Pseudo-turbulence in steady state flows through random particle suspensions at finite Mach number.

Pseudo-turbulent fluctuations are an inherent part of flow through particle clouds. Meso-scale models, both Eulerian-Eulerian and Eulerian-Lagrangian formulations, require modeling of the pseudo-turbulence. Pseudo-turbulence is also linked to the variation in drag and lift forces in particle suspensions. Therefore, advanced modeling of particle forces can benefit greatly from a better understanding of the pseudo-turbulence. In this work, we analyze the pseudo-turbulence in steady state flows through particle clouds at finite Mach numbers, based on data obtained from particle resolved simulations. We examine the pseudo-turbulent kinetic energy, its anisotropy, and the various unresolved terms in the volume-averaged compressible Navier-Stokes equations. We compare the data to existing models for pseudo-turbulence in incompressible flows and propose extensions to account for the effects of compressibilty.