Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-10T09:57:09.476Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahn, J., Lee, J.H., Lee, J. & Kang, J.-H. 2015 Direct numerical simulation of a 30R long tubrulent pipe flow at $Re_{\tau }=3008$. Phys. Fluids 27, 065110.CrossRefGoogle Scholar
Barkley, D. 2016 Theoretical perspective on the route to turbulence in a pipe. J. Fluid Mech. 803, P1.CrossRefGoogle Scholar
Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M. & Hof, B. 2015 The rise of fully turbulent flow. Nature 526, 550–553.CrossRefGoogle ScholarPubMed
Del Álamo, J.C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor's approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
Dimitropoulos, C.D., Sureshkumar, R., Beris, A.N. & Handler, R.A. 2001 Budgets of Reynolds stress, kinetic energy and streamwise enstrophy in viscoelastic turbulent channel flow. Phys. Fluids 13, 1016.CrossRefGoogle Scholar
Duguet, Y., Willis, A.P. & Kerswell, R.R. 2010 Slug genesis in cylindrical pipe flow. J. Fluid Mech. 663, 180–208.CrossRefGoogle Scholar
Durst, F. & Ünsal, B. 2006 Forced laminar to turbulent transition in pipe flows. J. Fluid Mech. 560, 449–464.CrossRefGoogle Scholar
El Khoury, G.L., Schlatter, P., Noorani, A., Fischer, P.F., Brethouwer, G. & Johansson, A.V. 2013 Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers. Flow Turbul. Combust. 91, 475–495.CrossRefGoogle Scholar
Hof, B., De Lozar, A., Avila, M., Tu, X. & Schneider, T.M. 2010 Eliminating turbulence in spatially intermittent flows. Science 327, 1491–1494.CrossRefGoogle ScholarPubMed
Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502.CrossRefGoogle Scholar
Holzner, M., Song, B., Avila, M. & Hof, B. 2013 Lagrangian approach to laminar-turbulent interfaces. J. Fluid Mech. 723, 140–162.CrossRefGoogle Scholar
Kanazawa, T. 2018 Lifetime and growing process of localized turbulence in plane channel flow. PhD thesis, Osaka University.Google Scholar
Lindgren, E.R. 1957 The transition process and other phenomena in viscous flow. Ark. Fys. 12, 1–169.Google Scholar
Lindgren, E.R. 1969 Propagation velocity of turbulent slugs and streaks in transition pipe flow. Phys. Fluids 12, 418.CrossRefGoogle Scholar
Nishi, M., Ünsal, B., Durst, F. & Biswas, G. 2008 Laminar-to-turbulent transition of pipe flows through puffs and slugs. J. Fluid Mech. 614, 425–446.CrossRefGoogle Scholar
Pei, J., Chen, J., She, Z.-S. & Hussain, F. 2012 Model for propagation speed in turbulent channel flows. Phys. Rev. E 86, 046307.CrossRefGoogle ScholarPubMed
Peixinho, J. & Mullin, T. 2007 Finite amplitude thresholds for transition in pipe flow. J. Fluid Mech. 582, 169–178.CrossRefGoogle Scholar
Rinaldi, E., Canton, J. & Schlatter, P. 2019 The vanishing of strong turbulent fronts in bent pipes. J. Fluid Mech. 866, 487–502.CrossRefGoogle Scholar
Ritter, P., Zammert, S., Song, B., Eckhardt, B. & Avila, M. 2018 Analysis and modeling of localized invariant solutions in pipe flow. Phys. Rev. Fluids 3, 013901.CrossRefGoogle Scholar
Shimizu, M. & Kida, S. 2009 A driving mechanism of a turbulent puff in pipe flow. Fluid Dyn. Res. 41, 045501.CrossRefGoogle Scholar
Song, B. 2014 Direct numerical simulation of transition to turbulence and turbulence control in pipe flow. PhD thesis, Gerog-August-Universität Göttingen.Google Scholar
Song, B., Barkley, D., Hof, B. & Avila, M. 2017 Speed and structure of turbulent fronts in pipe flow. J. Fluid Mech. 813, 1045–1059.CrossRefGoogle Scholar
Willis, A.P. 2017 The Openpipeflow Navier–Stokes solver. SoftwareX 6, 124–127.CrossRefGoogle Scholar
Willis, A.P. & Kerswell, R.R. 2009 Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarisation and localised ‘edge’ states. J. Fluid Mech. 619, 213–233.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2012 Direct numerical simulation of a 30R long turbulent pipe flow at $R^+$=685: large-and very large-scale motions. J. Fluid Mech. 698, 235–281.CrossRefGoogle Scholar
Wygnanski, I.J. & Champagne, F.H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281–335.CrossRefGoogle Scholar

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