Critical threshold in pipe flow transition

2008 ◽  
Vol 367 (1888) ◽  
pp. 545-560 ◽  
Author(s):  
Fernando Mellibovsky ◽  
Alvaro Meseguer
Keyword(s):  
Pipe Flow ◽  
Basin Of Attraction ◽  
Reynolds Numbers ◽  
Travelling Wave ◽  
Computational Method ◽  
Critical Threshold ◽  
Krylov Method ◽  
Numerical Characterization ◽  
Wide Range ◽  
Critical Amplitudes

This study provides a numerical characterization of the basin of attraction of the laminar Hagen–Poiseuille flow by measuring the minimal amplitude of a perturbation required to trigger transition. For pressure-driven pipe flow, the analysis presented here covers autonomous and impulsive scenarios where either the flow is perturbed with an initial disturbance with a well-defined norm or perturbed by means of local impulsive forcing that mimics injections through the pipe wall. In both the cases, the exploration is carried out for a wide range of Reynolds numbers by means of a computational method that numerically resolves the transitional dynamics. For , the present work provides critical amplitudes that decay as Re −3/2 and Re −1 for the autonomous and impulsive scenarios, respectively. For Re =2875, accurate threshold amplitudes are found for constant mass-flux pipe by means of a shooting method that provides critical trajectories that never relaminarize or trigger transition. These transient states are used as initial guesses in a damped Newton–Krylov method formulated to find periodic travelling wave solutions that either travel downstream or exhibit a helicoidal advection.

scholarly journals On the transient nature of localized pipe flow turbulence

2010 ◽  
Vol 646 ◽  
pp. 127-136 ◽  
Author(s):  
MARC AVILA ◽  
ASHLEY P. WILLIS ◽  
BJÖRN HOF
Keyword(s):  
Pipe Flow ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Critical Threshold ◽  
Lifetime Data ◽  
Low Reynolds Numbers ◽  
Transient Nature ◽  
Detailed Statistical Analysis ◽  
Flow Turbulence ◽  
Shed Light

The onset of shear flow turbulence is characterized by turbulent patches bounded by regions of laminar flow. At low Reynolds numbers localized turbulence relaminarizes, raising the question of whether it is transient in nature or becomes sustained at a critical threshold. We present extensive numerical simulations and a detailed statistical analysis of the lifetime data, in order to shed light on the sources of the discrepancies present in the literature. The results are in excellent quantitative agreement with recent experiments and show that turbulent lifetimes increase super-exponentially with Reynolds number. In addition, we provide evidence for a lower bound below which there are no meta-stable characteristics of the transients, i.e. the relaminarization process is no longer memoryless.

NUMERICAL CHARACTERIZATION OF THE FLOW FIELD IN A FOUR-GENERATION AIRWAY

2008 ◽  
Vol 08 (01) ◽  
pp. 55-74 ◽  
Author(s):  
T. C. LAI ◽  
Y. S. MORSI ◽  
M. SINGH
Keyword(s):  
Reynolds Numbers ◽  
Bronchial Tree ◽  
Secondary Flows ◽  
Fourth Generation ◽  
Numerical Characterization ◽  
Wide Range ◽  
Symmetrical Model ◽  
Computational Fluid Dynamics Cfd ◽  
Insight Into

In this paper, various aspects of respiratory airflow generated from the branching network of tubes that make up the tracheal-bronchial tree are numerically analyzed using the computational fluid dynamics (CFD) package CFX. The model used is a four-generation airway that is geometrically similar to Weibel's symmetrical model. In the present analysis, two different models (in-plane and off-plane) are examined for a wide range of Reynolds numbers that correspond to human breathing conditions. The findings indicate that the secondary flow patterns generated become more significant as the flow passes from the trachea to the fourth-generation airway. Moreover, comparison between in-plane and off-plane models shows that the skewed velocity profiles and secondary flows for the in-plane model are more prominent than those for the off-plane one. In general, the model developed in this study is capable of providing an overall insight into the effect of fluid flow in multiple generations of the human upper respiratory airways.

Experimental Modeling of Circular Hydraulic Jump by the Impingement of a Water Column on a Horizontal Disk

1999 ◽  
Vol 121 (1) ◽  
pp. 86-92 ◽  
Author(s):  
Mehdi N. Naraghi ◽  
M. Karim Moallemi ◽  
M. H. N. Naraghi ◽  
Sunil Kumar
Keyword(s):  
Experimental Study ◽  
Pipe Flow ◽  
Hydraulic Jump ◽  
Film Flow ◽  
Characteristic Length ◽  
Reynolds Numbers ◽  
Sudden Increase ◽  
Wide Range ◽  
The Relationship ◽  
Impingement Point

An experimental study is performed to investigate the relationship between an unsub-merged water jet impinging onto a horizontal surface and radius of hydraulic jump. Experiments are undertaken over a wide range of pipe Reynolds numbers for which the pipe flow is laminar. The laminar impinging jet produced a smooth circular hydraulic jump, at which the film thickness experienced a sudden increase in thickness. Effects of various parameters on a stable and stationary hydraulic jump are studied. The impingement point radius ri, is taken as a characteristic length of the film flow, and correlations are obtained for radius of hydraulic jump in terms of various dimensionless parameters.

A swirling spiral wave solution in pipe flow

2013 ◽  
Vol 737 ◽  
Author(s):  
K. Deguchi ◽  
A. G. Walton
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Wave Solution ◽  
Asymptotic Theory ◽  
Spiral Wave ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Travelling Wave ◽  
Navier Stokes ◽  
Nonlinear Solution

AbstractA numerically exact full Navier–Stokes counterpart of the asymptotic nonlinear solution in Hagen–Poiseuille flow proposed by Smith & Bodonyi (Proc. R. Soc. A, vol. 384, 1982, pp. 463–489) is discovered. The solution takes the form of a spiral travelling wave, with a novel feature being a strong induced component of swirl. Our solution shows excellent quantitative agreement with the asymptotic theory at Reynolds numbers of the order of $1{0}^{8} $.

scholarly journals Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids

1998 ◽  
Vol 377 ◽  
pp. 267-312 ◽  
Author(s):  
A. A. DRAAD ◽  
G. D. C. KUIKEN ◽  
F. T. M. NIEUWSTADT
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Polymer Solutions ◽  
Reynolds Numbers ◽  
Cylindrical Pipe ◽  
Turbulent Transition ◽  
Wide Range ◽  
Flow Changes ◽  
Transition Points ◽  
The Stability

A cylindrical pipe facility with a length of 32 m and a diameter of 40 mm has been designed. The natural transition Reynolds number, i.e. the Reynolds number at which transition occurs as a result of non-forced, natural disturbances, is approximately 60 000. In this facility we have studied the stability of cylindrical pipe flow to imposed disturbances. The disturbance consists of periodic suction and injection of fluid from a slit over the whole circumference in the pipe wall. The injection and suction are equal in magnitude and each distributed over half the circumference so that the disturbance is divergence free. The amplitude and frequency can be varied over a wide range.First, we consider a Newtonian fluid, water in our case. From the observations we compute the critical disturbance velocity, which is the smallest disturbance at a given Reynolds number for which transition occurs. For large wavenumbers, i.e. large frequencies, the dimensionless critical disturbance velocity scales according to Re−1, while for small wavenumbers, i.e. small frequencies, it scales as Re−2/3. The latter is in agreement with weak nonlinear stability theory. For Reynolds numbers above 30 000 multiple transition points are found which means that increasing the disturbance velocity at constant dimensionless wavenumber leads to the following course of events. First, the flow changes from laminar to turbulent at the critical disturbance velocity; subsequently at a higher value of the disturbance it returns back to laminar and at still larger disturbance velocities the flow again becomes turbulent.Secondly, we have carried out stability measurements for (non-Newtonian) dilute polymer solutions. The results show that the polymers reduce in general the natural transition Reynolds number. The cause of this reduction remains unclear, but a possible explanation may be related to a destabilizing effect of the elasticity on the developing boundary layers in the entry region of the flow. At the same time the polymers have a stabilizing effect with respect to the forced disturbances, namely the critical disturbance velocity for the polymer solutions is larger than for water. The stabilization is stronger for fresh polymer solutions and it is also larger when the polymers adopt a more extended conformation. A delay in transition has been only found for extended fresh polymers where delay means an increase of the critical Reynolds number, i.e. the number below which the flow remains laminar at any imposed disturbance.

Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized ‘edge’ states

2009 ◽  
Vol 619 ◽  
pp. 213-233 ◽  
Author(s):  
ASHLEY P. WILLIS ◽  
RICH R. KERSWELL
Keyword(s):  
Pipe Flow ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Edge State ◽  
Travelling Wave ◽  
Edge States ◽  
Huge Number ◽  
Laminar And Turbulent Flow ◽  
Flow Through

Fully three-dimensional computations of flow through a long pipe demand a huge number of degrees of freedom, making it very expensive to explore parameter space and difficult to isolate the structure of the underlying dynamics. We therefore introduce a ‘2+ε-dimensional’ model of pipe flow, which is a minimal three-dimensionalization of the axisymmetric case: only sinusoidal variation in azimuth plus azimuthal shifts are retained; yet the same dynamics familiar from experiments are found. In particular the model retains the subcritical dynamics of fully resolved pipe flow, capturing realistic localized ‘puff-like’ structures which can decay abruptly after long times, as well as global ‘slug’ turbulence. Relaminarization statistics of puffs reproduce the memoryless feature of pipe flow and indicate the existence of a Reynolds number about which lifetimes diverge rapidly, provided that the pipe is sufficiently long. Exponential divergence of the lifetime is prevalent in shorter periodic domains. In a short pipe, exact travelling-wave solutions are found near flow trajectories on the boundary between laminar and turbulent flow. In a long pipe, the attracting state on the laminar–turbulent boundary is a localized structure which resembles a smoothened puff. This ‘edge’ state remains localized even for Reynolds numbers at which the turbulent state is global.

Pipe flow measurements over a wide range of Reynolds numbers using liquid helium and various gases

2002 ◽  
Vol 461 ◽  
pp. 51-60 ◽  
Author(s):  
CHRIS J. SWANSON ◽  
BRIAN JULIAN ◽  
GARY G. IHAS ◽  
RUSSELL J. DONNELLY
Keyword(s):  
Liquid Helium ◽  
Pipe Flow ◽  
Scaling Laws ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Flow Measurements ◽  
Wide Range ◽  
Flow Apparatus ◽  
Stokes Fluid

We demonstrate that an unusually small pipe flow apparatus using both liquid helium and room temperature gases can span an enormous range of Reynolds numbers. This paper describes the construction and operation of the apparatus in some detail. A wide range of Reynolds numbers is an advantage in any experiment seeking to establish scaling laws. This experiment also adds to evidence already in hand that the normal phase of liquid helium is a Navier–Stokes fluid. Finally, we explore recent questions concerning the influence of molecular motions on the transition to turbulence (Muriel 1998) and are unable to observe any influence.

Pulsatile pipe flow pseudoplastic materials; The flow enhancement for Re ≪ 1

1983 ◽  
Vol 48 (6) ◽  
pp. 1579-1587 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Small Parameter ◽  
Pipe Flow ◽  
Quantitative Estimation ◽  
Reynolds Numbers ◽  
Power Law Model ◽  
Viscosity Function ◽  
Small Reynolds Numbers ◽  
Title Problem ◽  
Flow Enhancement ◽  
Method Of Small Parameter

Solution of the title problem for the power-law model of viscosity function is constructed by the method of small parameter in the region of small Reynolds numbers. The main result of the paper is a quantitative estimation of the values of Re, when the influence of inertia on flow enhancement may be quite neglected.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals Experimental and theoretical progress in pipe flow transition

2008 ◽  
Vol 366 (1876) ◽  
pp. 2671-2684 ◽  
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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