The Viewfactor boundary condition in Patran was designed to support modeling a media participating in the thermal radiation interchange. This interchange could take place between two surfaces or between a surface and an ambient or space node representing the background thermal radiation conditions. The participating medium is assumed to be isothermal and gray within each waveband and to be diffusely emitting and absorbing without photoactive effects.

The VFAC boundary condition also provides support for some capabilities in Viewfactor which are used to reduce the CPU time required to calculate the viewfactors. This support comes in the form of the CNVSID and nonobstruction FLAG parameters in the VFAC LBC form which are used to identify convex surfaces and nonobstructing surfaces, respectively, in Patran.

These features of the VFAC boundary condition are described in this section.

The participating medium is assumed to be at a uniform temperature, gray in a waveband, and diffuse. It is assumed to be weakly absorbing (i.e., the exact exponential absorption function may be accurately replaced with a linear approximation). It is assumed that the medium does not obscure itself or the other surfaces.

The Patran Thermal user is free to assign the temperature or heat flux to the participating media node as a simple constant or in more complicated situations as functions of time and temperatures of other nodes. The participating media node will be treated as any other node in the thermal resistor network.

When the participating media node is present, the Viewfactor code makes three resistors instead of the usual one resistor between the surface subareas. One of the resistors will still be between the surface subareas. But it will have been modified to account for the portion of the radiant energy which will be absorbed as it traverses between the two surfaces. The second and third resistors will be between the surface subareas for each surface and the participating media node. They will account for the radiant interchange between the surfaces and the participating media. Refer to the MSC Patran Thermal User’s Guide for an explanation of resistor networks and subareas. Two resistor networks are shown in Figure 3‑15, one without a participating medium and one with a medium.

The participating media node must be defined in the Patran model before it can be referenced in the VFAC LBC form. If the participating media node does not already exist, it may be created with the Patran Finite Element form:

In the node location list box, point to a convenient grid point.

Frequently in thermal radiation analysis we encounter a problem which has an enclosure with an opening to space or to the ambient environment. In order to facilitate modeling this situation, Viewfactor and Patran Thermal provide for ambient thermal radiation nodes. The Patran Viewfactor boundary condition provides support for entering this part of the model through the Patran preprocessing.

In the present analysis scheme for a given enclosure, each surface may see at most one ambient node. This implies that each surface in the enclosure sees an isothermal ambient environment. If there is a participating media present, it is assumed to exchange radiant energy with the ambient environment also. The distance from the ambient node to the participating media node is not well defined. Therefore, this combination cannot be used with Patran Thermal resistor types which calculate the media absorption and emittance from Beer’s Law of Absorption (i.e., resistor subtypes 7, 8, 11, and 12).

There is a way to produce a more accurate model of the thermal radiation interchange between a surface and the ambient radiation through an opening in the enclosure. This is done by covering the openings in the enclosure with surfaces having the temperature of the ambient environment. The viewfactor from the surface to the ambient environment is calculated by taking one minus the sum of the viewfactors to all other surfaces that the first surface can see. This summing process introduces the possibility of cumulative errors. By filling the enclosure openings with ambient surfaces, the error is only the error occurring in the viewfactor calculation from the first surface to the ambient surface.

This method does in general require more CPU time, but this increase in CPU time will be relatively small if the ambient surfaces needed to close the open enclosure are few compared to the total number of surfaces in the enclosure. This method also has another advantage. There are no restrictions on the use of Patran Thermal radiation resistors which use Beer’s Law to calculate the interaction with the participating media (see Role of Ambient Radiation Nodes). This method allows you to have nonuniform ambient temperatures and to model the radiative surface properties of the ambient environment.

Some examples of open enclosures and how they might be closed by ambient surfaces are shown in Figure 3‑16.

Whenever there is an ambient node present in an enclosure and the sum of the viewfactors from a surface to all other surfaces it can see in that enclosure is not one, then an Patran Thermal radiation resistor is created from that surface to the ambient node. In addition, if there is a participating media node and the previous resistor to the ambient node was made, then a resistor will be made from the participating media node to the ambient node. A simple example network is shown in Figure 3‑17 for an enclosure with participating media and an ambient node. Note the presence of the media transmissivity, , in the resistors to the ambient node. Since the distance to the ambient node is not well defined, this transmissivity cannot be calculated from Beer’s Law and thus Patran Thermal radiative resistor subtypes 7, 8, 11, and 12 are not permitted in an enclosure with both a participating medium and an ambient node.

The ambient node must be defined in the Patran model before it can be referenced in the VFAC boundary condition. If the ambient node does not already exist, it may be defined with the Patran finite element create menu. See example in Figure 3‑18.

 

Since the calculation of viewfactors is computationally expensive, we have provided the user with the ability to identify convex surfaces in the thermal radiation portion of the model. A convex surface is one for which no pair of points on the surface can see each other by direct line of sight. Thus the exterior of a sphere and the exterior of a cylinder are convex surfaces. Plane surfaces are also considered to be convex. Thus, for example, the faces of a cube are all convex, and the entire exterior of a cube is convex, while the interior of the cube has six separate convex surfaces, one for each face. Caution must be exercised when specifying convex surfaces in axisymmetric models (see Caveats Regarding Convex Surfaces in Axisymmetric Models, 48.

To calculate viewfactors, each surface must be paired with every other surface in the enclosure and a determination made regarding whether there is a direct line of sight view between pairs of points on these two surfaces, one point on each surface. By the nature of convex surfaces, we know a priori that a pair of surfaces, element faces in our case, on a convex surface do not have a direct line of sight view of each other.

This determination of whether one surface has a line of sight view of another surface from geometrical considerations is computationally significant. If the determination can be made simply by comparing convex surface IDs (a computationally trivial test) a significant amount of CPU time can be saved on problems which have a large number of element faces on convex surfaces in an enclosure.

This requires that the convex surfaces be identified by the user before they are submitted to Viewfactor for analysis. This of course is not required in order to run Viewfactor. You will have to decide whether it is an economical use of your time to identify convex surfaces in order to save some computational time. People seem to be more efficient than machines at identifying convex surfaces and are able to group large numbers of element faces into convex surfaces merely by looking briefly at the model.

In certain situations, you must take special care not to identify as convex surfaces which are not really convex. A simple example of this is the exterior of a torus, which appears convex when the axisymmetric model is drawn, but in reality, due to its double curvature, is partially not convex. This example is illustrated in Figure 3‑20. Such situations are common in axisymmetric models and also can occur in three-dimensional models. Viewfactor has no way to check the correctness of convex surface identification and so the user must take care not to make mistakes. When in doubt, it is best not to use the convex surface ID.

In calculating viewfactors, we must check to see if the view between two surfaces is obstructed or blocked by one or more other surfaces in the enclosure. In the worst case, this requires checking all of the surfaces in the enclosure as potential obstructions between every pair of surfaces in the enclosure. Anything that can be done to reduce the number of surfaces that must be considered as potential obstructions of the view between surface pairs is of interest to the user who has a limited amount of CPU time available.

By setting the nonobstruction flag, you can indicate that a surface cannot obstruct the view between any pair of surfaces in the enclosure. Viewfactor checks the nonobstruction flag. If the flag is set for a surface, that surface is not included in the potential obstruction list. Thus the number of potential obstructions to be checked is reduced and CPU time is conserved.

In the example shown in Figure 3‑18, none of the surfaces can obstruct the view between any other pair of surfaces. Thus all of the surfaces with VFAC boundary condition may have their nonobstruction flag set for the lower plate.

For the example shown in Figure 3‑19, the inner surface of the outer spherical shell does not obstruct the view of any other pair of surfaces in the enclosure and we may set the nonobstruction flag for the VFAC boundary condition on element faces on this surface.

Nonobstructing surfaces may be particularly difficult to identify in axisymmetric models. You may wish to forgo the use of the nonobstruction flag for axisymmetric models. The nature of the difficulty is illustrated in Figure 3‑21 with a simple example. The object being modeled is a solid cylinder surrounded by an annulus and a larger, hollow cylinder. Referring to the axisymmetric model of the object in the figure, it appears at first inspection that there are not obstructing surfaces in the model. However, a top view of the object, as seen in the figure, reveals that the solid cylinder does indeed obstruct the view between parts of the outer cylinder.

This type of situation can be difficult to correctly identify in more complicated axisymmetric models. You are urged Surface to exercise caution.