Quantitative measurement of the lifetime of localized turbulence in pipe flow

The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study such fluctuations in order to measure the time-scale of the transition efficiently. The method is composed of two parts: (i) the measurement of typical fluctuations (the bulk part of an accumulative probability function) and (ii) the measurement of rare fluctuations (the tail part of the probability function) by employing dynamics where a feedback control of the Reynolds number is implemented. We apply this method to a chaotic model of turbulent puffs proposed by Barkley and confirm that the time-scale of turbulence decay increases super-exponentially even for high Reynolds numbers up to Re = 2500, where getting enough statistics by brute-force calculations is difficult. The method uses a simple procedure of changing Reynolds number that can be applied even to experiments.

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“…[22] for the observation of this law within this model, and also see Refs. [8][9][10][11][12] in more realistic settings).…”

Section: Numerical Examplementioning

confidence: 99%

Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows

Nemoto

Alexakis

2018

Phys. Rev. E

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“…For that reason the helical pipe has been set up similar to straight-pipe-flow facilities which have proven an excellent performance in this respect (see e.g. Hof et al 2006;Kuik et al 2010). Figure 3a provides a schematic overview of the main parts of the helical-pipe facility: Coming from a reservoir the fluid driven by a constant pressure head first enters a calming section.…”

Section: Helical Pipementioning

confidence: 99%

Subcritical versus supercritical transition to turbulence in curved pipes

Kühnen¹,

Braunshier²,

Schwegel³

et al. 2015

J. Fluid Mech.

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Transition to turbulence in straight pipes occurs in spite of the linear stability of the laminar Hagen-Poiseuille flow if the amplitude of flow perturbations as well as the Reynolds number exceed a minimum threshold (subcritical transition). As the pipe curvature increases centrifugal effects become important, modifying the basic flow as well as the most unstable linear modes. If the curvature (tube-to-coiling diameter d/D) is sufficiently large a Hopf bifurcation (supercritical instability) is encountered before turbulence can be excited (subcritical instability). We trace the instability thresholds in the Re − d/D parameter space in the range 0.01 d/D 0.1 by means of laser-Doppler velocimetry and determine the point where the subcritical and supercritical instabilities meet. Two different experimental setups were used: a closed system where the pipe forms an axisymmetric torus and an open system employing a helical pipe. Implications for the measurement of friction factors in curved pipes are discussed. †

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“…For the unsteady cases, the total measurement time is long compared to the survival time of a puff. 35 As a result, the statistics average out with little influence of individual puffs. For the steady case, however, the total measurement time is short compared to the survival time.…”

Section: -9mentioning

confidence: 99%

An experimental study of transitional pulsatile pipe flow

et al. 2012

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The transitional regime of a sinusoidal pulsatile flow in a straight, rigid pipe is investigated using particle image velocimetry. The main aim is to investigate how the critical Reynolds number is affected by different pulsatile conditions, expressed as the Womersley number and the oscillatory Reynolds number. The transition occurs in the region of Re ¼ 2250-3000 and is characterized by an increasing number of isolated turbulence structures. Based on velocity fields and flow visualizations, these structures can be identified as puffs, similar to those observed in steady flow transition. Measurements at different Womersley numbers yield similar transition behavior, indicating that pulsatile effects do not play a role in the regime that is investigated. Variations of the oscillatory Reynolds number also appear to have little effect, so that the transition here seems to be determined only by the mean Reynolds number. For larger mean Reynolds numbers, a second regime is observed: here, the flow remains turbulent throughout the cycle. The turbulence intensity varies during the cycle, but has a phase shift with respect to the mean flow component. This is caused by a growth of kinetic energy during the decelerating part and a decay during the accelerating part of the cycle. Flow visualization experiments reveal that the flow develops localized turbulence at several random axial positions. The structures quickly grow to fill the entire pipe in the decelerating phase and (partially) decay during the accelerating phase.

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Quantitative measurement of the lifetime of localized turbulence in pipe flow

Cited by 40 publications

References 19 publications

Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows

Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows

Subcritical versus supercritical transition to turbulence in curved pipes

An experimental study of transitional pulsatile pipe flow

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