Toward a mesoscale‐structure‐based kinetic theory for heterogeneous gas‐solid flow: Particle velocity distribution function

Abstract

Mesoscience has recently been proposed as a possible general concept for describing complex systems far from equilibrium, however, concrete formulations are needed, and particularly, a statistical mechanics foundation of mesoscience remains to be explored. To this end, the mathematical theory of stochastic geometry is combined with the energy minimization multi-scale (EMMS) principle under the concept of mesoscience to propose a statistical mechanics framework. An EMMS-based particle velocity distribution function is then derived as an example to show how the proposed framework works, and more importantly, as a first key step toward a generalized kinetic theory for heterogeneous gas-solid flow. It was shown that the resultant EMMS-based distribution is bimodal, instead of the widely-used Maxwellian distribution, but it reduces to the Maxwellian distribution when the gas-solid system is homogeneous. The EMMS-based distribution is finally validated by comparing its prediction of the variance of solid concentration fluctuation and granular temperature with experimental data available in literature.

Data‐driven modeling of mesoscale solids stress closures for filtered two‐fluid model in gas–particle flows

“…Assuming that the particles in a grid are homogeneous, the interaction among particles is mainly related to the deformation of particle phase. However, there is a velocity distribution of particles in a coarse grid 21,60 . During this solution process, the local flow information is reduced.…”

“…Several subgrid models (SGMs) have been proposed to examine the effect of mesoscale structures, such as filtered two‐fluid model (fTFM), 13,15‐18 the energy minimization multi‐scale (EMMS), 19‐22 the spatially averaged two‐fluid model (SA‐TFM), 23‐25 and the gradient‐based method 26,27 . The development of those SGMs enables an acceptable computational overhead and a fairly good accuracy as well.…”

CFD simulation methodology for gas-solid flow in bypass pneumatic conveying – A review

“…The kinetic theory based description of gas-solid flows has been an active area of research for the past years [88][89][90][91][92] . Rao and Nott [93] derived a kinetic theory for rough inelastic particles.…”

A Bubble-Based Drag Model at the Local-Grid Level for Eulerian Simulation of Bubbling Fluidized Beds

“…A possible path is to reformulate the structure-based kinetic theory for heterogeneous gas-solid system. In the latest report [59], the EMMS group proposed their promising works on velocity distribution function as a first key step toward a generalized kinetic theory for gas-solid flow. As for the empiricism in the EMMS model, more work is required to reduce model's dependence upon correlations.…”