Drag reduction of turbulent flow over thin rectangular riblets

Direct numerical simulations of low-Reynolds number turbulent channel flow are carried out where thin rectangular riblets are distributed uniformly at only one of the channel walls. A second-order accurate finite volume code is modified in order to reconstruct the adjacent cells to the riblets at Cartesian coordinates. A quadratic interpolation scheme is used to estimate the fluxes at the reformed cells. The riblets height/spacing ratio is fixed at 0.5 which doubles the surface area at the ribbed wall and the thickness/spacing ratio is set to 0.02. The riblet spacing ranges from 13 to 41 viscous units. Comparison with experiments shows excellent agreement in detecting both reduction and the increase of drag at the studied range of spacings. The maximum drag reduction obtained is about 11% which occurs at a spacing of 18 viscous units. The increase of drag is addressed when the spacing is larger than 30 wall units. Wide spacing permits the near-wall eddies to reside inside the riblet-to-riblet span which in turn makes them interacting with larger wetted area and increases the friction drag.