Compressibility Corrections to Rotor Performance

The assumption that the lift-curve-slope of the blade airfoil sections and the drag coefficients are independent of Mach number is questionable. To examine the effects of compressibility on Cj, consider a correction to the lift-curve-slope of each blade element according to Glauert’s rule in which

We see that as Mtjp -> 0 then К -> 1 and the incompressible result given previously in Eq. 3.64 is obtained. If it assumed that an averaged compressible lift-curve-slope can be used for the entire rotor then

QJ Af=0.1

уі-^Мар)2’

where re is an effective radius. It can be shown that re = 1 /л/2 = 0.707 when Mtip —> 0, increasing to a value of re = 0.75 for A/tip = 0.8. This is in close agreement with Payne

(1959) , who suggests using an effective lift-curve-slope at 70% radius, which is probably accurate enough for Mtip < 0.6. Peters & Ormiston (1975) suggest using the value of the lift-curve-slope at 75% radius, which is realistic for the normal operational tip Mach numbers of most helicopters. Generally, the effects of compressibility will increase the rotor thrust coefficient by about 10% for a given collective pitch setting. However, tip relief effects (a 3-D effect) tends to reduce these compressibility effects somewhat (see discussion in Section 5.4.3).

Compressibility effects become more important for helicopter rotors when they are operated in forward flight, and especially where the advancing blade tip Mach numbers approach transonic conditions. In forward flight conditions, the idea of a mean lift-curve – slope corrected for compressibility becomes less applicable, and compressibility corrections must be included inside the thrust integral and for other quantities – that is, compressibility modeling must be considered separately at each blade element, and the net effect is obtained by numerical integration. This is the essence of the approach used in nearly all forms of modern helicopter analysis.