Turbulent drag reduction by spanwise wall forcing. Part 2. High-Reynolds-number experiments

Abstract

We present measurements of turbulent drag reduction (DR) in boundary layers at high friction Reynolds numbers in the range of $4500 \le Re_\tau \le 15\ 000$ . The efficacy of the approach, using streamwise travelling waves of spanwise wall oscillations, is studied for two actuation regimes: (i) inner-scaled actuation (ISA), as investigated in Part 1 of this study, which targets the relatively high-frequency structures of the near-wall cycle, and (ii) outer-scaled actuation (OSA), which was recently presented by Marusic et al. (Nat. Commun., vol. 12, 2021) for high- $Re_\tau$ flows, targeting the lower-frequency, outer-scale motions. Multiple experimental techniques were used, including a floating-element balance to directly measure the skin-friction drag force, hot-wire anemometry to acquire long-time fluctuating velocity and wall-shear stress, and stereoscopic particle image velocimetry to measure the turbulence statistics of all three velocity components across the boundary layer. Under the ISA pathway, DR of up to 25 % was achieved, but mostly with net power saving (NPS) losses due to the high-input power cost associated with the high-frequency actuation. The low-frequency OSA pathway, however, with its lower input power requirements, was found to consistently result in positive NPS of 5–10 % for moderate DRs of 5–15 %. The results suggest that OSA is an attractive pathway for energy-efficient DR in high-Reynolds-number applications.

On the relationship between manipulated inter-scale phase and energy-efficient turbulent drag reduction

“…It is important to note here that a discretised imposition of the streamwise travelling sinusoidal waves inevitably introduces high wavenumber harmonics of low amplitudes on the turbulent boundary layer (Auteri et al 2010). However, considering that the present experiments regard fundamental modes with very low wavenumbers (κ + x 0.0014; table 1), the corresponding higher harmonics are expected to only marginally influence the DR estimates (Gatti & Quadrio 2016;Chandran et al 2023). Further details regarding the characterisation and validation of the SATB can be found in Marusic et al (2021) and Chandran et al (2023).…”

“…As discussed by Duvvuri & McKeon (2015) and Jacobi & McKeon (2017), this inter-scale coupling offers an opportunity to control and manipulate the near-wall inner scales (Jiménez & Moin 1991;Waleffe, Kim & Hamilton 1993;Hamilton, Kim & Waleffe 1995;Jiménez & Pinelli 1999) by exciting the triadically coupled outer scales, with potential implications for drag reduction. For instance, the inner-scaled eddies near the wall are a major contributor to the total skin-friction drag across the practically relevant Reynolds-number range (Deck et al 2014;Chandran et al 2023). It is challenging, however, to actuate these eddies owing to their very small time/length scales in physical units (Quadrio & Ricco 2011;Ricco, Skote & Leschziner 2021).…”

“…Considering the inverse relationship between power cost and oscillation time period, previous studies performed at low Reynolds numbers (Gatti & Quadrio 2016; some cases in Marusic et al 2021) have attempted to reduce skin-friction drag by targeting the outer scales, associated with large T + osc . However, these attempts were proven less effective at such low Reynolds numbers, wherein the contributions of outer scales to the skin-friction drag are statistically insignificant (Chandran et al 2023). Based on the premise that outer-scale contributions to the turbulent skin friction increase with Reynolds number, Marusic et al (2021) demonstrated that large-time scale spanwise wall actuation targeting these outer scales can, however, yield DR for a sufficiently high-Reynolds-number flow.…”

“…Based on the premise that outer-scale contributions to the turbulent skin friction increase with Reynolds number, Marusic et al (2021) demonstrated that large-time scale spanwise wall actuation targeting these outer scales can, however, yield DR for a sufficiently high-Reynolds-number flow. More importantly, this outer-scaled actuation (OSA) strategy (Chandran et al 2023) required considerably lower input power, thereby yielding DR with net power savings. The exact mechanism behind this new DR strategy, however, remains unknown.…”

“…The present study investigates whether this energy-efficient DR via the OSA strategy is facilitated by the manipulation of the inter-scale phase of the triadically coupled inner and outer scales. To this end, statistical analysis, based on the arguments of McKeon and co-workers (Duvvuri & McKeon 2015;Jacobi & McKeon 2017), is conducted on the experimental data of Chandran et al (2023). The same analysis is also extended for the ISA strategy to confirm whether the triadically coupled scales can be influenced from either end of the frequency spectrum.…”