Numerical modal analysis of bulk-reactive lined duct with shear flow

Abstract

In this paper, the eigenmodes of bulk-reactive lined duct with shear flow are calculated and analyzed by a wave and finite element (WFE) method. Using this method, the eigenmodes can be calculated based on commercially available finite element (FE) matrices, which is of considerable practical interest when dealing with complicated cases. The proposed method is validated by comparing results with Chebyshev collocation method. It is shown that the axial wavenumbers obey the convergence rate of Se4 for all kinds of modes, where Se is the mesh size. The calculated eigenmodes can be divided into air-borne modes, lining-borne modes and surface modes, where air-borne modes mainly propagate in air domain; lining-borne modes propagate in both air and lining domains; surface modes propagate near the interface between air and lining domains. It is found that, for air-borne and lining-borne modes, boundary layer thickness has small effect on lower order modes, but has relatively large effect on mode shapes of higher order modes. For the surface modes, boundary layer thickness can greatly change their mode properties. In the calculated example, with perforated panel considered, two coupled modes emerge. With perforation ratio evolving from large to small, one coupled mode evolves from a lower-order air-borne mode to a higher-order air-borne mode, and the other evolves from a lining-borne mode to an air-borne mode. Generally, the perforation ratio has small effect on air-borne and lining-borne modes; while it has large effect on surface modes and the coupled mode, especially in the range of [3%, 13%].