Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers

Abstract

Turbulent boundary layer measurements above a smooth wall and sandpaper roughness are presented across a wide range of friction Reynolds numbers, δ + 99 , and equivalent sand grain roughness Reynolds numbers, k + s (smooth wall: 2020 δ + 99 21 430, rough wall: 2890 δ + 99 29 900; 22 k + s 155; and 28 δ + 99 /k + s 199). For the rough-wall measurements, the mean wall shear stress is determined using a floating element drag balance. All smooth-and rough-wall data exhibit, over an inertial sublayer, regions of logarithmic dependence in the mean velocity and streamwise velocity variance. These logarithmic slopes are apparently the same between smooth and rough walls, indicating similar dynamics are present in this region. The streamwise mean velocity defect and skewness profiles each show convincing collapse in the outer region of the flow, suggesting that Townsend's (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) wall-similarity hypothesis is a good approximation for these statistics even at these finite friction Reynolds numbers. Outer-layer collapse is also observed in the rough-wall streamwise velocity variance, but only for flows with δ + 99 14 000. At Reynolds numbers lower than this, profile invariance is only apparent when the flow is fully rough. In transitionally rough flows at low δ + 99 , the outer region of the inner-normalised streamwise velocity variance indicates a dependence on k + s for the present rough surface.

Large-eddy simulation and modelling of Taylor–Couette flow

“…When (u θ u θ ) + is plotted versus r + , all present LES with η = 0.909 show an inner peak in the range 10 < r + < 15. This is consistent with the peak location at r + ≈ 12 in TC flow experiments with η = 0.716 and with Reynolds number up to 1.5 × 10 6 (Huisman et al 2013), with a peak location at about y + ≈ 15 in experiments of boundary layer flows up to Re τ = 21, 430 (Squire et al 2016) and with super-pipe experiments up to Re τ = 98, 187 (Hultmark et al 2012). DNS of channel flow (Lee & Moser 2015) shows a weak increase in the location of the peak value of turbulent intensities from y + ≈ 15.0 at Re τ = 1, 000 to y + ≈ 15.6 at Re τ ≈ 5, 200.…”

Investigation of the flow inside an urban canopy immersed into an atmospheric boundary layer using laser Doppler anemometry

“…This trend is supported by the results of Squire et al (2016) who compared the interaction mechanisms in a smooth wall turbulent boundary layer and in a sand-rough boundary layer, in the framework of the MMH model (Marusic et al 2010). It was found that the presence of a sand-rough wall reduces the linear interactions mechanisms (superposition mechanism) and enhanced the non-linear interactions (via an amplitude modulation mechanism).…”

Turbulent flow over a long flat plate with uniform roughness

“…It is possible to find proof of this tendency in the literature. Figure 3 shows data from [12] for smooth and rough surfaces (P36 grit sandpaper). Figure 3(b) shows the boundary-layer thickness at x = 21.7 m downstream of the inlet to the working section (δ 21.7 ) for both the smooth and rough surfaces as a function of the freestream velocity U ∞ .…”

“…(9) and (4). It should be noted that the experiments of [12] are unique in the sense that (i) they studied a high-Reynolds-number boundary layer [we note from Fig. 1 that Re x ≈ O(10 7 ) is required to observe constant C f at fixed k s /x], (ii) they used an independent and accurate measurement of C f using a floating plate drag balance, (iii) they had a sufficiently small blockage k/δ such that assumptions of outer layer similarity (and assumptions about the logarithmic form of the mean velocity profile) were unlikely to be violated, (iv) they employed testing at fixed x and multiple different unit Reynolds numbers U ∞ /ν, and (v) they presented boundary-layer thickness data in tabulated form.…”