Spatial correlations and relative velocities of polydisperse droplets in homogeneous isotropic turbulence

Abstract

We investigate the motions of polydisperse droplets in homogeneous and isotropic turbulence at Reynolds numbers [Formula: see text]–300. The emphasize is put on the parameter dependences of spatial velocity correlations (SVCs) and relative velocities (RVs) of droplets, which are relevant to particle transport and dispersion in turbulence and have been less studied in experiments. The Kolmogorov-scale Stokes number is [Formula: see text]–[Formula: see text], and the settling parameter, i.e., the ratio of particle settling velocity to fluid velocity fluctuations, is [Formula: see text]–2.0. Using high-resolution measurements, we can resolve the motions of turbulence and droplet over a wide range of scales ([Formula: see text] to [Formula: see text], η is Kolmogorov length). The parabolic behavior in droplet SVCs near the origin is observed, similar to turbulence. The droplet SVCs are smaller than turbulence for all scales and decrease with both [Formula: see text] and [Formula: see text]. At large scales, the droplet RVs, smaller than those of turbulence due to the inertial filtering effect, also decrease with [Formula: see text] and [Formula: see text]. At small scales, the path-history effect leads to larger droplet RVs than fluid RVs. Interestingly, we find RVs present a non-monotonic trend with [Formula: see text] and reach a valley at [Formula: see text]. It may originate from particle clustering and preferential sweeping effects, which both prevail at [Formula: see text]. It is also found that droplet motions are less intermittent than turbulence. This is in contrast to the previous observations by simulations with the gravity effect being ignored. The intermittency of droplet RVs decreases with [Formula: see text] due to the diminished droplet–turbulence interactions, and it presents opposite trends with [Formula: see text] for small and large scales. Finally, the balance between the effects of path histories and turbulent structures makes the velocity statistics of droplets quasi-independent from the scale in the range of the dissipative scale ([Formula: see text]).