The interaction of droplet dynamics and turbulence cascade

TL;DR

This paper presents a numerical study of droplet fragmentation in turbulence at high Reynolds numbers, identifying the Hinze scale via spectral analysis and linking droplet size distribution to turbulent dissipation.

Contribution

It introduces a fully-coupled numerical approach to analyze droplet dynamics in turbulence, revealing the role of the Hinze scale and energy flux in droplet breakup and coalescence.

Findings

The Hinze scale is where net capillary energy exchange is zero.

Droplets larger than the Hinze scale tend to break up, absorbing energy.

Smaller droplets oscillate and coalesce, releasing energy.

Abstract

The dynamics of droplet fragmentation in turbulence is described in the Kolmogorov-Hinze framework. Yet, a quantitative theory is lacking at higher concentrations when strong interactions between the phases and coalescence become relevant, which is common in most flows. Here, we address this issue through a fully-coupled numerical study of the droplet dynamics in a turbulent flow at high Reynolds number. By means of time-space spectral statistics, not currently accessible to experiments, we demonstrate that the characteristic scale of the process, the Hinze scale, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than this scale preferentially break up absorbing energy from the flow; smaller droplets, instead, undergo rapid oscillations and tend to coalesce releasing energy to the flow. Further, we link the droplet-size-distribution with the probability distribution of the turbulent dissipation. This shows that key in the fragmentation process is the local flux of energy which dominates the process at large scales, vindicating its locality.