Yuanzineng kexue jishu (Dec 2024)
Research on Fast Spectrum Resonance Calculation Method Based on Subgroup Method
Abstract
With the rapid development of digital technology and the rapid improvement of computer performance, the high-fidelity deterministic transport calculation method represented by the method of characteristics (MOC) has received extensive attention in numerical reactor projects at home and abroad. Resonance calculation is a necessary part of the two-step or three-step physical calculation, and the traditional method is usually based on the geometric simplification model in dealing with the fast spectrum resonance calculation problem, which cannot accurately match the advantage of the MOC on the fine geometric processing ability, especially with the rapid development of advanced reactor research in recent years, many reactor schemes with fine structure have been proposed, including a large number of core schemes characterized by fast spectrum, for this type of problem, the traditional method is difficult to give high-precision multi-group constants under fine geometry. Compared with the equivalence theory, the subgroup method has good geometric adaptability because it can be combined with the MOC transport solver, and can obtain the same calculation accuracy as the ultrafine group method with fewer subgroups, so it has higher computational efficiency. Therefore, based on the subgroup method, the calculation of fast spectrum resonance under fine geometry was studied. In the fast spectrum resonance calculation problem, the resonance interference effect among multiple nuclides was more significant than that of the thermal spectrum problem, and it was very important to deal with the resonance interference effect accurately. The Bondarenko iterative method was commonly used in traditional methods, but when combined with the subgroup method to solve the fine geometry, its computational efficiency was low, so the pseudo resonance nuclide method was introduced to treat all nuclides in the same material as one pseudo resonance nuclide, which could avoid iterative solving of the subgroup flux of different resonant nuclides, so as to greatly reduce the number of subgroup equations that needed to be solved, and then effectively reduced the computational cost. The computational efficiency was improved, and the pseudo resonance nuclide method had higher computational accuracy than the Bondarenko iterative method because the resonance interference effect was processed at the point cross-section scale in advance. One of the key steps of the subgroup method was to solve the subgroup parameters, combined with the particle swarm optimization to solve the subgroup parameters of the pseudo resonance nuclide and the subgroup parameters of each sub-resonance nuclide composed of it, and the obtained subgroup parameters had high precision, and at the same time, due to the constraints added to the value range of the variables in the solution process, the shortcomings of the traditional method such as numerical instability and initial value sensitivity could be effectively avoided. Finally, based on the MOC, the fast spectrum single pin-cell problems of the China Experimental Fast Reactor (CEFR) and the fission surface power (FSP) system were verified. Compared with the reference solution obtained by the Monte Carlo program MCNP, the relative error of the total cross section of the fuel zone is within 1%, the calculation accuracy of the absorption cross section in the high energy region is almost 0.5%, and the calculation accuracy of the absorption cross section in the low energy region is slightly lower, with the maximum relative error within 2% and 3%, respectively, and the absolute errors of the eigenvalues of the two problems are 54 pcm and 146 pcm, respectively. Based on the above numerical verification results of cross section and eigenvalue, the proposed pseudo resonance nuclide subgroup method combined with particle swarm optimization can effectively deal with the problem of resonance cross-section calculation in fast spectrum.
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