Machine learning models for unresolved capillary effects in multiphase flows*

The multi-scale nature of many two-phase flows makes it practically impossible to capture all scales within a single simulation. For instance, the capillary breakup processes producing the smallest drops/bubbles often require resolutions below the Kolmogorov scale. Hence, unresolved capillary effects must be modeled in simulations of practical multiphase flows. We present two machine-learning (ML) models for this purpose. First, we present a physics-informed ML model for predicting the statistics of daughter drops generated during the breakup of under-resolved drops. By training on high-resolution simulations, the model learns to predict breakup outcomes from under-resolved input fields. Compared to baseline alternatives, our approach achieves superior accuracy in predicting drop size distribution and critical quantities of interest, such as surface area. This model can be considered the first step toward developing embedded ML models for primary and secondary breakup. Second, we present an ML model for predicting the unresolved surface area density in LES of multiphase flows. We explain how this model can be incorporated into Eulerian spray models, replacing phenomenological models typically used for closure of surface area density.