Direct measurement of skin friction using TSP data

We provide a proof-of-concept about the direct measurement of skin friction ? by means of a TemperatureSensitive Paint (TSP). To this aim, the relationships between the time-resolved measure of the surface temperature Tw(x, y,t) below a turbulent boundary layer and the span- and time-averaged streamwise friction velocity u?(x) is firstly assessed. Then, the focus is placed on the turbulent region after the Laminar Separation Bubble (LSB) which develops on the suction side of a NACA 0015 hydrofoil model, investigated experimentally at chord Reynolds number Re = 1.8×105 and angle of attack AoA = 10o . At spatial scales of the order of the LSB width, almost steady thermal footprints Tw(x, y,t) of the fluid, slowly evolving around their averaged position, unveil a flow regime subject to small 2D disturbances. The LSB-induced spatial gradients of Tw(x, y,t) are linked to almost fixed positions in time and any evidence of three-dimensional disturbance is missing. At smaller spatial scales, the legs of the turbulent structures rubbing the surface (hairpin vortexes) impress their thermal footprint on the TSP while they propagate in the streamwise direction. They act like a tracer and their strong preferential streamwise orientation suggests the application of a two-points cross-correlation algorithm, whose maximum provides the time-lag ?t between the appearance of a disturbance at the two streamwise aligned locations, and thus the propagation velocity upT of the Tw perturbation T 0 w . The relationship between upT and the friction velocity u? feeds a physics-based criterion for the identification of span- and time-averaged separation xS and reattachment xR locations grounded on the sign of u? (and ?) itself. In the paper we report: o The relationship between the velocity of propagation of the velocity disturbances upU and the friction velocity u? o The relationship between the velocity of propagation of the temperature disturbances upT and upU o The algorithm for the extraction of the propagation velocity of temperature perturbations upT o The resulting friction velocity u? and friction coefficient Cf profiles