Charge-Velocity Correlation Transport Equation Model with Triboelectric Effect for Gas-Solid Fluidized Bed N-Euler Simulation

The modelling and simulation of gas-solid fluidized bed is complex due to the multi-physical nature of particle-laden flows. A non-exhaustive list includes particle-turbulence interaction, inter-particle collisions or particle bouncing on smooth or rough walls. In addition, although long neglected in modelling approaches, the effect of electrical charges on the macroscopic behavior of gas-solid fluidized can be very important. The objective of this paper is to present some recent advances in modelling and simulation of electrically charged particles with triboelectric effect in gas-solid fluidized beds.

The kinetic theory of granular flows is used to derive the separate transport equations for the mean particle electric charge, the charge–velocity covariance and the charge variance for monodisperse particles in gas flow with tribocharging effect. The collision terms are closed by assuming that the electrostatic interaction does not modify the collision dynamics and without presuming explicitly the form of the dependence of the joint charge-velocity PDF on the particle electric charge. The full second-order transport equation model is tested in a one-dimensional periodic domain with nonuniform initial mean charge distribution. The results show that this model is able to capture important physical mechanisms that are neglected by simple algebraic models proposed for the particle charge-velocity correlation derived in previous works. An in-depth analysis of the transport equations is also performed. This study reveals that, for sufficiently small covariance characteristic destruction time scales, the transient and third-order moments terms can be safely neglected. In addition, reduced-order models are derived and analyzed. In particular, a semi-algebraic model that only resolves a transport equation for the charge variance coupled with an algebraic model for the covariance is proposed. Such a model is found to be a suitable alternative for sufficiently small value of a dimensionless interparticle collision time.