In-phase instabilities in BWR with sub-cooled boiling, direct heating, and spacers effects

In this paper a time dependent model for studying BWR in phase instabilities in the nonlinear regime has been developed. This model solves: the neutron point kinetic equations with void and Doppler reactivity feedback, the two node lumped parameter model equations for the volumetric weighted clad and fuel average temperatures, the recirculation loop dynamic equation, and the conservation equations for the mass, energy and momentum in the single phase and the two phase regions of the boiling channels. Special attention has been devoted to the dynamic equations of the sub-cooled and bulk boiling regions. The influence on the stability of the sub-cooling degree and the direct heating by neutrons and gamma rays has been carefully studied, also the effect of the spacers, located in the single and two phase regions, on the stability has been considered. The number of spatial nodes considered in the axial direction is up to 30, so we have studied with great detail the spatial and temporal evolution of the density wave oscillations and its effect on the reactor stability.