Law of incipient separation for turbulent flows over airfoils as inferred by RANS

Lu, Aithal & Ferrante (AIAA J., 2021) discovered a law that predicts the incipience of flow separation over curved ramps by knowing only a few geometrical parameters of the ramp and the Reynolds number of the flow. In that spirit, we have discovered a similar law for airfoils by performing Reynolds averaged Navier-Stokes (RANS) simulations of incompressible turbulent flows over thirty-two NACA airfoils. First, we have carried out verification and validation of RANS against the experimental measurements by A. J. Wadcock (NASA-CR 177450, 1987) which show the accuracy of the RANS prediction at small angles of attack when flow separation begins to occur on the upper side of the airfoil. Then, we have investigated the effects of the angle of attack, airfoil thickness, and camber on the incipience of flow separation for Reynolds number based on airfoil chord Re_c∈[1.64×10⁶, 6×10⁶]. From the analysis of the RANS results, we have determined a law for predicting the incipience of turbulent flow separation over airfoils that relies only on airfoil's newly defined characteristic slope, thickness, camber and Re_c (Huang, Aithal & Ferrante, Phys. Fluids, 2022).