A schematic of a twin-spool turbofan engine is given below. The engine is designed to cruise at a Mach number of 0.89 and an altitude of 37,500 ft. The inlet has an adiabatic efficiency of 0.92. The fan has a by-pass ratio of 1.37 and adiabatic efficiency of 0.95, while the compressor and both turbine stages have a polytropic efficiency of 0.95. The compressor is designed to supply 27 times compression, while the fan is designed to supply 1.65 times compression. All components have a mechanical efficiency of 0.99. The nozzle is of a converging-only type and has an adiabatic efficiency of 0.94. Combustion processes have an efficiency of 0.97 and a pressure loss of 4.5% of the supplied pressure. The assumption can be made that the velocities of all internal engine flows are negligibly small. Under cruise conditions, the engine operates at 65.0% maximum throttle position. For this analysis, throttle and fuel flow rate are interchangeable. The stoichiometric fuel-oxidizer ratio is 0.068 and the maximum allowable turbine inlet temperature is 3500 R. The ratio of specific heats can be taken to be 1.4 at all cold flow stations and 1.35 at all hot flow stations. The energy content of the JP-8 fuel is 19359.5 BTU/lbm. The frontal intake area of the engine is 6.2 ft2 and is equal to the total exhaust area. The fan exhaust area is 1.65 times larger then the core exhaust area.

(a) Draw a temperature-entropy (i. e. T-s) and normalized enthalpy-normalized kinentic energy (i. e. H-K) diagram for the engine cycle under both cruise and afterburning operation.

(b) Under cruise conditions what is the total specific thrust and thrust specific fuel consumption of this engine. What is the proportion of thrust developed by the fan flow stream alone as compared to the hot engine-core flow stream?

(c) What are the thermal, propulsive and overall efficiencies of this engine at cruise?

(d) During take-off this engine is designed to function with afterburners operating, such as would be required of an aircraft carrier based fighter. What is the fuel equivalence ratio of the engine as a whole and of the afterburner only if the temperature in the afterburner and entrance to the nozzle is not limited by material considerations?

(e) What is the specific thrust and thrust specific fuel consumption, as well as the thermal, propulsive and overall efficiencies of this engine under this afterburning operation?