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.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
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.

A Coupled Overlapping Domain Method for the Computation of Transitional Flow Through Artificial Heart Valves

2012 ◽  
Author(s):  
A. C. Verkaik ◽  
A. C. B. Bogaerds ◽  
F. Storti ◽  
F. N. van de Vosse
Keyword(s):  
High Speed ◽  
Heart Valves ◽  
Reynolds Numbers ◽  
Transitional Flow ◽  
Small Scale ◽  
High Deformation ◽  
Artificial Heart Valves ◽  
Laminar And Turbulent Flow ◽  
Flow Through ◽  
Dependent Flow

When blood is pumped through the aortic valves, it has a time dependent flow with a relatively high speed, resulting in Reynolds numbers between 1500 and 3000. Hence, flow is in the transitional regime between laminar and turbulent flow. Transitional flow contains small scale fluctuations, see Figure 1, and may result in local high deformation rates.

Analysis of a Novel Y-Y Micromixer for Mixing at a Wide Range of Reynolds Numbers

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Vladimir Viktorov ◽  
Carmen Visconte ◽  
Md Readul Mahmud
Keyword(s):  
Three Dimensional ◽  
Interfacial Area ◽  
Reynolds Numbers ◽  
Mixing Efficiency ◽  
Change Of Direction ◽  
Analysis Technique ◽  
Wide Range ◽  
Passive Micromixer ◽  
In Series ◽  
Flow Through

A novel passive micromixer, denoted as the Y-Y mixer, based on split-and-recombine (SAR) principle is proposed and studied both experimentally and numerically over Reynolds numbers ranging from 1 to 100. Two species are supplied to a prototype via a Y inlet, and flow through four identical elements repeated in series; the width of the mixing channel varies from 0.4 to 0.6 mm, while depth is 0.4 mm. An image analysis technique was used to evaluate mixture homogeneity at four target areas along the mixer. Numerical simulations were found to be a useful support for observing the complex three-dimensional flow inside the channels. Comparison with a known mixer, the tear-drop one, based on the same SAR principle, was also performed, to have a point of reference for evaluating performances. A good agreement was found between numerical and experimental results. Over the examined range of Reynolds numbers Re, the Y-Y micromixer showed at its exit an almost flat mixing characteristic, with a mixing efficiency higher than 0.9; conversely, the tear-drop mixer showed a relevant decrease of efficiency at the midrange. The good performance of the Y-Y micromixer is due to the three-dimensional 90 deg change of direction that occurs in its channel geometry, which causes a fluid swirling already at the midrange of Reynolds numbers. Consequently, the fluid path is lengthened and the interfacial area of species is increased, compensating for the residence time reduction.

Enhanced Mixing at Low Reynolds Numbers Through Elastic Turbulence

2011 ◽  
Vol 66 (6-7) ◽  
pp. 450-456
Author(s):  
Chris Goddard ◽  
Ortwin Hess
Keyword(s):  
Turbulent Flow ◽  
Three Dimensional ◽  
Maxwell Model ◽  
Reynolds Numbers ◽  
Cavity Flow ◽  
Driven Cavity ◽  
Low Reynolds Numbers ◽  
Tracer Particles ◽  
Laminar And Turbulent Flow ◽  
Spatio Temporal

A generic nonlinear Maxwell model for the stress tensor in viscoelastic materials is studied under mixing scenarios in a three-dimensional steady lid-driven cavity flow. Resulting laminar and turbulent flow profiles are investigated to study their mixing efficiencies. Massless tracer particles and passive concentrations are included to show that the irregular spatio-temporal chaos, present in turbulent flow, is useful for potential mixing applications. A Lyapunov measure for filament divergence confirms that the turbulent flow is more efficient at mixing

scholarly journals Turbulence Modeling in Three-Dimensional Stenosed Arterial Bifurcations

2006 ◽  
Vol 129 (1) ◽  
pp. 40-50 ◽  
Author(s):  
J. Banks ◽  
N. W. Bressloff
Keyword(s):  
Carotid Artery ◽  
Turbulence Modeling ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Shape Variation ◽  
Severe Stenosis ◽  
Carotid Artery Bifurcation ◽  
Inflow Turbulence ◽  
Flow Through

Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional k−ω model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG k−ϵ model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the k−ϵ model, whereas the velocity profiles in the transitional k−ω model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional k−ω model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity.

scholarly journals Flow through pipe orifices at low Reynolds numbers

1930 ◽  
Vol 126 (801) ◽  
pp. 231-245 ◽  
Keyword(s):  
Turbulent Flow ◽  
Discharge Coefficient ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Orifice Diameter ◽  
Vortex System ◽  
Low Reynolds Numbers ◽  
Commercial Practice ◽  
Flow Through ◽  
Low Reynolds

Most of the experimental work in connection with the flow of fluids through diaphragm orifices in pipe lines has been directed to the establishment of the orifice as a flow meter, and has been carried out at the velocities of flow commonly encountered in commercial practice. As a result of such research the coefficients relating the volumetric discharge of incompressible fluids to the differential head across an orifice are well known over a large range of high Reynolds numbers. For a particular diameter ratio ( i. e., orifice diameter ÷ diameter of pipe line) the discharge coefficient is nearly constant under conditions of turbulent flow. Over the range from steady to turbulent flow, however, very appreciable variations occur in the value of the discharge coefficient, suggest­ing that the accompanying variations in the nature of the flow through and beyond the orifice will be no less marked. As regards the turbulent flow pattern, an investigation, in which the author collaborated, of the airflow downstream of a flat plate suggests that an orifice in a pipe will in general give rise to a vortex system, probably having some points of resemblance to the well-known Kármán street which is a feature of the two-dimensional flow past a bluff obstacle, but doubtless exhibiting interesting differences arising from the symmetrical and three-dimensional character of the flow through an orifice. At sufficiently low Reynolds numbers, on the other hand, perfect flow free from periodic vorticity will occur. The stages connecting these two extreme conditions present many points of interest not only as regards the nature of the vortex system downstream of the orifice and the conditions of flow covering its inception, but also as regards the accom­panying pressure-velocity relation during the transition.

Laminar Flow through a Rectangular Horizontal Channel with Asymmetrical Contraction

2009 ◽  
Vol 15 ◽  
pp. 21-26
Author(s):  
O.A. Morales-Contreras ◽  
J.G. Barbosa-Saldaña ◽  
J.A. Jiménez-Bernal ◽  
Claudia del Carmen Gutiérrez Torres
Keyword(s):  
Numerical Simulation ◽  
Laminar Flow ◽  
Recirculation Zone ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Step Height ◽  
Axial Component ◽  
Parabolic Profile ◽  
Flow Through ◽  
Stream Direction

Numerical simulation for the three-dimensional laminar flow through a forward facing step channel was simulated by Fluent 6.3 code. Four Reynolds numbers and four step lengths were analyzed. The results showed that the length of the recirculation zone upstream the step depends on Reynolds number, as well as on the step height (h), while the height of the recirculation zone extends about 70% of the step height. In addition, it was found that the velocity profile in the stream direction at the channel exit presents a fully developed profile for the axial component. Nonetheless, the profile along the transversal direction does not have a parabolic profile, even for a length of 60h

scholarly journals Localised turbulence in a circular pipe flow with gradual expansion

2015 ◽  
Vol 771 ◽  
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.

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} $.

Edge states intermediate between laminar and turbulent dynamics in pipe flow

2008 ◽  
Vol 367 (1888) ◽  
pp. 577-587 ◽  
Author(s):  
Tobias M Schneider ◽  
Bruno Eckhardt
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Chaotic Dynamics ◽  
Energy Content ◽  
Edge State ◽  
Spontaneous Decay ◽  
Edge States

We studied the dynamics near the boundary between laminar and turbulent dynamics in pipe flow. This boundary contains invariant dynamical states that are attracting when the dynamics is confined to the boundary. These states can be found by controlling a single quantity, in our case the energy content. The edge state is dominated by two downstream vortices and shows intrinsic chaotic dynamics. With increasing Reynolds number the separation between the edge state and turbulence increases. We can track it down to Re =1900, where the turbulent lifetimes are short enough that spontaneous decay can also be seen in experiments.

Sign in / Sign up

Export Citation Format

Share Document