National advisory committee

Abstract

SUMMARY A method is presented for calculating the aerodynamic lifts and moments experienced by a cascade or two-dimensional approximation to a compressor or turbine blade row in subsonic flow under harmonic oscil- lation. The most significant features of the method stem from the utilization of Fourier transforms of blade pressure-jump functions. This permits expres- sion in closed form of the kernel function appearing in the integral equa- tion relating upwash to the pressure-jump transform. phenomena, first discovered in connection with the subsonic wall inter- ference problem, are shown to occur in the case of cascade oscillation even in the presence of stagger and arbitrary interblade phase-lag angles. The resonance points are shown to be related to the poles of the kernel function for the Fourier transform formulation of the problem. techniques are developed for the direct solution of the transform rather than of the pressure jump proper, and it is shown that lift and moment niay be easily expressed in terms of the pressure-jump transform without requiring any inversion. The method is applied to computation of a zero- stagger cascade in antiphase motion (corresponding to the tunnel-wall interference problem) in order to permit comparison of results with those obtained by solution of the more conventional integral equation based upon the Hankel function series type of kernel. obtained in all cases. Arbitrary stagger and interblade phase-lag angles are permitted. So-called resonance Numerical Excellent agreement is INTRODUCTION The aerodynamic forces and moments experienced by compressor blades undergoing oscillatory motion or in the presence of certain classes of oscillatory inflow are of interest to the aircraft-jet-engine'industry for several reasons. First, while the occurrence of classical flutter in compressor blades