Stability boundary analysis of boiling flow in a narrow vertical annulus heated by counterflow fluids from inner and outer surfaces

The analysis of density wave instability boundary is carried out to investigate the boiling flow in a narrow vertical annular channel, which is heated simultaneously from the inner and the outer sides of the channel by two streams of primary countercurrent flow. The model developed on the basis of the method of weighted residuals, which reduces the channel partial differential equations to seven time-dependent nonlinear ordinary equations, considers the heat-flux coupling between the primary and the secondary channel in space. The derived dynamical system is studied using bifurcation theory to obtain the Hopf bifurcation points, i.e. the stability boundary. The effects of varying the inlet and exit pressure loss coefficients, the inlet subcooling and the system pressure for the channel on the stability boundary are obtained and discussed.