High Temperature

, Volume 56, Issue 5, pp 767–773 | Cite as

A Method to Calculate Mixed MHD Convention in a Vertical Channel

  • I. A. BelyaevEmail author
  • N. G. Razuvanov
  • V. G. Sviridov


A method is proposed for the numerical simulation of heat transfer in a liquid metal flow in a vertical channel with consideration of the effects of a coplanar magnetic field and natural convection. It is demonstrated that, for a downward flow in a heated rectangular channel with an aspect ratio of 3 : 1, the counteraction of natural convection induces strong velocity and temperature fluctuations that can be taken into account with the proposed method. The first stage of the development of a modeling procedure deals with a numerical solution to a simplified, nonstationary 2D problem of a downward flow in a flat, slot-like channel with uniform heating of one or two walls. At the second stage, the predicted characteristics of the nonstationary 2D flow are used to calculate the averaged characteristics of a 3D flow. The numerical results are verified against experimental data obtained under conditions similar to those used in the calculations.



This work was supported by the Russian Science Foundation (grant no. 14-50-00124). We are grateful to the personnel of the Joint Supercomputer Center, an affiliate of the Federal Governmental Agency, Federal Scientific Center, Scientific Research Institute of System Development, Russian Academy of Sciences, where the calculations were performed.


  1. 1.
    Wong, C.P.C., Salavy, J.F., Kim, Y., et al., Fusion Eng. Des., 2008, vol. 83, no. 7, p. 850.CrossRefGoogle Scholar
  2. 2.
    Kovalenko, V.G., Leshukov, A.Y., Tomilov, S.N., Razmerov, A.V., Strebkov, Y.S., Sviridenko, M.N., and Vitkovsky, I.V., Fusion Eng. Des., 2016, vol. 35, p. 142.CrossRefGoogle Scholar
  3. 3.
    Genin, L.G., Listratov, Ya.I., Sviridov, V.G., Zhilin, V.G., Ivochkin, Yu.P., Sviridov, E.V., and Razuvanov, N.G., Vopr. At. Nauki Tekh., Ser.: Termoyad. Sint., 2003, no. 4, p. 35.Google Scholar
  4. 4.
    Genin, L.G. and Sviridov, V.G., Gidrodinamika i teploobmen MGD-techenii v kanalakh (Hydrodynamics and Heat Transfer of MHD Flows in Channels), Moscow: Mosk. Energ. Inst., 2001.Google Scholar
  5. 5.
    Belyaev, I.A., Ivochkin, Yu.P., Listratov, Ya.I., Razuvanov, N.G., and Sviridov, V.G., High Temp., 2015, vol. 53, no. 5, p. 734.CrossRefGoogle Scholar
  6. 6.
    Poddubnyi, I.I., Pyatnitskaya, N.Yu., Razuvanov, N.G., Sviridov, V.G., Sviridov, E.V., Leshukov, A.Yu., Aleskovskii, K.V., and Obukhov, D.M., Vopr. At. Nauki Tekh., Ser.: Termoyad. Sint., 2015, vol. 38, no. 3, p. 5.Google Scholar
  7. 7.
    Razuvanov, N.G., Sviridov, V.G., Sviridov, E.V., Belyaev, I.A., Pyatnitskaya, N.Y., and Zagorsky, V.S., Magnetohydrodynamics, 2016, vol. 52, no. 1, p. 17.Google Scholar
  8. 8.
    Kirillov, I.R., Obukhov, D.M., Genin, L.G., Sviridov, V.G., Razuvanov, N.G., Batenin, V.M., Belyaev, I.A., and Pyatnitskaya, N.Y., Fusion Eng. Des., 2016, vol. 104, p. 1.CrossRefGoogle Scholar
  9. 9.
    Branover, G.G. and Tsinober, A.B., Magnitnaya gidrodinamika neszhimaemykh sred (Magnetic Hydrodynamics of Incompressible Media), Moscow: Nauka, 1970.Google Scholar
  10. 10.
    Sommeria, J. and Moreau, R., J. Fluid Mech., 1982, vol. 118, p. 507.ADSCrossRefGoogle Scholar
  11. 11.
    Smolentsev S. and Moreau R. Proceedings of the 2006 Summer Program, CTR, Stanford University, 2006, p. 419.Google Scholar
  12. 12.
    Zimin, V.D. and Khripchenko, S.Yu., Magnetohydrodynamics, 1979, vol. 15, no. 4, p. 461.Google Scholar
  13. 13.
    Sommeria, J., J. Fluid Mech., 1986, vol. 170, p. 139.ADSCrossRefGoogle Scholar
  14. 14.
    Khripchenko, S.Yu., Vychisl. Mekh. Sploshnykh Sred, 2010, no. 3, p. 116.Google Scholar
  15. 15.
    Liu, L. and Zikanov, O., Phys. Fluids, 2015, vol. 27, no. 4, 044103.ADSCrossRefGoogle Scholar
  16. 16.
    Smolentsev, S., Vetcha, N., and Abdou, M., Fusion Eng. Des., 2013, vol. 88, no. 6, p. 607.CrossRefGoogle Scholar
  17. 17.
    Belyaev, I.A., Listratov, Y.I., Melnikov, I.A., Razuvanov, N.G., Sviridov, V.G., and Sviridov, E.V., Magnetohydrodynamics, 2016, vol. 52, no. 3, p. 287.CrossRefGoogle Scholar
  18. 18.
    Smolentsev, S.Yu., Magnetohydrodynamics, 1997, vol. 33, no. 1, p. 42.Google Scholar
  19. 19.
    Artemov, V.I., Yan’kov, G.G., Karpov, V.E., and Makarov, M.V., Teploenergetika, 2000, no. 7, p. 52.Google Scholar
  20. 20.
    Kovalev, S.I., Murav’ev, E.V., and Sviridov, V.G., Vopr. At. Nauki Tekh., Ser.: Termoyad. Sint., 1990, no. 1, p. 32.Google Scholar
  21. 21.
    Sudakov, A.V., Nadezhnost Bezop. Energ., 2008, no. 9, p. 10.Google Scholar
  22. 22.
    Poddubnyi, I.I., Cand. Sci. (Eng.) Dissertation, Moscow: Moscow Energy Inst., 2016.Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • I. A. Belyaev
    • 1
    Email author
  • N. G. Razuvanov
    • 1
  • V. G. Sviridov
    • 1
  1. 1.Joint Institute for High Temperatures, Russian Academy of SciencesMoscowRussia

Personalised recommendations