Simulation of instability and sound production in a turbulent channel flow with an acoustic liner

Abstract

Acoustic liners are used to absorb sound waves in ducts with flow. These liners can become unstable and some experiments have shown that in this case they do not damp sound as they should. This situation is addressed numerically. A turbulent plane channel flow at a friction Reynolds number of about 400 is computed using direct numerical simulation of the compressible Navier–Stokes equations. The channel is in spatial development, and the inflow is fully turbulent, non-reflecting, and can inject an incident acoustic wave. The liner is modeled by an acoustic impedance placed on a portion of the channel bottom wall. Several liners are simulated, stable or unstable. Spatial instabilities are observed and well modeled by a linear spatial stability analysis. The scattering of the instability at the liner trailing edge triggers backpropagating acoustic waves, as well as sound emission downstream of the liner. Backpropagating waves make a feedback loop possible on the liner, so that instabilities are observed even in convectively unstable situations without excitation. The effect of an incident acoustic wave is discussed.