The radiosity solver method works for general radiation problems involving two or more surfaces receiving and emitting radiation. The method is supported by all 3D and 2D elements having a temperature degree of freedom.
Elements supported for the radiosity method include:
| PLANE293 -- 2D 8-Node Thermal Solid |
| PLANE292 -- 2D 4-Node Thermal Solid |
| SOLID279 -- 3D 20-Node Thermal Solid |
| SOLID278 -- 3D 8-Node Thermal Solid |
| SOLID291 -- 3D 10-Node Tetrahedral Thermal Solid |
| PLANE222 -- 2D 4-Node Coupled-Field Solid |
| PLANE223 -- 2D 8-Node Coupled-Field Solid |
| SOLID225 -- 3D 8-Node Coupled-Field Solid |
| SOLID226 -- 3D 20-Node Coupled-Field Solid |
| SOLID227 -- 3D 10-Node Coupled-Field Solid |
| SHELL157 -- 3D Thermal-Electric Shell |
| SHELL132 -- 3D 8-Node Thermal Shell |
| SHELL131 -- 3D 4-Node Thermal Shell |
| SHELL294 -- 3D 4-Node Thermal Shell |
| SOLID98 -- Tetrahedral Coupled-Field Solid |
| SOLID90 -- 3D 20-Node Thermal Solid |
| SOLID87 -- 3D 10-Node Tetrahedral Thermal Solid |
| SOLID70 -- 3D Thermal Conduction Solid |
| PLANE77 -- 2D 8-Node Thermal Solid |
| PLANE55 -- 2D Thermal Solid |
| PLANE35 -- 2D 6-Node Triangular Thermal Solid |
| PLANE13 -- 2D Coupled-Field Solid |
| SOLID5 -- 3D Coupled-Field Solid |
The following radiosity topics are available:
- 5.5.1. Process for Using the Radiosity Solver Method
- 5.5.2. Recommendations for Using Space Nodes
- 5.5.3. Further Options for Static Analysis
- 5.5.4. View Factor Updating at the Substep Level for a Coupled-Field Analysis Including Large-deflection Effects
- 5.5.5. Troubleshooting with View Factor Diagnostics
The process for using the radiosity solver method involves these steps:
Define the radiating surfaces as follows:
Build the thermal model in the preprocessor (PREP7). Radiating surfaces support symmetry conditions in some cases. See Advanced Radiosity Options for information on modeling symmetry for radiating surfaces. Radiating surfaces are considered to be the faces of a 3D model or the sides of a 2D model.
Flag the radiation surfaces for a given emissivity and enclosure number using the SF, SFA, SFE, or SFL command. For all surface or line facets radiating to each other, specify the same enclosure number.
To specify temperature-dependent emissivity, issue the SF, SFA, SFE, or SFL command with
VALUE= -N. Emissivity values are from the EMIS property table for material N (MP).Since radiation can pass through a fluid region and impact on a solid, you can apply the surface-to-surface radiation load on a fluid/solid interface, as well as on external model boundaries. In this case, you should apply the RDSF load to either the fluid or solid element faces, or the solid entity defining the interface.
Verify the flagged radiation surfaces for properly specified emissivity, enclosure number and direction of radiation using the /PSF command.
To apply radiation surface loads on the SHELL131 (KEYOPT(3) = 2) or SHELL157 elements, you must specify the face number with the exterior or interior orientation to properly flag it. You can use the SF, SFA, or SFE commands to apply these loads. The SF and SFA commands apply the radiation surface loads only on face 1 of the shell element. To apply radiation surface loads on face 2 or on both faces of the shell elements, use the SFE command. See SHELL131 and SHELL157 in the Element Reference for information on face orientation and numbering.
Although the radiosity solution can be obtained by flagging element surfaces with RDSF flags (RDEC), a faster solution is possible by superimposing radiation surface-effect elements on those surfaces (RSURF). The radiosity solution is calculated on the surface-effect elements, which can be less accurate than is the case with the RDSF-flagged surface but requires fewer computational resources. If you choose the superimposition method for a faster solution and you wish to
The following table lists commands used to define solution options in a thermal analysis using the radiosity solver method. See the individual command descriptions for more details.
Table 5.1: Commands for setting Solution Options (Radiosity Solver Method)
| Commands | used to perform these steps in specifying the analysis[a] |
|---|---|
| STEF | Define the Stefan-Boltzmann constant in the appropriate units. |
| TOFFST | Specify the temperature offset (required for models with temperatures entered as degrees Fahrenheit or degrees Celsius). |
| /AUX12 | Enter the processor that supports the radiosity solver method. |
| RADOPT | Choose a direct solver or an iterative solver (default). Specify a relaxation factor and convergence tolerance for the heat flux. |
| SPCTEMP[b] | Specify the ambient (or space) temperature. List or delete all specified space temperatures. |
| SPCNOD[b] | Specify a space node for each enclosure[c]. List or delete all specified space nodes. |
[a] Multiple tasks that can be issued choosing different argument options for the same command are separated with a semicolon.
[b] For an open enclosure problem, you must specify the ambient temperature (SPCTEMP) or the ambient node (SPCNOD) for each enclosure.
[c] Radiation to ambient space can be simulated as another body in the model by specifying a space node for each enclosure. The radiosity solver retrieves the nodal temperature for the specified space node as the ambient temperature. See Recommendations for Using Space Nodes for a more detailed discussion on the use of space nodes in numerical radiation modeling.
The program uses different algorithms to calculate view factors for 2D and 3D models (See View Factor Calculation (2D) in the Theory Reference and View Factor Calculation (3D): Hemicube Method in the Theory Reference). It assumes a 3D model by default.
Specify options to calculate new view factors using the following commands:
Options for 2D Models
2D models may be either planar
(GEOM = 0 on V2DOPT), or
axisymmetric (GEOM = 1), with planar as the default.
Axisymmetric models are expanded internally to a 3D
model with the number of axisymmetric sections that is specified for
NDIV on V2DOPT (see View Factors of Axisymmetric Bodies in the Theory Reference). For example, the
default value of NDIV = 20 indicates twenty
sections, each spanning 18 degrees. This expansion is done only for view factor
calculation, and not for the thermal solution.
The V2DOPT command also allows you to select hidden or non-hidden viewing option (defaults to hidden).
The non-hidden method calculates the view factors from every element to every other element regardless of any blocking elements (See Non-Hidden Method in the Theory Reference).
The hidden method (default) first uses a hidden-line algorithm to determine which elements are "visible" to every other element (see Hidden Method in the Theory Reference). (A "target" element is visible to a "viewing" element if their normals point toward each other and there are no blocking elements.) Then, view factors are calculated as follows:
Each radiating or "viewing" element is enclosed with a unit hemisphere (or a semicircle in 2D).
All target or "receiving" elements are projected onto the hemisphere or semicircle.
To calculate the view factor, a predetermined number of rays are projected from the viewing element to the hemisphere or semicircle. Thus, the view factor is the ratio of the number of rays incident on the projected surface to the number of rays emitted by the viewing element. In general, accuracy of the view factors increases with the number of rays. You can increase the number of rays via the
NZONEargument on the V2DOPT command.
For more information, see the discussion on hidden and non-hidden options and axisymmetric geometry in Recommendations for Using Space Nodes and Radiation Matrix Method in the Theory Reference.
Other View Factor Options and Considerations
You can specify whether new view factors should be computed or if existing values should be used via the VFOPT command. VFOPT,NEW computes new view factors, stores them in the database, and writes them to a file. This calculation is not performed in parallel even if you are running in distributed-memory parallel (DMP) mode. If view factors already exist in the database, you can deactivate the view factor computation by issuing VFOPT,OFF, which is the default upon encountering the second and subsequent SOLVE commands in /SOLU. After the first SOLVE command, the program uses view factors existing in the database, unless they are overwritten by the VFOPT command.
The Jacobi iterative solver (SOLVER = 2) is the
only solver choice that runs in a fully distributed parallel fashion. Therefore,
it is typically the best choice for optimal performance when running in DMP
mode. Since the Jacobi iterative solver is not available for 2D models, it is
not possible to run 2D models in DMP mode.
For 3D analyses using distributed-memory parallel processing (DMP), you can specify parallel or serial mode for view factor calculations. View factors are calculated in parallel only if the following are true:
The view factor calculation occurs as part of the solution by issuing a SOLVE command in the /SOLU processor.
View factors were not previously calculated.
VFOPT allows you to output view factors in ASCII or binary file format. Binary is the default.
Solution time can be significantly reduced for models with symmetry by turning on view factor condensation via the VFCO command. For an example problem that uses view factor condensation, see Example of a 3D Open Enclosure with Symmetry: Radiation Analysis with Condensed View Factor Calculation, and for a description of the underlying theory, see View Factor Matrix for a Model with Symmetry in the Theory Reference and Radiosity Equations Simplified for Models with Symmetry in the Theory Reference.
To ensure a good energy balance, you need to satisfy both the row sum relationship as well as the reciprocity relationship for the view factor matrix. View factor smoothing (VFSM command) can be used to adjust the view factor matrix to satisfy reciprocity and/or row sum properties.
For a perfect enclosure, each row of the generated view factor matrix should sum to a value of 1. For a leaky enclosure, the sum across any row can be less than or equal to one, depending on the amount and characteristics of the leakiness.
The VFSM command must be used before VFOPT is issued, or /SOLU is initiated.
Important: Errors related to reciprocity violation can be severe, especially when the mesh resolution of various facets in the model are different. To calculate accurate view factors keep the mesh resolution as similar as possible. See Figure 5.1: Keep Mesh Resolution Similar to Reduce Reciprocity Violation Errors.
Next, you calculate the view factors. You can also query the view factor database and calculate an average view factor.
Compute and store the view factors using the VFOPT command
List the calculated view factors for the selected source and target elements by querying the view factor database and calculate the average view factor via the VFQUERY command.
You can retrieve the calculated average view factor using
*GET,Par,RAD,,VFAVG.
Specify an initial temperature if your model starts at a uniform temperature, then specify the number or size of the time steps and specify a ramped boundary condition.
To assign a uniform temperature to all nodes, use the TUNIF command.
Solution accuracy is governed by the time step size you use and the convergence criterion you chose. When using auto-time stepping, review the transient results carefully. The radiosity method works best when there are other forms of heat transfer besides radiation determining the temperature of a body.
Set the number or size of time steps, using either the NSUBST or DELTIM.
Due to the highly nonlinear nature of radiation, you should specify ramped boundary conditions via the KBC command.
Although modeling radiation does not always require a space node, the decision to include one or not can affect the accuracy of your thermal analysis results. Keep the following recommendations about space node usage in mind as you build your model.
Generally, you should specify a space node for an open system. Especially when modeling an open system which includes gray body radiation (emissivity is less than 1), you must use a space node to ensure accurate results. Conversely, do not specify a space node if you are modeling a closed system where all of the radiating surfaces form an enclosure and do not radiate to space.
For the hidden method of view factor calculation, the accuracy of the view factor calculations can affect the accuracy of the radiation calculated to the space node. Because inaccuracies in the calculations accumulate at the space node, the relative error in the space node view factor can be exaggerated in a closed or nearly closed system.
When using the hidden method, you may need to increase the number of divisions used in the view factor calculation and refine the mesh in order to make the view factors more accurate. To increase the number of divisions used in the view factor calculation:
If this is not possible, consider the following tips when defining the space node:
For a closed system in which all radiating surfaces form an enclosure and do not radiate to space, do not use a space node.
If the nature of the problem makes it acceptable to simulate radiation between the radiating surfaces only (ignoring radiation to space), then do not specify a space node. This approach is valid only when modeling black body radiation (where emissivity = 1).
To account for radiation to space in a nearly closed system, mesh the opening and constrain the temperature of the nodes in the opening to the temperature of space. The view factor to space will then be calculated explicitly and more accurately.
For an open system where there are significant losses to space, you can use a space node (with a specified boundary condition) to capture the lost radiation with acceptable accuracy using moderate mesh refinement and a moderate number of divisions.
You can also solve a static problem using a false transient approach.
The analysis would include the following three steps:
Issue a constant density and specific heat for the model using the MP command. You should use a typical value of unit density and specific heat for the approach. The exact value for density and specific heat are not important as the problem finally approaches a steady-state solution.
Specify a transient analysis using the ANTYPE command.
Run the quasi static radiation analysis to steady-state, using the QSOPT command.
You can set the tolerance for the steady-state temperature via the OPNCONTROL command.
Depending on the material properties of the model (that is, density, specific heat, and thermal conductivity), temperature changes may be small at the beginning of a transient. With QSOPT on and the final time set to the default value (TIME = 1), you may obtain a solution before the true steady-state is reached. To obtain the true steady-state solution, use one of the following strategies:
Tighten the steady-state temperature tolerance on the OPNCONTROL command. Be aware, though, it may take a long time to reach the true steady-state solution.
Increase the final time (TIME) and the time step size (DELTIM) so that large temperature changes are captured at later time.
Deformation and/or motion of radiating surfaces may cause inaccuracies in radiation calculations if the view factors are not updated as radiating surfaces deform and/or move. Issue the VFUP command to enable view factor updates at the substep level and improve simulation accuracy.
To enable view factor updating via VFUP, all of the following conditions are required:
The analysis must include coupled-field elements with at least structural and thermal degrees of freedom (PLANE222, PLANE223, SOLID225, SOLID226, or SOLID227).
Large-deflection effects must be included (NLGEOM,ON).
KEYOPT(1) must be set to 1 on radiosity surface elements (SURF251 / SURF252) so that they deform with the underlying solid mesh. You can specify KEYOPT(1) on radiosity surface elements when they are generated (
DKEYon the RSURF command) or after they are generated (KEYOPT command in PREP7).
Set OPT2 and OPT3 on
VFUP to control the frequency of view factor updates at the end
of substeps or in the multipass radiation loop. See the command definition for
details.
In general, view factor computations are expensive, both in memory and time. The time cost is compounded when the VFUP command is used to improve simulation accuracy. For a detailed description of different strategies you can follow to optimize the trade-off between improved accuracy at the expense of increased solution time, see the notes of the VFUP command description. Restrictions and limitations are also described in the VFUP notes.
The following example shows the ability to model radiative heat transfer between a moving bar and a fixed plate using the VFUP command.
Example 5.1: Radiative Heat Transfer Between a Bar Moving Over a Plate
The following results were calculated using the VFUP command to update view factors at the substep level. The simulation accurately models radiative heat transfer between a tool held at a constant temperature of 822 °C and a rectangular plate that is initially at ambient temperature (22 °C). The cylindrical tool moves in a prescribed rectangular pattern above the surface of the plate without touching its surface. The view factors are updated as the tool moves to accurately model radiative heat transfer between the tool and the plate. The animation shows the calculated transient temperature field in the plate as the high temperature tool moves above its surface.
See the following example problems that provide modeling details and command listings demonstrating the use of the VFUP command:
If you do not enable view factor updates at the substep level, results may be inaccurate because view factors are only updated at the beginning of a load step via the SOLVE command. There is an alternative way to update view factors in between load steps rather than at the substep level, but this strategy is more time consuming than using the VFUP command to enable view factor updates at the substep level. The alternative method requires the following steps:
You can use this alternative method as a comparison to check the accuracy of the more efficient VFUP approach.
To diagnose a solution failure, the view factor matrix must satisfy both the row sum and reciprocity relationships (see View Factors in the Theory Reference). Violation of the row sum relationship introduces error in the analysis and may cause the simulation to exit with a "space node not specified" error message. To identify where the problem may be in a model with complex geometry, you can specify view factor diagnostic options using the VFDI command to write diagnostic information the next time view factors are created by a subsequent VFOPT,NEW or SOLVE command. The following example problem illustrates its use.
Example 5.2: Using VFDI to Write View Factor Diagnostic Information
This simple open enclosure example problem demonstrates how to use the VFDI command to create a component containing view factor row sums within a specified range. See the problem description and command listing below for details.
Problem Description
Radiation between two rectangles and their surrounding space is considered as illustrated in the figure below. The rectangular bodies are modeled with PLANE292 thermal 2D solid elements (depicted blue in the figure). There is a constant temperature boundary condition, T = 300 ℃, on the left vertical surface of the larger rectangle, and radiosity surface elements (depicted purple in the figure) are created on all remaining vertical surfaces (SF commands followed by RSURF) to simulate radiation. Two enclosures are defined by issuing SPCTEMP twice, setting their free-space ambient temperature to the same value of 100 ℃:
Enclosure 1 accounts for radiation between the two facing surfaces of the rectangles and the ambient atmosphere.
Enclosure 2 accounts for radiation between the far right surface of the smaller rectangle and the ambient atmosphere.
When VFOPT,NEW is issued, view factor summations are written to the view factor (.vf) file for each radiation surface element (see callouts in yellow and their values written near their respective surfaces in (B) of the figure below). Issuing the VFDI command before VFOPT,NEW enables view factor diagnosis. Because VFDI,3,0,1,0.5,0.8 is issued in the command listing below, upon issuing VFOPT,NEW a component containing all surfaces with view factor sums between 0.5 and 0.8 is created, and they are written to the database and the Jobname.vfd file. For this illustrative example problem, two out of six radiosity surface elements are identified in the specified range: elements 9 and 10, each with view factor sums = 0.7025. This diagnostic tool is useful for larger models with complex surfaces, which can have thousands of surfaces and large view factor files, to find which surfaces have view factor sums in a specified range.
Command listing
/prep7 ! Create the geometry and the mesh et,1,292 rect,0,1,-1,5 rect,2,3,0,4 esize,,2 amesh,all eplot ! Assign material properties mp,kxx,1,8 ! Apply constant temperature boundary condition nsel,s,loc,x,0 d,all,temp,300 allsel ! Flag radiation surfaces and specify their emissivity and enclosure number nsel,s,loc,x,1 sf,all,rdsf,.2,1 nsel,all nsel,s,loc,x,2 sf,all,rdsf,.2,1 nsel,all nsel,s,loc,x,3 sf,all,rdsf,.2,2 nsel,all ! Set the offset temperature from absolute zero toffst,273 fini /aux12 ! Specify the Stefan-Boltzmann constant stef,5.67e-8 ! Define space temperature spctemp,1,100.0 spctemp,2,100.0 ! Generate SURF251 elements and store in database rsurf ! Issue VFDI to diagnose all enclosures and create a component of VF row sums between 0.5-0.8. vfdi,3,0,1,0.5,0.8 vfdi,stat ! Calculate view factors vfopt,new,,,,ascii ! List the component(s) created by VFDI command cmlist,all,1,elem fini