An Efficient Nodal Method for Transient Calculations in Light Water Reactors

Abstract

An efficient nodal method for the solution of two-group, multidimensional neutron kinetics problems is presented. In this method, correction factors called discontinuity factors are calculated in advance by the nodal expansion method (NEM) at steady-state conditions, and the nodewise flux and power distributions during steady-state and transient conditions are calculated based on the discontinuity factors. The nodal balance equation using the discontinuity factors is expressed logically in a less complicated manner than in other nodal methods since the factors reflect all of the approximations, including classic spatial truncations. Additionally, the convergence of the transient problem can be greatly accelerated through a thermal leakage-to-absorption ratio (TLAR) scheme.

The test results for the two-group, two-dimensional benchmark problems demonstrate that this new method has acceptable accuracy and is about two times faster without the TLAR scheme and about ten times faster with the TLAR scheme than other nodal methods (NEM or analytic nodal method) for transient applications in which assemblysize coarse nodes are used.