Turbulent boundary layer flow subject to streamwise oscillation of spanwise wall-velocity

Abstract

Direct numerical simulations have been performed to study the effect of a stationary distribution of spanwise wall-velocity that oscillates in the streamwise direction on a turbulent boundary layer. For the first time, a spatially developing flow with this type of forcing is studied. The part of the boundary layer which flows over the alternating wall-velocity section is greatly affected with a drag reduction close to 50% which exhibits an oscillatory distribution with a wavenumber which is twice that of the imposed wall-velocity. The maximum in drag reduction occurs where the wall velocity is at its maximum (or minimum) and the minimum occurs where the wall velocity is zero. Comparisons of the mean spanwise velocity profiles with the analytical solution to the laminar Navier-Stokes equations show very good agreement. The streamwise velocity profile indicates a thickening of the viscous sub-layer when scaled with the local friction velocity and an upward shifting of the logarithmic region when scaled with the reference (unmanipulated) friction velocity. An estimation of the idealized power consumption shows that—with the present wall forcing magnitude—more energy is required for the spatial oscillation than what is saved by drag reduction.