Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 67

The axial thrust T on the disc can be determined using the Kutta–Joukowski theorem:

where V is the tangential velocity component at the disc. If V = rΩ(1 + a′), then, using Eq. (3.32) ignoring any additional inflow at the disc caused by the centrifugal pressure reduction due to wake swirl discussed at the end of Section 3.3.2:

(3.41)

Integration of Eq. (3.41) over the entire disc gives the thrust coefficient as

(3.42)

That is, the same as for the simple momentum theory and so in balance with the rate of change of axial momentum. Note that if the induced tangential velocity a^′rΩ is included in V as it is in blade‐element/momentum (BEM) theory and the blade circulation is constant from the axis to the tip, there is a singularity in the axial force on the blade section at the axis as there is also at the outer tip. This points to the failure of a simple constant strength bound vortex model at the blade ends as discussed in the section on tip‐loss corrections.