Learning time-averaged turbulent flow field of jet in crossflow from limited observations using physics-informed neural networks

Physics-informed neural networks (PINNs) are becoming popular in solving fluid mechanics problems forwardly and inversely. However, under limited observations, the application of PINNs was found to be difficult in solving the inverse problems of three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations. In this study, the classical turbulent case of jet in crossflow was representatively adopted into the investigation. The dataset was obtained from a high-fidelity large-eddy simulation. The tensor-basis eddy viscosity (t-EV) model was imported first into the structure of PINNs as prior knowledge. Observations of five measured planes were preliminarily used to reconstruct the time-averaged turbulent flow field. After embedding the t-EV model, the highest absolute error and the relative L2 error of streamwise velocity were reduced by 11.1% and 31.4%, respectively. To cut down the volume of limited observations, a more effective training dataset containing only two planes and two pairs of lines was determined based on the flow characteristics (e.g., shear layer and counter-rotating vortex pair). Compared with those of five planes, the highest absolute error and the relative L2 error of streamwise velocity were further reduced by 30.0% and 6.4%, respectively. The investigation in this study provided an alternative to resolve the inverse problems of three-dimensional RANS equations with limited observations, which extended the deep learning application in fluid mechanics.