Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T22:04:20.773Z Has data issue: false hasContentIssue false
  • English
  • Français

Condensation of water vapour during supersonic expansion in nozzles

Published online by Cambridge University Press:  28 March 2006

Philip G. Hill
Philip G. Hill
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Abstract

Existing data on the condensation of steam and moist air in supersonic nozzles are compared with predictions based on nucleation and drop-growth theory. It is concluded that, if the surface tension is assumed independent of curvature, and the classical liquid-drop theory (based on a stationary liquid drop) is used, the theory is in general agreement with the data. The effects of uncertainties in cluster surface energy and also of the large corrections to nucleation theory due to the ‘gasification’ concept are examined. The gasification correction is in accord with experimental data only if the surface tension is considered to rise significantly with curvature. In neither case can the Tolman or Kirkwood–Buff equations be supported. A review of existing data shows that there is some question as to the appropriate value of the condensation coefficient but this is of little consequence as long as the accommodation coefficient for the liquid–vapour surface is taken to be unity. The usefulness of the nozzle experiments for testing the validity of nucleation theory is demonstrated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 3 , July 1966 , pp. 593 - 620
Copyright
© 1966 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

Alty, T. 1936 The exchange of energy between a gas and a solid or liquid surface. Science Progress 31, 436.Google Scholar
Alty, T. & Mackay, C. A. 1935 The accommodation coefficient and the evaporation coefficient of water. Proc. Roy. Soc., A 149, 104.Google Scholar
Baranaev, M. K. 1946 J. Phys. Chem. (U.S.S.R), 20, 399.
Barnard, A. J. 1953 Proc. Roy. Soc., A 220, 132.
Becker, R. & Döring, W. 1935 Ann. der Phys. 24, 71.
Binnie, A. M. & Green, J. R. 1943 An electrical detector of condensation in high velocity steam. Proc. Roy. Soc., A 181, 134.Google Scholar
Binnie, A. M. & Woods, M. W. 1938 The pressure distribution in a convergent-divergent steam nozzle. Proc. Inst. Mech. Eng. 138, 229.Google Scholar
Buhler, R. D. 1952 Condensation of air components in hypersonic wind tunnels—theoretical calculations and comparison with experiment. Ph.D. Thesis, California Institute of Technology.
Burrows, G. 1957 Evaporation at low pressures. J. Appl. Chem. 7, 375.Google Scholar
Clark, J. V. & Rodebush, W. R. 1953 Ph.D. Thesis of J. V. Clark, University of Illinois.
Courtney, W. G. 1962a J. Chem. Phys. 36, 200.
Courtney, W. G. 1962b J. Chem. Phys. 36, 201.
Courtney, W. G. 1965 To be published.
Feder, J., Russell, K. C., Lothe, J. & Pound, G. M. 1966 Homogeneous nucleation and growth of droplets in vapors. Adv. in Physics 15, 1.Google Scholar
Frenkel, J. 1946 Kinetic Theory of Liquids, chap. 7. Oxford University Press.(Also 1955, Dover Press.)
Gyarmathy, G. & Meyer, H. 1965 Spontane Kondensation. V.D.I. Forschungsheft, p. 508.Google Scholar
Head, R. M. 1949 Investigation of spontaneous condensation phenomena. Ph.D. Thesis, California Institute of Technology.
Hickman, K. C. D. 1954 Maximum evaporation coefficient of water. Ind. Eng. Chem. 46, 1442.Google Scholar
Hickman, K. C. D. & Trevoy, D. J. 1952 Studies in high vacuum evaporation. Ind. Eng. Chem. 44, 1882.Google Scholar
Kantrowitz, A. R. 1951 J. Chem. Phys. 19, 1097.
Knacke, A. & Stranski, I. N. 1956 The mechanism of evaporation. Progr. Metal Phys. 6, 181.Google Scholar
Knudsen, M. 1915 Ann. der Phys. 47, 69.
Kramers, H. & Stemerding, S. 1953 The sublimation of ice in a vacuum. Appl. Sci. Res. (Hague. A 3, 73.Google Scholar
Kuhrt, F. 1952 Das Tröpfchenmodell ubersattigen realer Gase. Z. Physik, 131, 205.Google Scholar
Littlewood, R. & Rideal, E. 1956 On the evaporation coefficient. Trans. Faraday Soc. 52, 1598.Google Scholar
Lothe, J. & Pound, G. M. 1962 Reconsiderations of nucleation theory. J. Chem. Phy. 36, 2080.Google Scholar
Madden, A. J. 1959 The influence of heat transfer on mass transfer at low pressures J. A.I.Ch.E. 5, 13.Google Scholar
Oriani, R. A. & Sundquist, B. E. 1963 Emendations to nucleation theory and the homogeneous nucleation of water from the vapor. J. Chem. Phys. 38, 2082.Google Scholar
Oswatitsch, K. 1942 Z. angew. Math. Mech. 22, 1.
Paul, B. 1962 Compilation of evaporation coefficients. A.R.S.J. 32, 1321.Google Scholar
Pound, G. M., Madonna, L. A. & Sciulli, C. M. 1955 Proc. Conf. on Interfacial phenomena: and Nucleation. Vol. I. Conference on nucleation. (Ed. H. Reiss). AFCRC Rept, no. 55–211, 85.
Powell, C. F. 1928 Proc. Roy. Soc., A 119, 55.
Probstein, R. F. 1951 J. Chem. Phys. 19, 61.
Prueger, W. 1940 Die Verdampfungsgeschwindigkeit der Fluessigkeiten. Z. Physik, 115, 202.Google Scholar
Rettaliata, J. T. 1936 Trans. A.S.M.E. 58, 59.
Sander, A. & Damkoehler, G. 1943 Naturwissenschaften 31, 46.
Schmidt, B. 1962 Beobachtungen über das Verhalten der durch Wasserdampfkondensation ausgelösten Störungen in einer Überschall-Windkanelduse. Thesis, Karlsruhe.
Sherwood, T. K. & Cooke, N. E. 1957 Mass transfer at low pressures. J. A.I.Ch.E. 3, 37.Google Scholar
Sherwood, T. K. & Johannes, C. 1962 The maximum rate of sublimation of solids. J. A.I.Ch.E. 8, 590.Google Scholar
Stever, H. G. 1958 Condensation in high speed flows. In High Speed Aerodynamics and Jet Propulsion, vol. III, p. 526. Princeton University Press.
Stodola, A. 1927 Steam and Gas Turbines, pp. 117–28, 1034–73. New York: McGraw-Hill.
Strickland-Constable, R. F. & Bruce, E. W. 1954 The mechanism of drying of solids, part IV: the sublimation of pure ice. Trans. Inst. Chem. Engrs 32, 19.Google Scholar
Tschudin, K. 1946 Helv. Phys. Acta 19, 9.
Volmer, M. 1939 Kinetik der Phasenbildung, chap. 4. Dresden and Leipzig: Steinkopf.
Wachman, H. Y. 1962 The thermal accommodation coefficient: a critical survey. A.R.S.J. 32, 2.Google Scholar
Wegener, P. P. & Mack, L. M. 1958 Condensation in supersonic and hypersonic wind tunnels. Adv. Appl. Mech. 5, 307–447.Google Scholar
Wegener, P. P. & Parlange, J. V. 1964 Surface tension of liquids from water bell experiments. Z. Phys. Chem. 43, 245.Google Scholar
Wegener, P. P. & Pouring, A. A. 1964 Experiments on condensation of water vapor by homogeneous nucleation in nozzles. Phys. Fluids 7, 352.Google Scholar
Whytlaw-Gray, R. W. 1932 Smoke. London: Arnold.
Wilson, C. T. R. 1899 Phil. Trans. Roy. Soc., Lond. A, 192, 403. (Also 1900 Phil. Trans. Roy. Soc., Lond., A 193, 289.)
Yang, W. T. 1963 D.Eng. Thesis, Yale University.
Yellot, J. I. 1934 Trans. A.S.M.E. 56, 41.
Yellot, J. I. & Holland, C. K. 1937 Trans. A.S.M.E. 59, 17.
Zeldovich, J. 1942 J. Exp. Theor. Phys. (U.S.S.R.), 12, 525.