LINEARIZED NAVIER-STOKES EQUATIONS AS ACOUSTIC PROPAGATION MODEL

An acoustical model based on the Linearized Navier-Stokes (LNS) equations is proposed. The inclusion of the viscous terms enables to represent hydrodynamic-acoustic interactions responsible of the generation of vorticity associated with hydrodynamic modes. The LNS equations are solved with a high-order accurate and low-dispersive numerical scheme. Time integration is performed using a fourth-order, six-stage Runge-Kutta scheme which has low dispersion and dissipation errors, the space discretization is based on a Discontinuous Galerkin formulation on unstructured grids and sponge-layer boundary conditions are introduced to avoid spurious wave reflections. The model is applied to the analysis of the acoustic propagation of an incoming perturbation inside a circular duct with a sudden area expansion in presence of a mean flow. At corners, the acoustic oscillations are strongly affected by viscous effects, vortical perturbations are generated at the wall and convected into the duct by the mean flow field. The computed coefficients of the scattering matrix are compared with experimental data for a convective Mach number equal to 0.29.