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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, rod-like 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.
Highlights
Many forms of irregular roughness found on engineering surfaces display some degree of anisotropy
The flow statistics are further discussed in the context of visualisations of the local streamwise and spanwise dispersive and Reynolds stresses within the roughness canopy
Considering that all surfaces have been scaled to an identical mean peak-to-valley height and share near-Gaussian height distributions, the sharp rise in ΔU + underlines the impact that surface anisotropy can have upon the drag penalty incurred by a rough surface
Summary
Many forms of irregular roughness found on engineering surfaces display some degree of anisotropy. Anisotropic roughness is encountered on in-service turbine vanes [2], bio-fouled ship hulls [3] and can often be observed in geo- and astrophysical contexts, e.g. in the form of ripple-patterns, which for example affect sand-transporting winds on Mars [4]. In the direct numerical simulations (DNS) of Leonardi et al [9], the spacing of bars was shown to affect the coherence of the near-wall flow as well as the levels of turbulence anisotropy Another widely studied form of regular anisotropic roughness are wavy walls. In the experimental study of Hamed et al [10] fundamental differences for flow over two- and three-dimensional large-scale wavy walls were found that have practical implications for bed erosion and sediment transport
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