GATE AE 2019 • Q39 MCQ • 2 Marks Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Subsonic & Supersonic Inlets

Question Statement:

In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. For a fixed turbine inlet temperature (TIT), how does this affect the turbine work output and the cycle thermal efficiency?

Options:

  • (A) Turbine work increases, thermal efficiency increases
  • (B) Turbine work decreases, thermal efficiency increases
  • (C) Turbine work remains unchanged, thermal efficiency decreases
  • (D) Turbine work decreases, thermal efficiency decreases

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2019 Q.39 / AE Q.29)** **1. Intuitive Physical Setup & Given Parameters**: - Real turbojet engine: compressor isentropic efficiency $\eta_c < 1$. - Fixed Turbine Inlet Temperature: $T_{04} = \text{TIT} = \text{constant}$. **2. Step-by-Step Thermodynamic Derivation**: 1. **Compressor Work Required**: With lower $\eta_c$, for a given pressure ratio, compressor discharge temperature $T_{03}$ rises because of internal aerodynamic friction: w_c = C_p (T_{03} - T_{02}) = \frac{C_p T_{02}}{\eta_c} \left( r_p^{\frac{\gamma-1}{\gamma}} - 1 \right) Higher $w_c$ is required to achieve the pressure ratio. 2. **Turbine Expansion & Work Output**: In a turbojet, the turbine is matched to drive the compressor (and accessories): w_t = w_c However, considering the turbine work capability per unit mass expansion for fixed pressure ratio and fixed TIT ($T_{04}$), the total enthalpy drop across the turbine is fixed by its own expansion ratio. 3. **Cycle Thermal Efficiency**: Because of compressor irreversibilities, more entropy is generated and fuel energy is wasted as internal reheat, causing the overall thermal efficiency $\eta_{th}$ to decrease. **3. Comprehensive Options & Distractor Analysis**: - **(A)** (both increase): ❌ Incorrect. Irreversibility degrades cycle efficiency. - **(B)** (thermal efficiency increases): ❌ Incorrect. - **(C)** (turbine work remains unchanged, thermal efficiency decreases): ✅ **CORRECT**. Matches official key C. - **(D)** (turbine work decreases): ❌ Incorrect distractor. **4. Official Master Key & Exam Takeaway**: - **Official Answer**: **C** - **Exam Rule**: Compressor inefficiency increases compressor discharge temperature and decreases overall thermal efficiency.
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