Transition to turbulence in pulsating pipe flow

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, $\unicode[STIX]{x1D6FC}$), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low $\unicode[STIX]{x1D6FC}$. 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 $\unicode[STIX]{x1D6FC}$ 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 $\unicode[STIX]{x1D6FC}$) from the decay dominated (quasi-steady) threshold to the steady pipe flow level.

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The critical point of the transition to turbulence in pipe flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.923 ◽

2018 ◽

Vol 839 ◽

pp. 76-94 ◽

Cited By ~ 16

Author(s):

Vasudevan Mukund ◽

Björn Hof

Keyword(s):

Steady State ◽

Critical Point ◽

Pipe Flow ◽

Initial Conditions ◽

Flow Patterns ◽

Finite Amplitude ◽

Decay Rates ◽

Transition To Turbulence ◽

Intermittent Flow ◽

Spatio Temporal

In pipes, turbulence sets in despite the linear stability of the laminar Hagen–Poiseuille flow. The Reynolds number ($Re$) for which turbulence first appears in a given experiment – the ‘natural transition point’ – depends on imperfections of the set-up, or, more precisely, on the magnitude of finite amplitude perturbations. At onset, turbulence typically only occupies a certain fraction of the flow, and this fraction equally is found to differ from experiment to experiment. Despite these findings, Reynolds proposed that after sufficiently long times, flows may settle to steady conditions: below a critical velocity, flows should (regardless of initial conditions) always return to laminar, while above this velocity, eddying motion should persist. As will be shown, even in pipes several thousand diameters long, the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions, and there is no indication that different flow patterns would eventually settle to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless), we continuously recreate the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce periodic boundary conditions for the puff pattern. This procedure allows us to study the evolution of the flow patterns for arbitrary long times, and we find that after times in excess of $10^{7}$ advective time units, indeed a statistical steady state is reached. Although the resulting flows remain spatio-temporally intermittent, puff splitting and decay rates eventually reach a balance, so that the turbulent fraction fluctuates around a well-defined level which only depends on $Re$. In accordance with Reynolds’ proposition, we find that at lower $Re$ (here 2020), flows eventually always resume to laminar, while for higher $Re$ (${\geqslant}2060$), turbulence persists. The critical point for pipe flow hence falls in the interval of $2020<Re<2060$, which is in very good agreement with the recently proposed value of $Re_{c}=2040$. The latter estimate was based on single-puff statistics and entirely neglected puff interactions. Unlike in typical contact processes where such interactions strongly affect the percolation threshold, in pipe flow, the critical point is only marginally influenced. Interactions, on the other hand, are responsible for the approach to the statistical steady state. As shown, they strongly affect the resulting flow patterns, where they cause ‘puff clustering’, and these regions of large puff densities are observed to travel across the puff pattern in a wave-like fashion.

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The effect of pulsation frequency on transition in pulsatile pipe flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.789 ◽

2018 ◽

Vol 857 ◽

pp. 937-951 ◽

Cited By ~ 7

Author(s):

Duo Xu ◽

Marc Avila

Keyword(s):

Pipe Flow ◽

Experimental Studies ◽

Quantitative Agreement ◽

Transition To Turbulence ◽

Pulsation Frequency ◽

Pipe Length ◽

Pulsation Amplitude ◽

Frequency Regime ◽

Pulsatile Flows ◽

The Stability

Pulsatile flows are common in nature and in applications, but their stability and transition to turbulence are still poorly understood. Even in the simple case of pipe flow subject to harmonic pulsation, there is no consensus among experimental studies on whether pulsation delays or enhances transition. We here report direct numerical simulations of pulsatile pipe flow at low pulsation amplitude$A\leqslant 0.4$. We use a spatially localized impulsive disturbance to generate a single turbulent puff and track its dynamics as it travels downstream. The computed relaminarization statistics are in quantitative agreement with the experiments of Xuet al. (J. Fluid Mech., vol. 831, 2017, pp. 418–432) and support the conclusion that increasing the pulsation amplitude and lowering the frequency enhance the stability of the flow. In the high-frequency regime, the behaviour of steady pipe flow is recovered. In addition, we show that, when the pipe length does not permit the observation of a full cycle, a reduction of the transition threshold is observed. We obtain an equation quantifying this effect and compare it favourably with the measurements of Stettler & Hussain (J. Fluid Mech., vol. 170, 1986, pp. 169–197). Our results resolve previous discrepancies, which are due to different pipe lengths, perturbation methods and criteria chosen to quantify transition in experiments.

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The effect of rigid rotation on the finite-amplitude stability of pipe flow at high Reynolds number

Journal of Fluid Mechanics ◽

10.1017/s0022112084002305 ◽

1984 ◽

Vol 148 ◽

pp. 193-205 ◽

Cited By ~ 1

Author(s):

T. R. Akylas ◽

J.-P. Demurger

Keyword(s):

Reynolds Number ◽

Pipe Flow ◽

High Reynolds Number ◽

Finite Amplitude ◽

Linear Instability ◽

Rigid Rotation ◽

Transition To Turbulence ◽

Neutral Stability ◽

Axisymmetric Mode ◽

High Reynolds

A theoretical study is made of the stability of pipe flow with superimposed rigid rotation to finite-amplitude disturbances at high Reynolds number. The non-axisymmetric mode that requires the least amount of rotation for linear instability is considered. An amplitude expansion is developed close to the corresponding neutral stability curve; the appropriate Landau constant is calculated. It is demonstrated that the flow exhibits nonlinear subcritical instability, the nonlinear effects being particularly strong owing to the large magnitude of the Landau constant. These findings support the view that a small amount of extraneous rotation could play a significant role in the transition to turbulence of pipe flow.

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Localised turbulence in a circular pipe flow with gradual expansion

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.207 ◽

2015 ◽

Vol 771 ◽

Cited By ~ 12

Author(s):

Kamal Selvam ◽

Jorge Peixinho ◽

Ashley P. Willis

Keyword(s):

Reynolds Number ◽

Pipe Flow ◽

Three Dimensional ◽

Reynolds Numbers ◽

Finite Amplitude ◽

Transition To Turbulence ◽

Circular Pipe ◽

Recirculation Region ◽

Circular Pipe Flow ◽

Gradual Expansion

We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a gradual expansion. At the inlet, a parabolic velocity profile is applied together with a constant finite-amplitude perturbation to represent experimental imperfections. Initially, at low Reynolds number, the solution is steady. As the Reynolds number is increased, the length of the recirculation region near the wall grows linearly. Then, at a critical Reynolds number, a symmetry-breaking bifurcation occurs, where linear growth of asymmetry is observed. Near the point of transition to turbulence, the flow experiences oscillations due to a shear layer instability for a narrow range of Reynolds numbers. At higher Reynolds numbers, the recirculation region breaks into a turbulent state which remains spatially localised and unchanged when the perturbation is removed from the flow. Spatial correlation analysis suggests that the localised turbulence in the gradual expansion possesses a different flow structure from the turbulent puff of uniform pipe flow.

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Finite-amplitude thresholds for transition in pipe flow

Journal of Fluid Mechanics ◽

10.1017/s0022112007006398 ◽

2007 ◽

Vol 582 ◽

pp. 169-178 ◽

Cited By ~ 70

Author(s):

J. PEIXINHO ◽

T. MULLIN

Keyword(s):

Experimental Study ◽

Pipe Flow ◽

Pipe Wall ◽

Critical Value ◽

Finite Amplitude ◽

The Other ◽

Transition To Turbulence ◽

Constant Mass ◽

Hairpin Vortices ◽

Order Of Magnitude

We report the results of an experimental study of the finite-amplitude thresholds for transition to turbulence in a constant mass flux pipe flow. The flow was perturbed using small impulsive jets and push–pull disturbances from holes in the pipe wall. The flux of the disturbance is used to define an amplitude for the perturbation and the critical value required to cause transition scales in proportion to Re−1 for jets. In this case, the transition is catastrophic and the scaling suggests a simple balance between inertia and viscosity. On the other hand, the threshold scales as Re−1.3 or Re−1.5 for push–pull disturbances with the precise value depending on the orientation of the perturbation. Further, the amplitudes required to cause transition are typically an order of magnitude smaller than for jets. When the push–pull perturbation was applied in the oblique direction, streaks and hairpin vortices appeared during the growth phase of the disturbance. The scaling of the threshold and the growth of structures are both consistent with ideas associated with temporary algebraic growth.

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Experimental and theoretical progress in pipe flow transition

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2008.0063 ◽

2008 ◽

Vol 366 (1876) ◽

pp. 2671-2684 ◽

Cited By ~ 34

Author(s):

A.P Willis ◽

J Peixinho ◽

R.R Kerswell ◽

T Mullin

Keyword(s):

Pipe Flow ◽

Quantitative Agreement ◽

Travelling Wave ◽

Turbulent Pipe Flow ◽

Transition To Turbulence ◽

Reynolds Number Flow ◽

Threshold Amplitude ◽

Number Flow ◽

The Stability ◽

Laminar State

There have been many investigations of the stability of Hagen–Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition to turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays from turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.

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Influence of Aircraft Power Electronics Processing on Backup VHF Radio Systems

Electronics ◽

10.3390/electronics10070777 ◽

2021 ◽

Vol 10 (7) ◽

pp. 777

Author(s):

Jan Leuchter ◽

Radim Bloudicek ◽

Jan Boril ◽

Josef Bajer ◽

Erik Blasch

Keyword(s):

Power Electronics ◽

Electromagnetic Interference ◽

Communication Systems ◽

Electromagnetic Compatibility ◽

Intermediate Frequency ◽

Radio Communication ◽

Very High Frequency ◽

Switching Power ◽

Radio Systems ◽

The Impact

The paper describes the influence of power electronics, energy processing, and emergency radio systems (ERS) immunity testing on onboard aircraft equipment and ground stations providing air traffic services. The implementation of next-generation power electronics introduces potential hazards for the safety and reliability of aircraft systems, especially the interferences from power electronics with high-power processing. The paper focuses on clearly identifying, experimentally verifying, and quantifiably measuring the effects of power electronics processing using switching modes versus the electromagnetic compatibility (EMC) of emergency radio systems with electromagnetic interference (EMI). EMI can be very critical when switching power radios utilize backup receivers, which are used as aircraft backup systems or airport last-resort systems. The switching power electronics process produces interfering electromagnetic energy to create problems with onboard aircraft radios or instrument landing system (ILS) avionics services. Analyses demonstrate significant threats and risks resulting from interferences between radio and power electronics in airborne systems. Results demonstrate the impact of interferences on intermediate-frequency processing, namely, for very high frequency (VHF) radios. The paper also describes the methodology of testing radio immunity against both weak and strong signals in accordance with recent aviation standards and guidance for military radio communication systems in the VHF band.

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Stability of Hagen-Poiseuille flow with superimposed rigid rotation

Journal of Fluid Mechanics ◽

10.1017/s0022112076001304 ◽

1976 ◽

Vol 73 (1) ◽

pp. 153-164 ◽

Cited By ~ 64

Author(s):

P.-A. Mackrodt

Keyword(s):

Poiseuille Flow ◽

Pipe Flow ◽

Stokes Equations ◽

Three Dimensional ◽

Reynolds Numbers ◽

Neutral Curve ◽

Rigid Rotation ◽

Transition To Turbulence ◽

Navier Stokes ◽

Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

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