Small particles in homogeneous turbulence: Settling velocity enhancement by two-way coupling

Abstract

The gravitational settling of an initially random suspension of small solid particles in homogeneous turbulence is investigated numerically. The simulations are based on a pseudospectral method to solve the fluid equations combined with a Lagrangian point-particle model for the particulate phase ͑Eulerian-Lagrangian approach͒. The focus is on the enhancement of the mean particle settling velocity in a turbulent carrier fluid, as compared to the settling velocity of a single particle in quiescent fluid. Results are presented for both one-way coupling, when the fluid flow is not affected by the presence of the particles, and two-way coupling, when the particles exert a feedback force on the fluid. The first case serves primarily for validation purposes. In the case with two-way coupling, it is shown that the effect of the particles on the carrier fluid involves an additional increase in their mean settling velocity compared to one-way coupling. The underlying physical mechanism is analyzed, revealing that the settling velocity enhancement depends on the particle loading, the Reynolds number, and the dimensionless Stokes settling velocity if the particle Stokes number is about unity. Also, for particle volume fractions ⌽ v տ 10 −5 , a turbulence modification is observed. Furthermore, a direct comparison with recent experimental studies by Aliseda et al. ͓J. Fluid Mech. 468, 77 ͑2002͔͒ and Yang and Shy ͓J. Fluid Mech. 526, 171 ͑2005͔͒ is performed for a microscale Reynolds number Re Ϸ 75 of the turbulent carrier flow.

Numerical Study on the Influence of Particle Inertia in Particle‐Driven Gravity Currents

“…strain-rate (see e.g. [2] or [5]). If particle inertia is neglected, no accumulation is observed since the particle velocity field is divergence-free for this approach.…”

“…The governing dimensionless parameters are the Reynolds number Re, the normalized Stokes settling velocity v s and the particle Stokes number St. For more details on the governing equations, see e.g. [2] and [3]. For comparison, we also present one simulation where particle inertia is neglected.…”

“…The particles are tracked individually using a Lagrangian point-particle approach as used e.g. in [2]. We only consider dilute suspensions in order to neglect particle-particle interactions and the particle volume displacement in the continuity equation.…”

“…by using a tent function (see e.g. [2]). The Poisson equation for the pressure is solved using a multigrid method.…”

Large-eddy simulation of particle-laden turbulent flows

“…Numerical studies concerning accumulation and dispersion of heavy particles in forced plane mixing layers have been carried out in a series of works: Martin & Meiburg (1994); Raju & Meiburg (1995); Marcu & Meiburg (1996a, b); Marcu, Meiburg & Raju (1996); they all reported the formation of highly concentrated particle streaks in the region between two vortices. The behaviour of heavy particles in homogeneous isotropic turbulence has been studied experimentally by Aliseda et al (2002) and numerically by Bosse, Kleiser & Meiburg (2006) where it is shown that the settling velocity is enhanced by the turbulence and that large temporal and spatial inhomogeneities in the particle concentration fields arise; the particles concentrate preferentially in certain regions of the flow.…”