Abstract: Heterogeneous roughness in the form of streamwise aligned strips is known to generate large scale secondary motions under turbulent flow conditions that can induce the intriguing feature of larger flow rates above rough than smooth surface parts. The hydrodynamical definition of a surface roughness includes a large scale separation between the roughness height and the boundary layer thickness which is directly related to the fact that the drag of a laminar flow is not altered by the presence of roughness. Existing simplified approaches for direct numerical simulation (DNS) of roughness strips do not fulfill this requirement of an unmodified laminar base flow compared to a smooth wall reference. It is shown that disturbances induced in a modified laminar base flow can trigger large scale motions with resemblance to turbulent secondary flow.
We propose a simple roughness model that allows to capture the particular features of turbulent secondary flow without impacting the laminar base flow. The roughness model is based on the prescription of a spanwise slip length, a quantity that can directly be translated into the Hama roughness function for a homogeneous rough surface. The heterogeneous application of the slip length boundary condition results in very good agreement with existing experimental data in terms of the secondary flow topology.
In addition, the proposed modelling approach allows to quantitatively evaluate the drag increasing contribution of the secondary flow. Both the secondary flow itself and the related drag increase reveal a very small dependence on the gradient of the transition between rough and smooth surface parts only. Interestingly, the observed drag increase due to secondary flows above the modelled roughness is significantly smaller than the one previously reported for roughness resolving simulations. We hypothesize that this difference arises from the fact that roughness resolving simulations cannot truly fulfill the requirement of large scale separation.
TechnicalRemarks: The data for all simulations discussed in the main paper are provided as Numpy npz files. See the readme file for a detailed description of the file contents.
