The stability of a family of Jeffery–Hamel solutions for divergent channel flow

Eagles, P. M.

doi:10.1017/s0022112066000582

Cited by 57 publications

(30 citation statements)

References 2 publications

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“…[2][3][4][6][7][8][9][10][11][12][13][14][15] However, an analysis of the results in Ref. 5 suggests that they do not contain a rigorous formulation of the boundary value problem with the condition of constancy of the fluid flow rate and boundary conditions.…”

Section: Formulation Of the Problem And Introductory Remarksmentioning

confidence: 99%

Bifurcation of multimode flows of a viscous fluid in a plane diverging channel

Акуленко¹,

Kumakshev²

2008

Journal of Applied Mathematics and Mechanics

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Section: Formulation Of the Problem And Introductory Remarksmentioning

confidence: 99%

Bifurcation of multimode flows of a viscous fluid in a plane diverging channel

Акуленко¹,

Kumakshev²

2008

Journal of Applied Mathematics and Mechanics

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“…Putkaradze et al 16 studied experimentally the velocity profile and the related instabilities and bifurcation of the flows through diverging channels and concluded, in a heuristic manner, that the solutions revealed absolute instability. Swaminathan et al 3 were the first to study the spatially developing global linear stability analysis problem to reveal that the disturbance modes are not the wave-like perturbations postulated in earlier work 5,6,2,1,8,7,9,11,13,15,16,12 as assumed by local parallel or weakly non-parallel analyses and question the relation between the Re cr and the α, but rather are large-scale structures filling the entire computational domain.…”

Section: Ia Background and Previous Studymentioning

confidence: 99%

“…For global linear stability analysis the flow, q is solved without any weakly nonparallel flow assumptions as in Eagles. 1 The base flow has two velocity components u & v in the x and y directions respectively. The governing equations can be given as below:…”

Section: Iib Global Linear Stability Analysismentioning

confidence: 99%

On Global Instability of Variable Aspect Ratio Channel Flows

Jotkar

Swaminathan

Theofilis

et al. 2012

42nd AIAA Fluid Dynamics Conference and Exhibit

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The linear global stability of a flow of an incompressible fluid through a diverging channel is studied. Stability of such flows in a local context has been studied a long time ago, using the Jeffery-Hamel (JH) similarity profiles and a locally parallel flow approximation. The velocity profiles thus obtained include a parabolic profile of plane Poisuelle flow (PPF), when the divergence angle α = 0. At high α these profiles present a single region of flow reversal at each of the walls. The JH profiles are solutions to steady, laminar, two-dimensional flow of incompressible fluid within an infinite wedge driven by a line source/sink situated at the intersection of the rigid planes that form the wedge. However, these similarity solutions are not valid in finite channels. In this paper the base flow is obtained by solving for the two-dimenisonal Navier-Stokes equation (NSE) using a multi-grid Poisson equation solver (MPES) which employs the vorticity stream-function formulation. Here the stability is carried out using a global approach. The two-dimensional linearized Navier-Stokes equations (LNSE) are solved as a generalized eigenvalue problem using Arnoldi iteration and validated against previously obtained solutions employing the QZ algorithm. The Arnoldi iteration allows for faster computing of the eigenspectrum. This permits complementing our earlier global instability analyses in the small angle-of-divergence limit and extending the work to finite values of this parameter.

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“…Some theorems stating that the classical single-mode profile is unique for asymptotically small Reynolds numbers were proved in [68]. When the number Re is sufficiently large, the steady motion of the viscous medium in a diffuser becomes unstable [57], resulting in turbulence.…”

Section: Rementioning

confidence: 99%

Deformation of a Bingham viscoplastic fluid in a plane confuser

et al. 2006

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A review is given to and comprehensive numerical-analytic study is carried out of the problem of steady Bingham viscoplastic flow in a plane confuser. The solution is constructed in the first approximation with the yield stress as a small parameter and the solution of the Jeffery-Hamel problem (steady radial motion of an incompressible viscous material in a plane confuser) as the zero-order approximation. The numerical analysis is based on the modified accelerated-convergence method proposed earlier by the authors. The bifurcations of the deformation pattern occurring when the parameters reach some critical values are discussed and commented on. The asymptotic boundaries of the rigid zones that appear at infinity upon perturbation of the yield stress are determined Introduction. Recently, the journal Prikladnaya Mekhanika (International Applied Mechanics) has published review papers on solid mechanics and related subject areas [60, 63, 66, etc.], which is of practical interest for scientists who solve important problems based on recent achievements in mathematics and mechanics. This paper outlines and analyzes the theoretical results from solution of one specific problem.This problem describes the stationary deformation of a Bingham viscoplastic medium in a plane confuser. To solve it, we will use numerical and analytical methods. The solution will be found in the first approximation with the yield stress as a small parameter and the solution of the Jeffery-Hamel problem (steady radial motion of a viscous incompressible medium in a flat-walled converging channel) as the zero-order approximation. We will determine and discuss the main characteristics of the process-asymptotic (first-order) quasi-rigid and deformed zones and analyze their behavior over a wide range of parameters. New mechanical effects will be revealed (bifurcations in the deformation pattern, shape and position of the asymptotic quasi-rigid zones, and the behavior of the velocity of the medium at their boundaries).Moreover, we will also perform a complete numerical and analytic study of the Jeffery-Hamel problem over the whole range of dimensionless parameters-the opening angle of the confuser and the Reynolds number. The numerical analysis is based on the modified accelerated-convergence method proposed by the authors.

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The stability of a family of Jeffery–Hamel solutions for divergent channel flow

Cited by 57 publications

References 2 publications

Bifurcation of multimode flows of a viscous fluid in a plane diverging channel

Bifurcation of multimode flows of a viscous fluid in a plane diverging channel

On Global Instability of Variable Aspect Ratio Channel Flows

Deformation of a Bingham viscoplastic fluid in a plane confuser

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