Finite element solution of the nonlinear coupled neutronic-energy equations for a fast reactor fuel cell.

Abstract

A transient overpower (TOP) accident in a Liquid Metal Fast Breeder Reactor (LMFBR) is considered. The analysis is formulated to model the dynamic response of the reactor fuel subassembly during the initial period of the postulated overpower transient. An equivalent cylindrical cell is used to model the fuel subassembly. The governing neutronic and heat transport equations for each region (fuel, clad, and coolant) of the equivalent cylindrical cell are developed. Nuclear Doppler broadening feedback is included in the dynamic model making the coupled equations non-linear. The resulting non-linear partial differential field equations are transformed into a system of ordinary differential equations by the finite element method. An isoparametric, quadratic, rectangular element is used for the discretization of the spatial domain. When using the finite element method, large system matrices may result. To facilitate solution of these large systems, an optimum compacting scheme is utilized. The implicit Gear's method is used for the solution of the system of ordinary differential equations. The results for a sample problem are presented.