On variation of absorption factor due to measurement method and correction factors for conversion between methods
Anna Färma) Ragnar Glavb)
Acoustics department, Scania CV AB, Södertälje, Sweden
KTH Royal Institute of Technology, School of Engineering Science,
Department of Aeronautical and Vehicle Engineering, Centre for ECO2 Vehicle Design, MWL 100 44 Stockholm, Sweden
Susann Boijc)
KTH Royal Institute of Technology, School of Engineering Science,
Department of Aeronautical and Vehicle Engineering, Centre for ECO2 Vehicle Design, MWL 100 44 Stockholm, Sweden
Sound absorbing materials are used in many applications to reduce sound, and their sound absorbing characteristics are most often determined experimentally since theoretical determination is difficult. Sound absorption factors are used in material specifications as well as input to numerical simulations.
Several methods for experimental determination of the absorption factor exist, two of them standardized and frequently used. It is commonly known that the absorption factor obtained by these two methods differs as different sound fields are prescribed by the standards. However, the size of the differences has not been so well described. Due to this difference, the choice of method is critical in order to avoid errors in simulations and specifications of material properties.
Experimental determination of absorption factors for three commonly used absorbers was performed, resulting in significant differences between the two methods. Correction factors to compensate the absorption factor determined at one acoustic state and used in another are given. Theory verifying the differences is also presented.
a) email: anna.farm@scania.com
b) email: ragnar.glav@scania.com
c) email: sboij@kth.se
1 INTRODUCTION
Porous material is used in many applications to reduce sound. The absorption factor of the material determines its quality and is most often determined experimentally. Experimental determination of the absorption factor is performed by either of two standardized methods, each based on a specific acoustic state. The obtained value on the absorption factor will depend on the acoustic state, either normal incidence or diffuse field excitation. Thus, systematic differences are to be expected in absorption for a specific material determined by the two different methods1. No thorough investigation has to the authors’ knowledge been made to determine the size of the differences.
This paper discusses the significance of these differences and also suggests correction factors between methods. It is shown that the choice of measurement method is indeed crucial.
Theory confirming differences obtained experimentally is provided and the results are discussed.
2 MATERIAL
The absorption factor is studied for isotropic porous foams with open pores, without any covering films or layers of different porosity. These are rather simple materials where viscous losses in the medium are the dominating characteristic. Structural motion of the material is often negligible.
The flow resistivity, σ, is a parameter often used to describe its acoustic properties. Typical values on commercially used absorbers are 1.0 k – 100 kNs/m4. The thickness is typically about a few centimetres.
3 EXPERIMENTAL METHODS
Two standardized methods, one based on normally and one based on randomly incident sound waves are used to experimentally determine the absorption factor of the materials. The methods also differ considerably concerning required measurement facilities and amount of sample material needed. Obviously these two issues often largely influence the choice of method in practice.
3.1 Normal incidence
The standing wave tube measurement2 is based on plane waves normally incident on the measurement sample. The pressure is measured at two positions, and the impedance of the surface is obtained using the wave decomposition technique. The absorption factor for normal incidence, αn, is then obtained from the surface impedance. The method is based on plane waves in the tube, why tubes of different diameters have to be used to cover a wider frequency range.
The method solely requires the impedance tube and relatively small measurements samples;
no dedicated acoustic measurement room is needed. The mounting in the tube will alter the stiffness of the sample, hence, for materials where the structural motion is significant compared to the viscous losses, the mounting affects the obtained absorption. In such cases, different results are obtained for different tube diameters. This implies that the method is preferably used for materials where viscous losses are dominant.
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As expected the absorption factor determined at normal incidence and at diffuse field excitation respectively differs significantly for all tested materials. The absorption at normal incidence for two of the materials, A and B, show the anticipated characteristics of a porous absorber with viscous losses due to fluid motion inside the pores. The third material C, however, differs from that pattern.
For material C, a clear peak in the absorption factor at normal incidence indicates that the structural motion in the material has significant impact on the resulting absorption. The flow resistivity for this foam is high which by definition means that the material resists fluid motion, instead forcing the structure to move. Structural motion in material C is further verified when results from the wide and narrow tubes are compared (thin and thick solid black line) since the resonance occurs at a higher frequency for the narrow tube where the sample is smaller and hence stiffer due to the mounting at the edges.
For the two materials A and B, the relation between the absorption factors obtained by the two methods show the same pattern for both materials. The absorption for diffuse field excitation is larger than the absorption for normal incidence except at the highest frequency bands measured. For even higher frequencies it is expected that the absorption for diffuse field excitation is smaller than for normal incidence1. At normal incidence the absorption increases slowly with frequency up to a certain value where it stabilizes. For diffuse field excitation, the absorption increases faster with frequency up to about the same value of the absorption factor as for normal incidence. This behaviour is to be expected since the apparent thickness of the absorber is larger for sound incident at oblique angle of incidence, increasing the absorption at low frequencies. Since the absorption factor is rather small in the low frequency region, this difference in absorption is significant in a wide frequency range. Relative differences as large as 100 % are seen and this is indeed substantial.
For the kind of material studied, where viscous losses due to fluid motion inside the pores are dominating and the structural motion is negligible, correction on absorption factors between methods would be of great use. In Figure 2 below, the correction factor K, according to Eq. (1) is given for materials A and B. Numerical values of K are given in Table 2.
(1)
Fig. 2 –
Table 2 diffuse f
Thr i) the pr amount interacti differen i) T This is t reflected increase
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ree mechani ropagation d
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[Hz]
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the materia the material ifferent mec obtained fr nce at norm istance a wa gles of inci eading to in
etween abso m thick mater
etween abso terials of dif nd A: Grey
KA 0.06 0.12 0.19 0.22 0.23 0.24 0.32 0.27 0.21 0.15 0.09 -0.03 -0.31 e total amou al, ii) the p
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orption facto rials of diffe orption fact ifferent flow y B: Light KB 0.02 0.09 0.22 0.30 0.32 0.31 0.38 0.36 0.30 0.19 0.14 0.04 -0.24 unt of visco article velo ng on the will dominate
methods co e equals twi vel inside the
the propaga sorption.
or for norma ferent flow re tor for norm w resistivity,
t grey 2 9 2 0 2 1 8 6 0 9 4 4
4
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al incidence esistivity, σ.
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related to ab material, an and the so he explanati this paper.
kness of the with an incid nce in the m
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dent and a material is
ii) High particle velocity gives high absorption. The particle velocity is zero at the backing rigid wall, hence small amounts of sound is absorbed there. Away from the rigid wall the velocity increases and is maximized one fourth of a wave length from the wall. The amount of absorption is hence coupled to the material thickness relative to the wavelength.
iii) When the angle of incidence increases the amount of sound energy reflected directly at the surface increases leading to smaller amount of sound energy entering the material. This phenomenon can e.g. be observed at the interface between air and an infinitely thick absorber (i.e. no rigid backing and no reflected wave inside the absorber). In that case the absorption is determined solely from the reflection at the interface, since all energy that enters the material is absorbed.
5 THEORETICAL RESULTS
There are many different material models that can be used to determine the sound absorption of porous materials. These models have various levels of complexity, ranging from semi-empirical Equivalent Fluid Models, EFM, (such as Delany and Bazley4), limp models neglecting motion in the structure5 down to models capturing the microstructure of the material such as Biot6 and Attenborough7. The latter models require assumptions on the microstructure properties and knowledge of material parameters which in many cases are hard to estimate.
Here, an EFM suggested by Delany and Bazley is used to calculate the absorption via the wave decomposition technique and the transfer matrix method (TMM)8 on a 20 mm thick material fronting a rigid wall. The absorption factor is calculated for angles of incidence ranging from normal to grazing incidence, from which the random incidence absorption is calculated as
0 2 sin 2 . (2) The absorption factor for normal incidence corresponds to the absorption determined in the standing wave tube, αn = α(0), whereas the randomly incident absorption approximately corresponds to the absorption for diffuse field excitation, αr ≈ αd.
For the flow resistivity according to materials A and B in this paper, the absorption factor at normal and random incidence is calculated. Since structural motion occur in material C, the behaviour of the material is not captured properly by the simplified model used, why the absorption is not calculated for material C.
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incidence creases for ted. These rent sound ossible be tion factor nly. If the pplication, ctions. For
this purpose, correction factors between diffuse field excitation and normal incidence are given for the two porous absorbers investigated in this work.
Theoretical determination of the correction factor from the thickness and flow resistivity of the material would be a useful tool in the future why further investigation on this are to be made.
The relation between the absorption factors for different acoustic states could also be measured for this purpose.
7 ACKNOWLEDGEMENTS
This research was supported by the Center for ECO2 Vehicle Design, and Scania CV AB provided material for experiments.
8 REFERENCES
1. Färm A., Boij S. and Glav R. “On Sound Absorbing Characteristics and suitable Measurement methods”. Proceedings of the 7th International Styrian Noise, Vibration and Harshness Congress, 2012.
2. ISO 354:2003. Acoustics -- Measurement of sound absorption in a reverberation room.
3. International standard ISO 10534-1:1996. Acoustics - Determination of sound absorption coefficient and impedance in impedance tubes -- Part 1: Method using standing wave ratio 4. Delany M. E. and Bazley, E. N., “Acoustic properties of fibrous absorbent materials”,
Applied Acoustics, 3: 105-116, 1970.
5. Corcos, G.M., “The Structure of the Turbulent Pressure Field in Boundary Layer Flows”, J.
of Fluid Mechanics, 18, 1964.
6. Biot, M. A. ”Generalized theory of acoustic propagation in porous dissipative media”, Journal of the Acoustical Society of America, 34 (9): 1254 - 1264, 1962.
7. Attenborough K., “ Acoustical characterization of porous materials” Physics Reports, 82 (3):
179-227, 1982.
8. Sastry J.S., Munjal M.L., “A transfer matrix approach for evaluation of the response of a multi-layer infinite plate to a two-dimensional pressure excitation”, Journal of Sound and Vibration, 182 (1):109–128, 1995.
