Prediction of liquid jet atomization using Gaussian process based machine learning techniques

Abstract

This study focuses on the development of a framework to predict liquid jet atomization process using Gaussian Process (GP) based machine learning techniques. The machine learning algorithm is trained using results obtained from experimentally validated high-fidelity numerical simulations of diesel jet injected into a quiescent nitrogen environment in an Eulerian-Eulerian (E-E) framework. A volume-of-fluid interface capturing algorithm is used in the E-E formulation to treat the liquid-gas interface and adaptive mesh refinement technique is adopted to ensure computational efficiency. The overall algorithm proceeds in five steps: 1) experimentally validate high-fidelity numerical simulations; 2) extraction of dominant energetic modes, basis functions and corresponding time coefficients using proper orthogonal decomposition (POD) technique such that 99% of the energy content is captured; 3) training the Gaussian stochastic process using the modal data extracted from the POD analysis for the range of operating conditions under consideration; 4) prediction of energetic modes (basis functions and time coefficients) using the learned algorithm, within the bounds of the training range; and 5) prediction and error estimation of results from the learned algorithm for test conditions (not used in training) with numerical/experimental data. It should be noted that our machine learning framework can predict both the spatial basis functions and the time coefficients, thus, predicting the entire flowfield in time and space. Two test cases are considered to demonstrate the capabilities and robustness of the developed framework: 1) flow over a circular cylinder for a range of Reynolds numbers from 10 to 200; and 2) diesel injection in quiescent environment at chamber pressure of 30 atm and room temperature conditions, and injection velocities from 10 to 55 m/s, corresponding to a range of Weber numbers from 11.5 to 348. The emulations from the learned GP algorithm show excellent agreement with high-fidelity numerical data for test conditions for both, flow over a cylinder and diesel injection cases. The resulting GP emulator is expected to significantly improve the design process of devices based on multiphase flow processes, such as fuel injectors, by enabling otherwise unaffordable studies, including sensitivity analysis and uncertainty quantification, that are critical for the development of such devices.