Abstract
The previous chapter dealt with the flows arising when an electric current radially diverges through the fluid from a small electrode. In spite of the simplicity of the physical model with a point current source, which was successfully combined with the similarity solution of equations of motion and magnetic field, it was found to be impossible to describe the flows for magnitudes of electric current higher than a certain critical magnitude. The source of failure may be sought in the similarity of the equations, which greatly restrict the form of the motions. However it should be recalled that the similarity is not an artificial assumption to describe the flows at a point electrode, it is derived by the dimensional analysis of the given physical quantities entering the problem [26]. Moreover, as was demonstrated in Section 2.10, the description of analogous flows without the assumption of similarity, e.g. in a closed hemispherical container, also led to serious difficulties. Consequently, the cause of difficulties should be sought in the physical statement of the problem, which probably does not take into account an essential mechanism limiting the growth of velocities in the flow when the critical magnitude of electric current is reached. The limiting mechanism cannot be related to the flow induced electric current since, even for excessive magnitudes of electrical condictivity (by 6–7 orders of magnitude compared to real materials) the critical magnitude of the electric current is not appreciably increased.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atthey D. R.: A mathematical model for fluid flow in a weld pool at high currents. J. Fluid Mech. (1980), 98, pp. 787–801.
Batchelor G. K.: An Introduction to Fluid Dynamics. Cambridge at the University Press, 1970.
Bershadskij A. G.: Stability of axisymmetric meridional flows to azimuthal rotations. Magnitnaya Gidrodinamika (1985), No. 1, pp. 49–54.
Bojarevičs V. V.: MHD flows at an electric current point source. Part I. Magnitnaya Gidrodinamika (1981), No. 1, pp. 21–28.
Bojarevičs V. V.: MHD flows at an electric current point source. Part II. Magnitnaya Gidrodinamika (1981), No. 2, pp. 41–44.
Bojarevičs V. V. and Millere R.: Amplification of rotation of meridional electrovortex flow in a hemisphere. Magnitnaya Gidrodinamika (1982), No. 4, pp. 51–56.
Bojarevičs V. V., Sharamkin V. I., and Shcherbinin E. V.: Effect of longitudinal magnetic field on the medium motion in electrical arc welding. Magnitnaya Gidrodinamika (1977), No. 1, pp. 115–120.
Bojarevics V. and Shcherbinin E. V.: Azimuthal rotation in the axisymmetric meridional flow due to an electric current source. J. Fluid Mech. (1983), 126, pp. 413–430.
Burgers J. M.: A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. (1948), 1, pp. 197–198.
Chow Ch. Y. and Uberoi M. S.: Stability of an electrical discharge surrounded by a free vortex. Phys. Fluids (1972), 15(12), pp. 2187–2192.
Craine R. E. and Weatherill N. P.: Fluid flow in a hemispherical container induced by a distributed source of current and superimposed uniform magnetic field. J. Fluid Mech. (1980), 99, pp. 1–12.
Dudko D. A. and Rublevskij I. N.: Electromagnetic mixing of slag and metal bath in electroslag process. Avtomaticheskaya Svarka (1960), No. 9, pp. 12–16.
Gagen Yu. G. and Taran V. D.: Welding by the Magnetically Controlled Arc. Moscow: Mashinostroenie, 1970 (In Russian).
Howells P. and Smith R. K.: Numerical simulations of tornado-like vortices. Geophys. Astrophys. Fluid Dynamics (1983), 27, pp. 253–284.
Kawakubo T., Tsutchiya Y., Sugaya M., and Matsumura K.: Formation of a vortex around a sink. Phys. Letters (1978), A68(l), pp. 65–66.
Kawakubo T., Shingubara S., and Tsutchiya Y.: Coherent structure formation of vortex flow around a sink. J. Phys. Soc. Jpn. (1983), 52 (Suppl.), pp. 143–146.
Lavrent’ev M. A. and Shabat B. V.: Problems in Hydrodynamics and Mathematical Models. Moscow: Nauka, 1977 (In Russian).
Levakov V. S. and Lyubavskij K. V.: Effect of longitudinal magnetic field on electric arc with nonmelting tungsten cathode. Svarochnoe Proizvodstvo (1965), No. 10, pp. 9–12.
Millere R. P., Sharamkin V. I., and Shcherbinin E. V.: Effect of longitudinal magnetic field on electrovortex flow in the cylindrical volume. Magnitnaya Gidrodinamika (1980), No. 1, pp. 81–85.
Moffatt H. K.: Some problems in the magnetohydrodynamics of liquid metals. Ztschr. Angew. Math. Mech. (1978), 58, T65–T71.
Morton B. R.: The strength of vortex and swirling core flows. J. Fluid Mech. (1969), 38, pp. 315–333.
Okorokov N. V.: Electromagnetic Mixing of Metal. Moscow: Metallurgizdat, 1961 (In Russian).
Orszag S.: Numerical simulation of incompressible flows within simple boundaries. 1. Galerkin (spectral) representations. Studies Appl. Math. (1971), 50, pp. 293–327.
Rotunno R.: Vorticity dynamics of a convective swirling boundary layer. J. Fluid Mech. (1980), 97(3), pp. 623–640.
Ryan R. T. and Vonnegut B.: Miniature whirlwinds produced in the laboratory by high-voltage electrical discharges. Science (1970), 168, pp. 1349–1351.
Shcherbinin E. V.: Viscous Fluid Jet Flows in Magnetic Field. Riga: Zinatne, 1973 (In Russian).
Shercliff J. A.: Fluid motion due to an electric current source. J. Fluid Mech. (1970), 40(2), pp. 241–250.
Shercliff J. A.: The dynamics of conducting fluids under rotational magnetic forces. Sci. Progress (1979), 66, pp. 151–170.
Shivamoggi B. K.: Method of matched asymptotic expansions — asymptotic matching principle for high approximations. Ztschr. Angew. Math. Mech. (1978), 58(8), S. 354–356.
Smyslov Yu. N. and Shcherbinin E. V.: Nonlinear magnetohydrodynamic model of tornado. Problems of Mathematical Physics. Ed. by Tuchkevich V. M. Leningrad: Nauka, 1976, pp. 271–282 (In Russian).
Sozou C. and English H.: Fluid motion induced by an electric current discharge. Proc. Roy. Soc. London (1972), A329, pp. 71–81.
Sozou C. and Pickering W. M.: Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container. J. Fluid Mech. (1976), 73(4), pp. 641–650.
Torrance K.: Natural convection in the thermally stratified enclosures with localized heating from below. J. Fluid Mech. (1979), 95, pp. 474–495.
Van Dyke M. D.: Perturbation Methods in Fluid Mechanics. New York: Academic Press, 1964.
Weir A. D.: Axisymmetric convection in a rotating sphere. 1. J. Fluid Mech. (1976), 75(1), pp. 49–79.
Wilson T. and Rotunno R.: Numerical simulation of a laminar endwall vortex and boundary layer. Phys. Fluids (1986), 29(12), pp. 3993–4005.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
Bojarevičs, V., Freibergs, J.A., Shilova, E.I., Shcherbinin, E.V. (1989). Electrically induced vortex flow at a point electrode and azimuthal rotation. In: Electrically Induced Vortical Flows. Mechanics of Fluids and Transport Processes, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1163-5_4
Download citation
DOI: https://doi.org/10.1007/978-94-009-1163-5_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7017-1
Online ISBN: 978-94-009-1163-5
eBook Packages: Springer Book Archive