Development of kinetic-theory-based models accounting for charge transport in polydisperse gas-solid flows

Abstract

Kinetic-theory-based transport models are developed for polydisperse granular and gas-solid flows with contact electrification. Starting with the Boltzmann-Enskog kinetic equations, a transport equation for the solid phase charge is introduced into kinetic theory for granular flows with, first, monodisperse particles and, latter, binary solid mixtures. For binary mixture, each solid phase possesses its own macroscopic quantities (i.e. solid volume fraction, mean velocity, granular temperature, mean charge and charge variance) using the non-equipartitioning of random fluctuating kinetic energy. The primary model is extended for dilute regime where self-diffusion of charge is modelled via a charge-velocity correlation. The model is further extended for granular flows far away from equilibrium conditions by applying a perturbation to the Maxwellian state of particle velocities. The hydrodynamic and the additional charge transport models are assessed through hard-sphere simulation results at each stage of the model development. The charge evolution is well predicted for granular flows at equilibrium conditions, while predictions of the flows at non-equilibrium conditions are less accurate. The mathematical models are implemented into an open-source multiphysics computational framework (OpenFOAM) with developing a new solver. This solver is then used to study the effect of vessel size on charge build-up in gas-solid suspensions and to model lightning during volcanic eruptions.