Stability of Pipe Poiseuille Flow

Lessen, Martin; Sadler, Stanley G.; Liu, Ting‐Yung

doi:10.1063/1.1692122

Cited by 80 publications

(56 citation statements)

References 9 publications

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“…The analytically-known basic flow,ū = 1 − r 2 , has been recovered on the same unstructured mesh as that on which the BiGlobal instability analysis has been performed. The eigenvalues presented by Lessen Lessen et al (1968) and Salwen Salwen et al (1980) at four Reynolds numbers have been calculated and excellent agreement with the literature has been obtained; some results are shown in table 2. The corresponding amplitude functions at Re = 100 are shown in figure 9; The (rather coarse, but adequate for convergence) mesh utilized is superimposed in these figures, further underlining the power of the spectral/hp method.…”

Section: High-order Spectral/hp Elements Karniadakis and Sherwin (2005)supporting

confidence: 57%

“…Several confined flows have been analyzed next, starting with the well-studied Hagen Poiseuille flow (HPF) in a circular pipe. While from a physical point of view this is probably the most prominent example of failure of modal linear theory to predict transition, the corresponding one-dimensional eigenvalue problem (of the Orr-Sommerfeld class) has been studied exhaustively over the years Lessen et al (1968); Salwen et al (1980), thus serving for the present validation work. The analytically-known basic flow,ū = 1 − r 2 , has been recovered on the same unstructured mesh as that on which the BiGlobal instability analysis has been performed.…”

Section: High-order Spectral/hp Elements Karniadakis and Sherwin (2005)mentioning

confidence: 99%

See 1 more Smart Citation

High-Order Numerical Methods for BiGlobal Flow Instability Analysis and Control

Vicente¹,

Rodríguez²,

González³

et al. 2011

Aeronautics and Astronautics

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Section: High-order Spectral/hp Elements Karniadakis and Sherwin (2005)supporting

confidence: 57%

Section: High-order Spectral/hp Elements Karniadakis and Sherwin (2005)mentioning

confidence: 99%

High-Order Numerical Methods for BiGlobal Flow Instability Analysis and Control

Vicente¹,

Rodríguez²,

González³

et al. 2011

Aeronautics and Astronautics

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“…T his work explores the effect of wall roughness on the long known contradiction between the linear stability analysis result of infinitely stable flow in pipes with smooth boundaries and the experimental observation (1) that flows become unstable at a Reynolds number of Ϸ2,000 for ordinary pipes (2)(3)(4). A hint that wall roughness may be important can be gathered from experiments which show that for smoothed pipes, the onset of the instability can greatly exceed 2,000 (5).…”

mentioning

confidence: 99%

Instability in pipe flow

Cotrell

McFadden

Alder

2008

Proc. Natl. Acad. Sci. U.S.A.

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The long-puzzling, unphysical result that linear stability analyses lead to no transition in pipe flow, even at infinite Reynolds number, is ascribed to the use of stick boundary conditions, because they ignore the amplitude variations associated with the roughness of the wall. Once that length scale is introduced (here, crudely, through a corrugated pipe), linear stability analyses lead to stable vortex formation at low Reynolds number above a finite amplitude of the corrugation and unsteady flow at a higher Reynolds number, where indications are that the vortex dislodges. Remarkably, extrapolation to infinite Reynolds number of both of these transitions leads to a finite and nearly identical value of the amplitude, implying that below this amplitude, the vortex cannot form because the wall is too smooth and, hence, stick boundary results prevail.

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“…Many references concerning the linear stabil ity of pipe flow can be found in Drazin and Reid's book [2], Lessen, Saddler, and Liu [4], in particular. underlined the necessity to look for disturbances with out axial symmetry.…”

Section: Even the Most Ordinary Things Are Not Understoodmentioning

confidence: 99%

Onset of Turbulence in a Pipe

Boberg

Brösa

1988

Zeitschrift Für Naturforschung A

206

167

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Turbulence in a pipe is derived directly from the Navier-Stokes equation. Analysis of numerical simulations revealed that small disturbances called 'mothers' induce other much stronger distur bances called 'daughters'. Daughters determine the look of turbulence, while mothers control the transfer of energy from the basic flow to the turbulent motion. From a practical point of view, ruling mothers means ruling turbulence. For theory, the mother-daughter process represents a mechanism permitting chaotic motion in a linearly stable system. The mechanism relies on a property of the linearized problem according to which the eigenfunctions become more and more collinear as the Reynolds number increases. The mathematical methods are described, comparisons with experi ments are made, mothers and daughters are analyzed, also graphically, with full particulars, and the systematic construction of small systems of differential equations to mimic the non-linear process by means as simple as possible is explained. We suggest that more then 20 but less than 180 essential degrees of freedom take part in the onset of turbulence.PACS number: 47.25. Ae O n s e t o f T u rb u le n c e in a P ip e

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Stability of Pipe Poiseuille Flow

Abstract: The stability of pipe Poiseuille flow with respect to linear azimuthally periodic disturbances is investigated. It is found that many radial modes of disturbance exist for each azimuthal periodicity. No linear instability is found for the mode sets with azimuthal periodicity of one.

Cited by 80 publications

References 9 publications

High-Order Numerical Methods for BiGlobal Flow Instability Analysis and Control

High-Order Numerical Methods for BiGlobal Flow Instability Analysis and Control

Instability in pipe flow

Onset of Turbulence in a Pipe

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