Stability analysis and nonlinear dynamics of natural circulation boiling water reactors

Numerous experimental and numerical investigations have been reported in literature on the effect of various parameters on the dynamics of natural circulation boiling water reactors (NCBWRs). Different findings were reported in literature regarding the effect of void reactivity coefficient and fuel time constant on Type-I and Type-II instabilities. The present work contains stability analysis and nonlinear dynamics of NCBWR using a lumped parameter model. The purpose of the stability analysis is to resolve different, seemingly contradictory parametric trends reported by previous authors. Stability analysis for three different system configurations has been done using the same mathematical model and compared with the findings reported in literature. It has been observed that the effects of void reactivity coefficient and fuel time constant are influenced by geometrical parameters and are different for different systems. Nonlinear dynamics and bifurcations have been studied numerically, for one of the system configurations, for boiling channels with and without riser. The possibility of existence of stable and unstable limit cycles, period doublings, and chaotic oscillations has been investigated. The effect of void reactivity coefficient on the nonlinear dynamics has been studied in both Type-I and Type-II regions. In the Type-I region, subcritical Hopf bifurcation leading to unstable limit cycle, as well as supercritical Hopf bifurcation leading to stable limit cycle have been found. The boiling channels with and without riser have been observed to undergo chaotic oscillations under strong reactivity feedback in the Type-II region. It has been found that the presence of riser aggravates chaotic oscillations.