Data-driven surrogate modelling of drop-size distribution*

The accurate prediction of the drop size distribution (DSD) in liquid atomization and sprays is key to the optimization of multi-phase flows, from gas-turbine combustion, through agriculture to healthcare. The DSD is characterized from experiments and high-fidelity simulations, which provide data for surrogate modelling. With this data, we propose a multi-task Gaussian process regression (GPR) to model the DSD as a function of the spray angle, the Reynolds, and the Weber number of the jet. The prior knowledge of the approximate statistics of the distribution is embedded in the learning algorithm to provide physical predictions that conserve the total probability. We enforce conservation laws while reproducing the complex features of the surrogate model (i.e., a sharply peaked, long-tailed distribution) by including the uncertainty on the data. This model outputs predictions on the drop-size distribution with confidence intervals. The work opens up opportunities for data-driven surrogate modelling and optimization of atomizers.