Gas-Turbine Powerplants For Two-Phase Hydropropulsion 



(e) Mass balance: 



1 + a' + a" - (ffj + 0(2 + ttg) ~ '^u ~ ^ ' (conventional turbine) 



-• ■■■ 1 + a' + a" - a^ = , 1 (33) 



I (bypass turbine) . 



a' (1 + S) - ttf ^ , J 



(f) Pressure balance (first gas-dynamical constraint): 



/3' + hjB = /3 (one-extraction turbine) 



= /S (multiple-extraction turbine) 

 = /Sj. (bypass turbine) . 



(g) Definitions: 



e - (a.+a.+ttg) 7, (second gas-dynamical constraint) 



/3 = /Si/?^ • 



(34) 



(35) 



The previous balance equations, which have been written in thermal form, 

 can be more usefully written in baric form, that is, in terms of the pressure 

 ratios, by making use of the isentropic laws and of the equation of state, for 

 perfect gases; the one real parameter introduced is the Cp, to which different 

 constant values have been given in different ranges. For the matching of the 

 powerplant and propulsor solutions, which are independent, it will be necessary 

 to evaluate the density p^-, of the gas injected at the chamber pressure p^. By 

 means of the hypotheses previously made, one obtains 



(a^ + a2 + 0(3) 



n = ' (conventional turbine) 



= K ' (bypass turbine) 



(36) 



where: 



P, Ps^ ^^ 



'' "''^^" Ufa, ' ""^ fifn, ' (37) 



Pa Pa 



1143 



