Centrifugal compressor design: for identical diameter, blade inlet angle, and rotational speed, which blade orientation typically yields the maximum pressure rise across the stage?

Introduction / Context:
In turbomachinery, the achievable pressure rise of a centrifugal compressor stage depends strongly on impeller blade orientation for a given tip speed, flow coefficient, and overall diameter. The three classic orientations are forward-curved, radial (90°), and backward-curved. Understanding how each affects the Euler head and the diffusion process is key for preliminary design and exam problems.

Given Data / Assumptions:

• Same overall impeller and diffuser dimensions (fixed diameter and width).
• Same blade inlet angle and the same rotational speed.
• Idealized comparison at the same flow coefficient, ignoring detailed loss variations beyond the first order trend.

Concept / Approach:
The stage ideal head is approximated by the Euler relation: Delta h_E ≈ U_2 * V_theta2 - U_1 * V_theta1With similar inlets, the dominant term is U_2 * V_theta2. Forward-curved blades increase the whirl component at exit (V_theta2), radial blades yield an intermediate whirl, and backward-curved blades reduce the whirl at exit for the same U_2. Therefore, the pressure coefficient and pressure rise trend is typically: forward-curved > radial > backward-curved (for identical boundaries).

Step-by-Step Solution:
Fix U_2 (same speed and radius) and geometry.Note that changing blade exit metal angle changes V_theta2.Forward-curved → higher V_theta2 → higher Euler head → greater pressure rise.Radial → moderate V_theta2 → moderate head.Backward-curved → reduced V_theta2 → lowest head among the three for same U_2.

Verification / Alternative check:
Velocity-triangle sketches confirm that, at fixed U_2 and mass flow, a forward exit metal angle adds to the tangential component, raising the specific work. Backward-curved blades are popular for efficiency and stable characteristic, not for maximum theoretical pressure rise.

Why Other Options Are Wrong:

• Backward curved blades: usually give a lower pressure rise for the same speed but are more efficient and stable.
• Radial blades: intermediate head; not the maximum.
• All orientations same: contradicts Euler head dependence on V_theta2.
• Mixed-flow blades: not comparable under the stated “same overall dimensions and angles”.

Common Pitfalls:
Confusing “maximum pressure rise” with “best efficiency.” Backward-curved blades often yield higher efficiency and a non-overloading power characteristic but not the maximum head.

Final Answer:
Forward curved blades