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.
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On a speed line, low mass flow / high pressure ratio is near surge and high mass flow is near choke; efficiency falls as the operating point moves toward the choke end.
In comparison to point B, point A is closer to the surge point
In comparison to point A, point B is closer to the choke point
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The Correct Option isA, C, D
Solution and Explanation
Step 1: Read the Positions of A and B on the Speed Line.
The figure plots pressure ratio \(\pi\) against mass flow rate \(\dot m\) for one constant speed line of a multi-stage axial compressor. As we move along this line from left to right, mass flow \(\dot m\) increases while pressure ratio \(\pi\) rises to a peak and then falls. Point A sits near the top of the curve, close to the peak pressure ratio and low mass flow end. Point B sits further along the curve, at a lower pressure ratio and a higher mass flow rate.
Step 2: Recall What Surge and Choke Mean on This Map.
Surge is an instability that occurs at the LOW mass flow, HIGH pressure ratio end of a speed line, where the flow can no longer support the adverse pressure gradient across the blade rows and breaks down. Choke happens at the opposite, HIGH mass flow end, where the flow in the narrowest passage of the compressor, usually the first rotor throat, reaches the local sonic (Mach 1) condition, so no more mass flow can pass through no matter how much the back pressure is lowered; the speed line becomes nearly vertical there.
Step 3: Locate A and B Relative to Surge and Choke.
Since A is near the peak-pressure-ratio, low mass flow end of the curve, it sits closer to the surge boundary than B does. Since B is further along toward the high mass flow, falling pressure ratio end of the curve, it sits closer to the choke condition than A does. This directly makes option (C), A is closer to surge than B, TRUE, and option (D), B is closer to choke than A, TRUE.
Step 4: Compare the Isentropic Efficiencies.
Isentropic efficiency contours on a compressor map form closed, roughly oval regions with the best efficiency located near the middle to upper part of each speed line, not right at either extreme. As operation moves away from that good-efficiency region toward choke, the relative velocities inside the narrow blade passages rise toward sonic values, so shock losses and flow separation increase quickly and efficiency drops sharply. Point B, being pushed further toward the choke end of the curve, sees this efficiency penalty, while point A, staying closer to the well-behaved part of the speed line near peak pressure ratio, retains a higher efficiency. So \(\eta_A > \eta_B\), making option (A) TRUE and option (B) FALSE.
Final Answer:
\[ \boxed{\eta_A > \eta_B, \ A \text{ is closer to surge}, \ B \text{ is closer to choke, i.e. options (A), (C) and (D)}} \]
