Abstract
We perform large-eddy simulations of turbulent flow in a channel constricted by streamwise periodically distributed hill-shaped protrusions. Two Reynolds number cases, i.e. $Re_h=10\,595$ (Fröhlich et al., J. Fluid Mech., vol. 526, 2005, pp. 19–66) and $Re_h=33\,000$ (Kähler et al., J. Fluid Mech., vol. 796, 2016, pp. 257–284), are repeated and utilized to verify and validate our numerical results, including the pressure and skin friction coefficients on bottom and top walls of the channel, mean velocity profiles and Reynolds stresses. All comparisons show reasonable agreement, providing a measure of validity that enables us to further probe simulation results at higher Reynolds number ($Re_h=10^5$) into aspects of flow physics that are not available from experiments. Effects of variation of Reynolds number are studied, with emphasis on the mean skin friction coefficients, separation bubble size and pressure fluctuations that are related to separation and reattachment. In addition, the main large-scale features of the separation behind the hill, including the scaling of the mean velocity profiles, are discussed. Furthermore, the instantaneous near-wall flow field is analysed in terms of skin friction portraits, and we confirm the existence of the local very small separation bubble on the hill crest as observed in experimental and numerical investigations. The flow field at the top wall, which is generally not given sufficient attention, is evaluated with the empirical friction law and universal logarithmic law as in planar channel flows. It is found that these empirical laws compare well with the large-eddy simulation results, although the hill constrictions behave as a perturbation source and the developed shear layer has some effects on the flow field near the top wall.