Spectral analysis of preferential concentration in turbulent flows: parametric dependence on Reynolds, stokes, and froude numbers

Abstract

Understanding the preferential concentration of inertial particles in turbulent flows is crucial for a wide range of natural and industrial processes. This study advances our understanding of turbulence-particle interactions by systematically evaluating the combined effects of turbulent Reynolds number (Re_λ), Stokes number (Stk), and Froude number (Fr) on particle clustering through direct numerical simulations (DNS). Our analysis demonstrates that particle clustering intensity peaks at Stk ∼ 1, where particles optimally interact with turbulent eddies. While previous research often overlooks the influence of Reynolds number, our findings reveal that this assumption holds for small Stk, but for larger Stk, Reynolds number significantly impacts clustering behaviour. Gravitational effects, quantified by Fr, also play a critical role in clustering dynamics. For Stk << 1, gravity's impact is minimal for Fr < 5.0; however, as Stk increases, gravity enhances large-scale clustering and modulates small-scale clustering—diminishing it for intermediate Stk ∼ 1 and enhancing it for Stk >> 1. Here, large-scale clustering refers to particle clustering at scales comparable to the largest energy-containing eddies, while small-scale clustering involves particle clustering at the dissipative scales of turbulence. We introduce a novel empirical model that predicts particle concentration spectra within 12 % relative error across a wide range of conditions $\left(0.1\le Stk\le 5.0;57\le Re\le 111;0.0\le Fr\le 5.0\right),$validated against current and previous studies. This model provides a practical tool for analysing particle-laden turbulent flows in large spaces and has substantial implications for atmospheric science, chemical engineering, and environmental studies, offering improved predictions of droplet clustering in clouds, particulate dispersion in reactors, and pollutant transport.