Theoretical analysis of fluctuating lift on the rotor of an axial turbomachine

Abstract

A theoretical analysis is presented for the determination of the fluctuating lift generated by a moving blade-row interacting with the potential flow disturbances of an upstream blade-row. This analysis is an extension of the existing theories, Refs. 1 and 2, for an isolated airfoil moving through transverse and chord-wise gusts to include the effects due to a cascade of airfoils. When the case of infinite spacing between the airfoils of the cascade is considered the present analysis gives the same results as the isolated airfoil theory. The mathematical representation of the cascade of airfoils is by a continuous distribution of vorticity on a reference blade and in the wakes of all the other blades. The effect of the bound vorticity of the neighbouring blades is simulated by a vortex at their quarter chord points. This representation is suggested by the steady state cascade analysis of Tanabe and Horlock and the present analysis gives the same results as Reference 11 for steady flow. Using thin airfoil theory an expression for the unsteady lift acting on a two-dimensional cascade of thin, slightly cambered airfoils moving through a sinusoidal disturbance in through flow velocity, is derived. This expression can be expressed as a function of a reduced frequency (as for an isolated airfoil Ref. 7) and other parameters representing the effects of the neighbouring blades. The resulting expression for the fluctuating lift for a cascade of airfoils with circular arc camber lines at small angle of incidence is presented.