Localized turbulence structures in transitional rectangular-duct flow

Takeishi, K., Kawahara, G., Wakabayashi, H., Uhlmann, M. & Pinelli, A. (2015). Localized turbulence structures in transitional rectangular-duct flow. Journal of Fluid Mechanics, 782, pp. 368-379. doi: 10.1017/jfm.2015.546

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Abstract

Direct numerical simulations of transitional flow in a rectangular duct of cross-sectional aspect ratio A≡s/h=1–9 (s and h being the duct half-span and half-height, respectively) have been performed in the Reynolds number range Re≡ubh/ν=650–1500 (ub and ν being the bulk velocity and the kinematic viscosity, respectively) in order to investigate the dependence on the aspect ratio of spatially localized turbulence structures. It was observed that the lowest Reynolds number ReT, estimated in a specific way, for localized (transiently sustaining) turbulence decreases monotonically from ReT=730 for A=1 (square duct) with increasing aspect ratio, and for A=5 it nearly attains a minimal value ReT≈670 that is consistent with the onset Reynolds number of turbulent spots in a plane channel (A=∞). Turbulent states consist of localized structures that undergo a fundamental change around A=4. At Re=ReT turbulence for A=1–3 is streamwise-localized similar to turbulent puffs in pipe flow, while for A=5–9 turbulence at Re=ReT is also localized in the spanwise direction, similar to turbulent spots in plane channel flow. This structural change in turbulent states at Re=ReT is attributed to the exclusion of turbulence from the vicinity of the duct sidewalls in the case of a wide duct with A≳4: here the friction length on the sidewalls is so long that the size (around 100 times the friction length) of a self-sustaining minimal flow unit of streamwise vortices and streaks is larger than the duct height and, therefore, it cannot be accommodated.

Item Type: Article
Additional Information: Copyright Cambridge Journals, 2015. Content and layout follow Cambridge University Press’s submission requirements. This version may have been revised following peer review but may be subject to further editorial input by Cambridge University Press.
Uncontrolled Keywords: Transition to turbulence, Turbulent flows
Subjects: T Technology > TL Motor vehicles. Aeronautics. Astronautics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/14266

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