Abstract: The fast scattering method (FSM) is a fast and flexible way to predict the sound propagation and radiation from a ducted-fan by solving the Helmholtz equation with specific boundary conditions and no flow. For the design of the ducted-fan acoustic liner, the method is applied to the simulation of sound propagation in a varying cross-section duct. The time harmonic and linearized acoustic equation is employed in the present study, and the flow field is assumed to be a uniform flow from the far field. By introducing a 3D Lorentz transformation, the acoustic scattering problem with flow is transformed to a problem of no flow described by the exterior Helmholtz equation with specific boundary conditions. The direct boundary element method (DBEM) is used for solving the homogeneous linear Helmholtz equation, which can avoid solving the reflection coefficients at the inlet and outlet duct surfaces and thus save much computational time. In addition, the effects of different impedances of the liner in a varying cross-section ducted-fan on sound propagation are also investigated. A comparison of numerical results by using the fast scattering method and by using the acoustic analogy method is also performed. Finally, the method is applied to an examination of the noise reduction by the duct liner in a real high-speed rotor. The results demonstrate that the fast scattering method is suitable for application to the design of a duct liner in aero engines.

Key words: direct boundary element method, fast scattering method, aeroengine nacelle, acoustic liner, noise reduction