The settling velocity of heavy particles in an aqueous near-isotropic turbulence

Abstract

The ensemble-average settling velocity, V s , of heavy tungsten and glass particles with different mean diameters in an aqueous near-isotropic turbulence that was generated by a pair of vertically oscillated grids in a water tank was measured using both particle tracking and particle image velocimetries. Emphasis is placed on the effect of the Stokes number, St, a time ratio of particle response to the Kolmogorov scale of turbulence, to the particle settling rate defined as (V s ϪV t)/ V t where V t is the particle terminal velocity in still fluid. It is found that even when the particle Reynolds number Re p is as large as 25 at which V t /v k Ϸ10 where v k is the Kolmogorov velocity scale of turbulence, the mean settling rate is positive and reaches its maximum of about 7% when St is approaching to unity, indicating a good trend of DNS results by Wang and Maxey ͑1993͒ and Yang and Lei ͑1998͒. This phenomenon becomes more and more pronounced as values of V t /v k decrease, for which DNS results reveal that the settling rate at V t /v k ϭ1 and Re p Ͻ1 can be as large as 50% when StϷ1. However, the present result differs drastically with Monte Carlo simulations for heavy particles subjected to nonlinear drag (Re p Ͼ1) in turbulence in which the settling rate was negative and decreases with increasing St. Using the wavelet analysis, the fluid integral time (I), the Taylor microscale (), and two heavy particles' characteristic times (c1 , c2) are identified for the first time. For StϽ1, c1 Ͻ I and c2 Ͻ , whereas c1 Ϸ I and c2 Ϸ for StϷ1. This may explain why the settling rate is a maximum near StϷ1, because the particle motion is in phase with the fluid turbulent motion only when StϷ1 where the relative slip velocities are smallest. These results may be relevant to sediment grains in rivers and aerosol particles in the atmosphere.

Turbulence as a driver for vertical plankton distribution in the subsurface upper ocean

“…Numerical modelling has shown that turbulence could enhance the sedimentation (flotation) velocities of heavy (light) particles (Wang and Maxey 1993, Yang and Lei 1998, Bosse et al 2006, De Lillo et al 2008. There are also several laboratory studies that examine how turbulence can modify the vertical velocity of small particles (Aliseda et al 2002, Brucato et al 1998, Ruiz et al 2004, Ross 2006, Schimdt and Seuront 2008, Yang and Shy 2003, Zhou and Cheng 2009. Some studies show a reduction of the sedimentation velocity of synthetic particles in turbulent waters (e.g.…”

Particle–fluid interactions in grid-generated turbulence

“…Aliseda et al (2002) and Yang & Shy (2005). These studies are closely related, but their focus is on different aspects of two-way coupling (i.e.…”

“…Because of the low number of particles, it is difficult to determine if preferential concentration effects are absent or if the particle statistics are insufficient. However, one could argue that preferential concentration effects will not be significant owing to the relatively high values of the ratio of the particle terminal velocity and the fluid fluctuations, β = u tv /u (Yang & Shy 2005). This corresponds to a low 'residence time' of the particles in a typical vortical structure.…”

“…Geiss et al (2004) performed comparable experiments, but did not find any changes in the spectrum. A study by Yang & Shy (2005) describes particle-turbulence interaction in stationary homogeneous and isotropic turbulence. They find significant changes in the shape of the spectra, depending on the Stokes number of the particle: (1) for small particles (St p = 0.36), they find an attenuation at large scales and augmentation at scales larger than the Taylor microscale (in both the horizontal and vertical velocity spectrum), (2) for intermediate particles no changes are observed at large scales, while there is again an increase at scales larger than the Taylor microscale (again both horizontal and vertical), (3) for heavy particles (St p > 1.9), the large scales are damped and small scales are augmented in the horizontal direction, while all scales are augmented in the vertical direction.…”

“…Another example is the ratio of the terminal velocity of a particle and a typical fluid fluctuation (β ≡ u T V /u ), which can be used to evaluate the influence of gravity (Yang & Shy 2005). Many different regimes exist in particle-laden turbulence, but a precise classification or prediction is currently difficult.…”