Predicting Energy Budgets in Droplet Dynamics: A Recurrent Neural Network Approach

TL;DR

This work addresses predicting transient and static aspects of the energy budget in droplet dynamics using an LSTM trained on geometric time-series data, applied to two regimes: non-spherical droplet impact and droplet coalescence. It combines a physics-based numerical solver (projection method for incompressible Navier–Stokes with surface tension) with front-tracking geometry to generate datasets and trains a three-layer LSTM to predict $E_k$, $E_s$, and $E_d$ over time, achieving high accuracy across a range of $Re$ and $We$. A two-phase sequential neural network is introduced to first predict energies from geometry and then infer nondimensional numbers $Re$ and $We$, enabling energy-budget inference from experimental video data alone; direct geometry-to-number predictions are found to be less reliable. The approach shows promise for experimental applicability and practical tasks in inkjet printing, sprays, and related technologies, and it points toward extensions to non-Newtonian fluids and physics-informed architectures in future work.

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.

Figures (17)

• Figure 1: Dataset is extracted from numerical simulations of two droplet dynamic problems.
• Figure 2: Different initial droplet shapes and the train-validation-test splits. The more complex shapes were specifically chosen for the validation and test sets.
• Figure 3: Effect of drop shape (shapes 1 and 10 from Fig \ref{['fig:conjunto1_1']}) on impact when varying Re and We: morphology for the first (a) and second (b) set of parameters and diameter time variation for both shapes from the first (c) and second set (d).
• Figure 4: Droplet collision dynamics with different impact parameters and varying Re and We: morphology for the first (a), second (b) and third (c) set of parameters and time variation in diameter $D$ and height $H$ for the first (d), second (e) and third set (f).
• Figure 5: LSTM Cell structure.