On the stability of slowly varying flow: the divergent channel

Eagles, P. M.; Weissman, Michael A.

doi:10.1017/s0022112075001425

Cited by 47 publications

(13 citation statements)

References 17 publications

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“…The second type of mean velocity profile analysed here is that in a 'slightly converging tube', where the angle between the tube wall and the axial direction α 1 and the product αRe ∼ 1. A similar limit was considered in the papers of Eagles & Weissman (1975) and Eagles & Smith (1980) where the stability of slowly varying two-dimensional rigid channels was considered. This parameter regime is of interest for the following reason.…”

Section: Problem Formulation and Governing Equationsmentioning

confidence: 98%

Stability of non-parabolic flow in a flexible tube

Shankar

Kumaran

1999

J. Fluid Mech.

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Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

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Section: Problem Formulation and Governing Equationsmentioning

confidence: 98%

Stability of non-parabolic flow in a flexible tube

Shankar

Kumaran

1999

J. Fluid Mech.

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“…The base state under consideration is plane Poiseuille flow parallel to the local wall orientation and is therefore susceptible to 2D Tollmien–Schlichting waves with properties varying locally in ; see, for example, Hall (1982 b ) and Eagles & Weissman (1975). Here, we concentrate on the potentially much more dangerous modes driven by centrifugal effects associated with streamline curvature.…”

Section: The Base Flow and Stability Equationsmentioning

confidence: 99%

Centrifugal/elliptic instabilities in slowly varying channel flows

Gajjar

Hall

2020

J. Fluid Mech.

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“…Earlier studies by Eagles [4], Eagles and Weissman [5] and Eagles and Smith [6] show that for channel flow, instabilities occurred at R = 215 for a = 0.01 and R = 40 for a = 0.1, where a is the semi-divergence angle of the channel. A similar pattern was expected for the DE profiles.…”

Section: Introductionmentioning

confidence: 95%