Impact of system pressure on the characteristics of stability boundary for a single-channel flow boiling system

Abstract

The two-phase flow boiling channel as a nonlinear dynamical system has very interesting features. Parametric stability analysis of a flow boiling thermal hydraulic system has been extensively studied in the past. Linear stability analysis provides a stability boundary which is a demarcation between stable and unstable region. The studies on the impact of system pressure on the stability boundary are limited. Moreover, the variation of subcritical and supercritical Hopf region on stability boundary with respect to pressure is not available in the literature. Nonlinear dynamics is used here to characterize the stability boundary(Hopf curve) for a single-channel flow boiling thermal hydraulic system. In the current work, focus is on the effect of the system pressure on the location of the generalized Hopf (GH) point over the Hopf curve which divides subcritical and supercritical Hopf region. The disappearance of the GH point with increasing system pressure, such that the stability boundary is completely subcritical, in the operating parameter range is one of the interesting features observed. The complete subcritical boundary is identified by noting that the first Lyapunov coefficient is always positive on the stability boundary for higher system pressures. The subcritical Hopf bifurcation indicates the presence of unstable limit cycle in the (linearly) stable region which is of prime concern as finite perturbation in this region leads to system instability. Numerical simulations are carried out around the stability boundary to verify its characteristics.