Nonlinear stability domain analysis of a CANDU reactor

Abstract

The asymptotic stability domain of a CANDU reactor was estimated for the various values of feedback and design parameters utilizing the expansion method. The expansion method for identifying nonlinear stability domain requires only a positive definite function and it is particularly useful for stiff systems such as a nuclear reactor. From a large starting region, the entire stability domain is estimated effectively after sufficient iterations. The dynamic equations for a CANDU reactor with four reactivity feedbacks are developed from the relation of energy balance and nonlinear analysis is performed for the steady-state solution. By analysis of bifucation theory, nonlinear phenomena are observed for various distributions of reactivity feedback coefficients. Hopf bifurcation point are situated on the dynamic stability boundary and stable limit cycles and unstable limit cycles of the steady-state solutions exist for certain values of the reactivity coefficients. We observed that feedback and design parameters change the size of the stability domain. In a CANDU reactor, the stability is determined chiefly by the extent of void at saturated state of coolant. It is noteworthy that the stability domain is scarcely affected by the moderator temperature coefficient. The stability domain increases as the fuel temperature coefficient decreases (in negative values) and the coolant temperature coefficient decreases (in positive values). As the mass flow rate of the coolant increases, the stability domain becomes large, and as the reactor power increases, the stability domain becomes small.