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.
Show Hint
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
Show Solution
The Correct Option isA, C, D
Solution and Explanation
A compressor map plots pressure ratio against mass flow rate for a set of constant speed lines, bounded on the left by the surge line and on the right by the choke condition. This question is about reading where points A and B sit on one such speed line, and reasoning what that means for stability and efficiency.
(A) $\eta_A > \eta_B$: Efficiency contours on a compressor map are closed loops, best near the middle of the useful operating range and worse toward either extreme. Point B lies further toward the high flow, low pressure ratio end of the curve where the compressor is closer to choking; near choke, blade passage velocities approach sonic values and losses from shocks and separation climb fast. Point A sits closer to the well-behaved, higher pressure ratio part of the line, so it keeps a higher efficiency. This statement is TRUE.
(B) $\eta_B > \eta_A$: This is the opposite of (A), and since (A) is correct, (B) is FALSE.
(C) A is closer to the surge point than B: Surge sits at the low mass flow, high pressure ratio end of a speed line. Point A is positioned right near the peak of the curve, exactly that low flow, high pressure ratio region, so A is nearer the surge boundary than B is. This statement is TRUE.
(D) B is closer to the choke point than A: Choke sits at the high mass flow end where the curve turns almost vertical. Point B is placed further along the curve toward that high flow region than A is, so B is nearer the choke boundary. This statement is TRUE.
Put together, moving from A to B along the speed line means moving away from the surge side and toward the choke side, mass flow rises, pressure ratio falls, and efficiency drops because the flow is getting pushed harder through the same fixed geometry.
Let's summarize:
Surge is the low flow, high pressure ratio end of a speed line; choke is the high flow end where the line goes nearly vertical.
A sits nearer the surge side, B sits nearer the choke side, on the same speed line.
Efficiency falls as the operating point is pushed toward choke, so $\eta_A > \eta_B$.
