Effects of particle inertia and flow structure inhomogeneities on the micro-scale fluid-particle drag force

Abstract

In fluidization, the fluid-particle drag force balances the buoyant weight of the particles, and so achieving accurate numerical predictions of the complex flow behavior of fluidized systems is heavily reliant on the validity of the micro-scale constitutive drag model that is employed. While prior models for the dimensionless drag force (actual drag force normalized by the Stokes drag force) in low-Reynolds-number flows with spherical, monodisperse particles have only been dependent on the particle volume fraction, the current work has found that the drag is also a function of the particle inertia and the extent of inhomogeneities. The insights in the current work have been obtained through the use of lattice Boltzmann method (LBM) simulations, in which the drag force is directly computed at the particle surface by enforcing a no-slip boundary condition. In this study, the particle inertia is quantified through the Stokes number (St), while the extent of inhomogeneities is quantified through one of two sub-grid-scale measures: the scalar variance of the particle volume fraction or the drift flux, which is the correlation between the particle volume fraction and slip velocity. These sub-grid scale quantities are estimated using a scale-similar approach, which was originally developed for the purposes of turbulence modeling. As the particle inertia, or St, increases, the particles are not able to react as quickly to the surrounding flow, and so the drag increases, with a plateauing effect observed at both the low and high St limits. Furthermore, the drag, over a range of length scales, has been found to significantly decrease as the extent of inhomogeneities increases, as the flow is able to more easily by-pass the inhomogeneous structures. Since prior drag models have not accounted for St and the extent of inhomogeneities, the current work represents a meaningful advancement in the field of multiphase flow, as the resulting drag models are applicable to a much wider range of fluidized systems than their prior counterparts. By employing these new drag relations as closures in larger-scale simulations, the accuracy of the numerical predictions can be significantly improved.