Analysis of Nonsteady Two-Phase Flow

Abstract

The techniques for solving problems of nonsteady, quasi-one-dimensional flows by the method of characteristics have been extended to flows of suspensions of small solid or liquid particles in a gas. The particles cannot follow the rapid velocity and temperature changes that are produced by pressure waves, and complicated relaxation processes result. Such flows are described by six simultaneous differential equations, and their characteristics and associated compatibility equations have been obtained. Terms are included to allow for variable duct area, for external forces that may act on the particles or on the gas, and for heat addition to the particles or the gas. To illustrate the application of the results, two flows in a pipe, filled with a suspension of small particles, are analyzed with the help of a small digital computer. In the first example, one end of the pipe is suddenly opened to a low-pressure reservoir, and the resulting expansion wave is computed. In the second example, a piston in the pipe is impulsively accelerated, and the flow between the resulting shock wave and the piston is obtained. A striking feature of this flow is the slow adjustment of the shock strength from its initial to its equilibrium value.