What does the actual path of air within a turbojet engine look like? While Wikipedia describes the flow path as axial, I wonder if the path could be helical instead. Wikipedia explanation is described first in section 1, section 4 is for what could be the actual flow path, and sections 2 and 3 list the reasons for that. Section 5 is my question.



1. Usual high-level explanation

Wikipedia explains air flow in a jet engine this simplified way:


Flow path, Wikipedia, author: Jeff Dahl

Not obvious on the picture, there is a stator with vanes after each rotor, to create the pressure increase on vanes pressure side, and to straighten the flow for the next stage of the cascade, else there would be no compression and the engine would be an expensive fan. See this question for a picture showing the stators.



2. Taking into account blade and vanes

Usual depiction of the path, taking into account blades and vanes, is zigzagging, similar to:

  

The path above seems valid for motionless blades and vanes, ignoring blades are in rotational motion. If we dive into a bit more detailed explanation, the path would be refined like this:

  

Vanes pressure side is upward while blades pressure side is downward.



3. Taking into account blade rotation

With blades rotation, blades of the second stage do move while air is traveling across the first stage. While rotating, second stage blades deflect older air,  which now exits the second stage using a vane which is lower than the vane it exited the first stage (during this time air of the first stage has reached the second stage, but is deflected by an upper blade, etc):

  

Air path is therefore spiraled a bit, the exact amount of the helical displacement depending of the ratio between air axial speed and blades angular speed. This is not necessarily the exact vane angular spacing (or a multiple of it).



4. Seemingly more consistent depiction of air path

If this was the correct way it works, then the overall flow would rather be helical than axial, something more like this:

  



5. Question: How blades and vanes impact overall air path? How the air path can be better explained, taking into account blades are not fixed?

I'm looking for some details, perhaps blade/vanes geometry and airspeed, not an over-simplified view.
(Source) Image shows CFD simulation for a jet engine carried out by Northern Arizona University.

Pretty much as your illustration, but more turbulent and not as many complete turns.

Let's take one rotor disk at a time.

Each blade on each disk is like a wing. Air is rushing in at it. And it, is moving down on the air (or up from the other side). Giving the blade an angle of attack.

In a wing, air is pushed down.

So, one disk will push down on the air on one side, up the other, left and right top and bottom—the stator disk will straighten it out for the following rotor. And so on, i.e., a stepping swirl.

If the stator reversed the flow, it will be an immense angle of attack for the receiving rotor, i.e., the rotor will stall. So, a stepping swirl makes more sense.

While a propeller, an axial compressor, and a turbine are different in what they do, I don't see why the shape of the corkscrew of the propeller I asked about here—would change for any rotating disk carrying airfoil blades—



(Source)

—except in magnitude and thermodynamic properties.

To complement the earlier CFD image, here are two more:



(Original image) Three stage transonic compressor.



(Source) Analysis of Rotor-Stator-Interaction and Blade-to-Blade Measurements in a Two Stage Axial Flow Compressor