Two-Way Coupling Effects in Dilute Gas-Particle Flows

A general analysis of gas-particle flows, under the hypotheses of number of particles large enough to consider the solid phase as a continuum and of volume fraction small enough to consider the suspension as dilute, is presented. The Stokes number Sk and the particle loading ratio β are shown to be the basic parameters governing the flow. Depending on the values of these two parameters, in one case the reciprocal interaction of the fluid and solid phases must be considered (two-way coupling), in the second case only the effect of the fluid field on the particle motion is relevant (one-way coupling). In the more general case of two-way coupling, the flow is governed by two sets of Navier-Stokes equations, one for each phase, which are coupled together through the particle volume fraction and the momentum interchange forces. The two systems of equations, expressed in the variables velocity, pressure, and particle volume fraction, are solved numerically by a finite difference scheme. The model has been applied to a duct with a sudden restriction, simulating a flow metering device. The coupling effect both on fluid and solid phase fields, the increase of pressure drop, and the energy dissipated in the fluid-solid interaction have been determined as functions of the governing parameters, Sk and β. The parametric study also indicates the ranges of β and Sk in which simplified formulations may be assumed.