A general acoustic energy-spectral method for axisymmetric cavity with arbitrary curvature edges

Abstract

An efficient acoustic energy-spectral method for axisymmetric cavity with arbitrary curvature edges is proposed in this study. The multi-segment strategy and multi-point mapping technique are used to formulate the acoustic model, which can overcome the geometric difficulties of using orthogonal polynomials to construct sound pressure functions in irregular physics fields. In order to ensure the conditions of acoustic compatibility between sub-cavities and improve the accuracy of the solution, an acoustic penalty parameter is firstly introduced. The mixed series, consisting of orthogonal polynomials and Fourier series for circumferential variables, is applied to expand the sound pressure variables. The effects of some key parameters, including mapping node, penalty parameter, truncated terms as well as number of segments, on the convergence of the developed formulation are elucidated in detail. After that, two segmented acoustic cavities with variable curvature edges is investigated, in which the consistent FEM reference solutions are also involved. All these investigations exhibit the excellent accuracy and potential of the present formulation in analyzing the acoustic mode and response of axisymmetric cavity with arbitrary curvature edges. And the presented numerical results from the developed method can also serve as a reference for further acoustic study of axisymmetric cavity with complex geometry.