Hydrodynamic Problems Solved by Rheoelectric Analogies 



where cr = (P^ - p^ )/(pVoV2) is the usual cavitation number. Having this, there 

 is no difficulty in expressing boundary conditions corresponding to a super- 

 cavitating blade. :i 



Analog Solution— The rheoelectric solution of this problem requires the 

 construction of a special tank. The electrolyte is contained within the volume 

 between two helicoids. The tank is thus made up of two helicoidal surfaces 

 (Fig. 23) covered with electrodes, the radial angle between them being 27t/p. One 

 surface represents the lower surface of the blade as well as the lower surface of 

 the cavity and/or the lower side of the free vortex sheet; the other surface rep- 

 resents the upper surface of the blade and/or the upper surface of the cavity as 

 well as the upper side of the wake of the adjacent blade. The two helicoidal sur- 

 faces are elongated and follow a radial direction to a radius sufficiently large 

 that the perturbations are negligible. Small electrodes placed on these surfaces 

 and symmetrically short-circuited assure the potential continuity. Upstream of 

 the blade the symmetry can be assured more simply by constructing two surfaces 

 a period apart and passing through the axis. A central core and a flat sector 

 perpendicular to the axis complete the tank. 



The tank comprises 160 small helicoidal components moulded in resin, each 

 one containing 20 electrodes. Certain of these components are removable for 

 better presentation of the geometry of the blades and cavities. A total of 3600 

 electrodes is required for each calculation. For this purpose there is an elec- 

 tric setup which consists of about 250 transformers, 200 potentiometers or volt- 

 age dividers, and interconnecting units which allow information to be collected at 

 about 250 points on the lower and upper surfaces of the blade. 



The geometry of the helicoid is characterized by the speed ratio Vq/uj, which 

 here is equal to 6.6 cm/rad (or 4.8 cm per revolution). 



Subcavitating Propellers — The rheoelectric installation just described is 

 especially useful for the solution of the inverse problem, because of the possi- 

 bility of regulating and controlling precisely the pressure distribution on each 

 section of the blade. To illustrate this, we shall describe the different stages of 

 a complete propeller design that permitted a useful experimental verification in 

 free water and in a cavitation tunnel. 



The characteristics of the propeller were the following: 



Advance velocity V^ = 7.25 m/sec 



Number of revolutions n = 3.75 t/sec (w = 25.36 rad/sec) 



Blade radius R = 1.20 m 



Advance coefficient x. = — =0.256, \ = -^= 0.805 



V V 



— = 0.256 , \ = — 

 jR nD 



Thrust T = 7200 kg 



399 



