A computational framework for droplet size distribution in liquid jets into crossflow via deep learning and image-based analysis

In this work, we develop a two-stage machine learning framework for predicting droplet size distributions (DSDs) resulting from liquid jet-in-crossflow (JIC) atomization. The framework integrates a Convolutional Neural Network (CNN), which extracts relevant flow features from jet breakup images, with a Mixture Density Network (MDN) that maps these features to corresponding DSDs represented as Gaussian mixtures, including uncertainty estimates. The training dataset is generated from Large Eddy Simulations (LES) coupled with a stochastic fields transported-probability density function (PDF) method, covering 27 LES cases across a range of Weber numbers (We=250,500,1000), momentum flux ratios (q=1,5,10), and density ratios (rρ=10,100,1000). The CNN predicts flow parameters with over 97% accuracy on the validation set, while the MDN achieves a mean absolute error of 0.0003, representing a 72.7% improvement over a benchmark multilayer perceptron. Furthermore, the pipeline reduces computational cost by more than 99.9% relative to LES. Here, LES acts as a labelled generator to train an image to DSD model, to enable fast, uncertainty-aware distribution-level inference directly from breakup images, with potential to extend it in cases where ground-truth diameters are unavailable (as experiments or legacy image archives). While this study is trained and evaluated exclusively on LES-generated data, the framework can be applied to other high-fidelity simulations, and is designed with experimental deployment in mind, though this is left as the subject of future studies.