Bifurcation analysis of pressure-drop oscillations and the Ledinegg instability

Abstract

Pressure-drop oscillations and the Ledinegg instability are analyzed from the perspective of dynamical systems theory. An integral formulation is developed to model the two-phase flow system. Instability criteria independent of the actual two-phase flow model are derived for the two phenomena. It is shown that the pressure-drop oscillation limit-cycles occur after a super-critical Hopf bifurcation. In an extension of the analysis, an effort is made to clarify the mechanisms of the pressure-drop type oscillations and Ledinegg instability. The two phenomena are classified from the angle of bifurcation theory, and the differences are outlined.