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On the flow between a rotating and a porous fixed disk with suction

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Abstract

Numerical self-similar solutions are reported for the laminar, incompressible flow between a rotating disk and a porous, fixed one with suction. Validation of the method is obtained through the numerical integration of the full Navier-Stokes equations applied to a reference radially confined geometry, and also with hot-wire measurements of the tangential velocity component. The flow structure is analysed for different values of the rotational and suction Reynolds numbers. It is shown that suction causes an important angular acceleration of the rotating core, whose velocity may thus considerably exceed that of the rotating disk. The physical reason for this unusual behavior is discussed in detail.

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References

  1. Batchelor, G.K., Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow, Quart. J. Mech. Appl. Math., 1951, 4, 29.

    Google Scholar 

  2. Stewartson, K., On the flow between two rotating coaxial disks, Math. Proc. Cambridge Philos. Soc., 1953, 49, 333.

    Google Scholar 

  3. Mellor, G.L., Chapple, P.J., and Stokes, V.K., On the flow between a rotating and a stationary disk, J. Fluid Mech., 1968, 31, 95.

    Google Scholar 

  4. Nguyen, N.D., Ribault, J.P., and Florent, P., Multiple solutions for flow between coaxial disks, J. Fluid Mech., 1975, 68, 369.

    Google Scholar 

  5. Holodniok, M., Kubicek, M., and Hlavacek, V., Computation of the flow between two rotating coaxial disks: multiplicity of steady-state solutions, J. Fluid Mech., 1981, 108, 227.

    Google Scholar 

  6. Dijkstra, D., and Van Heijst, G.J.F., The flow between two finite rotating disks enclosed by a cylinder, J. Fluid Mech., 1983, 128, 123.

    Google Scholar 

  7. Oliveira, L.A., Pécheux, J., and Restivo, A.O., On the flow between a rotating and a coaxial fixed disc: numerical validation of the radial similarity hypothesis, Theoret. Comput. Fluid Dynamics, 1991, 2, 211.

    Google Scholar 

  8. Wilson, L.O., and Schryer, N.L., Flow between a stationary and a rotating disk with suction, J. Fluid Mech., 1978, 85, 479.

    Google Scholar 

  9. Goldshtik, M.A., and Javorsky, N.I., On the flow between a porous rotating disk and a plane, J. Fluid Mech., 1989, 207, 1.

    Google Scholar 

  10. Elkrat, A.R., On the flow between a rotating disk and a porous disk, Arch. Rational Mech. Anal., 1980, 73, 63.

    Google Scholar 

  11. Pécheux, J., Contribution à l'étude de l'écoulement entre deux disques produit par débit radial, rotation, soufflage ou aspiration, Doctorat-ès-Sciences Physiques, University of Poitiers, 1976.

  12. Bien, F., and Penner, S.S., Velocity profiles in steady and unsteady rotating flows for a finite cylindrical geometry, Phys. Fluids, 1970, 13, 1665.

    Google Scholar 

  13. Owen, J.M., and Pincombe, J.R., Velocity measurements inside a rotating cylindrical cavity with a radial outflow of fluid, J. Fluid Mech., 1980, 99, 111.

    Google Scholar 

  14. Oliveira, L.A., Bousgarbiès, J.L., and Pécheux, J., Étude expérimentale de l'écoulement entre un disque fixe et un disque tournant, C. R. Acad. Sci. Paris, 1982, 294, 1163.

    Google Scholar 

  15. Pearson, C.E., Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks, J. Fluid Mech., 1965, 21, 623.

    Google Scholar 

  16. Smith, G.D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, Oxford, 1978.

    Google Scholar 

  17. Oliveira, L.A., Contribuição para o estudo do escoamento axissimétrico entre discos rotativos, Doctoral Thesis, University of Coimbra, 1986.

  18. Gosman, A.D., and Ideriah, F.J.K., TEACH-T: A general computer program for two-dimensional, turbulent, recirculating flow, Department of Mechanical Engineering Report, Imperial College, London, 1976.

    Google Scholar 

  19. Reshotko, E., and Rosenthal, R.L., Laminar flow between two infinite disks, one rotating and the other stationary, Israel J. Tech., 1971, 9, 93.

    Google Scholar 

  20. Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, 1968.

    Google Scholar 

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Authors and Affiliations

  1. Departamento de Engenharia Mecânica, Universidade de Coimbra, Coimbra, Portugal

    L. A. Oliveira

  2. Laboratoire d'Etudes Aérodynamiques (UA CNRS 191), Université de Poitiers, Poitiers, France

    J. Pécheux

  3. Departamento de Engenharia Mecânica, Universidade de Coimbra, Coimbra, Portugal

    M. C. Silva

Authors
  1. L. A. Oliveira
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  2. J. Pécheux
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  3. M. C. Silva
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Communicated by M.Y. Hussaini

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Oliveira, L.A., Pécheux, J. & Silva, M.C. On the flow between a rotating and a porous fixed disk with suction. Theoret. Comput. Fluid Dynamics 4, 119–127 (1993). https://doi.org/10.1007/BF00417936

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  • DOI: https://doi.org/10.1007/BF00417936

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