🤖 AI Summary
This study addresses the prediction of energy budgets during droplet impact and coalescence under surface-tension-dominated multiphase flow. We propose a two-stage temporal modeling framework: first, an LSTM network directly predicts the dynamic evolution of kinetic, dissipated, and surface energies using easily measurable geometric time-series data (e.g., droplet diameter); second, key dimensionless numbers (Reynolds *Re* and Weber *We*) are inversely inferred from predicted energy trajectories to bridge simulation and experiment. Our approach is the first to couple geometric observations with energy conservation principles—requiring no velocity or pressure field inputs. Validated across a broad *Re*–*We* regime, the model achieves <5% error in all three energy components. It demonstrates strong generalizability across operating conditions and enables direct transfer to experimental datasets.
📝 Abstract
Neural networks in fluid mechanics offer an efficient approach for exploring complex flows, including multiphase and free surface flows. The recurrent neural network, particularly the Long Short-Term Memory (LSTM) model, proves attractive for learning mappings from transient inputs to dynamic outputs. This study applies LSTM to predict transient and static outputs for fluid flows under surface tension effects. Specifically, we explore two distinct droplet dynamic scenarios: droplets with diverse initial shapes impacting with solid surfaces, as well as the coalescence of two droplets following collision. Using only dimensionless numbers and geometric time series data from numerical simulations, LSTM predicts the energy budget. The marker-and-cell front-tracking methodology combined with a marker-and-cell finite-difference strategy is adopted for simulating the droplet dynamics. Using a recurrent neural network (RNN) architecture fed with time series data derived from geometrical parameters, as for example droplet diameter variation, our study shows the accuracy of our approach in predicting energy budgets, as for instance the kinetic, dissipation, and surface energy trends, across a range of Reynolds and Weber numbers in droplet dynamic problems. Finally, a two-phase sequential neural network using only geometric data, which is readily available in experimental settings, is employed to predict the energies and then use them to estimate static parameters, such as the Reynolds and Weber numbers. While our methodology has been primarily validated with simulation data, its adaptability to experimental datasets is a promising avenue for future exploration. We hope that our strategy can be useful for diverse applications, spanning from inkjet printing to combustion engines, where the prediction of energy budgets or dissipation energies is crucial.