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National Advisory Committee for Aeronautics, Technical Notes - Theoretical Investigation of Subsonic Oscillatory Blade-Row Aerodynamics

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. Arbitrary stagger and interblade phase—lag angles are permitted.
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. So-called resonance
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. Numerical
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
may 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. Excellent agreement is
obtained in all cases.

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 has not been a matter of concern up to this time,
it is conceivable that current design trends may lead to configurations
and flow conditions in which the avoidance of classical flutter must
become a consideration.