Is this image of Compressor aerodynamics correct?

Question

Image Source: Air Gas Turbine Technology by Treager, Chapter 5

The rotation direction of rotor shown seems opposite. If it is correct, these are the questions I would like to ask:

1. Why the Y vector is in opposite direction?
2. How will the pressure zones (high and low) will form on the rotor and stator airfoils?

Answer 1

@Federico reminder has complicated a bit the answering process, but now we understand your actual problem, I can provide a focused answer immediately below, I've moved other elements at the end, you may ignore them as they were aimed to clarify your question and are indeed no more relevant.

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If I consider Y as relative velocity, Then X should also be the same, though in opposite direction, right?

Good point, they are the same magnitude. There is some approximation in the drawing:

I am not able to understand the term defined by X

The convention used for velocities in this drawing seems to be: Velocities relative to rotors are drawn as dotted lines and velocities relative to stators are drawn as plain lines. As stators are fixed to the engine, plain line velocities may be seen as "absolute".

• Y is the tangential velocity of IGV, and stators in general, relatively to the first stage rotor, and to rotors in general. Y is the apparent velocity of the stators.
  
• X is the tangential velocity of R1 (first stage rotor) relatively to S1 (first stage stator). X is the true velocity of the rotors.

In the Note, the relative velocity is shown by D, which I think is similar to C, making C relative velocity

• If you look at R1, there are arrows to emphasize the rotor channel is a diverging duct:
  
  The channel slows down air and at the same time it increases pressure.

• E described as "absolute" is linked to the fact it is relative to stator S1, which can be seen as being in the same reference frame than the engine, and "absolute".
  

  • D is the velocity of the flow relatively to R1, and E is the same velocity relatively to S1. The difference is: For the stator, D is affected by the rotation X.
  • For the rotor R1: C was transformed into D. D magnitude is smaller because of the deceleration by R1 diverging channel.
  • For the stator S1: B was transformed into E. E magnitute is larger because of the downwash created by R1.
  • As the mass is the same, and force is mass times acceleration, there is an excess of energy at the inlet of S1. This is the key to understand the compressor principle.

• S1 stator channel is again a diverging duct. It converts the energy added by the rotation into pressure, slowing down air from E to F velocity:
  

• This process ends here for the first stage, it will be repeated the same for the other stages, except IGV are not required, as the stator is designed to provide the correct angle of attack and velocity G for R2.

Bottom line, if we look at the process from the compressor standpoint, that is from the stators standpoint, for the stage R1/S1:

• Air at the outlet of the stage has the same velocity it has at its inlet, F ≈ B
• Pressure at the outlet is a bit larger than at inlet, due to addition of rotational kinetic energy (which source is the turbine, and ultimately fuel).
• Adding stages allows to incrementally increase pressure. The pressure ratio of a stage is limited by the angle of attack on blades and vanes. Increasing pressure means decreasing (axial) velocity. A smaller axial velocity at the outlet conjugated with a constant X/Y tangential velocity increases the angle of attack on the next airfoil, possibly past the stall angle.

IGV have no velocity-to-pressure conversion function, their role is only to create the correct angle of attack for R1. The equal length arrows emphasize an IGV channel is neither diverging nor converging:

If the velocity magnitude at the first stage inlet has to be adjusted relatively to the ram velocity, with such IGV, this must be done by the engine inlet duct, prior to the IGV.

The stator vanes have a double role, the one explained above for IGV, and the one to convert energy added by X into pressure.

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Your initial questions are answered below.

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Why the Y vector is in opposite direction?

Y velocity is the relative velocity of air for the rotor, it's opposed to the rotor actual rotation. It's like air coming from front when a wing moves forward:

How will the pressure zones (high and low) will form on the rotor and stator airfoils?

Blades and vanes are simple airfoils, which here are subject to chordwise winds C, E and G, exactly like regular wing airfoils. Pressure gradients will form like on any airfoil. E.g. for C and the first rotor blades, on the left your drawing, on the right the same drawing rotated:

Answer 2

C, E, and G are the relative winds as 'seen' by the blades of the 1st stage rotor, the blades of the 1st stage stator and the blades of the 2nd stage rotor, respectively.

C is the result of the vector addition of B and Y

E is the result of the vector addition of D and X

G is the result of the vector addition of F and Y

Answer 3

This one sort of reminds one of the physics quandary of whether light is a particle or a wave. Let's treat the incoming air as a continuous energy wave.

One can see, although the incoming airflow is 90 degrees to the next part of the inlet/rotor/stator/rotor diagram, the trailing edge of the "top wing" would "bounce" the wave right into the oncoming next set of "wings" at the proper (relative) angle of attack.

Keep in mind there are a whole ring of "wings" for each stage, and that jet compressors can be "stalled" by a sudden change in inlet airflow (to be avoided). This is why jet nacelles protect the compressor inlet.

At first the inlet vanes look "backwards", compared with the stator vanes, but the diagram is correct. It may be questionable as to why they alternate solid and dashed lines for each stage discharge, but that can be figured out.

How will low and high pressure zones (high and low) .. form on the rotor and stator airfoils?

Pressure increases and volume decreases as air is compressed from top of the diagram to bottom. In this case, higher pressure underneath the airfoils transfers the mechanical energy of the rotor into compressing the air. Each stage compresses more and more. The stator "lines up" the airflow for another rotor pass.

Finally, the concept of "relative wind" can be reviewed for this application. With ice boats, the (side wind) pushing the boat is not the same as that (from the movement of the boat) which creates the thrust from the sail, which allows it to go much faster than the wind. The relative wind from the rotor (at thousands of rpm) would be the major vector.

It might help to draw the vectors to scale.