Hydrodynamic Problems Solved by Rheoelectric Analogies 



THREE-DIMENSIONAL PROBLEMS 



We will consider first the problems involved in the calculation of super- 

 cavitating wings. Sub- and supercavitating screw propeller problems will then 

 be considered next. 



Supercavitating Hydrofoil with Non- Zero Cavitation 

 Number in Unbounded Flow 



The inverse problem was defined earlier in the section on the Hydrodynamic 

 Problem (paragraph 3B). To simplify the analog representation, the velocity po- 

 tential may be written in the form 



(I>(x,y,z)=x+-|-x+szS(x,y,z). 



The perturbation velocity potential is then defined by boundary conditions 

 slightly different from those corresponding to the function ^ = O - x. These 

 conditions are: on the upper and lower surface of the cavity, B^^t/Bx = o; on the 

 lower surface of the wing the pressure is higher than or at least equal to the 

 cavitation pressure. We thus have the condition B0/Bx > o, and to define the 

 distribution of 4> we will have, according to Eq. (5a), 



^o(y) + y Cj(y)g(x-xj,y) , .. . .. (5c) 



where g is given and fulfills the conditions indicated in paragraph 3B. At infinity 

 we should find the velocity of the undisturbed flow; hence 



The closure cavity condition is conveyed in any section y = cte, by ^(B0/3x) dx = 0. 

 With the overall boundary conditions we have just established, the ordinates of 

 the lower surface of the wing and of the contour of the cavity are given, if we 

 take, as Tulin suggested, the tangential velocities condition in the form dz/dx 

 = v/(Vq +u) instead of dz/dx = v/V^, by 



2 + Cr 



J Bz 



The rheoelectric simulation can be simplified still more if the potential 4> 

 is subdivided into three parts 



"El "" ^E2 



where -p^i and ^gj represent two even- potential functions characterizing the 

 cavity thickness effect, ^qd represents an odd potential function corresponding 

 to the general camber effect. The representation of these functions is extremely 



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