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Transonic flows of Bethe—Zel'dovich—Thompson fluids

Published online by Cambridge University Press:  26 April 2006

M. S. Cramer  and
G. M. Tarkenton
M. S. Cramer
Affiliation:
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219, USA
G. M. Tarkenton
Affiliation:
Department of Physics, University of Texas at Austin, Austin, TX 78741, USA
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Abstract

Bethe–Zel'dovich–Thompson fluids are ordinary, single-phase fluids in which the fundamental derivative of gasdynamics is negative over a finite range of temperatures and pressures. We examine the steady transonic flow of these fluids over two-dimensional thin wings and turbine blades. The free-stream state is taken to be in the neighbourhood of one of the zeros of the fundamental derivative. It is shown that a modified form of the classical transonic small-disturbance equation governs such flows. Critical Mach number estimates are provided which take into account the non-monotone variation of the Mach number with pressure predicted in previous investigations. Critical Mach numbers well over 0.95 are predicted for conventional airfoil sections. Numerical solutions reveal substantial reductions in the strength of the compression shocks occurring in supercritical flows. Further new results include the prediction of expansion and compression shocks in the same flow and compression bow shocks in flows with subsonic free streams.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 197 - 228
Copyright
© 1992 Cambridge University Press

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