Macroscopic Streamline Integral Relations for Two-Phase Flows

[+] Author and Article Information
D. A. Drew

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, N. Y.

J. Appl. Mech 42(4), 766-770 (Dec 01, 1975) (5 pages) doi:10.1115/1.3423702 History: Received August 01, 1974; Revised April 01, 1975; Online July 12, 2010


A spout-fluidized bed is an example of a situation where a nonuniform fluid flow through a bed of particles causes particle circulation. Several integral relations are derived from a steady, two-dimensional two-phase flow model. The vorticity of the particle motion enclosed by a particle streamline is shown to be equal to the fluid vorticity enclosed by that streamline. The net flux of fluid vorticity through a particle streamline is shown to be equal to zero. The pressure drop along a fluid streamline is related to the net drag force along that streamline. The net flux of particle vorticity through a fluid streamline is given in terms of the pressure drop. Implications of these relations to the mechanics of particle-fluid flows are discussed. Relations giving the particle vorticity in terms of an integral of the fluid vorticity, and vice versa, are presented. A possible numerical scheme for calculation of the flow fields is discussed.

Copyright © 1975 by ASME
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