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.