Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 59

The values of a and a^′ that will provide the maximum possible efficiency can be determined by differentiating Eq. (3.19) by either factor and putting the result equal to zero.

Hence

(3.23)

From Eq. (3.18)

giving

(3.24)

The combination of Eqs. (3.18) and (3.21) gives the required values of a and a^′ that maximise the incremental power coefficient:

(3.25)

The axial flow induction for maximum power extraction is the same as for the non‐rotating wake case, that is, , and is therefore uniform over the entire disc. However, a^′varies with radial position.

From Eq. (3.20) the power coefficient for the whole rotor is

Substituting for the expression for a^′ in Eq. (3.25) gives maximum power as

(3.26)

which is precisely the same as for the non‐rotating wake case.