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Design and in-situ measurement of the acoustic performance of a metasurface ventilation window
Applied Acoustics 152 (2019) 127–132
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Design and in-situ measurement of the acoustic performance of a metasurface ventilation window Xiang Yu Institute of High Performance Computing, A*STAR, 138632, Singapore
a r t i c l e
i n f o
Article history: Received 11 December 2018 Received in revised form 1 April 2019 Accepted 2 April 2019 Available online 6 April 2019 Keywords: Acoustic metasurface Noise control Finite element analysis Transmission loss Acoustic façade
a b s t r a c t Recent studies have discovered that acoustic metasurfaces possess great versatility in designing novel acoustic systems. An earlier theoretical study pointed out that acoustic metasurface constructed using an array of resonant-duct unit cells can provide superior sound insulation while allowing air to ventilate through the openings distributed on the surface. By using such a principle, a full-scale metasurface ventilation window is designed and experimentally demonstrated in this study. The primary goal of this paper is to detail the acoustic design methodology for developing this window prototype and to characterize its sound insulation performance in-situ. The dimensions of the metasurface window and its unit cells are tuned based on acoustic Finite Element (FE) analysis to enhance its noise reduction for traffic noise frequency, as well as to increase the single number quantity (SNQ) noise rating. The measured transmission loss (TL) shows a consistent behavior with the prediction in the design frequency range. Comparing the proposed window to a conventional casement window with an equal opening area, the SNQ from measurement for the metasurface window is 22 dB, which is 7 dB higher than the casement window at 15 dB. The substantial improvement shows the benefit of incorporating metasurface concept into the design of sound insulation components, such as building façade, noise barriers, etc. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Building façades integrated with natural ventilation technology are promising solutions to ease the increasing environmental problems caused by energy consumption for air conditioning. However, public still have concern about utilizing ventilation windows as they often result in poor noise insulation. With greater emphasis on energy-efficient building and tighter restriction on noise, windows that are naturally ventilated, yet capable of providing the same acoustic comfort as closed windows are crucially needed. Conventional windows, such as casement, top-hung and sliding windows, offer minimal noise reduction when they are opened, as airborne sound can transmit freely through the aperture. Some studies have proposed special acoustic treatments on the window opening, such as using staggered window construction to alter the sound transmission path [1], applying acoustic resonators [2] and absorbers [3] to reduce airborne sound transmission. Despite these efforts, new innovations are strongly needed to fundamentally advance the window design philosophy, so that the long-awaited features such as transparency, noise reduction, reduced thickness,
E-mail address: [email protected] https://doi.org/10.1016/j.apacoust.2019.04.003 0003-682X/Ó 2019 Elsevier Ltd. All rights reserved.
adjustable ventilation volume, and easy operation can become reality. Recent studies have discovered that acoustic metasurfaces could open up new opportunities for manipulating sound waves and designing novel acoustic devices [4]. For example, phase gradient metasurfaces enable unusual wavefront modulations, such as anomalous refraction [5], full control of reflected waves [6] and sub-wavelength absorption [7]. Gradient-index metasurface can achieve omnidirectional sound shielding in selected frequencies while permits airflow [8]. Although the physical principles have been demonstrated, few studies have extended the proof-ofconcept to real-world applications. Recently, a theoretical study pointed out that using an acoustic metasurface composed of an array of resonant-duct unit cells can achieve superior sound insulation while allowing air/fluid transport through the openings distributed on the surface [9]. One of the potential applications mentioned earlier was a ventilation window system, whose acoustic frequency can be flexibly tuned to cope with different noise spectra. A computationally efficient sub-structuring approach has been proposed to characterize the Sound Reduction Index (SRI)/ Transmission Loss (TL) of the metasurface system. Here, SRI and TL are interchangeable terms for describing the airborne sound insulation ability, which is defined as the reduction of acoustic
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energy between sound incidence and transmission in the decibel scale. In this study, the metasurface design philosophy is employed to the real design of the ventilation window prototype. The primary goals are to verify the design methodology, validate the numerical prediction and demonstrate the window performance using a fullscale experiment. Similar studies on sonic crystal sound barriers have been performed earlier [10,11]. We have chosen 800 to 1400 Hz as the design frequency range to be focused, since the peak of traffic noise usually appears at 1000 Hz. The A-weighted noise levels in this range are generally higher than the other frequencies [12]. One important consideration in designing the window performance is to raise the single number quantity (SNQ) rating covering the broadband frequency from 100 to 3150 Hz. This paper is organized as follows. Section 2 elaborates the window design methodology to choose the appropriate geometric parameters with respect to the design frequency range. Finite element (FE) models are employed to analyze the frequency characteristics of the unit cells, and the TL of the designed metasurface window is predicted using the unique sub-structuring approach developed earlier to overcome the computational cost. In Section 3, the window prototype is fabricated and its TL is measured in-situ using a partition wall between two rooms. The experimentally measured TL shows overall good agreement with prediction, and the single-number rated TL of the metasurface is significantly improved compared to that of a normal casement window with the same opening area. The experimental results reported in this study are encouraging, and the proposed metasurface window design strategy can potentially solve the challenging problem between ventilation and noise reduction. The design philosophy can be extended to many other systems to overcome the limitations of traditional acoustic devices.
2. Acoustic design methodology 2.1. Design of unit cell frequency Fig. 1(a) shows a rectangular aperture on the partition wall for designing and testing the metasurface window. The aperture dimension is 0:76 0:56m, located in the center of a set of window panes. Except for the aperture, the other window sashes are fully closed and considered as acoustically rigid. The first step to design the metasurface window is to split the aperture into grids. In Fig. 1 (b), four grids options of up to 3 3 cells are illustrated. For sound insulation purpose, even grid subdivision is applied here as we expect identical unit cells with the same acoustic property to
provide united effect without any weak point. The unit cell at each grid is a multi-layer resonant-chamber with a central rectangular hole. Such design allows air/fluid to flow freely while enables sound wave attenuation by means of impedance mismatching in the design frequency, like a reactive duct silencer [13]. We first omit the physical thickness of the chamber walls and simply analyze the air cavity in the resonant chambers. The unit cell’s height and width a b are related to the division of grids, as the aperture size is kept constant. A square hole with size c c is assumed for the sake of simplicity. As the total window thickness is preferable to be thin, only two chamber layers with equal thickness d are considered. Thus, the geometric parameters to be specified for one unit cell include height a, width b, opening size c, and thickness d of the two sub-chambers. The acoustic characteristics of the unit cell with varying geometric parameters are first analyzed using FE simulations. Given the fixed aperture size, Table 1 lists the unit cell dimensions a and b with respect to the grid subdivisions as illustrated in Fig. 1 (b). To maintain adequate ventilation, the length of the square hole c is required to be at least half of a or b, whichever is smaller. The maximum c is set as minimum c plus 0.06 m. Thicknesses of the two sub-chambers d are both 0.02 m to keep the window thin and flat. The FE model to predict the TL of a unit cell has been developed and validated in the previous paper, thus the detailed method will not be repeated here [9]. It is worth mentioning again that the unit cell TL refers to the attenuation behavior of a single element alone, which is calculated in a confined duct with normal sound incidence as illustrated in Fig. 2. The difference with the metasurface TL to be determined later (in between two rooms) is that the latter case considers random incidence from a diffuse sound field and involves interactions between the unit cells. It is already known that the hole size c not only affects ventilation but also has great influence on the TL performance and effective frequencies of the unit cell. To determine the optimal attenuation frequency that could be offered by each grid option, the unit cell TLs with respect to varying c are simulated, and the resultant TLs are plotted as contours to show the applicable frequency range for each case. Fig. 2(a)–(d) present the TL contours for 2 2, 3 2, 2 3, 3 3 grids, respectively. In each TL contour, the common trend is that noise reduction is higher with smaller opening c, and the working frequency is slightly shifted towards higher with an increasing c. It is clearly seen that the applicable frequency ranges for the four cases are quite different. By picking the frequency interval where TL is greater than 15 dB (with the smallest c), Table 1 compares their optimal operating frequencies for selecting the most suitable case for traffic noise. The lowest frequency range is achieved by 2 3
Fig. 1. (a) Dimensions of the aperture for designing the metasurface window; (b) Splitting the aperture area into different grids. The unit cell at each grid is a thin two-layer resonant-chamber with a central square hole. Geometric parameters can be tuned to enhance sound insulation for the desired frequency range.
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X. Yu / Applied Acoustics 152 (2019) 127–132 Table 1 Dimensions of the unit cells for the grid options illustrated in Fig. 1(b). Grids
ab
22 32 23 33
0:38 0:28 0:25 0:28 0:38 0:18 0:25 0:18
m m m m
Min c
Max c
Frequency with TL > 15 dB
0.14 m 0.13 m 0.09 m 0.09 m
0.2 m 0.19 m 0.15 m 0.15 m
600–950 Hz 900–1200 Hz 500–850 Hz 850–1400 Hz
Fig. 2. Design charts showing the TL contours of one unit cell with respect to varying opening size c, subdivision of grids are: (a) 2 2; (b) 3 2; (c) 2 3; (d) 3 3, respectively.
grid, because it has tall and slender chamber (long a and narrow b) to effectively lower the resonant frequency. Targeting traffic noise peak at 1000 Hz, both 3 2and 3 3 grids can provide a suitable attenuation zone. Further comparing Fig. 2(b) and (d), the TL contours of 15 dB and 20 dB are deeper and broader with 3 3 grid. Hence, 3 3 grid with square hole c = 0.09 m is chosen for prototyping and testing, which could provide sound attenuation of more than 10 dB in the design frequency range from 800 to 1400 Hz by a
single cell. The inner dimensions of the resonant chamber chosen for fabrication are: a = 0.25 m, b = 0.18 m, c = 0.09 m, and two air cavities with d = 0.02 m each. 2.2. Prediction of metasurface TL The final geometry of the metasurface ventilation window is sketched in Fig. 3(a). Since acrylic panels of thickness 2 mm will
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be used to fabricate the window prototype, the outer dimension of the unit cell is slightly increased to 0:254 0:184 0:046 m. With 3 3grid, the size of the metasurface window is 0:762 0:552 0:046 m, which fits well into the aperture as shown in Fig. 1(a). In the experimental test, the metasurface window is mounted at the center of a partition wall of size 2:55 2:85m between two reverberation rooms with rigid walls. The length of the two rooms on the left and right sides are 2 m and 5 m, as depicted in Fig. 3(b). A unique sub-structuring approach was developed in the previous study [9] to fully couple the metasurface with the acoustic fields in the adjacent rooms and to predict the TL/SRI of the system. The sub-structuring approach can overcome the computation challenge caused by the three-dimensional problem. Numerically, the unit cell of the metasurface is modeled using FE model to extract its wave propagation parameters, and the acoustic fields in the two rooms are modeled based upon modal expansion theory to reduce the computational cost. Then the metasurface and room modes are coupled together through pressure-velocity continuity conditions to solve the system response and predict airborne sound transmission. The TL of the partition with metasurface ventilation window is first calculated in the linear frequency range from 400 to 1600 Hz in order to correlate with the design frequency in Fig. 2. The metasurface TL (with two rooms) and the unit cell TL (with duct condition under normal incidence, as analyzed in Section 2.1) are plotted in Fig. 3(c). It can be seen that both curves exhibit fast increasing behavior from 700 Hz. The peak is reached at around 900 Hz and then the curve starts to descend. The predicted metasurface TL is above 20 dB from 700 Hz to 1600 Hz. The dome-like TL is attributed to the reactive sound attenuation behavior of the resonant chamber, where incident waves are strongly reflected back due to large impedance mismatch near the resonant frequency. With the attached rooms, the TL of the metasurface partition is higher than the unit cell TL, especially at frequencies outside the main peak. The reason is that although the unit cell is not isolating sound at 400–800 Hz and 1400–1600 Hz, the metasurface window only occupies 1/17 of the total partition area. With the other parts being assumed as rigid, reduction of energy transmission based on area difference supposed to give TL = 10log (17) = 12 dB. This possibly explains the higher metasurface TL at those frequencies. Overall,
the predicted metasurface TL shows it has great potential to provide excellent noise reduction in the design frequency range from 800 to 1400 Hz. 3. In-situ TL measurement In this section, the metasurface window prototype is fabricated and its TL characteristics are measured in-situ to confirm the prediction. Fig. 4(a) shows the window structure made of transparent acrylic panels. The panels are cut by CNC machine and glued together firmly to form one unit cell. Then 3 3 cells are stacked up by applying 3 M VHB tape to ensure the connections are airtight. The dashed lines indicate the apertures for air ventilation, occupying about 1/5 of the total window area. Although we haven’t quantified the airflow performance, good ventilation can be expected as the openings are large, allowing direct air exchange across the window surface. The partition wall with metasurface window is situated in between two rooms, with one being used as the source room and the other as the receiving room. The room dimensions are as sketched in Fig. 3(b). To measure the TL, omnidirectional loudspeaker placed in the source room is excited with a white noise signal. The source signal is at least 40 dB higher than the background noise to keep a sufficient signal-to-noise ratio. It should be noted that the room dimensions do not fully meet the requirements as specified in the lab measurement standard ISO 10140-5 [14], especially the small source room cannot provide an ideal diffuse field condition at very low frequency. The testing condition is more close to the field measurement standard ISO 16283-1 [15]. Thus, the measured TL is not strictly standardized and it is more suitable to be called ‘‘in-situ TL”, or ‘‘apparent SRI” as described in ISO 16283-1. The reverberation time in the source room with negligible absorption is typically between 1.1 s and 1.4 s. The airborne TL of the partition is measured according to ISO 10140-2 [16]. Three measurements in both rooms were taken to obtain the level difference (LD):
LD ¼ Ls Lr
ð1Þ
where Ls and Lr are the averaged sound pressure levels in the source room and receiving room, respectively. The absorption in the
Fig. 3. (a) Dimensions of the chosen unit cell and the metasurface window with 3 3 grid; (b) Dimensions of the two rooms and the partition wall to evaluate the TL of metasurface window. (c) Predicted TL of the metasurface with two rooms and the TL of the constituting unit cell itself.
X. Yu / Applied Acoustics 152 (2019) 127–132
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Fig. 4. (a) Metasurface window prototype being tested between two rooms. (b) Comparison between predicted TL using the numerical approach proposed in Ref. [9] and the measured TL in experiment in 1/3 octave bands. The black dashed curve is the single-number rating according to ISO 717.
receiving room needs to be taken into account, and the partition TL is calculated by correcting LD using the measured reverberation time, as:
ST TL ¼ Ls Lr þ 10log 0:16V
where S is the total area of the partition S = 7.25 m2, V is the total volume of the receiving room V = 36.3 m3. T is the reverberation time of the receiving room measured in 1/3 octave band frequency. The measured TL in 1/3 octave band and the predicted TL using the sub-structuring approach (as introduced in Section 2.2) are compared in Fig. 4(b). It can be observed that the behavior and magnitude of the two curves are consistent, both showing an increasing trend with frequency and an enhanced region between 800 and 1600 Hz. The enhanced region matches with design expectation, which can provide stronger attenuation effect to the main frequencies of typical traffic noise spectra. Below 200 Hz, diverging trends of the predicted and measured TL curves are observed. This could be due to the low modal density in the experimental facilities at low frequencies, but it is also worth noting that it is the predicted trend that is unexpected: decreasing with increasing frequency. Above 800 Hz, the measured partition TL is greater than 20 dB, which agrees with the initial design. The exact TL numbers in each frequency band do show some discrepancies between prediction and measurement, which can be possibly caused by a few reasons: 1) room conditions, such as insufficient source room volume to generate diffuse sound field; 2) neglected vibro-acoustic coupling effect and structure-borne sound transmission, as the window is fabricated using thin acrylic panels; 3) damping of the system, which is difficult to estimate or measure; 4) flanking transmission due to insufficient structural isolation by the other parts of partition walls. These facts are however limited by the current ‘‘in-situ” measurement conditions. The frequency-dependent TLs are further converted into single-number TL to characterize the acoustical performance of the metasurface. The single-number TLs of the prediction and experiment are rated by ISO 717 [17] and given in Table 2. Rw is the weighted sound reduction index calculated using the standard adaption terms within the frequency from 100 to 3150 Hz. Rw + C
Table 2 Single-number quantities derived from 1/3 octave band TL values of the metasurface window (prediction and measurement), and a normal casement window (measurement). SNQ
Meta-window (Prediction)
Meta-window (Measurement)
Normal window (Measurement)
Rw Rw + C Rw + Ctr
22 20 18
22 20 19
15 14 14
and Rw + Ctr are two more single-number quantities to account for different types of noise sources [17]. Generally, Rw is based on A-weighted sound pressure levels, Rw + C and Rw + Ctr are more suitable for describing highway and urban road traffic, respectively. The SNQ values derived from prediction and measurement results are very close. Overall, it can be concluded that the acoustical performance of the metasurface window measured in-situ follows our design, and the airborne sound insulation rating is generally 20 dB. Finally, the sound insulation performance of the metasurface window is compared to a normal casement window to demonstrate the acoustic benefit. Fig. 5(a) illustrates the two comparison cases. The TLs of the metasurface window and the normal window adjacent to it are measured individually using the same steps as described earlier. The normal window is deliberately opened at 15° to provide an aperture equal to the sum of the open surfaces of the metasurface window. The measured TLs of the two cases in 1/3 octave band are compared in Fig. 5(b). It can be seen that the normal window TL is a relatively flat curve with a mean value of around 14 dB. This attenuation value is obtained because the window opening size is much smaller than the whole partition. In contrast, the metasurface window TL is higher at all frequencies, especially a significantly improved region from 800 to 1600 Hz can be identified. The weighted SNQ Rw for the partition with metasurface window is 22 dB, which is 7 dB higher than the partition with normal casement window at 15 dB. To demonstrate the improvement in a more realistic case, we have also tested on real traffic noise signals fed to a loudspeaker. With metasurface window open (normal window closed), the average reading on a sound level meter in the receiving room is 7–8 dB/dBA lower than the case with normal window open (metasurface window closed). The substantial improvement shows the advantage and potential of using the proposed methodology for real ventilation window designs. 4. Conclusions This study has presented an experimental investigation on the sound insulation of a novel ventilation window designed using acoustic metasurface principle. The new window design may overcome the long-standing challenges of traditional ventilation windows such as poor sound insulation, insufficient ventilation, bulky window size and lack of transparency. The design strategy is to use a set of resonant-chamber unit cells periodically arranged in a plane to form an acoustic metasurface with high reflection. The geometric parameters associated with the constituting unit cells were assessed by FE simulations to understand their acoustic characteristics, which were further tuned to provide the best performance for traffic noise reduction. Using the sub-structuring numerical approach developed earlier, the TL of the metasurface
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Fig. 5. (a) Comparison of the in-situ noise reduction performance between metasurface window and normal casement window; the casement window is deliberately opened at 15° to provide an aperture equal to the sum of the open surfaces of the metasurface window. (b) The TL of metasurface window shows significant improvement in 1/3 octave frequency bands, especially between 800 and 1600 Hz.
window was predicted before fabrication, showing excellent noise reduction potential in the desired frequency range. The window prototype has a dimension of 0:76 0:55 m and a thickness of 0.046 m, with 9 square holes of size 0:09 0:09 m each distributed on its surface for ventilation. The sound insulation performance of the window prototype has been determined in-situ using the two-room testing method. The experimental results agree with the predictions and demonstrate the superior noise reduction ability of the proposed window. More specifically, the measured TL of the partition with metasurface window (partition area S = 7.25 m2) is above 20 dB from 800 to 3150 Hz, and the weighted single-number TL is 22 dB. Comparing to a traditional casement window with similar opening size, the TL values in 1/3 octave bands are significantly improved, and overall the single-number rating is increased by 7 dB. Further tests on real traffic noise signals confirm that the metasurface window can produce extra 7–8 dB attenuation on room interior noise compared with the normal window. The proposed methodology can be applied to other noise signals to flexibly tune the focused frequency range and provide desired noise attenuation. Beyond the high sound insulation quantity, the metasurface window also shows a few preferable features, such as simplicity, tunable frequency range, large ventilation area, and low manufacturing cost. The proposed design strategy based on acoustic metasurface can be extended or transferred into other categories of applications, such as noise barriers, controllable acoustic devices and underwater acoustics, etc. Acknowledgement This work is supported by Singapore Agency for Science, Technology and Research (grant No. A1820g0092) and Ministry of National Development (award No. L2NICCFP1-2013-9). The author thanks Dr. Du Liangfen for conducting the TL measurement. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.apacoust.2019.04.003.
References [1] Kang J, Brocklesby MW. Feasibility of applying micro-perforated absorbers in acoustic window systems. Appl Acoust 2005;66(6):669–89. [2] Kim S-H, Lee S-H. Air transparent soundproof window. AIP Adv 2014;4 (11):117123. [3] Yu X, Lau S-K, Cheng L, Cui F. A numerical investigation on the sound insulation of ventilation windows. Appl Acoust 2017;117(Part A):113–21. [4] Assouar B, Liang B, Wu Y, Li Y, Cheng J-C, Jing Y. Acoustic metasurfaces. Nat Rev Mater 2018;3(12):460–72. [5] Xie Y, Wang W, Chen H, Konneker A, Popa B-I, Cummer SA. Wavefront modulation and subwavelength diffractive acoustics with an acoustic metasurface. Nat Commun 2014;5. [6] Li Y, Jiang X, Li R-Q, Liang B, Zou X-Y, Yin L-L, et al. Experimental Realization of Full Control of Reflected Waves with Subwavelength Acoustic Metasurfaces. Phys Rev Appl 2014;2(6):064002. [7] Fang Y, Zhang X, Zhou J. Acoustic porous metasurface for excellent sound absorption based on wave manipulation. J Sound Vib 2018;434:273–83. [8] Shen C, Xie Y, Li J, Cummer SA, Jing Y. Acoustic metacages for sound shielding with steady air flow. J Appl Phys 2018;123(12):124501. [9] Yu X, Lu Z, Cheng L, Cui F. On the sound insulation of acoustic metasurface using a sub-structuring approach. J Sound Vib 2017;401:190–203. [10] García-Chocano VM, Sánchez-Dehesa J. Optimum control of broadband noise by arrays of cylindrical units made of a recycled material. Appl Acoust 2013;74 (1):58–62. [11] Morandi F, Miniaci M, Marzani A, Barbaresi L, Garai M. Standardised acoustic characterisation of sonic crystals noise barriers: Sound insulation and reflection properties. Appl Acoust 2016;114:294–306. [12] Garai M, Guidorzi P. European methodology for testing the airborne sound insulation characteristics of noise barriers in situ: Experimental verification and comparison with laboratory data. J Acoust Soc Am 2000;108(3):1054–67. [13] Yu X, Cheng L. Duct noise attenuation using reactive silencer with various internal configurations. J Sound Vib 2015;335:229–44. [14] ISO. 10140–5: Acoustics-Laboratory measurement of sound insulation of building elements-Part 5: Requirements for test facilities and equipment. International Organization for Standardization (ISO); 2010. [15] ISO. Acoustics – Field measurement of sound insulation in buildings and of building elements – Part 1: Airborne sound insulation. International Organization for Standardization (ISO); 2014. p. 16283–91. [16] ISO, 10140-2: Acoustics–Laboratory measurement of sound insulation of building elements–Part 2: Measurement of airborne sound insulation, International Organization for Standardization (ISO), (2010) 1–13. [17] ISO. Acoustics – Rating of sound insulation in buildings and of building elements – Part 1: Airborne sound insulation. International Organization for Standardization (ISO); 2013. p. 717–21.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Design and in-situ measurement of the acoustic performance of a metasurface ventilation window Xiang Yu Institute of High Performance Computing, A*STAR, 138632, Singapore
a r t i c l e
i n f o
Article history: Received 11 December 2018 Received in revised form 1 April 2019 Accepted 2 April 2019 Available online 6 April 2019 Keywords: Acoustic metasurface Noise control Finite element analysis Transmission loss Acoustic façade
a b s t r a c t Recent studies have discovered that acoustic metasurfaces possess great versatility in designing novel acoustic systems. An earlier theoretical study pointed out that acoustic metasurface constructed using an array of resonant-duct unit cells can provide superior sound insulation while allowing air to ventilate through the openings distributed on the surface. By using such a principle, a full-scale metasurface ventilation window is designed and experimentally demonstrated in this study. The primary goal of this paper is to detail the acoustic design methodology for developing this window prototype and to characterize its sound insulation performance in-situ. The dimensions of the metasurface window and its unit cells are tuned based on acoustic Finite Element (FE) analysis to enhance its noise reduction for traffic noise frequency, as well as to increase the single number quantity (SNQ) noise rating. The measured transmission loss (TL) shows a consistent behavior with the prediction in the design frequency range. Comparing the proposed window to a conventional casement window with an equal opening area, the SNQ from measurement for the metasurface window is 22 dB, which is 7 dB higher than the casement window at 15 dB. The substantial improvement shows the benefit of incorporating metasurface concept into the design of sound insulation components, such as building façade, noise barriers, etc. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Building façades integrated with natural ventilation technology are promising solutions to ease the increasing environmental problems caused by energy consumption for air conditioning. However, public still have concern about utilizing ventilation windows as they often result in poor noise insulation. With greater emphasis on energy-efficient building and tighter restriction on noise, windows that are naturally ventilated, yet capable of providing the same acoustic comfort as closed windows are crucially needed. Conventional windows, such as casement, top-hung and sliding windows, offer minimal noise reduction when they are opened, as airborne sound can transmit freely through the aperture. Some studies have proposed special acoustic treatments on the window opening, such as using staggered window construction to alter the sound transmission path [1], applying acoustic resonators [2] and absorbers [3] to reduce airborne sound transmission. Despite these efforts, new innovations are strongly needed to fundamentally advance the window design philosophy, so that the long-awaited features such as transparency, noise reduction, reduced thickness,
E-mail address: [email protected] https://doi.org/10.1016/j.apacoust.2019.04.003 0003-682X/Ó 2019 Elsevier Ltd. All rights reserved.
adjustable ventilation volume, and easy operation can become reality. Recent studies have discovered that acoustic metasurfaces could open up new opportunities for manipulating sound waves and designing novel acoustic devices [4]. For example, phase gradient metasurfaces enable unusual wavefront modulations, such as anomalous refraction [5], full control of reflected waves [6] and sub-wavelength absorption [7]. Gradient-index metasurface can achieve omnidirectional sound shielding in selected frequencies while permits airflow [8]. Although the physical principles have been demonstrated, few studies have extended the proof-ofconcept to real-world applications. Recently, a theoretical study pointed out that using an acoustic metasurface composed of an array of resonant-duct unit cells can achieve superior sound insulation while allowing air/fluid transport through the openings distributed on the surface [9]. One of the potential applications mentioned earlier was a ventilation window system, whose acoustic frequency can be flexibly tuned to cope with different noise spectra. A computationally efficient sub-structuring approach has been proposed to characterize the Sound Reduction Index (SRI)/ Transmission Loss (TL) of the metasurface system. Here, SRI and TL are interchangeable terms for describing the airborne sound insulation ability, which is defined as the reduction of acoustic
128
X. Yu / Applied Acoustics 152 (2019) 127–132
energy between sound incidence and transmission in the decibel scale. In this study, the metasurface design philosophy is employed to the real design of the ventilation window prototype. The primary goals are to verify the design methodology, validate the numerical prediction and demonstrate the window performance using a fullscale experiment. Similar studies on sonic crystal sound barriers have been performed earlier [10,11]. We have chosen 800 to 1400 Hz as the design frequency range to be focused, since the peak of traffic noise usually appears at 1000 Hz. The A-weighted noise levels in this range are generally higher than the other frequencies [12]. One important consideration in designing the window performance is to raise the single number quantity (SNQ) rating covering the broadband frequency from 100 to 3150 Hz. This paper is organized as follows. Section 2 elaborates the window design methodology to choose the appropriate geometric parameters with respect to the design frequency range. Finite element (FE) models are employed to analyze the frequency characteristics of the unit cells, and the TL of the designed metasurface window is predicted using the unique sub-structuring approach developed earlier to overcome the computational cost. In Section 3, the window prototype is fabricated and its TL is measured in-situ using a partition wall between two rooms. The experimentally measured TL shows overall good agreement with prediction, and the single-number rated TL of the metasurface is significantly improved compared to that of a normal casement window with the same opening area. The experimental results reported in this study are encouraging, and the proposed metasurface window design strategy can potentially solve the challenging problem between ventilation and noise reduction. The design philosophy can be extended to many other systems to overcome the limitations of traditional acoustic devices.
2. Acoustic design methodology 2.1. Design of unit cell frequency Fig. 1(a) shows a rectangular aperture on the partition wall for designing and testing the metasurface window. The aperture dimension is 0:76 0:56m, located in the center of a set of window panes. Except for the aperture, the other window sashes are fully closed and considered as acoustically rigid. The first step to design the metasurface window is to split the aperture into grids. In Fig. 1 (b), four grids options of up to 3 3 cells are illustrated. For sound insulation purpose, even grid subdivision is applied here as we expect identical unit cells with the same acoustic property to
provide united effect without any weak point. The unit cell at each grid is a multi-layer resonant-chamber with a central rectangular hole. Such design allows air/fluid to flow freely while enables sound wave attenuation by means of impedance mismatching in the design frequency, like a reactive duct silencer [13]. We first omit the physical thickness of the chamber walls and simply analyze the air cavity in the resonant chambers. The unit cell’s height and width a b are related to the division of grids, as the aperture size is kept constant. A square hole with size c c is assumed for the sake of simplicity. As the total window thickness is preferable to be thin, only two chamber layers with equal thickness d are considered. Thus, the geometric parameters to be specified for one unit cell include height a, width b, opening size c, and thickness d of the two sub-chambers. The acoustic characteristics of the unit cell with varying geometric parameters are first analyzed using FE simulations. Given the fixed aperture size, Table 1 lists the unit cell dimensions a and b with respect to the grid subdivisions as illustrated in Fig. 1 (b). To maintain adequate ventilation, the length of the square hole c is required to be at least half of a or b, whichever is smaller. The maximum c is set as minimum c plus 0.06 m. Thicknesses of the two sub-chambers d are both 0.02 m to keep the window thin and flat. The FE model to predict the TL of a unit cell has been developed and validated in the previous paper, thus the detailed method will not be repeated here [9]. It is worth mentioning again that the unit cell TL refers to the attenuation behavior of a single element alone, which is calculated in a confined duct with normal sound incidence as illustrated in Fig. 2. The difference with the metasurface TL to be determined later (in between two rooms) is that the latter case considers random incidence from a diffuse sound field and involves interactions between the unit cells. It is already known that the hole size c not only affects ventilation but also has great influence on the TL performance and effective frequencies of the unit cell. To determine the optimal attenuation frequency that could be offered by each grid option, the unit cell TLs with respect to varying c are simulated, and the resultant TLs are plotted as contours to show the applicable frequency range for each case. Fig. 2(a)–(d) present the TL contours for 2 2, 3 2, 2 3, 3 3 grids, respectively. In each TL contour, the common trend is that noise reduction is higher with smaller opening c, and the working frequency is slightly shifted towards higher with an increasing c. It is clearly seen that the applicable frequency ranges for the four cases are quite different. By picking the frequency interval where TL is greater than 15 dB (with the smallest c), Table 1 compares their optimal operating frequencies for selecting the most suitable case for traffic noise. The lowest frequency range is achieved by 2 3
Fig. 1. (a) Dimensions of the aperture for designing the metasurface window; (b) Splitting the aperture area into different grids. The unit cell at each grid is a thin two-layer resonant-chamber with a central square hole. Geometric parameters can be tuned to enhance sound insulation for the desired frequency range.
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X. Yu / Applied Acoustics 152 (2019) 127–132 Table 1 Dimensions of the unit cells for the grid options illustrated in Fig. 1(b). Grids
ab
22 32 23 33
0:38 0:28 0:25 0:28 0:38 0:18 0:25 0:18
m m m m
Min c
Max c
Frequency with TL > 15 dB
0.14 m 0.13 m 0.09 m 0.09 m
0.2 m 0.19 m 0.15 m 0.15 m
600–950 Hz 900–1200 Hz 500–850 Hz 850–1400 Hz
Fig. 2. Design charts showing the TL contours of one unit cell with respect to varying opening size c, subdivision of grids are: (a) 2 2; (b) 3 2; (c) 2 3; (d) 3 3, respectively.
grid, because it has tall and slender chamber (long a and narrow b) to effectively lower the resonant frequency. Targeting traffic noise peak at 1000 Hz, both 3 2and 3 3 grids can provide a suitable attenuation zone. Further comparing Fig. 2(b) and (d), the TL contours of 15 dB and 20 dB are deeper and broader with 3 3 grid. Hence, 3 3 grid with square hole c = 0.09 m is chosen for prototyping and testing, which could provide sound attenuation of more than 10 dB in the design frequency range from 800 to 1400 Hz by a
single cell. The inner dimensions of the resonant chamber chosen for fabrication are: a = 0.25 m, b = 0.18 m, c = 0.09 m, and two air cavities with d = 0.02 m each. 2.2. Prediction of metasurface TL The final geometry of the metasurface ventilation window is sketched in Fig. 3(a). Since acrylic panels of thickness 2 mm will
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be used to fabricate the window prototype, the outer dimension of the unit cell is slightly increased to 0:254 0:184 0:046 m. With 3 3grid, the size of the metasurface window is 0:762 0:552 0:046 m, which fits well into the aperture as shown in Fig. 1(a). In the experimental test, the metasurface window is mounted at the center of a partition wall of size 2:55 2:85m between two reverberation rooms with rigid walls. The length of the two rooms on the left and right sides are 2 m and 5 m, as depicted in Fig. 3(b). A unique sub-structuring approach was developed in the previous study [9] to fully couple the metasurface with the acoustic fields in the adjacent rooms and to predict the TL/SRI of the system. The sub-structuring approach can overcome the computation challenge caused by the three-dimensional problem. Numerically, the unit cell of the metasurface is modeled using FE model to extract its wave propagation parameters, and the acoustic fields in the two rooms are modeled based upon modal expansion theory to reduce the computational cost. Then the metasurface and room modes are coupled together through pressure-velocity continuity conditions to solve the system response and predict airborne sound transmission. The TL of the partition with metasurface ventilation window is first calculated in the linear frequency range from 400 to 1600 Hz in order to correlate with the design frequency in Fig. 2. The metasurface TL (with two rooms) and the unit cell TL (with duct condition under normal incidence, as analyzed in Section 2.1) are plotted in Fig. 3(c). It can be seen that both curves exhibit fast increasing behavior from 700 Hz. The peak is reached at around 900 Hz and then the curve starts to descend. The predicted metasurface TL is above 20 dB from 700 Hz to 1600 Hz. The dome-like TL is attributed to the reactive sound attenuation behavior of the resonant chamber, where incident waves are strongly reflected back due to large impedance mismatch near the resonant frequency. With the attached rooms, the TL of the metasurface partition is higher than the unit cell TL, especially at frequencies outside the main peak. The reason is that although the unit cell is not isolating sound at 400–800 Hz and 1400–1600 Hz, the metasurface window only occupies 1/17 of the total partition area. With the other parts being assumed as rigid, reduction of energy transmission based on area difference supposed to give TL = 10log (17) = 12 dB. This possibly explains the higher metasurface TL at those frequencies. Overall,
the predicted metasurface TL shows it has great potential to provide excellent noise reduction in the design frequency range from 800 to 1400 Hz. 3. In-situ TL measurement In this section, the metasurface window prototype is fabricated and its TL characteristics are measured in-situ to confirm the prediction. Fig. 4(a) shows the window structure made of transparent acrylic panels. The panels are cut by CNC machine and glued together firmly to form one unit cell. Then 3 3 cells are stacked up by applying 3 M VHB tape to ensure the connections are airtight. The dashed lines indicate the apertures for air ventilation, occupying about 1/5 of the total window area. Although we haven’t quantified the airflow performance, good ventilation can be expected as the openings are large, allowing direct air exchange across the window surface. The partition wall with metasurface window is situated in between two rooms, with one being used as the source room and the other as the receiving room. The room dimensions are as sketched in Fig. 3(b). To measure the TL, omnidirectional loudspeaker placed in the source room is excited with a white noise signal. The source signal is at least 40 dB higher than the background noise to keep a sufficient signal-to-noise ratio. It should be noted that the room dimensions do not fully meet the requirements as specified in the lab measurement standard ISO 10140-5 [14], especially the small source room cannot provide an ideal diffuse field condition at very low frequency. The testing condition is more close to the field measurement standard ISO 16283-1 [15]. Thus, the measured TL is not strictly standardized and it is more suitable to be called ‘‘in-situ TL”, or ‘‘apparent SRI” as described in ISO 16283-1. The reverberation time in the source room with negligible absorption is typically between 1.1 s and 1.4 s. The airborne TL of the partition is measured according to ISO 10140-2 [16]. Three measurements in both rooms were taken to obtain the level difference (LD):
LD ¼ Ls Lr
ð1Þ
where Ls and Lr are the averaged sound pressure levels in the source room and receiving room, respectively. The absorption in the
Fig. 3. (a) Dimensions of the chosen unit cell and the metasurface window with 3 3 grid; (b) Dimensions of the two rooms and the partition wall to evaluate the TL of metasurface window. (c) Predicted TL of the metasurface with two rooms and the TL of the constituting unit cell itself.
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Fig. 4. (a) Metasurface window prototype being tested between two rooms. (b) Comparison between predicted TL using the numerical approach proposed in Ref. [9] and the measured TL in experiment in 1/3 octave bands. The black dashed curve is the single-number rating according to ISO 717.
receiving room needs to be taken into account, and the partition TL is calculated by correcting LD using the measured reverberation time, as:
ST TL ¼ Ls Lr þ 10log 0:16V
where S is the total area of the partition S = 7.25 m2, V is the total volume of the receiving room V = 36.3 m3. T is the reverberation time of the receiving room measured in 1/3 octave band frequency. The measured TL in 1/3 octave band and the predicted TL using the sub-structuring approach (as introduced in Section 2.2) are compared in Fig. 4(b). It can be observed that the behavior and magnitude of the two curves are consistent, both showing an increasing trend with frequency and an enhanced region between 800 and 1600 Hz. The enhanced region matches with design expectation, which can provide stronger attenuation effect to the main frequencies of typical traffic noise spectra. Below 200 Hz, diverging trends of the predicted and measured TL curves are observed. This could be due to the low modal density in the experimental facilities at low frequencies, but it is also worth noting that it is the predicted trend that is unexpected: decreasing with increasing frequency. Above 800 Hz, the measured partition TL is greater than 20 dB, which agrees with the initial design. The exact TL numbers in each frequency band do show some discrepancies between prediction and measurement, which can be possibly caused by a few reasons: 1) room conditions, such as insufficient source room volume to generate diffuse sound field; 2) neglected vibro-acoustic coupling effect and structure-borne sound transmission, as the window is fabricated using thin acrylic panels; 3) damping of the system, which is difficult to estimate or measure; 4) flanking transmission due to insufficient structural isolation by the other parts of partition walls. These facts are however limited by the current ‘‘in-situ” measurement conditions. The frequency-dependent TLs are further converted into single-number TL to characterize the acoustical performance of the metasurface. The single-number TLs of the prediction and experiment are rated by ISO 717 [17] and given in Table 2. Rw is the weighted sound reduction index calculated using the standard adaption terms within the frequency from 100 to 3150 Hz. Rw + C
Table 2 Single-number quantities derived from 1/3 octave band TL values of the metasurface window (prediction and measurement), and a normal casement window (measurement). SNQ
Meta-window (Prediction)
Meta-window (Measurement)
Normal window (Measurement)
Rw Rw + C Rw + Ctr
22 20 18
22 20 19
15 14 14
and Rw + Ctr are two more single-number quantities to account for different types of noise sources [17]. Generally, Rw is based on A-weighted sound pressure levels, Rw + C and Rw + Ctr are more suitable for describing highway and urban road traffic, respectively. The SNQ values derived from prediction and measurement results are very close. Overall, it can be concluded that the acoustical performance of the metasurface window measured in-situ follows our design, and the airborne sound insulation rating is generally 20 dB. Finally, the sound insulation performance of the metasurface window is compared to a normal casement window to demonstrate the acoustic benefit. Fig. 5(a) illustrates the two comparison cases. The TLs of the metasurface window and the normal window adjacent to it are measured individually using the same steps as described earlier. The normal window is deliberately opened at 15° to provide an aperture equal to the sum of the open surfaces of the metasurface window. The measured TLs of the two cases in 1/3 octave band are compared in Fig. 5(b). It can be seen that the normal window TL is a relatively flat curve with a mean value of around 14 dB. This attenuation value is obtained because the window opening size is much smaller than the whole partition. In contrast, the metasurface window TL is higher at all frequencies, especially a significantly improved region from 800 to 1600 Hz can be identified. The weighted SNQ Rw for the partition with metasurface window is 22 dB, which is 7 dB higher than the partition with normal casement window at 15 dB. To demonstrate the improvement in a more realistic case, we have also tested on real traffic noise signals fed to a loudspeaker. With metasurface window open (normal window closed), the average reading on a sound level meter in the receiving room is 7–8 dB/dBA lower than the case with normal window open (metasurface window closed). The substantial improvement shows the advantage and potential of using the proposed methodology for real ventilation window designs. 4. Conclusions This study has presented an experimental investigation on the sound insulation of a novel ventilation window designed using acoustic metasurface principle. The new window design may overcome the long-standing challenges of traditional ventilation windows such as poor sound insulation, insufficient ventilation, bulky window size and lack of transparency. The design strategy is to use a set of resonant-chamber unit cells periodically arranged in a plane to form an acoustic metasurface with high reflection. The geometric parameters associated with the constituting unit cells were assessed by FE simulations to understand their acoustic characteristics, which were further tuned to provide the best performance for traffic noise reduction. Using the sub-structuring numerical approach developed earlier, the TL of the metasurface
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Fig. 5. (a) Comparison of the in-situ noise reduction performance between metasurface window and normal casement window; the casement window is deliberately opened at 15° to provide an aperture equal to the sum of the open surfaces of the metasurface window. (b) The TL of metasurface window shows significant improvement in 1/3 octave frequency bands, especially between 800 and 1600 Hz.
window was predicted before fabrication, showing excellent noise reduction potential in the desired frequency range. The window prototype has a dimension of 0:76 0:55 m and a thickness of 0.046 m, with 9 square holes of size 0:09 0:09 m each distributed on its surface for ventilation. The sound insulation performance of the window prototype has been determined in-situ using the two-room testing method. The experimental results agree with the predictions and demonstrate the superior noise reduction ability of the proposed window. More specifically, the measured TL of the partition with metasurface window (partition area S = 7.25 m2) is above 20 dB from 800 to 3150 Hz, and the weighted single-number TL is 22 dB. Comparing to a traditional casement window with similar opening size, the TL values in 1/3 octave bands are significantly improved, and overall the single-number rating is increased by 7 dB. Further tests on real traffic noise signals confirm that the metasurface window can produce extra 7–8 dB attenuation on room interior noise compared with the normal window. The proposed methodology can be applied to other noise signals to flexibly tune the focused frequency range and provide desired noise attenuation. Beyond the high sound insulation quantity, the metasurface window also shows a few preferable features, such as simplicity, tunable frequency range, large ventilation area, and low manufacturing cost. The proposed design strategy based on acoustic metasurface can be extended or transferred into other categories of applications, such as noise barriers, controllable acoustic devices and underwater acoustics, etc. Acknowledgement This work is supported by Singapore Agency for Science, Technology and Research (grant No. A1820g0092) and Ministry of National Development (award No. L2NICCFP1-2013-9). The author thanks Dr. Du Liangfen for conducting the TL measurement. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.apacoust.2019.04.003.
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