Suppression of the Spatial Hydrodynamic Instability in Scale-Resolving Simulations of Turbulent Flows Inside Lined Ducts

Abstract

This paper addresses one of the major obstacles arising in the high-fidelity scale-resolving simulations of turbulent flows inside ducts with the walls covered by acoustic liners in order to attenuate the sound radiated from the duct. It consists of the development of spatial hydrodynamic (convective) instability over the treated walls at the low values of the acoustic resistance of the liner. For reasons that remain unclear, the growth rate of this instability and its effect on sound propagation through the duct is strongly overestimated by the CFD simulations using the macroscopic concept of the locally reacting acoustic impedance. A new damping volume source term (“body force”) is proposed, whose introduction into the momentum equation resolves this issue by means of artificially suppressing the instability while remaining within the framework of the computationally efficient model of the impedance wall, i.e., without trying to simulate the liner microscopically. Examples are presented of the application of the developed methodology to the flows in the grazing impedance tubes with two different liners. They suggest that the proposed form of the damping source term can be considered universal and that the suppression of the hydrodynamic instability ensured by this term is not accompanied by any significant distortion of the propagation of the sound waves and the turbulence statistics, except for a very narrow near-wall region.