Question Statement:
A multi-stage axial compressor can be operated at two points, A and B, both of
which lie on the same speed line, as shown in the figure below. If $\eta$ is the
isentropic efficiency of the compressor, select the statements that is/are TRUE.
Scientific schematic diagram reproduced from official IIT paper
Options:
-
(A) $\eta$A > $\eta$B
-
(B) $\eta$B > $\eta$A
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(C) In comparison to point B, point A is closer to the surge point
-
(D) In comparison to point A, point B is closer to the choke point
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2026 Q.28)**
**1. Intuitive Physical Setup & Given Parameters**:
The problem illustrates a multi-stage axial compressor characteristic curve ($\pi_c$ vs mass flow rate $\dot{m}$) along a constant speed line.
Two operating points, A and B, are indicated on the same speed line:
- **Point A**: Located at lower mass flow rate and higher pressure ratio (towards the left of the characteristic).
- **Point B**: Located at higher mass flow rate and lower pressure ratio (towards the right of the characteristic, approaching the vertical drop).
We need to identify all TRUE statements concerning efficiency, surge, and choke (MSQ).
**2. Step-by-Step Aerodynamic & Compressor Derivation**:
1. **Surge and Choke Boundaries**:
- **Surge limit**: Occurs at the low mass-flow end (left side of the characteristic curve) where adverse pressure gradients cause flow breakdown, blade stall, and violent flow reversal. Since point A is located to the left of point B, point A is closer to the surge line. Statement C is **TRUE**.
- **Choke limit**: Occurs at the high mass-flow end (right side of the curve) where Mach number reaches unity at the blade throat, choking the flow and causing the pressure ratio to drop vertically. Since point B is located to the right of point A, point B is closer to the choke point. Statement D is **TRUE**.
2. **Isentropic Efficiency Distribution**:
- On a typical compressor speed line, peak isentropic efficiency $\eta$ occurs near the design point (mid-to-upper portion of the speed line, closer to point A).
- As the compressor approaches choke (point B), shock losses, large incidence mismatches, and viscous dissipation drastically degrade isentropic efficiency:
\eta_A > \eta_B
- Statement A is **TRUE**, Statement B is **FALSE**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A) $\eta$A > $\eta$B**: ✅ **CORRECT**. Point A operates near optimal design incidence and high pressure ratio, whereas point B is deeply deteriorated by choke losses.
- **(B) $\eta$B > $\eta$A**: ❌ **INCORRECT**. Choked/near-choked compressor stages suffer huge drop in efficiency.
- **(C) In comparison to point B, point A is closer to the surge point**: ✅ **CORRECT**. The surge line defines the low mass flow boundary to the left.
- **(D) In comparison to point A, point B is closer to the choke point**: ✅ **CORRECT**. The choke line defines the high mass flow boundary to the right.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A, C, D**
- **Exam Takeaway**: Along any compressor speed line: Left = Surge (stall-limited, high $\pi$), Right = Choke (sonic throat, $\pi o 1$). Peak efficiency lies safely between surge and choke, dropping sharply toward choke.