The streamwise drag-reduction response of a boundary layer subjected to a sudden imposition of transverse oscillatory wall motion

Abstract

A DNS study is presented, which examines the response of a spatially developing boundary layer to oscillatory spanwise wall motion imposed over a limited streamwise stretch. At the heart of the study is the dependence of the streamwise variations in skin friction and turbulence properties on the period of the oscillatory motion, with particular emphasis placed on the behaviour downstream of the start of the actuation. The friction Reynolds number just upstream of the actuation is Re τ = 520, and the wall-scaled actuation period, T + = T u τ 2 /ν, covers the range 80-200. In contrast to channel flow, the present configuration allows the processes during the transition stretch from the unactuated state to the low-drag state and the recovery from the low-drag state to be studied. Attention focuses primarily on the former. Results are included for the time-averaged turbulent stresses, their budgets and PDFs, as well as a range of phase-averaged properties. The study brings out, for low-drag conditions, a number of features and processes that are common with those in actuated channel flow, but suggests that the maximum drag-reduction margins are lower than those in equivalent channel flow, and that the optimum actuation period is significantly shorter. The transition to the low-drag state occurs over about 5 boundary-layer thicknesses, and is characterized by substantial oscillations in all phase-averaged properties. These oscillations, provoked at the start of the spanwise motion, propagate convectively as waves and decay as the low-drag state is approached. The interactions contributing to the oscillations are discussed as part of the analysis of phase-averaged quantities.

The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves

“…As already mentioned, no Reynolds number effect was observed in the boundary-layer experiment of Ricco & Wu (2004). Numerical simulations of the turbulent boundary layer with wall oscillation have been performed in a few studies (Yudhistira & Skote 2011;Skote 2012;Lardeau & Leschziner 2013). A drag reduction of DR = 29.4% was obtained at Re θ = 500 (or Re τ = 260) for A + = 12 and T + = 132 (Skote 2012).…”

“…In these numerical studies, a single Reynolds number was used, making a direct comparison for the Reynolds number effect between different studies less straightforward. Comparing Skote (2012) and Lardeau & Leschziner (2013) gives a change of ∆DR = 4.4% between Re τ = 260 and Re τ = 520, but it should be noted that different T + values were used in their simulations. Skote (2012) compared his boundary-layer DNS results at Re θ = 500 with channel flow data available in literature using an equivalent Re θ numbers for the channel flow.…”

“…A drag reduction of DR = 29.4% was obtained at Re θ = 500 (or Re τ = 260) for A + = 12 and T + = 132 (Skote 2012). DNS of turbulent boundary layer at Re τ = 520 was conducted by Lardeau & Leschziner (2013) for A + = 12 at four different oscillation frequencies: T + = 80, 100, 120 and 200, with the largest drag reduction of DR = 25% at T + = 80. In these numerical studies, a single Reynolds number was used, making a direct comparison for the Reynolds number effect between different studies less straightforward.…”

“…The maximum drag reduction is found at 48%, also by a forward travelling wave, and the maximum net power saving is found as 18% (ω ≈ 0.15, κ x ≈ 1), with an even larger saving of 26% for a lower value of A + = 6. Since the first direct numerical simulation (DNS) study of wall oscillation for flow control by Jung et al (1992), a number of DNS studies have been performed for the channel flow (Baron & Quadrio 1996;Choi et al 2002;Ricco & Quadrio 2008;Quadrio et al 2009;Viotti et al 2009;Ricco et al 2012;Touber & Leschziner 2012), pipe flow (Orlandi & Fatica 1997;Quadrio & Sibilla 2000) and boundary-layer flow (Yudhistira & Skote 2011;Skote 2012Skote , 2013Lardeau & Leschziner 2013). Although the drag reduction of wall oscillation has been found to decrease as the Reynolds number increases, the majority of previous studies have been confined to lower Reynolds numbers, and also the Reynolds number range investigated has not been wide enough to give a clear indication of the Reynolds number effect on the drag reduction.…”

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

“…The specific case of spanwise-forcing techniques for drag reduction includes the wellknown spanwise-oscillating wall (Jung et al 1992) and its generalizations made by the spanwise-travelling waves (Du et al 2002) and streamwise-travelling waves (Quadrio et al 2009); although most of the available information concerns internal flows, numerical experiments (Skote 2011;Lardeau & Leschziner 2013;Skote 2013;Mishra & Skote 2015) have shown that the forcing is effective in external flows too. The streamwise-travelling waves, in particular, yield larger maximum drag reduction and, more importantly, improved energetic efficiency, which is essential if drag reduction is motivated by the need to save energy.…”