Quantitative detection of unsteady leading-edge flow separation.

We propose here a method to quantitatively detect unsteady leading-edge flow separation on aerofoils with finite thickness. The methodology relies on a leading-edge suction parameter based on the inviscid flow theory and defined by a partial circulation around the leading-edge and the stagnation point location. We validate the computation of the leading-edge suction parameter for both numerical and experimental data under steady and unsteady flow conditions. The first-order approximation of the definition of the leading-edge suction parameter is proven to be sufficiently accurate for the application to thinner aerofoils such as the NACA0009 without a-priori knowledge of the stagnation point location. The second-order terms including the stagnation point location are required to reliably compute the leading-edge suction on thicker aerofoils such as the NACA0015. In our approach, we do not need to impose the Kutta condition at the trailing edge. This allows us to apply the method to separated flows and to connect the experimental measurements and the inviscid flow theory by the shear layer height. The relation between the evolution of the shear layer height and the leading-edge suction parameter are studied in two different unsteady flow conditions, a fixed aerofoil in a fluctuating free-stream velocity and a pitching aerofoil in a steady free-stream. The instantaneous value of the leading-edge suction parameter obtained through partial circulation is unambiguously defined for a given flow field and can serve a directly quantitative measure of the degree of unsteady flow separation at the leading edge.