Quandt 



considerable heat transfer and poor combustion result, thus giving low ther- 

 modynamic efficiency. 



In the past several years interest has developed in continuous air-water jets 

 for ship propulsion. Muench and Keith (5) describe the results of an analysis of 

 propulsive efficiencies possible with augmentation of a basic air jet and con- 

 clude that reasonable efficiencies are predictable at higher speeds. Davidson 

 and Sadowski (6) discuss similar computations directed toward modification of a 

 particular aircraft turbofan engine for ship propulsion. These detailed analyses 

 have been made possible through the development of a large body of data and 

 analytical techniques suitable for predicting the behavior of enclosed two-phase 

 systems. For example, Quandt (7) has developed a rational method of predicting 

 natural flow patterns which control the heat, mass, and momentum -transfer 

 characteristics of these mixtures. Levy (8) has provided a basis for computing 

 friction losses and mean density in dispersed flows, while Elliott (9) has re- 

 ported a satisfactory analytical description for predicting liquid droplet accel- 

 eration in an expanding gas stream. 



The purpose of this paper is to assemble some of the more recent theoreti- 

 cal and experimental techniques required to understand the gas -phase -continuous 

 two -phase jet system. The development will be that needed to predict thrust 

 performance for a water-droplet-air-jet system, and is similar to that of 

 Muench and Keith (8). It is intended that this paper will serve to illustrate a 

 formal basis for the analysis of air -water jets and to suggest the potential of 

 these variable density fluids as ship propulsion media. 



THEORY 



In order to satisfactorily construct a two -phase thrust device, it is neces- 

 sary to ingest each phase, add energy to one or both phases, form the mixture, 

 and eject it in the rearward direction. Significant differences arise in the anal- 

 ysis techniques used for the nozzle description in a single- and two -phase sys- 

 tems because in the latter the separate phases do not generally flow with the 

 same velocity. This velocity difference or "slip" between the phases has a sig- 

 nificant effect upon mixture density, momentum flux, energy transfer efficiency, 

 and consequently the size of apparatus needed to produce a given thrust. This 

 section will follow a development based upon separate ingestion and energy ad- 

 dition to each phase, since this may be accomplished with existing components 

 and analysis techniques. A two-phase analysis will be developed for the mixing 

 and ejection nozzle stages to predict thrust augmentation, thrust intensity, and 

 propulsive efficiency. Certain simplifying assumptions will be made to facili- 

 tate a first-order solution, so that the essential features of the two-phase jet 

 may be illustrated. 



Figure 1 presents a schematic of the air-water thrust system to be ana- 

 lyzed. Here, the water -handling component is characterized by a simple scoop, 

 duct, and injection nozzle station capable of delivering dispersed liquid to the 

 two-phase nozzle area at a velocity slightly less than the forward speed of the 

 ship. Air is taken in through a compressor, which, in this example, adds the 

 energy required to accelerate both the air and water phases. This air is ducted 

 to the vicinity of the water injection nozzles and mixed with the water, and the 



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