Characterisation of backflow events over a wing section

ABSTRACT

Rare backflow (negative wall-shear stress) events have recently been found and quantified in the near-wall region of canonical wall-bounded turbulent flows. Although their existence and correlation with large-scale events have been established beyond numerical and measurement technique uncertainties, their occurrence at numerically high Reynolds numbers is still rare (less than 1 per thousand and 1 per million at the wall and beyond the viscous sublayer, respectively). To better quantify these rare events, the turbulent boundary layer developing over the suction side of a wing section, experiencing an increasing adverse pressure gradient (APG) without separation along its chord c, is considered in the present work. We find that the backflow level of 0.06% documented in turbulent channels and zero-pressure-gradient (ZPG) turbulent boundary layers is already exceeded on the suction side for x/c > 0.3, at friction Reynolds numbers three times lower, while close to the trailing edge the backflow level reaches 30%. Conditional analysis of extreme events indicates that for increasing Clauser pressure-gradient parameters (reaching β ≃ 35), the flow reaches a state in which the extreme events are more likely aligned with or against the freestream, and that the otherwise strong spanwise component of the wall-shear stress reduces towards the vicinity of the trailing edge. Backflow events subjected to moderate up to strong APG conditions (0.6 < β < 4.1) exhibit an average width of Δz⁺ ≃ 20, and an average lifetime of Δt⁺ ≃ 2. This directly connects with the findings by Lenaers et al., and implies that there is a connection between high-Re ZPG and strong APG conditions.

KEYWORDS:

• Turbulent boundary layers
• adverse pressure gradient
• wings
• separation
• backflow

Acknowledgments

This research article is based on a presentation by the first author (R. Vinuesa) during the JJ70 Symposium held at Salamanca in September 2015. The authors acknowledge financial support from the Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation. Computer time was provided by SNIC (Swedish National Infrastructure for Computing).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation.