The Effect of Training Data on Predicting Turbulent Flow Through a Linear Cascade Using Physics-Informed Neural Networks

Abstract This article investigates the effect of training data on the accuracy of turbulent flow predictions in the wake region of a linear turbine cascade using physics-informed neural networks (PINNs). While it is well known that PINNs can solve the unclosed Reynolds-averaged Navier–Stokes (RANS) equations when sufficient training data are available, the specific characteristics of the data—such as the quantity and location—required for accurate predictions remain largely uncertain. To explore this, a PINN is constructed to solve the unclosed compressible RANS equations, leveraging training data from a computational fluid dynamics (CFD) solution of a turbine blade. The training data are then selectively sampled with future optical test campaigns in mind. This sampling includes varying the pitchwise surveys with evenly spaced training points, randomly sampled points, and CFD-guided sampling. For each case, the PINN is trained on data for the velocity components, temperature, pressure, and Reynolds stresses. A good agreement is seen between the PINNs-predicted quantities and the CFD solution, even in areas where the PINN was not provided training data and excellent agreement in regions where data were provided. It is shown that the PINN can provide acceptable solutions to the unclosed compressible RANS equations with roughly 100 data points downstream of the blade, and even better results when provided with roughly 200 points. This shows promise for future test campaigns that seek to combine artificial intelligence-based tools with experimental techniques.