Nonlinear analysis of a reduced-order model with relaxation effects for BWRs

Abstract

The aim of this work is the derivation of a nonlinear reduced-order mathematical model for boiling water reactors with relaxation effects in the propagation phenomena (P-ROM). The nonlinear BWR system is modeled by a set of ordinary differential equations (ODEs) which describe the dynamics of neutron density, the precursor concentration of delayed neutrons, the fuel temperature and the void reactivity. The reduced-order model with relaxation effects is a novel approximation where the neutron density is a second order ODE derived with P1 approximation of transport theory. Furthermore, the fuel temperature is a second order ODE obtained by considering a non-Fourier type constitute law. The void reactivity corresponds to that used in the classic reduced-order model (C-ROM), as it considers voids propagation at a finite velocity. Essentially, the P-ROM considers delay times or relaxation times in the dynamic description of the neutron density, heat transfer in the fuel, and void fraction reactivity. Nonlinear stability analysis with the estimation of the largest Lyapunov exponents (LLE) of the novel P-ROM for different times of relaxation is discussed and compared with classic approximation. We report evidence that suggests that the relaxation effects strongly determine not only the dynamic evolution of BWRs but their global stability in terms of a bifurcation parameter.