Lyapunov stability and numerical analysis of excursive instability for forced two-phase boiling flow in a horizontal channel

Lyapunov stability theory in dynamic systems and numerical analysis are combined to investigate dynamic features of excursive instability for forced two-phase boiling flow in a horizontal channel. The system model consists of two first-order nonlinear ordinary differential equations that are obtained via the lumped parameter method. Lyapunov analysis defines the dynamic stability types of equilibrium solutions of the system. The solution in the negative slope of the internal characteristic curve is an unstable node and the other two solutions in the positive slope are stable nodes. Excursive instability can be represented from the unstable node to two stable nodes. An initiation boundary (IB) is constructed with several key eigenvectors in the phase space of mass flux vs. pressure drop. Numerical simulation demonstrates the results from Lyapunov stability analysis. In addition, excursive instability is a multi-solution problem that is closely associated with the initial states of the system. The initiation boundary (IB) determines the correspondence between the initial states and the steady-state solutions, and the existence of the hysteresis phenomenon in the single-channel system.