Data Assimilation of Transitional and Separated Turbomachinery Flows With Physics-Informed Neural Networks

Abstract Despite the demonstrated utility of Reynolds-averaged Navier–Stokes (RANS) calculations for many industrially relevant problems, the method yields unsatisfactory representations of many flows of engineering interest, such as nonequilibrium turbulence, massive flow separation, coherent unsteadiness, and secondary flow features. Due to the Reynolds-averaging process, a turbulence model is required to close the RANS equations, and the simple physical arguments and approximations used in many turbulence models can cause erroneous results when applied to the flows that feature strong pressure gradients, sudden changes in mean-strain-rate, surface curvature, and turbulence anisotropy. Physics-informed neural networks (PINNs) offer a way to model aerodynamic problems without explicitly requiring turbulence closure. The network can use sparse training data and unclosed RANS equations to reconstruct the flow without a turbulence model. In this work, PINNs are applied to two problems of relevance in the turbomachinery community. First, we consider a variable area channel known as the periodic hills, which features a shear layer, a separation bubble, as well as favorable and adverse pressure gradients. Second, a PINN is applied to the T106C low-pressure turbine blade with two different levels of inlet turbulence intensity, featuring the additional challenges of transition and laminar separation. We demonstrate that PINNs are capable of modeling wall-bounded quantities such as Cf and Cp in such complex flows, capturing sensitive features such as the change in separation length when the turbulent inlet conditions are altered. This article undertakes a considered and pragmatic assessment of the state of PINNs when applied to complex high Reynolds number flows, highlighting where the method is comparable to the quality of high-fidelity simulations, and conversely where the method degrades with a lack of training data around regions of interest.