Motion of a cylinder in a viscous electroconductive medium with a magnetic field
- 18 Downloads
The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.
The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.
Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.
There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in . This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.
KeywordsMagnetic Field Circular Cylinder Uniform Magnetic Field Hartmann Number Magnetic Reynolds Number
Unable to display preview. Download preview PDF.
- 1.S. I. Syrovatskii, “Magnetohydrodynamics,” Usp. fiz. n., vol. 52, no. 3, 1957.Google Scholar
- 2.A. G. Kulikovskii and G. A. Lyubimov, Magnetohydrodynamics [in Russian], Fizmatgiz, 1962.Google Scholar
- 3.W. Chester, “The effect of a magnetic field on the flow of a conducting fluid past a body of revolution,” J. Fluid Mech., vol. 10, pt. 3, 1961.Google Scholar
- 4.Josinobu Hirowo, “A linearized theory of magnetohydrodynamic flow past a fixed body in a parallel magnetic field,” J. Phys. Soc., Japan, vol. 15, no. 1, 1960.Google Scholar
- 5.F. N. Frenkiel and W. R. Sears, “Proceedings of the symposium on magnetofluid dynamics,” Rev. Modern Phys., vol. 32, no. 4, 1960.Google Scholar
- 6.V. P. Dokuchaev, “The linear theory of flow about bodies. Method of force sources,” PMM, vol. 30, no. 6, 1966.Google Scholar
- 7.T. Cowling, Magnetohydrodynamics [Russian translation], Izd. inostr. lit., 1959.Google Scholar
- 8.N. E. Kochin, I. A. Kibel, and N. V. Roze, Theoretical Hydromechanics [in Russian], 4-th edition, Fizmatgiz, part 2, 1963.Google Scholar
- 9.I. N. Sneddon, Fourier Transforms [Russian translation], Izd. inostr. lit., 1955.Google Scholar
- 10.P. M. Morse and H. Feshbach, Methods of Theoretical Physics [Russian translation], vol. 1, Izd. inostr. lit., 1958.Google Scholar
- 11.G. N. Watson, Theory of Bessel Functions [Russian translation], Izd. inostr. lit., 1949.Google Scholar
- 12.M. B. Glauert, “Magnetohydrodynamic wakes,” J. Fluid Mech., vol. 15, pt. 1, 1963.Google Scholar
- 13.D. N. Fan, “Aligned-fields in magnetogasdynamic wakes,” J. Fluid Mech., vol. 20, pt. 3, 1964.Google Scholar