A fully analytical model for virtual mass force in mixture flows

Abstract

Virtual mass force plays important role in the dynamics of the mixture mass flow composed of viscous fluid and the solid particles. Often in practice, calibrated numerical values of the virtual mass force are used to validate the simulation results but largely without any further physical basis. Such values are limited to some lower limit of the solid volume fraction. This has restricted its applicability both in small scale and in large scale natural flow simulations where the virtual mass force should be automatically determined and controlled by the mechanical parameters and the flow dynamical variables involved in the mass movements. This requires a full analytical description of the virtual mass force in application that covers the whole domain of particle concentration distribution, from the vanishing limit to any upper limit that is needed. Based on a two-phase general mixture mass flow model (Pudasaini, 2012), here, we present a first-ever, fully analytical, smooth and well bounded model for the virtual mass force that overcomes these deficiencies, and thus the model is more appropriate for application in real flow simulations. The novel virtual mass force is general, evolves automatically as a function of solid volume fraction, is much more realistic and covers the whole spectrum of the flow as governed by the physical parameters, mechanics and dynamics of the mixture flow, including the concentration distribution, material densities and the mass fluxes. So, the new virtual mass force presents the most advanced model that exists for mixture mass flows. The strikingly novel observation and understanding is that the virtual mass force is maximum somewhere between dilute to dense distribution of the solid particles, or the dispersed phase, but not at the maximum solid volume fraction.