Abstract
Large-eddy simulation has been used to model turbulent channel flow over a range of surfaces featuring a prominent spatial heterogeneity; the flow streamwise direction is aligned relative to the heterogeneity at a range of angles, defined herein with . Prior work has established that a sharp roughness heterogeneity orthogonal to the flow streamwise direction ( ) induces formation of an internal boundary layer, which originates at the heterogeneity and thickens in the downflow direction before being homogenized via ambient shear. In contrast, more-recent studies have shown that a sharp roughness heterogeneity parallel to the flow streamwise direction ( ) induces streamwise-aligned, Reynolds-averaged secondary cells, where the spacing between adjacent surface heterogeneities regulates the spatial extent of secondary cells. No prior study has addressed intermediate (oblique) cases, . Results presented herein show that the momentum penalty exhibits a nonlinear dependence upon obliquity, where internal boundary layer-like flow processes persist over a range of obliquity angles before abruptly vanishing for spanwise roughness heterogeneity ( ). This result manifests itself within effective roughness lengths recovered a posteriori: the traditional approach to roughness modelling – predicated upon dependence with surface geometric arguments including height root-mean-square, skewness, frontal- and plan-area index, effective slope. and combinations thereof – is insufficient. A revised model incorporating dependence upon roughness frontal area index and flow-heterogeneity obliquity angle is able to accurately predict effective roughness length a priori.
Highlights
Inertia-dominated rough-wall turbulence figures prominently in engineering and geophysical flows; in engineering flows, roughness affects thermal efficiency and aero-/hydro-dynamic performance of lifting surfaces, while roughness in geophysical flows affects, for example, land–atmosphere interactions and benthic sequestration rates in the ocean bottom-boundary layer
Beginning with figure 2(a), which corresponds with a canonical spanwise-heterogeneous roughness, there is a distinct pattern of downwelling and upwelling above relatively more and less rough regions of the surface, which has been widely reported in preceding studies under similar inertial conditions (Willingham et al 2013)
IBL dynamics has been the topic of substantial prior work: IBLs are a product of streamwise roughness heterogeneity, from low-to-high or high-to-low roughness, originate at the surface heterogeneity, and thicken in the downstream before homogenizing via ambient, background shear
Summary
Inertia-dominated rough-wall turbulence figures prominently in engineering and geophysical flows; in engineering flows, roughness affects thermal efficiency and aero-/hydro-dynamic performance of lifting surfaces, while roughness in geophysical flows affects, for example, land–atmosphere interactions and benthic sequestration rates in the ocean bottom-boundary layer. One can envision that scenarios wherein the flow is aligned precisely parallel (figure 1a) or orthogonal (figure 1e) to a roughness heterogeneity are likely the exception, not the norm: cases of practical importance in engineering and geophysics are expected to encounter roughness heterogeneities at oblique angles, i.e. 0 < θ < π/2. Nugroho, Hutchins & Monty (2013) have performed experimental measurement of turbulent boundary layer flow over a ‘herringbone’ roughness pattern, composed of riblets in a converging–diverging pattern; this work is one exception to the sparsity of prior efforts on oblique roughness. Previous work has established that that this spacing is optimal for maintaining δ-scale streamwise rolls; our sole focus was reconciling the flow response to variable obliquity for idealized cases. Results of resolution sensitivity testing are provided in Appendix, which demonstrate no discernible influence of computational mesh resolution
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