Centrifugal compressor flow: location of highest Mach number leading to shock In a radial-flow (centrifugal) compressor, the flow accelerates through the impeller and then is decelerated in the diffuser. Considering where transonic conditions are most likely and where shocks originate, identify the location at which the highest Mach number typically occurs, leading to shock formation in the subsequent passage.

Introduction / Context:
Centrifugal compressors accelerate air within the impeller and then recover static pressure in the diffuser. At high tip speeds and pressure ratios, the flow leaving the impeller can reach transonic conditions. Understanding where the peak Mach number occurs is essential for diagnosing losses, diffuser surge margin, and shock-related efficiency penalties.

Given Data / Assumptions:

• Machine: centrifugal (radial) compressor with an impeller and a downstream diffuser.
• Operating at a high loading where local Mach numbers approach unity.
• Focus: location of peak Mach number that precipitates shocks.

Concept / Approach:
The impeller imparts kinetic energy to the fluid; thus absolute velocity (and often relative velocity near the blade trailing edge) peaks at the impeller exit. The diffuser immediately receives this high-speed flow and attempts controlled deceleration. If the incoming flow is transonic or supersonic, shocks appear in the diffuser inlet or passages, but the highest Mach number causing those shocks is achieved at the impeller outlet radius.

Step-by-Step Solution:
Recognise energy addition: impeller raises velocity most strongly toward its outlet radius.Assess Mach distribution: maximum Mach commonly occurs at or just as the flow leaves the impeller (tip region).Infer shock origin: deceleration in the diffuser produces shocks when inlet Mach is too high; however, the peak Mach value that triggers this is reached at impeller exit.Therefore, select the impeller outlet radius.

Verification / Alternative check:
Design practice limits tip relative Mach and uses vaneless spaces/contoured diffusers to manage shocks. Performance maps often show increased loss near choke, consistent with impeller-exit transonics.

Why Other Options Are Wrong:

• Diffuser inlet/outlet: shocks appear here, but the absolute maximum Mach originates at the impeller exit that feeds the diffuser.
• Impeller inlet: modern designs keep inlet Mach subsonic to avoid leading-edge shocks.
• Mid-diffuser hub: by this point, the flow is already decelerating.

Common Pitfalls:
Confusing the location of shocks with the location of peak Mach. Shocks can sit in the diffuser, yet the highest Mach that causes them is reached at the impeller’s outlet radius.

Final Answer:
impeller outlet radius