An effective correction method for droplet volume conservation in direct numerical simulation of droplet-laden turbulence

TL;DR

This paper evaluates existing phase-field models for droplet volume conservation in turbulent flows and introduces a curvature-dependent correction to improve volume preservation without adverse effects.

Contribution

It proposes a novel modification to the Allen-Cahn equation that enhances droplet volume conservation in turbulent simulations.

Findings

Existing models fail at high Weber numbers to preserve droplet volume.

The proposed correction achieves statistical volume conservation in turbulent flows.

The new model avoids numerical instability and other common issues.

Abstract

Accurately preserving the volume of the dispersed droplets remains a significant challenge in phase-field simulations of droplet-laden turbulence, especially under conditions that feature strong interfacial deformation and breakup. While modified phase-field equations have been developed to mitigate volume loss, their effectiveness has not been systematically assessed in the context of fully developed turbulent flows. In this work, we first evaluate the performance of several representative volume-corrected phase-field models in direct numerical simulations of droplet-laden homogeneous isotropic turbulence. Our results reveal that, at sufficiently high Weber numbers, none of the existing models provides satisfactory droplet-volume preservation. To address this limitation, we then propose a simple yet effective modification of the conservataive Allen-Cahn equation by incorporating a curvature-dependent counter-diffusion correction. Direct numerical simulations in turbulent regimes demonstrate that the proposed model achieves conservation of droplet volume in a statistical sense, while avoiding common adverse effects, such as numerical instability, violation of global mass conservation, increased computational cost, artificial coarsening, or enhanced spurious velocities.