Power Estimates for the Rotor

For a real rotor, the nonuniformity of A over the disk means that the induced power must be calculated by numerically integrating the equation

pr= N

CPi= XdCT «УХдСгп (3.113)

Jr=0 n=l

using the actual induced velocity distribution computed using the BEMT. This equation also allows the calculation of the induced power factor, к, for different twist distributions, that is,

4/2/V2

-5 0 5 10

Section angle of attack (AoA), a – deg.

For a more accurate calculation of the rotor profile power, we must consider the variation in sectional drag coefficient with blade section AoA – see Bailey & Gustafson (1944). For most airfoils the sectional drag coefficient below stall2 can be approximated by

Cd = Cdo + da + d2a2, (3.115)

as shown in Fig. 3.14. Clearly, the coefficients of this expression are also a function of airfoil section, Mach number, Reynolds number, and surface finish, and the behavior cannot easily be generalized. In practice, it is found sufficiently accurate to use 2-D airfoil measurements for the Reynolds and Mach numbers corresponding to those at 75% radius on the rotor. Yet, caution should be exercised when analyzing subscale rotors. If measurements for the airfoil in question are not available at low Reynolds number, then catalogs of airfoil data such as those compiled by Althaus (1972) and Miley (1982) are often useful in estimating the anticipated effects.

Cjr[15] dr.

The profile part of the rotor power is given by

Cp° = Ї L ^ + d'(e – ф) + Лг(в – ^[16]]r3 dr

r3 dr.

Proceeding on the basis that Eq. 3.115 is valid, then substituting gives

By including the higher-order approximation for the airfoil drag, improvements in rotor power prediction at higher values of Cj are usually obtained. Results from the experiments of Knight & Hefner (1937) are shown again in Fig. 3.15, but with the modified drag expression. Notice the better agreement than that shown previously in Fig. 3.3 when a constant drag coefficient was assumed, although power is perhaps now somewhat overpredicted for higher solidities and shows the limitations of this approximate approach.