Wind flow before and after a wind turbine
Wind turbine retards wind even before the wind reaches it. So, wind
turbine experiences wind speed slower than the original which is somewhere
between the upstream and downstream velocity. From the theory shown below,
the wind speed is found to be the average value between the upstream and
downstream velocity or in another word the upstream velocity decrement
equals to the downstream decrement. This relationship is proved by first
applying the Bernoulli equation to both the upstream and downstream streamline
and also applying the momentum equation on the whole flow as control volume.
By canceling out all the pressure terms from these 3 equations, the resulting
final equation shows the velocities relationship. A further probe by replacing
the velocity result back into the Bernoulli equation, we will find that
the pressure right after the rotor (downwind pressure) is actually a suction
(pressure lower than atmosphere) with magnitude equals to the ‘real’
pressure right in front of the rotor (upwind pressure).
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