A STUDY ON THE ACOUSTICAL ABSORPTION BEHAVIOR OF COIR FIBER USING MIKI MODEL

Transcription

1 International Journal of Mechanical and Materials Engineering (IJMME), Vol.6 (2), No.3, A STUDY ON THE ACOUSTICAL ABSORPTION BEHAVIOR OF COIR FIBER USING MIKI MODEL M. Ayub, R. Zulkifli, M.H. Fouladi 3, N. Amin 2, 4 and M.J.M. Nor Department of Mechanical and Materials Engineering, 2 Department of Electrical, Electronic and System Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, 436, UKM Bangi, Selangor, Malaysia. 3 School of Engineering, Taylor's University, 475, Subang Jaya, Selangor, Malaysia. 4 Center of Excellence for Research in Engineering Materials (CEREM), College of Engineering, King Saud University, Riyadh 42, Saudi Arabia. mxayub2@gmail.com; rozli@eng.ukm.my Received 2 December 2, Accepted 8 November 2 ABSTRACT Sound absorption capacity of natural coir fiber collected from coconut husk has been explored and predicted using Miki s empirical model. Experiments are conducted in impedance tube to validate the analytical outcomes for three samples having different thickness backed with and without air gap. Results show that the empirical model can estimate the absorption coefficient of coir fiber favourably well and shows higher accuracy than the Delany-Bazley model. Discrepancies between the predicted and measured absorption coefficient is very low although some inevitable irregularities is observed in the peak positions. However, presented Miki model can evaluate the overall acoustic behavior of coir fiber. This approach can be considered as a very simple and preliminary analytical solution for coir fiber acoustical characterization without considering several physical parameters of porous media. In addition, as a result, no complicated measuring procedure has to be followed to initiate the preliminary study for this material. Keywords: Noise absorption, Natural coir fiber, Empirical model, Miki model.. INTRODUCTION The absorption characteristics of porous material are well known to vary with type of porous materials. There are various types of porous materials which are generally categorized as fibrous medium and porous foam. They consist of various synthetic materials like glass wool to minerals, agro-based foams and fibers. Numerous studies had been done on the sound absorption of porous material like wood based material (Wassilieff, 996), tea-leaf-waste material (Ersoy & Kucuk, 29), melamine foam (Kino et al., 29) and fabric (Dias et al., 27). At the present time, green technology is widely used to manufacture materials from agricultural as substitute to synthetic fiber and wood based material for noise absorption purposes. Natural fibers such as coir fiber can be used as a potential acoustic material since they are easily obtained as an agricultural waste. Coir 343 fiber is a natural organic resource which is the seed-hair fiber obtained from the outer shell (endocarp) or husk of the coconut. The mechanical performance of these composites such as coir, kenaf or palm oil frond may suffer when the material is exposed to adverse environments for long periods of time (Rashdi et al., 2) and the comparison between acoustic properties of coir and oil palm fibre has been studied (Zulkifli et al., 29). In this paper, sound absorption behavior of coir fiber are explored and described by empirical models such as Miki model (Miki, 99a). The absorption phenomenon of porous material was examined theoretically by numerous authors. Various models were proposed to study the sound propagation in porous materials. A simplified model was developed by Delany and Bazley (97) and proposed a normalized model based on dimensionless groups. They developed an empirical formula to estimate the characteristics impedance and wave propagation constant of fibrous absorbent material. Their method was very simple and considered as the easy approximation to the solution as this method use only flow resistivity parameter which is an intrinsic property of the material. Subsequently this model was improved by Morse and Ingard (968) and Attenbourgh (983). Dunn and Davern (986) utilized the same method to define empirical relations between characteristics impedance and propagation constant of porous foam materials and multilayer absorbers. Qunli (988) gathered a large amount of experimental data and calculated those relations for foam materials with a wider range of flow resistivity. However, there are restrictions on the applicability of these Delany- Bazley formulations. These are only applicable where (Cox & D Antonio, 29): The porosity is close to, which most purpose built fibrous absorbers achieve. The limits of the flow resistivity in the measurements were: -

2 Miki (99a) showed that sometimes the real part of surface impedance that is computed by Delany and Bazley model converges to negative values at low frequencies. He modified that model to have a real positive value even in wider frequency range. Moreover, Miki (99b) generalized those models with respect to porosity, tortuosity and the pore shape factor ratio. Recently, Komatsu (28) proposed improvements for both conventional models Delany-Bazley and Miki which enables more precise prediction of acoustical properties of fibrous material. Equivalent electrical circuit approach (EECA) (Lee & Swenson, 992; Congyun & Qibai, 25) is an usual method to analyze the multilayer panel, in which surface acoustic impedance of back air gap is assumed as the acoustic impedance of rigid wall even when the air space were actually backed with perforated plates. Lee & Swenson (992) studied the assembly with two layers of perforated plates backed with air spaces by EECA. Lee and Chen (2) further studied the transmission analysis for multilayer absorbers consisting of several layer of porous material, air gap and perforated plate using a new technique named ATA (Acoustic-Transmission Approach). The effects of the back air gap and porous material was considered in ATA method. Results showed that ATA method can give the better result than the conventional EECA method for multilayer absorber. However, the microscopic model of sound propagation is more complicated. More sophisticated models like Biot Model (Biot, 962; Zwikker & Koston, 949; Allard, 993) will not be considered in this analysis because they feature a large number of parameters which are rarely available. They require uncommon procedures for their determination and can't be deduced from simple acoustic measurements. Empirical models are used in this work to predict the absorption coefficient of coir fiber as a preliminary study and as a simple method. However, this model is not suitable for very low and high frequency. sound propagation of coir fiber can be analyzed more accurately based on Biot model (Biot, 962), Johnson- Allard model (Allard, 993). A version of this paper is presented at 8 th ICME held in Bangladesh (Ayub et al., 29). This is the extended version of that work along with more enriched analyses for the acoustical characteristics prediction approach supported by the comparison between empirical models: Delany-Bazley and Miki model. 2. ACOUSTIC IMPEDANCE OF POROUS MATERIAL 2. Empirical model was first developed by Delany-Bazley. However, Miki (Miki, 99a) noticed that the real part of the surface impedance for multilayer combinations sometimes become negative at low frequencies when computed with the original Delany-Bazley model (Delany & Bazley, 97), which he denoted as a non-physical result. Based on Delany and Bazley measurements data on fibrous materials with porosities close to., Miki proposes to use the following expressions for the wave propagation constant and characteristic impedance (Miki, 99a): If the porous material is backed with a rigid wall, the surface acoustic impedance of the porous material can be expressed as (Miki, 99a; 99b): Where, is the air density, is the sound speed in the air, f is the frequency of the sound wave, is the thickness of porous layer. () (2) (3) (4) The sound absorption of coir fiber was investigated previously in Automotive Research Group Laboratories, Universiti Kebangsaan Malaysia (Nor et al., 24; Zulkifli et al., 28). Those studies were based on simulation program WinFLAG TM and compared with experimental data obtained in reverberation room using diffuse sound field of noise source. This present study is analytical and compared with experimental data obtained by impedance tube with normal incidence sound field of noise source. The purpose of this current study is to explore the absorption capacity of coir fiber and to establish an analytical technique which can be able to describe the acoustic characteristics of coir fiber. A panel composed of coir fiber layer with and without air gap backed by rigid wall was used to analyze the acoustic absorption performance of coir fiber. This paper is just the preliminary study based on empirical models to make an analytical technique for coir fiber. For further improvement, 344 These models are considered to give good agreement between the theoretical and experimental results for the following limitations as explained in Ref. (Miki, 99a; 99b),. (5) 3. ACOUSTIC IMPEDANCE OF AIR GAP The complex wave propagation constant and characteristic impedance of air spaces can also be expressed similar to porous material as, (6) (7)

3 If the air gap is backed with a rigid wall, the surface acoustic impedance of the air space can be expressed as Eq. (8), where, is the thickness of air space, ka is the wave number of air (Lee & Chen, 2). 4. CALCULATION OF ABSOPRTION COEFFICIENT In this work, a panel composed of porous material (Coir Fiber) and backed with rigid wall was considered for the analytical estimation of absorption coefficient of single layer coir fiber. Thereafter, a fixed layer of air is placed between the layer of porous material and rigid plate for constructing multilayer structure similar as shown in Figure. To calculate the surface impedance of single layer coir fiber, Eq. (4) is used customized with Eqs. () to (3). Porous Layer Air Gap Rigid back plate (8) 5. MATERIALS AND METHODS In this study, industrially treated coir fibers were used for experimental validation. Industrial coir fiber was prepared industrially using binder as a mixer with the fiber to keep it in shape. Coir fiber sample was collected industrially as a large rectangular sheet and then cut into suitable circular shape for impedance tube. Raw fiber thickness of the material was measured by dial thickness gauge meter in the scale of one hundredth of millimeter. Fifteen randomly selected fibers were used to measure the average thickness and weight of the fiber. Average diameter and density of the fiber was taken as 252 μm and 82 kg/m 3 respectively as found from the experimental measurements. The shape of the fiber was considered as cylindrical shape. Bulk density of the material was measured from mass and volume of the sample. Flow resistivity of the material was estimated using the empirical Eq. (2) based on mass, thickness and fiber diameter of each sample (Attenborough, 983), Z r = Figure : Schematic of the cross-section of absorber panel. For the multilayer structure as considering the geometry of Figure, that illustrates a cross section of the panel, the resultant surface acoustic impedance of the panel can be expressed as (Dunn & Davern, 986; Lee & Chen, 2), where,, and are calculated according to Eqs. (), (2) and (8) respectively. The total surface acoustic impedance of the panel or, is calculated from Eqs. (4) and (9) based on different modeling criteria. This result can be expressed as, (9) () where, and is the real and imaginary parts of impedance or. Having the surface acoustic impedance, acoustic absorption coefficient of the porous layer can be calculated as Eq. () for a normal incident plane sound wave as (Lee & Swenson, 992; Dunn & Davern, 986): () 345 (2) In this work, impedance tube is used to measure the normal incident sound absorption of coir fiber based on two microphones transfer function method to make the measurement according to ISO (ISO 534-2, 998) standard. The configuration of the system is shown in Figure 2. The components of the system mainly include the following:. Two impedance tube (size 28 mm and mm). Each contains two ¼" microphones type GRAS- 4BP, plane wave source and two channel data acquisition system db. Small Tube (dia. 28 mm) is used for acoustic properties measurements in the high frequency range (6 Hz 63 Hz). Vice versa Large Tube (dia. mm) is used for measurements in the low frequency range (3.5 Hz 6 Hz). The acoustic absorber sample is placed inside the tube. 2. One calibrator type GRAS-42AB at 4 db level and khz frequency for microphone sensitivity calibration. 3. The personal computer system which includes the frequency analysis system using SCS8 Software Package for Alfa coefficient calculation (SCS8, 28).. A random noise is created by the acoustic signal driver and it transmitted into the impedance tube. Two microphones detect the frequency and measure the sound pressure. By frequency analysis system obtaining the transfer function, the experimental acoustic absorption coefficient can be obtained in graphical form.

4 [βc a /ω]- [αc a /ω] - [X/ρ a c a ] [R/ρ a c a ]- a) [R/ρ a c a ]-=.699 () b).... [X/ρ a c a ]= -.7 () Figure 2: Schematic of experimental set up for coir fiber acoustic absorption measurement. Before starting the measurements, the two microphones used in the impedance tube were calibrated relatively to each other using the standard switching technique by mounting a sample in the sample holder to make sure that the sound field inside the tube is well defined. The range of measured frequency is 3.5 Hz 63 Hz and the acoustic absorption co-efficient α is calculated with an interval 3 Hz and sample records of finite duration about s in this measurement. 6. RESULTS AND DISCUSSIONS In the modeling of single layer coir fiber using Miki s empirical formula, the calculated flow resistivity from Eq. (2) was utilized in Eqs. () and (2) to estimate the characteristic impedance and propagation constant of fiber. These two equations constructed the surface impedance relation of single layer fiber backed by rigid wall in Eq. (4) which was implemented to calculate absorption coefficient in Eq. (). Validity of the model is checked by the normalized real and imaginary parts of characteristic impedance and propagation. is considered to give good agreement between the theoretical and experimental results for the following limitations: c) d) [αc a /ω]=.6 () [βc a /ω]-=.9 () -.68 (3). To verify the validity of this model for coir fiber, real and imaginary component of characteristics impedance and propagation constant is normalized into two dimensionless groups with free field wave impedance and plotted against normalized frequency group as shown in Figure 3. It can be seen that the frequency range is within the given limit of. to. for the majority of the normalized real and imaginary components of. and Figure 3: a) Normalized real component of characteristic impedance, b) Normalized imaginary component of characteristic impedance, c) Normalized real component of propagation coefficient, d) Normalized imaginary component of propagation coefficient ; (for 35 mm industrial coir fiber layer thickness).

5 Absorption Coefficient Absorption Coefficient Absorption Coefficient Verification of estimated absorption coefficient using the empirical model was done for three samples of industrial coir fiber. Thicknesses of samples are 2, 35 and 5 mm; measured mass of those sample are found as 5.5, and 34.3 gm, respectively. Comparison of the experimental and analytical results for 2, 35 and 5 mm industrial coir fiber layer backed with rigid wall is plotted in Figures 4, 5 and 6, respectively. The measured plots agree fairly well with analytical prediction. The profiles of the graphs are well behaved with the measured absorption coefficient despite some inevitable irregularities in the high frequency range Frequency (Hz) Frequency (Hz) Figure 4: Experimental data compared to numerical simulations of the absorption coefficient of single layer industrial coir fiber backed with rigid wall having layer thickness of 2 mm (Mass = 5.5 gm and Flow resistivity = 68.2 Nsm -4 )..8 Figure 6: Experimental data compared to numerical simulations of the absorption coefficient of single layer industrial coir fiber backed with rigid wall having layer thickness of 5 mm (Mass = 34.3 gm and Flow resistivity = Nsm-4). Moreover, the results were also compared with the estimated absorption plot obtained by Delany-Bazley model (Ayub et al., 29a) to show how much Miki model improved the prediction rate specifically in low frequency range. Results indicate that both models can justify the overall trend of absorption coefficient of coir fiber perfectly as demonstrated in this study. However, it was noticed that between both empirical models, Miki model shows better agreement with the measured absorption coefficient as expected according to the developed models (Miki, 99a; 99b). Discrepancies between the experimental and theoretical absorption plot can be described as the fact of improper measurement procedure and the maladjustment in the size of sample such as circular diameter and thickness of the fiber layer. Moreover, the flow resistivity (around 5 Nsm -4 ) and porosity (less than ) of the material is very low which may be another reason for the large prediction error rate (Komatsu, 28) for that empirical model Frequency (Hz) Figure 5: Experimental data compared to numerical simulations of the absorption coefficient of single layer industrial coir fiber backed with rigid wall having layer thickness of 35 mm (Mass = gm and Flow resistivity = Nsm-4). 347 The graph in Figs. 4 to 6, also shows that analytical plot gives better agreement with experimental measurements at larger thickness of the sample increases from 2 to 5 mm. Moreover, the prediction becomes more accurate at high frequency. It may be due to the reason was addressed by Delany-Bazley (Delany & Bazley, 97) to show this type of behavior, at lower value of many materials exhibit significant structural non-rigidity and under these circumstances simple normalization is not possible as (considered by both empirical models) shown in Figure 3. In case of these three samples of industrial fiber, it is found that increasing the fiber layer (sample) thickness decreases the flow resistivity from 68 Nsm -4 to 359 Nsm -4 and those samples maintain almost equal thickness to mass ratio (TMR) between.3 to.45. Although, flow resistivity

6 Absorption Coefficient Absorption Coefficient should be increased with increased thickness, but in this case flow resistivity is decreased because of bulk density. Bulk density is a factor of both mass and thickness, which is also decreased with increased layer thickness due to constant TMR. As a result, for larger thickness with the same TMR, gives a higher value of ratio compare to smaller thickness of the same material, which produces a better agreement of analytical model with experimental results. Similarly, for high frequency this ratio becomes higher which resulted in good approximation with the experimental results. To show the versatility of the presented method, absorption coefficient of multilayer coir fiber backed with air gap is also verified using both empirical models. Eqs. (6) and (7) were employed to calculate the characteristics impedance and propagation constant of air gap; and they were implemented in Eq. (8) to develop the surface impedance of air gap backed with rigid wall. As the air gap is placed between coir fiber layer and back wall, surface impedance of such combination was estimated using Eq. (9) customized by Eqs. (6) and (7) along with property of coir fiber calculated by Eqs. () and (2). Figures 7 and 8 exhibit the obtained results (from previous study Ayub et al., 29b) of absorption coefficient for 2 and 35 mm thickness coir fiber layer backed with 2 mm air gap, respectively. Eventually, again theoretical predictions by both of these models agree favorably with the experimental data. In brief summary, predicted acoustic response of each type of coir fiber obtained by two analytical approaches are presented and elaborated in above discussion. Based on these results, it can be suggested that empirical model is an easy solution for industrially treated fibers with such layer combinations with and without air gap Freqency (Hz) Figure 7: Experimental data compared to numerical simulations of the absorption coefficient of 2 mm coir fiber backed with 2 mm air gap Freqency (Hz) Figure 8: Experimental data compared to numerical simulations of the absorption coefficient of 35 mm coir fiber backed with 2 mm air gap. 7. CONCLUSION An analytical approach for theoretical prediction of acoustic absorption coefficient has been demonstrated based on an empirical formula. This analytical method has provided a closer and consistent agreement with the impedance tube data for the most of the coir fiber samples in two different conditions backed with and without air gap. It is capable to capture the overall absorption behavior despite the model relies on many assumptions and developed based on the experimental data only. Moreover, it did not consider any inside of the physics of porous media. It is a simplified tool based on empirical formula which avoids going through the tedious process of calculating and measuring all parameters. However, it is anticipated that considering the whole physics of porous media and measuring some of the physical parameters (such as flow resistivity) will give the best approximation for validation of the results. Therefore, for accurate prediction of overall absorption including the resonance frequencies, more sophisticated model like Johnson-Allard or Biot-Allard model can be used which take the consideration of different physical elements. REFERENCES Allard, J.F Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials. Elsevier Applied Science, London. Attenborough, K Acoustical characteristics of rigid fibrous absorbents and granular materials. Journal of Acoustical Society of America 73: Ayub, M., Nor, M. J. M., Amin, N., Zulkifli, R., & Ismail, A. R. 29b. A preliminary study of effect of air gap on sound absorption of natural coir fiber. Proceedings of the Regional Engineering Postgraduate Conference (EPC 29), 2-2 October, Putrajaya, Malaysia. Ayub, M., Nor, M. J. M., Amin, N., Zulkifli, R., Hosseini Fouladi, M. & Ismail, A. R. 29a. Analysis on sound absorption of natural coir fiber using Delany-Bazley 348

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