Aerodynamic Interference of Cascade Blades in Synchronized Oscillation

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Abstract
The failure of a compressor is sometimes due to flutter of the blades. Essentially, this problem is equivalent to a cascade in oscillation. The present analysis is to find the aerodynamic load on cascade in synchronized harmonic oscillations, pitching, and flapping. Conformal mapping is used. Two characteristic parameters are involved in the force and moment. One is μ which is related to the gap-chord ratio. The other is k which is known as reduced frequency. The main results are expressed in terms of these two parameters. Most can be reduced to closed form. The rest are given in graphs. The wake interference involves one new function C(μ,k) which is related to a ratio of two hypergeometric functions and which reduces to Theodorsen’s function C(k) in the limit of infinite gap. In a certain range of frequency and gap-chord ratio, the analysis shows quantitatively that single-oscillation airfoil theory may lead to inaccurate estimation of interference effect between blades.

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