Hydrodynamic Problems Solved by Rheoelectric Analogies 



Another method must be used, which will be described in the section on Three- 

 Dimensional Problems. 



Supercavitating Cascades '■ • ■■' -* c 



The study of supercavitating cascades is of practical interest in the field of 

 hydraulic machines such as pumps and turbines. It has been possible to design 

 convergent or divergent cascades constituted by supercavitating foils which sup- 

 port imposed pressure distribution. Here, the rheoelectric method shows the 

 possibilities open to the design of supercavitating propellers. 



Suppose that the foil camber is small. It is possible to consider, as in the 

 case of isolated profiles, the linearized flow with respect to the velocity far up- 

 stream. The periodicity of the velocity field allows the study of the function ^ 

 in a bounded strip (Fig. 13). The boundary conditions are defined, no longer on 

 a slit as in the preceding cases, but on the two surfaces limiting the strip. The 

 flow is supposed independent of the gravity field, and the boundary conditions are 

 given by Eqs. (3), (5a), (7), and (10a). A supplementary condition which takes 

 into account the periodicity of the field is conveyed by ^g = 4^,, where B and B' 

 are two points periodically apart upstream of the foils. 





rz 



^ 



fc-'Pc'^Ci 



LAA 



jL / 





control of Ci_ 



^ n^ttif*^- 



confrol of _^ 



UnJ ^^ ^I UmJ limJ Un 



Uhul 



^..I? 



m\ 



lft_ITTIT,TT-LI-LI"IZ 



I 



I 



(WIT 



.1 



i-t-uJ-id-nl-i^ 



_r 



.r 



Fig. 13 - Supercavitating cascade: function of (/> in a bounded strip 



385 



