Analytic Solution for the Phase Change in a Suddenly Pressurized Liquid-Vapor System

  • P. D. Thomas
  • F. H. Morse
Conference paper
Part of the Advances in Cryogenic Engineering book series (ACRE, volume 8)


To prevent boil-off of a cryogenic liquid in a nonperfectly insulated container, it is necessary to pressurize the ullage region. This is most conveniently accomplished by introducing a small quantity of gas at an elevated temperature. The amount of pressurizing gas required is inversely proportional to the temperature at which it enters the tank, since the pressurization requirement manifests itself as an energy requirement. The introduction of pressurant has two effects on the liquid-vapor system: it raises the interface temperature to the saturation temperature corresponding to the elevated ullage pressure, and it increases the vapor temperature. The liquid-vapor system, if isolated, will adjust to this nonequilibrium condition by transferring thermal energy from the vapor to the liquid. However, unlike two solids at different temperatures in thermal contact, the controlling temperature difference is not governed by the initial liquid and vapor temperatures alone. It is the interface temperature that controls the net heat flow into the liquid or vapor. Any imbalance of heat flow across the liquid-vapor interface is accounted for by a phase change, i.e., by energy being released at the interface by condensation or absorbed by evaporation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. I. Sedov, Similarity and Dimensional Methods in Mechanics, Academic Press, New York (1959).Google Scholar
  2. 2.
    H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford University Press, London (1959).Google Scholar
  3. 3.
    E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill Book Co., New York (1955).Google Scholar
  4. 4.
    W. C. Reynolds and T. A. Dolton, “The Use of Integral Methods in Transient Heat Transfer Analysis,” Stanford University Technical Report 36, Stanford, Calif. (Sept. 1958).Google Scholar

Copyright information

© Springer Science+Business Media New York 1963

Authors and Affiliations

  • P. D. Thomas
    • 1
  • F. H. Morse
    • 1
  1. 1.Lockheed Missiles and Space CompanyPalo AltoUSA

Personalised recommendations