Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 81

The blade design of Figure 3.19 is efficient but complex to build and therefore costly. Suppose the plan‐form was prescribed to have a uniform taper such that the outer part of the blade corresponds closely to Figure 3.19b. The straight line given by Eq. (3.75) and shown as the solid line in Figure 3.20 has been derived to minimise the departure from the true curve [Eq. (3.72))] in the outer region 0.7 < r/R < 0.9. This linear taper not only simplifies the plan‐form but removes a lot of material close to the root.

Figure 3.19 Optimum blade design for three blades and λ = 6: (a) blade twist distribution, and (b) blade plan‐form.

Figure 3.20 Uniform taper blade design for optimal operation.

The expression for this chord distribution approximation to the optimum plan‐form (Figure 3.20) is

(3.75)

The 0.8 in Eq. (3.75) refers to the 80% point, approximating in this case the solid line between target points 0.7 and 0.9 by the tangent at 0.8, which is very close to it.

Equation (3.75) can then be combined with Eq. (3.72) to give the modified spanwise variation of C_l for optimal operation of the uniformly tapered blade (Figure 3.21):

Close to the blade root the lift coefficient approaches the stalled condition and drag is high, but the penalty is small because the adverse torque is small in that region.

Assuming that stall does not occur, for the aerofoil in question, which has a 4% camber (this approximates to a zero lift angle of attack of −4^o), the lift coefficient is given approximately by

where α is in degrees and 0.1 is a good approximation to the gradient of the C_l vs α^o for most aerofoils, so _.

The blade twist distribution can now be determined from Eqs. (3.74) and (3.45) and is shown in Figure 3.22.

Figure 3.21 Spanwise distribution of the lift coefficient required for the linear taper blade.

Figure 3.22 Spanwise distribution of the twist in degrees required for the linear taper blade.

The twist angle close to the root is still high but lower than for the constant C_l blade.