Super cavitating Propeller Theory 



making use of the boundary condition that p* = at x* = -co. 



Green's theorem for the case of a propeller with Q equally spaced 

 blades gives 



(A3) 



p(x=* 



"■"'■'' -^t{i!"-''M^y' 





(A4) 



[p(x,r,0)] dS, 



So "0 



$„ ""o 



where 



R^ = [(x*-x)2 + r2 + r*2 - 2rr* cos <5J 







2tt 



The control point, considered fixed in space, is (x*, r*, 0*) and (x, r, e^ + a^) 

 is a point on the moving surface s^. Sq is the enclosed surface which, for the 

 supercavitating propeller, consists of the face and cavity boundaries of a blade. 

 In Eq. (A4) the direction of the normal is into the fluid. 



In accordance with linearization procedure S^ is assumed to be a surface 

 composed of helical lines possessing a continuously varying pitch angle 

 tan"i (R\(r)/r) in the r direction, see Fig. A2. 



PRESSURE 

 SIDE 



SUCTION 

 SIDE 



Fig. A2 - The linearization surface 



951 



