Question

Which of the following statements is/are TRUE for a single-stage axial compressor?

• A. Starting from design condition and keeping the mass flow rate constant, if the blade RPM is increased, the compressor rotor may experience \emph{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

Hint:

Incidence follows the rotor inlet triangle: \(\tan\beta_1=V_x/(U-V_{\theta1})\). \(\uparrow \dot m \Rightarrow \uparrow V_x \Rightarrow \uparrow \beta_1\) (positive incidence). \(\uparrow\) RPM at fixed \(\dot m\) \(\Rightarrow \downarrow \beta_1\) (negative incidence). Surge is approached by decreasing mass flow on a speed line.

Answer 1

The Correct Option is B

Step 1: Use the rotor inlet velocity triangle.
Let \(U\) be blade speed, \(V_x\) the axial velocity (set by mass flow \(\dot m=\rho A V_x\)), and \(V_{\theta 1}\) the inlet whirl. The rotor inlet relative flow angle \(\beta_1\) satisfies \[ \tan\beta_1=\frac{V_x}{U-V_{\theta 1}}. \] At the design point, the metal angle equals the relative flow angle so the incidence is zero. 

Step 2: Effect of changing RPM at constant mass flow (Option A).
Holding \(\dot m\) fixed keeps \(V_x\) essentially constant; increasing RPM raises \(U\Rightarrow (U-V_{\theta1})\) increases \(\Rightarrow \tan\beta_1\) decreases. Hence the actual \(\beta_1\) becomes smaller than the design angle (i.e., negative incidence), not positive. \(\Rightarrow\) (A) is False. 

Step 3: Effect of increasing mass flow at the same RPM (Option B).
Here \(U\) is fixed and \(V_x\) increases with \(\dot m\). Therefore \(\tan\beta_1\) increases and \(\beta_1\) becomes larger than the design blade angle \(\Rightarrow\) positive incidence, which can lead to leading-edge separation. \(\Rightarrow\) (B) is True. 

Step 4: Surge tendencies (Options C and D).
On a given speed line, surge is approached as the mass flow is reduced toward the left of the map, not when it is increased. Thus at fixed RPM, increasing \(\dot m\) moves away from surge \(\Rightarrow\) (D) False. At fixed \(\dot m\), merely increasing RPM does not by itself cause surge; surge is fundamentally tied to operating a speed line at too low flow (or excessive back-pressure). Without reducing \(\dot m\), increasing RPM does not meet this condition. \(\Rightarrow\) (C) is False. \[ \boxed{\text{Only (B) is correct.}} \]