A Mechanism of Eddy Generation in A Single Lid-Driven T-Shaped Cavity

Ali Deliceoğlu; Ebutalib Çelik

doi:10.17776/csj.569655

TR EN

A Mechanism of Eddy Generation in A Single Lid-Driven T-Shaped Cavity

Abstract

The two-dimensional (2D) steady, incompressible, Stokes flow is considered in a T-shaped cavity which has the upper-lid moving in horizontal directions. A Galerkin finite element method is used to investigate a new eddy generation and flow bifurcation. The flow in a cavity is controlled by two parameters and which are associated with the heights of the T-shaped domain. By varying and , the second eddy formation mechanism and the control space diagram are obtained.

Keywords

A T-shaped cavity,Stokes flow

Supporting Institution

TÜBİTAK

Project Number

114F525

Thanks

This study was supported by Scientific and Technological Research Council of Turkey (TÜBİTAK) [project number 114F525]

References

[1] Shankar, P. N., The eddy structure in Stokes ﬂow in a cavity, Journal of Fluid Mechanics, 250 (1993) 371–383.
[2] Gaskell, P. H., Gürcan, F., Savage, M. D., Thompson, H. M., Stokes ﬂow in a double-lid-driven cavity with free surface side walls, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 212(5) (1998) 387–403.
[3] Gürcan, F., Gaskell, P. H., Savage, M. D., Wilson, M. C. T., Eddy genesis and transformation of Stokes ﬂow in a double-lid driven cavity, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 217(3) (2003) 353–364.
[4] Liu, C., Joseph, D., Stokes ﬂow in wedge-shaped trenches, Journal of Fluid Mechanics, 80(3) (1977) 443-463.
[5] R Schreiber, H.B Keller, Driven cavity ﬂows by eﬃcient numerical techniques, Journal of Computational Physics, 49(2) (1983) 310-333.
[6] Erturk, E., Gokcol, O., Fine Grid Numerical Solutions of Triangular Cavity Flow, Applied Physics, 38(1) (2007) 97–105.
[7] Deliceoğlu, A., Aydin, S. H. Topological ﬂow structures in an L-shaped cavity with horizontal motion of the upper lid, Journal of Computational and Applied Mathematics, 259(PART B) (2014) 937–943.
[8] Gürcan, F., Bilgil, H., Bifurcations and eddy genesis of Stokes ﬂow within a sectorial cavity, European Journal of Mechanics, B/Fluids, 39 (2013) 42-51.

[9] Brøns, M., Hartnack, J. N., Streamline topologies near simple degenerate critical points in two-dimensional ﬂow away from boundaries, Physics of Fluids, 11(2) (1999) 314–324.
[10] Gürcan, F., Deliceoğlu, A., Bakker, P. G., Streamline topologies near a non-simple degenerate critical point close to a stationary wall using normal forms, Journal of Fluid Mechanics, 539 (2005) 299–311.
[11] Gürcan, F., Deliceoğlu, A., Streamline topologies near non-simple degenerate points in two-dimensional ﬂows with double symmetry away from boundaries and an application, Physics of Fluids, 17(9) (2005) 1–7.
[12] Hartnack, J. N., Streamlines topologies near a ﬁxed wall using normal forms, Acta Mechanica, 75 (1999) 55–75.
[13] Erturk, E., Corke, T. C. and Gökçöl, C., Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers. Int. J. Numer. Meth. Fluids, 48 (2005) 747-774.
[14] Botella, O., Peyret, R., Benchmark Spectral Results on the Lid Driven Cavity Flow, Computers and Fluids, 27(4) (1998) 421–433.
[15] Driesen, CH, Kuerten, JGM and Streng, M., Low-Reynols-Number ﬂow over partially covered cavities, J. Eng. Math., 34 (1998) 3-20.
[16] Gaskell, PH, Savage, MD, Summers, JL and Thompson, HM., Stokes ﬂow in closed, rectangular domains, Applied Mathematical Modelling, 22 (1998) 727-743.
[17] Ghia, U, Ghia, KN and Shin, CT., High-Re solution for incompressible ﬂow using the Navier-Stokes equations and a multigrid method, J. Comp. Physics, 48 (1982) 387-411.
[18] Gürcan, F., Eﬀect of the Reynolds number on streamline bifurcations in a double-lid-driven cavity with free surfaces, Computers and Fluids, 32 (2003) 1283-1298.
[19] Gürcan, F., Flow bifurcations in rectangular, lid-driven, cavity ﬂows. PhD. Thesis (1996), University of Leeds.
[20] William D. McQuain, Calvin J. Ribbens, C.-Y. Wang, Layne T. Watson., Steady viscous ﬂow in a trapezoidal cavity, Computers and Fluids, 23(4) (1994) 613-626.
[21] Gaskell, P., Savage, M., Wilson, M., Stokes ﬂow in a half-ﬁlled annulus between rotating coaxial cylinders, Journal of Fluid Mechanics, 337 (1997) 263-282.
[22] Ribbens, C. J., Watson, L. T., Wang, C.-Y., Steady Viscous Flow in a Triangular Cavity, Journal of Computational Physics, 112(1) (1994) 173–181.
[23] Gaskell, P.H., Thompson, H, Savage, M., A finite element analysis of steady viscous flow in triangular cavities, Proceedings of The Institution of Mechanical Engineers Part C-journal of Mechanical Engineering Science, 213 (1999) 263-276.
[24] Gurcan, F., Bilgil, H., Bifurcations and eddy genesis of Stokes flow within a sectorial cavity PART II: Co-moving lids, European Journal of Mechanics- B/Fluids, 56 (2015) 42–51.
[25] Bilgil, H., Gürcan, F., Eﬀect of the Reynolds number on ﬂow bifurcations and eddy genesis in a lid-driven sectorial cavity, Japan Journal of Industrial and Applied Mathematics, 33(2) (2016) 343–360.
[26] Deliceoğlu, A., Aydin, S. H., Flow bifurcation and eddy genesis in an L-shaped cavity, Computers and Fluids, 73 (2013) 24-46.
[27] E.B. Becker, G.F. Carey and J.T. Oden, Finite Elements, An introduction Vol. I. Prentice-Hall, 1981, New Jersey.
[28] Aydın, S. H., The Finite Element Method Over a Simple Stabilizing Grid Applied to Fluid Flow Problems, PhD Thesis (2008).

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Ali Deliceoğlu ^*
0000-0003-0863-6276
Türkiye

Ebutalib Çelik
0000-0002-4500-4465
Türkiye

Publication Date

September 30, 2019

Submission Date

May 24, 2019

Acceptance Date

August 15, 2019

Published in Issue

Year 2019 Volume: 40 Number: 3

DOI

https://doi.org/10.17776/csj.569655

IZ

https://izlik.org/JA39FS65WZ

Cite

RIS / Bibtex

APA

Deliceoğlu, A., & Çelik, E. (2019). A Mechanism of Eddy Generation in A Single Lid-Driven T-Shaped Cavity. Cumhuriyet Science Journal, 40(3), 583-594. https://doi.org/10.17776/csj.569655

Computational analysis of Newtonian fluid in a 2-D square cavity with kinetic energy, enstrophy, and palinstrophy in the presence of bottom corner obstacle

Results in Physics

https://doi.org/10.1016/j.rinp.2024.108086

Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid

Karaelmas Science and Engineering Journal

https://doi.org/10.7212/karaelmasfen.888991

A Mechanism of Eddy Generation in A Single Lid-Driven T-Shaped Cavity

Tek Kapağı Sürgülü T-Şeklindeki Kaviti İçerisindeki Girdap Oluşum Mekanizması

Öz

Anahtar Kelimeler

A Mechanism of Eddy Generation in A Single Lid-Driven T-Shaped Cavity

Abstract

Keywords

Supporting Institution

Project Number

Thanks

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

Cited By

Lid-Driven Butterfly Cavity for a Controllable Viscous Flow

Analytical solution and flow topology in a lid-driven S-shaped cavity

A decoupled finite element scheme for simulating the dynamics of red blood cells in an L-shaped cavity

Computational analysis of Newtonian fluid in a 2-D square cavity with kinetic energy, enstrophy, and palinstrophy in the presence of bottom corner obstacle

Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid