In this work, acoustical methods were derived from the Johnson et al. and Wilson dynamic density models to characterize the parameters governing viscous dissipation in open-cell porous media. The methods were tested on three materials covering a wide range of static flow resistivities (2300–150 100 Ns/m4), frame rigidities (soft and rigid), and pore geometries (cells and fibers). To operate, the methods require an acoustical measurement of the dynamic density of the tested material.
From the Johnson et al. model, two methods were derived: (i) an analytical method and (ii) an extrapolation method. To use the analytical method, the static airflow resistivity and open porosity of the material must be known. To use the extrapolation method, only the open porosity needs to be known. Both methods allow characterization of the geometrical tortuosity and viscous characteristic dimension. In addition, the extrapolation method can be used to characterize the static airflow resistivity of the material. Tests on the three porous materials have shown that both methods yield statistically the same results. Moreover, the static flow resistivities found from the extrapolation method were very close to the directly measured ones.
To estimate the precision of the analytical method using the Johnson et al. model, the method was applied on two virtual materials of theoretically known properties (dynamic density, geometrical tortuosity, viscous characteristic dimension, and static airflow resistivity). From this study, it was found that the method should yield small relative errors on the tortuosity (maximum error less than 2% in absolute value). Similarly, small relative errors (less than 1% in absolute value) are expected for the static airflow resistivity if the extraction proceeds at low frequencies. For the viscous characteristic dimension, if the method is applied in the low-frequency viscosity-controlled regime, a systematic error is introduced. From the tested virtual materials, this systematic error is expected to be no more than 20% (in absolute value)—which is quite acceptable since this parameter is difficult to obtain with accuracy using other existing methods. However, if the method is applied in the higher-frequency mass-controlled regime, the error tends rapidly to zero. In addition to the assessment of the precision of the method, Fig. 1 obtained from this error analysis can be used to select the frequency range in which the extraction should proceed to minimize the error of the method.
For the Wilson model, the derived analytical method was found to be a secure characterization method to infer representative values for and in the Wilson dynamic density. Also, it was shown that relations =0/ and, more particularly, =02/2 or =20/, as proposed by Wilson, may be misleading. For the second relation, it was found to be more appropriate to use J. One advantage of the Wilson model over the Johnson et al. model is that the characterization of the two Wilson's parameters does not require prior knowledge of any other physical properties.
Moreover, it was found that both models, once their parameters are carefully characterized, predict similar dynamic densities and compare well with measurements. Also, for both models, relative constancy in the characterized parameters in the function of the frequency was noted. This constancy can be used to assess the validity of (1) the descriptive models in a given frequency range; and (2) the characterized parameters found from the proposed characterization methods. Also, it supports the relaxation process as suggested by Wilson and the Johnson et al. dissipation function GJ.
Once again, these good correlations with measurements, together with the noted constancy in the found parameters with the frequency, reinforce the fact that the proposed characterization methods offer an elegant alternative to existing characterization methods. Moreover, since the methods only rely on equations and a widespread apparatus (impedance tube), this makes the characterization of porous materials possible for many acoustic laboratories.
To conclude, the authors believe that comparisons with ultrasound techniques are necessary to complete this work—this was not possible here using the available laboratory equipments. Also, similar methods15 could be developed for characterizing the parameters relative to the thermal losses (i.e. thermal characteristic dimension, static thermal permeability, Wilson entropy-mode relaxation time, Wilson compressibility parameter). To improve the reliability of the proposed methods, work on improving the accuracy of the measurements of the dynamic properties (characteristic impedance, propagation constant, dynamic density) and on the minimization of frame vibrations, is necessary.
