New insight into flow development and two dimensionality of turbulent channel flows

Abstract

The experimental conditions required for a turbulent channel flow to be considered fully developed and nominally two dimensional remain a challenging objective. In this study, we show that the flow obtained in a high-aspect-ratio channel facility cannot be reproduced by direct numerical simulations (DNSs) of spanwise-periodic channel flows; therefore, we reserve the term “channel” for spanwise-periodic DNSs and denote the experimental flow by the term “duct.” Oil film interferometry (OFI) and static pressure measurements were carried out over the range \(200 < Re_{\tau } < 900\) in an adjustable-geometry duct flow facility. Three-dimensional effects were studied by considering different aspect ratio (AR) configurations and also by fixing the AR and modifying the hydraulic diameter \(D_{\mathrm{H}}\) of the section. The conditions at the centerplane of the duct were characterized through the local skin friction from the OFI and the centerline velocity at four different streamwise locations and through the wall shear based on the streamwise global pressure gradient. The skin friction obtained from pressure gradient overestimated the local shear measurements obtained from the OFI and did not reproduce the same AR dependence observed with OFI. Differences between the local and global techniques were also reflected in the flow development. For the range of Reynolds numbers tested, the development length of high-aspect-ratio ducts scales with the duct full-height \(H\) and is around \(200H\), much larger than the values of around 100–150H previously reported in the literature.