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Comparison to TRASYS models Fence Problem Before a comparison between the RADKs of a TRASYS run and a MCRT solution run is done, it should be pointed out what kind of differences are expected. The differences in the theory behind the Gebhart solution and Monte Carlo ray tracing can produce different results. The ray tracing result will always approach the correct answer, provided enough sampling (number of rays shot) has been taken. On the other hand, the Gebhart method will give poor results for models that are not nodalized correctly. Consider the following example:
The Gebhart method will calculate a view factor from surface 1 to 2 and from surface 1 to 3. When the radiation network is calculated there will be a RADK from 2 to 3, which is physically impossible. This is due to the assumption that the radiation is spread over the entire node. In MCRT, when a ray leaves surface 2 and hits surface 1, it is re-radiated from the point of intersection on surface 1. And thus the ray can only reflect back to surface 2 or to space. Therefore, the ray tracing method would not predict a RADK from 2 to 3. Nodalization Problem This following example shows how nodalization can play a big part in the answer obtained from the Gebhart method.
For the above model, TRASYS gives a RADK from 1 to 4 of 3.36e-3. If the user combines surfaces 2 and 3 into one surface (in the SURFACE data block), then the RADK becomes 3.77e-03. The difference in the RADK based on nodalization is 12%. The TRASYS view factors (using default inputs) agree with closed form solutions. MCRT obtained a value of 3.28e-03, which is independent of the breakdown of surfaces 2 and 3. While it is very worthwhile to test ray tracing methods verses
the Gebhart method; it should not be alarming that the results do
not match perfectly. View Factor Calculation Consider the geometry shown in Figure 3.
The following table shows how TRASYS compares to the closed form solution for this geometry. The interesting thing about the data is that there seems to be a magical number somewhere between 6.6 and 6.7 that makes the TRASYS numbers give better answers. Looking at this makes one wonder, what other magical numbers are undocumented that could cause problems with a model?
Consider the geometry in Figure 4.
By varying d, the TRASYS view factor calculation from node 1 to 3 can be compared against the MCRT solution, as shown in the following table. With 100K rays shot, the MCRT solution can be considered extremely accurate.
These errors have to do with the scheme that TRASYS uses to determine if shadowing has occurred. At smaller values of d, TRASYS is doing shadowing, but is over predicting the amount of shadowing. At the higher values of d, TRASYS is predicting no shadowing and hence the view factor is too high. Gebhart Solution – Propagated Error The Gebhart solution will propagate errors from the view factor calculations. Consider the geometry in Figure 5.
The Gebhart solution was then run twice, once with view factors of .5 and then a second time with view factors of .49, or only 2% in error. The results are in the following table.
Users experienced in TRASYS should use this information to realize that their models always contained some error, but still got accurate results. New users to MCRT should use this information so as not to shoot millions and millions of rays, trying to get accuracy down to zero percent error.
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