AbstractClustering (or preferential concentration) of weakly inertial particles suspended in a homogeneous isotropic turbulent flow is driven primarily by the smallest eddies at the so-called Kolmogorov scale. In particle-laden large-eddy simulations (LES), these small scales are not resolved by the grid and hence their effect on both the resolved flow scales and the particle motion have to be modelled. In order to predict clustering in a particle-laden LES, it is crucial that the subgrid model for the particles captures the mechanism by which the subgrid scales affect the particle motion (Ray & Collins, J. Fluid Mech., vol. 680, 2011, pp. 488–510). In this paper, we describe novel satellite particle simulations (SPS), in which we study the clustering and relative velocity statistics of inertial particles at separation distances well below the Kolmogorov length scale. SPS is designed to isolate pairwise interactions of particles, and is therefore well suited for developing two-particle models. We show that the power-law dependence of the radial distribution function (RDF), a statistical measure of clustering, is predicted by the SPS in excellent agreement with direct numerical simulations (DNS) for Stokes numbers up to 3, implying that no explicit information from the inertial range is required to accurately describe particle clustering. This result further explains our successful prediction of the RDF power using the drift-diffusion model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219–251) for $\mathit{St}\leq 0. 4$. We also consider the second-order longitudinal relative velocity structure function for the particles; we show that the SPS is able to capture its power-law exponent for $\mathit{St}\leq 0. 5$ and attribute the disagreement at larger $\mathit{St}$ to the effect of the larger scales of motion not captured by the SPS. Further, the SPS is able to capture the ‘caustic activation’ of the structure function at zero separation and predict the critical $\mathit{St}$ and rate of activation in agreement with the DNS (Salazar & Collins, J. Fluid. Mech., vol. 696, 2012, pp. 45–66). We show comparisons between filtered DNS and equivalently filtered SPS, and the findings are similar to the unfiltered case. Overall, SPS is an efficient and accurate computational tool for investigating particle pair dynamics at small separations, as well as an interesting platform for developing LES subgrid models designed to accurately reproduce particle clustering.
Integrated random processes exhibiting long tails, finite moments, and power-law spectra
