Stability of transonic two-phase flow

Abstract

The nature of a singular point in the stability of one-dimensional transonic flow of a vapor-drop mixture in a channel of variable cross section is considered within the framework of a two-lquid hydrodynamical model. It is shown that the singular point in the case of any lags of the drops preserves the nature of a saddle inherent to homogeneous gas flow, shifting only towards the divergent part of the channel if the content of condensed phase is not too high. Here the transition of subsonic two-phase flow into supersonic flow is stable and the predominance of drop agglomeration over fragmentation and the positive curvature of the channel profile are stabilizing factors. The saddle nature of the singularity is possible only if the lag of the drops is not too high in the case of flows with a higher content of condensed phase. In the opposite case, the point at which the speed of sound is attained loses the nature of a saddle point.