Research Article
PDF Zotero Mendeley EndNote BibTex Cite

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

Year 2019, Volume 40, Issue 3, 583 - 594, 30.09.2019
https://doi.org/10.17776/csj.569655

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.

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).

Tek Kapağı Sürgülü T-Şeklindeki Kaviti İçerisindeki Girdap Oluşum Mekanizması

Year 2019, Volume 40, Issue 3, 583 - 594, 30.09.2019
https://doi.org/10.17776/csj.569655

Abstract

Üst kapağı yatay yönde hareket eden T şeklindeki kaviti içerisindeki iki boyutlu (2D) durağan, sıkıştırılamaz, Stokes akış ele alındı. Yeni girdap oluşumunu ve akış çatallanmasını araştırmak için Galerkin sonlu elemanlar yöntemi kullanıldı. Kaviti içersindeki akış, T-şeklindeki bölgenin  ve  yükseklik parametreleri tarafından kotrol edilir.  ve  yüksekliklerinin değişmesiyle meydana gelen girdap oluşum mekanizması ve  kontrol uzay diyagramı elde edildi.

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 Basic Sciences
Journal Section Natural Sciences
Authors

Ali DELİCEOĞLU (Primary Author)
Erciyes University, Science Faculty, Department of Mathematics
0000-0003-0863-6276
Türkiye


Ebutalib ÇELİK
Erciyes University, Science Faculty, Department of Mathematics
0000-0002-4500-4465
Türkiye

Supporting Institution TÜBİTAK
Project Number 114F525
Thanks This study was supported by Scientific and Technological Research Council of Turkey (TÜBİTAK) [project number 114F525]
Publication Date September 30, 2019
Application Date May 24, 2019
Acceptance Date August 15, 2019
Published in Issue Year 2019, Volume 40, Issue 3

Cite

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 . DOI: 10.17776/csj.569655