The nature of “slow” rarefaction waves accompanying the escape of a boiling liquid

Abstract

The depressurization of a high-pressure container in the form of a tube closed at both ends and initially filled with water not heated to the boiling point is studied. At the zero time, one of the ends of the tube is opened, and the liquid begins to escape into the atmosphere. Since the atmospheric pressure is less than the saturation pressure of the liquid, its escape is accompanied by boiling. It is known from experiments [1, 2] that after depressurization a rarefaction wave travels into the channel with the speed of sound in the pure liquid. After it has passed, a two-phase mixture is formed in the container. A “slow” (or “secondary”) rarefaction wave (Fig. 1a) moves through this mixture with a velocity relative to the tube walls of order 10 m/sec, transforming the two-phase mixture to the equilibrium state. To explain the features of the escape process, we propose a new mathematical model of a boiling liquid that takes into account two mechanisms of vapor formation —boiling at nucleating centers present in the liquid and fragmentation of the formed bubbles. If the second mechanism is to be realized, a certain relationship must be established between the bubble size and the difference of the velocities of the phases. The slow rarefaction wave is described by means of the proposed model.