Efficient Treatment of Anisotropic Scattering in Method of Characteristics Calculations

Abstract

In order to consider anisotropic neutron scattering effect in the method of characteristics (MOC) codes, improved transport correction method so called in-scatter based transport correction was examined and explicit high order scattering moment treatment scheme was implemented and investigated. The in-scatter based transport correction was derived from the P1 first moment equation with less assumption compared to well-established out-scatter based transport correction based on the inconsistent P1 equation. And the high order scattering source expansion based on spherical harmonics upto 3rd order was derived and successfully implemented in MOC code. To treat high order scattering source terms, two different calculation schemes were compared. One is flux moment storage scheme and the other one is angular flux storage scheme. The flux moment storage scheme shows better performances in case of P0 MOC with transport corrected cross sections. On the other hand, in case of Pn MOC with expanded high order scattering sources, the angular flux storage scheme are much faster than the flux moment storage scheme and gives better efficiency with more high order flux moments. This performance gap comes from memory structures for saving essential variables and the number of operations during ray tracing calculations in MOC. As a consequence, the angular flux storage scheme was chosen for default option in the Pn MOC calculation module although this scheme requires additional virtual memories to save averaged angular fluxes at each flat source region (FSR). To analyze the effectiveness of transport corrections and the Pn MOC, selected benchmark problems of VERA and BEAVRS were calculated using direct whole core transport code nTRACER. Faithful input decks for each problem were prepared with sufficient details including all geometrical structures. These benchmark problems were investigated by five different methods: the out and in-scatter based transport corrections, P1 through P3 MOC. With the VERA benchmark, these five solvers show almost same results in case of typical lattice problems which dont have large neutron currents at all FSRs. However, the out-scatter transport correction method could not give accurate solutions with large neutron current cases such as heavily control rodded lattice problems or quarter core cases in both eigenvalue and power distributions. On the other hand, with improved methods, results were drastically improved in case of lattice with control rod problem. Still there is some consistent power tilt of about 2% errors with the Pn MOC and this is suspected that theses consistent errors come from other causes such as multi-group cross section data. With the BEAVRS benchmark, in-core detector signal measurements from 3-D BEAVRS quarter core were compared using two transport correction methods and the P2 MOC. Since the BEARS core was designed quite similar to the VERA core, although improved methods gives better accuracy, same tendencies such as overall power tilt were also shown with this problem. From these performance examinations, it can be concluded that the anisotropic scattering treatment in nTRACER was improved by the in-scatter based transport correction as well as successful implementation of explicit Pn MOC.