Experimental quantification of unsteady leading-edge flow separation

We propose here a method to experimentally quantify unsteady leading-edge flow separation on aerofoils with finite thickness. The methodology relies on the computation of a leading-edge suction parameter based on measured values of the 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 leading-order approximation of the definition of the leading-edge suction parameter is proven to be sufficiently accurate for the application to thin aerofoils such as the NACA0009 without a-priori knowledge of the stagnation point location. The higher-order terms including the stagnation point location are required to reliably compute the leading-edge suction parameter on thicker aerofoils such as the NACA0015. The computation of the leading-edge suction parameter from inviscid flow theory does not assume the Kutta condition to be valid at the trailing edge which allows us to compute its value for separated flows. The relation between the leading-edge suction parameter and the evolution of the shear layer height is 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. We demonstrate here that the instantaneous value of the leading-edge suction parameter based on the partial circulation around the leading edge is unambiguously defined for a given flow field and can serve as a directly quantitative measure of the degree of unsteady flow separation at the leading edge.Comment: 21 pages, 9 figures, first revision submitted to Journal of Fluid Mechanics on 11th February 202