Advertisement

Instabilities in Extreme Magnetoconvection

  • Oleg ZikanovEmail author
  • Yaroslav Listratov
  • Xuan Zhang
  • Valentin Sviridov
Chapter
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 50)

Abstract

Thermal convection in an electrically conducting fluid (for example, a liquid metal) in the presence of a static magnetic field is considered in this chapter. The focus is on the extreme states of the flow, in which both buoyancy and Lorentz forces are very strong. It is argued that the instabilities occurring in such flows are often of unique and counter-intuitive nature due to the action of the magnetic field, which suppresses conventional turbulence and gives preference to two-dimensional instability modes not appearing in more conventional convection systems. Tools of numerical analysis suitable for such flows are discussed.

Keywords

Magnetohydrodynamics Convection Instability 

Notes

Acknowledgements

The authors are thankful to Dmitry Krasnov for the continuing support of the computational tools used for the simulations presented in this paper. The work was supported by the US NSF (Grants CBET 1232851 and 1435269) and by the Ministry of Education and Science of the Russian Federation (Project No. 13.9619.2017/8.9).

References

  1. 1.
    Abdou, M.A., Team, T.A.: Exploring novel high power density concepts for attractive fusion systems. Fusion Eng. Des. 45, 145–167 (1999)CrossRefGoogle Scholar
  2. 2.
    Abdou, M., Morley, N.B., Smolentsev, S., Ying, A., Malang, S., Rowcliffe, A., Ulrickson, M.: Blanket/first wall challenges and required R&D on the pathway to DEMO. Fusion Eng. Des. 100, 2–43 (2015)CrossRefGoogle Scholar
  3. 3.
    Batchelor, G.K., Nitsche, J.M.: Instability of stratified fluid in a vertical cylinder. J. Fluid Mech. 252, 419–448 (1993)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Boeck, T., Krasnov, D., Thess, A., Zikanov, O.: Large-scale intermittency of liquid-metal channel flow in a magnetic field. Phys. Rev. Lett. 101, 244,501 (2008)Google Scholar
  5. 5.
    Calzavarini, E., Doering, C.R., Gibbon, J.D., Lohse, D., Tanabe, A., Toschi, F.: Exponentially growing solutions of homogeneous Rayleigh-Bénard flow. Phys. Rev. E 73, R035,301 (2006)Google Scholar
  6. 6.
    Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford (1961)Google Scholar
  7. 7.
    Cioni, S., Chaumat, S., Sommeria, J.: Effect of a vertical magnetic field on turbulent rayleigh-bénard convection. Phys. Rev. E 62(4), R4520 (2000)CrossRefGoogle Scholar
  8. 8.
    Davidson, P.A.: Introduction to Magnetohydrodynamics. Cambridge University Press, Cambridge (2016)Google Scholar
  9. 9.
    Di Piazza, I., Ciofalo, M.: MHD free convection in a liquid-metal filled cubic enclosure. I. differential heating. Int. J. Heat Mass Trans. 45(7), 1477–1492 (2002)Google Scholar
  10. 10.
    Di Piazza, I., Ciofalo, M.: MHD free convection in a liquid-metal filled cubic enclosure. II. internal heating. Int. J. Heat Mass Trans. 45(7), 1493–1511 (2002)Google Scholar
  11. 11.
    Dolan, T.J., Moir, R.W., Manheimer, W., Cadwallader, L.C., Neumann, M.J.: Magnetic Fusion Technology. Springer, Berlin (2013)Google Scholar
  12. 12.
    Dong, S., Krasnov, D., Boeck, T.: Secondary energy growth and turbulence suppression in conducting channel flow with streamwise magnetic field. Phys. Fluids 24(7), 074,101 (2012)CrossRefGoogle Scholar
  13. 13.
    Evtikhin, V.A., Lyublinski, I.E., Vertkov, A.V., Yezhov, N.I., Khripunov, B.I., Sotnikov, S.M., Mirnov, S.V., Petrov, V.B.: Energy removal and MHD performance of lithium capillary-pore systems for divertor target application. Fusion Eng. Des. 49, 195–199 (2000)CrossRefGoogle Scholar
  14. 14.
    Genin, L.G., Zhilin, V.G., Ivochkin, Y.P., Razuvanov, N.G., Belyaev, I.A., Listratov, Y.I., Sviridov, V.G.: Temperature fluctuations in a heated horizontal tube affected by transverse magnetic field. In: Proceedings of 8th PAMIR Conference on Fundamental and Applied MHD, pp. 37–41. Borgo, Corsica, France (2011)Google Scholar
  15. 15.
    Gershuni, G.Z., Zhukhovitskii, E.M.: Convective Stability of Incompressible Fluids. Nauka, Moscow (1986)Google Scholar
  16. 16.
    Kelley, D.H., Sadoway, D.R.: Mixing in a liquid metal electrode. Phys. Fluids 26(5), 057,102 (2014)CrossRefGoogle Scholar
  17. 17.
    Kim, H., Boysen, D.A., Newhouse, J.M., Spatocco, B.L., Chung, B., Burke, P.J., Bradwell, D.J., Jiang, K., Tomaszowska, A.A., Wang, K., Wei, W., Ortiz, L.A., Barriga, S.A., Poizeau, S.M., Sadoway, D.R.: Liquid metal batteries: past, present, and future. Chem. Rev. 113(3), 2075–2099 (2013)CrossRefGoogle Scholar
  18. 18.
    Kirillov, I.R., Obukhov, D.M., Genin, L.G., Sviridov, V.G., Razuvanov, N.G., Batenin, V.M., Belyaev, I.A., Poddubnyi, I.I., Pyatnitskaya, N.Y.: Buoyancy effects in vertical rectangular duct with coplanar magnetic field and single sided heat load. Fusion Eng. Des. 104, 1–8 (2016)CrossRefGoogle Scholar
  19. 19.
    Krasnov, D., Zikanov, O., Boeck, T.: Comparative study of finite difference approaches to simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number. Comp. Fluids 50, 46–59 (2011)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Krasnov, D.S., Zikanov, O., Boeck, T.: Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers. J. Fluid Mech. 704, 421–446 (2012)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Liu, L., Zikanov, O.: Elevator mode convection in flows with strong magnetic fields. Phys. Fluids 27(4), 044,103 (2015)CrossRefGoogle Scholar
  22. 22.
    Mas de les Valls, E., Sedano, L., Batet, L., Ricapito, I., Aiello, A., Gastaldi, O., Gabriel, F.: Lead-lithium eutectic material database for nuclear fusion technology. J. Nucl. Mater. 376(3), 353–357 (2008)Google Scholar
  23. 23.
    Mas de les Valls, E., Batet, L., de Medina, V., Sedano, L.A.: MHD thermofluid flow simulation of channels with a uniform thermal load as applied to HCLL breeding blankets for fusion technology. Magnetohydrodynamics (0024-998X) 48(1) (2012)Google Scholar
  24. 24.
    Melnikov, I.A., Sviridov, E.V., Sviridov, V.G., Razuvanov, N.G.: Experimental investigation of MHD heat transfer in a vertical round tube affected by transverse magnetic field. Fusion Eng. Des. 112, 505–512 (2016)CrossRefGoogle Scholar
  25. 25.
    Moffatt, K.: On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 23, 571–592 (1967)CrossRefGoogle Scholar
  26. 26.
    Morinishi, Y., Lund, T.S., Vasilyev, O.V., Moin, P.: Fully conservative higher order finite difference schemes for incompressible flow. J. Comp. Phys. 143, 90–124 (1998)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Müller, U., Bühler, L.: Magnetohydrodynamics in Channels and Containers. Springer, Berlin (2001)CrossRefGoogle Scholar
  28. 28.
    Ni, M.J., Munipalli, R., Huang, P., Morley, N.B., Abdou, M.A.: A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: On a rectangular collocated grid system. J. Comp. Phys. 227, 174–204 (2007)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Ozoe, H.: Magnetic Convection. Imperial College Press, London (2005)CrossRefGoogle Scholar
  30. 30.
    Ruzic, D. N., Xu, W., Andruczyk, D., Jaworski, M. A.: Lithium-metal infused trenches (LiMIT) for heat removal in fusion devices. Nucl. Fusion 51(10), 102,002 (2011)CrossRefGoogle Scholar
  31. 31.
    Schmidt, L.E., Calzavarini, E., Lohse, D., Toschi, F., Verzicco, R.: Axially homogeneous Rayleigh-Bénard convection in a cylindrical cell. J. Fluid Mech. 691, 52–68 (2012)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Shen, Y., Zikanov, O.: Thermal convection in a liquid metal battery. Theor. Comp. Fluid Dyn. 30(4), 275–294 (2016)CrossRefGoogle Scholar
  33. 33.
    Sommeria, J., Moreau, R.: Why, how and when MHD-turbulence becomes two-dimensional. J. Fluid Mech. 118, 507–518 (1982)CrossRefGoogle Scholar
  34. 34.
    Stefani, F., Gundrum, T., Gerbeth, G.: Contactless inductive flow tomography. Phys. Rev. E 70, 056,306 (2004)Google Scholar
  35. 35.
    Thess, A., Zikanov, O.: Transition from two-dimensional to three-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 579, 383–412 (2007)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Thess, A., Votyakov, E., Knaepen, B., Zikanov, O.: Theory of the lorentz force flowmeter. New J. Phys. 9(8), 299 (2007)CrossRefGoogle Scholar
  37. 37.
    Vorobev, A., Zikanov, O., Davidson, P.A., Knaepen, B.: Anisotropy of magnetohydrodynamic turbulence at low magnetic Reynolds number. Phys. Fluids 17(12), 125,105 (2005)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Weiss, N.O., Proctor, M.R.E.: Magnetoconvection. Cambridge University Press, Cambridge (2014)CrossRefGoogle Scholar
  39. 39.
    Zhang, X., Zikanov, O.: Mixed convection in a horizontal duct with bottom heating and strong transverse magnetic field. J. Fluid Mech. 757, 33–56 (2014)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Zhang, X., Zikanov, O.: Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor. J. Fluid Mech. 779, 36–52 (2015)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Zhang, X., Zikanov, O.: Thermal convection in a duct with strong axial magnetic field. Magnetohydrodynamics 53(1) (2017)Google Scholar
  42. 42.
    Zhang, X., Zikanov, O.: Thermal convection in a toroidal duct of a liquid metal blanket. Part I. Effect of poloidal magnetic field. Fusion Eng. Des. 116, 52–60 (2017)CrossRefGoogle Scholar
  43. 43.
    Zhang, X., Zikanov, O.: Thermal convection in a toroidal duct of a liquid metal blanket. Part II. Effect of axial mean flow. Fusion Eng. Des. 116, 40–46 (2017)CrossRefGoogle Scholar
  44. 44.
    Zhao, Y., Tao, J., Zikanov, O.: Transition to two-dimensionality in magnetohydrodynamic turbulent Taylor-Couette flow. Phys. Rev. E 89, 033,002 (2014)Google Scholar
  45. 45.
    Zikanov, O., Listratov, Y.: Numerical investigation of MHD heat transfer in a vertical round tube affected by transverse magnetic field. Fusion Eng. Des. 113, 151–161 (2016)CrossRefGoogle Scholar
  46. 46.
    Zikanov, O., Thess, A.: Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number. J. Fluid Mech. 358, 299–333 (1998)CrossRefGoogle Scholar
  47. 47.
    Zikanov, O., Thess, A.: Direct numerical simulation as a tool for understanding MHD liquid metal turbulence. Appl. Math. Mod. 28(1), 1–13 (2004)CrossRefGoogle Scholar
  48. 48.
    Zikanov, O., Listratov, Y., Sviridov, V.G.: Natural convection in horizontal pipe flow with strong transverse magnetic field. J. Fluid Mech. 720, 486–516 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Oleg Zikanov
    • 1
    Email author
  • Yaroslav Listratov
    • 2
  • Xuan Zhang
    • 3
  • Valentin Sviridov
    • 4
  1. 1.University of Michigan - DearbornDearbornUSA
  2. 2.National Research University “Moscow Power Engineering Institute”MoscowRussia
  3. 3.Max Plank Institute for Dynamics and Self-OrganizationGöttingenGermany
  4. 4.Joint Institute for High Temperatures RASMoscowRussia

Personalised recommendations