Question

Consider a turbofan engine with a bypass ratio of 6. The cruising Mach number is 0.85 at an altitude of 12000 m with an ambient temperature of 217 K. The ratio of stagnation pressure and ambient pressure for the fan and the core engine is 1.6. The stagnation temperature is 600 K at the exit of the core engine and 340 K at the exit of the fan. (a) If the fan and core streams expand in separate nozzles to ambient pressure, what is the specific thrust? (b) If the fan and core streams are mixed first to a uniform stagnation temperature and then expanded to the atmosphere in a single nozzle, what is the specific thrust? For simplicity, assume that the specific heat ratio and the gas constant are the same inde- pendent of the fluid's composition. Use 1.4 for 7 and 0.287 kJ/kg/K for R. The fuel-air ratio for the core engine is about 0.018. Neglect the losses in the nozzle.

Answer 1

& flight velocity l= M from table u= дӘ) l ca Me z 14 2 UX4 u. MORTA Ma) 0.85 82104 0.85 70•4)(287) (216-65) 250.8mis velocity of cone stream 2) co Joctefi- () 2 (1005) 1600) [. J1206 1206 000x [ 1 - (0.625 10.286 u? 389.5 m/s Velocity of fan stream (pal 2x(1005) (340) illf=V6 683400 (01257 ly =) 293.1 m/s F Es (1+the+ Belz=(1+3]u (1+0.018) (399.5) +61293.1)-8 (146) (25018) z) 399051) NS-leg Mf= you мү? 1•4-) 1-4 By pas ratio Trust z 6 m

come stream expand in 6 when they expand in single nozzel so thrust when fan, seper ate nozels 399.5 nsky t (1++) Toc + B7ct stagnation (1+B+4) - (+0.018)6600)+6)(340) uniform 1+6+ 0.018 » 2650.8 7,018 3770.7k Stagnation temperature Velocity of mixed Stream zce Tst ( 11 Pa 2 ठ um ) po. Mm= 14 261005)(3777) (1-67.) Moms (159177 [1-(0.62570286 J95467.83 -) velocity mitech 2) 2) 309 mis

I= (x+ B+ f) Um- (1+Bu Chorust 2) (1+ 6+000187 (304) - [1+6 ) (250.8) ) 2168.56 - 17556 m 6/Ns/kg