Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness

Abstract

The influence of surface anisotropy upon the near-wall region of a rough-wall turbulent channel flow is investigated using direct numerical simulation (DNS). A set of nine irregular rough surfaces with fixed mean peak-to-valley height, near-Gaussian height distributions and specified streamwise and spanwise correlation lengths were synthesised using a surface generation algorithm. By defining the surface anisotropy ratio (SAR) as the ratio of the streamwise and spanwise correlation lengths of the surface, we demonstrate that surfaces with a strong spanwise anisotropy (SAR <1) can induce an over 200% increase in the roughness function ΔU + , compared to their streamwise anisotropic (SAR >1) equivalent. Furthermore, we find that the relationship between the roughness function ΔU + and the SAR parameter approximately follows an exponentially decaying function. The statistical response of the near-wall flow is studied using a "double-averaging" methodology in order to distinguish form-induced "dispersive" stresses from their turbulent counterparts. Outer-layer similarity is recovered for the mean velocity defect profile as well as the Reynolds stresses. The dispersive stresses all attain their maxima within the roughness canopy. Only the streamwise dispersive stress reaches levels that are comparable to the equivalent Reynolds stress, with surfaces of high SAR attaining the highest levels of streamwise dispersive stress. The Reynolds stress anisotropy also shows distinct differences between cases with strong streamwise anisotropy that stay close to an axisymmetric, rodlike state for all wall-normal locations, compared to cases with spanwise anisotropy where an axisymmetric, disk-like state of the Reynolds stress anisotropy tensor is observed around the roughness mean plane. Overall, the results from this study underline that the drag penalty incurred by a rough surface is strongly influenced by the surface topography and highlight its impact upon the mean momentum deficit in the outer flow as well as the Reynolds and dispersive stresses within the roughness layer.

Investigation of rough-wall turbulence over barnacle roughness with increasing solidity using direct numerical simulations

“…The levels attained by the wall-normal dispersive stresses (see figure 10 (b)) are also significantly lower than for the corresponding Reynolds stresses, an observation that is consistent with results for other irregular rough surfaces [69,70]. It is noticeable that the peak values of the wall-normal stress and the levels sustained above the maximum barnacle height are higher for the lower coverage surfaces, especially the 15% and 30% coverage cases.…”

“…The peak spanwise Reynolds stresses (see figure 9 the peak location moves above the rough surface and a reduction of spanwise velocity fluctuations can be observed within the rough surface which is consistent with the decrease in the streamwise velocity fluctuations within the rough surface. In contrast to the results for the streamwise velocity component, the levels of the spanwise dispersive stresses are significantly lower, reaching peak values of less than 40% of the equivalent Reynolds stresses, which is comparable to the levels observed for other forms of irregular roughness [69,70]. As the coverage increases, the peak values first increase before attaining approximately constant levels for the 15% to 60% cases before decreasing again.…”

“…The depth of this minimum decreases with increasing coverage, and no negative values for − ũ w are observed for the higher coverage cases. While, typically, positive values − ũ w are reported for rough surfaces, negative values for − ũ w have been previously observed in other rough-wall related studies, see e.g., for flow over superhydrophobic surfaces with streamwise grooves [73] and for irregular rough surfaces with strong spanwise anisotropy [69].…”

Modelling of three-dimensional particle rebound from an anisotropic rough wall

“…In pure fluid turbulent flow, it has been found that surface anisotropy is an important parameter that influences skin friction and anisotropy of Reynolds stresses [6].…”

The Effects of Anisotropic Surface Roughness on Turbulent Boundary-Layer Flow

“…The case of isotropic roughness, where ES x = ES y , has been studied and extensively characterised for both regular [4] and irregular geometries [9]. Recent studies have shown that spanwise anisotropy strongly affects the near-wall region of the flow [2]. However, studies on the effect of anisotropy where the ratio ES x /ES y is systematically varied remain scarce.…”