The 21st International Congress on Sound and Vibration 13-17 July, 2014, Beijing/China
MICROPERFORATED PANEL ABSORBER DESIGN: A TUTORIAL D. W. Herrin, X. Hua, and J. Liu University of Kentucky, Lexington, KY e-mail:
[email protected] A microperforated panel absorber is best thought of as a noise control system consisting of both the panel itself and the air space behind the panel. This work looks at practical design aspects related to both the panel and the air space. The work by Maa for determining the transfer impedance of the panel is relied on heavily, and it is shown that his equations are useful for characterizing microperforated panels consisting of slit type perforations and for non-uniform hole diameters. Because panels are often placed in dirty environments, the effect of contamination is discussed and it is noteworthy that performance of a panel can sometimes be improved when polluted. The second part of this paper will focus on the design of backings behind the panel. It has been shown that both partitioning and varying the backing cavity depth can greatly improve microperforated panel performance. A number of schemes that Wirt suggested over 30 years ago are used to enhance both the low and broadband frequency sound absorption.
1.
Introduction
Industry by and large addresses mid and high frequency noise issues by using sound absorbing materials like fibers and foams to reduce noise. They are inexpensive, sometimes provide a thermal function, and have excellent sound absorption. However, there are numerous drawbacks. First, low frequency absorption remains a problem unless very thick absorbers are used. Moreover, fibers and foams often become laden with oils and other contaminants that are flammable. Sometimes protective covers are placed over the fiber or foam, but then acoustic performance is compromised. Likewise, sound absorbers are often desired in harsh or high temperature environments in which protective covers are easily damaged. Additionally, the long-term health consequences of fibers in buildings are concerning. Bearing that in mind, the interest in microperforated panel (MPP) absorbers is understandable. Most commercially available microperforated panel absorbers are made from metals, like aluminium or steel, or plastic. In view of that, sound attenuation can be accomplished without exposing building occupants to potentially dangerous airborne fiber and mold issues. Absorbers can be easily cleaned and sterilized for hygienic applications such as medical or food preparation facilities. Additionally, panels can be manufactured from materials that have a high fire rating (i.e., not flammable or smoke generating). First generation MPP absorbers consisted of circular shaped holes what were less than 1 mm in diameter. Nowadays, many MPP absorbers are manufactured by etching, shearing slits into metal or plastics, or grinding. As a result, MPP absorbers are steadily decreasing in price and are being
ICSV21, Beijing, China, 13-17 July 2014
1
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014 used in a number of industrial, transportation, and architectural applications. Nevertheless, they remain a niche solution since they are generally more costly than fibers and foams. While cost is perhaps most important, fibers and foams have another advantage over MPP absorbers. They are generally effective at mid to high frequencies without regard to their placement. As a result, NVH engineers can use them to effectively treat problems with very little thought. Additionally, the properties of many fibers and foams are readily available from the manufacturers and can be measured easily. Though designers recognize the advantages of MPP absorbers, they often struggle with employing them to solve their specific noise problems. This is primarily due to the fact that an MPP absorber is a system consisting of the MPP itself and the environment it is placed in. This paper is intended to serve as a general tutorial for designing with MPP absorbers. It is particularly geared towards engineers who are considering implementing MPP absorbers in their products. The work herein assumes that a backing cavity is placed behind the MPP since MPP absorbers are most often configured in this way.
2.
Designing MPP absorbers
When designing MPP absorbers, the following steps should be taken to guarantee an effective implementation. 1. Select an MPP and measure the transfer impedance. It is beneficial to use a nonlinear least squares curve fit to determine effective MPP parameters based on Maa’s theory. This aids the designer in better understanding the MPP in use and can point to redesign of the panel to improve the performance or the selection of another panel. 2. Consider the environment the MPP is placed in. The effective parameters determined in Step 1 can be used to estimate the transfer impedance of the MPP in flow, for high sound pressures, and also for contamination or dust build-up. 3. Partition the backing cavity so that the MPP behaves in a local reacting manner. An MPP absorber will be ineffective at attenuating grazing waves if it is not partitioned. 4. Vary the depth of the backing cavity to improve the low and broadband frequency attenuation. Wirt proposed a number of creative approaches to vary cavity depth without increasing the total volume of the absorber.
3.
Select an MPP and measure transfer impedance
3.1 Transfer impedance equations including grazing flow Maa first developed MPP absorbers with high temperature and flow environments in mind. In the course of his work, he developed equations to characterize MPP absorbers; first for circular holes and later for elliptical shaped perforations1-2. In doing so, he paved the way for much of the subsequent engineering work on applying MPP absorbers to solve noise problems. The real ( ) and imaginary ( ) parts of the transfer impedance ( ) for circular perforations, according to Maa and including adjustments for grazing flow suggested by researchers at KTH3-4, can be expressed as Re
1
2
2
|
|
(1)
and
ICSV21, Beijing, China, 13-17 July 2014
2
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
Im
1
2
0.85
1
|
| (2)
for a panel with hole diameter , porosity and thickness . is the dimensionless shear wave number which relates the hole diameter to the viscous boundary layer thickness. It is expressed as (3) /4 , and are the kinematic viscosity, mass density, and speed of sound of the medium respectively. is the grazing flow Mach number and | | is the absolute value of the peak particle velocity in the hole. and are zeroth and first order Bessel functions of the first kind respectively. is the surface resistance and is defined as √2 (4) 2 where is the dynamic viscosity. is equal to 2 for holes with rounded edges and 4 for holes with sharp edges. is related to the flow effect on reactance and is expressed as 1 (5) 1 12.6 0.15 0.0125. The above equations are for circular holes though researchers at KTH have developed similar equations for elliptical shaped slits. The impedance of the perforate plus backing cavity is (6) cot where is the cavity depth. Once the surface impedance ( ) is determined, the normal incident absorption coefficient can be expressed as 4 (7) 1 and are the real and imaginary parts of the surface impedance ( ) in Equation (6). where 3.2 Measurement Though a number of methods have been proposed for measuring transfer impedance, it is straightforwardly measured using the impedance difference method suggested by Wu et al.5. A sample is cut to fit in an impedance tube and the impedance is measured for the sample and backing air cavity. The impedance in front of the panel is the combined impedance of the panel itself and the cavity. The impedance behind the panel is the impedance of the backing cavity, which is directly measured without the panel in the tube (or can be calculated). Both of these impedances can be measured using the two-microphone method6-7 and the transfer impedance is the difference between the two. 3.3 Determination of effective parameters The perforations in first generation MPP were often cut using lasers. However, cheaper manufacturing approaches are being used for second generation MPP. There are a number of commercially available MPP with slit-shaped perforations where perforations are sheared into the material. Figure 1 shows a magnified view and a cross-sectional view of a single slit. Notice that the crosssectional area of the slit varies with depth, and the slit is angled through the material. In a MPP of this type, geometric parameters like slit size and porosity, are difficult to determine and Equations (1) and (2) are not directly applicable. However, prior work by the authors8 showed that a nonlinear least squares data fitting (NLLSF) algorithm could be used to determine an effective hole diameter and porosity using EquaICSV21, Beijing, China, 13-17 July 2014
3
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014 tions (1) and (2) as a basis. The procedure is as follows. The sound absorption coefficient of a sample with known cavity depth is first measured in an impedance tube. The algorithm takes a function , , defined according to Equation (7) using assumed values of and and compares that against the measured sound absorption . The NLLSF can be expressed as min‖ ,
‖
,
min
, ,
,
(8)
subjected to reasonable constraints for the porosity ( ) and hole diameter ( ) where quency at the th data point.
is the fre-
Thickness
a.
b.
Figure 1. a) Photo of a micro-slit absorber b) Section view of a slit.
Figure 2a compares the measured sound absorption to the NLLSF for a MPP with slit perforations. Figure 2b compares the real and imaginary parts of the transfer impedance. Notice the excellent agreement in each case. There are a number of advantages to characterizing the MPP using the NLLSF. First, the sound absorption coefficient can be extrapolated to higher frequencies than the impedance tube measurement would allow. Similarly, data can be extrapolated to lower frequencies where measured data using an impedance tube is noisy due to low sound absorption and source strength. Additionally, knowing the effective parameters can point to making modifications to the MPP itself if the performance is judged to be insufficient. Normalized Transfer Impedance
Absorption Coefficient
1 0.8 0.6 0.4 Measured 0.2
NLLSF
0 0
1000
2000
3000
4000
4 Real (Measured) Real (NLLSF) Imag (Measured) Imag (NLLSF)
3 2 1 0 0
1000
Frequency (Hz)
a.
2000
3000
4000
Frequency (Hz)
b.
Figure 2. Comparison of measured and NLLSF a) sound absorption coefficient and b) transfer impedance.
4.
Consider the environment the MPP is placed in
The designer should also consider the environment the MPP is placed within. After determining NLLSF fitted geometric parameters, the designer can then adjust the transfer impedance for temperature, flow, particle velocity amplitude, and contamination effects using Equations (1) and (2). In most situations, the engineer should have some idea of the first three of these for a particular ICSV21, Beijing, China, 13-17 July 2014
4
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014 application, and Equations (1) and (2) can be used directly to predict the adjusted transfer impedance. KTH4 has performed work of this sort with some success. However, determining the effect of contamination is less obvious. Prior work by the authors8 has shown that dust contamination will mostly reduce the effective porosity while the effective hole diameter remains relatively constant. Figures 3a and 3b show the sound absorption with dust accumulation for two different MPP absorbers. The effective porosities and hole diameters are indicated in the legends. Notice that dust accumulation deteriorates the performance in the case of Figure 3a and improves the performance in Figure 3b. The first MPP absorber is 1 mm thick with slit perforations whereas the second is 0.3 mm thick with circular perforations. 1
1
Absorption Coefficinet
Absorption Coefficinet
0.8 0.6 0.4
0.9% Porosity, 0.2 mm Diameter 2.0% Porosity, 0.2 mm Diameter 2.3% Porosity, 0.2 mm Diameter 2.0% Porosity, 0.2 mm Diameter 4.2% Porosity, 0.2 mm Diameter
0.2 0 0
1000
2000 Frequency (Hz)
3000
a.
0.8
0.6
0.4
1.4% Porosity, 0.3 mm Diameter 1.7% Porosity, 0.3 mm Diameter
0.2
2.0% Porosity, 0.4 mm Diameter 2.8% Porosity, 0.4 mm Diameter
0 4000
0
1000
2000 Frequency (Hz)
3000
4000
b.
Figure 3. Measured sound absorption for different levels of contamination for a) 1.0 mm thick MPP with slit perforations and b) 0.3 mm thick MPP with circular perforations.
These results indicate that the MPP absorber performance will depend on the level of dust accumulation. The following steps are suggested. For a particular application, the effective parameters should be determined for the MPP absorber clean and then after use (i.e. dirty). In doing so, a range of transfer impedances and corresponding performances can be established. After doing so, the engineer can determine the importance of contamination for a given application and recommend cleaning regimes. Alternatively, the engineer may select an MPP absorber that will perform well for a typical amount of dust contamination.
5.
Partition the backing cavity
Attenuation can be enhanced by partitioning the backing cavity behind the MPP. Yairi et al.9, and Toyoda and Takahashi10 demonstrated that MPP absorbers have comparable sound absorption to foams and fibers in certain frequency bands if the backing cavity is partitioned. The authors performed two studies examining the effect of partitioning11-12. In the latter study12, the authors investigated the mechanism for the improved performance with partitioning using both experimentation and boundary element simulation. The test case considered was a sealed plenum (0.96 m 0.57 m 0.42 m) with a loudspeaker attached via a short tube on one end. The MPP was placed on the other side with a backing cavity depth of 65 mm. Honeycomb partitioning as shown in Figure 4a was placed behind the MPP. A type of insertion loss was defined as being the difference between average sound pressure on a plane anterior to the MPP untreated and treated. The insertion loss with and without partitioning is shown in Figure 4b. The acoustic modes of the plenum are also indicated in the plot as well. The attenuation for the lateral and or grazing modes is markedly improved by on average 8 dB if partitioning is used. The effect on longitudinal ( ) modes is noticeable but less pronounced. ICSV21, Beijing, China, 13-17 July 2014
5
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014 These conclusions were confirmed using boundary element analysis. The results indicate that partitioning of some type should be used if broadband attenuation is required12. 30 MPP with Partitioning MPP
(2,1,0) (1,0,1) (3,1,0) (3,0,0) (0,0,1)
20
IL (dB)
(1,0,0)
(0,1,0)
(4,0,0)
(0,3,0) (0,0,2)
(2,0,0)
10
0
-10 0
200
400
600
800
1000
Frequency (Hz)
Figure 4. a) Photo showing honeycomb partitioning posterior to MPP b) Insertion loss due to MPP absorber with and without partitioning.
6.
Vary the depth of the backing cavity
Nearly 40 years ago, Les Wirt, from Lockheed, developed a number of novel absorbers that were intended as alternatives to fibers and foams13. These absorbers were developed to meet the unique durability, space, and temperature needs of the aerospace industry. Wirt gave attentiongrabbing names to these absorbers like parasones, bicores, permobliques, and schizophoniums. The primary intent of each of these concepts was to creatively vary and/or increase the tube length of a reactive absorber. Moreover, Wirt suggested placing a permeable sheet or perforate in front of or within the tubes to create a resistive attenuator. Though mostly overlooked in the intervening years, these concepts are directly applicable to improving the performance of MPP absorbers. Using the electrical analogy, the MPP absorber can be thought of as being in series with the impedance of the backing cavity. Figure 5a illustrates the analogous electrical circuit. In a similar manner, consider the case where the cavity is partitioned into a series of channels with varying depths as shown in Figure 5b. It can be assumed that the sound pressure is constant on the front surface of the MPP. In that case, the combined transfer impedance and reactance for each channel may be considered in parallel with its neighbor as shown in Figure 5b. Ztr Plane Wave
Zcavity
Cavity
a. 1 …
Plane Wave
Ztr
Ztr
Ztr
2
Zcavity.1
Zcavity.n
n
b. Figure 5. Equivalent circuit analogy for a) single cavity and b) multiple cavities.
ICSV21, Beijing, China, 13-17 July 2014
6
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014 The backing partitioned substrate can be designed so that cavity depth is increased which provides lower frequency absorption without adding additional volume. Simultaneously, the cavity depth is varied so that broadband frequency absorption is achieved. One candidate design called a three-channel configuration is shown in Figures 6a and 6b. Notice that one channel wraps around the middle channel. This effectively creates one channel that has a length that is twice the cavity depth. The sound absorption of the MPP with three-channel backing was measured in an impedance tube and is compared with both a plane wave model and boundary element analysis with good agreement in Figure 6c. Additionally, the sound absorption with no backing is also shown for comparison. The results indicate that both the low frequency and broadband sound absorption is substantially improved with the backing.
1.0
Absorption Coefficient
0.8
MPP
a.
0.6
0.4 Measurement Empty Backcing
0.2
BEM
95 mm
Plane Wave 0.0 0
b.
500
1000 Frequency (Hz)
1500
2000
c.
100 mm
Figure 6. a) Photo showing three-channel backing b) Schematic showing three-channel backing, and b) sound absorption of three-channel backing.
Another candidate backing termed a schizophonium is shown in Figure 7a. It consists of a cone as shown. There is a small gap between the mouth of the cone and the end of the cavity. The sound absorption is compared in Figure 7b. Though the broadband absorption is similar to a standard MPP, the low frequency absorption is substantially improved. See Reference 14 for additional information about this backing configuration. 1.0
MPP Absorption Coefficient
0.8
Open Mouth
0.6 0.4 Measured
0.2
Plane Wave Measured (Empty Cavity)
0.0 0
500
1000
1500
2000
Frequency (Hz)
a. b. Figure 7. a) Schematic showing schizophonium backing, and b) sound absorption comparison.
ICSV21, Beijing, China, 13-17 July 2014
7
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
7.
Conclusions
In this paper, a suggested process for designing MPP absorbers has been outlined. The MPP should first be characterized by measuring the transfer impedance and determining effective geometric parameters using a NLLSF. These effective parameters can be used to adjust the transfer impedance in accordance with the environment (including temperature, grazing flow, and high sound pressure levels) the MPP is placed in. After selecting and characterizing the MPP, attention should then be shifted to the backing cavity. It should be partitioned, and additional performance can be achieved by creatively varying the backing cavity depth.
ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of the Vibro-Acoustics Consortium.
REFERENCES 1 2 3
4 5
6 7 8 9
10 11
12 13 14
Maa, D. Y., Theory and Design of Microperforated-Panel Sound-Absorbing Construction, Scientia Sinica XVIII, pp. 55-71, 1975. Maa, D. Y., Theory of Microslit Absorbers, Acta Acustica Peking, Vol. 25, No. 6, pp. 481485 (2000) [in Chinese]. Allam, S., Guo, Y., and Åbom, M. Acoustical Study of Micro-Perforated Plates for Vehicle Applications, SAE Noise and Vibration Conference, Paper No. 2009-01-2037, St. Charles, IL, 2009. Allam, S. and Åbom, M. A New Type of Muffler Based on Microperforated Tubes, ASME Journal of Vibration and Acoustics, Vol. 133, 2013. Wu, T. W., Cheng, C. Y. R. and Tao, Z., Boundary Element Analysis of Packed Silencers with Protective Cloth and Embedded Thin Surfaces, Journal of Sound and Vibration, Vol. 261, No. 1, pp. 1-15, 2003. Chung, J. Y. and Blaser, D. A. Transfer function method of measuring in-duct acoustic properties. I. Theory. J. Acoust. Soc. Am., Vol. 68 No. 3, 907-913 (1980). Chung, J. Y. and Blaser, D. A. Transfer function method of measuring in-duct acoustic properties. II. Experiment. J. Acoust. Soc. Am. Vol. 68, No. 3, 914-921 (1980). Liu, J., Hua, X., and Herrin, D. W. Estimation of Effective Parameters for Microperforated Panel Absorbers and Applications, Applied Acoustics, Vol. 75, pp. 86-93, 2014. Yairi, M., Sakagami, K., Morimoto, M. and Minemura, A. Acoustical Properties of Microperforated Panel Absorbers with Various Configurations of the Back Cavity, 12th International Congress on Sound and Vibration, Lisbon, Portugal, 2005. Toyoda, M. and Takahashi, D. Sound Transmission through a Microperforated Panel Structure with Subdivided Air Cavities, J. Acoust. Soc. Am. 124, pp. 3594-3603, 2008. Liu, J., Herrin, D. W., and Seybert, A. F. Application of Micro-Perforated Panels to Attenuate Noise in a Duct”, SAE Transactions Journal of Passenger Cars: Mechanical Systems, pp. 1629-1633, 2007. Liu, J. and Herrin, D. W. Enhancing Micro-perforated Panel Attenuation by Partitioning the Adjoining Cavity” Applied Acoustics, Vol. 71, pp. 120-127, 2010. Wirt, L. S. Sound-Absorptive Materials to Meet Special Requirements, Journal of the Acoustical Society of America, Vol. 57, No. 1, pp. 126-143, 1975. Hua, X., Herrin, D. W., and Jackson, P., “Varying Backing Cavity Depths to Achieve Broadband Absorption using Micro-Perforated Panels,” Noise-Con 2013, Denver, CO, August 2628, 2013.
ICSV21, Beijing, China, 13-17 July 2014
8
