Modelling turbulent collision of bidisperse inertial particles

Abstract

We study finite-inertia effects on the collision rate of bidisperse heavy particles in a turbulent gas, using direct numerical simulations and kinematic descriptions. As shown previously for a monodisperse system (Sundaram & Collins 1997; Wang, Wexler & Zhou 2000), a statistical mechanical description of the average collision kernel consists of two parts, namely a description of the relative velocity between two colliding particles (the turbulent transport effect) and of the non-uniform particle distribution due to dynamic interaction of particles with coherent vortex structures (the accumulation effect). We first show that this description remains valid and accurate for a bidisperse system involving two groups of particles of inertial response time τp1 and τp2, respectively. Numerical results for the turbulent transport effect and the accumulation effect have been obtained as a function of τp1 and τp2. Interestingly, the accumulation effect in a bidisperse system is bounded above by that of a monodisperse system. An explanation for this observation is given, in terms of the correlation between concentration fields of the two size groups. Simulations show that particles from two size groups were found in different regions of a vortex, thus reducing the net accumulation effect in a bidisperse system. The turbulent transport effect, on the other hand, is bounded below by the level in a monodisperse system, due to a differential inertia effect. The above observations imply that the size polydispersity enhances the turbulent transport effect but weakens the accumulation effect, relative to a monodisperse system.A simple eddy–particle interaction (EPI) model was developed and shown to give a reasonable prediction of the collision kernel, except for a small parametric region where both τp1 and τp2 are on the order of the ow Kolmogorov time τk and thus the accumulation effect must be included. A more accurate model incorporating both the turbulent transport effect and the accumulation effect has also been developed. The model would provide an upper bound on the collision rates for a non-dilute bidisperse system, since turbulence modulation and particle-particle interactions are not considered in this model.Finally, some consideration is given to the effect of nonlinear drag on the collision kernel. The results show that the drag nonlinearity can increase the collision kernel slightly (less than 10%) at large particle inertia.