(A) solution decomposition approach to reactor kinetics calculation under space-dependent feedbacks in the analytic function expansion nodal method

Abstract

During the last several years, the analytic function expansion nodal (AFEN) method has been developed and successfully applied to static reactor analysis. In this thesis, we develop kinetics calculational capability of the AFEN method. We propose a novel method with the time-dependent solution decomposed into an analytic part and a polynomial correction part. The analytic part consists of the analytic solutions of the "quasi-static" diffusion equation. The polynomial correction part is determined applying a Galerkin scheme. The kinetic equations are discretized in time after exponential transformation of the neutron fluxes. This enables the method to use larger time step size than the case of direct differencing of the fluxes. The relation of delayed neutron precursor densities between time steps is obtained analytically by using the transformed fluxes and assuming linear variations of the fission rates within a time step. After the discretization in time and space, we use no more approximations except the solution decomposition. During transient, the cross sections within a node change due to the space-dependent feedbacks. In conventional nodal methods, rehomogenization or four nodes/assembly calculation are needed to overcome this problem. However, in our method, we only need to add the weighted integrals of space-dependent terms in the equation. All other types of space-dependent cross sections can be treated in the same manner. In this thesis, we model the cross section variation using Legendre polynomial bases. The computing time increase due to space-dependent feedback is marginal, and it becomes negligible with infrequent update of the correction part. For the acceleration of the method, coarse group rebalance (CGR) scheme is modified and applied. The computing time is greatly reduced by applying this scheme. In three-dimensional problems, we incorporate the bilinear weighting method to treat the control rod cusping problem occurring in the partially rod...