The high-order parabolic equation to solve propagation problems in aeroacoustics

Abstract

The parabolic equation (PE) has proved its capability to deal with the long range sound propagation in the atmosphere. It also represents an attractive alternative to the ray model to handle duct propagation in high frequencies, for the noise radiated by the nacelle of aero-engines. It was recently shown that the High-Order Parabolic Equation (HOPE), based on a Padé expansion with an order of 5, significantly increases the aperture angle of propagation compared to the standard and the Wide-Angle PEs, allowing prediction close to cut-off frequency of the duct. This paper concerns the propagation using the HOPE in heterogeneous flows, including boundary layers above a wall and in shear layers. The thickness of the boundary layer is about dozens of centimeters while outside it, the Mach number reaches 0.5. The boundary layer effects are investigated showing the refraction effects on a range propagation of 30 m, up to 4 kHz. In the shear layer, discontinuities in the directivity patterns occur significant differences of the directivity patterns occur. Comparisons with the Euler solutions are considered, establishing the domain of application of the HOPE on a set of flow configurations, including beyond its theoretical limits. [Work supported by Airbus-France.]