Transport of condensing droplets in Taylor-Green vortex flow in the presence of thermal noise

TL;DR

This study investigates how phase change and thermal noise influence the transport of condensing droplets in a turbulent Taylor-Green vortex flow, revealing conditions under which droplets escape vortices and transition to ballistic motion.

Contribution

It introduces a toy model combining phase change, thermal noise, and vortex flow to analyze droplet transport, highlighting the effects of noise and growth on droplet dynamics.

Findings

Thermal noise enables droplets with small Stokes numbers to escape vortices.

Growing droplets tend to achieve ballistic motion as their Stokes number approaches one.

Thermal noise effects diminish for larger, growing droplets.

Abstract

We study the role of phase change and thermal noise in particle transport in turbulent flows. We employ a toy model to extract the main physics: condensing droplets are modelled as heavy particles which grow in size, the ambient flow is modelled as a two-dimensional Taylor-Green (TG) flow consisting of an array of vortices delineated by separatrices, and thermal noise are modelled as uncorrelated Gaussian white noise. In general, heavy inertial particles are centrifuged out of regions of high vorticity and into regions of high strain. In cellular flows, we find, in agreement with earlier results, that droplets with Stokes numbers smaller than a critical value, $St < St_{\rm{cr}}$, remain trapped in the vortices in which they are initialised, while larger droplets move ballistically away from their initial positions by crossing separatrices. We independently vary the P\'eclet number $Pe$ characterising the amplitude of thermal noise and the condensation rate $\Pi$ to study their effects on the critical Stokes number for droplet trapping, as well as on the final states of motion of the droplets. We find that the imposition of thermal noise, or of a finite condensation rate, allows droplets of $St < St_{\rm{cr}}$ to leave their initial vortices. We find that the effects of thermal noise become negligible for growing droplets, and that growing droplets achieve ballistic motion when their Stokes numbers become $\mathcal{O}(1)$. We also find an intermediate regime prior to attaining the ballistic state, in which droplets move diffusively away from their initial vortices in the presence of thermal noise.