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 ΔU^+(k^+_(s∞)) that depends on some geometric roughness height k_(s∞) 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 Re_b based on the bulk flow speed in the range 10^4–10^(10) with the equivalent Re_τ, based on the wall-drag velocity u_τ varying from 650 to 10^8. Results include a Moody-like diagram for the friction factor f = f(Re_b, ∈), ∈ = k_(s∞)/δ, mean velocity profiles, and turbulence statistics. In the fully rough regime, at sufficiently large Re_b, 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 u_τ 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 u_τ are bounded above by the sum of a logarithmic profile plus a finite function across the whole channel suggests that the infinite Re_b 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.

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