Subtopic: Dutch Roll, Spiral & Roll Subsidence Modes
Question Statement:
Which of the following statements is/are TRUE for a single stage axial compressor?
Options:
(A) Starting from design condition and keeping the mass flow rate constant, if the blade
RPM is increased, the compressor rotor may experience positive incidence flow
separation (actual relative flow angle greater than the design blade angle)
(B) Starting from design condition at the same blade RPM , if the mass flow rate is
increased, the compressor rotor may experience positive incidence flow separation
(actual relative flow angle greater than the design blade angle)
(C) Keeping the mass flow rate constant, if the blade RPM is increased, the compressor
may experience surge
(D) At the same blade RPM, if the mass flow rate is increased, the compressor may
experience surge
Official Answer Key:
A, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.50)**
**1. Governing Concept & Theory**:
Governed by principles of **Dynamic Stability** (Aircraft Performance & Stability, 2 Mark, MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **A, C**.
**3. Official Answer Verification**:
- **Official Result**: **A, C**
- **Evaluation Status**: Matches official GATE 2024 master key with 100% accuracy.
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