2 Adding bypass to an engine (35 pts) a) Core stage only (10 pts) Compute the propulsive efficiency and spe- cific thrust for a turbojet engine with an exhaust velocity of

450 m/s, an air mass flow rate of 250 kg/s, an exit area of 2 m², and an exit pressure of 35,000 Pa if the aircraft is flying at 200 m/s at an ambient pressure of 30,000 Pa. The fuel fraction is 2.0%. b) with bypass (20 pts) We want to add bypass to this turbojet to adapt it into a turbofan with the original turbojet as a core. The airstream coming from the fan has an exhaust velocity of 250 m/s and its exit pres- sure is matched to the ambient. The flow rate ingested by the fan m, is related to the air passing through the core me by m = 3me, where 3 is the bypass ratio. i) Efficiency (15 pts) Given that the heat of reaction of the fuel used by the engine is 43 MJ/kg, plot its thermal efficiency, propulsive effi- ciency, and total efficiency as a function of bypass ratio over 3 € [0, 15]. Render all efficiencies on the same plot. ii) Thrust (5 pts) Plot the specific thrust and thrust specific fuel con- sumption as a function of bypass ratio over 3 € [0, 15]. Render both on the same plot (multiple y axes). c) Comparison (5 pts) Based on your results, for which applications would we want to use a high-bypass turbofan? A low-bypass turbofan? Justify your answer.