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Tutorial 5. Modeling Radiation and Natural Convection Introduction: In this tutorial, combined radiation and natural convec- tion are solved in a two-dimensional square box on a mesh consist- ing of quadrilateral elements. In this tutorial you will learn how to: Use the radiation models in FLUENT (Rosseland, P-1, DTRM, discrete ordinates (DO), and surface-to-surface (S2S)) and un- derstand their ranges of application Use the Boussinesq model for density Set the boundary conditions for a heat transfer problem in- volving 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 segregated 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 solved Tutorial 1. Some steps in the setup and solution procedure will not be shown explicitly. Problem Description: The problem to be considered is shown schemat- ically 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 points downwards. A buoyant flow devel- ops because of thermally-induced density gradients. The medium c Fluent Inc. November 29, 2001 5-1
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Page 1: Tutorial 5 Fluent

Tutorial 5. Modeling Radiation and

Natural Convection

Introduction: In this tutorial, combined radiation and natural convec-tion are solved in a two-dimensional square box on a mesh consist-ing of quadrilateral elements.

In this tutorial you will learn how to:

• Use the radiation models in FLUENT (Rosseland, P-1, DTRM,discrete ordinates (DO), and surface-to-surface (S2S)) and un-derstand their ranges of application

• Use the Boussinesq model for density

• Set the boundary conditions for a heat transfer problem in-volving 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 segregated solver

• Display velocity vectors and contours of stream function andtemperature for flow visualization

Prerequisites: This tutorial assumes that you are familiar with themenu structure in FLUENT, and that you have solved Tutorial 1.Some steps in the setup and solution procedure will not be shownexplicitly.

Problem Description: The problem to be considered is shown schemat-ically in Figure 5.1. A square box of side L has a hot right wall atT = 2000 K, a cold left wall at T = 1000 K, and adiabatic top andbottom walls. Gravity points downwards. A buoyant flow devel-ops because of thermally-induced density gradients. The medium

c© Fluent Inc. November 29, 2001 5-1

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Modeling Radiation and Natural Convection

contained in the box is assumed to be absorbing and emitting, sothat the radiant exchange between the walls is attenuated by ab-sorption and augmented by emission in the medium. All walls areblack. The objective is to compute the flow and temperature pat-terns in the box, as well as the wall heat flux, using the radiationmodels available in FLUENT, and to compare their performancefor different values of the optical thickness aL.

The working fluid has a Prandtl number of approximately 0.71, andthe Rayleigh number based on L is 5× 105. This means the flow isinherently laminar. The Boussinesq assumption is used to modelbuoyancy. The Planck number k/(4σLT 3

0 ) is 0.02, and measuresthe 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., gravitational acceleration) have been adjusted to yield thedesired Prandtl, Rayleigh, and Planck numbers.

ρ = 1000 kg/m3

k = 15.309 W/mK

µ = 10 kg/ms- 3

β = 10 1/K- 5

g = -6.96 x 10 m/s- 5 2

c = 1.1030x10 J/kgKp4

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 = 2000 Kh

T =

100

0 K

c

Figure 5.1: Schematic of the Problem

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Modeling Radiation and Natural Convection

Preparation

1. Copy the file rad/rad.msh from the FLUENT documentation CDto your working directory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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 windowreporting the progress of the reading. The mesh size will be reportedas 2500 cells.

2. Check the grid.

Grid −→Check

FLUENT performs various checks on the mesh and reports the progressin the console window. Pay particular attention to the minimumvolume. Make sure this is a positive number.

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3. Display the grid (Figure 5.2).

Display −→ Grid...

Note: All the walls are currently contained in a single wall zone,wall-4. You will need to separate them out into four differentwalls so that you can specify different boundary conditions foreach wall.

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GridFLUENT 6.0 (2d, segregated, lam)

Jul 25, 2001

Figure 5.2: Graphics Display of Grid

4. Separate the single wall zone into four wall zones.

Grid −→ Separate −→Faces...

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(a) Select the Angle separation method (the default) under Op-tions.

(b) Select wall-4 in the Zones list.

(c) Specify 89◦ as the significant Angle.

(d) Click on the Separate button.

Faces with normal vectors that differ by more than 89◦ will be placedin separate zones. Since the four wall zones are perpendicular (an-gle = 90◦), wall-4 will be separated into four zones.

5. Display the grid again.

(a) Select all Surfaces and click on Display.

Notice that you now have four different wall zones instead ofonly one.

Extra: You can use the right mouse button to check whichwall zone number corresponds to each wall boundary. Ifyou click the right mouse button on one of the boundariesin the graphics window, its zone number, name, and typewill be printed in the FLUENT console window. This fea-ture is especially useful when you have several zones ofthe same type and you want to distinguish between themquickly. In some cases, you may want to disable the dis-play of the interior grid so as to more accurately selectthe boundaries for identification.

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Step 2: Models

As discussed earlier, in this tutorial you will enable each radiation modelin turn, obtain a solution, and postprocess the results. You will startwith the Rosseland model, then use the P-1 model, the discrete transferradiation model (DTRM), and the discrete ordinates (DO) model. Atthe end of the tutorial, you will use the surface-to-surface (S2S) model.

1. Keep the default solver settings.

Define −→ Models −→Solver...

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Modeling Radiation and Natural Convection

2. Turn on the Rosseland radiation model.

Define −→ Models −→Radiation...

When you click OK in the Radiation Model panel, FLUENT willpresent an Information dialog box telling you that new materialproperties have been added for the radiation model. You will besetting properties later, so you can simply click OK in the dialogbox to acknowledge this information.

Note: FLUENT will automatically enable the energy calculationwhen you enable a radiation model, so you need not visit theEnergy panel.

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3. Add the effect of gravity on the model.

Define −→Operating Conditions...

(a) Turn on Gravity.

The panel will expand to show additional inputs.

(b) Set the Gravitational Acceleration in the Y direction to -6.94e-5m/s2.

As mentioned earlier, the gravitational acceleration has beenadjusted to yield the correct dimensionless quantities (Prandtl,Rayleigh, and Planck numbers). See Figure 5.1 and the asso-ciated comments.

(c) Set the Operating Temperature to 1000 K.

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

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Step 3: Materials

The default fluid material is air, which is the working fluid in this prob-lem. However, since you are working with a fictitious fluid whose prop-erties have been adjusted to give the desired values of the dimensionlessparameters, you must change the default properties for air. You will usean optical thickness aL of 0.2 for this calculation. (Since L = 1, the ab-sorption coefficient a will be set to 0.2.) Later in the tutorial, results foran optically thick medium with aL = 5 and non-participating mediumwith aL = 0 are computed to show how the different radiation modelsbehave for different optical thicknesses.

Define −→Materials...

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1. Select boussinesq in the drop-down list next to Density, and thenset the Density to 1000 kg/m3.

For details about the Boussinesq model, see the User’s Guide.

2. Set the specific heat, Cp, to 1.103e4 J/kg-K.

3. Set the Thermal Conductivity to 15.309 W/m-K.

4. Set the Viscosity to 0.001 kg/m-s.

5. Set the Absorption Coefficient to 0.2 m−1.

Hint: Use the scroll bar to access the properties that are not ini-tially visible in the panel.

6. Keep the default settings for the Scattering Coefficient and the Scat-tering Phase Function, since there is no scattering in this problem.

7. Set the Thermal Expansion Coefficient (used by the Boussinesq model)to 1e-5 K−1.

8. Click on Change/Create and close the Materials panel.

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Step 4: Boundary Conditions

Define −→Boundary Conditions...

1. Set the boundary conditions for the bottom wall (wall-4.006).

Note: The bottom wall should be called wall-4.006, but to be surethat you have the correct wall, use your right mouse button toclick on the bottom wall in the graphics window. When youdo this, the corresponding zone will be selected automaticallyin the Zone list in the Boundary Conditions panel. You can dothis when you set boundary conditions for the other walls aswell, to be sure that you are defining the correct conditions.

(a) Change the Zone Name to bottom.

(b) Retain the default thermal conditions (heat flux of 0) to spec-ify an adiabatic wall.

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Note: The Rosseland model does not require you to set a wallemissivity. Later in the tutorial, you will need to define thewall emissivity for the other radiation models.

2. Set the boundary conditions for the left wall, wall-4.

(a) Change the Zone Name to left.

(b) Select Temperature under Thermal Conditions and set the Tem-perature to 1000 K.

3. Set the boundary conditions for the right wall, wall-4:007.

(a) Change the Zone Name to right.

(b) Select Temperature under Thermal Conditions and set the Tem-perature to 2000 K.

4. Set the boundary conditions for the top wall, wall-4:005.

(a) Change the Zone Name to top.

(b) Retain the default thermal conditions (heat flux of 0) to spec-ify an adiabatic wall.

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Step 5: Solution for the Rosseland Model

1. Set the parameters that control the solution.

Solve −→ Controls −→Solution...

(a) Retain the default selected Equations (all of them) and Under-Relaxation Factors.

(b) Under Discretization, select PRESTO! for Pressure, and SecondOrder Upwind for Momentum and Energy.

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2. Initialize the flow field.

Solve −→ Initialize −→Initialize...

(a) Set the Temperature to 1500 K and click on Init.

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3. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click OK.

Note: There is no extra residual for the radiation heat transferbecause the Rosseland model does not solve extra transportequations for radiation; instead, it augments the thermal con-ductivity in the energy equation. When you use the P-1 andDO radiation models, which both solve additional transportequations, you will see additional residuals for radiation.

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4. Save the case file (rad ross.cas).

File −→ Write −→Case...

5. Start the calculation by requesting 200 iterations.

Solve −→Iterate...

The solution will converge in about 180 iterations.

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

File −→ Write −→Data...

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Step 6: Postprocessing for the Rosseland Model

1. Display velocity vectors (Figure 5.3).

Display −→Vectors...

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Modeling Radiation and Natural Convection

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, lam)

Jul 25, 2001

2.11e-04

1.90e-04

1.68e-04

1.47e-04

1.26e-04

1.05e-04

8.42e-05

6.32e-05

4.21e-05

2.11e-05

2.61e-09

Figure 5.3: Velocity Vectors for the Rosseland Model

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Modeling Radiation and Natural Convection

2. Display contours of stream function (Figure 5.4).

Display −→Contours...

The recirculatory patterns observed are due to the natural convec-tion in the box. At a low optical thickness (0.2), radiation shouldnot have a large influence on the flow. The flow pattern is ex-pected 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 natu-ral convection case. This discrepancy occurs because the Rosselandmodel is not appropriate for small optical thickness.

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Modeling Radiation and Natural Convection

Contours of Stream Function (kg/s)FLUENT 6.0 (2d, segregated, lam)

Jul 25, 2001

6.95e-02

6.26e-02

5.56e-02

4.87e-02

4.17e-02

3.48e-02

2.78e-02

2.09e-02

1.39e-02

6.95e-03

0.00e+00

Figure 5.4: Contours of Stream Function for the Rosseland Model

Extra: If you want to compute the results without radiation your-self, turn off all the radiation models in the Radiation Modelpanel, set the under-relaxation factor for energy to 0.8, andcalculate until convergence. (Remember to reset the under-relaxation factor to 1 before continuing with the tutorial).

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Modeling Radiation and Natural Convection

Contours of Stream Function (kg/s)FLUENT 6.0 (2d, segregated, lam)

Jul 25, 2001

1.97e-02

1.77e-02

1.57e-02

1.38e-02

1.18e-02

9.84e-03

7.87e-03

5.90e-03

3.94e-03

1.97e-03

0.00e+00

Figure 5.5: Contours of Stream Function with No Radiation

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Modeling Radiation and Natural Convection

3. Display filled contours of temperature (Figure 5.6).

Display −→Contours...

The Rosseland model predicts a temperature field (Figure 5.6) verydifferent from that obtained without radiation (Figure 5.7). For thelow optical thickness in this problem, the temperature field predictedby the Rosseland model is not physical.

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Modeling Radiation and Natural Convection

Contours of Static Temperature (k)FLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

2.00e+03

1.90e+03

1.80e+03

1.70e+03

1.60e+03

1.50e+03

1.40e+03

1.30e+03

1.20e+03

1.10e+03

1.00e+03

Figure 5.6: Contours of Temperature for the Rosseland Model

Contours of Static Temperature (k) Nov 28, 2001FLUENT 6.0 (2d, segregated, lam)

2.00e+03

1.00e+03

1.10e+03

1.20e+03

1.30e+03

1.40e+03

1.50e+03

1.60e+03

1.70e+03

1.80e+03

1.90e+03

Figure 5.7: Contours of Temperature with No Radiation

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4. Plot the y velocity along the horizontal centerline of the box.

(a) Create an isosurface at y = 0.5, the horizontal line throughthe center of the box.

Surface −→Iso-Surface...

i. Select Grid... in the Surface of Constant drop-down listand select Y-Coordinate from the list below.

ii. Click on Compute to see the extents of the domain.

iii. Set a value of 0.5 in the Iso-Values field, and change theNew Surface Name to y=0.5.

iv. Click on Create to create a surface at y = 0.5.

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(b) Create an XY plot of y velocity on the isosurface.

Plot −→XY Plot...

i. Check that the Plot Direction for X is 1, and the PlotDirection for Y is 0.

With a Plot Direction vector of (1,0), FLUENT will plotthe selected variable as a function of x. Since you areplotting the velocity profile on a cross-section of constanty, the x direction is the one in which the velocity varies.

ii. Select Velocity... and Y Velocity under Y Axis Function.

iii. Select y=0.5 in the Surfaces list.

iv. Click on Plot.

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Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 25, 2001

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 hotright wall, and the falling plume at the cold left wall.Compared to the case with no radiation, the profile pre-dicted by the Rosseland model exhibits thicker wall layers.As discussed before, the expected profile for aL = 0.2 issimilar to the case with no radiation.

(c) Save the plot data to a file.

i. Select the Write to File option, and click the Write... pushbutton.

ii. In the resulting Select File dialog box, specify rad ross.xyin the XY File text entry box and click OK.

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5. Compute the total wall heat flux on each lateral wall.

Report −→Fluxes...

(a) Select Total Heat Transfer Rate under Options.

(b) Select right and left under Boundaries.

(c) Click the Compute button.

The total wall heat transfer rate is reported for the hot andcold walls as approximately 7.43 × 105 W. The sum of theheat fluxes on the lateral walls is a negligible imbalance.

6. 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 con-vection problem using the Rosseland model to compute radiation. Youhave also learned to postprocess the results. You will now turn on theP-1 model and compare the results so computed with those of the Rosse-land model.

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Step 7: P-1 Model Definition, Solution, and Post-processing

You will now repeat the above calculation using the P-1 radiation model.The main steps are identical to the procedure described above for theRosseland model.

1. Enable the P-1 model.

Define −→ Models −→Radiation...

2. Confirm that the wall emissivity is 1 for all walls.

Define −→Boundary Conditions...

For each wall boundary, there will be a new entry, Internal Emis-sivity, in the Thermal section of the Wall panel. Retain the defaultvalue of 1.

3. Modify the under-relaxation parameters.

Solve −→ Controls −→Solution...

(a) Under Under-Relaxation Factors, set the factor for P1 to 1.0,and retain the default factors for Pressure, Momentum, andEnergy (0.3, 0.7, and 1.0).

Note that an additional equation, P1, appears because the P-1model solves an additional radiation transport equation. Thisproblem is relatively easy to converge for the P-1 model sincethere is not much coupling between the radiation and tempera-ture equations at low optical thicknesses. Consequently a highunder-relaxation factor can be used for P-1.

4. Save the case file (rad p1.cas).

File −→ Write −→Case...

5. Continue the calculation by requesting another 200 iterations.

Solve −→Iterate...

The P-1 model reaches convergence after about 115 additional it-erations.

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

File −→ Write −→Data...

7. Examine the results of the P-1 model calculation.

Note: The steps below do not include detailed instructions becausethe procedure is the same one that you followed for the Rosse-land model postprocessing. See Step 6: Postprocessing forthe Rosseland Model if you need more detailed instruc-tions.

(a) Display velocity vectors (Figure 5.9).

Display −→Vectors...

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

2.87e-04

2.58e-04

2.29e-04

2.01e-04

1.72e-04

1.43e-04

1.15e-04

8.61e-05

5.75e-05

2.89e-05

2.27e-07

Figure 5.9: Velocity Vectors for the P-1 Model

(b) Plot the y velocity along the horizontal centerline (Figure 5.10),and save the plot data to a file called rad p1.xy.

Plot −→XY Plot...

! You will need to reselect Y Velocity under Y Axis Function.Also, remember to turn off the Write to File option so thatyou can access the Plot button to generate the plot.

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Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

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

(c) 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 heat imbalance at the lateral walls is negligiblysmall. You will see later that the Rosseland and P-1 wall heattransfer rates are substantially different from those obtainedby the DTRM and the DO model.

Notice how different the velocity vectors and y-velocity profile are fromthose obtained using the Rosseland model. The P-1 velocity profiles showa clear momentum boundary layer along the hot and cold walls. Theseprofiles 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 forthis optically thin limit, it yields the correct velocity profiles since theradiation source in the energy equation, which is proportional to the ab-sorption coefficient, is small. The Rosseland model uses an effectiveconductivity to account for radiation, and yields the wrong temperaturefield, which in turn results in an erroneous velocity field.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

2.16e-04

1.94e-04

1.73e-04

1.51e-04

1.29e-04

1.08e-04

8.63e-05

6.47e-05

4.31e-05

2.16e-05

8.78e-09

Figure 5.11: Velocity Vectors with No Radiation

Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

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

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Step 8: DTRM Definition, Solution, and Post-processing

1. Turn on the discrete transfer radiation model (DTRM) and definethe ray tracing.

Define −→ Models −→Radiation...

(a) Select Discrete Transfer under Model.

The panel will expand to show additional inputs.

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(b) Accept the defaults by clicking OK.

The Ray Tracing panel will open automatically.

(c) Accept the default settings for Clustering and Angular Dis-cretization by clicking OK.

When you click OK, FLUENT will open a Select File dialogbox so you can specify a name for the ray file used by theDTRM. A detailed description of the ray tracing procedure canbe found in the User’s Guide. In brief, the number of Cells PerVolume Cluster and Faces Per Surface Cluster control the totalnumber of radiating surfaces and absorbing cells. For a small2D problem, the default number of 1 is acceptable. For a largeproblem, however, you will want to increase these numbersto reduce the ray tracing expense. The Theta Divisions andPhi Divisions control the number of rays being created fromeach surface cluster. For most practical problems, the defaultsettings will suffice.

(d) In the Ray File text entry box in the Select File dialog box,enter rad dtrm.ray for the name of the ray file. Then clickOK.

FLUENT will print an informational message describing theprogress of the ray tracing procedure.

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2. Retain the current under-relaxation factors for pressure, momen-tum, and energy (0.3, 0.7, and 1.0).

Solve −→ Controls −→Solution...

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

File −→ Write −→Case...

4. 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...

6. Examine the results of the DTRM calculation.

Note: The steps below do not include detailed instructions becausethe procedure is the same one that you followed for the Rosse-land model postprocessing. See Step 6: Postprocessing forthe Rosseland Model if you need more detailed instruc-tions.

(a) Display velocity vectors (Figure 5.13).

Display −→Vectors...

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

2.88e-04

2.59e-04

2.30e-04

2.02e-04

1.73e-04

1.44e-04

1.15e-04

8.65e-05

5.77e-05

2.90e-05

2.08e-07

Figure 5.13: Velocity Vectors for the DTRM

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(b) Plot the y velocity along the horizontal centerline (Figure 5.14),and save the plot data to a file called rad dtrm.xy.

Plot −→XY Plot...

! You will need to reselect Y Velocity under Y Axis Function.Also, remember to turn off the Write to File option so thatyou can access the Plot button to generate the plot.

Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

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

(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

The total heat transfer rate reported on the right wall is 6.06×105 W. Note that this is substantially lower than the valuespredicted by the Rosseland and P-1 models.

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Step 9: DO Model Definition, Solution, and Post-processing

1. Turn on the discrete ordinates (DO) radiation model and definethe angular discretization.

Define −→ Models −→Radiation...

(a) Select Discrete Ordinates under Model.

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

(b) Set the number of Flow Iterations Per Radiation Iteration to 1.

This is a relatively simple flow problem, and will convergeeasily. Consequently it is useful to do the DO calculation everyiteration of the flow solution. For problems that are difficult to

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converge, it is sometimes useful to allow the flow solution toestablish itself between radiation calculations. In such cases,it may be useful to set Flow Iterations Per Radiation Iterationto a higher value, such as 10.

(c) Retain the default settings for Angular Discretization and Non-Gray Model.

For details about the angular discretization used by the DOmodel, see the User’s Guide. The Number of Bands for theNon-Gray Model is zero because only gray radiation is beingmodeled in this tutorial.

Note: When you click OK in the Radiation Model panel, FLU-ENT will present an Information dialog box telling you thatnew material properties have been added for the radiationmodel. The property that is new for the DO model is therefractive index, which is relevant only when you are mod-eling semi-transparent media. Since you are not modelingsemi-transparent media here, you can simply click OK inthe dialog box to acknowledge this information.

2. Retain the current under-relaxation factors for pressure, momen-tum, and energy (0.3, 0.7, and 1.0), as well as the default under-relaxation of 1 for the discrete ordinates transport equation.

Solve −→ Controls −→Solution...

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

File −→ Write −→Case...

4. Continue the calculation by requesting another 100 iterations.

Solve −→Iterate...

The solution will converge after about 25 additional iterations.

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

File −→ Write −→Data...

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6. Examine the results of the DO calculation.

Note: The steps below do not include detailed instructions becausethe procedure is the same one that you followed for the Rosse-land model postprocessing. See Step 6: Postprocessing forthe Rosseland Model if you need more detailed instruc-tions.

(a) Display velocity vectors (Figure 5.15).

Display −→Vectors...

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

2.89e-04

2.61e-04

2.32e-04

2.03e-04

1.74e-04

1.45e-04

1.16e-04

8.70e-05

5.80e-05

2.91e-05

1.91e-07

Figure 5.15: Velocity Vectors for the DO Model

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Modeling Radiation and Natural Convection

(b) Plot the y velocity along the horizontal centerline (Figure 5.16),and save the plot data to a file called rad do.xy.

Plot −→XY Plot...

! You will need to reselect Y Velocity under Y Axis Function.Also, remember to turn off the Write to File option so thatyou can access the Plot button to generate the plot.

Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

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

(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

The total heat transfer rate reported on the right wall is 6.12×105 W. Note that this is about 1.5% higher than that predictedby the DTRM. The DO and DTRM values are comparableto each other, while the Rosseland and P-1 values are bothsubstantially different. The DTRM and DO models are validacross the range of optical thickness, and the heat transferrates computed using them are expected to be closer to thecorrect heat transfer rate.

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Step 10: Comparison of y-Velocity Plots

In this step, you will read the plot files you saved for all the solutionsand compare them in a single plot.

Plot −→File...

1. Read in all the XY plot files.

(a) Click on the Add... button.

(b) In the resulting Select File dialog box, select rad do.xy,rad dtrm.xy, rad p1.xy, and rad ross.xy in the Files list.

They will be added to the XY File(s) list. If you accidentallyadd an incorrect file, you can select it in this list and clickRemove.

(c) Click OK to load the 4 files.

2. Click on Plot.

Extra: You can click Curves... in the File XY Plot panel to openthe Curves panel, where you can define different styles for dif-ferent plot curves. In Figure 5.17, different symbols have beenselected for each curve.

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Modeling Radiation and Natural Convection

3. Resize and move the legend box so that you can read the informa-tion inside it.

(a) To resize the box, press any mouse button on a corner anddrag the mouse to the desired position.

(b) To move the legend box, press any mouse button anywhereelse on the box and drag it to the desired location.

Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

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_do.xy)Y Velocity (rad_dtrm.xy)Y Velocity (rad_p1.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 model are nearly identical even though the reported wall heattransfer rates are different. This is because in an optically thin problem,the velocity field is essentially independent of the radiation field, and allthree models give a flow solution very close to the non-radiating case. TheRosseland model gives substantially erroneous solutions for an opticallythin case.

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Step 11: Comparison of Radiation Models for anOptically Thick Medium

In the previous steps, you compared the results of four radiation modelsfor an optically thin (aL = 0.2) medium. It was found that, as a result ofthe 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 werevery close to each other, and substantially different from those obtainedwith the Rosseland and P-1 models. In this step, you will recalculatea solution (using each radiation model) for an optically thick (aL = 5)medium. This is accomplished by increasing the value of the absorptioncoefficient from 0.2 to 5. You will repeat the process outlined below foreach set of case and data files that you saved earlier in the tutorial.

1. For each radiation model, calculate a new solution for aL = 5.

(a) Read in the case and data file saved earlier (e.g., rad ross.casand rad ross.dat).

File −→ Read −→Case & Data...

(b) Set the absorption coefficient to 5.

This will result in an optical thickness aL of 5, since L = 1.

Define −→Materials...

(c) Calculate until the new solution converges.

Solve −→Iterate...

! For the DTRM calculation, you may need to click the It-erate button repeatedly until the radiation field is updated.Since the number of Flow Iterations Per Radiation Iterationin the Radiation Model panel is 10, it is possible that theradiation field will not be updated for as many as 9 iter-ations, although FLUENT will report that the solution isconverged. If this happens, keep clicking the Iterate but-ton until the radiation field is updated and the solutionproceeds for multiple iterations.

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(d) Save the new case and data files using a different file name(e.g., rad ros5.cas and rad ros5.dat).

File −→ Write −→Case & Data...

(e) Compute the total wall heat transfer rate.

Report −→Fluxes...

(f) Plot the y velocity along the horizontal centerline, and savethe plot data to a file (e.g., rad ros5.xy).

Plot −→XY Plot...

2. Compare the computed heat transfer rates for the four models.

The wall heat transfer rates predicted by the four radiation modelsrange from 3.50 × 105 to 3.97 × 105 W.

3. Compare the y-velocity profiles in a single plot (Figure 5.18).

Plot −→File...

Note: Use the Delete button in the File XY Plot panel to removethe old XY plot data files.

The XY plots of y velocity are nearly identical for the P-1 model,DO model, and DTRM. The Rosseland model gives somewhat dif-ferent velocities, but is still within 10% of the other results. TheRosseland and P-1 models are suitable for the optically thick limit;the DTRM and DO models are valid across the range of opticalthicknesses. Consequently, they yield similar answers at aL = 5.For many applications with large optical thicknesses, the Rosselandand P-1 models provide a simple low-cost alternative.

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Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

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_do5.xy)Y Velocity (rad_dtr5.xy)Y Velocity (rad_p15.xy)Y Velocity

Y Velocity

Figure 5.18: Comparison of Computed y Velocities for aL = 5

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Modeling Radiation and Natural Convection

Step 12: S2S Model Definition, Solution and Post-processing for a Non-Participating Medium

In the previous steps, you compared the results of four radiation modelsfor optically thin (aL = 0.2) and optically thick (aL = 5) media. Thesurface-to-surface (S2S) radiation model cannot be used to model partic-ipating radiation problems, but it is suitable for modeling the enclosureradiative transfer without participating media. The S2S model assumesthat all surfaces are gray and diffuse. Thus, according to the gray-bodymodel, if a certain amount of radiation is incident on a surface, a frac-tion is reflected, a fraction is absorbed, and a fraction is transmitted.

For most applications the surfaces in question are opaque to thermalradiation (in the infrared spectrum), so the surfaces can be consideredopaque. The transmissivity, therefore, can be neglected. Effectively, forthe S2S model the absorption coefficient can be considered to be zero.

In this step, you will calculate a solution for aL = 0 using the S2Sradiation model. In the next step, you will use the DTRM and DO modelsfor aL = 0, and compare the results of the three models. The Rosselandand P-1 models are not considered here as they have been shown (earlierin the tutorial) to be inappropriate for optically thin media.

1. Turn on the surface-to-surface (S2S) radiation model and definethe view factor and cluster parameters.

Define −→ Models −→Radiation...

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(a) Select Surface to Surface under Model.

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

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(b) Set the view factor and cluster parameters.

i. Click Set... under Parameters.

The View Factor and Cluster Parameters panel will openautomatically.

ii. Click OK to accept the default settings.

The S2S radiation model is computationally very expen-sive when there are a large number of radiating surfaces.The number of radiating surfaces is reduced by cluster-ing surfaces into surface “clusters”. The surface clustersare made by starting from a face and adding its neighborsand their neighbors until a specified number of faces persurface cluster is collected. For a small 2D problem, thedefault value of 1 for Faces Per Surface Cluster is accept-able. For a large problem, you can increase this number

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to reduce the memory requirement for the view factor filethat is saved in a later step. This may also lead to somereduction in the computational expense. However, this isat the cost of some accuracy.

Using the Blocking option ensures that any additional sur-face that is blocking the view between two opposite surfacesis 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 op-tion will produce the same result. The default setting forSmoothing is None, which is appropriate for small prob-lems. The Least Square option is more accurate, but alsomore computationally expensive. See the User’s Guide fordetails about view factors and clusters for the S2S model.

(c) Compute the view factors for the S2S model.

This step is required only if the problem is being solved forthe first time. For subsequent calculations, you can read theview factor and cluster information from an existing file (byclicking Read... instead of Compute/Write...).

i. Click Compute/Write... under Methods in the RadiationModel panel.

FLUENT will open a Select File dialog box so you can spec-ify a name for the file where the cluster and view factorparameters are stored.

ii. In the S2S File text entry box in the Select File dialog box,enter rad s2s.s2s for the name of the S2S file. Then clickOK.

FLUENT will print an informational message describingthe progress of the view factor calculation.

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2. Retain the current under-relaxation factors for pressure, momen-tum, and energy (0.3, 0.7, and 1.0).

Solve −→ Controls −→Solution...

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

File −→ Write −→Case...

4. 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 s2s.dat).

File −→ Write −→Data...

6. Examine the results of the S2S calculation.

Note: The steps below do not include detailed instructions becausethe procedure is the same one that you followed for the Rosse-land model postprocessing. See Step 6: Postprocessing forthe Rosseland Model if you need more detailed instruc-tions.

(a) Display velocity vectors (Figure 5.19).

Display −→Vectors...

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

2.47e-04

2.22e-04

1.98e-04

1.73e-04

1.48e-04

1.24e-04

9.89e-05

7.43e-05

4.96e-05

2.49e-05

1.92e-07

Figure 5.19: Velocity Vectors for the S2S Model

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(b) 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 will have to reselect Y Velocity under Y Axis Function.Also, remember to turn off the Write to File option toaccess the Plot button to generate the plot.

Y VelocityFLUENT 6.0 (2d, segregated, lam)

Jul 26, 2001

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

(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

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

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Step 13: Comparison of Radiation Models for aNon-Participating Medium

In this step, you will calculate a solution for the aL = 0 case, usingthe DTRM and DO models, and then compare the results with the S2Sresults.

1. For the DTRM and DO models, calculate a new solution for aL =0.

(a) Read in the case and data files saved earlier (e.g., rad dtrm.casand rad dtrm.dat).

File −→ Read −→Case & Data...

(b) Set the absorption coefficient to 0.

This will result in an optical thickness aL of 0.

Define −→Materials...

(c) Calculate until the new solution converges.

Solve −→Iterate...

(d) Save the new case and data files using a different file name(e.g., rad dtr0.cas and rad dtr0.dat).

File −→ Write −→Case & Data...

(e) Compute the total wall heat transfer rate.

Report −→Fluxes...

(f) Plot the y velocity along the horizontal centerline, and savethe plot data to a file (e.g., rad dtr0.xy)

Plot −→XY Plot...

2. Compare the computed heat transfer rates for the three models.

For the S2S model, the total heat transfer rate on the right wallwas 6.77 × 105 W. This is about 5% higher than that predicted bythe DTRM and 1.5% higher than DO. Although the S2S, DO, andDTRM values are comparable to each other, this problem involvesenclosure radiative transfer without participating media. Therefore,the S2S model provides the most accurate solution.

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3. 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 theold XY plot data files.

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

(c) Click on Plot.

Y VelocityFLUENT 6.0 (2d, segregated, lam)

Aug 02, 2001

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_dtr0.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 modelsare almost identical even though the wall heat transfer rates are different.

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Summary: In this tutorial, you studied combined natural convectionand radiation in a square box and compared the performance offour radiation models in FLUENT for optically thin and opticallythick cases, and the performance of three radiation models for anon-participating medium.

• For the optically thin case, the Rosseland and P-1 models arenot appropriate; the DTRM and the DO model are applicable,and yield similar results.

• In the optically thick limit, all four models are appropriateand yield similar results. In this limit, the less computationally-expensive Rosseland and P-1 models may be adequate formany engineering applications.

• The S2S radiation model is appropriate for modeling the en-closure radiative transfer without participating media, wherethe methods for participating radiation may not always beefficient.

For more information about the applicability of the different radi-ation models, see the User’s Guide.

5-56 c© Fluent Inc. November 29, 2001