Modeling Radiation and Natural Convection

Transcription

1 Tutorial 5. Modeling Radiation and Natural Convection Introduction In this tutorial combined radiation and natural convection are solved in a two-dimensional square box on a mesh consisting of quadrilateral elements. This tutorial demonstrates how to do the following: Use the radiation models in FLUENT (Rosseland, P-1, DTRM, discrete ordinates (DO), and surface-to-surface (S2S)) and understand their ranges of application. Use the Boussinesq model for density. Set the boundary conditions for a heat transfer problem involving natural convection and radiation. Separate a single wall zone into multiple wall zones. Change the properties of an existing fluid material. Calculate a solution using the pressure-based solver. Display velocity vectors and contours of stream function and temperature for flow visualization. Prerequisites This tutorial assumes that you are familiar with the menu structure in FLUENT and that you have completed Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description The problem to be considered is shown schematically in Figure 5.1. A square box of side L has a hot right wall at T = 2000 K, a cold left wall at T = 1000 K, and adiabatic top and bottom walls. Gravity acts downwards. A buoyant flow develops because of thermally-induced density gradients. The medium contained in the box is assumed to be absorbing and emitting, so that the radiant exchange between the walls is attenuated by absorption and augmented by emission in the medium. All walls are black. The objective is to compute the flow and temperature patterns in the box, as well as the wall heat flux, c Fluent Inc. September 21,

2 using the radiation models available in FLUENT, and to compare their performance for different values of the optical thickness al. The working fluid has a Prandtl number of approximately 0.71, and the Rayleigh number based on L is This means the flow is inherently laminar. The Boussinesq assumption is used to model buoyancy. The Planck number k/(4σlt0 3 ) is 0.02, and measures the relative importance of conduction to radiation; here T 0 = (T h + T c )/2. Three values for the optical thickness are considered: al = 0, al = 0.2, and al = 5. Note that the values of physical properties and operating conditions (e.g., gravitational acceleration) have been adjusted to yield the desired Prandtl, Rayleigh, and Planck numbers. T = 1000 K c y x Adiabatic L g T = 2000 K h ρ = 1000 kg/m 3 c = x10 p k = W/mK µ = 10-3 kg/ms β = /K g = x 10-5 m/s 2 a = 0, 0.2, 5 1/m L = 1 m 5 Ra = 5 x 10 Pr = 0.71 Pl = 0.02 τ = 0.2, 5 4 J/kgK Figure 5.1: Schematic of the Problem Setup and Solution Preparation 1. Download radiation_natural_convection.zip from the Fluent Inc. User Services Center or copy it from the FLUENT documentation CD to your working folder (as described in Tutorial 1). 2. Unzip radiation_natural_convection.zip. rad.msh can be found in the radiation natural convection folder created after unzipping the file. 3. Start the 2D (2d) version of FLUENT. 5-2 c Fluent Inc. September 21, 2006

3 Step 1: Grid 1. Read the mesh file rad.msh. File Read Case... As the mesh is read in, messages will appear in the console reporting the progress of the reading. The mesh size will be reported as 2500 cells. 2. Check the grid. Grid Check FLUENT will perform various checks on the mesh and report the progress in the console. Make sure that the minimum volume reported is a positive number. 3. Display the grid. Display Grid... (a) Retain the default settings. (b) Click Display to view the grid in the graphics display window (Figure 5.2). (c) Close the Grid Display panel. Note: All of the walls are currently contained in a single wall zone, wall-4. You will need to separate them out into four different walls in the next step so that you can specify different boundary conditions for each wall. c Fluent Inc. September 21,

4 Grid FLUENT 6.3 (2d, pbns, lam) Figure 5.2: Graphics Display of Grid 4. Separate the single wall zone into four wall zones. Grid Separate Faces... Faces with normal vectors that differ by more than 89 are placed in separate zones. Since the four wall zones are perpendicular (angle = 90 ), wall-4 will be separated into four zones when you set the angle to 89 in this step. (a) Retain the default Angle separation method in the Options list. (b) Select wall-4 from the Zones selection list. (c) Enter 89 for the Angle. (d) Click Separate to split the single wall into four zones. There are now four wall zones for wall-4 listed under Zones in the Separate Face Zones panel. The new zone information is also reported in the console. 5-4 c Fluent Inc. September 21, 2006

5 (e) Close the Separate Face Zones panel. 5. Display the grid again. Display Grid... (a) Select all of the surfaces to display by clicking the shaded icon to the right of Surfaces. (b) Click Display to view the grid in the graphics window. Verify that you now have four different wall zones instead of only one. To do this, right-click on one of the wall boundaries in the graphics window to check which wall zone number corresponds to each wall boundary. Information will be displayed in the FLUENT console about the associated zone, including the name of the zone. This feature is especially useful when you have several zones of the same type and you want to distinguish between them quickly. In some cases, you may want to disable the display of the interior grid so as to more accurately select the boundaries for identification. (c) Close the Grid Display panel. c Fluent Inc. September 21,

6 Step 2: Models As discussed earlier, in this tutorial you will define each radiation model in turn, obtain a solution, and then postprocess the results. You will start with the Rosseland model, then use the P-1 model, the discrete transfer radiation model (DTRM), and the discrete ordinates (DO) model. At the end of the tutorial, you will use the surface-to-surface (S2S) model. 1. Retain the default solver settings. Define Models Solver Define the Rosseland radiation model. Define Models Radiation c Fluent Inc. September 21, 2006

7 (a) Select Rosseland in the Model list. (b) Click OK to close the Radiation Model panel. FLUENT will present an Information dialog box telling you that new material properties have been added for the radiation model. You will be setting properties later so you can simply click OK in the dialog box to acknowledge this information. Note: FLUENT will automatically enable the energy calculation when you select a radiation model, so you need not visit the Energy panel. 3. Add the effect of gravity to the model. Define Operating Conditions... (a) Enable the Gravity option in the Gravity group box. The panel will expand to show additional inputs. (b) Enter -6.94e-5 m/s 2 for Y in the Gravitational Acceleration group box. As previously mentioned, the gravitational acceleration is adjusted to yield the correct dimensionless quantities for Prandtl, Rayleigh, and Planck numbers. See Figure 5.1 and the associated comments. (c) Enter 1000 K for Operating Temperature in the Boussinesq Parameters group box. The operating temperature will be used by the Boussinesq model which you will enable in the next step. (d) Click OK to close the Operating Conditions panel and set the parameters. c Fluent Inc. September 21,

8 Step 3: Materials The default fluid material is air which is the working fluid in this problem. However, since you are working with a fictitious fluid whose properties have been adjusted to give the desired values of the dimensionless parameters, you must change the default properties for air. You will use an optical thickness al of 0.2 for this calculation. (Since L = 1, the absorption coefficient a will be set to 0.2.) Later in the tutorial, results for an optically thick medium with al = 5 and non-participating medium with al = 0 are computed to show how the different radiation models behave for different optical thicknesses. 1. Define the material properties. Define Materials... (a) Select boussinesq from the drop-down list for Density and then enter 1000 to set the density to 1000 kg/m 3. For details about the Boussinesq model, see the User s Guide. (b) Enter 1.103e4 J/kg-K for Cp to set the specific heat. (c) Enter W/m-K for Thermal Conductivity. (d) Enter kg/m-s for Viscosity. 5-8 c Fluent Inc. September 21, 2006

9 (e) Enter 0.2 m 1 for Absorption Coefficient Use the scroll bar to access the properties that are not initially visible in the panel. (f) Retain the default values for Scattering Coefficient, Scattering Phase Function, and Refractive Index since there is no scattering in this problem. (g) Enter 1e-5 K 1 for Thermal Expansion Coefficient (used by the Boussinesq model). (h) Click Change/Create and then close the Materials panel. Step 4: Boundary Conditions Define Boundary Conditions... c Fluent Inc. September 21,

10 1. Set the boundary conditions for the left wall (wall-4). (a) Enter left-wall for Zone Name. (b) Click the Thermal tab. i. Select Temperature from the Thermal Conditions list. ii. Enter 1000 K for Temperature. (c) Click OK to set the conditions and close the Wall panel c Fluent Inc. September 21, 2006

11 2. Set the boundary conditions for the top wall (wall-4:005). (a) Enter top-wall for Zone Name. (b) Click the Thermal tab and retain the default thermal conditions (Heat Flux of 0) to specify an adiabatic wall. (c) Click OK to set the conditions and close the Wall panel. 3. Set the boundary conditions for the bottom wall (wall-4:006). Note: The bottom wall should be called wall-4:006, but to be sure that you have the correct wall use your right mouse button to click on the bottom wall in the graphics window. When you do this, the corresponding zone will be selected automatically in the Zone list in the Boundary Conditions panel. You can do this when you set boundary conditions for the other walls as well to be sure that you are defining the correct conditions. (a) Enter bottom-wall for Zone Name. (b) Click the Thermal tab and retain the default thermal conditions (Heat Flux of 0) to specify an adiabatic wall. (c) Click OK to set the conditions and close the Wall panel. Note: The Rosseland model does not require you to set a wall emissivity. Later in the tutorial you will need to define the wall emissivity for the other radiation models. c Fluent Inc. September 21,

12 4. Set the boundary conditions for the right wall (wall-4:007). (a) Enter right-wall for Zone Name. (b) Click the Thermal tab. i. Select Temperature from the Thermal Conditions list. ii. Enter 2000 K for Temperature. (c) Click OK to set the conditions and close the Wall panel. 5. Close the Boundary Conditions panel. Step 5: Solution for the Rosseland Model 1. Set the parameters that control the solution. Solve Controls Solution... (a) Retain the default selected Equations and the default Under-Relaxation Factors. (b) Select PRESTO! from the Pressure drop-down list in the Discretization group box. (c) Select Second Order Upwind from the Momentum and Energy drop-down lists. (d) Click OK to set the parameters and close the Solution Controls panel c Fluent Inc. September 21, 2006

13 2. Initialize the flow field. Solve Initialize Initialize... (a) Enter 1500 K for Temperature to set the initial temperature. (b) Click Init and then close the Solution Initialization panel. 3. Enable the plotting of residuals during the calculation. Solve Monitors Residual... c Fluent Inc. September 21,

14 (a) Enable Plot in the Options group box. (b) Click OK to set the conditions and close the Residual Monitors panel. Note: There is no extra residual for the radiation heat transfer because the Rosseland model does not solve extra transport equations for radiation; instead, it augments the thermal conductivity in the energy equation. When you use the P-1 and DO radiation models, which both solve additional transport equations, you will see additional residuals for radiation. 4. Save the case file (rad ross.cas). File Write Case Start the calculation by requesting 200 iterations. Solve Iterate... (a) Enter 200 for Number of Iterations. (b) Click Iterate. The results of the solution will be reported in the console. The solution will converge in approximately 180 iterations. (c) Close the Iterate panel. 6. Save the data file (rad ross.dat). File Write Data c Fluent Inc. September 21, 2006

15 Step 6: Postprocessing for the Rosseland Model 1. Display velocity vectors. Display Vectors... (a) Retain the default settings. (b) Click Display to view the vectors in the graphics display window (Figure 5.3). (c) Close the Vectors panel. c Fluent Inc. September 21,

16 2.11e e e e e e e e e e e e e e e e e e e e e-09 Velocity Vectors Colored By Velocity Magnitude (m/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.3: Velocity Vectors for the Rosseland Model 2. Display contours of stream function. Display Contours... (a) Select Velocity... and Stream Function from the Contours of drop-down lists. (b) Click Display to view the contours in the graphics display window (Figure 5.4) c Fluent Inc. September 21, 2006

17 (c) Close the Contours panel. The recirculatory patterns observed are due to the natural convection in the box. At a low optical thickness (0.2), radiation should not have a large influence on the flow. The flow pattern is expected to be similar to that obtained with no radiation (Figure 5.5). However, the Rosseland model predicts a flow pattern that is very symmetric (Figure 5.4), and quite different from the pure natural convection case. This discrepancy occurs because the Rosseland model is not appropriate for small optical thickness. 7.02e e e e e e e e e e e e e e e e e e e e e+00 Contours of Stream Function (kg/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.4: Contours of Stream Function for the Rosseland Model Extra: If you want to compute the results without radiation yourself, turn off all the radiation models in the Radiation Model panel, set the under-relaxation factor for energy to 0.8 in the Solution Controls panel, and iterate the solution until convergence. (Remember to reset the under-relaxation factor to 1 (the default value) before continuing with the tutorial). Compare the stream function contours without radiation (Figure 5.5) to the plot with the Rosseland radiation model enabled (Figure 5.4). c Fluent Inc. September 21,

18 1.97e e e e e e e e e e e e e e e e e e e e e+00 Contours of Stream Function (kg/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.5: Contours of Stream Function with No Radiation 3. Display filled contours of temperature. Display Contours... (a) Enable Filled in the Options group box c Fluent Inc. September 21, 2006

19 (b) Select Temperature... and Static Temperature from the Contours of drop-down lists. (c) Click Display to view the filled contours in the graphics display window (Figure 5.6). (d) Close the Contours panel. 2.00e e e e e e e e e e e e e e e e e e e e e+03 Contours of Static Temperature (k) FLUENT 6.3 (2d, pbns, lam) Figure 5.6: Contours of Temperature for the Rosseland Model The Rosseland model predicts a temperature field (Figure 5.6) very different from that obtained without radiation (Figure 5.7). For the low optical thickness in this problem, the temperature field predicted by the Rosseland model is not physical. c Fluent Inc. September 21,

20 2.00e e e e e e e e e e e e e e e e e e e e e+03 Contours of Static Temperature (k) FLUENT 6.3 (2d, pbns, lam) Figure 5.7: Contours of Temperature with No Radiation 4. Create an isosurface at y = 0.5, the horizontal line through the center of the box. Surface Iso-Surface... (a) Select Grid... and Y-Coordinate from the Surface of Constant drop-down lists. (b) Click Compute to calculate the extents of the domain. (c) Enter 0.5 for Iso-Values. (d) Enter y=0.5 for New Surface Name c Fluent Inc. September 21, 2006

21 (e) Click Create to create a surface at y = 0.5. The new isosurface at y=0.5 will appear in the From Surface list. (f) Close the Iso-Surface panel. 5. Create an XY plot of y velocity on the isosurface. Plot XY Plot... (a) Retain the default selection of Node Values in the Options group box. If you prefer to display the cell values, disable the Node Values option. Note, however, that you will need to ensure that whatever option you choose for Node Values is used throughout the tutorial for displaying and saving XY plots. This will enable you to correctly compare the XY plots for different radiation models in a later step, as they will use identical options. (b) Retain the default values of 1 for X and 0 for Y in the Plot Direction group box. With a Plot Direction vector of (1, 0), FLUENT will plot the selected variable as a function of x. Since you are plotting the velocity profile on a cross-section of constant y, the x direction is the one in which the velocity varies. (c) Select Velocity... and Y Velocity from the Y Axis Function drop-down lists. (d) Select y=0.5 from the Surfaces selection list. (e) Click Plot to display the x-y plot in the graphics display window (Figure 5.8). c Fluent Inc. September 21,

22 y= e e e e e-05 Velocity Y (m/s) 0.00e e e e e e Position (m) Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.8: XY Plot of Centerline y Velocity for the Rosseland Model The velocity profile reflects the rising plume at the hot right wall, and the falling plume at the cold left wall. Compared to the case with no radiation, the profile predicted by the Rosseland model exhibits thicker wall layers. As discussed before, the expected profile for al = 0.2 is similar to the case with no radiation. (f) Enable Write to File in the Options group box and save the plot data to a file. (g) Click Write... to open the Select File dialog box. (h) Enter rad ross.xy for XY File and click OK. This will save the xy plot file named rad ross.xy to your working folder. (i) Close the Solution XY Plot panel c Fluent Inc. September 21, 2006

23 6. Compute the total wall heat flux on each lateral wall. Report Fluxes... (a) Select Total Heat Transfer Rate in the Options list. (b) Select left-wall and right-wall from the Boundaries selection list. (c) Click Compute. The total wall heat transfer rate is reported for the hot and cold walls as approximately W. The net heat flux on the lateral walls is a negligible imbalance. This is reported in the panel as well as displayed in the console. (d) Close the Flux Reports panel. 7. Save the case and data files (rad ross.cas and rad ross.dat). File Write Case & Data... Thus far in this tutorial, you have learned how to set up a natural convection problem using the Rosseland model to compute radiation. You have also learned to postprocess the results. You will now enable the P-1 model, run a simulation, and compare the results to the Rosseland model. c Fluent Inc. September 21,

24 Step 7: P-1 Model Setup, Solution, and Postprocessing You will now repeat Step 2 through Step 6 to define, solve, and postprocess a P-1 radiation model problem. The main steps are identical to the Rosseland model case. 1. Define the P-1 radiation model. Define Models Radiation... (a) Select P-1 in the Model list and click OK. 2. Define the boundary conditions. Define Boundary Conditions... (a) Retain the default value of 1 for Internal Emissivity for all walls. Remember to click the Thermal tab to view emissivity in the Wall boundary condition panel. (b) Close the Wall and Boundary Conditions panels. 3. Set the solution parameters. Solve Controls Solution... (a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, and 1.0 for Energy in the Under-Relaxation Factors group box. (b) Enter 1.0 for P1 in the Under-Relaxation Factors group box. Scroll down to view the P1 factor. Note that the P1 factor appears in the list because the P-1 model solves an additional radiation transport equation. This problem is relatively easy to converge for the P-1 model since there is not much coupling between the radiation and temperature equations at low optical thicknesses. Consequently a high under-relaxation factor can be used for P-1. (c) Click OK to set the parameters and close the Solution Controls panel. 4. Save the case file (rad p1.cas). File Write Case Continue the calculation by requesting another 200 iterations. Solve Iterate... The P-1 model reaches convergence after approximately 115 additional iterations. 6. Save the data file (rad p1.dat). File Write Data c Fluent Inc. September 21, 2006

25 7. Display velocity vectors (Figure 5.9) of the P-1 model calculation. Display Vectors... Note: The following postprocessing steps do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model for details. 2.86e e e e e e e e e e e e e e e e e e e e e-07 Velocity Vectors Colored By Velocity Magnitude (m/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.9: Velocity Vectors for the P-1 Model c Fluent Inc. September 21,

26 8. Plot the y velocity along the horizontal centerline y = 0.5 (Figure 5.10) and then save the plot data to a file called rad p1.xy. Plot XY Plot... You may need to reselect Velocity... and Y Velocity in the Y Axis Function drop-down lists. Also, remember to deselect the Write to File option so that you can access the Plot button to generate the plot. y= e e e e e-05 Velocity Y (m/s) 0.00e e e e e e e Position (m) Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.10: XY Plot of Centerline y Velocity for the P-1 Model 9. Compute the total wall heat transfer rate. Report Fluxes... The total heat transfer rate reported on the right wall is W. The heat imbalance at the lateral walls is negligible. You will see later that the Rosseland and P-1 wall heat transfer rates are substantially different from those obtained by the DTRM and the DO model. Notice how different the velocity vectors and y-velocity profile are from those obtained using the Rosseland model. The P-1 velocity profiles show a clear momentum boundary layer along the hot and cold walls. These profiles are much closer to those obtained from the non-radiating case (Figures 5.11 and 5.12). Though the P-1 model is not appropriate for this optically thin limit, it yields the correct velocity profiles since the radiation source in the energy equation, which is proportional to the absorption coefficient, is small. The Rosseland model uses an effective conductivity to account for radiation, and yields the wrong temperature field, which in turn results in an erroneous velocity field c Fluent Inc. September 21, 2006

27 2.16e e e e e e e e e e e e e e e e e e e e e-08 Velocity Vectors Colored By Velocity Magnitude (m/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.11: Velocity Vectors with No Radiation y= e e e e e-05 Velocity Y (m/s) 0.00e e e e e e Position (m) Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.12: XY Plot of Centerline y Velocity with No Radiation c Fluent Inc. September 21,

28 Step 8: DTRM Setup, Solution, and Postprocessing 1. Define the DTRM and the ray tracing. Define Models Radiation... (a) Select Discrete Transfer (DTRM) in the Model list. The Radiation Model panel will expand to show additional inputs. (b) Retain the default parameters. (c) Click OK in the Radiation Model panel to open the DTRM Rays panel. i. Retain the default settings for Clustering and Angular Discretization. The number of Cells Per Volume Cluster and Faces Per Surface Cluster control the total number of radiating surfaces and absorbing cells. For a small 2D problem, the default number of 1 is acceptable. For a large problem, however, you will want to increase these numbers to reduce the ray tracing expense. The Theta Divisions and Phi Divisions control the number of rays being created from each surface cluster. For most practical problems, however, the default settings will suffice. ii. Click OK to open the Select File dialog box. See Section of the User s Guide for a more detailed description of the ray tracing procedure c Fluent Inc. September 21, 2006

29 iii. Enter rad dtrm.ray for the Ray File in the Select File dialog box. iv. Click OK to write the ray file. FLUENT will report on the status of the ray tracing in the console. 2. Set the parameters that control the solution. Solve Controls Solution... (a) Retain the default solution values of 0.3 for Pressure, 0.7 for Momentum, and 1.0 for Energy in the Under-Relaxation Factors list. 3. Save the case file (rad dtrm.cas). File Write Case Continue the calculation by requesting another 100 iterations. Solve Iterate... The solution will converge after about 80 additional iterations. 5. Save the data file (rad dtrm.dat). File Write Data Display velocity vectors (Figure 5.13) of the DTRM calculation. Display Vectors... Note: The following postprocessing steps do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model for details. 7. Plot the y velocity along the horizontal centerline y = 0.5 (Figure 5.14), and save the plot data to a file called rad dtrm.xy. Plot XY Plot... You may need to reselect Velocity... and Y Velocity from the Y Axis Function dropdown lists. Also, remember to deselect the Write to File option so that you can access the Plot button to generate the plot. 8. Compute the total wall heat transfer rate. Report Fluxes... The total heat transfer rate reported on the right wall is W. Note that this is substantially lower than the values predicted by the Rosseland and P-1 models. c Fluent Inc. September 21,

30 2.88e e e e e e e e e e e e e e e e e e e e e-07 Velocity Vectors Colored By Velocity Magnitude (m/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.13: Velocity Vectors for the DTRM y= e e e e e-05 Velocity Y (m/s) 0.00e e e e e e e Position (m) Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.14: XY Plot of Centerline y Velocity for the DTRM 5-30 c Fluent Inc. September 21, 2006

31 Step 9: DO Model Setup, Solution, and Postprocessing 1. Define the DO model and the angular discretization. Define Models Radiation... (a) Select Discrete Ordinates (DO) in the Model list. The Radiation Model panel will expand to show additional inputs for the DO model. (b) Enter 1 for Flow Iterations per Radiation Iteration in the Iteration Parameters group box. This is a relatively simple flow problem and will converge easily. Consequently it is useful to do the DO calculation every iteration of the flow solution. For problems that are difficult to converge it is sometimes useful to allow the flow solution to establish itself between radiation calculations. In such cases it may be useful to set Flow Iterations Per Radiation Iteration to a higher value, such as 10. (c) Retain the default settings for Angular Discretization and Non-Gray Model. The Number of Bands for the Non-Gray Model is zero because gray radiation, only, is being modeled in this tutorial. See Section of the User s Guide for details about the angular discretization used by the DO model. (d) Click OK. Note: FLUENT will present an Information dialog box telling you that new material properties have been added for the radiation model. The property that is new for the DO model is the refractive index, which is relevant only c Fluent Inc. September 21,

32 when you are modeling semi-transparent media. Since you are not modeling semi-transparent media here you can simply click OK in the dialog box to acknowledge this information. 2. Set the parameters that control the solution. Solve Controls Solution... (a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, 1.0 for Energy, and 1.0 for Discrete Ordinates in the Under-Relaxation Factors group box. Note that the Discrete Ordinates factor appears in the list because the DO model solves an additional radiation transport equation. (b) Retain the default setting of First Order Upwind in the Discrete Ordinates dropdown list for Discretization. 3. Save the case file (rad do.cas). File Write Case Continue the calculation by requesting another 100 iterations. Solve Iterate... The solution will converge after approximately 25 additional iterations. 5. Save the data file (rad do.dat). File Write Data Display velocity vectors of the DO calculation (Figure 5.15). Display Vectors... Note: The following postprocessing steps do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model for details. 7. Plot the y velocity along the horizontal centerline y = 0.5m (Figure 5.16), and save the plot data to a file called rad do.xy. Plot XY Plot... You may need to reselect Velocity... and Y Velocity in the Y Axis Function drop-down lists. Also, remember to disable the Write to File option so that you can access the Plot button to generate the plot c Fluent Inc. September 21, 2006

33 2.89e e e e e e e e e e e e e e e e e e e e e-07 Velocity Vectors Colored By Velocity Magnitude (m/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.15: Velocity Vectors for the DO Model y= e e e-04 Velocity Y (m/s) 0.00e e e e Position (m) Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.16: XY Plot of Centerline y Velocity for the DO Model c Fluent Inc. September 21,

34 8. Compute the total wall heat transfer rate. Report Fluxes... The total heat transfer rate reported on the right wall is W. Note that this is about 1.5% higher than that predicted by the DTRM. The DO and DTRM values are comparable to each other, while the Rosseland and P-1 values are both substantially different. The DTRM and DO models are valid across the range of optical thickness, and the heat transfer rates computed using them are expected to be closer to the correct heat transfer rate. Step 10: Comparison of y-velocity Plots In this step, you will read the plot files you saved for all the solutions and compare them in a single plot. 1. Read in all the XY plot files. Plot File... (a) Click Add... to open the Select File dialog box. i. Select rad do.xy, rad dtrm.xy, rad p1.xy, and rad ross.xy from the Files list in the Select File dialog box. They will be added to the XY File(s) list. If you accidentally add an incorrect file, you can select it in this list and click Remove. ii. Click OK in the Select File dialog box to load the 4 files. The files will be listed in the Files list in the File XY Plot panel. (b) Click Plot in the File XY Plot panel c Fluent Inc. September 21, 2006

35 Extra: You can click Curves... to open the Curves panel, where you can define different styles for different plot curves. In Figure 5.17, different symbols have been selected for each curve. (c) Close the File XY Plot panel. Extra: You can resize and move the legend box in the XY plot displayed in the graphics window so that you can read the information inside it. To resize the box, press any mouse button on a corner and drag the mouse to the desired position. To move the legend box, press any mouse button anywhere else on the box and drag it to the desired location. Y Velocity Y Velocity Y Velocity (ra 3.00e-04 Y Velocity (ra Y Velocity (ra 2.00e e-04 Velocity Y 0.00e e e e Position Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.17: Comparison of Computed y Velocities for al = 0.2 Notice in Figure 5.17 that the velocity profiles for the P-1 model, DTRM, and DO model are nearly identical even though the reported wall heat transfer rates are different. This is because in an optically thin problem, the velocity field is essentially independent of the radiation field, and all three models give a flow solution very close to the non-radiating case. The Rosseland model gives substantially erroneous solutions for an optically thin case. c Fluent Inc. September 21,

36 Step 11: Comparison of Radiation Models for an Optically Thick Medium In the previous steps you compared the results of four radiation models for an optically thin (al = 0.2) medium. It was found that as a result of the low optical thickness, the velocity fields predicted by the P-1, DTRM, and DO models were very similar and close to that obtained in the non-radiating case. The wall heat transfer rates for DO and DTRM were very close in value, and substantially different from those obtained with the Rosseland and P-1 models. In this step you will recalculate a solution (using each radiation model) for an optically thick (al = 5) medium. This is accomplished by increasing the value of the absorption coefficient from 0.2 to 5. You will repeat the process outlined in the steps that follow for each set of case and data files that you saved earlier in the tutorial. 1. Read in the case and data file saved earlier (e.g., rad ross.cas and rad ross.dat). File Read Case & Data Define the new material property. Define Materials... (a) Enter 5 for the Absorption Coefficient in the Materials panel. This will result in an optical thickness al of 5, since L = 1. (b) Click Change/Create and then close the panel. 3. Calculate the new solution until it converges. Solve Iterate... For the DTRM calculation you may need to click Iterate repeatedly until the radiation field is updated. Since the number of Flow Iterations Per Radiation Iteration in the Radiation Model panel is 10, it is possible that the radiation field will not be updated for as many as 9 iterations, although FLUENT will report that the solution is converged. If this happens, continue to click the Iterate button until the radiation field is updated and the solution proceeds for multiple iterations. 4. Save the new case and data files using a different file name (e.g., rad ross5.cas and rad ross5.dat). File Write Case & Data Compute the total wall heat transfer rate. Report Fluxes Plot the y velocity along the horizontal centerline, and save the plot data to a file (e.g., rad ross5.xy). Plot XY Plot c Fluent Inc. September 21, 2006

37 7. Compare the computed heat transfer rates for the four models by plotting the y-velocity profiles in a single plot (Figure 5.18). The wall heat transfer rates predicted by the four radiation models range from to W. Plot File... Note: Click Delete in the File XY Plot panel to remove the old XY plot data files. Y Velocity Y Velocity Y Velocity (ra 5.00e-04 Y Velocity (ra Y Velocity (ra 4.00e e e e-04 Velocity Y 0.00e e e e e e Position Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.18: Comparison of Computed y Velocities for al = 5 The XY plots of y velocity are nearly identical for the P-1 model, DO model, and DTRM. The Rosseland model gives somewhat different velocities, but is still within 10% of the other results. The Rosseland and P-1 models are suitable for the optically thick limit; the DTRM and DO models are valid across the range of optical thicknesses. Consequently, they yield similar answers at al = 5. For many applications with large optical thicknesses, the Rosseland and P-1 models provide a simple low-cost alternative. c Fluent Inc. September 21,

38 Step 12: S2S Setup, Solution, and Postprocessing for a Non-Participating Medium In the previous steps you compared the results of four radiation models for optically thin (al = 0.2) and optically thick (al = 5) media. The Surface-to-Surface (S2S) radiation model can be used to account for the radiation exchange in an enclosure of gray-diffuse surfaces. The energy exchange between two surfaces depends in part on their size, separation distance, and orientation. These parameters are accounted for by a geometric function called a view factor. The S2S model assumes that all surfaces are gray and diffuse. Thus according to the graybody model, if a certain amount of radiation is incident on a surface, then a fraction is reflected, a fraction is absorbed, and a fraction is transmitted. The main assumption of the S2S model is that any absorption, emission, or scattering of radiation by the medium can be ignored. Therefore surface-to-surface radiation, only, needs to be considered for analysis. For most applications the surfaces in question are opaque to thermal radiation (in the infrared spectrum), so the surfaces can be considered opaque. For gray, diffuse, and opaque surfaces it is valid to assume that the emissivity is equal to the absorptivity and that reflectivity is equal to 1 minus the emissivity. When the S2S model is used, you also have the option to define a partial enclosure which allows you to disable the view factor calculation for walls with negligible emission/absorption or walls that have uniform temperature. The main advantage of this option is to speed up the view factor calculation and the radiosity calculation. In this step you will calculate a solution for al = 0 using the S2S radiation model without partial enclosure. In the next step you will use the DTRM and DO models for al = 0, and compare the results of the three models. The Rosseland and P-1 models are not considered here as they have been shown (earlier in the tutorial) to be inappropriate for optically thin media. Later in the tutorial you will calculate a solution for S2S model with partial enclosure and compare the results with the solution for S2S model for a non-participating medium that is calculated here c Fluent Inc. September 21, 2006

39 1. Define the S2S model and the view factor and cluster parameters. Define Models Radiation... (a) Select Surface to Surface (S2S) in the Model list. The Radiation Model panel will expand to show additional inputs for the S2S model. c Fluent Inc. September 21,

40 (b) Click Set... for Parameters in the View Factors group box to open the View Factor and Cluster Parameters panel. You will define the view factor and cluster parameters. i. Click OK to accept the default settings and close the View Factor and Cluster Parameters panel. The S2S radiation model is computationally very expensive when there are a large number of radiating surfaces. The number of radiating surfaces is reduced by clustering surfaces into surface clusters. The surface clusters are made by starting from a face and adding its neighbors and their neighbors until a specified number of faces per surface cluster is collected. For a small 2D problem, the default value of 1 for Faces Per Surface Cluster is acceptable. For a large problem you can increase this number to reduce the memory requirement for the view factor file that is saved in a later step. This may also lead to some reduction in the computational expense. However, this is at the cost of some accuracy. Using the Blocking option ensures that any additional surface that is blocking the view between two opposite surfaces is considered in the view factor calculation. In this case there is no obstructing surface between the opposite walls so selecting either the Blocking or the Nonblocking option will produce the same result. The default setting for Smoothing is None which is appropriate for small problems. The Least Square option is more accurate, but also more computationally expensive c Fluent Inc. September 21, 2006

41 See Section of the User s Guide for details about view factors and clusters for the S2S model. (c) Click Compute/Write... for Methods in the View Factors group box to open the Select File dialog box and to compute the view factors. You will specify a file name where the cluster and view factor parameters will be stored. This step is required if the problem is being solved for the first time, only. For subsequent calculations you can read the view factor and cluster information from an existing file (by clicking Read... instead of Compute/Write...). i. Enter rad s2s.gz as the file name for S2S File and click OK in the Select File dialog box. Note: The size of the viewfactor file can be very large if not compressed. It is highly recommended to compress the view factor file by providing.gz or.z extension after the name (i.e. rad s2s.gz or rad s2s.z). For small files, you can provide the.s2s file after the name. FLUENT will print an informational message describing the progress of the view factor calculation in the console. (d) Click OK to close the Radiation Model panel. 2. Set the parameters that control the solution. Solve Controls Solution... (a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, 1.0 for Energy in the Under-Relaxation Factors list. 3. Save the case file (rad s2s.cas). File Write Case Continue the calculation by requesting another 200 iterations. Solve Iterate Save the data file (rad s2s.dat). File Write Data Display velocity vectors of the S2S calculation (Figure 5.19). Display Vectors... Note: The following postprocessing steps do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model if you need more details. c Fluent Inc. September 21,

42 2.48e e e e e e e e e e e e e e e e e e e e e-07 Velocity Vectors Colored By Velocity Magnitude (m/s) FLUENT 6.3 (2d, pbns, lam) Figure 5.19: Velocity Vectors for the S2S Model 7. Plot the y velocity along the horizontal centerline (Figure 5.20), and save the plot data to a file called rad s2s.xy. Plot XY Plot... You may have to reselect Y Velocity from the Y Axis Function drop-down lists. Also, remember to deselect the Write to File option to access the Plot button to generate the plot. y= e e e e e-05 Velocity Y (m/s) 0.00e e e e e e Position (m) Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.20: XY Plot of Centerline y Velocity for the S2S Model 5-42 c Fluent Inc. September 21, 2006

43 8. Compute the total wall heat transfer rate. Report Fluxes... The total heat transfer rate on the right wall is W. Step 13: Comparison of Radiation Models for a Non-Participating Medium In this step you will calculate a solution for the al = 0 case using the DTRM and DO models and then compare the results with the S2S results. 1. Read in the case and data files saved earlier for the DTRM and DO models (e.g., rad dtrm.cas and rad dtrm.dat). File Read Case & Data Define the new material property. Define Materials... (a) Enter 0 for the Absorption Coefficient. This will result in an optical thickness al of 0. (b) Click Change/Create and then close the Materials panel. 3. Calculate the new solution until it converges. Solve Iterate... For the DTRM calculation you may need to click the Iterate button repeatedly until the radiation field is updated. Since the number of Flow Iterations Per Radiation Iteration in the Radiation Model panel is 10, it is possible that the radiation field will not be updated for as many as 9 iterations, although FLUENT will report that the solution is converged. If this happens, keep clicking the Iterate button until the radiation field is updated and the solution proceeds for multiple iterations. 4. Save the new case and data files using a different file name (e.g., rad dtrm0.cas and rad dtrm0.dat). File Write Case & Data Compute the total wall heat transfer rate. Report Fluxes Plot the y velocity along the horizontal centerline, and save the plot data to a file (e.g., rad dtrm0.xy) Plot XY Plot... c Fluent Inc. September 21,

44 7. Compare the computed heat transfer rates for the three models. For the S2S model, the total heat transfer rate on the right wall was W. This is about 5% higher than that predicted by the DTRM and 1.5% higher than DO. Although the S2S, DO, and DTRM values are comparable to each other, this problem involves enclosure radiative transfer without participating media. Therefore, the S2S model provides the most accurate solution. 8. Compare the y-velocity profiles in a single plot (Figure 5.21) Plot File... (a) Use the Delete button in the File XY Plot panel to remove the old XY plot data files. (b) Read in all the XY plot files you saved for the S2S, DTRM, and DO models. (c) Click Plot. (d) Close the File XY Plot panel. 2.50e e e-04 Y Velocity Y Velocity Y Velocity (rad_dtrm0.xy) Y Velocity (rad_do0.xy) 1.00e e-05 Velocity Y 0.00e e e e e e Position Y Velocity FLUENT 6.3 (2d, pbns, lam) Figure 5.21: Comparison of Computed y Velocities for al = 0 In Figure 5.21, the velocity profiles for the DTRM, DO, and S2S models are almost identical even though the wall heat transfer rates are different c Fluent Inc. September 21, 2006

45 Step 14: S2S Definition, Solution and Postprocessing with Partial Enclosure As mentioned earlier, when the S2S model is used, you also have the option to define a partial enclosure ; i.e., you can disable the view factor calculation for walls with negligible emission/absorption, or walls that have uniform temperature. Even though the view factor will not be computed for these walls, they will still emit radiation at a fixed temperature called the partial enclosure temperature. The main advantage of this is to speed up the view factor and the radiosity calculation. For this problem, specify the left wall boundary as the non-participating wall in S2S radiation. Consequently, you need to specify the partial enclosure temperature for the wall boundary that is not participating in S2S radiation. Note that if multiple wall boundaries are not participating in S2S radiation and each has a different temperature, then the partial enclosure option may not yield accurate results. This is because the same partial enclosure temperature is specified for each of the non-participating walls. 1. Read in the case and data file saved earlier for the S2S model (rad s2s.cas and rad s2s.dat). File Read Case & Data Set the partial enclosure parameters for the S2S model. Define Models Radiation... (a) Enter 1000 for Temperature in the Partial Enclosure group box. (b) Click OK to close the Radiation Model panel. c Fluent Inc. September 21,

46 Previous radiation model setups for this problem specified the left wall temperature as 1000 k. Therefore set the partial enclosure to this temperature. 3. Define the boundary conditions for the left-wall. Define Boundary Conditions (a) Click the Radiation tab and disable Participates in S2S Radiation in the S2S Parameters group box. (b) Click OK to close the Wall panel. (c) Close the Boundary Conditions panel. 4. Compute the view factors for the S2S model. Define Models Radiation... The view factor file will store the view factors for the radiating surfaces only. This may help you control the size of the view factor file as well as the memory required to store view factors in FLUENT. Furthermore, the time required to compute the view factors will reduce as only the view factors for radiating surfaces will be calculated. You should compute the view factors only when you have specified the boundaries that will participate in the radiation model using the Boundary Conditions panel. If you first compute the view factors and then make a change to the boundary conditions, FLUENT will use the view factor file stored earlier for calculating a solution, in which case, the changes that you made to the model will not be used for the calculation. Therefore, you should recompute the view factors and save the case file whenever you modify the number of objects that will participate in radiation c Fluent Inc. September 21, 2006

47 (a) Click Compute/Write... under Methods to open the Select File dialog box. You will specify a file name where the view factor parameters are stored. i. Enter rad s2spe.gz as file name for S2S File and click OK. (b) Click OK to close the Radiation Model panel. FLUENT will print an informational message describing the progress of the view factor calculation. 5. Set the parameters that control the solution. Solve Controls Solution... (a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, and 1.0 for Energy in the Under-Relaxation Factors list. 6. Save the case file (rad s2spe.cas). File Write Case Continue the calculation by requesting another 100 iterations. Solve Iterate... The solution will converge after approximately 80 additional iterations. 8. Save the data file (rad s2spe.dat). File Write Data Display velocity vectors of the S2S calculation (Figure 5.22). Display Vectors... Note: The following postprocessing steps do not include detailed instructions because the procedure is the same one that you followed for the Rosseland model postprocessing. See Step 6: Postprocessing for the Rosseland Model if you need more details. 10. Plot the y velocity along the horizontal centerline (Figure 5.23), and save the plot data to a file called rad s2spe.xy. Plot XY Plot... You may have to reselect Y Velocity from the Y Axis Function drop-down lists. Also, remember to deselect the Write to File option to access the Plot button to generate the plot. c Fluent Inc. September 21,