Reynolds number dependence of heavy particles clustering in homogeneous isotropic turbulence

The preferential concentration of heavy inertial point particles in homogeneous isotropic turbulence is investigated with direct numerical simulations. The particle clustering is measured by the standard deviation of normalized Voronoi volumes. With the particle number, large-scale time and length fixed, it is found that the degree of particle clustering is reduced with the increase of Taylor Reynolds number (R-lambda) for 52 <= R-lambda <= 139 when the Stokes number (St) is small (e.g., St <2.0), where St is the ratio of particle response time (tau(p)) to the Kolmogorov timescale (tau(eta)). On the contrary, the clustering of high-St particles tends to become stronger with the increase of R-lambda in the same R-lambda range. Quantities invoked for low-St particle clustering include tau(eta), the characteristic time (tau(f)) of particles being trapped by "shear structures" and the strength of "shear structures" quantified by the second invariant of velocity gradient tensor (Q = SijSij - Omega(ij)Omega(ij)). While the increase of Q with Reynolds number enhances preferential concentration, tau(eta) and tau(f) both decrease as Reynolds number increases, which could moderate the level of particle clustering. Then the observable reduction in the clustering of low-St particles with increasing R-lambda emerges as the dominance of tau(eta) and tau(f) over Q effects. In addition, we find that the strain rate cannot directly affect the spatial inhomogeneous distribution of low-St particles, but instead it impacts low-St particle clustering indirectly due to its correlation with the rotation rate. Unlike low-St particles dominated by small-scale eddies, the clustering of high-St particles is mainly influenced by large-scale eddies due to the "resonant" effect between particles and eddies.