PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Acoustic simulation for high intensity sound source with Helmholtz
resonatorZinan LI1; Bo ZHANG1,2; Qiqi CHEN1; Liheng WANG1; Yutian BAI1
12

School of Mechanical Engineering, Ningxia University, China

CAE Key Laboratory for Intelligent Equipment of Ningxia, China

ABSTRACTTo study acoustic radiation characteristics of high intensity sound source used for the acoustic test of soundabsorbing materials, a simulation model in the combination of horn-type loudspeaker and Helmholtz
resonator, which are conceived for the design of a high intensity sound source in acoustic impedance tube, isdeveloped by using software COMSOL. Fully couplings among multiple physical fields such as
electromagnetic, mechanical, and acoustic ones are considered in this model, letting voltage be the input andsound pressure the output. Without the help of any simplified lumped parameter and only through theacoustic model constructed in COMSOL and accurate material parameters, the signal frequency response
characteristics, output sound pressure, and electroacoustic transformation efficiency of the high intensity
sound source can be obtained. The results show that the acoustic radiation characteristic of this high intensity
sound source depends on the interactions between horn-type loudspeaker and Helmholtz resonator, and its
equivalent acoustic impedance characteristics is mainly dominated by Helmholtz resonator. It is also shown
from results that the resonances of both horn-type loudspeaker and Helmholtz resonator may not only
strengthen sound radiation of sound source system, but enhance its electroacoustic transformation efficiency
observably.
Keywords: Sound Source, Acoustic Simulation

1. INTRODUCTION
In recent years, researches on porous metal materials have received more and more attentionˈandthe sound absorption performance of porous metal materials under high pressure and high intensity
has become a research hotspot as well. To conduct nonlinear acoustic research of porous metalmaterials under high sound pressure levels, it is necessary to construct a qualified high intensity
sound field, and high intensity sound sources are the key to solve this problem. Cone typeloudspeaker is usually selected as acoustic testing sound source, but because it directly generates
acoustic radiation through the vibration of cone wall of loudspeaker, which is less efficient and theexcited the sound pressure level cannot meet the test requirements. On the other hand, the siren isused as the sound source as well. Although it can generate a large amount of sound power, its biggest
disadvantage is that it cannot control the frequency response of the signal. In addition, someresearchers have also used the method of adding a horn to sound source system to improve theacoustic radiation of the speaker (1).The Helmholtz resonator is a special kind of acoustic component
designed for acoustic amplification (2). In this work, authors adopt COMSOL as tool to build asimulation model, combining the horn-type loudspeaker with the Helmholtz resonator, which
provides a new idea for the design of high intensity sound source.

2. COMPOSITION OF SOUND SOURCE
2.1 Compression DriverCompression driver is the most commonly used acoustic device for the fabrication of sound127288zhangb@nxu.edu.cn
12712580@qq.com

source system that mainly works in high frequency range, as shown in Fig. 1. The acoustic excitation
mechanism of compression driver is the same as that of cone type loudspeaker, and the membrane isusually dome shaped. Unlike the cone type loudspeaker, the membrane of compression driver does
not directly radiate sound in free air, but through a thin system called the phase plug. The system acts
to collect sound radiation energy from different parts of the dome in correct phase relation and toimprove the acoustic load and transduction efficiency (1, 3). And horn is connected to outlet of phaseplug.

Figure 1 – Internal structure of a compression driver
2.2 Helmholtz Resonator
In engineering applications, Helmholtz resonator is regarded as an acoustic device of locallycollecting sound energy for other purposes such as radiation. It usually consists of a cavity and aspool piece acoustic performance parameters of which are related to the structural configuration.
When the sound signal enters the cavity and its frequency is the same as the resonant frequency of
the resonator, the air in the cavity will be activated to generate so-called resonance, as a result ofenhancing the incident acoustic signal. Consider the typical structure of a Helmholtz resonator,
where S is the cross sectional area of inlet hole of the resonator and l is the effective length, and V isthe volume of the resonator. Therefore, the resonant frequency f of the resonator is given by Eqn. (1),where c 0 is the sound velocity.

fc02S

SlV

(1)

This formula is utilized in the following simulation and modeling of high intensity sound source.
2.3 Horn
The sound waves from the output of the resonator radiate into the open space after entering thehorn throat and the horn mouth, and the sound radiation is again enhanced.
When the horn throat radius is a 0 and f >>fc, its acoustic impedance is approximately equal to:

za0 |

U0 c0
S (a0 ) 2

Provided that horn mouth radius is al and kal
as:

zal |

(2)

5 , its acoustic impedance is approximately given

U 0 c0S (al ) 2

(3)

Moreover, the acoustic impedance at point x (being the distance away from the horn throat) isdefined as:

Za x

pvS

(4)

And particle velocity at position x is written as follows:

7289vA ª§m ·  jJ x B §m · jJ x º  m2 x jZt
J  j ¸e  ¨J  j ¸ e » e eU0c0 k «¬¨©
A©
2¹2¹¼(5)The sound pressure at horn mouth is N times as large as that at horn throat, which is expressed byNplp0Z al vl Sl
Z a0 v0 S0(6)3. MODEL IMPLEMENTATION ON COMSOL
3.1 2D Model
Considering the typical geometry of a horn loudspeaker, it is simplified and constructed as anaxisymmetric 2D model without the phase plug, as shown in Fig. 2. This paper uses the PML domain
to calculate the far sound pressure field.

Figure 2 – 2D model without the phase plug
By modeling its electromagnetic, structural and acoustic properties, the model combines themagnetic field interface of the AC/DC module with the acoustic-structure interaction multiple
physics interface of the acoustic module, see Refs. (4, 7). The AC/DC module is responsible forsimulating the generator, which firstly sets the voltage driven by the system and then calculates thevibrational speed of membrane. The velocity at frequency of analysis is then applied to membrane inpressure acoustic frequency domain.
3.2 Mathematical Description
In this work, one may assume that the excitation voltage V0 = 4V, the sound source is driven by atime harmonic voltage and finally connected to the voice coil, as follows:

VV0e jZt(7)

For a wire of length l and electric current I in a magnetic field of induction density B, the Lorentz
force F generated is given by:(8)
F lB u I
The voice coil consists of N turns of wire, so the resultant driving force on the coil hence
becomes:FeI2S N
rBr dAA ³

where Br is the r-component of the magnetic flux density and A is the cross section of coil.
The current through the voice coil is related to the applied voltage, i.e,7290

(9)

I

V0  VbeZb(10)

In Eqn. (10), Z b is the blocking electrical impedance and −Vbe is the back EMF (the voltage inducedin the coil due to its movement through the permanent magnetic field in air gap).
The force factor BL in loudspeaker system is expressed by:

Bl

2S N
rBr dAA ³(11)After arrangement, one may obtain the expression for the driving force F e :FeBl

V0  BLvZb(12)3.3 Model Mesh
To mesh such geometries, the main issue is on how to set maximum element size and try to keep
the number of elements relatively low to reduce computation time (5, 6).
There are three types of meshes for model meshing. The first is suitable for the static magnetic
mode of having very simple geometries. The magnet, pole and the top plate can be easily meshed bymanually defining a fine mesh throughout the magnetic circuit. The second is often used for theelectromagnetic domain. This is a much more complicated grid that must be considered carefully.
The third one is used for the mechanical and acoustic domains because in this case, the two domains
are fully coupled with and those neighboring meshes must be tailored to merge.
3.4 Multiple-Physics Coupling
Usually, there is a direct coupling relation between magnetic field and mechanics fields. For
example, the Lorentz force comes from the voice coil vibration. In return, the vibration of voice coilproduces a counter electromotive force. To calculate the values of factors BL and Zb , the resultant
driving force on the coil can be obtained. Then the result can be plugged directly into theacoustic-structure coupling calculation of the horn-type loudspeaker performance. The first couplingsolves the electromagnetic part of the problem. The second coupling is a full model, including therelevant multiple physics interactions from the drive voltage to the calculated sound pressure level(6).

4. RESUITS
4.1 The Variation of Sound Pressure Level
According to the analysis of acoustic-structure interaction, the distribution of sound pressurelevels inside and outside the sound source at different frequencies is calculated , as shown in Fig. 3.

(a)

(b)

7291

(c)(d)

(e)

(f)

(g)

(h)

Figure 3 – Sound pressure level at different frequencies: (a) 110.59Hz, (b) 201.67Hz, (c) 316.48Hz, (d)577.14Hz, (e) 670.67Hz, (f) 779.37Hz, (g) 905.68Hz, and (h) 1052.5Hz
4.2 SPL Response
The sound pressure level is the main and direct reference measurement for designers to predict
sound radiation properties of a loudspeaker (1, 5). Comparing the frequency response curves of thehigh intensity sound source with those of the cone loudspeaker, see Fig. 4, it is found that the highintensity sound source having a Helmholtz resonance structure reaches a high sound pressure level inthe range of 50-200 Hz, but gets significantly declined SPL at high frequencies.

7292

(a)

(b)

Figure 4 – SPL response of (a) high intensity sound source and (b) cone type loudspeaker.

5. CONCLUSIONSIn this paper, one coupled simulation model for the design of a high-intensity sound source isdeveloped by using COMSOL. Theoretical deduction and finite element simulation conducted to theloudspeakers help to establish the relationship between the electromagnetic field and mechanicalvibration and sound field.
The results show that the COMSOL simulation model can clearly reflect the tendency of theacoustic pressure field, and compare the sound pressure level curve between the high intensity soundsource and the cone loudspeaker of the same size and the same input voltage.
The parameters used in this model are taken from the COMSOL Acoustic Module User Guide,
which can be studied more precisely.
The shortcomings in this paper is that authors do not carefully analyze the structural dimensionsof Helmholtz resonator, just highlighting the effect of resonance on the sound pressure level. Hence,the presented simulation model need to refine further.
Many obstacles have been encountered in developing model, which are mainly caused by theform of geometric inaccuracy and uncertainty of material parameters.

ACKNOWLEDGEMENTS
The authors gratefully acknowledge supports for this work from the Graduate Innovative
Educational Project of Ningxia (Grant No. YKC201606), Research Project of CAE Key Laboratory
for Intelligent Equipment of Ningxia, Project of National Natural Science Foundation of China(Grant No. 51365046), and Graduate Innovative Project of Ningxia University (Grant No.
GIP2018055).

REFERENCES
1. Dario Cinanni. Simulation of horn driver response by direct combination of compression driverfrequency response and horn FEA. Proceedings of the COMSOL Conference. 2015.
2. Ma Dayou. Helmholtz Resonator. Technical Acoustic, 2002, 21(1/2), 2-3.
3. Michael J.D. Hedges, Yiu Lam. Accuracy of fully coupled loudspeaker simulation using COMSOL.
Proceedings of the COMSOL Conference, 2009.
4. COMSOL5.4. Acoustics Module User Guide.
5. Riccardo Balistreri. PA loudspeaker system design using multiphysics simulation. Proceedings of theCOMSOL Conference, 2015.
6. Roberto Magalotti. A multiphysics approach to the design of loudspeaker drivers. Proceedings of theCOMSOL Conference, 2015.
7. M. Cobianchi, Dr. M. Rousseau, S. Xavier. Modelling the electrical parameters of a loudspeaker motor
system with the AC-DC module – (MEPLMSAM). Proceedings of the COMSOL Conference, 2015.

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