A slip-transpiration-vortex model for riblets past the viscous regime

A new boundary condition at a plane, fictitious wall, meant to simulate the presence of small-scale streamwise-aligned riblets is outlined and tested. The need for an approach which extends beyond the viscous regime stems from the high cost of numerically resolving microscopic flow details within micro-ribs, and from the desire to rapidly optimize a variety of wall textures. A multiscale homogenization technique which accounts for advection is coupled to a synthetic vortex model which mimics the transverse flow in the near-wall region. The proposed wall model captures the non-monotonic behavior of the skin-friction drag over ribleted surfaces with the increase in \(\ell ^+\) (the pitch distance measured in viscous units), including the performance degradation and the eventual drag increase beyond some \(\ell ^+\) threshold.