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Calculation of the self-oscillations arising as a result of the loss of stability by the spiral flow of a viscous liquid in an annular tube

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Abstract

The spiral flow of a viscous liquid in an annular gap (formed by concentric cylinders) due to the rotation of the inner cylinder and the axial pressure gradient is considered; the stability of the flow is discussed in relation to small but finite rotationally symmetrical perturbations.

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Literature cited

  1. 1.

    S. Goldstein, “The stability of viscous fluid between rotating cylinders,” Proc. Cambridge Phil. Soc.,33, 41–61 (1937).

  2. 2.

    R. C. Di Prima, “The stability of a viscous fluid between rotating cylinders with an axial flow,” J. Fluid Mech.,9, No. 4, 621–629 (1960).

  3. 3.

    S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford (1961).

  4. 4.

    E. R. Krueger and R. C. Di Prima, “The stability of a viscous fluid between rotating cylinders with an axial uow,” J. Fluid Mech.,19, No. 4 (1964).

  5. 5.

    S. K. Datta, “Stability of spiral flow between concentric cylinders at low axial Reynolds numbers,” J. Fluid Mech.,21, No. 4 (1965).

  6. 6.

    T. H. Hughes and W. H. Reid, “The stability of spiral flow between rotating cylinders,” Phil. Trans. Roy Soc.,A263, No. 1135, 57–91 (1968).

  7. 7.

    E. Wedemeyer, “Stability of a spiral flow in a cylindrical annular space,” Mitt. M. Planck Inst. Strömungsforsch. Aerodyn. Versuch.,44 (1969).

  8. 8.

    W. L. Hung, D. D. Joseph, and B. R. Munson, “Global stability of spiral flow. Part 2,” J. Fluid Mech.,51, No. 3, 593–612 (1972).

  9. 9.

    R. I. Cornisch, “Flow of water through fine clearances with relative motion of the boundaries,” Proc. Roy. Soc.,A140, 227–240 (1933).

  10. 10.

    A. Fage, “The influence of wall oscillations, wall rotation, and entry eddies on the breakdown of laminar flow in an annular pipe,” Proc. Roy. Soc.,A165, 513–517 (1938).

  11. 11.

    J. Kaye and E. C. Elgar, “Modes of adiabatic and diabatic flow in an annulus with an inner rotating cylinder,” Trans. ASME,80, No. 3 (1958).

  12. 12.

    R. J. Donnelly and D. Fultz, “Experiments of the stability of spiral flow between rotating cylinders,” Proc. Nat. Acad. Sci.,46, No. 8, 1150–1154 (1960).

  13. 13.

    M. A. Snyder, “Experiments on the stability of spiral flow at low axial Reynolds numbers,” Proc. Roy. Soc.,A265, No. 1321 (1962).

  14. 14.

    K. W. Schwartz, B. E. Springett, and R. J. Donnelly, “Modes of instability of spiral flow between rotating cylinders,” J. Fluid Mech.,20, Part 2 (1964).

  15. 15.

    T. A. Liseikina, “Stability of spiral flows,” Candidate's Dissertation, Institute of Thermophysics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1973).

  16. 16.

    T. A. Vil'gel'mi and V. N. Shtern, “Stability of spiral flow in an annular gap,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 35–44 (1974).

  17. 17.

    V. I. Yudovich, “Mathematical problems in the theory of stability of liquid flows,” Doctoral Dissertation, Institute of the Problems of Mechanics, Academy of Sciences of the USSR, Moscow (1972).

  18. 18.

    A. L. Urintsev, “Self-oscillations in a liquid heated from below,” in: Communications to the Second Conference of the Rostov Mathematical Society [in Russian], Rostov-on-Don (1968), pp. 153–157.

  19. 19.

    V. I. Yudovich, “Development of self-oscillations in a liquid,” Prikl. Mat. Mekh.,35, No. 4 (1971).

  20. 20.

    V. I. Yudovich, “Study of the self-oscillations of a continuous medium arising after the loss of stability of a steady-state situation,” Prikl. Mat. Mekh.,36, No. 3 (1972).

  21. 21.

    I. P. Andreichikov and V. I. Yudovich, “Self-oscillatory modes branching from Poiseuille flow in a plane channel,” Dokl. Akad. Nauk SSSR,202, No. 4, 791 (1972).

  22. 22.

    S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk,16, No. 3(99), 171–174 (1961).

  23. 23.

    S. D. Conte, “The numerical solution of linear boundary-value problems,” SIA Review, 8, No. 3, 309–321 (1966).

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Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 57–63, May–June, 1976.

The author wishes to thank V. I. Yudovich for interest in this work.

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Urintsev, A.L. Calculation of the self-oscillations arising as a result of the loss of stability by the spiral flow of a viscous liquid in an annular tube. J Appl Mech Tech Phys 17, 344–349 (1976). https://doi.org/10.1007/BF00853567

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Keywords

  • Mathematical Modeling
  • Mechanical Engineer
  • Pressure Gradient
  • Industrial Mathematic
  • Viscous Liquid