Wind Energy Handbook. Michael Barton Graham

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(3.20)

      where _.

Knowing how a and a^′ vary radially [Eq. (3.20)] can be integrated to determine the overall power coefficient for the disc for a given tip speed ratio λ.

It was argued by Glauert (1935b) that the rotation in the wake required energy that is taken from the flow and is unavailable for extraction, but this can be shown not to be the case. The residual rotation in the far wake is supplied by the rotation component a′Ω induced at the rotor. The lift forces on the blades forming the rotor disc are normal to the resultant velocity relative to the blades, and so no work is done on or by the fluid. Therefore, Bernoulli's theorem can be applied to the flow across the disc, relative to the disc spinning at angular velocity Ω, to give for an annulus of radius r

      where w is the radial component of velocity. which is assumed continuous across the disc.

      Consequently,

      The pressure drop across the disc clearly has two components. The first component

(3.21)

is shown to be, from Eq. (3.18), the same as that given by Eq. (3.9) in the simple momentum theory in which rotation plays no part. The second component is

(3.22)

      Δp_D2 can be shown to provide a radial, static pressure gradient

in the rotating wake that balances the centrifugal force on the rotating fluid, because [see Eq. (3.33) a^′(r) = a′(R)R²/r². This pressure causes a small discontinuity in the pressure at the wake boundary equal to 2ρ(a′(R)ΩR)², which in reality, along with the other discontinuities there, is smeared out.

      The kinetic energy per unit volume of the rotating fluid in the wake is СКАЧАТЬ