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

Abstract 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 $$\ell ^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> (the pitch distance measured in viscous units), including the performance degradation and the eventual drag increase beyond some $$\ell ^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> threshold.