Turbulence closure in Reynolds-averaged Navier–Stokes and flow inference around a cylinder using physics-informed neural networks 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 ( $3900$ – $100\,000$ ) and Mach numbers ( $0$ – $0.3$ ), encompassing incompressible and weakly compressible regimes, with the goal of improving predictions of mean velocity and Reynolds forces. 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 direct numerical simulation and large eddy simulation. 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 and the numerical solver OpenFOAM, significantly improves RANS predictions of both mean flow and turbulence statistics relative to conventional models.