Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms

Abstract

Direct numerical simulations for fully developed channel flow, subjected to oscillatory spanwise wall motion, have been performed and analysed in an effort to illuminate the fundamental mechanisms responsible for the reduction in turbulent friction drag, observed to result from the spanwise wall motion. A range of statistical data are discussed, including second-moment budgets, joint-probability-density functions, enstrophy and energy-spectra maps. Structural features are also investigated by reference to the response of streak properties to the oscillatory forcing. The unsteady cross-flow straining is shown to cause major spanwise distortions in the streak nearwall structures, leading to a pronounced reduction in the wall-normal momentum exchange in the viscous sublayer, hence disrupting the turbulence contribution to the wall shear stress. The response of the streaks, in terms of their periodic reorientation in wall-parallel planes, the decline and recovery of their intensity during the cyclic actuation, and their wall-normal coherence, is shown to be closely correlated with the temporal variation of the shear-strain vector. Furthermore, a modulating 'top-to-bottom' effect, associated with large-scale outer-layer structures, is highlighted and deemed responsible for the observed reduction in the actuation efficiency as the Reynolds number is increased.

Direct Numerical Simulation of Supersonic Turbulent Boundary Layer with Spanwise Wall Oscillation

“…According to previous research in SWO [43][44][45], the near-wall spanwise velocity profile agrees well with the laminar Stokes solution, even though the main flow is fully turbulent. We are considering a static fluid in a space with a half-infinite spanwise oscillating wall.…”

“…Then the N-S equations can be simplified as, To investigate the influence of the Stokes layer on the WHF, the solution of one dimensional (1D) laminar Stokes layer is used to estimate the temperature field and WHF. According to previous research in SWO [43][44][45], the near-wall spanwise velocity profile agrees well with the laminar Stokes solution, even though the main flow is fully turbulent. We are considering a static fluid in a space with a half-infinite spanwise oscillating wall.…”

On the influence of outer large-scale structures on near-wall turbulence in channel flow

“…At an actuation period close to an optimum value, at which the drag-reduction margin is maximised, the near-wall streaks are weak, and the effect of the large-scale structures on the near-wall streaks is very prominent, even at low Reynolds numbers. This is demonstrated by Touber & Leschziner 26 and Agostini et al 25 for Re τ = 500 and 1025, respectively. In particular, there is clear evidence of near-wallstreak modulation that leads to a virtual annihilation of the streaks in patches subjected to low-velocity footprints during periods of high rates of change in the spanwise Stokes-strain.…”

Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing

“…In this paper, we will indicate with the customary + superscript the "reference" wall units, whereas a * superscript will indicate the "actual" wall units. Limiting to the literature where more than one value of Re was considered, quantities have been scaled through either reference + units (Quadrio et al 2009;Touber & Leschziner 2012;Gatti & Quadrio 2013;Hurst et al 2014) or actual actual * units (Moarref & Jovanović 2012). The choice of nondimensionalization is particularly delicate and may cause spurious Re effects, since R is function of all control parameters including Re.…”

“…Quadrio et al (2009) for the streamwise-travelling waves measured γ = 0.24. Touber & Leschziner (2012) went up to Re τ = 1000 for the oscillating wall and suggested γ = 0.20. This is a rather strong decrease rate: with γ = 0.24, the 58% drag reduction of the travelling waves at Re τ = 200 would become a mere 7% at Re τ = 10 6 .…”