Data-driven surrogate modeling of multiphase flows using machine learning techniques

This study focuses on the development of a theoretical framework and corresponding algorithms to establish spatio-temporal surrogate models for multiphase flow processes using Gaussian process (GP) based machine learning technique trained by direct numerical simulation (DNS) data. The training (and testing) datasets are obtained by solving the incompressible form of the Navier Stokes equations with surface tension in an Eulerian reference frame. The liquid-gas interfacial evolution is resolved using a volume-of-fluid (VOF) interface capturing method. The overall framework proceeds in four steps: 1) design of experiments study to identify the training and testing points and generation of corresponding datasets using DNS calculations; 2) dimensionality reduction using proper orthogonal decomposition; 3) Gaussian process regression (supervised training) over the reduced training dataset over the entire range of operating conditions under consideration; and 4) Galerkin reconstruction and error quantification by comparing the emulated flowfields (at test conditions) with the testing dataset. The machine learning framework predicts both the spatial basis-functions and the time-coefficients, thus, predicting the entire flowfield in time and space. The capabilities of the algorithm are demonstrated for two canonical flow configurations: 1) flow over a circular cylinder for a range of Reynolds numbers from 10 to 200; and 2) diesel jet injected into a quiescent nitrogen 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 gas-based 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; average error (in both space and time) at the testing point of Re = 185 for the flow over cylinder case is 4.4%, and for the diesel jet injection configuration at a testing point corresponding to velovity of 22.5 m/s is found to be 15.5%. The tip penetration location of the diesel jet is predicted within 2.5% of the DNS calculations. Corresponding to these two representative test points, speedup of 256 and 8000 is achieved for flow over cylinder and diesel jet atomization configurations, respectively. This paper represents the first effort of its kind on the development of a general machine learning framework to predict multiphase flows. (C) 2020 Elsevier Ltd. All rights reserved.