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Characterization of Sheep Wool as a Sustainable Material for Acoustic Applications Romina del Rey 1, * 1 2

*

ID

, Antonio Uris 2 , Jesús Alba 1

ID

and Pilar Candelas 2

Centro de Tecnologías Físicas, Universitat Politècnica de València, EPS Gandia, C/Paraninf, 1, 46730 Grao de Gandia, Valencia, Spain; [email protected] Centro de Tecnologías Físicas, Universitat Politècnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain; [email protected] (A.U.); [email protected] (P.C.) Correspondence: [email protected]; Tel.: +34-962849302

Received: 29 September 2017; Accepted: 3 November 2017; Published: 7 November 2017

Abstract: In recent years, natural materials are becoming a valid alternative to traditional sound absorbers due to reduced production costs and environmental protection. This paper reports the acoustical characterization of sheep wool. Measurements on normal incidence and diffuse-incidence sound absorption coefficients of different samples are reported. The airflow resistance has also been measured. The results prove that sheep wool has a comparable sound absorption performance to that of mineral wool or recycled polyurethane foam. An empirical model is used to calculate the sound absorption of sheep wool samples. A reasonable agreement on the acoustic absorption of all sheep wool samples is obtained. Keywords: natural material; sound absorption; flow resistance; sheep wool; delany-bazley model

1. Introduction In conventional construction, most of the materials used respect little or do not respect at all the environment, since they require high energy expenditure for their extraction, transport, and transformation. In addition, they incorporate chemicals that can be detrimental to human health into materials to improve their technical characteristics. At present, the demand for a more sustainable construction has gone from being a matter of personal choice to being a regulated sector in order to implement measures that improve the environmental behavior of infrastructures and buildings. Construction activity is a great consumer of natural resources. Buildings continue to be a direct cause of pollution after they have been built due to their emissions and their impact on territory. Sustainable construction takes into account the consumption of resources, the environmental impact it produces, and the specific risks to human health. Thus, ecological materials must be natural, renewable, and durable, and they must have a low environmental impact for their manufacture, placement, and maintenance. In recent years, the development of new renewable materials has focused the attention of the research community. The origin of these materials can be vegetable or animal so their manufacture has a low environmental impact due to the energy saved in the production process. Several papers focused their investigations on thermal insulation [1–8]. Other authors have studied natural fibers for acoustic applications [9–17]. This paper describes the work carried out as part of the BIAEFIREMAT project to develop a new eco-materials and sustainable constructive solutions based on the use of waste and renewable raw materials. It is based on the fact that sheep wool is an excellent natural material, with very good characteristics for thermal insulation, moisture management, and sound absorption. However, due to their natural origin, the homogeneity of the fibers is not controlled and each hair or wool fiber can come

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from different sheep, breeds, or skin areas. It is intended to convert residues of sheep wool into new materials with acoustic applications both in both architectural and environmental acoustics. acoustics. The sheepskin new materials with acoustic applications in architectural and environmental The generates wool fiberswool that fibers are used make materials. These materials could be sheepskinwell-known generates well-known thattoare usednatural to make natural materials. These materials substitutes of others of more aggressive with the environment. could be substitutes others more aggressive with the environment. The aim of this this paper paper is is to to examine examinethe theairflow airflowresistance resistanceand andsound soundabsorption absorptioncoefficient coefficientofofa anatural naturaland andrenewable renewablematerial materialsuch suchasassheep sheepwool woolas asan an alternative alternative to to classical classical sound sound absorbers. absorbers. The sound absorption capabilities of the sheep wool presented in this paper were measured in an impedance tube and in aa reverberation reverberation chamber. chamber. The sound absorption coefficient has also been calculated by using an empirical model. model. 2. 2. Recall Recall of of the the Sheep Sheep Wool Wool Fiber Fiber Characteristics Characteristics and and the the Manufacturing Manufacturing Process Process Sheep Sheep wool wool comes comes in in the the form form of of aa corrugated corrugated fiber fiber having having aa diameter diameter of of 16 16 to to 40 40 µm μm and and aa total total length of 35–350 mm. Figure 1 shows electronic microscope details of sheep wool fibers. A sheep wool length of 35–350 mm. Figure 1 shows electronic microscope details of sheep wool fibers. A sheep wool fiber fiber of of 16 16 µm μm would would have have aa size size similar similar to to mineral mineral fibers. fibers. A A 33–36 33–36 µm μm sheep sheep wool wool fiber fiber would would be be roughly the same size as PET polyester fibers (33 µm) [18] or Kenaf fibers (36 µm) [19]. Unlike synthetic roughly the same size as PET polyester fibers (33 μm) [18] or Kenaf fibers (36 μm) [19]. Unlike fibers, sheep fibers do not have fixedhave thickness. thickness range has a standard of synthetic fibers, sheep fibers doa not a fixedTheir thickness. Their thickness range hasdeviation a standard 2deviation µm, according to the consulted scientific works [20]. Theworks fiber diameter the depends breed of of 2 μm, according to the consulted scientific [20]. The also fiberdepends diameteronalso the sheep. Merina is the predominant breed in Spain. In the Merina and related breeds, the is on the breed of the sheep. Merina is the predominant breed in Spain. In the Merina and relatedfleece breeds, closed and the wool has no brightness and presents variable uniformity: 60–80 mm length, 18–20 µm the fleece is closed and the wool has no brightness and presents variable uniformity: 60–80 mm fineness, of 100 mm. The wash performance after shearing to remove natural impurities length, 18and –20 ripple μm fineness, and ripple of 100 mm. The wash performance after shearing to remove such as remains of vegetation, urine, and above all grease was 38–42%. It is considered fine fiber. natural impurities such as remains of vegetation, urine, and above all grease was 38a–42%. It is A priori, it would be comparable to mineral fibers such as fiberglass, and studies of this type of wool considered a fine fiber. A priori, it would be comparable to mineral fibers such as fiberglass, and should focus on the same applications. This is the best quality sheep wool. studies of this type of wool should focus on the same applications. This is the best quality sheep wool.

(a)

(b)

Figure 1. Electronic microscope details of sheep wool fibers. (a) 200 μm rank; (b) 50 μm rank. Figure 1. Electronic microscope details of sheep wool fibers. (a) 200 µm rank; (b) 50 µm rank.

Another type of ovine breed is known as Entrefino group. These are of wide geographic Another of ovineproductive breed is known as Entrefino group. of main wide geographic diffusion diffusion andtype of varied orientation. When first These bred, are their objective was wool and of varied productive orientation. When first bred, their main objective was wool production, production, but today, production has been diversified with meat-wool or meat-milk-wool but today, production has have beena diversified meat-wool or The meat-milk-wool exploitations. exploitations. These animals semi-closedwith medium-size fleece. wool is characterized by its These animals have a semi-closed medium-size fleece. The wool is characterized by varying brightness, variable uniformity, 70–80 mm length, 28–30 μm fineness, ripple of its 40–varying 60 mm, brightness, variable 28–30would µm fineness, ripple of 40–60 mm, and a and a thorough washuniformity, performance70–80 of 42–mm 48%.length, These fibers be comparable with polyester fibers thorough wash performance of 42–48%. These fibers would be comparable with polyester fibers (PET) [18]. (PET)Finally [18]. there is another sheep breed called Churro. The Churro breed is characterized by wool there another breed called Churro. The Churro is characterized by wool thata that Finally is shiny, hasisvery lowsheep uniformity, 80–120 mm length, 35–40breed μm fineness, a low ripple and is shiny, has very low uniformity, 80–120 mm length, 35–40 µm fineness, a low ripple and a thorough thorough wash performance of 46–50%. These fibers would be comparable with other natural fibers wash performance 46–50%. These comparable withwool. other natural fibers such as such as Kenaf fibersof(36 μm) [19]. Thisfibers is thewould secondbe best quality sheep KenafThe fibers (36 µm) [19]. This is the second best quality sheep wool. manufacturing process of sheep wool is the classic of a nonwoven. It is carried out via dry and thermo-fusion. Sheep wool fibers are “combed” and introduced into the machinery, where they are mixed with polyester fibers obtained from recycled PET flakes. The caula ends up generating sheep wool by the thermo-fusion of the PET fiber that acts as a binder (the fiber melts at 140–150 °C).

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The manufacturing process of sheep wool is the classic of a nonwoven. It is carried out via dry and thermo-fusion. Materials 2017, 10, 1277 Sheep wool fibers are “combed” and introduced into the machinery, where3they of 11 are mixed with polyester fibers obtained from recycled PET flakes. The caula ends up generating The material out compressed the desired density depending on melts the capacity of ◦the sheep wool bycomes the thermo-fusion of the to PET fiber that acts as a binder (the fiber at 140–150 C). machinery. is a process similar toto the manufacture of conventional PET The difference is that The materialItcomes out compressed the desired density depending on the[18]. capacity of the machinery. theisfinal product has 80% sheep wool fiber of (first quality, second ordifference blend), andisthe remaining It a process similar to the manufacture conventional PET quality, [18]. The that the final 20% is PET An important that the machinery for these fibers is the same as product has fiber. 80% sheep wool fiberissue (first is quality, second quality,used or blend), andnew the remaining 20% is PET that used in the textile sector for non-woven materials. The machine should be cleaned only if fibers fiber. An important issue is that the machinery used for these new fibers is the same as that used in the are changed. textile sector for non-woven materials. The machine should be cleaned only if fibers are changed. 3. Acoustic Measurement Set-Up 3.1. Airflow Resistance Resistance 3.1. Airflow To To evaluate evaluate the the airflow airflow resistance resistance of of sheep sheep wool wool samples, samples, two two indirect indirect measurement measurement methods methods were used: Ingard & Dear's indirect method [21] and the Dragonetti et al. method [22]. Both of were used: Ingard & Dear's indirect method [21] and the Dragonetti et al. method [22]. Both of them them allow us to obtain the specific airflow resistance of sound absorbing materials. Ingard & Dear’s allow us to obtain the specific airflow resistance of sound absorbing materials. Ingard & Dear’s method et al. al. method is is based based on on measurements measurements with with an an impedance impedance tube tube and and two two microphones. microphones. The The Dragonetti Dragonetti et method is based on measurement through cavities with different volumes. Details of each of these two method is based on measurement through cavities with different volumes. Details of each of these measurement methods, similarities and and differences between themthem and and the normalized procedure can two measurement methods, similarities differences between the normalized procedure be in [23]. Figure 2 shows bothboth airflow measurement systems. canfound be found in [23]. Figure 2 shows airflow measurement systems.

(a)

(b)

Figure 2. 2. Airflow measurementsystems. systems. Ingard & Dear’s indirect method; (b) Dragonetti al. method. Figure Airflow measurement (a)(a) Ingard & Dear’s indirect method; (b) Dragonetti et al. et method.

3.2. Sound Absorption Coefficient at Normal Incidence 3.2. Sound Absorption Coefficient at Normal Incidence The sound absorption coefficient at normal incidence, α, is the quotient between the acoustic The sound absorption coefficient at normal incidence, α, is the quotient between the acoustic energy absorbed by the surface of the test sample and the incident acoustic energy, for a plane energy absorbed by the surface of the test sample and the incident acoustic energy, for a plane acoustic acoustic wave at normal incidence. ISO 10534-2 standard [24] establishes a test procedure to determine wave at normal incidence. ISO 10534-2 standard [24] establishes a test procedure to determine the the sound absorption coefficient for normal incidence of acoustic absorbers by means of an sound absorption coefficient for normal incidence of acoustic absorbers by means of an impedance impedance tube, two microphone positions, and a digital analysis system signal. The measurements tube, two microphone positions, and a digital analysis system signal. The measurements described in described in the standard procedure are useful in basic research and product development. the standard procedure are useful in basic research and product development. 3.3. Sound Measurement in in Reverberation Reverberation Chamber Chamber 3.3. Sound Absorption Absorption Coefficient Coefficient Measurement ISO ISO 354 354 standard standard [25] [25] establishes establishes the the measurement measurement procedure procedure of of the the sound sound absorption absorption coefficient coefficient in a diffuse field. This coefficient is obtained from measurements of the reverberation time, with in a diffuse field. This coefficient is obtained from measurements of the reverberation time, with and and without sample, inside a reverberation chamber. Measurements were carried out in the normalized without sample, inside a reverberation chamber. Measurements were carried out in the normalized reverberation chamber reverberation chamber at at the the EPS EPS Gandia Gandia at at the the Universitat Universitat Politécnica Politécnica de de València València (EPSG-UPV). (EPSG-UPV). 2 This measurement method requires large samples. Each sample size under investigation This measurement method requires large samples. Each sample size under investigation had had 12 12 m m2.. Figure 3 shows an image of the normalized reverberation chamber at the EPS Gandia at the Universitat Politécnica de València.

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Figure 3 shows an image of the normalized reverberation chamber at the EPS Gandia at the Universitat Politécnica Materials 2017,de 10,València. 1277 4 of 11

Figure 3. Normalized reverberation chamber at the EPS Gandia at the Universitat Politécnica de Figure 3. Normalized reverberation chamber at the EPS Gandia at the Universitat Politécnica de València. València.

ISO ISO 11654 11654 standard standard [26] [26] establishes establishes aa procedure procedure for for obtaining obtaining aa single single parameter, parameter, the the weighted weighted sound absorption coefficient, α , to evaluate the degree of sound absorption provided by the w sound absorption coefficient, αw, to evaluate the degree of sound absorption providedmaterial. by the This weighted is obtained the 1/3 octave band absorption coefficient valuescoefficient measured material. Thisvalue weighted value from is obtained from the 1/3sound octave band sound absorption in the reverberation The weighted sound allows to rate the absorbent values measured in chamber. the reverberation chamber. Theabsorption weighted coefficient sound absorption coefficient allows to material as indicated in Table 1. rate the absorbent material as indicated in Table 1. Table 1. Rating of sound absorption according to ISO 11654, 1997. Table 1. Rating of sound absorption according to ISO 11654, 1997. Sound Rating SoundAbsorption Absorption Rating AA BB CC D D E E No qualify

No qualify

αwαw 0.900.90 or or higher higher between and 0.85 between 0.80.8 and 0.85 between and 0.75 between 0.60.6 and 0.75 between 0.3 and 0.55 between 0.3 and 0.55 between 0.15 and 0.25 between0.10 0.15 0.25 or and lower 0.10 or lower

3.4. Tested Samples 3.4. Tested Samples In the study reported here, seven sheep wool samples with different compositions were used. In the studyofreported here, seven sheep wool with differentof compositions weresecond used. The composition all samples included 20% PET andsamples a variable percentage wool of first and The composition of all samples included 20% PET and a variable percentage of wool of first and quality. Table 2 shows the composition of each considered sample, its density, weight, and thickness, second Table 2 shows the composition of each considered sample, its density, weight, and and the quality. code used for each sample. thickness, and the code used for each sample. Table 2. Composition and the code used for each sample. Table 2. Composition and the code used for each sample. Composition

Composition

Sample Pet Bi-Co

Sample20 S1 S2 S3 S4 S5 S6 S7

S1 S2 S3 S4 S5 S6 S7

20 20 20 20 20 20

1st Quality Wool

Pet Bi-Co 20 20 20 20 20 20 20

1st 80 Quality 40 40Wool 40 40 80 40 0 40 40 40 40 40 0

2nd Quality Wool

2nd 0 Quality 40 40 Wool 40 0 40 40 40 80 40 40 40 40 80

Density (Kg/m3 )

Weight (g/m2 )

Density 30 30 3) (Kg/m

Weight 1500 15002) (g/m

25 30 30 40 30

1250 1200 1800 2000 1500

25 30 3030 40 3030

1250 1200 1500 1800 2000 1500 1500

Nominal Thickness (mm) Nominal 50 Thickness 50 50 (mm) 40 50 60 50 50 50 50 40 60 50 50

Test Thickness (mm)

Test 43 Thickness 53 43 (mm) 53 43 55 54 53 44 43 53 55 54 44

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4. Results and Discussion Materials 2017, replicates 10, 1277 Three

of 11 of each sample were prepared and measured so that three values of 5flow resistance for each sample were obtained. The largest and smallest values are taken as the interval if theResults typicaland deviation was lower than 2%. Table 3 presents the results of airflow resistance for the 4. Discussion seven samples considered. By comparing different samples results, it is found that there are no great Three replicates of resistance. each sampleThis wereisprepared andfact measured so that values of flow resistance variations on airflow due to the that there is athree close relationship between for each sample were obtained. The largest and smallest values are taken as the interval if the typical airflow resistance, density, and fiber diameter [9]. In this case, there are no large variations in density deviation was lower than 2%. Table 3 presents results airflow between resistance for the The seven samples or fiber diameter, so the airflow resistance valuesthe have littleof variation samples. differences considered. By comparing different samples results, it is found that there are no great variations on are caused by the material heterogeneity, which increases the dispersion of the results [23]. airflow resistance. This is due to the fact that there is a close relationship between airflow resistance, Figure 4 shows the measured normal incidence sound absorption coefficients of the seven density, fiber diameter [9]. In show this case, there are absorption no large variations in density samplesand considered. The results high sound coefficient values or at fiber mid diameter, and high so the airflow resistance values have little variation between samples. The differences caused by frequencies, making it an excellent sound absorbing material. It is observed that the are higher sound the material heterogeneity, which increases the dispersion of the results [23]. absorption coefficients are obtained for the higher thicknesses. Figure 4 shows the measured normal incidence sound absorption coefficients of the seven samples considered. The results show sound absorption coefficient values at mid and high frequencies, Tablehigh 3. Specific airflow resistance measurement results. making it an excellent sound absorbing material. It is observed that the higher sound absorption Nominal Test coefficients are obtained for the higher thicknesses. Ingard & Dear Dragonetti Density Weight Thickness Thickness Sample 3 2 (rayls/m) × 1000 (rayls/m) × 1000 (Kg/m ) (g/m ) (mm) Table 3. Specific(mm) airflow resistance measurement results. S1 30 1500 50 43 9.29–9.31 6.89–7.11 Ingard & Dear Dragonetti Nominal 3 2 S2 30 1500 50 53 7.59–7.61 5.26–5.61 Test Thickness (mm) Sample Density (Kg/m ) Weight (g/m ) (rayls/m) × 1000 (rayls/m) × 1000 Thickness (mm) S3 25 12501500 50 50 43 9.33–9.47 6.70–6.90 S1 30 43 9.29–9.31 6.89–7.11 S2 30 53 7.59–7.61 5.26–5.61 S4 30 12001500 40 50 53 9.28–9.32 6.34–6.47 S3 25 1250 50 43 9.33–9.47 6.70–6.90 S5 30 1800 60 55 7.18–7.22 5.85–6.05 S4 30 1200 40 53 9.28–9.32 6.34–6.47 S5 30 55 7.18–7.22 5.85–6.05 S6 40 20001800 50 60 54 7.38–7.42 7.55–7.59 S6 40 2000 50 54 7.38–7.42 7.55–7.59 S7 30 44 9.09–9.13 7.52–7.68 S7 30 15001500 50 50 44 9.09–9.13 7.52–7.68

Figure 4. Measured normal incidence sound absorption coefficients. Figure 4. Measured normal incidence sound absorption coefficients.

For room acoustics and environmental applications, normal incidence sound absorption is not For usable. room acoustics environmental normal sound absorption is not directly It is moreand practical and moreapplications, representative of the incidence performance of the material to use directly usable. It is more practical and more representative of the performance of the material to use diffuse-field sound absorption. The measured diffuse field sound absorption coefficients are shown diffuse-field sound absorption. The measured diffuse field sound absorption coefficients arethan shown in Figure 5. As expected, the diffuse field sound absorption coefficient values are higher the in Figure 5. As expected, the diffuse field sound absorption coefficient values are higher than the normal incidence sound values for the same samples. Figure 5 reveals that there are no great normal incidence sound values for the same samples. Figure 5 reveals that there arefact no great variations variations between sound absorption properties of measured samples due to the that differences between sound absorption properties of measured samples due to the fact that differences between between densities and thicknesses in all measured samples are relatively small: samples densities densities and thicknesses in all measured samples are relatively small: samples densities range between 25–40 kg/m3 while sample thicknesses range between 40–60 mm. By comparing samples S1, S2, and S7,

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range between 25–40 kg/m33 while sample thicknesses range between 40–60 mm. By comparing range between 25–40quality kg/m on while sample thicknesses range between –60 mm.80% By percentage comparing the influence of and wool sound canon be sound observed. Sample40can S1 has samples S1, S2, S7, the influence ofabsorption wool quality absorption be an observed. Sample samples S1, S2, and S7, the influence of wool quality on sound absorption can be observed. Sample of has firstan quality sheep wool,ofwhereas sample S2 wool, has a 40% percentage sheep wool S1 80% percentage first quality sheep whereas sampleof S2first has quality a 40% percentage ofand firsta S1 has an 80% percentage of first quality sheep wool, whereas sample S2 has a 40% percentage of first 40% percentage of second quality sheep wool. Finally, sample S7 has an 80% percentage of second quality sheep wool and a 40% percentage of second quality sheep wool. Finally, sample S7 has an quality sheep wool and a 40% percentage of second quality sheep wool. Finally, sample S7 has an quality sheep wool. As observed the quality of sheep wool6,does not have influence 80% percentage of second qualityfrom sheepFigure wool.6,As observed from Figure the quality of an sheep wool 80% percentage of second quality sheep wool. As observed from Figure 6, the quality of sheep wool on the absorption coefficient. low quality sheepTherefore, wool, which used wool, in the which textile does not have an influence onTherefore, the absorption coefficient. lowcannot qualitybesheep does not have an influence on the absorption coefficient. Therefore, low quality sheep wool, which industry, beinused as a sound absorbing cannot be can used the textile industry, can bematerial. used as a sound absorbing material. cannot be used in the textile industry, can be used as a sound absorbing material.

Figure 5. Measured field sound absorption coefficients. Figure Measureddiffuse diffuse Figure 5. 5. Measured diffuse field field sound sound absorption absorption coefficients. coefficients.

Figure 6. Measured diffuse field sound absorption coefficients of samples S1, S2, and S7. Figure 6. Measured field sound sound absorption absorption coefficients coefficients of of samples samples S1, S1, S2, S2, and and S7. S7. Figure 6. Measured diffuse diffuse field

The comparison between the diffuse field sound absorption coefficients of sheep wool sample The comparison between the diffuse field sound absorption coefficients of sheep wool sample S4, mineral wool, recycled poliurethane [27], and PET is shown in Figure 7. Allwool samples have The comparison between the diffusefoam field sound absorption coefficients of sheep sample S4, S4, mineral wool, recycled poliurethane foam [27], and PET is shown in Figure 7. All samples have 3, recycled the same thickness of 40 mm. The bulk densities of the samples were mineral wool 30 kg/m mineral wool, recycled poliurethane foam [27], and PET is shown in Figure 7. All samples3 have the the same thickness of 40 mm. The bulk densities of the samples were mineral wool 30 kg/m3 , recycled 3. The sound absorption curves have similar shapes and foam kg/m3, and kg/m values, same 80 40PET mm.35 The bulk of the samples were mineral wool 30 kg/m , recycled 3. densities foam thickness 80 kg/m33, of and PET 35 kg/m The sound absorption curves have similar shapes and values, 3 except for the PET sample. There are some differences in the low frequency range where PET and foam 80 kg/m , and PET 35 kg/m . The sound absorption curves have similar shapes and values, except for the PET sample. There are some differences in the low frequency range where PET and sheep wool have higher values thanare mineral wool and recycled foam. except for the PET sample. There some differences in the low frequency range where PET and sheep wool have higher values than mineral wool and recycled foam. sheep wool have higher values than mineral wool and recycled foam.

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Figure 7. 7. Comparison Comparisonbetween betweenthe thediffuse diffusefield fieldsound sound absorption coefficients of sheep wool sample Figure absorption coefficients of sheep wool sample S4, S4, mineral wool, recycled poliurethane foam and polyester fibers (PET). mineral wool, recycled poliurethane foam and polyester fibers (PET).

From the measured diffuse field sound absorption coefficients, and in accordance with ISO From the measured diffuse field sound absorption coefficients, and in accordance with ISO 11654 11654 standard [26], the weighted sound absorption coefficient, αw, can be obtained for all the standard [26], the weighted sound absorption coefficient, αw , can be obtained for all the measured measured samples in the reverberation chamber. Table 4 shows the weighted sound absorption samples in the reverberation chamber. Table 4 shows the weighted sound absorption coefficient, αw . coefficient, αw. It is observed that sheep wool samples have the same or, in samples S2, S5, and S6, It is observed that sheep wool samples have the same or, in samples S2, S5, and S6, even higher sound even higher sound absorbing capacity than mineral wool or recycled polyurethane foams. absorbing capacity than mineral wool or recycled polyurethane foams. Table 4. Measured rating of sound absorption according to ISO 11654. Table 4. Measured rating of sound absorption according to ISO 11654.

Sample Sample S1 S1S2 S2S3 S3 S4 S4 S5S5 S6S6 S7S7 Mineral MineralWool Wool Recicled Foam Recicled Foam PET

PET

αw (11654:1958) Absorption Class αw (11654:1958) Absorption Class 0.75 C 0.80 B C 0.75 0.80 0.75 C B 0.75 0.75 C C 0.75 C 0.85 B B 0.85 0.80 B B 0.80 0.75 0.75 C C 0.65 0.65 C C 0.65 C 0.65 C C 0.70 0.70 C

5. Calculation of the Sound Absorption Coefficient of Sheep Wool 5. Calculation of the Sound Absorption Coefficient of Sheep Wool It is desirable to have a method for predicting sound absorbing performance of sheep wool due It is desirable to have a method for predicting sound absorbing performance of sheep wool due to to the fact that it is impossible to measure every possible sample. In this section, a summary of the the fact that it is impossible to measure every possible sample. In this section, a summary of the model model for predicting the sound absorbing performance of sheep wool is given. This model is based on for predicting the sound absorbing performance of sheep wool is given. This model is based on the the empirical model proposed by Delany and Bazley [28]. Two complex values determine the sound empirical model proposed by Delany and Bazley [28]. Two complex values determine the sound propagation through a homogeneous and isotropic material in the frequency domain. They are the propagation through a homogeneous and isotropic material in the frequency domain. They are the characteristic wave impedance (Z) and the characteristic propagation constant (k'). Delany and Bazley characteristic wave impedance (Z) and the characteristic propagation constant (k'). Delany and Bazley model determines the real constants Ci (i = 1 . . . 8) that best fit the following Equations (1) and (2): model determines the real constants Ci (i = 1 … 8) that best fit the following Equations (1) and (2):    2C 2 −C −C4 C 4 ZZ=Z0Z 011+CC1 χ − jC χ (1)   jC  3 3 1











   −C6 C 6 k0 k=' k kCC j 1j + 1 C7Cχ7−C8 C8 5 χ5  + 

(2)

where ρc is isthe thecharacteristic characteristicimpedance impedanceofofair, air,χχ= =ρf/σ ρf /σ a dimensionless parameter, is the is aisdimensionless parameter, ρ isρthe air where Z00 == ρc 3 ), f is the sound frequency, σ is the airflow resistivity 3 air density at room temperature ( ≈ 1.2 kg/m density at room temperature (≈1.2 kg/m ), f is the sound frequency, σ is the airflow (rayls/m), is the the speed speed of of sound sound in in air air at at room room temperature temperature (≈343 (≈343m/s), m/s), and = ω/c = 2πfis/c the (rayls/m), cc is and k =k ω/c = 2πf/c theisfree free wavenumber. range which the model is valid is 0.012 χ ≤ 1.2. fieldfield wavenumber. The The range overover which the model is valid is 0.012  χ ≤1.2. The normal-incidence sound absorption coefficient, α, can be determined by Equation (3) [19]:

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The normal-incidence sound absorption coefficient, α, can be determined by Equation (3) [19]: α=

4Z0 ZdR

(3)

2

| Zd | + 2Z0 ZdR + Z02

where the rigid-backing specific surface impedance of the material is given by Zd = Z0 coth(k0d) = ZdR + jZdI

(4)

where d is the material layer thickness and ZdR and ZdI are the real and imaginary parts of Zd , respectively. The regression coefficients, Ci , are determined from the normal-incidence sound absorption coefficients in the frequency domain of the measured data for a known airflow resistivity of the material sample. An iterative method based on a minimization of a quadratic error function is used to obtain the regression coefficients that best fit the measured sound absorption coefficient. The quadratic error function used in the iterative process is defined as N

ε=

∑ (αi − aˆ i )2

(5)

i =1

where αi is the measured normal-incidence sound absorption coefficient for a material sample at the i-th frequency and âi is the corresponding value estimated from Equations (1) and (2). Minimization of Equation (5) implies that N ∂ε ∂ aˆ = 2 ∑ (αi − aˆ i ) i = 0 (6) ∂Ci ∂C i i =1 for all i = 1 . . . 8. To minimize the nonlinear Equation (6) and to obtain the corresponding values of Ci , a MATLAB computer program was implemented. The Nelder-Mead simplex method [29] was used for the optimization process. Acceptable values of χ were constrained to fall between 0.04 and 1.0. The regression coefficients of the empirical model proposed by Delany and Bazley [28] were used as initial values in the iterative method. Table 5 reports the obtained coefficients, while Figure 8 shows the results of the best-fit curves normal incidence sound absorption coefficient for the sheep wool samples considered. It is interesting to emphasize that the empirical model proposed by Delany-Bazley, as it can be observed from Figure 8h, does not adjust to the absorption coefficient measurements for one of the sheep wools analyzed in this work. In the same figure, it can be observed that the model developed in this work, specific for sheep wool, adjusts much better to the experimental values. Table 5. Values of coefficients Ci . Model

C1

C2

C3

C4

C5

C6

C7

C8

Delany & Bazley First Quality Sheep Wool Second Quality Sheep Wool Sheep Wool Mixture

0.057 0.0574 −0.0298 0.0560

0.754 0.3808 0.4829 0.3640

0.087 0.0222 0.0249 0.0164

0.732 0.8552 0.7419 0.9325

0.189 0.1999 0.2653 0.1915

0.595 0.8906 1.1107 0.7863

0.098 0.1031 0.0965 0.1201

0.700 0.8687 1.0131 1.1163

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 8. Best-fit curves for the different sheep wool samples measured in this paper. (a): sample S1; Figure 8. Best-fit curves for the different sheep wool samples measured in this paper. (a): sample S1; (b): sample S2; (c): sample S3; (d): sample S4; f; (e): sample S5; (f): sample S6; (g): sample S7 and (b): sample S2; (c): sample S3; (d): sample S4; f; (e): sample S5; (f): sample S6; (g): sample S7 and (h): (h): sample S8. sample S8.

6. Conclusions 6. Conclusions In this paper, the sound absorption performance of sheep wool has been investigated. Seven In this paper, the sound absorption performance of sheep wool has been investigated. Seven sheep sheep wool samples with different wool compositions and densities have been used. Airflow wool samples with different wool compositions and densities have been used. Airflow resistance resistance and sound absorption coefficients at normal and diffuse incidence measurements were and sound absorption coefficients at normal and diffuse incidence measurements were carried out. carried out. From the measurements results, it has been demonstrated that sheep wool is a good From the measurements results, it has been demonstrated that sheep wool is a good sound absorbing sound absorbing material at medium and high frequencies. It is also shown that sheep wool has material at medium and high frequencies. It is also shown that sheep wool has comparable sound comparable sound absorption performance to that of mineral wool or recycles polyurethane foams. absorption performance to that of mineral wool or recycles polyurethane foams. An empirical model An empirical model proposed by Delany-Bazley has been used to predict the sound absorption of the proposed by Delany-Bazley has been used to predict the sound absorption of the sheep wool samples. sheep wool samples. A reasonable agreement for sound absorption has been obtained. A reasonable agreement for sound absorption has been obtained. Acknowledgments: This work was financially supported by the project BIA2013-41537-R (BIAEFIREMAT Acknowledgments: This work was financially supported by the project BIA2013-41537-R (BIAEFIREMAT “Development of of new new eco-materials eco-materials and and sustainable sustainable constructive constructive solutions solutions based based on on the the use use of of waste waste and and “Development renewable raw materials”), materials”), funded by the Ministry Ministry of of Economy Economy and and Competitiveness Competitiveness of Spain and co-financed co-financed with with ERDF ERDF funds, funds, within within the the National National RDI RDI Programme Programmefocused focusedon onthe theChallenges Challengesof ofSociety Society2013. 2013. Author Alba conceived andand designed the the experiments; Romina del Rey Author Contributions: Contributions: Romina Rominadel delRey Reyand andJesús Jesús Alba conceived designed experiments; Romina del performed the experiments; Antonio Uris and Pilar Candelas analyzed the data and participated in the analysis of Rey performed the experiments; Antonio Uris and Pilar Candelas analyzed the data and participated in the the state-of-the-art and in the design of some experiments, as well as in the drafting of the manuscript. analysis of the state-of-the-art and in the design of some experiments, as well as in the drafting of the manuscript. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design Conflicts of Interest: The authors declareor nointerpretation conflict of interest. Theinfounding sponsors no role in and the design of the study; in the collection, analyses, of data; the writing of thehad manuscript, in the decision to publish the results. of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

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