Читать книгу Wind Energy Handbook - Michael Barton Graham - Страница 87

At the root of a blade the circulation must fall to zero as it does at the blade tip, and so it can be presumed that a similar process occurs. The blade root will be at some distance from the rotor axis, and the air flow through the disc inside the blade root radius will be at the free‐stream velocity. Actually, the vortex theory of Section 3.4 can be extended to show that the flow through the root disc is somewhat higher than the free‐stream velocity. It is usual, therefore, to apply the Prandtl tip‐loss function at the blade root as well as at the tip (see Figure 3.35).

Figure 3.35 Spanwise variation of combined tip/root loss factor for a three blade turbine optimised for a tip speed ratio of 6 and with a blade root at 20% span.

If μ_R is the normalised root radius, then the root loss factor can be determined by modifying the tip‐loss factor of Eq. (3.82):

(3.84)

If Eq. (3.82) is now termed f_T(r) the complete tip/root loss factor is

(3.85)