Predicting the three-dimensional separating flow in a diffuser using physics-informed neural networks

We study the capabilities of physics-informed neural networks (PINNs) that are trained to capture the three-dimensional mean flow of a turbulent separation bubble that occurs inside a one-sided diffuser. The network output is constrained by the three-dimensional Reynolds-averaged Navier-Stokes equations on the one hand and an extensive experimental database on the other. The latter contains the mean wall pressure field on the diffuser surface as well as approximately 730,000 three-component velocity vectors spanning the entire flow domain. In addition, the mean two-component wall shear-stress field acquired on the diffuser surface is employed to assimilate the velocity gradient at the wall. It is shown that measurement artefacts pertaining to the velocity field data are rectified thanks to the physics-informed approach. Furthermore, the velocity can be predicted reliably in the near-wall region where no measurement data are available. Here, a PINN trained with wall shear-stress data showed a better performance than an alternative model where this data was not provided. Leveraging the training data at the boundaries of the flow domain, we also demonstrate that the complex three-dimensional velocity field can be reconstructed with reasonable accuracy requiring as few as 0.01 % of the velocity training dataset (i.e., only 100 vectors). This gives rise to less elaborate acquisitions of three-dimensional flow fields where extensive velocity field measurements can be substituted with a few single-point measurements.