On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug
TL;DR: In this paper, hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence, where the pipe was smooth and carefully aligned so that turbulent slugs appeared naturally at Re > 5 × 104.
Abstract: Conditionally sampled hot-wire measurements were taken in a pipe at Reynolds numbers corresponding to the onset of turbulence. The pipe was smooth and carefully aligned so that turbulent slugs appeared naturally at Re > 5 × 104. Transition could be initiated at lower Re by introducing disturbances into the inlet. For smooth or only slightly disturbed inlets, transition occurs as a result of instabilities in the boundary layer long before the flow becomes fully developed in the pipe. This type of transition gives rise to turbulent slugs which occupy the entire cross-section of the pipe, and they grow in length as they proceed downstream. The leading and trailing ‘fronts’ of a turbulent slug are clearly defined. A unique relation seems to exist between the velocity of the interface and the velocity of the fluid by which relaminarization of turbulent fluid is prevented. The length of slugs is of the same order of magnitude as the length of the pipe, although the lengths of individual slugs differ at the same flow conditions. The structure of the flow in the interior of a slug is identical to that in a fully developed turbulent pipe flow. Near the interfaces, where the mean motion changes from a laminar to a turbulent state, the velocity profiles develop inflexions. The total turbulent intensity near the interfaces is very high and it may reach 15% of the velocity at the centre of the pipe. A turbulent energy balance was made for the flow near the interfaces. All of the terms contributing to the energy balance must vanish identically somewhere on the interface if that portion of the interface does not entrain non-turbulent fluid. It appears that diffusion which also includes pressure transport is the most likely mechanism by which turbulent energy can be transferred to non-turbulent fluid. The dissipation term at the interface is negligible and increases with increasing turbulent energy towards the interior of the slug.Mixed laminar and turbulent flows were observed far downstream for
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2000 < Re < 2700
\]
when a large disturbance was introduced into the inlet. The flow in the vicinity of the inlet, however, was turbulent at much lower Re. The turbulent regions which are convected downstream at a velocity which is slightly smaller than the average velocity in the pipe we shall henceforth call puffs. The leading front of a puff does not have a clearly defined interface and the trailing front is clearly defined only in the vicinity of the centre-line. The length and structure of the puff is independent of the character of the obstruction which created it, provided that the latter is big enough to produce turbulent flow at the inlet. The puff will be discussed in more detail later.
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TL;DR: In this paper, the authors investigated the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, and compared the results obtained from a channel flow simulation.
Abstract: Direct numerical simulations (DNS) and experiments are carried out to study fully developed turbulent pipe flow at Reynolds number Rec ≈ 7000 based on centreline velocity and pipe diameter The agreement between numerical and experimental results is excellent for the lower-order statistics (mean flow and turbulence intensities) and reasonably good for the higher-order statistics (skewness and flatness factors) To investigate the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, the present DNS results are compared to those obtained from a channel flow simulation Beside the mean flow properties and turbulence statistics up to fourth order, the energy budgets of the Reynolds-stress components are computed and compared The present results show that the mean velocity profile in the pipe fails to conform to the accepted law of the wall, in contrast to the channel flow This confirms earlier observations reported in the literature The statistics on fluctuating velocities, including the energy budgets of the Reynolds stresses, appear to be less affected by the axisymmetric pipe geometry Only the skewness factor of the normal-to-the-wall velocity fluctuations differs in the pipe flow compared to the channel flow The energy budgets illustrate that the normal-to-the-wall velocity fluctuations in the pipe are altered owing to a different ‘impingement’ or ‘splatting’ mechanism close to the curved wall
732 citations
TL;DR: In this paper, it is argued that the border separating in space two possible solutions of the flow equations (as turbulent and laminar in pipe flows or boundary layers) moves with a constant mean velocity, depending on the control parameter.
605 citations
TL;DR: It is shown that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point and is intrinsic to the nature of fluid turbulence.
Abstract: Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even for the well-studied case of pipe flow, it has not been possible to determine at what Reynolds number the motion will be either persistently turbulent or ultimately laminar. We show that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point. Through extensive experiments and computer simulations, we were able to identify and characterize the processes ultimately responsible for sustaining turbulence. In contrast to the classical Landau-Ruelle-Takens view that turbulence arises from an increase in the temporal complexity of fluid motion, here, spatial proliferation of chaotic domains is the decisive process and intrinsic to the nature of fluid turbulence.
588 citations
TL;DR: Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile as discussed by the authors, which can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space.
Abstract: Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile. Experiments on pipe flow, as well as plane Couette and plane Poiseuille flow, show that triggering turbulence depends sensitively on initial conditions, that between the laminar and the turbulent states there exists no intermediate state with simple spatial or temporal characteristics, and that turbulence is not persistent, i.e., it can decay again, if the observation time is long enough. All these features can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space. The goal of this review is to explain this concept, summarize the numerical and experimental evidence for pipe flow, and outline the consequences for related flows.
548 citations
Cites background from "On transition in a pipe. Part 1. Th..."
...…i.e., localized turbulent patches in boundary layers (Gad el Hak & Hussain 1986, Schumacher & Eckhardt 2001), turbulent sections in pipe flow (Wygnanski & Champagne 1973, Wygnanski et al. 1975), or banded turbulence in plane Couette and Taylor-Couette flow (Barkley & Tuckerman 2005, Prigent…...
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...…transition to turbulence in pipe flow that is not addressed: For the intermediate Reynolds numbers considered here a localized perturbation will induce turbulence in localized sections of the pipe only (see Wygnanski & Champagne 1973 and Wygnanski et al. 1975 for seminal observations and studies)....
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TL;DR: In this paper, the authors proposed a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100-140 for turbulent mixing.
Abstract: Data on turbulent mixing and other turbulent-flow phenomena suggest that a (mixing) transition, originally documented to occur in shear layers, also occurs in jets, as well as in other flows and may be regarded as a universal phenomenon of turbulence. The resulting fully-developed turbulent flow requires an outer-scale Reynolds number of Re = U[delta]/v [greater, similar] 1–2 × 104, or a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100–140, to be sustained. A proposal based on the relative magnitude of dimensional spatial scales is offered to explain this behaviour.
546 citations
Cites background from "On transition in a pipe. Part 1. Th..."
...This sensitivity to initial conditions diminishes, however, at a Reynolds number in the vicinity of 104 (Wygnanski & Champagne 1973)....
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Book•
19 Dec 1975
TL;DR: In this paper, the authors present a method to find the optimal set of words for a given sentence in a sentence using the Bibliogr. Index Reference Record created on 2004-09-07, modified on 2016-08-08
Abstract: Note: Bibliogr. : p. 413-424. Index Reference Record created on 2004-09-07, modified on 2016-08-08
3,758 citations
TL;DR: In this article, the authors describe the formation of low-speed streaks in the region very near the wall, which interact with the outer portions of the flow through a process of gradual lift-up, then sudden oscillation, bursting, and ejection.
Abstract: Extensive visual and quantitative studies of turbulent boundary layers are described. Visual studies reveal the presence of surprisingly well-organized spatially and temporally dependent motions within the so-called ‘laminar sublayer’. These motions lead to the formation of low-speed streaks in the region very near the wall. The streaks interact with the outer portions of the flow through a process of gradual ‘lift-up’, then sudden oscillation, bursting, and ejection. It is felt that these processes play a dominant role in the production of new turbulence and the transport of turbulence within the boundary layer on smooth walls.Quantitative data are presented providing an association of the observed structure features with the accepted ‘regions’ of the boundary layer in non-dimensional co-ordinates; these data include zero, negative and positive pressure gradients on smooth walls. Instantaneous spanwise velocity profiles for the inner layers are given, and dimensionless correlations for mean streak-spacing and break-up frequency are presented.Tentative mechanisms for formation and break-up of the low-speed streaks are proposed, and other evidence regarding the implications and importance of the streak structure in turbulent boundary layers is reviewed.
2,753 citations
TL;DR: In this paper, the authors show that a large-scale orderly pattern may exist in the noiseproducing region of a round subsonic jet by observing the evolution of orderly flow with advancing Reynolds number.
Abstract: Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.
2,108 citations
TL;DR: In this article, it was shown that the general character of the motion of fluids in contact with solid surfaces depends on the relation between a physical constant of the fluid and the product of the linear dimensions of the space occupied by the fluid.
Abstract: 1. Objects and results of the investigation.—The results of this investigation have both a practical and a philosophical aspect. In their practical aspect they relate to the law of resistance to the motion of water in pipes, which appears in a new form, the law for all velocities and all diameters being represented by an equation of two terms. In their philosophical aspect these results relate to the fundamental principles of fluid motion; inasmuch as they afford for the case of pipes a definite verification of two principles, which are— that the general character of the motion of fluids in contact with solid surfaces depends on the relation between a physical constant of the fluid and the product of the linear dimensions of the space occupied by the fluid and the velocity.
1,820 citations
TL;DR: In this article, an experimental investigation is described, in which principal emphasis is given to revealing the nature of the motions in the non-linear range of boundary-layer instability and the onset of turbulence, and it is demonstrated that the actual breakdown of the wave motion into turbulence is a consequence of a new instability which arises in the aforementioned three-dimensional wave motion.
Abstract: An experimental investigation is described in which principal emphasis is given to revealing the nature of the motions in the non-linear range of boundary-layer instability and the onset of turbulence. It has as its central purpose the evaluation of existing theoretical considerations and the provision of a sound physical model which can be taken as a basis for a theoretical approach. The experimental method consisted of introducing, in a two-dimensional boundary layer on a flat plate at ‘incompressible’ speeds, three-dimensional disturbances under controlled conditions using the vibrating-ribbon technique, and studying their growth and evolution using hot-wire methods. It has been definitely established that longitudinal vortices are associated with the non-linear three-dimensional wave motions. Sufficient data were obtained for an evaluation of existing theoretical approaches. Those which have been considered are the generation of higher harmonics, the interaction of the mean flow and the Reynold stress, the concave streamline curvature associated with the wave motion, the vortex loop and the non-linear effect of a three-dimensional perturbation. It appears that except for the latter they do not adequately describe the observed phenomena. It is not that they are incorrect or may not play a role in some aspect of the local behaviour, but from the over-all point of view the results suggest that it is the non-linear effect of a three-dimensional perturbation which dominates the behaviour. A principal conclusion to be drawn is that a new perspective, one that takes three-dimensionality into account, is required in connexion with boundary-layer instability. It is demonstrated that the actual breakdown of the wave motion into turbulence is a consequence of a new instability which arises in the aforementioned three-dimensional wave motion. This instability involves the generation of ‘hairpin’ eddies and is remarkably similar in behaviour to ‘inflexional’ instability. It is also shown that the results obtained from the study of controlled disturbances are equally applicable to ‘natural’ transition.
1,045 citations