Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at

Abstract

A DNS-based study is presented, which focuses on the response of near-wall turbulence and skin friction to the imposition of an oscillatory spanwise wall motion in channel flow.One point of contrast to earlier studies is the relatively high Reynolds number of the flow, namely Re τ =1000. Another is the focus on transients in the drag that are in the form of moderate oscillatory variations in the skin friction and near-wall turbulence around the low-drag state at a sub-optimal actuation period. These conditions allow phase-averaged statistics to be extracted, during the periodic drag decline and rise, that shed light on the interaction between turbulence and the unsteady Stokes strain. Results are presented for, among others, the phase-averaged second-moments of stochastic fluctuations and their budgets, enstrophy components and joint PDFs. The study identifies velocity skewnessthe wall-normal derivative of the angle of the velocity vector -as playing a significant role † Email address for correspondence: l.agostini@imperial.ac.uk 2 L. Agostini, E. Touber and M. A. Leschzinerin the streak-damping process during the drag-reduction phase. Furthermore, the phasewise asymmetry in the skewness is identified as the source of a distinctive hysteresis in all properties, wherein the drag decline progresses over a longer proportion of the actuation cycle than the drag increase. This feature, coupled with the fact that the streakgeneration time scale limits the ability of the streaks to re-establish themselves during the low-skewness phase when the actuation period is sufficiently short, is proposed to drive the drag-reduction process. The observations in the study thus augment a previously identified mechanism proposed by two of the present authors, in which the drag-reduction process was linked to the rate-of-change in the Stokes strain in the upper region of the viscous sublayer where the streaks are strongest. Furthermore, an examination of the stochastic-stress budgets and the enstrophy lead to conclusions contrasting those recently proposed by other authors, according to which the drag-reduction process is linked to increases in enstrophy and turbulence-energy dissipation. It is shown, both for the transient drag-reduction phase and the periodic drag fluctuations around the lowdrag state, that the drag decrease/increase phases are correlated with decreases/increases in both enstrophy and dissipation.

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

“…The adequacy of the resolution and convergence of phase-averaged quantities were investigated in various ways, including a simulation of the flow over a grid of 1200 M cells, an examination of the resolved dissipation, relative to the imbalance of other terms in the turbulence-energy budget, an evaluation of the ratio of cell distances to the Kolmogorov length scale, and comparisons of the turbulence energy budget to results by Moser et al 28 and Hoyas and Jimenez 29 . As is demonstrated by Agostini et al 25 , the present budget agrees closely with the previously published data for the near-wall layer, within which resolution quality is the most critical. Moreover, Agostini et al 25 show that the ratio of the cell volume (∆x + × ∆y + × ∆z + ) 1/3 to the Kolmogorov length scale, η, is close to 2 over the entire flow, with the x-directed ratio ∆x/η -the highest of the three directional ratios -being around 4 at y/h=0.15 and declining with y.…”

“…As is demonstrated by Agostini et al 25 , the present budget agrees closely with the previously published data for the near-wall layer, within which resolution quality is the most critical. Moreover, Agostini et al 25 show that the ratio of the cell volume (∆x + × ∆y + × ∆z + ) 1/3 to the Kolmogorov length scale, η, is close to 2 over the entire flow, with the x-directed ratio ∆x/η -the highest of the three directional ratios -being around 4 at y/h=0.15 and declining with y. Hence, the resolution in the outer part of the boundary layer is as good as, if not better than, in the near-wall layer.…”

“…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.…”

“…In this paper, we examine various aspects of eq. 1, as well as the validity of Chernyshenko et al's proposal 24 , focusing on the statistical properties of the velocity fluctuations, which are derived from DNS data for channel flow at Re τ = 1025, reported in Agostini et al 25 . Although this Reynolds number is relatively low -certainly in comparison with experimental configurations -the flow is appropriate to the aims pursued in this study.…”

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

“…The motivation of investigating the possibility to use the QSQH hypothesis for developing means of extrapolating the results of direct numerical simulations of flows with drag reduction to higher Re led us to choosing the set of data containing the drag-reduction case, described in detail in [33] and provided to us by the authors of that paper. In the present the points are obtained from our dataset, and the curves are from [7].…”