Time-Domain Simulation of Nonlinear Acoustic Propagation in a Lined Duct

Abstract

The nonlinear behavior of finite amplitude acoustic waves, such as attenuation through shocks and energy transfer between frequencies, are important considerations in the prediction of the inlet fan noise. In this study, a time-domain nonlinear acoustic propagation code with an impedance boundary condition representing the acoustic liners is presented. The full Euler equations are utilized as a model equation for nonlinear wave propagation. Spatial discretization of the equations is accomplished using a high-order conservative scheme on a cell-centered finite volume grid. A time-domain impedance boundary condition is implemented based on a characteristic boundary approach, which is equivalent to the use of a reflection relation in the linear case. The order of accuracy of the broadband impedance model using the z-transform is improved over previous implementations. The NASA Langley grazing impedance tube configuration with a ceramic tubular (CT) liner is adopted for the nonlinear simulation of a lined duct. For the nonlinear simulations, impedance nonlinearity is ignored and only propagation nonlinearity is considered. Simulations of nonlinear propagation for two types of source waveforms are conducted. For saw-tooth wave sources, the energy transfer between the harmonic components is clearly observed during the propagation in the lined duct. For sinusoidal sources at 1 kHz, the attenuation rate by the acoustic liner at the fundamental frequency is the same regardless of source amplitude. Nonlinearity of the liner is discussed by comparison with experimental data.