Impact of spanwise effective slope upon rough-wall turbulent channel flow

Abstract

Whereas streamwise effective slope ( $ES_{x}$ ) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart ( $ES_{y}$ ) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of $ES_{y}$ is studied using direct numerical simulation. All simulations were performed at a fixed friction Reynolds number 395, corresponding to a viscous-scaled roughness height $k^{+}\approx 65.8$ (where $k$ is the mean peak-to-valley height). A surface generation algorithm is used to synthesise a set of ten irregular surfaces with specified $ES_{y}$ for three different values of $ES_{x}$ . All surfaces share a common mean peak-to-valley height and are near-Gaussian, which allows this study to focus on the impact of varying $ES_{y}$ , since roughness amplitude, skewness and $ES_{x}$ can be eliminated simultaneously as parameters. Based on an analysis of first- and second-order velocity statistics, as well as turbulence co-spectra and the fractional contribution of pressure and viscous drag, the study shows that $ES_{y}$ can strongly affect the roughness drag penalty – particularly for low- $ES_{x}$ surfaces. A secondary observation is that particular low- $ES_{y}$ surfaces in this study can lead to diminished levels of outer-layer similarity in both mean flow and turbulence statistics, which is attributed to insufficient scale separation between the outer length scale and the in-plane spanwise roughness wavelength.

Effect of high skewness and kurtosis on turbulent channel flow over irregular rough walls

“…For the positively skewed cases, which result all in approximately in the same value for the roughness function, a higher scatter can be seen in the relationship between U + and F p /F tot . An approximately linear dependency between the fractional contribution of the pressure drag and the roughness function has previously been observed for irregular rough surfaces with different streamwise and spanwise effective slopes and approximately Gaussian height distributions [47].…”

“…To associate physical mechanisms to changes in the Hama roughness function (Figure 5(a)), the total drag force was partitioned into its pressure and viscous components. After some manipulation, the mean pressure and viscous forces per unit area acting on the surface can be expressed as [47]…”

Direct numerical simulation of turbulent flow in pipes with realistic large roughness at the wall

“…Owing to the large relative roughness, the fields do not show any symmetry, thus confirming that for R/k 40 the effect of the wall is felt throughout the wall layer (Jiménez 2004). Furthermore, according to Chung et al (2021) and Jelly et al (2022), the diameter and the strength of the secondary flows is sensitive to the spanwise length scale of the roughness in proportion to the outer scale of the problem, say δ. Specifically, Chung et al (2021) state that the diameter of the secondary flows is about δ when the spanwise wavelength of the roughness matches or exceeds the outer scale, here the pipe radius.…”

Direct numerical simulation of Taylor–Couette flow with vertical asymmetric rough walls

“…2021; Jelly et al. 2022) and reviews (Flack & Schultz 2014; Chung et al. 2021) have explored the effects of wall roughness in (pipe or channel) turbulence.…”

“…Nikuradse (1933) was the first to study how local wall roughness (sand glued to the wall) affects global transport properties in pipe flow. Since then, numerous studies (Chan et al 2018;Rouhi, Chung & Hutchins 2019;Ma et al 2020;Modesti et al 2021;Jelly et al 2022) and reviews (Flack & Schultz 2014;Chung et al 2021) have explored the effects of wall roughness in (pipe or channel) turbulence. Instead of using open-channel or pipe flow with rough walls, we employ a Taylor-Couette (TC) apparatus, which is a closed system with an exact balance between energy input and dissipation.…”