On the rotationally symmetric laminar flow of Newtonian fluids induced by rotating disks

  • Antonio Delgado
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 549)


This paper deals with the flow induced by rotating disks. Such flows are subject of a large number of contributions in the twentieth century. Most of them are based on the famous von Kármán transform. In the last three decades the applicability of this transform has been proved in sophisticated experimental and theoretical investigations. The present paper focuses on theoretical investigations treating a pair of disks rotating concentrically. In addition to classical solutions given by Batchelor and Stewartson, the problem of solutions being multiple, unstable and even aphysical is briefly addressed. Furthermore, some approaches dealing with moderate Reynolds-numbers are presented for which the equations of motion are linearized starting from a known creeping flow solution. A comparison of the results with those obtained from the solution of the complete Navier-Stokes equation is carried out.


Reynolds Number Constant Angular Velocity Wall Shear Rate Small Reynolds Number Circumferential Velocity 
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  1. 1.
    T. von Kármán: ZAMM 1, 233–254 (1921)CrossRefGoogle Scholar
  2. 2.
    W.G. Cochran: Proc. Camb. Phil. Soc. 30, 365–375 (1934)zbMATHCrossRefGoogle Scholar
  3. 3.
    K.G Batchelor: Q. J. Mech. Maths 4, 29–41 (1951)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    K. Stewartson: Proc. Camb. Phil. Soc. 49, 333–341 (1953)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    K.G. Picha, E.R.G. Eckert: ‘Study of the air flow between coaxial disks rotating with arbitrary velocities in an open or enclosed space’. In: Proc. Third U.S. Natl. Cong. Appl. Mech., 791–798 (1958)Google Scholar
  6. 6.
    S.M. Roberts, J.S. Shipman: J. Fluid Mech. 73, 53–63 (1976)zbMATHCrossRefADSGoogle Scholar
  7. 7.
    G.L. Mellor, P.J. Chapple, V.J. Stokes: J. Fluid Mech. 68, 95–112 (1968)CrossRefADSGoogle Scholar
  8. 8.
    M. Holodniok, M. Kubicek, V. Hlavácek: J. Fluid Mech. 81, 689–699 (1977)zbMATHCrossRefADSMathSciNetGoogle Scholar
  9. 9.
    D. Dijkstra, G.J.F. van Heijst: J. Fluid Mech. 128, 123–154 (1983)zbMATHCrossRefADSGoogle Scholar
  10. 10.
    A. Delgado, H.J. Rath: Archives of Mech. 42, 4–5, 443–462 (1990)zbMATHGoogle Scholar
  11. 11.
    A. Delgado: ‘Gravitationskompensierte Strömungen rotierender newtonscher und nichtnewtonscher Fluide’. In: Fortschr.-Ber. VDIR eihe 7 Nr. 264, VDI-Verlag (1995)Google Scholar
  12. 12.
    H.P. Greenspan: ‘The theory of rotating fluids’. In: Cambridge University Press, Cambridge (1980)zbMATHGoogle Scholar
  13. 13.
    L. van Wijngaarden: Fluid Dynamics Transactions 12, 157–179 (1985)Google Scholar
  14. 14.
    P.J Zandbergen, D. Dijkstra: Annual Rev. Fluid Mech. 19, 465–491 (1987)CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    S.V. Parter: ‘On the swirling flow between coaxial rotating disks: a survey’. In: MCR Technical Report 2332 (1982)Google Scholar
  16. 16.
    M.H. Rogers, G.N. Lance: J. Fluid Mech. 7, 617–631 (1960)zbMATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    U.T. Bödewadt: ZAMM 20, 241–253 (1940)zbMATHCrossRefGoogle Scholar
  18. 18.
    R.J. Bodonyi, B.S. Ng: J. Fluid Mech. 144, 311–328 (1984)zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    A. Delgado, H.J. Rath: ZAMM 69/6, T614–T616 (1989)Google Scholar
  20. 20.
    A. Delgado, B. Petri, H.J. Rath: Appl. Microgravity Technology 1, 4, 188–201 (1988)Google Scholar
  21. 21.
    J. Wu, A. Delgado, H.J. Rath: ‘Linearized numerical solution method for rotating coaxial disk flows at moderate Reynolds numbers’. In: Proc. 7th Int. Conf. Numerical Methods in Laminar and Turbulent Flows, 15–19. July1991,Stanford, CA, USA, Vol VII, 1, pp. 480–490 (1991)ADSGoogle Scholar
  22. 22.
    J.F. Brady, L.J. Durlofsky: J. Fluid Mech. 175, 363–394 (1987)CrossRefADSGoogle Scholar
  23. 23.
    A.Z. Szeri, A. Giron, S.J. Schneider, H.N. Kaufman: J. Fluid Mech. 134, 133–154 (1983)CrossRefADSGoogle Scholar
  24. 24.
    L.J Durlofsky: Topics in fluid mechanics: I. Flow between finite rotating disks, II. Simulation of hydrodynamically interacting particles in Stokes flow. Ph.D. Thesis, Massachussets Institute of Technology (1986)Google Scholar
  25. 25.
    H. Schlichting: Grenzschicht-Theorie, 8nd edn. (Braun, Karlsruhe 1982)zbMATHGoogle Scholar
  26. 26.
    M. Holodniok, M. Kubicek, V. Hlavácek: J. Fluid Mech. 108, 227–240 (1981)zbMATHCrossRefADSGoogle Scholar
  27. 27.
    E. Reshotko, R.L. Rosenthal: Israel J. Tech. 9, 93–103 (1971)zbMATHGoogle Scholar
  28. 28.
    F. Schultz-Grunow: ZAMM 14, 191–204 (1935)Google Scholar
  29. 29.
    R.K.-H. Szeto: The flow between rotating coaxial disks. Ph.D. Thesis, California Institute of Technology (1978)Google Scholar
  30. 30.
    S. Bhattacharyya, A. Pal: Acta Mechanica 135/1, 27–40 (1999)zbMATHCrossRefGoogle Scholar
  31. 31.
    A. Delgado, H.J. Rath: ‘Theoretical investigation of the rotating disks flow of oneand two-phase fluids in microgravity’. In. Proc. IUTAM Symp. Microgravity Fluid Mech., 2.–6. September1991, Springer, Heidelberg, pp.185–193 (1992)Google Scholar
  32. 32.
    W.M. Yan, C.Y. Soong: International J. of Heat and Mass Transfer 40/4, 773–784 (1997)zbMATHCrossRefGoogle Scholar
  33. 33.
    G. Leneweit, K.G. Roesner, R. Koehler: Exp. Fluids 26, 75–85 (1999)CrossRefGoogle Scholar
  34. 34.
    W. Hort: Zeitschrift für Technische Physik 1/10, 213–221 (1920)Google Scholar
  35. 35.
    P.C. Ray, B.S. Dandapat: The quarterly J. of Mech. and appl. Math. 47/1, 297–304 (1994)zbMATHCrossRefGoogle Scholar
  36. 36.
    M. Kilic, X. Gan, J.M. Owen: J. of Fluid Mech. 281, 119–135 (1994)CrossRefADSGoogle Scholar
  37. 37.
    J.S. Roy, S. Padhy, L.K. Bhopa: Acta Mechanica 108/14, 111–120 (1995)zbMATHCrossRefGoogle Scholar
  38. 38.
    C.Y. Soong, H.L. Ma: International J. of Heat and Mass Transfer 38, 1865–1878 (1995)zbMATHCrossRefGoogle Scholar
  39. 39.
    C.Y. Soong, W.M. Yan: J. of Thermophysics and Heat Transfer 7/1, 165–170 (1993)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Antonio Delgado
    • 1
  1. 1.Technische Universität MünchenFreisingGermany

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