Question

How does the propulsion efficiency of a turbofan engine, operating at a given Mach number and altitude, change with increase in compressor pressure ratio?

• A. Remains constant
• B. Increases monotonically
• C. Decreases monotonically
• D. First decreases and then increases

Hint:

Propulsion efficiency depends on how close jet speed is to flight speed; increasing CPR first increases the mismatch, then improves thermal efficiency.

Answer 1

The Correct Option is D

Propulsion efficiency measures how effectively the engine converts kinetic energy into useful thrust power. It is given by: \[ \eta_p = \frac{2V_0}{V_j + V_0} \] where \(V_0\) = flight speed and \(V_j\) = jet velocity.
1. Effect of increasing compressor pressure ratio (CPR):
Higher CPR increases the stagnation temperature at the compressor exit. Therefore, the turbine must extract more work. To maintain the same turbine inlet temperature, more fuel is burned, raising the jet exhaust velocity.
2. Initial behaviour (efficiency decreases):
As the compressor pressure ratio starts increasing, the jet velocity increases more sharply than the flight velocity. Since propulsion efficiency decreases when the jet becomes much faster than the aircraft: \[ \eta_p \downarrow \] In this region, kinetic energy wasted in the jet increases significantly.
3. Later behaviour (efficiency increases):
At very high CPR, thermal efficiency increases substantially. Higher CPR improves Brayton-cycle efficiency, meaning more of the fuel's energy is converted into useful work. Even though jet velocity remains high, the ratio of useful thrust power to fuel energy increases. This raises propulsion efficiency.
Thus, the curve is non-monotonic:
\[ \text{Efficiency} = \begin{cases} \text{decreases initially},
\text{then increases with high CPR}. \end{cases} \] Hence, the correct trend is: first decreases, then increases.