I am trying to use Blade Element Momentum Theory to run some power calculations for a turbine I built, however, I'm having trouble with one value in particular.

I derived the following equation for power from Blade Element Momentum theory. $$P_{Actual}=4a'(1-a)\rho V \pi \Omega^2\int_{R_h}^{R_r}{r^3 dr}$$

In this case, $a'=\frac{\omega}{2\Omega}$. I have everything but $\omega$, which is angular velocity of the wake, which is the following.

If the wind imparts a torque on the blades then the blades must be imparting a torque on the wind. This torque would then cause the flow to rotate. Thus the flow in the wake has two components, axial and tangential. This tangential flow is referred to as wake rotation.).

I cannot find this value experimentally and I was told by someone that I can approximate.

Upon searching Wikipedia, I also found:

There is a lot of variation between different versions of BEM theory. First, one can consider the effect of wake rotation or not.

This tells me that I can either approximate or use an alternative form of BEM. I cannot find information on either of these options and so any advice, (ie. how to approximate this value) or (an alternative equation without $\omega$), would be sincerely appreciated.

I tried using the same value as $\Omega$ (which I found experimentally and is the angular velocity of the blades) for $\omega$, however, my actual power yield is greater than my theoretical by a factor of 1.45.


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