Aerodynamics of loaded cascades in subsonic flows subject to unsteady three-dimensional vortical disturbances

A highly efficient numerical method is developed for three-dimensional, periodic, vortical flows around a cascade of loaded airfoils. The method linearizes Euler's equations about the mean flow of the cascade and thus fully accounts for the effects of distortion of the vortical disturbances as they propogate and interact with the cascade mean flow. The numerical scheme is based on splitting the unsteady velocity into vortical and potential parts. The latter is governed by a non-constant coefficient inhomogeneous convective wave equation. A new and computationally suitable out-flow conditions are derived and avoid the difficulties associated with the singular velocity downstream. Solutions were obtained in the frequency domain by using a body-fitted coordinate system. Results are presented to demonstrate the effects of the out-flow boundary conditions, cascade spacing, mean blade loading and gust upstream conditions on the aerodynamics response and unsteady pressure field of a cascade.