Skin-friction from temperature and velocity data around a wall-mounted cube

Abstract

This paper reports an algorithm for measuring the time-averaged skin friction vector field starting from time-resolved temperature maps, acquired by a functional coating of Temperature Sensitive Paint (TSP). The algorithm is applied to a large area around a wall-mounted cube, immersed in the turbulent boundary layer over a flat plate. The method adopts a relaxed version of the Taylor Hypothesis operating on time-resolved maps of temperature fluctuations T' measured on the slightly warmer bounding surface. The procedure extracts UT(X), the celerity of displacement of T', as the best approximation of the forecasting provided by the frozen turbulence assumption near the wall, where its rigorous application is inappropriate. The skin friction estimation is based on the hypothesis of a linear relationship between U_T (X) and U_U(X), chained to the one between U_U(X) and U_{tau}(X). We assess the outcomes of the proposed algorithm against those derived by the 2D and 3D Lagrangian particle tracking (LPT) methodology ’Shake-The-Box’ (STB), whose advent has made available high-quality near-wall flow field information. Furthermore, data from high-density 2D time-resolved LPT allows exploring the suitability of the linear relationships chain between U_T(X) and U_{tau}(X) in the proposed context.