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January 31, 2007, 09:11 
Monte Carlo  Number of Iterations?

#1 
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Hi, I am trying to use the Monte Carlo radiation model in order to calculate, at a first stage, geometric view factors for complex geometries based on radiation heat transfer values from one surface to another. From what I've read in the manuals (CFX10) and tried with some simple geometries (with known analytical solutions like two perpendicular planes), it seams to me that the results that come from the first iteration (radiation variables like Radiation Wall Heat Flux) are, probably, better (or worse depending on the geometry parameters) than those of the second ore of the nth iteration. In other words, it seams to me that more iterations don't obligatory bring to better radiation results once we are dealing with a statistical (MC) model (no rms) that has to be completely solved each iteration. Is this so? Could any one say something about this?
To calculate the Geometric View Factors based on the heat exchanges between the surfaces (transparent medium), I'm assuming air absorption coef. equal to 0. Even with a great number of histories (1.000.000) the %SD stays by 100% for some cases. Does any one knows what really means this parameter and how is it calculated? Once I verify for this cases that the numerical solution is quite good (near the analytical one)? Thanks in advance. tsimon 

January 31, 2007, 16:48 
Re: Monte Carlo  Number of Iterations?

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Dear tsimon,
The heat exchange between boundaries is recomputed every iteration.. As you said, the statistical nature of MC model will not give you the same results between iterations. You mentioned that %SD is 100%, is is for the surfaces, or fo r the volume? %SD stands for standard deviation. At each radiation surface/volume a mean value is obtained by averaging the solution of "several accumulators" (multiple calculations for the same quantity). Then, a standard deviation is computed. The maximum standard deviation among all surfaces, or volumes is then reported. Opaque.. 

February 1, 2007, 06:22 
Re: Monte Carlo  Number of Iterations?

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Dear Opaque, Thank you very much for your prompt answer (from what I've seen in this forum, and I am new here, you are really the radiation specialist).
About %SD, in some simulations it stays 100% both for Surface and for Volume in all iterations. Also in these iterations the %imbal and lost (which I also know what they mean) is zero. But my question was also in another sense, that is, the fact that the results are different at every iteration, doesn't means that the results are better in the later iterations…. Is this so??? There is a CFX Technical Report (which I presume you know) that calculates View Factors Using the MC and DTM radiation models. It is mentioned in that report that all simulations were made until rms < 1e5. My question is why? Is this really necessary? Are radiation results of the last simulation better than of the first when using this models? I've studied MC statistical model (theoretically) and so I can have an "Idea" (but only a weak idea, even reading CFX manuals) about what are those SD values in CFX… But let me put the things another way: Once the rms value of the energy eq. is not dependent on the radiation values (MC model), I've tried (and think achieved) to calculate only radiation by establishing the Thermal conductivity (k) equal to zero in the material properties. With this and with laminar flow, no inlets, no outlets, V=0, the runs stop at the first iteration with rms =0 for all variables (vel., p, H) giving the radiation results for this first and only iteration. Once the boundary conditions are only definition of wall temperatures (for emitting radiation), aren't this radiation results so good as those I would get if k was not zero and I waited for 10 or a 100 iterations until the rms of the energy equation gets bellow some established value? Another question, related with these last and which I think of interest for many people (from what I've read in this forum) is if the number of histories is the same thing as the number of photons simulated, i.e., after coarsening the mesh, imagine there are 10 boundary radiation surfaces, if we have 100 histories it means that the model will take (randomly in terms of direction and optical deph â€" here appears the SD values) 10 photons (100 hist/10 surfaces) to be emitted by each surface and follow them history in terms of scattering and absorption until they die?? Thanks again (and I hope my questions are also the questions of other people and maybe also will bring light to someone)… tsimon 

February 8, 2007, 09:17 
Re: Monte Carlo  Number of Iterations?

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Dear tsimon,
My apologies I did not answer earlier.. you asked: " ..doesn't means that the results are better in the later iterations?" Assuming the temperature distribution has not changed, the MC results should be nearly as good as the previous iterations. Any RMS target used for a radiation calculation (no flow) using MC/DTM only applies to the energy equation. Again, if the k is not zero you need iterations to solve the temperature for the radiation solution to be valid. I assume that your media is absorbing radiation. For a transparent material with all temperature specified boundaries, the radiation solution is obtained in one iteration. Well, distributing the histories (photons) among the boundaries is kind of an art.. ANSYS CFX does not distribute them randomly, but it uses the emission as a weigth.. That is, if one of those 10 surfaces emitts 90% of the total emission in the domain, it will get 90 photons out of 100. Leaving the other boundaries to divide last 10 among themselves (again base on their contribution to the total emission). The main assumption is that boundaries that do not emitt enough energy are not assigned any photons (the minimum is 10 if recall correctly). Basically, the photon distribution is selfadaptive. Hope the information helps, Opaque.. 

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