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.

A suspension drop is a swarm of particles that are suspended in initially still fluid. When settling under the influence of gravity a suspension drop may undergo a complex shape evolution including the formation of a torus and eventual disintegration. In the present work the settling process of initially spherical suspension drops is investigated numerically for low and moderate drop Reynolds numbers Re d . In the simulations a pseudospectral method is used for the liquid phase combined with a Lagrangian point-particle model for the particulate phase. In the case of low Reynolds numbers ͑Re d Ͻ 1͒ the suspension drop retains a roughly spherical shape while settling. A few particles leak away into a tail emanating from the rear of the drop. Due to the use of periodic boundaries a hindered settling effect is observed: the drop settling velocity is decreased compared to a suspension drop in infinite fluid. In the Reynolds number range 1 ഛ Re d ഛ 100 the suspension drop deforms into a torus that eventually becomes unstable and breaks up into a number of secondary blobs. This Reynolds number range has not been investigated systematically in previous studies and is the focus of the present work. It is shown that the number of secondary blobs is primarily determined by the Reynolds number and the particle distribution inside the initial drop. An increased number of particles making up the suspension, i.e., a finer drop discretization, may result in a delayed torus disintegration with a larger number of secondary blobs. The influence of the initial particle distribution as a source of ͑natural͒ perturbations and the effect of initially imposed ͑artificial͒ shape perturbations on the breakup process are examined in detail. To gain a better understanding of the substructural effects ͑inside the suspension͒ leading to torus breakup, the particle field is analyzed from a spectral point of view. To this end, the time evolution of the Fourier coefficients associated with the particle distribution in the azimuthal direction of the torus is studied.

The feasibility of large‐eddy simulations (LES) of particle‐laden homogeneous turbulence is investigated for both one‐way and two‐way coupling using a high‐pass filtered Smagorinsky model. The LES results are compared with our recent direct numerical simulations (DNS) as well as data in the literature. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A suspension drop is an initially spherical swarm of small particles that are suspended in fluid at rest. Under the influence of gravity this drop settles, and it can undergo a complex shape evolution with subsequent disintegration. We performed numerical simulations of suspension drops settling at moderate drop Reynolds numbers 1 ഛ Re d ഛ 100. 1 Here, we show two typical examples of the drop breakup. Figure 1 displays the initial drop ͑left͒ and the settling drop very shortly after the release ͑right͒. The particles are colorcoded to visualize their motion inside the drop. This initial stage is similar for all drop Reynolds numbers. However, the subsequent shape evolution and disintegration strongly depend on the Reynolds number. In the case of very small Reynolds numbers, Re d Ӷ 1, the drop retains a compact spherical shape and a few particles leak into a tail emanating from the rear of the drop ͑not shown here͒. In the case of Re d = 1 the drop deforms into a torus that grows in diameter while settling. Eventually two bulges form and the torus breaks up into two secondary blobs ͑Fig. 2͒. In the case of Re d = 100 the disintegration process occurs much faster than in the foregoing example. Also, the torus is now spanned by a membrane of dilute particles and finally breaks up into a larger number of secondary blobs ͑Fig. 3͒. 1 T. Bosse, C. Härtel, E. Meiburg, and L. Kleiser, "Numerical simulation of finite Reynolds number suspension drops settling under gravity," Phys. Fluids 17, 037101 ͑2005͒. FIG. 1. ͑Enhanced online͒. Initial drop ͑left͒ and settling drop very shortly after the release ͑right͒. FIG. 2. Breakup of suspension drop settling at Re d =1. FIG. 3. Breakup of suspension drop settling at Re d =100.