Modelling of sound propagation in a non-uniform lined duct using a Multi-Modal Propagation Method

Abstract

Liner non-uniformities, such as distributed impedances, may have a direct influence on the performance of turbofan engine liners. A relevant problem to study these effects is that of sound propagation in a hard-walled duct of circular cross-section, fitted with a region of non-uniform liner. Given the complex modal input amplitudes at one end of the hard-walled duct, the problem is to compute the complex modal output amplitudes at the other end. In the present paper, a Multi-Modal Propagation Method (MMPM) is proposed to solve this problem in the absence of mean flow. For simplicity, the liner impedance is set piecewise constant along the duct, while being arbitrarily variable along the circumference of each segment. The principle of the method is to expand the sound pressure and axial velocity into double infinite series using the rigid duct modal basis, and then to follow the projection coefficients evolution along the duct axis. Scattering matrices are obtained for individual segments and then combined to construct a global scattering matrix. It is numerically shown that the convergence rate of the infinite series is at least O ( M - 2 ) and O ( N - 1.5 ) , where M and N refer to the maximum circumferential and radial mode orders, respectively. Validation of the method is done in 2D by comparison with FEM. The present MMPM is shown to deal with realistic turbofan engine configurations with spliced liners, up to relatively high reduced wavenumbers K ∼ 50 .