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

The law of incipient separation over ramps by Lu, Aithal & Ferrante (AIAA J., 2021) requires the knowledge of only few geometrical parameters of the ramp and the Reynolds number of the incoming flow. In that spirit, we have performed two-dimensional RANS wall-resolved simulations of incompressible turbulent flows over airfoils. We have also developed a new grid generation method, and have carried out verification and validation of RANS using the Spalart-Allmaras model against the experimental measurements by Wadcock (NASA-CR-177450, 1987) for a NACA4412 airfoil at Re_c = 1.64×10⁶. From such comparison, we have found that although the RANS prediction fails at α≧13^○, the incipient separation occurs at only α≅1^○.Thus, we have investigated the effects of angle of attack, airfoil thickness, and camber on the incipiency of flow separation for eleven different airfoils and Re_c ∈[1.64×10⁶, 6×10⁶]. From the RANS results, we have determined a law for predicting incipient turbulent flow separation that relies only on a few key airfoil's geometrical parameters and the Reynolds number of the flow.