Drag Reduction Via Spanwise Transversal Surface Waves at High Reynolds Numbers

Abstract

The impact of transversal spanwise traveling surface waves on the wall-shear stress distribution of high Reynolds number turbulent boundary layer flows is analyzed using high-resolution large-eddy simulations. The Reynolds numbers based on the friction velocity are Ret = 540, 906, 1908, and 2250. The surface wave motion defined by the amplitude, the wavelength, and the phase speed in inner coordinates is constant for the investigated Ret range. When the Reynolds number is increased, the drag reduction decreases from 11 % to 1 %. That is, in contrast to the result in the literature for actuated channel flow, which shows the drag reduction (DR) as a function of the Reynolds number based on the friction velocity to be proportional to \(Re_{\tau }^{-0.2}\) for Ret = 1000, the current analysis for evolving turbulent boundary layers over actuated surfaces leads to DR\(\sim Re_{\tau }^{-1}\). The detailed analysis of the velocity profiles in the viscous sublayer clearly shows that the major difference in the velocity gradient occurs above the trough where the velocity gradient is reduced by increasing Reynolds number. At low Reynolds numbers, the peak value of the wall-normal vorticity distribution above the moving wave crest and above the moving wave trough is much smaller than that of the non-actuated wall resulting in a pronounced drag reduction. At increasing Reynolds number, the difference in the wall-normal vorticity distribution in the near-wall region for the actuated and the non-actuated wall becomes smaller leading to a lower drag reduction. The analysis of the anisotropy map shows that the wall actuation excites the two-component turbulence in the viscous sublayer above the crest and the trough. That is, unlike passively controlled flow, the drag reducing mechanism is related not to the one-component but to the two-component state in the anisotropy map.