A relaxation approach for time domain modelling of sound propagation in porous media

In the present study a relaxation approach to modelling sound propagation in porous media has been developed. A frequency domain model has been formulated and is shown to allow an analytical transformation of the governing equations in the time domain. The model proposed is an extension of an earlier work by Wilson at al. (1997) and is based on the use of two relaxation times. The model presented requires a set of six measurable parameters, e.g. static flow resistivity, porosity, tortuosity, thermal permeability, viscous and thermal characteristic lengths. It will be shown that the model satisfies the physically correct low and high frequency limits evaluated by Johnson et al. (1987) and therefore allows the prediction of a porous material's behaviour in a wide range of frequencies (and pulse durations when used in time domain). It will also be demonstrated that two different model formulations are necessary depending on the material shape factor values and physical reasons for this are identified. The model has been validated by performing laboratory measurements and numerical simulations in both frequency and time domains for a range of granular and fibrous porous materials. The well-known equivalent fluid model by Johnson et al. (1987), Champoux and Allard (1991) and Lafarge et al. (1997) has been formulated analytically in the time domain and its predictions are compared with those of the relaxation model and the data. In the last section of the work a nonlinear model is developed for finite amplitude sound propagation in porous media and validated using laboratory data for acoustic pulses with different durations and amplitudes