Assimilating experimental data of a mean three-dimensional separated flow using physics-informed neural networks

In this article, we address the capabilities of physics-informed neural networks (PINNs) in assimilating the experimentally acquired mean flow of a turbulent separation bubble occurring in a diffuser test section. The training database contains discrete mean pressure and wall shear-stress fields measured on the diffuser surface as well as three-component velocity vectors obtained with particle image velocimetry throughout the volumetric flow domain. Imperfections arise from the measurement uncertainty and the inability to acquire velocity data in the near-wall region. We show that the PINN methodology is suited to handle both of these issues thanks to the incorporation of the underlying physics that, in the present study, are taken into account by minimizing residuals of the three-dimensional incompressible Reynolds-averaged Navier–Stokes equations. As a result, measurement errors are rectified and near-wall velocity profiles are predicted reliably. The latter benefits from the incorporation of wall shear-stress data into the PINN training, which has not been attempted so far to the best of our knowledge. In addition to demonstrating the influence of this novel loss term, we provide a three-dimensional, highly resolved, and differentiable model of a separating and reattaching flow that can be readily used in future studies.