On the influence of wavy riblets on the slip behaviour of viscous fluids

Matthieu Bonnivard (1) , Francisco J Suarez-Grau (2) , Giordano Tierra (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Departemento Ecuaciones Diferenciales y Analisis Numerico
3 Mathematical Institute

In this work, we use the homogenization theory to investigate the capability of wavy riblet patterns to influence the behaviour of a viscous flow near a ribbed boundary. Starting from perfect slip conditions on the wall, we show that periodic oscillations of wavy riblets in the lateral direction may induce a friction effect in the direction of the flow, contrary to what happens with straight riblets. Finally, we illustrate this effect numerically by simulating riblet profiles that are widely used in experimental studies: the V-shape, U-shape, and blade riblets.

Mots clés: rough boundary; straight riblets; viscous fluids; slip condition; wavy riblets; homogenization Mathematics subject classifications (2000): 35B27; 35Q35; 74A55

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Bonnivard, Francisco J Suarez-Grau, Giordano Tierra. On the influence of wavy riblets on the slip behaviour of viscous fluids. 2015. ⟨hal-01161634⟩