Foa 



10 15 2,0 ^ , 2.5 3.0 35 



Fig. 13 - Performance of a bladeless propeller with a 

 large coning angle 



(c) a constant-area mixing phase is added, as in Ref. 9. The primary gas par- 

 ticles are assumed to move, during the deflection phase, along the surface of 

 the cone defined by the initial coning angle of the nozzle axes. Of particular in- 

 terest here is the effect of mixing during the deflection phase. Jet cascade 

 tests by Palmieri at R.P.I. (Ref. 13) and velocity surveys in jet injection tests 

 at the McDonnell Propulsion Laboratory (Ref. 5) have shown that the mutual de- 

 flection of the two flows can be completed before mixing has made substantial 

 progress. This, however, has yet to be accomplished in the actual operating 

 conditions of the bladeless propeller, mainly because mixing is promoted by the 

 curl components which are introduced in both flows by the rotation of F ^ . Mix- 

 ing in the deflection phase is described in Ref. 12 as a mass transfer which is 

 assumed to progress at a constant rate per unit length of the primary jet. The 

 mass transferred from the secondary to the primary flow during the deflection 

 phase is related nondimensionally to the length of the primary jet through an 

 "entrainment coefficient" \ , the value of which varies from zero (for the case 

 of no mixing) to 0.05 for the worst condition considered. Some of the numerical 

 results of the analysis of Ref. 12 are shown in Fig. 14. The adverse effect of 

 entrainment increases, as expected, with increasing spin angles. An increase 

 of primary-to -secondary stagnation temperature ratio (hence of secondary-to- 

 primary density ratio) is again found to increase the augmentation ratio and to 

 decrease the optimum spin angle for any given area ratio. 



Special attention to the interaction of a gaseous primary with a liquid sec- 

 ondary fluid has been given in recent years at Grumman Aircraft Engineering 

 Corp. in an extensive study of underwater propulsion applications of the blade- 

 less propeller (Refs. 14 and 15). In such interactions, the collision angle be- 

 tween the two flows is generally very much larger than the spin angle, and the 

 Grumman study has revealed that the best performance is obtained, as a conse- 

 quence, with very small spin angles. In Refs. 14 and 15 the deflection phase is 



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