The Analysis of Global Stability Boundary and Multistability in the Nonlinear Dynamical System of an Advanced Heavy Water Reactor

Abstract

The nonlinear stability analysis of an advanced heavy water reactor (AHWR) is performed to investigate global stability. The global stability perspective predicts the exact stability boundary of the system, which is valid for small as well as large disturbances in the system. Recently, the local or linear stability boundary and bifurcation of limit cycles has been discussed for an AHWR. However, the studies were not sufficient to predict global stability of the system. In this work, advanced bifurcation analysis is carried out for an AHWR, which unfolds multistable or unstable states. The region of multistability is observed due to the presence of steady states and multiple limit cycles. The global stability boundary is marginally away from the local stability boundary, the region beyond which the global stability boundary is safe for operation due to the nonexistence of nonlinear phenomena, such as limit cycles. The local stability boundary is basically a Hopf bifurcation boundary as limit cycles (i.e., nonlinear phenomena) emerge from these points. Subcritical or supercritical Hopf bifurcations excite unstable limit cycles (ULCs) or stable limit cycles (SLCs), respectively, and these limit cycles end on the global stability boundary. The subcritical Hopf bifurcation is considered as hard or dangerous bifurcation due to the presence of ULCs in the linearly stable region, which gains stability on the global stability boundary and in which SLCs surround ULCs. Therefore, a region of bistability between the local and global stability boundary is present for subcritical Hopf. The supercritical Hopf is generally considered as the soft and safe bifurcation because of SLCs in the linearly unstable region. Due to this fact, it is assumed that in the supercritical Hopf region the global and local stability boundaries are the same. However, in this work ULCs in the linearly stable region for supercritical Hopf bifurcation are observed along with SLCs, which is an uncommon phenomenon in nuclear reactors. The presence of ULCs surrounding SLCs are observed both in the stable and unstable side on the parameter plane for supercritical Hopf. For the safe operation of a nuclear reactor, identification of the region of global stability is of paramount interest.

Keywords:

• Global stability boundary
• generalized Hopf bifurcation
• multistability

Nomenclature

=	=	steady state precursor concentration of delayed neutrons ()
=	=	precursor concentration of the delayed neutrons ()
=	=	heat capacity of the fuel element in the reactor core ()
=	=	specific enthalpy of evaporation at saturation pressure ()
=	=	steady state neutron density ()
=	=	neutron density ()
=	=	steady-state reactor power (W)
=	=	reactor power (W)
=	=	average fuel temperature (K)
=	=	steady-state fuel temperature (K)
=	=	saturation temperature of the coolant (K)
U =	=	overall heat transfer coefficient including fuel conductivity ()
=	=	specific volume of saturated vapor at saturation pressure
=	=	steady-state void volume ()
=	=	void volume ()
	=	Greek
=	=	fuel temperature coefficient of reactivity
=	=	void coefficient of reactivity (dimensionless)
=	=	delayed neutrons fraction (dimensionless)
=	=	neutron generation time (s)
=	=	decay constant for the delayed neutron precursors (s–1)
=	=	reactivity multiplication factor
=	=	time (s)