Dependence of turbulent wall-shear stress on the amplitude of spanwise transversal surface waves

Drag Reduction and Energy Saving by Spanwise Traveling Transversal Surface Waves for Flat Plate Flow

“…The numerical method has thoroughly been validated by computing a wide variety of internal and external flow problems [43,3,39,46]. Analyses of drag reduction have been performed for riblet structured surfaces [24] and for traveling transversal surface waves in canonical turbulent boundary layer flow [26,27,28,34] and in turbulent airfoil flow [2]. The quality of the results confirms the validity of the approach for the current flow problem.…”

“…Instead of directly introducing spanwise velocity, the surface is wavily deflected in the wall-normal direction to generate a secondary flow field of periodic wallnormal and spanwise fluctuations. Positive drag reduction using this technique was achieved experimentally [20,47,30] and numerically for channel flow [48], boundary layer flow [26,28,27,19], and airfoil flow [2]. Tomiyama and Fukagata [48] observed a possible shielding effect of quasi-streamwise vortices from the wall by the wave-like deformations and showed that a combination of the thickness of the Stokes layer, i.e., the actuation period, and the actuation velocity amplitudes scales reasonably well with drag reduction.…”

“…Note that case N 80 has a wavelength of λ + = 3000, the images for this case are thus compressed for lack of space. of spanwise forcing [11], spanwise velocity at the wall [54], or spanwise transversal surface waves [25,28].…”

Closed‐loop control of turbulent boundary layers using spanwise traveling surface waves

“…Another promising approach is spanwise transversal traveling surface waves which impose a secondary flow field in the near-wall region. Studies in channel flows have shown drag reductions of 30 percent [3], while the effect in external flows, i.e., turbulent boundary layers, is in the range of 10 percent [4].…”

Drag reduction via spanwise transversal traveling waves of smooth and structured surfaces

“…By comparing both setups which were excited by the same mechanism, Klumpp et al were able to show that the reduction of wall-normal vorticity is a key-indicator for drag reduction. More recently, the effect of changing amplitude in the range A + = 30 − 70 in inner units at increasing Reynolds number (1000 ≤ Re θ ≤ 7000) on the drag reduction of a transversal traveling surface wave with a wave length of λ + = 500 in inner coordinates was investigated by Koh et al [4]. It was shown that increasing the amplitude can compensate the weakening of the drag reduction observed at increasing Reynolds number.…”