This method works for general radiation problems involving two or more surfaces receiving and emitting radiation. The method involves generating a matrix of form factors (view factors) between radiating surfaces and using it to create a superelement in the thermal analysis. You also can include hidden or partially hidden surfaces, as well as a "space node" that can absorb radiation energy.
The following AUX12 topics are available:
The Radiation Matrix Method consists of three steps:
Define the radiating surfaces.
Generate the radiation matrix.
Use the radiation matrix in the thermal analysis.
To define the radiating surfaces, you create a superimposed mesh of LINK33 elements in 2D models and SHELL131 (KEYOPT(3) = 2) elements in 3D models. To do so, perform the following tasks:
Build the thermal model in the preprocessor (PREP7). Since radiating surfaces do not support symmetry conditions, models involving radiating surfaces cannot take advantage of geometric symmetry and must therefore be modeled completely (except for 2D axisymmetric cases). Radiating surfaces are usually faces of a 3D model and edges of a 2D model, as shown below:
Superimpose the radiating surfaces with a mesh of SHELL131 (KEYOPT(3) = 2) elements in 3D models or LINK33 elements in 2D models, as shown in the graphic below. The best way to do this is to first create a subset of the surface nodes, and then generate the surface elements using the ESURF command
Make sure to first activate the proper element type for the surface elements. Also, if the surfaces are to have different emissivities, assign different material reference numbers before creating the elements.
Caution: Radiating surface mesh of SHELL131 or LINK33 elements must match (node for node) the underlying solid element mesh. If it does not match, the resulting thermal solution will be incorrect. Therefore, the underlying solid elements must not have midside nodes.
The orientation of the superimposed elements is important. The AUX12 radiation matrix generator assumes that the "viewing" direction (direction of radiation) is along +Ze for SHELL131 elements and along +Ye for LINK33 elements (where e denotes the outward normal direction of the element coordinate system). Therefore, you must mesh the superimposed elements so that the radiation occurs from (or to) the proper face. The order in which the element's nodes are defined controls the element orientation, as shown below:
For an open enclosure problem, if you want to simulate radiation to the ambient space as a body in your model, define a space node. The location of this space node is not important. (For a more detailed discussion on space nodes, see Recommendations for Using Space Nodes).
Calculating the radiation matrix requires the following inputs:
Nodes and elements that make up the radiating surfaces
Model dimensionality (2D or 3D)
Emissivity and Stefan-Boltzmann constant
The method used to calculate the view factors (hidden or visible)
A space node, if desired.
To generate the matrix, perform these steps:
Enter AUX12 using the /AUX12 command.
Select the nodes and elements that make up the radiation surfaces. An easy way to do this is to select elements by type and then select all attached nodes using the ESEL,S,TYPE and NSLE commands. If you have defined a space node, remember to select it.
Specify whether this is a 2D model or a 3D model (GEOM).
The AUX12 radiation matrix generator uses different algorithms to calculate the form factors for 2D and 3D models respectively. It assumes a 3D model by default. The 2D models may be either planar (by default, or
NDIVvalue = 0), or axisymmetric (NDIVvalue > 0). Axisymmetric models are expanded internally to a 3D model, withNDIVrepresenting the number of axisymmetric sections. For example, settingNDIVto 10 indicates ten sections, each spanning 36 degrees.Define the emissivity (EMIS).
Define the Stefan-Boltzmann constant (STEF). The Stefan-Boltzmann constant defaults to 0.119E-10 Btu/hr-in2-R4. (In S.I. Units, the constant has the value 5.67E-8 W/m2-K4.)
Specify how to calculate view factors, using the VTYPE command to choose between the hidden or non-hidden methods.
The non-hidden method calculates the view factors from every element to every other element regardless of any blocking elements.
The hidden method (default) first uses a hidden-line algorithm to determine which elements are "visible" to every other element. (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 NZONE field on the VTYPE command or the menu option. Both indicate the number of radial sampling zones.
If necessary, designate the space node (SPACE).
Use either the WRITE command or the menu option to write the radiation matrix to the file Jobname.sub. If you want to write more than one radiation matrix, use a separate filename for each matrix. To print your matrices, issue the command MPRINT,1 before issuing the WRITE command.
Reselect all nodes and elements (ALLSEL).
You now have the radiation matrix written as a superelement on a file.
After writing the radiation matrix, re-enter the preprocessor (PREP7) and read the matrix in as a superelement following these steps:
Re-enter the preprocessor (/PREP7).
Switch the element type pointer to the superelement (TYPE).
Read in the superelement matrix (SE).
Delete the superimposed mesh of SHELL131 or LINK33 elements (EDELE) since the thermal analysis does not require these elements.
Exit the preprocessor and enter the SOLUTION processor.
Assign the known boundary condition to the space node using either the D or F command.
This boundary typically is a temperature (such as ambient temperature), but it may also be a heat flow, depening on the actual environmental conditions being modeled.
Proceed with the thermal analysis as explained in the other chapters of this manual.
Below are some general guidelines for using the AUX12 radiation matrix generator approach to radiation analysis:
The non-hidden method can be used if all the radiating surfaces see each other fully. If the non-hidden method is used for cases where any blocking effect exists, there will be significant inaccuracies in the view factor calculations and the subsequent results, and the problem may fail to converge.
The hidden method requires significantly longer computer time than the non-hidden method. Therefore, use it only if blocking surfaces are present or if surfaces cannot be grouped.
In some cases, you may be able to group radiating surfaces so that each group is isolated completely from the other groups in terms of radiation heat transfer. In such cases, you can save significant time by creating a separate radiation matrix for each group using the non-hidden method. (This is true so long as no blocking effects exist within a group.) Do this by selecting the desired group of radiating surfaces before writing the matrix.
For the hidden method, increasing the number of rays usually produces more accurate view factors.
For both hidden and non-hidden methods, a finer mesh of the radiating surface elements will calculate more accurate view factors. It is particularly important to have a more refined mesh when using the hidden method in order to obtain the same level of accuracy in view factor computation as the non-hidden method. Even though increasing the number of rays used (controlled by
NZONEargument of the VTYPE command) tends to improve accuracy, for a coarse mesh, increasingNZONEto even its maximum limit may still not yield an accurate solution for the hidden method.For axisymmetric models, about 20 axisymmetric sectors provide reasonably accurate view factors. Elements should have reasonable aspect ratios whey they are expanded to a 3D model.
LINK33 elements, which are used as superimposed radiation surface elements in 2D planar or axisymmetric models, do not directly support the axisymmetric option. In axisymmetric models, therefore, be sure to delete (or unselect) them before doing the thermal analysis.
Theoretically, the summation of view factors from any radiating surface to all
other radiating surfaces should be 1.0 for a closed system. This is printed as
***** FORM FACTORS ***** TOTAL =
Value for each radiating surface if the view factors for
radiating surfaces are printed using the MPRINT,1 command. For
open systems, the summation should always be less than 1.0. One way of checking
whether the view factor calculations are correct or not is to use the
MPRINT,1 command, and check if the summation of view factors
for any radiating surface exceeds 1.0. This can happen if the non-hidden method is
inadvertently used for calculating view factors between radiating surfaces with
blocking effects.
For more information, see the discussion on hidden and non-hidden options and axisymmetric geometry in Recommendations for Using Space Nodes in this chapter and Radiation Matrix Method in the Theory Reference.