On the Flow of Vapor Between Liquid Surfaces

Author: Mathews, Warren Edward

Year: 1953

Degree: Dissertation (Ph.D.)

Advisor: Plesset, Milton S.

Committee Member: Unknown, Unknown

Option: Physics; Mathematics

DOI: 10.7907/EHV7-1W20

Abstract

An analysis of the one-dimensional flow of vapor between parallel liquid surfaces of identical composition but different temperatures is presented. The low velocity steady flow analysis reported previously by Plesset is extended to steady flows in which the Mach number approaches unity, and to low velocity flows in which the liquid surface spacing and temperatures are allowed to vary slowly with time. More important among the new results obtained are 1) an exact solution in closed form of the (non-linear) steady-flow equations, subject only to the condition [gamma]M[superscript 2] <= 1, and 2) a relatively simple approximate form of the nonsteady-flow perturbation solution which applies whenever the product of liquid surface spacing and unperturbed current density is not unusually small.

The perturbation technique developed for the one-dimensional problem is extended also to cylindrically symmetric two-dimensional and spherically symmetric three-dimensional flows. In addition, an alternative solution for the pressure perturbation is obtained by a method which, while clearly non-exact, does not explicitly involve a neglect of higher order terms.

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