A physics-informed machine learning model for the prediction of drop breakup in two-phase flows

Predictive simulations of two-phase flows are highly sought after because of their widespread applications in propulsion, energy, agriculture, and medicine. One crucial goal for many of these simulations is the accurate and efficient prediction of the size distribution and number density of atomized drops. The multi-scale nature of these flows makes it practically impossible to capture all scales within a single simulation. In particular, the breakup processes producing the smallest drops through secondary breakup often necessitate resolutions far below the Kolmogorov scale. Consequently, models must be employed for secondary breakup. Existing physics- based and stochastic breakup models are not universal and fail to account for the local and instantaneous flow field and drop geometry. We present a physics-informed machine learning model for predicting the statistics of daughter drops generated during the breakup of under-resolved drops. By training on high-fidelity simulations, the model can predict breakup outcomes from severely under-resolved input fields. This is made possible by a careful choice of quantities of interest and by taking inspiration from the discrete nature of breakup events to encode the temporal evolution via a mixture of sigmoid functions. We showcase proof-of-concept results from the canonical settings of 3D Taylor-Green vortex flows and homogeneous isotropic turbulence. Compared to results generated by low-resolution simulations (i.e., without a model) and baseline state-of-the-art models, our approach achieves superior accuracy in predicting drop size distribution and critical quantities of interest, such as surface area. This work paves the path towards the development of embedded machine learning models for the prediction of primary and secondary breakup.