Investigation of Physics-Informed Neural Networks Based Solution Techniques for Internal Flows

Abstract In this work, we explore for the first time the possibility and potentials of employing the emerging PINNs approach in internal flow configurations, solving the steady state Euler equations in two dimensions for forward and inverse problems. In addition to a simple bump test case, the PINNs results of a highly loaded transonic linear turbine guide vane cascade are presented. For forward problems, we investigate different formulations of the transport equations and boundary conditions. Overall, PINNs approximate the solution with acceptable accuracy; however, conventional CFD methods are far superior in forward settings. Finally, we demonstrate the capabilities and the tremendous potentials of PINNs regarding hidden fluid mechanics in two distinct inverse settings, intractable for conventional CFD methods. Firstly, we infer complete flow fields based on partial, possible noisy, solution data, e.g., partial surface pressure and velocity field data; even approximating the exit condition of the cascade using only the measured blade pressure distribution is possible. Secondly, we also infer an unknown parameter of the governing equations.