PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Comparison of characterization methods for rigid porous materials
Ferina SAATI, Christian A. GEWETH and Steffen MARBURG
Technical University of Munich, Germany

ABSTRACTOne of the most common problems in the development of silencers is to provide sufficient absorptive
behavior using less costly materials that are effective over the desired wide frequency band and are thin,lightweight and application-friendly [1]. Theoretical and empirical models for the acoustic properties ofporous or granular media allow inverse determination of some porous properties. In this work, classicaldescription of porous media as a homogeneous equivalent fluid is assumed, and are applied using a numericalpredictive model for a porous granular medium consisting of a face centered cubic sphere packing on whichmeasurements were taken [2]. The comparative absorption result of the numerical versus experimental
models are discussed.
Keywords: Porous, Absorption, Impedance tube

1. INTRODUCTION
Material parameters in a porous acoustics materials are sometimes difficult or not directly
measurable [3], especially in the case of a medium consisting of pores with a wide scale range andrandom compounds. To describe the acoustic behavior of porous or granular materials, soundpropagation models are used. The prediction of several parameters by such models is applicable tovarious fields, for which, equivalent fluid models are used in many situations [4]. Here, the main
assumption is that the solid part of the material is rigid and immovable. Therefore, the behavior of thematerial as a mass medium is of interest. Such models focus on macroscopic behaviors and do notzoom into the microscopic occurrences in the pore scale. There are several microscopic scale studies
on the subject none of which upon the authors’ knowledge, have made the ends meet and given an athorough analysis of what each and every parameter involved in macro-scale physically means inmicro-scale.
Absorptance is usually tested with a standard 2-microphone impedance tube in accordance with an
ISO 2001 standard. The tube in this study is fixed in a vertical state to avoid the influence of gravity
on granular material for reasons of surface symmetry. Measurements are carried out in the frequency
range from 100 Hz to 4.5 kHz. The sample is mounted in the sample holder, supported by a rigid plate.

2. FINITE ELEMENT MODELLING
A finite element model was created on a stack of beads (Figure 1). Each spherical bead has 3 mmradius and the distance between them range from 200 to 500 ߤ݉. The diameter of the impedance tube
is 44 mm. The length of the pipe must be more than three times the diameter. The network is set veryfine and network convergence is complete. Stack layer has the thickness of 30 mm. For the case of300 micrometer distance, the created mesh consists of 1.2 million domain elements, 400 thousandboundary elements, and 33 thousand edge elements. The absorption coefficient is calculated using theequation 4.4 in Kampinga’s thesis [5].

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Figure 1- Model of an impedance tube in Comsol Multiphysics with the full-scale beads in thesample-holder
Although the crosslinking and solution process is quite costly, we hope that comparing thesimulation and measurement results with inversion and direct methods will allow us to find patternsof morphology versus the porous acoustic behavior of our samples. In Table 1 we see the peakabsorption occurring at various distances of the beads.
Table 1- Seeking for higher absorption peak by decreasing the distance among beads
Distance between 6mm diameter beads
Maximum Absorption
500
0.24
375
0.31
300
0.37
250
0.43
200
0.48
If we do a linear curve fitting using the data from the above table, we will see that according tosuch a calculation, at around 14 ߤ݉, we should get the absorption 1. Since the experimental resultsof a stack of the same layer thickness as in the model consisting of glass beads of the same diameter,in the same tube results in absorption peak of close to 1, we would need to decrease the distancefurther down. Given the amount of time such a solution will take, such a solution is not yet
accomplished and is under

3. CONCLUSIONS
Granular materials are typically characterized using acoustic models. However, the accuracy of theprediction depends heavily on the input parameters and the chosen method. Three-dimensional finite
element modeling was shown on an sample of a stack of glass beads in an impedance tube, and theresulting absorption curve was calculated as a result. It is concluded that the distance among the beads
needs to be further increased in order for the measurement and simulation to become potentiallycomparable.

ACKNOWLEDGEMENTS
The authors would like to thank Prof. Kirill V. Horoshenkov and Alistair I. Hurrel for their help
with the original idea and the measurements

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REFERENCES
1. Paulo H. Mareze, Eric Brandao, William D’A. Fonseca, Olavo M. Silva and Arcanjo Lenzi.
“Modeling of acoustic porous material absorber using rigid multiple micro-ducts network:validation of the proposed model.” Journal of Sound and Vibration 443 (2019): 376-396
2. S. Gasser and F. Paun. “Absorptive properties of rigid porous media: Application to facecentered cubic sphere packing.” The Journal of the Acoustical Society of America 117.4(2005): 2090-2099
3. Bonfiglio Paolo, Pompoli Francesco. “Comparison of Different Inversion Techniques for
Determining Physical Parameters of Porous Media.” 19th International Congress on Acoustics,
ICA 2007 Madrid
4. Atalla, Youssef, and Raymond Panneton. “Inverse acoustical characterization of open cellporous media using impedance tube measurements.” Canadian acoustics 33, no. 1 (2005): 1124.
5. W.R. Kampinga. “Viscothermal acoustics using finite elements - Analysis tools for engineers”

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