An efficient computation of cascade-gust interaction noise based on a hybrid analytical and boundary element method

Abstract

This paper presents a hybrid analytical and boundary element method to compute the airfoil cascade-gust interaction noise. We assume that the acoustic response of an airfoil to the oncoming gust depends on the locally non-uniform mean flow such that the analytical solution based on a generalised Prandtl-Glauert transformation is utilised to compute the sound generation. The radiation of sound from an airfoil is scattered by other airfoils, which is resolved by a high-efficiency boundary element method. An averaging approach is proposed to efficiently compute the periodic Green's function due to the cascade. The predicted results are validated against numerical simulations for flat plate cascades, and the results match reasonably well. The cut-off properties due to the geometry restriction are discussed, and the critical gust wavelengths for the different orders of acoustic mode are derived. The low-frequency components are trapped in the space between the blades if the stagger angle is zero, while the plane waves are likely to propagating otherwise. For cascades with real airfoil geometry, the background mean flows are computed based on the potential theory. The omission of the refraction effect and approximation errors in the analytical solution of the acoustic response can cause errors for real airfoils, but the hybrid method can capture the sound reduction due to the finite thickness, and yield closer agreement with the numerical solution than the flat plate.