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

This paper reports an algorithm for measuring the time-averaged skin friction vector field τ¯(X) starting from time-resolved temperature maps, acquired by a functional coating of temperature-sensitive paint. 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 U¯T(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 τ¯(X) 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¯τ(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’, 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¯τ(X) in the proposed context.