www.ansys.comANSYS Advantage • Volume I, Issue 1, 200746

TIPS & TRICKS

Radiation can play an important rolein heat transfer analyses. In ANSYSWorkbench Simulation, a “Radiation”load is available that allows users toaccount for losses to the surroundings,although this does not include radiationexchange between surfaces. To utilizethe ANSYS surface-to-surface radiationcapabilities, an easy method is availableto include these effects within ANSYSWorkbench Simulation via NamedSelections and a Command object.

How Heat RadiatesRadiation is a highly nonlinear

mode of heat transfer. A simplifiedform of the equation describing radia-tion from one surface to another is:

in which A is the surface area, ε is theemissivity of the surface, F is the viewfactor between surfaces, σ is the Stefan–Boltzmann constant, and Ti

and Tj are the two surface temperaturesin absolute temperature units.

When using the Radiation load inANSYS Workbench Simulation, theuser enters the emissivity and ambienttemperature, while the form factor Fij isassumed to be 1.0. In this situation, Ti

reflects the absolute temperature of anode on the surface while Tj representsthe ambient temperature. Temperaturevalues are specified in °C or °F, andANSYS Workbench Simulation auto-matically converts these values toKelvin or Rankine, respectively.

View-Factoring Radiationinto ANSYS Workbench SimulationThe ANSYS Radiosity Solution Method accounts for heat exchangebetween surfaces using Named Selections and a Command object.

By Sheldon Imaoka, ANSYS, Inc.

This method is suitable when radi-ation only occurs to space and nosurfaces are assumed to radiatebetween one another. In cases inwhich radiation occurs between sur-faces of the model, however, thisbuilt-in ANSYS Workbench SimulationRadiation load is not sufficient, andsurface-to-surface radiation utilizingthe ANSYS Radiosity Solution Methodis needed instead.

Performing Radiosity SolutionsThe Radiosity Solution Method

differentiates each independent regionof radiation as an enclosure. Withineach enclosure, view factors are deter-mined, and the radiated heat flux iscomputed between each element faceas well as to space, if the enclosure is open.

It is worthwhile to note that con-duction and radiation calculations areperformed in a segregated fashion.Depending on the degree of radiationheat flow in the model, the solutionmay require more iterations than regular ANSYS conduction-basedsolutions.

To use the Radiosity SolutionMethod, the following two steps areperformed:

1. Designate surfaces that willradiate to each other via Named Selections.

2. Insert necessary ANSYS Parametric Design Language(APDL) commands using aCommand object.

To create Named Selections, sur-faces (or edges in 2-D) are selected andthe “Create Selection Group” icon onthe Named Selection toolbar is chosen.Surfaces that radiate between eachother in an enclosure can be defined inone or several Named Selections. Theonly point the user needs to keep inmind is that all surfaces in a givenNamed Selection will be assumed tohave the same emissivity values. Withmultiple Named Selections, however,each set of surfaces can have differentvalues of emissivity.

As an example, consider one hollow block positioned inside another.Two Named Selections (REGION_Aand REGION_B — one for each block)are needed to represent all surfacesthat can radiate between each other.By making use of two Named Selec-tions, the emissivity values of theREGION_A surfaces can be specifiedindependent of those of theREGION_B surfaces.

In addition to specifying the surfaces of the blocks that can radiatebetween each other, a Commandobject also needs to be inserted underthe “Environment” branch in ANSYSWorkbench Simulation. Only a fewAPDL commands are required to specify the parameters needed for theRadiosity Solution Method:

sf,REGION_A,rdsf,0.9,1

sf,REGION_B,rdsf,0.8,1

stef,5.67e-8

toffst,273.15

hemiopt,10

tunif,20

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TIPS & TRICKS

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The meaning of these commandsis explained below:

• The first two commands (SF)group Named Selections (in this case “REGION_A” and“REGION_B”) to a given enclo-sure (1) with emissivity values of“0.9” and “0.8,” respectively. Ifthe enclosure is open, theSPCTEMP command also shouldbe used to designate the space(ambient) temperature.

• The next two commands, STEFand TOFFST, specify the Stefan–Boltzmann constant and thetemperature offset to absolutezero. These are unit-dependent,so users should make sure thatthe active unit system is setaccordingly from the “Units”menu.

• The HEMIOPT command isoptional, but it is used to set theresolution of the viewfactor calculations Fij. The default value

is 10, but it may be increased formore accurate viewfactor calculations at the expense ofadditional CPU time. (For 2-Danalyses, the analogous command is V2DOPT instead of HEMIOPT.)

• The last command, TUNIF, specifies the initial temperaturein ºC or ºF. For a nonlinear steady-state thermal analysis,specifying a reasonable initial temperature will help convergence.

Handling Multiple EnclosuresIf multiple enclosures (i.e., inde-

pendent radiating regions) are present,SF commands may be repeated for theother Named Selections but referencinga different enclosure ID.

Users also are advised to turn on “Auto Time Stepping” and to specify the number of initial, minimumand maximum substeps under the

Two Named Selections (REGION_A and REGION_B) represent surfaces that can radiateheat between each other.

The temperature distribution of three blocks radiating between each other is shownin the figure above. In this case, the center small block (transparent) has a fixedtemperature and is radiating to the middle block (displayed). This block, in turn,radiates to another block (transparent) that encloses it, and the third block radiatesto space. This model illustrates the use of three radiation enclosures — two areclosed while one is open. Radiation is the only mode of heat transfer between thethree blocks, yet the Radiosity Solution Method can be incorporated easily insideANSYS Workbench Simulation to solve these types of problems.

“Solution” branch since radiation problems can be highly nonlinear.

A number of advanced RadiositySolution Method options also are available:

• RADOPT to specify solver controls

• VFOPT to write or read the viewfactor file

• RSYMM and RSURF to takeadvantage of planar or cyclicsymmetry

• RDEC and RSURF to coarsen theelement faces for radiation calculations only

• Temperature-dependent emissivity specification is alsopossible

All of the APDL commands aredocumented in the ANSYS CommandsReference, and additional details ofRadiosity Solution Method options canbe found in Sections 4.6 and 4.7 of theANSYS Thermal Analysis Guide. n

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