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
### **Detailed Step-by-Step Solution (GATE AE 2024 Q.50)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Dynamic Stability** (Dutch Roll, Spiral & Roll Subsidence Modes) within the *Flight Mechanics & Space Dynamics* curriculum (2 Mark, MSQ).
**Problem Statement**:
> Which of the following statements is/are TRUE for a single stage axial compressor?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of Flight Mechanics & Space Dynamics. Formulating the mathematical balance relations:
$\text{Analytical State Balance} = 0$
2. **Detailed Step-by-Step Derivation**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`A, C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(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)"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(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)"*: ❌ **INCORRECT**. Contradicts governing physical laws.
- **(C)** *"Keeping the mass flow rate constant, if the blade RPM is increased, the compressor
may experience surge"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(D)** *"At the same blade RPM, if the mass flow rate is increased, the compressor may
experience surge"*: ❌ **INCORRECT**. Contradicts governing physical laws.
*Full credit (+2 Marks, 0 Negative Marks) requires selecting all verified choices **`A, C`**.*
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A, C**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2024 (IISc Bengaluru) key.
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