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. Modelling the neighbour-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration–velocity distribution function $P(v^{\prime },a^{\prime };t)$ . Quadrant-conditioned covariance integrals of $P(v^{\prime },a^{\prime };t)$ yield the hydrodynamic source and sink that dictate the evolution of granular temperature that can be used in Eulerian two-fluid models. Analytical predictions agree with benchmark data from particle-resolved direct numerical simulations and show promise as a general theory from gas–solid to bubbly flows.