pilot-jet

Tutorial: Simulation of a Piloted Jet Flame using Unsteady

Laminar Flamelet Model

Introduction

The purpose of this tutorial is to demonstrate the setup and solution for simulation of apiloted jet flame using the unsteady laminar flamelet model in FLUENT 6.3.

The steady laminar flamelet model can simulate local chemical non-equilibrium due to theaerodynamic straining of the flame by the turbulent flow-field. Species that respond quicklyto this turbulent straining (such as the OH radical) can be modeled accurately. However,slow kinetic species like NOx, and in some cases CO, cannot be modeled directly withthe steady laminar flamelet model since their concentrations depend on their history ofmolecular mixing and subsequent reaction.

As an alternative, NOx can be modeled in FLUENT with the pollutant postprocessingmodel. NOx and CO can also be modeled with the laminar finite-rate, eddy-dissipation-concept (EDC) or PDF transport models. However, these three models are computationallyexpensive since the chemistry is computed in every cell.

A prerequisite to running the unsteady flamelet model is to obtain a converged steadyflamelet solution.

This tutorial demonstrates how to do the following:

Set up and solve the steady laminar flamelet case by importing a CHEMKIN mecha-nism and generating steady flamelets.

Obtain a converged steady flamelet solution. Calculate a solution for unsteady flamelet model. Examine results using graphics.

Pre-requisites

This tutorial assumes that you are familiar with the FLUENT interface, and that you havea good understanding of model setup and solution procedures. You are expected to have agood understanding of modeling turbulence, species transport and chemical reaction. Fordetails, refer to Chapter 12: Modeling Turbulence and Section 14.1: Volumetric Reactionsof the FLUENT 6.3 Users Guide.

c Fluent Inc. November 15, 2006 1

Simulation of a Piloted Jet Flame using Unsteady Laminar Flamelet Model

Problem Description

The unsteady laminar flamelet approach can model slow species formation, such as NO ingas-phase reactors and product compounds in liquid reactors. Expensive chemical kineticcalculations are performed in one-dimension, so complex 3D geometries can be economicallysimulated with detailed chemical mechanisms.

A diagram of the piloted jet flame simulated in this tutorial is shown in the Figure 1.

Pilot JetMain Jet

Inlet Outlet

Figure 1: Problem Schematic

Preparation

1. Copy the files flameD-sfla.msh.gz and gri30.che to your working folder.

2. Start the 2D (2d) version of FLUENT.

Setup and Solution

Step 1: Grid

1. Read in the mesh file, flameD-sfla.msh.gz.

File Read Case...2. Check the grid.

Grid Check...FLUENT will perform various checks on the mesh and will report the progress in theconsole. Make sure the minimum volume reported is a positive number.

3. Display the mesh.

Display Grid...

2 c Fluent Inc. November 15, 2006


(a) Click Display and close the Grid Display panel.Retain the default values to display the mesh.

GridFLUENT 6.3 (2d, pbns, lam)

Figure 2: Piloted Jet Flame

Step 2: Models

1. Select axisymmetric solver settings.

Define Models Solver...

(a) Enable Axisymmetric from the Space list.

(b) Click OK to close the Solver panel.

2. Enable the realizable k- model.

Define Models Viscous...



(a) Select k- Model from the Model list and enable Realizable under k- Model.

(b) Click OK to close the Viscous Model panel.

3. Enable non-premixed combustion species model.

Define Models Species Transport & Reaction...



(a) Enable Non-Premixed Combustion under Model in the Species Model panel.

Although the inlet stream is a mixture of air and methane (in order to minimizesooting so that the flame species and temperature can be measured with laserdiagnostics), this mixture is so rich that the flame behaves much like a non-premixed flame.



(b) Enable Create Table under PDF Options.

(c) Select Steady Flamelets in the Chemistry tab.

(d) Enable Adiabatic in the Chemistry tab.

(e) Click the Import CHEMKIN Mechanism button to open the CHEMKIN MechanismImport panel.

i. Click the Browse button next to Gas-Phase CHEMKIN Mechanism File.

ii. Load gri30.che.

iii. Retain the default Gas-Phase Thermodynamic Database File.

iv. Click Import and close the CHEMKIN Mechanism Import panel.

(f) Click the Boundary tab in the Species Model panel.



i. Select Mole Fraction under Species Unit.

ii. Enter 0.1575 for o2 under Fuel.

iii. Enter 0.5925 for n2 under Fuel.

iv. Enter 0.25 for ch4 under Fuel.

v. Enter 294 K for Fuel and 291 K for Oxid under Temperature.

In order to save time in this tutorial, the chemistry will be modeled with a singleflamelet instead of a library of flamelets.

(g) Click the Control tab in the Species Model panel.

i. Enter 1.1 for Fourier Number Multiplier under Flamelet Controls.

The flamelet equations are integrated in time until convergence (or the time ex-ceeds the maximum integration time). The time-step for flamelet integration ismultiplied by the fourier number multiplier at each step. Decreasing this numbertowards 1 improves stability.

(h) Click Flamelet tab in Species Model panel.



i. Enter 1 for Maximum Number of Flamelets under Flamelet Parameters.

ii. Enter 33/s for Initial Scalar Dissipation under Flamelet Parameters.

This is the average scalar dissipation on the stochiometric surface, which canbe verified after convergence.

iii. Click the Calculate Flamelets button.

Note: A dialog box appears and asks whether you want to save the flamelet.Click Yes to save the flamelet to a file.

(i) Click the Table tab in the Species Model panel.



i. Verify that Include Equilibrium Flamelet is not selected.

ii. Click the Calculate PDF Table button.

iii. Save the PDF file.

File Write PDF...

(j) Click OK to close the Species Model panel.

Step 3: Boundary Conditions

Define Boundary Conditions...

1. Set boundary conditions for inlet (jet).

(a) Select jet under Zone and velocity-inlet under Type.

(b) Click the Set... button to open the Velocity Inlet panel.



i. Enter 49.6 m/s for Velocity Magnitude.

ii. Select Intensity and Hydraulic Diameter from the Specification Method drop-down list under Turbulence.

iii. Enter 10% for Turbulent Intensity.

iv. Enter 0.0072 m for Hydraulic Diameter.

v. Click the Species tab and enter 1 for the Mean Mixture Fraction.

(c) Click OK to close the Velocity Inlet panel.



2. Set boundary conditions for inlet (pilot).

(a) Select pilot under Zone and velocity-inlet under Type.



ii. Select Intensity and Hydraulic Diameter from the Specification Method drop-down list under Turbulence.


iv. Enter 0.0165 m for Hydraulic Diameter.

v. Click the Species tab and enter 0.2755 for the Mean Mixture Fraction.


3. Set boundary conditions for inlet (coflow).

(a) Select coflow under Zone and velocity-inlet under Type.



ii. Select Intensity and Viscosity Ratio from the Specification Method drop-downlist under Turbulence.


iv. Enter 10 as Turbulent Viscosity Ratio.

v. Click on the Species tab and enter 0 for the Mean Mixture Fraction.




4. Set boundary conditions for outlet (outlet).

(a) Select outlet under Zone and pressure-outlet under Type.

(b) Click the Set... button to open the Pressure Outlet panel.

i. Select Intensity and Viscosity Ratio from the Specification Method drop-downlist under Turbulence.

ii. Enter 10% for Backflow Turbulent Intensity.

iii. Enter 10 for Backflow Turbulent Viscosity Ratio.

(c) Click OK to close the Pressure Outlet panel.

5. Close the Boundary Conditions panel.



Step 4: Solution for Steady Flamelet Model

1. Initialize the solution.

Solve Initialize Initialize...(a) Select all-zones from the Compute From drop-down list.

(b) Click Init and close the Solution Initialization panel.

2. Enable the plotting of residuals during the calculation.

Solve Monitors Residual...(a) Enable Plot in the Options group box.

(b) Retain the default values and click OK to close the Residual Monitors.

3. Set the solution parameters.

Solve Controls Solution...

(a) Enter 0.7 for Density in the Under-Relaxation Factors group box.

(b) Select PRESTO! from the drop-down list of Pressure under Discretization.

(c) Select Second Order Upwind for all remaining parameters.



4. Start the calculation by requesting 500 iterations.

Solve Iterate...(a) Enter 500 for the Number of Iterations.

(b) Click Iterate.

The solution converges before 500 iterations are completed.

5. Save the case and data files (flameD-sfla-1.cas.gz and flameD-sfla-1.dat.gz).

File Write Case & Data...

Step 5: Solution for Unsteady Laminar Flamelet Model

1. Define the species model.

Define Models Species Transport & Reaction...

(a) Enable Create Table under PDF Options in Species Model panel.

(b) Click the Chemistry tab and enable Unsteady Flamelet.

The unsteady laminar flamelet model can be enabled in a steady-state FLUENTcase file that employs steady flamelets generated in FLUENT.

(c) Click the Boundary tab.

The Fuel and Oxid compositions for unsteady flamelet model are the same as forthe steady flamelet model and are not editable.



(d) Click the Control tab.

i. Accept the default species under Species Zeroed in Initial Unsteady Flamelet.

The unsteady flamelet requires an ignition profile to initiate combustion, whichis taken as a steady strained flamelet. However, the steady flamelet solution forslow species (such as NOx), is incorrect, and these species should be set to zeroin the initial flamelet. The slow species to be zeroed in initial unsteady flameletcan be set by the user. Since the NOx species are already included in the defaultlist, accept the default list.

(e) Click the Flamelet tab.



i. Accept the default value of 32 for Number of Grid Points in Flamelet.

ii. Enter 0.4 for Mixture Fraction Lower Limit for Initial Probability.

The unsteady flamelet model convects (and diffuses) a marker probabilityequation through the steady-state FLUENT flow field in an unsteady manner.This marker is initialized to 1 above the Mixture Fraction Lower Limit forInitial Probability, and 0 below this value. In general, it should be set to avalue greater than the stochiometric mixture fraction. For this methane-airfuel mixture, the stochiometric mixture fraction is about 0.35. So set theMixture Fraction Lower Limit for Initial Probability to 0.4.

iii. Enter 600/s for Maximum Scalar Dissipation.

Flamelets can extinguish at scalar dissipation rates greater than the extinc-tion scalar dissipation. To prevent excessive scalar dissipation, FLUENTallows you to specify the maximum scalar dissipation during the flameletevolution, which should be set to approximately the extinction scalar dissi-pation. The extinction scalar dissipation can be calculated in FLUENT usingthe steady flamelet generator. For this flame, this has been performed beforeand the extinction scalar dissipation rate is 600/s.

iv. Retain the default Courant Number of 1.

The marker probability equation convects/diffuses out of the domain overtime. The time-step is calculated automatically based on a Courant Number,and the default of unity is almost always sufficient.

v. Click Initialize Unsteady Flamelet Probability

This initializes the marker probability, enables the unsteady solver in FLU-ENT, and disables all equations except the probability equation.

(f) Click OK to close the Species Model panel.



FLUENT will enable the unsteady solver and disable all equations except the un-steady flamelet probability.

2. Enable plotting at the outlet.

Monitor the average probability at the outlet to gauge when it has convected/diffusedout of the domain. We run the calculation until the probability has been diffuse/convectedout of the domain, and there is no convergence criteria for other models/equations inFLUENT.

Solve Monitors Surface...

(a) Set Surface Monitors to 1.

(b) Enable Plot, Print, and Write for monitor-1.

(c) Select Time Step from When drop-down list.

(d) Click the Define... button to open the Define Surface Monitor panel.



i. Select Mass-Weighted Average from the Report Type drop-down list.

ii. Select Unsteady Flamelet and Probability from Report of drop-down list.

iii. Select outlet under Surfaces.

iv. Set the Plot Window to 2.

v. Click OK to close the Surface Monitors panel.

3. Set the solution parameters.

Solve Controls Solution...

(a) Select Second Order Upwind from the Unsteady Flamelet Probability drop-downlist under Discretization.

(b) Click OK to close the Solution Controls panel.

4. Save the case file (flameD-ufla-1.cas.gz).

File Write Case....5. Run the solution.

Solve Iterate...(a) Enter 100 for Number of Time Steps.

(b) Click Iterate.

6. Save the data file (flameD-ufla-1.dat.gz).

File Write Data...



Convergence history of Probability on outlet (in SI units) (Time=7.2150e-01)FLUENT 6.3 (axi, pbns, pdf20, rke, unsteady)

Time Step

ProbabilityAverage

Mass-Weighted

1009080706050403020100

4.50e-04

4.00e-04

3.50e-04

3.00e-04

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

Figure 3: Convergence History of Probability on outlet.

Figure 3 is the monitor plot of outlet average probability, which shows probability increasingwith time, peaking, then decreasing to zero as the probability convects and diffuses out ofthe domain.

Step 6: Postprocessing for Unsteady Laminar Flamelet Model.

1. Display the contours of probability. (see Figure 4).

Display Contours...



(a) Select Unsteady Flamelet... and Probability from the Contours of drop-down lists.

(b) Click Display.

Contours of Probability (Time=7.2150e-01)FLUENT 6.3 (axi, pbns, pdf20, rke, unsteady)

5.13e-074.88e-074.62e-074.36e-074.11e-073.85e-073.59e-073.34e-073.08e-072.82e-072.57e-072.31e-072.05e-071.80e-071.54e-071.28e-071.03e-077.70e-085.13e-082.57e-080.00e+00

Figure 4: Contours of Probability

Note that most of the probability marker has convected out of the domain with only asmall probability remaining near the outlet.

2. Display the contours of mean temperature. (see Figure 5).



(a) Select Unsteady Flamelet... and Mean Temperature from the Contours of drop-down lists.

(b) Click Display.

Contours of Mean Temperature (Time=7.2150e-01)FLUENT 6.3 (axi, pbns, pdf20, rke, unsteady)

1.89e+031.81e+031.73e+031.65e+031.57e+031.49e+031.41e+031.33e+031.25e+031.17e+031.09e+031.01e+039.29e+028.49e+027.70e+026.90e+026.10e+025.30e+024.51e+023.71e+022.91e+02

Figure 5: Contours of Mean Temperature

The contours of unsteady flamelet mean temperature differ slightly from the steadyflamelet temperature, which can be displayed under the contours of temperaturedrop-down list.



3. Display the contours of the unsteady flamelet mean mass fraction of no. (see Figure 6).

(a) Select Unsteady Flamelet... and Mean Mass fraction of no from the Contours ofdrop-down lists.

(b) Click Display.

Contours of Mean Mass fraction of no (Time=7.2150e-01)FLUENT 6.3 (axi, pbns, pdf20, rke, unsteady)

1.15e-041.10e-041.04e-049.80e-059.23e-058.65e-058.07e-057.50e-056.92e-056.34e-055.77e-055.19e-054.61e-054.04e-053.46e-052.88e-052.31e-051.73e-051.15e-055.77e-060.00e+00

Figure 6: Contours of Mass fraction of no

The NO species is far from chemical equilibrium. The unsteady flamelet NO values arein much better agreement with experimental data than the steady flamelet NO values,which can be displayed under the contours of species drop-down list.

4. Click Close to exit the Contours panel.



Summary

This tutorial has demonstrated set up and solution of the unsteady laminar flamelet modelfor a gas-phase, piloted jet diffusion flame. Kinetically limited species, in particular NOxcan be modeled using detailed kinetic mechanisms. Chemistry calculations are performed inone dimension, allowing economic calculations for detailed kinetics with complex geometry.


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