Propeller Pressure Field in a Nonuniform Flow 



1 A 



Fig. 2 - Propeller blade vortex system: 

 1, propeller blade; 2, bound vortex; 3, heli- 

 coidal free vortices; 4, radial free vortices 



where 



OJt. 



Thus in the case of a lightly loaded propeller the pressure generated by a 

 propeller blade in a nonuniform flow is related to the circulation in the same 

 manner as in uniform -inflow conditions. The only difference lies in the fact that 

 the constant circulation r(r' ) is replaced by its instantaneous value r(r',t). 

 The latter in general should be determined taking into account the nonstationary 

 flow conditions. 



Pl = 



For a z-bladed propeller one obtains 



4Tr 



277 . 



-wr'x + V r sin [y - 6 



277 



dr' 



:2+ r2+ r'2- 2i 



rr cos \j- 6 - — - ] 



Let us express the pressure in the dimensionless form: 



- ^ P p 



'" ^0 "PV^2 



^^o') 



where Pq is the mean propeller thrust and bp = Pq/{pW^/2) ttR^ is the propeller 

 loading coefficient; and let us nondimensionalize all lengths with respect to the 

 propeller radius R^ . 



Then we may write the expression for the propeller vibratory pressure due 

 to loading: 



