ACOUSTIC PERFORMANCE OF MICROPERFORATED
PANEL ABSORBER ARRAY SUBJECTED TO HIGH INTENSITY SOUND
Y. K. Chiang and Y. S. Choy
Department of Mechanical Engineering, The Hong Kong Polytechnic University, HKSAR
email: [email protected]
Microperforated panel (MPP) absorber is a promising fiber-free alternative to the porous materials. It is widely applied in the air-conditioning systems and aircraft engines which are the environments with high sound pressure. The present study focuses on the acoustic properties of the
parallel arranged MPP absorber array at high incident sound intensity. A different impedance
model instead of the traditional linear impedance model is required such that the effects of jets
and vortex rings formed at the exit of orifices on the acoustic properties are taken into account.
The absorption performance are investigated by adopting the empirical acoustic impedance
model, in which the excitation pressure is considered. The MPP absorber array with different
designed geometric parameters are studied. The preliminary results show that a broader frequency
range is obtained by the MPP absorber array by comparing with a single MPP absorber. Also, a
better acoustic absorption performance is achieved at high sound intensity. Experimental studies
are conducted to verify the empirical model for the array of MPP absorber. The prototype is tested
under normal incident. The estimated and measured results show good agreement.
1.
Introduction
Microperforated panels (MPPs) are thin plates with numerous orifices whose diameter is reduced
to sub-millimeter scale in order to provide sufficient acoustic resistance and low acoustic reactance
for sound absorption. Maa [1, 2] introduced the theoretical basis of MPP and also an empirical impedance model to predict the acoustic performance of such a device in the linear regime. However,
in many practical applications, MPP is utilized in extreme environments at moderate or high sound
pressure level such as aircraft engines and launcher fairings [3, 4]. In the case of high intensity of the
incident sound, a high particle velocity is induced in the orifices of MPPs. Hence, flow separation
occurred at the edges of the perforations. A number of researchers [5, 6] have investigated the acoustic
behaviour of the orifice in the nonlinear regime. From the flow visualizations, Ingard and Labate [7]
observed the acoustic circulation at moderate acoustic intensity. When the sound excitation further
increases, flow separation and the jet formation are observed at the outlet of orifice [8, 9]. The acoustic energy converted to the vertical energy due to the vortex ring formation. This results in an increase
of acoustic resistance of the orifices.
The acoustic impedance is greatly dependent on the particle velocity in the orifice or in front of
the panel at high sound pressure levels. Several theoretical models were developed to study the nonlinear acoustic resistance or energy loss. Cummings [10] has studied the acoustic power losses induced by the production of vorticity at the orifice lip by means of a one-dimensional numerical timedomain model. By introducing the empirical vena contracta coefficient, Cummings and Eversman
[11] improved the quasi-steady model to investigate the nonlinear acoustic resistance in the absence
of mean flow. Kraft, Yu and Kwan [3] adopted the discharge coefficient, which is defined as the
actual discharge (affected by the friction as the jet passes through the orifice) divided by the ideal
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discharge (without friction), as the nonlinear parameter to predict the nonlinear acoustic impedance.
Later on, Maa [12] introduced a nonlinear impedance which is a combination of the linear impedance
and the end correction which is related to the particle velocity inside the orifices. Park [4] then improved the empirical nonlinear impedance such that the dependence of impedance on the geometric
parameters is included.
Although the MPP provide higher absorption performance at high sound pressure level, the absorption bandwidth can be even broader by using the parallel arranged multiple micro-perforated
panel absorbers. Zha et al. [13] proposed a two parallel arranged MPP absorbers to enhance the sound
absorption capability in linear regime. In the latter work, Wang and Huang [14] established a finite
element model to simulate the acoustic behaviour of three parallel arranged MPP absorbers. It shows
that a broader absorption bandwidth can be achieved by combining different frequency bands. The
acoustic absorption performance of the array of absorbers with different backing cavity depths which
are partially filled with three different types of polymer materials is studied [15]. However, most of
the existing works concentrated on the acoustic behaviour of the MPP absorber array in the linear
regime. This study is conducted to exam the sound absorption performance of the MPP absorber array
with different cavity depths in the nonlinear regime.
In this study, a finite element model is established to study the acoustic behaviour of the MPP
absorber array that is subjected to the high intensity of normal incident sound. Section 2 describes the
finite element modelling of the present study. The numerical predictions and discussions of the sound
absorption performance are given in Section 3. Section 4 describes the experimental studies. Finally,
the conclusions are given in Section 4.
2.
Finite element modelling
Figure 1 shows the two-dimensional configuration of the MPP absorber array which consists of an
MPP and two partitioned rectangular cavities with widths W1, and W2 and depths D1 and D2 respectively. A finite element model is established to investigate the acoustic performance of the MPP absorber array when it is subjected to high intensity sound.
Figure 1: Schematic diagram of MPP absorber array with two different cavity depths.
The acoustic impedance of the MPP can be determined by an empirical acoustic model which is
related to the panel thickness t, the orifice diameter d, the perforation ratio σ and also the nonlinear
term due to the high sound pressure [4],
0.06


2 2 pi
32 t 
K2
2  d 
d 
0.155


Z
1


K

1.59

0.25


0.5

 
 


0c0 d 2 
32 32  t  
0c0 2 2
t


,
(1)
1


2 1/2

2



2 2 pi 1  
t  
K 
1

d 
 0.25 
i
 0.5   
1   9 
  0.85   1 
2
2
2
 
 c0  
2 
0c0 
 t   1   
 


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where K  d 0 / 4 , pi is the rms normal incident pressure, ω is the angular frequency, ρ0 is the
air density, c0 is the sound speed and η is the coefficient of viscosity. The acoustic field inside the
backed cavity and the duct is governed by the Helmholtz equation,
(2)
 2  k 2    0 ,
where k is the acoustic wavenumber and ϕ is the velocity potential.
The duct wall, partitioning wall and backing walls are assumed to be acoustically rigid, which
means that the particle velocity normal to the walls vanishes such that the boundary condition can be
expressed as

(3)
 0,
n
where n represents the outward normal direction to the boundary.
The incident pressure is assumed to plane wave with the amplitude pi . The governing Eq. (2)
together with the relevant boundary conditions of the incident wave and the acoustically rigid wall is
solved by using COMSOL Multiphysics.
3.
Numerical results
According to the finite element model presented above, the absorption coefficient, α and the nonlinear acoustic resistance, zr of MPP which d = 1 mm, t = 1 mm and σ = 5.14% are predicted and
compared with the empirical results given by Park [4] in Fig. 2 as a preliminary validation.
Figure 2: Comparison of the predicted results from the finite element model and the analytical solution. The
depth of the backing cavity is D = 100 mm. The sound pressure level is 115 dB.
In the present study, the acoustic absorption performances are studied for the MPP absorber array
with two subcavities only. The widths of each subcavity are assumed to be the same. It means that
for the case of two subcavities, W1 = W2 = 50 mm.
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3.1 Comparison the absorption performance between the single MPP absorber and
dual MPP absorber array at high sound pressure level
Although the acoustic absorption performance of the MPP can be improved at high sound pressure
level, the enhancement might not sufficient enough for the linear to absorb half of the acoustic energy,
α = 0.5. The properties of MPP examined are d = 1 mm, t = 1 mm and σ = 5.14%. The absorption
coefficients of the single MPP backed by the cavity of D = 100mm (dash line), D = 50 mm (dot line)
and the MPP absorber array of D1 = 100mm and D2 = 50 mm (solid line) at SPL = 115 dB are shown
in Fig. 3(a). The maximum value of α is only ~0.43 and ~0.45 for single MPP of D = 100 mm and D
= 50 mm respectively. In contrast, for the MPP absorber array, the absorption coefficient is maintained at 0.5 from frequency f = 510 to 1020 Hz. The half-absorption bandwidth is improved to 2.
Fig. 3(b) shows the change of half-absorption bandwidth with the orifice diameter of the single MPP
and the dual MPP absorber array. It indicates that, without changing the thickness and the perforation
ratio of the MPP, the d should be reduced to 0.45 mm, in order to achieve the similar absorption
performance of the MPP absorber array for both D = 100 mm and D = 50 mm.
Figure 3: Comparison of the absorption performance between the MPP absorber array and single MPPs. (a)
Absorption coefficient; (b) Half-absorption bandwidth. The results are predicted at 115dB.
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3.2 Comparison the absorption performance of dual MPP absorber array between
linear and nonlinear regimes
The acoustic behaviours of the MPP absorber array are compared between the linear and nonlinear
regimes as shown in Figs. 4(a) and 4(b) respectively. The MPP properties are d = 0.8 mm, t = 0.5 mm
and σ = 1% which are the same as that of Ref. 14. It indicates that, for both linear and nonlinear cases,
the MPP absorber array with two different cavity depths can provide a higher absorption level, say,
α > 0.8, when comparing the performance given by the single MPPs. Although, in the linear regime,
the absorption coefficient can even reach to α > 0.95, such performance can only be achieved for
some narrow bandwidth around the frequencies of local resonances, i.e., f = 420 Hz and 860 Hz.
However, for the MPP absorber array which is subjected to high intensity sound, the absorption coefficient can be maintained at high level α > 0.75 from f = 360 Hz to 1250 Hz. This frequency range
with high sound absorption performance is wider than that achieved by the linear case which is separated into two frequency ranges from f = 365 Hz to 500 Hz and 765 Hz to 990 Hz. The half-absorption bandwidth is also improved from 3.50 to 5.44.
Figure 4: Comparison of the absorption performance of the MPP absorber array between the linear and nonlinear regimes. (a) Linear; (b) High sound pressure level at 115 dB.
Also, from Fig. 4(a), there are two peaks at frequencies f = 420 Hz and 860 Hz. Such enhanced
absorption peaks associated with the local resonance are insignificant for case in nonlinear regime.
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Figs. 5(a) and (b) depict the acoustic intensity of two corresponding local resonance frequencies as
shown in Fig. 4(a) in the linear regime. It is observed that most of the acoustic energy at each resonance frequency is absorbed by different corresponding cavity. However, Fig. 5(d) shows that, at the
local resonance frequency f = 860 Hz, the sound energy is not only absorbed by one subcavity. The
cavity 2 of D2 = 25 mm also absorbs parts of the sound energy with cavity 1. As such, there is no
significant peak at the local resonance frequency in Fig. 4(b) due to the inter-resonator interaction
between subcavities.
Figure 5: The acoustic intensity in the duct at f = 420 Hz and 860 Hz. (a)-(b) Linear; (c)-(d) High sound pressure level at 115 dB. The depths of cavity 1 and 2 are 100mm and 25mm respectively.
4.
Experimental studies
The normal incident absorption coefficients are measured experimentally using a standing wave
tube in order to validate the finite element simulation established for the MPP absorber array at high
sound intensity. A prototype made of acrylic is partitioned into two subcavities by an aluminium plate
of thickness 1 mm. The depths of two subcavities are D1 = 75mm and D2 = 100mm. The cross section
of the rectangular duct is 100 × 100 mm. A pair of 1/2-in. microphones (B&K 4189) are used to
measure the acoustic pressure inside the duct.
The comparisons of normal absorption coefficient predicted by the finite element model and the
results measured from the experiments are shown in Fig. 6. Two MPP samples are tested at 110 dB.
The MPP absorber array of d = 1.05mm, t = 0.4mm and σ = 0.78% are measured and its result is
shown as Fig. 6(a). Fig. 6(b) shows the measured absorption coefficient of the MPP absorber array
that two subcavites, i.e., D1 and D2, are covered by the sample with two different properties d1 =
1.05mm, t1 = 0.4mm, σ1 = 0.92% and d2 = 1.05mm, t2 = 0.4mm, σ2 = 1.23% respectively. For both
Figs. 6(a) and 6(b), the estimated and measured results are in good agreement.
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Figure 6: The absorption coefficient of the MPP absorber array at 110 dB. (a) d = 1.05mm, t = 0.4mm and σ
= 0.78%; (b) d1 = 1.05mm, t1 = 0.4mm, σ1 = 0.92%, d2 = 1.05mm, t2 = 0.4mm and σ2 = 1.23%. The depths of
subcavities are D1 = 75mm and D2 = 100mm.
5.
Conclusions
A finite element model has been developed for investigating the acoustic behaviour of the microperforated panel absorber array in the nonlinear regime. Experimental studies are conduct to verify the
presented model. A more comprehensive study of the acoustic performance of the MPP absorber
array with more subcavities in the nonlinear regime is carrying on. Major conclusions can be summarized as follows:
(1) The MPP absorber array enhances the acoustic absorption when comparing the performance of
the single MPP absorber at high sound pressure level. The half-absorption bandwidth is improved to
2 by using the MPP absorber array of d = 1 mm, t = 1 mm and σ = 5.14% instead of reducing the
orifices into smaller diameter.
(2) Compared with the MPP absorber array in linear regime, the sound absorption by the non-resonating MPP absorbers is no longer trivial. Amount of acoustic energy is absorbed non-resonating
MPP absorbers such that a more even and broader absorption is obtained.
(3) The absorption coefficients of MPP absorber array with two subcavities at 110 dB are experimentally studied. The numerical predictions and the experimental measurements are in good agreement.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the General research Grant from the Hong Kong SAR government 514013 (B-Q39B) and the first author thanks the Hong Kong Polytechnic University for the
research studentship.
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The 23rd International Congress on Sound and Vibration
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