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I am having hard time understanding how does the axial component stay constant through the rotor. Every resource i look just says it is due to mass conservation but never gives the actual conservation equation and i can't write it.

For clarity, i am talking about wake rotation theory and not the simplified 1D momentum theory.

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  • $\begingroup$ You don't post links to any references. If the rotor is considered as a disk, or as a cylinder with no flow through the sides, then the net axial flow pretty much must be constant. I could certainly see doing the analysis such that there's a constant axial flow plus some circulation flow centered on the turbine blades and extending outward from them. This would mean that the flow at some point in the rotor disk would vary, but mathematically you could claim it as the sum of a constant flow + circulation. $\endgroup$
    – TimWescott
    Commented May 20, 2019 at 17:00
  • $\begingroup$ So, think about the Betz limit... $\endgroup$
    – Solar Mike
    Commented May 20, 2019 at 17:05
  • $\begingroup$ It stays constant because you assume that there in negligible radial flow. That makes the model self-consistent. The value of this constant velocity is the average of the freestream (axial) velocity and the (fully contracted) wake (axial) velocity. Does this fit with the model you are studying? $\endgroup$
    – Phil Sweet
    Commented May 20, 2019 at 21:02
  • $\begingroup$ Should have been "fully expanded". Turbines have expanded wakes, propellers have contracted wakes. $\endgroup$
    – Phil Sweet
    Commented Jun 14, 2020 at 10:27
  • $\begingroup$ This is not to answer your question directly, as I am laking the expertise, but to bring up an article that may be in your interest. Per the linked wiki article, "Two velocity parameters of importance for the wake pattern are: v is the relative velocity of the water and the surface object that causes the wake. c is the phase velocity of a wave, varying with wave frequency." If the above is relevant to your question, you shall address which velocity is in your question with references or citations. [link](en.wikipedia.org/wiki/… $\endgroup$
    – r13
    Commented Jun 9, 2021 at 20:46

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The windmills based on lift action don't change the speed of air passing through them same as an airplane's wing flying through the air, the air stream washing around the wing's top and bottom doesn't pick up any speed. It Just gets bent down.

The blades of the windmill in this case work like a wing they let the air stream through but they bend it by twisting it as a screw driver, albeit that twisting will calm down rather fast by the viscosity of the air.

A crude example of the flux of the air before and after the windmill would be like those striped colored toothpaste, going straight till it hits the blades then twists a quarter of circle then keeps roping out straight behind not turning anymore, and getting mixed with the rest of the wind. this is kind of cleaned up version of the affair, other wise there is some turbulence and a bit of drag, etc.

So the axial speed of the air remains the same but the tangential speed changes for the transit time starting from the encountering the tip of the blade till some time after leaving the trailing edge of the blade.

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  • $\begingroup$ I'm pretty sure that is the 1D momentum model that the OP isn't interested in. $\endgroup$
    – Phil Sweet
    Commented May 21, 2019 at 9:32

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