Subgrid Scale Modeling of the Scalar Transport Equation in Multiphase Flows

In multi-phase systems with heat or mass transfer at large Peclet numbers, thin boundary layers form at the interface. These are potentially orders of magnitude smaller than the smallest hydrodynamic length scales, making a true DNS of the system infeasible. We present a subgrid-scale (SGS) model for the scalar transport equation which corrects transport for advective and diffusive fluxes near the interface from a DNS for the flow. This allows us to predict heat and mass transfer correctly even if the boundary layer is fully contained in a single cell layer around the interface. We demonstrate how a shallow neural network can be used to approximate a boundary layer profile, allowing the user to quickly develop a model for the boundary layer and integrate it into the overall framework. The modeling framework is integrated into an existing open-source multiphase flow solver with adaptive mesh resolution which computes the velocity field used in the scalar transport equation. We apply our SGS framework to a variety of problems including bubble dissolution, nucleate boiling, and liquid-liquid transfer in a gas-blown ladle. The method allows us to recover known scaling regimes with very coarse grids compared to what would be required with traditional methods.