• Energy Research

Based on the observation that ignoring the angle dependency of multigroup resonance cross sections within a fuel pellet would result in nontrivial underestimation of the spatial self-shielding of flux, a parametrized spectral superhomogenization (SPH) factor library (PSSL) method is developed as a practical means of resolving the problem. Region-wise spectral SPH factors are calculated by the normal and transport corrected SPH iterations after ultrafine group slowing down calculations over various light water reactor pin-cell configurations. The parametrization is done with fuel temperature, U-238 number density, fuel radius, moderator source represented by ΣmodVmod, and the number density ratio of resonance nuclides to that of U-238 in a form of resonance interference correction factors. The parametrization is successful in that the root mean square errors of the interpolated SPH factors over the fuel regions of various pin-cells are within 0.1%. The improvement in reactivity error of the PSSL method is shown to be superior to that by the original SPH method in that the reactivity bias of −200 pcm to −300 pcm vanishes almost completely. It is demonstrated that the environment effect takes only about 4% in the reactivity improvement so that the pin-cell based PSSL method is effective in the assembly problems.

Based on the observation that ignoring the angle dependency of multigroup resonance cross sections within a fuel pellet would result in nontrivial underestimation of the spatial self-shielding of flux, a parametrized spectral superhomogenization (SPH) factor library (PSSL) method is developed as a practical means of resolving the problem. Region-wise spectral SPH factors are calculated by the normal and transport corrected SPH iterations after ultrafine group slowing down calculations over various light water reactor pin-cell configurations. The parametrization is done with fuel temperature, U-238 number density, fuel radius, moderator source represented by ΣmodVmod, and the number density ratio of resonance nuclides to that of U-238 in a form of resonance interference correction factors. The parametrization is successful in that the root mean square errors of the interpolated SPH factors over the fuel regions of various pin-cells are within 0.1%. The improvement in reactivity error of the PSSL method is shown to be superior to that by the original SPH method in that the reactivity bias of −200 pcm to −300 pcm vanishes almost completely. It is demonstrated that the environment effect takes only about 4% in the reactivity improvement so that the pin-cell based PSSL method is effective in the assembly problems.

Abstract The Macro Level Grid scheme for the efficient application of the subgroup method is presented, that employs the number density consideration factor and the temperature consideration factor for the treatment of non-uniform number densities and temperature distributions in a core. This scheme provides the efficient resonance treatment in direct whole core calculations of power reactors that involve thermal feedback and isotopic depletion. The new method solves the subgroup fixed source problem only 8 times per energy group with 8 macroscopic subgroup levels, regardless of the number of resonance isotopes in the problem of interest. The escape cross section of each isotope is obtained by interpolation using the pre-calculated ones at the specified macroscopic subgroup levels. This scheme turns out to be superior to the conventional scheme in terms of computing time and accuracy. More than 30% of the computing time for fixed source problems is saved compared to the conventional one with negligible reactivity errors of about a few pcm, whereas the conventional one has consistent reactivity errors of about +60 ∼ +150 pcm for typical pin-cell problems in a light water reactor. Moreover, it turns out that the new method provides high accuracy not only for very heterogeneous uranium dioxide and mixed oxide pin-cell checkerboard problems, but also for the depletion calculation of a multi-assembly problem involving hot full power thermal feedback with significantly shortened times.

Abstract The Macro Level Grid scheme for the efficient application of the subgroup method is presented, that employs the number density consideration factor and the temperature consideration factor for the treatment of non-uniform number densities and temperature distributions in a core. This scheme provides the efficient resonance treatment in direct whole core calculations of power reactors that involve thermal feedback and isotopic depletion. The new method solves the subgroup fixed source problem only 8 times per energy group with 8 macroscopic subgroup levels, regardless of the number of resonance isotopes in the problem of interest. The escape cross section of each isotope is obtained by interpolation using the pre-calculated ones at the specified macroscopic subgroup levels. This scheme turns out to be superior to the conventional scheme in terms of computing time and accuracy. More than 30% of the computing time for fixed source problems is saved compared to the conventional one with negligible reactivity errors of about a few pcm, whereas the conventional one has consistent reactivity errors of about +60 ∼ +150 pcm for typical pin-cell problems in a light water reactor. Moreover, it turns out that the new method provides high accuracy not only for very heterogeneous uranium dioxide and mixed oxide pin-cell checkerboard problems, but also for the depletion calculation of a multi-assembly problem involving hot full power thermal feedback with significantly shortened times.

Abstract This paper presents the PROTEUS-NODAL capabilities developed for modeling and simulation of molten salt reactors (MSRs) with flowing fuel. Steady-state and transient solvers were developed to solve the coupled neutron flux and delayed neutron precursor concentration equations for a given velocity field. A variational nodal solver for cylindrical geometries was also developed. For thermal feedback calculations, a standalone thermal-hydraulics solver for flowing fuel was implemented. Verification and validation tests were performed using the Molten Salt Fast Reactor (MSFR) benchmark and the available experimental data of the Molten Salt Reactor Experiments (MSRE). The MSFR solution of PROTEUS-NODAL agreed well with the open literature solutions for all transients. The PROTEUS-NODAL results for static and transient experiments of the MSRE were in good agreement with measured values. These results indicate that the PROTEUS-NODAL code can be used reliably for steady-state and transient analyses of fast and thermal spectrum MSRs.

Abstract This paper presents the PROTEUS-NODAL capabilities developed for modeling and simulation of molten salt reactors (MSRs) with flowing fuel. Steady-state and transient solvers were developed to solve the coupled neutron flux and delayed neutron precursor concentration equations for a given velocity field. A variational nodal solver for cylindrical geometries was also developed. For thermal feedback calculations, a standalone thermal-hydraulics solver for flowing fuel was implemented. Verification and validation tests were performed using the Molten Salt Fast Reactor (MSFR) benchmark and the available experimental data of the Molten Salt Reactor Experiments (MSRE). The MSFR solution of PROTEUS-NODAL agreed well with the open literature solutions for all transients. The PROTEUS-NODAL results for static and transient experiments of the MSRE were in good agreement with measured values. These results indicate that the PROTEUS-NODAL code can be used reliably for steady-state and transient analyses of fast and thermal spectrum MSRs.

The whole-core transport code nTRACER has made many advances in recent years. Several innovative cross section treatment methods were developed, a new axial transport solver was introduced for stabilizing the 2D/1D scheme, and substantial computational enhancements were achieved using NVIDIA CUDA and Intel Math Kernel Library (MKL). In addition, gamma transport solver was implemented to predict the power distributions more physically, and the flexibility of the restart calculation was improved using an offline processing code nTIG (nTRACER Input Generator). This paper is the compilation of the recent progresses in nTRACER developments.