Unification of particle velocity distribution functions in gas-solid flow

Continuum models have been extensively used in CFD simulation of gas-solid flow, which is usually closed with a kinetic theory of granular flow for particulate phase stresses and a correlation for interphase drag force. Particle velocity distribution function (PVDF) is the cornerstone of kinetic theory of granular flow and the PVDFs in gas-solid flow can be Maxwellian, bimodal and/or non-Maxwellian with an overpopulated high-energy tail, depending on the physical nature of gas-solid flow. Here we theoretically show that the different PVDFs can be unified under the umbrella of a recently proposed kinetic theory framework (Wang et al., 2016) and the root of different PVDFs lies in the different characteristics of mesoscale structures. Validation of theoretical analysis is then carried out by comparing the theoretical prediction with experimental and DNS data available in literature. The findings of present study offer a possibility of developing a unified kinetic theory for gas-solid flows.