Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction

Abstract

Steady forcing at the wall of a channel flow is studied via direct numerical simulation to assess its ability of yielding reductions in turbulent friction drag. The wall forcing consists of a stationary distribution of spanwise velocity that alternates in the streamwise direction. The idea behind the forcing builds on the existing technique of the spanwise wall oscillation and exploits the convective nature of the flow to achieve an unsteady interaction with turbulence. The analysis takes advantage of the equivalent laminar flow, which is solved analytically to show that the energetic cost of the forcing is unaffected by turbulence. In a turbulent flow, the alternate forcing is found to behave similarly to the oscillating wall; in particular an optimal wavelength is found which yields a maximal reduction in turbulent drag. The energetic performance is significantly improved, with more than 50% of maximum friction saving at large intensities of the forcing, and a net energetic saving of 23% for smaller intensities. Such a steady, wall-based forcing may pave the way to passively interacting with the turbulent flow to achieve drag reduction through a suitable distribution of roughness, designed to excite a selected streamwise wavelength. © 2009 American Institute of Physics. ͓doi:10.1063/1.3266945

Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction

“…In the oscillating-wall case, the space-averaged velocity profile follows closely the laminar solution, which has led to a scaling parameter for drag reduction (Choi et al 2002;Quadrio & Ricco 2004). Analogously, Viotti et al (2008) have found that the laminar layer induced by the standing waves agrees well with the space-averaged turbulent profile. Future work should therefore be directed at extending these results to the traveling-wave case to estimate the modification of drag.…”

“…While purely spatial and purely temporal oscillations have been shown by Viotti et al (2008) to be largely analogous to each other, the flow response to the traveling waves is found to be interestingly complex when examined as a function of ω and κ x . Both drag reduction (DR) and drag increase (DI) may occur.…”

“…(1.4) reduces to the steady wave case (1.2). Some of these points are taken from Viotti et al (2008), who employed the same Re and discretization parameters. As discussed there, DR behaves very similarly on the two axes, once frequency is converted into wavenumber through Eq.…”

“…(Hereinafter, the + superscript indicates scaling by the friction velocity u τ of the reference flow and the kinematic viscosity ν of the fluid.) Viotti et al (2008) have shown that the optimal frequency ω opt for (1.1) translates into an optimal wavenumber κ x,opt for (1.2) through the relation…”

“…At lower A, the energy balance between the power saved thanks to the oscillation and the power spent to activate the wall motion against the viscous stresses may be positive at about 7% when ω = ω opt . In a recent work, Quadrio et al (2007) (see also Viotti et al 2008) have addressed one of the drawbacks of the oscillating-wall technique, i.e. its unsteady nature.…”