Lattice Boltzmann simulations of impedance tube flows

An original time-domain surface acoustic impedance condition for Lattice Boltzmann methods has been developed. The basis for this method is the extension proposed by Delattre et al. [Delattre G, Manoha E, Redonnet S, Sagaut P. Time-domain simulation of sound absorption on curved wall. 13th AIAA/CEAS Aeroacoustics conference, Rome, Italy, AIAA-2007-3493; 2007] of the z-transform approach suggested by Özyörük et al. [Özyörük Y, Long LN, Jones M. Time-domain numerical simulation of a flow impedance tube. J Comput Phys 1998;146:29–57]. Using this boundary condition that links the normal velocity and the pressure, the basic idea consists in calculating the Lattice Boltzmann populations at a boundary node thanks to the gradients of the fluid velocity. This paper describes the proposed LBM boundary conditions and its assessment on the NASA Langley flow-impedance tube with a constant depth ceramic tubular liner. We performed both single and broadband-frequency simulations, without mean flow and with sheared mean flows. Excellent agreement is shown with both experimental data and other simulation results at various frequencies up to a Mach number equal to 0.5.