B1 and INF difference in critical state version 2.1.28

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B1 and INF difference in critical state version 2.1.28

Postby jan.frybort » Tue May 16, 2017 12:15 pm

Hello, I was expecting agreement between B1 and INF DIFFCOEF values in critical fuel assembly model in infinite geometry. I was changing the multiplication factor by enrichment. There are results for fast group diffusion coefficient:

kinf B1 INF difference
0.9904 1.4063 1.5120 7.52 %
0.9927 1.4061 1.5121 7.54 %
0.9957 1.4058 1.5120 7.56 %
0.9984 1.4055 1.5121 7.58 %
1.0012 1.4055 1.5121 7.59 %
1.0039 1.4052 1.5123 7.62 %
1.0067 1.4052 1.5125 7.63 %
1.0092 1.4049 1.5124 7.65 %
1.0115 1.4044 1.5122 7.67 %
1.0141 1.4045 1.5125 7.69 %
1.0166 1.4044 1.5126 7.71 %
1.0192 1.4039 1.5122 7.72 %
1.0218 1.4038 1.5124 7.74 %
1.0241 1.4038 1.5127 7.76 %
1.0266 1.4034 1.5125 7.77 %
1.0293 1.4033 1.5126 7.78 %
1.0316 1.4030 1.5125 7.80 %
1.0340 1.4029 1.5126 7.82 %
1.0363 1.4027 1.5126 7.84 %
1.0387 1.4026 1.5127 7.85 %
1.0409 1.4025 1.5128 7.87 %
1.0633 1.4009 1.5132 8.02 %
1.0837 1.3995 1.5135 8.14 %
1.1028 1.3985 1.5141 8.26 %
1.1204 1.3972 1.5141 8.37 %
1.1366 1.3963 1.5145 8.47 %

I did similar calculation in SCALE 6.2.1 and if the system is critical INF and B1 result are the same. What might be the reason for this behaviour in Serpent? Thank you.

Best regards
Jan Frybort
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Re: B1 and INF difference in critical state version 2.1.28

Postby Jaakko Leppänen » Tue May 16, 2017 5:23 pm

B1_DIFFCOEF is obtained from the solution of the B1 equations, so it is not calculated similar to INF_DIFFCOEF (i.e. collapsing the micro-group inverse transport cross section with spectrum). So even though the B1 spectrum should be very close to the infinite spectrum, there are fundamental differences in the definition of the diffusion coefficient.

However, Serpent does collapse the transport cross section with the B1 spectrum. What do you get if you compare B1_TRANSPXS and INF_TRANSPXS?

Also note that the B1 solution fails if you are too close to criticality.
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Re: B1 and INF difference in critical state version 2.1.28

Postby jan.frybort » Wed May 17, 2017 12:54 am

Hi Jaakko, thank you for the explanation. You are right, the TRANSPXS exhibits increasing agreement between B1 and INF values close to critical state. Do I understand it correctly that the B1_DIFFCOEF is designed to produce values similar to deterministic codes, where B1_TRANSPXS is using the genuine Monte-Carlo approach to few-group data generation? Which of these values should be used for macroscopic data generation? Thank you.
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Re: B1 and INF difference in critical state version 2.1.28

Postby Jaakko Leppänen » Wed May 17, 2017 9:30 am

The methodology used for the B1 leakage correction is described in the text book by Stamm'ler and Abbate, and it is also used in HELIOS. This also applies to B1_DIFFCOEF. The method used for calcuating B1_TRANSPXS may be used by other codes (maybe SCALE?). Both methods are based on approximations, and which approach works better really depends on how the diffusion solver is implemented. There is a great paper related to this topic by Kord Smith from PHYSOR 2016:

Smith, K. "Nodal Diffusion Methods: Understanding Numerous Unpublished Details." In Proc. PHYSOR 2016, Sun Valley, ID, May 1-5, 2016.
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