Bifurcations and eddy genesis of Stokes flow within a sectorial cavity

Gürcan, Fuat; Bilgil, Halis

doi:10.1016/j.euromechflu.2012.11.002

Cited by 12 publications

(3 citation statements)

References 33 publications

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“…Stokes flow in lid-driven cavities for different geometries has been studied by several authors. 1–3 Apart from serving the test problem for the assessment of numerical methods, 4–7 they are encountered in industrial applications such as roll coating, 8 polymer processing, 9 and ceramics casting. 10…”

Section: Introductionmentioning

confidence: 99%

“…Stokes flow in lid-driven cavities for different geometries has been studied by several authors. [1][2][3] Apart from serving the test problem for the assessment of numerical methods, [4][5][6][7] they are encountered in industrial applications such as roll coating, 8 polymer processing, 9 and ceramics casting. 10 One of the different geometries is a rectangular cavity driven by the uniform motion of the upper side wall with three rigid walls, which is considered here.…”

Section: Introductionmentioning

confidence: 99%

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Singular treatment of viscous flow near the corner by using matched eigenfunctions

Deliceoğlu

Çelik

Gürcan

2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, the local singular behavior of Stokes flow is solved near the salient and re-entrant corners by the matching eigenfunction method. The flow in a rectangular and an L-shaped cavity are considered as a model for the flow generated by the motion of the upper lid. The solutions of the Stokes equation in polar coordinates are matched with a velocity vector components obtained by analytic or numerical solution for the streamfunction developed for any values of the heights of the rectangular and an L-shaped cavity. Streamline patterns near the corner are simulated for a different aspect ratio A. The techniques are tested on a flow problem undergoing Stokes or Navier–Stokes equations in a square cavity. It is seen that the method appears to be cheaper and more accurate than the numerical and analytical methods. It is expected that the study will lead to useful insights into the understanding of the flow topology near a re-entrant corner from a combined analytical-numerical method. Attention is then focused on the topological behavior near the re-entrant corner of the L-shaped cavity. Careful analysis of the streamlines of streamfunction near the re-entrant corner by using wall shear stress allows us to give a possible flow bifurcation of dividing streamline.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Singular treatment of viscous flow near the corner by using matched eigenfunctions

Deliceoğlu

Çelik

Gürcan

2018

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Bakker (1991), Brøns & Bisgaard (2006), Brøns (2007), Brøns et al (2007), Gürcan & Bilgil (2013), Balci et al (2015) for theory and various applications. However, streamline patterns are not Galilean invariant and are therefore affected by a change of frame.…”

Section: Introductionmentioning

confidence: 99%

Topological fluid mechanics of the formation of the Kármán-vortex street

et al. 2016

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We explore the two-dimensional flow around a circular cylinder with the aim of elucidating the changes in the topology of the vorticity field that lead to the formation of the Kármán vortex street. Specifically, we analyse the formation and disappearance of extremal points of vorticity, which we consider to be feature points for vortices. The basic vortex creation mechanism is shown to be a topological cusp bifurcation in the vorticity field, where a saddle and an extremum of the vorticity are created simultaneously. We demonstrate that vortices are first created approximately 100 diameters downstream of the cylinder, at a Reynolds number, Re K , which is slightly larger than the critical Reynolds number, Re crit ≈ 46, at which the flow becomes time periodic. For Re slightly above Re K , the newly created vortices disappear again a short distance further downstream. As Re is further increased, the points of creation and disappearance move rapidly upstream and downstream, respectively, and the Kármán vortex street persists over increasingly large streamwise distances.

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The Lid-Driven Cavity

Kuhlmann

Romanò

2018

Computational Methods in Applied Sciences

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Bifurcations and eddy genesis of Stokes flow within a sectorial cavity

Cited by 12 publications

References 33 publications

Singular treatment of viscous flow near the corner by using matched eigenfunctions

Singular treatment of viscous flow near the corner by using matched eigenfunctions

Topological fluid mechanics of the formation of the Kármán-vortex street

The Lid-Driven Cavity

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