Interaction of Upstream Flow Distortions With High-Mach-Number Cascades

This analytical study models features of the interaction of flow distortions, such as gusts and wakes, with blade rows of advance-type fans and compressors having high-tip Mach numbers. A typical distortion is assumed to have harmonic time dependence and is described, at a far upstream location, in three orthogonal spatial coordinates by a double Fourier series. It is convected at supersonic velocity relative to a linear cascade described as an unrolled annulus. Conditions are selected so that the component of this velocity parallel to the axis of the turbomachine is subsonic, permitting interaction between blades through the upstream as well as downstream flow media. A strong, nearly normal shock is considered in the blade passages which is allowed curvature and displacement. The flows before and after the shock are linearized relative to uniform mean velocities in their respective regions. Solution of the descriptive equations is by adaptation of the Wiener-Hopf technique. This enables a determination of distortion patterns through and downstream of the cascade, and of pressure distributions on the blade surfaces. Details of interaction of the distortion with the in-passage shock are discussed. Influences of amplitude, wavelength, and phase of the distortion on lifts and moments of cascade configurations are presented. Numerical results are clarified by reference to an especially orderly pattern of upstream vortical motion in relation to the cascade parameters.