Codes to calculate diffusion parameters of homogeneous reactor

[DeltaMed910]

TL;DR Summary

What codes can calculate diffusion coefficient D and thermal diffusion area L^2 of a given homogeneous, reflected sphere reactor?

For a novice research problem, I am approximating a system as a spherical reactor of homogenized natural uranium and heavy water, reflected by infinite graphite. I was attempting to find the critical mass and dimensions for it (very similarly to Lamarsh 3e Ex.6.7-8). To do so, I need to calculate the diffusion coefficients D and thermal diffusion area L^2 of the homogenized core and the reflector.

While Lamarsh lays out how to do it by hand, I am also interested in what codes can calculate this for a given mixture. I do not see any entries about diffusion parameters in the MCNP manual (I have a copy of MCNP6.2).

This source has pretty much what I'm looking for, a code that calculates thermal neutron diffusion parameters for arbitrary mixtures, but it seems to have problems with hydrogenous media.
https://inis.iaea.org/collection/NCLCollectionStore/_Public/27/017/27017643.pdf

 

[Astronuc]

TL;DR Summary: What codes can calculate diffusion coefficient D and thermal diffusion area L^2 of a given homogeneous, reflected sphere reactor?

I do not see any entries about diffusion parameters in the MCNP manual (I have a copy of MCNP6.2).

MCNP is a general-purpose, continuous-energy, generalized-geometry, time-dependent, Monte Carlo radiation transport code designed to track many particle types over broad ranges of energies, so one will not find diffusion coefficients as input.

I would imagine a diffusion theory based code would calculate, and perhaps output, diffusion coefficients, if the code is so designed.

 

[Alex A]

I'd say the chief advantage of a one group analytical solution is that it can be done on a bit of paper and produce an answer. MCNP however simulates the physics and so doesn't use any of that analytical maths internally. I did a little doodle in MCNP which may help if you want to play with the numbers.

Reflected homogeneous sphere.
1 1 -1.11 -1
2 2 -1.8 1 -2
3 0 2

1 so 50
*2 so 10000

mode n
imp:n 1 1 0
kcode 10000 1.0 10 30
ksrc 0 0 0
m1 92235 8.7E-5 01002 2 08016 1
mt1 hwtr.10t
m2 06012 99 06013 1

That's a 50cm sphere of D2O surrounded by a 100m sphere of d1.8 graphite. 8.7e-5 molar amount is just under critical and 8.8 is just over critical. The 100m sphere is reflecting but changing this makes no difference to the result so it's as close to infinite as it needs to be I think.

Changing the material to natural U will require a big change in geometry.
m1 92235 8.7E-5 01002 2 08016 1 92238 0.01234
Would be the equivalent with natural U, but this may be hopelessly dilute and you may need to alter the density in the cell section.

Edit, added S(alpha,beta) table which affects the answer slightly. 8.7 now shown to be a bit overcritical.

 

[rpp]

What is the purpose of these calculations?

One-group diffusion theory is going to have "limited accuracy". If you are just doing a back of the envelope calculation, this is fine and you can find values of one-group cross sections and L^2 and D in most introductory reactor physics books. (The older Lamarsh and Duderstadt and Hamilton have tables for many different fuel and reflector material). There is also an older (and very big) report called ANL-5800 that has tables of one-group cross sections.

If you want something more accurate, the easiest thing to do would be use MCNP, or some other Continuous Energy Monte Carlo code. Like @Alex A demonstrated, the input is fairly easy for simple geometry with no feedback.

If you want to go one step further, you can use the Serpent or OpenMC Monte Carlo codes, and these codes will produce one-group cross sections and diffusion coefficients as edits.