Fluid-mediated sources of granular temperature at finite Reynolds numbers

TL;DR

This paper develops an analytical framework for understanding how hydrodynamic interactions influence granular temperature in suspensions at finite Reynolds numbers, validated by numerical simulations.

Contribution

It introduces an exact solution for the joint distribution of fluctuating acceleration and velocity, linking hydrodynamic sources to granular temperature evolution.

Findings

Analytical solutions match particle-resolved simulation data.

Hydrodynamic sources significantly influence granular temperature.

The theory applies across gas-solid and bubbly flow regimes.

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.