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Transonic nozzle flow of dense gases

Published online by Cambridge University Press:  26 April 2006

A. Kluwick
A. Kluwick
Affiliation:
Institut für Strömungslehre und Wärmeübertragung, Technische Universität Wien, A-1040 Wien, Austria
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Abstract

The paper deals with the flow properties of dense gases in the throat area of slender nozzles. Starting from the Navier–Stokes equations supplemented with realistic equations of state for gases which have relatively large specific heats a novel form of the viscous transonic small-perturbation equation is derived. Evaluation of the inviscid limit of this equation shows that three sonic points rather than a single sonic point may occur during isentropic expansion of such media, in contrast to the case of perfect gases. As a consequence, a shock-free transition from subsonic to supersonic speeds cannot, in general, be achieved by means of a conventional converging–diverging nozzle. Nozzles leading to shock-free flow fields must have an unusual shape consisting of two throats and an intervening antithroat. Additional new results include the computation of the internal thermoviscous structure of weak shock waves and a phenomenon referred to as impending shock splitting. Finally, the relevance of these results to the description of external transonic flows is discussed briefly.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 247 , February 1993 , pp. 661 - 688
Copyright
© 1993 Cambridge University Press

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References

Bethe, H. A. 1942 The theory of shock waves for an arbitrary equation of state. Office Sci. Res. Dev. Rep. 545.Google Scholar
Chandrasekar, D. & Prasad, P. 1991 Transonic flow of a fluid with positive and negative nonlinearity through a nozzle. Phys. Fluids A 3, 427– 438.Google Scholar
Cramer, M. S. 1989 Negative nonlinearity in selected fluorocarbons. Phys. Fluids A1, 1894– 1897.Google Scholar
Cramer, M. S. 1991a Transonic flows of BZT fluids. In Proc. 13th World Congr. on Computation and Applied Mathematics (IMACS 91), pp. 570– 571.
Cramer, M. S. 1991b Nonclassical dynamics of classical gases. In Nonlinear Waves in Real Fluids (ed. A. Kluwick). pp. 91– 145. Springer.
Cramer, M. S. & Crickenberger, A. B. 1991 The dissipative structure of shock waves in dense gases. J. Fluid Mech. 223, 325– 355.Google Scholar
Cramer, M. S. & Kluwick, A. 1984 On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142, 9– 37.Google Scholar
Cramer, M. S. & Tarkenton, G. M. 1992 Transonic flows of Bethe–Zel'dovich–Thompson fluids. J. Fluid Mech. 240, 197– 228.Google Scholar
Kluwick, A. 1991 Small-amplitude finite-rate waves in fluids having both positive and negative nonlinearity In Nonlinear Waves in Real Fluids (ed. A. Kluwick), pp. 1– 43. Springer.
Lambrakis, K. C. & Thompson, P. A. 1972 Existence of real fluids with a negative fundamental derivative Γ. Phys. Fluids 5, 933– 935.
Liepmann, H. W., Ashkenas, H. I. & Cole, J. D. 1950 Experiments in transonic flow. Wright Air Dev. Cent. Tech. Rep. 5667.Google Scholar
Martin, J. J. & Hou, Y. C. 1955 Development of an equation of state for gases. AIChE J. 1, 142– 151.Google Scholar
Messiter, A. F. & Adamson, T. C. 1981 Transonic small disturbance theory for lightly loaded cascades. AIAA J. 19, 1047– 1054.Google Scholar
Oleinik, O. A. 1959 Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation. Usp. Mat. Nauk 14, 165– 170. (English Transl.) Am. Math. Soc. Transl. Ser 2, 33, 285–290.Google Scholar
Thompson, P. A. 1971 A fundamental derivative in gasdynamics. Phys. Fluids 14, 1843– 1849.Google Scholar
Thompson, P. A. & Lambrakis, K. C. 1973 Negative shock waves. J. Fluid Mech. 60, 187– 207.Google Scholar
Zel'Dovich, Ya. B. 1946 On the possibility of rarefaction shock waves. Zh. Eksp. Tear. Fiz. 4, 363– 364Google Scholar