Large eddy simulation of smooth–rough–smooth transitions in turbulent channel flows

Abstract

We describe a high Reynolds number large-eddy-simulation (LES) study of turbulent flow in a long channel of length 128 channel half heights, δ, with the walls consisting of roughness strips where the long stream-wise extent invites a full relaxation of the mean velocities within each strip. The channel is stream-wise periodic and strips are oriented transverse to the flow resulting in repeated transitions between smooth and rough surfaces along the stream-wise direction. The present LES uses a wall model that contains Colebrook's empirical formula as a roughness correction to both the local and dynamic calculation of the friction velocity and also the LES wall boundary condition. This operates point-wise across wall surfaces, and hence changes in the outer flow can be viewed as a response to the temporally and/or spatially variant roughness distribution. At the wall surface, dynamically calculated levels of time- and span-wise-averaged friction velocity u_τ[bar](x) over/undershoot and then fully recover towards their smooth or rough state over a stream-wise distance of order 10–30 δδ depending on both roughness and Reynolds number. Also, the initial response rate in u_τ[bar] shows Reynolds number and roughness dependence over both transitions. The growth rate of the internal boundary layer (IBL), defined by the abrupt change in stream-wise turbulent intensity, is found to grow as x^0.70 on average over multiple simulation conditions for the case of a smooth-to-rough transition, which agrees with the experimental results of Antonia and Luxton (1971) [1] and Efros and Krogstad (2011) [2]. IBL profiles demonstrate a good collapse on δ/log(Re^(*)_(τ)), where View the Re^(*)_(τ) is the local Reynolds number based on u_τ[bar] at the point of full recovery.

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