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

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 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(cr) remain trapped in the vortices in which they are initialized, while larger droplets move ballistically away from their initial positions by crossing separatrices. We independently vary the Peclet number Pe characterizing the amplitude of thermal noise and the condensation rate 11 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(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 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.

Automated summary

We study the effect of phase change and thermal noise on particle transport in turbulent flows. By using a toy model, we find that heavy particles are centrifuged out of high vorticity regions and into high strain regions. In cellular flows, droplets with small Stokes numbers remain trapped in vortices, while larger droplets move ballistically away from their original positions. The imposition of thermal noise or a finite condensation rate allows droplets with small Stokes numbers to leave their initial vortices. Thermal noise becomes negligible for growing droplets and they achieve ballistic motion when their Stokes numbers reach O(1). Before reaching the ballistic state, droplets move diffusively away from their initial vortices in the presence of thermal noise.