Design Space Exploration of Turbulent Multiphase Flows Using Machine Learning-Based Surrogate Model

This study focuses on establishing a surrogate model based on machine learning techniques to predict the time-averaged spatially distributed behaviors of vaporizing liquid jets in turbulent air crossflow for momentum flux ratios between 5 and 120. This surrogate model extends a previously developed Gaussian-process-based framework applicable to laminar flows to accommodate turbulent flows and demonstrates that in addition to detailed fields of primitive variables, second-order turbulence statistics can also be predicted using machine learning techniques. The framework proceeds in 3 steps—(1) design of experiment studies to identify training points and conducting high-fidelity calculations to build the training dataset; (2) Gaussian process regression (supervised training) for the range of operating conditions under consideration for gaseous and dispersed phase quantities; and (3) error quantification of the surrogate model by comparing the machine learning predictions with the truth model for test conditions (i.e., conditions not used for training). The framework was trained using data generated by high-fidelity large eddy simulation (LES)-based calculations (also referred to as the truth model), which solves the complete set of conservation equations for mass, momentum, energy, and species in an Eulerian reference frame, coupled with a Lagrangian solver that tracks the dispersed phase. Simulations were conducted for the range of momentum flux ratios between 5 and 120 for liquid water injected into crossflowing air at a pressure of 1 atm and temperature of 600 K. Results from the machine-learned surrogate model, also called emulations, were compared with the truth model under testing conditions identified by momentum flux ratios of 7 and 40. L1 errors for time-averaged field quantities, including velocity magnitudes, pressure, temperature, vapor fraction of the evaporated liquid, and turbulent kinetic energy in the gas phase, and spray penetration and Sauter mean diameters in the dispersed phase are reported. Speedup of 65 was achieved with this emulator when compared against LES simulation of the same test conditions with errors for all quantities below 14%, thus demonstrating the potential benefits of using machine learning techniques for design space exploration of devices that are based on turbulent multiphase fluid flows. This is the first effort of its kind in the literature that demonstrates the application of machine learning techniques on turbulent multiphase flows.