A Linearized Unsteady Aerodynamic Analysis for Real Blade Supersonic Cascades

The prediction capabilities of a linearized unsteady potential analysis have been extended to include supersonic cascades with subsonic axial flow. The numerical analysis of this type of flows presents several difficulties. First, complex oblique shock patterns exist within the cascade passage. Second, the acoustic response is discontinuous and propagates upstream and downstream of the blade row. Finally, a numerical scheme which is based on the domain of dependence is required for numerical stability. These difficulties are addressed by developing a discontinuity capturing scheme and matching the numerical near-field solution to an analytical far-field solution. Comparisons with semi-analytic results for flat plate cascades show that reasonable predictions of the unsteady aerodynamic response at the airfoil surfaces are possible, but aeroacoustic response calculations are difficult. Comparisons between flat plate and real blade cascade results show that one effect of real blades is the impulsive loads due to motion of finite strength shocks.