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SOUND ABSORPTION MEASUREMENTS OF SOME POROUS LOOSE GRANULAR MATERIALS Ayoub BOUBEL1; Said BOUSSHINE1; Mohammed GAROUM1; Bybi Abdelmajid1; Najma Laaroussi1 ¹ Structure LEME l’EST, Salé -CED de l’EMI, Mohammed V University in Rabat-Morocco B.P 227, Avenus du Prince Héritier Sidi Mohammed Sortie des Arcs, Salé Morroco
ABSTRACT This work deals with the study of the basic acoustic properties of five expanded loose granular materials (cork, perlite, clay, vermiculite and glass) as a function of granular size distributions and thickness. Direct measurements of the normal incidence sound absorption coefficient were conducted in the impedance tube based on the transfer method. In addition numerical inverse estimation of the main quantities involved in most outstanding acoustic model of porous materials (b. e. flow resistivity, tortuosity and porosity) was performed using constrained global nelder Mead algorithm. For a given grains size, results show that the expanded perlite and glass exhibit the best absorption performances. Keywords: loose granular materials, impedance tube acoustic, numerical inverse estimation.
1. INTRODUCTION The acoustic wave propagation in fibrous and granular porous materials has been the object of many works ( 1, 2, 3, 4). If fibrous materials are usually used in a variety of acoustical absorbing applications, the granular ones are however less used. For these reasons, this work addresses the acoustical characterization of five granular bulk materials in order to examine their potential uses as alternative absorbers to usually used fibrous materials. In this way, the normal sound absorption coefficient of five expanded commercial granular materials (cork, perlite, glass, vermiculite and clay) was measured and compared for several grain sizes and thicknesses. The experimental data were then completed by a numerical inverse estimation of physical parameters related to Johnson-Stinson-Champoux model (JSCM) widely used to predict the acoustical absorbing properties of granular materials.
2. Samples preparation For each loose granular material were sieved to produce several characteristic bands GS i of grain sizes (Figure 1).Table 1 shows these different bands with their corresponding densities. For each band a set of five loose cylindrical samples of 0.10 m diameter has been tested. The thicknesses considered are 0.04 m, 0.08 m, 0.12 m, 0.16 m and 0.2 m. All samples were first
dried in an oven at 60 °C and weighted at regular intervals until that their masses remain constant.
Grain size(mm) GS 1 [0.160-0.315] GS 2 [0.315-0.63]
0.139
0.110 0.102
-
-
-
GS 3
[0.63-1.25]
0.132
0.089
-
-
-
GS 4 GS 5
[1.25-2.5] [2.5-5]
0.106 0.096
0.079 0.074
0.187
0.171 0.130
0.603
GS 6
[5-6.3]
0.088
0.072
0.173
-
0.528
-
0.156
-
0.516
GS 7 [6.3-8] 0.085 1
Clay
[email protected]
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Density(g/cm3 )
Table 1–Grain sizes, materials and densities . Material Cork Perlite Glass Vermiculite
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Material Grain size(mm) GS 8 [8-10] GS 9 [10-12.5] GS 10 [12.5-16] GS11 [16-20]
Cork
Perlite
Glass
Vermiculite
Clay
0.080 0.0787 0.077 0.0752
-
0.151 0.149 -
-
0.450 0.414 0.367 -
Figure 1 – Different grain size of loose materials. (a): Cork, (b): Perlite, (c): Glass,(d):Vermiculite, (e): Clay
3. Experimental setup and results 3.1. Experimental setup Normal sound absorption measurements were performed using an acoustic impedance tube arranged vertically (figure 2) using the twomicrophone method described in the ISO 10534-2:2001 standard. This apparatus consists of a rigid tube of circular section with 100 mm in diameter and 1.20 m in length. The frequency range explored is 50 Hz -1600 Hz. The upper limit is the cut of frequency of the tube. All measurements were achieved with rigidly backed samples at an ambient temperature and relative humidity of about 18° C and 50% respectively.
Figure 2 – Acoustic impedance tube
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3.2. Experimental results 3.2.1: Loose cork and perlite The experimental measuremeents of sound absorption of cork as a function of grain size, has been made with ten different graain sizes (GS2 to GS11). For a given thickness of coork sample, the first frequency resonance shiffted to the lower frequency and the corresponding absorption coefficient increases as grain size decreases except for GS 2 which consists of a pow wdered cork. For example, figure 3 gives the abssorption coefficient spectra for samples made from GS 2 to GS11 with d= 0.08m. There is a lower limit grain size GS 2=[0.315-0.63]mm below whhich the absorption behaviour of cork disappe ars as a granular material. Indeed, for this band, the peak of the first frequency resonance in noot well identified. This band can be considered ass the boundary between the granular and powdder behaviours of cork. It should be noticed thatt the maximum is reached for GS 4 which givves an absorption coefficient very close to 1 aboutt 678 Hz. ϭ
'^Ϯ '^ϯ '^ϰ '^ϱ '^ϲ '^ϳ '^ϴ '^ϵ '^ϭϬ '^ϭϭ
Ϭ͕ϵ Absorption coefficient Į
Ϭ͕ϴ Ϭ͕ϳ Ϭ͕ϲ Ϭ͕ϱ Ϭ͕ϰ Ϭ͕ϯ Ϭ͕Ϯ Ϭ͕ϭ Ϭ Ϭ
ϱϬϬ
Frequency Hz
ϭϬϬϬ
ϭϱϬϬ
Figure3– Experimental absorrption coefficient spectra of granular cork with diffeerent grain sizes Thickness: d=0.08m. For the loose perlite tests sam mples were prepared from six grains sizes (GS1 to t GS6). Like cork, the same interpreetation can be made for perlite as shown in figgure 4. The band GS 3= [0.63-1.25] gives the best sound absorption results with a maximum absoorption coefficient of 0.97 about 650Hz.
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ϭ
'^ϭ '^Ϯ '^ϯ '^ϰ '^ϱ '^ϲ
Absorption coefficient Į
Ϭ͕ϵ Ϭ͕ϴ Ϭ͕ϳ Ϭ͕ϲ Ϭ͕ϱ Ϭ͕ϰ Ϭ͕ϯ Ϭ͕Ϯ Ϭ͕ϭ Ϭ Ϭ
ϱϬϬ
ϭϬϬϬ
ϭϱϬϬ
Frequency Hz
Figure4 – Experimental absorpption coefficient spectra of granular perlite with diffferent grain sizes Thickness: d= 0.08 m In order to highlight the transition between the granular and powder absorpttion behaviours of cork and perlite, the figure 5 shhows the absorption coefficient is plotted as fun ction of the mean radius Rm of each grains size baand at the neighbouring of the first resonance frequency(800 f Hz for cork and 700 Hz for perlite ) .
Figure5 – Variation V of acoustic absorption as function of Rm 3.2.2. Loose glass, clay and verrmiculite measurements For glass samples, five grainn sizes were studied (GS5 to GS9 ). We present heere only the effect of the thickness on the absorptioon coefficient for GS5 band. It can be seen from figure 6 that there is a lag of the first resonance maaximum to low frequency as thickness increases..
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Absorption coefficient Į
ϭ
ϰĐŵ
Ϭ͕ϵ
ϴĐŵ ϭϮĐŵ
Ϭ͕ϴ
ϭϲĐŵ ϮϬĐŵ
Ϭ͕ϳ Ϭ͕ϲ Ϭ͕ϱ Ϭ͕ϰ Ϭ͕ϯ Ϭ͕Ϯ Ϭ͕ϭ Ϭ Ϭ
ϮϬϬ
ϰϬϬϬ
ϲϬϬ
ϴϬϬ
ϭϬϬϬ
ϭϮϬϬ
ϭϰϬϬ
ϭϲϬϬ
Frequency Hz
Figure6– Experimental absorrption coefficient spectra of granular glass for differrent Thickness: grain sizes: GS 5 (2.5-5) mm For clay and vermiculite the same behaviours was observed concerning the e ffect of grain size and thickness. 3.2.3. Comparison between exp perimental data The comparison between thhe five loose granular materials was perform med for GS5 with d=0.08m. Figure 7 show that clay and cork exhibit less performance than perlite, p glass and F all samples, the maximum reached at the frequency resonance vermiculite at low frequency. For is greater than 0.92 in the range [600,740] Hz. ϭ
ůĂLJ
Ϭ͕ϵ
'ůĂƐƐ ŽƌŬ
Absorption coefficient Į
Ϭ͕ϴ
ƉĞƌůŝƚĞ
Ϭ͕ϳ
ǀĞƌŵŝĐƵůŝƚĞ
Ϭ͕ϲ Ϭ͕ϱ Ϭ͕ϰ Ϭ͕ϯ Ϭ͕Ϯ Ϭ͕ϭ Ϭ Ϭ
ϮϬϬ
ϰ ϰϬϬ
ϲϬϬ
ϴϬϬ
ϭϬϬϬ
ϭϮϬϬ
ϭϰϬϬ
ϭϲϬϬ Ϭ
Frequency Hz
Figure 7–Comparison between noormal sound absorption coefficient Įexp spectra forr loose perlite, cork, clay, glass and vermiculite: Thicknessd= 0.08m and grain size GS S5
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4. Theoretical model The theoretical normal sound absorption coefficient α th is given by the following formulas α th = 1 −
Zs −1 Zs +1
2
(1)
Where
Z z = −i
Zc cot(k c d ) , Z c = ρ (ω )K (ω ) and kc = ω ρ (ω ) / K (ω ) ρ 0 .c
(2)
Zc, kc, ρ( ω) and K (ω) are the characteristic acoustic impedance, the propagation constant, the complex density, the bulk modulus respectively. Z0=ρ0.c is the specific impedance of the unconstrained air and d is the thickness of the sample and ω the circular frequency. Many theoretical and empirical models have been developed to predict the acoustical proprieties of granular porous materials such as the Johnson-Stinson-Champoux (JSCM) below. (5, 6).
§ β12 ·¸ 2 σ .θ ¨ tŝƚŚ A = ρ (ω ) = ρ 0 .τ 1 − iA 1 + i /θ (3) ¨ ¸ 2A ¹ ω .ρ 0 .τ © K (ω ) =
γP0 γ −1
γ− 1− i
β 22 Pr
A. 1 + i.
(4)
Pr 2 Aβ 22
ρ ŝƐthe dynamical density and K the bulk modulus. Where γ=1.4 is the ratio of specific heats. Pr=0.706 is the Prandtl number. In this model the five non acoustical parameters namely, the porosity (θ), the tortuosity (τ), the flow resistivity (σ) and the two adjustable parameters (β)1 and (β2) corresponding to the viscous an thermal effects will be estimated from experimental data.
5. Numerical identification of non acoustical parameters The numerical estimation of η=(θ, τ, σ, β1, β2) was performed using the constrained direct search Nelder–Mead minimization algorithm. This algorithm allows a fast convergence than Differential Evolution and Simulating Annealing global inversion algorithms (7).The objective function to be minimized is:
N
(
S (η , d ) = ¦ α exp ( f j ) − αth ( f j ,η , d ) j =1
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)
2
(5)
͘
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Table 2 below give an example of the predicted parameters of loose granular materials.
Table 2 – Estimated parameters (Grain size: GS5, d= 0.08 m) τ
θ
Parameters σ (N.s.m−4)
β1
β2
1.76
0.56
748
3
1
2.39
0.96
1907
2.23
0.54
2.27
0.69
3088
1.49
0.69
1.95
0.72
4014
1.16
0.64
1.83
0.47
917
2
1.4
Materials Expanded cork expanded perlite Expanded glass Expanded vermiculite Expanded clay
Figure 8 – Comparison between measured and predicted sound absorption coefficient For Grain size GS5 and d=0.08m ___
:Predicted,ŸŸŸ : Corck, ŽŽŽ : Perlite, ƔƔƔ: Glass, ŽŽŽ͗Vermiculite͕זזזǣ
The estimated values of η is then injected into the JSCM model to in order to compare theoretical and experimental data. For example, figure 7 shows the predicted (continuous lines) and measured (markers) absorption coefficient spectra for grain size GS5 and d=0.08m. There is a good agreement between theoretical and experimental data over the whole frequency range.
6. CONCLUSION In this article we studied the acoustic absorption behavior of five kinds of loose granular materials: perlite, cork, glass, clay and vermiculite with several sizes and thickness. The experimental data have been fitted using the Johnson-Stinson-Champoux model (JSCM). A contribution to the numerical estimation of the granular materials parameters has been investigated for the model, using the constrained direct search Nelder–Mead minimization algorithm. In addition, granular materials can offer good absorption combined with good mechanical strength. They can be used as an alternative to usually used fibrous absorbers.
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7. REFERENCES 1. Garoum, M., Simón, F., Pfretzschner, J. and Moreno, A. Characterisation of non-consolidated cork crumbs as a basic sound absorber raw material , Proceedings of the Twelfth International Congress on Sound and Vibration Lisbon, Portugal, 11-15 July, (2005). 2. Asdrubali, F. and Horoshenkov, K.V. The acoustic properties of expanded clay granulates, Building Acoustics, 9 (02), 85-98, (2002). 3. Voronina, V.V. and Horochenkov, K.V. Acoustic properties of unconsolidated granular mixes, Applied Acoustics, 65, 673-69, (2004). 4. Garoum.M et al,"Sound absorption characteristics of some non-agglomerated sustainable materials" ICSV 20 Bangkok,Thailand 7-11 July 2013 5. D.L.Johnson, D.Koplik and R.Daschen. "Theory of dynamic permeability and tortuosity in fluidsatured porous media."J.Fluid.Mech., 176 : 379 - 402, (1987). 6. Stinson, M.R. and Champoux, Y. Propagation of sound and the assignment of shape factors in model porous materials having simple geometries, JASA, 91 (2), 685-695, (1992). 7. Garoum Mohammed, Boubel Ayoub, Bousshine Said, Bybi Abdelmajid, Najma Laaroussi Investigation of sound absorption characteristics of loose and agglomerated perlite granulate Proceedings of the 23rd International Congress on Sound and Vibration Athens, Greece, 10-14 July, (2016).
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