Turbulence Closure in RANS and Flow Inference around a Cylinder using PINNs and Sparse Experimental Data

Traditional Reynolds-averaged Navier-Stokes (RANS) closures, based on the Boussinesq eddy viscosity hypothesis and calibrated on canonical flows, often yield inaccurate predictions of both mean flow and turbulence statistics. Here, we consider flow past a circular cylinder over a range of Reynolds numbers (3,900-100,000) and Mach numbers (0-0.3), encompassing incompressible and weakly compressible regimes, with the goal of improving predictions of mean velocity and Reynolds stresses. To this end, we assemble a cross-validated dataset comprising hydrodynamic particle image velocimetry (PIV) in a towing tank, aerodynamic PIV in a wind tunnel, and high-fidelity spectral element DNS and LES. Analysis of these data reveals a universal distribution of Reynolds stresses across the parameter space, which provides the foundation for a data-driven closure. We employ physics-informed neural networks (PINNs), trained with the unclosed RANS equations, to infer the velocity field and Reynolds-stress forcing from boundary information alone. The resulting closure, embedded in a forward PINN solver, significantly improves RANS predictions of both mean flow and turbulence statistics relative to conventional models.