Diffusion coefficient calculation and average cosine of scattering angle

User Support
1

Hi,
I’m interested in calculating the average cosine of scattering angle and diffusion coefficient D. Is there any way to do it by use of OpenMC?

Regards

Tarek

2

Hello Tarek,

You have a few options for how to calculate the average cosine and the diffusion coefficient. The average cosine is scatter-1 / scatter-0 and therefore if you include those scores in a tally you can post-process to get the average scattering cosine.
There are multiple definitions of the diffusion coefficient, I’ll assume you simply mean the classical 1/(3 * Sigma_transport). To be able to generate this, you can use the definition of Sigma_transport as Sigma_total - Sigma-s,1. In terms of score types that is: total - scatter-1. Alternatively you can get this from the TransportXS MGXS object in the python API (Documented for ver 0.7.1 here with example notebooks to demonstrate their use).

Adam

3

Tarek,

You should be cautious of computing the diffusion coefficient using the transport cross-section as Adam mentioned above. The reason is that the energy condensation must be applied to the ratio 1/(3Sigma_tr) rather than Sigma_tr - i.e., one must tally 1/(3Sigma_tr) directly in Monte Carlo (and account for a number of other subtleties).

If you compute the diffusion coefficient from the transport cross section it may be very wrong - in an LWR spectra this approach results in diffusion coefficients that are hundreds of percent off. The magnitude of the error depends on the spectrum and core configuration. But should you use use tallied transport cross sections to compute diffusion coefficients, you do so at your own risk since this is not an approach that we recommend.

At the moment we do not support any robust approach to compute diffusion coefficients in OpenMC (that I know of). The Serpent MC code is equipped to compute coarse mesh diffusion coefficients for nodal diffusion, but those methods are not implemented in OpenMC at this time. We do have a student working on a new flexible approach to computing diffusion tallies, but this is still experimental and not available in a release version of OpenMC.

Best,

Will

4

Thank you Adam

Tarek

5

Thank you Will,
Your remarks will be taken into account.

Regards

Tarek