I'm having a hard time conceptualizing this statement from "The Jet Engine" by Rolls-Royce

Question

This is taken from section 21 of Chapter 3, Compressors that discusses axial flow compressors in turbine jet engines.

The more the pressure ratio of a compressor is increased the more difficult it becomes to ensure that it will operate efficiently over the full speed range. This is because the requirement for the ratio of inlet area to exit area, at the high speed case, results in an inlet area that becomes progressively too large relative to the exit area as the compressor speed and hence pressure ratio is reduced. The axial velocity of the inlet air in the front stages thus becomes low relative to the blade speed, this changes the incidence of the air onto the blades and a condition is reached where the flow separates and the compressor flow breaks down

I'm trying to draw a connection to something I already understand, is this similar to the phenomenon that limits propellers to low speed? In order to produce positive thrust they need to spin faster and faster?

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• https://www.wiley.com/en-it/The+Jet+Engine%2C+5th+Edition-p-9781119065999 (also here)

Answer 1

Variable pitch propellers can help explain this.

When the aircraft speed is slow, the blade pitch is finer. At faster air speeds the blades must be opened more in the direction of the airstream.

This is due to the fact that the velocity of the airstream contributes to the relative wind on the propeller. The rotational velocity of the prop is the other contributor.

If the propeller is opened but the airstream velocity drops, then the angle of attack of the relative wind on the prop will increase. If the AoA gets too high, flow will begin to separate from the prop airfoil.

The compressor blades are all little airfoils. They will behave exactly the same way if incoming airflow slows down too much.

Answer 2

Picture 3.9, which is related to the text you copied in your question, is helpful in understanding the concept:

First of all note that with "inlet" they mean the beginning of the axial compressor and not the inlet of the whole engine.

Now, going from the inlet toward the outlet, the section of the compressor becomes smaller and smaller: that's simply because air gets compressed and occupies a smaller and smaller volume. Obviously the outlet area cannot become indefinitely small: there are mechanical and aerodynamic limitations that cannot be overcome. That implies that if you want/need to add compression stages then you have to add them to the left, by the inlet section. But each section added to the left has a bigger and bigger area i.e. blade span. A bigger blade span is achieved both increasing its outer radius (Ro) and decreasing its inner radius (Ri). But higher radius means bigger rotating velocity while smaller radius means smaller rotating velocity, which are both bad since:

1. Higher rotating velocity at the tip means getting closer and closer to transonic or even supersonic speeds: drag and noise increase and lift decreases.
2. Lower rotating velocity at the base of the blade means lower Reynolds numbers and higher AoA to get enough lift despite the lower velocity: drag increases as well as the chance to get the blade stalled.