Verification and Validation of the SP_L Module of the Deterministic Code AZNHEX through the Neutronics Benchmark of the CEFR Start-Up Tests

Round 1

Reviewer 1 Report

 In this paper, the authors give the derivation and implementation of the transport equation in SP method. And use Serpent to generate the group-constants and verify the continuous-energy cross-section databases. Finally, the accuracy of AZNHEX is proved by comparing the experimental measurements and the results of Monte-Carlo code – Serpent. The overall logic of this article is rigorous, but the following comments still need to be answered:

1.     Page 5, line 114 to 116. Whether authors can provide some basis or references to prove that even if the SP7 approximation is used, the cost of computation is still much less than that of solving the transport equation directly. Through more specific description or reference to make the article more objective.

2.     Equation (7), the multiplication operator should be written as “”, and not as the italics of the letter “x”.

3.     In Table 4, can authors supply the computation time which required for these calculations by AZNHEX? If we consider the computation time and accuracy comprehensively, which model has the best comprehensive performance?

4.     In section 4.3.1, the mesh sensitivity analysis has been carried out. In line 232 and 233, authors analysis that the main reason of the finer radial mesh, the worse calculation result is that the increase in dimensions ratio between axial and radial nodes. The authors only describe this phenomenon, the specific reason is still not explained.

5.     The authors can add some comparison of power distribution or neutron scalar flux distribution of the whole core, and the comparison can be made between the AZNHEX and Serpent.

6.     If possible, we hope that authors could tabulate the group constants of CEFR which are generated by Serpent, to facilitate the calculation and verification for other deterministic programs in the future.

Comments for author File: Comments.pdf

Author Response

Dear reviewer.

First of all, I would like to thank you for devoting the time to review the manuscript we submitted to the Journal of Nuclear Engineering. The work team that prepared it gave the corresponding answers to their comments and corrections. As a PDF file, an attached table was designed to describe the response or the requested modification to facilitate a follow-up. 

Sincerely yours

Prof. Edmundo del Valle Gallegos

Author Response File: Author Response.pdf

Reviewer 2 Report

Well-prepared article. Helpful models description. I just recommend to avoid passive voice.

Author Response

Dear reviewer.

First of all, I would like to thank you for devoting the time to review the manuscript we submitted to the Journal of Nuclear Engineering. The work team that prepared it gave the corresponding answers to their comments and corrections. As a PDF file, an attached table was designed to describe the response or the requested modification to facilitate a follow-up. 

Sincerely yours

Prof. Edmundo del Valle Gallegos

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the implementation of a module, based on SPL numerical scheme, in the AZNHEX code is presented. Implementation is validated with experimental data from the CEFR sodium reactor. Sensitivity analysis on radial and axial meshing are also performed, showing a good agreement with experimental results for high-order expansions and refined radial and axial meshing.

Corrections:

 - Ln. 129: allows -> allow

 - Ln. 139: which density -> whose density

 - Ln. 143: Evaluated -> evaluated

 - Ln. 146: BROND3.1, CENDL-3.1, ENDFB-7.1, ENDFB-8.0 -> BROND-3.1, CENDL-3.1, ENDF/B-VII.1, ENDF/B-VIII.0. Modify x axis in Fig. 2 accordingly for these and the rest of the libraries.

  - Ln. 152, 155 and 157: ENDFB-8.0 -> ENDF/B-VIII.0

  - Ln. 242: The constant improvement is part of the software development. -> Constant improvement is part of software development.

 - Ln. 243 - 245: set of exercises, when it was used in a smaller core it failed, creating the need for an improvement. In this work, it was presented (along with its validation process) a recently developed SPL solver (based on the Spherical Harmonics Theory), -> set of exercises, it failed when used in a smaller core; therefore, an improvement on the mathematical solvers was needed. In this work, a recently developed SPL solver (based on the Spherical Harmonics Theory), along with its validation process, were presented.

 - Ln 254: codes of the AZTLAN Platform since there is only -> codes of the AZTLAN Platform, since there is only

 - Ln. 263: neutron energy groups reducing also considerably -> neutron energy groups. This resulted in a considerable reduction of the computing time in both codes and in to getting very accurate results with AZNHEX, as can be seen

 - Ln. 274 - 275: Despite it is expected that the deviation goes smaller as the refinement and the SPL order increase -> Although a reduction of the deviation with increased SPL refinements was expected, many

 - Ln. 317 - 319: Finally, another implementation in AZNHEX is a Discrete Ordinates SN module, further work will be aimed to compare these new solvers against stochastic and experimental data -> Finally, a Discrete Ordinates SN module has been also implemented in AZNHEX. Further work will be performed to compare these new solvers against stochastic and experimental data.

Comments:

 - Ln. 134 - 136: assumption on linear expansion coefficient was defined in benchmark specifications of was taken just for this work? Please clarify in the text.

 - Ln. 146 - 147: please add corresponding references to each of the libraries.

 - Ln. 143 - 144: authors state that “A study on the selection of the Evaluated data library was done to ensure that nodal XS generated with Serpent are appropriated.” However, generation of appropriate nodal XS should be independent of the nuclear data library used. Authors selected as a reference library the one yielding closest results to the experimental value for keff. I would rephrase this statement.

 - I would recommend the authors introducing Section 3.2.2 inside Section 4.2. In Section 4, the experiment is detailed, and equation for reactivity is presented. This is used implicitly before in Sec. 3.2.2. Moreover, a detailed CR about core critical state is given in Sect. 4.1, which is used in Sec. 3.2.2. In my opinion, it would make more sense to introduce selection of library after experiment has been described since everything is more clear for the reader. I would insert it just after Eq. 8.

 - Tables 3, 4, 5, 6 and 7: Is experimental uncertainty on rho_exp available? If so, please include it in pcm for rho_exp. When comparing against experimental data, uncertainties should always be considered. Depending on the precision of the experiments, results for SP5 and SP7 may even be in agreement with experimental data (for sure in Table 7 when a combination of radial and axial refinement is performed).

 - Fig. 5: why keff is only overestimated for SP3, while the rest of L values underestimate it? Could you please elaborate on this and provide an explanation in the text?

 - Ln. 231: not positive impact = decrease in reactivity? I would rephrase this sentence.

 - Ln. 251 - 252: indeed. Please provide a couple of examples and references of such reactors to illustrate your point.

 - Ln. 256 -260: I would mention these limitations in Sec. 3.1.1 too.

 - Ln. 272: several times a comment is given on computational cost in the paper. It would be a good idea to provide a reference on the increase of time (and memory?) for the use of high-order SPL. What do you consider expensive? minutes, hours, days, weeks?

 - Ln. 273 - 274: following my previous comment, what is the “cost” of the refined radial and axial mesh?

Author Response

Dear reviewer.

First of all, I would like to thank you for devoting the time to review the manuscript we submitted to the Journal of Nuclear Engineering. The work team that prepared it gave the corresponding answers to their comments and corrections. As a PDF file, an attached table was designed to describe the response or the requested modification to facilitate a follow-up. 

Sincerely yours

Prof. Edmundo del Valle Gallegos

Author Response File: Author Response.pdf