Low-Reynolds-number turbulent boundary layers

Abstract

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.