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Computation and measurement of Hall potentials and flow-field perturbations in magnetogasdynamic flow of an axisymmetric free jet

Published online by Cambridge University Press:  28 March 2006

David R. Otis
David R. Otis
Affiliation:
University of California, Berkeley Present address: Mechanical Engineering Department, University of Wisconsin, Madison, Wisconsin.
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Abstract

The interaction was observed between a supersonic free jet of partially ionized argon and the magnetic field of a coil concentric with the jet. Nominal values of the parameters were: Mach number, 3; Reynolds number, 1000; magnetic Reynolds number, 0·2; magnetic interaction parameter, 1; Hall parameter, 1. The jet was strongly channelled. Axial and radial electric fields were observed in the jet with a net rise in potential across the interaction.

These observations were consistent with predictions based on the single fluid, macroscopic equations, and a simple slug flow model. The current equation was solved to second order in the Hall parameter giving a closed form expression for the Hall potential which agreed with the experiments for weak fields. Flow perturbations were calculated for Mach numbers of 3.11, 6.08, and 10.05, neglecting Hall currents; the calculations are in qualitative agreement with the experiments and show Joule heating to be the main factor in perturbing the flow at high Mach numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 1 , January 1966 , pp. 41 - 63
Copyright
© 1966 Cambridge University Press

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References

Brundin, C. L. 1964 The application of Langmuir probe techniques to flowing ionized gases. Univ. Calif. Aero. Sci. Div. Tech. Rep. no. AS-64–9.Google Scholar
Brundin, C. L., Talbot, L. & Sherman, F. S. 1960 Flow studies in an arc heated low density supersonic wind tunnel. Univ. of Calif. Eng. Proj. Rep. no. HE-150–181.Google Scholar
Courant, R. 1962 Methods of Mathematical Physics, vol. II, Partial Differential Equations, ch. 5. New York: Interscience.
Ehlers, F. E. 1961 Linearized magnetogasdynamic channel flow with axial symmetry. ARS J. 31, 334–42.Google Scholar
Fishman, F., Lothrop, J. W., Patrick, R. M. & Petschek, H. E. 1959 Supersonic two-dimensional magnetohydrodynamic flow. The Magnetohydrodynamics of Conducting Fluids, ed. D. Bershader, p. 120. Stanford University Press.
Gilleo, M. A. 1961 Flow of low-density high-speed plasma through a magnetic barrier. Phys. Fluids, 4, 1399–1406.Google Scholar
Hains, F. D. & Yoler, Y. A. 1962 Axisymmetric magnetohydrodynamic channel flow. J. Aero. Sci. 29, 143–50.Google Scholar
Hains, F. D., Yoler, Y. A. & Ehlers, E. E. 1959 Axi-symmetric hydromagnetic channel flow. Boeing Res. Lab. Rep. no. DI-82–0025. Presented at ARS Northwestern Gas Dynamics Symposium, Northwestern Univ., 24–26 August.Google Scholar
Hasimoto, H. 1964 Swirl of a conducting gas due to the Hall effect. J. Phys. Soc. Japan, 19, 1457–63.Google Scholar
Kemp, N. H. & Petschek, H. E. 1958 Two-dimensional incompressible magnetohydrodynamic flow across an elliptical solenoid. J. Fluid Mech. 4, 553–84.Google Scholar
Lai, W., Gustavson, J. & Talbot, L. 1958 Design considerations and initial evaluation of Model B plasma generator. Univ. of Calif. Eng. Proj. Rep. no. HE-150–161.Google Scholar
Landshoff, R. 1949 Transport phenomena in a completely ionized gas in presence of a magnetic field. Phys. Rev. 76, 904–9.Google Scholar
Otis, D. R. 1963 Computation and measurement of Hall potentials and flow-field perturbations in magnetogasdynamic flow of an axisymmetric free jet. Ph.D. thesis, University of California.
Podolsky, B. & Sherman, A. 1962 Influence of tensor conductivity on end currents in crossed field MHD channels with skewed electrodes. J. Appl. Phys. 33, 1414–18.Google Scholar
Resler, E. L. & McCune, J. E. 1960 Some exact solutions in linearized magnetoaerodynamics for arbitrary magnetic Reynolds number. Rev. Mod. Phys. 32, 848–54.Google Scholar
Sherman, F. S. & Talbot, L. 1962 Diagnostic studies of a low-density arc-heated wind tunnel stream. In Hypersonic Flow Research, ed. F. R. Riddell, vol. 7, p. 581. New York: Academic Press.
Sneddon, I. N. 1946 Finite Hankel transforms. Phil. Mag. 37, 17–25.Google Scholar
Spitzer, L. 1956 Physics of Fully Ionized Gases, chs. 2 and 5. New York: Interscience.
Talbot, L., Katz, J. E. & Brundin, C. L. 1963 Comparison between Langmuir probe and microwave electron density measurements in an arc-heated low-density wind tunnel. Phys. Fluids, 6, 559–65.Google Scholar
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions, 2nd edition, ch. 18. Cambridge University Press.
Robben, F. A. 1963 A spectrographic study of recombination in a helium plasma. Univ. of Calif. Eng. Proj. Rep. no. HE-150–211.Google Scholar
Scott, F. R. & Voorhies, H. G. 1961 Plasma injection into a magnetic field. Phys. Fluids, 4, 600–6.Google Scholar
Shapiro, A. H. 1953 The Dynamics and Thermodynamics of Compressible Fluid Flow, vol. I, ch. 8. New York: The Ronald Press Co.