Refined cf relation for turbulent channels and consequences for high-Re experiments

Abstract

There have been rising concerns regarding the accuracy of measurements in turbulent channel flows, in particular, measurements of the skin-friction results. In the present study, two different methods, namely, mean streamwise pressure gradient (PG) and oil film interferometry (OFI), are used to estimate the wall skin-friction relation, cf = f(Rem), for fully developed turbulent plane-channel flow over a wide range of Reynolds numbers. The channel skin-friction data are then fitted to the well-known logarithmic friction law, providing outstanding agreement with values for the constants of the logarithmic law of the mean velocity profile. A revised logarithmic skin-friction relation is developed, providing good agreement with our skin-friction results and data from the literature, when constants of the logarithmic friction relation adopted from the recent work of Zanoun et al (2003 Phys. Fluids 15 3079–89, 2005 4th Int. Conf. on Heat Transfer, Fluid Mechanics and Thermodynamics, HEAT2005, 19–22 September, Cairo, Egypt) are utilized. A new experimental channel facility is proposed, allowing measurements at high Reynolds numbers well beyond those achieved previously in laboratories, i.e. over five times the highest Rem reached in the present study, while maintaining sufficiently high spatial resolution.