Two-Layer Wall Model for Large-Eddy Simulations of Mow over Rough Surfaces

Two-layer zonal near-wall treatment for flow over rough surfaces is proposed in a generalized coordinate large-eddy simulation framework. Rotta's [Rotta, J. C., "Turbulent Boundary Layers in Incompressible Flow," Progress in Aeronautical Sciences, Vol. 2, 1962, pp. 1-220.] approach to amplify the mixing length near the wall is used to model the eddy viscosity in the inner layer. Calculations are performed in a rod-roughened channel at high flow Reynolds numbers in the range of 6000 to 56,000 and in the fully rough regime. An equivalent sand-grain roughness is used to correlate the amplification in the wall shear stress with the roughness geometry. The roughness wall model predicts the skin-friction coefficient and the mean velocity profile, in close agreement with experiments. Turbulence statistics are also predicted with good accuracy. For the lowest Reynolds number investigated in the current study, the spatial resolution required by wall-modeled large-eddy simulation is three orders of magnitude smaller than with a direct simulation on the same geometry that resolves the roughness elements. This results in large savings in computational cost.