# In horizontal axis wind turbines, why does axial component of absolute velocity stay constant (wake rotation theory)

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.

• 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. May 20, 2019 at 17:00
• So, think about the Betz limit... May 20, 2019 at 17:05
• 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? May 20, 2019 at 21:02
• Should have been "fully expanded". Turbines have expanded wakes, propellers have contracted wakes. Jun 14, 2020 at 10:27
• 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/…
– r13
Jun 9, 2021 at 20:46