Nonlinear dynamics in multi-phase flow

Flow problems in vertical channels e.g. pipes, in which there simultaneously are single-phase and two-phase flow regions in the interior and heat is supplied through the side walls, have been studied as nonlinear dynamical systems. In this paper we summarize some of our results on the linear, quasi-linear and nonlinear analyses of these systems. The linear and quasi-linear analyses show that in most of the autonomous dynamical systems supercritical Hopf bifurcations occur so that perturbations about equilibria evolve to finite-amplitude oscillatory limit cycles. These analyses also provide a theoretical basis for the interpretation of the results of the numerical simulations of both autonomous and non-autonomous systems. The numerical simulations also are used to determine the interactions among various attracting sets that exist simultaneously for the same fixed set of heated channel parameter values.