Direct Numerical Simulation of Finite-Inertia Particle Collision in Isotropic Turbulent Flow

In this paper, direct numerical simulations (DNS) were conducted to study particle collisions in a stationary isotropic homogeneous turbulent flow, with the aim to investigate the influence of turbulence on particle collision rates of various finite-inertia particles. It is found that the behavior of finite-inertial particle collision is very complicated, both the Saffman & Turner theory(Stk=τp/τk =0) and kinetic theory( Stk=￥) can't correctly predict it. For particles of Stk <1 the collision rate increases sharply as Stk increases; at Stk ~1, collision rate reaches a peak value; As Stk continues to increase, collision rate slowly decreases at first and then increases to reach another peak at Stk ~3 (corresponding to Eulerian integral time scale). As particle inertia continues to increase, collision rate begins to decrease slowly to reach the kinetic theory. Both of the peak value is about 30 times of zero inertia limit. To further understand the mechanism of finite-inertia particle collision in isotropic turbulence, two major effects of turbulent flow on particle collision, namely turbulent transport effect and preferential concentration effect, are investigated and are represent qualitatively using radial relative velocity <|wr|> and radial distribution function g(R) of colliding particle pairs respectively. Both effects tend to increase collision rates, leading to the observed complex behavior. The results showed that preferential concentration effect is the main contribution factor for the peak of particle collision rate near Stk~1, while both preferential concentration effect and turbulent transport effect contributing to the peak near Stk~3, with much stronger turbulent transport effect herein. Statistical analysis of the data also showed that the probability density function(pdf) of relative radial velocity between two colliding particles does not fit for Gaussian distribution for different Stokes number. Instead, due to the effect of different scales of motions in turbulent flow, the shape of the pdf appears to belong to a family of exponential distributions with powers in the exponent that vary with the Stokes number.Keywords: Isotropic Turbulence, DNS, Finite Inertia, Particle Collision Rate, Preferential Concentration Effect, Turbulent Transport Effect