Diffusion Coefficients at Different Reactor Regions

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danhsiu
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Diffusion Coefficients at Different Reactor Regions

Post by danhsiu » Fri Feb 21, 2020 6:47 pm

Hi, I'm quite particularly new to Serpent, and I would say my reactor physics knowledge is... scrappy. It would be appreciated if I could get some comments pointing me in the right direction, or any critique on my methodology.

I have a cylindrical molten salt reactor input file that runs correctly, and the output file gives me two diffusion coefficients "CMM_DIFFCOEF" and "INF_DIFFCOEF" from the two calculation methods noted in the output parameters page http://serpent.vtt.fi/mediawiki/index.p ... arameters .

I was wondering, it is possible for serpent to compute different regions of a reactor according to input geometry?

To illustrate using the picture below, I want to calculate the diffusion coefficients for 1) the volume of the inner core, and 2) other "n" cylindrical sectors extending outwards the reactor core to "nodalize" my results.

Image

I know I can compute macroscopic cross sections for a region of the core by defining a detector and an MT number throughout the reactor, but I'm not certain on computing the diffusion coefficient at a specified region. The reactor design is non-homogenous extending outward of the core, so my understanding is that different sections should have different diffusion coefficients.

Any path forward?

Ville Valtavirta
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Re: Diffusion Coefficients at Different Reactor Regions

Post by Ville Valtavirta » Mon Feb 24, 2020 11:18 am

Hi,

Serpent can evaluate group constants such as homogenized cross sections and diffusion coefficients separately for different universes. You can thus get the data separately for the different regions of a reactor by making the different parts be a different universe.

You can consider this already while building your geometry, but if you have a ready made geometry, you could simply do something like in the example below.

However, you should note that the Cumulative Migration Method (CMM) approach does not work for finite/partial geometries. Thus far there is no formulation of the method that could be used to obtain diffusion coefficients for subsets of a system.

-Ville

Code: Select all

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --- Assuming geometry is already defined in universe 0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% --- Set a new root universe, so that we can use universe 0 as any other universe
%     (we'll still need to define new_root_universe)

set root new_root_universe

% --- Create a surface at infinity

surf sINF inf

% --- Create an infinite copy of universe 0, named inner (fill it with universe 0)

cell  c91  inner  fill 0  -sINF

% --- Create an infinite copy of universe 0, named outer (fill it with universe 0)

cell  c92  outer  fill 0  -sINF

% --- Use these two copies to define the inner and outer core

surf sBOUND cylz 0.0 0.0 100.0

% --- Fill the two universe 0 copies to inner and outer core

cell cINNER  new_root_universe  fill inner  -sBOUND
cell cOUTER  new_root_universe  fill outer   sBOUND

% --- Generate group constants in the two universes

set gcu inner outer

danhsiu
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Re: Diffusion Coefficients at Different Reactor Regions

Post by danhsiu » Mon Feb 24, 2020 6:21 pm

Thank you for the detailed reply and pointers to a great example, Ville.

I have my geometry currently set-up and I am defining subset universes to calculate group-constants. I suppose this means that if I use the "set gcu" function to calculate homogenized cross-sections that all the three diffusion parameters "1) INF_DIFFCOEF, 2) B1_DIFFCOEF, and 3) CMM_DIFFCOEF", are garbage results and cannot be approximated?

Ville Valtavirta
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Re: Diffusion Coefficients at Different Reactor Regions

Post by Ville Valtavirta » Tue Feb 25, 2020 10:59 am

Hi,

the INF_DIFFCOEF is based on the out-scatter approximation that can be applied separately at the sub regions. However, the out-scatter approximation itself does not give the best diffusion coefficients.

B1_DIFFCOEF is the leakage corrected diffusion coefficient and as you are not generating diffusion coefficients in an infinite lattice geometry, you should not apply leakage correction.

CMM_DIFFCOEF as noted gives very good diffusion coefficients in infinite lattice geometries, but the results in sub-regions are nonsensical.

Currently the best way to calculate diffusion coefficients in sub-regions is to use the transport correction approach, where a pre-calculated transport correction curve is given for each material that exhibits important non-isotropic scattering using the set trc card. This requires some additional work to set up however.

The transport correction curve is the energy dependent ratio of Sigma_{tr}/Sigma_{tot}, i.e. the ratio of transport cross section to the total cross section of the material or nuclide.

One method for doing this is to run an external source simulation for an infinite homogeneous system consisting of the material to be evaluated with a fixed source of neutrons according to a suitable fission spectrum. If you switch cmm on in this calculation, you'll get the homogenized transport cross section (CMM_TRANSPXS) as well as total cross section (INF_TOT) as an output and can use them to evaluate the transport correction.

This transport correction curve needs to be pre-calculated on a fine enough energy grid so you'll need to choose a fine few group structure.

For LWR calculations the transport correction needs to be applied at least for the water in the problem.

-Ville

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