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

Yıl 2019, Cilt: 40 Sayı: 3, 583 - 594, 30.09.2019
https://doi.org/10.17776/csj.569655

Öz

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.

Destekleyen Kurum

TÜBİTAK

Proje Numarası

114F525

Teşekkür

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

Kaynakça

  • [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

Yıl 2019, Cilt: 40 Sayı: 3, 583 - 594, 30.09.2019
https://doi.org/10.17776/csj.569655

Öz

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.

Proje Numarası

114F525

Kaynakça

  • [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).
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Natural Sciences
Yazarlar

Ali Deliceoğlu 0000-0003-0863-6276

Ebutalib Çelik 0000-0002-4500-4465

Proje Numarası 114F525
Yayımlanma Tarihi 30 Eylül 2019
Gönderilme Tarihi 24 Mayıs 2019
Kabul Tarihi 15 Ağustos 2019
Yayımlandığı Sayı Yıl 2019Cilt: 40 Sayı: 3

Kaynak Göster

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