ANSYS Fluid Analysis Guide

ANSYS Fluids AnalysisGuideANSYS Release 9.0

002114November 2004

ANSYS, Inc. is aUL registeredISO 9001: 2000Company.

ANSYS Fluids Analysis Guide

ANSYS Release 9.0

ANSYS, Inc.Southpointe275 Technology DriveCanonsburg, PA [email protected]://www.ansys.com(T) 724-746-3304(F) 724-514-9494

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Table of Contents

I. CFD

1. Overview of FLOTRAN CFD Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–11.1. What Is FLOTRAN CFD Analysis? .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–11.2. Types of FLOTRAN Analyses ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–1

1.2.1. Laminar Flow Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–11.2.2. Turbulent Flow Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–21.2.3. Thermal Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–21.2.4. Compressible Flow Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–21.2.5. Non-Newtonian Fluid Flow Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–21.2.6. Multiple Species Transport Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–21.2.7. Free Surface Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–2

1.3. About GUI Paths and Command Syntax ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–22. The Basics of FLOTRAN Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–1

2.1. Characteristics of the FLOTRAN Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–12.1.1. Other Element Features ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–1

2.2. Considerations and Restrictions for Using the FLOTRAN Elements .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–12.2.1. Limitations on FLOTRAN Element Use ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–2

2.3. Overview of a FLOTRAN Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–32.3.1. Determining the Problem Domain ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42.3.2. Determining the Flow Regime ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42.3.3. Creating the Finite Element Mesh ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42.3.4. Applying Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–52.3.5. Setting FLOTRAN Analysis Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–52.3.6. Solving the Problem .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–52.3.7. Examining the Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–5

2.4. Files the FLOTRAN Elements Create ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–52.4.1. The Results File .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–62.4.2. The Print File (Jobname.PFL) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–62.4.3. The Nodal Residuals File .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–62.4.4. The Restart File .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–72.4.5. The Domain File .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–72.4.6. Restarting a FLOTRAN Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–7

2.5. Convergence and Stability Tools .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–82.5.1. Relaxation Factors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–82.5.2. Inertial Relaxation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–82.5.3. Modified Inertial Relaxation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–92.5.4. Artificial Viscosity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–92.5.5. DOF Capping ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–92.5.6. The Quadrature Order ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–10

2.6. What to Watch For During a FLOTRAN Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–102.6.1. Deciding How Many Global Iterations to Use ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–102.6.2. Convergence Monitors .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–112.6.3. Stopping a FLOTRAN Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–132.6.4. Pressure Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–13

2.7. Evaluating a FLOTRAN Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–142.8. Verifying Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–14

3. FLOTRAN Laminar and Turbulent Incompressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–13.1. Characteristics of Fluid Flow Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–13.2. Activating the Turbulence Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–2

ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

3.2.1. The Role of the Reynolds Number ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–23.2.2. Determining Whether an Analysis Is Turbulent ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–33.2.3. Turbulence Ratio and Inlet Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–33.2.4. Turbulence Models .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–3

3.2.4.1. Standard k-epsilon Model (default) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–43.2.4.2. Zero Equation Turbulence Model (ZeroEq) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–63.2.4.3. Re-Normalized Group Turbulence Model (RNG) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–63.2.4.4. k-epsilon Model Due to Shih (NKE) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–73.2.4.5. Nonlinear Model of Girimaji (GIR) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–73.2.4.6. Shih, Zhu, Lumley Model (SZL) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–83.2.4.7. k-omega Turbulence Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–83.2.4.8. Shear Stress Transport Model (SST) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–9

3.3. Meshing Requirements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–93.4. Flow Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–113.5. Strategies for Difficult Problems ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–143.6. Example of a Laminar and Turbulent FLOTRAN Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–16

4. FLOTRAN Thermal Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–14.1. Thermal Analysis Overview ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–14.2. Meshing Requirements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–14.3. Property Specifications and Control .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–14.4. Thermal Loads and Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–1

4.4.1. Applying Loads ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–24.4.1.1. Applying Loads Using Commands ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–24.4.1.2. Applying Loads Using the GUI ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–34.4.1.3. Solutions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–3

4.5. Solution Strategies ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–44.5.1. Constant Fluid Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–44.5.2. Forced Convection, Temperature Dependent Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–44.5.3. Free Convection, Temperature Dependent Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–54.5.4. Conjugate Heat Transfer .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–5

4.6. Heat Balance ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–74.7. Surface-to-Surface Radiation Analysis Using the Radiosity Method .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–8

4.7.1. Procedure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–84.7.2. Heat Balances ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–8

4.8. Examples of a Laminar, Thermal, Steady-State FLOTRAN Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–84.8.1. The Example Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–94.8.2. Doing the Buoyancy Driven Flow Analysis (GUI Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–104.8.3. Doing the Buoyancy Driven Flow Analysis (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–16

4.9. Example of Radiation Analysis Using FLOTRAN (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–174.10. Where to Find Other FLOTRAN Analysis Examples ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–18

5. FLOTRAN Transient Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–15.1. Time Integration Method ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–15.2. Time Step Specification and Convergence ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–15.3. Terminating and Getting Output from a Transient Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–35.4. Applying Transient Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–3

6. Volume of Fluid (VOF) Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–16.1. Overview ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–16.2. VFRC Loads ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–1

6.2.1. Initial VFRC Loads ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–16.2.2. Boundary VFRC Loads ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–2

6.3. Input Settings ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–36.3.1. Ambient Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–3

ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.vi


6.3.2. VFRC Tolerances ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–46.3.3. VOF Time Steps ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–4

6.4. Postprocessing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–56.5. VOF Analysis of a Dam .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–5

6.5.1. The Problem Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–56.5.2. Building and Solving the Model (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–5

6.6. VOF Analysis of Open Channel with an Obstruction ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–66.6.1. The Problem Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–66.6.2. Building and Solving the Model (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–7

6.7. VOF Analysis of an Oscillating Droplet .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–106.7.1. The Problem Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–106.7.2. Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–106.7.3. Building and Solving the Model (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–126.7.4. Where to Find Other Examples ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–13

7. Arbitrary Lagrangian-Eulerian (ALE) Formulation for Moving Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17.1. Introduction ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17.2. Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–37.3. Mesh Updating ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–57.4. Remeshing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–67.5. Postprocessing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–77.6. ALE Analysis of a Simplified Torsional Mirror .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–8

7.6.1. The Problem Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–87.6.2. Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–87.6.3. Forces and Moments ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–97.6.4. Building and Solving the Model (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–12

7.7. ALE/VOF Analysis of a Vessel with a Moving Wall .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–157.7.1. The Problem Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–157.7.2. Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–167.7.3. Building and Solving the Model (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–16

7.8. ALE Analysis of a Moving Cylinder ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–187.8.1. The Problem Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–187.8.2. Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–197.8.3. Building and Solving the Model (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–19

8. FLOTRAN Compressible Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–18.1. Requirements for Compressible Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–18.2. Property Calculations ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–18.3. Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–28.4. Structured vs. Unstructured Mesh ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–28.5. Solution Strategies ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–3

8.5.1. Inertial Relaxation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–48.6. Example of a Compressible Flow Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–4

8.6.1. The Example Described ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–48.6.1.1. Fluid Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–48.6.1.2. Approach and Assumptions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–4

8.7. Doing the Example Compressible Flow Analysis (GUI Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–58.8. Doing the Example Compressible Flow Analysis (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–11

9. Specifying Fluid Properties for FLOTRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–19.1. Guidelines for Specifying Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–19.2. Fluid Property Types ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–1

9.2.1. Property Types for Specific Heat ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–29.2.2. Property Types for Density and Thermal Conductivity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–29.2.3. Property Types for Viscosity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–3


viiANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

9.2.4. Property Types for Surface Tension Coefficient ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–39.2.5. Property Types for Wall Static Contact Angle ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–39.2.6. General Guidelines for Setting Property Types ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–3

9.2.6.1. Using a Fluid Property Table ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–39.2.6.2. Specifying Property Types ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–4

9.2.7. Density ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–59.2.8. Viscosity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–69.2.9. Specific Heat ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–79.2.10. Thermal Conductivity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–89.2.11. Surface Tension Coefficient ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–89.2.12. Wall Static Contact Angle ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–9

9.3. Initializing and Varying Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–99.3.1. Activating Variable Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–10

9.4. Modifying the Fluid Property Database ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–109.5. Using Reference Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–129.6. Using the ANSYS Non-Newtonian Flow Capabilities .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–13

9.6.1. Activating the Power Law Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–139.6.2. Activating the Carreau Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–149.6.3. Activating the Bingham Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–14

9.7. Using User-Programmable Subroutines ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–1410. FLOTRAN Special Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–1

10.1. Coordinate Systems ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–110.2. Rotating Frames of Reference ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–210.3. Swirl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–310.4. Distributed Resistance/Source ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–4

11. FLOTRAN CFD Solvers and the Matrix Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–111.1. Which Solver Should You Use? ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–111.2. Tri-Diagonal Matrix Algorithm .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–111.3. Semi-Direct Solvers .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–2

11.3.1. Preconditioned Generalized Minimum Residual (PGMR) Solver .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–311.3.2. Preconditioned BiCGStab (PBCGM) Solver .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–5

11.4. Sparse Direct Method ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–512. Coupling Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–1

12.1. Overview ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–112.2. Algorithm Settings ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–1

12.2.1. Advection Scheme ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–112.2.2. Solver .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–212.2.3. Relaxation Factors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–2

12.3. Performance ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–213. Multiple Species Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–1

13.1. Overview of Multiple Species Transport .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–113.2. Mixture Types ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–1

13.2.1. Dilute Mixture Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–113.2.2. Composite Mixture Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–113.2.3. Composite Gas Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–2

13.3. Doing a Multiple Species Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–213.3.1. Establish the Species ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–213.3.2. Choose an Algebraic Species ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–313.3.3. Adjust Output Format ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–313.3.4. Set Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–313.3.5. Specify Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–413.3.6. Set Relaxation and Solution Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–4

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13.4. Doing a Heat Exchanger Analysis Using Two Species ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–513.5. Example Analysis Mixing Three Gases ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–7

14. Advection Discretization Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–114.1. Introduction ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–114.2. Using SUPG and COLG ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–114.3. Strategies for Difficult Solutions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14–2

II. Acoustics

15. Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–115.1. What Is Acoustics? .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1

15.1.1. Types of Acoustic Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–115.2. Solving Acoustics Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–115.3. Building the Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1

15.3.1. Harmonic Acoustic Analysis Guidelines ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–215.3.1.1. FLUID29 and FLUID30 ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–215.3.1.2. FLUID129 and FLUID130 ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–2

15.4. Meshing the Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–415.4.1. Step 1: Mesh the Interior Fluid Domain ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–415.4.2. Step 2: Generate the Infinite Acoustic Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–415.4.3. Step 3: Specify the Fluid-Structure Interface ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–5

15.5. Applying Loads and Obtaining the Solution ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–615.5.1. Step 1: Enter the SOLUTION Processor ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–615.5.2. Step 2: Define the Analysis Type ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–615.5.3. Step 3: Define Analysis Options ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–615.5.4. Step 4: Apply Loads on the Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–7

15.5.4.1. Applying Loads Using the GUI ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–815.5.4.2. Applying Loads Using Commands ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–815.5.4.3. Load Types ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–9

15.5.5. Step 5: Specify Load Step Options ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–915.5.5.1. Dynamics Options ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1015.5.5.2. General Options ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1015.5.5.3. Output Controls .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–10

15.5.6. Step 6: Back Up Your Database ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1015.5.7. Step 7: Apply Additional Load Steps (Optional) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1115.5.8. Step 8: Finish the Solution ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–11

15.6. Reviewing Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1115.7. Fluid-Structure Interaction ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1115.8. Sample Applications ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1215.9. Example 1: Fluid-Structure Coupled Acoustic Analysis (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1215.10. Example 2: Room Acoustic Analysis (Command Method) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–13

III. Thin Film

16. Thin Film Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–116.1. Elements for Modeling Thin Films ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–116.2. Squeeze Film Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1

16.2.1. Static Analysis Overview ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–216.2.2. Harmonic Response Analysis Overview ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–316.2.3. Flow Regime Considerations ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–416.2.4. Modeling and Meshing Considerations ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–416.2.5. Analysis Settings and Options ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–516.2.6. Loads and Solution ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–5


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16.2.7. Review Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–616.2.8. Example Problem .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–6

16.3. Modal Projection Method for Squeeze Film Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1016.3.1. Modal Projection Method Overview ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1016.3.2. Steps in Computing the Damping Parameter Using the Modal Projection Tech-nique ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–11

16.3.2.1. Modeling and Meshing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1216.3.2.2. Perform Modal Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1216.3.2.3. Extracting Eigenvectors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1216.3.2.4. Performing a Harmonic Response Analysis and Extracting Damping Paramet-ers .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–12

16.3.3. Example Problem Using the Modal Projection Method ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1316.3.4. Damping Extraction for Large Signal Cases ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–18

16.4. Slide Film Damping ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1816.4.1. Slide Film Damping Example ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–20

Index ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index–1

List of Figures2.1. Convergence Monitors Displayed by the GST Feature ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–123.1. Internal Flow ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–13.2. External Flow ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–13.3. Structured Mesh ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–103.4. Unstructured Mesh ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–104.1. Diagram of the Square Cavity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–94.2. Plot of the Temperature Solution ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–134.3. Plot of Streamline Contours ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–144.4. Plot of Velocity Vectors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–154.5. Plot of Flow Trace ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–166.1. Instantaneous Pressure Distributions at 0.001 ms ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–116.2. Instantaneous Pressure Distributions at 0.012 ms ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–117.1. Torsional Mirror at t = 0 Seconds ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–17.2. Torsional Mirror at t = 2.5 Seconds ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–27.3. Torsional Mirror at t = 7.5 Seconds ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–27.4. Boundary Conditions for Moving Walls .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–37.5. Torsional Mirror Problem Description ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–87.6. Torsional Mirror Problem - Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–107.7. Square Vessel with a Moving Wall .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–157.8. Left Wall Displacement and Velocity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–167.9. Moving Cylinder ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–187.10. Elements at 0 Seconds ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–197.11. Elements at 22 Seconds ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–197.12. Elements at 44 Seconds ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–198.1. Three Types of Meshing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8–310.1. Direction of Positive Swirl Velocity VZ for Axisymmetric Models .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–110.2. Rotating Flow Problem .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–310.3. Problem Schematic with Rotating Coordinate ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–311.1. Typical Debug Files .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11–313.1. Environment for a Typical Heat Exchanger Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13–515.1. Example of a 2-D Acoustic Model (Fluid Within a Structure) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–215.2. Example of Absorption Element Application ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–3

ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.x


15.3. Submerged Cylindrical Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–315.4. Mesh the Fluid Domain ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–415.5. Add the Absorption Element on the Boundary ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–515.6. Specify Fluid-Structure Interface ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–616.1. Moving Plate above a Fixed Wall .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–216.2. Perforated Plate Structure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–216.3. Pressure Distribution on a Plate at a Low Driving Frequency ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–316.4. Damping and Squeeze Stiffness Coefficients vs. Frequency ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–316.5. Coupling of Nodes at the Hole Periphery with the Center Node of a FLUID138 Element ... . . . . . . . . . . . . . . . . . 16–516.6. Pressure Distribution (Real Component) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–716.7. Pressure Distribution (Imaginary Component) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–816.8. Modal Projection Technique for Damping Characterization ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1016.9. Damping and Squeeze Stiffness Parameters for a Rectangular Plate ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1116.10. Fluidic Cross-Talk between Transverse and Rotational Motion ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1316.11. Time-Transient Response from Voltage Pulse ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1716.12. Slide Film Damping at Low and High Frequencies ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–1916.13. Viscous Slide Film Element FLUID139 ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–2016.14. Comb Drive Resonator ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–2116.15. Displacement of Central Mass ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–2116.16. Real and Imaginary Current ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–22

List of Tables2.1. 2-D Solid Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–13.1. Boundary Conditions at Intersections ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–134.1. Command Family and GUI Path Used to Apply Loads ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–24.2. Load Commands for a FLOTRAN Thermal Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–25.1. Specifying Values for Time Steps ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–25.2. Saving Analysis Results for Processing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–37.1. Interface Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–47.2. Element Qualities .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–67.3. Remeshing Limitations ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–77.4. Quality Requirements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7–189.1. Units for Thermal Quantities .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–19.2. Energy Units for Incompressible Analyses with Viscous Heating ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–29.3. Units for the AIR Property Type ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–29.4. Property types for Value ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–49.5. Property Database Format ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9–1110.1. Coordinate System Specification ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10–112.1. Advection Scheme Defaults .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–112.2. SIMPLEF and SIMPLEN Performance Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12–215.1. Loads Applicable in an Acoustic Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–715.2. Commands for Applying Loads in Acoustic Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–815.3. Load Step Options for a Harmonic Acoustic Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15–1016.1. Thin Film Fluid Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–116.2. Load Options for Thin Film Fluid Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–516.3. Beam Model Results Considering Perforated Holes ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–716.4. Modal Damping Parameters for First Two Eigenfrequencies ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16–14


xiANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

Part I. CFD

Chapter 1: Overview of FLOTRAN CFD Analyses

1.1. What Is FLOTRAN CFD Analysis?

The ANSYS FLOTRAN derived product and the FLOTRAN CFD (Computational Fluid Dynamics) option to theother ANSYS products offer you comprehensive tools for analyzing 2-D and 3-D fluid flow fields. Using eitherproduct and the FLOTRAN CFD elements FLUID141 and FLUID142, you can achieve solutions for the following:

• Lift and drag on an airfoil

• The flow in supersonic nozzles

• Complex, 3-D flow patterns in a pipe bend

In addition, you can use the features of ANSYS and ANSYS FLOTRAN to perform tasks including:

• Calculating the gas pressure and temperature distributions in an engine exhaust manifold

• Studying the thermal stratification and breakup in piping systems

• Using flow mixing studies to evaluate potential for thermal shock

• Doing natural convection analyses to evaluate the thermal performance of chips in electronic enclosures

• Conducting heat exchanger studies involving different fluids separated by solid regions

1.2. Types of FLOTRAN Analyses

You can perform these types of FLOTRAN analyses:

• Laminar or turbulent

• Thermal or adiabatic

• Free surface

• Compressible or incompressible

• Newtonian or Non-Newtonian

• Multiple species transport

These types of analyses are not mutually exclusive. For example, a laminar analysis can be thermal or adiabatic.A turbulent analysis can be compressible or incompressible.

To solve any analysis involving the flow of fluid, use either of the following:Command(s): FLDATA1,SOLU,FLOW,TRUEGUI: Main Menu> Solution> FLOTRAN Set Up> Solution Options

1.2.1. Laminar Flow Analysis

In these analyses, the velocity field is very ordered and smooth, as it is in highly viscous, slow-moving flows. Theflow of some oils also can be laminar.


1.2.2. Turbulent Flow Analysis

Turbulent flow analyses deal with problems where velocities are high enough and the viscosity is low enoughto cause turbulent fluctuations. The two-equation turbulence model in ANSYS enables you to account for theeffect of the turbulent velocity fluctuations on the mean flow.

Laminar and turbulent flows are considered to be incompressible if density is constant or if the fluid expendslittle energy in compressing the flow. The temperature equation for incompressible flow neglects kinetic energychanges and viscous dissipation.

1.2.3. Thermal Analysis

Often, the solution for the temperature distribution throughout the flow field is of interest. If fluid properties donot vary with temperature, you can converge the flow field without solving the temperature equation. In a con-jugate heat transfer problem, the temperature equation is solved in a domain with both fluid and non-fluid (thatis, solid material) regions. In a natural convection problem, the flow results mainly or solely from density gradientsbrought about by temperature variations. Most natural convection problems, unlike forced convection problems,have no externally applied flow sources.

1.2.4. Compressible Flow Analysis

For high velocity gas flows, changes in density due to strong pressure gradients significantly influence the natureof the flow field. ANSYS uses a different solution algorithm for compressible flow.

1.2.5. Non-Newtonian Fluid Flow Analysis

A linear relationship between the stress and rate-of-strain cannot describe many fluid flows adequately. For suchnon-Newtonian flows, the ANSYS program provides three viscosity models and a user-programmable subroutine.

1.2.6. Multiple Species Transport Analysis

This type of analysis is useful in studying the dispersion of dilute contaminants or pollutants in the bulk fluidflow. In addition, you can use multiple species transport analysis for heat exchanger studies where two or morefluids (separated by walls) may be involved.

1.2.7. Free Surface Analysis

Free surface analyses deal with problems involving a unconstrained gas-liquid surface. You can use this type ofanalysis to solve two dimensional planar and axisymmetric problems such as flow over a dam and tank sloshing.

1.3. About GUI Paths and Command Syntax

Throughout this document, you will see references to ANSYS commands and their equivalent GUI paths. Suchreferences use only the command name, because you do not always need to specify all of a command's arguments,and specific combinations of command arguments perform different functions. For complete syntax descriptionsof ANSYS commands, consult the ANSYS Commands Reference.

The GUI paths shown are as complete as possible. In many cases, choosing the GUI path as shown will performthe function you want. In other cases, choosing the GUI path given in this document takes you to a menu ordialog box; from there, you must choose additional options that are appropriate for the specific task being per-formed.

ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.1–2

Chapter 1: Overview of FLOTRAN CFD Analyses

For the thermal related analyses described in this guide, specify the material you will be simulating using an in-tuitive material model interface. This interface uses a hierarchical tree structure of material categories, which isintended to assist you in choosing the appropriate model for your analysis. See Section 1.2.4.4: Material ModelInterface in the ANSYS Basic Analysis Guide for details on the material model interface.

Section 1.3: About GUI Paths and Command Syntax

1–3ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

Chapter 2: The Basics of FLOTRAN Analysis

2.1. Characteristics of the FLOTRAN Elements

The ANSYS FLOTRAN elements, FLUID141 and FLUID142, solve for 2-D and 3-D flow, pressure, and temperaturedistributions in a single phase viscous fluid. For these elements, the ANSYS program calculates velocity compon-ents, pressure, and temperature from the conservation of three properties: mass, momentum, and energy.

Table 2.1 2-D Solid Elements

DOFsShape or CharacteristicDimens.Element

Fluid velocity, pressure, temperature, turbu-lent kinetic energy, turbulent energy dissip-ation, multiple species mass fractions for upto six fluids

Quadrilateral, four nodes or triangle, threenodes

2-DFLUID141

Fluid velocity, pressure, temperature, turbu-lent kinetic energy, turbulent energy dissip-ation, multiple species mass fractions for upto six fluids

Hexahedral, eight nodes or tetrahedral, fournodes or wedge, six nodes or pyramid, fivenodes; tetrahedral and hexahedral elementscan be combined by pyramids

3-DFLUID142

2.1.1. Other Element Features

Other features of the FLOTRAN elements include:

• A two-equation turbulence model for simulating turbulent flows.

• Derived results, such as Mach number, pressure coefficient, total pressure, shear stress, y plus at walls,and stream function for fluid analyses and heat flux and heat transfer (film) coefficient for thermal analyses.

• Fluid boundary conditions, including velocities, pressures, and the turbulence quantities kinetic energyand kinetic energy dissipation rate. You may supply specific values of the turbulence quantities at theinlet, but the FLOTRAN default boundary conditions suffice if the entrance is not close to the regions ofprimary interest.

• Thermal boundary conditions, including temperature, heat flux, volumetric heat sources, and heat transfer(film) coefficient.

You can solve problems in Cartesian, cylindrical, polar, and axisymmetric coordinate systems. If a problem isaxisymmetric, activating a swirl option allows you to calculate a velocity component normal to the axisymmetricplane.

2.2. Considerations and Restrictions for Using the FLOTRAN Elements

The FLOTRAN elements have some limitations:

• You cannot change the problem domain during a single analysis.

• Certain features of the ANSYS program do not work with the FLOTRAN elements.

• You cannot use certain commands or menu paths with the FLOTRAN elements.

• If you use the ANSYS GUI, only the features and options called for in the FLOTRAN SetUp portion of themenus and dialog boxes will appear.


2.2.1. Limitations on FLOTRAN Element Use

When you are using the FLOTRAN elements, you should avoid using certain ANSYS features and commands, orif you do choose to use them, be aware that they have slightly different uses with the FLOTRAN elements. Thisdoes not mean that every command not listed here will work with FLOTRAN elements. ANSYS informs you if you tryto issue a command that is invalid.

When using the FLOTRAN elements, keep the following points in mind:

• You cannot combine the FLOTRAN elements with other elements.

• The nodal coordinate system must be identical to the global coordinate system.

• The /CLEAR command does not destroy an existing FLOTRAN results file (Jobname.RFL), thus preventingyou from inadvertently destroying a results file that took much time and effort to create. Existing Job-name.RFL file names will become Jobname.RFO file names if the number of nodes in the model haschanged since the Jobname.RFL file creation. You should remove unwanted results files at the systemlevel.

• In FLOTRAN, the CP command enforces periodic boundary conditions by coupling all degrees of freedombetween two nodes. You should not use the CP command to couple more than two nodes or to couplea subset of the degrees of freedom. You should only use this command to couple all degrees of freedomof one node on a periodic boundary face to one other node on another periodic boundary face.

You cannot couple nodes on the same element, and you may have difficulty coupling nodes on adjacentelements.

• The ADAPT macro does not work with FLOTRAN.

• You cannot use the ANTYPE command to invoke a transient analysis with the FLOTRAN element. (SeeChapter 5, “FLOTRAN Transient Analyses”.)

• FLOTRAN analyses do not support automatic time stepping. For more information, see Chapter 5, “FLOTRANTransient Analyses”.

• If you specify nodal heat generation loads via commands BFCUM, BFDELE, or BFUNIF, ANSYS uses loadvalues specified with the BFE command instead.

• The commands CE, CECMOD, CEDELE, and CEINTF do not work with FLOTRAN.

• The CNVTOL command does not set convergence tolerances with FLOTRAN as it does for other analyses.For information about FLOTRAN convergence, see Section 2.6.1: Deciding How Many Global Iterations toUse.

• The symmetry and antisymmetry conditions that the DSYM command specifies are not appropriate forFLOTRAN. Chapter 3, “FLOTRAN Laminar and Turbulent Incompressible Flow” explains how to specifyflow symmetry boundary conditions for FLOTRAN.

• FLOTRAN does not support angular acceleration vectors for rotating coordinate systems.

• In a FLOTRAN analysis, the command FLDATA4,TIME (rather than the DELTIM command) specifies a timestep for a load step.

• For FLOTRAN, you cannot use the DESOL command or the PRESOL command to modify HEAT, FLOW, orFLUX nodal results.

• FLOTRAN does not permit extrapolation of integration point results to nodes (via the ERESX command).

• FLOTRAN does not allow you to generate elements through reflections. Although not recommended,FLOTRAN will execute properly if you generate reflected elements using a different element type and yousubsequently switch to the FLOTRAN element type.



• In FLOTRAN analyses, you cannot ramp loads via the KBC command. The FLOTRAN commandFLDATA4,TIME,BC, however, is analogous to the ANSYS command KBC, except that the default for FLOTRANis a step change.

• Load case operations, such as those performed by the LCCALC, LCDEF, LCFACT, and LCFILE commands,are not allowed in a FLOTRAN analysis.

• Do not use the LSWRITE or LSSOLVE command in a FLOTRAN analysis. Use the SOLVE command to starta FLOTRAN solution.

• The convergence tool invoked with the NCNV command does not apply to the FLOTRAN segregatedsolver.

• Do not use the NEQIT command, which defines the number of equilibrium iterations for a nonlinearsolution, in a FLOTRAN analysis.

• FLOTRAN requires the nodal and global Cartesian coordinate systems to be the same. Therefore, youcannot use the rotational fields on the N, NMODIF, and NROTAT commands.

• In a FLOTRAN analysis, the commands FLDATA2,ITER, FLDATA4,TIME, and FLDATA4A,STEP control itemswritten to the results files (Jobname.RFL and Jobname.PFL

• FLOTRAN does not permit user programmable elements, such as those specified via the NSVR command.

• In a FLOTRAN analysis, the commands FLDATA2,ITER and FLDATA4,TIME control items written to thedatabase.

• The PRNLD command does not apply to FLOTRAN, because it does not store boundary conditions asprintable element nodal loads.

• Node reaction solutions, such as those produced by the PRRSOL command, are not available for FLOTRAN.

• The partial and predefined solution option (called by the PSOLVE command) does not apply to the FLO-TRAN segregated solver.

• The TIME command, which associates boundary conditions with a particular time value, does not applyto FLOTRAN.

• FLOTRAN analyses use the FLDATA1,SOLU command instead of the TIMINT command to specify transientload steps.

• FLOTRAN analyses use the FLDATA4,TIME command instead of the TRNOPT command to specify transientanalysis options.

• The RESCONTROL command does not apply to FLOTRAN. Some of the functionality of RESCONTROL isprovided with the FLDATA32,REST command.

• For FLOTRAN, you cannot use the DK command to define DOF constraints at keypoints.

2.3. Overview of a FLOTRAN Analysis

A typical FLOTRAN analysis consists of seven main steps:

1. Determine the problem domain.

2. Determine the flow regime.

3. Create the finite element mesh.

4. Apply boundary conditions.

5. Set FLOTRAN analysis parameters.

6. Solve the problem.

Section 2.3: Overview of a FLOTRAN Analysis


7. Examine the results.

2.3.1. Determining the Problem Domain

You need to determine the proper domain for each problem you analyze. Locate the boundaries of the problemwhere conditions are known. If you do not know precise conditions and must make assumptions about them,do not locate boundaries too close to the regions of greatest interest or near regions that have steep gradientsin the solution variables.

Sometimes, you may not realize that steep gradients occur too near the outlet or in some other region until yousee the analysis results. Should this happen, you can re-analyze the problem with a different problem domain.

For specific recommendations on determining problem domain, see the sections discussing the various flowphenomena.

2.3.2. Determining the Flow Regime

You need to estimate the character of the flow. The character is a function of the fluid properties, geometry, andthe approximate magnitude of the velocity field.

Fluid flow problems that FLOTRAN solves will include gases and liquids, the properties of which can vary signi-ficantly with temperature. The flow of gases is restricted to ideal gases. You must determine whether the effectof temperature on fluid density, viscosity, and thermal conductivity is important. In many cases, you can getadequate results with constant properties.

To assess whether you need the FLOTRAN turbulence model, use an estimate of the Reynolds number, whichmeasures the relative strengths of the inertial and viscous forces. (See Chapter 3, “FLOTRAN Laminar and TurbulentIncompressible Flow” for more information.)

To determine whether you need to use the compressible option, estimate the Mach number. (See Chapter 8,“FLOTRAN Compressible Analyses”) The Mach number at any point in the flow field is the ratio of the fluid speedand the speed of sound. At Mach numbers above approximately 0.3, consider using the compressible solutionalgorithm. At Mach numbers above approximately 0.7, you can expect significant differences between incom-pressible and compressible results. You may want to compare results from each algorithm for a representativeproblem.

2.3.3. Creating the Finite Element Mesh

You will need to make assumptions about where the gradients are expected to be the highest, and you mustadjust the mesh accordingly. For example, if you are using the turbulence model, then the region near the wallsmust have a much denser mesh than would be needed for a laminar problem. If it is too coarse, the original meshmay not capture significant effects brought about through steep gradients in the solution. Conversely, elementsmay have very large aspect ratios with the long sides along directions with very low gradients.

For the most accurate results, use mapped meshing. It more effectively maintains a consistent mesh patternalong the boundary. You can do this by issuing the command MSHKEY,1 (Main Menu> Preprocessor> Meshing>Mesh> entity> Mapped).

In some cases, you may wish to use hexahedral elements to capture detail in high-gradient regions and tetrahedralelements in less critical regions. As described in Section 7.3.9: Creating Transitional Pyramid Elements in theANSYS Modeling and Meshing Guide you can instruct ANSYS to automatically create pyramid elements at the in-terface.



For flow analysis, especially turbulent, you should not use pyramid elements in the region near the walls becauseit may lead to inaccuracies in the solution.

Wedge elements can be useful when a complex area can be easily meshed with triangles that are then extruded.For a quick solution, you can use wedge elements in the region near the walls. However, for accurate results,you should use hexahedral elements in those regions.

Wedge elements are considered to be degenerate hexahedral elements. When using the ANSYS MeshTool (MainMenu> Preprocessor> Meshing> MeshTool) to sweep triangles into wedges, you must select Hex elements.

2.3.4. Applying Boundary Conditions

You can apply boundary conditions before or after you mesh the domain. Consider every model boundary. If acondition is not specified for a dependent variable, a zero gradient of that value normal to the surface is assumed.

You can change boundary conditions between restarts. If you need to change a boundary condition or accidentallyomit it, you do not need to restart your analysis unless the change causes instabilities in the analysis solution.

2.3.5. Setting FLOTRAN Analysis Parameters

In order to use options such as the turbulence model or solution of the temperature equation, you must activatethem. Specific items to be set, such as fluid properties, are a function of the type of flow problem at hand. Othersections in this document recommend parameter settings for various types of flow.

2.3.6. Solving the Problem

You can monitor solution convergence and stability of the analysis by observing the rate of change of the solutionand the behavior of relevant dependent variables. These variables include velocity, pressure, temperature, and(if necessary) turbulence quantities such as kinetic energy (degree of freedom ENKE), kinetic energy dissipationrate (ENDS), and effective viscosity (EVIS).

An analysis typically requires multiple restarts.

2.3.7. Examining the Results

You can postprocess output quantities and examine the results in the output files. Use your engineering judgmentwhen examining the results to evaluate the plausibility and consistency of the overall analysis approach, howspecific properties are used, and the conditions imposed.

2.4. Files the FLOTRAN Elements Create

You perform most fluid flow analyses in ANSYS by stopping the analysis job and then restarting it multiple times.Often, analysts change parameters such as relaxation factors or turn options (such as solution of the temperatureequation) on or off between restarts. Each time you continue a job, the ANSYS program appends data to all ofthe files that its FLOTRAN element creates.

The following list explains all files that a FLOTRAN element creates. A discussion of the residual file appears atthe end of this section.

• The results file, Jobname.RFL, contains nodal results.

• The print file, Jobname.PFL, contains input convergence monitors, and inlet/outlet summaries.

• The wall file, Jobname.RSW, contains wall shear stress and Y-plus information.

Section 2.4: Files the FLOTRAN Elements Create


• The residual file, Jobname.RDF, contains the nodal residuals.

• The debug file, Jobname.DBG, contains information about algebraic solver performance.

• The results backup file, Jobname.RFO, contains a copy of the results file data.

• The restart file, Jobname.CFD, contains FLOTRAN data structures.

• The domain file, (jobname.pv_0000n) for use by ICEM CFD's PV3 postprocessing visualization tool.

2.4.1. The Results File

The results of a FLOTRAN analysis are not stored in the ANSYS database automatically. At the end of every solution,the ANSYS program adds a set of results to the results file, Jobname.RFL. You have some control over the contentof the results file and how often ANSYS updates it. The defaults given in the description of the FLDATA5,OUTPcommand in the ANSYS Commands Reference reflect FLOTRAN's determination of what the results file shouldstore based on the options you choose.

The ANSYS program is flexible about how many sets of results you can store for a steady-state FLOTRAN analysis.Keeping sets of results from earlier executions has advantages: you can compare changes that occurred betweensets of results, and you can continue an analysis from its earlier stages using different options or relaxationparameters.

The ANSYS program stores a set of results when you begin an analysis (before the first iteration), then storesresults again when one of the termination criteria is reached. Between those events, you can append the resultsto the Jobname.RFL file. Storing intermediate sets of results enables you to continue the analysis from anearlier stage with different options and features activated, for example to enhance stability.

We recommend that you use ANSYS' overwrite frequency option because it allows you to periodically store andupdate a temporary set of results. Using this option ensures that a useful set of results will exist should you needto restart an analysis after a power failure or other system interruption. The next regularly scheduled output ofresults overwrites the temporary results set. You can accomplish the same thing by instructing ANSYS to appenddata to the results file more often; however, this method inflates the size of the results file.

To set the overwrite frequency, use either of the following:Command(s): FLDATA2,ITER,OVER,ValueGUI: Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl

To set the append frequency, use either of the following:Command(s): FLDATA2,ITER,APPE,ValueGUI: Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl

2.4.2. The Print File (Jobname.PFL)

The Jobname.PFL file contains a complete record of all FLOTRAN input parameters, including properties andsolution options. This information is recorded each time a SOLVE is issued so as to provide a complete accountof the analysis history. In addition, all convergence monitors are recorded for all active values. A results summary,showing maximum and minimum values of each property and degree of freedom, is provided at a user-determinedfrequency. Average values are also recorded. The mass flow boundaries are identified and a mass balance iscalculated. Finally, all heat transfer information is summarized for all heat transfer and heat sources.

2.4.3. The Nodal Residuals File

The nodal residuals file, Jobname.RDF, shows you how well the current solution is converged. At every stagein the solution procedure, the flow, property, and temperature fields are used to calculate coefficient matrices



and forcing functions for each DOF. If a solution is converged completely, these matrices and forcing functionswill produce the same velocity field used to generate them and the residuals of the matrix equation will be verysmall. You must request at least one global iteration to obtain a nodal residual file.

If a solution oscillates, however, the magnitude of the residuals shows where the maximum errors are. (The maindiagonal entries of the matrix normalize the residuals.) This normalization enables you to compare directly thevalue of the DOF and the value of its residual.

To calculate residuals for every active degree of freedom and output them to the residuals file, do either of thefollowing:

Command(s): FLDATA5,OUTP,RESI,TRUEGUI: Main Menu> Solution> FLOTRAN SetUp> Additional Out> Residual File

To read the residuals file, either issue the FLREAD command (Main Menu> General Postproc> FLOTRAN 2.1A).The residuals are postprocessed with the label associated with the DOF (for instance, TEMP or PRES for thetemperature or pressure residuals).

2.4.4. The Restart File

By default, FLOTRAN calculates data structures at the beginning of a restart of an analysis. These calculationsmay take considerable time for large models. To avoid recalculation, you can opt to have FLOTRAN store thedata structures in the Jobname.CFD file. FLOTRAN creates this file from information in the ANSYS database (butthe file is not required for restarts).

To write to or read from the Jobname.CFD file, use either of the following methods before the restart:Command(s): FLDATA32,REST,RFIL,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Restart Options> CFD Restart File

You can toggle the RFIL state on (TRUE) or off (FALSE). If is on, ANSYS reads the restart file when FLOTRAN beginsto execute. If no restart file exists, one will be created.

If you are restarting an analysis with updated boundary conditions, you must overwrite an existing .CFD file inorder to use the new conditions. To overwrite the file, use either of the following methods:

Command(s): FLDATA32,REST,WFIL,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Restart Options> CFD Restart File

This will cause FLOTRAN to create a new restart file during the next load step, and automatically sets the RFILstate to False. After the restart that has created the new file completes, issue the FLDATA32,REST,RFIL,TRUEcommand so that subsequent restarts use the new Jobname.CFD restart file.

2.4.5. The Domain File

Domain files are used by ICEM CFD's PV3 postprocessor visualization tool. In addition to nodal results these filescontain information to define the finite element model, including node locations, element topology, elementconnectivity, and family information concerning predefined ANSYS components. They also contain load step,substep, cumulative iteration, and time point values.

2.4.6. Restarting a FLOTRAN Analysis

You can restart the FLOTRAN analysis from any set of results in the Jobname.RFL file or from a different .RFLfile. You can base the restart on the set number (Label = NSET), the global iteration number (Label = ITER), theload step/subset numbers (Label = LSTP), or the transient analysis time (Label = TIME). You determine the restartcriteria by doing either of the following:

Section 2.4: Files the FLOTRAN Elements Create


• Issue the command FLDATA32,REST,Label,Value. Specify one of the labels listed above in place of Label.The Value argument causes values associated with the other criteria to be zeroed. Once invoked, thebehavior is turned off in the database by setting all the criteria to zero. If you are restarting from a differentresults file, you also need to specify the filename, extension, and directory of that file.

• Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Restart Options> Restart/Iteration(or Restart/Load step, Restart/Set, etc.)

If you specify invalid criteria, ANSYS notifies you and (if the program is operating in batch mode) terminates theanalysis.

When you restart an analysis, ANSYS copies the original results file to the file Jobname.RSO and places the restartpoint, all previous results sets, and all subsequent results sets in the new Jobname.RFL file. If the Value inputon the FLDATA32,REST command is negative, creation of the Jobname.RSO file is blocked. FLOTRAN uses theabsolute value of the number specified for Value.

If a results file name is entered in the Fname field of the FLDATA32,REST command, FLOTRAN interpolates thoseresults onto the current mesh in the database, regardless of whether or not the mesh has changed. This causesthe convergence monitors to start again from zero. This restart is different than a restart without a file namespecification. However, the results quickly converge to the original solution.

2.5. Convergence and Stability Tools

The ANSYS program offers several tools to help with convergence and solution stability. The ANSYS, Inc. TheoryReference explains how they are implemented.

2.5.1. Relaxation Factors

The relaxation factor is the fraction of the change between the old solution and the newly calculated solutionthat is added to the old solution, giving the results for the new global iteration. The relaxation factors for everycomponent must be between 0.0 (resulting in no update to the degree of freedom or property) and 1.0 inclusive.You set relaxation factors via either of the following:

Command(s): FLDATA25,RELX,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> DOF RelaxationMain Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Prop RelaxationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> DOF RelaxationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation

Note — See the description of the FLDATA25,RELX command in the ANSYS Commands Reference for listsof degree of freedom and property component names.

2.5.2. Inertial Relaxation

Inertial relaxation of the equation set for a DOF provides diagonal dominance to make a solution stable. Hypo-thetically, when a solution is converged in the absence of round off-error, the inertial relaxation applied doesnot affect the value of the answer. However, in real situations, some round off-error always occurs, so the inertialrelaxation may affect your solution.

You can apply inertial relaxation to the momentum equations (MOME), turbulence equations (TURB), the pressureequation (PRES), and the temperature equation (TEMP). To do so, use either of these methods:

Command(s): FLDATA26,STAB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Stability ParmsMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms



The inertial relaxation factor is in the denominator of the term added, so smaller values have a greater effect.

Typical useful values range between 1.0 (mild) and 1.0 x 10-7 (severe).

2.5.3. Modified Inertial Relaxation

Modified inertial relaxation adds a local positive value to the diagonal term to guarantee a positive diagonal.

You can apply modified inertial relaxation to the momentum equations (MOME), turbulence equations (TURB),and the temperature equation (TEMP). To do so, use either of these methods:

Command(s): FLDATA34,MIR,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> MIR StabilizationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization

A larger modified inertial relaxation factor gives a more robust scheme, but it may yield a slower convergence.The recommended range is 0.1 to 1.0.

You should consider inertial relaxation and modified inertial relaxation to be mutually exclusive.

2.5.4. Artificial Viscosity

Artificial viscosity smooths the velocity solution in regions of steep gradients. It has proven useful in aidingconvergence of compressible problems and in smoothing velocity solutions in incompressible problems withdistributed resistances. For incompressible analyses, you should keep the artificial viscosity within an order ofmagnitude of the effective viscosity.

To apply artificial viscosity, use either of these methods:Command(s): FLDATA26,STAB,VISC,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Stability ParmsMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms

2.5.5. DOF Capping

DOF capping allows you to prevent variables from going out of boundaries you specify. You can limit the velo-cities, pressure, and temperature degrees of freedom (VY, VY, VZ, PRES, TEMP). To do this, use either of thesemethods:

Command(s): FLDATA31,CAPPGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Results CappingMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Results Capping

Velocity capping eliminates the effects of velocity spikes on properties, which may occur in the early stages ofconvergence. Capping is especially suited to compressible analyses, where velocity spikes can cause kinetic energyterms great enough to produce negative static temperatures. When a degree of freedom is capped, ANSYS printsa message along with the convergence monitor printout.

The pressure value calculated by the solution of the pressure equation is capped, not the relaxed value. Therefore,if you introduce pressure capping upon restarting an analysis, pressure values may still be outside the caps.

Capping applies to relative values of pressure and absolute values of temperature.

You should cap the total temperature when performing compressible thermal analyses. It will help ensure neg-ative properties do not enter the calculations.

Caution: When velocities are capped, conservation of mass may not be enforced.

Section 2.5: Convergence and Stability Tools


2.5.6. The Quadrature Order

You have control over the quadrature order. In axisymmetric problems, the quadrature order automatically isset to 2 upon solution. This is because quadrature orders of 2 produce more accurate results for problems withirregularly shaped elements. The quadrature order is also automatically set to 2 upon solution for 3-D problemsusing cylindrical coordinates.

If you notice anomalous results near a region of skewed hexahedral elements, reset the quadrature order to 2.There might be a problem with the results when the included angles of the hexahedra exceed 120 degrees.

You can change the quadrature order for momentum diffusion or source, pressure diffusion or source, thermaldiffusion or source, turbulent diffusion or source, using either of the following:

Command(s):FLDATA30,QUAD,Label,Value

(Label is the element integral to change quadrature for, and Value is the number of integration points).

GUI:

Main Menu> Preprocessor> FLOTRAN Set Up> Mod Res/Quad Ord> CFD Quad OrdersMain Menu> Solution> FLOTRAN Set Up> Mod Res/Quad Ord> CFD Quad Orders

For more information on quadrature order, refer to the description of the FLDATA30,QUAD command in theANSYS Commands Reference.

2.6. What to Watch For During a FLOTRAN Analysis

This section describes what happens in a FLOTRAN analysis and how to evaluate how the analysis is proceeding.

2.6.1. Deciding How Many Global Iterations to Use

A FLOTRAN analysis is nonlinear and uses a sequential solution, so the first thing you must do is decide howmany global iterations should be executed. A global iteration is the solution, in sequence, of all relevant governingequations followed by any fluid property updates that are needed.

In a transient simulation, a time step loop exists around the global iteration loop.

During a global iteration, the ANSYS Multiphysics program or ANSYS FLOTRAN obtains approximate solutionsto the momentum equation and uses them as forcing functions to solve a pressure equation based on conservationof mass. ANSYS uses the resulting pressures to update the velocities so that the velocity field conserves mass. Ifyou request it, the ANSYS program solves the temperature equation and updates temperature dependentproperties.

Finally, if you have activated the turbulence model, the equations are solved and the program uses the turbulentkinetic energy and dissipation rate to calculate the effective viscosity and thermal conductivity. Effective viscosityand thermal conductivity replace, respectively, the laminar viscosity and thermal conductivity to model the effectof turbulence on the mean flow.

To specify how many global iterations a FLOTRAN analysis should execute, use either of the following:Command(s): FLDATA2,ITER,EXEC,Value (Value is the number of iterations.)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl



2.6.2. Convergence Monitors

As a FLOTRAN simulation proceeds, ANSYS calculates convergence monitors for each degree of freedom everyglobal iteration. Convergence monitors are computed for velocities (VY, VY, VZ), pressure (PRES), temperature(TEMP), turbulent kinetic energy (ENKE), kinetic energy dissipation rate (ENDS), and any active species transportequations (SP01-SP06).

The convergence monitors are a normalized measure of the solution's rate of change from iteration to iteration.Denoting by the general field variable, Φ, any DOF, the convergence monitor is defined as follows:

ConvMon=− −

=

=

∑

∑

φ φ

φ

ik

ik

i

N

ik

i

N

1

1

1

The convergence monitor represents the sum of changes of the variable calculated from the results between

the current kth iteration and the previous (k-1)th iteration, divided by the sum of the current values. The summationis performed over all n nodes, using the absolute values of the differences.

Available in both batch and interactive sessions, the Graphical Solution Tracking (GST) feature displays thecomputed convergence monitors while the solution is in process. Be default, GST is ON for interactive sessionsand OFF for batch runs. To turn GST on or off, use either of the following:

Command(s): /GSTGUI: Main Menu> Solution> Load Step Opts> Output Ctrls> Grph Solu Track

Figure 2.1: “Convergence Monitors Displayed by the GST Feature” shows two typical GST displays:

Section 2.6: What to Watch For During a FLOTRAN Analysis


Figure 2.1 Convergence Monitors Displayed by the GST Feature

(a) Steady-state simulation, (b) Transient simulation

In Figure 2.1: “Convergence Monitors Displayed by the GST Feature” (b), a plot of a transient FLOTRAN solution,each "spike" on the plot indicates the beginning of a new time step.



After perhaps some initial fluctuations, convergence monitors will decrease as the analysis approaches conver-gence. How small the numbers become depends on several factors, such as:

• Complexity of the geometry

• Adequacy of the finite element mesh in regions with steep gradients

• The severity of the turbulence levels, indicated by the flow Reynolds number

• Development of the flow near outlet boundaries

Points to remember when using graphical solution tracking include:

• The GST feature is available for FLOTRAN analyses and also for structural, thermal, and electromagneticanalyses containing nonlinearities. For information about using GST to track convergence in non-FLOTRANanalyses, see the ANSYS Thermal Analysis Guide, the ANSYS Low-Frequency Electromagnetic Analysis Guide,and the ANSYS Structural Analysis Guide.

• GST can display up to ten curves at the same time. (Your model can include more than ten DOFs, but onlythe first ten will be displayed.)

• When the GST begins its plotting, ANSYS displays a dialog box with a STOP button. You can stop thesolution at any time by clicking on this button. To restart it, issue SOLVE or choose Main Menu> Solution>Run FLOTRAN.

• The time label which is positioned above the graph reveals the time at the last iteration.

2.6.3. Stopping a FLOTRAN Analysis

You can choose a target value for terminating a FLOTRAN analysis, based on the convergence monitors for eachdegree of freedom falling below a certain value. To specify these values, use the following:

Command(s): FLDATA3,TERM,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl

See the ANSYS Commands Reference for the default values. Termination checks do not include inactive degreesof freedom or degrees of freedom set to a negative value.

The analysis must satisfy convergence criteria for all active degrees of freedom, or complete the specified numberof global iterations requested. FLOTRAN terminates on the first condition satisfied. For information on terminatingtransient analyses, see Chapter 5, “FLOTRAN Transient Analyses”.

To stop a FLOTRAN batch or background job in progress, place a file named Jobname.ABT in the subdirectoryfrom which the ANSYS job has been executed. The first line of this file should contain the word "terminate," andshould be left-justified. On Windows systems, you should also add a blank line at the end of the Jobname.ABTfile. FLOTRAN looks for the Jobname.ABT file during every global iteration. If it finds the file and reads the word"terminate," it will finish that global iteration and terminate normally, writing the results to the Jobname.RFLfile and extending the Jobname.PFL file.

2.6.4. Pressure Results

For locked tetrahedral elements (those at a corner where two walls meet) there is a slight pressure anomaly.ANSYS takes those elements out of the solution domain because all the nodes have boundary conditions. Thesolution is correct in the domain. Use hexahedral elements to avoid this pressure anomaly.

Section 2.6: What to Watch For During a FLOTRAN Analysis


2.7. Evaluating a FLOTRAN Analysis

The two basic questions an analyst must answer are:

1. When is the analysis completed?

2. Has it been done correctly?

These questions are interrelated, since convergence may not be achieved it you have not set up and executedthe analysis correctly.

If you have set the input parameters and boundary conditions correctly, the analysis is complete when the con-vergence monitors for all variables stop decreasing and the average, maximum, and minimum values of thesolution variables no longer increase or decrease. There is no guarantee, however, that you will achieve a singleexact answer because nature does not guarantee that a single exact answer exists. Oscillatory problems (for ex-ample, vortex shedding behind a cylinder) may not yield stationary results from a steady-state or a transientsolution algorithm. You may wish to continue executing the analysis to verify whether a solution has a stable ora fluctuating nature.

The ANSYS program stores the average, minimum, and maximum values of the solution variables in the fileJobname.PFL. This file also records the FLOTRAN input plus the convergence monitors which have been calcu-lated. The results summary includes all the DOF, as well as laminar and effective properties. You determine howoften ANSYS issues the results summary by using one of these methods:

Command(s): FLDATA5,OUTP,SUMF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Additional Out> RFL Out DerivedMain Menu> Solution> FLOTRAN Set Up> Additional Out> RFL Out Derived

The Value argument is the number of global iterations that pass before ANSYS issues the next results summary.

You may also want to map your results onto a path through your model. See Section 5.3.5: Mapping Results ontoa Path in the ANSYS Basic Analysis Guide for more information on reviewing results along a path.

2.8. Verifying Results

You, the analyst, are responsible for verifying results. If your FLOTRAN analysis produces unexpected results,take the actions listed below. You can accomplish many of these actions at the beginning of the analysis. ANSYScreates a Jobname.PFL file and checks inputs even if the number of iterations executed is zero.

1. Check the mass balance printed as part of the results summary. Internal checks will determine if anymass flow can potentially cross a model boundary. Boundary conditions admitting mass flow are:

• Specified velocity boundaries

• Specified pressure boundaries

• Unspecified boundaries (These can result if you inadvertently omit a boundary condition.)

The ANSYS program tabulates the number of inlets/outlets, which should correspond to expectations.

2. Check boundary conditions within ANSYS to ensure that they are accurate.

3. Check that you specified the properties correctly and that they can vary with temperature and pressureif necessary. The results summary in the Jobname.PFL file is a convenient place to check this.

4. Check that the length units used to build the model are consistent with those used in specifying properties.

5. In some cases, you need to verify that equations associated with the options chosen are solved correctly(for instance, the pressure equation in compressible flow).



6. If the unexpected result of your analysis is divergence, the finite element mesh may not have sufficientresolution, or significant gradients may exist near outlets. To resolve this, you may need to use conver-gence aids such as relaxation. Later sections in this document discuss various relaxation techniques.

7. If you get a diverged solution for a particular variable, you can re-initialize that variable to a single valueand continue. To do so, use one of these methods:

Command(s): FLDATA29,MODVGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Mod Res/Quad Ord> Modify ResultsMain Menu> Solution> FLOTRAN Set Up> Mod Res/Quad Ord> Modify Results

Section 2.8: Verifying Results


2–16

Chapter 3: FLOTRAN Laminar and TurbulentIncompressible Flow

3.1. Characteristics of Fluid Flow Analysis

A laminar or turbulent flow analysis calculates the flow and pressure distribution in a 2-D or 3-D geometry. Flowproblems require you to specify density and viscosity. Problems may be internal or external in nature. For internalflows, wall or symmetry planes bound the flow (for example, flow in a pipe), except for the inlet and outletboundaries. (Figure 3.1: “Internal Flow” shows an example). The boundaries of external problems generally areeither far-field velocity or pressure boundary conditions. The flow surrounding an airfoil is an external flow (SeeFigure 3.2: “External Flow”).

Figure 3.1 Internal Flow

Figure 3.2 External Flow


The distinction between incompressible and compressible flow lies in both the equation of state and the solutionalgorithm.

• In an incompressible flow, density variations can drive the flow only through gravitational acceleration.Temperature changes cause variations of density.

• In a compressible flow, the density changes caused by pressure variations significantly affect the momentumand temperature equations.

In any event, the incompressible algorithm can measure flow of an ideal gas, complete with small density changesdue to pressure. See Chapter 8, “FLOTRAN Compressible Analyses” for more information.

3.2. Activating the Turbulence Model

The distinction between laminar and turbulent flow lies in the ratio of the inertial transport to the viscoustransport. As this ratio increases, instabilities develop and velocity fluctuations begin to occur. A turbulentmodel accounts for the effect of these fluctuations on the mean flow by using an increased viscosity, the effectiveviscosity, in the governing equations. The effective viscosity is the sum of the laminar viscosity (which is a propertyof the fluid) and turbulent viscosity (which is calculated from a turbulence model).

µe = µ + µt

Generally, the more turbulent the flow field, the higher the effective viscosity.

3.2.1. The Role of the Reynolds Number

The dimensionless Reynolds number measures the ratio of inertial and viscous forces to help determine whetheror not the turbulence model should be activated. The Reynolds number is defined in terms of the properties ofthe fluid, a characteristic velocity, and a characteristic dimension:

RE = ρµ

VLc

The density ρ (mass/length3) and absolute viscosity µ (mass/length-time) are properties of the fluid. For internalflow problems, the characteristic dimension is the hydraulic diameter, defined as:

L =D =4 (Cross-Sectional Flow Area)

Wetted Perimeterc h

For example, the hydraulic diameter of a pipe is simply the diameter. As a general guideline for internal flowproblems such as flow in pipes, the turbulence model should usually be activated if the Reynolds number is inexcess of about 2300.

For an external flow problem, such as the flow over an airfoil, the characteristic length is a parameter such as thelength of the airfoil (wing cross section for a 2-D analysis).

For flow over a flat plate, the dimension is the length along the plate from the leading edge, with the transitionto turbulence occurring at a Reynolds number of approximately 500,000.

For more information, see the ANSYS, Inc. Theory Reference.


Chapter 3: FLOTRAN Laminar and Turbulent Incompressible Flow

3.2.2. Determining Whether an Analysis Is Turbulent

Determining if an analysis is laminar or turbulent is your responsibility. What happens if turbulence is not activatedwhen it should be, or vice versa? What are the indications and the consequences?

If turbulence is needed but not activated, the analysis probably will diverge. If this occurs, the momentum andpressure convergence parameters will approach 1.0 and the values of velocities and pressure will become verylarge. You should start over with the turbulence model activated.

In some cases, convergence occurs even without the turbulence model. This can happen if no geometrical featuressuch as bends disturb the flow. Physically, some flows retain laminar characteristics unless they are slightly dis-turbed in some fashion.

Conversely, although the turbulence models are not low Reynolds number models and do not "automatically"resort to laminar behavior at low Reynolds numbers, in such cases the turbulence models predict low values ofeffective viscosity. If the final average effective viscosity is less than five times greater than the laminar value,you should rerun the case without the turbulence model and evaluate the differences.

You can postprocess the effective viscosity with the label EVIS. It is also tabulated in the results summary outputprovided in the Jobname.PFL file. Therefore, you can observe the average behavior of effective viscosity as thesolution proceeds. You also can postprocess it to see its variation throughout the flow field.

3.2.3. Turbulence Ratio and Inlet Parameters

Be aware that when an analysis begins, the effective viscosity initializes as a multiple of the laminar value. Thisinitialization occurs whether a turbulence model is or is not active. The default value of this multiple (also calledthe turbulence ratio) is 1000; a reasonable value for most turbulent analyses. The algorithm calculates lower orhigher values as conditions dictate. However, the accuracy of the initial estimate affects how long the programtakes to compute the final value.

To set the turbulence ratio, use either of these methods:Command(s): FLDATA24,TURB,RATI,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

The two-equation turbulence models require boundary conditions for the turbulent kinetic energy (ENKE) andturbulent kinetic energy dissipation rate (ENDS) at an inlet. If known values are available at the inlet, you canspecify ENKE and ENDS, Otherwise, you must specify an inlet intensity (ININ), which is the ratio of the fluctuatingvelocity to the inlet velocity, and an inlet scale factor (INSF), which is the ratio of a length scale inlet region tothe hydraulic diameter of the inlet. ININ and INSF default to 0.01.

To set the inlet intensity and inlet scale factor, you use either of the following:Command(s): FLDATA24,TURB,ININ,Value FLDATA24,TURB,INSF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

3.2.4. Turbulence Models

FLOTRAN offers several turbulence models:

1. Standard k-ε Model

2. Zero Equation Turbulence Model (ZeroEq)

3. Re-Normalized Group Turbulence Model (RNG)

4. k-ε Model due to Shih (NKE)

Section 3.2: Activating the Turbulence Model


5. Nonlinear Model of Girimaji (GIR)

6. Shih, Zhu, Lumley Model (SZL)

7. k-ω Turbulence Model

8. Shear Stress Transport Turbulence Model (SST)

Turbulence modeling is activated by either of the following:Command(s): FLDATA1,SOLU,TURB,TGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution OptionsMain Menu> Solution> FLOTRAN Setup> Solution Options

To select a model, you use either of the following:Command(s): FLDATA24,TURB,MODL,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

Normally, the Standard k-ε Model is the first model to apply. It usually provides a realistic picture of the flow. Itis fine for the analysis of turbulent flow in pipes and channels. However, it over predicts the amount of turbulencein a number of situations. For example, the flow in a converging nozzle undergoes significant normal strain andthe Standard k-ε Model over predicts the amount of turbulence. The resulting kinetic energy is over predicted,and the resulting effective viscosity prevents simulation of shock waves in some cases.

In general, the RNG, NKE, GIR, and SZL turbulence models produce significantly more realistic and reliable resultsin regions of large strain. This is particularly important for cases where the flow is strongly accelerated or decel-erated (e.g. a converging nozzle) or where there is significant separation or recirculation (e.g. a duct that goesthrough a 180 degree change of direction). Other situations where the Standard k-ε Model encounters difficultiesinclude flows with stagnation points.

The RNG, NKE, GIR, and SZL turbulence models control the excess turbulence by applying adjustments to C µand the source term of the dissipation equation. The adjustments are made in accordance with the local rate ofstrain.

The k-ω turbulence model has the advantage near the walls to accurately predict the turbulence length scale inthe presence of an adverse pressure gradient. The k-ω model is much more sensitive to the free-stream turbulencelevels than the k-ε model. The Shear Stress Transport model (SST) combines the k-ω model near the wall and thek-ε model away from the wall to overcome the deficiencies of both models.

See the ANSYS Commands Reference and the ANSYS, Inc. Theory Reference for more information on the models.

3.2.4.1. Standard k-epsilon Model (default)

The Standard k-ε Model, the Zero Equation Turbulence Model, and the k-ω Model are the simplest models. Theother models are all extensions of the Standard k-ε Model and the k-ω Model. The Standard k-ε Model is the defaultmodel.

To select the Standard k-ε Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,1GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

Cµ, C1, C2, SCTK, and SCTD are Standard k-ε Model constants that are defined as follows:

Cµ - Value is the k-ε turbulence model constant



µ ρεµt Ck=

2

which is used in the update of the turbulent viscosity.

C1 - Value is the k-ε turbulence model C1 constant. It is the multiplier of the shear rate generation term of theturbulent kinetic energy dissipation rate equation.

C2 - Value is the k-ε turbulence model C2 constant. It is the multiplier of the dissipation source term in the tur-bulent kinetic energy dissipation rate equation.

SCTK - Value is the Schmidt number for the turbulent kinetic energy. The diffusion term in the turbulent kineticenergy equation is divided by this factor.

SCTD - Value is the Schmidt number for the kinetic energy dissipation rate. The diffusion term in the dissipationrate equation is divided by this factor.

To set the Standard k-ε Model constants Cµ, C1, C2, SCTK, and SCTD, you use either of the following:Command(s): FLDATA24,TURB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

The following five wall parameters control turbulence wall modeling. The wall parameters apply for all turbulencemodels except the Zero Equation Turbulence Model.

KAPP - Value is the law of the wall constant. It is the slope of the plot of normalized shear velocity (u+) versus

the nondimensionalized distance from the wall (y+). See ANSYS, Inc. Theory Reference for details.

EWLL - Value is the law of the wall constant. It is related to the y intercept value for a plot of normalized shear

velocity (u+) versus the nondimensionalized distance from the wall (y+). See the ANSYS, Inc. Theory Reference formore details.

WALL - Value is the choice of wall conductivity model. The default model is the Van Driest model (Value =VAND), used most often for high Prandtl number fluids. The second choice is the Spalding model (Value = SPAL),applicable to low Prandtl number fluids. The third choice is the Equilibrium model (Value = EQLB). The equilib-rium model is also automatically invoked for the wall viscosity by this command.

VAND - Value is the constant in the Van Driest wall conductivity model. See the ANSYS, Inc. Theory Reference fordetails.

TRAN - Value is the magnitude of y+ marking the outer boundary of the laminar sublayer. Used only for theEquilibrium Wall model.

To set the wall parameters KAPP, EWILL, WALL, VAND and TRAN, you use either of the following:Command(s): FLDATA24,TURB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Wall ParametersMain Menu> Solution> FLOTRAN Setup> Turbulence> Wall Parameters

The following three buoyancy terms control buoyancy modeling. The buoyancy terms apply for all turbulencemodels except the Zero Equation Turbulence Model.



BUC3 - Value is the k-ε buoyancy model constant. A value of zero means that there is no contribution to theturbulent kinetic energy dissipation rate equation. The default value of one is appropriate for stable thermallystratified flows. A value of zero is appropriate for unstable thermally stratified flows.

BUC4 - Value is the k-ε multiplier applied to the buoyancy term of the turbulent kinetic energy equation. A valueof 1.0 is appropriate for the calculation of stable thermally stratified flows. The default value is zero.

BETA - Value is β, the coefficient of thermal expansion

βρ

ρ= ∂∂

1T

This term is used in the buoyancy terms of the k-ε model.

To set the buoyancy terms BUC3, BUC4, and BETA, you use either of the following:Command(s): FLDATA24,TURB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Buoyancy TermsMain Menu> Solution> FLOTRAN Setup> Turbulence> Buoyancy Terms

See the ANSYS, Inc. Theory Reference and the ANSYS Commands Reference for more information.

3.2.4.2. Zero Equation Turbulence Model (ZeroEq)

The Zero Equation Turbulence Model (ZeroEq) is the simplest and fastest turbulence model. It applies to problemswith fairly simple geometry and flow characteristics. The model does not give accurate results if there is significantseparation or recirculation.

To select the Zero Equation Turbulence Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,2GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

The Zero Equation Turbulence Model contains an automatic calculation of the length scale or you can specifythe length scale. Generally, the turbulence ratio can be set to 2.0 when you are using the Zero Equation TurbulenceModel.


3.2.4.3. Re-Normalized Group Turbulence Model (RNG)

The Re-Normalized Group Turbulence Model (RNG) is effective where the geometry has a strong curvature (e.g.,a duct that goes through a 180 degree change in direction. If you have tried the SZL Model and the results areunsatisfactory, it is generally recommended that you try the RNG Model.

To select the RNG Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,3GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

To set the constants for the RNG Model, you use either the FLDATA24A,RNGT command or the foregoing GUI.

The RNG Model is an extension of the Standard k-ε Model. Seven constants are assigned values. The Cµ, C1, C2,SCTK, and SCTD constants are assigned values that are separate from the Standard k-ε Model. The following twoconstants are added:



BETA -Value is the RNG model constant, β∞

ETAI -Value is the asymptotic value of the strain rate parameter eta.

Inlet parameters and wall parameters are the same as the Standard k-ε Model.


3.2.4.4. k-epsilon Model Due to Shih (NKE)

The k-ε Model due to Shih (NKE) features a variable Cµ term which helps to reduce the excess normal strain termsin the Standard k-ε Model. The NKE model also employs a different dissipation source term than the Standardk-ε Model.

The NKE and GIR models are recommended for rotating flows.

To select the NKE Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,4GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

To set the constants for the NKE Model, you use either the FLDATA24B,NKET command or the foregoing GUI.

The NKE Model is an extension of the Standard k-ε Model. Four constants are assigned values. The C2, SCTK, andSCTD constants are assigned values that are separate from the Standard k-ε Model. The following constant isadded:

C1MX - Value is the maximum allowed value of the C1 constant in the turbulent kinetic energy dissipation rateequation.



3.2.4.5. Nonlinear Model of Girimaji (GIR)

The Nonlinear Model of Girimaji (GIR) is suggested for cases with secondary vortices in the flow. The GIR and NKEmodels are recommended for rotating flows.

To select the GIR Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,5GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

To set the constants for the GIR Model, you use either the FLDATA24C,GIRT command or the foregoing GUI.

The GIR Model is an extension of the Standard k-ε Model. Seven constants are assigned values. The SCTK, andSCTD constants are assigned values that are separate from the Standard k-ε Model. The following five constantsare added:

G0 - Value is the C10

constant.

G1 - Value is the C11

constant.G2 - Value is the C2 constant.



G3 - Value is the C3 constant.

G4 - Value is the C4 constant.



3.2.4.6. Shih, Zhu, Lumley Model (SZL)

The SZL Model is simpler than the NKE and GIR models. It produces the lowest level of turbulence. The SZLmodel is numerically efficient, but in some cases the resulting low effective viscosity has an adverse effect onstability. Generally, if the SZL model does not give satisfactory results, it is recommended that you try the RNGmodel.

If conditions of large strain exist in the flow field, you may want to try the SZL Model after trying the RNG, NKEor GIR models. If the SZL Model gives significantly different results, it is recommended that you refine the meshin the regions where the turbulence field is strongly altered.

To select the SZL Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,6GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

To set the constants for the SZL Model, you use either the FLDATA24D,SZLT command or the foregoing GUI.

The SZL Model is an extension of the Standard k-ε Model. Five constants are assigned values. The SCTK, and SCTDconstants are assigned values that are separate from the Standard k-ε Model. The following three constants areadded:

SZL1 - Value is the numerator constant used in the calculation of Cµ. It is the Aszl1 constant.

SZL2 - Value is the denominator constant used in the calculation of Cµ. It is the Aszl2 constant.

SZL3 - Value is the strain rate multiplier. It is the Aszl3 constant.



3.2.4.7. k-omega Turbulence Model

The k-ω model is one of the simplest turbulence models. It provides better modeling of the turbulent boundarylayer than the standard k-ε model, but is more sensitive to the free-stream turbulence levels.

To select the k-ω Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,7GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

To set the constants for the k-ω Model, use either the FLDATA24E,SKWT command or the foregoing GUI.

The k-ω Model solves for the ω equation rather than the ε equation in the standard k-ε Model. Four constantsare assigned values. The SCTK constant is an assigned value that is separate from the Standard k-ε Model. Thefollowing three constants are added:

SCTW - Value is the Schmidt number for the specific dissipation rate.BETA - Value is the BETA factor.



GAMA - Value is the GAMMA factor.



3.2.4.8. Shear Stress Transport Model (SST)

The SST Model combines advantages of both the Standard k-ε Model and the k-ω Model. It automatically switchesto the k-ω Model in the near region and the Standard k-ε Model away from the walls.

To select the SST Model, you use either of the following:Command(s): FLDATA24,TURB,MODL,8GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence ModelMain Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

To set the constants for the SST Model, use the FLDATA24F,SST1, FLDATA24G,SST1 and FLDATA24H,SST2commands, or the foregoing GUI. Similar to the k-ω Model, the SST Model solves for the ω equation rather thanthe ε equation in the Standard k-ε Model. Nine constants are assigned values. The SCTK1 and the SCTK2 constants

are assigned values that are separate from the Standard k-ε Model. The following seven constants are added.

CLMT - Value is the turbulent production clip factor.SCTW1 - Value is the Schmidt number for the specific dissipation rate in the k-ω regime.

SCTW2 - Value is the Schmidt number for the specific dissipation rate in the k-ε regime.

BETA1 - Value is the BETA factor in the k-ω regime.

BETA2 - Value is the BETA factor in the k-ε regime.

GAMA1 - Value is the GAMMA factor in the k-ω regime.

GAMA2 - Value is the GAMMA factor in the k-ε regime.



3.3. Meshing Requirements

The meshing requirements for turbulence are more restrictive than those for laminar flow. The most importantareas obviously are those with the higher gradients, in particular the regions near walls.

Structured meshes, as contrasted with free meshes, can provide more consistent representation at the walls.Figure 3.3: “Structured Mesh” and Figure 3.4: “Unstructured Mesh” compare the structured and unstructuredmeshes for a region near the wall.

Section 3.3: Meshing Requirements


Figure 3.3 Structured Mesh

This mesh was produced with MSHAPE,0,2D and MSHKEY,1 commands.

Figure 3.4 Unstructured Mesh

This mesh was produced with MSHAPE,1,2D and MSHKEY,0 commands.



You can evaluate the adequacy of the mesh near the walls. Applying the turbulence model near walls involves

the "Log Law of the Wall," the relationship between a nondimensionalized distance from the wall Y+, and thelog of a nondimensionalized velocity in a region near the wall. This law calculates a near wall viscosity that is

consistent with experimentally determined velocity profiles near the wall. Values of Y+ are relevant only for wallnodes and are available for postprocessing (YPLU).

Optimum values of Y+ are between approximately 30 and 1000. If the pressure is decreasing in the direction of

flow, values up to 5000 are acceptable. FLOTRAN handles the case where Y+ is less than 30 for the near wall nodeby assuming that the near wall node is in the laminar sublayer or the overlap region. In the former case, the nearwall viscosity is simply the laminar value.

If Y+ is very small, perhaps below 1, more elements than necessary are being used to resolve the flow distribution

field. If Y+ is greater than 5000, decrease the mesh spacing near the wall.

Caution: Use enough elements to resolve the flow field in the regions of interest. You should use atleast four elements to span the cross sections of long thin channels. Use more than four elements wherethin channels connect to larger regions.

3.4. Flow Boundary Conditions

Each boundary of the problem domain requires treatment. You specify some combination of DOF (VX, VY, VZand PRES) at the boundary types listed below. (If suitable values are available, you can specify turbulent kineticenergy (ENKE) and turbulent kinetic energy dissipation rate (ENDS) at an inlet.) The derivative of all dependentvariables normal to the surface is zero if you apply no conditions at the boundary surface.

To set DOF constraints at nodes, use either of the following:Command(s): DGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> boundary condition type

You can set boundary conditions on the solid model using any of the following:Command(s): DA and DLGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> boundary condition type> OnAreasMain Menu> Solution> Define Loads> Apply> boundary condition type> On AreasMain Menu> Preprocessor> Loads> Define Loads> Apply> boundary condition type> On LinesMain Menu> Solution> Define Loads> Apply> boundary condition type> On Lines

This enables you to redo the analysis with a different mesh, without reapplying boundary conditions on a nodalbasis. These commands or GUI paths allow you to specify the condition on the endpoints of a line or the edgeof an area.

Take care to ensure that the proper conditions are applied at intersecting boundaries. You have control overwhether or not boundary conditions are applied at the ends of lines or at the edges of areas. A nonzero velocitycomponent at the end of a line or at the edge of an area will not replace an existing zero velocity condition atthe associated nodes. Where a wall intersects an inlet, the wall condition will automatically prevail.

If you apply new (and different) boundary conditions to a solid model of a finite element mesh, you should deleteexisting nodal boundary conditions before transferring the new loads.

Specified Flow: You specify all velocity components at the boundary. Use this method to specify a flow at aninlet. Knowledge of the mass flow at the inlet requires you to know the density.

Section 3.4: Flow Boundary Conditions


Specified Pressure: Typically, you apply a relative pressure (usually zero) as an outlet boundary condition. Inthe absence of gravity and a rotating reference frame, the absolute pressure is the sum of the FLOTRAN (relative)pressure and the reference pressure. See the ANSYS, Inc. Theory Reference for a more complete discussion ofpressure. A problem may also be pressure driven, in which case one of the pressure boundaries is an inlet.

Note — If significant gradients are calculated near a boundary, a mass imbalance can occur. This is dueto the implied condition of fully developed flow for a constant pressure boundary. If the flow has notfully developed, FLOTRAN is forced to adjust it across the last row of elements to satisfy the boundarycondition. Occasionally, this adjustment may cause a mass imbalance.

To prevent this from occurring, you can add a development length to the exit. This addition does not actuallyneed to match the physical flow geometry. You can subtract the pressure drop in this "chimney" to obtain thedesired pressure drop. The pressure drop in the "chimney" will vary over its full cross section. You will have tochoose a representative value of the pressure drop to match the desired outlet conditions. You will not knowthis pressure drop, of course, until after you examine the results from the chimney. You can opt to apply an exitpressure profile, based on these results, to the original geometry.

You can calculate the required length of the chimney (L) using the characteristic diameter (D) from the develop-ment length formula:

Laminar flow: L/D ~ 0.06 Re

Turbulent flow: L/D ~ 4.4 Re1/6

Typically, a chimney 20 to 25 diameters long will be sufficient. Although the mesh in this region may be coarse,you should avoid drastic changes in element size by using a size ratio in the chimney. The important feature isthe chimney length, not the number of nodes in it.

Symmetry Boundary: The velocity component normal to the boundary is specified as zero. Leave all other degreesof freedom unspecified.

Generalized Symmetry Boundary Conditions: You can also apply generalized symmetry boundary conditions.Velocity components are set tangential to the symmetry surface if the ALE formulation is not activated. They areset equal to the mesh velocity if the ALE formulation is activated. To apply generalized symmetry boundaryconditions, use one of the following commands or the GUI equivalent:

D,NODE,ENDS,-1DL,LINE,AREA,ENDS,-1,Value2DA,AREA,ENDS,-1,Value2

With one exception, if any velocity component is specified at the same boundary, the generalized symmetryboundary conditions are overwritten. In a 2-D swirl problem, specification of a velocity component VZ does notoverwrite generalized symmetry conditions.

Stationary Wall: This is also referred to as a no-slip condition. All the velocity components are set to zero.

Moving Wall: Specify the velocity component tangent to the wall and set all other velocity components to zero.As a flag to indicate this is a moving wall, set the turbulent kinetic energy to -1 on a moving wall. This specificationis as a flag only; it does not affect the performance of the wall turbulence model. If you are using the GUI, indicatea moving wall when specifying the velocities.

Unspecified Boundary: In this case, neither the relative pressure nor the velocities are known. The most commonapplication for this is at downstream boundaries in compressible supersonic flow.



Periodic Boundary: Conditions are unknown but identical at two boundaries. You select the nodes at oneboundary and then issue the macro PERI,DX, DY, DZ, where DX, DY, and DZ are the offsets of the secondboundary from the first. The offsets are input in the established FLOTRAN coordinate system. The meshes at thetwo boundaries must be identical.

Intersections: At the intersection of surfaces where two different boundary conditions are applied, either theboundary conditions are merged or one takes precedence over the other. The following table provides guidanceon what boundary conditions are applied at the intersection.

Table 3.1 Boundary Conditions at Intersections

ActionIntersecting Boundary 2Intersecting Boundary 1

Overwrite inflow with wallWall:VX, VY, VZ = 0

Inflow:VX, VY, VZ values specified

Combine inflow with symmetrySymmetry:VX or VY or VZ = 0


Enforce inflow condition, not outflowOutflow:P = 0


Combine symmetry and outflowOutflow:P = 0

Symmetry:VX or VY or VZ = 0

Overwrite symmetry with the wallWall:X, VY, VZ = 0

Symmetry:VX or VY or VZ = 0

Combine wall and outflow conditionsOutflow:P = 0

Wall:VX, VY, VZ = 0

Combine the generalized symmetry and outflowconditions

Outflow:P = 0

Generalized Symmetry

Note — Inflow, symmetry , and wall boundary conditions all overwrite generalized symmetry conditions.

Inlet Values: If you activate the turbulence model, boundary conditions are required. The ANSYS program suppliesdefault values based on the inlet velocity and a scale factor. Given an inlet velocity magnitude V, the inlet kineticenergy is specified as:

k [(ININ)V]inlet2= 3

2

The default value of the factor ININ is 0.01, corresponding to a level of turbulence of 1 percent at the inlet. Theinlet value of the kinetic energy dissipation rate ε is calculated from:

ε µinlet

INSF L=

C k32

( )

The INSF value is a user-controlled scale factor. To specify the factors ININ and INSF, use either of the followingmethods:

Command(s): FLDATA24,TURB,ININ,Value and FLDATA24,TURB,INSF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

Section 3.4: Flow Boundary Conditions


Main Menu> Solution> FLOTRAN Set Up> Turbulence> Turbulence Param

You can set specific values of the turbulent kinetic energy (ENKE) or the dissipation rate (ENDS) using either theFLDATA24 command or the menu paths in Section 3.2.2: Determining Whether an Analysis Is Turbulent.

Occasionally, you may wish to activate the turbulence model for the case, but deactivate it for certain regions.To deactivate the turbulence model in regions, set the kinetic energy (ENKE) to zero and the dissipation rate(ENDS) to 1.0. It is never valid to set the dissipation rate to zero, and FLOTRAN prohibits it. ENDS will be set to1.0, if ENKE is set to zero.

Wall Roughness:

The FLOTRAN default condition is smooth walls. To specify wall roughness values, you must use the equilibriumwall turbulence model. You activate it using the FLDATA24,TURB,WALL,EQLB command.

To apply a uniform wall roughness in length units to all walls, you can use the FLDATA24,TURB,KS,Value command.In addition to being the actual roughness, the KS parameter determines the regime of roughness (smooth,transitional, or fully rough). The default value of 0.0 implies a smooth wall.

You can also apply an empirical dimensionless factor (CKS) between 0.5 and 1.0 that specifies the degree ofnonuniformity of the surface. The default value of 0.5 means that the roughness signified by KS is uniformlydistributed. Higher values increase the roughness losses without changing the flow regime implied by the valueof KS. You can use the FLDATA24,TURB,CKS,Value command to specify this factor.

The following two methods are available if you have surfaces that require different roughness values.

The first method utilizes real constants for all the wall elements. You apply suitable KS and CKS values to the nearwall elements as real constants. A different real constant set will exist for each set of wall roughnesses. Note thatroughness constants applied to elements that are not near wall will be ignored. Also, any KS and CKS valuesspecified by the FLDATA24,TURB command will be ignored.

The second method is for cases where most of the surfaces have the same roughness condition and only a feware different. First, set the values appropriate for most of the surfaces with the FLDATA24,TURB command. Thenuse real constants to apply roughnesses to the walls that have different conditions. The real constants willoverwrite the FLDATA24,TURB values. Note that if the same value of CKS is applied to all the surfaces (as is typ-ical), it can be controlled with the FLDATA24,TURB command and the real constant can be omitted.

3.5. Strategies for Difficult Problems

The most common problems are divergence or oscillation of the pressure and/or velocity field.

The following strategies have proven helpful in getting difficult turbulent problems to converge.

1. Activate the turbulence option if you have not done so.

Turbulence modeling is activated by either of the following:Command(s): FLDATA1,SOLU,TURB,TGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution OptionsMain Menu> Solution> FLOTRAN Setup> Solution Options

2. Use a mapped mesh if a free mesh has given poor results. Resolve the boundary layer so that the value

of Y+ is less than 5000.

To set the Y+ output option, use the following:Command(s): FLDATA5,OUTPUT,YPLU,Value



GUI: Main Menu> Preprocessor> FLOTRAN Setup> Additional Out> RFL Out DerivedMain Menu> Solution> FLOTRAN Setup> Additional Out> RFL Out Derived

3. Set the turbulence inertial relaxation factor to 1.0. Values as low as 1.0-2 may help. (For incompressibleflow problems, you may not need to vary this factor.)

To set the turbulence inertial relaxation factor, use the following:Command(s): FLDATA26,STAB,TURB,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Stability ParmsMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms

4. Use pressure and momentum relaxation factors less than 0.5. If values as low as 0.2 do not help, goinglower probably will not help either.

To set the pressure and momentum relaxation factors, use the following:Command(s): FLDATA25,RELX,PRES,Value FLDATA25,RELX,VX (or VY, VZ),ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> DOF RelaxationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> DOF Relaxation

5. Begin the problem with a higher turbulence ratio (meaning a higher initial effective viscosity). Do not

set values for this parameter, which takes effect only at problem startup, above 1.0 x 107. The ratio setcontrols the initial effective viscosity no matter when you activate the turbulence model.

To set the turbulence ratio, use either of these methods:Command(s): FLDATA24,TURB,RATI,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence ParamMain Menu> Solution> FLOTRAN Set Up> Turbulence> Turbulence Param

6. After initializing with the correct properties, solve the problem with a higher viscosity and the turbulencemodel turned off. When the flow field is partially converged, the turbulence model is activated. You mayneed to reduce the relaxation factor of the effective viscosity to 0.1 or 0.0 for some global iterations toallow partial convergence of the turbulence equations. Refer to the foregoing strategies for commandinformation.

7. Difficulties can involve large changes in properties due to large fluctuations in pressure or temperature.Preventing property variations early in the analysis (until the large fluctuations calm down) can stabilizethe analysis significantly.

You also can invoke velocity capping to prevent large values of velocities or pressures. This is particularlyuseful in compressible analyses, where velocity spikes can cause negative static temperatures.

To implement velocity capping, use either of the following methods:Command(s): FLDATA31,CAPP,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Results CappingMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Results Capping

If you use the FLDATA31 command, Label represents a capping parameter such as VELO (velocity), orTEMP (temperature). Value is either the capping flag (T or F) or the capping parameter value. Pressurecapping applies to relative values of pressure. Temperature capping applies to absolute values of tem-perature.

8. Problems involving pyramid, wedge or in particular tetrahedral element shapes may require tighterconvergence of the pressure equation. Values as low as 1.E-18 may be required (FLDATA21,CONV,PRES,1.E-18). You should reduce the convergence criterion until, from one global iteration to the next, the numberof iterations required to solve the equation varies by less than 10 percent (as per the Jobname.DBG file).

Section 3.5: Strategies for Difficult Problems


9. The solution of the pressure equation may affect the mass balance. The mass balance may be incorrect(as per the Jobname.PFL file) if large aspect ratio elements are near significant flow area changes. Massimbalances may also occur if inlet or outlet regions are too coarsely meshed or if the flow tends to exitat an angle at outlets.

10. If FLOTRAN displays a message stating that the coefficient matrix has a negative diagonal and the solutionis probably divergent, try turning on modified inertial relaxation in the momentum equation or turbulenceequation. Set the Value between 0.1 and 1.0. To achieve a faster convergence rate, use the smallestValue possible.

To set the turbulence inertial relaxation factor, use the following:Command(s): FLDATA34,MIR,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> MIR StabilizationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization

11. If you notice anomalous results for 3-D problems, you should increasing the quadrature order to 2.

12. Specifying the Streamline Upwind/Petrov-Galerkin (SUPG) approach for momentum may help conver-gence. Specifying the SUPG approach for temperature may also yield more accurate energy solutionsand hence more accurate energy balances. For more information on the SUPG approach, see Chapter 14,“Advection Discretization Options”.

3.6. Example of a Laminar and Turbulent FLOTRAN Analysis

Access the CFD Tutorial to perform an example analysis of laminar and turbulent flow in a 2–D duct.

Before you begin the laminar/turbulent example, note the following:

• The example problem is only one of many possible FLOTRAN analyses. It does not illustrate every techniqueyou might use in a FLOTRAN analysis, and is intended only to show the kinds of tasks a FLOTRAN analysistypically requires.

• You can use many techniques in a FLOTRAN analysis that are not shown in this problem. For example,you can integrate pressure and shear stress on an airfoil to determine the lift and drag forces (see thedescription of the INTSRF command in Section 5.3.3: Integrating Surface Results in the ANSYS Basic Ana-lysis Guide).

• The values you enter in this example are specific values for this example only. The characteristics of theindividual problem you are solving dictate what values you should specify for a particular FLOTRAN ana-lysis.



Chapter 4: FLOTRAN Thermal Analyses

4.1. Thermal Analysis Overview

In a thermal analysis, you solve the temperature equation to determine temperature. Even if the temperatureitself is not important, the variation of fluid properties with temperature may be important enough to warranta thermal analysis.

In addition to calculating a temperature field, a thermal analysis provides heat fluxes at problem boundaries andheat transfer coefficients based on an assumed bulk or ambient temperature.

You activate solution of the temperature equation via one of the following:Command(s): FLDATA1,SOLU,TEMP,TRUEGUI: Main Menu> Solution> FLOTRAN Set Up> Solution Options

FLOTRAN automatically includes viscous heating for compressible flows. For information on activating viscousheating for incompressible flows, see Section 4.5.2: Forced Convection, Temperature Dependent Properties andthe description of the FLDATA1 command in the ANSYS Commands Reference.

4.2. Meshing Requirements

The ANSYS program has no formal criteria for evaluating the finite element mesh. However, thermal gradientsare often extremely high near thermal boundaries, especially heat flux boundaries. Therefore, the mesh shouldusually be denser near thermal boundaries.

4.3. Property Specifications and Control

In addition to density and viscosity, thermal flow problems require the specification of thermal conductivity andspecific heat. You must determine whether or not fluid properties should vary with temperature.

To set properties for non-fluid regions, use one of these methods:Command(s): MPGUI: Main Menu> Preprocessor> Loads> Load Step Opts> Other> Change Mat PropsMain Menu> Preprocessor> Material Props> Material Models> CFD> Conductivity> IsotropicMain Menu> Preprocessor> Material Props> Material Models> CFD> Specific HeatMain Menu> Solution> Load Step Opts> Other> Change Mat Props

4.4. Thermal Loads and Boundary Conditions

The ANSYS program supports six types of thermal boundary conditions:

1. Constant temperatures

2. Constant heat fluxes

3. Applied heat transfer (film) coefficients with associated ambient temperatures

4. Ambient radiation with associated surface emissivities and ambient temperatures

5. Surface-to-surface radiation with associated emissivities and enclosure number.

6. Adiabatic boundaries (the default condition)

In addition, constant volumetric heat sources may be located in both fluid and non-fluid regions.


The applicable commands are summarized below.

You can apply your boundary conditions via TABLE type array parameters (see Section 2.3.4.2.1: Applying LoadsUsing TABLE Type Array Parameters in the ANSYS Basic Analysis Guide). You can also apply your boundary conditionsusing function boundary conditions (see Section 2.6.15: Applying Loads Using Function Boundary Conditionsin the ANSYS Basic Analysis Guide).

You can define a TABLE type array parameter to apply your boundary conditions in a FLOTRAN analysis. Attemptingto use tabular boundary conditions in a FLOTRAN analysis will create erroneous results.

4.4.1. Applying Loads

The table below lists the loads you can apply in a thermal FLOTRAN analysis.

Table 4.1 Command Family and GUI Path Used to Apply Loads

GUI PathCmdFamily

CategoryLoad Type

Main Menu> Solution> Define Loads> Apply> TemperatureDConstraintsTemperature (TEMP)

Main Menu> Solution> Define Loads> Apply> Thermal>ConvectionMain Menu> Solution> Define Loads> Apply> Thermal>Heat FluxMain Menu> Solution> Define Loads> Apply> Thermal>Ambient RadMain Menu> Solution> Define Loads> Apply> Thermal>Surface Rad

SFSurface LoadsConvection (CONV),Heat Flux (HFLU),Radiation (RAD),Surface-to-surface radiation (RDSF)

Main Menu> Solution> Define Loads> Apply> Fluid/CFD>Heat Generat

BFBody LoadsHeat Generation Rates(HGEN)

In an analysis, you can apply, remove, operate on, or list loads.

4.4.1.1. Applying Loads Using Commands

The table below lists all the commands in detail you can use to apply loads in a FLOTRAN thermal analysis.

Table 4.2 Load Commands for a FLOTRAN Thermal Analysis

Apply Set-tings

OperateListDeleteApplyEntitySolid Modelor FE

Load Type

--DLISTDDELEDNodesFinite ElementTemperature

---SFLDELESFLLinesSolid ModelConvection, HeatFlux, Ambient Radi-ation, or Surface-to-surface Radiation

SFGRADSFTRANSFALISTSFADELESFAAreasSolid Model

--SFLISTSFDELESFNodesFinite Element

-SFSCALESFELISTSFEDELESFEElementsFinite Element

-SFSCALESFELISTSFEDELESFEElementsFinite ElementHeat GenerationRates -BFTRANBFLLISTBFLDELEBFLLinesSolid Model

-BFTRANBFALISTBFADELEBFAAreasSolid Model

-BFTRANBFVLISTBFVDELEBFVVolumesSolid Model

--BFLISTBFDELEBFNodesFinite Element



-BFSCALEBFELISTBFEDELEBFEElementsFinite Element

Note — You must use tabular boundary conditions if you are applying tapered heat flux or convectionloads.

4.4.1.2. Applying Loads Using the GUI

You access all operations except List through a series of cascading menus. From the Solution Menu, you choosethe operation (Apply, Delete, etc.), then the load type (temperature, heat flux, etc.), and then the object (node,line, or area) to which you are applying the load.

For example, to apply a temperature load to lines, follow this GUI path:

Main Menu> Solution> Define Loads> Apply> Thermal> Temperature> On Lines

To list loads, follow this GUI path:

Utility Menu> List> Loads> load type

4.4.1.3. Solutions

The following list describes what is known and what is calculated as a function of the type of boundary specified.

• For temperature boundary conditions, heat flux and heat transfer coefficient are calculated.

• For heat flux boundary conditions, temperature and heat transfer coefficient are calculated.

• For ambient radiation boundary conditions, temperature and heat flux are calculated.

• For surface-to-surface radiation boundary conditions, temperature and heat flux are calculated.

• For heat transfer boundary conditions, temperature and heat flux are calculated.

• For adiabatic boundary conditions, temperature is calculated.

When you apply a heat transfer (film) coefficient, you also specify an associated ambient temperature. The ANSYSprogram uses this along with the surface temperature to calculate the heat flux at that boundary.

You specify heat flux and heat transfer coefficients at external model boundaries. You cannot specify them atgeneral internal surfaces. You can specify heat flux and heat transfer coefficients at internal boundary faces (suchas fluid/solid interface surfaces), but FLOTRAN will issue a warning because they are probably incorrect. In astandard FLOTRAN analysis the heat transfer at a fluid/solid boundary is a desired result, not a boundary condition.If you wish to apply a heat flux or a heat transfer coefficient, you should apply it at the external solid materialboundary, or at the edge of the fluid region without modeling the solid material in the analysis. If you specify afilm coefficient or a heat flux at an internal fluid/solid interface, FLOTRAN interprets it to be a line/area heatsource or sink. You can prescribe temperatures anywhere.

In cases where you must calculate the heat transfer coefficient at a surface, ANSYS uses the surface temperaturealong with the bulk temperature you specify using either of the following methods:

Command(s): FLDATA14,TEMP,BULK,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref ConditionsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

If the analysis is compressible, boundary condition temperatures are in terms of total temperature, and thetemperature equation is formulated and solved in terms of total temperature.

Section 4.4: Thermal Loads and Boundary Conditions


The FLOTRAN ambient radiation load simulates radiation heat transfer to space at a constant temperature. Youspecify the constant temperature with the SF command. You specify the Stefan-Boltzmann constant with the

STEF command (defaults to 0.119E-10 Btu/hr/in2/ °R4). The form factor is 1.0 by assumption.

Since radiation can pass through a fluid region and impact on a solid, you can apply the ambient radiation loadon a fluid/solid interface, as well as on external model boundaries. In this case, you should apply the surface loadto either the fluid or solid element faces, or the solid model entity defining the interface. If you apply the loadto more than one face, FLOTRAN applies the boundary conditions on only one face and issues a message thatit skipped duplicate boundary conditions.

4.5. Solution Strategies

The most efficient way to solve thermal-flow problems depends on the degree to which the fluid propertiesdepend on the temperature.

4.5.1. Constant Fluid Properties

In this case, the flow solution does not depend at all on the temperature field and can be converged withoutactivating the temperature equation solution.

Once the flow solution is complete, the temperature equation become linear. You can then solve it in oneglobal iteration after you set the relaxation factor for temperature to 1 using either method shown below:

Command(s): FLDATA25,RELX,TEMP,1.0GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap/DOF RelaxationMain Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap/Prop RelaxationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap/DOF RelaxationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap/Prop Relaxation

This is often best accomplished with a semi-direct solution algorithm.

See Chapter 11, “FLOTRAN CFD Solvers and the Matrix Equation” for more information.

The flow equations need not be solved during the solution of the temperature equation. Executing two globaliterations should result in a very small change, if any, in the answer during the second calculation. This will bereflected in a large decrease in the convergence monitors for temperature in the second iteration.

4.5.2. Forced Convection, Temperature Dependent Properties

The flow pattern will be a mild function of the temperature field. You can choose to solve the temperatureequation every global iteration or converge the flow field calculations before activating solution of the temper-ature equation. In the latter case, you will still need to solve the flow and temperature equations together to refinethe flow field with the property variations. If difficulties with the temperature equation are encountered early inthe solution, it is then best to start over and partially converge the flow solution before allowing the propertiesto vary with temperature.

For incompressible flows, viscous heating is generally not important for cases with low Prandtl numbers or lowto moderate velocities. However, you should turn on viscous heating whenever the Prandtl number is greaterthan 2 or the velocities are high (e.g., greater than 100 m/s in air). FLOTRAN automatically includes viscousheating for compressible flows. To include viscous heating for incompressible flows, use one of the following:

Command(s): FLDATA1,SOLU,IVSH,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution OptionsMain Menu> Solution> FLOTRAN Set Up> Solution Options



For information on the energy units required for thermal quantities when an incompressible analysis includesviscous heating, refer to Section 9.2: Fluid Property Types.

4.5.3. Free Convection, Temperature Dependent Properties

In this case, the driving force for the flow is the density change brought about by temperature variations. Youmust turn on both options.

You also must do the following:

• Specify acceleration due to gravity, using one of the following:Command(s): ACELGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> GravityMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Gravity

• Activate the variable density option using one of the following:Command(s): FLDATA13,VARY,Label,TRUE (Label = fluid property)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid propertiesMain Menu> Solution> FLOTRAN Set Up> Fluid properties

Buoyancy property types, which use a constant pressure to evaluate the density from the ideal gas law areprovided for AIR. (See Chapter 9, “Specifying Fluid Properties for FLOTRAN”.) Pressure fluctuations are thus pre-vented from causing instabilities in density calculations. Natural convection cases converge slowly, and may bemore stable if the TDMA algorithm is used for pressure and temperature. The number of sweeps used may beset to Number of Nodes/10, but should be at least 100.

4.5.4. Conjugate Heat Transfer

When the thermal properties of the non-fluid material are several orders of magnitude different from those ofthe fluid, this is called an ill-conditioned conjugate heat transfer problem. In this situation, the TDMA methodprobably will not yield useful results, no matter how many sweeps you specify. You access the TDMA methodusing either of the following:

Command(s): FLDATA18,METH,TEMP,1GUI: Main Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> Temp Solver CFD

The Conjugate Residual method offers more functionality and requires little more memory than the Tri-DiagonalMatrix Algorithm (TDMA) method. To access it, use either of the following:


You can control several parameters, such as convergence criteria and the number of search vectors used, to en-hance performance. (See the discussion of FLDATA18 in the ANSYS Commands Reference for more informationabout these parameters.) However, the conjugate residual method, although fairly fast, is not suited for difficultproblems.

A more robust choice for solving ill-conditioned heat transfer problems is the Preconditioned Conjugate Residualmethod, which requires much more memory than either the TDMA or Conjugate Residual methods. The PCRmethod allows you to control the number of search vectors used, up to a maximum of 30. To use it, use eitherof the following:


Note — For nodes connected only to solid nodes, the value stored in the Jobname.RFL file under thedensity (DENS) label is the product of the density and specific heat.

Section 4.5: Solution Strategies


You can evaluate performance of the Conjugate Residual and Preconditioned Conjugate Residual methods bylooking at the Jobname.DBG file (described in Chapter 11, “FLOTRAN CFD Solvers and the Matrix Equation”).

The most robust, but most memory-intensive, method for solving conjugate heat transfer problems is the Pre-conditioned Generalized Minimum Residual method. You can access it via either of the following:


The Preconditioned Generalized Minimum Residual (PGMR) solution method is the default choice for temperature.

Although the same user controls exist for the PGMR method as for the PCCR solver, the default values are different.For PGMR, the least restrictive convergence criterion allowed is 1.E-10. If you try to use a less restrictive convergencecriterion, FLOTRAN will change it to 1.E-10. A convergence criterion as low as 1.E-20 may be necessary for someproblems. In addition, you should use at least 12 search vectors, and FLOTRAN ensures this. For the PGMR solver,12 search vectors is the default and the allowable range is 12 to 20.

FLOTRAN non-fluid elements support both temperature dependence and orthotropic variation. That is, KXX,KYY, and KZZ can assume different values and temperature variations. FLOTRAN considers conductivity as anelement quantity, evaluated at the quadrature points in the element. However, in fluid elements, FLOTRANconsiders thermal conductivity to be a nodal quantity.

To specify the variable and orthotropic conductivities, you use the following commands or GUI paths:Command(s): MP or MPDATAGUI: Main Menu> Preprocessor> Loads> Load Step Opts> Other> Change Mat PropsMain Menu> Preprocessor> Material Props> Material Models> CFD> Conductivity> OrthotropicMain Menu> Solution> Load Step Opts> Other> Change Mat PropsMain Menu> Preprocessor> Loads> Load Step Opts> Other> Change Mat Props

Note — Thermal analysis problems having variable thermal conductivity are nonlinear and require multipleiterations to solve. Variable solid thermal conductivities are not relaxed.

For a conjugate heat transfer problem, it is wise to obtain an initial temperature solution before solving thecoupled energy/momentum equations. To achieve the temperature solution, use the following:

Command(s): FLDATA1,SOLU,FLOW,FGUI: Main Menu> Solution> FLOTRAN Set Up> Solution OptionsCommand(s): FLDATA1,SOLU,TEMP,TGUI: Main Menu> Solution> FLOTRAN Set Up> Solution OptionsCommand(s): FLDATA25,RELX,TEMP,1.0GUI: Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> DOF RelaxationCommand(s): FLDATA2,ITER,EXEC,1GUI: Main Menu> Solution> FLOTRAN Set Up> Execution CtrlCommand(s): FLDATA18,METH,TEMP,3GUI: Main Menu> Solution> FLOTRAN Set Up> CFD Solver Contr> TEMP Solver CFD

In the above steps, an initial temperature solution is obtained from a solution of the heat conduction equation.

FLOTRAN can calculate film coefficients at walls in conjugate heat transfer problems. Two algorithms are availablefor this purpose: the conductivity matrix algorithm and the temperature field algorithm. The conductivity matrixalgorithm uses the thermal conductivity matrix to calculate heat fluxes and film coefficients. It is the default.Generally, it produces satisfactory results for well shaped elements. However, if the elements are not well shaped,it can produce non-smooth results. You should then switch to the temperature field algorithm. It calculates filmcoefficients directly from thermal gradients. To set the algorithm, use the following:

Command(s): FLDATA37,ALGR,HFLM,Value



GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Algorithm CtrMain Menu> Solution> FLOTRAN Set Up> Algorithm Ctr

4.6. Heat Balance

Using information in the Jobname.PFL file, you can calculate a heat balance for your problem. For any flowproblem with the thermal option activated, the energy flow into and out of the problem domain at the inlets/out-lets is calculated and tabulated. Also calculated for the flow boundaries is the heat conduction across theboundary faces. The difference between the energy flow into the system and out of the system at the flowboundaries should equal the total energy added through sources and sinks.

The accuracy of the energy balance depends on the approach used to discretize the advection term in the energyequation. In general, the Streamline Upwind/Petrov-Galerkin (SUPG) approach provides a more accurate energybalance than the Monotone Streamline Upwind (MSU) approach. If you desire an exact energy balance, use theCollocated Galerkin (COLG) approach. For steady-state incompressible flows, it provides an exact energy balance,even with a coarse mesh. However, SUPG or COLG may suffer from oscillatory thermal solution near walls witha coarse mesh. Use the FLDATA40,WADV command to minimize such spatial oscillation.

Energy flowing into or out of the system at mass flow boundaries is equal to the product of the mass flow, thespecific heat, and the temperature. A temperature offset specified by the TOFFST command does not enter thiscalculation. Positive numbers mean heat flows into the system.

Energy sources include volumetric heat sources in either fluids or solids. Specified wall temperatures and specifiedfilm coefficient boundaries are either sources or sinks, depending on the temperature gradient. Heat fluxes aresources or sinks depending on the sign.

Heat transfer to/from wall faces refers to boundaries of fluid regions which are not inlets or outlets.

Heat transfer at wall faces refers to fluid boundaries, regardless of whether or not the boundary is a no-fluidelement or simply a no-slip condition. Positive numbers mean heat flows into the fluid.

Volumetric heat generation can be applied to solid regions or fluid regions. Be careful, when calculating theenergy balance to avoid accounting for heat generation in solids twice.

For example, suppose a conjugate heat transfer problem featured a volumetric heat source in a solid regionwhich is cooled by a fluid flow. The difference between the energy flow in and out should equal heat transfer towall faces. This number should also match the volumetric heat generation in the solid.

For all cases, the difference between the energy flowing into the system at flow boundaries and flowing out atthe boundaries should equal heat transfer to wall faces plus fluid volumetric heat sources plus the heat conductioneffects normal to the flow direction at the flow boundaries.

Essentially, FLOTRAN performs a heat balance on the fluid region only. Heat fluxes and film coefficients aresolution outputs for the external fluid boundaries only. Heat fluxes applied on external boundaries are not partof the solution output.

The effects of viscous dissipation on a heat balance are not explicitly tabulated. The associated heat generationis manifested in terms of an increased temperature, which in turn affects the energy departure at the outlet andthe heat transfer at wall faces if applicable. With adiabatic walls, for example, the temperature of the fluid willincrease from viscous dissipation, even though no heat sources will be apparent.

Section 4.6: Heat Balance


4.7. Surface-to-Surface Radiation Analysis Using the Radiosity Method

Surface-to-surface radiation analysis in FLOTRAN can be used for solving generalized radiation problems involvingtwo or more radiating surfaces in single or multiple open or closed enclosures. The method is supported for both3-D and 2-D FLOTRAN elements FLUID141 and FLUID142. The thermal solution option has to be on for radiationanalysis. You can switch radiation analysis off using the FLDATA1, SOLU, RDSF command. The command defaultsto on.

Surface-to-surface radiation analysis in 2-D is supported for planar and axisymmetric geometry about YR and XRcoordinate systems. Radiation analysis is not supported for 3-D/2-D compressible flow thermal analysis and forR-θ and R-θ-Z coordinate system in 2-D and 3-D analysis respectively.

Elements supported for the radiosity method include:

FLOTRAN

FLUID141FLUID142

4.7.1. Procedure

The Radiosity Solution method consists of four steps:

1. Define the radiating surfaces.

2. Define Solution options.

3. Define View Factor options.

4. Calculate and query view factors.

See Section 4.7: Using the Radiosity Solver Method in the ANSYS Thermal Analysis Guide for a detailed explanationof these steps.

4.7.2. Heat Balances

Jobname.PFL file provides information of the net positive and negative radiation heat transfer from both solidand fluid surfaces.

See Section 4.9: Example of Radiation Analysis Using FLOTRAN (Command Method)

4.8. Examples of a Laminar, Thermal, Steady-State FLOTRAN Analysis

This chapter describes a laminar, thermal, steady-state fluid flow problem and two ways to solve it: by choosingitems on the ANSYS GUI menus or by issuing a series of ANSYS commands.

Before you begin reading about the example, note the following:

• The example problem described is only one of many possible FLOTRAN analyses. It does not illustrateevery technique you might use in a FLOTRAN analysis, and is intended only to show the kinds of tasks aFLOTRAN analysis typically requires.

• The values you enter in this example via commands or dialog boxes are specific values for this exampleonly. The characteristics of the individual problem you are solving dictate what values you should specifyfor a particular FLOTRAN analysis.



4.8.1. The Example Described

This example evaluates buoyancy-driven flow in a square cavity with differentially heated vertical sides. It is alaminar steady-state analysis that uses the FLUID141 2-D element. The physics modeled in this problem governa number of practical problems, including solar energy collection, the ventilation of rooms, and so on.

Figure 4.1 Diagram of the Square Cavity

Density variations resulting from the temperature difference across the cavity drive the laminar flow. The Rayleighnumber for this flow is 1.01E+05, and is defined as follows:

Ra = g β ∆TL3 ρ2Cp/k µ

The symbols in this equation are:

g = gravitational accelerationβ = 1/T∆T = THOT - TCOLD

L = cavity lengthρ = densityCp = specific heat

k = thermal conductivityµ = viscosity

Other example analysis conditions are:

• Cavity: dimensions 0.03m x 0.03m; gravitational acceleration 9.81 m/s2

• Operating conditions: nominal temperature 193K; reference pressure 1.0135E+05 Pa

• Fluid: Air in SI units

• Loads: no slip walls (Vx = Vy = 0); left wall of cavity maintained at THOT = 320K; right wall of cavity maintained

at TCOLD = 280K

Section 4.8: Examples of a Laminar, Thermal, Steady-State FLOTRAN Analysis


4.8.2. Doing the Buoyancy Driven Flow Analysis (GUI Method)

To do the example buoyancy-driven flow analysis using the menus, perform the steps discussed in the next fewsections.

Step 1: Establish an Analysis Title and Preferences

When you have entered the ANSYS program, do these tasks:

1. Choose menu path Utility Menu> File> Change Title. The Change Title dialog box appears.

2. Enter the text "Buoyancy driven flow in a square cavity."

3. Click on OK.

4. Choose menu path Main Menu> Preferences. The Preferences for GUI Filtering dialog box appears.

5. Click the button for FLOTRAN CFD to "On."

6. Click on OK. You have just instructed the ANSYS program to do a FLOTRAN analysis.

Step 2: Define Element Types

Next, you need to specify which elements your analysis will use. The example uses only one element, FLUID141.To define it:

1. Choose menu path Main Menu> Preprocessor> Element Type> Add/Edit/Delete. The Element Typesdialog box appears.

2. Click on Add. The Library of Element Types dialog box appears.

3. In the two scrollable lists, highlight (click on) FLOTRAN CFD and "2D FLOTRAN 141."

4. Click on OK. ANSYS returns you to the Element Types dialog box.

5. Click on Close.

Step 3: Create Areas

Next, create the areas you need. Our example requires an area representing the square cavity. To create it, performthese tasks:

1. Choose menu path Main Menu> Preprocessor> Modeling> Create> Areas> Rectangle> By Dimen-sions. The Create Rectangle by Dimensions dialog box appears.

2. Enter the X coordinates from 0.0 to 0.03.

3. Enter the Y coordinates from 0.0 to 0.03.

4. Click on OK. The square area you have just created will appear in the Graphics Window.

Step 4: Define Lines, Mesh, and Plot Elements

This step meshes the square cavity area so that you can apply temperature loads to it. Follow these steps:

1. Choose menu path Main Menu> Preprocessor> Meshing> MeshTool. Under the Size Controls sectionof the MeshTool, click Lines,Set. The Element Size on Picked Lines picking menu appears.

2. Click Pick All. The Element Size on Picked Lines dialog box appears.

3. Set the number of element divisions to 25.



4. Click on OK.

5. In the MeshTool, select Areas from the Mesh drop down menu. Then click Quad and Free. Then clickMESH. The Mesh Areas picking menu appears.

6. Click on Pick All to generate the mesh.

7. Click on Close on the MeshTool.

8. Click SAVE_DB on the ANSYS Toolbar.

Step 5: Apply Velocity Boundary Conditions

In this step and Step 6, you apply boundary conditions to your model, starting with the exterior nodes. Do thefollowing:

1. Choose menu path Utility Menu> Select> Entities. The Select Entities dialog box appears.

2. Select Nodes and Exterior.

3. Click on OK.

4. Choose menu path Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Velocity>On Nodes. The Apply V on Nodes picking menu appears.

5. On the picking menu, click on Pick All. The Velocity Constraints on Nodes dialog box appears.

6. Set the VX velocity component and VY velocity component fields to 0.

7. Click on OK.

Step 6: Apply Thermal Boundary Conditions

Now you need to apply temperature loads on the left and right edges of the model. To do so:

1. Choose menu path Main Menu> Preprocessor> Loads> Define Loads> Apply> Thermal> Temperat-ure> On Nodes. The Apply TEMP on Nodes picking menu appears.

2. Click on Box. Doing this enables you to select the nodes to which you are applying loads by drawing abox around them.

3. Press and drag your left mouse button to draw a box around the nodes on the left edge of the meshedarea.

4. Click on OK.

5. In the Apply TEMP on Nodes dialog box, enter 320 as the temperature value.

6. Click on OK.

7. Choose menu path Main Menu> Preprocessor> Loads> Define Loads> Apply> Thermal> Temperat-ure> On Nodes. The Apply TEMP on Nodes picking menu appears.

8. On the menu, click on Box. Doing this enables you to select the nodes to which you are applying loadsby drawing a box around them.

9. Press and drag your left mouse button to draw a box around the nodes on the right edge of the meshedarea.

10. Click on OK.

11. In the Apply TEMP on Nodes dialog box, enter 280 as the temperature value.

12. Click on OK.



13. Choose menu path Utility Menu> Select> Everything. This step is important; it ensures that ANSYSincludes all nodes and elements in the analysis.

14. Click on the SAVE_DB button on the Toolbar.

Step 7: Set FLOTRAN Solution Options and Execution Controls

In this step and the next few steps, you set up conditions for the FLOTRAN analysis. You first specify what typeof FLOTRAN analysis you are doing and what values will control FLOTRAN execution.

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options. The FLOTRANSolution Options dialog box appears.

2. Set the "Adiabatic or thermal?" field to Thermal.

3. Click on OK.

4. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl. The Steady StateControl Settings dialog box appears.

5. Set the Global Iterations (EXEC) field to 200.

6. Set the .RFL File Overwrite Freq field to 50.

7. Set the Output summary frequency (SUMF) field to 50.

8. Click on OK.

Step 8: Set Fluid Properties

To set the fluid properties for the example analysis, do the following:

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties. The Fluid Prop-erties dialog box appears.

2. Set the "Density," "Viscosity," "Conductivity," and "Specific heat" fields to AIR-SI.

3. Set the "Allow density variations?" field to Yes.

4. Click on Apply. The CFD Flow Properties dialog box appears.

5. Read the information about how coefficients will be calculated, then click on OK.

Step 9: Set FLOTRAN Flow Environment Parameters

To set the flow environment parameters, follow these steps:

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Gravity. TheGravity Specification dialog box appears.

2. Set the "Accel in Y direction" field to 9.81.

3. Click on OK.

Step 10: Solve the Problem

Set controls for the FLOTRAN solver before you initiate the solution process. Follow these steps:

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Contr> PRES SolverCFD. The PRES Solver CFD dialog box appears.

2. Choose TDMA.



3. Click on OK. The TDMA Pressure dialog box appears.

4. Make sure that the value of the "No. of TDMA sweeps for pressure" field is 100. If so, click on OK.

5. Click on the SAVE_DB button in the Toolbar.

6. Choose menu path Main Menu> Solution> Run FLOTRAN.

7. Wait for the solution to finish, then review the information in the ANSYS Output Window. Click Close inthe Solution is done window.

Step 11: Read In Results and Plot the Temperature Solution

Perform these steps:

1. Choose menu path Main Menu> General PostProc> Read Results> Last Set.

2. Choose menu path Main Menu> General PostProc> Plot Results> Contour Plot> Nodal Solu. TheContour Nodal Solution Data dialog box appears.

3. In the "Item to be Contoured" list, click on (highlight) DOF Solution.

4. In the scrollable list, scroll down and choose TEMP.

5. Click on OK. The Graphics Window shows you the following contour plot:

Figure 4.2 Plot of the Temperature Solution

Step 12: Plot Streamline Contours

1. Choose menu path Main Menu> General PostProc> Plot Results> Contour Plot> Nodal Solu. TheContour Nodal Solution Data dialog box appears.

2. Click on (highlight) "Other quantities."

3. In the scrollable list, select "Strm func2D STRM" (stream function).



4. Click on OK. The Graphics Window shows you the following contour plot:

Figure 4.3 Plot of Streamline Contours

Step 13: Plot Velocity Vectors

For better viewing of the analysis results for the example, switch to vector plotting as described below:

1. Choose menu path Utility Menu> PlotCtrls> Device Options. The Device Options dialog box appears.

2. Set Vector mode (wireframe) to "On."

3. Click on OK.

4. Choose menu path Main Menu> General PostProc> Plot Result> Vector Plot> Predefined. The VectorPlot of Predefined Vectors dialog box appears.

5. Verify that the items "DOF solution" and "Velocity" are highlighted. If so, click on OK. The display in theGraphics Window now looks similar to the one below.



Figure 4.4 Plot of Velocity Vectors

Step 14: Plot Particle Traces Contoured by Temperature

In the example analysis, the dimensions of the problem are small (.03 x .03). Therefore, before plotting particletrace points, you should change the working plane to give a better view from which to choose those points.

1. Choose menu path Utility Menu> WorkPlane> WP Settings. The WP Settings dialog box appears.

2. Set Snap Increment to 0.0005.

3. Set Spacing to 0.0001.

4. Set Tolerance to 0.00005.

5. Click on OK.

6. Choose menu path Utility Menu> Plot> Elements.

7. Choose menu path Main Menu> General Postproc> Plot Results> Flow Trace> Defi Trace Pt.

8. Using your mouse, pick five or six points anywhere within the upper half of the problem domain.

9. Click on OK in the picking menu.

10. Choose menu path Main Menu> General Postproc> Plot Results> Flow Trace> Plot Flow Trace. ThePlot Flow Trace dialog box appears.

11. In the scrollable list, click on (highlight) "Temperature TEMP".

12. Click on OK. The Graphics Window shows a plot that resembles the plot shown below. Your plot maylook different, depending on the location of the points you picked. If a warning message appears tellingyou that the maximum number of loops has been exceeded, review it and click Close. For the purposes of thisproblem, the particle trace is stuck in a loop by definition, so you can ignore this message.



Figure 4.5 Plot of Flow Trace

Step 15: Plot Particle Traces Contoured by Velocity Magnitude

1. Choose menu path Main Menu> General PostProc> Plot Results> Flow Trace> Plot Flow Trace. ThePlot Flow Trace dialog box appears.

2. In the scrollable list, choose "VSUM."

3. Click on OK. The plot shown in the Graphics Window is now contoured by velocity magnitude. How yourplot looks will depend on the location of the points you picked. If you receive another warning messageabout the maximum number of loops being exceeded, click Close.

4. If you wish, you can use animation to enhance your analysis of particle flow. Choose menu path Util-ity Menu> PlotCtrls> Animate> Particle Flow. When the Animate Flow Trace dialog box appears, enterthe desired animation data and click OK. (To animate particle flow, you must have at least one trace pointdefined. To complete the sample analysis, simply take the defaults and click on OK.)

5. When you are done viewing the animation, click Stop and then Close in the Animation Controller. If ad-ditional warning messages appear, close them.

6. To exit ANSYS, click Quit on the ANSYS Toolbar. Choose an exit option and then click on OK.

See Section 5.10, Doing the Sample Analysis (Command Method), for an example problem.

4.8.3. Doing the Buoyancy Driven Flow Analysis (Command Method)

To do the example buoyancy-driven flow analysis, you issue these ANSYS commands:

/TITLE,Buoyancy driven flow in a square cavity/PREP7ET,1,FLUID141 ! Set 2-D fluid element type



RECTNG,,0.03,,0.03 ! Create square areaLPLOTLESIZE,ALL, , ,25,1,0 ! Define line divisions and mesh areaAMESH,1EPLOTNSEL,S,EXT ! Apply velocity b.c. on exterior nodesD,ALL,,,,,,VX,VYNSEL,S,NODE,,1 ! Apply thermal b.c. on left edgeNSEL,A,NODE,,52NSEL,A,NODE,,77,100D,ALL,TEMP,320NSEL,S,NODE,,2 ! Apply thermal b.c. on right edgeNSEL,A,NODE,,27,51D,ALL,TEMP,280NSEL,ALLESEL,ALLFLDATA1,SOLU,TEMP,1 ! Set solution option to thermalFLDATA2,ITER,EXEC,200 ! Set FLOTRAN execution controlsFLDATA2,ITER,OVER,50FLDATA5,OUTP,SUMF,50!*FLDATA13,VARY,DENS,1 ! Set fluid propertiesFLDATA7,PROT,DENS,AIR-SIFLDATA7,PROT,VISC,AIR-SIFLDATA7,PROT,COND,AIR-SIFLDATA8,NOMI,COND,-1FLDATA7,PROT,SPHT,AIR-SI!*ACEL,0,9.81,0 ! Set flow environment gravityFLDATA18,METH,PRES,1 ! Set FLOTRAN solver controlsFLDATA19,TDMA,PRES,100FINISH/SOLUSOLVE ! Solve modelFINISH/POST1SET,LASTPLNSOL,TEMP ! Plot temperature solutionPLNSOL,STRM ! Plot streamline contours/DEVICE,VECTOR,1!*PLVECT,V, , , ,VECT,ELEM ! Plot velocity vectorswpstyle,0.0005,0.0001,-1,1,0.00005,0,2,,5EPLOTTRPOIN,P ! The P argument enables graphical picking ! of trace points via the GUIPLTRAC,FLUID,TEMP ! Plot particle traces contoured byPLTRAC,FLUID,V,SUM ! temperature and velocity magnitudeFINISH

4.9. Example of Radiation Analysis Using FLOTRAN (Command Method)

The following is an example of a laminar, thermal, steady-state FLOTRAN analysis with surface-to-surface radiationusing the radiosity solution method (command method). In this example a buoyancy-driven flow in a squarecavity with differentially heated vertical walls is considered. All walls of the cavity are radiating surfaces with anemissivity of 0.9. The final temperature distribution in the cavity effected by the presence of the radiating wallsin the fluid domain.

To do the surface-to-surface radiation problem, you issue these ANSYS commands:

/prep7et, 1, 141 ! 2-D Fluid elementrectng, , .027744, , .027744 ! Create square cavityesize, , 20 ! Set number of elementsamesh, all ! Mesh areansel, s, ext ! Select external nodesd, all,,,,,,vx,vy ! Set all external wall velocities to zero allsel lsel, s, loc, x, 0.0

Section 4.9: Example of Radiation Analysis Using FLOTRAN (Command Method)


nsll, s, 1d, all, temp, 500 ! Set wall temperature at x = 0.0 to 500 Klsel, s, loc, x, .027744nsll, s, 1d, all, temp, 200 ! Set wall temperature at x = 0.027744 to 200 Knsel, allesel, allfldata1, solu, temp, 1 ! Set solution option to thermalfldata2, iter, exec, 200 ! Set FLOTRAN execution controlfldata2, iter, over, 50 fldata5, outp, sumf, 50! fldata13, vary, dens, 1 ! Set fluid propertiesfldata7, prot, dens, air-sifldata7, prot, visc, air-sifldata7, prot, cond, air-sifldata8, nomi, cond, -1fldata7, prot, spht, air-si!acel, 0, 9.81, 0 ! Set flow environment gravityfldata18, meth, pres, 1fldata19, tdma, pres, 100fldata18, meth, temp, 6stef,5.67e-8 ! Set Stefan-Boltzmann constanttoff,0 ! Set temperature offset to zero radopt,.5,0.0001 ! Set radiosity solver optionsfinish/soluallselnsel,s,ext ! Select all external nodessf, all, rdsf, 0.9, -1 ! Apply radiation on external faces facing inwardsallselsolve ! Solvefinish/post1set lastplnsol, temp ! Plot temperature solutionplnsol, strm ! Plot streamline contours

4.10. Where to Find Other FLOTRAN Analysis Examples

Another example of a FLOTRAN analysis is the CFD Tutorial. Also, the ANSYS Verification Manual contains severaladditional examples of FLOTRAN analyses. The ANSYS Verification Manual examples include:

VM46 - Flow Between Rotating Concentric CylindersVM121 - Laminar Flow Through a Pipe with Uniform Heat FluxVM178 - Plane Poiseuille FlowVM209 - Multiple Species Flow Entering A Circular PipeVM219 - Non-Newtonian Pressure Driven Sector Flow



Chapter 5: FLOTRAN Transient AnalysesYou activate the transient algorithm by setting the solution option, using one of these methods:

Command(s): FLDATA1,SOLU,TRAN,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution OptionsMain Menu> Solution> FLOTRAN Set Up> Solution Options

You must make decisions regarding the time step, the method of converging the analysis during a time step,the length of execution of the job and the frequency of output.

What you specify via one of the following methods determines the transient execution and output:Command(s): FLDATA4,TIME and FLDATA4A,STEPGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl

The final section of this chapter explains how to apply transient boundary conditions for FLOTRAN.

5.1. Time Integration Method

There are two methods available for the time integration: Backward (the default) and Newmark. The Newmarkmethod is more accurate than the Backward method. To specify the Newmark method, use one of the following:

Command(s): FLDATA4,TIME,METH,NEWMGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Transient Contrl> Time Integration MethMain Menu> Solution> FLOTRAN Set Up> Transient Contrl> Time Integration Meth

When using the Newmark method, you can introduce numerical damping to stabilize the solution.Command(s): FLDATA4,TIME,DELT,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Transient Contrl> Time Integration MethMain Menu> Solution> FLOTRAN Set Up> Transient Contrl> Time Integration Meth

The Newmark parameter must be ≥ 0.5. It defaults to 0.5. The recommended range is 0.5 to 0.6. Higher valuesare more stable because there is more damping. Lower values result in more accurate results with 0.5 correspond-ing to second order accuracy. For more information on the Newmark method, see Section 17.2: Transient Ana-lysis in the ANSYS, Inc. Theory Reference.

There are two mass types that you can set for the transient analysis: lumped (the default) and consistent. Theconsistent type is more dissipative than the lumped type. To specify the consistent type, use one of the following:

Command(s): FLDATA38,MASS,Label,CONS MSMASS,SPNUM,CONSGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Transient Contrl> Mass TypeMain Menu> Solution> FLOTRAN Set Up> Transient Contrl> Mass TypeMain Menu> Solution> FLOTRAN Set Up> Multiple Species

5.2. Time Step Specification and Convergence

Because the algorithm is implicit in nature, no stability restrictions exist on the time step size. You specify a timestep or elect to have FLOTRAN calculate a time step. To do so, use either of the following:

Command(s): FLDATA4A,TIME,STEP,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl

The graphical user interface will require you to set the time step if you choose the User Defined option.


The table below shows the values you can specify. A brief description of the FLOTRAN calculation follows thetable.

Table 5.1 Specifying Values for Time Steps

MeaningValue to Specify

User Specified Time StepAny value > 0

Advection Limit-1

Pressure Wave Limit-2

Smaller of Pressure wave and Advection-3

Conduction Limit-4

The advection limit prevents a particle of fluid from passing completely through a finite element during a timestep.

The pressure wave limit means the time step is chosen small enough to prevent a pressure wave from passingall the way through a finite element during a single time step. This option is active only if you choose the com-pressible solution algorithm.

The choice of -3 (again valid only for compressible analyses) means that the more restrictive (that is, smaller)time step criterion will be imposed.

The conduction limit is calculated to prevent the conductive diffusion of a parcel of energy completely throughan element during a time step. The limit applies only to problems that include conduction, and is valid forproblems with both fluid and non-fluid elements.

FLOTRAN must execute global iterations to converge within a time step. The time step terminates when eitherof the following happens:

• The convergence criteria are met.

• The maximum number of global iterations allowed per time step executes.

You set the maximum number of global iterations per time step using one of the following:Command(s): FLDATA4A,TIME,GLOB,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl

The convergence criteria are values below which the convergence monitors for each active degree of freedommust drop to cause the time step to terminate. You specify these values using the following commands or menupaths:

Command(s): FLDATA4,TIME,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl

As soon as all the convergence criteria are met, the time step terminates. The time step terminates on the numberof global iterations allowed if the convergence monitor criteria are not met.

If the problem is adiabatic, only the pressure equation monitor is checked. Both the pressure and temperatureequation monitors must be reduced below the convergence criteria values if the temperature equation also issolved.


Chapter 5: FLOTRAN Transient Analyses

As soon as the convergence monitor criteria are met, the time step terminates. The time step terminates on thenumber of global iterations allowed if the convergence monitor criteria are not met.

5.3. Terminating and Getting Output from a Transient Analysis

You can either specify an end time for a transient FLOTRAN analysis or have it end after a specified number oftime steps. To specify an end time, use either method shown below.

Command(s): FLDATA4,TIME,TEND,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl

To specify a number of time steps, either use one of the menu paths listed above or issue the following command:

Command(s):FLDATA4,TIME,NUMB,Value

The event that occurs first (end time or reaching the time step threshold) terminates the analysis.

You determine how often ANSYS saves the analysis results for processing and how often it writes informationto the Jobname.PFL file. You do this by choosing from the following commands or menu paths:

Command(s): FLDATA4,TIME,Label,Value and FLDATA4A,STEP,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution CtrlMain Menu> Solution> FLOTRAN Set Up> Execution Ctrl

The table below shows you how the values you specify affect analysis output:

Table 5.2 Saving Analysis Results for Processing

Meaning of ValueName, Label, Value

Output results to Jobname.RFL every n time stepsSTEP,APPE,n

Output results to Jobname.RFL every x secondsTIME,APPE,x

Add output summary to Jobname.PFL every n time stepsSTEP,SUMF,n

Add output summary to Jobname.PFL every x secondsTIME,SUMF,x

Overwrite the temporary results set every n time stepsSTEP,OVER,n

Overwrite the temporary results set every x secondsTIME,OVER,x

If you wish to control the output based on time, you must first defeat the default controls which set APPE andSUMF to ten steps.

5.4. Applying Transient Boundary Conditions

When any boundary conditions are changed, FLOTRAN assumes either a step change (default) or a ramp change.The ramp is chosen by setting the BC label in the TIME item to 1 via one in the following:

Command(s): FLDATA4,TIME,BC,1GUI: Main Menu> Preprocessor> FLOTRAN Setup> Execution Control

The ramp will occur for the next execution over the period of time for execution specified by the user. This is thedifference between the current time (i.e., the beginning in the execution) and the end time as specified by thefollowing:

Command(s): FLDATA4,TIME,TEND,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Execution Control

Section 5.4: Applying Transient Boundary Conditions


The ramp is between the “old” boundary conditions and the “new” boundary conditions. A boundary conditionis considered old as soon as FLOTRAN has gone through the calculational loop. This means that to use a rampedcondition at the beginning of an analysis, a zero iteration execution (which may be accomplished with theFLOCHECK command) should be done with the initial condition (applied as a boundary condition) and then theboundary condition value(s) are changed to those at the end in the ramp.

Note that the ramp is calculated with the value of TEND as specified above, NOT the actual ending time in thecase. For this reason, it is recommended that the user terminate the case with the TIME controls rather than theSTEP controls. Ensure that the case will not terminate prematurely due to an insufficient number of time steps.If the case terminates before the time specified by TEND, upon restart the boundary conditions will be immediatelychanged from where they were when the run terminated to what the current boundary condition setting is. Ifyou use the STEP controls in the GUI to set the number of time steps, you need to set TEND in that same dialog

box. Otherwise, TEND defaults to 1.0 x 106 and the ramp is almost nonexistent.

Transient boundary conditions on velocity DOF (VX, VY, and VZ) must not be ramped from zero to a nonzerovalue. A very small velocity must be used instead of zero so that FLOTRAN recognizes the face as an inlet oroutlet rather than a wall.

At any time, you can change the applied boundary conditions to the "old" state with one of the following:Command(s): FLOCHECK,2GUI: Main Menu> Preprocessor> FLOTRAN Setup> Flocheck

FLOCHECK,2 has no effect on the Jobname.RFL file.

Caution: FLOTRAN has no record of boundary conditions at earlier times. That is, if you want to restartfrom an earlier point in time and simulate a ramped boundary condition it is necessary to apply theboundary condition appropriate for the beginning of the ramp, make it an old condition via the FLOCHECKcommand, and then apply the condition at the end of the ramp.


Chapter 5: FLOTRAN Transient Analyses

Chapter 6: Volume of Fluid (VOF) Analyses

6.1. Overview

In a Volume of Fluid (VOF) analysis, FLOTRAN uses an advection algorithm for the volume fraction (VFRC) to trackthe evolution of the free surface. The VFRC value for each element varies from zero to one, where zero denotesan empty or void element and one denotes a full or fluid element. The values between zero and one indicatethat the corresponding elements are the partially full or surface elements (henceforth called partial elements),and the free surface can thus be determined by the distribution of the VFRC field.

For the dynamic behavior at the interface between a gas and liquid, FLOTRAN uses a continuum surface force(CSF) method to model the surface tension. Surface tension is an inherent characteristic of material interfaces.It is a localized surface force acting on the interface. FLOTRAN reformulates this surface force into an equivalentvolumetric force in the momentum equation. This force consists of two components: a normal component tothe interface due to local curvature and a tangential component to the interface due to local variations of thesurface tension coefficient.

Currently, VOF capability is available only for quadrilateral elements for two dimensional planar or axisymmetricanalyses. For a VOF analysis, boundary conditions are required for boundary nodes that belong to at least onenon-empty (partial or full) element.

To activate a VOF analysis in FLOTRAN and model the surface tension effect, use the following commands or GUImenu paths:

Command(s): FLDATA1,SOLU,VOF,Value FLDATA1,SOLU,SFTS,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution OptionsMain Menu> Solution> FLOTRAN Setup> Solution Options

In FLOTRAN, the VOF algorithm first computes the motion of the polygon of fluid in a Lagrangian sense and thenutilizes the computational geometry of the intersection of two polygons to determine the VFRC fluxes. Thismethod is referred to as the Computational Lagrangian-Eulerian Advection Remap (CLEAR) method. See theANSYS, Inc. Theory Reference for information on the theoretical background. This CLEAR-VOF method tracks thefree surface explicitly in time, and it is therefore necessary to activate the transient solution option for a VOFanalysis. Refer to Chapter 5, “FLOTRAN Transient Analyses” for information on the selection of the transientparameters, such as the time step, converging method, execution length and the output frequency. For accuracy,you should use the Streamline Upwind Petrov-Galerkin (SUPG) approach described in Chapter 14, “AdvectionDiscretization Options”. If you encounter a convergence difficulty, the time increment may be reduced, and themodified inertial relaxation (MIR) scheme may also be activated for robustness.

Caution: You should avoid using quadrilateral elements with only one node on the inflow or outflowboundary.

6.2. VFRC Loads

When performing a VOF analysis, you need to apply both initial and boundary VFRC loads. In most cases, defaultvalues are appropriate.

6.2.1. Initial VFRC Loads

You impose initial conditions for the velocity and other degrees of freedom in the usual manner. For the initialVFRC field, you can define each element as initially full, partially full or empty. Take care when initially settingpartial elements. Each partial element must be adjacent to at least one full element and one empty element.


During the analysis, if a partial element does not have any full elements as neighbors, it will be reset to empty.You should also include at least one layer of empty elements above the free surface to allow the surface to evolvein time.

To set the initial volume fraction field, use one of the following:Command(s): ICE,ELEM,VFRC,ValueGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Volume Fract> InitLoads> On ElementsMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Fract> Init Loads> On Elements

By default, the volume fraction is zero. Therefore, if there is fluid initially inside the problem domain, you mustset the VFRC field accordingly.

To set the initial volume fraction for a given geometry, use one of the following:Command(s): ICVFRC,GEOM,VAL1,VAL2,VAL3,VAL4GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Volume Fract> Init Loads> ByGeomMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Frac> Init Loads> By Geom

ICVFRC automatically calculates the volume fraction value for all selected elements that are either inside thegiven geometry or intersect with it. The volume fraction is:

• One for elements completely within the geometry

• A fraction equal to the element area within the geometry for elements intersected by the boundary ofthe geometry

Currently, there are two valid geometries: circle (CIRC) and ellipse (ELPT). For a circle or ellipse, VAL1 and VAL2are the x and y coordinates of the center, respectively. For a circle, VAL3 is the radius and VAL4 is not used. Foran ellipse, VAL3 and VAL4 are the x and y semiaxes, respectively.

To display the initial volume fraction loads, use the following:Command(s): /PICE,VFRC,,KEYGUI: Utility Menu> PlotCtrls> Symbols

The /PBF and /PSF commands override the /PICE command.

6.2.2. Boundary VFRC Loads

You impose boundary conditions for the velocity and other degrees of freedom in the usual manner. Althoughboundary conditions outside the fluid region have no physical meaning initially, these conditions will becomeactive if the fluid touches these boundaries. Accordingly, you should apply all appropriate boundary conditionson all boundaries potentially touched by the fluid. FLOTRAN treats unspecified boundaries with natural conditions.

Boundary conditions for VFRC loads consist of the boundary VFRC value and the wetting status. FLOTRAN onlyallows zero (empty) and one (full) values for the boundary VFRC values. By default, boundary VFRC values areset to one (full). FLOTRAN uses the boundary VFRC values to determine the normal surface direction in the VOFreconstruction stage, when the boundary is adjacent to the surface elements. The wetting status specifieswhether the fluid can be advected into the problem domain. A zero value indicates a non-wetting boundary,whereas a unity value indicates a wetting boundary. By default, wetting status is set to zero (non-wettingboundary). On a wetting boundary, fluid advection into the problem domain takes place. The correspondingboundary VFRC value must be set to unity to be meaningful. On a non-wetting boundary, advection of the fluidor void elements into the problem domain does not take place. The boundary VFRC value only acts passively tohelp determine the normal surface direction.

To set boundary VFRC loads, use one of the following:



Command(s): SFL,LINE,VFRC,VALI,VALJ,VAL2I,VAL2J SFE,ELEM,LKEY,VFRC,KVAL,VAL1,VAL2,VAL3,VAL4GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Volume Fract> BoundLoads> On LinesMain Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Volume Fract> BoundLoads> On ElementsMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Fract> Bound Loads> On LinesMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Fract> Bound Loads> On Elements

For the SFL command, VALI specifies the boundary VFRC value and (defaults to 1) VAL2I specifies the wettingstatus (defaults to non-wetting). If Lab = VFRC, a VAL2I setting of 1 indicates a wetted boundary. For the SFEcommand, VAL1 specifies the boundary VFRC value (defaults to 1) when KVAL = 0 or 1, and VAL1 specifies theboundary wetting status (defaults to non-wetting) when KVAL = 2. If Lab = VFRC and KVAL = 2, a VAL1 settingof 1 indicates a wetted boundary. At a wetted boundary, the fluid upstream keeps the associated elements full.

6.3. Input Settings

When performing a VOF analysis, you may set the environmental conditions regarding the ambient conditions,the VFRC tolerances, and the time stepping strategy.

When studying surface tension effects, you need set the proper values for the surface tension coefficient andthe wall static contact angle. Refer to Chapter 9, “Specifying Fluid Properties for FLOTRAN” for information onthese property types.

6.3.1. Ambient Conditions

Set the ambient nodal values outside the fluid region for the following variables:

VX - U velocityVY - V velocityVZ - W velocityTEMP - TemperatureENKE - Turbulent Kinetic EnergyENDS - Turbulent Dissipation Rate

using one of the following:Command(s): FLDATA36,AMBV, Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> VOF Environment> Ambient Condit'nMain Menu> Solution> FLOTRAN Setup> VOF Environment> Ambient Condit'n

When a boundary node with Dirichlet Condition lies outside the fluid region, the assigned ambient values onthis node are ignored. The prescribed Dirichlet Condition will become active once its associate element becomespartially full or full. Except for pressure, the ambient values are only set for postprocessing purposes. Pressureacts as an actual boundary condition.

Unlike other FLOTRAN analyses, the pressure field for a VOF analysis will include both the dynamic pressure andthe static pressure and the static pressure will be in balance with the gravitational acceleration terms. For example,in a VOF analysis, the pressure contours for a parallel uniform flow with gravity will consist of parallel lines witha gradient balancing gravity, whereas they remain constant for other FLOTRAN analyses.

In a VOF analysis, an outlet can have specified pressures or it can have natural conditions. When outlet pressuresare specified, the values will differ from those in other FLOTRAN analyses by the offsets of the static pressure (orelevation head). For natural boundary conditions the outlet pressures will adjust automatically. In that case, if asteady state solution exists, the outlet pressures will converge to the correct values.

Section 6.3: Input Settings


6.3.2. VFRC Tolerances

Ideally, a VFRC value of one signifies a full or fluid element and a value of zero signifies an empty or void element.In reality, however, exact values of one and zero are difficult to maintain in the VOF advection algorithm due tovarious types of error accumulations. Hence, FLOTRAN introduces small cutoff values to determine the full andempty elements. An element is considered full if its VFRC value is greater than or equal to 1 - VOFU, where VOFUis the upper tolerance for the VOF advection algorithm. An element is considered empty if its VFRC value is lessthan or equal to VOFL, where VOFL is the lower tolerance for the VOF advection algorithm. By default, VOFL and

VOFU are both set to 10-5.

In the FLOTRAN solution routines, a nearly empty element adjacent to a nearly full element may introduce anabrupt change in the locally rescaled meshes. This can make the stiffness matrix more ill-conditioned and canadversely affect the quality of the desired solution. To avoid this, FLOTRAN introduces another tolerance to notassemble the finite element equations for those elements with VFRC values less than or equal to LAML for lam-inar flows and TRBL for turbulent flows, where LAML and TRBL are the lower tolerances for laminar and turbulentflows, respectively. Similarly, elements with VFRC values greater than or equal to 1 - LAMU for laminar flows and1 - TRBU for turbulent flows are considered full when assembling the finite element equations. You can set any

of these tolerance values. By default, LAML and LAMU are set to 10-2 and TRBL and TRBU are set to 10-1.

To set any of the tolerance values, use one of the following:Command(s): FLDATA35,VFTOL,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> VOF Environment> VFRC ToleranceMain Menu> Solution> FLOTRAN Setup> VOF Environment> VFRC Tolerance

6.3.3. VOF Time Steps

Because the CLEAR-VOF is explicit in time, it must use a time step for the VOF advection algorithm that correspondsto a CFL number less than one. On the other hand, selecting the time step based on the VOF constraint may betoo restrictive sometimes because the FLOTRAN transient solution algorithm is implicit in time, and there is nostability restriction on the time step size. Accordingly, FLOTRAN allows multiple VOF advection steps per solutionstep. The VOF advection time step is set equal to the solution time step divided by a factor that you specify. Ifthe VOF advection time step is still too large, FLOTRAN will automatically reduce the VOF time step by half. Thisautomatic reduction in the VOF time step continues until the local imbalance of the VFRC field during the VOFadvection computations is less than the VOFL tolerance. A good input parameter guess makes the calculationmore efficient by removing some checks on the time step.

To set the number of VOF advection time steps per solution time step, use one of the following:Command(s): FLDATA4,TIME,NTVF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> VOF Environment> Time SteppingMain Menu> Solution> FLOTRAN Setup> VOF Environment> Time Stepping

For a VOF analysis, the density is constant. Therefore, mass conservation is equivalent to the conservation of thetotal fluid volume (or area in two dimensions). Ideally, the difference between the volume coming into theproblem domain and going out of the domain should be equal to the increase or decrease of the total volumeinside the domain. In an actual finite element analysis, however, continuity satisfaction is expressed in a Galerkinweak form. Therefore, in general, each element has a small mass imbalance. The local mass imbalance is usuallyof the order of the discretization error, and this error is a major source of the global VFRC imbalance introducedin a VOF analysis. Even though this imbalance may be very small compared to the total volume, it can accumulateexponentially as the number of time steps increases. Hence, FLOTRAN performs a global adjustment of the VFRCfield at each VOF time step. It proportionally increases or decreases the VFRC values of the partial elements toguarantee the global VFRC balance. It prints the final VFRC imbalance in the Jobname.PFL file.



6.4. Postprocessing

The volume fraction is stored as a non-summable miscellaneous record in the element data section of the resultsfile. If you want to view the volume fraction, issue the command:

Command(s):PLESOL,NMISC,1

Since the volume fraction is essentially an element based quantity, it is discontinuous across elements. If youwish to see a smooth and continuous volume fraction, you should first store the results in an element table, usingone of the following:

Command(s): ETABLE,VFRC,NMISC,1GUI: Main Menu> General Postproc> Element Table> Define Table

You can then plot the results with an averaging operation, using one of the following:Command(s): PLETAB,VFRC,1GUI: Main Menu> General Postproc> Element Table> Plot Elem Table

However, instead of using the foregoing commands, you can use one of the following:Command(s): PLVFRC,CONTGUI: Main Menu> General Postproc> Plot Results> Contour Plot> Element Solu

The PLVFRC macro issues the ETABLE and PLETAB commands. When CONT = 0, PLVFRC uses contour levels of0.5 and 1.0 to indicate the free surface and fluid regions. When CONT = 1, it uses the current contour settings.

You can also animate your results. To obtain an animation over a time sequence by interpolation between timesteps, use the PLVFRC command macro along with one of the following:

Command(s): PLVFRC,CONT ANTIME,NFRAM, DELAY, NCYCL, AUTOCNTRKY, RSLTDAT, MIN, MAXGUI: Utility Menu> PlotCtrls> Animate> Over Time

To produce an animation based on the time steps without interpolation, use the PLVFRC command macro alongwith one of the following:

Command(s): PLVFRC,CONT ANDATA,DELAY,NCYCL, RSCLDAT, MIN, MAX, INCR, FRCLST, AUTOCNTRKYGUI: Utility Menu> PlotCtrls> Animate> Over Results

Note that if CONT = 0, the animation is based on two contour levels of 0.5 and 1.0. If CONT = 1, the animation isbased on AUTOCNTRKY setting.

6.5. VOF Analysis of a Dam

6.5.1. The Problem Described

In this example, two vertical walls confine a rectangular column of stationary water. When the right wall is removed,the water flows out onto a rigid horizontal plane. The ICE command sets the initial volume fraction field.

6.5.2. Building and Solving the Model (Command Method)

The following command stream shows all the relevant parameters and solution strategy. All text prefaced withan exclamation point (!) is a comment.

/BATCH,LIST/title, broken dam problem by the VOF solution./com/com ------------------------------------------------------------------/com ** Reference: "Part IV: An Experimental Study of the Collapse of

Section 6.5: VOF Analysis of a Dam


/com ** Liquid Columns on a Rigid Horizontal Plane" /com ** By Martin and Moyce, Phil. Trans. Roy. Soc. /com ** (London,A244, pp. 312-324, 1952./com ** "Volume of Fluid (VOF) Method for the Dynamics of/com ** Free Boundaries" By C.W. Hirt and B.D. Nichols,/com ** J. Comput. Physics, Vol. 39, pp. 201-225, 1981./com **/prep7 !!!!! Define some dimensions and gravity LX = 5.0 ! X lengthLY = 2.5 ! Y lengthDELX = 0.2 ! X spacingDELY = 0.05 ! Y spacinggrav = 9.81 ! Gravityet,1,141!!!! meshingrect,0,LX,0,LYlsel,s,,,2,4,2lesize,all,DELYlsel,s,,,1,3,2lesize,all,DELXamesh,all

nsel,s,loc,y,0.0 ! Wall boundary conditions nsel,a,loc,x,0.0d,all,vx,0.0d,all,vy,0.0

nsel,s,loc,x,0.0,1.0 ! Setup initial VFRCnsel,r,loc,y,0.0,2.0esln,s,1ice,all,vfrc,1.0

alls ! Initial conditions for vx & vyic,all,vx,0ic,all,vy,0savefini

/solu!!!! FLOTRAN inputacel,0.0,grav,0FLDA,NOMI,DENS,1.0e3FLDA,NOMI,VISC,1.0d-3FLDA,SOLU,FLOW,TFLDA,SOLU,TRAN,TFLDA,SOLU,turb,Fflda,solu,vof,tflda,time,glob,5flda,time,numb,70flda,time,step,0.01flda,time,appe,0.1flda,advm,mome,supgflda,relx,vx,0.5flda,relx,vy,0.5flda,relx,pres,1.0solve finiexit,nosa

6.6. VOF Analysis of Open Channel with an Obstruction


In this example, water flows in an open channel with a semicircular obstruction on the bottom. The computationuses the standard k-ε turbulence model since the turbulence model is not very important for the prediction ofthe free-surface shape. The solution domain extends five cylinder diameters upstream and five diameters



downstream of the obstruction. The fluid starts to fill the domain at the beginning of the simulation. The SFEand SFL commands set a wetting boundary on the left inlet.



/BATCH,LIST/title, initial development of flow over a bump./com/com ------------------------------------------------------------------/com ** Initial development of flow over a semicircular bump /com ** Reference: "Critical Free-Surface Flow Over a Semi-Circular/com ** Obstruction" By L.K. Forbes, J. Eng. Math., /com ** vol. 22, pp. 3-13, 1998./com ** "Computation of free-surface flows using the /com ** finite-volume method and moving grids", /com ** By S. Muzaferija and M. Peric, Numerical Heat/com ** Transfer, Part B, 32:369-384, 1997./com ------------------------------------------------------------------!!! Property and parameter inputrho = 1.0e0 ! Densitygrav = 9.81 ! Gravity mu = 1.0e-6 ! Viscosity!R = 0.03 ! Bump radiusL = 2*RH = 0.075 ! Inlet heightH0 = R ! Height above the Inletoutlen = 5.0*R ! Outlet lengthinlen = 5.0*R ! Inlet lengthny1 = 8 ! Number of elements in line 1ny2 = 2 ! Number of elements in line 2ny3 = 4 ! Number of elements in line 3ry2 = 1.0 ! Ratio of element size in line 2ry3 = 1.0 ! Ratio of element size in line 3nx1 = 15 ! Number of elements in line 13nx2 = 15 ! Number of elements in line 21nx3 = 20 ! Number of elements in line 17rx1 = 0.5 ! Ratio of element size in line 13rx2 = 1.0 ! Ratio of element size in line 25rx3 = 1.5 ! Ratio of element size in line 17nr1 = 10 ! Number of elements in radial direction near bump!!/prep7et,1,141k,1,-inlen,0.0 ! KP 1 - 4 are at the inletk,2,-inlen,Lk,3,-inlen,Hk,4,-inlen,H+H0!l,1,2 ! Lines 1-3 are the inlet linel,2,3l,3,4!k,5,-L,0.0 ! KP 5 - 8 are before the bump k,6,-L,Lk,7,-L,Hk,8,-L,H+H0!l,5,6 ! Lines 4-6 before the bumpl,6,7l,7,8!k,9,L,0.0 ! KP 9 - 12 are after the bumpk,10,L,Lk,11,L,H

Section 6.6: VOF Analysis of Open Channel with an Obstruction


k,12,L,H+H0!l,9,10 ! Lines 7-9 after the bumpl,10,11l,11,12!k,13,outlen,0.0 ! KP 13 - 16 are at the outletk,14,outlen,Lk,15,outlen,Hk,16,outlen,H+H0!l,13,14 ! Lines 10-12 at the outletl,14,15l,15,16!l,1,5 ! Lines 13-16 are horizontal lines near inlet

l,2,6 l,3,7l,4,8!l,9,13 ! Lines 17-20 are horizontal lines near outlet l,10,14l,11,15l,12,16!l,6,10 ! Lines 21-23 are horizontal lines near the bump l,7,11l,8,12! k,17,R,0.0 ! KP 17 to 23 are for the semicircular bumpk,18,0.0,0.0circle,18,R,,17,180,4lcomb,25,26,0!l,19,9 ! Lines 26, 28-30 in radial direction near bumpl,20,10l,22,6l,23,5!

! Select lines and establish line divisions! lsel,s,,,1,4,3lesize,all,,,ny1! lsel,s,,,2,11,3lesize,all,,,ny2,ry2! lsel,s,,,3,12,3lesize,all,,,ny3,ry3! lsel,s,,,13,16lesize,all,,,nx1,rx1! lsel,s,,,21,23lesize,all,,,nx2,1.0/rx2lsel,s,,,25lesize,all,,,nx2,rx2! lsel,s,,,17,20lesize,all,,,nx3,rx3! lsel,s,,,27lesize,all,,,ny1!lsel,s,,,26lsel,a,,,28,30lesize,all,,,nr1!! define the y-direction meshlsel,s,,,24



lsel,a,,,7lsel,a,,,10lesize,all,,,nx2,1.5!alls! Create areas....a,1,5,6,2 ! Inleta,2,6,7,3a,3,7,8,4a,9,13,14,10 ! Outleta,10,14,15,11a,11,15,16,12 a,6,10,11,7 ! Bumpa,7,11,12,8a,19,9,10,20a,20,10,6,22a,5,23,22,6allsamesh,all!! Inlet boundary conditionlsel,s,,,1,2nsll,,1d,all,vx,0.32d,all,vy,0.0!nsel,s,loc,x,-inlennsel,r,loc,y,0.0d,all,vx,0.001!! boundary volume fraction (SFL and SFE commands)sfl,1,vfrc,1,,1sfl,2,vfrc,1,,1!!!!!! The wallslsel,s,,,13lsel,a,,,17lsel,a,,,24,25lsel,a,,,27lsel,a,,,26lsel,a,,,30nsll,,1d,all,vx,0d,all,vy,0alls/solu!!!! FLOTRAN Input acel,0.0,grav,0.0 FLDA,SOLU,VOF,ON FLDA,SOLU,FLOW,ONFLDA,SOLU,TRAN,ONFLDA,SOLU,TURB,ONFLDA,TIME,GLOB,3FLDA,TIME,NUMB,50FLDA,TIME,STEP,1e-2FLDA,TIME,APPE,0.1FLDA,TIME,PRES,1.0E-6FLDA,ADVM,MOME,SUPGflda,relx,vx,0.5flda,relx,vy,0.5flda,relx,pres,1.0flda,prot,dens,constant ! Constant density flda,prot,visc,constant ! Constant viscosityflda,nomi,dens,rho ! Density set earlier flda,nomi,visc,mu ! Viscosity set earliersolvefiniexit,nosa

Section 6.6: VOF Analysis of Open Channel with an Obstruction


6.7. VOF Analysis of an Oscillating Droplet


This example examines the interesting phenomenon of a liquid droplet oscillating in an dynamically inactivegas. For small amplitudes, the angular frequency, ω, is given by the following formula from A. Prosperetti, ("FreeOscillations of Drops and Bubbles: The Initial-Value Problem," Journal of Fluid Mechanics, Vol. 100, p. 333, 1980):

ω σρ

2 2

F3

= [8 - 5 / Re ]R

( )

where ρ is the density, σ is the surface tension coefficient, and RF is the radius of the drop at its equilibrium state.

Here, Re is the Reynolds number given by:

Re =ρσ

µRF

where µ is the dynamic viscosity of the liquid.

When the oscillation is fully damped by the viscosity, the droplet takes a spherical shape and the droplet pressureis given by:

P =2RF

theoryσ

The droplet analyzed here is initially elliptical with major and minor semiaxes of 24.69 mm and 18 mm, respectively.

This corresponds to a final radius of RF of 20 mm. The time increment, ∆t, is set to 2 x 10-4 ms.

The material properties of the droplet are:

• ρ = 10 9 mg/(µm)3

• µ = 10 6 mg/(µm)(ms)

• σ = 0.073 mg/(ms)2

The Prosperetti formula gives an oscillation frequency of 43.0 kHz.

6.7.2. Results

Figure 6.1: “Instantaneous Pressure Distributions at 0.001 ms” and Figure 6.2: “Instantaneous Pressure Distributionsat 0.012 ms” show the instantaneous pressure distributions at 0.001 ms and 0.012 ms, respectively. Rather thana pressure jump across the interface, the pressure is observed to vary smoothly in a thin transition region nearthe interface. Initially, the maximum pressure occurs at the top and bottom portion of the droplet due to a highlocal curvature. The resulting pressure gradient forces the fluid inward and redirects it to the sides. As the dropletmoves, the pressure starts to rise at the sides due to the increasing local curvature. This slows down the movementof the droplet and eventually forces the fluid back inward from the sides. The pressure distribution controls thedroplet oscillation by balancing the kinetic energy and the potential energy due to the surface tension. Thesimulation produces a free surface profile every 5 time steps. The frequency is 42.6 kHz (two cycles occur in 0.047ms). This agrees quite well with the 43.0 kHz predicted by the Prosperetti formula. The oscillation amplitude



decreases with time and damps out at 0.2 ms due to viscosity. Averaging the pressure values on interior nodesattached to only full elements gives the numerical droplet pressure. The difference between the numerical andthe analytical pressure is approximately 1%. There are some noises in the velocity field near the interface due tothe so-called parasitic currents inherent in the CSF formulation.

Figure 6.1 Instantaneous Pressure Distributions at 0.001 ms

Figure 6.2 Instantaneous Pressure Distributions at 0.012 ms

Section 6.7: VOF Analysis of an Oscillating Droplet




/title, oscillating axisymmetric drop problem by the VOF/CSF solution./noprLX = 30 ! x length in micrometer (um)LY = 30 ! y length in micrometer (um)RadF = 20 ! radius of the final sphere in micrometer (um)aRad = 18 ! x radius in micrometer (um)bRad = RadF**3/aRad**2 ! y radius in micrometer (um)DELX = 0.1*RadF ! x spacing in micrometer (um)DELY = 0.1*RadF ! y spacing in micrometer (um)DELT = 2.0e-4 ! time increment in millisecond (ms)APPT = DELT*5 ! append time in millisecond (ms)NDT = 1000 ! total number of time stepsSigm = 0.073 ! SFTS coefficient in unit of (mg)/(ms)^2rho = 1.0e-9 ! density in unit of (mg)/(um)^3mu = 1.0e-6 ! viscosity in unit of (mg)/(um)(ms)pexact=2*Sigm/RadF ! theoretical pressure in equilibrium/prep7 et,1,141,,,1 ! RY geometryrect,0,LX,-LY,LYlsel,s,,,2,4,2lesize,all,DELYlsel,s,,,1,3,2lesize,all,DELXamesh,all

nsel,s,loc,x,0 ! symmetry conditiond,all,vx,0.0

allsicvf,elpt,0.0,0.0,aRad,bRad ! initial VFRCic,all,vx,0 ! initial velocityic,all,vy,0savefini

/soluflda,solu,tran,tflda,solu,vof,tflda,solu,sfts,tflda,nomi,sfts,sigmflda,nomi,dens,rhoflda,nomi,visc,muflda,time,glob,10flda,time,numb,NDTflda,time,step,DELTflda,advm,mome,supgflda,mir,mome,1.0flda,relx,pres,1.0flda,time,appe,APPTsolve fini/post1set,lastPLVFRC,0ANDATA,0.1, ,2,1,51,1,0.0,1

set,last*GET,VFAdvU,FLDA,VFTO,VOFUVFAdvU=1.0-VFAdvU

alls*get,elmmax,elem,0,count ! Get the number of elements*get,elmi,elem,0,num,min ! Get the lowest elem number in the set*get,vfval,elem,elmi,nmis,1 ! Get the VFRC for the element*IF,vfval,LE,VFAdvU,thenesel,u,,,elmi ! Remove elmi from the active set



*ENDIF

*do,ilop,2,elmmax ! Loop over selected elements *get,elmn,elem,elmi,nxth ! Get the next higher elem number in the set *get,vfval,elem,elmn,nmis,1 ! Get the VFRC for the element *IF,vfval,LE,VFAdvU,then esel,u,,,elmn ! Remove elmn from the active set *ELSE elmi=elmn *ENDIF*enddo

nsle,s,all ! select all node attached to elementsnsel,u,ext ! unselect ext. nodes of prev. selected nodes

pavg=0.0prms=0.0*get,nodmax,node,0,count ! Get the number of selected nodes*do,ilop,1,nodmax ! Loop over the number of nodes*get,nodi,node,0,num,min ! Get the lowest node number in the set*get,pval,node,nodi,pres ! Get the ypavg=pavg+pval ! pressure sumprms=prms+(pval-pexact)**2 ! pressure rmsnsel,u,,,nodi ! Remove node from the active set*enddopavg=pavg/nodmaxprms=sqrt(prms/nodmax)/pexact

/go*vwrite(9x,'DelX/Rad ', 3x, 'PRES / Pexact ',3x,'Prms ')*vwrite,DELX/RadF,pavg/pexact,prms(3(4x,1pe12.5))finiexit,nosa

6.7.4. Where to Find Other Examples

For more examples on the VOF analysis of free surface problems with surface tension, refer to G. Wang, (“FiniteElement Simulations of Gas-Liquid Flows with Surface Tension,” International Mechanical Engineering Congress& Exposition, November 5-10, 2000, Orlando, Florida).

Section 6.7: VOF Analysis of an Oscillating Droplet


6–14

Chapter 7: Arbitrary Lagrangian-Eulerian (ALE)Formulation for Moving Domains

7.1. Introduction

Fluid flow problems often involve moving interfaces. The interfaces can be moving internal walls (for example,a solid moving through a fluid), external walls, or free surfaces. In such problems, the fluid domain changes withtime and the finite element mesh must move to satisfy the boundary conditions at the moving interfaces. Youcan use the Arbitrary Lagrangian-Eulerian (ALE) formulation to solve problems of this type.

Figure 7.1: “Torsional Mirror at t = 0 Seconds” illustrates a typical fluid flow problem requiring the ALE formulation.It involves a micro-electromechanical system (MEMS) device with a viscous fluid between two rigid plates. Initially,the plates are parallel and the fluid is at rest.

Figure 7.1 Torsional Mirror at t = 0 Seconds

The top plate begins to oscillate about its centerline setting the fluid in motion. The ALE formulation allows thefluid domain to change with time and the finite element mesh to move to satisfy the boundary conditions atthe moving plate. Figure 7.2: “Torsional Mirror at t = 2.5 Seconds” and Figure 7.3: “Torsional Mirror at t = 7.5Seconds” show the finite element mesh at later times.


Figure 7.2 Torsional Mirror at t = 2.5 Seconds

Figure 7.3 Torsional Mirror at t = 7.5 Seconds

To perform a transient analysis employing the ALE formulation, you must activate the ALE formulation and thetransient solution algorithm. To activate the ALE formulation, you use one of the following:

Command(s): FLDATA1,SOLU,ALE,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution OptionsMain Menu> Solution> FLOTRAN Setup> Solution Options

To activate the transient algorithm, you use one of the following:Command(s): FLDATA1,SOLU,TRAN,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution OptionsMain Menu> Solution> FLOTRAN Set Up> Solution Options

For more information on transient analyses and the transient algorithm, see Chapter 5, “FLOTRAN TransientAnalyses”.

To do an ALE analysis, you need to use one of the following elements:


Chapter 7: Arbitrary Lagrangian-Eulerian (ALE) Formulation for Moving Domains

FLUID141, KEYOPT(3) = 0 (Cartesian coordinates), 1 (axisymmetric about Y-axis), or 2 (axisymmetic about X-axis).

FLUID142, KEYOPT(3) = 0 (Cartesian coordinates). You cannot use a cylindrical coordinate system (KEYOPT(3) =3) with ALE.

You will need to activate KEYOPT(4) to specify boundary motions (displacement DOFs). To define the elementtype, use one of the following:

Command(s): ET,ITYPE,Ename,KOP1,KOP2,KOP3,KOP4,KOP5,KOP6 KEYOPT,ITYPE,KNUM,VALUEGUI: Main Menu> Preprocessor> Element Type> Add/Edit/Delete

Currently, free surfaces are not a part of the ALE formulation. However, you can use the Volume of Fluid (VOF)method in conjunction with the ALE formulation to simulate flows involving free surfaces and moving walls.(Refer to Chapter 6, “Volume of Fluid (VOF) Analyses”.)

7.2. Boundary Conditions

Generally, either slip or stick boundary conditions apply for moving internal or external walls (See Fig-ure 7.4: “Boundary Conditions for Moving Walls”.)

Figure 7.4 Boundary Conditions for Moving Walls

! #"$"%&'(" "!

)

*

+ -, ./0

*

Table 7.1: “Interface Boundary Conditions” shows the required displacement and velocity specifications for slipand stick boundary conditions.

Section 7.2: Boundary Conditions


Table 7.1 Interface Boundary Conditions

Stick[1]Slip[1]Boundary Condi-tion

Specify all displacement components for fluid nodes.

That is, specify the following:

Specify normal compon-ent of displacement forfluid nodes.

That is, specify the follow-ing:

D = d nn ⋅

Displacement

3-D2-D

D = d nn ⋅

D = dτ τ1 1⋅

D = dτ τ2 2⋅

or Dx; Dy; Dz

D = d nn ⋅

D = dτ τ⋅

or Dx; Dy

Viscous Flow

Specify all velocity components for fluid nodes.

That is, specify the following:

Inviscid Flow

Specify normal compon-ent of velocity for fluidnodes.

That is, specify the follow-ing:

V = nn υ ⋅

Velocity

3-D2-D

V = nn υ ⋅

V =1 1τ υ τ⋅

V =2 2τ υ τ⋅

or Vx; Vy; Vz

V = nn υ ⋅

V =τ υ τ⋅

or Vx; Vy

1. The time derivative of the normal displacement must be equal to the normal velocity, dDn/dt = Vn.

Slip or stick boundary conditions can apply for displacement. For velocity, slip boundary conditions apply forinviscid flow and stick boundary conditions apply for viscous flow. In all cases, the time derivative of the normaldisplacement must be equal to the normal velocity. In FLOTRAN, only stick boundary conditions are currentlyvalid.

To set displacement or velocity boundary conditions at nodes, you can use either of the following:Command(s): DGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement (orVelocity)> On NodesMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Displacement (or Velocity)> OnNodes

To set boundary conditions on the solid model, you can use any of the following:Command(s): DL and DAGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement (orVelocity)> On LinesMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Displacement (or Velocity)> On Lines



Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement (or Velo-city)> On AreasMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Displacement (or Velocity)> On Areas

If a node is part of a distributed resistance or a fan model or part of a solid region composed of FLUID141 orFLUID142 elements, homogenous displacement boundary conditions are automatically applied (that is,D,ALL,UX,0.0 and D,ALL,UY,0.0 for 2-D and D,ALL,UX,0.0, D,ALL,UY,0.0, and D,ALL,UZ,0.0 for 3-D).

You can specify partial displacement boundary conditions to make external nodes move along a global axis. Forexample, D,ALL,UX,0.0 will make a set of nodes slide along the y-axis in a 2-D model. Currently, normal and tan-gential components of displacement can not be specified for an external boundary.

You can also specify generalized symmetry boundary conditions. If the ALE formulation is activated, velocitycomponents are then set equal to the mesh velocity. To do so, use one of the following commands or the GUIequivalent:

D,NODE,ENDS,-1DL,LINE,AREA,ENDS,-1,Value2DA,AREA,ENDS,-1,Value2

7.3. Mesh Updating

The ALE formulation uses the displacement boundary conditions applied by the D, DL, and DA commands toupdate the finite element mesh. It determines the displacement at the beginning of each time step relative tothe previous time step. For each time step, an elasticity based morphing algorithm updates the mesh. The al-gorithm ensures that boundary layers are retained (that is, nodes in a fine mesh area move less than nodes in acoarse mesh area).

A transient analysis cannot proceed if morphing fails. If morphing is independent of the fluid flow solution, youcan step through the morphing algorithm before doing a fluid flow analysis to determine whether morphingwill fail. To do so, issue the following command sequence:

/solu...fldata,solu,turb,ffldata,solu,temp,ffldata,solu,spec,ffldata,solu,ale,tfldata,solu,flow,fsolve

You can not check for morphing failure in advance if the time step size depends on the fluid flow variables orthe problem involves a free surface.

Mesh morphing is currently available for the following element shapes:

• Pure quadrilaterals, pure triangles, or a combination for FLUID141

• Pure hexahedrals, pure tetrahedrals, pure pyramids, pure wedges, or any combination for FLUID142

Sometimes mesh morphing produces poor quality elements (for example, when a fluid domain is extremelysqueezed by a moving wall). The birth and death feature can then be useful. To implement this feature, you assigna birth/death tolerance to the candidate elements using the real constant BDTOL. A node is automatically deac-tivated if the distance from it to the center of any element face on the wall becomes less than the assignedBDTOL. A element is deactivated if all of its nodes are deactivated. Conversely, a node is reactivated if the distance

Section 7.3: Mesh Updating


from it to the center of the closest element face on the wall becomes greater than or equal to the assignedBDTOL. A element is reactivated if all of its nodes are reactivated.

7.4. Remeshing

Large fluid domain changes can produce poor quality elements and mesh morphing failure. To avoid elementfailure, you must remesh.

To accomplish remeshing, issue one of the following:Command(s): FLDATA39,REMESHGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Remesh Ctrl

FLDATA39,REMESH will automatically remesh the fluid elements and linearly interpolate the nodal solutionfrom the old mesh to the new mesh. Use it to specify one of the following three ways of remeshing:

• Remesh all defined fluid elements if the quality of the worst defined element falls below any specifiedquality requirement listed in Table 7.2: “Element Qualities”.

Whole domain remeshing is suitable when the moving boundary affects all of the fluid elements (all thefluid elements may become distorted during solution).

• Remesh defined fluid elements that have a quality below any specified quality requirement.

Partial domain remeshing is suitable when the distorted elements are locally distributed and the locationof the distorted elements is not known before solution or it changes during solution.

• Remesh all grouped fluid elements with a specified component name if the quality of the worst selectedelement falls below any specified quality requirement.

Selected component remeshing is suitable when the distorted elements are locally distributed, but thelocation of the distorted elements is known before solution and it does not change during solution.

There are three maximum allowable element qualities that you need to specify for remeshing: aspect ratio,change of element size, and change of element aspect ratio.

Table 7.2 Element Qualities

TetrahedronsTrianglesElement Quality

AR = ((lavg)3 / V) / 8.48AR = ((lavg)2 / A) / 2.3Generalized Aspect Ratio (AR)

VOCH = exp | log (V(t) / V(0)) |VOCH = exp | log (A(t) / A(0)) |Change of Element Size (VOCH)

ARCH = exp | log (AR(t) / AR(0)) |Change of Aspect Ratio (ARCH)

where:

lavg = average length of the element edges

A = element areaV = element volumeA(t) and V(t) = element area and volume at time tA(0) and V(0) = element area and volume at time 0

You may also specify the following remeshing inputs:

• Elements Excluded



You can exclude all elements connected to boundary nodes from remeshing. For a fluid-structure interactionanalysis, you can exclude the elements connected to fluid-solid interfaces.

• Element Size

The element remeshing size defaults to 0. The element size at the nearest boundary is then used forremeshing.

• Area Expansion or Contraction

You can size internal elements so that they are approximately the size of the boundary elements timesan expansion or contraction factor.

• Checkpoints

You can specify element quality checkpoints in three ways: every time step, every Nth time step, or at asingle time point. The fluid elements will automatically remesh if any quality requirement is not met at acheckpoint.

After each remesh, new databases and results files are written with the extensions .rfl0n and .dbn, where n isthe remesh file number (Jobname.rfl01, Jobname.rfl02, ... and Jobname.db01, Jobname.db02,...). Use theANMRES command to create an animation across the results files.

Note — The original database file is Jobname.db0. The Jobname.db01, Jobname.db02, ... files haveelements that are detached from the solid model.

You can use the FLOTRAN remeshing capability in a pure fluid flow analysis or a fluid-solid interaction analysis.For information on fluid-solid interaction analyses, see Chapter 3, “Fluid-Solid Interaction Solver” and Chapter 4,“ANSYS Multi-field (TM) Solver” in the ANSYS Coupled-Field Analysis Guide.

Some important remeshing limitations are listed in the following table.

Table 7.3 Remeshing Limitations

DescriptionLimitation

Remeshing supports models meshed with triangular or tetrahedral elements. It only worksfor element groups with one element type and one real constant.

Elements

Remeshing will not work for extreme area or volume changes.Area/Volume Changes

2-D problems can have multiple domains; 3-D problems require a single domain. Do not allowtwo separate domains without distance (e.g., when solving a FSI problem with a beam or shellelement, at least one side elements connected to the beam or shell elements must be excludedfrom remeshing).

Domains

Remeshing can treat nodal loads on the boundary, but it cannot treat body loads applied tointerior nodes. Fluid-solid interaction is the only valid element based load.

Loads

Nodes on the boundary cannot be remeshed. Therefore, remeshing will not work if morphingfailed on surface nodes.

Boundary Nodes

See ALE Analysis of a Moving Cylinder for a problem using remeshing.

7.5. Postprocessing

For postprocessing, you can use the following contour and vector command sequence for the reference domainor the current deformed domain:

Section 7.5: Postprocessing


set,load step,substep ! sets the set number for processing/dscal,,1.0 ! sets the scaling for displayplns,pres,,0 ! display pressure contours on deformed domainplve,v,,,,,,,1 ! display velocity vectors on the deformed domain

To view the deformed mesh , issue the following command sequence:

set,load step,substep ! sets the set number for processing/dscal,,1.0 ! sets the scaling for displaypldi,2 ! display the deformed mesh overlayed with undeformed ! edges

To produce an animated sequence of the results, issue the ANTIME macro with the above commands.

Note — The displacements of non-structural elements are mesh (or grid) displacements to avoid meshdistortion but have no physical meaning except at the interface between the fluid and the structure.

7.6. ALE Analysis of a Simplified Torsional Mirror


This is an Arbitrary Lagrangian-Eulerian (ALE) analysis of a micro-electromechanical system (MEMS) device. Thedevice consists of a viscous fluid between two rigid plates. Initially, the plates are parallel and the fluid is at rest.The top plate begins to oscillate about its centerline setting the fluid in motion. The top plate oscillates with avery small angular amplitude.

You must determine the torque on the moving plate in order to develop a reduced order model for this device.

Figure 7.5 Torsional Mirror Problem Description

! " # $!%'& ( )*

+ ), ( -./ % ( /-)"/0/ %'& ( )* 132 / /

/ /

7.6.2. Boundary Conditions

This section derives formulas for the displacement and velocity boundary conditions.

The angle of rotation is: θ = θosinωt

Differentiating, the angular velocity is: &θ = ωθocosωt



The position of any point on the plate is given by:

x(t) = xo + Rcosθy(t) = yo + Rsinθ

where:

R = xr x o and xr is the x coordinate on the plate at time equals zero.

Therefore, the displacements of the plate are given by:

UX(t) = x(t) x(o) = x x r R

UY(t) = y(t) y(o) = y y o

Substituting the expressions for x and y gives:

UX = R(cosθ 1)UY = Rsinθ

Note — As θ approaches 0, UX approaches 0 and UY approaches Rθ.

Differentiating displacements gives the following velocity equations:

UX UX R

VY UY R

= = −

= =

& &

& &sin

cos

θθ

θθ

Note — As θ approaches 0, VX approaches R θ &θ ∝ θo2 and VY approaches R

&θ ∝ θo. Therefore, VX ap-

proaches 0 faster than VY.

The command listing in Section 7.6.4: Building and Solving the Model (Command Method) uses the above ex-pressions for UX, UY, VX, and VY in the boundary condition tables.

7.6.3. Forces and Moments

This section derives formulas for the forces and moments acting on the torsional mirror.

Section 7.6: ALE Analysis of a Simplified Torsional Mirror


Figure 7.6 Torsional Mirror Problem - Boundary Conditions

! " #$%

&

'(*) " " #$+ ,-! " #$%

!./!00!./! 0

12314 12314 5 6 65

.712312.75

6

Assuming the flow is 2-D and neglecting inertia terms, the Navier-Stokes equation reduces to the Reynoldsequation for incompressible flow:

∂∂

∂∂

∂∂x

hpx

= 6x

hU + 12 V3 µ µ( )

where: h = h (x,t) is the gap height and U and V are the velocity components of the moving plate.

Assuming that the angular displacement of the mirror is small gives:

U ≈ 0

V ≈ R &θ

R ≈ x

Substituting these values in the Reynolds equation and assuming that U variations with x are small gives:

∂∂

∂∂

x

hpx

= 12 V = 12 x3 µ µ θ&

Integrating gives:

p dx= +∫ ∫6x

h

C

hdx + C

2

313 2µθ&

where C1 and C2 are constants to be determined.

Substituting ho for h for small angular displacements and completing the integration gives:

p =

6

h

x3

+C x

h+ C

o3

31

o3 2

µθ&

Substituting p = po at x = ± L/2 gives:



po =

2

h

L2

+C

h

L2

+ Co3

31

o3 2

µθ&

po =

-2

h

L2

-C

h

L2

+ Co3

1

o3 2

µθ& 3

Solving these two equations for C1 and C2 gives:

C2 = po

C1 = 2 µ&θ (L/2)2

Substituting the C1 and C2 values into the pressure equation gives:

p po= +

2

hx -

2

h

L2

xo3

3

o3

µθ µθ& & 2

( )p - p2

hx -

L2o

o3

=

µθ&x2

2

Thus, the force and moment on the torsional mirror are given by:

F = (p - p ) dx = 0p o- L/2

L/2

∫

M = p - p xdx = -1

60L

hp o

- L/2

L/2 5

o3

( )∫ µθ&

The flow field at any x coordinate is given by:

U x,y,t =1

2px

y y -( ) ( )µ

∂∂

h

Accordingly, the shear stress on the torsional mirror is:

µ µθ∂∂

∂∂

Uy

=px

=h

3x -L2y = h

o2

22h

2

&

Thus, the force and moment due to shearing stresses are:

F =Uy

dx = 0s- L/2

L/2

y = hµ ∂∂∫



M =Uy

xdx = 0s

- L/2

L/2

y = hµ ∂∂∫


The following command stream shows all the relevant parameters and solution strategy. All text prefaced withan exclamation point (!) is a comment. Please refer to Figure 7.5: “Torsional Mirror Problem Description”.

/BATCH,LIST/tit,Torque Mirror Problem /noprLX = 1.0 ! Plate Length in X directionNDX = 40 ! Number of X divisionsH = 0.01 ! Gap in Y-direction NDY = 10 ! Number of Y divisionsPOUT = 0.0 ! Outlet relative pressureRHO = 1.0000 ! Fluid densityMU = 1.00 ! Fluid viscositynts = 40 ! number of time stepstime = 10. ! total simulation timedelta = time/nts ! time step sizeappf = delta ! append results every time step*AFUN,RAD ! angles are in radiansAMAX = (2*H/LX)/8 ! adjust angular amplitude << 1OMEGA = 2*3.14159/time ! complete 1 cycle in given timeX0 = LX/2 ! pivot point x-coordY0 = H ! pivot point y-coordH0 = H

! use function builder/tables (refer to Section 2.6.15: Applying Loads Using Function BoundaryConditions in the ANSYS Basic Analysis Guide)

! for displacements/velocities of oscillating plate

*DIM,UXTAB,TABLE,6,4,1UXTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX, 0.0, 0.0UXTAB(0,1,1) = 1.0,-1 , 0, 1.0 , 27 , 2 , 17 ! Radius = XR - X0UXTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 ! Angle=amax*sin(omega*t) UXTAB(0,3,1) = 0.0,-3 , 10, 1.0 ,-2 , 3 ,-1 ! Radius*cos(Angle) UXTAB(0,4,1) = 0.0,99 , 0, 1.0 ,-3 , 2 ,-1 ! Radius*cos(Angle)-Radius *DIM,UYTAB,TABLE,6,3,1UYTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX, 0.0, 0.0UYTAB(0,1,1) = 1.0,-1 , 0, 1.0 , 27 , 2 , 17 ! Radius = XR - X0UYTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 ! Angle=amax*sin(omega*t) UYTAB(0,3,1) = 0.0,99 , 9, 1.0 ,-2 , 3 ,-1 ! Radius*sin(Angle) *DIM,VXTAB,TABLE,6,5,1VXTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX,OMEGA*AMAX, 0.0VXTAB(0,1,1) = 1.0,-1 , 0,-1.0 , 27 , 1 , 17 ! -Radius = -(XR-X0)VXTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 ! Angle=amax*sin(omega*t) VXTAB(0,3,1) = 0.0,-3 , 10,OMEGA, 1, 3 , 19 ! Angle speed= ! amax*omega*cos(omega*t)VXTAB(0,4,1) = 0.0,-4 , 9, 1.0 ,-2 , 3 , -1 ! -Radius*sin(angle)VXTAB(0,5,1) = 0.0,99 , 0, 1.0 ,-4 , 3 , -3 !-Radius*sin(angle)*angle speed*DIM,VYTAB,TABLE,6,5,1VYTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX,OMEGA*AMAX, 0.0VYTAB(0,1,1) = 1.0,-1 , 0, 1.0 , 27 , 2 , 17 !Radius = XR - X0VYTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 !Angle=amax*sin(omega*t)VYTAB(0,3,1) = 0.0,-3 , 10,OMEGA, 1, 3 , 19 !Angle speed= !amax*omega*cos(omega*t)VYTAB(0,4,1) = 0.0,-4 , 10, 1.0 ,-2 , 3 , -1 !Radius*cos(angle)VYTAB(0,5,1) = 0.0,99 , 0, 1.0 ,-4 , 3 , -3 !Radius*cos(angle)*angle speed

/PREP7 $smrt,off et,1,141 ! 2-D XY systemkeyopt,1,4,1 ! allow disp. DOFs



esha,2 ! Quad elementsrect,,LX,,Hlesize,1,,,NDX,lesize,3,,,NDX,lesize,2,,,NDY,-10lesize,4,,,NDY,-10allsamesh,all

lsel,s,,,3 ! Moving top plate nsll,s,1d,all,VX,%VXTAB%d,all,VY,%VYTAB%d,all,enke,-1d,all,ux,%UXTAB%d,all,uy,%UYTAB%

lsel,s,,,2 ! Left & Right Outlets lsel,a,,,4 nsll,s,1d,all,pres,POUT

lsel,s,,,1 ! Stationary bottom plate nsll,s,1d,all,vx, d,all,vy, d,all,ux,0.0d,all,uy,0.0

allsfini

/SOLUFLDA,NOMI,DENS,RHO ! Nominal densityFLDA,NOMI,VISC,MU ! Nominal viscosityFLDA,OUTP,TAUW,T ! Output wall shear stressflda,quad,momd,2 ! increased quadrature for deformedflda,quad,moma,2 ! elementsflda,quad,moms,2flda,quad,prsd,2flda,quad,prss,2flda,solu,tran,tflda,time,step,deltaflda,time,numb,ntsflda,time,tend,timeflda,time,glob,25flda,time,appe,appfflda,solu,ale,t ! Turn ALE onsaveSOLVEfini

!do the comparison with analytical solution here/post1!moving wall*dim,RES1,,NDX+1,15*do,j,1,nts,1 ! loop over the time stepsrsys,0 csys,0set,1,j ! get the results of step j*get,curtime,active,0,set,time ! get the time of this substeptheta = amax*sin(omega*curtime) ! get the plate anglethetad = amax*omega*cos(omega*curtime) ! get plate angular speednsel,s,loc,y,H ! select moving wall nodes*do,i,1,NDX+1 ! loop over these nodes *get,XMAX,node,,mxloc,x n = node(XMAX,H,0) RES1(i,1) = n ! Node number RES1(i,2) = NX(n) ! X-coordinate RES1(i,3) = NY(n) ! Y-coordinate RES1(i,4) = UX(n) ! UX Rn = NX(n)-X0



RES1(i,10) = Rn*(cos(theta)-1.0) ! UX exact RES1(i,5) = UY(n) ! UY RES1(i,11) = Rn*sin(theta) ! UY exact RES1(i,6) = VX(n) ! VX RES1(i,12) = -Rn*sin(theta)*thetad ! VX exact RES1(i,7) = VY(n) ! VY RES1(i,13) = Rn*cos(theta)*thetad ! VY exact RES1(i,8) = PRES(n) ! Pressure c1 = 2.0*MU*thetad/H0**3 c2 = NX(n) - X0 RES1(i,14) = c1*(c2**3 - c2*(LX/2)**2) ! Exact Pressure *get,RES1(i,9),node,n,TAUW ! Shear stress c0 = NX(n) - X0 c1 = H0 + theta*c0 c2 = 3*c0**2 - (LX/2)**2 RES1(i,15) = ABS(c1*mu*thetad*c2/H0**3) ! Exact shear stress nsel,u,,,n*enddo/com Compare disps/velocities/pressures/shears on moving wall(X,H,0)/com*status,curtime*status,theta *vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'UX (FLOTRAN)',5x,'UX (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,4),RES1(1,10)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'UY (FLOTRAN)',5x,'UY (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,5),RES1(1,11)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'VX (FLOTRAN)',5x,'VX (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,6),RES1(1,12)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'VY (FLOTRAN)',5x,'VY (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,7),RES1(1,13)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'PRE (FLOTRAN)',5x,'PRE (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,8),RES1(1,14)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'TAU (FLOTRAN)',5x,'TAU (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,9),RES1(1,15)(3x,f5.0,4(1pe17.5))/comnsel,s,loc,y,H ! select nodes on moving platelocal,11,0,X0,Y0,0 ! setup local coord system for moment calcsrsys,11/com compute pressure force/moments on the wallintsrf,pres*get,forcex,intsrf,0,item,fx*get,forcey,intsrf,0,item,fy*get,forcez,intsrf,0,item,fz*get,momx,intsrf,0,item,mx*get,momy,intsrf,0,item,my*get,momz,intsrf,0,item,mz*status,forcex*status,forcey ! should be zero*status,forcez*status,momx*status,momy*status,momz ! FlotranMoment = -0.0166*mu*thetad*LX**5/H0**3 ! Exact*status,moment/com compute shear force/moments on the wall should be zero



intsrf,tauw*get,forcex,intsrf,0,item,fx *get,forcey,intsrf,0,item,fy*get,forcez,intsrf,0,item,fz*get,momx,intsrf,0,item,mx*get,momy,intsrf,0,item,my*get,momz,intsrf,0,item,mz*status,forcex ! should be zero*status,forcey*status,forcez*status,momx*status,momy*status,momz ! should be zero*enddofini/exit,nosa

7.7. ALE/VOF Analysis of a Vessel with a Moving Wall


This problem involves a moving wall and a free surface. A square vessel is half filled with liquid and at t = 0 theleft wall begins to move to the right. The wall stops moving after a short time and the fluid comes to restgradually. The total analysis time is 2 seconds. The left wall comes to rest at 0.125 * (time) = 0.125*(2 seconds) =0.25 seconds. The left wall displacement and velocity are input as tabular boundary conditions (see Figure 7.8: “LeftWall Displacement and Velocity”). The simulation uses the Volume of Fluid (VOF) method in conjunction withthe ALE formulation.

Figure 7.7 Square Vessel with a Moving Wall

!#" $&%

! '()

!

!* + ,$.-/ %$.-/ %

!#"0 $&%/ -1243657 89

!* + ,

!#"

:;

,<

$95 89

!* + ,

Section 7.7: ALE/VOF Analysis of a Vessel with a Moving Wall


Figure 7.8 Left Wall Displacement and Velocity

"!$# %&

&

')(

*(

7.7.2. Results

The initial fluid volume is 1/2 H times LX. Since H and LX are both equal to 1, the initial fluid volume is 0.500000000.The calculated final fluid volume is 0.499999673.



/BATCH,LIST/title,ALE-VOF combination - container with moving wall & free surface/noprLX = 1.0 ! Initial width in X directionNDX = 10 ! Number of X divisionsH = 1.0 ! Height of container NDY = 10 ! Number of Y divisionsRHO = 1.0000 ! Fluid densityMU = 1.00 ! Fluid viscosityLXF = 0.750 ! Final X-Length time = 2. ! Total simulation timents = 200 ! Total number of time stepsdelta = time/nts ! Time step sizeappf = delta ! Results append frequencyVEL = (LX-LXF)/(0.125*time) ! left wall moves for 12.5% of ! simulation time with velocity VEL

*dim,timutab,table,3,,,time ! left wall displacement historytimutab(1,0)=0,0.125*time,time timutab(1,1)=0,(LX-LXF),(LX-LXF)*dim,timvtab,table,4,,,time ! left wall fluid velocity historytimvtab(1,0)=0,0.125*time,0.125*time+0.000001,time timvtab(1,1)=VEL,VEL,1.e-12,1.e-12



/PREP7 $smrt,off et,1,141 ! 2-D XY systemkeyopt,1,4,1 ! enable disp DOFsesha,2 ! Quad elementsrect,,LX,,Hlesize,1,,,NDX,-10lesize,3,,,NDX,-10lesize,2,,,NDY,lesize,4,,,NDY,allsamesh,all

lsel,s,,,4 ! Moving left wall nsll,s,1d,all,VX,%timvtab%d,all,VY,d,all,enke,-1d,all,ux,%timutab%d,all,uy,0.0

lsel,s,,,1 ! bottom wallnsll,s,1d,all,vxd,all,vy

lsel,s,,,3 ! top wall nsll,s,1d,all,vxd,all,vy

lsel,s,,,2 ! Stationary right wall nsll,s,1d,all,vx, d,all,vy, d,all,ux,0.0d,all,uy,0.0

alls

nsel,s,loc,y,0,0.5*H ! select lower half elementsesln,s,1ice,all,vfrc,1.0 ! apply vof initial conditionsallsel

fini

/SOLUFLDA,NOMI,DENS,RHO ! Nominal densityFLDA,NOMI,VISC,MU ! Nominal viscosityacel,,9.8 ! Apply gravity loadingflda,step,sumf,1flda,solu,tran,tflda,time,step,deltaflda,time,numb,nts flda,time,tend,timeflda,time,glob,25flda,time,appe,appf flda,solu,ale,t ! Ale onflda,solu,vof,t ! Vof onsaveSOLVEfini

!do the comparison here for final fluid volume/post1set,lastfvol = 0. ! initialize volume to zero*do,i,1,NDX*NDY ! loop over elements n1 = nelem(i,1) ! 4 nodes of this element n2 = nelem(i,2) n3 = nelem(i,3) n4 = nelem(i,4)

Section 7.7: ALE/VOF Analysis of a Vessel with a Moving Wall


x1 = nx(n1)+ux(n1) ! current coords of the 4 nodes y1 = ny(n1)+uy(n1) x2 = nx(n2)+ux(n2) y2 = ny(n2)+uy(n2) x3 = nx(n3)+ux(n3) y3 = ny(n3)+uy(n3) x4 = nx(n4)+ux(n4) y4 = ny(n4)+uy(n4) evol1 = x1*y2+y1*x3+y3*x2 ! compute volume of triangle 123 evol1 = evol1-y2*x3-y1*x2-x1*y3 evol1 = abs(0.5*evol1) ! first triangle volume evol2 = x1*y4+y1*x3+y3*x4 ! compute volume of triangle 143 evol2 = evol2-y4*x3-y1*x4-x1*y3 evol2 = abs(0.5*evol2) ! second triangle volume *get,frac,elem,i,nmisc,1 ! get VOF of this quad fvol = fvol + (evol1+evol2)*frac!increment the total fluid volume*enddo*status,fvol ! print the final fluid volumetarget = 0.5*H*LX*status,target ! print the expected fluid volume/comfini/exit,nosa

7.8. ALE Analysis of a Moving Cylinder


This problem involves a cylinder passing through a channel with a constant velocity VX = 1.0. FLUID141 triangleelements model the fluid. The simulation uses the ALE formulation and remeshing. FLDATA39,REMESH,Label,Valuespecifies the quality requirements shown in the following table.

Table 7.4 Quality Requirements

FLDATA39,REMESH,Label,Value CommandElement Quality

FLDATA39,REMESH,ARMA,5.0Aspect Ratio (AR)

FLDATA39,REMESH,VOCH,3.0Change of Element Size (VOCH)

FLDATA39,REMESH,ARCH,3.0Change of Aspect Ratio (ARCH)

FLDATA39,REMESH,ELEM,ALL sets the remeshing to all defined fluid elements if the quality of the worst definedelement falls below any quality requirement. The total analysis time is 44 seconds.

Figure 7.9 Moving Cylinder

"!

ρ#

µ#



7.8.2. Results

The ten results files are file.rfl01 through file.rfl10. They were created when one of the remeshing criteria weremet. The following figures display the remeshed elements at 0, 22, and 44 seconds.

Figure 7.10 Elements at 0 Seconds





/batch,list/verify,dv-1101c/title, dv-1101c, Flotran Remeshing: Cylinder pass through a channel/COM,****************************************************/COM,* Cylinder pass through a channel (pure fluid flow)/COM,* Verify partial domain re-meshing/COM,****************************************************r1 = 2.5l1 = 5.0l2= 20.0l3=60.0h = 10.0rx0= l1+(l2-l1)/2.0

Section 7.8: ALE Analysis of a Moving Cylinder


ry0 = h/2.0nl1 = 5nl3 = 10nr=8nc=8/PREP7

*DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNC_C1*SET,_FNCNAME,'DIS'*DIM,_FNC_C1,,1 *SET,_FNC_C1(1),1.0! /INPUT,force.func *DIM,%_FNCNAME%,TABLE,6,3,1 ! ! Begin of equation: a*TIME *SET,%_FNCNAME%(0,0,1), 0.0, -999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), %_FNC_C1(1)%*SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, -1, 0, 1, 17, 3, 1 *SET,%_FNCNAME%(0,2,1), 0.0, 99, 0, 1, -1, 0, 0 *SET,%_FNCNAME%(0,3,1), 0 ! End of equation: a*TIME !-->

RECTNG,0,l1,0,h, RECTNG,l1,l2,0,h, RECTNG,l2,l3,0,h, aglue,all

CYl4,rx0,ry0,0,45,r1,135 CYl4,rx0,ry0,0,135,r1,225 CYl4,rx0,ry0,0,225,r1,315 CYl4,rx0,ry0,0,315,r1,405 asel,s,,,2asel,a,,,3asel,a,,,6asel,a,,,7allsel,below,areaaglue,all allselFLST,3,4,5,ORDE,3 FITEM,3,2 FITEM,3,8 FITEM,3,-10 ASBA, 4,P51Xaplot

et,1,141KEYOPT,1,4,1type,1mat,1asel,s,,,1esize,.5mshape,1,2dmshkey,0amesh,all

et,2,141KEYOPT,2,4,1type,2mat,1asel,s,,,3esize,.5mshape,1,2dmshkey,0amesh,all



et,3,141KEYOPT,3,4,1type,3mat,1asel,s,,,5esize,2.0mshape,1,2dmshkey,0amesh,allnsel,s,loc,x,0D,ALL,VX,0.0, D,ALL,VY, 0.0D,ALL,UX,0.0, D,ALL,UY, 0.0nsel,s,loc,x,l3D,ALL,pres,0.0D,ALL,UX,0.0, D,ALL,UY, 0.0nsel,s,loc,y,0D,ALL,vy,0.0D,ALL,UX,0.0, D,ALL,UY, 0.0nsel,s,loc,y,hD,ALL,vy,0.0D,ALL,UX,0.0, D,ALL,UY,0.0,lsel,s,,,5lsel,a,,,23lsel,a,,,25lsel,a,,,27nsll,s,1d,all,UX,%DIS%d,all,UY,0.0d,all,VX,1.0d,all,VY,0.0allselcdwrite,db,fluid,cdb,fini! Flotran Setup/soluFLDATA30,QUAD,MOMD,2, FLDATA30,QUAD,MOMS,2, FLDATA30,QUAD,PRSD,2, FLDATA30,QUAD,PRSS,2, FLDATA30,QUAD,THRD,0, FLDATA30,QUAD,THRS,0, FLDATA30,QUAD,TRBD,0, FLDATA30,QUAD,TRBS,2, /soluFLDATA4,TIME,NUMB,100000, FLDATA4,TIME,TEND,44.0, FLDA,SOLU,ALE,T ! ALE solutionFLDATA1,SOLU,FLOW,1FLDATA1,SOLU,TRAN,1!FLDATA1,SOLU,TURB,1FLDATA2,TIME,GLOB,5

FLDATA7,PROT,DENS,CONSTANTFLDATA8,NOMI,DENS,1.0FLDATA7,PROT,VISC,CONSTANTFLDATA8,NOMI,VISC,1.0!FLDA,BULK,BETA,1.0e5FLDA,TIME,STEP, 2.0!!!! Newmark method!FLDATA,OUTP,TAUW,TFLDATA,TIME,METH,NEWMFLDATA,TIME,DELT,0.5!

Section 7.8: ALE Analysis of a Moving Cylinder


!! Set ANSYS-STRUCTURE commandsSAVE/COM /COM Re-meshing Commands/COM FLDATA,REMESH,ELEM,ALL ! all defined element re-meshingFLDATA,REMESH,ARMA,10.0 ! maximum aspect ratioFLDATA,REMESH,VOCH,5.0 ! maximum volume changeFLDATA,REMESH,ARCH,5.0 ! maximum aspect ratio changeSOLVESAVEfinish



Chapter 8: FLOTRAN Compressible Analyses

8.1. Requirements for Compressible Analysis

As is true with turbulence, activating the compressible algorithm is at your discretion. You should activate turbu-lence for virtually all compressible analyses, (although in principle the Reynolds number can be in the laminarrange for high Mach numbers). Differences in results (pressure, density, velocity distributions) between the in-compressible and compressible algorithms can exist at Mach numbers as low as 0.3, and are quite pronouncedwhen the Mach number is as high as 0.7.

The speed of sound is a function of the equation of state of the fluid and its absolute temperature. For a constantdensity fluid, the speed of sound is infinite. For an ideal gas, regardless of whether the incompressible or com-pressible solution algorithm is used, the relationship is:

C RT= γ

In the preceding equation:

• R is the Universal Gas Constant

• γ is the ratio of specific heats (Cp/Cv)

• T is the absolute temperature

For 2-D compressible analyses, meshes using quadrilateral elements are highly recommended. Hexagonal elementsare recommended for 3-D cases. For more information, see Section 8.4: Structured vs. Unstructured Mesh.

8.2. Property Calculations

The compressible algorithm takes into account the kinetic energy changes of the fluid as it accelerates. The for-mulation is in terms of the total temperature.

In an adiabatic analysis, the total temperature remains constant throughout the problem domain. You specifythe temperature using either of the following methods:

Command(s): FLDATA14,TEMP,TTOT,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref ConditionsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

The conservation of energy is then a balance between thermal storage (static temperature) and kinetic energy.

The total (stagnation) temperature is the temperature of the fluid after it has been brought isentropically to azero velocity. Typically, you choose the conditions at the inlet. Knowledge of the static temperature and the ve-locity magnitude |V| at the inlet enables you to calculate the total temperature via the following equation,

T TV

Co staticp

= +2

2

This relationship is sometimes useful when cast in terms of the Mach number (M):

T T Mo = + −( )1

12

2γ

You must specify the specific heat and the ratio of specific heats γ. (To enter this ratio, use one of the following:)


Command(s): FLDATA17,GAMM,COMP,GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref ConditionsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

The ANSYS program uses the resulting static temperature and the absolute pressure to calculate the densityfrom the equation of state.

Note — Unlike incompressible analyses, where freezing the density calculation for the early global itera-tions can be an advantage, compressible analyses automatically involve the variable density option.Another difference between these types of analysis is that for compressible analyses, initial propertiesare calculated from the calculated static temperature, not from the nominal temperature.

8.3. Boundary Conditions

Typically, you will know the Mach number or the velocity or the mass flow along with the static temperature forthe inlet. Knowing the velocity or Mach number enables you, using the above equations, to calculate of the ap-propriate total temperature. If you know only the mass flow rate, you can approximate the pressure at the inletby the reference pressure and use it with the equation of state to approximate the inlet density and thus thevelocity.

For subsonic problems, the boundary condition strategy is similar to that used for incompressible flow problems,that is, velocity or pressure at the inlet and pressure at the outlet. For supersonic problems, however, the natureof the equations changes and the effects of downstream boundary conditions cannot propagate upstream. It iscommon in such cases to apply both pressure and velocity to upstream locations. Leave the downstreamboundary unspecified.

Free stream conditions are often applied as far field boundary conditions for external flow problems. Oftenspecification of pressure at these boundaries helps. However, as the solution develops, phenomena such asshock waves propagate to these boundaries. In this case, you should remove the boundary conditions. Failureto do so could adversely affect the resultant mass balance. Also, if the boundary is too close to the region of interest(e.g. the airfoil the flow is moving past), the velocity solution near the boundary will tend to be greater than thefree stream velocity. In such cases, a better choice for the velocity boundary conditions is the symmetry condition(only specify the velocity normal to the boundary as zero).

If the problem is thermal, ANSYS takes all of the applied boundary conditions to be total temperature, not statictemperature. Conversely, if a problem is adiabatic, thermal boundary conditions are ignored.

If you use a thermal incompressible solution as a starting point for a thermal compressible problem, you mustchange the boundary conditions so that they are specified in terms of total temperature.

8.4. Structured vs. Unstructured Mesh

As noted at the beginning of this chapter, for 2-D compressible flow problems, quadrilateral mesh is the best touse. Consider Figure 8.1: “Three Types of Meshing”:



Figure 8.1 Three Types of Meshing

(a) Quadrilateral mesh, (b) Triangular mesh with a random pattern, (c) Triangular mesh with asymmetrical pattern

In 2-D compressible analyses, mesh (a), the quadrilateral mesh, produces the most accurate results. Mesh (b)yields 2-D, not 1-D results, and mesh (c) yields 1-D results.

Similarly, in a 3-D compressible analysis, a hexagonal mesh (the equivalent of quadrilateral mesh in 2-D) producesthe best results. A tetrahedral mesh with a random pattern (the 3-D equivalent of mesh (b)) yields only 3-D results,not 1-D. And a tetrahedral symmetric mesh, the 3-D equivalent of mesh (c), gives you 1-D results.

8.5. Solution Strategies

You must solve compressible analyses as pseudo-transient or transient problems. This is due to the non-ellipticnature of supersonic problems. The pseudo-transient approach is quite adequate when the time-history of thedeveloping transient is not of interest. In that approach, you apply inertial relaxation to the pressure equation(see Section 8.5.1: Inertial Relaxation).

For an ideal gas, the density is always calculated from an equation of state involving the absolute pressure andthe absolute temperature. Because of this, you must prevent negative values of absolute pressure and absolutestatic temperature from being encountered during the iterative process, as these would lead to a negativedensity. One way to do this is to use a converged incompressible solution as a starting point. Another way is touse capping to specify a minimum FLOTRAN (relative) pressure. For example, to keep the absolute pressure ata minimum of 1 psi, you would cap the relative pressure at -13.7 psi for a reference pressure of 14.7 psi. Cappingis not a stability control and by itself it will not control the solution progression. It only helps prevent negativeproperties.

Artificial viscosity helps to prevent negative temperatures. You set it at the beginning of the analysis, and mustreduce it slowly for subsequent continuations of the analysis. You will probably encounter divergence if you in-crease the viscosity between runs. The magnitude of the artificial viscosity required can vary greatly. The smallerthe starting value, the fewer the global iterations required. But if it is not large enough, you may encounternegative static temperatures. You can use the laminar and effective viscosities to gauge a good starting value.It is typically a couple orders of magnitude higher than the effective viscosity, which in turn is initialized as a

Section 8.5: Solution Strategies


multiple of the laminar value. Generally, a value 3 or 4 orders of magnitude higher than the laminar viscosity isa good approximate starting point.

In a compressible problem, the final answer would be a function of the artificial viscosity if it were not removed.Therefore, after stability has been achieved, gradually remove the artificial viscosity during repeated analysiscontinuations.

8.5.1. Inertial Relaxation

Inertial relaxation helps to stabilize a solution by increasing the magnitude of the main diagonal of the matrixequation along with a corresponding increase in the forcing function. Values used are generally between 1.0 x

10-3 (less relaxation) and 1.0 x 10-6 (more relaxation) for pressure. The smaller values provide more diagonaldominance and thus equation stability. The cost of this is slower convergence since it de-emphasizes the influenceof the cross-coupling terms present in the equations.

Unlike artificial viscosity, the inertial relaxation does not affect the answer if the problem is converged and thus

does not have to be removed. It is best to reduce the magnitude to the range of 1 x 10-4 later in the analysis. Youcan measure the effectiveness of the relaxation by observing the performance of the parameter RTR in the Job-name.DBG file.

All the techniques discussed so far involve the steady state algorithm. It is common for supersonic problems,even if they are posed as steady state to be solved with the transient algorithm. An initial velocity field can beimposed as a first guess. The inertial relaxation acts similarly to the transient algorithm and its use is consideredredundant in transient analyses. Do note that problems involving moving shocks may lead to inaccurate solutionswhen using the transient algorithm. With the current set of governing partial differential equations and the dis-cretization techniques used, the transient algorithm has demonstrated solutions that are qualitatively correctbut may yield quantitatively inaccurate results.

8.6. Example of a Compressible Flow Analysis

8.6.1. The Example Described

This example evaluates compressible flow in a converging-diverging nozzle. The nozzle is axisymmetric withinlet, throat, and outlet radii of 2.432 cm, 0.5 cm and 0.80 cm, respectively. The nozzle inlet pressure is given as

6.13769e+6 dynes/cm2.

8.6.1.1. Fluid Properties

The analysis uses density, viscosity, thermal conductivity, and specific heat properties for air in units of cm-g-sec.

8.6.1.2. Approach and Assumptions

The compressible flow analysis is a turbulent analysis that uses the FLUID141 2-D Fluid-Thermal element.

The analysis assumes atmospheric pressure conditions at the outlet. It assumes a stagnation temperature of 550K.

Inlet and outlet pressure boundary conditions are set to 6.13769e+6 dynes/cm2 and 0, respectively. The VY velocitycomponent is set to 0 along the axis of symmetry and the VX and VY velocity components are set to 0 along theouter surface.



The analysis starts with 20 iterations at an artificial viscosity of 10. It then continues for 20 iterations at artificialviscosity values of 1, .1, .01, .001, .0001, and .00001 to give a total of 140 iterations. The analysis then continuesfor another 160 iterations at an artificial viscosity of 0. After 300 iterations of slowly reducing the viscosity to 0,the analysis continues for 100 iterations with increased momentum and pressure inertial relaxation factors. Finally,the analysis converges to a final solution with the momentum and pressure inertial relaxation factors increasedto higher values for 400 iterations.

8.7. Doing the Example Compressible Flow Analysis (GUI Method)

You perform the following steps to analyze the converging diverging nozzle using the GUI Method.

Step 1: Establish an Analysis Title and Preferences

1. Choose Utility Menu> File> Change Title. The Change Title dialog box appears.

2. Enter the text "Compressible Flow in a Converging Diverging Nozzle."

3. Click on OK.

4. Choose Main Menu> Preferences. The Preferences for GUI Filtering dialog box appears.

5. Click the button for FLOTRAN CFD to "On."

6. Click on OK.

Step 2: Define Element Types

1. Choose Main Menu> Preprocessor> Element Type> Add/Edit/Delete. The Element Types dialog boxappears.

2. Click on Add. The Library of Element Types dialog box appears.

3. In the two scrollable lists, highlight (click on) "FLOTRAN CFD" and "2D FLOTRAN 141."

4. Click on OK. ANSYS returns you to the Element Types dialog box.

5. Click on Close.

Step 3: Create Keypoints

1. Choose Main Menu> Preprocessor> Modeling> Create> Keypoints> In Active CS. The Create Keypointsin Active Coordinate System dialog box appears.

2. In the "Keypoint number (NPT)" field enter 1 and in the "Location in active CS (X and Y)" fields enter 0and 2.432, respectively. Click on Apply.

3. Repeat the previous substep for the following sets of keypoint numbers and (X, Y) locations: 2 (0, 0), 3(1, 2.432), 4 (1, 0), 5 (2, 2.232), 6 (2, 0), 7 (5, 0), 8 (5, 0.7), 9 (6, 0), 10 (6, 0.5), 11 (14, 0), 12 (14, 0.8). After en-tering each set, click on Apply. After entering the last set, click on OK.

4. Click on SAVE_DB on the ANSYS Toolbar.

Step 4: Create Lines

1. Choose Utility Menu> PlotCtrls> Numbering. The Plot Numbering Controls dialog box appears.

2. Click the button for "Line Numbers (LINE)" to "On" and click OK.

3. Choose Main Menu> Preprocessor> Modeling> Create> Lines> Lines> In Active Coord. The Linesin Active Coord picking menu appears.

Section 8.7: Doing the Example Compressible Flow Analysis (GUI Method)


4. Pick the keypoint numbers 2 and 4 and click on Apply.

5. Repeat steps 3 and 4 for the following sets of keypoint numbers: 3 and 4; 1 and 3; 1 and 2; and 5 and 8.After entering each set, click on Apply. After entering the last set, click on OK.

6. Choose Main Menu> Preprocessor> Modeling> Create> Lines> Lines> Tan to 2 Lines. The LineTangent to 2 Lines picking menu appears.

7. Pick line number 3 and click on Apply. The Line Tangent to 2 Lines picking menu reappears.

8. Pick keypoint number 3 and click on Apply. The Line Tangent to 2 Lines picking menu reappears.


10. Pick keypoint number 5 and click on OK.


12. Pick the keypoint numbers 10 and 12 and click on OK.

13. Choose Main Menu> Preprocessor> Modeling> Create> Lines> Lines> Tan to 2 Lines. The LineTangent to 2 Lines picking menu appears.


15. Pick keypoint number 8 and click on Apply. The Line Tangent to 2 Lines picking menu reappears.


17. Pick keypoint number 10 and click on OK.


19. Pick the keypoint numbers 4 and 6 and click on Apply.

20. Enter the following sets of keypoint number by repeating steps 18 and 19: 6 and 7; 7 and 9; and 9 and11. After entering each set, click on Apply. After entering the last set, click on OK.

Step 5: Create Areas

1. Choose Main Menu> Preprocessor> Modeling> Create> Areas> Arbitrary> Through KPs. The CreateArea thru KPs picking menu appears.

2. Pick the keypoint numbers (2, 4, 3, 1) and click on Apply.

3. Repeat the previous substep for the following sets of keypoint numbers: (4, 6, 5, 3), (6, 7, 8, 5), (7, 9, 10,8), and (9, 11, 12, 10). After entering each set, click on Apply. After entering the last set, click on OK.

4. Click on SAVE_DB on the ANSYS Toolbar.

Step 6: Define Scalar Parameters

1. Choose Utility Menu> Parameters> Scalar Parameters. The Scalar Parameters dialog box appears.

2. Type in the parameter values shown below. (Press ENTER after entering each value.)

ntran = 24rtran = 10na = 10nb = 10nc = 25nd = 10



ne = 100re = -1.5

3. Click on Close to close the dialog box.

Step 7: Mesh the Model

1. Choose Main Menu> Preprocessor> Meshing> Size Cntrls> Lines> Picked Lines. The Element Sizeon Picked Lines picking menu appears.

2. Pick line number 4 and click on Apply. The Element Sizes on Picked Lines dialog box appears.

3. In the "No. of element divisions (NDIV)" field, enter ntran, and in the "Spacing ratio (SPACE)" field enterrtran. Click on Apply.

4. Repeat steps 2 and 3 for line number 2.


6. In the "No. of element divisions (NDIV)" field, enter ntran, and in the "Spacing ratio (SPACE)" field enter1/rtran. Click on Apply.

7. Repeat steps 5 and 6 for line numbers 14, 15, and 16.


9. In the "No. of element divisions (NDIV)" field, enter na, and in the "Spacing ratio (SPACE)" field enter 1.Click on Apply.



12. In the "No. of element divisions (NDIV)" field, enter nb, and in the "Spacing ratio (SPACE)" field enter 1.Click on Apply.



15. In the "No. of element divisions (NDIV)" field, enter nc, and in the "Spacing ratio (SPACE)" field enter 1.Click on Apply.



18. In the "No. of element divisions (NDIV)" field, enter nd, and in the "Spacing ratio (SPACE)" field enter 1.Click Apply.



21. In the "No. of element divisions (NDIV)" field, enter ne, and in the "Spacing ratio (SPACE)" field enter re.Click on Apply.

22. Repeat steps 20 and 21 for line number 12 but this time click OK.

23. Choose Main Menu> Preprocessor> Meshing> Mesh> Areas> Mapped> 3 or 4 sided. A picking menuappears.

24. Click on Pick All. The meshed model appears.



Step 8: Compress Numbers

1. Choose Main Menu> Preprocessor> Numbering Ctrls> Compress Numbers. The Compress Numbersdialog box appears.

2. Select Nodes as the "Item to be compressed" and click on Apply.

3. Select Elements as the "Item to be compressed" and click on OK.

Step 9: Apply Boundary Conditions

1. Choose Utility Menu> Select> Entities. The Select Entities dialog box appears.

2. Choose "Lines" and "By Num/Pick," then click on OK. A Select Lines picking menu appears.

3. Choose Utility Menu> Plot>Lines.

4. Pick lines 1, 9, 10, 11, and 12 and click on OK.


6. Choose "Nodes" and "Attached to," click on Lines, all, and then click on OK.

7. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Velocity> On Nodes.The Apply V on Nodes picking menu appears.

8. Click on Pick All. The Velocity Constraints on Nodes dialog box appears.

9. In the "Velocity component (VY)" field, enter 0, and click on OK.


11. Choose "Lines" and "By Num/Pick," then click on the Sele All button. Click on OK. The Select Lines pickingmenu appears.

12. Pick line number 4 and click on OK.



15. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Pressure DOF> OnNodes. The Apply PRES on Nodes picking menu appears.

16. Click on Pick All. The Pressure Constraint on Nodes dialog box appears.

17. In the "Pressure value (PRES)" field, enter 6.13769e+6, and click on OK.

18. Choose Utility Menu> Select> Entities.

19. Choose "Lines" and "By Num/Pick," then click on the Sele All button. Click on OK. The Select Lines pickingmenu appears.

20. Pick line numbers 3, 5, 6, 7, and 8 and click on OK.

21. Choose Utility Menu> Select> Entities.


23. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Velocity> On Nodes.The Apply V on Nodes picking menu appears.

24. Click on Pick All. The Velocity Constraints on Nodes dialog box appears.

25. In the "Velocity component (VX)" field and in the "Velocity component (VY)" enter 0, and click on OK.




27. Choose "Lines" and "By Num/Pick," click on the Sele All button, and then click on OK. The Select Linespicking menu appears.

28. Pick line number 16 and click on OK.



31. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Pressure DOF> OnNodes. The Apply PRES on Nodes picking menu appears.

32. Click on Pick All. The Pressure Constraint on Nodes dialog box appears.

33. In the "Pressure value (PRES)" field, enter 0, and click on OK.

Step 10: Set Fluid Properties

1. Choose Utility Menu> Select> Everything.

2. Choose Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties. The Fluid Properties dialogbox appears.

3. Set the "Density (DENS)," "Viscosity (VISC)," "Conductivity (COND)," and "Specific heat (SPHT)" fields toAIR-CM.

4. Set the "Allow density variations?" field to yes.

5. Click on Apply. The CFD Flow Properties dialog box appears.

6. Read the information about how coefficients will be calculated, and click on OK.

Step 11: Set Flow Environment Parameters

1. Choose Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions. TheReference Conditions dialog box appears.

2. Set the "Reference pressure (REFE)" field to 1.01325e+6 and the "Nominal temperature (NOMI)" and"Stagnation (total) temperature (TTOT)" fields to 550, and then click on OK.

Step 12: Set Solution Options and CFD Solver Controls

1. Choose Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options. The FLOTRAN SolutionOptions dialog box appears.

2. Set the "Laminar or turbulent (TURB)" field to Turbulent and the "Incompress or compress (COMP)" fieldto Compressible. Click OK.

3. Choose Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Contr> PRES Solver CFD. ThePRES Solver CFD dialog box appears.

4. Choose Precond conj res.

5. Click on OK. The Semi Direct Solver Options for Pressure dialog box appears.

6. In the "Convergence criterion" field, enter 1.e-12, and click on OK.

Step 13: Solve

1. Choose Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation. The PropertyRelaxation dialog box appears.

2. Set the "Density relaxation" field to 1.0 and click on OK.



3. Choose Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization. The ModifiedInertial Relaxation (MIR) dialog box appears.

4. Set the MIR values for the momentum and turbulence equations to 0.2

5. Choose Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms. The StabilityParameters dialog box appears.

6. Set the "Momentum inertia" field to 1.0, the "Pressure inertia" field to 1.e-4, and the "Artificial viscosity"field to 10, and then click on OK.

7. Choose Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl. The Steady State Control Settingsdialog box appears.

8. Set the "Global iterations (EXEC) field to 20 and click on OK.

9. Choose Main Menu> Solution> Run FLOTRAN.

10. After 20 iterations finish, the Solution is done message appears. Close it. Choose Main Menu> Solution>FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms. The Stability Parameters dialog box appears.

11. Set the "Artificial viscosity" field to 1 and click on OK.


13. Repeat the previous 3 substeps and continue to reduce the "Artificial viscosity" to .1, .01, .001, .0001, and.00001.

14. After 140 total iterations finish, the Solution is done message appears. Close it. Choose Main Menu>Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms. The Stability Parameters dialog boxappears.

15. Set the "Artificial viscosity" field to 0 and click on OK.





20. Set the "Momentum inertia" field to 10, the "Pressure inertia" field to 1.e-2, and then click on OK.





25. Set the "Momentum inertia" field to 1e+15, the "Pressure inertia" field to 1.e+15, and then click on OK.



28. Choose Main Menu> Solution> Run FLOTRAN. When the Solution is done message appears, close it.



29. Click QUIT on the ANSYS Toolbar. Choose an exit option and click OK.

8.8. Doing the Example Compressible Flow Analysis (Command Method)

You issue the following ANSYS commands to perform a compressible flow analysis of the converging divergingnozzle. Text preceded by an exclamation point (!) is a comment.

/title, Compressible Flow in a Converging Diverging Nozzle/prep7!! Assign Element Type!et,1,141!! Create the Model Geometry!/pnum,line,1k,1,0,2.432k,2,0,0k,3,1,2.432k,4,1,0k,5,2,2.232k,6,2,0k,7,5,0k,8,5,.7k,9,6,0k,10,6,.5k,11,14,0k,12,14,.8l,2,4l,3,4l,1,3l,1,2l,5,8l2tan,3,5l,10,12l2tan,5,7l,4,6l,6,7l,7,9l,9,11a,2,4,3,1a,4,6,5,3a,6,7,8,5a,7,9,10,8a,9,11,12,10!! !Mesh the Model and Compress Numbers!ntran=24rtran=10na=10nb=10nc=25nd=10ne=100re=-1.5lesize,4,,,ntran,rtranlesize,2,,,ntran,rtranlesize,13,,,ntran,1/rtranlesize,14,,,ntran,1/rtranlesize,15,,,ntran,1/rtranlesize,16,,,ntran,1/rtranlesize,1,,,nalesize,3,,,nalesize,6,,,nblesize,9,,,nblesize,5,,,nclesize,10,,,nclesize,8,,,nd

Section 8.8: Doing the Example Compressible Flow Analysis (Command Method)


lesize,11,,,ndlesize,7,,,ne,relesize,12,,,ne,reamesh,allnumcmp,nodenumcmp,elem!! Apply Boundary Conditions!lsel,s,,,1lsel,a,,,9,12,1nsll,,1d,all,vy,0lsel,alllsel,s,,,4nsll,,1d,all,pres,6.13769e+6lsel,alllsel,s,,,3lsel,a,,,5,8,1nsll,,1d,all,vx,0d,all,vy,0lsel,alllsel,s,,,16nsll,,1d,all,pres,0!! Set Fluid Properties!alls/soluflda,prot,dens,air-cmflda,prot,visc,air-cmflda,prot,cond,air-cmflda,prot,spht,air-cmflda,vary,dens,t!! Set Flow Environment Parameters!flda,pres,refe,1.01325e+6flda,temp,ttot,550flda,temp,nomi,550!! Set Solution Options and CFD Solver Controls!flda,solu,turb,tflda,solu,comp,tflda,meth,pres,3flda,conv,pres,1e-12!! Solve!flda,relx,dens,1flda,mir,mome,0.2flda,mir,turb,0.2flda,stab,mome,1flda,stab,pres,1e-4flda,stab,visc,10flda,iter,exec,20solveflda,stab,visc,1solveflda,stab,visc,.1solveflda,stab,visc,.01solveflda,stab,visc,.001solveflda,stab,visc,.0001solveflda,stab,visc,.00001



solveflda,stab,visc,0flda,iter,exec,160solveflda,stab,mome,10flda,stab,pres,1e-2flda,iter,exec,100solveflda,stab,mome,1e+15flda,stab,pres,1e+15flda,iter,exec,400solve

Section 8.8: Doing the Example Compressible Flow Analysis (Command Method)


8–14

Chapter 9: Specifying Fluid Properties forFLOTRAN

9.1. Guidelines for Specifying Properties

Every flow analysis requires the fluid properties density and viscosity. Thermal analyses, in addition, require thefluid's thermal conductivity as well as specific heat. Volume of Fluid (VOF) analyses, in addition, might requirethe fluid properties surface tension coefficient and wall static contact angle. You specify fluid properties usingone of the following:

Command(s): FLDATA7,PROT,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

The command shown above simply sets the fluid property type. After choosing the property type, you may haveto set values.

To specify non-fluid properties (density, specific heat, and thermal conductivity), use one of the following:Command(s): MPGUI: Main Menu> Preprocessor> Loads> Other> Change Mat Props> PolynomialMain Menu> Preprocessor> Material Props> Material Models> Thermal> DensityMain Menu> Preprocessor> Material Props> Material Models> Thermal> Specific HeatMain Menu> Preprocessor> Material Props> Material Models> Thermal> Conductivity> IsotropicMain Menu> Solution> Other> Change Mat Props> Polynomial

Non-fluid thermal conductivities can vary with temperature. Orthotropic variation of non-fluid thermal conduct-ivity also is supported. For further information, see the descriptions of the MP and MPDATA commands, andrelated commands.

ANSYS provides no default values for density or viscosity properties. This prevents default properties from puttingthe analysis into an unexpected flow regime.

A value of -1 will appear in the user interface for properties that must be set. If you submit an analysis withoutsetting these properties, an error message results and you will be reminded that you must specify properties.

9.2. Fluid Property Types

A "fluid property type" defines how the particular fluid property will vary with temperature (and pressure, in thecase of density for a gas). You choose the fluid property type separately for density, viscosity, thermal conduct-ivity, specific heat, surface tension coefficient, and wall static contact angle.

You must use a consistent set of units for all the data that you enter. All thermal quantities must have the sameenergy unit as shown in the following table:

Table 9.1 Units for Thermal Quantities

UnitsThermal Quantity

energy/length-temperature-timeThermal Conductivity

energy/mass-temperatureSpecific Heat

energy/length2-timeHeat Flux


UnitsThermal Quantity

energy/length3-timeVolumetric Heat Source

energy/length2-temperature-timeHeat Transfer Coefficient

Except for incompressible flow analyses including viscous heating, you can use any energy unit as long as youuse the same unit for all thermal quantities. The metric and English property types defined below use joules andBTUs, respectively, as the energy unit for thermal conductivity and specific heat. For an incompressible analysisincluding viscous heating, you must use the energy unit for the system as shown in the following table:

Table 9.2 Energy Units for Incompressible Analyses with Viscous Heating

Energy Unit[1]System

JouleSI (meter-kg-sec)

ErgCGS (cm-g-sec)

Centi-ergmm-g-sec

lbf-ftBritish (ft-slug-sec)

lbf-inPSI

1. 1 Joule = 1.0E9 Centi-ergs; 1 BTU = 778.26 lbf-ft.

9.2.1. Property Types for Specific Heat

For specific heat, you can choose among the following property types: CONSTANT, CMIX, TABLE, user-definedthrough a file (floprp.ans), user-programmable subroutine (USER), and the variations of AIR shown below inTable 9.3: “Units for the AIR Property Type”.

9.2.2. Property Types for Density and Thermal Conductivity

For density and thermal conductivity, the property types you can choose are CONSTANT, CMIX, TABLE, GAS, LIQUID,user-defined through a file (floprp.ans), and the variations of AIR shown below. (To learn how to add more, seeSection 9.4: Modifying the Fluid Property Database.) A user-programmable subroutine (USER) also is available.For density only, you have one other property type option: CGAS.

Table 9.3 Units for the AIR Property Type

Viscosity UnitsDensity UnitsPressure UnitsUnitsPROT

kg/m-seckg/m3Pascalsmeter-kg-secAIR

kg/m-seckg/m3Pascalsmeter-kg-secAIR-SI

g/cm-sec (poise)g/cm3dynes/cm2cm-g-secAIR-CM

g/mm-secg/mm3Pascalsmm-g-secAIR-MM

slug/ft-secslugs/ft3lbf/ft2ft-slug-secAIR-FT

lbf-s/in2lbf-sec2/in4psiin-(lbf-s2/in)-secAIR-IN

ANSYS automatically supplies for you, in the property database, the relevant input for the AIR property types.


Chapter 9: Specifying Fluid Properties for FLOTRAN

9.2.3. Property Types for Viscosity

For viscosity, you can choose the property types CMIX, TABLE, CONSTANT, LIQUID, GAS, Power Law (POWL),Bingham (BING), Carreau (CARR), user-defined through a file (floprp.ans), and a user-programmable subroutine(USER or USRV). The AIR and GAS property types assume that the fluid is an ideal gas with constant specific heat.The viscosity and thermal conductivity variations with temperature are assumed to follow Sutherland's laws forgases, the form of which is shown below. A LIQUID assumes up to a second order polynomial for the variationof density with temperature, a constant value for specific heat, and Sutherland's laws for a liquid for viscosityand thermal conductivity.

Viscosity as a function of the velocity gradient is represented by the non-Newtonian viscosity types: Power Law,Bingham, and Carreau. Refer to Section 9.6: Using the ANSYS Non-Newtonian Flow Capabilities for more inform-ation.

9.2.4. Property Types for Surface Tension Coefficient

For surface tension coefficient, you can choose among the following property types: CONSTANT, LIQUID, anduser-programmable subroutine (USER).

9.2.5. Property Types for Wall Static Contact Angle

For wall static contact angle, CONSTANT is the only valid property type.

9.2.6. General Guidelines for Setting Property Types

You must use a consistent set of units (the gravitational constant gc must be unity.) Of course, the proper length

unit must be assumed when building the finite element model. Additional choices are available for air as per thetable shown below. Units for density are simply mass/volume; the table omits them.

Set the property type using the following:Command(s): FLDATA7,PROT,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

For Label, you specify one of the following: DENS (density), VISC (viscosity), COND (thermal conductivity), SPHT(specific heat), or SFTS (surface tension coefficient).

For Value, you specify any of the property types listed in Table 9.4: “Property types for Value”, or you can specifya table of fluid properties. To specify a table, enclose the table name in percent signs (%) (for example,FLDATA7,PROT,DENS,%Table%).

9.2.6.1. Using a Fluid Property Table

If working interactively, you define a new table prior to using the table to apply loads. You can define a tableinteractively via the Utility Menu> Parameters> Array Parameters> Define/Edit menu path, or in batch modevia the *DIM command. If working interactively, you will be asked to define the table through a series of dialogboxes. If working in batch mode, you need to define the table before issuing any of the loading commands.

For more information on defining tables, see the discussion of table array parameters in the ANSYS APDL Program-mer's Guide.

When you define the table, you can define the following primary variables:

Section 9.2: Fluid Property Types


• Temperature (TEMP)

• Pressure (PRESSURE)

• Time (TIME)

• X-coordinate (X)

• Y-coordinate (Y)

• Z-coordinate (Z)

• Velocity (VELOCITY)

• Reference X-coordinate (Xr) (ALE formulation only)

• Reference Y-coordinate (Yr) (ALE formulation only)

• Reference Z-coordinate (Zr) (ALE formulation only)

The valid labels used by the *DIM command are shown in parentheses.

If you need to specify a variable other than one of the primary variables listed, you can do so by defining an in-dependent variable. To specify an independent variable, define an additional table for the independent variable.That table must have the same name as the independent variable and can be a function of either a primaryvariable or another independent variable.

9.2.6.2. Specifying Property Types

The following table describes the property types that you can specify.

Table 9.4 Property types for Value

ArgumentProperty Type

CONSTANTConstant properties

GASGas properties

LIQUIDLiquid properties

TABLETable of property values and corresponding temperature values (which you enter using theMPDATAand MPTEMP commands)

AIR or AIR-SIAir properties in units of meter-kg-sec

AIR_B or AIR-SI_BAir properties in units of meter-kg-sec, with pressure set to the reference pressure for theevaluation of density

AIR-CMAir properties in units of cm-g-sec

AIR-CM_BAir properties in units of cm-g-sec, with pressure set to the reference pressure for the evalu-ation of density

AIR-MMAir properties in units of mm-g-sec

AIR-MM_BAir properties in units of mm-g-sec, with pressure set to the reference pressure for theevaluation of density

AIR-FTAir properties in units of fl-slug-sec

AIR-FT_BAir properties in unites of fl-slug-sec, with pressure set to the reference pressure for theevaluation of density

AIR-INAir properties in units of in-(lbf-s**2/in)-sec (results in units of psi for pressure)

AIR-IN_BAir properties in units of in-(lbf-s**2/in)-sec (results in units of psi for pressure), with pressureset to the reference pressure for the evaluation of density

POWLPower Law non-Newtonian viscosity type



ArgumentProperty Type

CARRCarreau non-Newtonian viscosity type

BINGBingham non-Newtonian viscosity type

CMIXProperty is mass fraction average of the species component

USERUser-programmable via subroutines:UserVisLaw for viscosityUserSpht for specificheatUserDens for densityUserCond for conductivityUserSfts for surface tension

CGASA variation of ideal gas law based on species mass fractions. Available for density only.

Once you choose property types, you do not need to specify any coefficients for the properties. If the characters_B are added to these property types (as in the AIR types listed above), the pressure in the ideal gas law calculationis at a constant density corresponding to atmospheric pressure. The length and time units of conductivity andspecific heat must be consistent with the rest of the properties. The energy units in these quantities are unres-tricted.

If using property types CONSTANT, GAS, or LIQUID, you must specify property coefficients. To do so, either issuethe commands shown below or choose one of the following menu paths:

Command(s): FLDATA8,NOMI,Label,Value FLDATA9,COF1,Label,Value FLDATA10,COF2,La-bel,Value FLDATA11,COF3,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

If you use the commands, you enter the property in the Label field of each command and enter the value itselfin each command's Value field.

The format of the equations for GAS and LIQUID input is oriented towards calculating constants based on chosendata points. All cases take COF1 to be the absolute temperature at which the chosen property has the value setby NOMI. (Section 9.5: Using Reference Properties discusses the use of relative temperatures and an offset tem-perature to calculate absolute temperatures.) This is not used in the COF1 specification; COF1 should always bean absolute temperature.

Once values are inserted into the relationships below for NOMI and COF1, the values of COF2 and COF3, if neces-sary, follow from knowledge of one or two additional data points, respectively. When calculating COF2 and COF3for GAS and LIQUID property types, you must use absolute temperatures and pressures in these relationships.If COF1 is set to zero, the property will become constant at the value set by NOMI. For GAS and LIQUID propertytypes, the specific heat is constant and therefore the parameters COF1, COF2 and COF3 are not needed. For vis-cosity types Power Law, Bingham, and Carreau, NOMI, COF1, COF2, and COF3 have different interpretations. Thisis discussed in the ANSYS, Inc. Theory Reference and in Section 9.2.8: Viscosity.

9.2.7. Density

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the density to 1.205 via:

Command(s):FLDATA8,NOMI,DENS,1.205

If the property type is GAS, the ideal gas law is used for the density. You specify density for this choice as:

Density = NOMI * (P/COF2) / (T/COF1)

If the choice is LIQUID, then a second order polynomial as a function of temperature is used for density.



Density = NOMI + COF2*(T - COF1) + COF3*(T - COF1)2

If the property type is CMIX, then:

Density ==∑ Yi ii

Nρ

1

In the equation shown above, N is the defined number of species, Yi is the mass fraction of the ith species, and

ρi is the density of the ith species.

If the property is CGAS, then:

Density =∑

P

RT Y Mi ii

N( / )

In the CGAS equation shown above, N is the defined number of species, Yi is the mass fraction of the ith species,

Mi is the molecular weight of the ith species, R is the universal gas constant, and P is the absolute pressure.

If the property type is TABLE, the density is interpolated linearly between the data points provided via theMPTEMP or MPDATA commands (or their GUI equivalents).

If the choice is USER, the density is computed in the user-programmable subroutine UserDens. The four coefficientsNOMI, COF1, COF2, and COF3 are available in this routine.

9.2.8. Viscosity

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the viscosity to 1.205 via:

Command(s):FLDATA8,NOMI,VISC,1.205

If the choice is GAS, Sutherland's law for gases is used for viscosity. You can enter the parameters NOMI, COF1,and COF2.

The ideal gas constant R is defined as (COF2/NOMI*COF1)

Viscosity ("Property"):

Property/NOMI = (T/COF1)1.5 * (COF1 + COF2)/(T + COF2)

As an example of using this relationship, suppose that there are two data points available for the calculation ofviscosity as a function of temperature:

Viscosity = 4.18 x 10-5 at T = 760

Viscosity = 5.76 x 10-5 at T = 1010

Consider the first data point as the nominal value. This means that NOMI = 4.18 x 10-5 and COF1 = 760. Usingthese in the Sutherland relationship yields:

Property/4.18 x 10-5 = (T/760)1.5 (760 + COF2)/(T + COF2)



Use the remaining data point to calculate COF2 by setting "Property" to 5.76 x 10-5 and T = 1010. Thus, the con-stants are calculated from the data points.

If the choice is LIQUID, then Sutherland's liquid law is used for the viscosity.

Viscosity ("Property"):

Property/NOMI = EXPCOF2*(1/T - 1/COF1) + COF3(1/T - 1/COF1)2

If the choice is POWL, then the non-Newtonian Power Law model is used for the viscosity:

Viscosity =NOMI*COF2*D ,D>COF1

NOMI*COF2*COF1

(COF3-1)

(COF3-1) ,,D COF1≤

If the choice is BING, then the non-Newtonian Bingham model is used for the viscosity:

Viscosity =

NOMI+COF1

D,D

COF1

COF2 NOMI

COF2 ,D<COF1

COV2-NOMI

≥−

If the choice is CARR, the non-Newtonian Carreau model is used for the viscosity:

Viscosity =COF1+(NOMI-COF1)*(1+(COF2*D) )2COF3-1

2


Viscosity ==∑ Yi ii

Nµ

1


µi is the viscosity of the ith species.


If the choice is USRV or USER, then the viscosity is computed in the user programmable subroutine UserVisLaw.The four coefficients NOMI, COF1, COF2, and COF3 are available in this routine.

9.2.9. Specific Heat

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the specific heat to 1.205 via:

Command(s):FLDATA8,NOMI,SPHT,1.205

If the choice is USER, specify specific heat via user-programmable subroutine UserSpht. For specific heat, NOMI,COF1, COF2, and COF3 are available in the user-programmable subroutine UserSpht.




Specific Heat ==∑ Y Ci pi

N

i1


Cpi is the specific heat of the ith species.

If the property type is TABLE, the specific heat is interpolated linearly between the data points provided via theMPTEMP or MPDATA commands (or their GUI equivalents).

9.2.10. Thermal Conductivity

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the thermal conductivity to 1.205 via:

Command(s):FLDATA8,NOMI,COND,1.205

If the choice is GAS, Sutherland's law for gases is used for conductivity. You can enter the parameters NOMI,COF1, and COF2.

The ideal gas constant R is defined as (COF2/NOMI*COF1)

Thermal Conductivity ("Property"):

Property/NOMI = (T/COF1)1.5 * (COF1 + COF2)/(T + COF2)

If the choice is LIQUID, then Sutherland's liquid law is used for conductivity.

Thermal Conductivity ("Property"):

Property/NOMI = EXPCOF2*(1/T - 1/COF1) + COF3(1/T - 1/COF1)2


Conductivity ==∑ Y Ki ii

N

1


Ki is the conductivity of the ith species.


If the choice is USER, then the thermal conductivity is computed in the user programmable subroutine UserCond.The four coefficients NOMI, COF1, COF2, and COF3 are available in this routine.

9.2.11. Surface Tension Coefficient

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the surface tension coefficient to 73.0 via:



Command(s):FLDATA8,NOMI,SFTS,73.0

If the choice is LIQUID, then a second order polynomial as a function of temperature is used for surface tensioncoefficient.

Surface tension coefficient = NOMI + COF2*(T - COF1) + COF3*(T - COF1)2

If the choice is USER, the surface tension coefficient is computed in the user-programmable subroutine UserSfts.The four coefficients NOMI, COF1, COF2, and COF3 are available in this routine.

9.2.12. Wall Static Contact Angle

To set the constant value use the FLDATA8,NOMI command or the equivalent menu path. For example, set thewall static contact angle to 120.0 degrees via:

Command(s):FLDATA8,NOMI,WSCA,120.0

The wall static contact angle defaults to 90 degrees. Angles less than 90 degrees describe an adhesive wall con-dition and angles between 90 and 180 degrees describe a nonadhesive wall condition. In reality, the angle is notonly a material property of the fluid, but also depends on the local fluid and wall conditions. FLOTRAN treats itas a single input constant for simplicity.

9.3. Initializing and Varying Properties

When an analysis begins, ANSYS calculates properties based on the specified property type and the appropriateconstants. To set the initial temperature, choose one of the following:

Command(s): FLDATA14,TEMP,NOMI,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref ConditionsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

You can choose to treat this temperature as an absolute or a relative temperature. If it is a relative temperature,the difference between the relative and the absolute temperature is the offset from absolute zero set by one ofthe following:

Command(s): TOFFST,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref ConditionsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

Either way, FLOTRAN initializes the absolute nominal temperature as the sum of the values set by theFLDATA,TEMP,NOMI and TOFFST commands or their equivalent menu paths.

Unless otherwise specified through boundary or initial condition commands, the initial relative pressure is zero.In the absence of gravity and rotation the absolute pressure is the sum of the reference and relative pressures.Therefore, the initial absolute pressure is the reference pressure.

For specific heat, density, surface tension coefficient, and thermal conductivity, the ANSYS program uses initialvalues of absolute nominal temperature and absolute pressure to calculate the initial properties. However, fornon-Newtonian viscosity, you specify initial properties using either the command FLDATA12,PROP,IVISC,Value(Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties). If you specify a value less than or equal tozero, the NOMI coefficient described in the previous section is used to initialize the viscosity.

Section 9.3: Initializing and Varying Properties


9.3.1. Activating Variable Properties

Once the analysis begins, the properties will vary only between global iterations as the temperature and pressurechange if the property variations are activated. This is accomplished with the FLDATA13,VARY,Label,Valuecommand with the labels SPHT, DENS, VISC, SFTS, and COND. Allowable Values are TRUE and FALSE (T or F). TheVARY setting has no effect if the property type are set to CONSTANT or COF1 is zero for a GAS or LIQUID.

9.4. Modifying the Fluid Property Database

Choices other than CGAS, CMIX, TABLE, USER, GAS, LIQUID, CONSTANT or AIR for density, thermal conductivity,viscosity, and specific heat imply that all the properties will be obtained from the information in the floprp.ansfile (a text file), where the data for AIR resides. This file is provided with ANSYS, and you should make a local copyif you plan additions to it. You can make the copy at the system level with a text editor. The procedure for makingadditions requires you to:

1. Choose a property name.

2. Specify functional form and constants.

id Integer equation identifier (two digit number)n Number of coefficientsCi Equation coefficients

You can access the following forms through the property database by specifying the appropriate ID. The variable"y" refers to the value of the property of interest, T is the absolute temperature, and P is the absolute pressure.

Polynomial ID: 01

y = C1 + C2T + C3T2 + ... + CnTn-1

Inverse Polynomial ID: 02

y CCT

C

T

C

Tn

n= + + + + −1

2 32 1

…L L

Exponential Polynomial ID: 03

In(y) = C1 + C2T + C3T2 + ... + CnTn-1

Exponential Inverse Polynomial ID: 04

In y CCT

C

T

C

Tn

n( ) = + + + + −1

2 32 1

…L L

Power Law ID: 05

y = C1TC2

Ideal Gas Law ID: 11

yP

C T=

1L

Sutherland's Formula ID: 12



yC TT C

=+1

2

3

2

Pressure based variation ID: 15

yC C P

C C P

C

C= +

+1 2

3

4 56

Non-Newtonian Power Law ID: 16 (applies to viscosity only)

y C C D D C

y C C C D C

C

C

= >

= ≤

−

−

1 31

2

1 3 21

2

4

4

( )

( )

,

,

where D I= 2 , I2 is the second invariant of the strain rate tensor.

Non-Newtonian Bingham Model ID: 17 (applies to viscosity only)

y CCD

DC

C C

y C DC

C C

= + ≥−

= <−

12 2

3 1

32

3 1

,

,

Carreau Model ID: 18 (applies to viscosity only)

y C C C C D

C

= + − +−

2 1 2 321

4 1

2( ) * ( ( ) )

User-programmable subroutine: 19

y = y (C1, C2, C3, C4)

Because you can use the subroutine to describe property variations, you can use the four coefficients in any waywithin the subroutine.

The format of the property database file floprp.ans is provided in the table below:

Table 9.5 Property Database Format

DescriptionLine

Fluid Name [A8] and optional comments1

nLines [I6]2

Proplab, tProp, nProp

(PropCF(i)=1,nProp)

[A4, 1x, 2I6, 5E12.5/6E 12.5]

nLines

Section 9.4: Modifying the Fluid Property Database


DescriptionLine

Fluid Name=Fluid property type

nLines=Number of properties to be read

Proplab=Property label (one of the following):

SPHT - Specific heatDENS - DensityVISC - ViscosityCOND - ConductivityGAMM - GammatProp - Equation identifier for propertynProp - Number of coefficients for propertyPropCF - Coefficients for property calculation

9.5. Using Reference Properties

The following properties are part of the flow environment:

• The ratio of specific heats, Cp/Cv, known as gamma, is a reference property that applies only to compressible

problems. Currently it is a constant. Specify this property using one of these methods:Command(s): FLDATA17,GAMM,COMP,VALUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions

File:Edit the file floprp.ans and set the value of GAMM.

• The pressures FLOTRAN calculates are relative pressures. A reference pressure is added to the relativepressure to calculate the absolute pressure. Rotational and gravitational terms also are added as needed.For more information, see Chapter 10, “FLOTRAN Special Features”.

To specify the reference pressure, use one of the following:Command(s): FLDATA15,PRES,REFE,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref ConditionsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

• You can use a relative temperature (for example, degrees Fahrenheit rather than degrees Rankine). In thiscase, an offset temperature is set so that property calculations include absolute temperatures. This is ne-cessary, for instance, for calculating densities from the ideal gas law. ANSYS automatically adds the offsettemperature to all of the boundary condition temperatures applied.

To set the offset temperature, use one of the followingCommand(s): TOFFST,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref ConditionsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

• The nominal temperature is that at which the properties initialize. It may be a relative temperature if youuse the TOFFST command or an equivalent menu path. If the viscosity is not stored in the results file (thedefault condition) and is now allowed to vary, ANSYS recalculates it when the analysis continues at thenominal temperature.

To specify the nominal temperature, use one of the following:Command(s): FLDATA14,TEMP,NOMI,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions



Main Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

• You can specify gravitational accelerations using one of the following:Command(s): ACEL,ACELX,ACELY,ACELZGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> GravityMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Gravity

The sign convention of the gravitational acceleration denotes as positive the direction of the reaction force.

9.6. Using the ANSYS Non-Newtonian Flow Capabilities

The ANSYS program enables you to specify viscosity for non-Newtonian fluid flows. (You can use this capabilityonly with FLUID141 and FLUID142 elements.) You can choose among four types of models:

• The Power Law model, useful for modeling polymers, blood, rubber solutions, etc.

• The Carreau model, which removes some of the deficiencies associated with the Power Law model. Usethis model when fluid has intermediate values of shear rate but remains bounded for zero/infinite shearrates.

• The Bingham model, useful for modeling slurries and pastes.

• A user-programmable subroutine UserVisLaw, which gives you greater flexibility in choosing viscositymodels.

Typically, you select one of these models after you have built and meshed the model for your problem and afteryou have applied the boundary conditions.

9.6.1. Activating the Power Law Model

To activate the Power Law viscosity model, issue the command or use one of the menu paths shown below:Command(s): FLDATA7,PROT,VISC,POWLGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

Choosing any of the above automatically issues other commands which set output and storage controls and theproperty variation flag. For details, see the descriptions of the FLDATA commands in the ANSYS CommandsReference.

To specify the four coefficients associated with the Power Law model, choose either of the menu paths shownabove (and specify the appropriate coefficients), or issue the following commands:

Command(s):

FLDATA8,NOMI,VISC,Value (specifies nominal viscosity)FLDATA9,COF1,VISC,Value (specifies the cutoff shear rate)FLDATA10,COF2,VISC,Value (specifies the consistency coefficient)FLDATA11,COF3,VISC,Value (specifies the power)

The ANSYS, Inc. Theory Reference describes these coefficients.

Once you have specified the coefficients, you can issue the SOLVE command or choose menu path Main Menu>Solution> Run FLOTRAN.

Section 9.6: Using the ANSYS Non-Newtonian Flow Capabilities


9.6.2. Activating the Carreau Model

To activate the Carreau viscosity model, issue the command or use one of the menu paths shown below:Command(s): FLDATA7,PROT,VISC,CARRGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

Choosing one of the above automatically issues commands which set output and storage controls and theproperty variation flag. For more information about the FLDATA commands, see the ANSYS Commands Reference.

You need to specify the four coefficients associated with the Carreau model, using either of the menu pathsshown above or the following commands:

Command(s):

FLDATA8,NOMI,VISC,Value (specifies the zero shear viscosity)FLDATA9,COF1,VISC,Value (specifies the infinite shear viscosity)FLDATA10,COF2,VISC,Value (specifies the time constant)FLDATA11,COF3,VISC,Value (specifies the power)

The ANSYS, Inc. Theory Reference describes these coefficients. Once you have specified them, you can issue theSOLVE command or choose menu path Main Menu> Solution> Run FLOTRAN.

9.6.3. Activating the Bingham Model

To activate the Bingham viscosity model, issue the command or choose one of the menu paths shown below:Command(s): FLDATA7,PROT,VISC,BINGGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

Choosing one of the items shown above automatically issues commands that set output and storage controlsand the property variation flag.

To set the coefficients associated with the Bingham model, either use one of the menu paths shown above orissue the following commands:

FLDATA8,NOMI,VISC,Value (specifies the plastic viscosity)FLDATA9,COF1,VISC,Value (specifies the plastic/yield stress)FLDATA10,COF2,VISC,Value (specifies the Newtonian viscosity)

The ANSYS, Inc. Theory Reference describes these coefficients.

You can also specify an initial viscosity to accelerate convergence. Typically, you can set this to be the Newtonianviscosity (that is, COF2) via one of the following:

Command(s): FLDATA12,PROP,VISC,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

9.7. Using User-Programmable Subroutines

User-programmable subroutines are available for specific heat, density, viscosity, surface tension coefficient,and thermal conductivity of fluid regions. Since the procedures are quite similar, only one property will be de-scribed in depth here.



If you wish to use the user-programmable viscosity subroutine, USERVISLAW, you will need to customize it forthe particular model you are analyzing. You compile the subroutine, link it with the ANSYS libraries, and makean executable copy available. Then, you can resume the model to be analyzed and activate the viscosity modelyou have defined. To do so, use one of the following:

Command(s): FLDATA7,PROT,VISC,USRV (or USER)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

At this point, you may want to specify that properties are updated every iteration and that you want viscosityoutput to go to the results file. To do so, issue the following commands or use the following menu paths:

Command(s): FLDATA12,PROP,UFRQ,1 and FLDATA5,OUTP,VISC,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

Next, you need to specify the four coefficients associated with the user-defined viscosity model. To do so, useeither of the menu paths shown above or issue the following commands:

Command(s):

FLDATA7,NOMI,VISC,Value (specifies coefficient 1)FLDATA6,COF1,VISC,Value (specifies coefficient 2)FLDATA9,COF2,VISC,Value (specifies coefficient 3)FLDATA10,COF3,VISC,Value (specifies coefficient 4)

These coefficients are available within the UserVisLaw subroutine. By default, this subroutine produces a PowerLaw viscosity model using the coefficients you define. To see a copy of the subroutine, see the Guide to ANSYSUser Programmable Features.

You can also specify an initial viscosity to accelerate convergence, via one of the following:Command(s): FLDATA12,PROP,IVISC,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties

Once you have specified the coefficients, and, optionally, an initial viscosity, you can solve your model by issuingthe SOLVE command or choosing Main Menu> Solution> Run FLOTRAN.

Section 9.7: Using User-Programmable Subroutines


9–16

Chapter 10: FLOTRAN Special Features

10.1. Coordinate Systems

You set the coordinate system via one of the following:Command(s): KEYOPTGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> FLOTRAN Coor SysMain Menu> Solution> FLOTRAN Set Up> Flow Environment> FLOTRAN Coor Sys

The table below shows you how to select various coordinate systems and describes the velocities representedby DOFs VX, VY, and VZ in these systems. The default value of the KEYOPT is zero, which selects Cartesian coordin-ates.

Figure 10.1 Direction of Positive Swirl Velocity VZ for Axisymmetric Models

Table 10.1 Coordinate System Specification

VZVYVXKEYOPT(3)Coordinate System

ZYX0Cartesian

swirlaxialradial12-D - Axisymmetric about Y axis

swirlradialaxial22-D - Axisymmetric about X axis

N/Athetaradial32-D - Polar Coordinates

axialthetaradial33-D - Cylindrical Coordinates


For axisymmetric problems, the sign convention for the swirl (VZ) component conforms to positive rotationabout the axis of symmetry, as defined by the right hand rule. Thus, for a model that is axisymmetric about theY axis, a nonnegative swirl velocity VZ is considered to be pointing "into the page." Similarly, for a model that isaxisymmetric about the X axis, a nonnegative swirl velocity VZ is considered to be pointing "out of the page."This should be accounted for when you apply boundary conditions in rotating coordinates.

Note — Based on the definition of directions for the cylindrical coordinate system, gravity is only appro-priate for the Z direction when KEYOPT(3) is set to 3.

10.2. Rotating Frames of Reference

You can choose to solve your problem in a rotating reference frame. In this case, the velocities are calculatedand specified with respect to a coordinate system which is rotating at constant angular velocity. Such an approachis useful for pump blade passage analysis. Figure 10.2: “Rotating Flow Problem” shows a schematic of a rotatingproblem which requires moving coordinate systems. Figure 10.3: “Problem Schematic with Rotating Coordinate”shows the problem schematic in the rotating coordinate system.

The pressures specified by boundary conditions are in terms of the static pressure observable by the stationaryanalyst, not in terms of the rotating coordinate system. The transformations necessary to solve the equations inthe rotating coordinate frame are done internally.

You can set rotational speeds using any of the following:Command(s): CGOMGAGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Rotating CoordsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Rotating Coords

For all but 3-D Cartesian coordinate systems, you must specify the axis of rotation as being about the Z axis. For2-D axisymmetric systems, the ANSYS program automatically interprets the specified Z-axis rotation as actuallyacting about the correct axis of symmetry (that is, about either the X or Y axis). For 3-D Cartesian geometries, therotational axis need not be in the same direction as one of the principal axes of the global coordinate system,and may be offset from the origin of the global coordinate system.

To specify offsets for the axis of rotation, use one of the following:Command(s): CGLOCGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Rotating CoordsMain Menu> Solution> FLOTRAN Set Up> Flow Environment> Rotating Coords



Figure 10.2 Rotating Flow Problem

Figure 10.3 Problem Schematic with Rotating Coordinate

10.3. Swirl

Swirl applies only to axisymmetric problems and refers to motion perpendicular to the X-Y plane. To activateswirl, choose one of the following:

Section 10.3: Swirl


Command(s): FLDATA1,SOLU,SWIRL,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution OptionsMain Menu> Solution> FLOTRAN Set Up> Solution Options

Either a moving wall (for instance, a rotating shaft) or a component of swirl at an inlet can cause the motion inthe swirl direction (with velocity component VZ).

In a swirl problem, there are no changes in the "theta" direction since it is axisymmetric.

The swirl component is calculated through solution of the momentum equation in the swirl direction. With nopressure gradient in the swirl direction, nothing contributes to the swirl velocity directly from the velocity updatestep in the segregated solution algorithm. It is thus sometimes useful to accelerate the convergence of swirlproblems by solving the momentum in the swirl direction equation with a relaxation factor of 1.0 for a fewglobal iterations.

10.4. Distributed Resistance/Source

Distributed resistances are macroscopic representations of geometric features not directly concerned with theregion of interest and considered too detailed for exact representation. A typical example is pipe flow whichencounters a screen.

You apply distributed resistance on an element basis through the use of real constants. See the ANSYS ElementsReference for the formulation and the list and meaning of the real constants.

Since the distributed resistance parameters will describe the known behavior of the flow in the region, the useof the turbulence model is redundant. You should deactivate it in the distributed resistance region by settingENKE to 0.0 and ENDS to 1.0.

To do so, choose one of the following:Command(s): DGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Turbulence> On NodesMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Turbulence> On Nodes

The distributed resistances referred to above are used to describe losses to the system. You can model momentumsources in similar fashion. Such sources can be used to represent fans or pumps in a system. Typical characteriz-ation of these components is a "Head-Capacity Curve," representing the pressure rise as a function of flow for aconstant speed pump. The fan or pump model is not intended to describe the details of the flow in the pumpregion, but rather to approximate its effects on the rest of the system. You can use any coordinate system orFLOTRAN element shape, but Cartesian coordinate systems with hex shaped elements in three dimensions andquadrilateral elements in two dimensions tend to give more stable results.

The fan model input takes the form of element real constants, and is described in detail in the ANSYS ElementsReference.

The ANSYS program supports two types of fan model. A "Type Four" fan model acts only along a specific coordinatedirection, while a "Type Five" model enables the user to align the fan or pump in an arbitrary direction. Coefficientsare assigned for each coordinate direction.

The equation for the fan model is in terms of a pressure gradient applied in the direction of flow. You thereforemust know over what length the fan model is to be applied in order to achieve the correct total pressure rise.The relationship defining the momentum source for an arbitrary direction "s" is as follows:

dPds

C C V C V= + +1 2 32



In the above equation, V is the velocity through the fan. If the given data is in terms of volumetric flow, you mustknow the area of the actual pump. The actual velocity at the outlet of the pump as well as the volumetric flowrate should be preserved. Consistent units must be used, that is, the gravitational conversion constant must be1.0. If, for example, the pressure drop is in psi, the velocity units are in/sec.

Generally, you determine the fan or pump coefficients by taking three pairs of pressure-velocity points on the"fan curve" and solving for the coefficients. If the flow is to be in the negative direction, the signs of all the coef-ficients change.

The type 5 model is used for pumps not aligned with one of the coordinate directions. Given V as the velocityin the S arbitrary direction and the pump constants C1, C2, and C3; the directional coefficients can be calculated.

If θx is the angle between the arbitrary direction S and the x coordinate direction, the directional constants are:

C C

C C

CC

x x

x

xx

1 1

2 2

33

==

=

cos

cos

θ

θ

Similarly, if θy and θz are defined as the angles between the fan direction and the y and z coordinate direction

respectively:

C C

C C

CC

C C

C C

CC

y y

y

yy

z z

z

zz

1 1

2 2

33

1 1

2 2

33

=

=

=

==

=

cos

cos

cos

cos

θ

θ

θ

θ

Section 10.4: Distributed Resistance/Source


10–6

Chapter 11: FLOTRAN CFD Solvers and theMatrix Equation

11.1. Which Solver Should You Use?

In the sequential solution algorithm, you have three options for solving equations sets for degrees of freedom:

1. A fast, approximate solver

This solver, the Tri-Diagonal Matrix Algorithm (TDMA), performs a user-specified number of iterationsthrough the problem domain.

2. "Exact" solvers

The "exact" methods are semi-direct conjugate direction methods that iterate to a specified convergencecriterion.

These methods are:

• The Conjugate Residual (CR), Preconditioned Conjugate Residual (PCCR), Preconditioned GeneralizedMinimum Residual (PGMR), and Preconditioned BiCGStab (PBCGM) methods for non-symmetricmatrix equations.

• The preconditioned conjugate gradient method for the incompressible pressure equation.

3. Sparse Direct solver

This solver uses Gaussian elimination to factorize the matrix and then uses backward/forward substitutionto solve for the unknowns.

You choose the method for each DOF via one of the following:Command(s): FLDATA18,METH,Label,Value (Label = DOF)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> PRES Solver CFDMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> PRES Solver CFD

Valid choices are: 1 (TDMA), 2 (conjugate residual), 3 (preconditioned conjugate residual or gradient), 4 (precon-ditioned generalized minimum residual), 5 (sparse direct), or 6 (preconditioned BiCGStab). A choice of 0 indicatesthat the equation set is not to be solved. The preconditioned conjugate gradient method automatically appliesto the incompressible pressure equation for choices 2 or 3.

The default solver (TDMA) for the velocities and the turbulence equations is adequate for virtually every problemencountered. The number of sweeps (iterations) for the velocity is 1. Do not change this value. Experience hasshown that the default number of 10 sweeps for the turbulence equations is most efficient although you canincrease this number to see if better convergence is attained for a particular application.

In general, the solution of the pressure equation must be accurate and conjugate direction methods are used.However, the TDMA method can be successful for natural convection flows. The sections for the various typesof analyses discuss where to use solvers other than the default choices.

11.2. Tri-Diagonal Matrix Algorithm

You set the number of sweeps for the TDMA solver using one of the following:


Command(s): FLDATA19,TDMA,Label,Value (Label = DOF)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

In the GUI, you do not have access to this command unless the TDMA method has been requested for that DOF.It is not available in the GUI at all for velocities.

11.3. Semi-Direct Solvers

You can gauge the performance of the semi-direct solvers by the behavior during the solution process of theinner product of the residuals, referred to as RTR (or ZTR for the incompressible pressure equation.) RTR should

be reduced during the global iteration to a fraction, typically 1.0 x 10-7 of its initial value.

The fraction is the convergence criterion for the semi-direct methods, set with one of the following:Command(s): FLDATA21,CONV,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

To set the maximum number of iterations allowed during a global iteration, choose one of the following:Command(s): FLDATA22,MAXI,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

Data concerning how the semi-direct solvers are performing appears in the text file Jobname.DBG for everyDOF for which they are used, generally PRES, TEMP, or both.

The semi-direct algorithms may conclude in three different ways: convergence is achieved, the maximum numberof iterations has been reached without convergence, or the solution has stalled.

If the maximum number has been reached without convergence, more iterations may be required (for example,in a large or ill-conditioned problem). If so, increase the maximum number of iterations. The maximum numberalso may be reached if the convergence criterion has been set to a very small value (for example, less than 1.0 x

10-15), in which case the convergence criterion should be eased. It may also, however, mean that the solution is

diverging. If so, large values of RTR or ZTR (perhaps above 1.0 x 1020) will appear in the debug file; but increasingthe number of iterations will not help.

Stall occurs when the new iteration makes no progress towards the solution but the convergence criterion hasnot been achieved. If the rate of change is small enough the solution process stops.

Note — You specify the rate of change which leads to termination of the solver by using one of the fol-lowing:

Command(s): FLDATA23,DELT,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

The label refers to the DOF being solved. Stall can occur in the solution of the compressible pressure equationor in the solution of the temperature equation of some conjugate heat transfer problems. The value of RTR doesnot decrease significantly and at the last iteration the value of DelMax is less than the value you specified. Thismeans that the solution is essentially not changing, and further computational effort is wasted.


Chapter 11: FLOTRAN CFD Solvers and the Matrix Equation

You can resolve a stall situation by increasing the number of search directions or using inertial relaxation. To in-crease search directions, either use one of the menu paths described above (with the FLDATA23,DELT command),or issue the following command:

Command(s):FLDATA20,SRCH,Label,Value

The default value is 2, appropriate for well conditioned problems. The number of search directions required mayvary widely among problems. Values of 20 may be required, but be aware that each search direction specifiedrequires N compute storage locations in memory. (N is the number of finite element nodes in the problem). Thecomputer storage required for large values of SRCH could exceed the computational resources available, inwhich case inertial relaxation should be used.

Figure 11.1: “Typical Debug Files” shows typical debug files.

Figure 11.1 Typical Debug Files

11.3.1. Preconditioned Generalized Minimum Residual (PGMR) Solver

The PGMR method uses fill-in when constructing the L and U decomposition matrices. The PGMR method is aversion of the generalized minimum residual method that uses an LU preconditioning to transform the systemof equations into a set easier to solve. As with the PCCR method, the coefficient matrix is decomposed into anapproximate LU product. In the PCCR method, the sparsity pattern of the original matrix is preserved in the Land U matrices.

Accordingly, when you are using the Preconditioned Generalized Minimum Residual (PGMR) solver, you needto specify the amount of fill-in. You must also specify the number of search vectors.

The fill-in value represents the number of extra elements allowed in each row of the L and U decompositionmatrices. An extra element is defined as being in addition to the number of nonzero elements in the row of theoriginal matrix.

There are two PGMR algorithms available for FLOTRAN. The choice is automatically made by the program. Thedifference lies in the "fill-in". It is only required and only available for the PRES and TEMP degrees of freedom.

Section 11.3: Semi-Direct Solvers


To specify the amount of fill-in, use either of these methods:Command(s): FLDATA20A,PGMR,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

The allowable range for fill-in is 1 to 10. The default value is 6. A single fill-in value is input for all applicable DOF.

For some problems, it is unnecessary to obtain an exact solution to the energy equation every global iteration.To save some time, you can then employ the foregoing command with a Label of MODP. You use it to specify anumber of global iterations performed using the TDMA method between global iterations performed using thePGMR method for the temperature DOF.

The number of search directions required may vary widely among problems. If large values of SRCH result in therequired computer storage exceeding the computational resources, inertial relaxation should be used. To specifythe number of search vectors, use either of these methods:

Command(s): FLDATA20,SRCH,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

For the PGMR solver, the allowable range of search vectors is 12 to 20. The default value is 12.

The PGMR method is not recommended for velocity DOF.

The output associated with the solver is recorded in the Jobname.OUT file for non-FLOTRAN analyses. TheFLOTRAN iterative solver output is recorded in the jobname.dbg file.

The fact that the PGMR solver is being used is indicated in the Jobname.DBG file. The file shows if convergenceis reached, the maximum number of iterations is reached without convergence, or the solution is stalled.

The PGMR method output is in the same form as that provided in the jobname.out file for non-FLOTRAN analyses.The NORM referred to in the Jobname.OUT file is the square root of the convergence criterion specified in theFLOTRAN input. For example, a EQSLV command solver tolerance value of 1.E-5 corresponds to the FLOTRANdefault convergence criterion value of 1.E-10.

The PGMR method can fail for the following reasons:

• The problem is ill-conditioned.

• The problem is improperly formulated.

• The specified convergence criterion is too tight.

• An insufficient number of iterations is specified.

If the PGMR method stalls, it may be because the problem is ill-conditioned or improperly formulated. If theproblem is ill-conditioned, you can control several parameters to enhance performance. You can increase theamount of fill-in or the number of search vectors. You can also use inertial relaxation. If the problem is improperlyformulated, there may be an input error or the boundary conditions may be applied incorrectly. You need tocheck the input parameters and boundary conditions to ensure that they are accurate.

FLOTRAN does not allow a convergence criterion less restrictive than the default value. You can enter a highervalue, but FLOTRAN issues a warning message and changes it to the default value.

If the maximum number of iterations has been reached without convergence, it may mean more iterations arerequired. This could be the case if you see that the Norm has been lowered, but it is not quite to the target. If so,you can try increasing the maximum number of iterations.


Chapter 11: FLOTRAN CFD Solvers and the Matrix Equation

If the PGMR method converges and the results are questionable, reduce the convergence criterion below thedefault value of 1.E-10. A convergence criterion as low as 1.E-20 may be necessary for some problems.

11.3.2. Preconditioned BiCGStab (PBCGM) Solver

The PBCGM method is a version of the generalized bi-conjugate gradient method that uses two sets of vectorsconstructed from both the coefficient matrix and its real transpose matrix by making them orthogonal to eachother. At each iteration, a new vector is first generated orthogonal to some user-specified number of previousvectors (search directions) from the basis of the real transpose matrix. A minimization procedure is then used tostabilize the numerical procedure. Similar to PGMR, the PBCGM method uses fill-in when constructing the L andU decomposition matrices. This preconditioning procedure transforms the system of equations into a set easierto solve by decomposing the coefficient into an approximate LU product.

Accordingly, when you are using the Preconditioned BiCGStab (PBCGM) solver, you need to specify the amountof fill-in. You must also specify the number of search vectors.

The fill-in value represents the number of extra elements allowed in each row of the L and U decompositionmatrices. An extra element is defined as being in addition to the number of nonzero elements in the row of theoriginal matrix.

There are two PBCGM algorithms available for FLOTRAN. The difference lies in the fill-in value. When it is specifiedto be zero, the algorithm is parallelized except the LU preconditioning part. For other fill-in values, the algorithmis not parallelized at all.

To specify the amount of fill-in, use the following command or menu path:Command(s): FLDATA20B,PBCGM,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

The allowable range for fill-in is 0 to 10. The default value is 6. A single fill-in value is input for all applicable DOF.

The number of search directions required may vary widely among problems. If large values of SRCH result in therequired computer storage exceeding the computational resources, use inertial relaxation. In practice, you shouldusually use a value of 1 or 2 in order to save the memory storage. To specify the number of search vectors, usethe following command or menu path:

Command(s): FLDATA20,SRCH,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

For the PBCGM solver, the allowable range of search vectors is 1 to 8. The default value is 2.

11.4. Sparse Direct Method

The Sparse Direct method is memory intensive and you should only use it if all other methods have failed. Thismethod produces intermediate files during matrix factorization and it is difficult to predict the memory required.Ensure enough hard disk space exists for intermediate files.

If you choose the Sparse Direct method for the VX, VY, or VZ DOFs, FLOTRAN will reset the method to Precondi-tioned Conjugate Residual (PCCR). The Sparse Direct method is not suitable for the velocity degrees of freedom.

Section 11.4: Sparse Direct Method


11–6

Chapter 12: Coupling Algorithms

12.1. Overview

Chapter 11, “FLOTRAN CFD Solvers and the Matrix Equation” describes the linear solvers available to solve eachindividual equation. To obtain a final solution, you must usually account for the coupling between the individualequations. In FLOTRAN, this nonlinear coupling is handled in a segregated or decoupled manner. The couplingalgorithms belong to a general class referred to as the Semi-Implicit Method for Pressure Linked Equations(SIMPLE). For more information on this general class of algorithms, see S.V. Patankar, D.B. Spalding, ("A calculationprocedure for heat, mass and momentum transfer in 3-D parabolic flows," International Journal of Heat and MassTransfer, Vol 15, pp. 1787-1806, 1972).

To handle the coupling between the pressure and momentum equations, there are two segregated solution al-gorithms: SIMPLEF and SIMPLEN. For many years, SIMPLEF was the sole pressure-velocity coupling algorithm. Itwas developed by R.J. Schnipke and J.G. Rice ("Application of a new finite element method to convection heattransfer," Fourth International Conference on Numerical Methods in Thermal Problems, Swansea, U.K., July 1985).The SIMPLEF algorithm has been improved by utilizing some ideas from the SIMPLEC algorithm developed byJ.P. Van Doormaal and G.D. Raithby ("Enhancements of the SIMPLE method for predicting incompressible fluidflows," Numerical Heat Transfer, Vol. 7, pp. 147-163, 1984). To improve the rate of convergence, the SIMPLEN al-gorithm has been added to FLOTRAN. It was developed by G. Wang ("A fast and robust variant of the SIMPLE al-gorithm for finite-element simulations of incompressible flows," Computational Fluid and Solid Mechanics, Vol.2, pp. 1014-1016, Elsevier, 2001).

SIMPLEF is the default algorithm. To activate the SIMPLEN algorithm, use one of the following:Command(s): FLDATA37GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Algorithm ControlMain Menu> Solution> FLOTRAN Set Up> Algorithm Control

12.2. Algorithm Settings

In general, FLOTRAN automatically set defaults suited for the two segregated algorithms. However, for someproblems, you may need to reset the advection scheme, solver choice, or relaxation factors.

12.2.1. Advection Scheme

You can discretize the advection term using three approaches: Monotone Streamline Upwind (MSU), StreamlineUpwind/Petrov-Galerkin (SUPG), or Collocated Galerkin (COLG). Refer to Chapter 14, “Advection DiscretizationOptions” for information on how to select a proper advection scheme.

Refer to the following table for a list of the defaults.

Table 12.1 Advection Scheme Defaults

SIMPLEN AlgorithmSIMPLEF AlgorithmTransport Equation

SUPGSUPGMomentum

MSUSUPGTurbulence

MSUMSUPressure

SUPGSUPGEnergy

SUPGSUPGSpecies


12.2.2. Solver

For the SIMPLEF algorithm, the TDMA solver is the default for the momentum and turbulence equations. Noneof the other solvers will improve the overall rate of convergence. Even when exact solutions are obtained onthose individual equations, the overall rate of convergence will not improve. This is due to weak coupling betweenthe pressure and momentum equations.

For the SIMPLEN algorithm, the overall rate of convergence can be improved considerably when more exactsolutions are obtained for each individual equation. Therefore, when SIMPLEN is activated, FLOTRAN automaticallyresets the solver option to the preconditioned BiCGStab method (PBCGM) for the momentum, turbulence andenergy equations. Furthermore, it will reset the fill-in parameter for PBCGM to zero for computational efficiency.

12.2.3. Relaxation Factors

Due to the nonlinear coupling between equations, in order to stabilize the overall solution procedure, relaxationis usually necessary to moderate changes from one global iteration to the next. Experience indicates that relax-ation factors greater than 0.5 for the velocity and pressure degrees of freedom will generally cause instabilityand divergence for the SIMPLEF algorithm. On the other hand, the SIMPLEN algorithm provides more consistentcoupling between the pressure and velocity degrees of freedom. For incompressible flow problems, SIMPLENremoves the need for relaxation for the pressure equation and allows a relaxation factor close to 1.0 for the mo-mentum equations. For compressible flow problems, relaxation is usually needed for the pressure equation inorder to obtain a convergent solution. The default for SIMPLEF is 0.5 for the pressure and velocity degrees offreedom. When SIMPLEN is activated, FLOTRAN automatically resets the relaxation factor to 1.0 for the incom-pressible pressure equation, 0.5 for the compressible pressure equation, and 0.8 for the momentum equations.

12.3. Performance

Table 12.2: “SIMPLEF and SIMPLEN Performance Results” presents results for laminar flow in a 2-D square cavity.The Reynolds number is 100 based on the length of the cavity side and the velocity at the top. The uniform grid

consists of 322 = 1024 elements.

Table 12.2 SIMPLEF and SIMPLEN Performance Results

SIMPLENSIMPLEF

0.990.980.950.90.80.5RELX

1761146681153325Iter. No.

8.95.73.34.07.212.9CPU (sec)

For the SIMPLEN algorithm , the total number of global iterations and the computational time decrease as therelaxation factor (RELX) increases from 0.8 to 0.95. As RELX increases above 0.95, the iteration number andcomputational time increase. The optimal RELX value is 0.95. At this value, the SIMPLEN convergence rate isabout 4 times faster than SIMPLEF. The SIMPLEN computational time is about 1/4 of the SIMPLEF computationaltime.

Results for a finer mesh of 1282 = 16,384 elements show an even better SIMPLEN performance. At an optimalRELX value of 0.99, the SIMPLEN computational time is about 1/40 of the SIMPLEF computational time.

SIMPLEN significantly improves the rate of convergence if pressure-velocity coupling dominates the convergence.If other factors affect the overall rate of convergence, SIMPLEN will not increase the rate of convergence as sig-nificantly. However, for those problems, SIMPLEN will generally be more robust than SIMPLEF, and it will usuallygive a better convergence behavior. For more comparisons, see Wang G., "A fast and robust variant of the SIMPLE



algorithm for finite-element simulations of incompressible flows," Computational Fluid and Solid Mechanics,vol. 2, pp. 1014-1016, Elsevier, 2001.

Below is the command input listing used to perform this analysis. All text preceded by an exclamation point (!)is a comment.

/title, Lid driven cavity flow analysis using SIMPLEF/SIMPLEN algorithmsNDL = 32 ! Number of line divisionsMU = 0.010 ! Fluid viscosityRHO = 1.0L = 1.0sL = 1.0e-8Vel = 1.000niter = 10000

/PREP7et,1,141 ! 2-D XY systemesha,2 ! Quad elementsrect,,L,,Llesi,all,,,NDLamesh,1alls! Apply Boundary Conditionsnsel,s,ext ! Wall boundary conditionsd,all,vxd,all,vynsel,r,loc,y,L-sL,L+sL !topd,all,vx,veld,all,vyd,all,enke,-1allsd,1,PRESfinisave

/SOLU ! SIMPLEF algorithmflda,iter,exec,niter ! No. of global iterationsflda,nomi,visc,MUflda,nomi,dens,RHOflda,term,pres,1.e-6solvefini/delete,,rfl

/SOLU ! SIMPLEN algorithmflda,algr,segr,simplensolvefini/delete,,rfl

/SOLUflda,relx,vx,0.9flda,relx,vy,0.9solvefini/delete,,rfl



Section 12.3: Performance


/SOLUflda,relx,vx,0.99flda,relx,vy,0.99solvefini



Chapter 13: Multiple Species Transport

13.1. Overview of Multiple Species Transport

The multiple species transport capability enables you to track several different fluids at once, subject to thelimitation that a single momentum equation is solved for the flow field. Transport equations are solved for eachspecies. The properties used in the momentum equation can be those of a "main" fluid, a "bulk" fluid (dilutemixture analysis), or a combination of component fluids. Momentum effects such as advection and diffusioncause the fluid transport.

The following restrictions apply to this type of analysis:

• Currently, no reactions are modeled among the species.

• Solid model boundary /initial conditions are not supported for species mass fractions.

• Also, you must postprocess multiple species results by issuing commands instead of via the GUI.

13.2. Mixture Types

In terms of property variations, the strategies for solving multiple species problems parallel those for thermalproblems. The key issue is determining how large a mass fraction of the overall flow field the species to be tracedrepresents. You can choose among three mixture types for analysis: dilute mixture, composite mixture, andcomposite gas. For each mixture type, the properties may be a function of temperature.

13.2.1. Dilute Mixture Analysis

In a dilute mixture analysis, small mass fractions of species fluids are tracked in a flow field, and the speciesproperties do not significantly influence the flow field. The fluid properties are set and the bulk fluid analysisproceeds as in any other FLOTRAN analysis. You solve the transport equations for species using the bulk densityand the velocities from the bulk fluid analysis.

If the analysis problem is isothermal or the properties are assumed not to vary with temperature, you can convergethe flow field completely before the species transport option is activated. The number of species to be solved isa feature of the element and is controlled via a key option on the element. The appropriate KEYOPT setting mustbe defined during the PREP7 phase of the analysis. Once the element type and number of species has been set,the multiple species input commands (e.g., MSSPEC) can be issued from either PREP7 or SOLUTION phases.However, the multiple species menus are accessible only from PREP7.

To activate multiple species transport, use one of the following:Command(s): FLDATA1,SOLU,SPEC,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution OptionsMain Menu> Solution> FLOTRAN Set Up> Solution Options

13.2.2. Composite Mixture Analysis

A composite mixture analysis calculates the properties used in the solution from a linear combination of thespecies, weighted by mass fraction as a function of space. The solution of the momentum equation depends onthe species distribution, so the momentum and transport equations are strongly coupled.

You initialize the species mass fractions using either the MSNOMF command (which has no GUI menu equivalent)or (typically for a transient analysis) one of the following:

Command(s): IC,Label,Value


GUI: Main Menu> Preprocessor> Loads> Analysis Type> Analysis OptionsMain Menu> Solution> Define Loads> Apply> Initial Condit'n> Define

The mass fractions specified must add up to 1.0. To activate the composite mixture option for an individualproperty, use one of the following:

Command(s): FLDATA7,PROT,Label,CMIXGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

13.2.3. Composite Gas Analysis

In a composite gas analysis, at each node the fluid density is calculated as a function of the mass fractions andmolecular weights of the gases:

ρ =

=∑

P

RTYM

i

ii

N

1

In the equation above:

• R is the Universal Gas constant. You can set it using one of the following:Command(s): MSDATAGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

• Mi is the molecular weight of the ith species. You set this weight using one of the following:

Command(s): MSSPECGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

• N is the total number of species defined.

• P is pressure degree of freedom (PRES).

• T is the absolute temperature (TEMP).

To invoke the composite gas option for the bulk fluid, use one of the following:Command(s): FLDATA7,PROT,DENS,CGASGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid PropertiesMain Menu> Solution> FLOTRAN Set Up> Fluid Properties

13.3. Doing a Multiple Species Analysis

The procedure for a multiple species analysis has six steps:

1. Establish the number of species to model and assign species names.

2. Designate an algebraic species.

3. Adjust output format if desired.

4. Set properties.

5. Specify boundary conditions and nominal mass fractions.

6. Set relaxation and solution parameters for the solution of the transport equations (if necessary).

13.3.1. Establish the Species

To set the number of species, use one of these methods:



Command(s): KEYOPT,1,1,n (n = number of species (at least 2, but no more than 6))GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

To name each species, use the menu paths shown above or the following command:

Command(s):MSSPEC

FLOTRAN uses these names for assigning boundary conditions and in postprocessing listings and plots. Thedefault names for species are SP01, SP02, and so on.

13.3.2. Choose an Algebraic Species

The transport equations solve for the mass fractions of each species. You must choose one as the algebraic species,using the value set by the ALGEB argument or one of the following:

Command(s): MSDATAGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

The transport equation for the algebraic species is not solved, but its concentration as a function of space iscalculated by ensuring that the mass fractions of all the species add up to 1.0 everywhere.

Note — The MSDATA command also sets the universal gas constant. Every issuance of the commandsets both numbers.

13.3.3. Adjust Output Format

You can set the format of the convergence monitors on the file Jobname.PFL to list columns of values for allthe degrees of freedom for a single iteration. (This also affects the ANSYS output file.) To adjust output, use oneof the following:

Command(s): FLDATA6GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Additional Out> Print ControlsMain Menu> Solution> FLOTRAN Set Up> Additional Out> Print Controls

13.3.4. Set Properties

For a dilute mixture analysis, set the bulk property type as appropriate (CONSTANT, Liquid, etc.).

If the bulk properties are to be a linear combination of the species properties, set the bulk property type to CMIX.For example, you would use the following command:

Command(s):FLDATA7,PROT,Label,Type

In the preceding command, Label can be DENS, VISC, COND, or SPHT, and Type is CMIX. If Label = DENSE, Typemay be CGAS. Using CGAS requires you to enter a molecular weight for the gas via the MSSPEC command or itsequivalent GUI path.

You handle individual species property variations the same way, and with the same options as, the bulk fluid.The CONSTANT, LIQUID, and GAS fluid types are available. Specify them, along with coefficients, using one ofthe following:

Command(s): MSPROPGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

Section 13.3: Doing a Multiple Species Analysis


For all analyses, you must enter the mass diffusion coefficient data for each species. For a dilute mixture, thedensity is the only other relevant property because the bulk or main fluid properties govern the solution of themomentum equation. For the CMIX and CGAS options, you need to specify density and viscosity using MSPROPor an equivalent menu path. Also specify conductivity if the energy equation is to be solved.

The form of the diffusion term is:

∇⋅ ∇( )ρD Ymi i

The value Dmi is the diffusion coefficient, and Yi is the mass fraction being solved.

Sometimes, the available data is expressed as a Schmidt number. The following equality enables expression ofthe diffusion portion of transport in terms of laminar viscosity µ, the density ρ, and the Schmidt number:

ρ µD Y

SCYmi i

ii∇ = ∇

Note — The input must be in terms of the mass diffusion coefficient, not the Schmidt number. The Schmidtnumber relating the diffusion coefficient to the density and viscosity differs from the turbulent Schmidtnumber discussed below.

In addition, the flow field may be turbulent. Another representation of the diffusion term, this time includingthe effect of the turbulent viscosity µ, is:

∇⋅ +

∇µ µ

SC SCY

i

t

Tii

The quantity SCTi is the turbulent Schmidt number, which you specify via one of the following:

Command(s): MSSPECGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

The normal default value of 1.0 is sufficient unless you want to regulate explicitly the effect of turbulence on thetransport.

13.3.5. Specify Boundary Conditions

The default boundary condition is zero gradient of the mass fraction at the boundaries. You can specify the massfraction at a boundary, such as the inlet, by entering the species name in the LAB field of one of the following:

Command(s): DGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement> OnNodesMain Menu> Solution> Define Loads> Apply> Fluid/CFD> Displacement> On Nodes

Initialize the mass fractions for every species, including the algebraic species. The fractions must sum to 1.0.

13.3.6. Set Relaxation and Solution Parameters

Relaxation factors for the property calculations and the mass fraction update default to 0.5. To change the factors,use one of the following:

Command(s): MSRELAXGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

You can set modified inertial relaxation factors for multiple species. To do so, use one of the following:Command(s): MSMIR,SPNUM,Value



GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

A larger modified inertial relaxation factor gives a more robust scheme, but it may yield a slower convergence.The recommended range is 0.1 to 1.0.

You can change parameters for the algebraic solvers for the transport equation and choose a solver by usingone of the following commands or menu paths:

Command(s): MSSOLU, MSMETHGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

Activating mass fraction capping is recommended to prevent intermediate calculations from producing unreal-istic results. Use either of the following for each species:

Command(s): MSCAPGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

Finally, you activate the multiple species option using one of the following:Command(s): FLDATA1,SOLU,Spec,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution OptionsMain Menu> Preprocessor> FLOTRAN Set Up> Solution Options

13.4. Doing a Heat Exchanger Analysis Using Two Species

Although FLOTRAN permits only one fluid region to correspond to material number 1 (using the commandMAT,1 or an equivalent GUI path), you can simulate multiple fluids within this restriction. To do so, you set allfluid property types to CMIX, then set the appropriate species mass fraction to 1.0 in a particular region. Thesesettings enable all properties in that region to correspond to that of species with mass fraction 1.0. For suchmultiple fluid simulations, the mass fractions must remain constant throughout the analysis; that is, the analysisshould not turn on the species solution.

A typical heat exchanger analysis consists of two fluids flowing in opposite directions, separated by a wall asshown in Figure 13.1: “Environment for a Typical Heat Exchanger Analysis”:

Figure 13.1 Environment for a Typical Heat Exchanger Analysis

The sample command stream that follows shows you how to set up the model shown in Figure 13.1: “Environmentfor a Typical Heat Exchanger Analysis”, apply boundary conditions, set up appropriate properties, etc. It is important

Section 13.4: Doing a Heat Exchanger Analysis Using Two Species


to note that, although two species are defined, the species transport has not been activated. In addition, all fluidproperties must be declared variable so that the initial value (the same in regions 1 and 2) is reset based on themass fraction.

/BATCH,LIST/tit,heat exchanger problem !two different fluids separated by a solid wall!cartesian geometry, pressure-driven flow!solve by 2 speciesLX = 10 ! Length in X directionNDX = 10 ! Number of X divisionsLY1 = 2 ! fluid 1 widthLY2 = 0.1 ! solid widthLY3 = 1.0 ! fluid 2 widthNDY1 = 10NDY2 = 3 NDY3 = 10 YOFFSET = 0 !offset from X-axis /prep7 $smrt,offet,1,141 ! 2-D XY system!specieskeyopt,1,1,2 ! 2 species!axisymm!keyopt,1,3,2 !use for axisymm RY system onlyesha,2 !Quad elementsrect,,LX,YOFFSET,YOFFSET+LY1 !fluid 1 arearect,,LX,YOFFSET+LY1,YOFFSET+LY1+LY2 !solid arearect,,LX,YOFFSET+LY1+LY2,YOFFSET+LY1+LY2+LY3` !fluid 2 areanummrg,allnumcmp,alllsel,s,,,3,9,3lsel,a,,,1lesi,all,,,NDX,

lsel,s,,,2,4,2lesi,all,,,NDY1,-5.0 lsel,s,,,5,7,2lesi,all,,,NDY2,-5.0 lsel,s,,,8,10,2lesi,all,,,NDY3,-5.0 allselmat,1 !for fluids material must be 1amesh,1 !mesh fluid 1 regionamesh,3 !mesh fluid 2 regionmat,2 !for solid set material to 2amesh,2 !mesh solid region!inner region 1!bc inletlsel,s,,,4nsll,s,1d,all,pres,10 !inlet pressure & temp specified for fluid 1d,all,temp,100!bc outletlsel,s,,,2nsll,s,1d,all,pres,0. !outlet pressure specified for fluid 1!symmlsel,s,,,1nsll,s,1d,all,vy,0 !symmetry surface for fluid 1 only!region 2!bc inletlsel,s,,,8nsll,s,1d,all,pres,10. !inlet pressure & temp specified for fluid 2d,all,temp,400!bc outletlsel,s,,,10nsll,s,1d,all,pres,0. !outlet pressure specified for fluid 2!top wall



lsel,s,,,9 nsll,s,1d,all,vx,0 !wall boundary conditions d,all,vy,0 allsel!solid propertiesmp,dens,2,5. !specify solid region 3 propertiesmp,kxx,2,100mp,c,2,13/SOLU!ic for speciesnsel,s,loc,x,,lx !select nodes for fluid 1nsel,s,loc,y,o,ly1ic,all,sp01,1.0 !set mass fraction for fluid 1ic,all,sp02,0.0nsel,s,loc,x,,lxnsel,s,loc,y,ly1+ly2,ly1+ly2+ly3 !select nodes for fluid 2ic,all,sp01,0.0 !set mass fraction for fluid 2ic,all,sp02,1.0allselFLDA,ITER,EXEC,200 FLDA,PROT,DENS,CMIX ! Fluid densityFLDA,PROT,VISC,CMIX ! Fluid viscosity FLDA,PROT,COND,CMIX ! Fluid conductivityFLDA,PROT,SPHT,CMIX ! Fluid specific heatflda,vary,dens,t !all properties MUST be variableflda,vary,visc,tflda,vary,cond,tflda,vary,spht,tFLDA,NOMI,DENS,1.0 ! initial density for all fluid regionFLDA,NOMI,VISC,2.0 ! initial viscosity for all fluid regionFLDA,NOMI,COND,3.0 ! initial conductivity for all fluid regionFLDA,NOMI,SPHT,4.0 ! initial specific heat for all fluid regionmsprop,1,spht,constant,1 !sp heat for fluid 1msprop,2,spht,constant,2 !sp heat for fluid 2msprop,1,dens,constant,1 !density for fluid 1msprop,2,dens,constant,2 !density for fluid 2msprop,1,visc,constant,1.0 !viscosity for fluid 1msprop,2,visc,constant,2.0 !viscosity for fluid 2msprop,1,cond,constant,.1 !conductivity for fluid 1msprop,2,cond,constant,.2 !conductivity for fluid 2FLDA,CONV,PRES,1.0E-10 ! PCCR convergence criterionFLDA,TERM,PRES,1.E-09FLDA,OUTP,SP01,TFLDA,OUTP,SP02,TsaveSOLVE !solve for flow onlyFLDA,SOLU,ENRG,TFLDA,SOLU,FLOW,FFLDA,METH,ENRG,3 FLDA,ITER,EXEC,50FLDA,RELX,TEMP,1.SOLVE !solve for temperature onlyfini/exit,nosa

13.5. Example Analysis Mixing Three Gases

The following example analysis mixes three gases: oxygen (O2), nitrogen (N2), and hydrogen (H2). The mass

fractions of the gases are set at each inlet along with the velocity. For the three inlets:

Section 13.5: Example Analysis Mixing Three Gases


Bottom:Left:Top:

VX = 0

VY = 0.1

TEMP = 300

O2 = 0.0

N2 =0.0

H2 = 1.0

VX = 0.1

VY = 0

TEMP = 400

O2 = 0.0

N2 = 1.0

H2 = 0.0

VX = 0

VY = -0.1

TEMP = 300

O2 = 1.0

N2 = 0.0

H2 = 0.0

The command stream for the example (shown below) shows all the relevant properties and the solution strategy.

/batch,list/filename,spec/com ** Analysis Types Laminar and Turbulent, Incompressible/com 2-D - quadrilateral and triangular elements/com ** Features Thermal, Multiple Species Transport/com ** Options Dilute mixtures, composite property types (CGAS, CMIX)/com ** Variable laminar properties/com ** Turbulence/com ** Construction of geometry/prep7!!!!!!! Define some dimensions - SI units are usedlenin=.3half=lenin/2.width=.1hfwid=width/2.outlen=1.2!!!!!!! Define inlet and outlet rectanglesrect,-lenin,0,-hfwid,hfwidrect,.2,.3,.25,.25+leninrect,.2,.3,-.25,-.25-leninrect,.4,.4+outlen,-.15,.15!!!!!!! Lines that border the mixing areal2tan,-3,-8l2tan,-6,-15l2tan,-13,-10l2tan,-12,-1!!!!!!! Parameters defined for meshingnlcurv=16rlcurv=1nscurv=9rscurv=1nispan=8rispan=-1.5nospan=13rospan=-2nilen=10rilen=-2nolen=24rolen=4!!!!!!!!flst,2,2,4,orde,2!fitem,2,17!fitem,2,20lsel,s,,,17,20,3lesize,all,,,nlcurv,rlcurvlsel,s,,,18,19!fitem,2,18!fitem,2,-19lesize,19,,,nscurv,rscurv!flst,2,3,4,orde,3!fitem,2,2!fitem,2,5!fitem,2,11lsel,s,,,2,5,3



lsel,a,,,11lesize,all,,,nispan,1!flst,2,3,4,orde,3!fitem,2,4!fitem,2,7!fitem,2,9lsel,s,,,4,7,3lsel,a,,,9lesize,all,,,nispan,rispan!flst,2,6,4,orde,6!fitem,2,1!fitem,2,3!fitem,2,6!fitem,2,8!fitem,2,10!fitem,2,12lsel,s,,,1,3,2lsel,a,,,6,12,2lesize,all,,,nilen,rilenlsel,s,,,13,16lesize,13,,,nolen,rolenlesize,15,,,nolen,1./rolenlesize,16,,,nospan,rospanlesize,14,,,nospan,rospanalls!!!!!!! Define the mixing area...!flst,2,8,3!fitem,2,2!fitem,2,12!fitem,2,11!fitem,2,13!fitem,2,16!fitem,2,6!fitem,2,5!fitem,2,3a,2,12,11,13,16,6,5,3alls/com ** CONSTRUCTION OF THE MESH!!!!!!! Put triangles in the mixing area (5)asel,s,,,5et,1,141mshape,1,2damesh,5!!!!!!! Put a mapped mesh in the rectangles (quads)asel,s,,,1,4mshape,0,2dmshkey,1amesh,all/com ** BOUNDARY CONDITIONS!!!!!!! Wall boundary conditionslsel,s,,,1,3,2lsel,a,,,6,12,2lsel,a,,,13,17,2lsel,a,,,18,20nsll,,1d,all,vx,0d,all,vy,0!!!!!!! Define velocities, temperature at top, bottom, leftvtop=.1vbot=.1vlef=.1lsel,s,,,7nslld,all,vx,0d,all,vy,-vtopnsll,,1d,all,temp,300lsel,s,,,4nslld,all,vx,vlefd,all,vy,0nsll,,1



d,all,temp,400lsel,s,,,9nslld,all,vx,0d,all,vy,vbotnsll,,1d,all,temp,300lsel,s,,,14nsll,,1d,all,pres,0flda,conv,iter,5savefinishalls/solu/com ** FLOTRAN INPUTflda,iter,exec,40flda,temp,nomi,300 ! Initial temperature field is 300Kflda,prot,dens,air-si ! Initial solution will be for AIRflda,vary,dens,trueflda,prot,visc,air-siflda,vary,visc,trueflda,prot,cond,air-siflda,vary,cond,trueflda,prot,spht,air-sisavesolve ! Solve 40 iterations with air at 300Kfinish ! Prepare for species transport .../prep7flda,prot,dens,cmix ! Composite mixture for densityflda,prot,visc,cmix ! Composite mixture for viscositykeyopt,1,1,3 ! Specify that there are 3 species

flda,solu,spec,t ! Turn on solution for multiple species transportmsdata,2 ! Specify species 2 (N2) as the algebraic species!!!!!!!! Species Property Inputmsspec,1,o2,31.999msprop,1,DENS,GAS,1.2998,300,1.01325E+5msvary,1,dens,tmsnomf,1,.3msprop,1,VISC,CONSTANT,1.2067E-5msprop,1,mdif,CONSTANT,2.149E-5msprop,1,cond,CONSTANT,.02674mscap,1,1!msspec,2,n2,28.018msprop,2,DENS,GAS,1.1381,300,1.01325E+5msvary,2,dens,tmsnomf,2,.3msprop,2,VISC,CONSTANT,1.786E-5msprop,2,mdif,CONSTANT,1.601E-5msprop,2,cond,CONSTANT,.02598mscap,2,1!msspec,3,h2,2.016msprop,3,DENS,GAS,0.0819,300,1.01325E+5msvary,3,dens,tmsnomf,3,.4msprop,3,VISC,CONSTANT,8.94E-6msprop,3,mdif,CONSTANT,4.964E-5msprop,3,cond,CONSTANT,.1815mscap,3,1!msrelx,1,1.0msrelx,3,1.0msmeth,1,3mssolu,1,,,2,1.e-8msmeth,3,3mssolu,3,,,2,1.e-8alls!!!!!!! Species boundary conditions



lsel,s,,,7nsll,,1d,all,o2,1.0d,all,n2,0.0d,all,h2,0.0lsel,s,,,4nsll,,1d,all,o2,0.0d,all,n2,1.0d,all,h2,0.0lsel,s,,,9nsll,,1d,all,o2,0.0d,all,n2,0.0d,all,h2,1.0alls!!!!!!! End of species boundary conditionsflda,iter,exec,20 ! Ask for 20 global iterationsflda,conv,outp,land ! Adjust convergence monitor output stylesavefinish/solusolve ! 20 iterations with species activated!!Prepare for energy solutionflda,solu,temp,t ! Achieve a constant flow temperature solutionflda,solu,flow,f ! Freeze the flow fieldflda,meth,temp,3 ! Activate PCCR solverflda,conv,temp,1.e-10 ! Convergence criterion for PCCRflda,iter,exec,5 ! Need only a few iterations for solution...flda,relx,temp,1.0 ! no relaxation on temperaturesavesolve!! Prepare for coupled solution

flda,iter,exec,35 ! Achieve a flow and thermal solutionflda,solu,flow,tsolveflda,iter,exec,50 ! Run 50 more iterations to refine solutionsavesolve



13–12

Chapter 14: Advection Discretization Options

14.1. Introduction

When momentum, energy, species transport, turbulence or the compressible pressure equations are solved, theadvection term plays a significant role in the solution. When the advection term dominates over other terms inthe governing equations, it can lead to numerical instabilities. Accordingly, you must be careful with the discret-ization of this particular term.

You can discretize the advection term using three approaches: monotone streamline upwind (MSU), streamlineupwind/Petrov-Galerkin (SUPG), or collocated Galerkin (COLG). For the momentum, energy, turbulence orcompressible pressure equations, you specify the approach using one of the following:

Command(s): FLDATA33,ADVM,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> AdvectionMain Menu> Solution> FLOTRAN Set Up> Advection

For the species transport equation, you specify the approach using one of the following:Command(s): MSADV,SPNUM,MTHAGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple SpeciesMain Menu> Solution> FLOTRAN Set Up> Multiple Species

MSU tends to be first order accurate while SUPG and COLG are second order accurate. MSU produces diagonallydominant matrices and is generally quite robust. SUPG and COLG provide less diagonal dominance, but aregenerally more accurate. COLG provides an exact energy balance for incompressible flows, even with a coarsemesh. Special techniques may be required to achieve convergence using SUPG or COLG.

For more information on the approaches, consult the ANSYS, Inc. Theory Reference.

14.2. Using SUPG and COLG

For simple geometries and simple flows, the SUPG or COLG approach provides a convergent solution in a straightforward fashion.

For laminar flow past obstacles, which generally produce regions of recirculation in the wake, you may need toturn on modified inertial relaxation in the momentum equation using one of the following:

Command(s): FLDATA34,MIR,MOME,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> MIR StabilizationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization

For turbulent problems, FLOTRAN will sometimes display a message stating that the coefficient matrix has anegative diagonal and the solution is probably divergent. You should then try turning on modified inertial relax-ation in the momentum equation or turbulence equation.

Command(s):FLDATA34,MIR,MOME,Value or FLDATA34,MIR,TURB,Value

The modified inertial relaxation Value should be between 0.1 and 1.0. A larger Value leads to more relaxation.To achieve a faster convergence rate, use the smallest Value possible.

For complex geometries with turbulence and complex flow fields, you can employ the following techniques toachieve a convergent solution with SUPG or COLG.


• Set the turbulence ratio to a high value of 1 x 106 and the effective viscosity relaxation factor to a low valueof 0.1 using the following commands. These conditions provide the necessary diagonal dominance untilthe solution enters the radius of convergence.

Command(s): FLDATA24,TURB,RATI,1.0E6GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence ModelMain Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence ParamMain Menu> Solution> FLOTRAN Set Up> Turbulence ModelMain Menu> Solution> FLOTRAN Set Up> Turbulence ParamCommand(s): FLDATA25,RELX,EVIS,0.1GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Prop RelaxationMain Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation

• Achieve a convergent solution using MSU on all variables. Then, using the following command, performa restart employing SUPG or COLG on the momentum variables only. After achieving a convergent solution,you can perform a restart again employing SUPG or COLG on the turbulence, pressure, temperature andspecies variables.

Command(s): FLDATA33,ADVM,MOME,SUPG FLDATA33,ADVM,MOME,COLGGUI: Main Menu> Preprocessor> FLOTRAN Set Up> AdvectionMain Menu> Solution> FLOTRAN Set Up> Advection

• Although the foregoing techniques might work on a coarse mesh, both may fail on a fine mesh. In thiscase, you may have to resort to a transient algorithm which has the necessary diagonal dominance dueto the inertia term.

14.3. Strategies for Difficult Solutions

Although SUPG and COLG are more accurate than MSU, they may lead to spurious oscillations in the solution.This may lead to nonphysical solutions or convergence difficulties. You may encounter negative temperaturesin the energy equation solution. In this case, you should refine the mesh in that region. You may also encounternegative turbulence values. Internally, FLOTRAN tries to reset these values to some realistic numbers, but thismay lead to a situation where the solution stalls. In this situation, you should try using MSU on turbulence variableswhile retaining SUPG or COLG on momentum variables. The solution to the species transport equation must bebounded between 0 and 1.0, and oscillations in the SUPG or COLG solution may make this difficult to achieveeven though capping has been turned on. If convergence is not achieved, you should then refine the mesh.

A poor mesh, recirculating regions, or a strong swirl might cause the SUPG technique to have strong oscillationsin an axisymmetric analysis. Temperatures (or species concentrations) could be higher or lower than any appliedboundary conditions. The mesh should be refined or another advection discretization method should be used.


Chapter 14: Advection Discretization Options

Part II. Acoustics

Chapter 15: Acoustics

15.1. What Is Acoustics?

Acoustics is the study of the generation, propagation, absorption, and reflection of sound pressure waves in afluid medium. Applications for acoustics include the following:

• Sonar - the acoustic counterpart of radar

• Design of concert halls, where an even distribution of sound pressure is desired

• Noise minimization in machine shops

• Noise cancellation in automobiles

• Underwater acoustics

• Design of speakers, speaker housings, acoustic filters, mufflers, and many other similar devices.

• Geophysical exploration

15.1.1. Types of Acoustic Analysis

An acoustic analysis, available in the ANSYS Multiphysics and ANSYS Mechanical programs only, usually involvesmodeling the fluid medium and the surrounding structure. Typical quantities of interest are the pressure distri-bution in the fluid at different frequencies, pressure gradient, particle velocity, the sound pressure level, as wellas, scattering, diffraction, transmission, radiation, attenuation, and dispersion of acoustic waves. A coupledacoustic analysis takes the fluid-structure interaction into account. An uncoupled acoustic analysis models only thefluid and ignores any fluid-structure interaction.

The ANSYS program assumes that the fluid is compressible, but allows only relatively small pressure changeswith respect to the mean pressure. Also, the fluid is assumed to be non-flowing and inviscid (that is, viscositycauses no dissipative effects). Uniform mean density and mean pressure are assumed, with the pressure solutionbeing the deviation from the mean pressure, not the absolute pressure.

15.2. Solving Acoustics Problems

You can solve many acoustics problems by performing a harmonic response analysis. The analysis calculates thepressure distribution in the fluid due to a harmonic (sinusoidally varying) load at the fluid-structure interface. Byspecifying a frequency range for the load, you can observe the pressure distribution at various frequencies. Youcan also perform modal and transient acoustic analyses. (See the ANSYS Structural Analysis Guide for more inform-ation on these types of analyses.)

The procedure for a harmonic acoustic analysis consists of three main steps:

• Build the model.

• Apply boundary conditions and loads and obtain the solution.

• Review the results.

15.3. Building the Model

In this step, you specify the jobname and analysis title and then use the PREP7 preprocessor to define the elementtypes, element real constants, material properties, and the model geometry. These tasks, common to most analyses,are described in the ANSYS Basic Analysis Guide.


15.3.1. Harmonic Acoustic Analysis Guidelines

For a harmonic acoustic analysis, consider the following points:

Element Types - Four ANSYS element types are specifically designed for acoustic analyses: FLUID29 and FLUID30are used to model the fluid portion of 2-D and 3-D models respectively. FLUID129 and FLUID130, companionelements to FLUID29 and FLUID30, are used to model an infinite envelope around the FLUID29 and FLUID30elements. Use these element types to model the fluid portion, and then use a corresponding structural element(PLANE42, SOLID45, etc.) for the solid. Only FLUID29 and FLUID30 elements can be in contact with structuralelements (either on the inside or outside of the structure); FLUID129 and FLUID130 can contact only the FLUID29and FLUID30 elements, and not the structural elements directly.

15.3.1.1. FLUID29 and FLUID30

For acoustic elements that are in contact with the solid, be sure to use KEYOPT(2) = 0, the default setting that allowsfor fluid-structure interaction. This results in unsymmetric element matrices with UX, UY, UZ, and PRES as thedegrees of freedom. For all other acoustic elements, set KEYOPT(2) = 1, which results in symmetric elementmatrices with the PRES degree of freedom. (See Figure 15.1: “Example of a 2-D Acoustic Model (Fluid Within aStructure)”.) Symmetric matrices require much less storage and computer time, so use them wherever possible.For more information on fluid-structure interaction, see the ANSYS, Inc. Theory Reference.

Figure 15.1 Example of a 2-D Acoustic Model (Fluid Within a Structure)

15.3.1.2. FLUID129 and FLUID130

These infinite acoustic elements absorb the pressure waves, simulating the outgoing effects of a domain thatextends to infinity beyond the FLUID29 and FLUID30 elements. FLUID129 and FLUID130 provide a second-orderabsorbing boundary condition so that an outgoing pressure wave reaching the boundary of the model is absorbedwith minimal reflections back into the fluid domain.

FLUID129 is used to model the boundary of 2-D fluid regions and as such is a line element. FLUID130 is used tomodel the boundary of 3-D fluid regions and as such is a plane surface element.

Material Properties - The acoustic elements require density (DENS) and speed of sound (SONC) as material prop-erties (FLUID129 and FLUID130 require only SONC). If sound absorption at the fluid-structure interface exists,use the label MU to specify boundary admittance β (absorption coefficient). Values of β are usually determinedfrom experimental measurements. For the structural elements, specify the Young's modulus (EX), density (DENS),and Poisson's ratio (PRXY or NUXY).

Real Constants - When using FLUID129 and FLUID130, the boundary of the underlying finite element mesh mustbe circular (2-D and axisymmetric) or spherical (3-D), and the radius of the circular or spherical boundary of the



finite domain must be specified as real constant RAD. (See Figure 15.2: “Example of Absorption Element Applic-ation”.) The center of the circle or sphere is also specified using real constants:

R,3,RAD,X0,Y0!REAL set 3 for FLUID129R,3,RAD,X0,Y0,Z0!REAL set 3 for FLUID130

If the coordinates (X0, Y0) for the 2-D and axisymmetric cases or (X0, Y0, Z0) for the 3-D case of the center of thecircle or sphere are not specified via real constants, ANSYS assumes the center to be the origin of the global co-ordinate system.

Figure 15.2 Example of Absorption Element Application

Figure 15.3 Submerged Cylindrical Shell

Section 15.3: Building the Model


15.4. Meshing the Model

A typical meshing procedure using the 2-D infinite acoustic elements follows. The procedure is the same with3-D elements. If you have a structural component as well, the structural elements must lie next to the FLUID29elements, and cannot lie next to the infinite fluid elements (FLUID129).

This process automatically adds the FLUID129 elements on the boundary of the finite domain. Here an annularstructural ring is meshed with PLANE42 structural elements. The layer of fluid elements in touch with PLANE42elements is modeled using FLUID29 with UX and UY DOFs and with the fluid-structure interface turned on. Theouter layers of fluid are modeled using FLUID29 without the UX and UY DOFs. The radius for placing FLUID129is 0.31242 (see Section 15.4.2: Step 2: Generate the Infinite Acoustic Elements) with X0 = Y0 = 0. You define theFLUID129 elements using:

Command(s): ESURFGUI: Main Menu> Preprocessor> Modeling> Create> Elements> Inf Acoustic

15.4.1. Step 1: Mesh the Interior Fluid Domain

Mesh the interior fluid domain that is bounded by a circular or spherical boundary (PLANE42) with FLUID29elements.

Figure 15.4 Mesh the Fluid Domain

15.4.2. Step 2: Generate the Infinite Acoustic Elements

Follow these steps:

1. Select the nodes on the circular or spherical boundary.Command(s): NSELGUI: Utility Menu> Select> Entities



2. Specify FLUID129 as the infinite fluid element type associated with the FLUID29 element.Command(s): TYPE, REALGUI: Main Menu> Preprocessor> Meshing> Mesh Attributes> Default AttribsMain Menu> Preprocessor> Real Constants> Add/Edit/Delete

The infinite elements perform well for low as well as high frequency excitations. Numerical experimentshave determined that the placement of the absorbing elements at a distance of approximately 0.2 λbeyond the region occupied by the structure or source of vibration can produce accurate solutions.Here λ = c/f is the dominant wavelength of the pressure waves. c is the speed of sound (SONC) in thefluid and f is the dominant frequency of the pressure wave. For example, in the case of a submergedcircular or spherical shell of diameter D, the radius of the enclosing boundary, RAD, should be at least(D/2) + 0.2 λ. Also, for acoustic analysis in general, the mesh must be fine enough to resolve the smallestdominant frequency.

3. Generate the absorption elements (FLUID129) on the boundary.Command(s): ESURFGUI: Main Menu> Preprocessor> Modeling> Create> Elements> Inf Acoustic

Figure 15.5 Add the Absorption Element on the Boundary

15.4.3. Step 3: Specify the Fluid-Structure Interface

Specify the fluid-structure interface:

1. Select all nodes on the interface.Command(s): NSELGUI: Utility Menu> Select Entities

2. Select the fluid elements attached to this set of nodes.Command(s): ESELGUI: Utility Menu> Select> Entities

3. Specify the selected nodes as fluid-structure interface nodes.Command(s): SF

Section 15.4: Meshing the Model


GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid-Struct Intr> On Nodes

Note — Be sure to reselect all nodes before solving your analysis.

Figure 15.6 Specify Fluid-Structure Interface

15.5. Applying Loads and Obtaining the Solution

In this step, you define the analysis type and options, apply loads, specify load step options, and initiate the finiteelement solution. The next few sections explain how to do these tasks.

15.5.1. Step 1: Enter the SOLUTION Processor

Enter the SOLUTION processor by choosing GUI path Main Menu> Solution or by executing the /SOLU command.

15.5.2. Step 2: Define the Analysis Type

Using either the GUI or a set of commands, define the analysis type and analysis options.

To define the analysis type, use one of the following:Command(s): ANTYPE,HARMICGUI: Main Menu> Solution> Analysis Type> New Analysis

You must choose New Analysis because restarts are not valid in a harmonic response analysis. If you need toapply additional harmonic loads, do a new analysis each time (or use the "partial solution" procedure describedin the ANSYS Basic Analysis Guide).

15.5.3. Step 3: Define Analysis Options

To specify the solution method, use one of the following:



Command(s): HROPTGUI: Main Menu> Solution> Analysis Options

Although full, reduced, or mode superposition methods are options, choose the full method because it alonecan handle unsymmetric matrices.

To define the solution listing format, use one of the following:Command(s): HROUTGUI: Main Menu> Solution> Analysis Options

This option determines how ANSYS lists the harmonic degree-of-freedom solution in the printed output (Job-name.OUT).

To specify the equation solver to be used, use one of the following:Command(s): EQSLVGUI: Main Menu> Solution> Analysis Options

You can choose the frontal solver (default), the sparse direct solver (SPARSE), the Jacobi Conjugate Gradient(JCG) solver, or the Incomplete Cholesky Conjugate Gradient (ICCG) solver. The JCG solver is recommended formost models.

15.5.4. Step 4: Apply Loads on the Model

A harmonic analysis, by definition, assumes that any applied load varies harmonically (sinusoidally) with time.To completely specify a harmonic load in an acoustic analysis, two pieces of information are usually required:the amplitude and the forcing frequency. The amplitude is the maximum value of the load, which you specify usingthe commands shown in Table 15.2: “Commands for Applying Loads in Acoustic Analysis”. The forcing frequencyis the frequency of the harmonic load (in cycles/time). You specify it later as a load step option with the HARFRQcommand (Main Menu> Solution> Time/Frequenc> Freq & Substeps). Section 15.5.5: Step 5: Specify LoadStep Options describes this task.

Table 15.1: “Loads Applicable in an Acoustic Analysis” shows all possible loads for a harmonic acoustic analysisand the commands to define, list, and delete them. Notice that except for inertia loads, you can define loadseither on the solid model (keypoints, lines, and areas) or on the finite element model (nodes and elements). Fora general discussion of solid-model loads versus finite-element loads, see Chapter 2, “Loading” and Chapter 3,“Solution” in the ANSYS Basic Analysis Guide.

Table 15.1 Loads Applicable in an Acoustic Analysis

GUI PathCmd FamilyCategoryLoad Type

Main Menu> Preprocessor> Define Loads>Apply> Structural> Displacement or PotentialMain Menu> Solution> Define Loads> Apply>Structural> Displacement

DConstraintsDisplacement(UX,UY,UZ),

Pressure (PRES)

Main Menu> Preprocessor> Define Loads>Apply> Force/MomentMain Menu> Solution> Define Loads> Apply>Force/Moment

FForcesForce (FX,FX,FZ),

Moment(MX,MY,MZ),

Flow loading

Section 15.5: Applying Loads and Obtaining the Solution


GUI PathCmd FamilyCategoryLoad Type

Main Menu> Preprocessor> Define Loads>Apply> load typeMain Menu> Solution> Define Loads> Apply>load type

SFSurface LoadsPressure (PRES)

Impedance (IMPD)

Fluid-structure inter-action flag (FSI)

Main Menu> Preprocessor> Define Loads>Apply> load typeMain Menu> Solution> Define Loads> Apply>load type

ACEL, OMEGA,DOMEGA, CG-LOC, CGOMGA,DCGOMG, IRLF

Inertia LoadsGravity, Spinning,etc.

In an analysis, you can apply, remove, operate on, or list loads.

15.5.4.1. Applying Loads Using the GUI

You access all loading operations except List (see below) through a series of cascading menus. From the Solutionmenu, you choose the operation (apply, etc.), then the load type (displacement, force, etc.), and then the object(keypoint, etc.) to which you are applying the load.

For example, to apply a displacement load to a line, follow this GUI path: Main Menu> Solution> Define Loads>Apply> Displacement> On Lines

To list loads, use this GUI path: Utility Menu> List> Loads> load type

15.5.4.2. Applying Loads Using Commands

Table 15.2: “Commands for Applying Loads in Acoustic Analysis” lists all the commands you can use to applyloads in an acoustic analysis.

Table 15.2 Commands for Applying Loads in Acoustic Analysis

Apply SettingsOperateListDeleteApplyEntitySolidModel or

FE

Load Type

-DTRANDKLISTDKDELEDKKeypointsSolidModel

Displace-ment, Pres-sure -DTRANDLLISTDLDELEDLLinesSolid

Model

-DTRANDALISTDADELEDAAreasSolidModel

DCUMDSCALEDLISTDDELEDNodesFiniteElem

-FTRANFKLISTFKDELEFKKeypointsSolidModel

Force, Mo-ment

FCUMFSCALEFLISTFDELEFNodesFiniteElem

SFGRADSFTRANSFLLISTSFLDELESFLLinesSolidModel

Pressure,Impedance,Fluid- Struc-ture Interac-tion Flag

SFGRADSFTRANSFALISTSFADELESFAAreasSolidModel



SFCUM , SFGRADSFSCALESFLISTSFDELESFNodesFiniteElem

SFBEAM, SFCUM,SFFUN, SFGRAD

SFSCALESFELISTSFEDELESFEElementsFiniteElem

Apply SettingsOperateListDeleteApplyEntitySolidModel or

FE

Load Type

----ACEL, CGLOC,CGOMGA,DCGOMG,OMEGA, DO-MEGA, IRLF

--Inertia

15.5.4.3. Load Types

Displacements (UX, UY, UZ) and pressures (PRES)

These are DOF (degree-of-freedom) constraints. For example, you specify zero displacements at a rigid fluid-structure interface. You may also specify nonzero displacements, but remember that they are assumed to beharmonic. You usually specify zero pressures at free fluid boundaries (where the fluid is not enclosed, such as atan opening).

Forces (FX, FY, FZ) and moments (MX, MY, MZ)

Usually, you specify these loads on the solid portion of the model to "excite" the fluid.

Flow Load

This is a mass flow rate per unit time (for example, kg/sec/sec in SI units). It represents a pulsating mass flow rateat a node. Specify it using the FLOW force label:

Command(s): F,,FLOWGUI: Main Menu> Solution> Define Loads> Apply> Structural> Force/Moment> On Nodes

Pressure (PRES)

You can specify surface loads on the solid portion instead of forces and moments.

Impedance (IMPD)

These are not really loads but indicate surfaces that absorb sound. Specify the degree of sound absorption asthe material property MU (boundary admittance or absorption coefficient).

Fluid-structure interaction flag (FSI)

This denotes an interface surface between the fluid and structure part of the model.

For problems with fluid-structure interaction on both sides of a structure (e.g., a submerged plate), mesh thestructure with solid elements to provide two distinct fluid-interaction surfaces. For problems with fluid-structureinteraction on only one side of a structure, mesh the structure with shell or solid elements.

15.5.5. Step 5: Specify Load Step Options

You have the following options for a harmonic acoustic analysis:

Section 15.5: Applying Loads and Obtaining the Solution


Table 15.3 Load Step Options for a Harmonic Acoustic Analysis

GUI PathCom-mand

Option

Dynamics Options

Main Menu> Solution> Load Step Opts> Time/Frequenc> Freq& Substeps

HARFRQForcing frequency range

General Options


NSUBSTNumber of harmonic solu-tions


KBCStepped or ramped loads

Output Controls

Main Menu> Solution> Output Ctrls> Solu PrintoutOUTPRControl of printed output

Main Menu> Solution> Output Ctrls> DB/Results FileOUTRESDatabase and results fileoutput

Main Menu> Solution> Output Ctrls> Integration PtERESXExtrapolation of results

15.5.5.1. Dynamics Options

The only valid option in this category is the forcing frequency range, which must be defined (in cycles/time) fora harmonic analysis. Within this range, you then specify the number of solutions to be calculated. (See "GeneralOptions.")

15.5.5.2. General Options

You can request any number of harmonic solutions (via the NSUBST command or its equivalent GUI path) to becalculated. The solutions (or substeps) will be evenly spaced within the previously specified frequency range.For example, if you specify 10 solutions in the range 30 to 40 Hz, the program will calculate the response at 31,32, 33, ..., 39, and 40 Hz. No response is calculated at the lower end of the frequency range.

The loads may be stepped or ramped (via KBC or its GUI counterpart). By default, they are ramped; that is, theload value increases gradually with each substep. By stepping the loads, you maintain the same load value forall substeps in the frequency range.

15.5.5.3. Output Controls

Use OUTPR or its GUI equivalent if you want to include any results data on the printed output file (Jobname.OUT).OUTRES and its GUI counterpart control the data on the results file (Jobname.RST). ERESX and its GUI path allowyou to review element integration point results by copying them to the nodes instead of extrapolating them(default).

Note — By default, the program writes only the last substep of each load step to the results file. If youwant all substeps (the solution at all frequencies) on the results file, be sure to set the FREQ field onOUTRES to ALL (or 1).

15.5.6. Step 6: Back Up Your Database

Save a backup copy of the database on a named file using Utility Menu> File> Save as or the SAVE command.Doing so enables you to retrieve your model should your computer abort during the solution. (To retrieve amodel, reenter ANSYS and then issue the RESUME command or choose Utility Menu> File> Resume.)



15.5.7. Step 7: Apply Additional Load Steps (Optional)

If you wish to apply additional load steps, repeat steps 5 and 6.

15.5.8. Step 8: Finish the Solution

Solve the analysis and then finish.Command(s): SOLVEGUI: Main Menu> Solution> Solve> Current LSCommand(s): FINISHGUI: Main Menu> Finish

15.6. Reviewing Results

The ANSYS program writes results from a harmonic acoustic analysis to the structural results file, Jobname.RST.Results consist of the following data, all of which vary harmonically at each forcing frequency for which thesolution was calculated:

• Primary data

– Nodal pressures

– Nodal displacements

• Derived data

– Nodal and element pressure gradients

– Nodal and element stresses

– Element forces

– Nodal reaction forces

You can review this information using POST1 or POST26.

15.7. Fluid-Structure Interaction

The interaction of the fluid and the structure at a mesh interface causes the acoustic pressure to exert a forceapplied to the structure and the structural motions produce an effective "fluid load." The governing finite elementmatrix equations then become:

[ ] [ ] [ ]

[ ] [ ] [ ]

M U K U F R P

M P K P F R

s s s

f f f oT

&&

&&+ = +

+ = −ρ &&U

[R] is a "coupling" matrix that represents the effective surface area associated with each node on the fluid-structure interface (FSI). The coupling matrix [R] also takes into account the direction of the normal vector definedfor each pair of coincident fluid and structural element faces that comprises the interface surface. The positivedirection of the normal vector, as the ANSYS program uses it, is defined to be outward from the fluid mesh andin towards the structure. Both the structural and fluid load quantities that are produced at the fluid-structureinterface are functions of unknown nodal degrees of freedom. Placing these unknown "load" quantities on theleft hand side of the equations and combining the two equations into a single equation produces the following:

Section 15.7: Fluid-Structure Interaction


M O

R M

U

P

K R

O K

U

P

F

Fs

oT

f

s

f

s

fρ

+−

=

&&&&

Equation 3 implies that nodes on a fluid-structure interface have both displacement and pressure degrees offreedom.

15.8. Sample Applications

The two example problems presented here illustrate the application of the acoustic elements. The first exampleshows the use of the acoustic absorption elements in modeling far-field problems. The second example is a near-field problem showing the use of standing wave prediction in an enclosed space.

15.9. Example 1: Fluid-Structure Coupled Acoustic Analysis (CommandMethod)

In this problem you will determine the first flexural mode (egg mode) frequency of an annular ring submergedin water which extends to infinity. You will perform a harmonic analysis using a frequency sweep between 34and 38 Hz. The distance from the center of the ring to the infinite elements will at least be equal to (D/2) + 0.2λwhere D is the outer diameter of the ring and λ = c/f is the dominant wavelength of the pressure waves. Using0.26035 for the outer radius of the ring, 1460 for the speed of sound (c), and 36 for the estimated dominant fre-quency (f), gives (D/2) + 0.2λ = 0.26035 + (0.2)(1460)/36 = 8.37146. However, this is much greater than the distancerequired when using the acoustic infinite element and a distance of 2 times the outer radius of the ring will beused ( 2 x .26035 = .5207), as shown in the command listing.

/BATCH,LIST/VERIFY,EV129-1S/PREP7/TITLE,AMA,EV129-1S,FLUID129,HARMONIC ANALYSISET,1,PLANE42 ! structural elementET,2,FLUID29 ! acoustic fluid element with ux & uyet,3,129 ! acoustic infinite line elementr,3,0.5207,0,0ET,4,FLUID29,,1,0 ! acoustic fluid element without ux & uy! material propertiesMP,EX,1,2.068e11MP,DENS,1,7929MP,NUXY,1,0MP,DENS,2,1030MP,SONC,2,1460! create inner and outer quarter circlesCYL4,0,0,0.254,0,0.26035,90 CYL4,0,0,0.26035,0,0.5207,90! select, assign attribute to and mesh area 1ASEL,S,AREA,,1AATT,1,1,1,0LESIZE,1,,,16,1LESIZE,3,,,16,1LESIZE,2,,,1,1LESIZE,4,,,1,1MSHKEY,1MSHAPE,0,2D ! mapped quad meshAMESH,1! select, assign attribute to and mesh area 2ASEL,S,AREA,,2AATT,2,1,2,0LESIZE,5,,,16,1LESIZE,7,,,16,1LESIZE,6,,,5LESIZE,8,,,5MSHKEY,0MSHAPE,0,2D ! mapped quad meshAMESH,2



! reflect quarter circle into semicircle about x-axisnsym,x,1000,all ! offset node number by 1000esym,,1000,all! reflect semicircle into full circle about y-axisnsym,y,2000,all ! offset node number by 2000esym,,2000,allNUMMRG,ALL ! merge all quantities! modify outer 2 layers of el29 into type 4esel,s,type,,1nsle,sesln,s,0nsle,sesel,invensle,semodif,all,type,4esel,allnsel,all! define el129 line elementcsys,1nsel,s,loc,x,0.5207type,3real,3mat,2esurfesel,allnsel,all! flag interface as fluid-structure interfacensel,s,loc,x,0.26035esel,s,type,,2sf,all,fsi,1nsel,allesel,allFINISH! enter solution module/SOLUANTYPE,harmic ! select harmonic analysishropt,fullf,19,fx,1000.f,1019,fx,-1000.harfrq,34.,38.nsubst,100kbc,1SOLVEFINISH! postprocess/post26plcplx,0nsol,2,1,u,x,d1uxstoreconjug,3,2prod,4,2,3sqrt,5,4*get,uxmx,vari,5,extrem,tmax/COM -------------------------------------------------------------/COM Expected Result:/COM/COM The following "uxmx" should equal 35.24 Hz./COM -------------------------------------------------------------*status,uxmxfinish

15.10. Example 2: Room Acoustic Analysis (Command Method)

This sample problem demonstrates the use of FLUID30 to predict the acoustic standing wave pattern of a typicalenclosure representing a room. A sound-absorption material is located at the bottom surface of the enclosureand a vibrating structure with a cylindrical surface is located at the top right hand corner of the enclosure. Thisproblem will determine the acoustic pressure wave pattern when the structure vibrates at an excitation frequencyof 80 HZ.

Section 15.10: Example 2: Room Acoustic Analysis (Command Method)


/batch,list/com, Harmonic Analysis - Room Acoustics

/PREP7/TITLE,Room Acoustic AnalysisANTYPE,HARMET,1,30 ! Acoustic elements in contact with walls and vibrating surfaceET,2,30,,1 ! Acoustic elements in interior (not in contact with walls)

! Set parameters for mesh generation

XDIV=29 ! Number of divisions along x-axisYDIV=19 ! Number of divisions along y-axisZDIV=1 ! Number of divisions along z-axisCDIV=2 ! Number of divisions along radius

! Dimensions of the room

LEN=27HGT=20RAD=0.9

! Mesh generation

K,1K,2,LENK,3,LEN,HGTK,4,,HGTK,5,,,-1K,6,LEN,,-1K,7,LEN,HGT,-1K,8,,HGT,-1L,1,5,1L,2,6,1L,3,7,1L,4,8,1CIRC,3,RAD,7,2,90,2ADRAG,5,6,,,,, 3PIO4=ATAN(1)LENC=COS(PIO4)LENC=LENC*RADHGTC=HGT-LENCLENC=LEN-LENCK,15,,HGTCK,16,,HGTC,-1K,17,LENCK,18,LENC,,-1L,1 ,17,XDIVL,10,15,XDIVL,11,4 ,XDIVL,17,10,YDIVL,15, 1,YDIVL,2 ,9 ,YDIVL,5 ,18,XDIVL,13,16,XDIVL,14,8 ,XDIVL,18,13,YDIVL,16,5 ,YDIVL,6 ,12,YDIVESIZE,,CDIVV,1 ,17,10,15, 5,18,13,16V,15,10,11,4 ,16,13,14,8V,17,2 ,9 ,10,18,6 ,12,13VMESH,ALL

! Material properties

MP,DENS,1,2.35E-3 ! (Rho) density of air (lb/ft**3)MP,SONC,1,1100.0 ! (C) speed of sound in air (ft/sec)MP,MU,1,0.04 ! (Beta) absorption coefficient of the walls ! ('Beta' should be between 0 - 1)MP,DENS,2,2.35E-3



MP,SONC,2,1100.0MP,MU,2,0.70 ! (Beta) absorption coefficient of ! the absorbing material on the floor ! ('Beta' should be between 0 -1)MP,DENS,3,2.35E-3MP,SONC,3,1100.0MP,MU,3,0.0 ! (Beta) zero absorption coefficient for interior elementsNSEL,S,LOC,Y,0.0NSEL,R,LOC,X,12,15ESLNMAT,2EMODIF,ALL ! Elements which have the absorbing material on the floor

! Boundary conditions

ALLSNSEL,S,LOC,X,0.0NSEL,A,LOC,Y,0.0NSEL,A,LOC,X,LENNSEL,A,LOC,Y,HGTD,ALL,UX,,,,,UY,UZ! Constrain all displacements to zero at the wallsLOCAL,11,1,27,20NSEL,A,LOC,X,RADESLNESEL,INVETYPE,2MAT,3EMODIF,ALL ! Interior elements are specified as Type=2 & material=3ALLS

! Fluid-Structure Interface (FSI)

NSEL,S,LOC,X,RAD ! Select interface (FSI) surface nodesESLN ! Select elements attached to interface surfaceSF,ALL,FSI ! Specify vibrating surface as Fluid-structure interfaceNROTAT,ALLD,ALL,UX,.01 ! Radial vibration amplitude of Vibrating surfaceD,ALL,UY,,,,,UZ

! Impedance Surface (IMPD)

CSYS,0ALLSNSEL,S,LOC,X,0.0NSEL,A,LOC,X,LENNSEL,A,LOC,Y,0.0NSEL,A,LOC,Y,HGTSF,ALL,IMPD,1 ! Specify the walls as Impedance Surface flag ! to activate absorptionALLSFINISH/SOLU

! Excitation Frequency for Harmonic Analysis

HARF,80,80 ! Frequency of excitation = 80 HzSOLVEFINISH

! Plot the Standing Wave Pattern (f = 80 Hz)

/POST1/SHOW,ENCL1,GRPH,1SET,1,1 ! plot the real part of pressure responseEPLOT/EDGE,1/TITLE,-ROOM ACOUSTICS- * REAL PART OF PRESSUREPLNS,PRESSET,1,1,,1 ! plot the imag. part of pressure response/TITLE,-ROOM ACOUSTICS- * IMAG. PART OF PRESSUREPLNS,PRESFINISH

Section 15.10: Example 2: Room Acoustic Analysis (Command Method)


15–16

Part III. Thin Film

Chapter 16: Thin Film AnalysisA thin film is a small gap of fluid between moving surfaces. This thin layer of fluid can alter the structural responseof the structure by adding stiffness and/or damping to the system. Movement normal to the gap produces asqueeze film effect. Movement tangential to the gap produces a slide film effect.

Thin film effects are important in macrostructures, but they are particularly critical in microstructures where thedamping and stiffening effects of thin layers of air can significantly affect the behavior of devices used in micro-electromechanical systems (MEMS). Squeeze film effects are important in devices such as accelerometers andmicromirrors. Slide film effects are important in devices such as comb drives.

One method for assessing the effect of thin films is to use thin film fluid elements based on the Reynolds number(which is known from lubrication technology and rarified gas physics) to calculate the stiffening and dampingeffects. These effects can then be added to the overall system model. Separate element types are used to assesssqueeze and slide film effects.

The governing Reynolds equation limits the application of thin film analyses to structures with lateral dimensionsmuch greater than the gap separation. In addition, the pressure change across the gap must be much smallerthan the ambient (i.e., surrounding) pressure, and any viscous heating effects must be ignored. If these threeconditions are not satisfied, then the effects of the thin film cannot be assessed using thin film elements. Forthose situations, the Navier Stokes equations must be solved using FLOTRAN to assess the effect of the fluid.

16.1. Elements for Modeling Thin Films

The ANSYS program has three elements for modeling thin film effects. FLUID136 and FLUID138 are used tomodel squeeze film effects. FLUID139 is used to model slide film effects.

Table 16.1 Thin Film Fluid Elements

DOFShape or CharacteristicDimens.Element

PRESQuadrilateral, 4 or 8-node3-DFLUID136

PRESLine, 2-node3-DFLUID138

UX or UY or UZLine, 2-node1-DFLUID139

16.2. Squeeze Film Analysis

Squeeze film analysis simulates the effects of fluid in small gaps between fixed surfaces and structures movingperpendicular to the surfaces. Depending on the operating frequencies, the fluid can add stiffening and/ordamping to the system. At low frequencies, the fluid can escape before it compresses. Therefore, the fluid onlyadds damping to the system. At high frequencies, the fluid compresses before it can escape. Therefore, the fluidadds both stiffening and damping to the system.

A static analysis is used to determine the damping effects at low frequencies. A harmonic analysis is used to de-termine the stiffening and damping effects at high frequencies.

The FLUID136 element is used to model the fluid domain between a fixed surface and a structure moving normallyto that surface. The fluid domain is modeled by overlaying FLUID136 elements on the moving surface of thestructure (i.e., lower surface of the structure adjacent to the fixed wall).


Figure 16.1 Moving Plate above a Fixed Wall

The FLUID138 element is used to model the pressure drop through holes in a moving structure. Microstructuresare commonly perforated to reduce the damping effects of the fluid layer. FLUID138 elements are used in con-junction with FLUID136 elements to obtain a consistent pressure distribution, including the effects of holes.

Figure 16.2 Perforated Plate Structure

A squeeze film analysis can be performed on structures with known velocities or unknown velocities. If the velocityprofile is known, you can apply it directly to the fluid elements. If the velocity profile is not known (or is toocomplicated), it can be determined from the mode-frequency response of the structure (model projectionmethod). This section deals with directly applying the velocities. Section 16.3: Modal Projection Method forSqueeze Film Analysis covers the modal projection method.

16.2.1. Static Analysis Overview

Use a static analysis to calculate the pressure distribution for low operating frequencies, where the compressionof the fluid (and thus the stiffening effect) is negligible. The resulting pressure distribution can then be used toextract a damping coefficient that reflects the damping effect of the fluid.

CFvz

=


Chapter 16: Thin Film Analysis

F is the total pressure force at the fluid structure interface and vz is the normal velocity component of the moving

structure. A typical pressure distribution on a rectangular plate is shown in Figure 16.3: “Pressure Distributionon a Plate at a Low Driving Frequency”.

Figure 16.3 Pressure Distribution on a Plate at a Low Driving Frequency

16.2.2. Harmonic Response Analysis Overview

Use a harmonic analysis to calculate the complex pressure distribution for high operating frequencies. Thecomplex pressure distribution can be used to extract a damping coefficient and a stiffness coefficient. The phaseshift between the pressure and the velocity is caused by compression of the fluid. The real pressure componentcontributes to the damping of the system. The imaginary pressure component contributes to the stiffening ofthe system.

CFv

KF

vz z= =

Re Imω

FRe is the real component of the pressure force. FIm is the imaginary component of the pressure force. Omega(ω) is the frequency (rad/sec). The damping and stiffness coefficients are frequency-dependent. Figure 16.4: “Damp-ing and Squeeze Stiffness Coefficients vs. Frequency” illustrates the frequency dependency for a typical microsys-tem application.

Figure 16.4 Damping and Squeeze Stiffness Coefficients vs. Frequency

The DMPEXT command is used to extract frequency-dependent damping parameters for use with the MDAMP,DMPRAT, ALPHAD, and BETAD command inputs.

Section 16.2: Squeeze Film Analysis


16.2.3. Flow Regime Considerations

The Reynolds squeeze film approach assumes a continuous fluid flow regime. To ensure a continuous flow regime,the characteristic length (i.e., gap thickness) must be more than one hundred times larger than the mean freepath of the fluid particles.

L pL P

pm( )00 0

0=

Lm(po) is the mean free path of the fluid at the operating pressure P0, and L0 is the mean path at reference pressure

P0. If the fluid is air at atmospheric pressure (1.01325*105), then by definition L0 is approximately 64*10-9 meters

(64 µm). So, for continuum theory to be directly applicable (without modification) to air at atmospheric pressure,

the gap should be greater than 6.4 µm (64*10-9 meters * 100).

The applicability of the continuum theory is generally assessed using the Knudsen number, which is equal tothe mean free fluid path divided by the gap. For continuum theory to be valid, the Knudsen number should beless than 0.01.

KnLd

L Pp d

m= = 0 0

0

For high Knudsen numbers, the continuum theory is not valid. However, the dynamic viscosity can be adjustedto simulate the high Knudsen number flow regime. The default flow regime for FLUID136 and FLUID138 is con-tinuum theory (KEYOPT(1) = 0). Set KEYOPT (1) = 1 to specify the high Knudsen number flow regime.

The type of reflection of the gas molecules at the wall interface is specified using accommodation factors. Squeezefilm models assume diffuse reflection of the gas molecules at the wall interface (accommodation factor = 1). Thisassumption is valid for most metals, but is less accurate for micromachined surfaces, particularly those fabricatedfrom silicon. Materials such as silicon cause specular reflection. Typical accommodation factors for silicon arebetween 0.80 and 0.90.

16.2.4. Modeling and Meshing Considerations

The methods used to model and mesh the fluid domain depend on the squeeze film analysis method. If the ve-locities are directly applied to the fluid elements, the fluid elements can be independent of the structure. If thevelocities are determined from the mode-frequency response of the structure (modal projection method), thefluid elements cannot be independent of the structure.

In the modal projection method, the FLUID136 elements must lie on the surface of the structural mesh. Use theESURF command to overlay FLUID136 elements on the surface of an existing structural mesh. FLUID136 supports4-node and 8-node options, along with degenerative triangles.

The FLUID138 element is used to model the pressure drop in the channels (holes) in a structure as shown inFigure 16.2: “Perforated Plate Structure”. The element supports a circular hole configuration and a rectangularhole configuration (KEYOPT(3)). The element works in conjunction with FLUID136 to correctly compute thepressure distribution on the structure's surface and through the channels. To correctly model the FLUID138element:

1. Use a single FLUID138 element for each hole.

2. Align the FLUID138 element at the center of the hole. The element should extend through the depth ofthe hole and have a length equal to the depth of the hole.



3. Assume the pressure at the center of the hole (flush with the plate surface in the thin film region) is atthe same pressure as the nodes modeled at the periphery of the hole. Couple the nodes of the FLUID136element at the whole periphery with the node of the FLUID138 element as shown in Figure 16.5: “Couplingof Nodes at the Hole Periphery with the Center Node of a FLUID138 Element”.

Figure 16.5 Coupling of Nodes at the Hole Periphery with the Center Node of a FLUID138Element

! #"%$# &(' $ &*)+ ' $ $ " ' &* , #" $

- (& /. &1023 $ $# + 4!56 * 7 ' #&(#0/ $ $ 8& /. &9 : $ $ ' " ' ; & " 0 . ,4

16.2.5. Analysis Settings and Options

A thin film analysis using FLUID136 and FLUID138 is a linear solution for both a static and a harmonic responseanalysis. No special analysis options or load step options are required. See the ANSYS Basic Analysis Guide forgeneral guidelines on solving a static analysis.

For a harmonic response analysis, you must use the full method.

16.2.6. Loads and Solution

The fluid elements support pressure loads at the nodal PRES degrees of freedom and velocity body loads (FLUE)at the node or element as shown in Table 16.2: “Load Options for Thin Film Fluid Elements”. Pressure loads areapplied using the D family of commands. The velocity load is applied using the BF family of commands. For thevelocity load, a positive velocity load will cause a positive pressure. For a harmonic response analysis, a positivevelocity load will cause a positive in-phase pressure load. See Section 2.6.8: Body Loads for details on applyingbody loads.

Note — Velocity body loads (FLUE) are the velocities of the moving wall in a direction normal to the wall.They are not in-plane velocities of the fluid.

Table 16.2 Load Options for Thin Film Fluid Elements

ANSYS LabelTypeLoad

PRESNodal DOFPressure

FLUEBody LoadNormal Velocity

The recommended equation solvers for the fluid elements are the Sparse Direct Solver (SPARSE), the JacobiConjugate Gradient Solver (JCG) and the Incomplete Cholesky Conjugate Gradient Solver (ICCG).



16.2.7. Review Results

Results from a thin film fluid analysis are stored on the Jobname.RST file. The primary result from the fluid ana-lysis is the nodal pressures. For a harmonic response analysis, the pressures are stored as complex values (Realand Imaginary components). Chapter 5, “The General Postprocessor (POST1)” discusses reading results into thedatabase and viewing the nodal degree of freedom (pressure) results.

Each fluid element computes and stores results for the mid-plane fluid velocity (PG) and effective viscosity. Usethe element table to retrieve and view these results.

To compute the damping and squeeze stiffness coefficients from the resulting pressure distribution on the surfaceof a structure, use the element table tools to compute the force on a per-element basis, then sum over all elementsto compute the coefficients. The following command sequence demonstrates how to do this task. This exampleassumes parameters “omega” and “velo” exist (frequency and normal velocity (FLUE loading), respectively).

set,1,1 ! store Real solutionetable,presR,temp ! extract "Real" pressureetable,earea,volu ! extract element areasmult,forR,presR,earea ! compute "Real" forcessum ! sum over all elements*get,Fre,ssum,,item,forR ! get the total "real" forceset,1,1,,1 ! store Imaginary solutionetable,presI,temp ! extract "Imaginary" pressuresmult,forI,presI,earea ! compute "Imaginary" forcessum ! sum over all elements *get,Fim,ssum,,item,forI ! get the total "imaginary" force

K=abs(Fim*omega/velo) ! Compute squeeze stiffness coefficientC=abs(Fre/velo) ! Compute damping coefficient

/com, ** Equivalent squeeze stiffness coefficient ** *stat,K/com, ** Equivalent damping coefficient ** *stat,C

16.2.8. Example Problem

A rectangular beam with perforated holes under transverse motion is modeled to compute the effective dampingand squeeze stiffness coefficients. The thin film surface of the structure is modeled with FLUID136 elements.FLUID138 elements are used to model the hole regions. By altering the boundary condition of the free FLUID138node, we can simulate different pressure boundary conditions of the hole region. The purpose of the analysis isto compute the equivalent squeeze stiffness and damping coefficient for an assumed uniform plate velocity. Aharmonic response analysis is performed at 150 kHz. A previous modal analysis indicated that the pertinent ei-genfrequency was 150 kHz. Since the analysis is linear, the magnitude of the velocity can be arbitrary for com-puting the coefficients.

Three cases were considered:

1. Holes modeled with no resistance (pressure = 0 at hole location, no FLUID138 elements ).

2. Holes modeled with finite resistance (FLUID138 elements modeled, pressure set to zero on fluid nodeat top of plate).

3. Holes modeled with infinite resistance (no pressure specification at hole location, no FLUID138 elements).

Case 1 is typical for large diameter holes compared to the hole depth. Case 3 is typical for very high flow resistance,which happens in the case of narrow and long holes. Case 2 is the most accurate case where the fluid pressuredrop is taken into account by the FLUID138 elements.



Table 16.3: “Beam Model Results Considering Perforated Holes” lists the damping and squeeze coefficient results.Figure 16.6: “Pressure Distribution (Real Component)” and Figure 16.7: “Pressure Distribution (Imaginary Com-ponent)” illustrate the real and imaginary pressure distribution. The input file for case 2 is listed.

Table 16.3 Beam Model Results Considering Perforated Holes

Squeeze stiffness coefficientDamping CoefficientHole optionFrequency (kHz.)

1.2012.016e-5Infinite resistance150

.54651.325e-5Finite resistance150

.46071.165e-5No resistance150

Figure 16.6 Pressure Distribution (Real Component)



Figure 16.7 Pressure Distribution (Imaginary Component)

The input file for this example is shown below for the finite-resistance Case 2

/batch,list/PREP7/title, Damping and Squeeze film stiffness calculations for a rigid /com, plate with holes/com uMKS units

ET, 1,136,1 ! 4-node option, High Knudsen NumberET, 2,138,1 ! Circular hole option, Hugh Knudsen Number

s_l=100 ! Half Plate length (um)s_l1=60 ! Plate hole locations_w=20 ! Plate widths_t=1 ! Plate thicknessc_r=3 ! Hole radiusd_el=2 ! Gappamb=.1 ! ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)velo=2000 ! arbitrary velocity (um/s)freq=150000 ! Frequency (Hz.)pi=3.14159omega=2*pi*freq ! Frequency (rad/sec)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! mean free path (um)Knud=mfp/d_el ! Knudsen number

mp,visc,1,visc ! Dynamic viscosity gapmp,visc,2,visc ! Dynamic viscosity holes

r,1,d_el,,,pamb ! Real constants - gaprmore,pref,mfp

r,2,c_r,,,pamb ! Real constants - holermore,pref,mfp

! Build the model

rectng,-s_l,s_l,-s_w,s_w ! Plate domainpcirc,c_r ! Hole domain



agen,3,2,,,-s_l1/3agen,3,2,,,s_l1/3ASBA, 1, all

TYPE, 1MAT, 1smrtsize,4AMESH, all ! Mesh plate domain

! Begin Hole generation*do,i,1,5 nsel,all *GET, numb, node, , num, max ! Create nodes for link elements N, numb+1,-s_l1+i*s_l1/3,, N, numb+2,-s_l1+i*s_l1/3,, s_t TYPE,2 MAT, 2 REAL,2 NSEL, all E, numb+1, numb+2 ! Define 2-D link element ESEL, s, type,,1 NSLE,s,1 local,11,1,-s_l1+i*s_l1/3 csys,11 NSEL,r, loc, x, c_r ! Select all nodes on the hole circumference NSEL,a, node, ,numb+1 *GET, next, node, , num, min CP, i, pres, numb+1, next nsel,u,node, ,numb+1 nsel,u,node, ,next CP, i, pres,all !Coupled DOF set for constant pressure csys,0 *enddo ! End hole generation

nsel,s,loc,x,-s_lnsel,a,loc,x,s_lnsel,a,loc,y,-s_wnsel,a,loc,y,s_wnsel,r,loc,z,-1e-9,1e-9d,all,pres ! Fix pressure at outer plate boundarynsel,all

esel,s,type,,2nsle,s,1nsel,r,loc,z,s_td,all,pres,0 ! P=0 at top of plate dlist,all

allsel

bfe,all,flue,,velo ! Apply arbitrary velocity fini

finish/soluantyp,harm ! Full Harmonic analysisharfrq,freqsolvefinish/post1esel,s,type,,1set,1,1etable,presR,pres ! extract "Real" pressureetable,earea,volusmult,forR,presR,earea ! compute "Real" forcessum*get,Fre,ssum,,item,forRset,1,1,,1etable,presI,pres ! extract "Imaginary" pressuresmult,forI,presI,earea ! compute "Imaginary" pressure



ssum*get,Fim,ssum,,item,forI

K=abs(Fim*omega/velo) ! Compute equivalent stiffnessC=abs(Fre/velo) ! Compute equivalent damping

/com, ******* Equivalent stiffness *************************stat,K/com, ******* Equivalent damping ***************************stat,Cfinish

16.3. Modal Projection Method for Squeeze Film Analysis

Modal projection techniques provide an efficient method for computing damping parameters for flexible bodies.The Modal Projection Technique is the process of calculating the squeeze stiffness and damping coefficients ofthe fluid using the eigenvectors of the structure. In the modal projection method, the velocity profiles are de-termined from the mode-frequency response of the structure.

16.3.1. Modal Projection Method Overview

For a structure undergoing flexible body dynamics, the displacement and velocity vary along the structure. Fora thin-film fluid adjacent to the structure, there is a true dependency between the structural velocity and thefluid pressure. A modal analysis of a structure provides information on the fundamental eigenfrequencies andmode shapes (eigenvectors). For each mode, i, we can impress the distributed eigenvector values as velocityloads and compute the resulting pressure distribution and hence the fluid force acting on mode j. Therefore, wecan compute a matrix of modal squeeze stiffness coefficients, Kij, and modal damping coefficients, Cij. The diag-

onal terms of these matrices are the coefficients of each mode, the off-diagonal terms represent the "cross-talk"coefficients between modes. Figure 16.8: “Modal Projection Technique for Damping Characterization” illustratesthe modal projection technique.

Figure 16.8 Modal Projection Technique for Damping Characterization



From the modal squeeze and stiffness coefficients for the main diagonal terms (source mode = target mode),other useful damping parameters can be calculated. For example, the modal damping ratio, ξ , and the modalsqueeze to stiffness ratio, kri, can be computed by:

ξ ω ωi ii i i i ii iC m kr K= =/( ) /2 2

Where mi is the modal mass and ωi the eigenfrequency. The damping ratio can be used to compute ALPHAD

and BETAD parameters for Rayleigh damping (see ABEXTRACT command), or to specify constant and modaldamping by means of the DMPRAT or MDAMP commands.

The squeeze to stiffness ratio represents the relative stiffening of the mechanical system due to fluid compressionand resonance shift. If the squeeze-to-stiffness ratio is small (e.g., <.02), then the squeeze stiffness affects thestructural stiffness by less than 2%, which may be negligible. At higher frequencies, the ratio can be much larger,indicating a significant stiffening of the structure.

The stiffness and damping coefficients may be strongly frequency-dependent. Figure 16.9: “Damping and SqueezeStiffness Parameters for a Rectangular Plate” shows a typical frequency dependency of the squeeze and dampingforces on a flat plate, and the resulting stiffness and damping constant. The frequency where the forces intersectis known as the cut-off frequency. Below this frequency, structures may be accurately characterized by a constantdamping coefficient, and stiffness effects can be ignored. Structures which operate far above the cut-off can bedescribed by a constant stiffness coefficient, and damping effects can be ignored.

Figure 16.9 Damping and Squeeze Stiffness Parameters for a Rectangular Plate

16.3.2. Steps in Computing the Damping Parameter Using the Modal ProjectionTechnique

The basic steps in performing the analysis are as follows:

1. Build a structural and thin-film fluid model and mesh.

2. Perform a modal analysis on the structure.

3. Extract the desired mode eigenvectors.

4. Select the desired modes for damping parameter calculations.

5. Perform a harmonic analysis on the thin-film elements.

6. Compute the modal squeeze stiffness and damping parameters.

7. Compute modal damping ratio and squeeze stiffness coefficient.

8. Display the results.

Section 16.3: Modal Projection Method for Squeeze Film Analysis


Steps 4-7 have been automated using the DMPEXT command macro. Step 8 is available through the MDPLOTcommand macro.

16.3.2.1. Modeling and Meshing

Model preparation for the modal projection method for damping parameter extraction follows very closely tothe method outlined in Section 16.2.4: Modeling and Meshing Considerations. Both the structural model andthe thin-film fluid model need to be defined simultaneously. Group the fluid nodes on the structure surface intoa node component named "FLUN". This component should only include nodes attached to FLUID136 elements.This component defines the nodes for which the eigenvector values will be extracted from the mode-frequencyanalysis.

16.3.2.2. Perform Modal Analysis

A modal analysis of the structure is required to obtain the eigenvectors of the desired modes. The modal analysisshould be set up with the following options:

1. Use the Block Lanczos method (MODOPT command).

2. Extract the eigenmodes of interest (MODOPT command).

3. Expand the eigenmodes of interest (MXPAND command).

The expanded eigenmodes will compute the necessary eigenvectors required for the modal projection technique.Note: The thin-film fluid elements may be left active in the model when performing the modal analysis. Theseelements will not contribute to the modal solution.

16.3.2.3. Extracting Eigenvectors

The eigenvectors from the modal analysis must be retrieved and stored in a format appropriate for use by thethin-film fluid elements for a subsequent harmonic fluid analysis. Use the RMFLVEC command in POST1 to retrievethe eigenvectors. The data is stored in the file Jobname.EFL.

16.3.2.4. Performing a Harmonic Response Analysis and Extracting DampingParameters

The command macro DMPEXT performs a harmonic response analysis with the thin-film fluid elements usingthe eigenvector information for the desired mode(s). The macro also extracts damping parameter informationfor use in subsequent dynamic structural analysis. Damping parameters extracted include the modal dampingcoefficient, modal squeeze stiffness coefficient, damping ratio, and the squeeze-to-stiffness ratio.

DMPEXT requires a "source" mode number and a "target" mode number. The source mode is the mode for whichthe eigenvectors are used to impart a velocity field on the fluid elements. The target mode is the mode which isacted on by the pressure solution (fluid forces). For transverse oscillations and a uniform gap, there is little modeinteraction and hence only diagonal terms are required (source mode (i) = target mode (j)). For transverse motionwith nonuniform gaps, or asymmetric plate motion, mode interaction effects (cross-talk) can be significant andshould be computed (source mode .ne. target mode). Typical cross-talk scenarios are shown in Figure 16.10: “Flu-idic Cross-Talk between Transverse and Rotational Motion”.



Figure 16.10 Fluidic Cross-Talk between Transverse and Rotational Motion

Damping parameter extraction can be selected over a desired frequency range or at the eigenfrequencies of thestructure. Damping results are computed and stored in an array parameter.

Computed damping ratios may be used in subsequent dynamic structural analyses. A constant damping ratiocan be applied using DMPRAT for a subsequent harmonic or mode-superposition transient analysis. Modedamping ratios may be applied using the MDAMP command for use in mode-superposition harmonic andtransient analyses. Note: Subsequent structural analysis using these damping parameters do not require thethin-film fluid elements in the model.

The command macro ABEXTRACT (like DMPEXT) extracts alpha and beta damping parameters for use in theALPHAD and BETAD commands. These commands define Rayleigh damping and can be used in time-transientstructural analysis to model damping effects. The damping parameters are computed from two modes definedby the user.

The command macro MDPLOT may be used to display the frequency-dependent damping parameters.

16.3.3. Example Problem Using the Modal Projection Method

A rectangular beam with perforated holes is modeled to compute the effective damping coefficient, stiffnesscoefficient, and damping ratio. The surface of the structure is modeled with FLUID136 elements to represent thethin film. The structure is modeled with SOLID45 elements. This example computes the Rayleigh dampingcoefficients (α and β) and modal damping ratios ξi for use in a transient dynamic analysis.

The problem is defined as an extension to the earlier squeeze film example. After modeling the fluid domain,the structure of the beam is modeled and meshed with SOLID45 elements. A modal analysis is performed onthe structure and the first two eigenvalues and eigenvectors are computed. RMFLVEC is used to extract the ei-genvectors for use in the modal projection method to compute the thin-film damping parameters. The command



macro ABEXTRACT is used to compute the Rayleigh parameters from the lowest two eigenmodes . Modaldamping ratios are also provided by the ABEXTRACT macro for the two eigenmodes.

Table 16.4: “Modal Damping Parameters for First Two Eigenfrequencies” lists the results from the dampingparameter extraction. Computed Rayleigh parameters are: ALPHAD=65212, BETAD=1.829e-8. The input file forthis example is shown below.

Table 16.4 Modal Damping Parameters for First Two Eigenfrequencies

Stiffness RatioDamping RatioModal Squeeze StiffnessCoefficient

Modal Damping Coeffi-cient

Frequency (Hz.)

.2285e-2.9703e-1.2758e96741955294

.3644e-2.4200e-1.3568e1083123157497

The input file for this example is shown below.

/batch,list/PREP7/title, Damping Ratio and Rayleigh Damping Calculations for a Perforated Plate/com uMKS units

ET, 1,136,1 ! 4-node option, High Knudsen NumberET, 2,138,1 ! Circular hole option, Hugh Knudsen Number ET,3,45 ! Structural element

s_l=100 ! Half Plate length (um)s_l1=60 ! Plate hole locations_w=20 ! Plate widths_t=1 ! Plate thicknessc_r=3 ! Hole radiusd_el=2 ! Gappamb=.1 ! ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! mean free path (um)Knud=mfp/d_el ! Knudsen number

mp,visc,1,visc ! Dynamic viscosity gapmp,visc,2,visc ! Dynamic viscosity holesmp,ex,3,79e3 ! Goldmp,dens,3,19300e-18mp,nuxy,3,.1

r,1,d_el,,,pamb ! Real constants - gaprmore,pref,mfp

r,2,c_r,,,pamb ! Real constants - holermore,pref,mfp

! Build the model

rectng,-s_l,s_l,-s_w,s_w ! Plate domainpcirc,c_r ! Hole domainagen,3,2,,,-s_l1/3agen,3,2,,,s_l1/3ASBA, 1, all


! Begin Hole generation*do,i,1,5



nsel,all *GET, numb, node, , num, max ! Create nodes for link elements N, numb+1,-s_l1+i*s_l1/3,, N, numb+2,-s_l1+i*s_l1/3,, s_t TYPE,2 MAT, 2 REAL,2 NSEL, all E, numb+1, numb+2 ! Define 2-D link element ESEL, s, type,,1 NSLE,s,1 local,11,1,-s_l1+i*s_l1/3 csys,11 NSEL,r, loc, x, c_r ! Select all nodes on the hole circumference NSEL,a, node, ,numb+1 *GET, next, node, , num, min CP, i, pres, numb+1, next nsel,u,node, ,numb+1 nsel,u,node, ,next CP, i, pres,all !Coupled DOF set for constant pressure csys,0 *enddo ! End hole generation

esize,,2type,3mat,3real,3vext,all,,,,,s_t ! Extrude structural domain

nsel,s,loc,x,-s_lnsel,a,loc,x,s_lnsel,a,loc,y,-s_wnsel,a,loc,y,s_wnsel,r,loc,z,-1e-9,1e-9d,all,pres ! Fix pressure at outer plate boundarynsel,all

esel,s,type,,2nsle,s,1nsel,r,loc,z,s_td,all,pres,0 ! P=0 at top of plate dlist,all

esel,s,type,,1nsle,s,1nsel,u,cp,,1,5cm,FLUN,nodeallsel

nsel,s,loc,x,-s_lnsel,a,loc,x,s_ld,all,uxd,all,uyd,all,uz

allsel

fini

/soluantype,modal ! Modal analysismodopt,lanb,2 ! Extract lowest two eigenmodeseqslv,sparsemxpand,2 ! Expand lowest two eigenmodessolvefini

/post1RMFLVEC ! Extract eigenvectors



fini

/soluabextract,1,2 ! Extract damping ratios and Rayleigh constantsfinish

A transient dynamic analysis on the switch can be performed using the extracted damping parameters. The fol-lowing input illustrates a coupled electrostatic-structural time-transient solution. The electrostatic field is assumedto be normal to the plate in the gap, and fringing effects are ignored. TRANS126 elements are used to model thecoupled electrostatic-structural interaction with the switch. The EMTGEN command is used to generate thetransducer elements. A step voltage pulse is applied over a short duration (65 micro-seconds) then released.Rayleigh damping parameters, when used, are applied to the global mass (ALPHAD parameter) and stiffness(BETAD parameter) matrices. We want to apply these only to the mass and stiffness matrix of the SOLID45 elements,and not the TRANS126 elements, because doing so may overdamp the system. The TRANS126 elements producea damping matrix and a stiffness matrix only. Hence, we can use the ALPHAD parameter for the global massmatrix since there is no contribution from the TRANS126 elements. To isolate the SOLID45 elements for betadamping, we can apply the beta damping via a material damping option (MP,DAMP). Figure 16.11: “Time-Tran-sient Response from Voltage Pulse” illustrates the displacement of a node near the center of the plate over time.The maximum amplitude of displacement (0.11 microns) is small enough to ignore large deflection dampingeffects.

/batch,list/PREP7/title, Damped Transient Dynamic Response of an RF MEMS switch/com uMKS units/com, Small deflection assumption

et,1,200,6ET,3,45 ! Structural element

s_l=100 ! Plate length (um)s_l1=60 ! Plate hole locations_w=20 ! Plate widths_t=1 ! Plate thicknessc_r=3 ! Hole radiusd_el=2 ! Gappamb=.1 ! ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! mean free path (um)Knud=mfp/d_el ! Knudsen number

mp,ex,3,79e3 ! Goldmp,dens,3,19300e-18mp,nuxy,3,.1mp,damp,1,1.829e-8 ! Material damping (from squeeze film results)! Build the model

rectng,-s_l,s_l,-s_w,s_w ! Plate domainpcirc,c_r ! Hole domainagen,3,2,,,-s_l1/3agen,3,2,,,s_l1/3ASBA, 1, all


esize,,2type,3mat,3real,3vext,all,,,,,s_t ! Extrude structural domain

nsel,s,loc,x,-s_lnsel,a,loc,x,s_l



d,all,uxd,all,uyd,all,uz

allselaclear,allsave

nsel,s,loc,zcm,base,nodesemtgen,'base',,,'uz',-d_el ! generate Transducer elementsallsel,allnsel,s,loc,z,-d_eld,all,uz,0d,all,volt,0cmsel,s,base d,all,volt,10allsel,allfini/soluantyp,transalphad,65211 ! alpha damping computed from Squeeze-film theorykbc,1time,.000065deltime,2.0e-6outres,all,noneoutres,nsol,allsolvetime,.0002cmsel,s,based,all,volt,0allsel,allsolvefinin1=node(0,2,0)/post26nsol,2,n1,uzprvar,2plvar,2finish

Figure 16.11 Time-Transient Response from Voltage Pulse



16.3.4. Damping Extraction for Large Signal Cases

If a structure does not undergo significant deformation, the gap between the structure and the fixed wall maybe assumed to be constant (small signal case). If the structural deformation in the gap is significant, the changein the gap may effect the damping of the structure (large signal case). The gap is defined as a real constant inthe thin-film fluid elements. Use SETFGAP to automatically define and/or update the gap real constants for thethin-film FLUID136 elements. The command can be used to:

• Create real constant table entries for every selected FLUID136 element (large signal case).

• Update an existing real constant table according to structural displacements for every FLUID136 element(large signal case).

This option allows you to check the dependence of the damping parameters over the deflection range of thestructure.

16.4. Slide Film Damping

Slide film damping occurs if two surfaces separated by a thin fluid film move tangentially with respect to eachother, because energy is dissipated due to viscous flow. Typical applications are damping between the fingersof comb drives and horizontally-moving seismic masses.

FLUID139 is used to model slide film damping. FLUID139 can model Couette and Stokes flow (Figure 16.12: “SlideFilm Damping at Low and High Frequencies”). Couette flow assumes a constant velocity gradient across thefluid gap. Tangentially moving surfaces at low frequencies produce a nearly constant velocity gradient in thefluid, so Couette flow is applicable to low frequencies.

Stokes flow assumes that the velocity gradient is not constant across the fluid gap. Tangentially moving surfacesat high frequencies do not produce a constant velocity gradient, so the Stokes flow is applicable to high frequen-cies. The transition from Couette to Stokes flow occurs near the cut-off frequency.

fd

c = ηπρ2 2

where ρ is the fluid density, η the dynamic viscosity and d the gap separation.

Couette flow does not occur at high frequencies, because inertial effects are important and viscous friction isonly able to accelerate a thin fluid layer near the moving surface. The penetration depth is given by

δ ηρ

= 2Ω



Figure 16.12 Slide Film Damping at Low and High Frequencies "!$#% %

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νρ( ) ( )( ) ( )

FLUID139 models the effect of viscous flow in the thin film with a series of mass-damper elements, as shown inFigure 16.13: “Viscous Slide Film Element FLUID139”. Couette flow is modeled using a two-node option. Stokesflow is modeled using a 32-node option. In the 32-node option, the end nodes (node 1 and 32) are connectedto the structural portion of the model with structural degrees of freedom, and the series of mass-damper elementsare contained within "auxiliary" nodes (nodes 2-31).

The gap separation distance (GAP) and the overlap area of the surfaces (AREA) are specified as real constants forFLUID139. If the overlap area changes during the analysis, the area change rate (DADU) must also be specifiedas a real constant. A changing overlap area is typical in lateral comb drives.

A AdAdu

u unew initial n i= + −( )

AREA is the initial overlap area, DADU is the change in the overlap area with respect to the surface displacement,and un and ui are the location of the interface nodes (1 and 32). Note: For a constant surface area, DADU is the

width of the overlap surface.

FLUID139 may be used for a prestress static analysis in conjunction with a prestress harmonic analysis, as wellas a full transient analysis. Prestress analysis is required if the plate area changes due to the structural displacement.A typical command sequence for a prestress harmonic analysis would include the following:

/solu antyp,static pstress,on . . solve fini

Section 16.4: Slide Film Damping


/solu antyp,harmonic pstress,on . . solve finish

KEYOPT(3) specifies the continuous flow options. For a no-slip assumption at the wall, use the continuum theory(KEYOPT(3) = 0). For slip flow where the Knudsen number is much less or much greater than 1.0, use the first orderslip flow condition (KEYOPT(3) = 1). For slip flow with a Knudsen number of approximately 1.0, use the extendedslip flow option (KEYOPT(3) = 2).

Figure 16.13 Viscous Slide Film Element FLUID139

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16.4.1. Slide Film Damping Example

Comb drive resonators are a common application for slide film damping. Figure 16.14: “Comb Drive Resonator”illustrates a typical comb drive assembly consisting of fixed and moving comb drives, springs, and a central mass.



Figure 16.14 Comb Drive Resonator

Details on the comb drive geometry are given in the input file listed below. The electrostatic behavior of themoving comb drives are represented by two TRANS126 transducer elements with prescribed Stroke vs. Capacitancedata obtained from finite element runs. The structural behavior of the crab legs is modeled by a spring element.The inertial effects of the central mass are modeled with a mass element. Damping occurs between the combteeth (lateral dimension), and between the comb teeth and the substrate (vertical dimension). Four FLUID139elements are used to model the lateral and vertical damping (two per comb drive). The cut-off frequency is wellbelow the frequency range for the analysis; therefore, Couette flow is assumed. Since the comb drive effectivesurface area changes with displacement, the DADU real constant is used (equal to the width of the plate area).

A static prestress analysis is run using a DC bias voltage on the input and output fixed comb drives. A harmonicanalysis sweep is then performed using a small AC voltage. The displacement (magnitude and phase angle) ofthe central mass is shown in Figure 16.15: “Displacement of Central Mass”. Figure 16.16: “Real and ImaginaryCurrent” shows the current.

Figure 16.15 Displacement of Central Mass



Figure 16.16 Real and Imaginary Current

/prep7/title Comb drive resonator with FLUID139 Couette damping

! DRIVE COMB! |! | ! CRAB LEG SPRING --- CENTRAL MASS --- CRAB LEG SPRING! |! |! PICK-UP COMB

! Reference:! "Microelectromechanical Filters for Signal Processing",! Lin, L., Howe, R.T., J. Microelectromechanical Systems,! VOL 7, No. 3, Sept 1998

! beam parameters (uMKS units)E = 190e3 !Young modulusd = 2.33e-15 ! densityhb = 2 ! beam thicknesswb = 2 ! beam width Lb = 100 ! beam lengthk = 5.699 ! mechanical stiffness



! comb parametern= 9 ! number of fingernp=n*2 ! number of finger pairsx0= 10 ! initial finger overlapL0= 26 ! finger length (stator comb)L=20 ! finger length (moving comb)gi= L0-x0 ! initial gapw= 4 ! finger widthh= hb ! finger thicknessgp=3 ! finger gap (lateral)g= 3 ! comb gap (vertical)Mr = 1.96563e-11 ! mass

! Lateral gap areaareal=np*h*x0! Vertical gap areaareav=n*w*x0

! Stroke vs. Capacitance data

x1 = 14cx1 = 0.97857e-2x2 = 15cx2 = 0.96669e-2x3 = 16cx3 = 0.95445e-2x4 = 17cx4 = 0.94185e-2x5 = 18cx5 = 0.93384e-2

! Voltage conditions

Vi = 40 ! input dc biasVo = 60 ! output dc biasVac = 10 ! input ac bias

! Damping parmeters

nu=18.3e-12 ! dynamic viscositypo=0.1 ! reference pressuredens=1.17e-18 ! densityfc=nu/(2*3.14159*dens*(g**2)) ! cutoff frequency daduv=w*n ! change in plate area - verticaldadul=h*np ! change in plate area - lateral

! Model

n,1,0n,2,0n,3,0n,4,0

et,1,126,,0,1 !Trans126, UX-Volt DOFr,1,,,gi,,rmore,x1,cx1,x2,cx2,x3,cx3rmore,x4,cx4,x5,cx5

e,1,2e,2,3

et,2,21,,,4 ! Mass elementr,2,Mrtype,2real,2e,2

et,3,14,,1 ! linear spring, UX DOFr,3,ktype,3real,3



e,2,4

! Lateral damperset,4,139 ! Slide-film damper, Couette flow, Continuum theorymp,visc,4,nump,dens,4,densr,4,g,areal,-dadul,potype,4mat,4real,4e,1,2e,2,3

! Vertical dampersr,5,g,areav,-daduv,poreal,5e,1,2e,2,3

d,1,ux,0d,3,ux,0d,4,ux,0d,2,uy,0d,2,volt,0

! Prestress static analysis

/solud,1,volt,Vid,3,volt,Vopstres,onsolvefini

! Harmonic Frequency Sweep

fr0=60000fr1=120000/soluantyp,harmd,1,volt,Vac ! AC voltage component on capacitord,3,volt,0pstres,on ! prestressharfrq,fr0,fr1nsubs,60outres,all,allkbc,1solve

/post26nsol,2,2,u,x,ux2esol,3,2,,nmisc,24,iresol,4,2,,nmisc,25,ii

/axlab,x,Frequency (Hz) ! label of x axisplcplx,0/axlab,y, Displacement (um)plvar,2 ! plot displacement versus time (frequency)plcplx,1/axlab,y, Phase angleplvar,2plcplx,2/axlab,y, Current (pA)plvar,3,4fini



IndexAacceleration, 9–12ACEL command, 4–5, 9–12acoustic analysis, 15–1

load step options, 15–9loads for, 15–7reviewing results from, 15–11

acoustics, 15–1absolute pressure, 15–1absorbing boundary condition, 15–2amplitude, 15–7applications of, 15–1axisymmetric cases, 15–2boundary admittance, 15–2circular or spherical boundary (RAD), 15–2compressible fluid, 15–1coupled acoustic analysis, 15–1coupling matrix, 15–11definition of, 15–1density, 15–2far-field problems, 15–12fluid load, 15–11fluid-structure interaction, 15–1, 15–11fluid-structure interface, 15–5forcing frequency, 15–7harmonic acoustic analysis, 15–2infinite acoustic elements, 15–2inviscid fluid, 15–1mean pressure, 15–1meshing the model, 15–4modal analysis, 15–1outgoing pressure wave, 15–2particle velocity, 15–1pressure changes, 15–1pressure gradient, 15–1sample fluid-structure acoustic analysis (batch),15–12sample room acoustic analysis, 15–13solving acoustics problems, 15–1sound-absorption material, 15–13speed of sound (SONC), 15–2standing wave pattern, 15–13transient acoustic analysis, 15–1uncoupled acoustic analysis, 15–1unsymmetric matrices, 15–6wavelength, 15–4

ADAPT command, 2–2adiabatic boundaries, 4–1advection limit, 5–1

advection term, 14–1ambient radiation, 4–1amplitude, 15–7analysis options

acoustics, 15–6analysis type

acoustics, 15–1angular acceleration vectors, 2–2ANTYPE command, 2–2Arbitrary Lagrangian-Eulerian analysis, 7–1

boundary conditions, 7–3mesh updating, 7–5remeshing, 7–6

arbitrary Lagrangian-Eulerian analysisexample problems, 7–8

artificial viscosity, 2–9, 8–3axis of rotation, 10–2

Bbackward time integration method, 5–1BFCUM command, 2–2BFDELE command, 2–2BFE command, 2–2BFUNIF command, 2–2Bingham viscosity model, 9–3, 9–6, 9–14boundary conditions, 2–5, 8–2

laminar and turbulent flow, 3–11thermal analysis, 4–1transient analysis, 5–3

bulk temperature, 4–3buoyancy, 4–5

CCarreau viscosity model, 9–3, 9–6, 9–14CE command, 2–2CECMOD command, 2–2CEDELE command, 2–2CGLOC command, 10–2CGOMEGA command, 10–2/CLEAR command, 2–2CNVTOL command, 2–2collocated Galerkin approach, 4–7, 14–1compressible flow analysis, 1–2, 2–4, 3–1, 8–1compressible fluid, 15–1conduction limit, 5–1conductivity matrix algorithm, 4–5conjugate heat transfer, 1–2, 4–5convergence, 2–6, 2–8, 2–11, 5–1, 11–2coordinate systems, 2–1, 2–2, 10–1Couette flow, 16–18coupled acoustic analysis, 15–1coupling algorithms, 12–1


CP command, 2–2cross-talk, 16–12

DD command, 3–11, 7–3, 10–4, 13–4DA command, 3–11, 7–3database

backing up, 15–10DELTIM command, 2–2density, 4–1, 9–2DESOL command, 2–2displacements, 15–9distributed resistance, 10–4divergence, 2–14, 8–3DK command, 2–2DL command, 3–11, 7–3DOF capping, 2–9domain file, 2–7drag, 3–16DSYM command, 2–2

Eeffective viscosity, 2–5, 3–2elements, 2–1ERESX command, 2–2example problems

arbitrary Lagrangian-Eulerian analysis, 7–8compressible flow, 8–4incompressible flow, 3–16modal projection method, 16–13multiple species, 13–5slide film, 16–20squeeze film, 16–6thermal analysis, 4–8volume of fluid analysis, 6–5

Ffiles

Jobname.RST, 15–11FLDATA1 command, 3–3, 4–1, 5–1FLDATA10 command, 9–4FLDATA11 command, 9–4FLDATA12 command, 9–9, 9–14FLDATA13 command, 4–5, 9–10FLDATA14 command, 4–3, 8–1, 9–9FLDATA15 command, 9–12FLDATA17 command, 8–1, 9–12FLDATA18 command, 4–5, 11–1FLDATA19 command, 11–1FLDATA2 command, 2–2, 2–6, 2–10FLDATA20 command, 11–2, 11–3FLDATA21 command, 11–2

FLDATA22 command, 11–2FLDATA23 command, 11–2FLDATA24 command, 3–3, 3–11, 3–14, 14–1FLDATA25 command, 2–8, 4–4, 14–1FLDATA26 command, 2–8, 2–9FLDATA29 command, 2–14FLDATA3 command, 2–13FLDATA30 command, 2–10FLDATA31 command, 2–9, 3–14FLDATA32 command, 2–2, 2–7FLDATA33 command, 14–1FLDATA34 command, 2–9, 3–14, 14–1FLDATA35 command, 6–4FLDATA36 command, 6–3FLDATA37 command, 4–5, 12–1FLDATA38 command, 5–1FLDATA4 command, 2–2, 5–3, 6–4FLDATA4A command, 5–1, 5–1FLDATA5 command, 2–6, 2–6, 2–14FLDATA7 command, 9–1, 9–3, 9–13, 13–1FLDATA8 command, 9–4FLDATA9 command, 9–4FLOCHECK command, 5–3FLOTRAN analysis

applications, 1–1characterizing flow, 3–3compressible flow, 1–2, 8–1evaluating, 2–14files , 2–5fluid properties, 9–1free surface, 1–2incompressible flow, 1–2laminar flow, 1–1multiple species transport, 1–2non-Newtonian fluid flow, 1–2overview, 2–3restarting, 2–7setting parameters, 2–5solvers, 11–1special features, 10–1stopping, 2–13thermal analysis, 1–2, 4–1transient analysis, 5–1turbulent flow, 1–2types, 1–1verifying results, 2–14

FLOTRAN elements, 2–1flow regime, 2–4

thin film, 16–4FLREAD command, 2–6fluid analyses

acoustics (see acoustics)

ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.Index–2

Index

slide film, 16–18squeeze film, 16–1thin film, 16–1

fluid propertiesinitializing and varying, 9–9specifying, 9–1tables, 9–3user-defined file, 9–2, 9–10user-programmable subroutines, 9–2, 9–14

fluid property types, 9–1fluid-structure interaction, 15–1, 15–9, 15–11fluid-structure interface, 15–5forced convection, 1–2, 4–4forces, 15–9forcing frequency, 15–7free convection, 4–5free surface analysis, 1–2

Ggeneralized symmetry boundary conditions, 3–11, 7–3global iterations, 2–10, 5–1, 11–2graphical solution tracking, 2–11gravitational acceleration, 9–12

Hharmonic acoustic analysis, 15–2harmonic acoustic analysis guidelines, 15–2heat balance, 4–7, 4–8heat fluxes, 4–1heat transfer (film) coefficients, 4–1hydraulic diameter, 3–2

IIC command, 13–1ICE command, 6–1ICVFRC command, 6–1impedance, 15–9incompressible flow analysis, 1–2, 3–1

boundary conditions, 3–11difficult problems, 3–14example problem, 3–16meshing requirements, 3–9

inertial relaxation, 2–8, 8–4infinite acoustic elements, 15–2inlet parameters, 3–3inlet values, 3–11intersections, 3–11INTSRF command, 3–16

KKBC command, 2–2KEYOPT command, 10–1, 13–2

kinetic energy, 2–5Knudsen number, 16–4

Llaminar flow, 1–1, 3–1, 3–3large signal cases, 16–18LCCALC command, 2–2LCDEF command, 2–2LCFACT command, 2–2LCFILE command, 2–2lift, 3–16load step options

acoustics, 15–9loads, 4–2, 15–6

Mmass imbalances, 3–11mass types, 5–1material model interface, 1–2meshing, 2–4, 3–9, 4–1mixture types, 13–1modal projection method, 16–10modified inertial relaxation, 2–9, 13–4moments, 15–9monotone Streamline Upwind approach, 4–7monotone streamline upwind approach, 14–1moving wall, 3–11MP command, 4–1, 9–1MSADV command, 14–1MSCAP command, 13–4MSDATA command, 13–2, 13–3MSMETH command, 13–4MSNOMF command, 13–1MSPROP command, 13–3MSRELAX command, 13–4MSSOLU command, 13–4MSSPEC command, 13–1, 13–2, 13–3multiple species transport, 1–2, 13–1

NN command, 2–2natural convection, 1–2NCNV command, 2–2NEQIT command, 2–2Newmark time integration method, 5–1NMODIF command, 2–2nodal residuals file, 2–6non-fluid properties, 4–1, 9–1non-Newtonian fluid flow analysis, 1–2, 9–13non-Newtonian viscosity models, 9–3, 9–6NROTAT command, 2–2NSVR command, 2–2

Index

Index–3ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

Ooverwrite frequency option, 2–6

Pparticle velocity, 15–1PERI command, 3–11periodic boundaries, 3–11/PICE command, 6–1PLVFRC command, 6–5power law viscosity model, 9–3, 9–6, 9–13preconditioned bicgstab solver, 11–5preconditioned generalized minimum residual solver,11–3PRESOL command, 2–2pressure gradient, 15–1pressure surface loads, 15–9pressure wave limit, 5–1print file, 2–6PRNLD command, 2–2problem domain, 2–4property calculations, 8–1property types, 9–1, 9–4PRRSOL command, 2–2PSOLVE command, 2–2

Qquadrature order, 2–10

Rradiosity solver method, 4–8ratio of specific heats, 8–1, 9–12reference pressure, 9–12reference properties, 9–12relaxation factors, 2–8, 4–4, 13–4RESCONTROL command, 2–2residuals, 2–6restart file, 2–7results file, 2–6reviewing results

acoustics, 15–11Reynolds number, 3–2rotating reference frames, 10–2rotational speeds, 10–2

Ssample acoustic analysis

batch method, 15–12search directions, 11–2semi-direct solvers, 11–2SFE command, 6–2SFL command, 6–2SIMPLEF algorithm, 12–1

SIMPLEN algorithm, 12–1slide film, 16–1, 16–18solution, 15–6Solvers, 11–1, 15–6sparse direct solver, 11–5, 15–6species mass fractions, 13–1specific heat, 4–1, 8–1, 9–2, 9–7specified flow, 3–11specified pressure, 3–11squeeze film, 16–1squeeze stiffness effect, 16–1stationary wall, 3–11stepped or ramped loads, 15–10Stokes flow, 16–18streamline upwind/Petrov-Galerkin approach, 4–7,14–1surface tension coefficient, 6–1, 9–1, 9–3, 9–8surface-to-surface radiation, 4–1, 4–8Sutherland's law, 9–6swirl, 10–3symmetry boundary, 3–11

Ttemperature equation, 4–1temperature field algorithm, 4–5temperature load, 4–1temperature offset, 9–9thermal analysis, 1–2

example problems, 4–8loads and boundary conditions, 4–1property specifications, 4–1

thermal boundary conditions, 4–1thermal conductivity, 4–1, 9–2, 9–8thin film analysis, 16–1

Couette vs. Stokes flow, 16–18cross-talk, 16–12flow regime, 16–4harmonic response analysis, 16–3large signal cases, 16–18modal projection method, 16–10slide film, 16–18squeeze film, 16–1static analysis, 16–2

TIME command, 2–2time steps, 5–1TIMINT command, 2–2TOFFST command, 9–9, 9–12total temperature, 8–1transient analysis, 5–1

boundary conditions, 5–3settings, 5–1terminating, 5–3

ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.Index–4

Index

tri-diagonal matrix algorithm, 11–1TRNOPT command, 2–2turbulence model, 2–4, 2–10, 3–2, 3–3turbulence ratio, 3–3, 3–14turbulent flow, 1–2, 3–1turbulent kinetic energy, 3–3, 3–11

Uuncoupled acoustic analysis, 15–1units, 9–1unspecified boundary, 3–11

Vvariable density option, 4–5velocity capping, 3–14viscosity, 4–1

artificial, 2–9Bingham model, 9–3, 9–6, 9–14Carreau model, 9–3, 9–6, 9–14effective, 2–5, 3–2power law model, 9–3, 9–6, 9–13

viscous heating, 4–4volume of fluid analysis, 6–1

boundary conditions, 6–2example problems, 6–5input settings, 6–3loads, 6–1postprocessing, 6–5

Wwall roughness, 3–11wall static contact angle, 9–1, 9–3, 9–9

Index

Index–5ANSYS Fluids Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

ANSYS Fluid Analysis Guide

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