Polyflow-Intro 13.0 Tut-03 Fluid Solid

Tutorial 3. Fluid Flow and Conjugate heat Transfer

ANSYS Inc., December 2010 3-1

Introduction This tutorial illustrates the setup and solution of a problem involving heat transfer between a Newtonian fluid and a cooled circular die. Along with a good die design, rheological and thermo physical properties of the melt and the thermal settings in the die are very important in obtaining a geometrically well-defined polymer product. The heat transfer calculation is important when temperature-sensitive polymers are shaped and when product surface qualities are of critical importance. The temperature field at the die exit influences the swelling and drawing behavior of the product. In this tutorial, you will solve the non-isothermal flow problem for the fluid and the heat conduction in the die, making some assumptions regarding the rheological and thermo physical properties of the melt. In this tutorial you will learn how to: Start POLYDATA from Workbench. Create a new task. Create multiple sub-tasks. Define a Newtonian non-isothermal flow problem. Define a heat conduction problem. Set material properties and boundary conditions for a fluid-solid heat conduction and flow problem. Prerequisites This tutorial assumes that you are familiar with the menu structure in POLYDATA and Workbench and that you have solved or read Tutorial 1. Some steps in the setup procedure will not be shown explicitly. Problem Description This tutorial examines the coupled problem of non-isothermal flow of a Newtonian fluid and heat conduction in an axisymmetric steel die. As shown in Figure 3.1, the melt enters the domain at a fixed temperature and a given flow rate of T = 180C and Q =0.6e06 m3/s, respectively. The problem involves flow, heat transfer by conduction and convection, and heat generation by viscous dissipation. Energy, momentum, and

Fluid Flow and Conjugate heat transfer

3-2 ANSYS Inc., December 2010

incompressibility equations are solved in the fluid domain. The energy equation for heat conduction is solved in the solid domain. To solve the coupled problem, two sub-tasks are defined: one for the fluid (sub-task 1) and the other for the solid (sub-task 2). Each sub-task will contain a particular model, domain of definition, material properties, and boundary conditions, including interface conditions with the other sub-task. The sub-tasks are coupled, because the global solution of the problem depends on the values of the solution variables at the intersection of the fluid and solid domains.

Figure 3.1: A Schematic Diagram of the Fluid and the Circular Die

The material properties for the fluid are: = density (950 kg/m3) = Newtonian viscosity (2500 Pa s) Cp = heat capacity per unit mass (2300 J/kg-K) k = thermal conductivity (0.5 W/m-K) Viscous heating is taken into account. For the solid region, the thermal conductivity k is 35 W/m-K.



The boundary sets for the problem are shown in Figure 3.2, and the conditions at the boundaries of the domains are: boundary 1: flow inlet, T = 180C, Q = 0.6 106 m3/s intersection of subdomain 1 and subdomain 2: interface boundary 2: insulated boundary 3: T = 100C boundary 4: insulated boundary 5: flow exit boundary 6: symmetry axis

Figure 3.2: Boundaries and Sub-domains Preparation 1. Copy the file, flusol/flusol.msh from the POLYFLOW documentation CD or installation area to your working directory (as described in Tutorial 1). 2. Start Workbench from startAll ProgramsAnsys13.0Workbench.



Step 1: Project and Mesh 1. Create a Polyflow Analysis system by drag and drop in workbench, import the mesh file (flusol.msh), and double-click the Setup cell of the analysis to start POLYDATA. Hint: For detailed information on how to do this, refer to Tutorial 1. When POLYDATA starts, the Create a new task menu item is be highlighted, and the geometry for the problem is displayed in the Graphics Display window. Step 2: Models, Material Data, and Boundary Conditions In this step, define a new task representing the fluid flow and conjugate heat transfer problem. The flow problem for the fluid and the heat conduction in the solid is solved in two different sub-tasks. However, the task attributes are the same for both the sub-tasks, so define a single task for the coupled problem. 1. Create a task for the model. Create a new task (a) Select the following options: F.E.M. task Steady-state problem 2D axisymmetric geometry

Since the problem involves an axisymmetric steel die, the computational domain for the problem is chosen to be a 2D cylindrical reference frame (r,z) with r=0 as the axis of symmetry, and involves two velocity components (u,v); hence 2D axisymmetric geometry has been chosen. A Steady-state condition is assumed for the problem.

(b) Select Accept the current setup. The Create a sub-task menu item is highlighted.



Step 2a: Definition of Sub-Task 1 In this step, define the flow problem, identify the domain of definition, set the relevant material properties for the Newtonian fluid, and define boundary conditions along its boundaries. 1. Create the sub-task for the fluid flow. Create a sub-task (a) Select Generalized Newtonian non-isothermal flow problem. A panel appears asking for the title of the problem.

(b) Enter fluid as the New value and click OK. The Domain of the sub-task menu item is highlighted. 2. Define the domain where the sub-task applies. To solve the coupled problem, the computational domain is divided into two sub-domains with a common intersection. A sub-task with its own model, material properties, and boundary conditions is defined on each of the non-overlapping subdomains. Sub-task 1 is defined for Subdomain 1, since Subdomain 1 represents the fluid (as shown in Figure3.2). Domain of the sub-task (a) Select Subdomain 2 and click Remove.



Subdomain 2 is moved from the top list to the bottom list, indicating that subtask 1 is defined on subdomain 1.

(b) Click on Upper level menu at the top of the panel. The Material data menu item is highlighted. 3. Specify the material properties for the fluid. POLYDATA indicates which material properties are relevant for your sub-task by graying out the irrelevant properties. In this sub-task, POLYFLOW solves energy, incompressibility and momentum equations, so you have to define viscosity, density, thermal conductivity, heat capacity per unit mass, and viscous heating. For a non-isothermal flow problem, the viscosity can depend on both shear rate and temperature. In this case, the viscosity is constant, so it depends on neither of them. Material data (a) Select Shear-rate dependence of viscosity. Since the fluid flow is Newtonian, specify a constant value for the viscosity.



i. Select Constant viscosity. ii. Specify the value for Modify fac POLYDATA prompts for the new value of

iii. Enter 2500 as the New value and click OK. iv. Select Upper level menu two times to continue the Material Data specification. (b) Select Temperature dependence of viscosity. i. Select No temperature dependence.

POLYDATA displays the following message, confirming that there is no temperature dependence for the viscosity.



ii. Click OK. iii. Select Upper level menu to continue the Material Data specification. (c) Select Density. In this problem, specify a constant value for the density. Modification of density

i. Enter 950 as the New value and click OK. ii. Select Upper level menu to continue the Material Data specification. (d) Select Thermal conductivity.



As shown at the top of the menu, the thermal conductivity is defined as a non-linear function of the temperature:

k = a + bt + ct2 + dt3 (3.1)

In this problem, the thermal conductivity is assumed to be a constant for the fluid, so only the constant coefficient a is modified.

Modify a

i. Enter 0.5 as the New value and click OK. ii. Select Upper level menu to continue the Material Data specification. (e) Select Heat capacity per unit mass.

As shown at the top of the menu, the heat capacity per unit mass is defined as a non-linear function of temperature:

cp = a + bt + ct2 + dt3 (3.2)

The temperature variation of cp differs with the nature of the polymer melts. In this problem, cp is assumed to be constant, so only the constant coefficient a is modified.



Modify a

i. Enter 2300 as the New value and click OK. ii. Select Upper level menu to continue the Material Data specification. (f) Select Viscous heating.

When shearing occurs in a flow, the friction of the different fluid layers creates heat. When the fluid is highly viscous and/or the shear rate is high, the heating of the fluid due to this phenomenon is important and must be taken into consideration.

i. Select Viscous heating will be taken into account. ii. Select Upper level menu to return to the Material Data specification. (g) Select Upper level menu to leave the Material Data specification. The Flow boundary conditions menu item is highlighted. 4. Specify the flow boundary conditions for subdomain 1.



Flow boundary conditions

(a) Set the conditions along the intersection of subdomain 1 and subdomain 2.

The intersection acts as a wall for the fluid, and since the fluid is assumed to stick to the wall, zero normal and tangential velocities is imposed along this boundary.

i. Select Zero wall velocity (vn=vs=0) along subdomain 2 and click Modify. ii. Select Zero wall velocity (vn=vs=0). (b) Set the conditions at the flow inlet (boundary 1). i. Select Zero wall velocity (vn=vs=0) along boundary 1 and click Modify. ii. Select Inflow. POLYDATA prompts for the new value of the volumetric flow rate.



iii. Enter 0.6e-06 as the New value and click OK. The flow rate of the melt is very low due to the highly viscous nature of the melt. iv. Select Automatic.

When the Automatic option is selected, POLYDATA automatically chooses the most appropriate method to compute the inflow condition.

(c) Set the conditions at the flow exit (boundary 5).

It is assumed that a fully developed velocity profile is reached at the exit, so the outflow condition is most appropriate. This condition imposes a zero normal force, fn (which includes a pressure term), and zero tangential velocity, vs.

i. Select Zero wall velocity (vn=vs=0) along boundary 5 and click Modify. ii. Select Outflow.

(d) Retain the default condition Axis of symmetry at the symmetry axis (boundary 6).

For axisymmetric models, POLYDATA recognizes the axis of symmetry from the mesh file, and automatically imposes the symmetry condition along the line r=0. This condition imposes a zero normal velocity vn and zero tangential force fs along this boundary.

(e) Click on Upper level menu at the top of the panel to leave the Flow boundary conditions panel.

The Thermal boundary conditions menu item is highlighted.



5. Specify the thermal boundary conditions for subdomain 1. For non-isothermal problems, specify either the temperature or the heat flux on each boundary segment. The temperature along a given boundary can be a constant or a prescribed function of coordinates. Thermal boundary conditions

(a) Set the conditions at the intersection of subdomain 1 and subdomain 2.

An interface condition is set at the intersection of subdomain 1 and subdomain 2. This condition ensures continuity of the temperature field and of the heat flux along the interface. Since you are solving a coupled problem, this condition of continuity is essential for the global solution of the temperature and heat flux variables.

i. Select Temperature imposed along subdomain 2 and click Modify. ii. Select Interface.



iii. Select Upper level menu to accept the default setting (continuous heat flux along the interface).

In the case of an interface condition, both the heat flux and temperature are usually continuous along the interface. It is possible to specify a nonzero value for the heat flux jump (dq), but this is mainly used in problems where internal radiation is simulated. Here, accept the default value for the definition of heat flux discontinuity, i.e., dq = 0.

(b) Set the conditions at the flow inlet (boundary 1). A constant value for the temperature is imposed along this boundary. i. Select Temperature imposed along boundary 1 and click Modify. ii. Select Temperature imposed. iii. Select Constant. POLYDATA prompts you for the new value of the constant temperature.

iv. Enter 180 as the New value and click OK. v. Select Upper level menu to return to the Thermal boundary conditions panel. (c) Set the conditions at the flow outlet (boundary 5). A zero conductive heat flux is imposed along this boundary. i. Select Temperature imposed along boundary 5 and click Modify. ii. Select Outflow.



(d) Keep the default condition Axis of symmetry at the symmetry axis (boundary 6). (e) Click on Upper level menu at the top of the Thermal boundary conditions panel. (f) Select Upper level menu at the top of the fluid sub-task menu. Step 2b: Definition of Sub-Task 2 In this step, define the heat conduction problem, identify the domain of definition, set the relevant material properties for the solid, and define the boundary conditions along its boundaries. 1. Create a sub-task for the solid. Create a sub-task (a) POLYDATA asks if you want to copy data from an existing sub-task.

(b) Click No, since this sub-task has different parameters associated with it. (c) Select Heat conduction problem. A small panel appears asking for the title of the problem. i. Enter solid as the New value and click OK. The Domain of the sub-task menu item is highlighted. 2. Define the domain where the sub-task applies (subdomain 2). Domain of the sub-task (a) Select Subdomain 1 and click Remove.



(b) Click on Upper level menu at the top of the panel. The Material data menu item is highlighted. 3. Specify the material properties for the solid. Material data In this problem, specify a constant value for the thermal conductivity k. (a) Select Thermal conductivity.

In this problem, thermal conductivity is assumed to be a constant, so only the constant coefficient a is modified.



i. Enter 35 as the New value and click OK. (b) Select Upper level menu two times to leave the Material Data specification. 4. Specify the thermal boundary conditions for subdomain 2. In this step, set the conditions at each of the boundaries of the domain. When a boundary set is selected, it is highlighted in red in the graphics window. Thermal boundary conditions (a) Set the conditions at the intersection of subdomain 1 and subdomain 2. An interface condition is set at the intersection of the sub-domains. i. Select Temperature imposed along subdomain 1 and click Modify. ii. Select Interface. iii. Select Upper level menu to accept the default option for continuity of temperature and heat flux. (b) Set the conditions at the bottom boundary of the solid (boundary 2). A zero conductive heat flux is imposed along this boundary. i. Select Temperature imposed along boundary 2 and click Modify. ii. Select Insulated boundary / symmetry. (c) Set the conditions at the outer boundary of the solid (boundary 3).



A constant value for the temperature is imposed along this boundary. i. Select Temperature imposed along boundary 3 and click Modify. ii. Select Temperature imposed. iii. Select Constant. POLYDATA prompts you for the new value of the constant temperature. iv. Enter 100 as the New value and click OK. v. Select Upper level menu to return to the Thermal boundary conditions panel. (d) Set the conditions at the top boundary of the solid (boundary 4). A zero conductive heat flux is imposed along this boundary. i. Select Temperature imposed along boundary 4 and click Modify. ii. Select Insulated boundary / symmetry. (e) Click on Upper level menu to leave the Thermal boundary conditions panel. (f) Select Upper level menu two times to return to the top-level POLYDATA menu. Step 3: Save the Data and Exit POLYDATA After defining your model in POLYDATA, save the data file. In the next step, read this data file into POLYFLOW and calculate a solution. Save and exit POLYDATA asks you to confirm the current system units and fields that are to be saved to the results file for post-processing. 1. Select Upper level menu This confirms that the default units are correct.



2. Select Accept. This confirms that the default Current field(s) are correct. 3. Select Continue. This accepts the default names for graphical output files (cfx.res) that are to be saved for postprocessing, and the POLYFLOW format results file (res). Step 4: Solution Run POLYFLOW to calculate a solution for the model you just defined using POLYDATA. 1. Run POLYFLOW by righ click on Solution cell of the simulation and click on Update button. This executes POLYFLOW using the data file as standard input, and writes information about the problem description, calculations, and convergence to a listing file (listingFile). 2. Check for convergence in the listing file. Right click on Solution cell and click on Listing Viewer Workbench opens View listing file panel, which displays the listing file. Step 5: Post-processing Use CFDPost to view the results of the POLYFLOW simulation. 1. Double click on Results cell in the workbench analysis and read the results files saved by POLYFLOW. CFDPost reads the solution fields that were saved to the results file. 2. Align the view.



(a) Select View Towards z. The central-mouse button allows you to zoom in and zoom out. The left-mouse button allows to rotate the image. The right-mouse button allows you to translate the image. 3. Display contours of pressure in the fluid region (sub domain 1). (a) Select the domain. Outline tab Unroll Mesh regions

i. under Mesh Regions, select SD_1 Hex. (b) Select the variable and display the results. ii. In the graphic window, right-click on the left-hand domain iii. Under Colour, select PRESSURE.



Most of the pressure drop occurs in the upper part of the die where the cross section is smallest (Figure 3.3). The pressure is linear except in the contraction zone. The isobars are perpendicular to the flow direction, as expected for the fully developed flow that occurs in the second part of the die.

Figure 3.3: Pressure Contours

4. Display contours of velocity in the fluid region (sub domain1). ii. In the graphic window, right-click on the left-hand domain iii. Under Colour, select VELOCITIES.

The velocity is higher in the second part of the die where the cross-section is smaller (Figure 3.4). It reaches a maximum value in the center of the thin tube.

5. Display of the velocity vectors. (a) In the Outline tab, under Mesh Regions, unselect SD_1 Hex. (b) Define the vectors. Insert Vector or click on the button i. Under the tab Geometry, click on next to Location ii. Select the location SD_1 iii. Under the tab Symbol, select Arrow 3D.



iv. Click on apply.

The flow is fully developed in the downstream part of the die (Figure 3.5). Observe the classical parabolic velocity profile. The Poiseuille flow is rapidly reached after the contraction because inertia is not taken into account here.

6. Display of the temperature distribution in the solid and the fluid regions. (a) Unselect the vectors.

Outline tab under User locations and plots, unselect Vector 1. (b) Select the domain. Outline tab under Mesh Regions, select SD_1 Hex and SD_2 Hex. (c) Define the contour plot. i. In the graphic window, right-click on the left-hand domain ii. Under Colour, select TEMPERATURE. iii. Repeat the above operations i and ii for the right-hand domain.

As expected, the temperature gradients are larger in the fluid than in the die, i.e., the isolines are closer together in the fluid than in the die (Figure 3.6). This is because the conductivity of the fluid is much lower than the conductivity of the solid. The temperature isolines are perpendicular to the boundaries where the (normal) flux becomes zero. The heating of the fluid due to viscous dissipation can be clearly seen.



Figure 3.4: Velocity distribution

Figure 3.5: Velocity vectors



Figure 3.6: Temperature distribution

7. Plot the temperature along a line y = 0.0006. For this, we first create a line and subsequently ask a plot on that line. (a) Define the line of the plot with the starting and ending points for y = 0.0006.

i. Under Location, select Line, enter a name.



ii. Define the line by two points (0,0.006,0) and (0.008,0.006,0). iii. Click on Apply. (b) Create a plot. i. Click on the Chart button , enter a name, and click on OK.

ii. In the Details of chart, select the tab Chart Line 1 iii. Select the location: the line defined above. iv. Select X along the X-axis and TEMPERATURE along the Y-axis. v. Under the tab Chart, modify the title, if needed.



vi. Click on Apply.

Figure 3.7: Temperature profile along the Line y = 0.006

The thermal boundary layer located along the die wall is clearly visible. This boundary layer is the result of the low thermal conductivity and high heat capacity of the fluid. The temperature of the fluid at the center is not affected by the low temperature of the solid. The heat does not diffuse quickly enough through the fluid layer to reach the axis of symmetry, before the fluid exits the die. Summary This tutorial introduced the coupling of sub-tasks of different types: a non-isothermal flow problem and a heat conduction problem in a solid. Coupled calculations like this are very useful in polymer processing applications where thermal effects are critical (e.g., extrusion, coating, fiber spinning). Coupling can also be applied through fields other than temperature (e.g., electrical potential and pressure in porous media).

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Polyflow-Intro 13.0 Tut-03 Fluid Solid

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