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The vanishing of strong turbulent fronts in bent pipes

Published online by Cambridge University Press:  13 March 2019

Enrico Rinaldi Open the ORCID record for Enrico Rinaldi [Opens in a new window] ,
Jacopo Canton Open the ORCID record for Jacopo Canton [Opens in a new window]  and
Philipp Schlatter Open the ORCID record for Philipp Schlatter [Opens in a new window]
Enrico Rinaldi
Affiliation:
Linné FLOW Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden
Jacopo Canton*
Affiliation:
Linné FLOW Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden
Philipp Schlatter
Affiliation:
Linné FLOW Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden
*
†Email address for correspondence: jcanton@mech.kth.se
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Abstract

Isolated patches of turbulence in transitional straight pipes are sustained by a strong instability at their upstream front, where the production of turbulent kinetic energy (TKE) is up to five times higher than in the core. Direct numerical simulations presented in this paper show no evidence of such strong fronts if the pipe is bent. We examine the temporal and spatial evolution of puffs and slugs in a toroidal pipe with pipe-to-torus diameter ratio $\unicode[STIX]{x1D6FF}=D/d=0.01$ at several subcritical Reynolds numbers. Results show that the upstream overshoot of TKE production is at most one-and-a-half times the value in the core and that the average cross-flow fluctuations at the front are up to three times lower if compared to a straight pipe, while attaining similar values in the core. Localised turbulence can be sustained at smaller energies through a redistribution of turbulent fluctuations and vortical structures by the in-plane Dean motion of the mean flow. This asymmetry determines a strong localisation of TKE production near the outer bend, where linear and nonlinear mechanisms optimally amplify perturbations. We further observe a substantial reduction of the range of Reynolds numbers for long-lived intermittent turbulence, in agreement with experimental data from the literature. Moreover, no occurrence of nucleation of spots through splitting could be detected in the range of parameters considered. Based on the present results, we argue that this mechanism gradually becomes marginal as the curvature of the pipe increases and the transition scenario approaches a dynamical switch from subcritical to supercritical.

JFM classification

Instability: Nonlinear instability Boundary Layers: Pipe flow boundary layer Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , pp. 487 - 502
Copyright
© 2019 Cambridge University Press 

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Rinaldi et al. supplementary movie 1

Effect of the secondary motion on the upstream front of a puff.

Download Rinaldi et al. supplementary movie 1(Video)
Video 25.4 MB

Rinaldi et al. supplementary movie 2

Upstream front of a puff in a straight pipe for Re = 2600.

Download Rinaldi et al. supplementary movie 2(Video)
Video 8 MB

Rinaldi et al. supplementary movie 3

Upstream front of a puff in a bent pipe for Re = 3100.

Download Rinaldi et al. supplementary movie 3(Video)
Video 7.4 MB

Rinaldi et al. supplementary movie 4

Upstream front of a puff in a bent pipe for Re = 3300.

Download Rinaldi et al. supplementary movie 4(Video)
Video 11.1 MB

Rinaldi et al. supplementary movie 5

Upstream front of a puff in a bent pipe for Re = 5000.

Download Rinaldi et al. supplementary movie 5(Video)
Video 16.7 MB