Interphase coupling for gas-droplet flows using the fully Lagrangian approach
C. P. Stafford, O. Rybdylova
TL;DR
This work presents a fully Lagrangian approach (FLA) augmented by kernel regression to enable robust two-way coupling between evaporating droplets and an incompressible carrier flow, implemented in OpenFOAM. By treating the droplet phase as a dilute continuum and reconstructing interphase source terms $S_{ ext{Mass}}$ and $\bm{S}_{\text{Mom}}$ from Lagrangian trajectories via a Nadaraya–Watson-like estimator with adaptive kernel scale, the method achieves high fidelity comparable to PSI-CELL while reducing the required droplet seeding by ~100×. The framework handles both steady and transient regimes, with evaporating droplets introducing mass transfer and vapour diffusion through $S_{ ext{Mass}}$ and a vapour field $\rho_v$ governed by $\partial_t\rho_v + \nabla\cdot(D\nabla\rho_v) + \nabla\cdot(\bm{u}\rho_v) = S_{ ext{Mass}}$, enabling detailed analysis of wake modulation, vortex dynamics, and vapour transport. The results demonstrate accurate reproduction of flow features and significant computational savings, positioning the FLA-kernel regression approach as a practical tool for complex gas–droplet flows and enabling future exploration of boundaries, turbulence, and multi-component droplets.
Abstract
A novel method combining the fully Lagrangian approach (FLA) and kernel regression has been developed for two-way coupled simulations of evaporating sprays. The carrier phase is incompressible viscous flow described by the Navier-Stokes equations. The admixture is considered to be a cloud of monodisperse evaporating droplets, which is treated as a continuum in the FLA. All droplet parameters are calculated along selected trajectories with the number density calculated using the Lagrangian form of the continuity equation. To enable two-way coupling, the momentum and mass phase exchange terms must be calculated in each volume element of an Eulerian mesh. This is achieved by using kernel regression in conjunction with the FLA trajectory data, which retains the detail of complex structures in droplet clouds by adaptively scaling the kernel support according to the local droplet field deformation. In this work, the mass and momentum coupling source terms obtained using the FLA are assessed against reference values calculated using a standard Lagrangian particle tracking simulation that incorporates a PSI-CELL box-counting method. It is shown that the FLA retains the same level of fidelity and smoothness as the reference PSI-CELL case, whilst also providing a computational speedup factor of around 100 times due to the decreased droplet seeding.