Fluid-mediated sources of granular temperature at finite Reynolds numbers

Abstract

We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modeling the neighbor-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration-velocity distribution function $P\left(v^{\prime},a^{\prime};t\right)$. Quadrant-conditioned covariance integrals of $P\left(v^{\prime},a^{\prime};t\right)$ yield the hydrodynamic source and sink that dictate the evolution of granular temperature. Analytical predictions are in agreement with benchmark data obtained from particle-resolved direct numerical simulations and show promise as a general theory from gas--solid to bubbly flows.