Effect of nonlinear drag on the settling velocity of particles in homogeneous isotropic turbulence

Abstract

We study the average settling velocity of small spherical particles under gravity through a Gaussian random velocity field generated by Fourier modes with a von Kárman energy spectrum. The particles are subjected to the effects of a linear (Stokes) or nonlinear drag force, inertia and gravity. It is shown that the effect of drag nonlinearity is a function of the particle to fluid density ratio ρp/ρf and a function of the ratio τp/τk of the particle time constant to the Kolmogorov timescale of the fluid. Simulations show that as ρp/ρf decreases from 877 to 2.65 or as τp/τk increases from 1 to 2.74, the drag nonlinearity increases as a result of the increase in particle Reynolds numbers. Hence the settling velocity changes from larger to smaller as compared with the still fluid settling velocity, showing that one of the major mechanisms governing the fall velocity reduction in a turbulent flow is the drag nonlinearity. The maximum increase in settling rate occurs at VT/υk ≈ 2 for ρp/ρf ≥ 87 (where VT is the terminal velocity of the particle and υk is the Kolmogorov velocity); this is consistent with the results of Wang and Maxey [1993]. The maximum decrease in settling rate occurs at VT/VK ≈ 1 for ρp/ρf ≈ 2.65, consistent with the results of Fung [1993]. In addition, the role of the spatial and temporal variations of the flow field on the settling rate is investigated. Finally, the Gaussian velocity field is also simulated with an exponential energy spectrum, and similar results are observed.