tutorial 5. modeling radiation and natural convectionbarbertj/cfd training/fluent/fluent...

Tutorial 5. Modeling Radiation and Natural Convection

Introduction

In this tutorial combined radiation and natural convection are solved in a two-dimensionalsquare 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 convec-tion 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 flowvisualization.

Prerequisites

This tutorial assumes that you are familiar with the menu structure in FLUENT and thatyou have completed Tutorial 1 . Some steps in the setup and solution procedure will notbe shown explicitly.

Problem Description

The problem to be considered is shown schematically in Figure 5.1. A square box of sideL has a hot right wall at T = 2000 K, a cold left wall at T = 1000 K, and adiabatictop and bottom walls. Gravity acts downwards. A buoyant flow develops because ofthermally-induced density gradients. The medium contained in the box is assumed to beabsorbing and emitting, so that the radiant exchange between the walls is attenuated byabsorption and augmented by emission in the medium. All walls are black. The objectiveis to compute the flow and temperature patterns in the box, as well as the wall heat flux,

c© Fluent Inc. September 21, 2006 5-1

Modeling Radiation and Natural Convection

using the radiation models available in FLUENT, and to compare their performance fordifferent values of the optical thickness aL.

The working fluid has a Prandtl number of approximately 0.71, and the Rayleigh numberbased on L is 5 × 105. This means the flow is inherently laminar. The Boussinesqassumption is used to model buoyancy. The Planck number k/(4σLT 3

0 ) is 0.02, andmeasures the relative importance of conduction to radiation; here T0 = (Th + Tc)/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., gravitationalacceleration) have been adjusted to yield the desired Prandtl, Rayleigh, and Plancknumbers.

ρ = 1000 kg/m3

k = 15.309 W/mK

µ = 10-3

β = 10-5

g = -6.96 x 10-5 2

c = 1.1030x10p4

a = 0, 0.2, 5 1/mL = 1 m

5Ra = 5 x 10

Pl = 0.02Pr = 0.71

τ = 0.2, 5

Adiabatic

➢

➢L

x

y

g

T=

2000K

h

T=

1000

Kc

J/kgK

kg/ms1/K

m/s

Figure 5.1: Schematic of the Problem

Setup and Solution

Preparation

1. Download radiation_natural_convection.zip from the Fluent Inc. User Ser-vices Center or copy it from the FLUENT documentation CD to your workingfolder (as described in Tutorial 1).

2. Unzip radiation_natural_convection.zip.

rad.msh can be found in the radiation natural convection folder created afterunzipping the file.

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

5-2 c© Fluent Inc. September 21, 2006


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 progressof 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 theconsole. 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. Youwill need to separate them out into four different walls in the next step so thatyou can specify different boundary conditions for each wall.



GridFLUENT 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 separatedinto 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 SeparateFace Zones panel. The new zone information is also reported in the console.



(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 ofSurfaces.

(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 dothis, right-click on one of the wall boundaries in the graphics window to checkwhich wall zone number corresponds to each wall boundary. Information willbe displayed in the FLUENT console about the associated zone, including thename of the zone. This feature is especially useful when you have several zonesof the same type and you want to distinguish between them quickly. In somecases, you may want to disable the display of the interior grid so as to moreaccurately select the boundaries for identification.

(c) Close the Grid Display panel.



Step 2: Models

As discussed earlier, in this tutorial you will define each radiation model in turn, obtaina 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 discreteordinates (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...

2. Define the Rosseland radiation model.

Define −→ Models −→Radiation...



(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 materialproperties have been added for the radiation model. You will be setting prop-erties later so you can simply click OK in the dialog box to acknowledge thisinformation.

Note: FLUENT will automatically enable the energy calculation when you se-lect 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/s2 for Y in the Gravitational Acceleration group box.

As previously mentioned, the gravitational acceleration is adjusted to yield thecorrect 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 groupbox.

The operating temperature will be used by the Boussinesq model which you willenable in the next step.

(d) Click OK to close the Operating Conditions panel and set the parameters.



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 givethe desired values of the dimensionless parameters, you must change the default propertiesfor air. You will use an optical thickness aL of 0.2 for this calculation. (Since L = 1, theabsorption coefficient a will be set to 0.2.) Later in the tutorial, results for an opticallythick medium with aL = 5 and non-participating medium with aL = 0 are computed toshow 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 toset the density to 1000 kg/m3.

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 15.309 W/m-K for Thermal Conductivity.

(d) Enter 0.001 kg/m-s for Viscosity.



(e) Enter 0.2 m−1 for Absorption Coefficient

Use the scroll bar to access the properties that are not initially visible in thepanel.

(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 Boussinesqmodel).

(h) Click Change/Create and then close the Materials panel.

Step 4: Boundary Conditions

Define −→Boundary Conditions...



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.



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 of0) to specify an adiabatic wall.


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 thecorrect wall use your right mouse button to click on the bottom wall in thegraphics window. When you do this, the corresponding zone will be selectedautomatically in the Zone list in the Boundary Conditions panel. You can dothis when you set boundary conditions for the other walls as well to be surethat 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 of0) to specify an adiabatic wall.


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 theother radiation models.



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.


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 groupbox.

(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.



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...



(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 Rosse-land model does not solve extra transport equations for radiation; instead, itaugments the thermal conductivity in the energy equation. When you use theP-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...

5. 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 willconverge in approximately 180 iterations.

(c) Close the Iterate panel.

6. Save the data file (rad ross.dat).

File −→ Write −→Data...



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.



Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.3 (2d, pbns, lam)

2.11e-042.01e-041.90e-041.80e-041.69e-041.58e-041.48e-041.37e-041.27e-041.16e-041.06e-049.51e-058.45e-057.40e-056.34e-055.28e-054.23e-053.17e-052.11e-051.06e-053.34e-09

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) 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 theflow. 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 verysymmetric (Figure 5.4), and quite different from the pure natural convection case.This discrepancy occurs because the Rosseland model is not appropriate for smalloptical thickness.

Contours of Stream Function (kg/s)FLUENT 6.3 (2d, pbns, lam)

7.02e-026.67e-026.32e-025.97e-025.62e-025.26e-024.91e-024.56e-024.21e-023.86e-023.51e-023.16e-022.81e-022.46e-022.11e-021.75e-021.40e-021.05e-027.02e-033.51e-030.00e+00

Figure 5.4: Contours of Stream Function for the Rosseland Model

Extra: If you want to compute the results without radiation yourself, turn off allthe radiation models in the Radiation Model panel, set the under-relaxationfactor for energy to 0.8 in the Solution Controls panel, and iterate the solu-tion until convergence. (Remember to reset the under-relaxation factor to 1(the default value) before continuing with the tutorial). Compare the streamfunction contours without radiation (Figure 5.5) to the plot with the Rosselandradiation model enabled (Figure 5.4).



Contours of Stream Function (kg/s)FLUENT 6.3 (2d, pbns, lam)

1.97e-021.87e-021.77e-021.67e-021.58e-021.48e-021.38e-021.28e-021.18e-021.08e-029.85e-038.87e-037.88e-036.90e-035.91e-034.93e-033.94e-032.96e-031.97e-039.85e-040.00e+00

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.



(b) Select Temperature... and Static Temperature from the Contours of drop-downlists.

(c) Click Display to view the filled contours in the graphics display window (Fig-ure 5.6).

(d) Close the Contours panel.

Contours of Static Temperature (k)FLUENT 6.3 (2d, pbns, lam)

2.00e+031.95e+031.90e+031.85e+031.80e+031.75e+031.70e+031.65e+031.60e+031.55e+031.50e+031.45e+031.40e+031.35e+031.30e+031.25e+031.20e+031.15e+031.10e+031.05e+031.00e+03

Figure 5.6: Contours of Temperature for the Rosseland Model

The Rosseland model predicts a temperature field (Figure 5.6) very different fromthat obtained without radiation (Figure 5.7). For the low optical thickness in thisproblem, the temperature field predicted by the Rosseland model is not physical.



Contours of Static Temperature (k)FLUENT 6.3 (2d, pbns, lam)

2.00e+031.95e+031.90e+031.85e+031.80e+031.75e+031.70e+031.65e+031.60e+031.55e+031.50e+031.45e+031.40e+031.35e+031.30e+031.25e+031.20e+031.15e+031.10e+031.05e+031.00e+03

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.



(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 NodeValues is used throughout the tutorial for displaying and saving XY plots. Thiswill enable you to correctly compare the XY plots for different radiation modelsin 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 groupbox.

With a Plot Direction vector of (1, 0), FLUENT will plot the selected variableas a function of x. Since you are plotting the velocity profile on a cross-sectionof 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).



Y VelocityFLUENT 6.3 (2d, pbns, lam)

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

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 thefalling plume at the cold left wall. Compared to the case with no radiation,the profile predicted by the Rosseland model exhibits thicker wall layers. Asdiscussed before, the expected profile for aL = 0.2 is similar to the case withno 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.



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 ap-proximately 7.43× 105 W. The net heat flux on the lateral walls is a negligibleimbalance. 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 problemusing the Rosseland model to compute radiation. You have also learned to postprocess theresults. You will now enable the P-1 model, run a simulation, and compare the results tothe Rosseland model.



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-1radiation model problem. The main steps are identical to the Rosseland model case.

1. Define the P-1 radiation model.


(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 toclick 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.


(a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, and 1.0 forEnergy 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 thelist 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 notmuch coupling between the radiation and temperature equations at low opticalthicknesses. 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).


5. Continue the calculation by requesting another 200 iterations.


The P-1 model reaches convergence after approximately 115 additional iterations.

6. Save the data file (rad p1.dat).




7. Display velocity vectors (Figure 5.9) of the P-1 model calculation.


Note: The following postprocessing steps do not include detailed instructions be-cause the procedure is the same one that you followed for the Rosseland modelpostprocessing. See Step 6: Postprocessing for the Rosseland Modelfor details.



Figure 5.9: Velocity Vectors for the P-1 Model



8. Plot the y velocity along the horizontal centerline y = 0.5 (Figure 5.10) and thensave the plot data to a file called rad p1.xy.


You may need to reselect Velocity... and Y Velocity in the Y Axis Function drop-downlists. Also, remember to deselect the Write to File option so that you can access thePlot button to generate the plot.


Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

-3.00e-04

y=0.5

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 8.47 × 105 W. The heatimbalance at the lateral walls is negligible. You will see later that the Rosselandand P-1 wall heat transfer rates are substantially different from those obtained bythe DTRM and the DO model.

Notice how different the velocity vectors and y-velocity profile are from those obtainedusing the Rosseland model. The P-1 velocity profiles show a clear momentum boundarylayer along the hot and cold walls. These profiles are much closer to those obtained fromthe non-radiating case (Figures 5.11 and 5.12). Though the P-1 model is not appropriatefor this optically thin limit, it yields the correct velocity profiles since the radiation sourcein the energy equation, which is proportional to the absorption coefficient, is small. TheRosseland model uses an effective conductivity to account for radiation, and yields thewrong temperature field, which in turn results in an erroneous velocity field.





Figure 5.11: Velocity Vectors with No Radiation


Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

Figure 5.12: XY Plot of Centerline y Velocity with No Radiation



Step 8: DTRM Setup, Solution, and Postprocessing

1. Define the DTRM and the ray tracing.


(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 Clustercontrol the total number of radiating surfaces and absorbing cells. Fora small 2D problem, the default number of 1 is acceptable. For a largeproblem, however, you will want to increase these numbers to reduce theray tracing expense. The Theta Divisions and Phi Divisions control thenumber of rays being created from each surface cluster. For most practicalproblems, however, the default settings will suffice.

ii. Click OK to open the Select File dialog box.

See Section 13.3.5 of the User’s Guide for a more detailed description ofthe ray tracing procedure.



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.



(a) Retain the default solution values of 0.3 for Pressure, 0.7 for Momentum, and1.0 for Energy in the Under-Relaxation Factors list.

3. Save the case file (rad dtrm.cas).




The solution will converge after about 80 additional iterations.

5. Save the data file (rad dtrm.dat).


6. Display velocity vectors (Figure 5.13) of the DTRM calculation.



7. Plot the y velocity along the horizontal centerline y = 0.5 (Figure 5.14), and savethe plot data to a file called rad dtrm.xy.


You may need to reselect Velocity... and Y Velocity from the Y Axis Function drop-down lists. Also, remember to deselect the Write to File option so that you canaccess the Plot button to generate the plot.



The total heat transfer rate reported on the right wall is 6.07×105 W. Note that thisis substantially lower than the values predicted by the Rosseland and P-1 models.





Figure 5.13: Velocity Vectors for the DTRM


Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

-3.00e-04

y=0.5

Figure 5.14: XY Plot of Centerline y Velocity for the DTRM



Step 9: DO Model Setup, Solution, and Postprocessing

1. Define the DO model and the angular discretization.


(a) Select Discrete Ordinates (DO) in the Model list.

The Radiation Model panel will expand to show additional inputs for the DOmodel.

(b) Enter 1 for Flow Iterations per Radiation Iteration in the Iteration Parametersgroup box.

This is a relatively simple flow problem and will converge easily. Consequentlyit is useful to do the DO calculation every iteration of the flow solution. Forproblems that are difficult to converge it is sometimes useful to allow the flowsolution to establish itself between radiation calculations. In such cases it maybe useful to set Flow Iterations Per Radiation Iteration to a higher value, suchas 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 13.3.6 of the User’s Guide for details about the angular discretiza-tion used by the DO model.

(d) Click OK.

Note: FLUENT will present an Information dialog box telling you that newmaterial properties have been added for the radiation model. The propertythat is new for the DO model is the refractive index, which is relevant only



when you are modeling semi-transparent media. Since you are not mod-eling semi-transparent media here you can simply click OK in the dialogbox to acknowledge this information.



(a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, 1.0 forEnergy, and 1.0 for Discrete Ordinates in the Under-Relaxation Factors groupbox.

Note that the Discrete Ordinates factor appears in the list because the DO modelsolves an additional radiation transport equation.

(b) Retain the default setting of First Order Upwind in the Discrete Ordinates drop-down list for Discretization.

3. Save the case file (rad do.cas).




The solution will converge after approximately 25 additional iterations.

5. Save the data file (rad do.dat).


6. Display velocity vectors of the DO calculation (Figure 5.15).



7. Plot the y velocity along the horizontal centerline y = 0.5m (Figure 5.16), and savethe plot data to a file called rad do.xy.


You may need to reselect Velocity... and Y Velocity in the Y Axis Function drop-downlists. Also, remember to disable the Write to File option so that you can access thePlot button to generate the plot.





Figure 5.15: Velocity Vectors for the DO Model


Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

3.00e-04

2.00e-04

1.00e-04

0.00e+00

-1.00e-04

-2.00e-04

-3.00e-04

y=0.5

Figure 5.16: XY Plot of Centerline y Velocity for the DO Model





The total heat transfer rate reported on the right wall is 6.12 × 105 W. Note thatthis is about 1.5% higher than that predicted by the DTRM. The DO and DTRMvalues are comparable to each other, while the Rosseland and P-1 values are bothsubstantially different. The DTRM and DO models are valid across the range ofoptical thickness, and the heat transfer rates computed using them are expected tobe 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 themin 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 listin the Select File dialog box.

They will be added to the XY File(s) list. If you accidentally add an incor-rect 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.



Extra: You can click Curves... to open the Curves panel, where you can definedifferent styles for different plot curves. In Figure 5.17, different symbolshave 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 thegraphics window so that you can read the information inside it. To resize thebox, press any mouse button on a corner and drag the mouse to the desiredposition. To move the legend box, press any mouse button anywhere else onthe box and drag it to the desired location.


Position

VelocityY

10.90.80.70.60.50.40.30.20.10

3.00e-04

2.00e-04

1.00e-04

0.00e+00

-1.00e-04

-2.00e-04

-3.00e-04

Y Velocity (rad_ross.xy)Y Velocity (rad_p1.xy)Y Velocity (rad_dtrm.xy)Y Velocity

Y Velocity

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 modelare nearly identical even though the reported wall heat transfer rates are different. Thisis because in an optically thin problem, the velocity field is essentially independent of theradiation field, and all three models give a flow solution very close to the non-radiatingcase. The Rosseland model gives substantially erroneous solutions for an optically thincase.



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 velocityfields predicted by the P-1, DTRM, and DO models were very similar and close to thatobtained in the non-radiating case. The wall heat transfer rates for DO and DTRM werevery close in value, and substantially different from those obtained with the Rosselandand 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 ofthe absorption coefficient from 0.2 to 5. You will repeat the process outlined in the stepsthat 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 andrad ross.dat).

File −→ Read −→Case & Data...

2. Define the new material property.


(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.


For the DTRM calculation you may need to click Iterate repeatedly until the radi-ation field is updated. Since the number of Flow Iterations Per Radiation Iterationin the Radiation Model panel is 10, it is possible that the radiation field will not beupdated for as many as 9 iterations, although FLUENT will report that the solutionis converged. If this happens, continue to click the Iterate button until the radiationfield 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 andrad ross5.dat).




6. Plot the y velocity along the horizontal centerline, and save the plot data to a file(e.g., rad ross5.xy).




7. Compare the computed heat transfer rates for the four models by plotting they-velocity profiles in a single plot (Figure 5.18).

The wall heat transfer rates predicted by the four radiation models range from 3.50×105 to 3.98× 105 W.

Plot −→File...

Note: Click Delete in the File XY Plot panel to remove the old XY plot data files.


Position

VelocityY

10.90.80.70.60.50.40.30.20.10

5.00e-04

4.00e-04

3.00e-04

2.00e-04

1.00e-04

0.00e+00

-1.00e-04

-2.00e-04

-3.00e-04

-4.00e-04

-5.00e-04

Y Velocity (rad_ross5.xy)Y Velocity (rad_p15.xy)Y Velocity (rad_dtrm5.xy)Y Velocity

Y Velocity

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, andDTRM. The Rosseland model gives somewhat different velocities, but is still within10% of the other results. The Rosseland and P-1 models are suitable for the opti-cally thick limit; the DTRM and DO models are valid across the range of opticalthicknesses. Consequently, they yield similar answers at aL = 5. For many ap-plications with large optical thicknesses, the Rosseland and P-1 models provide asimple low-cost alternative.



Step 12: S2S Setup, Solution, and Postprocessing for a Non-ParticipatingMedium

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 ex-change in an enclosure of gray-diffuse surfaces. The energy exchange between two surfacesdepends in part on their size, separation distance, and orientation. These parameters areaccounted for by a geometric function called a “view factor”.

The S2S model assumes that all surfaces are gray and diffuse. Thus according to the gray-body model, if a certain amount of radiation is incident on a surface, then a fraction isreflected, a fraction is absorbed, and a fraction is transmitted. The main assumption ofthe S2S model is that any absorption, emission, or scattering of radiation by the mediumcan be ignored. Therefore “surface-to-surface” radiation, only, needs to be considered foranalysis.

For most applications the surfaces in question are opaque to thermal radiation (in theinfrared spectrum), so the surfaces can be considered opaque. For gray, diffuse, andopaque surfaces it is valid to assume that the emissivity is equal to the absorptivity andthat 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 emis-sion/absorption or walls that have uniform temperature. The main advantage of thisoption 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 withoutpartial 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 notconsidered here as they have been shown (earlier in the tutorial) to be inappropriate foroptically thin media. Later in the tutorial you will calculate a solution for S2S modelwith partial enclosure and compare the results with the solution for S2S model for anon-participating medium that is calculated here.



1. Define the S2S model and the view factor and cluster parameters.


(a) Select Surface to Surface (S2S) in the Model list.

The Radiation Model panel will expand to show additional inputs for the S2Smodel.



(b) Click Set... for Parameters in the View Factors group box to open the ViewFactor 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 andCluster Parameters panel.

The S2S radiation model is computationally very expensive when there area large number of radiating surfaces. The number of radiating surfaces isreduced by clustering surfaces into surface “clusters”. The surface clus-ters are made by starting from a face and adding its neighbors and theirneighbors 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 Clusteris acceptable. For a large problem you can increase this number to reducethe memory requirement for the view factor file that is saved in a laterstep. 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 block-ing the view between two opposite surfaces is considered in the view factorcalculation. In this case there is no obstructing surface between the oppo-site walls so selecting either the Blocking or the Nonblocking option willproduce the same result. The default setting for Smoothing is None whichis appropriate for small problems. The Least Square option is more accu-rate, but also more computationally expensive.



See Section 13.3.12 of the User’s Guide for details about view factors andclusters for the S2S model.

(c) Click Compute/Write... for Methods in the View Factors group box to open theSelect File dialog box and to compute the view factors.

You will specify a file name where the cluster and view factor parameters willbe stored.

This step is required if the problem is being solved for the first time, only. Forsubsequent calculations you can read the view factor and cluster informationfrom 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 SelectFile 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 ofthe view factor calculation in the console.

(d) Click OK to close the Radiation Model panel.



(a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, 1.0 forEnergy in the Under-Relaxation Factors list.

3. Save the case file (rad s2s.cas).




5. Save the data file (rad s2s.dat).


6. Display velocity vectors of the S2S calculation (Figure 5.19).


Note: The following postprocessing steps do not include detailed instructions be-cause the procedure is the same one that you followed for the Rosseland modelpostprocessing. See Step 6: Postprocessing for the Rosseland Model ifyou need more details.





Figure 5.19: Velocity Vectors for the S2S Model

7. Plot the y velocity along the horizontal centerline (Figure 5.20), and save the plotdata to a file called rad s2s.xy.


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 generatethe plot.


Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

Figure 5.20: XY Plot of Centerline y Velocity for the S2S Model





The total heat transfer rate on the right wall is 6.77× 105 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 DOmodels 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).


2. Define the new material property.


(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.


For the DTRM calculation you may need to click the Iterate button repeatedly untilthe radiation field is updated. Since the number of Flow Iterations Per RadiationIteration in the Radiation Model panel is 10, it is possible that the radiation fieldwill not be updated for as many as 9 iterations, although FLUENT will report thatthe solution is converged. If this happens, keep clicking the Iterate button until theradiation 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).




6. Plot the y velocity along the horizontal centerline, and save the plot data to a file(e.g., rad dtrm0.xy)




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 6.77× 105 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 probleminvolves enclosure radiative transfer without participating media. Therefore, theS2S 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 plotdata 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.


Position

VelocityY

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

Y Velocity (rad_do0.xy)Y Velocity (rad_dtrm0.xy)Y Velocity

Y Velocity

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 almostidentical even though the wall heat transfer rates are different.



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 definea “partial enclosure”; i.e., you can disable the view factor calculation for walls withnegligible emission/absorption, or walls that have uniform temperature. Even though theview factor will not be computed for these walls, they will still emit radiation at a fixedtemperature called the “partial enclosure temperature”. The main advantage of this is tospeed up the view factor and the radiosity calculation.

For this problem, specify the left wall boundary as the non-participating wall in S2Sradiation. Consequently, you need to specify the partial enclosure temperature for the wallboundary that is not participating in S2S radiation. Note that if multiple wall boundariesare not participating in S2S radiation and each has a different temperature, then thepartial enclosure option may not yield accurate results. This is because the same partialenclosure 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 andrad s2s.dat).


2. Set the partial enclosure parameters for the S2S model.


(a) Enter 1000 for Temperature in the Partial Enclosure group box.




Previous radiation model setups for this problem specified the left wall temperatureas 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 S2SParameters 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.


The view factor file will store the view factors for the radiating surfaces only. Thismay help you control the size of the view factor file as well as the memory required tostore view factors in FLUENT. Furthermore, the time required to compute the viewfactors 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 boundariesthat 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 boundaryconditions, FLUENT will use the view factor file stored earlier for calculating asolution, in which case, the changes that you made to the model will not be used forthe calculation. Therefore, you should recompute the view factors and save the casefile whenever you modify the number of objects that will participate in radiation.



(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.


FLUENT will print an informational message describing the progress of theview factor calculation.



(a) Retain the default values of 0.3 for Pressure, 0.7 for Momentum, and 1.0 forEnergy in the Under-Relaxation Factors list.

6. Save the case file (rad s2spe.cas).




The solution will converge after approximately 80 additional iterations.

8. Save the data file (rad s2spe.dat).


9. Display velocity vectors of the S2S calculation (Figure 5.22).


Note: The following postprocessing steps do not include detailed instructions be-cause the procedure is the same one that you followed for the Rosseland modelpostprocessing. See Step 6: Postprocessing for the Rosseland Model ifyou need more details.

10. Plot the y velocity along the horizontal centerline (Figure 5.23), and save the plotdata to a file called rad s2spe.xy.


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 generatethe plot.





Figure 5.22: Velocity Vectors for the S2S Model with Partial Enclosure


Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

Figure 5.23: XY Plot of Centerline y Velocity for the S2S Model with Partial Enclosure





The total heat transfer rate on the right wall is 6.78 × 105 W. Note that the totalheat transfer rate on the left wall is reported as zero because the report utility in thecurrent version of FLUENT does not account for the radiation heat transfer rate bythis wall, as it should.

Step 15: Comparison of S2S Models with and without Partial Enclosure

1. Compare the computed heat transfer rates for the two S2S models.

2. Compare the y-velocity profiles in a single plot (Figure 5.24).

Plot −→File...

(a) Use the Delete button in the File XY Plot panel to remove the old XY plotdata files.

(b) Read in all the XY plot files you saved for the S2S models.

(c) Click Plot.

(d) Close the File XY Plot panel.


Position

VelocityY

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

0.00e+00

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

Y Velocity (rad_s2s.xy)Y Velocity

Y Velocity

Figure 5.24: Comparison of Computed y Velocities for S2S models

In Figure 5.24, the velocity profiles for the S2S model without partial enclosure and theS2S model with partial enclosure are almost identical.



Summary

In this tutorial you studied combined natural convection and radiation in a square boxand compared the performance of four radiation models in FLUENT for optically thinand optically thick cases, and the performance of three radiation models for a non-participating medium.

• For the optically thin case, the Rosseland and P-1 models are not appropriate andthe DTRM and DO model are applicable and yield similar results.

• In the optically thick limit, all four models are appropriate and yield similar results.In this limit, the less computationally-expensive Rosseland and P-1 models may beadequate for many engineering applications.

• The S2S radiation model is appropriate for modeling the enclosure radiative transferwithout participating media whereas the methods for participating radiation maynot always be efficient.

See Section 13.3 of the User’s Guide for more information about the applicability of thedifferent radiation models.

Further Improvements

This tutorial guides you through the steps to reach an initial solution. You may be ableto obtain a more accurate solution by using an appropriate higher-order discretizationscheme and by adapting the grid. Grid adaption can also ensure that the solution isindependent of the grid. These steps are demonstrated in Tutorial 1.


tutorial 5. modeling radiation and natural convectionbarbertj/cfd training/fluent/fluent...

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