Convective instability and transient growth in steady and pulsatile stenotic flows

Blackburn, Hugh Maurice; Sherwin, Spencer J.; Barkley, Dwight

doi:10.1017/s0022112008001717

Cited by 69 publications

(71 citation statements)

References 17 publications

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“…Convective instabilities may be dominant in the related problem of flow in a partially constricted tube (stenotic flows) with a steady inlet velocity. 6,14,32,34 In addition, convective instabilities are identified in the two-dimensional flow over a bump, 2 the backward-facing step, [30][31][32][33] and separated boundary-layer. 10 In each of these problems, the base flow is strongly nonparallel.…”

Section: A Relation To a Convective Instabilitymentioning

confidence: 99%

A pressure-gradient mechanism for vortex shedding in constricted channels

Boghosian

Cassel

2013

Physics of Fluids

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Numerical simulations of the unsteady, two-dimensional, incompressible NavierStokes equations are performed for a Newtonian fluid in a channel having a symmetric constriction modeled by a two-parameter Gaussian distribution on both channel walls. The Reynolds number based on inlet half-channel height and mean inlet velocity ranges from 1 to 3000. Constriction ratios based on the half-channel height of 0.25, 0.5, and 0.75 are considered. The results show that both the Reynolds number and constriction geometry have a significant effect on the behavior of the post-constriction flow field. The Navier-Stokes solutions are observed to experience a number of bifurcations: steady attached flow, steady separated flow (symmetric and asymmetric), and unsteady vortex shedding downstream of the constriction depending on the Reynolds number and constriction ratio. A sequence of events is described showing how a sustained spatially growing flow instability, reminiscent of a convective instability, leads to the vortex shedding phenomenon via a proposed streamwise pressure-gradient mechanism. C 2013 AIP Publishing LLC. [http://dx

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Section: A Relation To a Convective Instabilitymentioning

confidence: 99%

A pressure-gradient mechanism for vortex shedding in constricted channels

Boghosian

Cassel

2013

Physics of Fluids

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“…This problem has been considered recently by Sherwin & Blackburn [26] et al [7] and also as a test problem in Cliffe et al [11]. In this setting, with a Poiseuille flow profile at the inlet, a steady O(2) symmetry breaking occurs with azimuthal wave number m = 1 when Re 0 = 721.05272346 to 8 decimal places.…”

Section: Meshes and Tracesmentioning

confidence: 99%

Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry

et al. 2011

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Access from the University of Nottingham repository:http://eprints.nottingham.ac.uk/1437/1/cliffe_et_al_o2_article.pdf Copyright and reuse:The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence. For more details see: http://eprints.nottingham.ac.uk/end_user_agreement.pdf A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Abstract. In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork bifurcation occurs when the underlying physical system possesses rotational and reflectional or O(2) symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual Weighted Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented. Here, particular attention is devoted to the problem of flow through a cylindrical pipe with a sudden expansion, which represents a notoriously difficult computational problem.Key words. Incompressible flows, bifurcation problems, a posteriori error estimation, adaptivity, discontinuous Galerkin methods, O(2) symmetry 1. Introduction. In this article, we study the stability of the three-dimensional incompressible Navier-Stokes equations in the case when the underlying system possesses both rotational and reflectional symmetry, or more precisely, O(2) symmetry. To this end, we are interested in numerically estimating the critical Reynolds number Re, at which a (pitchfork) bifurcation point first occurs; a review of techniques for bifurcation detection can be found in Cliffe et al. [13], for example. The work in this article expands upon our recent work in [12] and [10] to include problems whose geometries exhibit both rotational and reflectional symmetry. The detection of bifurcation points in this setting is now well understood, for example, see Golubitsky and Schaeffer [19]. For the purposes of this article, we assume that a symmetric steady state solution to the incompressible Navier-Stokes equations undergoes a steady pitchfork bifurcation at a critical value of the Reynolds number. Estimation of the critical...

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“…We consider the Reynolds number Re = 400 for which the base flow is asymptotically stable; the same Reynolds number was the main focus of attention in the transient growth study in [21]. At Re = 400, the maximum energy growth of initial perturbations, 8.94×10 4 , occurs for a dimensionless time horizon τ = 4.43 at azimuthal wavenumber m = 1 [21].…”

Section: Problem Descriptionmentioning

confidence: 99%

“…At Re = 400, the maximum energy growth of initial perturbations, 8.94×10 4 , occurs for a dimensionless time horizon τ = 4.43 at azimuthal wavenumber m = 1 [21]. In the remainder of this section, m = 1 is adopted and the outcome of the related global optimal initial perturbation at t = 4.43 is considered as the control target u iτ .…”

Section: Problem Descriptionmentioning

confidence: 99%

Optimal suppression of flow perturbations using boundary control

2015

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Convective instability and transient growth in steady and pulsatile stenotic flows

Cited by 69 publications

References 17 publications

A pressure-gradient mechanism for vortex shedding in constricted channels

A pressure-gradient mechanism for vortex shedding in constricted channels

Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry

Optimal suppression of flow perturbations using boundary control

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