Influence of Forchheimer's nonlinearity and transient effects on pulse propagation in air saturated rigid granular materials.

It has been shown in the earlier work of Umnova et al. [Noise Control Eng. 50, 204-210 (2002)] that interaction of a relatively long, high amplitude acoustic pulse with a rigid porous material can be accurately described accounting for the Forchheimer nonlinearity. In the present study, the goal is to determine whether the accuracy of the modeling can be improved in the case of a lower amplitude and a shorter pulse. A model that accounts for the Forchheimer's nonlinearity and the transient effects is developed. It is assumed that all the contributions to the viscous force are additive in the time domain. The governing equations are solved numerically using finite difference time domain scheme. The results are compared with the data for two granular materials. The latter are obtained in an impedance tube and in a shock tube experiments, where acoustic pulses with various amplitudes and durations are generated.