In Core LOCA-s: Analytical Solution for the Delayed Mixing Model for Moderator Poison Concentration

Abstract

Solutions to dynamic moderator poison concentration model with delayed mixing under single pressure tube/calandria tube rupture scenario are discussed. Such a model is described by a delay differential equation and for such equations the standard ways of solution are not directly applicable. In the paper an exact, direct time-domain analytical solution to the delayed mixing model is presented and discussed. The obtained solution has a "marching" form and is easy to calculate numerically. Results of the numerical calculations based on the analytical solution indicate that for the expected range of mixing times the existing uniform mixing model is a good representation of the moderator poison mixing process for single PT/CT breaks. However, for postulated multi-pipe breaks (which is very unlikely to occur) the uniform mixing model is not adequate any more; at the same time an "approximate" solution based on Laplace transform significantly overpredicts the rate of poison concentration decrease, resulting in excessive increase in the moderator dilution factor. In this situation the true, analytical solution must be used. The analytical solution presented in the paper may also serve as a bench-mark test for the accuracy of the existing poison mixing models. Moreover, because of the existing oscillatory tendency of the solution, special care must be taken in using delay differential models in other applications.