There is an ongoing discussion about if it is worth to implement the complicated Johnson-Champoux-Allard (JCA)[1] models or even the full Biot Model. Why not using the Delany-Bazley Model[3] or the modified version by Miki [4]. The Advantage of there empirical models is their **simplicity**, because the only parameter is the **flow resistivity**

In the current update of pyva the Delany-Bazley and Miki models are implemented as a subclass of Fluid (Delany class) and I take this as an opportunity to check if there are major differences in the three models. For the verification I chose Pannetons material from [2] where he has proven experimentally that the limp-fibre model is precise enough to describe such material.

## Equivalent density and speed of sound.

It can be seen in the above figure, that the complex density is well represented from 600Hz on. The black line denotes the frequency range of the Delany model, . Below 600 Hz both empirical models fail.

The complex speed of is not correctly represented over the full frequency range.

## Absorption

The main purpose of fibre material is absorption. So, let’s see of the poor equivalent material property results has consequences for the absorption paramters. I calculated the normal and diffuse field absorption of 10cm of fibre material.

The empirical models underestimate the normal absorption at low frequencies. The same is true for the diffuse field absorption

## Conclusion

For the example of Pannetons fibre material the quality of the Delany-Bazley-Miki model is low. In any case the model require the flow resistivity – a parameter that is not that easy to measure. When we keep in mind that you can get all the remaining parameters from impedance tube tests and curve fitting I would always recommend to use the equivalent fluid model for fibre material. Once the parameters are derived the model can be easily applied providing better quality of your simulation results.

## Literature

[1] Y. Champoux and J.-F. Allard, “Dynamic tortuosity and bulk modulus in air-satutrated porous media,” *Journal of Applied Physics*, vol. 70, no. 4, pp. 1975–1979, Aug. 1991.

[2] R. Panneton, “Comments on the limp frame equivalent fluid model for porous media,” *The Journal of the Acoustical Society of America*, vol. 122, no. 6, pp. EL217–EL222, 2007, doi: 10.1121/1.2800895.

[3] M. Delany and E. Bazley, “Acoustical properties of fibrous absorbent materials,” *Applied acoustics*, vol. 3, no. 2, pp. 105–116, 1970.

[4] Y. Miki, *Acoustical properties of porous materials – Modifications of Delany-Bazley models*, J. Acoust. Soc. Jpn (E). 11(1), 1990, pp. 19-24