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Propagation speed of turbulent fronts in pipe flow at high Reynolds numbers

Published online by Cambridge University Press:  25 January 2022

Kaiwen Chen ,
Duo Xu  and
Baofang Song Open the ORCID record for Baofang Song [Opens in a new window]
Kaiwen Chen
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China
Duo Xu
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Baofang Song*
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China
*
†Email address for correspondence: baofang_song@tju.edu.cn
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Abstract

We investigated the propagation of turbulent fronts in pipe flow at high Reynolds numbers by direct numerical simulation. We used a technique combining a moving frame of reference and an artificial damping to isolate the fronts in short periodic pipes, which enabled us to explore the bulk Reynolds number up to $Re=10^5$ with affordable computation power. We measured the propagation speed of the downstream front and observed that a fit of $1.971-(Re/1925)^{-0.825}$ (in unit of bulk speed) captures this speed above $Re\simeq 5000$ very well. The speed increases monotonically as $Re$ increases, in stark contrast to the decreasing trend above $Re\simeq 10\,000$ reported by Wygnanski & Champagne (J. Fluid Mech., vol. 59, 1973, pp. 281–335). The speed of the upstream front overall agrees with the former studies and $0.024+(Re/1936)^{-0.528}$ fits our data well, and those from the literature. Based on our analysis of the front dynamics, we proposed that both front speeds would keep their respective monotonic trends as the Reynolds number increases further. We show that, at high Reynolds numbers, the local transition at the upstream front tip is via high-azimuthal-wavenumber structures in the high-shear region near the pipe wall, whereas at the downstream front tip is via low-azimuthal-wavenumber structures in the low-shear region near the pipe centre. This difference is possibly responsible for the asymmetric speed scalings between the upstream and downstream fronts.

JFM classification

Instability: Shear-flow instability Instability: Transition to turbulence Turbulent Flows: Pipe flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A11
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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Chen et al. supplementary movie 1

Visualisation of the downstream front in a co-moving frame of reference at Re=25000. The transverse velocity is color-coded in a cut-plane along the pipe axis. The flow is from left to right and the domain shown in the movie is eight-diameters-long in the axial direction.

Download Chen et al. supplementary movie 1(Video)
Video 4.6 MB

Chen et al. supplementary movie 2

Visualisation of the upstream front in a co-moving frame of reference at Re=25000. The transverse velocity is color-coded in a cut-plane along the pipe axis. The flow is from left to right and the domain shown in the movie is eight-diameters-long in the axial direction.

Download Chen et al. supplementary movie 2(Video)
Video 4.5 MB

Chen et al. supplementary movie 3

Visualisation of the downstream front tip in a co-moving frame of reference at Re=25000. The transverse velocity is color-coded in a cut-plane along the pipe axis. The flow is from left to right and the domain shown in the movie is five diameters-long in the axial direction. The flow is damped at the left end of the domain in order to isolate the front tip.

Download Chen et al. supplementary movie 3(Video)
Video 7.6 MB

Chen et al. supplementary movie 4

Visualisation of the upstream front tip in a co-moving frame of reference at Re=25000. The transverse velocity is color-coded in a cut-plane along the pipe axis. The flow is from left to right and the domain shown in the movie is five diameters-long in the axial direction. The flow is damped at the left end of the domain in order to isolate the front tip which is at the right end of the domain in the movie.

Download Chen et al. supplementary movie 4(Video)
Video 5.8 MB