Stability and experimental velocity field in Taylor—Couette flow with axial and radial flow

  • Richard M. Lueptow
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 549)


The imposition of a radial or axial flow on cylindrical Couette flow alters the stability of the system and modifies the velocity field. An axial flow stabilizes cylindrical Couette flow. The supercritical flow includes a rich variety of vortical structures including helical and wavy vortices. An axial flow also results in translation of the vortices with the axial flow. A radial flow through porous cylinders stabilizes cylindrical Couette flow, whether the radial flow is inward or outward. An exception is that a small radial outward flow destabilizes the flow slightly. The radial flow results in displacing vortex centers toward the cylinder from which fluid exits the annulus. For combined axial and radial flow, the axial flow stabilizes the cylindrical Couette flow regardless of the radial flow. In addition, the radial flow stabilizes the flow compared to the situation with no radial flow. Above the supercritical transition a wide variety of flow regimes occur in the case where the inner cylinder is porous and the outer cylinder is nonporous. The velocity field for cylindrical Couette flow with axial flow and a radial inflow at the inner cylinder is altered very little for small radial flows. However, the vortices shrink in size as they translate in the annulus as fluid is lost through the inner cylinder.


Particle Image Velocimetry Axial Velocity Linear Stability Analysis Outer Cylinder Azimuthal Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    E.C. Johnson, R.M. Lueptow: Phys. Fluids 9, 3687 (1997)CrossRefADSGoogle Scholar
  2. 2.
    K.C. Chung, K.N. Astill: J. Fluid Mech. 81, 641 (1977)zbMATHCrossRefADSGoogle Scholar
  3. 3.
    P.R. Fenstermacher, H.L. Swinney, J.P. Gollub: J. Fluid Mech. 94, 103 (1979)CrossRefADSGoogle Scholar
  4. 4.
    C.D. Andereck, S.S. Liu, H.L. Swinney: J. Fluid Mech. 164, 155 (1986)CrossRefADSGoogle Scholar
  5. 5.
    K. Bühler, N. Polifke:’ Dynamical behavior of Taylor vortices with superimposed axial flow’. In: Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems ed. by F. H. Busse, L. Kramer (Plenum Press, New York 1990), vol. Series B:Physics Vol. 225, pp. 21Google Scholar
  6. 6.
    R.M. Lueptow, A. Docter, K. Min: Phys. Fluids A 4, 2446 (1992)CrossRefADSGoogle Scholar
  7. 7.
    G.I. Taylor: Phil. Trans. A 223, 289 (1923)CrossRefADSGoogle Scholar
  8. 8.
    S. Chandrasekhar: Hydrodynamic and Hydromagnetic Stability, (Oxford University Press, 1961)Google Scholar
  9. 9.
    R.C. DiPrima, H.L. Swinney:’ Instabilities and transition in flow between concentric rotating cylinders’. In: Topics in Applied Physics, Hydrodynamic Instabilities and the Transition to Turbulence, ed. by H. L. Swinney, J. P. Gollub (Springer-Verlag, Berlin, 1985) pp. 139–180Google Scholar
  10. 10.
    K. Kataoka:’ Taylor vortices and instabilities in circular Couette flows’. In Encyclopedia of Fluid Mechanics, ed. by N. P. Cheremisinoff (Gulf Publishing Company, 1986), vol. 1, pp. 237–273Google Scholar
  11. 11.
    E.L. Koschmieder: Benard Cells and Taylor Vortices (Cambridge University Press, 1993)Google Scholar
  12. 12.
    S. Chandrasekhar: Proc. Natl. Acad. Sci. 46, 141 (1960)zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    R.C. DiPrima: J. Fluid Mech. 9, 621 (1960)CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    M.A. Hasoon, B.W. Martin: Proc. R. Soc. Lond. A 352, 351 (1977)zbMATHADSCrossRefGoogle Scholar
  15. 15.
    R.C. DiPrima, A. Pridor: Proc. R. Soc. Lond. A 366, 555 (1979)ADSCrossRefGoogle Scholar
  16. 16.
    J. Kaye, E.C. Elgar: Trans ASME 80, 753 (1958)Google Scholar
  17. 17.
    H.A. Snyder: Proc. R. Soc. Lond. A 265, 198 (1962)ADSCrossRefGoogle Scholar
  18. 18.
    B.S. Ng, E.R. Turner: Proc. R. Soc. Lond. A 382, 83 (1982)zbMATHADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    K.L. Babcock, G. Ahlers, D.S. Cannell: Physical Review Letters 67, 3388 (1991)CrossRefADSGoogle Scholar
  20. 20.
    A. Recktenwald M. Lücke, H.W. Müller: Physical Review E 48, 4444 (1993)CrossRefADSGoogle Scholar
  21. 21.
    D.I. Takeuchi, D.F. Jankowski: J. Fluid Mech. 102, 101 (1981)CrossRefADSGoogle Scholar
  22. 22.
    K. Bühler: ZAMM 64, T180 (1984)Google Scholar
  23. 23.
    A. Tsameret, V. Steinberg: Physical Review Letters 67, 3392 (1991)CrossRefADSGoogle Scholar
  24. 24.
    A. Tsameret, V. Steinberg: Physical Review E 49, 1291 (1994)CrossRefADSGoogle Scholar
  25. 25.
    K.M. Becker, J. Kaye: J. Heat Transfer 84, 97 (1962)Google Scholar
  26. 26.
    K. Beranek, I. Streda, J. Sestak: Acta Technica CSA V 24, 665 (1979)Google Scholar
  27. 27.
    K.W. Schwarz, B.E. Springett, R.J. Donnelly: J. Fluid Mech. 20, 281 (1964)CrossRefADSGoogle Scholar
  28. 28.
    K. Kataoka, H. Doi, T. Komai: Int. J. Heat Mass Transfer 20, 57 (1977)CrossRefGoogle Scholar
  29. 29.
    S.T. Wereley, R.M. Lueptow: Phys. Fluids 11, 3637 (1999)CrossRefADSzbMATHGoogle Scholar
  30. 30.
    K.N. Astill: J. of Heat Transfer 86, 383 (1964)Google Scholar
  31. 31.
    D.A. Simmers, J.E.R. Coney: Int. J. Heat Fluid Flow 1, 177 (1979)CrossRefGoogle Scholar
  32. 32.
    K. Min, R.M. Lueptow: Exp. Fluids 17, 190 (1994)CrossRefGoogle Scholar
  33. 33.
    S.T. Wereley, R.M. Lueptow: Exp. Fluids 18, 1 (1994)CrossRefGoogle Scholar
  34. 34.
    R.M. Lueptow, A. Hajiloo: Am. Soc. Artif. Int. Organs J. 41, 182 (1995)Google Scholar
  35. 35.
    M. Stöckert, R.M. Lueptow: ‘Velocity field in Couette-Taylor flow with axial flow’. In 10th International Couette-Taylor Workshop, ed. by C. Normand, J. E. Wesfreid Paris, 1997 pp. 147–148.Google Scholar
  36. 36.
    S.T. Wereley, R.M. Lueptow: J. Fluid Mech. 364, 59 (1998)zbMATHCrossRefADSMathSciNetGoogle Scholar
  37. 37.
    P.S. Marcus: J. Fluid Mech. 146, 65(1984)zbMATHCrossRefADSGoogle Scholar
  38. 38.
    T.S. Chang, W.K. Sartory: J. Fluid Mech. 27, 65(1967)Google Scholar
  39. 39.
    T.S. Chang, W.K. Sartory: J. Fluid Mech. 36, 193 (1969)Google Scholar
  40. 40.
    S.K. Bahl: Def. Sci. J. 20, 89 (1970)Google Scholar
  41. 41.
    K. Bühler, ”Taylor vortex flow with superimposed radial mass flux”. In: Ordered and Turbulent Patterns in Taylor-Couette Flow, ed. by E. D. Andereck, F. Hayot (Plenum Press, New York, 1992) pp. 197–203.Google Scholar
  42. 42.
    P.G. Reddy, Y.B. Reddy: Def. Sci. J. 26, 47 (1976)zbMATHGoogle Scholar
  43. 43.
    P.G. Reddy, Y.B. Reddy, A.G.S. Reddy: Def. Sci. J. 28, 145(1978)zbMATHGoogle Scholar
  44. 44.
    K. Min, R.M. Lueptow: Phys. Fluids 6, 144 (1994)zbMATHCrossRefADSGoogle Scholar
  45. 45.
    A. Kolyshkin, R. Vaillancourt: Phys. Fluids 9, 910 (1997)zbMATHCrossRefADSMathSciNetGoogle Scholar
  46. 46.
    N. Gravas, B.W. Martin: J. Fluid Mech. 86, 385(1978)CrossRefADSGoogle Scholar
  47. 47.
    S.K. Bahl, K.M. Kapur: Def. Sci. J. 25, 139 (1975)zbMATHGoogle Scholar
  48. 48.
    F. Marques, J. Sanchez, P.D. Weidman: J. Fluid Mech. 347, 221 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Richard M. Lueptow
    • 1
  1. 1.Northwestern UniversityEvanstonUSA

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