Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-17T00:44:23.361Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic solution of shock tube flows with homogeneous condensation

Published online by Cambridge University Press:  26 April 2006

Can F. Delale ,
Günter H. Schnerr  and
Jürgen Zierep
Can F. Delale
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität Karlsruhe (TH), Germany
Günter H. Schnerr
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität Karlsruhe (TH), Germany
Jürgen Zierep
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität Karlsruhe (TH), Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The asymptotic solution of shock tube flows with homogeneous condensation is presented for both smooth, or subcritical, flows and flows with an embedded shock wave, or supercritical flows. For subcritical flows an analytical expression, independent of the particular theory of homogeneous condensation to be employed, that determines the condensation wave front in the rarefaction wave is obtained by the asymptotic analysis of the rate equation along pathlines. The complete solution is computed by an algorithm which utilizes the classical nucleation theory and the Hertz–Knudsen droplet growth law. For supercritical flows four distinct flow regimes are distinguished along pathlines intersecting the embedded shock wave analogous to supercritical nozzle flows. The complete global solution for supercritical flows is discussed only qualitatively owing to the lack of a shock fitting technique for embedded shock waves. The results of the computations obtained by the subcritical algorithm show that most of the experimental data available exhibit supercritical flow behaviour and thereby the predicted onset conditions in general show deviations from the measured values. The causes of these deviations are reasoned by utilizing the qualitative global asymptotic solution of supercritical flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 287 , 25 March 1995 , pp. 93 - 118
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, A. 1965 Handbook of Mathematical Functions. Dover.
Barschdorff, D. 1975 Carrier gas effects on homogeneous nucleation of water vapor in a shock tube. Phys. Fluids 18, 529–535.Google Scholar
Blythe, P. A. & Shih, C. J. 1976 Condensation shocks in nozzle flows. J. Fluid Mech. 76, 593–621.Google Scholar
Clarke, J. H. & Delale, C. F. 1986 Nozzle flows with nonequilibrium condensation. Phys. Fluids 29, 1398–1413.Google Scholar
Courtney, W. G. 1965 Condensation in a rarefaction wave. Tech. Rep. 2 ONR NR 092 517/4-29-65. Tiokol Chemical Corp., Denville, New Jersey.
Delale, C. F., Schnerr, G. H. & Zierep, J. 1993a Asymptotic solution of transonic nozzle flows with homogeneous condensation. I. Subcritical flows. Phys. Fluids A 5, 2969–2981.Google Scholar
Delale, C. F., Schnerr, G. H. & Zierep, J. 1993b Asymptotic solution of transonic nozzle flows with homogeneous condensation. II. Supercritical flows. Phys. Fluids A 5, 2982–2995.Google Scholar
Erdelyi, A. 1956 Asymptotic Expansions. Dover.
Glass, I. I., Kalra, S. P. & Sislian, J. P. 1977 Condensation of water vapor in rarefaction waves. III. Experimental results. AIAA J. 15, 686–693.Google Scholar
Glass, I. I. & Patterson, G. N. 1955 A theoretical and experimental study of shock tube flows. J. Aero. Sci. 22, 75–100.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Tables of Integrals, Series and Products. Academic.
Homer, J. B. 1971 Studies on nucleation and growth of metallic particles from supersaturated vapors. Shock Tube Research, Proc. Eighth Intl Shock Tube Symp., London (ed. J. L. Stollery, A. G. Gaydon & P. R. Owen). Chapman and Hall.
Kalra, S. P. 1975 Experiments on nonequilibrium, nonstationary expansion of water vapor/carrier gas mixture in a shock tube. University of Toronto, Institute for Aerospace Studies, Rep. 195.
Kawada, H. & Mori, Y. 1973 A shock tube study on condensation kinetics. Bull. JSME 16, 1053–1066.Google Scholar
Kotake, S. & Glass, I. I. 1977 Condensation of water vapor in rarefaction waves. II. Heterogeneous nucleation. AIAA J. 15, 215–221.Google Scholar
Lax, P. D. 1954 Weak solutions of nonlinear hyperbolic equations and their numerical computation. Commun. Pure Appl. Maths 7, 159–193.Google Scholar
Lee, C. F. 1977 Condensation of H2O and D2O in argon in the centred expansion wave in a shock tube. ASME Symp. on Condensation in High Speed Flows (ed. A. A. Pouring), pp. 83–96. US Naval Academy.
Moretti, G. 1987 Computation of flows with shocks. Ann. Rev. Fluid Mech. 19, 313–337.Google Scholar
Peters, F. 1987 Condensation of supersaturated water vapor at low temperatures in a shock tube. J. Phys. Chem. 91, 2487–2489.Google Scholar
Peters, F. & Paikert, B. 1989 Nucleation and growth rates of homogeneously condensing water vapor in argon from shock tube experiments. Exps. Fluids 7, 521–530.Google Scholar
Roe, P. L. 1986 Characteristic based schemes for the Euler equations. Ann. Rev. Fluid Mech. 18, 337–365.Google Scholar
Sirovich, L. 1971 Techniques of Asymptotic Analysis. Springer.
Sislian, J. P. 1975 Condensation of water vapor with or without a carrier gas in a shock tube. University of Toronto, Institute for Aerospace Studies, Rep. 201.
Sislian, J. P. & Glass, I. I. 1976 Condensation of water vapor in rarefaction waves. I. Homogeneous nucleation. AIAA J. 14, 1731–1737.Google Scholar
Smolders, H. J. 1992 Nonlinear wave phenomena in a gas-vapour-droplets mixture with phase transition. Proefschrift. Eindhoven University of Technology.
Smolders, H. J., Niessen, E. M. J. & Dongen, M. E. H. van, 1992 The random choice method applied to nonlinear wave propagation in gas-vapour-droplets mixtures. Computers Fluids 21, 63–75.Google Scholar
Sonntag, D. & Heinze, D. 1982 Sättigungsdampfdruck- und Sättigungsdampfdichtetafeln für Wasser und Eis. Leipzig: VEB Deutscher-Verlag.
Vincenti, G. W. & Kruger, C. H. 1965 Introduction to Physical Gas Dynamics. Wiley.
Wegener, P. P. & Lundquist, G. 1951 Condensation of water vapor in a shock tube below 150° K. J. Appl. Phys. 22, 233.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.
Wu, B. J. C. 1977 Analysis of condensation in the centred expansion wave in a shock tube. ASME Symp. on Condensation in High Speed Flows (ed. A. A. Pouring), pp. 73–82. US Naval Academy.
Zettlemoyer, A. C. 1969 Nucleation. Marcel Dekker.