Interaction of upstream flow distortions with high Mach number cascades
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 are modeled. A typical disturbance was assumed to have harmonic time dependence and was described, at a far upstream location, in three orthogonal spatial coordinates by a double Fourier series. It was convected at supersonic relative to a linear cascade described as an unrolled annulus. Conditions were selected so that the component of this velocity parallel to the axis of the turbomachine was subsonic, permitting interaction between blades through the upstream as well as downstream flow media. A strong, nearly normal shock was considered in the blade passages which was allowed curvature and displacement. The flows before and after the shock were linearized relative to uniform mean velocities in their respective regions. Solution of the descriptive equations was by adaption of the Wiener-Hopf technique, enabling a determination of distortion patterns through and downstream of the cascade as well as pressure distributions on the blade and surfaces. Details of interaction of the disturbance with the in-passage shock were discussed. Infuences of amplitude, wave length, and phase of the disturbance on lifts and moments of cascade configurations are presented. Numerical results are clarified by reference to an especially orderly pattern of upstream vertical motion in relation to the cascade parameters.