High Temperature

, Volume 55, Issue 5, pp 746–752 | Cite as

The stability of swirling flows with a heat source

  • I. P. Zavershinskii
  • A. I. Klimov
  • S. E. Kurushina
  • V. V. Maksimov
  • N. E. Molevich
  • S. S. Sugak
Heat and Mass Transfer and Physical Gasdynamics


The absolute instability of a Rankine vortex with an axial flow and paraxial heat source is investigated. The dispersion relation for vortex modes is derived analytically. The dependence of dispersion properties of the media on control parameters such as swirl parameter S, velocity a, and heat source power (density parameter Q) is studied. The frequency of helical waves increases and the increment decreases with increasing heat source power, accompanied by a decrease in the width of the neutral stability region. Numerical analysis also suggests that one of the dispersion curve branches could include an instability region of a parametric nature.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gupta, A.K., Lilley, D.G., Syred, N., Swirl Flows, Tunbridge Wells: Abacus, 1984.Google Scholar
  2. 2.
    Alekseenko, S.V., Kuibin, P.A., and Okulov, V.L., Vvedenie v teoriyu kontsentrirovannykh vikhrei (Introduction to the Theory of Concentrated Vortices), Novosibirsk: Inst. Teplofiz., Sib. Otd. Ross. Akad. Nauk, 2003.MATHGoogle Scholar
  3. 3.
    Syred, N., Prog. Energy Combust. Sci., 2006, vol. 32, p. 93.CrossRefGoogle Scholar
  4. 4.
    Hassa, C., Voigt, P., Lehmann, B., Schodl, R., and Carl, M., AIAA Pap., 2002, 2002–3709.Google Scholar
  5. 5.
    Jasinski, M., Dors, M., Nowakowska, H., and Mizeraczyk, J., Chem. Listy, 2008, vol. 102, p. 1332.Google Scholar
  6. 6.
    Bityurin, V.A., Klimov, A.I., Korshunov, O.V., and Chinnov, V.F., High Temp., 2015, vol. 53, no. 1, p. 21.CrossRefGoogle Scholar
  7. 7.
    Litvinov, I.V., Shtork, S.I., Kuibin, P.A., Alekseenko, S.V., and Hanjalic, K., Int. J. Heat Fluid Flow, 2013, vol. 42, p. 251.CrossRefGoogle Scholar
  8. 8.
    Fernandes, E.C., Heitor, M.V., and Shtork, S.I., Exp. Fluids, 2006, vol. 40, p. 177.CrossRefGoogle Scholar
  9. 9.
    Claypole, T.C., Pollutant Formation in Swirling Jets, PhD Thesis, Cardiff: Univ. Wales, 1980.Google Scholar
  10. 10.
    Syred, N. and Bee, J.M., Astronaut. Acta, 1972, vol. 17, p. 783.Google Scholar
  11. 11.
    Loiseleux, T., Chomaz, J.-M., and Huerre, P., Phys. Fluids, 1998, vol. 1, p. 1120.ADSCrossRefGoogle Scholar
  12. 12.
    Lim, D. and Redekopp, L., Eur. J. Mech., 1998, vol. 17, p. 165.CrossRefGoogle Scholar
  13. 13.
    Gallaire, F. and Chomaz, J.-M., Phys. Fluids, 2003, vol. 12, p. 2622.ADSCrossRefGoogle Scholar
  14. 14.
    Sipp, D., Fabre, D., Michelin, S., and Jacquin, L., J. Fluid Mech., 2005, vol. 526, p. 67.ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Fridman, A.M., Phys.—Usp., 2008, vol. 51, no. 3, p. 213.ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Meliga, P., Sipp, D., and Chomaz, J.-M., J. Fluid Mech., 2008, vol. 600, p. 373.ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Lesshafft, L. and Huerre, P., Phys. Fluids, 2007, vol. 19, 024102.ADSCrossRefGoogle Scholar
  18. 18.
    Di Pierro, B. and Abid, M., Eur. Phys. J. B, 2012, vol. 85, p. 69.ADSCrossRefGoogle Scholar
  19. 19.
    Yu, N. and Monkewitz, P.A., Phys. Fluids A, 1990, vol. 2, no. 7, p. 1175.ADSCrossRefGoogle Scholar
  20. 20.
    Uberoi, M., Chow, ChuenYen., and Narain, J., Phys. Fluids, 1972, vol. 15, p. 1718.ADSCrossRefGoogle Scholar
  21. 21.
    Di Pierro, B., Abid, M., and Amielh, M., Phys. Fluids, 2013, vol. 25, 084104.ADSCrossRefGoogle Scholar
  22. 22.
    Moralev, I.A., Klimov, A.I., Preobrazhenskii, D.S., Tolkunov, B.N., and Kutlaliev, V.A., Teplofiz. Vys. Temp., 2010, vol. 48, no. 1 (Suppl.), p. 136.Google Scholar
  23. 23.
    Zavershinskii, I.P., Klimov, A.I., Makaryan, V.G., Molevich, N.E., Moralev, I.A., and Porfir’ev, D.P., Tech. Phys. Lett., 2011, vol. 37, no. 12, p. 1120.CrossRefGoogle Scholar
  24. 24.
    Saffman P.G., Vortex Dynamics, New York: Cambridge Univ. Press, 1992.MATHGoogle Scholar
  25. 25.
    Ostrovskii, L.A., Rybak, S.A., and Tsimring, L.Sh., Phys.—Usp., 1986, vol. 29, no. 11, p. 1040.ADSCrossRefGoogle Scholar
  26. 26.
    Zavershinskii, I.P., Kogan, E.Ya., Makaryan, V.G., Molevich, N.E., Porfir’ev, D.P., and Sugak, S.S., Tech. Phys. Lett., 2013, vol. 39, no. 4, p. 333.ADSCrossRefGoogle Scholar
  27. 27.
    Dekterev, A.A., Gavrilov, A.A., and Dekterev, A.A., in Sb. tr. Mezhdunar. konf. “Sovremennye problemy prikladnoi matematiki i mekhaniki: teoriya, eksperiment i prilozheniya” (Proc. Int. Conf. “Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment, and Applications”), Novosibirsk, 2011, p. 1.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • I. P. Zavershinskii
    • 1
  • A. I. Klimov
    • 2
  • S. E. Kurushina
    • 1
  • V. V. Maksimov
    • 1
  • N. E. Molevich
    • 1
    • 3
  • S. S. Sugak
    • 1
  1. 1.Korolev Samara State Aerospace University (SGAU)SamaraRussia
  2. 2.Joint Institute for High Temperatures of the Russian Academy of SciencesMoscowRussia
  3. 3.Lebedev Physical Institute of the Russian Academy of SciencesSamaraRussia

Personalised recommendations