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Theoretical Considerations on Shrouded Propellers

Tho now and the forcos which aro gonoratod by a propu:sion system 
consisting of rotor, shroud end guido vanos aro analyzed. For this purposo, 
tho compononts of tho system aro replaced by singulariti08. From the 
component velocity fields Old fmm the characteristic constants of the singu- 
luities, the interaction forces between the components aco determined from 
which the net forcos of the unit follow. Tho deduced expressions for thrust 
and power input taken together with the pressure increase at the rotor, which 
uises from tho action of the shroud, and with tho condition of cavitation tree 
now form the basis for a method of design of a propulsion unit.. To apply this 
method, of boui lift vetSU3 angle of attack curves and of press"te 
curves of sections in cascado is necessary. 
Comparison of experimental results for ghe efficiency and the 
action force between rotor and shroud in fair agreement with tho respective 
expressions taking into account the lack of knowledge relativo to 
the drag of tho shroud.

Recent int«ogt by the U.S. Navy in the possible pplication ot shrouded propellers 
vuious typeg of naval vessels for purpose of delaying cavitation Uld propeller noise 
has led to a study of the avlilablo theory ot such 8 propulsion system. It was found desire 
able Co considor further tho thexetical upects of this problem which has resulted in the de• 
velopment ot the theory represented here. It ts planned supplement this work with a 
sentation of the theory as gppliod to a qecific dosign problem. 
The forces on the components of the system and the design data ate to be determined 
for a given net thrust of c propulsion system consisting of rotor, shroud, and guidc vanos 
(the latter two component8 being stationary) and for given quantities ot speed of advanco, 
numbøe of revolutions, rotor diameter, and pressure at tho rotor (duo to the action of.the 
shroud). For this problem, it ig necessary ascertain the mutual interaction betwoen the 
components of tho gygtem which follows when thon componont8, with respee, thair effect 
on the now, are replaced by propc: singularitios. In order deduco the component forces on 
the basis o: such a thøory, it iB nocegsuy to know the component velocity fields. This re. 
quires cereain appmximations which will bø mentioned first i'. connection with the singulari• 
ties.