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.

scholarly journals The effect of pulsation frequency on transition in pulsatile pipe flow

2018 ◽  
Vol 857 ◽  
pp. 937-951 ◽  
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.

On transition of the pulsatile pipe flow

1986 ◽  
Vol 170 ◽  
pp. 169-197 ◽  
Author(s):  
J. C. Stettler ◽  
A. K. M. Fazle Hussain
Keyword(s):  
Steady Flow ◽  
Pipe Flow ◽  
Three Dimensional ◽  
Building Blocks ◽  
Rate Of Change ◽  
Turbulent Pipe Flow ◽  
Dimensional Parameter ◽  
Pipe Length ◽  
The Mean ◽  
The Stability

Transition in a pipe flow with a superimposed sinusoidal modulation has been studied in a straight circular water pipe using laser-Doppler anemometer (LDA) techniques. This study has determined the stability–transition boundary in the three-dimensional parameter space defined by the mean and modulation Reynolds numbers Rem, Remω and the frequency parameter λ. Furthermore, it documents the mean passage frequency Fp of ‘turbulent plugs’ as functions of Rem’ Remω and λ. This study also delineates the conditions when plugs occur randomly in time (as in the steady flow) or phase-locked with the excitation. The periodic flow requires a new definition of the transitional Reynolds number Rer, identified on the basis of the rate of change of Fp with Rem. The extent of increase or decrease in Rer from the corresponding steady flow value depends on λ and Remω. At any Rem and Remω, maximum stabilization occurs at λ ≈ 5. With increasing Remω, the ‘stabilization bandwidth’ of modulation frequencies increases and then abruptly decreases after levelling off. The maximum stabilization bandwidth depends strongly on Rem, decreasing with increasing Rem. Previously reported observations of turbulence during deceleration, followed by a relaminarization during acceleration, can be explained in terms of a new phenomenon: namely, periodic modulation produces longitudinally periodic cells of turbulent fluid ‘plugs’ which differ in structural details from ‘puffs’ or ‘slugs’ in steady transitional pipe flows and are called patches. The length of a patch could be increased continuously from zero to the entire pipe length by increasing Rem. This tends to question the concept that all turbulent plugs (and even the fully-turbulent pipe flow) consists of many identical elementary plugs as basic ‘building blocks’.

Critical Reynolds Number in Constant-Acceleration Pipe Flow From an Initial Steady Laminar State

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Charles W. Knisely ◽  
Kazuyoshi Nishihara ◽  
Manabu Iguchi
Keyword(s):  
Reynolds Number ◽  
Flow Visualization ◽  
Pipe Flow ◽  
Laser Doppler Velocimetry ◽  
Critical Reynolds Number ◽  
Transition To Turbulence ◽  
Doppler Velocimetry ◽  
Constant Acceleration ◽  
Laminar State ◽  
Steady Laminar

The transition to turbulence in a constant-acceleration pipe flow from an initial laminar state was investigated in a custom-made apparatus permitting visual access to the water flow in the pipe. The apparatus allowed both laser Doppler velocimetry measurements and flow visualization using a tracer. The experiment was carried out by accelerating the flow from a steady laminar state to a steady turbulent state. The relation between the critical Reynolds number for transition to turbulence and the acceleration was found to be similar to that in a constant-acceleration pipe flow started from rest. In addition, with increased acceleration, the turbulent transition was found to be delayed to higher Reynolds numbers using flow visualization with simultaneous laser Doppler velocimetry measurements.

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} $.

COMPARING ENTROPIC AND MULTIPLE RELAXATION TIMES LATTICE BOLTZMANN METHODS FOR BLOOD FLOW SIMULATIONS

2009 ◽  
Vol 20 (05) ◽  
pp. 721-733
Author(s):  
JOOST B. W. GEERDINK ◽  
ALFONS G. HOEKSTRA
Keyword(s):  
Lattice Boltzmann ◽  
Optimization Technique ◽  
Relaxation Times ◽  
Lattice Boltzmann Methods ◽  
Reynolds Number Flow ◽  
Lattice Node ◽  
Time Harmonic ◽  
Number Flow ◽  
High Reynolds ◽  
The Stability

We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries. The Lattice BGK shows predictable stability and is the fastest method in terms of lattice node updates per second. The Multiple Relaxation Times LBM shows erratic stability which depends strongly on the relaxation times set chosen and is slightly slower. The Entropic LBM gives the best stability at the price of fewer lattice node updates per second. A parameter constraint optimization technique is used to determine which is the fastest model given a certain preset accuracy. It is found that the Lattice BGK performs best at most arterial flows, except for the high Reynolds number flow in the aorta, where the Entropic LBM is the fastest method due to its better stability. However we also conclude that the Entropic LBM with velocity/pressure inlet/outlet conditions shows much worse performance.

scholarly journals Revealing the state space of turbulent pipe flow by symmetry reduction

2013 ◽  
Vol 721 ◽  
pp. 514-540 ◽  
Author(s):  
A. P. Willis ◽  
P. Cvitanović ◽  
M. Avila
Keyword(s):  
State Space ◽  
Periodic Orbits ◽  
Pipe Flow ◽  
Travelling Wave ◽  
Symmetry Reduction ◽  
Turbulent Pipe Flow ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Unstable Manifolds ◽  
Reduced State

AbstractSymmetry reduction by the method of slices is applied to pipe flow in order to obtain a quotient of the streamwise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave solutions reduce to equilibria, and all relative periodic orbits reduce to periodic orbits. Projections of these solutions and their unstable manifolds from their infinite-dimensional symmetry-reduced state space onto suitably chosen two- or three-dimensional subspaces reveal their interrelations and the role they play in organizing turbulence in wall-bounded shear flows. Visualizations of the flow within the slice and its linearization at equilibria enable us to trace out the unstable manifolds, determine close recurrences, identify connections between different travelling wave solutions and find, for the first time for pipe flows, relative periodic orbits that are embedded within the chaotic saddle, which capture turbulent dynamics at transitional Reynolds numbers.

Transition to turbulence in constant-mass-flux pipe flow

1995 ◽  
Vol 289 ◽  
pp. 83-114 ◽  
Author(s):  
A. G. Darbyshire ◽  
T. Mullin
Keyword(s):  
Mass Flux ◽  
Pipe Flow ◽  
Critical Level ◽  
Transition To Turbulence ◽  
Constant Mass ◽  
Critical Amplitude ◽  
Injection Point ◽  
Driven Systems ◽  
The Stability ◽  
Transition Behaviour

We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number (Re) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re. This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.

scholarly journals The stability of a curved, heated boundary layer: linear and nonlinear problems

2005 ◽  
Vol 46 (4) ◽  
pp. 507-543 ◽  
Author(s):  
C. E. Watson ◽  
S. R. Otto
Keyword(s):  
Nonlinear Problems ◽  
Stable Stratification ◽  
Longitudinal Vortices ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
Linear And Nonlinear ◽  
High Reynolds ◽  
The Stability ◽  
Curved Walls ◽  
Nonlinear Regimes

AbstractWe consider the stability of high Reynolds number flow past a heated, curved wall. The influence of both buoyancy and curvature, with the appropriate sense, can render a flow unstable to longitudinal vortices. However, conversely each mechanism can make a flow more stable; as with a stable stratification or a convex curvature. This is partially due to their influence on the basic flow and also due to additional terms in the stability equations. In fact the presence of buoyancy in combination with an appropriate local wall gradient can actually increase the wall shear and these effects can lead to supervelocities and the promotion of a wall jet. This leads to the interesting discovery that the flow can be unstable for both concave and convex curvatures. Furthermore, it is possible to observe sustained vortex growth in stably stratified boundary layers over convexly curved walls. The evolution of the modes is considered in both the linear and nonlinear régimes.

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