Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 89

The BEM Eqs. (3.54a) and (3.55) are used to determine the flow induction factors for non‐optimal operation. With tip‐loss included the BEM equations have to be modified. The necessary modification depends upon whether the azimuthally averaged values of the flow factors are to be the determined or the maximum (local to a blade element) values. If the former alternative is chosen, then, in the momentum terms, the averaged flow factors a and a^′ remain unmodified, but in the blade element terms, the flow factors must appear as the average values divided by the tip‐loss factor. Choosing to determine the maximum values of the flow factors, i.e. a_b and a_b^′, means that they are not modified in the blade element terms but are multiplied by the tip‐loss factor in the momentum terms. The former choice allows the simpler modification of Eqs. (3.54a) and (3.55):

(3.54c)

(3.55a)

where the flow factor values determined are the averaged values a and a^′.

There remains the problem of the breakdown of the momentum theory when wake mixing occurs. The helicoidal vortex structure may not exist, and so Prandtl's approximation is less physically appropriate. Nevertheless, due to the finite length of the blades and radius of the vortex wake, the application of a tip‐loss factor is necessary. Prandtl's approximation is the only practical method available and so is commonly used. In view of the manner in which the experimental results of Figure 3.16 were gathered, it is the average value of a that should determine at which stage the momentum theory breaks down.