Large eddy simulation of smooth-wall, transitional and fully rough-wall channel flow

Abstract

Large eddy simulation (LES) is reported for both smooth and rough-wall channel flows at resolutions for which the roughness is subgrid. The stretched vortex, subgrid-scale model is combined with an existing wall-model that calculates the local friction velocity dynamically while providing a Dirichlet-like slip velocity at a slightly raised wall. This wall model is presently extended to include the effects of subgrid wall roughness by the incorporation of the Hama's roughness function \documentclass[12pt]{minimal}\begin{document}$\Delta U^+(k_{s\infty }^+)$\end{document}ΔU+(ks∞+) that depends on some geometric roughness height ks∞ scaled in inner variables. Presently Colebrook's empirical roughness function is used but the model can utilize any given function of an arbitrary number of inner-scaled, roughness length parameters. This approach requires no change to the interior LES and can handle both smooth and rough walls. The LES is applied to fully turbulent, smooth, and rough-wall channel flow in both the transitional and fully rough regimes. Both roughness and Reynolds number effects are captured for Reynolds numbers Reb based on the bulk flow speed in the range 104–1010 with the equivalent Reτ, based on the wall-drag velocity uτ varying from 650 to 108. Results include a Moody-like diagram for the friction factor f = f(Reb, ε), ε = ks∞/δ, mean velocity profiles, and turbulence statistics. In the fully rough regime, at sufficiently large Reb, the mean velocity profiles show collapse in outer variables onto a roughness modified, universal, velocity-deficit profile. Outer-flow stream-wise turbulence intensities scale well with uτ for both smooth and rough-wall flow, showing a log-like profile. The infinite Reynolds number limits of both smooth and rough-wall flows are explored. An assumption that, for smooth-wall flow, the turbulence intensities scaled on uτ are bounded above by the sum of a logarithmic profile plus a finite function across the whole channel suggests that the infinite Reb limit is inviscid slip flow without turbulence. The asymptote, however, is extremely slow. Turbulent rough-wall flow that conforms to the Hama model shows a finite limit containing turbulence intensities that scale on the friction factor for any small but finite roughness.