Condensation Phenomena in Supersonic Flows

Citation

Charyk, Joseph Vincent (1946) Condensation Phenomena in Supersonic Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/RSQH-W442. https://resolver.caltech.edu/CaltechETD:etd-11062003-165637

Abstract

With the very rapid development of jet propulsion systems, the attainment of speeds which seemed to be well beyond reach a few years ago now appears to be at hand. The war has produced many examples of guided missiles traveling at supersonic speeds such as the famed German A-4 rocket, more commonly referred to in this country as the V-2. Today a supersonic airplane is no longer a designer's dream but practically an accomplished fact. Despite the impressive array of symbols of apparent mastery of high speed flight, there exists a large gap of fundamental knowledge that the theoretician working with the experimentalist must fill before true mastery of transonic and supersonic speeds can be said to be at hand. It was only due to the efforts of pioneers in high speed fluid mechanics like de Laval, Riemann, Hugoniot, Lord Rayleigh and Tschaplygin (see for example Ref. 1 to 4) and later the applications of such basic knowledge to the new field of high speed aerodynamics by men with foresight such as Prandtl, Ackeret, von Karman Taylor and Busemann (see for example Ref. 5 to 9) that tools for the engineer and designer were available when the need for them suddenly arose.

Today the emphasis of the aeronautical profession is on the basic problems of transonic and supersonic flows. One of the important and at first mystifying phenomena that emerged from experimental investigations in supersonic wind tunnels was the condensation shock. Later such shocks were noticed in the flow over an airfoil in experiments conducted at the California Institute of Technology by Kate Liepmann in 1941. In more recent years their appearance has been noted in actual flight at high speeds. The importance of such shocks in connection with the aerodynamic characteristics of airfoils in supercritical transonic flow has been pointed out by Tsien and Fejer (Ref. 10). Apparently, however, no detailed investigation of the phenomenon has been made with a view to studying the fundamental aspects of the condensation shock in order to develop practical methods for predicting the occurrence, location, strength and effect of such shocks. It has been the basic purpose of this research to study the detailed aspects of this problem and to endeavor to develop a means of accomplishing the aims noted. It is felt that though crude in many respects, the results of this investigation can provide practical knowledge of basic importance in understanding and treating the problems of condensation shocks when they appear and can point the way towards more refined and detailed future analyses of this problem.

In attacking this problem, an examination of the phenomenon of the sudden collapse of the supersaturated state of the moist air is first made. The assumptions necessary for the determination of the critical stability limit of the supersaturated air are analyzed and the necessity for further investigation, especially from the kinetic point of view, is pointed out. The study reveals that the temperature of air at which this collapse occurs is approximately a function only of the amount of water contained in the air and does not depend upon the pressure. This enables an important simplification in the analysis to be made.

The condition for collapse of the supersaturated state is then applied to the special case of normal condensation shocks. Because of this relatively small amount of water present in air, the effect of the presence of the water on the properties of the air can be neglected except at the shock where the release of the latent heat of vaporization upon condensation is of vital importance. A simple consideration of this heating process yields the interesting result that the flow after the shock must always be supersonic. An important simplification in treating the general condensation problem is an approximation to the actual saturation vapor pressure versus temperature curve by means of an exponential curve. Mathematically this means an approximate integration of the Clausius-Clapeyron equation in the sense that the specific volume of the fluid phase is neglected as compared to the specific volume of the vapor phase. This simplification enables a closed form solution to be obtained.

The oblique condensation shock is then analyzed and its application to the flow over an airfoil or other body in a stream of moist air is treated.

The possibility of a continuous condensation instead of an abrupt condensation of a combination of the two is discussed for the case of a one-dimensional flow. Certain interesting results emerge from such a consideration and experimentation will be required to determine whether under certain conditions such a condensation process can take place.

A considerable number of charts are provided which may be of use in making calculations in practical cases. In instances where a different range of values is necessary, additional charts can readily be constructed.

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