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On the motion of thin airfoils in fluids of finite electrical conductivity

Published online by Cambridge University Press:  28 March 2006

James E. McCune
James E. McCune
Affiliation:
Cornell University, Ithaca, New York
Now with Aeronautical Research Associates of Princeton, Inc.
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Abstract

A two-dimensional, small-perturbation theory for the steady motion of thin lifting airfoils in an incompressible conducting fluid, with the uniform applied magnetic field perpendicular to (and in the plane of) the undisturbed, uniform flow field, is described. The conductivity of the fluid is assumed to be such that the magnetic Reynolds number, Rm, of the flow is large but finite. Within this assumption, a theory based on superposition of sinusoidal modes is constructed and applied to some simple thin airfoil problems.

It is shown that with this particular field geometry the Alfvén wave mechanism is important in making possible very deep penetration into the flow field of currents and their associated vorticity. It is also shown that the current penetration for an airfoil is much larger than for a wavy wall of wavelength equal to the airfoil chord.

A value of Rm = 5 is found to be a good approximation to infinity in this study; in fact, use of the present technique for values of Rm of the order of unity is permissible. These results provide an indication of what is meant by ‘large’ magnetic Reynolds number in two-dimensional magneto-aerodynamics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 3 , March 1960 , pp. 449 - 468
Copyright
© 1960 Cambridge University Press

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References

Cowling, T. G. 1957 Magnetohydrodynamics. London: Interscience.
Glauert, H. 1926 Aerofoil and Airscrew Theory. Cambridge University Press.
Lighthill, M. J. 1956 Surveys in Mechanics (ed. G. K. Batchelor and R. M. Davies). Cambridge University Press.
Rayleigh, Lord 1946 Theory of Sound II, 2nd ed. New York: Dover.
Resler, E. L. Jr., & McCune, J. E. 1960 Rev. Mod. Phys. (in the Press).
Resler, E. L. Jr., & Sears, W. R. 1958 J. Aero. Sci. 25, 235.
Rott, N. & Cheng, H. K. 1954 J. Rat. Mech. Anal. 3, 357.
Sears, W. R. & Resler, E. L. Jr., 1959 J. Fluid Mech. 5, 257.