Advertisement

Numerical investigation of the onset of axisymmetric and wavy Taylor-Couette flows between combinations of cylinders and spherocylinders

  • A. LalaouaEmail author
  • F. Naït Bouda
Regular Article
  • 32 Downloads

Abstract.

The Taylor-Couette flow, which is the flow that occurs between two rotating bodies, has become fundamental to the study of instability and nonlinear behaviour. Many modifications can be made to the Taylor-Couette flow resulting in much more complex flow structures, either by geometrical changes, or by combining different geometries. The main goal of this work is to numerically investigate the effect of the cylinders-spheres combinations on the onset of different instabilities of a fluid confined between two concentric bodies. The modelling strategy was developed by studying three types of flow configurations: cylindrical Taylor-Couette flow (with fixed endcaps), flow between two concentric cylinders with hemispheres on the lower end wall, and flow between two coaxial spherocylinders (cylinders with hemispheres on the upper and lower end surfaces). The inner element rotates while the outer one is at rest. The numerical calculations were carried out to determine the transition zone from a laminar Couette flow to the onset of Taylor vortices and wavy vortex flow. The parameter that determines the flow regimes is the Reynolds number based on the angular velocity of the inner element. The fluid dynamic behaviours for different flow configurations are characterized by the wall shear stress and the skin friction coefficient. Laminar, axisymmetric and wavy Taylor-Couette flows are predicted for different configurations. It is established that the different combinations deeply affect the flow behaviour and the appearance of the instabilities. The transition from LCF to TVF and then to WVF in the combined flow systems is substantially retarded compared to the cylindrical Taylor-Couette flow system.

References

  1. 1.
    A. Mallock, Philos. Trans. R. Soc. London A 187, 41 (1896)ADSCrossRefGoogle Scholar
  2. 2.
    M. Couette, Ann. Chim. Phys. 6, 433 (1890)Google Scholar
  3. 3.
    L. Rayleigh, Proc. R. Soc. London A 93, 148 (1916)ADSCrossRefGoogle Scholar
  4. 4.
    G.l. Taylor, Philos. Trans. R. Soc. London A 223, 289 (1923)ADSCrossRefGoogle Scholar
  5. 5.
    D. Coles, J. Fluid Mech. 21, 385 (1965)ADSCrossRefGoogle Scholar
  6. 6.
    S. Chandrasekhar, Proc. Natl. Acad. Sci. 46, 141 (1960)ADSCrossRefGoogle Scholar
  7. 7.
    P.R. Fenstermacher, H.L. Swinney, J.P. Gollub, J. Fluid Mech. 94, 103 (1979)ADSCrossRefGoogle Scholar
  8. 8.
    R.C. Diprima, H.L. Swinney, Instabilities and transition in flow between concentric rotating cylinders, in Hydrodynamic Instabilities and the Transition to Turbulence, Topics in Applied Physics, Springer, Vol. 45 (Springer, 1981) pp. 139--180Google Scholar
  9. 9.
    R.J. Donnelly, Phys. Today 44, 32 (1991)CrossRefGoogle Scholar
  10. 10.
    P.S. Marcus, J. Fluid Mech. 146, 45 (1984)ADSCrossRefGoogle Scholar
  11. 11.
    E.L. Koschmieder, Benard cells and Taylor vortices (Cambridge University, NewYork, 1993)Google Scholar
  12. 12.
    O. Czarny, E. Serre, P. Bontoux, R.M. Lueptow, Phys. Fluids 15, 467 (2003)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    K. Avila, B. Hof, Rev. Sci. Instrum. 84, 065106 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    B. Martinez-Arias, J. Peixinho, O. Crumeyrolle, I. Mutabazi, J. Fluid Mech. 748, 756 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    E. Adnane, A. Lalaoua, A. Bouabdallah, J. Appl. Fluid Mech. 9, 1097 (2016)CrossRefGoogle Scholar
  16. 16.
    Duccio Griffini, Massimiliano Insinna, Simone Salvadori, Andrea Barucci, Franco Cosi, Stefano Pelli, Giancarlo C. Righini, Fluids 2, 8 (2017)CrossRefGoogle Scholar
  17. 17.
    A. Froitzheim, S. Merbold, C. Egbers, J. Fluid Mech. 831, 330 (2017)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    H.J. Brauckmann, M. Salewsky, B. Eckhardt, J. Fluid Mech. 790, 419 (2016)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    A. Chouippe, E. Climent, D. Legendre, C. Gabillet, Phys. Fluids 26, 043304 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    S. Grossmann, D. Lohse, C. Sun, Annu. Rev. Fluid Mech. 48, 53 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    A. Lalaoua, Eur. Phys. J. Appl. Phys. 77, 11101 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    T. Mullin, M. Heise, G. Pfister, Phys. Rev. Fluids 2, 081901(R) (2017)ADSCrossRefGoogle Scholar
  23. 23.
    G.N. Khlebutin, Fluid Dyn. 3, 31 (1968)ADSCrossRefGoogle Scholar
  24. 24.
    I.M. Yavorskaya, Yu.N. Belyaev, A.A. Monakhov, Dokl. Akad. Nauk. SSSR 237, 804 (1977)ADSGoogle Scholar
  25. 25.
    K. Nakabavashi, ASME J. Fluids Eng. 100, 97 (1978)CrossRefGoogle Scholar
  26. 26.
    P.S. Marcus, L.S. Tuckerman, J. Fluid Mech. 185, 1 (1987)ADSCrossRefGoogle Scholar
  27. 27.
    P.S. Marcus, L.S. Tuckerman, J. Fluid Mech. 185, 31 (1987)ADSCrossRefGoogle Scholar
  28. 28.
    K. Bühler, Acta Mech. 81, 3 (1990)MathSciNetCrossRefGoogle Scholar
  29. 29.
    C. Egbers, H.J. Rath, Acta Mech. 111, 125 (1995)CrossRefGoogle Scholar
  30. 30.
    R. Hollerbach, Phys. Rev. Lett. 81, 3132 (1998)ADSCrossRefGoogle Scholar
  31. 31.
    C. Peralta, A. Melatos, M. Giacobello, A. Ooi, J. Fluid Mech. 609, 221 (2008)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    K. Bühler, J. Therm. Sci. 18, 109 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    Li. Yuan, Phys. Fluids 24, 124104 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    D.Yu. Zhilenko, O.E. Krivonosova, Fluid Dyn. 48, 452 (2013)ADSCrossRefGoogle Scholar
  35. 35.
    A. Lalaoua, A. Bouabdallah, ASME J. Fluids Eng. 138, 111201 (2016)CrossRefGoogle Scholar
  36. 36.
    M. Wimmer, Prog. Aerospace Sci. 25, 43 (1988)ADSCrossRefGoogle Scholar
  37. 37.
    M. Wimmer, Z. Angew. Math. Mech. 69, 616 (1989)Google Scholar
  38. 38.
    M. Wimmer: Vortex patterns between cones and cylinders, in Ordered and turbulent patterns in Taylor-Couette flow, edited by C.D. Andereck, F. Hayot, in NATO ASI Series B. Physics, Vol. 297 (Plenum Press N. Y., 1992) pp. 205--211Google Scholar
  39. 39.
    M. Abboud, Z. Angew. Math. Mech. 70, T441 (1990)Google Scholar
  40. 40.
    L. Ning, G. Ahlers, D.S. Cannel, Phys. Rev. Lett. 64, 1235 (1990)ADSCrossRefGoogle Scholar
  41. 41.
    B. Denne, M. Wimmer, Acta Mech. 133, 69 (1999)CrossRefGoogle Scholar
  42. 42.
    M.A. Sprague, P.D. Weidman, S. Macumber, P.F. Fischer, Phys. Fluids 20, 014102 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    M. Wimmer: Taylor vortices at different geometries, in Phys. Rotating Fluids, edited by C. Egbers, G. Pfister (Springer, New York, 2000) pp. 194--212CrossRefGoogle Scholar
  44. 44.
    J. Parker, P. Merati, Trans. ASME 118, 810 (1996)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of TechnologyUniversity of BejaiaBejaïaAlgeria

Personalised recommendations