Transition to turbulence in pulsating pipe flow Journal Article

Author(s): Xu, Duo; Warnecke, Sascha; Song, Baofang; Ma, Xingyu; Hof, Björn
Article Title: Transition to turbulence in pulsating pipe flow
Affiliation IST Austria
Abstract: Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, ), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low . In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence ('puffs') analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics is dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi-steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number (i.e. the dimensionless oscillation amplitude). In the high frequency limit on the other hand, puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing ) from the decay dominated (quasi-steady) threshold to the steady pipe flow level.
Keywords: Transition to turbulence; instability
Journal Title: Journal of Fluid Mechanics
Volume: 831
ISSN: 1469-7645
Publisher: Cambridge University Press  
Date Published: 2017-11-25
Start Page: 418
End Page: 432
DOI: 10.1017/jfm.2017.620
Notes: D.X. gratefully acknowledges the support from Max Planck Society and Humboldt Foundation (3.5-CHN/1154663STP) and IST Austria. B.H. acknowledges funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement 306589.
Open access: yes (repository)
IST Austria Authors
  1. Björn Hof
    46 Hof
  2. Baofang Song
    6 Song