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 \(\overline{\pmb {\tau }}(\pmb {X})\) $\overline{\mathit{\tau }}(\mathit{X})$ 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 \(T'\) $T^{\prime }$ measured on the slightly warmer bounding surface. The procedure extracts \({\overline{U}}_T(\pmb {X})\) ${\overline{U}}_T(\mathit{X})$ , the celerity of displacement of \(T'\) $T^{\prime }$ , as the best approximation of the forecasting provided by the frozen turbulence assumption near the wall, where its rigorous application is inappropriate. The \(\overline{\pmb {\tau }}(\pmb {X})\) $\overline{\mathit{\tau }}(\mathit{X})$ estimation is based on the hypothesis of a linear relationship between \({\overline{U}}_T(\pmb {X})\) ${\overline{U}}_T(\mathit{X})$ and \({\overline{U}}_U(\pmb {X})\) ${\overline{U}}_U(\mathit{X})$ , chained to the one between \({\overline{U}}_U(\pmb {X})\) ${\overline{U}}_U(\mathit{X})$ and \({\overline{U}}_\tau (\pmb {X})\) ${\overline{U}}_{\tau }(\mathit{X})$ . 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 \({\overline{U}}_T(\pmb {X})\) ${\overline{U}}_T(\mathit{X})$ and \({\overline{U}}_\tau (\pmb {X})\) ${\overline{U}}_{\tau }(\mathit{X})$ in the proposed context.