Collision Statistics of Inertial Particles in Two-Dimensional Homogeneous Isotropic Turbulence with an Inverse Cascade

This study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for small Stokes number (St) particles in 2D flows is proposed based on the model of Saffman & Turner (1956) (ST56 model). The DNS results agree with this 2D version of the ST56 model for St .0.1. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around three in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency free. Collision statistics for St=0.1, 0.4 and 0.6, i.e., for St<1, are obtained from the present 2D DNS and compared with those obtained from the 3D DNS of Onishi et al. (2013). We have observed that the 3D radial distribution function at contact (g(R), the so-called clustering effect) decreases for St=0.4 and 0.6 with increasing Reynolds number, while the 2D g(R) do not show a significant Reynolds number dependence. This observation supports the view that the Reynolds number dependence of g(R) observed in 3D is due to internal intermittency of the 3D turbulence. We have further investigated the local St, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds number dependence of g(R). Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for St 1 show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-St particle system. However, the PDF of local St at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when St is not much smaller than unity.