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An experimental study on the acoustic absorption of sand panels
Applied Acoustics 116 (2017) 238–248
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Technical note
An experimental study on the acoustic absorption of sand panels Lu Shuai a, Xu Weiguo a,b, Chen Yuxiao a, Yan Xiang a,b,⇑ a b
School of Architecture, Tsinghua University, Beijing 100084, PR China Key Laboratory of Urban-Rural Eco Planning and Green Building, Ministry of Education, Tsinghua University, PR China
a r t i c l e
i n f o
Article history: Received 30 July 2016 Received in revised form 1 September 2016 Accepted 1 September 2016
Keywords: Sand panels Acoustic absorption Flow resistivity Delany-Bazley Model Voronina Model
a b s t r a c t Potentially sand panels could be used as novel sound absorbing materials that are fire resistant, environmentally friendly, mechanically strong and have good durability. However, the performance of sand panels as sound absorbers has not yet been studied. Results of measurements in a reverberation chamber of the random-incidence absorption coefficients of 13 different sand panel compositions and configurations with air gaps are reported. Also the flow resistivities and bulk densities have been measured. The results prove that sand panels could offer effective and wide-band acoustic absorption. As is the case with conventional sound absorbing materials, adding an air space is found to be the most effective way to widen the absorption bands and improve the overall absorption. Comparisons of the measured sand panel absorption data with predictions of the Delany and Bazley and Voronina models reveal that, while neither model is very accurate, the former gives more accurate predictions especially for sand panels with lower flow resistivity and smaller thickness. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Research background As undesirable noise has been regarded as a severe problem for the environment and public health, sound absorption materials are widely used nowadays in many indoor and outdoor occasions. Therefore, materials with effective absorption and other virtues like fire resistance, environmental harmlessness and low cost are in large demand. Sand panels are an innovative class of absorption materials developed in recent years. They are made out of natural sands with inorganic silicon-based solvent by relatively simple manufacturing process. Test data has shown that sand panels are fire resistant, environment friendly, mechanically strong and with good durability in severe environments (Table 1). These are significant advantages of sand panels over traditional sound absorption materials such as glass wool or rock wool. Compared to metallic absorption materials like aluminum foams or micro-perforated steel plates, sand panels are far more economical since their main ingredient is widely-distributed and easily-acquired sands. Moreover, the finishing of sand panels can be in different colors and with different natural textures (Fig. 1). They could also be made into curved shapes. As a result, sand panels have already been used ⇑ Corresponding author at: School of Architecture, Tsinghua University, Beijing 100084, PR China. E-mail address: [email protected] (X. Yan). http://dx.doi.org/10.1016/j.apacoust.2016.09.002 0003-682X/Ó 2016 Elsevier Ltd. All rights reserved.
in many projects in recent years (Fig. 2, the projects shown here are designed by the Building Acoustic Lab of Tsinghua University). However, there is no existing research that reports the sound absorption characteristics that sand panels can offer with different values of material parameters (flow resistivity, thickness, etc.). This lack of knowledge makes it difficult to obtain sand panels with desirable absorption coefficients for specific requirements, and thus significantly affects the application of this material. This paper seeks to address this problem. 1.2. State of the art The sound absorption of materials is a topic that has been long studied. Delany and Bazley [1] investigated fibrous porous materials and provided a simple empirical model to predict the characteristic impedance and propagation coefficient based on flow resistivity. This model has been widely used for a long time because of its simplicity and good precision [2,3]. However, it is found to have the drawbacks of working well only for a limited variety of materials and being inaccurate for low frequencies due to its non-physical nature [4]. Some researchers have sought to modify the Delany and Bazley Model so that it could provide better fits for other specific materials [5,6]. Johnson et al. [7] and Allard [8] formulated a mathematical model to describe the propagation and absorption of sound in fluid-saturated porous materials based on Biot’s research [9,10]. This model has a better accuracy but needs more parameters. Compared to typical porous materials,
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Table 1 Physical characteristics of a typical simple of sand panel. Size 600 ⁄ 600 ⁄ 20 mm Tensile strength 13.3 Mpa
Density
Fire-resistance 3
3
1.51 ⁄ 10 kg/m Bending strength 24.7 MPa
TVOC (Total Volatile Organic Compounds) 3
Non-combustible Impact strength 15.6 kJ/m2
0.062 mg/m h Percentage of moisture expansion 0.16%
Compressive strength 29.1 Mpa Frost test (25 cycles) No wrecking occurred
Note: The test sample is manufactured by the Building Acoustic Lab of Tsinghua University. The fire-resistance is tested by the Tianjin Fire Research and Testing Center of the Ministry of Public Safety of the PR China. Other tests are conducted by the National Building Material Testing Center of the PR China.
(a) Sand panels with different colors
(b) Sand panels with different natural textures
(c) Sand panels made of large particles
(d) Sand panels made of small particles
Fig. 1. The appearance (a, b) and microstructure (c, d) of sand panels.
(a) The ceiling and columns are sand panels
(b) The ceiling is sand panels
Fig. 2. A dining hall (a) and a lecture hall (b) that applied sand panels.
the porosity of sand panels is much lower and the flow resistivity is much higher (detail information in Section 2.1). Therefore, whether sand panels share similar patterns of sound absorption with fibrous porous materials still needs to be tested. Besides porous materials, there are also many researches that investigated the acoustic characteristics of granular materials, which have more similar microstructures to sand panels. Voronina and Horoshenkov [11] studied granular materials based on experimental data and developed a model that can predict their acoustic features using
flow resistivity, porosity, tortuosity and structural characteristic. However, the predictive power of this semi-phenomenological model is found to be limited [12]. Moreover, the model is acquired from the data of only four kinds of granular materials (vermiculite, granulated rubber, perlite and granulated nitrile foam), and is found to be ineffective to predict the acoustic characteristics of polyurethane particles [13]. Therefore, whether this model is applicable to other materials like sand panels needs to be investigated. Horoshenkov and Swift [14] raised another model for granular
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materials, and the model was found to be effective to predict the acoustic characteristics of a similar material to sand panels (Coustone, a material made from flint particles consolidated with rubber-epoxy blinder). However, this model cannot be employed here, because the facility for measuring the pore size distribution (a water suction system [15]) is not available in the institute of the authors. Similar models regarding granular materials were also provided by Attenborough [16,17], but sand panels were not included in them either. In this research, the model of porous materials raised by Delany and Bazley (referred to as DelanyBazley Model) and the model of granular materials raised by Voronina (referred to as Voronina Model) are adopted to compare with the measurement data of sand panels, in order to investigate whether two existing models can provide reliable predictions for the acoustic absorption of sand panels. There are also many researches that revealed the acoustic absorption characteristics of a specific kind of materials. Swift et al. [18], Pfretzschner and Rodriguez [19], Horoshenkov and Swift [20] and Hong et al. [21] studied the acoustic absorption of rubber particle materials, uncovered the factors that are influential for absorption, or measured acoustical properties of specialcomposited rubber materials based on experimental data. Asdrubali and Horoshenkov [22] and Vasina et al. [23] investigated the acoustic feature of materials composed of expanded clay granules. Zhou et al. [13] studied the acoustic absorptions of polyurethane particles. And Cuiyun et al. [24] explored the absorption characteristics of sintering ceramic material, etc. However, there is no existing research that specifically devotes to the acoustic properties of sand panels found in archival publications, and this is the blank that this research aims to fill in. 1.3. Objective of this research
particles are well mixed with inorganic silicon-based solvent, and then poured into moulds. Finally, after about 15 min at room temperature, sand particles are aggregated together and sand panels are produced. In the research, 13 cases are investigated and 7 kinds of sand panels are involved. Their physical properties are presented in Table 2. The flow resistivity was measured by the direct airflow method introduced in ISO 9053-1991 [25]. A pressure depression system of the water reservoir was employed to produce airflow. For each kind of sand panels, three samples were made and three specimens were taken from each of the samples. The measurements of all the nine specimens were averaged. All the samples are with a diameter of 100 mm and a thickness of 20 mm. The bulk density was determined by its definition. The bulk volume of one piece of sand panel was known from its mold, and the mass was measured by weighing. The bulk density was calculated from dividing its mass by its bulk volume. The calculations of three specimens were averaged. The porosity was measured by the gas expansion method [26,27]. Two vessels of the same volume, one with a piece of sand panel inside and the other without, were pumped with the same amount of air. The air pressures of the two vessels were measured respectively, and then the effective volume of the pores in the sand panel was calculated according to the ideal gas law. Finally, the porosity was calculated from dividing the effective volume of the pores by the bulk volume. Similarly, the calculations of three specimens were averaged. It is found that samples made out of larger particles had smaller flow resistivity. However, the bulk densities of different samples are distributed within a very narrow range around 1.5 ⁄ 103 kg/m3, and the porosities of all samples are around 0.43 regardless of the dimensions of particles. 2.2. Sound absorption measurement
This research is an experiment-based investigation on the absorption characteristics of sand panels, and specifically pursues two goals: (1) to uncover the acoustic absorption characteristics that sand panels can offer with different values of material parameters; (2) to verify if existing models can provide reliable predictions for the acoustic absorption of sand panels. 2. Methodology 2.1. Manufacture of sand panel samples The samples of sand panels used in this research are manufactured in a process consisting of three stages. First, natural sands are sifted with meshes of different sizes, thus sand particles with dimensions in a certain range can be acquired. Second, sifted sand
The absorption coefficients of all samples are respectively measured in a reverberation chamber following ISO 354-2003 [28]. The volume of the reverberation chamber is 202 m3, and the area of each specimen is 10 m2. The frequency range of the measured absorption coefficients is 100–5000 Hz at 1/3 octave bands. As a nature of the reverberation chamber method, the absorption coefficient in this research refers to diffuse-field absorption coefficient instead of normal-incident absorption coefficient. For most architectural and environmental applications, the diffuse-field absorption coefficient is more practical [29, pp. 254]. The random-incidence absorption coefficient is also used as the basis for testing the adequacy of Delany-Bazley Model and Voronina Model for sand panels. Although the characteristic impedance and propagation constant measured by the impedance tube are more sensitive for testing the adequacy of models theoretically, using the
Table 2 Physical properties of the test samples in this research. Case no.
Characteristic particle size (mm)
Bulk density (kg/m3)
Porosity (%)
Flow resistivity (N s/m4)
Sand panel thickness (mm)
Air space thickness (mm)
1 2 3 4 5 6 7 1a 1b 4a 5a 6a 7a
0.30 0.30 0.30 0.59 0.27 0.23 0.19 0.30 0.30 0.59 0.27 0.23 0.19
1.51 ⁄ 103 1.51 ⁄ 103 1.51 ⁄ 103 1.53 ⁄ 103 1.50 ⁄ 103 1.49 ⁄ 103 1.49 ⁄ 103 1.51 ⁄ 103 1.51 ⁄ 103 1.53 ⁄ 103 1.50 ⁄ 103 1.49 ⁄ 103 1.49 ⁄ 103
43.0 43.0 43.0 42.3 43.4 43.8 43.8 43.0 43.0 42.3 43.4 43.8 43.8
92,450 92,450 92,450 49,300 135,100 210,500 274,500 92,450 92,450 49,300 135,100 210,500 274,500
20 30 50 20 20 20 20 20 20 20 20 20 20
0 0 0 0 0 0 0 20 100 100 100 100 100
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random-incidence absorption coefficient as the basis is more intuitive practically. It allows an easier understanding about how accurate the predictions for the acoustic absorption of sand panels could be. Another important reason for giving up the impedance tube method is that it is only applicable to locally reacting absorber, while sand panels with non-partitioned air spaces behind (Case 1a, 1b, 4a, 5a, 6a, 7a) are typical non-locally reacting absorbers that are only measurable by the reverberation chamber method [30].
where n is a dimensionless parameter, q is the tortuosity, k is the wave number in air, and Q is the structural characteristics. c0 is the sound velocity in air in m/s, l is the dynamic viscosity of air in N s/m2, while f is the frequency in Hz. With Eqs. (5)–(11), the characteristic impedance Z0 = R + jX and the propagation coefficient c = a + jb can be predicted by:
2.3. Prediction models (1) Delany-Bazley Model
R ¼ 1 þ Q; if f < f cr
ð12Þ
Or R ¼ q=H; if f P f cr
ð13Þ
X ¼ Q H=ð1 þ CÞ
ð14Þ
a ¼ k Q H=ð1 þ AÞ
ð15Þ
b ¼ k ½1 þ Q H ð1 þ BÞ
ð16Þ
Delany and Bazley presented an empirical model for estimating the properties of porous materials. The characteristic impedance Z0 = R + jX and the propagation coefficient c = a + jb can be predicted by [1]:
where coefficients A, B, C and the transition frequency fcr are defined as:
R ¼ q0 c0 1 þ 9:08
A¼
"
" X ¼ q0 c0 ð11:9Þ
0:75 # f
r 0:73 # f
r
0:59 x f a ¼ 10:3 c0 r b¼
x c0
" 1 þ 10:8
0:70 # f
r
ð1Þ
ð2Þ
In the model that Voronina raised [11], several physical parameters are required to predict the properties of granular materials:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D ¼ V g =0:5233
ð5Þ
H ¼ 1 qm =qg
ð6Þ
M¼
103 q0
D q0 c0
l
ð7Þ
ð8Þ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1H q¼ 1þ 2H
ð9Þ
2pf c0
ð10Þ
k¼
1H C ¼ pffiffiffiffi Q
ð19Þ
200 l ð1 HÞ2 ð1 þ HÞ4
p q0 D2 ðq HÞ2
ð20Þ
(3) Calculation of the diffuse-field absorption coefficient Both the Delany-Bazley Model and the Voronina Model provide predictions for the characteristic impedance (Z0) and the propagation coefficient (c), and they can be converted to the diffuse-field absorption coefficient in order to compare with the measurement data acquired in the reverberation chamber [29, pp. 253–254]:
Z ¼ Z 0 cothðc LÞ
ð21Þ
Z cos h q0 c0 2 ah ¼ 1 Z cos h þ q0 c0
ð22Þ
Z
p=2
a¼2 0
where D is the characteristic dimension of particles in mm, H is the porosity, and M is a dimensionless parameter. Vg is the number of particles in a unit volume. qm is the density of the granular material, qg is the density of the grain material, while q0 is the air density (all in kg/m3). Based on Eqs. (5)–(7), more parameters can be calculated:
n¼
ð18Þ
f cr ¼ ð4Þ
ð17Þ
1 B ¼ pffiffiffiffi Q ð1 þ HÞ ð1 þ Q 2 MÞ
ð3Þ
where q0 is the air density in kg/m3, c0 is sound velocity in air in m/s, r is the flow resistivity in g/(s cm3) (i.e., 1000 N s/m4), f is the frequency in Hz and is related to x by x = 2pf, while j is the imaginary unit. (2) Voronina Model
qg
ð1 HÞ M 1þQ
ah sin h cos h dh
ð23Þ
where Z is the impedance of a rigidly-backed material layer with finite thickness of L (in m). ah is the absorption coefficient at the incident angle of h, while a is the diffuse-field absorption coefficient. 3. Results and analysis The measurement data is presented in Table 3. Among all 13 test cases, the average value of the mean absorption coefficient over all frequencies is 0.49, and the average noise reduction coefficient (NRC) is 0.51. For cases without and with air space behind, the average values of the mean absorption coefficient over all frequencies are 0.43 and 0.54 respectively, with the mean NRC of 0.46 and 0.57. The highest value of the mean absorption coefficient over all frequencies is 0.66 (Case 1b), while the highest NRC is 0.7 (Case 1b and Case 4a). 3.1. Acoustic absorption with different flow resistivities
0:2 ð1 HÞ ð1 þ HÞ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q¼ H kDn
ð11Þ
Five cases with the same thickness and no air space behind are plotted in Fig. 3. The flow resistivities of Case 4, 1, 5, 6 and 7 increase from 49,300 N s/m4 to 274,500 N s/m4. It can be seen that
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Table 3 Measurement data of the test cases in this research. Frequency (Hz)
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
Mean
NRC
Case Case Case Case Case Case Case Case Case Case Case Case Case
0.05 0.03 0.02 0.02 0.06 0.00 0.00 0.11 0.29 0.15 0.27 0.15 0.05
0.03 0.05 0.05 0.00 0.04 0.03 0.00 0.12 0.38 0.20 0.47 0.22 0.00
0.03 0.04 0.04 0.00 0.01 0.00 0.00 0.18 0.51 0.23 0.35 0.32 0.14
0.01 0.07 0.12 0.06 0.07 0.03 0.01 0.16 0.56 0.43 0.43 0.35 0.30
0.03 0.12 0.17 0.07 0.07 0.08 0.10 0.19 0.60 0.65 0.45 0.43 0.39
0.08 0.23 0.31 0.07 0.12 0.12 0.23 0.29 0.77 0.71 0.51 0.46 0.38
0.12 0.26 0.44 0.11 0.22 0.13 0.27 0.46 0.97 0.82 0.54 0.55 0.43
0.18 0.36 0.58 0.17 0.32 0.26 0.36 0.65 0.90 0.83 0.54 0.50 0.45
0.28 0.50 0.66 0.28 0.44 0.31 0.40 0.82 0.85 0.88 0.62 0.54 0.40
0.38 0.63 0.65 0.37 0.54 0.49 0.44 0.96 0.85 0.83 0.49 0.51 0.35
0.59 0.72 0.62 0.53 0.63 0.54 0.50 0.93 0.72 0.73 0.48 0.49 0.33
0.79 0.78 0.67 0.79 0.73 0.71 0.50 0.82 0.64 0.69 0.47 0.52 0.42
0.95 0.79 0.63 0.86 0.75 0.75 0.53 0.77 0.58 0.57 0.53 0.51 0.50
0.99 0.86 0.73 0.99 0.81 0.69 0.55 0.67 0.60 0.59 0.62 0.58 0.48
0.90 0.79 0.72 0.93 0.67 0.76 0.59 0.62 0.55 0.67 0.68 0.62 0.56
0.83 0.78 0.77 0.81 0.80 0.67 0.58 0.56 0.62 0.69 0.73 0.69 0.61
0.79 0.81 0.86 0.81 0.87 0.79 0.57 0.70 0.72 0.80 0.79 0.80 0.58
0.79 0.86 0.93 0.85 0.87 0.71 0.70 0.79 0.82 0.83 0.83 0.74 0.60
0.43 0.48 0.50 0.43 0.45 0.39 0.35 0.54 0.66 0.63 0.54 0.50 0.39
0.45 0.50 0.55 0.45 0.45 0.40 0.40 0.60 0.70 0.70 0.50 0.50 0.40
1 2 3 4 5 6 7 1a 1b 4a 5a 6a 7a
1.0
Absorption Coefficient
0.8
Case 1 Case 4 Case 5 Case 6 Case 7
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 3. The absorption coefficient of cases with different flow resistivity.
sand panels with lower flow resistivities (e.g., Case 1 and Case 4) have effective absorption at high frequencies, and the absorption coefficient approaches 1 at 2000 Hz. At low frequencies, however, the absorption effectiveness is poor and the absorption coefficient stays below 0.2 at frequencies lower than 500 Hz. If the flow resistivity increases (e.g., Case 7), the absorption will improve at lower frequencies but the improvement is rather limited (still below 0.4 at 500 Hz). Moreover, the absorption will drop more significantly at high frequencies (below 0.6 at 2000 Hz), while the mean absorption coefficient over all frequencies and the NRC will also drop for about 0.1. In other words, the overall absorption of sand panels will get weaker if the flow resistivity increases. This is accordant with the common knowledge of porous materials. As a result, sand panels with lower flow resistivity are normally preferred to acquire better absorption properties. The measurement data and predictions of Case 1, 4, 5, 6 and 7 are respectively shown in Figs. 4–8. It can be seen that for sand panels with low flow resistivity (Case 4), both Delany-Bazley Model and Voronina Model can provide predictions with good accuracy. The
maximal errors of both models are below 0.2 over all frequencies. When the flow resistivity increases (Case 1 and Case 5), Delany-Bazley Model can still provide rather precise predictions, while estimations provided by Voronina Model turn inaccurate and cannot imitate the shape of the frequency diagram well. For the cases of high flow resistivities (Case 6 and Case 7), the prediction of each model approaches a straight line and cannot reflect the characteristics of the frequency diagrams of sand panels at all. In conclusion, Delany-Bazley Model can provide a better fit for sand panels than Voronina Model. This is an unexpected result because sand panels are more similar to granular materials instead of porous materials in terms of material nature. A possible explanation is that the materials that Voronina Model was derived from (vermiculite, granulated rubber, perlite and granulated nitrile foam) have larger particle sizes (0.4–3.5 mm) than sand panels (0.19–0.59 mm), so the patterns of absorption differ significantly. Another outcome is that sand panels with lower flow resistivities can be better predicted by Delany-Bazley Model than those with higher flow resistivities. This is accordant with anticipations because sand panels with
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 4. The absorption coefficient of Case 1.
1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 5. The absorption coefficient of Case 4.
lower flow resistivities are similar to (but still higher than) general porous materials in terms of flow resistivity.
3.2. Acoustic absorption with different thicknesses Case 1, 2 and 3, which have the same flow resistivity and no air space behind, are plotted in Fig. 9. Their thicknesses are 20 mm, 30 mm and 50 mm respectively. It can be seen that when the thickness of sand panels increases, the absorption will improve
244
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 6. The absorption coefficient of Case 5.
1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 7. The absorption coefficient of Case 6.
significantly at low frequencies while drop at frequencies around 2000 Hz. The absorption coefficient of 50 mm-thick sand panels (Case 3) stays above 0.6 at frequencies higher than 500 Hz, while the mean absorption coefficient and the NRC respectively increase by 0.07 and 0.08 compared with 20 mm-thick panels. In conclu-
sion, increasing thickness can enhance the general absorption of sand panels and also make them effective at wider bands. This is similar to the pattern observed with more conventional porous materials [31, pp. 249]. However, increasing thickness will
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 8. The absorption coefficient of Case 7.
1.0 Case 1 Case 2 Case 3
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 9. The absorption coefficient of cases with different thickness.
unavoidably cause heavier load and higher cost. Therefore, this method could be infeasible in some practical applications. The measurement data and predictions of Case 2 and 3 are respectively shown in Figs. 10 and 11. Together with Case 1
(Fig. 4), it can be seen that for sand panels with different thicknesses, Delany-Bazley Model is still more effective to provide estimations for the acoustic absorption than Voronina Model. It is also found that, when the thickness increases, the precision of predic-
246
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 10. The absorption coefficient of Case 2.
1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 11. The absorption coefficient of Case 3.
tions will decrease in terms of both the shape of frequency diagram and the general absorption (the mean absorption coefficient and the NRC).
3.3. Acoustic absorption with different air spaces Case 1, 1a and 1b are plotted in Fig. 12, in which the sand panels are the same but the thicknesses of the air spaces behind the panels are different (0 mm, 20 mm and 100 mm respectively). It can be seen that adding an air space is very effective in adjusting
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1.0 Case 1 Case 1a Case 1b
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 12. The absorption coefficient of cases with different air spaces.
1.0
Absorption Coefficient
0.8
Case 1b Case 4a Case 5a Case 6a Case 7a
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 13. The absorption coefficient of cases with the same air space but different flow resistivity.
the absorption of sand panels. With 100 mm air space behind (Case 1b), the sand panel becomes very effective in absorbing sound around 400 Hz (the absorption coefficient approaches 1). Moreover, its absorption coefficient stays larger than 0.5 at frequencies higher than 160 Hz, which makes it an efficient wide-band acoustic
absorber. The mean absorption coefficient and the NRC also respectively increase by 0.23 and 0.25 compared with sand panels without air space behind (Case 1). In case that there is no room for 100 mm air space, a much narrower air space is also found to be effective in adjusting the absorption. With only 20 mm air space
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behind (Case 1a), the first resonant frequency of the sand panel is moved to 800 Hz (where the absorption coefficient approaches 1), and the absorption coefficient stays larger than 0.5 at frequencies higher than 500 Hz. The mean absorption coefficient and the NRC also respectively increase by 0.11 and 0.15 compared with Case 1. Therefore, a 20 mm air space is already sufficient to acquire more effective and wider-band absorption of sand panels. In conclusion, air space is effective to adjust the shape of frequency diagram and improve the overall absorption of sand panels. Also this accords with existing knowledge of porous materials [31, pp. 251]. Fig. 13 presents the absorption of Case 1b, 4a, 5a, 6a and 7a. They all employ 20 mm-thick sand panels with 100 mm air space behind, but the flow resistivities of sand panels are different. Together with Fig. 3, it can be seen that each of the cases with 100 mm air space has better absorption at low- and mid- frequencies (especially around 400 Hz) compared with the corresponding case without air space behind. This further proves the effectiveness of air space in improving the absorption. It is also found that the improvements in the cases with lower flow resistivity (e.g., Case 1b, Case 4a) are much more significant than the cases with higher flow resistivity (e.g., Case 7a). Therefore, flow resistivity becomes a more important factor for the absorption of sand panels when there are air spaces behind, and panels with lower flow resistivity should be used with priority in order to acquire more effective absorption. 4. Conclusions Herein, the random-incidence absorption coefficients of sand panels with different flow resistivities, thicknesses, and air spaces are studied. The measured data are compared with the predictions provided by two existing models, and the precision of the predictions is analyzed. Several conclusions can be drawn from this research: (1) Sand panels manufactured from natural sands and inorganic solvent could serve as effective wide-band absorbers on the premise of proper choices of flow resistivity, thickness and air space. An average absorption coefficient over all frequencies of 0.66 and an NRC of 0.7 are reachable by sand panels according to the cases investigated in this research. (2) Flow resistivity, thickness and air space are influential for the absorption of sand panels. In order to acquire effective and wide-band absorption, adding an air space behind is recommended in priority. A 100 mm air space is capable to make the absorption coefficient of 20 mm sand panels stay above 0.5 at frequencies higher than 160 Hz, and a 20 mm air space is enough to make the absorption coefficient stay above 0.5 at frequencies higher than 500 Hz. Increasing thickness can also enhance the general absorption and widen the absorption bands, while the side effects of heavier load and higher cost are unavoidable. For the flow resistivity, lower values such as 49,300 or 92,450 N s/m4 are recommended, especially for cases with air spaces behind. (3) Delany-Bazley Model can provide a better fit for the acoustic absorption of sand panels than Voronina Model. Moreover, the predictions for sand panels with lower flow resistivities and smaller thicknesses are more accurate than those with
higher flow resistivities and larger thicknesses. Prediction methods that are more accurate and applicable for sand panels with air spaces behind will be investigated in the near future.
References [1] Delany ME, Bazley EN. Acoustical properties of fibrous absorbent materials. Appl Acoust 1970;3(2):105–16. [2] Chu RKM, Naguib HE, Atalla N. Synthesis and characterization of open cell foams for sound absorption with rotational molding method. Polym Eng Sci 2009;49(9):1744–54. [3] Fouladi MH, Ayub M, Nor MJM. Analysis of coir fiber acoustical characteristics. Appl Acoust 2011;72(1):35–42. [4] Kirby R. On the modification of Delany and Bazley fomulae. Appl Acoust 2014;86:47–9. [5] Cummings A, Beadle SP. Acoustic properties of reticulated plastic foams. J Sound Vib 1994;175(1):115–33. [6] Garai M, Pompoli F. A simple empirical model of polyester fibre materials for acoustical applications. Appl Acoust 2005;66(12):1383–98. [7] Johnson DL, Koplik J, Dashen R. Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J Fluid Mech 1987;176:379–402. [8] Allard JF. Propagation of sound in porous media. Elsevier Applied Science; 1993. [9] Biot MA. Theory of propagation of elastic waves in a fluid saturated porous solid. I. Low frequency range. J Acoust Soc Am 1956;28(2):168–78. [10] Biot MA. Theory of propagation of elastic waves in a fluid saturated porous solid. II. Higher frequency range. J Acoust Soc Am 1956;28(2):179–91. [11] Voronina NN, Horoshenkov KV. A new empirical model for the acoustic properties of loose granular media. Appl Acoust 2003;64(4):415–32 (2004). [12] Venegas R, Umnova O. Acoustical properties of double porosity granular materials. J Acoust Soc Am 2011;130(5):2765–76. [13] Zhou H, Li B, Huang G. Sound absorption characteristics of polymer microparticles. J Appl Polym Sci 2006;101(4):2675–9. [14] Horoshenkov KV, Swift MJ. The acoustic properties of granular materials with pore size distribution close to log-normal. J Acoust Soc Am 2001;110 (5):2371–8. [15] Leclaire P, Swift MJ, Horoshenkov KV. Determining the specific area of porous acoustic materials from water extraction data. J Appl Phys 1998;84 (12):6886–90. [16] Attenborough K. Acoustical characteristics of rigid fibrous absorbents and granular materials. J Acoust Soc Am 1983;73(3):785–99. [17] Attenborough K. Models for the acoustical properties of air-saturated granular media. Acta Acúst 1993;1:213–26. [18] Swift MJ, Bris P, Horoshenkov KV. Acoustic absorption in re-cycled rubber granulate. Appl Acoust 1999;57(3):203–12. [19] Pfretzschner J, Rodriguez RM. Acoustic properties of rubber crumbs. Polym Testing 1999;18(2):81–92. [20] Horoshenkov KV, Swift MJ. The effect of consolidation on the acoustic properties of loose rubber granulates. Appl Acoust 2001;62(6):665–90. [21] Hong Z, Bo L, Guangsu H. A novel composite sound absorber with recycled rubber particles. J Sound Vib 2007;304(1):400–6. [22] Asdrubali F, Horoshenkov KV. The acoustic properties of expanded clay granulates. Build Acoust 2002;9(2):85–98. [23] Vašina M, Hughes DC, Horoshenkov KV. The acoustical properties of consolidated expanded clay granulates. Appl Acoust 2006;67(8):787–96. [24] Cuiyun D, Guang C, Xinbang X. Sound absorption characteristics of a hightemperature sintering porous ceramic material. Appl Acoust 2012;73 (9):865–71. [25] ISO. Acoustics: materials for acoustical applications: determination of airflow resistance. ISO 9053-1991. [26] Washburn EW, Bunting EN. Porosity: VI. Determination of porosity by the method of gas expansion. J Am Ceram Soc 1922;5(2):112–30. [27] Dullien FAL. Porous media. Fluid transport and pore structure. Academic Press; 1992. [28] ISO. Acoustics: measurement of sound absorption in a reverberation room. ISO 354-2003. [29] Long M. Architectural acoustics. 2nd ed. Amsterdam: Elsevier; 2014. [30] Kuttruff H. Room acoustics. Oxon: Spon Press; 2009. [31] Beranek LL, Ver IL. Noise and vibration control engineering: principles and applications. John Wiley; 1992.
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Technical note
An experimental study on the acoustic absorption of sand panels Lu Shuai a, Xu Weiguo a,b, Chen Yuxiao a, Yan Xiang a,b,⇑ a b
School of Architecture, Tsinghua University, Beijing 100084, PR China Key Laboratory of Urban-Rural Eco Planning and Green Building, Ministry of Education, Tsinghua University, PR China
a r t i c l e
i n f o
Article history: Received 30 July 2016 Received in revised form 1 September 2016 Accepted 1 September 2016
Keywords: Sand panels Acoustic absorption Flow resistivity Delany-Bazley Model Voronina Model
a b s t r a c t Potentially sand panels could be used as novel sound absorbing materials that are fire resistant, environmentally friendly, mechanically strong and have good durability. However, the performance of sand panels as sound absorbers has not yet been studied. Results of measurements in a reverberation chamber of the random-incidence absorption coefficients of 13 different sand panel compositions and configurations with air gaps are reported. Also the flow resistivities and bulk densities have been measured. The results prove that sand panels could offer effective and wide-band acoustic absorption. As is the case with conventional sound absorbing materials, adding an air space is found to be the most effective way to widen the absorption bands and improve the overall absorption. Comparisons of the measured sand panel absorption data with predictions of the Delany and Bazley and Voronina models reveal that, while neither model is very accurate, the former gives more accurate predictions especially for sand panels with lower flow resistivity and smaller thickness. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Research background As undesirable noise has been regarded as a severe problem for the environment and public health, sound absorption materials are widely used nowadays in many indoor and outdoor occasions. Therefore, materials with effective absorption and other virtues like fire resistance, environmental harmlessness and low cost are in large demand. Sand panels are an innovative class of absorption materials developed in recent years. They are made out of natural sands with inorganic silicon-based solvent by relatively simple manufacturing process. Test data has shown that sand panels are fire resistant, environment friendly, mechanically strong and with good durability in severe environments (Table 1). These are significant advantages of sand panels over traditional sound absorption materials such as glass wool or rock wool. Compared to metallic absorption materials like aluminum foams or micro-perforated steel plates, sand panels are far more economical since their main ingredient is widely-distributed and easily-acquired sands. Moreover, the finishing of sand panels can be in different colors and with different natural textures (Fig. 1). They could also be made into curved shapes. As a result, sand panels have already been used ⇑ Corresponding author at: School of Architecture, Tsinghua University, Beijing 100084, PR China. E-mail address: [email protected] (X. Yan). http://dx.doi.org/10.1016/j.apacoust.2016.09.002 0003-682X/Ó 2016 Elsevier Ltd. All rights reserved.
in many projects in recent years (Fig. 2, the projects shown here are designed by the Building Acoustic Lab of Tsinghua University). However, there is no existing research that reports the sound absorption characteristics that sand panels can offer with different values of material parameters (flow resistivity, thickness, etc.). This lack of knowledge makes it difficult to obtain sand panels with desirable absorption coefficients for specific requirements, and thus significantly affects the application of this material. This paper seeks to address this problem. 1.2. State of the art The sound absorption of materials is a topic that has been long studied. Delany and Bazley [1] investigated fibrous porous materials and provided a simple empirical model to predict the characteristic impedance and propagation coefficient based on flow resistivity. This model has been widely used for a long time because of its simplicity and good precision [2,3]. However, it is found to have the drawbacks of working well only for a limited variety of materials and being inaccurate for low frequencies due to its non-physical nature [4]. Some researchers have sought to modify the Delany and Bazley Model so that it could provide better fits for other specific materials [5,6]. Johnson et al. [7] and Allard [8] formulated a mathematical model to describe the propagation and absorption of sound in fluid-saturated porous materials based on Biot’s research [9,10]. This model has a better accuracy but needs more parameters. Compared to typical porous materials,
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Table 1 Physical characteristics of a typical simple of sand panel. Size 600 ⁄ 600 ⁄ 20 mm Tensile strength 13.3 Mpa
Density
Fire-resistance 3
3
1.51 ⁄ 10 kg/m Bending strength 24.7 MPa
TVOC (Total Volatile Organic Compounds) 3
Non-combustible Impact strength 15.6 kJ/m2
0.062 mg/m h Percentage of moisture expansion 0.16%
Compressive strength 29.1 Mpa Frost test (25 cycles) No wrecking occurred
Note: The test sample is manufactured by the Building Acoustic Lab of Tsinghua University. The fire-resistance is tested by the Tianjin Fire Research and Testing Center of the Ministry of Public Safety of the PR China. Other tests are conducted by the National Building Material Testing Center of the PR China.
(a) Sand panels with different colors
(b) Sand panels with different natural textures
(c) Sand panels made of large particles
(d) Sand panels made of small particles
Fig. 1. The appearance (a, b) and microstructure (c, d) of sand panels.
(a) The ceiling and columns are sand panels
(b) The ceiling is sand panels
Fig. 2. A dining hall (a) and a lecture hall (b) that applied sand panels.
the porosity of sand panels is much lower and the flow resistivity is much higher (detail information in Section 2.1). Therefore, whether sand panels share similar patterns of sound absorption with fibrous porous materials still needs to be tested. Besides porous materials, there are also many researches that investigated the acoustic characteristics of granular materials, which have more similar microstructures to sand panels. Voronina and Horoshenkov [11] studied granular materials based on experimental data and developed a model that can predict their acoustic features using
flow resistivity, porosity, tortuosity and structural characteristic. However, the predictive power of this semi-phenomenological model is found to be limited [12]. Moreover, the model is acquired from the data of only four kinds of granular materials (vermiculite, granulated rubber, perlite and granulated nitrile foam), and is found to be ineffective to predict the acoustic characteristics of polyurethane particles [13]. Therefore, whether this model is applicable to other materials like sand panels needs to be investigated. Horoshenkov and Swift [14] raised another model for granular
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materials, and the model was found to be effective to predict the acoustic characteristics of a similar material to sand panels (Coustone, a material made from flint particles consolidated with rubber-epoxy blinder). However, this model cannot be employed here, because the facility for measuring the pore size distribution (a water suction system [15]) is not available in the institute of the authors. Similar models regarding granular materials were also provided by Attenborough [16,17], but sand panels were not included in them either. In this research, the model of porous materials raised by Delany and Bazley (referred to as DelanyBazley Model) and the model of granular materials raised by Voronina (referred to as Voronina Model) are adopted to compare with the measurement data of sand panels, in order to investigate whether two existing models can provide reliable predictions for the acoustic absorption of sand panels. There are also many researches that revealed the acoustic absorption characteristics of a specific kind of materials. Swift et al. [18], Pfretzschner and Rodriguez [19], Horoshenkov and Swift [20] and Hong et al. [21] studied the acoustic absorption of rubber particle materials, uncovered the factors that are influential for absorption, or measured acoustical properties of specialcomposited rubber materials based on experimental data. Asdrubali and Horoshenkov [22] and Vasina et al. [23] investigated the acoustic feature of materials composed of expanded clay granules. Zhou et al. [13] studied the acoustic absorptions of polyurethane particles. And Cuiyun et al. [24] explored the absorption characteristics of sintering ceramic material, etc. However, there is no existing research that specifically devotes to the acoustic properties of sand panels found in archival publications, and this is the blank that this research aims to fill in. 1.3. Objective of this research
particles are well mixed with inorganic silicon-based solvent, and then poured into moulds. Finally, after about 15 min at room temperature, sand particles are aggregated together and sand panels are produced. In the research, 13 cases are investigated and 7 kinds of sand panels are involved. Their physical properties are presented in Table 2. The flow resistivity was measured by the direct airflow method introduced in ISO 9053-1991 [25]. A pressure depression system of the water reservoir was employed to produce airflow. For each kind of sand panels, three samples were made and three specimens were taken from each of the samples. The measurements of all the nine specimens were averaged. All the samples are with a diameter of 100 mm and a thickness of 20 mm. The bulk density was determined by its definition. The bulk volume of one piece of sand panel was known from its mold, and the mass was measured by weighing. The bulk density was calculated from dividing its mass by its bulk volume. The calculations of three specimens were averaged. The porosity was measured by the gas expansion method [26,27]. Two vessels of the same volume, one with a piece of sand panel inside and the other without, were pumped with the same amount of air. The air pressures of the two vessels were measured respectively, and then the effective volume of the pores in the sand panel was calculated according to the ideal gas law. Finally, the porosity was calculated from dividing the effective volume of the pores by the bulk volume. Similarly, the calculations of three specimens were averaged. It is found that samples made out of larger particles had smaller flow resistivity. However, the bulk densities of different samples are distributed within a very narrow range around 1.5 ⁄ 103 kg/m3, and the porosities of all samples are around 0.43 regardless of the dimensions of particles. 2.2. Sound absorption measurement
This research is an experiment-based investigation on the absorption characteristics of sand panels, and specifically pursues two goals: (1) to uncover the acoustic absorption characteristics that sand panels can offer with different values of material parameters; (2) to verify if existing models can provide reliable predictions for the acoustic absorption of sand panels. 2. Methodology 2.1. Manufacture of sand panel samples The samples of sand panels used in this research are manufactured in a process consisting of three stages. First, natural sands are sifted with meshes of different sizes, thus sand particles with dimensions in a certain range can be acquired. Second, sifted sand
The absorption coefficients of all samples are respectively measured in a reverberation chamber following ISO 354-2003 [28]. The volume of the reverberation chamber is 202 m3, and the area of each specimen is 10 m2. The frequency range of the measured absorption coefficients is 100–5000 Hz at 1/3 octave bands. As a nature of the reverberation chamber method, the absorption coefficient in this research refers to diffuse-field absorption coefficient instead of normal-incident absorption coefficient. For most architectural and environmental applications, the diffuse-field absorption coefficient is more practical [29, pp. 254]. The random-incidence absorption coefficient is also used as the basis for testing the adequacy of Delany-Bazley Model and Voronina Model for sand panels. Although the characteristic impedance and propagation constant measured by the impedance tube are more sensitive for testing the adequacy of models theoretically, using the
Table 2 Physical properties of the test samples in this research. Case no.
Characteristic particle size (mm)
Bulk density (kg/m3)
Porosity (%)
Flow resistivity (N s/m4)
Sand panel thickness (mm)
Air space thickness (mm)
1 2 3 4 5 6 7 1a 1b 4a 5a 6a 7a
0.30 0.30 0.30 0.59 0.27 0.23 0.19 0.30 0.30 0.59 0.27 0.23 0.19
1.51 ⁄ 103 1.51 ⁄ 103 1.51 ⁄ 103 1.53 ⁄ 103 1.50 ⁄ 103 1.49 ⁄ 103 1.49 ⁄ 103 1.51 ⁄ 103 1.51 ⁄ 103 1.53 ⁄ 103 1.50 ⁄ 103 1.49 ⁄ 103 1.49 ⁄ 103
43.0 43.0 43.0 42.3 43.4 43.8 43.8 43.0 43.0 42.3 43.4 43.8 43.8
92,450 92,450 92,450 49,300 135,100 210,500 274,500 92,450 92,450 49,300 135,100 210,500 274,500
20 30 50 20 20 20 20 20 20 20 20 20 20
0 0 0 0 0 0 0 20 100 100 100 100 100
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random-incidence absorption coefficient as the basis is more intuitive practically. It allows an easier understanding about how accurate the predictions for the acoustic absorption of sand panels could be. Another important reason for giving up the impedance tube method is that it is only applicable to locally reacting absorber, while sand panels with non-partitioned air spaces behind (Case 1a, 1b, 4a, 5a, 6a, 7a) are typical non-locally reacting absorbers that are only measurable by the reverberation chamber method [30].
where n is a dimensionless parameter, q is the tortuosity, k is the wave number in air, and Q is the structural characteristics. c0 is the sound velocity in air in m/s, l is the dynamic viscosity of air in N s/m2, while f is the frequency in Hz. With Eqs. (5)–(11), the characteristic impedance Z0 = R + jX and the propagation coefficient c = a + jb can be predicted by:
2.3. Prediction models (1) Delany-Bazley Model
R ¼ 1 þ Q; if f < f cr
ð12Þ
Or R ¼ q=H; if f P f cr
ð13Þ
X ¼ Q H=ð1 þ CÞ
ð14Þ
a ¼ k Q H=ð1 þ AÞ
ð15Þ
b ¼ k ½1 þ Q H ð1 þ BÞ
ð16Þ
Delany and Bazley presented an empirical model for estimating the properties of porous materials. The characteristic impedance Z0 = R + jX and the propagation coefficient c = a + jb can be predicted by [1]:
where coefficients A, B, C and the transition frequency fcr are defined as:
R ¼ q0 c0 1 þ 9:08
A¼
"
" X ¼ q0 c0 ð11:9Þ
0:75 # f
r 0:73 # f
r
0:59 x f a ¼ 10:3 c0 r b¼
x c0
" 1 þ 10:8
0:70 # f
r
ð1Þ
ð2Þ
In the model that Voronina raised [11], several physical parameters are required to predict the properties of granular materials:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D ¼ V g =0:5233
ð5Þ
H ¼ 1 qm =qg
ð6Þ
M¼
103 q0
D q0 c0
l
ð7Þ
ð8Þ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1H q¼ 1þ 2H
ð9Þ
2pf c0
ð10Þ
k¼
1H C ¼ pffiffiffiffi Q
ð19Þ
200 l ð1 HÞ2 ð1 þ HÞ4
p q0 D2 ðq HÞ2
ð20Þ
(3) Calculation of the diffuse-field absorption coefficient Both the Delany-Bazley Model and the Voronina Model provide predictions for the characteristic impedance (Z0) and the propagation coefficient (c), and they can be converted to the diffuse-field absorption coefficient in order to compare with the measurement data acquired in the reverberation chamber [29, pp. 253–254]:
Z ¼ Z 0 cothðc LÞ
ð21Þ
Z cos h q0 c0 2 ah ¼ 1 Z cos h þ q0 c0
ð22Þ
Z
p=2
a¼2 0
where D is the characteristic dimension of particles in mm, H is the porosity, and M is a dimensionless parameter. Vg is the number of particles in a unit volume. qm is the density of the granular material, qg is the density of the grain material, while q0 is the air density (all in kg/m3). Based on Eqs. (5)–(7), more parameters can be calculated:
n¼
ð18Þ
f cr ¼ ð4Þ
ð17Þ
1 B ¼ pffiffiffiffi Q ð1 þ HÞ ð1 þ Q 2 MÞ
ð3Þ
where q0 is the air density in kg/m3, c0 is sound velocity in air in m/s, r is the flow resistivity in g/(s cm3) (i.e., 1000 N s/m4), f is the frequency in Hz and is related to x by x = 2pf, while j is the imaginary unit. (2) Voronina Model
qg
ð1 HÞ M 1þQ
ah sin h cos h dh
ð23Þ
where Z is the impedance of a rigidly-backed material layer with finite thickness of L (in m). ah is the absorption coefficient at the incident angle of h, while a is the diffuse-field absorption coefficient. 3. Results and analysis The measurement data is presented in Table 3. Among all 13 test cases, the average value of the mean absorption coefficient over all frequencies is 0.49, and the average noise reduction coefficient (NRC) is 0.51. For cases without and with air space behind, the average values of the mean absorption coefficient over all frequencies are 0.43 and 0.54 respectively, with the mean NRC of 0.46 and 0.57. The highest value of the mean absorption coefficient over all frequencies is 0.66 (Case 1b), while the highest NRC is 0.7 (Case 1b and Case 4a). 3.1. Acoustic absorption with different flow resistivities
0:2 ð1 HÞ ð1 þ HÞ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q¼ H kDn
ð11Þ
Five cases with the same thickness and no air space behind are plotted in Fig. 3. The flow resistivities of Case 4, 1, 5, 6 and 7 increase from 49,300 N s/m4 to 274,500 N s/m4. It can be seen that
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Table 3 Measurement data of the test cases in this research. Frequency (Hz)
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
Mean
NRC
Case Case Case Case Case Case Case Case Case Case Case Case Case
0.05 0.03 0.02 0.02 0.06 0.00 0.00 0.11 0.29 0.15 0.27 0.15 0.05
0.03 0.05 0.05 0.00 0.04 0.03 0.00 0.12 0.38 0.20 0.47 0.22 0.00
0.03 0.04 0.04 0.00 0.01 0.00 0.00 0.18 0.51 0.23 0.35 0.32 0.14
0.01 0.07 0.12 0.06 0.07 0.03 0.01 0.16 0.56 0.43 0.43 0.35 0.30
0.03 0.12 0.17 0.07 0.07 0.08 0.10 0.19 0.60 0.65 0.45 0.43 0.39
0.08 0.23 0.31 0.07 0.12 0.12 0.23 0.29 0.77 0.71 0.51 0.46 0.38
0.12 0.26 0.44 0.11 0.22 0.13 0.27 0.46 0.97 0.82 0.54 0.55 0.43
0.18 0.36 0.58 0.17 0.32 0.26 0.36 0.65 0.90 0.83 0.54 0.50 0.45
0.28 0.50 0.66 0.28 0.44 0.31 0.40 0.82 0.85 0.88 0.62 0.54 0.40
0.38 0.63 0.65 0.37 0.54 0.49 0.44 0.96 0.85 0.83 0.49 0.51 0.35
0.59 0.72 0.62 0.53 0.63 0.54 0.50 0.93 0.72 0.73 0.48 0.49 0.33
0.79 0.78 0.67 0.79 0.73 0.71 0.50 0.82 0.64 0.69 0.47 0.52 0.42
0.95 0.79 0.63 0.86 0.75 0.75 0.53 0.77 0.58 0.57 0.53 0.51 0.50
0.99 0.86 0.73 0.99 0.81 0.69 0.55 0.67 0.60 0.59 0.62 0.58 0.48
0.90 0.79 0.72 0.93 0.67 0.76 0.59 0.62 0.55 0.67 0.68 0.62 0.56
0.83 0.78 0.77 0.81 0.80 0.67 0.58 0.56 0.62 0.69 0.73 0.69 0.61
0.79 0.81 0.86 0.81 0.87 0.79 0.57 0.70 0.72 0.80 0.79 0.80 0.58
0.79 0.86 0.93 0.85 0.87 0.71 0.70 0.79 0.82 0.83 0.83 0.74 0.60
0.43 0.48 0.50 0.43 0.45 0.39 0.35 0.54 0.66 0.63 0.54 0.50 0.39
0.45 0.50 0.55 0.45 0.45 0.40 0.40 0.60 0.70 0.70 0.50 0.50 0.40
1 2 3 4 5 6 7 1a 1b 4a 5a 6a 7a
1.0
Absorption Coefficient
0.8
Case 1 Case 4 Case 5 Case 6 Case 7
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 3. The absorption coefficient of cases with different flow resistivity.
sand panels with lower flow resistivities (e.g., Case 1 and Case 4) have effective absorption at high frequencies, and the absorption coefficient approaches 1 at 2000 Hz. At low frequencies, however, the absorption effectiveness is poor and the absorption coefficient stays below 0.2 at frequencies lower than 500 Hz. If the flow resistivity increases (e.g., Case 7), the absorption will improve at lower frequencies but the improvement is rather limited (still below 0.4 at 500 Hz). Moreover, the absorption will drop more significantly at high frequencies (below 0.6 at 2000 Hz), while the mean absorption coefficient over all frequencies and the NRC will also drop for about 0.1. In other words, the overall absorption of sand panels will get weaker if the flow resistivity increases. This is accordant with the common knowledge of porous materials. As a result, sand panels with lower flow resistivity are normally preferred to acquire better absorption properties. The measurement data and predictions of Case 1, 4, 5, 6 and 7 are respectively shown in Figs. 4–8. It can be seen that for sand panels with low flow resistivity (Case 4), both Delany-Bazley Model and Voronina Model can provide predictions with good accuracy. The
maximal errors of both models are below 0.2 over all frequencies. When the flow resistivity increases (Case 1 and Case 5), Delany-Bazley Model can still provide rather precise predictions, while estimations provided by Voronina Model turn inaccurate and cannot imitate the shape of the frequency diagram well. For the cases of high flow resistivities (Case 6 and Case 7), the prediction of each model approaches a straight line and cannot reflect the characteristics of the frequency diagrams of sand panels at all. In conclusion, Delany-Bazley Model can provide a better fit for sand panels than Voronina Model. This is an unexpected result because sand panels are more similar to granular materials instead of porous materials in terms of material nature. A possible explanation is that the materials that Voronina Model was derived from (vermiculite, granulated rubber, perlite and granulated nitrile foam) have larger particle sizes (0.4–3.5 mm) than sand panels (0.19–0.59 mm), so the patterns of absorption differ significantly. Another outcome is that sand panels with lower flow resistivities can be better predicted by Delany-Bazley Model than those with higher flow resistivities. This is accordant with anticipations because sand panels with
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 4. The absorption coefficient of Case 1.
1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
0.4
0.2
0.0 100
125
160
200
250
315
400
500
630
800
1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 5. The absorption coefficient of Case 4.
lower flow resistivities are similar to (but still higher than) general porous materials in terms of flow resistivity.
3.2. Acoustic absorption with different thicknesses Case 1, 2 and 3, which have the same flow resistivity and no air space behind, are plotted in Fig. 9. Their thicknesses are 20 mm, 30 mm and 50 mm respectively. It can be seen that when the thickness of sand panels increases, the absorption will improve
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
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Frequency (Hz) Fig. 6. The absorption coefficient of Case 5.
1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
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0.2
0.0 100
125
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Frequency (Hz) Fig. 7. The absorption coefficient of Case 6.
significantly at low frequencies while drop at frequencies around 2000 Hz. The absorption coefficient of 50 mm-thick sand panels (Case 3) stays above 0.6 at frequencies higher than 500 Hz, while the mean absorption coefficient and the NRC respectively increase by 0.07 and 0.08 compared with 20 mm-thick panels. In conclu-
sion, increasing thickness can enhance the general absorption of sand panels and also make them effective at wider bands. This is similar to the pattern observed with more conventional porous materials [31, pp. 249]. However, increasing thickness will
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
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Frequency (Hz) Fig. 8. The absorption coefficient of Case 7.
1.0 Case 1 Case 2 Case 3
Absorption Coefficient
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0.4
0.2
0.0 100
125
160
200
250
315
400
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630
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1000 1250 1600 2000 2500 3150 4000 5000 Mean NRC
Frequency (Hz) Fig. 9. The absorption coefficient of cases with different thickness.
unavoidably cause heavier load and higher cost. Therefore, this method could be infeasible in some practical applications. The measurement data and predictions of Case 2 and 3 are respectively shown in Figs. 10 and 11. Together with Case 1
(Fig. 4), it can be seen that for sand panels with different thicknesses, Delany-Bazley Model is still more effective to provide estimations for the acoustic absorption than Voronina Model. It is also found that, when the thickness increases, the precision of predic-
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1.0 Measurement Model of Delany Model of Voronina
Absorption Coefficient
0.8
0.6
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Frequency (Hz) Fig. 10. The absorption coefficient of Case 2.
1.0 Measurement Model of Delany Model of Voronina
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Frequency (Hz) Fig. 11. The absorption coefficient of Case 3.
tions will decrease in terms of both the shape of frequency diagram and the general absorption (the mean absorption coefficient and the NRC).
3.3. Acoustic absorption with different air spaces Case 1, 1a and 1b are plotted in Fig. 12, in which the sand panels are the same but the thicknesses of the air spaces behind the panels are different (0 mm, 20 mm and 100 mm respectively). It can be seen that adding an air space is very effective in adjusting
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1.0 Case 1 Case 1a Case 1b
Absorption Coefficient
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Frequency (Hz) Fig. 12. The absorption coefficient of cases with different air spaces.
1.0
Absorption Coefficient
0.8
Case 1b Case 4a Case 5a Case 6a Case 7a
0.6
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Frequency (Hz) Fig. 13. The absorption coefficient of cases with the same air space but different flow resistivity.
the absorption of sand panels. With 100 mm air space behind (Case 1b), the sand panel becomes very effective in absorbing sound around 400 Hz (the absorption coefficient approaches 1). Moreover, its absorption coefficient stays larger than 0.5 at frequencies higher than 160 Hz, which makes it an efficient wide-band acoustic
absorber. The mean absorption coefficient and the NRC also respectively increase by 0.23 and 0.25 compared with sand panels without air space behind (Case 1). In case that there is no room for 100 mm air space, a much narrower air space is also found to be effective in adjusting the absorption. With only 20 mm air space
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behind (Case 1a), the first resonant frequency of the sand panel is moved to 800 Hz (where the absorption coefficient approaches 1), and the absorption coefficient stays larger than 0.5 at frequencies higher than 500 Hz. The mean absorption coefficient and the NRC also respectively increase by 0.11 and 0.15 compared with Case 1. Therefore, a 20 mm air space is already sufficient to acquire more effective and wider-band absorption of sand panels. In conclusion, air space is effective to adjust the shape of frequency diagram and improve the overall absorption of sand panels. Also this accords with existing knowledge of porous materials [31, pp. 251]. Fig. 13 presents the absorption of Case 1b, 4a, 5a, 6a and 7a. They all employ 20 mm-thick sand panels with 100 mm air space behind, but the flow resistivities of sand panels are different. Together with Fig. 3, it can be seen that each of the cases with 100 mm air space has better absorption at low- and mid- frequencies (especially around 400 Hz) compared with the corresponding case without air space behind. This further proves the effectiveness of air space in improving the absorption. It is also found that the improvements in the cases with lower flow resistivity (e.g., Case 1b, Case 4a) are much more significant than the cases with higher flow resistivity (e.g., Case 7a). Therefore, flow resistivity becomes a more important factor for the absorption of sand panels when there are air spaces behind, and panels with lower flow resistivity should be used with priority in order to acquire more effective absorption. 4. Conclusions Herein, the random-incidence absorption coefficients of sand panels with different flow resistivities, thicknesses, and air spaces are studied. The measured data are compared with the predictions provided by two existing models, and the precision of the predictions is analyzed. Several conclusions can be drawn from this research: (1) Sand panels manufactured from natural sands and inorganic solvent could serve as effective wide-band absorbers on the premise of proper choices of flow resistivity, thickness and air space. An average absorption coefficient over all frequencies of 0.66 and an NRC of 0.7 are reachable by sand panels according to the cases investigated in this research. (2) Flow resistivity, thickness and air space are influential for the absorption of sand panels. In order to acquire effective and wide-band absorption, adding an air space behind is recommended in priority. A 100 mm air space is capable to make the absorption coefficient of 20 mm sand panels stay above 0.5 at frequencies higher than 160 Hz, and a 20 mm air space is enough to make the absorption coefficient stay above 0.5 at frequencies higher than 500 Hz. Increasing thickness can also enhance the general absorption and widen the absorption bands, while the side effects of heavier load and higher cost are unavoidable. For the flow resistivity, lower values such as 49,300 or 92,450 N s/m4 are recommended, especially for cases with air spaces behind. (3) Delany-Bazley Model can provide a better fit for the acoustic absorption of sand panels than Voronina Model. Moreover, the predictions for sand panels with lower flow resistivities and smaller thicknesses are more accurate than those with
higher flow resistivities and larger thicknesses. Prediction methods that are more accurate and applicable for sand panels with air spaces behind will be investigated in the near future.
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