On the modelling and simulation of electrically charged particle-laden flows by Olivier Simonin (IMFT)

Turbulent particle-laden flows are encountered in many practical applications such as geophysical flows, engineering processes or health/medicine studies. The modelling and simulation of particle transport and dispersion 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 a smooth or rough wall. In addition, although long neglected in modelling approaches, the effect of electrical charges on the dynamics of particle flow can be very important. The objective of this talk is to present some recent advances in modelling and simulation of electrically charged particle flows for two very different particle-laden flow regimes.

The first part of the presentation is devoted to the effect of electrostatic forces on the dispersion of small inertial particles, with the same charge, carried by a homogeneous isotropic turbulent flow for very dilute configurations. This phenomenon is analyzed by means of direct numerical simulations (DNS) coupled with Lagrangian tracking of electrically charged particles. The simulation results show that the kinetic energy, self-dispersion and segregation of the particles decrease with increasing electrical charges. Statistical analysis of the simulation results in the framework of the joint fluid-particle PDF approach shows that the decrease in kinetic energy and self-dispersion of charged particles is due to a decorrelation effect between the turbulent velocities of the fluid and the particles by electrostatic forces. Such an effect can be modelled by introducing a Coulomb collision cross section by analogy with the elastic collision effect on particle dispersion in turbulent flows.

The second part of the presentation is devoted to the statistical modelling of the mean electric charge transport with triboelectric effects in mono-dispersed gas-particle flows for kinetic and collisional regimes. The kinetic theory of granular flows is used to derive the transport equations for the mean particle electric charge and for the secondorder moments: charge-velocity correlations and charge variance. The collision terms in these equations 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. A linear model for the mean electric charge conditioned by the instantaneous particle velocity is proposed to account for the charge–velocity correlations in the computation of the collision terms. First, a gradient dispersion model for the charge-velocity correlations is derived from the corresponding transport equation by using simplifying hypotheses. The gradient dispersion model is tested in a periodic box with non-uniform initial mean charge distribution. The results show that the dispersion phenomenon has two contributions: a kinetic contribution due to the electric charge transport by the random motion of particles and a collisional contribution due to the electric charge transfer during particle–particle collisions. Another phenomenon that contributes to the mean electric charge transport is a triboelectrical current density due to the tribocharging effect by particle–particle collisions in the presence of a global electric field. Second, a full second-moment transport equation model is tested in the periodic box with nonuniform initial mean charge distribution. The results show that this model is able to capture some important mechanism that are neglected in the gradient dispersion modelling approach and, in particular, allows to account for the coupling with the charge variance production and dissipation.