A lifting surface theory is developed for unsteady three-dimensional flow in rotating subsonic, transonic and supersonic annular cascades with fluctuating blade loadings. Application of a finite radial eigenfunction series approximation not only affords a clear insight into the three-dimensional structures of acoustic fields but also provides mathematical expressions advantageous to numerical work. The theory is applied to oscillating blades. Numerical examples are presented to demonstrate three-dimensional effects on aerodynamic characteristics. Three-dimensional effects in supersonic cascades are generally small and strip theory predicts local aerodynamic forces as well as total aerodynamic forces with good accuracy. In transonic flow, however, the strip theory approximation breaks down near the sonic span station and three-dimensional effects are of primary importance.

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