Validation of a Zonal Method Computing the Sound Radiation from Lined Ducts

Abstract

A hybrid method for the prediction of the far-field radiation from flows in lined ducts is investigated. The method combines a high-order computational aeroacoustics (CAA) scheme with the recently developed acoustic intensity-based method (AIBM) for the calculation of far-field radiations. A broadband time domain impedance boundary condition based on the extended Helmholtz resonator model and the Ingard/Myers boundary condition is implemented in the CAA code. The hybrid approach is similar to the application of an acoustic analogy, but allows an acoustic input from an open control surface. Two dierent analytical benchmark problems are taken from the literature to validate the hybrid zonal method. One considers the radiation from a semi-infinite two-dimensional duct of which a small fraction of the upper and lower wall close to outlet nozzle is lined. The impedance function in this case is found to be very similar to the extended Helmholtz resonator model so that the broadband properties of the model can be evaluated directly from the model. The other benchmark case is chosen from a recently published work about the radiation of tones from the bypass duct of an aeroengine with short cowl design and lined afterbody. The complex geometry is simplified to an annular duct with a semi-infinite hard cylindrical outer wall and a fully-lined, partially-lined or hard-walled cylindrical centerbody, respectively. Sheared flow conditions and moderate frequencies with a higher azimuthal mode are considered. The large variety of test cases well covers the condition in the bypass duct of an aeroengine even though the geometry is highly abstracted. All published test cases are considered for comparisons to obtain an overview about the capability of the current hybrid method. The agreement of analytical solutions and numerical results is found to be good for most of the cases. However, for the higher frequency cases, it would require a mesh refinement to improve the solution in case of the partially lined 2D duct.