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Acoustic properties of rubber crumbs
Polymer Testing 18 (1999) 81–92
Material Properties
Acoustic properties of rubber crumbs J. Pfretzschner*, R. Mª. Rodriguez Instituto de Acu´stica (CSIC), Serrano, 144 28006, Madrid, Spain Received 23 December 1997; accepted 13 February 1998
Abstract The purpose of this article is to demonstrate that in the actual state of the art, recycled rubber products can be used to form acoustic absorbent materials, applicable to control noise pollution. Their applicability in noise screens shows excellent performance of broadband acoustic absorption. The article summarises part of a recent research carried out in the ‘Instituto de Acu´stica (CSIC)’, that has concluded in a Spanish and EU patent about absorbing noise screens [1]. 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction Tire dumps are a growing problem. Americans discard about 20 million tires per year, and about 2 billion scrap tires have been accumulated in stock piles across the country. In Europe analogous situations can be found, and the piles of thousands of tires at junkyards, landfills and other places are an environmental, public safety and health problem. As a consequence of this situation, the environmental regulations in U.S., and the more restricted regulations in Germany and Holland in Europe, push many reclaimers to increase their efforts in order to find applications for making use of rubber waste in the form of recycled materials or energy production. The main ‘acoustical application’ of reutilizing rubber consists in its use in pavements, as modified asphalt with increased elasticity, crack resistance and lower emission levels. A noise reduction can be achieved by a porous road, through partial absorption of the acoustic energy at * Corresponding author. 0142-9418/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 4 1 8 ( 9 8 ) 0 0 0 0 9 - 9
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the road surface, reducing the noise which propagates close to its surface. Due to the necessary constitution of this type of asphalt (compatible with its mechanical performances), their absorption spectrum has narrow band characteristics centred at 1200 Hz. Nevertheless, and taking into account that this frequency band corresponds to the most sensitive frequency range of the human ear, the absorption sensation can reach between 3 and 5 A weighted dB for this kind of new surface. The possibility of reducing traffic noise by using porous road surfaces is nowadays well known, but the physical explanation of the acoustical performance remains rather empirical (it depends on size and distribution of the aggregates, type of binder, layer thickness, etc.). Another application is based on the use of rubber crumb in the construction of sound barriers along highways to reduce noise to neighbouring residential areas. In this case, the acoustical design of a new material should be made in such a way that its absorption characteristics are broadband and adequate to the energy band spectrum of the pollutant source; this means that the designed material should have its highest absorption bands in coincidence with those of maximum emission bands of the noise source. In this way, a high degree of noise reduction can be achieved. This article is focused on the problem involved in the use of this kind of waste material and on its application as appropriate acoustic noise screens. 2. Theoretical The acoustical absorption phenomena inside a fibrous or porous material are mainly due to dissipative processes of viscosity and thermal conductions in the fluid inside the material. For this kind of material, these processes are a function of several parameters involved in its microstructural characteristics: porosity (⍀), tortuosity (T) and air flow resistivity (). Several theoretical models [2–6] relate the above mentioned parameters to the macroscopic acoustic absorption coefficient. In order to design an acoustic material adequate for the characteristics of an incident noise (e. g. traffic noise), it is convenient to elaborate a physicomathematical model to predict its acoustical absorption as a function of the frequency; in this way, empirical solutions can be avoided, saving time and a lot of experimental test. Usually, fibrous materials (like fibre glass or rock wool) or open cell polyurethane foams are used as absorbents in order to mitigate high levels of environmental noise. In these kind of materials, high absorption rates with frequency are due to the combination of a high porosity (⍀ ⬵ 1) with a great air resistivity ( > 40000 Rayls/m), and a large amount of tables of acoustic characteristics and performances can be found in the literature. Also, the literature of mathematical prediction models is plentiful. On the contrary, the literature about the acoustic behaviour of granular materials is much more restricted, and almost all present works are based on the first investigations carried out by Zwikker and Kosten [7], and on those developed by Biot [8] applied to the propagation of elastic waves in fluid saturated porous solids. In these mathematical models, the porous structures are modelled by simple forms (spheres, cylinders, slits, etc.). In the general case of common porous materials (as rubber crumbs), the key question is to find an expression for the characteristic acoustic impedance of the material under study (relation
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83
between the propagation pressure and the velocity of an acoustic pressure wave in the material), that is function of the frequency dependent dynamic density, () and the bulk modulus, K() of the material: Zc() ⫽
P ⫽ √()·K() U
(1)
If the material can be considered as a rigid frame whose pores are filled with a known fluid (the frame is motionless in a wide range of frequencies), it can be replaced on the macroscopic scale by an equivalent fluid, and Biot’s effective density of the fluid (air) can be expressed as:
() ⫽ 0T ⫺
⍀ F()
(2)
where T is the macroscopic tortuosity of the material, ⫽ 2 f (f ⫽ incident wave frequency), 0 air density, and F() is a complex function related to Bessel’s functions of 0 and 1 order of the shape factor (adimensional): 8T0
冪 ⍀
⫽c
(3)
c being an adjustment parameter. In this paper we follow the simplification for F() established by Johnson [9] (GJ()):
再
() ⫽ T0 1 ⫹
冎
⍀ G () with GJ ⫽ c j0T j
冪
1⫹
2 ;j⫽√⫺1 16
(4)
This simplification has a sufficient degree of precision. For cylindrical pores without intersections among them, Eq. (4) gives exact solutions, and in this case the shape parameter c ⫽ 1. For the calculation of the bulk modulus, K, and in absence of a general model for the frequency dependence of K, we use the same dependence as for cylindrical pores, taking the expression of Zwikker-Kosten, and introducing Johnson’s simplification:
再
冋
K() ⫽ ␥P0 ␥ ⫺ (␥ ⫺ 1)/ 1 ⫹
册冎
c⬘⍀ G ⬘(N ) jNPr0T J Pr
−1
(5)
with: Gj ⬘(NPr,) ⫽
冪
冉 冊
1 ⫹ jNPr
2 , 4cc⬘
being NPr the Prandtl number and c⬘ another shape parameter related to the thermal gradients in the pores (c is related to viscous losses in the pores). In general c ⫽ 1/c⬘, and 0.3 ⬍ c ⬍ 3. Having and K, the specific impedance of the granular material can be evaluated as a function of the test frequency, (Eq. (1)). It is well known [5] that the relationship between the surface impedance of a layer of porous material with a thickness d, for normal incidence sound waves, considering rigid backing, is:
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Z ⫽ ⫺ jZc()cot(kd)
(6)
being k the wave number in the material: k ⫽ √()/K(). From this impedance, the acoustic reflection coefficient can be calculated through: R() ⫽
Z() ⫺ 0c Z() ⫹ 0c
(7)
where 0c is the air impedance at standard conditions 0c ⫽ 415 Rayls MKS. Finally, the acoustic absorption coefficient of the material can be obtained as follows:
␣() ⫽ 1 ⫺ 兩R()兩2
(8)
3. Experimental In order to evaluate the evolution of the absorption coefficient (Eq. (8)) of a predetermined granular material two ways of measurements can be established: 1. Direct methods. Given an acoustic material, its absorption coefficient can be obtained, in a direct experimental way, through two different well known standardised measuring methods which have been used for a long time to measure the reflection coefficient of materials and the surface impedance: 쐌 standing wave tube (Kundt’s tube) for small samples of a material (S ⬵ 0.03 m2) 쐌 reverberation room, for samples at actual scale (S > 10 m2) 2. Prediction methods. Basically they consist in numerical procedures, in which the absorption can be calculated with the aid of Eqs. (1)–(8). Nevertheless it is necessary to measure the involved characteristic magnitudes, ⍀, T and of the granular material. In what follows the method employed to measure the mentioned structural parameters of any granular material will be described, as well as the direct measurements of the acoustic absorption coefficient. 3.1. Porosity Porous materials with open cells consist of an elastic or rigid frame which is surrounded by air. The porosity, ⍀, is the ratio of the air volume, Va, inside the sample, to the total volume, VT, occupied by the porous material ⍀ ⫽ Va/VT. For most fibrous materials and plastic foams with open cells, the porosity lies very close to one. Methods for measuring porosity are given in ref. [7]. In the case of rubber crumbs, the porosity lies around 0.5, and a simple alternative to measure this magnitude can be carried out through density relations (rubber-air), or filling the material with a known fluid, being the sample vacuum impregnated whit the liquid, in order to avoid air bubbles inside the frame.
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3.2. Flow resistivity For acoustic materials, this measurement has been standardised in ISO 9053 [10]. The sample is placed in a pipe, and a differential pressure induces a controlled unidirectional steady flow of air through the test specimen. The flow resistivity , which is an intrinsic property of the material, is given by:
⫽
p2 ⫺ p1 S · d
in this equation, p2–p1 is the incremental pressure drop between the two free faces of the test specimen (in reference to the atmospheric one); , the mean flow of air; S and d the area and thickness of the material placed in the pipe respectively. The total height of the cell should be such that there is essentially laminar air flow entering and leaving the test specimen. The air flow source should provide air flow rates such that the resulting velocities will be low enough to ensure that the measured airflow resistances are independent of velocity. (It is recommended that the source be such as to permit airflow velocities down to 0.5 ⫻ 10−3 m/s.) In MKS units, is expressed in Nm−4s or Rayls/m. In granular rubber materials (that can be considered as homogeneous), the flow resistivity is highly dependent on the particles size and in general is much lower than those of fibre glass. For rubber crumbs we have found values between 1000 and 12000 Nm−4s (in fibre materials flow resistivities generally lie between 40000 and 100000 Nm−4s). For the test specimen used in this work, a bubble air flow meter has been used in order to measure very low volumetric air flow rates, that lie between 9 ⫻ 10−6 m3/s and 300 ⫻ 10−6 m3/s. The equipment used for differential pressures should permit measurements of pressures as low as 0.1 Pa, with an accuracy of ⫾ 5% of the indicated value. 3.3. Tortuosity In the simple ideal case of material layers having cylindrical pores tilted at an angle in directions symmetrical with respect to the normal of the surface, the tortuosity is T ⫽ 1/cos2, named ‘structure factor’ by Zwikker and Kosten. In the case of common porous materials, a modelling of the tortuosity from the geometry of the frame is generally impossible (as occurs with the bulk modulus and the effective mass of the air). This explains why the models that describe sound propagation in these materials are mostly phenomenological. In frames where the solid is non electrically conductive, a method for measuring tortuosity has been described by Brown [11], based in an electroacoustical analogy. The porous material is saturated with a conducting fluid, and the electrical resistivity (equivalent to the flow resistivity) is then calculated through current and voltage measurements. Let c and f be the measured resistivities of the saturated material and the fluid respectively, the tortuosity is then given by: T⫽⍀
c f
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In our case, a 10% dissolution of CuSO4 has been employed, using circular plates of copper as electrodes. In this way, voltage curves versus electrical current have been renamed, maintaining constant the interelectrodic distance for both circumstances (with and without the granular sample). From the slope of the experimental regression lines (R ⫽ V/i) the tortuosity is given by T ⫽ ⍀•Rc/Rf, ⍀ being the porosity of the sample, measured previously. Measurements have been made using both a direct voltage (d.c. power supply) and an alternating voltage generator (oscillator plus power amplifier) at several emission frequencies (20 Hz– 5 kHz). Better linearity of experimental points has been found when relative high frequency pure tones (5000 Hz) were used, due to the shorter time constant of the equivalent circuit (it works as a charged condenser). With a surface of the circular plate electrodes (S ⫽ 78 ⫻ 10−4 m2), a separation distance (0.1 m) and a concentration of the electrolyte (10% of CuSO4 in water), the obtained resistance of the electrolyte (Rf ⬇ 6 ⍀) changes for the granular sample as a function of the pore size of the material (e. g. Rc ⬇ 26 ⍀ for 1.4 mm rubber size crumb). The resulting ranges of tortuosities for the studied granules lie between 1.3 and 3. 3.4. Absorption coefficient measured in Kundt’s tube The standing wave tube (Kundt) has been largely used to measure the reflection coefficient of acoustic materials and the corresponding surface impedance. A sample of the material is set at one extremity of a cylindrical tube and a plane acoustic wave propagates parallel to the axis of the tube. The reflection coefficient and the surface impedance can be evaluated by measuring the pressure in the tube at different places with a moving probe microphone. In order to facilitate the measurements, another technique based on FFT transforms, using various microphones has also been implemented during the last decade. Both techniques are well documented in an ISO Draft [12], and the last one has also been reported in this Journal [13]. These methods are very fast and feasible, needing only small test specimens. On the other hand, it allows to compare the obtained experimental absorption coefficients as a function of the frequency with those calculated through Eqs. (1)–(8). 3.5. Absorption coefficient measured in a reverberant room The absorption coefficient is not only frequency dependent but also depends on the angle of incidence. The Kundt’s tube method cannot be used at oblique incidence and offers some drawbacks. The high frequency range can be reached only if the tube has a small diameter ( ⬍ /4) and the preparation of homogeneous samples of material can be difficult for these geometries. If the frame can not be considered as motionless, the vibrations inside the tube can distort the measurement. Moreover, the vibration modes of the sample in a Kundt tube differ from the response of a panel in situ. For all these reasons, when the measuring purposes are focused only to know the absorption coefficient at random incidence, it is usual to measure the absorption characteristics of large specimens ( > 10 m2) through the reverberation procedure. The method is based in the generation of an acoustic diffuse field inside a chamber (V > 200 m3)
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by a sound source. The level to which reverberant sound builds up, and the subsequent decay of reverberant sound when the source is stopped, are governed by the sound absorbing characteristics of the boundary surfaces and testing material. The equivalent sound absorption area A, in square meters, of the test specimen, shall be calculated using the formula: A(f) ⫽ 55.3
冉
冊
1 V 1 [m2] ⫺ c T2(f) T1(f)
where c is the sound velocity in air (c ⫽ 331 ⫹ 0.6t, t ⫽ air temperature in ºC); T1 and T2 are the reverberation times, in seconds, of the empty room and after the test specimen has been introduced. The absorption coefficient of the test specimen in function of the frequency is:
␣(f) ⫽ A/S where S is the area, in square meters, of the test specimen (not less than 10 m2). The measurements shall be carried out at the centre frequencies from the normalized 18 onethird octave band series: 100, 125,.....5000 Hz. This procedure is well reported in the ISO Standard 354.[14] Several attempts has been made to relate the absorption data obtained through the Kundt’s tube method to the corresponding one in a reverberant room.[15] No one gives exact correlation data, but they can offer a good approximation of the behaviour of the material when it is exposed to a diffuse acoustic field. The absorption coefficients ␣(f) obtained through this procedure normally are higher than those of the Kundt’s tube. 4. Results and discussions It has been checked in preceding paragraphs, that the acoustic absorption behaviour of a sample depends on the intrinsic characteristics of the pore sizes and on the thickness of the layer. The tested samples correspond to rubber crumbs obtained from waste tires (without metallic and textile residues) with granules that lie in the range of 1.4 to 7 mm. The following types of rubber crumbs have been studied: Sample
s1
s2
s3
s4
s5
s6
s7
Size ()
⫽ 1.4
⬍ 3.5
1⬍⬍3
3⬍⬍5
⫽ 3.5
5⬍⬍7
⬍7
being the size of the rubber crumbs in mm. The samples s2 and s7 include any size of grains (from powder to the limiting size of the mesh), and it has been found a content about 70% of samples s3 and s4, respectively. 4.1. Direct measurements In Fig. 1, the absorption coefficient for samples of rubber crumb s2 ( ⬍ 3.5 mm) with 2.5, 5 and 9 cm layer thickness measured in a Kundt’s tube are shown. It can be observed the displace-
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Fig. 1. Sound absorption coefficient of rubber crumb sample s2 (grain size ⬍ 3.5 mm) for different thickness 2.5 (— *), 5 (....⌬), and 9 cm.(— o).
ment to lower frequencies of the principal maximum when the thickness increases (one octave per doubling thickness), as Eq. (6) establishes. This constitutes the simplest way to get better absorption layers for a given material. For a given sample thickness, the absorption coefficient increases when the diameter of the grains decreases. In this way, Fig. 2a shows, for a layer of 9 cm, the absorption curves in function of the frequency for rubber crumbs samples: s1 (+), s4 (䊐), and s7 (䊊). In order to check the influence of small size components, in Fig. 2b the absorption of the polidisperse sample s2(—*) with the monodisperse s3 (...⌬) is shown in a comparative way. Fig. 2c shows analogous curves for the samples s7(–䉫) and s6(....⌬). It can be observed the influence of the small size components inside the polidisperse samples in the high frequency range. Analogous results have been found for other thicknesses of the studied samples. In order to show the behaviour of the rubber crumb material in a reverberation room, Fig. 3 presents the absorption coefficient as a function of frequency for sample s2 with a thickness d ⫽ 9 cm (dashed line). In the same figure the corresponding experimental values obtained in Kundt’s tube have been overprinted (continuous line). The reverberant room test can be considered the best one to find the actual behaviour in situ of the material and it only should be carried out when the designed material can be considered final. The measurement is not cumbersome with the appropriate installations and instrumentation facilities, but the preparation of the samples are tiresome due to the big size of the samples (e.g. a total weight of 600 kg. were necessary to prepare a sample of 12 ⫻ 0.09 m3 of rubber crumb). In the figure it can be observed that a smoother curve for the results obtained in the reverberation room is obtained, due to the spatial averaging of the incident acoustic field. 4.2. Indirect measurements For the different types of rubber crumb samples studied (s1-s7), the intrinsic parameters have been measured in accordance with the methodologies explained in Section 2.
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Fig. 2. Acoustic absorption coefficients versus frequency for the following types of samples (thickness 9 cm): 2 a) s1 (+), s4 (....䊐), and s6(o); 2 b) s2(— *), and s3(...⌬); 2 c) s7(—䉫) and s6(....⌬).
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J. Pfretzschner, R.Mª. Rodriguez / Polymer Testing 18 (1999) 81–92
Fig. 3. Comparison between measured absorption coefficients obtained in Kundt’s tube (— *) and in Reverberation Room (....o), for sample s2 (grain size ⬍ 3.5 mm) with thickness 9 cm.
It has been checked that when the grain size diminishes, the air flow resistivity and the tortuosity increases, decreasing the porosity. As an example, it is worth comparing the values obtained for two types of samples with different grain sizes. In this way, for the crumb of 1.4 mm (s1), the following values have been measured: ⫽ 11000 Rayls/m MKS, T ⫽ 3 and ⍀ ⫽ 44.3%, whereas for the rubber crumb with size diameter > 5 (s6) the measured values were: ⫽ 1200 Rayls/m MKS, T ⫽ 1.4 and ⍀ ⫽ 54.4%. In Fig. 4a, the absorption coefficients, calculated through Eqs. (1)–(8) (continuous line), for the test sample s6 (⍀ ⫽ 54.4%, ⫽ 1200, T ⫽ 1.38, c ⫽ 1.5, c⬘ ⫽ 0.4), and the corresponding ones (point line) obtained by means of the Kundt’s tube method are shown, for a 5 cm of the layer thickness. Fig. 4b shows the results obtained for the same sample with a thickness of 9 cm. Analogous figures have been reached for the rest of the sample types, showing a high degree of correlation between experimental and calculated curves, making evident the proper algorithms developed in this article for this kind of material. In this manner, and through the developed algorithms, an easy way to design new absorbent acoustic materials has been established, avoiding unnecessary and time consuming empirical procedures. 5. Conclusions It has been checked that rubber crumbs specially sorted and prepared can be a good acoustic material with a broadband absorption spectrum. The developed physicomathematical algorithms gives a good correlation with the experimental values obtained through the Kundt’s tube. These algorithms constitute a good tool in order to design a new absorption granular material, adequate to the noise spectrum of a pollutant source. The use of this kind of material in noise barriers on emplacements exposed to climate atmos-
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91
Fig. 4. Comparison between calculated (—–) and measured (.....) normal absorption coefficient for 5 cm (a) and 9 cm (b) thick rubber crumbs samples (s6) backed by a rigid wall.
pheric agents (specially rain) is advantageous compared to the classical ones (glass or rockwool fibres), because its performance is not lost with the impregnated water or dust. Also, it can be painted with appropriate colours and cleaned in an easy way. For all these reasons, it is recommended for use outdoors, being an excellent alternative to the current absorbent screens used for the protection against traffic noise, contributing at the same time to eliminate scrap tires.
Acknowledgements This work was supported by the Spanish Plan Nacional de I ⫹ D, Project Number AMB950101.
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References [1] Pfretzschner J, et al. Sound absorbing wall with refuse vulcanised rubber Patent application nº 9502536 (1995). Applicant: Consejo Superior de Investigaciones Cientı´ficas, Spain. [2] Hamet JF, Be´rengier M. Acoustical characteristics of porous pavements: A new phenomenological model, Internoise 93. [3] Be´rengier MC. et al. Porous road pavements: Acoustical characterisation and propagation effects. J Acoust Soc Am 1997;101(1):155–62. [4] Champoux Y, Stinson MR. On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors. J Acoust Soc Am 1992;92(2):1120–31. [5] Attenborough K. Acoustical characteristics of rigid fibrous absorbents and granular materials. J Acoust Soc Am 1983;73(3):785–99. [6] Attenborough K. Models for the acoustical properties of air-saturated granular media. Acta Acustica 1993;1:213–26. [7] Zwikker C, Kosten CW. Sound absorbing materials. Elsevier Publishing Company, Inc, 1949. [8] Biot MA. The theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. II. Higher frequency range. J Acoust Soc Am 1956;28:168–91. [9] Johnson DL. Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mechanics 1987;176:379–402. [10] Standard ISO, 9053 Materials for acoustical applications. Determination of airflow resistance, 1991. [11] Brown JS. Connection between formation factor for electrical resistivity and fluid-solid coupling factors in Biot’s equations for acoustic waves in fluid-filled porous media. Geophysics 1980;45(8):1269–75. [12] ISO/DIS 10534-2, Determination of sound absorption coefficient and impedance in impedance tubes, 1996. [13] Soto PF. Acoustic impedance and absorption coefficient measurements of porous materials used in the automotive industry. Polymer Testing 1994;13:77–88. [14] Standard ISO 354, Measurement of sound absorption in a reverberant room, 1985. [15] London A. The determination of reverberant sound absorption coefficients from acoustic impedance measurements. J Acoust Soc Am 1950;22(2):263–9.
Material Properties
Acoustic properties of rubber crumbs J. Pfretzschner*, R. Mª. Rodriguez Instituto de Acu´stica (CSIC), Serrano, 144 28006, Madrid, Spain Received 23 December 1997; accepted 13 February 1998
Abstract The purpose of this article is to demonstrate that in the actual state of the art, recycled rubber products can be used to form acoustic absorbent materials, applicable to control noise pollution. Their applicability in noise screens shows excellent performance of broadband acoustic absorption. The article summarises part of a recent research carried out in the ‘Instituto de Acu´stica (CSIC)’, that has concluded in a Spanish and EU patent about absorbing noise screens [1]. 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction Tire dumps are a growing problem. Americans discard about 20 million tires per year, and about 2 billion scrap tires have been accumulated in stock piles across the country. In Europe analogous situations can be found, and the piles of thousands of tires at junkyards, landfills and other places are an environmental, public safety and health problem. As a consequence of this situation, the environmental regulations in U.S., and the more restricted regulations in Germany and Holland in Europe, push many reclaimers to increase their efforts in order to find applications for making use of rubber waste in the form of recycled materials or energy production. The main ‘acoustical application’ of reutilizing rubber consists in its use in pavements, as modified asphalt with increased elasticity, crack resistance and lower emission levels. A noise reduction can be achieved by a porous road, through partial absorption of the acoustic energy at * Corresponding author. 0142-9418/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 4 1 8 ( 9 8 ) 0 0 0 0 9 - 9
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J. Pfretzschner, R.Mª. Rodriguez / Polymer Testing 18 (1999) 81–92
the road surface, reducing the noise which propagates close to its surface. Due to the necessary constitution of this type of asphalt (compatible with its mechanical performances), their absorption spectrum has narrow band characteristics centred at 1200 Hz. Nevertheless, and taking into account that this frequency band corresponds to the most sensitive frequency range of the human ear, the absorption sensation can reach between 3 and 5 A weighted dB for this kind of new surface. The possibility of reducing traffic noise by using porous road surfaces is nowadays well known, but the physical explanation of the acoustical performance remains rather empirical (it depends on size and distribution of the aggregates, type of binder, layer thickness, etc.). Another application is based on the use of rubber crumb in the construction of sound barriers along highways to reduce noise to neighbouring residential areas. In this case, the acoustical design of a new material should be made in such a way that its absorption characteristics are broadband and adequate to the energy band spectrum of the pollutant source; this means that the designed material should have its highest absorption bands in coincidence with those of maximum emission bands of the noise source. In this way, a high degree of noise reduction can be achieved. This article is focused on the problem involved in the use of this kind of waste material and on its application as appropriate acoustic noise screens. 2. Theoretical The acoustical absorption phenomena inside a fibrous or porous material are mainly due to dissipative processes of viscosity and thermal conductions in the fluid inside the material. For this kind of material, these processes are a function of several parameters involved in its microstructural characteristics: porosity (⍀), tortuosity (T) and air flow resistivity (). Several theoretical models [2–6] relate the above mentioned parameters to the macroscopic acoustic absorption coefficient. In order to design an acoustic material adequate for the characteristics of an incident noise (e. g. traffic noise), it is convenient to elaborate a physicomathematical model to predict its acoustical absorption as a function of the frequency; in this way, empirical solutions can be avoided, saving time and a lot of experimental test. Usually, fibrous materials (like fibre glass or rock wool) or open cell polyurethane foams are used as absorbents in order to mitigate high levels of environmental noise. In these kind of materials, high absorption rates with frequency are due to the combination of a high porosity (⍀ ⬵ 1) with a great air resistivity ( > 40000 Rayls/m), and a large amount of tables of acoustic characteristics and performances can be found in the literature. Also, the literature of mathematical prediction models is plentiful. On the contrary, the literature about the acoustic behaviour of granular materials is much more restricted, and almost all present works are based on the first investigations carried out by Zwikker and Kosten [7], and on those developed by Biot [8] applied to the propagation of elastic waves in fluid saturated porous solids. In these mathematical models, the porous structures are modelled by simple forms (spheres, cylinders, slits, etc.). In the general case of common porous materials (as rubber crumbs), the key question is to find an expression for the characteristic acoustic impedance of the material under study (relation
J. Pfretzschner, R.Mª. Rodriguez / Polymer Testing 18 (1999) 81–92
83
between the propagation pressure and the velocity of an acoustic pressure wave in the material), that is function of the frequency dependent dynamic density, () and the bulk modulus, K() of the material: Zc() ⫽
P ⫽ √()·K() U
(1)
If the material can be considered as a rigid frame whose pores are filled with a known fluid (the frame is motionless in a wide range of frequencies), it can be replaced on the macroscopic scale by an equivalent fluid, and Biot’s effective density of the fluid (air) can be expressed as:
() ⫽ 0T ⫺
⍀ F()
(2)
where T is the macroscopic tortuosity of the material, ⫽ 2 f (f ⫽ incident wave frequency), 0 air density, and F() is a complex function related to Bessel’s functions of 0 and 1 order of the shape factor (adimensional): 8T0
冪 ⍀
⫽c
(3)
c being an adjustment parameter. In this paper we follow the simplification for F() established by Johnson [9] (GJ()):
再
() ⫽ T0 1 ⫹
冎
⍀ G () with GJ ⫽ c j0T j
冪
1⫹
2 ;j⫽√⫺1 16
(4)
This simplification has a sufficient degree of precision. For cylindrical pores without intersections among them, Eq. (4) gives exact solutions, and in this case the shape parameter c ⫽ 1. For the calculation of the bulk modulus, K, and in absence of a general model for the frequency dependence of K, we use the same dependence as for cylindrical pores, taking the expression of Zwikker-Kosten, and introducing Johnson’s simplification:
再
冋
K() ⫽ ␥P0 ␥ ⫺ (␥ ⫺ 1)/ 1 ⫹
册冎
c⬘⍀ G ⬘(N ) jNPr0T J Pr
−1
(5)
with: Gj ⬘(NPr,) ⫽
冪
冉 冊
1 ⫹ jNPr
2 , 4cc⬘
being NPr the Prandtl number and c⬘ another shape parameter related to the thermal gradients in the pores (c is related to viscous losses in the pores). In general c ⫽ 1/c⬘, and 0.3 ⬍ c ⬍ 3. Having and K, the specific impedance of the granular material can be evaluated as a function of the test frequency, (Eq. (1)). It is well known [5] that the relationship between the surface impedance of a layer of porous material with a thickness d, for normal incidence sound waves, considering rigid backing, is:
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Z ⫽ ⫺ jZc()cot(kd)
(6)
being k the wave number in the material: k ⫽ √()/K(). From this impedance, the acoustic reflection coefficient can be calculated through: R() ⫽
Z() ⫺ 0c Z() ⫹ 0c
(7)
where 0c is the air impedance at standard conditions 0c ⫽ 415 Rayls MKS. Finally, the acoustic absorption coefficient of the material can be obtained as follows:
␣() ⫽ 1 ⫺ 兩R()兩2
(8)
3. Experimental In order to evaluate the evolution of the absorption coefficient (Eq. (8)) of a predetermined granular material two ways of measurements can be established: 1. Direct methods. Given an acoustic material, its absorption coefficient can be obtained, in a direct experimental way, through two different well known standardised measuring methods which have been used for a long time to measure the reflection coefficient of materials and the surface impedance: 쐌 standing wave tube (Kundt’s tube) for small samples of a material (S ⬵ 0.03 m2) 쐌 reverberation room, for samples at actual scale (S > 10 m2) 2. Prediction methods. Basically they consist in numerical procedures, in which the absorption can be calculated with the aid of Eqs. (1)–(8). Nevertheless it is necessary to measure the involved characteristic magnitudes, ⍀, T and of the granular material. In what follows the method employed to measure the mentioned structural parameters of any granular material will be described, as well as the direct measurements of the acoustic absorption coefficient. 3.1. Porosity Porous materials with open cells consist of an elastic or rigid frame which is surrounded by air. The porosity, ⍀, is the ratio of the air volume, Va, inside the sample, to the total volume, VT, occupied by the porous material ⍀ ⫽ Va/VT. For most fibrous materials and plastic foams with open cells, the porosity lies very close to one. Methods for measuring porosity are given in ref. [7]. In the case of rubber crumbs, the porosity lies around 0.5, and a simple alternative to measure this magnitude can be carried out through density relations (rubber-air), or filling the material with a known fluid, being the sample vacuum impregnated whit the liquid, in order to avoid air bubbles inside the frame.
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3.2. Flow resistivity For acoustic materials, this measurement has been standardised in ISO 9053 [10]. The sample is placed in a pipe, and a differential pressure induces a controlled unidirectional steady flow of air through the test specimen. The flow resistivity , which is an intrinsic property of the material, is given by:
⫽
p2 ⫺ p1 S · d
in this equation, p2–p1 is the incremental pressure drop between the two free faces of the test specimen (in reference to the atmospheric one); , the mean flow of air; S and d the area and thickness of the material placed in the pipe respectively. The total height of the cell should be such that there is essentially laminar air flow entering and leaving the test specimen. The air flow source should provide air flow rates such that the resulting velocities will be low enough to ensure that the measured airflow resistances are independent of velocity. (It is recommended that the source be such as to permit airflow velocities down to 0.5 ⫻ 10−3 m/s.) In MKS units, is expressed in Nm−4s or Rayls/m. In granular rubber materials (that can be considered as homogeneous), the flow resistivity is highly dependent on the particles size and in general is much lower than those of fibre glass. For rubber crumbs we have found values between 1000 and 12000 Nm−4s (in fibre materials flow resistivities generally lie between 40000 and 100000 Nm−4s). For the test specimen used in this work, a bubble air flow meter has been used in order to measure very low volumetric air flow rates, that lie between 9 ⫻ 10−6 m3/s and 300 ⫻ 10−6 m3/s. The equipment used for differential pressures should permit measurements of pressures as low as 0.1 Pa, with an accuracy of ⫾ 5% of the indicated value. 3.3. Tortuosity In the simple ideal case of material layers having cylindrical pores tilted at an angle in directions symmetrical with respect to the normal of the surface, the tortuosity is T ⫽ 1/cos2, named ‘structure factor’ by Zwikker and Kosten. In the case of common porous materials, a modelling of the tortuosity from the geometry of the frame is generally impossible (as occurs with the bulk modulus and the effective mass of the air). This explains why the models that describe sound propagation in these materials are mostly phenomenological. In frames where the solid is non electrically conductive, a method for measuring tortuosity has been described by Brown [11], based in an electroacoustical analogy. The porous material is saturated with a conducting fluid, and the electrical resistivity (equivalent to the flow resistivity) is then calculated through current and voltage measurements. Let c and f be the measured resistivities of the saturated material and the fluid respectively, the tortuosity is then given by: T⫽⍀
c f
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In our case, a 10% dissolution of CuSO4 has been employed, using circular plates of copper as electrodes. In this way, voltage curves versus electrical current have been renamed, maintaining constant the interelectrodic distance for both circumstances (with and without the granular sample). From the slope of the experimental regression lines (R ⫽ V/i) the tortuosity is given by T ⫽ ⍀•Rc/Rf, ⍀ being the porosity of the sample, measured previously. Measurements have been made using both a direct voltage (d.c. power supply) and an alternating voltage generator (oscillator plus power amplifier) at several emission frequencies (20 Hz– 5 kHz). Better linearity of experimental points has been found when relative high frequency pure tones (5000 Hz) were used, due to the shorter time constant of the equivalent circuit (it works as a charged condenser). With a surface of the circular plate electrodes (S ⫽ 78 ⫻ 10−4 m2), a separation distance (0.1 m) and a concentration of the electrolyte (10% of CuSO4 in water), the obtained resistance of the electrolyte (Rf ⬇ 6 ⍀) changes for the granular sample as a function of the pore size of the material (e. g. Rc ⬇ 26 ⍀ for 1.4 mm rubber size crumb). The resulting ranges of tortuosities for the studied granules lie between 1.3 and 3. 3.4. Absorption coefficient measured in Kundt’s tube The standing wave tube (Kundt) has been largely used to measure the reflection coefficient of acoustic materials and the corresponding surface impedance. A sample of the material is set at one extremity of a cylindrical tube and a plane acoustic wave propagates parallel to the axis of the tube. The reflection coefficient and the surface impedance can be evaluated by measuring the pressure in the tube at different places with a moving probe microphone. In order to facilitate the measurements, another technique based on FFT transforms, using various microphones has also been implemented during the last decade. Both techniques are well documented in an ISO Draft [12], and the last one has also been reported in this Journal [13]. These methods are very fast and feasible, needing only small test specimens. On the other hand, it allows to compare the obtained experimental absorption coefficients as a function of the frequency with those calculated through Eqs. (1)–(8). 3.5. Absorption coefficient measured in a reverberant room The absorption coefficient is not only frequency dependent but also depends on the angle of incidence. The Kundt’s tube method cannot be used at oblique incidence and offers some drawbacks. The high frequency range can be reached only if the tube has a small diameter ( ⬍ /4) and the preparation of homogeneous samples of material can be difficult for these geometries. If the frame can not be considered as motionless, the vibrations inside the tube can distort the measurement. Moreover, the vibration modes of the sample in a Kundt tube differ from the response of a panel in situ. For all these reasons, when the measuring purposes are focused only to know the absorption coefficient at random incidence, it is usual to measure the absorption characteristics of large specimens ( > 10 m2) through the reverberation procedure. The method is based in the generation of an acoustic diffuse field inside a chamber (V > 200 m3)
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by a sound source. The level to which reverberant sound builds up, and the subsequent decay of reverberant sound when the source is stopped, are governed by the sound absorbing characteristics of the boundary surfaces and testing material. The equivalent sound absorption area A, in square meters, of the test specimen, shall be calculated using the formula: A(f) ⫽ 55.3
冉
冊
1 V 1 [m2] ⫺ c T2(f) T1(f)
where c is the sound velocity in air (c ⫽ 331 ⫹ 0.6t, t ⫽ air temperature in ºC); T1 and T2 are the reverberation times, in seconds, of the empty room and after the test specimen has been introduced. The absorption coefficient of the test specimen in function of the frequency is:
␣(f) ⫽ A/S where S is the area, in square meters, of the test specimen (not less than 10 m2). The measurements shall be carried out at the centre frequencies from the normalized 18 onethird octave band series: 100, 125,.....5000 Hz. This procedure is well reported in the ISO Standard 354.[14] Several attempts has been made to relate the absorption data obtained through the Kundt’s tube method to the corresponding one in a reverberant room.[15] No one gives exact correlation data, but they can offer a good approximation of the behaviour of the material when it is exposed to a diffuse acoustic field. The absorption coefficients ␣(f) obtained through this procedure normally are higher than those of the Kundt’s tube. 4. Results and discussions It has been checked in preceding paragraphs, that the acoustic absorption behaviour of a sample depends on the intrinsic characteristics of the pore sizes and on the thickness of the layer. The tested samples correspond to rubber crumbs obtained from waste tires (without metallic and textile residues) with granules that lie in the range of 1.4 to 7 mm. The following types of rubber crumbs have been studied: Sample
s1
s2
s3
s4
s5
s6
s7
Size ()
⫽ 1.4
⬍ 3.5
1⬍⬍3
3⬍⬍5
⫽ 3.5
5⬍⬍7
⬍7
being the size of the rubber crumbs in mm. The samples s2 and s7 include any size of grains (from powder to the limiting size of the mesh), and it has been found a content about 70% of samples s3 and s4, respectively. 4.1. Direct measurements In Fig. 1, the absorption coefficient for samples of rubber crumb s2 ( ⬍ 3.5 mm) with 2.5, 5 and 9 cm layer thickness measured in a Kundt’s tube are shown. It can be observed the displace-
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Fig. 1. Sound absorption coefficient of rubber crumb sample s2 (grain size ⬍ 3.5 mm) for different thickness 2.5 (— *), 5 (....⌬), and 9 cm.(— o).
ment to lower frequencies of the principal maximum when the thickness increases (one octave per doubling thickness), as Eq. (6) establishes. This constitutes the simplest way to get better absorption layers for a given material. For a given sample thickness, the absorption coefficient increases when the diameter of the grains decreases. In this way, Fig. 2a shows, for a layer of 9 cm, the absorption curves in function of the frequency for rubber crumbs samples: s1 (+), s4 (䊐), and s7 (䊊). In order to check the influence of small size components, in Fig. 2b the absorption of the polidisperse sample s2(—*) with the monodisperse s3 (...⌬) is shown in a comparative way. Fig. 2c shows analogous curves for the samples s7(–䉫) and s6(....⌬). It can be observed the influence of the small size components inside the polidisperse samples in the high frequency range. Analogous results have been found for other thicknesses of the studied samples. In order to show the behaviour of the rubber crumb material in a reverberation room, Fig. 3 presents the absorption coefficient as a function of frequency for sample s2 with a thickness d ⫽ 9 cm (dashed line). In the same figure the corresponding experimental values obtained in Kundt’s tube have been overprinted (continuous line). The reverberant room test can be considered the best one to find the actual behaviour in situ of the material and it only should be carried out when the designed material can be considered final. The measurement is not cumbersome with the appropriate installations and instrumentation facilities, but the preparation of the samples are tiresome due to the big size of the samples (e.g. a total weight of 600 kg. were necessary to prepare a sample of 12 ⫻ 0.09 m3 of rubber crumb). In the figure it can be observed that a smoother curve for the results obtained in the reverberation room is obtained, due to the spatial averaging of the incident acoustic field. 4.2. Indirect measurements For the different types of rubber crumb samples studied (s1-s7), the intrinsic parameters have been measured in accordance with the methodologies explained in Section 2.
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Fig. 2. Acoustic absorption coefficients versus frequency for the following types of samples (thickness 9 cm): 2 a) s1 (+), s4 (....䊐), and s6(o); 2 b) s2(— *), and s3(...⌬); 2 c) s7(—䉫) and s6(....⌬).
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Fig. 3. Comparison between measured absorption coefficients obtained in Kundt’s tube (— *) and in Reverberation Room (....o), for sample s2 (grain size ⬍ 3.5 mm) with thickness 9 cm.
It has been checked that when the grain size diminishes, the air flow resistivity and the tortuosity increases, decreasing the porosity. As an example, it is worth comparing the values obtained for two types of samples with different grain sizes. In this way, for the crumb of 1.4 mm (s1), the following values have been measured: ⫽ 11000 Rayls/m MKS, T ⫽ 3 and ⍀ ⫽ 44.3%, whereas for the rubber crumb with size diameter > 5 (s6) the measured values were: ⫽ 1200 Rayls/m MKS, T ⫽ 1.4 and ⍀ ⫽ 54.4%. In Fig. 4a, the absorption coefficients, calculated through Eqs. (1)–(8) (continuous line), for the test sample s6 (⍀ ⫽ 54.4%, ⫽ 1200, T ⫽ 1.38, c ⫽ 1.5, c⬘ ⫽ 0.4), and the corresponding ones (point line) obtained by means of the Kundt’s tube method are shown, for a 5 cm of the layer thickness. Fig. 4b shows the results obtained for the same sample with a thickness of 9 cm. Analogous figures have been reached for the rest of the sample types, showing a high degree of correlation between experimental and calculated curves, making evident the proper algorithms developed in this article for this kind of material. In this manner, and through the developed algorithms, an easy way to design new absorbent acoustic materials has been established, avoiding unnecessary and time consuming empirical procedures. 5. Conclusions It has been checked that rubber crumbs specially sorted and prepared can be a good acoustic material with a broadband absorption spectrum. The developed physicomathematical algorithms gives a good correlation with the experimental values obtained through the Kundt’s tube. These algorithms constitute a good tool in order to design a new absorption granular material, adequate to the noise spectrum of a pollutant source. The use of this kind of material in noise barriers on emplacements exposed to climate atmos-
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Fig. 4. Comparison between calculated (—–) and measured (.....) normal absorption coefficient for 5 cm (a) and 9 cm (b) thick rubber crumbs samples (s6) backed by a rigid wall.
pheric agents (specially rain) is advantageous compared to the classical ones (glass or rockwool fibres), because its performance is not lost with the impregnated water or dust. Also, it can be painted with appropriate colours and cleaned in an easy way. For all these reasons, it is recommended for use outdoors, being an excellent alternative to the current absorbent screens used for the protection against traffic noise, contributing at the same time to eliminate scrap tires.
Acknowledgements This work was supported by the Spanish Plan Nacional de I ⫹ D, Project Number AMB950101.
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