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

Year 2019, Volume: 40 Issue: 3, 583 - 594, 30.09.2019

Ali Deliceoğlu Ebutalib Çelik

https://doi.org/10.17776/csj.569655
Cited By: 3

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).

Tek Kapağı Sürgülü T-Şeklindeki Kaviti İçerisindeki Girdap Oluşum Mekanizması

Year 2019, Volume: 40 Issue: 3, 583 - 594, 30.09.2019

Ali Deliceoğlu Ebutalib Çelik

https://doi.org/10.17776/csj.569655
Cited By: 3

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.

Keywords

T-şekilli kaviti Stokes akış

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).
There are 28 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Ali Deliceoğlu 0000-0003-0863-6276

Ebutalib Çelik 0000-0002-4500-4465

Project Number 114F525
Publication Date September 30, 2019
Submission Date May 24, 2019
Acceptance Date August 15, 2019
Published in Issue Year 2019Volume: 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. https://doi.org/10.17776/csj.569655

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