Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations

Abstract

Clustering (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 St 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 St 0.5 and attribute the disagreement at larger 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 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.

Fluid particles only separate exponentially in the dissipation range of turbulence after extremely long times

“…we may instead directly solve (4). In this way, the turbulence is specified through the single-point quantity Γ, and as discussed by Ray & Collins [41], such a method eliminates the aforementioned interpolation errors which could otherwise strongly affect the relative motion results when the particle separations are much smaller than the DNS grid spacing.…”

Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches

“…However, they have the obvious advantage of accounting for spatial correlations of the SGS fluid velocity components, which are crucial for phenomena such as pair dispersion, preferential concentration, collision, break-up, coalescence and agglomeration [105]. Future research efforts should be aimed at providing a sound assessment of the performance of structural models, particularly in high Reynolds number flows and at higher volume concentrations of the dispersed phase.…”

Collision dynamics of particles and bubbles in gravity‐driven flotation: A DNS investigation

“…The normalised particle–bubble collision kernel obtained from () is $$\Gamma _{pb}\tau _\eta /r_c^3=0.13$$. Due to the low turbulence level and the dominance of gravity, the collision kernel is small compared to previous studies [9].…”

“…The collision kernel is influenced by a variety of parameters that describe not only the characteristics of the two suspended species, but also the characteristics of the turbulent fluid motion. In a non-dimensional form, the relevant dependencies are [9,10] Γ 𝑝𝑏 𝑟…”

“…The expression without prefactor is therefore widely used to normalise the dimensional collision kernel. An overview of other models for collision kernels can be found in [1, 9,10,12].…”