Aerodynamic Properties of Rough Surfaces with High Aspect-Ratio Roughness Elements: Effect of Aspect Ratio and Arrangements

We examine the effect of varying roughness-element aspect ratio on the mean velocity distributions of turbulent flow over arrays of rectangular-prism-shaped elements. Large-eddy simulations (LES) in conjunction with a sharp-interface immersed boundary method are used to simulate spatially-growing turbulent boundary layers over these rough surfaces. Arrays of aligned and staggered rectangular roughness elements with aspect ratio >1 are considered. First the temporally- and spatially-averaged velocity profiles are used to illustrate the aspect-ratio effects. For aligned prisms, the roughness length (zo\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{o}$$\end{document}) and the friction velocity (u∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_*$$\end{document}) increase initially with an increase in the roughness-element aspect ratio, until the values reach a plateau at a particular aspect ratio. The exact value of this aspect ratio depends on the coverage density. Further increase in the aspect ratio changes neither zo\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{o}$$\end{document}, u∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_*$$\end{document} nor the bulk flow above the roughness elements. For the staggered cases, zo\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{o}$$\end{document} and u∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_*$$\end{document} continue to increase for the surface coverage density and the aspect ratios investigated. To model the flow response to variations in roughness aspect ratio, we turn to a previously developed phenomenological volumetric sheltering model (Yang et al., in J Fluid Mech 789:127–165, 2016), which was intended for low to moderate aspect-ratio roughness elements. Here, we extend this model to account for high aspect-ratio roughness elements. We find that for aligned cases, the model predicts strong mutual sheltering among the roughness elements, while the effect is much weaker for staggered cases. The model-predicted zo\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{o}$$\end{document} and u∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_*$$\end{document} agree well with the LES results. Results show that the model, which takes explicit account of the mutual sheltering effects, provides a rapid and reliable prediction method of roughness effects in turbulent boundary-layer flows over arrays of rectangular-prism roughness elements.