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Localized turbulence structures in transitional rectangular-duct flow

Published online by Cambridge University Press:  08 October 2015

Keisuke Takeishi ,
Genta Kawahara ,
Hiroki Wakabayashi ,
Markus Uhlmann  and
Alfredo Pinelli
Keisuke Takeishi
Affiliation:
Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan
Genta Kawahara*
Affiliation:
Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan
Hiroki Wakabayashi
Affiliation:
Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan
Markus Uhlmann
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany
Alfredo Pinelli
Affiliation:
School of Mathematics, Computer Science and Engineering, City University London, London EC1V 0HB, UK
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations of transitional flow in a rectangular duct of cross-sectional aspect ratio $A\equiv s/h=1$–9 ($s$ and $h$ being the duct half-span and half-height, respectively) have been performed in the Reynolds number range $\mathit{Re}\equiv u_{b}h/{\it\nu}=650$–1500 ($u_{b}$ and ${\it\nu}$ 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 $\mathit{Re}_{T}$, estimated in a specific way, for localized (transiently sustaining) turbulence decreases monotonically from $\mathit{Re}_{T}=730$ for $A=1$ (square duct) with increasing aspect ratio, and for $A=5$ it nearly attains a minimal value $\mathit{Re}_{T}\approx 670$ that is consistent with the onset Reynolds number of turbulent spots in a plane channel ($A=\infty$). Turbulent states consist of localized structures that undergo a fundamental change around $A=4$. At $\mathit{Re}=\mathit{Re}_{T}$ turbulence for $A=1$–$3$ is streamwise-localized similar to turbulent puffs in pipe flow, while for $A=5$–9 turbulence at $\mathit{Re}=\mathit{Re}_{T}$ is also localized in the spanwise direction, similar to turbulent spots in plane channel flow. This structural change in turbulent states at $\mathit{Re}=\mathit{Re}_{T}$ is attributed to the exclusion of turbulence from the vicinity of the duct sidewalls in the case of a wide duct with $A\gtrsim 4$: 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.

JFM classification

Instability: Instability Instability: Transition to turbulence Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 782 , 10 November 2015 , pp. 368 - 379
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Copyright
© 2015 Cambridge University Press 

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