Global linear stability analysis of flow in a lined duct

Eigenmodes of the linearised Euler equations are computed in order to study lined flow duct global stability. A simplified configuration is considered and the governing equations are discretised by means of the discontinuous Galerkin method. A biorthogonal technique is used to decompose the global eigenfunctions into local eigenmodes. The system dynamics switches from noise amplifier to resonator as the length of the liner is increased. The global mode in the liner region is shown to be mainly composed of a hydrodynamic unstable wave and a left-running acoustic mode.