Accounting for Pseudoturbulence in Eulerian-Lagrangian Simulations of Liquid-Solid Beds

An Eulerian-Lagrangian (EL) model is used for the simulation of liquid-solid flows to capture important features of the flow when particle trajectory crossing plays an important role. The basic EL model does not resolve pseudoturbulence in fluid, partially resolves coupling with particle velocity fluctuations, and thus requires closures for fluid velocity fluctuations and particle velocity fluctuations. A closure for fluid velocity fluctuations extracted from particle-resolved direct-numerical simulation is implemented in an EL code. A velocity Langevin model is then proposed for the effect of the fluid-phase pseudoturbulence on the particle velocity. When the fluid density is significant relative to the particle density, particle-particle interactions mediated by the fluid give rise to a non-negligible force in the particle equation of motion, which is called fluid-mediated particle-particle (PFP) force. The simulation results exhibit the significant contribution of pseudoturbulence and PFP terms.