Numerical Computation of a Lined Duct Instability Using the Linearized Euler Equations

Abstract

The two-dimensional linearized Euler equations in the time domain are computed to obtain the sound field in a channel with a rigid upper wall and an acoustic liner on the bottom wall in the presence of a shear flow. The liner is a simple mass–spring–damper system. The shear flow has a rather thin boundary layer, and the mesh has to be refined close to the walls. The objective is to assess whether an instability can be computed and whether a computed instability is physical. The computations are backed by a linear stability analysis of the flow that is performed by solving a matrix eigenvalue problem. By comparing the results of the simulations of the linearized Euler equations with the results of the stability analysis, it is found that the computed instabilities are physical and that their characteristics can be predicted. The effect of using selective filtering on the wave-number spectrum is also discussed.