Characterization and suppression of the hydrodynamic instability in the time domain for acoustic propagation in a lined flow duct

The gradient term suppression (GTS) method for removing the hydrodynamic instability appearing in the time-domain solutions of the linearized Euler equations (LEE) along a lined flow duct is assessed. For this, the characterization of a convective instability in the time domain, with the aid of a complementary modal analysis, is first presented. The effect of the mesh size and spatial filtering on the instability is investigated. In particular, a convergence of the instability in the time domain is achieved for a small enough grid size. The consequence of suppressing the mean flow gradient term on the modes is then investigated. It is shown that the unstable modes are indeed removed, but also that acoustic modes are significantly modified, especially for low Helmholtz numbers. The GTS method is finally applied to the NASA grazing impedance tube benchmark. It is found that tuning the weight of the mean flow gradient term within the LEE can be effective for suppressing the instability while conserving a reasonable accuracy of the acoustic component.