Drag reduction in turbulent boundary layers by in-plane wall motion

Abstract

Drag-reduction techniques capable of reducing the level of turbulent friction through wall-parallel movement of the wall are described, with special emphasis placed on spanwise movement. The discussion is confined to active open-loop control strategies, although feedback control is briefly mentioned with regard to peculiarities of spanwise sensing and/or actuation. Theoretical considerations are first given to explain why spanwise motion is expected to be particularly effective in skin-friction drag reduction. A review of the spanwise oscillating-wall technique is given next, with discussion of recent results and prospects. Last, waves of spanwise velocity are addressed, either spanwise-or streamwise-travelling. The latter include the oscillating wall as a special case. The generalized Stokes layer-i.e. the laminar, transverse oscillating boundary layer that develops under the action of the streamwise-travelling waves-is described, and its importance in determining turbulent drag reduction discussed. Finally, open issues like energetic efficiency and its dependence on Reynolds number are addressed.

Drag reduction: enticing turbulence, and then an industry

“…For instance, an active system presented with no discussion of the power needed to operate it has little appeal, as observed by Quadrio [12]. Preferably, the power will be expressed nondimensionally, for instance as an effective drag coefficient.…”

Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence

“…However, taking into account the Reynolds number effects using the classical universality hypothesis, as proposed by [10], shows [11] that the effective-ness of riblets is not sufficient for applications in aeronautics. The known active methods, involving suction and blowing through the wall [12], plazma actuation [13], and in-plane wall motion are nominally much more efficient [14]. However, the complexity of the practical implementation of these known active methods is too large [11].…”

“…For example, the frequency modulation of small scales by large scales, predicted by the quasi-steady hypothesis, is observed only for y + < 100 [24]. Fortunately, the drag reduction mechanism is concentrated in the area below 100 wall units [14,19,26]. Measuring the large-scale fluctuations at y + = 100 for the values of Re typical for aeronautical applications is a realistic task.…”

Turbulent boundary-layer control with plasma actuators

“…Streamwise travelling waves of spanwise velocity were studied by Quadrio et al [24], combining the spanwise oscillation and travellingwave control techniques. Further details of this technique are reviewed by Quadrio [25] in this Theme Issue. The Lorentz forcing was used for turbulent boundary-layer control in many DNS studies [26,27].…”