The 21st International Congress on Sound and Vibration
13-17 July, 2014, Beijing/China
NUMERICAL SIMULATION OF ACOUSTIC PROPERTIES
OF POROUS METALS UNDER HIGH SOUND PRESSURE LEVEL CONDITIONS
Bo Zhang, Xingbo Wang
School of Mechanical engineering, Ningxia University, Yinchuan, China 750021
e-mail: zhangbonxu@gmail.com
The sound propagation and absorption properties of porous media under high sound pressure
level conditions have been reported elsewhere. Also several analytical and semi-analytical
solutions have been developed; however, these solutions are relatively complicated and the
provided results are not accurate enough yet. In this work, the simulated results for the study
of the sound absorption properties of porous metals under the high sound pressure level conditions are presented by using the software COMSOL Multi-physics to clearly explore the
nonlinear coupling behaviors in sound field. While simulating, firstly, the amplitude of incidence wave is kept relatively low level, e.g. less than 90dB.Then, the amplitude of incidence
wave are gradually raised from 90 to 170dB.In the simulation, a rough nonlinear coupling relation is accepted for simplicity. Finally, the simulated results for the sound fields and sound
absorption properties are put forward to provide references for future works.
1.
Introduction
As a type of sound absorber porous metal has been applied in some harsh environments1-2,
with the developments of manufacturing technologies for materials. Besides, porous metal exhibits
other excellent properties such as ultra-light, durability, and multi-functions. Porous metals are also
called foam metals and normally are divided into two groups: open-cell metallic foam and close-cell
metallic foam. Therefore the properties of porous metal mainly depend on the micro-structure of
pores which are variable if the different manufacturing processes in engineering are applied. Up to
now, many manufacturing processes for porous metals are developed to manipulate the pore size,
porosity, and shape of pore to obtain some unique characteristics. For examples, foam metal with
independent closed cells can be obtained by means of foaming process; open-cell foam metal with
interconnected pores can be developed by using melt infiltration casting process. It should been
noted that as sound absorbent, open-cell foam metals are more popular in noise control applications,
in particular under some extreme conditions, e.g. high temperature 3-5, high sound pressure levels 6,
etc.
Moreover, it has been found out that the structural parameters affecting foam metals’ sound
absorbing capacities are the static and dynamic resistivity, porosity, pore size, tortuosity, etc. And
the planar acoustic wave will be attenuated as travelling in porous materials, mainly by means of
viscous loss and heat transfer in air; i.e., sound energy is transformed into the equivalent amount of
thermal energy. Specifically, for foam metals, according to the current investigations from many
literatures the sound absorbing mechanism of open-cell foam metals would be summarized as folICSV21, Beijing, China, 13-17 July 2014
1
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
lows: (1) sound scattering due to the rough surface of porous materials, (2) locally resonating in
semi-open cells inside foam metals after mechanical cutting and drilling, (3) the vibration of elastic
skeleton although its contribution is negligible for most porous metals, and (4) the thermal exchanges between the metallic skeleton and air in pores .
The aim of this work is to investigate the sound absorbing characteristics of porous metals at
normal and relatively high sound pressure levels by using software COMOL Multiphysics 7. The
involved experimental measurements for comparisons will be given in another article.
Figure 1 Typical micro-structure in porous materials with interconnected open pores
2.
Sound absorbing simulation by COMSOL Multiphysics
In this section, the acoustic module of COMSOL Mulitiphysics is introduced to simulate the
acoustic filed in porous metal and free air. In simulations, the amplitude of incidence wave is kept
constant at first and then gradually raised from 90 to 170dB in order to clearly explore the variation
tendencies of sound absorption of porous metal at different sound pressure levels by using the
commercial engineering software. We present a model of sound absorption by porous open-cell
foam; the material of skeleton is assumed to be a type of metal, e.g., stainless steel instead of melamine or other plastic. In the simulations, the porosity is 0.995, the static flow resistivity is 10500
Pa.s/m2, viscous and thermal characteristic lengths are, respectively, 240 and 470 micron, and tortuosity factor is 1.0059. Figure 2 depicts the geometry of the modelled system, in which an incident
sound field hits the porous foam metal at angle theta. As pointed out in Ref.7, the dotted line in figure 2 indicates the model domain’s boundaries and periodic Floquet boundary conditions on the left
and right boundaries are applied to extend the domain to infinity. The thickness of porous metal is
Hp=10cm and the height of the modelled air region is H=30cm.Also the porous metal could be defined as that backed by a rigid wall or an air gap.
ICSV21, Beijing, China, 13-17 July 2014
2
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
Figure 2 Geometry of the modelled system 7
2.1 Simulations for the incidence wave of constant amplitude
Firstly, the amplitude of incidence wave is set as 1 Pa. Then after several steps of simulations
and setups, the specific surface acoustic impedance, and sound absorption coefficient for different
incidence angles can be easily obtained, including the corresponding sound fields. Figures 3 and 4
showed the scattered fields for incidence angles 0 and 45 degree respectively at frequency
f=790Hz.Because of anti-resonance of acoustic waves inside porous metal, the sound absorbing
capacity is not very satisfactory at the frequency f=790Hz. Relatively, the sound absorption for incidence angle 45 degree is improved in comparison with that for 0 degree, see figures 3-4.
Figure 3 The sound field for incidence angle 0 degree and frequency f=790Hz.
ICSV21, Beijing, China, 13-17 July 2014
3
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
Figure 4 The sound field for incidence angle 45 degree and frequency f=790Hz.
2.2 Simulations for the incidence wave of high amplitude
On the basis of above simulations, one may gradually raise the amplitude of incidence wave
about from 90 to170dB to study the effect of the higher incidence sound pressure level on porous
metal’s sound absorbing capacity. For clarity, the incidence wave angle is kept 0 degree here. Also
it should be noticed that the static flow resistivity of porous metal is kept constant at relatively low
sound pressure levels, e.g., less than 90dB. However, its dynamic airflow resistance will increase
with the raise of sound pressure level. On other hand, the dynamic airflow resistivity σ or the effective density of air in pore inside porous metal would be coupled with particle velocity u or incidence sound pressure amplitude. For example, one may utilize the following relationship between
the dynamic flow resistivity σ and particle velocity u of air:
1.42(1   )
 0 
0 u
2 3 d a
(1)
In this equation, σ0 and ρ0 are the static flow resistivity and static density of air, θ the porosity, and
da the characteristic length of porous metals. In our simulation, a relationship between the dynamic
flow resistivity and the incidence sound pressure level was deduced and accepted for simplicity.
The simulated results are shown in figures 5-9.It was found out from these figures that the general
tendency is that the sound absorption coefficient of porous metal backed with rigid wall decreases
with increasing incidence sound pressure level, as shown in figures 5-6. For comparisons, the corresponding scattered sound fields are also plotted in figures 7-9.
ICSV21, Beijing, China, 13-17 July 2014
4
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
Figure 5 Sound absorption coefficient of porous metal at the sound pressure levels of 90-170dB, as a
function of frequency.
Figure 6 Sound absorption coefficient of porous metal at frequencies of about 596-4941Hz, as a function of sound pressure levels
ICSV21, Beijing, China, 13-17 July 2014
5
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
Figure 7 The scattered sound field at frequency f=10 kHz and sound pressure level 90dB
Figure 8 The scattered sound field at frequency f=10 kHz and sound pressure level 150dB
ICSV21, Beijing, China, 13-17 July 2014
6
21st International Congress on Sound and Vibration (ICSV21), Beijing, China, 13-17 July 2014
Figure 9 The scattered sound field at frequency f=10 kHz and sound pressure level 170dB
3.
Acknowledgements
The authors gratefully acknowledge support for this work from the Project of National Natural Science Foundation of China (grant No.51365046).
REFERENCES
1.
2.
3.
4.
5.
6.
7.
Rademaker, E. R., Vand der Wal, H.M.M., Geurts, E.G. M., Hot-stream in-situ acoustic impedance measurements on varies air-filled cavity and porous liners, The 16th International
Congress on Sound and Vibration, Krakow, Poland, 5-9 July ,(2009).
Nordin,P. ,Sarin,S. L. , Rademaker, E. R. , Development of new linear technology for
application hot stream areas of aero-engines, Proc. 10th AIAA/CEAS Aeroacoustics
Conference,1-13, (2004).
Sun, F. G., Chen, H. L., Wu, J. H., Feng, K., Sound absorbing characteristics of fibrous metal
materials at high temperatures, Applied Acoustics, 71, 221-235,(2010).
Zhang,J.F,Wang, Q.M., et al. Study on Acoustic of Double Layer Micro-perforated Panel
Absorber at High Temperature, Piezoelectrics & Acoustooptics, 31(1), 139-141,(2009).[in
Chinese].
Christie, D. R. A., Measurement of the acoustic properties of a sound absorbing material at
high temperatures, Journal of Sound and Vibration, 46(3), 347-355 ,(1976).
Zhou,H., Wu,J.H, et al. Acoustic Properties of Porous Metals at High Temperature and High
SPL, Chinese Journal of Theoretical and Applied Mechanics, 45(2), 229-235, (2013).
COMSOL Inc., Acoustics Module User’s Guide, Version 4.3, (2012)
ICSV21, Beijing, China, 13-17 July 2014
7