Development of Particle Resolved - Subgrid Corrected Simulations: Hydrodynamic force calculation and flow sub-resolution corrections

Abstract

Particle Resolved - Direct Numerical Simulation (PR-DNS) of fluid–solid particles is conducted to study hydrodynamic interactions at the interface between phases. An original distinction is proposed between Particle Resolved Simulation (PRS) and Particle Resolved - Direct Numerical Simulation (PR-DNS). In PR-DNS, velocity gradients and pressure are fully resolved, which required several dozens of meshes in the diameter of the particles (40 in Stokes configuration), whereas for PRS, with grid resolution of 10 meshes per diameter, the gradients are only partly resolved, resulting in a sub-resolution of hydrodynamic forces exerted by the fluid to the interface of solid particles. The very high computational cost, associated to PR-DNS, limits its application to academic cases, even though, it was originally developed to study the collective physical effects of a fluid–particle assembly. It explains why numerous simulations with a grid resolution of only a dozen meshes in the particle’s diameter – typically between 10 and 16 – referred to here as PRS, can be found in the literature. In these cases, the velocity gradients and pressure are not accurately computed, inducing an error in the hydrodynamic forces exerted by the fluid to the interface of particles. This paper aims to clarify the hydrodynamic interactions at this scale for a single particle settling in an infinite medium under Stokes configuration. For this purpose, an original method, designed for solid particles, is proposed to compute hydrodynamic forces. A mesh-dependent correlation is then built to numerically correct the partially resolved hydrodynamic forces obtained with PRS, in what we call Particle Resolved - Subgrid Corrected Simulations (PR-SCS). Finally, the correction is assessed for various Reynolds numbers and density ratios under the Stokes assumption.