Post-processing power normalization and 2-D temperature distribution

[andrewryh]

Hello,

I got an email asking about results in the initial paper: Introduction to Moltres: an application for simulation of Molten Salt Reactors

Unfortunately, I was unable to help with the questions below:

"A) I am attempting to reproduce the results from the paper using the input files already present in the Moltres/MOOSE repository under Problems/2017_annals_pub_msre_compare. When I try to recreate Fig. 3 (Group 1 flux), the spatial shape of the flux profile matches yours exactly – the normalized distribution looks correct – however, the absolute scale I obtain is of the order of 2.4×10⁻⁴, whereas in your published plot the flux is of the order of 10¹³ n·cm⁻²·s⁻¹.

Could you help me understand what accounts for this discrepancy in the absolute scale? Specifically, I would like to know:

1. Was a post-processing normalization applied to the raw eigenvalue flux to convert it to a physically meaningful power-normalized flux (e.g., using a target reactor power of ~8 MW_th)?
2. If so, could you share the normalization factor or the procedure used – for example, whether the flux was scaled by P / (∫ Σ_f φ dV · E_fission)?
3. Alternatively, were specific material cross-sections or source terms set in the input files that implicitly carried physical units?

The shape match but magnitude mismatch strongly suggests the simulation is solving the eigenvalue problem correctly, and the absolute flux simply needs to be normalized to the operating power. But I want to confirm this with you rather than assume.

This is the plot from your paper:

This is the plot we recreated using the input file 2group_eigen.i :

B) Fig. 5 shows a 2D temperature distribution over the reactor cross-section, with a reported maximum fuel temperature of approximately 955 K. However, in Fig. 11, which plots the axial temperature profiles along the reactor height, the fuel temperature at the exit (top of the core) appears to be closer to 970 K. This seems inconsistent, since one would expect the peak fuel temperature in the 2D map to be at least as high as the exit temperature in the axial profile.

Fig.5:

Fig.11:

Could you help me understand the source of this apparent discrepancy?

I would appreciate your clarification on these points. Thank you for your time and consideration."

I would appreciate it if anyone could address the reader's questions.

Thanks,
Andrei

[smpark7]

Hey Andrei, good to hear from you again. I wasn't on the first Moltres paper but I think I have the answers:

All input files in that directory apply a scaling factor of 1e13 to the fission heat source in the temperature advection-diffusion equation through the nt_scale input parameter. This accounts for the 1e13 magnitude difference. Also, the reader ran the k-eigenvalue input file instead of the coupled neutronics-temperature input file. If I'm not wrong, the plots in the paper were generated using the latter with a reactor height of 151.75cm.

On a related note, the paper used a 151.75 cm-tall MSRE model for neutronics and temperature plots in Figure 3-7. But the paper used a taller 162.56cm model for direct temperature comparisons with the ORNL MSRE numerical model data in Figures 11-13. If I'm not wrong, the taller model and figures were created in response to reviewer feedback for model verification.

I found a critical bug in MatINSTemperatureTimeDerivative (fix in PR arfc/squirrel#15) which prevents any of the coupled input files from converging. The reader will need to incorporate the bug fix to run the coupled input files.

@lindsayad Do you remember how to set up the 151.75cm model?

[andrewryh]

Hey Sun Myung,
Happy to hear from you!

Thanks for clarifying.
I think his question was why max(T_{fuel}) = 955K on Fig. 5, while Fig. 11 shows a ~970 K peak (blue line).
So, I will point out to him that the height was different for different figures.

@gridley, do you recall why that is?

[lindsayad]

I don't have very many answers as this has been lost from my memory. The only help I can offer is a search in the current repo

(base) lindad@INL429698:~/projects/moltres(devel)$ git grep -n "151\.75" -- *.geo
problems/060717_dimension_testing/2d_lattice_structured.geo:3:H = 151.75;

Perhaps that directory could be useful but it also only appears to use a single neutron group. So you'd probably have to synthesize that .geo\.msh file with the annals directory inputs and then maybe one could reproduce the 151.75 cm figures from the paper. I'm disappointed that I seem to have flubbed this up in the git history. You can apologize to your inquirer for me @andrewryh

[andrewryh]

All good @lindsayad
I sent an aggregate response from the grains of wisdom @smpark7 and you provided.
They should be able to reproduce it.

Thanks ALL

[lindsayad]

Thanks for being the conduit! Great hearing from you 😄 Miss ya!