Channel flow over large cube roughness: a direct numerical simulation study

Abstract

Computations of channel flow with rough walls comprising staggered arrays of cubes having various plan area densities are presented and discussed. The cube height h is 12.5 % of the channel half-depth and Reynolds numbers (u τ h/ν) are typically around 700 -well into the fully rough regime. A direct numerical simulation technique, using an immersed boundary method for the obstacles, was employed with typically 35 million cells. It is shown that the surface drag is predominantly form drag, which is greatest at an area coverage around 15 %. The height variation of the axial pressure force across the obstacles weakens significantly as the area coverage decreases, but is always largest near the top of the obstacles. Mean flow velocity and pressure data allow precise determination of the zero-plane displacement (defined as the height at which the axial surface drag force acts) and this leads to noticeably better fits to the log-law region than can be obtained by using the zero-plane displacement merely as a fitting parameter. There are consequent implications for the value of von Kármán's constant. As the effective roughness of the surface increases, it is also shown that there are significant changes to the structure of the turbulence field around the bottom boundary of the inertial sublayer. In distinct contrast to twodimensional roughness (longitudinal or transverse bars), increasing the area density of this three-dimensional roughness leads to a monotonic decrease in normalized vertical stress around the top of the roughness elements. Normalized turbulence stresses in the outer part of the flows are nonetheless very similar to those in smooth-wall flows.

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

“…The roughness length results, in figure 8(a), closely follow the skin friction trends as a function of both the solidities, as shown in table 1. The drag-peak location herein is partially in contrast with previous studies, for which it was found at λ P ≡ λ F ≈ 0.15 (Hagishima et al 2009;Leonardi & Castro 2010;Kanda et al 2004) and λ P ≡ λ F ≈ 0.16 (Santiago et al 2008;Coceal & Belcher 2004). These differences are perhaps not surprising giving the high uncertainty in the fitting procedure which results in the visible scatter of the data for different studies in figure 8(a), even when values of similar frontal and plan solidity are considered.…”

“…It is clearly visible in figure 9(b) that the virtual origin increases with an increase in plan solidity till it approaches its asymptote at d = h. The latter is qualitatively consistent with previous studies which have shown that the zero plane displacement tends to assume larger values (i.e. d tends to h) as the plan solidity increases (Kanda et al 2004;Hagishima et al 2009;Leonardi & Castro 2010). This trend is also consistent with the predictions from Macdonald (1998).…”

“…It is shown in figures 8(a) & (b) that the behaviour of the roughness length as a function of frontal and plan solidity is drastically different. Figure 8(a) shows that the roughness length (which is related to the total drag) increases in the sparse regime, and indicates a marginal decrease after the peak for increased values of frontal solidity, as in Leonardi et al (2003) and Leonardi & Castro (2010). Within the range of solidity explored herewith, the bulk drag seems to reach a peak at λ F = 0.21 for a fixed λ P = 0.27.…”

“…Dashed line represents λF ≡ λP (cubes), dot-dashed line represents variation of λP at fixed λF and dotted line stands for variation of λF at fixed λP . Filled symbols indicate the current experiment while empty symbols indicate respectively • Kanda et al (2004), ♦ Hagishima et al (2009) and Leonardi & Castro (2010). A cut along the dashed in figure (a) is presented in (b).…”

Selected Spectral Characteristics of Turbulence over an Urbanized Area in the Centre of Łódź, Poland

“…The constants a i estimated in this way for Łódź are close to those given by Kaimal et al (1972) Oncley et al 1996;Frenzen and Vogel 2001;Andreas et al 2006;Li et al 2008;Leonardi and Castro 2010;Kanda et al 2013) suggest that κ could be lower than 0.4, especially over rough surfaces (κ decreases with increasing roughness Reynolds number). The Kolmogorov constant, α u , also ranges from 0.36 to 0.56 (Högström 1990), which introduces additional imprecision in the estimation of φ ε (0).…”