Gas-Turbine Powerplants For Two-Phase Hydropropulsion 



At the exit, Eq. (15) becomes 



(a) aligned propulsor (p^ = p^; /3j = ^J: 



-u' '- K,/3- ^ . 



(16) 



(b) S-propulsor (p^ = P3; fi-, = /3j): 



K, 



/?; 



(l + \j/3!'")^ 



The local pseudo-Mach number M is defined as 



M = V/c . 



(16-) 



(17) 



It will be useful to identify the pseudosonic conditions, which can be obtained 

 by equalizing Eq. (8') to Eq. (15). The corresponding value of /3. = /3^ is the 

 critical expansion ratio 



1 + ^n - /^h 



/3r 



— k.fi ( 1 - /?-*) = - /3, — 1 ^— 1— 



(18) 



By numerical procedure it will be possible to deduce fi^ from Eq. (18). The 

 exit pseudo-Mach number can be obtained from Eqs. (10) [or (10')], (16) [or 

 (16')], and (17). The equations cannot show any useful solutions for the water- 

 jet in terms of M, because of the limits (14). The previous equations define all 

 the parameters necessary to the flow solutions when \i or e are fixed. 



In the present work we will, on the contrary, assign an exit value (m^), 

 and the values of Xj or e which are consistent with such exit value will be 

 determined. By matching Eqs. (10) [or (10')], (16) [or (16')], and (17), one ob- 

 tains the following equation: 



where 



B,\.2 - B,^. - B3 = , 



[2(^/-l) - M^2(u-i)] 



(aligned propulsor) 



[2(l+/eho)^(/3e'^- 1) - M^2(k_ 1)] , (S-propulsor) 



(19) 



(19') 



1117 



