Large eddy simulations and parameterisation of roughness element orientation and flow direction effects in rough wall boundary layers

We conduct a series of large eddy simulations (LES) of turbulent boundary layers over arrays of cuboidal roughness elements at arbitrary orientation angles (non-frontal orientations with the incident flow). Flow response to changing roughness orientation is systematically studied at two ground coverage densities, λ_p = 0.06 and 0.11. As expected, the effective roughness heights z_o measured from LES are higher for λ_p = 0.11 than for λ_p = 0.06, although appreciable changes both in z_o and wall shear stress (friction velocity) are observed at both ground coverage densities as the roughness orientation angle changes. This suggests the necessity of accounting for detailed rough wall topology (including more information than just λ_p, λ_f) when relating rough wall morphology to its aerodynamic properties. To this end, a recently developed analytical rough wall parameterisation is used to predict the aerodynamic properties of the simulated rough surfaces. In this rough wall model, wake interactions among roughness elements are explicitly modelled using the concept of sheltering height and exponential attenuation coefficient. As a result, the parameterisation is responsive to detailed ground roughness arrangements and flow conditions, including roughness height variations, element orientation, incident flow direction, transverse displacements, etc. Model-predicted effective roughness heights, wall stress, mean velocity at the height of the roughness, and in some cases displacement height, are compared against the LES measurements from this study as well as numerical/experiment measurements from other authors. The predictions from the model are found to agree well with the measurements both in trends and in absolute values, thus extending the applicability of the analytical rough wall model to more general surfaces than those previously tested.