Statistical mechanical description and modelling of turbulent collision of inertial particles

The collision rate of monodisperse solid particles in a turbulent gas is governed by a wide range of scales of motion in the flow. Recent studies have shown that large-scale energetic eddies are the dominant factor contributing to the relative velocity between two colliding particles (the turbulent transport effect), whereas small-scale dissipative eddies can enhance the collision rate significantly by inducing local nonuniform particle distribution (the accumulation effect). The turbulent transport effect is most noticeable when the particle inertial response time tau(p) is of the order of the flow integral timescale and the accumulation effect is most pronounced when tau(p) is comparable to the flow Kolmogorov time. We study these two contributions separately through direct numerical simulations. The two effects are quantified carefully with a numerical procedure that is independent of the computation of average collision rate. This facilitates the study of not only the statistical description of the collision kernel, but also the relative contributions and modelling of the two physical effects. Simulations at several flow Reynolds numbers were performed to suggest a model for the accumulation effect. The data show that the accumulation effect scales linearly with flow Taylor microscale Reynolds number R-i, while the theory for fully developed turbulence indicates that the maximum level of the turbulent transport effect scales with R-lambda(1/2). Finally, an integrated model has been developed to predict the collision rate at arbitrary flow Reynolds numbers and particle inertia.