High-fidelity simulation and data-driven machine-learning modeling of drop deformation and drag in aerodynamic breakup

When a freely moving droplet undergoes sudden acceleration due to a free-stream flow with non-zero relative velocity, the droplet experiences aerodynamic deformation and potential breakup if the surface tension is insufficient to resist the fluid inertia. The aerobreakup process relies on small-scale physics, which is extremely computationally costly in three-dimensional (3D) simulations. For practical spray applications involving a large number of droplets, it is infeasible to fully resolve the droplet-scale physics, and thus sub-scale Lagrangian point-droplet models are needed to predict the forces, heat transfer, and phase change, if it occurs. Traditional Lagrangian droplet models assume isolated spherical droplets, and this oversimplification limits the accuracy in predicting droplet forces. In the present study, we first perform detailed interface-resolved simulations of droplet aerobreakup using the Volume-of-Fluid method. Then, data-driven models for droplet deformation and forces are developed using the simulation data and neural networks. We test a simple MLP (Multi-Layer Perceptron) and a more sophisticated recurrent NARX (Non-linear Auto-Regressive with Exogenous Input) Neural Network. By incorporating important physical parameters of the droplet, including the Weber number, Reynolds number, and spherical harmonics modal coefficients that represent the droplet shape, the model predictions for droplet deformation and drag agree remarkably well with the simulation data. The simulation and modeling approaches are then extended to a droplet cloud with varying volume fractions to incorporate the effects of droplet-droplet interactions.