A semi-analytical method for oblique gust - cascade interaction

A semi-analytical method is proposed for calculating the response of a linear cascade with spanwise mean flow subject to oblique gusts. It is developed based on the boundary value problems defined by Lloyd and Peake (AIAA paper 2008-2840). A gust strength parameter is introduced and the correct three-dimensional (3-D) response is obtained. The classic similarity rules are extended; the approach can be used to extend any 2-D methods to account for oblique gusts and 3-D mean flows. It is validated against analytical approximations for single-airfoil and cascade responses. The method is used to investigate the effect of gust angle αg on the unsteady lift and the sound field. It is found that as αg increases, the 2-D equivalent response varies slightly. However, the 3-D lift is amplified by factor 1/cosαg, and the spanwise phase variation increases. Cascade effects are also studied. The inter-blade phase angle (IBPA) is important even for very low solidity. As the solidity increases, the chordwise distribution of lift is no longer leading-edge dominant. Cascade effects are small only when the cascade blade count is lower than a limit. A statistics analysis reveals that Mach number is the most important parameter for determining this blade count limit, and frequency is the least important.