A meshless wave-based method for modeling sound propagation in three-dimensional axisymmetric lined ducts

Theoretical modeling of sound propagation within lined ducts can help with interpreting the underlying mechanisms of waveguide physics. Herein, we present ESM-FLOW, a meshless, wave-based method in physical space for modeling sound propagation in 3D axisymmetric lined ducts. First, ESM-FLOW is applied to a 3D axisymmetric problem with uniform flow, in which the wall-reflected fields are replaced by a set of equivalent sources (ESs) surrounding the wall. A circumferential Fourier transform is employed to reduce this to a 2D problem in the circumferential modal domain. This enables efficient solving using a 2D equivalent-source method (ESM) scheme with circumferential modal Green's functions. Clenshaw-Curtis quadrature is used to accurately evaluate the oscillating circumferential integral. The unknown ES amplitudes are solved for through a linear system assembled by replacing the incident and wall-reflected fields with ESs satisfying the wall boundary conditions in the modal domain. Next, rigid-wall modes are derived as inputs for the 3D axisymmetric problem, enabling modal analysis-something with which most boundary-integral formulation (BIF) methods struggle. Finally, a multi-layer ESM-FLOW method is presented to address medium inhomogeneities, in which the non-uniform waveguide is divided into layers with piece-wise constant medium properties. ESM-FLOW is validated by comparison with a finite-element model, and additional simulations are presented to showcase its capabilities. The results demonstrate that ESM-FLOW combines the numerical efficiency and accuracy of typical BIF methods (including backscattering) while overcoming the limitations imposed by uniform media. This makes it highly applicable to the acoustic design of engines and ventilation systems.

Automated summary

This paper presents ESM-FLOW, a meshless, wave-based method for modeling sound propagation in 3D axisymmetric lined ducts. ESM-FLOW combines the numerical efficiency and accuracy of typical BIF methods while overcoming the limitations imposed by uniform media. It is highly applicable to the acoustic design of engines and ventilation systems.