Flow Inference and Turbulence Closure of Flow Past a Cylinder using PINNs and Data-Driven RANS Equations

Traditional Reynolds‐averaged Navier–Stokes (RANS) closures are tuned on canonical flows and often mispredict Reynolds stresses and forces in more complex configurations. We study flow past a circular cylinder over a broad range of Reynolds numbers in both incompressible and compressible regimes, with the aim of simultaneously improving estimates of Reynolds forces and the mean velocity field. We begin by assembling a diverse, high-quality, and well-validated dataset: hydrodynamic particle image velocity (PIV) in a towing tank, aerodynamic PIV in a wind tunnel, and high-fidelity spectral element DNS and LES. The Reynolds number range is 5,000-300,000, and the Mach number range is 0-0.8. We discovered a universal Reynolds‐stress distribution for cylinder flows across Reynolds and Mach numbers. This physical universality is the cornerstone for the generalization of the data-driven closure model. We then deploy physics‐informed neural networks (PINNs) with the unclosed form of the RANS equation to infer the full velocity field and the Reynolds‐force distribution based on limited data. We demonstrate that PINNs can accurately reconstruct flow fields from only boundary information. Finally, we map the inferred Reynolds forces into a data‐driven turbulence closure and integrate it into both the forward PINNs and the numerical solver OpenFOAM. The data-driven closure model embedded in the solver substantially improves RANS predictions of both turbulent forces and mean velocities.