Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-23T17:30:42.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-equilibrium vapour condensation on a shock-tube endwall behind a reflected shock wave

Published online by Cambridge University Press:  21 April 2006

Shigeo Fujikawa ,
Masahiko Okuda ,
Teruaki Akamatsu  and
Tomonobu Goto
Shigeo Fujikawa
Affiliation:
Department of Mechanical Engineering, Kyoto University, Kyoto 606, Japan
Masahiko Okuda
Affiliation:
Department of Mechanical Engineering, Kyoto University, Kyoto 606, Japan
Teruaki Akamatsu
Affiliation:
Department of Mechanical Engineering, Kyoto University, Kyoto 606, Japan
Tomonobu Goto
Affiliation:
Department of Mechanical Engineering, Kyoto University, Kyoto 606, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals theoretically with a filmwise condensation of a vapour on the endwall of a shock tube behind a reflected shock wave. The gas dynamics, accompanied by heat and mass transfer at the vapour-liquid interface, is treated by the method of matched asymptotic expansions. The first and second approximate solutions are obtained and evaluated numerically. It is clarified that there exists a transition process on the growth of a liquid film, that is, the liquid film grows approximately in proportion to the time t in the early stages after the reflection of the shock wave, and after some time, it grows in proportion to the square root of the time. This transition process from the t-dependent growth to the t½-dependent one is mainly controlled by the intensity of condensation. In the t-dependent growth region, the growth rate of the liquid film is proportional to the condensation parameter, depending both upon an initial condition and upon thermal properties of the vapour and the liquid film, while in the t½-dependent growth region it becomes independent of the condensation parameter and is controlled only by thermal properties of the vapour, liquid film and shock-tube endwall. This result suggests that the measurement of the condensation parameter by shock tubes should be made in the t-dependent growth region immediately after the reflection of the shock wave.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 293 - 324
Copyright
© 1987 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

Beylich, A. E. 1985 Dynamik und Thermodynamik von Sphärischen Dampfblasen. VDI-Forschungsheft 630, 1–27.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd edn. Clarendon Press.
Clarke, J. F. 1967 The reflexion of a plane shockwave from a heat-conducting wall. Proc. R. Soc. Lond. 299, 221–237.Google Scholar
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transformations, vol. 1. McGraw-Hill.
Fujikawa, S., Akamatsu, T., Yahara, J. & Fujioka, H. 1982 Condensation and thermal accommodation processes of a vapour by a shock tube. J. Japan Soc. Fluid Mech. 1, 166–180.Google Scholar
Fujikawa, S., Mizuno, I., Akamatsu, T. & Zhurin, V. V. 1985 Condensation and vapour-liquid interaction in a reflected shock region. In Rarefied Gas Dynamics (ed. O. M. Belotserkovskii, M. N. Kogan, S. S. Kutateladze & A. K. Rebrov), vol. 2, pp. 1019–1031. Plenum.
Goldstein, R. 1964 Study of water vapour condensation on shock-tube walls. J. Chem. Phys. 40, 2793–2799.Google Scholar
Grosse, F. A. & Smith, W. R. 1968 Vapour condensation in a shock tube. Electrostatic effects. Phys. Fluids 11, 735–739.Google Scholar
Hill, P. G. 1966 Condensation of water vapour during supersonic expansion in nozzles. J. Fluid Mech. 25, 593–620.Google Scholar
Kawada, H. & Mori, Y. 1973 A shock tube study on condensation kinetics. Bull. Japan Soc. Mech. Engrs 16, 1053–1065.Google Scholar
Kogan, M. N. & Makashev, N. K. 1971 Knudsen layer role in the theory of heterogeneous reactions and in the surface reaction flows. Izv. Akad. Nauk SSSR, Mekh. Zhid. iGaza 6, 3–11.Google Scholar
Labuntsov, D. A. & Kryukov, A. P. 1979 Analysis of intensive evaporation and condensation. Intl J. Heat Mass Transfer 22, 989–1002.Google Scholar
Mortensen, E. M. & Eyring, H. 1960 Transition coefficients for evaporation and condensation. J. Phys. Chem. 64, 846–849.Google Scholar
Ockendon, J. R. & Hodgkins, W. R. 1975 Moving Boundary Problems in Heat Flow and Diffusion. Clarendon Press.
Schrage, R. W. 1953 A Theoretical Study of Interphase Mass Transfer. Columbia University Press.
Sislian, J. P. & Glass, I. I. 1976 Condensation of water vapour in rarefaction waves: I. Homogeneous nucleation. AIAA J. 14, 1731–1737.Google Scholar
Smith, W. R. 1973 Vapour-liquid condensation in a shock tube. Proc. 9th Intl Shock Tube Symp. Stanford University, pp. 785–792.
Sone, Y. & Onishi, Y. 1973 Kinetic theory of evaporation and condensation. J. Phys. Soc. Japan 35, 1773–1776.Google Scholar
Sone, Y. & Onishi, Y. 1978 Kinetic theory of evaporation and condensation. Hydrodynamic equation and slip boundary condition. J. Phys. Soc. Japan 44, 1981–1994.Google Scholar
Spalding, D. B. 1956 The theory of flame phenomena with chain reactions. Phil. Trans. R. Soc. Lond. A 249, 1–25.Google Scholar
Wegener, P. P. & Pouring, A. A. 1964 Experiments on condensation of water vapour by homogeneous nucleation in nozzles. Phys. Fluids 7, 352–361.Google Scholar
Van Dyke, M. D. 1964 Perturbation Methods in Fluid Mechanics. Academic.