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Radiation Surface Check

In the thermal analysis, if [Surface-to-surface (accuracy prioritized)] is selected for radiation setting of the thermal boundary condition,

the radiation surface check is performed at the beginning of the analysis.

It is examined whether elements in each radiation group can be seen from nodes on the radiation surface.

 

There are three checking methods available: "triple-loop method", "mapping method", and "Hemicube method"..

The difference between them is explained here.

Triple-Loop Method

The checking process is as follows:

 

Note that the loops are for the same radiation group.

1. Element loop or node loop

2. Element loop in the Loop 1

3. Element loop in the Loop 2, which checks if there are obstructing elements between the nodes and the elements.

 

These loops constitute a triple-loop.

Calculations are performed up to e*e*e times for the face-to-face radiation solver (time prioritized), and up to n*e*n times for the point-to-face radiation solver (accuracy prioritized) where e is the number of elements and n is the number of nodes.

The triple-method has the disadvantage that the calculation time increases in proportion to the cubic law when the number of elements increases.

This disadvantage is especially notable in the 3D analysis.

Mapping Method

In the mapping method, the check precess is as follows:

 

Note that the loops are for the same radiation group.

1. Element loop or node loop (element or node is a viewpoint)

2. Element loop 1: Map the distance from the viewpoint to each element.

3. Element loop 2: Check whether each element is obstructed by other elements or not.

 

In contrast to the triple-loop method, Loop 3 begins after Loop 2 is finished completely.

Calculations are performed e*(2*e) times for the face-to-face radiation solver (time prioritized), and n*(2*e) times for the point-to-face radiation solver (accuracy prioritized) where e is the number of elements and n is the number of nodes.

The mapping method consists of a double-loop, whereas the triple-loop method consists of a triple-loop.

With the mapping method, the time reduction is significant when the number of elements is large in 3D analysis.

The time reduction is in proportion to the number of elements.

Mapping Method Setup

 

During Loop 1, the distance information is recorded in the 2D array variable.

The distance is compared to the recorded one, and the recorded distance is renewed

only if the new distance is shorter than the recorded one.

 

Mapping resolution is the resolution per 90-degree view angle.

The default value is 90, and the difference of the distance can be mapped every 1 degree.

 

During Loop 2,

the recorded distance on the map and the distance from the viewpoint to the element are examined.

If an element is obstructed by other elements, the recorded distance is shorter than the distance from the viewpoint to the element.

 

Tolerance of distance check sets the multiplying factor of the recorded distance against the distance from the viewpoint to the element.

It is the threshold to judge whether they are considered within the matching tolerance.

The difference between the triple-loop and mapping methods will be small

if this tolerance is set to a small value even if the mapping resolution is coarse.

 

Please note that too rough (or small) tolerance value might lead to

the misjudge that some obstructed elements are visible.

 

If "Evaluate the difference between triple-loop and mapping methods" is selected, the radiation surface check is performed with both methods,

and the difference between them is displayed by percentage. This setting is available only if the radiation solver is set with [Point - Face (Accuracy Prioritized].

This method takes long time as the radiation surface check is performed both with the triple-loop method and the mapping method.

If the difference is not negligible (ex. more than a few percent), the result of triple-loop method should be considered more reliable.

The result of the mapping method may become closer to that of the high-precision method

by setting higher resolution and looser tolerance for the distance check with the mapping method.

 

The Checking Time of Triple-Loop Method and Mapping Method

The figure below shows the checking time of triple-loop and mapping methods against the number of elements.

The model of thermal analysis example 9 is used.

 

 

The mapping method is more effective in the analysis with higher number of elements.

 

Hemicube Method

The Hemicube method can be applied only to surface-to-surface radiation.

In the Hemicube method, place a camera at the center of the element and conduct visibility check by drawing surrounding elements internally by GPU.

The Hemicube method is as follows:

 

1. Process each element in a loop (treating each element as a viewpoint)

2. Draw all element faces simultaneously using GPU.

3. Calculate the view factor by looping over each pixel.

 

The number of calculations equals the number of elements multiplied by the number of pixels (upper face and four side faces of Hemicube).

Since the element faces are drawn simultaneously by GPU, using a high-performance discrete GPU can reduce the calculation time.

Hemicube resolution is the number of pixels on one edge of a Hemicube face.