tutorial 5 - modeling radiation and natural convection - 12 juni 2014

8/21/2019 TUTORIAL 5 - Modeling Radiation and Natural Convection - 12 Juni 2014

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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 flow

visualization.

Prerequisites

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

Problem Description

The problem to be considered is shown schematically in Figure5.1. 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
http://tut01.pdf/


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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/(4LT3

0) is 0.02, and

measures 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, andaL = 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.

= 1000 kg/m3

k = 15.309 W/mK

= 10-3

= 10-5

g = -6.96 x 10-5 2

c = 1.1030x10p

4

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

5Ra = 5 x 10

Pl = 0.02

Pr = 0.71

= 0.2, 5

Adiabatic

L

x

y

g

T=2000K

h

T=100

0K

c

J/kgK

kg/ms

1/Km/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 Tutorial1).

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 ofFLUENT.

5-2 c Fluent Inc. September 21, 2006
http://-/?-


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Step 1: Grid

1. Read the mesh file rad.msh.

File Read Case...

As the mesh is read in, messages will appear in the console reporting the progress

of the reading. The mesh size will be reported as 2500 cells.

2. Check the grid.

Grid Check

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

3. Display the grid.

Display Grid...

(a) Retain the default settings.

(b) ClickDisplayto view the grid in the graphics display window (Figure5.2).

(c) Close the Grid Displaypanel.

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.



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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 than89 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 defaultAngle separation method in the Options list.

(b) Select wall-4 from the Zones selection list.

(c) Enter 89 for theAngle.

(d) ClickSeparate 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.



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(e) Close the Separate Face Zones panel.

5. Display the grid again.

Display Grid...

(a) Select all of the surfaces to display by clicking the shaded icon to the right of

Surfaces.

(b) ClickDisplayto 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 theFLUENT 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 Displaypanel.



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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...



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(a) Select Rosselandin the Model list.

(b) ClickOK 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 clickOK in the dialog box to acknowledge this

information.

Note: FLUENTwill automatically enable the energy calculation when you se-lect a radiation model, so you need not visit theEnergy panel.

3. Add the effect of gravity to the model.

Define Operating Conditions...

(a) Enable the Gravityoption in the Gravitygroup box.

The panel will expand to show additional inputs.

(b) Enter -6.94e-5m/s2 forY 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 Figure5.1and 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) ClickOK to close the Operating Conditions panel and set the parameters.



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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 properties

for air. You will use an optical thicknessaL of0.2for this calculation. (SinceL = 1, the

absorption coefficienta will be set to 0.2.) Later in the tutorial, results for an opticallythick medium withaL = 5 and non-participating medium withaL = 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 Users Guide.

(b) Enter 1.103e4 J/kg-K forCp to set the specific heat.

(c) Enter 15.309 W/m-K for Thermal Conductivity.

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



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(e) Enter 0.2 m1 forAbsorption 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,andRefractive Index since there is no scattering in this problem.

(g) Enter 1e-5 K1 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...



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1. Set the boundary conditions for the left wall (wall-4).

(a) Enter left-wall for Zone Name.

(b) Click the Thermal tab.

i. SelectTemperaturefrom the Thermal Conditions list.

ii. Enter 1000 K forTemperature.

(c) ClickOK to set the conditions and close the Wall panel.



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2. Set the boundary conditions for the top wall (wall-4:005).

(a) Enter top-wallfor Zone Name.

(b) Click the Thermaltab and retain the default thermal conditions (Heat Fluxof0) to specify an adiabatic wall.


3. Set the boundary conditions for the bottom wall (wall-4:006).

Note: The bottom wall should be calledwall-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 theBoundary 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-wallfor Zone Name.

(b) Click the Thermaltab and retain the default thermal conditions (Heat Fluxof

0) 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.



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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. SelectTemperaturefrom the Thermal Conditions list.

ii. Enter 2000 K forTemperature.(c) ClickOK to set the conditions and close the Wall panel.

5. Close the Boundary Conditions panel.

Step 5: Solution for the Rosseland Model

1. Set the parameters that control the solution.

Solve Controls Solution...

(a) Retain the default selectedEquationsand the defaultUnder-Relaxation Factors.

(b) Select PRESTO! from the Pressure drop-down list in the Discretization groupbox.

(c) SelectSecond Order Upwind from the MomentumandEnergydrop-down lists.

(d) ClickOK to set the parameters and close the Solution Controls panel.



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2. Initialize the flow field.

Solve Initialize Initialize...

(a) Enter 1500 K for Temperature to set the initial temperature.

(b) ClickInit and then close the Solution Initialization panel.

3. Enable the plotting of residuals during the calculation.

Solve Monitors Residual...



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(a) Enable Plotin theOptions group box.

(b) ClickOK 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) ClickIterate.

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...



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Step 6: Postprocessing for the Rosseland Model

1. Display velocity vectors.

Display Vectors...

(a) Retain the default settings.

(b) ClickDisplayto view the vectors in the graphics display window (Figure 5.3).

(c) Close the Vectors panel.



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

2.11e-04

2.01e-04

1.90e-04

1.80e-04

1.69e-04

1.58e-04

1.48e-04

1.37e-04

1.27e-04

1.16e-04

1.06e-04

9.51e-05

8.45e-05

7.40e-05

6.34e-05

5.28e-05

4.23e-05

3.17e-05

2.11e-05

1.06e-05

3.34e-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 ofdrop-down lists.

(b) ClickDisplayto view the contours in the graphics display window (Figure5.4).



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(c) Close the Contours panel.

The recirculatory patterns observed are due to the natural convection in the box.At a low optical thickness (0.2), radiation should not have a large influence on the

flow. The flow pattern is expected to be similar to that obtained with no radiation(Figure 5.5). However, the Rosseland model predicts a flow pattern that is very

symmetric (Figure5.4), 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-02

6.67e-02

6.32e-02

5.97e-02

5.62e-02

5.26e-02

4.91e-02

4.56e-02

4.21e-02

3.86e-02

3.51e-02

3.16e-02

2.81e-02

2.46e-02

2.11e-02

1.75e-02

1.40e-02

1.05e-02

7.02e-03

3.51e-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 yourself, turn off allthe radiation models in the Radiation Model panel, set the under-relaxation

factor for energy to 0.8 in the Solution Controls panel, and iterate the solu-tion until convergence. (Remember to reset the under-relaxation factor to 1(the default value) before continuing with the tutorial). Compare the stream

function contours without radiation (Figure5.5) to the plot with the Rosselandradiation model enabled (Figure5.4).



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

1.97e-02

1.87e-02

1.77e-02

1.67e-02

1.58e-02

1.48e-02

1.38e-02

1.28e-02

1.18e-02

1.08e-02

9.85e-03

8.87e-03

7.88e-03

6.90e-03

5.91e-03

4.93e-03

3.94e-03

2.96e-03

1.97e-03

9.85e-04

0.00e+0

Figure 5.5: Contours of Stream Function with No Radiation

3. Display filled contours of temperature.

Display Contours...

(a) Enable Filled in theOptions group box.



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(b) SelectTemperature... andStatic Temperature from the Contours ofdrop-downlists.

(c) ClickDisplayto view the filled contours in the graphics display window (Fig-ure5.6).

(d) Close theContours panel.

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

2.00e+0

1.95e+0

1.90e+0

1.85e+0

1.80e+0

1.75e+0

1.70e+0

1.65e+0

1.60e+0

1.55e+0

1.50e+0

1.45e+0

1.40e+0

1.35e+0

1.30e+0

1.25e+01.20e+0

1.15e+0

1.10e+0

1.05e+0

1.00e+0

Figure 5.6: Contours of Temperature for the Rosseland Model

The Rosseland model predicts a temperature field (Figure5.6) very different from

that obtained without radiation (Figure5.7). For the low optical thickness in thisproblem, the temperature field predicted by the Rosseland model is not physical.



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

2.00e+0

1.95e+0

1.90e+0

1.85e+0

1.80e+0

1.75e+0

1.70e+0

1.65e+0

1.60e+0

1.55e+0

1.50e+0

1.45e+0

1.40e+0

1.35e+0

1.30e+0

1.25e+0

1.20e+0

1.15e+0

1.10e+0

1.05e+0

1.00e+0

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) ClickCompute to calculate the extents of the domain.

(c) Enter 0.5 for Iso-Values.

(d) Enter y=0.5 for New Surface Name.



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(e) ClickCreate to create a surface at y = 0.5.

The new isosurface aty=0.5will appear in theFrom Surface list.

(f) Close the Iso-Surface panel.

5. Create an XY plot ofy velocity on the isosurface.

Plot XY Plot...

(a) Retain the default selection ofNode Values in the Optionsgroup box.

If you prefer to display the cell values, disable theNode Values option. Note,however, that you will need to ensure that whatever option you choose forNodeValuesis 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 ofx. Since you are plotting the velocity profile on a cross-section

of constanty, thex direction is the one in which the velocity varies.(c) SelectVelocity... and Y Velocityfrom the Y Axis Function drop-down lists.

(d) Select y=0.5 from the Surfaces selection list.

(e) ClickPlotto display the x-y plot in the graphics display window (Figure 5.8).



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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

= .

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 foraL = 0.2 is similar to the case withno radiation.

(f) EnableWrite to File in theOptionsgroup box and save the plot data to a file.

(g) ClickWrite... to open the Select File dialog box.

(h) Enter rad ross.xy for XY File and clickOK.This will save the xy plot file named rad ross.xy to your working folder.

(i) Close theSolution XY Plot panel.



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

Report Fluxes...

(a) Select Total Heat Transfer Rate in theOptions list.

(b) Select left-wall and right-wall from the Boundaries selection list.

(c) ClickCompute.

The total wall heat transfer rate is reported for the hot and cold walls as ap-proximately7.43 105 W. The net heat flux on the lateral walls is a negligible

imbalance. This is reported in the panel as well as displayed in the console.(d) Close theFlux 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.



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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 clickOK.

2. Define the boundary conditions.

Define Boundary Conditions...

(a) Retain the default value of 1for Internal Emissivity for all walls. Remember toclick theThermal tab to view emissivity in theWall boundary condition panel.

(b) Close theWall 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 Factorsgroup box.

(b) Enter 1.0 for P1 in the Under-Relaxation Factorsgroup 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) ClickOK to set the parameters and close the Solution Controls panel.

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 approximately 115 additional iterations.

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

File Write Data...



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7. Display velocity vectors (Figure5.9) of the P-1 model calculation.

Display Vectors...

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

for details.


2.86e-04

2.72e-04

2.58e-04

2.43e-04

2.29e-04

2.15e-04

2.00e-04

1.86e-04

1.72e-04

1.58e-04

1.43e-04

1.29e-04

1.15e-04

1.00e-048.60e-05

7.17e-05

5.74e-05

4.31e-05

2.88e-05

1.45e-05

1.94e-07

Figure 5.9: Velocity Vectors for the P-1 Model



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8. Plot the y velocity along the horizontal centerline y = 0.5 (Figure5.10) and thensave the plot data to a file called rad p1.xy.

Plot XY Plot...

You may need to reselectVelocity... andY Velocityin theY Axis Functiondrop-downlists. Also, remember to deselect theWrite to File option so that you can access the

Plot 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

=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 boundary

layer along the hot and cold walls. These profiles are much closer to those obtained fromthe non-radiating case (Figures5.11and5.12). Though the P-1 model is not appropriate

for 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.



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2.16e-0

2.05e-0

1.94e-0

1.83e-0

1.72e-0

1.62e-01.51e-0

1.40e-0

1.29e-0

1.19e-0

1.08e-0

9.70e-0

8.62e-0

7.55e-0

6.47e-0

5.39e-0

4.31e-0

3.24e-0

2.16e-0

1.08e-0

3.93e-0

Figure 5.11: Velocity Vectors with No Radiation

Y Velocity FLUENT 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

=0.5

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



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Step 8: DTRM Setup, Solution, and Postprocessing

1. Define the DTRM and the ray tracing.


(a) Select Discrete Transfer (DTRM) in the Model list.TheRadiation Model panel will expand to show additional inputs.

(b) Retain the default parameters.

(c) ClickOK in the Radiation Model panel to open the DTRM Rayspanel.

i. Retain the default settings for ClusteringandAngular 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 the

ray 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. ClickOK to open the Select File dialog box.

See Section13.3.5of theUsers Guidefor a more detailed description ofthe ray tracing procedure.

http://../ug/flug.pdfhttp://-/?-


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iii. Enter rad dtrm.ray for theRay File in the Select File dialog box.

iv. ClickOK to write the ray file.

FLUENTwill report on the status of the ray tracing in the console.



(a) Retain the default solution values of 0.3for Pressure, 0.7for Momentum, and1.0 for Energyin the Under-Relaxation Factorslist.

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

File Write Case...


Solve Iterate...

The solution will converge after about 80 additional iterations.5. Save the data file (rad dtrm.dat).

File Write Data...

6. Display velocity vectors (Figure5.13) of the DTRM calculation.

Display Vectors...


for details.

7. Plot the y velocity along the horizontal centerline y = 0.5 (Figure5.14), and savethe plot data to a file called rad dtrm.xy.

Plot XY Plot...

You may need to reselectVelocity... andY Velocity from theY Axis Function drop-down lists. Also, remember to deselect the Write to File option so that you canaccess thePlot button to generate the plot.


Report Fluxes ...The total heat transfer rate reported on the right wall is6.07105 W. Note that thisis substantially lower than the values predicted by the Rosseland and P-1 models.



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2.88e-04

2.73e-04

2.59e-04

2.44e-04

2.30e-04

2.16e-042.01e-04

1.87e-04

1.73e-04

1.58e-04

1.44e-04

1.30e-04

1.15e-04

1.01e-04

8.64e-05

7.21e-05

5.77e-05

4.33e-05

2.90e-05

1.46e-05

2.41e-07

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



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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, suchas10.

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

TheNumber of Bands for theNon-Gray Model is zero because gray radiation,only, is being modeled in this tutorial.

See Section13.3.6of theUsers Guidefor details about the angular discretiza-tion used by the DO model.

(d) ClickOK.

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



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when you are modeling semi-transparent media. Since you are not mod-eling semi-transparent media here you can simply clickOK 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 theDiscrete Ordinatesfactor appears in the list because the DO modelsolves an additional radiation transport equation.

(b) Retain the default setting ofFirst Order Upwindin theDiscrete Ordinatesdrop-down list for Discretization.

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

File Write Case...


Solve Iterate...

The solution will converge after approximately 25 additional iterations.

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

File Write Data...

6. Display velocity vectors of the DO calculation (Figure5.15).

Display Vectors...


for details.

7. Plot they velocity along the horizontal centerline y = 0.5m(Figure5.16), and savethe plot data to a file called rad do.xy.

Plot XY Plot...

You may need to reselectVelocity... andY Velocityin theY Axis Functiondrop-downlists. Also, remember to disable theWrite to File option so that you can access thePlot button to generate the plot.



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2.89e-04

2.75e-04

2.60e-04

2.46e-04

2.31e-04

2.17e-042.03e-04

1.88e-04

1.74e-04

1.59e-04

1.45e-04

1.30e-04

1.16e-04

1.01e-04

8.69e-05

7.25e-05

5.80e-05

4.36e-05

2.91e-05

1.47e-05

2.23e-07

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

=0.5

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



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Report Fluxes ...

The total heat transfer rate reported on the right wall is6.12 105 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 both

substantially 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 ofy-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) ClickAdd... 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 theXY File(s)list. If you accidentally add an incor-

rect file, you can select it in this list and clickRemove.ii. ClickOK in the Select File dialog box to load the 4 files.

The files will be listed in theFiles list in theFile XY Plot panel.

(b) ClickPlot in the File XY Plot panel.



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Extra: You can clickCurves... to open theCurvespanel, where you can definedifferent styles for different plot curves. In Figure5.17, 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 the

box, 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 (rY Velocity (rY Velocity (rY Velocity

Y Velocity

Figure 5.17: Comparison of Computed y Velocities for aL = 0.2

Notice in Figure5.17that the velocity profiles for the P-1 model, DTRM, and DO modelare nearly identical even though the reported wal l 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.



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Step 11: Comparison of Radiation Models for an Optically Thick Medium

In the previous steps you compared the results of four radiation models for an optically thin(aL= 0.2) medium. It was found that as a result of the low optical thickness, the velocity

fields predicted by the P-1, DTRM, and DO models were very similar and close to thatobtained in the non-radiating case. The wall heat transfer rates for DO and DTRM were

very close in value, and substantially different from those obtained with the 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.Define Materials...

(a) Enter 5 for the Absorption Coefficient in the Materialspanel.

This will result in an optical thicknessaLof 5, sinceL= 1.

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

3. Calculate the new solution until it converges.

Solve Iterate...

For the DTRM calculation you may need to clickIterate repeatedly until the radi-ation field is updated. Since the number ofFlow Iterations Per Radiation Iterationin theRadiation Model panel is 10, it is possible that the radiation field will not beupdated for as many as 9 iterations, althoughFLUENTwill report that the solutionis converged. If this happens, continue to click theIterate button until the radiation

field is updated and the solution proceeds for multiple iterations.

4. Save the new case and data files using a different file name (e.g.,rad ross5.casandrad ross5.dat).


5. Compute the total wall heat transfer rate.Report Fluxes...

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

Plot XY Plot...



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7. Compare the computed heat transfer rates for the four models by plotting they-velocity profiles in a single plot (Figure5.18).

The wall heat transfer rates predicted by the four radiation models range from3.50105 to 3.98 105 W.

Plot File...

Note: ClickDelete in theFile 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 (rY Velocity (rY Velocity (rY Velocity

Y Velocity

Figure 5.18: Comparison of Computed y Velocities foraL = 5

The XY plots ofy 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.



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

Medium

In the previous steps you compared the results of four radiation models for optically thin(aL= 0.2) and optically thick (aL= 5) media.

The Surface-to-Surface (S2S) radiation model can be used to account for the radiation 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 enclosurewhich 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 foraL = 0using the S2S radiation model without

partial enclosure. In the next step you will use the DTRM and DO models foraL= 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.



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


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

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



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(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 Parameterspanel.

The S2S radiation model is computationally very expensive when there are

a 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 of1 forFaces 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 theBlockingoption 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 theNonblocking option willproduce the same result. The default setting forSmoothing isNone whichis appropriate for small problems. TheLeast Square option is more accu-rate, but also more computationally expensive.



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See Section13.3.12of theUsers Guidefor details about view factors andclusters for the S2S model.

(c) ClickCompute/Write... forMethodsin theView Factorsgroup 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 will

be 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 information

from an existing file (by clickingRead... instead of Compute/Write...).

i. Enter rad s2s.gz as the file name forS2S File and clickOK 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 orrad 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) ClickOK 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 Factorslist.

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

File Write Case...


Solve Iterate...

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

File Write Data...

6. Display velocity vectors of the S2S calculation (Figure5.19).

Display Vectors...

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 Modelifyou need more details.



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2.48e-0

2.35e-0

2.23e-0

2.11e-0

1.98e-0

1.86e-0

1.73e-0

1.61e-0

1.49e-0

1.36e-0

1.24e-01.12e-0

9.92e-05

8.69e-05

7.45e-05

6.21e-05

4.97e-05

3.74e-05

2.50e-05

1.26e-05

2.28e-0

Figure 5.19: Velocity Vectors for the S2S Model

7. Plot the y velocity along the horizontal centerline (Figure5.20), and save the plotdata to a file called rad s2s.xy.

Plot XY Plot...

You may have to reselectY Velocityfrom theY Axis Function drop-down lists. Also,remember to deselect theWrite to File option to access thePlot 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



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Report Fluxes ...

The total heat transfer rate on the right wall is6.77 105 W.

Step 13: Comparison of Radiation Models for a Non-Participating MediumIn this step you will calculate a solution for theaL= 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.

Define Materials...(a) Enter 0 for the Absorption Coefficient.

This will result in an optical thicknessaLof 0.

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

3. Calculate the new solution until it converges.

Solve Iterate...

For the DTRM calculation you may need to click theIterate button repeatedly untilthe radiation field is updated. Since the number ofFlow Iterations Per Radiation

Iteration in the Radiation Model panel is 10, it is possible that the radiation fieldwill not be updated for as many as 9 iterations, althoughFLUENT will report thatthe solution is converged. If this happens, keep clicking theIterate 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.casand rad dtrm0.dat).



Report Fluxes...

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

Plot XY Plot...



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

For the S2S model, the total heat transfer rate on the right wall was6.77 105 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, the

S2S model provides the most accurate solution.

8. Compare the y-velocity profiles in a single plot (Figure5.21)

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) ClickPlot.

(d) Close theFile 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 foraL = 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.



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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 fixed

temperature 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 thePartial Enclosure group box.




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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 S2SParametersgroup box.

(b) ClickOK to close the Wall panel.

(c) Close the Boundary Conditions panel.

4. Compute the view factors for the S2S model.Define Models Radiation...

The view factor file will store the view factors for the radiating surfaces only. Thismay help you control the size of the view factor file as well as the memory required tostore view factors inFLUENT. Furthermore, the time required to compute the view

factors will reduce as only the view factors for radiating surfaces will be calculated.

You should compute the view factors only when you have specified the 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 case

file whenever you modify the number of objects that will participate in radiation.



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(a) Click Compute/Write... underMethods 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 clickOK.


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 Factorslist.

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

File Write Case...


Solve Iterate...

The solution will converge after approximately 80 additional iterations.

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

File Write Data...

9. Display velocity vectors of the S2S calculation (Figure5.22).

Display Vectors...

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 Modelifyou need more details.

10. Plot the y velocity along the horizontal centerline (Figure5.23), and save the plotdata to a file called rad s2spe.xy.

Plot XY Plot...

You may have to reselectY Velocityfrom theY Axis Function drop-down lists. Also,

remember to deselect theWrite to File option to access thePlot button to generatethe plot.



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2.47e-04

2.35e-04

2.22e-04

2.10e-04

1.98e-04

1.85e-041.73e-04

1.61e-04

1.48e-04

1.36e-04

1.24e-04

1.11e-04

9.90e-05

8.66e-05

7.43e-05

6.19e-05

4.96e-05

3.73e-05

2.49e-05

1.26e-05

2.27e-07

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



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Report Fluxes ...

The total heat transfer rate on the right wall is6.78 105 W. Note that the totalheat transfer rate on the left wall is reported as zero because the report utility in thecurrent version ofFLUENT does not account for the radiation heat transfer rate by

this 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 (Figure5.24).

Plot File...

(a) Use the Delete button in the File XY Plot panel to remove the old XY plot

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

(c) ClickPlot.

(d) Close theFile 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 Figure5.24, the velocity profiles for the S2S model without partial enclosure and theS2S model with partial enclosure are almost identical.



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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 Section13.3of theUsers Guidefor 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.
http://tut01.pdf/http://../ug/flug.pdfhttp://-/?-

tutorial 5 - modeling radiation and natural convection - 12 juni 2014

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