Introduction to Acoustics Module

VERSION 4.4

Introduction toAcoustics Module

C o n t a c t I n f o r m a t i o nVisit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact

Technical Support, or search for an address and phone number. You can also visit the Worldwide

Sales Offices page at www.comsol.com/contact/offices for address and contact information.

If you need to contact Support, an online request form is located at the COMSOL Access page at

www.comsol.com/support/case.

Other useful links include:

Support Center: www.comsol.com/support

Product Download: www.comsol.com/support/download

Product Updates: www.comsol.com/support/updates

COMSOL Community: www.comsol.com/community

Events: www.comsol.com/events

COMSOL Video Center: www.comsol.com/video

Support Knowledge Base: www.comsol.com/support/knowledgebase

Part number: CM020204

I n t r o d u c t i o n t o t h e A c o u s t i c s M o d u l e 19982013 COMSOL

Protected by U.S. Patents 7,519,518; 7,596,474; 7,623,991; and 8,457,932. Patents pending.

This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/sla) and may be used or copied only under the terms of the license agreement.

COMSOL, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/tm.

Version: November 2013 COMSOL 4.4

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

The Acoustics Module Physics Interfaces. . . . . . . . . . . . . . . . . . . . . . 3

The Physics Interface List by Space Dimension and Study Type . . 7

The Model Libraries Window . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Basics o

Gove

Lengt

Boun

Elasti

Mode

Model E

Mode

Dom

Boun

Resu

Refer

Additio

Gaus

Eigen

Piezo

Loud

The B | i

f Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

rning Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

h and Time Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

dary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

c Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

ls with Losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

xample: Absorptive Muffler . . . . . . . . . . . . . . . . . . . . . . 16

l Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

ain Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

dary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

lts and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

ences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

nal Examples from the Model Library. . . . . . . . . . . . . . . 43

sian Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

modes in a Muffler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

acoustic Transducer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

speaker Driver in a Vented Enclosure . . . . . . . . . . . . . . . . . . . 45

rel & Kjr 4134 Condenser Microphone . . . . . . . . . . . . . . 46

Introduction

The Acoustics Module consists of a set of physics interfaces, which enable you to simulate the propagation of sound in fluids and in solids. The interface applications include pressure acoustics, acoustic-solid interaction, aeroacoustics, and thermoacoustics.

Figure 1: COMSOL

Acoustic simulscattering, diffproblems are rinsulation for patterns like dacoustic-structand fluid-borninteraction is ssonar technoloindustry. Usindesign of electand receivers.Aeroacosutic plinearized poteused to modelfield, applicatiosensors and mIntroduction | 1

model of the sound pressure level distribution in a muffler system.

ations using this module can easily model classical problems such as raction, emission, radiation, and transmission of sound. These elevant to muffler design, loudspeaker construction, sound absorbers and diffusers, the evaluation of directional acoustic irectivity, noise radiation problems, and much more. The ure interaction features can model problems involving structure- sound and their interaction. For example, acoustic-structure imulated for detailed muffler design, ultrasound piezo-actuators, gy, and noise and vibration analysis of machinery in the automotive g the COMSOL Multiphysics capabilities enables the analysis and roacoustic transducers such as loudspeakers, sensors, microphones,

roblems can be analyzed and modeled by solving either the ntial flow equations or the linearized Euler equations. These are the one way interaction between an external flow and an acoustic ns range from jet-engine noise analysis to simulating acoustic flow

ufflers with flow.

2 | Introduction

The Thermoacoustic interface can accurately model systems where small geometrical dimensions are present, which is relevant to the mobile phone and hearing aid industries, and for all transducer designers. The Acoustics Module is of great benefit for engineers. By using 3D simulations, existing products can be optimized and new products more quickly designed with virtual prototypes. Simulations also help designers, researchers, and engineers gain insight into problems that are difficult to handle experimentally. And by testing a design before manufacturing it, companies also save time and money. The many physics interfaces available with this module are shown in Figure 2 and are available uThe Acousticinterface funct

Figure 2: The Acouthe Acoustic-Shell Structural Mechan

There are mansimple pressurwaves and presconcepts and tThe Acousticsfrom modelingnder the Acoustics branch in the Model Wizard. The next section s Module Physics Interfaces provides you with an overview of the ionality.

stics Module physics interfaces. Some interfaces require additional modulesboth of Interaction interfaces and the Thermoacoustic-Shell Interaction interface require the ics Module. The Pipe Acoustics, Transient interface requires the Pipe Flow Module.

y application areas where these interfaces are usedfrom modeling e waves in air to examining complex interactions between elastic sure waves in porous materials. For a brief introduction to the basic heory of acoustics see the Basics of Acoustics starting on page 12. Module model library has many examples of applications ranging sound insulation lining, modeling loudspeakers, microphones, and

mufflers. These examples show, among other things, how to simulate acoustic losses. The loss models range from homogenized empirical fluid models for fibrous materials to include thermal and viscous loss in detail using the Thermoacoustics interface.The Flow Duct model uses the Linearized Potential Flow interface to show the influence a flow has on the sound field in a jet engine. Predefined couplings can be used to model the interaction between acoustic, structure, and electric fields in piezoelectric materials (see The Model Libraries Window on page 11 for information about accessing these models). You can also get started with your own model bystarting on pag

The AcousticThere are fourInteraction, Ainterfaces are bphysics interfa

PRESSURE ACThe Pressure Ais described anvariations on tthe absence ofThe interfacesusing the PresHelmholtz eqAcoustics, TraThe Boundaryin waveguides a long distanceA large varietyimpedance conopen boundarseveral fluid mpropagation infibrous materistructures of cfeature), and fperfectly matcdomain. FinallIntroduction | 3

going to the tutorial Model Example: Absorptive Muffler e 16.

s Module Physics Interfaces main branchesPressure Acoustics, Acoustic-Structure eroacoustics, and Thermoacousticsand each of the physics riefly described here, followed by a table on page 7 listing the

ce availability by space dimension and preset study types.

OUSTICS

coustics branch ( ) has physics interfaces where the sound field d solved by the pressure p. The pressure represents the acoustic op of the ambient stationary pressure. The ambient pressure is, in flow, simply the static absolute pressure. enable solving the acoustic problem both in the frequency domain sure Acoustics, Frequency Domain interface ( ), where the uation is solved, and as a transient system using the Pressure nsient interface ( ), where the classical wave equation is solved. Mode Acoustics interface ( ) is used to study propagating modes and ducts (only a finite set of shapes, or modes can propagate over ). of boundary conditions are available, include hard walls and ditions, radiation, symmetry, and periodic conditions for modeling

ies, and conditions for applying sources. The interfaces also have odels, which, in a homogenized way, mimic the behavior of sound more complex media. This includes the propagation in porous or

als (the Poroacoustics domain feature), the propagation in narrow onstant cross section (the Narrow Region Acoustics domain luid models for defining bulk absorption behavior. So-called hed layers (PMLs) are also available to truncate the computational y, the far-field feature can be used to determine the pressure in any

4 | Introduction

point outside the computational domain. Dedicated results and analysis capabilities exist for visualizing the far-field in polar 2D, 2D, and 3D plots.

Figure 3: A 3D farLoudspeaker Encl

ACOUSTIC-STThe Acoustic-multiphysics psolid domain, acceleration acthe Acoustic-SInteraction, TDomain ( )Acoustic-PiezoAcoustic-PiezoAcoustic-Piezothe electric fiestress-charge oThe Pipe AcouDomain ( )These interfacflexible pipe syeffects of the pbackground fl-field polar plot of the loudspeaker sensitivity at 3000 Hz. From the Vented osure model found in the model library.

RUCTURE INTERACTIONStructure Interaction branch ( ) has interfaces that apply to a henomenon where the fluids pressure causes a fluid load on the and the structural acceleration affects the fluid domain as normal ross the fluid-solid boundary. The interfaces under this branch are olid Interaction, Frequency Domain ( ); the Acoustic-Solid ransient ( ); the Acoustic-Shell Interaction, Frequency ; the Acoustic-Shell Interaction, Transient ( ); the electric Interaction, Frequency Domain ( ); and the electric Interaction, Transient ( ) interfaces. The two electric Interaction interfaces also support solving and modeling

ld in a piezoelectric material. The piezoelectric coupling can be in r strain-charge form.stics, Transient ( ) and the Pipe Acoustics, Frequency

interfaces are available with the addition of the Pipe Flow Module. es are used for modeling the propagation of sound waves in 1D stems. The equations are formulated in a general way to include the ipe wall compliance and allow the possibility of a stationary

ow.

Two more physics interfaces are available under this branchElastic Waves ( ), for modeling elastic waves in solids, and Poroelastic Waves ( ), for precisely modeling the propagation of sound in a porous material. The latter includes the two-way coupling between deformation of the solid matrix and the pressure waves in the saturating fluid. The interface solves Biots equations in the frequency domain.With these interfaces you can model frequency domain and transient problems involving pressure acoustics and solid mechanics, with 3D, 2D, and 2D axisymmetric geometries.

AEROACOUSTThe one way icalled flow boAeroacoustics acoustics is bassolve for the abackground mequations undThe LinearizedPotential Flowbackground pocases where thbackground flinterface ( )The Linearizedboundary modto define sourcThe LinearizedEuler, Transieused to compupresence of a sideal gas flow.

THERMOACOThe interfacesmodel acoustithermal condulayer are createthermal conduIntroduction | 5

ICS

nteraction of a background fluid flow with an acoustic field (so rne noise/sound) is modeled using the interfaces found under the branch ( ). The coupling between the fluid mechanics and the ed on solving the set of linearized governing equations. In this way coustic variations of the dependent variables on top of a stationary ean-flow. Different interfaces exist that solve the governing er various physical approximations. Potential Flow, Frequency Domain ( ) and the Linearized , Transient ( ) interfaces model the interaction of a stationary tential flow with an acoustic field. This interface is only suited for

e flow is inviscid and, being irrotational, has no vorticity. The ow is typically solved for using the Compressible Potential Flow . Potential Flow, Boundary Mode interface ( ) is used to study e acoustic problems in a background flow field. It is typically used es at the inlet of ducts. Euler, Frequency Domain interface ( ) and the The Linearized

nt interface ( ) solve the Linearized Euler equations. They are te the acoustic variations in density, velocity, and pressure in the tationary background mean-flow that is well approximated by an

USTICS

under the Thermoacoustics branch ( ) are used to accurately cs in geometries with small dimensions. Near walls, viscosity and ction become important because a viscous and a thermal boundary d, resulting in significant losses. This makes it necessary to include ction effects and viscous losses explicitly in the governing

6 | Introduction

equations. This is done by solving the full set of linearized compressible flow equations, that is, the linearized Navier-Stokes, continuity, and energy equations.Because a detailed description is needed to model thermoacoustics, the interface simultaneously solve for the acoustic pressure p, the particle velocity vector u, and the acoustic temperature variation T.In the Thermoacoustics, Frequency Domain interface ( ), the governing equations are implemented in the time harmonic formulation and solved in the frequency domain. Both mechanical and thermal boundary conditions exist. Coupling the thermoacoustic domain to a pressure acoustic domain is also straightforwarA Thermoacoavailable to solto model smalPredefined boThe Thermoacfor modeling tThis can, for ehearing aids an

Figure 4: DeformaMicrophone moded, with a predefined boundary condition.ustic-Solid Interaction, Frequency Domain interface ( ) is ve coupled vibro-acoustic problems. This can, for example, be used l electroacoustic transducers or damping in MEMS devices. undary conditions exist between solid domains and fluid domains.oustic-Shell Interaction, Frequency Domain interface ( ) is used he interactions between shells and acoustics in small dimensions. xample, be used to analyze the damped vibrations of shells in d prevent feedback problems.

tion of the diaphragm (or membrane) at 12 kHz in the Axisymmetric Condenser l found in the model library.

The Physics Interface List by Space Dimension and Study TypeThe table below list the interfaces available specifically with this module in addition to those in the COMSOL Multiphysics basic license.

INTERFACE ICON TAG SPACE DIMENSION

AVAILABLE PRESET STUDY TYPE

Acoustics

Pressure Acoustics

Pressure AcoFrequency D

Pressure AcoTransient

Boundary MoAcoustics

Acoustic-Str

Acoustic-SoliInteraction, Frequency D

Acoustic-SoliInteraction, T

Acoustic-SheInteraction, Frequency D

Acoustic-SheInteraction, Transient2Introduction | 7

ustics, omain1

acpr all dimensions eigenfrequency; frequency domain; frequency-domain modal; mode analysis (2D and 1D axisymmetric models only)

ustics, actd all dimensions eigenfrequency; frequency domain; frequency-domain modal; time dependent; time-dependent modal; modal reduced order model; mode analysis (2D and 1D axisymmetric models only)

de acbm 3D, 2D axisymmetric

mode analysis

ucture Interaction

d

omain

acsl 3D, 2D, 2D axisymmetric

eigenfrequency; frequency domain; frequency-domain modal

d ransient

astd 3D, 2D, 2D axisymmetric

eigenfrequency; frequency domain; frequency-domain modal; time dependent; time-dependent modal; modal reduced order model

ll

omain2

acsh 3D eigenfrequency; frequency domain; frequency-domain modal

ll acshtd 3D eigenfrequency; frequency domain; frequency-domain modal; time dependent; time-dependent modal; modal reduced order model

8 | Introduction

Acoustic-Piezoelectric Interaction, Frequency Domain

acpz 3D, 2D, 2D axisymmetric


Acoustic-Piezoelectric Interaction, Transient

acpztd 3D, 2D, 2D axisymmetric

eigenfrequency; frequency domain; frequency-domain modal; time dependent; time-dependent modal; modal

Elastic Waves

Poroelastic W

Pipe AcousticFrequency D

Pipe AcousticTransient3

Aeroacoust

Linearized PoFlow, FrequeDomain

Linearized PoFlow, Transie

Linearized PoFlow, BoundaMode

CompressiblePotential Flow

Linearized EuFrequency D

Linearized EuTransient


AVAILABLE PRESET STUDY TYPEreduced order model

elw 3D, 2D, 2D axisymmetric


aves elw 3D, 2D, 2D axisymmetric


s, omain3

pafd 3D, 2D eigenfrequency; frequency domain

s, patd 3D, 2D time dependent

ics

tential ncy

ae all dimensions frequency domain; mode analysis (2D and 1D axisymmetric models only)

tential nt

aetd all dimensions frequency domain; time dependent mode analysis (2D and 1D axisymmetric models only)

tential ry

aebm 3D, 2D axisymmetric

mode analysis

cpf all dimensions stationary; time dependent

ler, omain

lef 3D, 2D axisymmetric, 2D, and 1D

frequency domain; eigenfrequency

ler, let 3D, 2D axisymmetric, 2D, and 1D

time dependent

Linearized Navier-Stokes, Frequency Domain4

lnsf 3D, 2D axisymmetric, 2D, and 1D

frequency domain; eigenfrequency

Linearized Navier-Stokes, Transient4

lnst 3D, 2D axisymmetric, 2D, and 1D

time dependent

Thermoacoustics

ThermoacouFrequency D

Thermoacoud Interaction,Frequency D

Thermoacoul Interaction2

Structura

Solid Mechanics1


AVAILABLE PRESET STUDY TYPEIntroduction | 9

stics, omain

ta all dimensions eigenfrequency; frequency domain; frequency domain modal; mode analysis (2D and 1D axisymmetric models only)

stic-Soli omain

tas 3D, 2D, 2D axisymmetric

eigenfrequency; frequency domain; frequency domain modal

stic-Shel tash 3D eigenfrequency; frequency domain; frequency domain modal

l Mechanics

solid 3D, 2D, 2D axisymmetric

stationary; eigenfrequency; prestressed analysis, eigenfrequency; time dependent; time-dependent modal; frequency domain; frequency-domain modal; prestressed analysis, frequency domain; modal reduced order model

10 | Introductio

Piezoelectric Devices pzd 3D, 2D, 2D axisymmetric

stationary; eigenfrequency; time dependent; time-dependent modal; frequency domain; frequency domain modal; modal reduced order model

1This physics interface is included with the core COMSOL package but has added functionality for this module.2 Requires both3 Requires both4 These physics


AVAILABLE PRESET STUDY TYPEn

the Structural Mechanics Module and the Acoustics Module.

the Pipe Flow Module and the Acoustics Module.

interfaces are available as a technology preview feature.

The Model Libraries Window

To open an Acoustics Module model library model, click Blank Model in the New screen. Then on the Home or Main toolbar click Model Libraries . In the Model Libraries window that opens, expand the Acoustics Module folder and browse or search the contents. Click Open Model to open the model in COMSOL Multiphysics or click Open PDF Document to read background about the model including the step-by-step inlibrary can hav Full MPH-f

window theexceeds 25Myou positio

Compact Mand solutiosolutions foand to meshversionswupdate youwindow witthe Model LMPH-file isincludes a D

To check all avLibrary ( ) f(Mac and LinuThe Absorptivstarting on pagavailable in theThe Model Libraries Window | 11

structions to build it. The MPH-files in the COMSOL model e two formatsFull MPH-files or Compact MPH-files.iles, including all meshes and solutions. In the Model Libraries se models appear with the icon. If the MPH-files size B, a tip with the text Large file and the file size appears when

n the cursor at the models node in the Model Libraries tree.PH-files with all settings for the model but without built meshes

n data to save space on the DVD (a few MPH-files have no r other reasons). You can open these models to study the settings and re-solve the models. It is also possible to download the full ith meshes and solutionsof most of these models when you

r model library. These models appear in the Model Libraries h the icon. If you position the cursor at a compact model in ibraries window, a No solutions stored message appears. If a full

available for download, the corresponding nodes context menu ownload Full Model item ( ).

ailable Model Libraries updates, select Update COMSOL Model rom the File>Help menu (Windows users) or from the Help menu x users). e Muffler model tutorial starts on page 16 and the last section, e 43, provides a brief overview of some of the other models also Acoustics Module model library.

12 | Basics of A

Basics of Acoustics

Acoustics is the physics of sound. Sound is the sensation, as detected by the ear, of very small rapid changes in the acoustic pressure p above and below a static value p0. This static value is the atmospheric pressure (about 100,000 pascals). The acoustic pressure variations are typically described as pressure waves propagating in space and time. The wave crests are the pressure maxima while the troughs represent the pressure minima.Sound is creatobject, such asof a bass speakmoves forwardpressure. Thenpressure. Thispressure at theThe frequencyperceived per ssuch peaks. Thfrequency andfrequency (Sfrequency to adefined as k = specific distaninformation abgeneral, the recalled the disp

Governing EThe equationsthe governingdescribed by toften referred the model conbetween thermwhich describeand adiabatic, state is used.Under these apressure p (SI coustics

ed when the air is disturbed by a source. An example is a vibrating a speaker cone in a sound system. It is possible to see the movement er cone when it generates sound at a very low frequency. As the cone it compresses the air in front of it, causing an increase in air it moves back past its resting position and causes a reduction in air

process continues, radiating a wave of alternating high and low speed of sound. f (SI unit: Hz = 1/s) is the number of vibrations (pressure peaks) econd and the wavelength l (SI unit: m) is the distance between two e speed of sound c (SI unit: m/s) is given as the product of the

the wavelength, c = f. It is often convenient to define the angular I unit: rad/s) of the wave, which is = 2f, and relates the full 360o phase shift. The wave number k (SI unit: rad/m) is 2/. The wave number, which is the number of waves over a ce, is also usually defined as a vector k, such that it also contains out the direction of propagation of the wave, with |k| = k. In lation between the angular frequency and the wave number k is ersion relation; for simple fluids it is /k = c.

quations that describe the propagation of sound in fluids are derived from equations of fluid flow. That is, conservation of mass, which is he continuity equation; the conservation of momentum, that is to as the Navier-Stokes equation; an energy conservation equation; stitutive equations; and an equation of state to describe the relation odynamic variables. In the classical case of pressure acoustics, s most acoustic phenomena accurately, the flow is assumed lossless viscous effects are neglected, and a linearized isentropic equation of

ssumptions, the acoustic field is described by one variable, the unit: Pa), and is governed by the wave equation

where t is time (SI unit: s), 0 is the density of the fluid (SI unit: kg/m3), and q and Q are possible acoustic dipole and monopole source terms (SI units: N/m3

and 1/s2, respectively).Acoustic problems often involve simple harmonic waves such as sinusoidal waves. More generally, any signal may be expanded into harmonic components via its Fourier series. The wave equation can then be solved in the frequency domain for one frequency

where the spatmay be written

where the actuthis assumptioto the well-kn

In the homogesolution to the

where P0 is thefrequency an

Length and TWhen solving length and timphysics of the The relative sizthe selection oWhen workingHelmholtz eqfrequency, T =geometric dim

1

0c2-----------2pt2---------

10------ p q + Q=Basics of Acoustics | 13

at a time. A harmonic solution has the form

ial p(x) and temporal sin(t) components are split. The pressure in a more general way using complex variables

(5)

al physical value of the pressure is the real part of Equation 5. Using n for the pressure field, the time-dependent wave equation reduces own Helmholtz equation

(6)

nous case where the two source terms q and Q are zero, one simple Helmholtz equation (Equation 6) is the plane wave

(7)

wave amplitude and it is moving in the k direction with angular d wave number k = |k|.

ime Scalesacoustic problems, it is important to think about the different basic e scales involved in the system. Some of the scales are set by the problem, while others are set by the numerical solution method. e of these scales may influence the accuracy of the solution, but also f the physics interface used to model the problem. with acoustics in the frequency domain, that is, solving the

uation, only one time scale T exists (the period) and it is set by the 1/f. Several length scales exist: the wavelength = c/f, the smallest ension Lmin, the mesh size h, and the thickness of the acoustic

p x t p x t sin=

p x t p x eit=

10------ p q

20c2-----------p Q=

p P0ei t k x

=

14 | Basics of A

boundary layer (the latter is discussed in Models with Losses on page 15). In order to get an accurate solution, the mesh should be fine enough to both resolve the geometric features and the wavelength. As a rule of thumb, the maximal mesh size should be less than or equal to /N, where N is a number between 5 and 10.For transient acoustic problems the same considerations apply. However, several new time scales are also introduced. One is given by the frequency contents of the signal and by the desired maximal frequency resolution: T = 1 fmax. The other is given by the size of the time step t used by the numerical solver. A condition on the so-called CFL number dictates the relation between the time step size and the minimal mesh

where c is the numbers of apinformation ison page 43.In order to ruphysical and ncorrectness of robustness of numerical timsolution, withimesh was prob

Boundary CoBoundary condomain. Someinterface. Othdomain. The aopen boundarsuch as a perfo

Elastic WaveThe propagatioscillations of to surroundininteraction, thstructural accefluid-solid boucoustics

size hmin, The CFL number is defined as

(8)

speed of sound in the system. It is good practice to have CFL proximately 0.2 (when using quadratic spatial elements). More included with the Gaussian Explosion tutorial model described

n accurate acoustic simulations it is important to think about these umerical scales and about their influence on the convergence and the numerical solution. A good practical approach is to test the a solution compared to changes in the mesh in all cases and the e stepping in the transient problems. If some measure of the n a given accuracy range, changes when the mesh is refined then the ably not good enough.

nditionsditions define the nature of the boundaries of the computational define real physical obstacles, like a sound hard wall or a moving ers, called artificial boundary conditions, are used to truncate the rtificial boundary conditions are, for example, used to simulate an

y where no sound is reflected. It may also mimic a reacting boundary rated plate.

son of sound in solids happens through small-amplitude elastic the solids shape and structure. These elastic waves are transmitted g fluids as ordinary sound waves. Through acoustic-structure e fluids pressure causes a fluid load on the solid domain, and the leration affects the fluid domain as a normal acceleration across the ndary.

CFL cthmin-----------=

The Acoustics Module has the Poroelastic Waves interface available to model poroelastic waves that propagate in porous materials. These waves result from the complex interaction between acoustic pressure variations in the saturating fluid and the elastic deformation of the solid porous matrix.

Models with LossesIn order to accurately model acoustics in geometries with small dimensions, it is necessary to include thermal conduction effects and viscous losses explicitly in the governing equations. Near walls, viscosity and thermal conduction become important becawhere losses aphenomena; ththe full linearizThe interface sthe acoustic tethe mean backThe length scathe thickness o

where is the is the specific hacoustic bounAnother way tequivalent fluihomogenized mimic differeninterfaces thatboundary layeconduction anfor simulatingdomain featurnarrow ducts (the equivalentexample, solviBasics of Acoustics | 15

use the acoustic field creates a viscous and a thermal boundary layer re significant. A detailed description is needed to model these e dedicated Thermoacoustics, Frequency Domain interface solves ed Navier-Stokes, continuity, and energy equations simultaneously. olves for the acoustic pressure p, the particle velocity vector u, and mperature variation T. These are the acoustic variations on top of ground values.le at which the thermoacoustic description is necessary is given by f the viscous (v) and thermal (th) boundary layers

dynamic viscosity, k is the coefficient of thermal conduction, and Cp eat capacity at constant pressure. These two length scales define an

dary layer that needs to be resolved by the computational mesh.o introduce losses in the governing equations is to use the d models available in the pressure acoustics interfaces. In a way, this introduces attenuation properties to the bulk fluid that t loss mechanism. This is in contrast to the thermoacoustics model losses explicitly where they happen, that is, in the acoustic r near walls. The fluid models include losses due to bulk thermal d viscosity (in the main Pressure Acoustics domain feature), models the damping in certain porous materials (in the Poroacoustics e), and models to mimic the boundary absorption losses in long the Narrow Region Acoustics domain feature). When applicable, fluid models are computationally much less heavy than, for ng a corresponding full poroelastic model.

v f---------= thk

fCp----------------=

16 | Model Exa

Model Example: Absorptive Muffler

This model describes the pressure-wave propagation in a muffler for an internal combustion engine. The approach is generally applicable to analyses of the damping of propagation of harmonic pressure waves.The purpose of this model is to show how to analyze both inductive and resistive damping in pressure acoustics. The main output is the transmission loss for the frequency range 50 Hz1500 Hz.

Model DefinThe muffler, schamber with first version ofwith 15 mm o

Figure 9: Geometrthe left pipe (inlet

Domain EquThis model soPressure Acoumodified versimple: Absorptive Muffler

itionchematically shown in Figure 9, consists of a 24-liter resonator a section of the centered exhaust pipe included at each end. In the the model, the chamber is empty. In the second version it is lined f absorbing glass wool.

y of the lined muffler with the upper half removed. The exhaust fumes enter through ) and exit through the right pipe (outlet).

ationslves the problem in the frequency domain using the time-harmonic stics, Frequency Domain interface. The model equation is a slightly on of the Helmholtz equation for the acoustic pressure, p:

pc-------

2pcc

2c-----------

0=

where c is the density, cc is the speed of sound, and gives the angular frequency. The subscript c refers to that these can be complex valued.In the absorbing glass wool, modeled as a Poroacoustics domain, the damping enters the equation as a complex speed of sound, cc/kc, and a complex density, ckc Zc/, where kc is the complex wave number and Zc equals the complex impedance. This is a so-called equivalent fluid model for the porous domain where the losses are modeled in a homogenized way.For a highly porous material with a rigid skeleton, the well-known Delany and Bazley model estimates these parameters as functions of frequency and flow resistivity. Usiexpressions are

where Rf is thewave number afor the Delanyfind flow resistglass-wool-like

where ap is thThis model us

Boundary CoThere are thre At the solid

and the pipcondition im

The boundaimposed plathe documeModel Example: Absorptive Muffler | 17

ng the original coefficients of Delany and Bazley (Ref. 1), the

flow resistivity, and where ka/ca and Zaa ca are the free-space nd impedance of air, respectively. This model is the default selected -Bazley-Miki model in the Poroacoustics domain feature. You can ivities in tables, see for example Ref. 4 or by measuring it. For materials, Bies and Hansen (Ref. 2) give an empirical correlation

e materials apparent density and dav is the mean fiber diameter. es a lightweight glass wool with ap12 kg/m3 and dav 10 m.

nditionse types boundary conditions used in this model. boundaries, which are the outer walls of the resonator chamber es, the model uses sound hard (wall) boundary conditions. The

poses that the normal velocity at the boundary is zero.ry condition at the inlet involves a combination of an incoming ne wave and an outgoing radiating plane wave (see Ref. 3 and ntation for details). This boundary condition is valid as long as

kc ka 1 0.098a fRf---------

0.7 i 0.189 a f

Rf---------

0.595 + =

Zc Za 1 0.057a fRf---------

0.734 i 0.087 a f

Rf---------

0.732 + =

Rf3.18 10 9 ap1.53

dav2

-------------------------------------------=

18 | Model Exa

the frequency is kept below the cutoff frequency for the second propagating mode in the tube.

At the outlet boundary, the model specifies an outgoing radiating plane wave.

Results and DiscussionFigure 10 shows the isosurface plot for the total acoustic pressure field. The pressure is represented as iso-barometric surfaces in the muffler. From the figure it is clear that transverse mod

Figure 10: The pre

An important defined as the attenuation dw

Here win and wat the outlet, rover the corremple: Absorptive Muffler

at this frequency longitudinal standing waves exist as well as es.

ssure distribution in the absorptive muffler without the liner is shown for f = 1500 Hz.

parameter for a muffler is the transmission loss or attenuation. It is ratio between the incoming and the outgoing acoustic energy. The (given in dB) of the acoustic energy is:

out denote the incoming power at the inlet and the outgoing power espectively. Each of these quantities can be calculated as an integral sponding surface:

dw 10winwout----------- log=

Figure 11: Attenuadips are due to lonpresent, but the g

Figure 11 shomuffler, the grfrequencies, wdisplays resonabehavior is mofor such frequcross-sectionalmodes that aremodes participunpredictable.described on presonance freq

woutp 2

2c---------- Ad= win p0

2

2c---------- Ad=Model Example: Absorptive Muffler | 19

tion (dB) in the empty muffler as a function of frequency (blue curve). The first four gitudinal resonances. In the muffler with absorbing liner (green curve) the dips are still eneral trend is that the higher the frequency, the better the damping.

ws the result of a parametric frequency study. For the undamped aph shows that the damping works rather well for most low ith the exception of a few distinct dips where the muffler chamber nces. At frequencies higher than approximately 1250 Hz, the plots re complicated and there is generally less damping. This is because

encies, the tube supports not only longitudinal resonances but also propagation modes. Slightly above this frequency, a range of combinations of this propagation mode and the longitudinal ate. This will make the damping properties increasingly For an analysis of these modes, see Eigenmodes in a Muffler age 43. The glass wool lining improves the attenuation at the uencies as well as at higher frequencies.

20 | Model Exa

References1. M. A. Delany and E. N. Bazley, Acoustic Properties of Fibrous Absorbent Materials, Appl. Acoust., vol. 3, pp. 105116, 1970.

2. D. A. Bies and C. H. Hansen, Flow Resistance Information for Acoustical Design, Appl. Acoust., vol. 13, pp. 357391, 1980.

3. D. Givoli and B. Neta, High-order Non-reflecting Boundary Scheme for Time-dependent Waves, J. Comp. Phys., vol. 186, pp. 2446, 2003.

4. T. J. Cox andand Francis, 20

Model Wi

The instructiocompletely hoglass wool.Note: These inminor differen

1 To start thethe softwareCOMSOL mthe Model WIf COMSONew fro

The Model next window

2 In the Space3 In the Selec

Acoustics, F4 Double-clic

select A5 Click Study6 On the Sele

Domain mple: Absorptive Muffler

P. DAntonio, Acoustic Absorbers and Diffusers, Second Edition, Taylor 09.

zard

ns take you through two versions of the model, first with a llow chamber with rigid walls, then where the chamber is lined with

structions are for the user interface on Windows but apply, with ces, also to Linux and Mac.

software, double-click the COMSOL icon on the desktop. When opens, you can choose to use the Model Wizard to create a new odel or Blank Model to create one manually. For this tutorial, click izard button.

L is already open, you can start the Model Wizard by selecting m the File menu and then click Model Wizard .

Wizard guides you through the first steps of setting up a model. The lets you select the dimension of the modeling space.

Dimension window click the 3D button .t physics tree, select Acoustics>Pressure Acoustics>Pressure requency Domain (acpr) .k the physics interface, click the Add button, or right-click and dd Physics. .ct Study window, in the tree, select Preset Studies>Frequency .

7 Click Done .

Global Definit ions

Note: The location of the text files used in this exercise vary based on the installation. For example, if the installation is on your hard drive, the file path might be simil

Parameters1 On the HomNote: On Linunear the top o

2 Go to the PFile .

3 Browse to thdouble-click

The parametersystem. The gedimension in tModel Example: Absorptive Muffler | 21

ar to C:\Program Files\COMSOL44\models\.

e toolbar, click Parameters .x and Mac, the Home toolbar refers to the specific set of controls

f the Desktop.

arameters settings window. Under Parameters click Load from

e model library folder (Acoustics_Module\Industrial Models) and the file absorptive_muffler_parameters.txt.

s define the physical values and the geometrical dimensions of the ometry is now parameterized and simply changing the value of a he parameters list updates the geometry automatically.

22 | Model Exa

Geometry 1

1 In the Model Builder under Component 1, click Geometry 1 .

2 Go to the Geometry settings window. Under Units from the Length unit list, choose mm.

Work Plane 11 On the Geo

Plane .2 Go to the W

Under Planlist, choose

Rectangle 11 In the Mode

and add a Rto the Mod

2 Go to the RUnder Size - Width fie- Height fi

3 Locate the Plist, choose

Fillet 11 On the Wor2 Click the Zo

Graphics tomple: Absorptive Muffler

metry toolbar, click Work

ork Plane settings window. e Definition, from the Plane yz-plane.

l Builder, right-click Plane Geometry ectangle . A Rectangle node is added el Builder.

ectangle settings window. in the:ld, enter W.eld, enter H.osition section. From the Base Center.

k plane toolbar, click Fillet .om Extents button on the

olbar.

3 On the object r1, select Points 1,2,3,4 only.

4 Go to the Fillet settings window. Under Radius in the Radius field, enter H/2.

Rectangle 21 Right-click 2 Go to the R

Under Size - Width fie- Height fie

3 Locate the PBase list, ch

Fillet 21 On the Wor

Fillet .2 On the obje3 Go to the F(H-2*D)/2.

4 On the Hombutton . Work Plane this point:

Extrude 11 On the Wor

Close .2 On the GeoModel Example: Absorptive Muffler | 23

Plane Geometry and choose Rectangle .ectangle settings window. in the: ld, enter W-2*D. ld, enter H-2*D.osition section. From the

oose Center.

k plane toolbar, click

ct r2, select Points 1,2,3,4 only.illet settings window. Under Radius in the Radius field, enter

e toolbar, click the Build All The node sequence under 1 should match this figure at

k plane toolbar, click

metry toolbar, click Extrude .

24 | Model Exa

3 Go to the Extrude settings window. Under Distances from Plane in the table under Distances (mm), enter L in the column.

Cylinder 11 On the Geo

Cylinder 2 Go to the C

Size and Sh- Radius fie- Height fi

3 Under Posit4 Under Axis,

Cartesian.5 Under Axis

- x field, en- z field, en

Cylinder 21 On the Geo

Cylinder 2 Go to the C

- Radius fie- Height fi

3 Under Posit4 Under Axis,5 Under Axis

- x field, en- z field, en

6 Click the Buthe Graphicmple: Absorptive Muffler

metry toolbar, click .

ylinder settings window. Under ape in the:ld, enter R_io.

eld, enter L_io.ion in the x field, enter -L_io. from the Axis type list, choose

in the: ter 1.ter 0.

metry toolbar, click .ylinder settings window. Under Size and Shape in the:ld, enter R_io.

eld, enter L_io.ion in the x field, enter L. from the Axis type list, choose Cartesian.in the:ter 1.ter 0.ild All button and then click the Zoom Extents button on

s toolbar.

The node sequence in the Model Builder should match the figure.

The finished geometry is shown in the figure below, the axis dimensystem of coor

Definit ion

Explicit 11 On the Defi2 In the Mod

Explicit 1 3 Go to the R4 Click OK.Model Example: Absorptive Muffler | 25

sions are in mm, as selected, and the dinates is also shown.

s

nitions toolbar, click Explicit .el Builder window, under Component 1>Definitions right-click

and choose Rename (or press F2). ename Explicit dialog box and enter Inlet in the New name field.

26 | Model Exa

5 Go to the Explicit settings window. Under Input Entities from the Geometric entity level list, choose Boundary.

6 Select Boundary 1 only.

Explicit 21 On the Definitions toolbar, click Explicit .2 In the Model Builder window, click Explicit 2 and press F2. In the Rename

Explicit dialog box, enter Outlet as the New name. Click OK.3 Go to the E

Under Inpuentity level

4 Select Boun

Integration 11 On the Def

ComponentIntegration

2 Go to the InUnder SourGeometric eBoundary.

3 From the Se

Integration 21 On the Def

Couplings aIntegration

2 Go to the InSource Selelist, choose mple: Absorptive Muffler

xplicit settings window. t Entities from the Geometric list, choose Boundary. dary 28 only.

initions toolbar, click Couplings and choose

.tegration settings window.

ce Selection from the ntity level list, choose

lection list, choose Inlet.

initions toolbar, click Component nd choose Integration . An 2 node is added to the Model Builder. tegration settings window. Under

ction from the Geometric entity level Boundary.

3 From the Selection list, choose Outlet.

You have now defined the integration coupling operators intop1 and intop2, for integration over the inlet and outlet, respectively. Use the operators in defining the in-going and out-going power, as defined in the Results and Discussion section.

Variables 11 In the Model Builder, right-click Definitions and choose Variables .2 Go to the V

following se

Materials

1 On the Hom2 Go to the A3 In the tree, 4 In the Add

to Compon5 Click the Ai

look at the Msettings win

NAME

w_in

w_outModel Example: Absorptive Muffler | 27

ariables settings window. Under Variables in the table, enter the ttings:

e toolbar, click Add Material .dd Material window.select Built-In>Air .material window, click Add ent .r node under Materials to

aterial Contents in the dow.

EXPRESSION DESCRIPTION

intop1(p0^2/(2*acpr.rho*acpr.c))

Power of the incoming wave

intop2(abs(p)^2/(2*acpr.rho*acpr.c))

Power of the outgoing wave

28 | Model Exa

The green check marks indicate which material parameters are necessary in the model.

Note: By defauscope settingsIn the second now, the muff

Pressure A

Plane Wave R1 On the Phys

2 Select Boun

Incident Press1 Under Press

Radiation 1mple: Absorptive Muffler

lt the first material added applies to all domains so the geometric do not need to be changed.version of this model, a lining material is inserted in Domain 2. For ler is completely hollow.

coustics, Frequency Domain

adiation 1ics toolbar, click Boundaries and choose Plane Wave Radiation .

daries 1 and 28 only.

ure Field 1ure Acoustics, Frequency Domain, right-click Plane Wave

and choose Incident Pressure Field . An Incident Pressure Field

node is added to the Model Builder. Nodes with a D in the upper left corner indicate it is a default node.

2 Go to the Incident Pressure Field settings window. Under Boundary Selection from the Se

3 Under Incidfield, enter p

You have nowradiation condinlet and outleincident wave boundaries bycondition.Now, add a sefor the absorpdeactivate this

Poroacous

1 On the Phy2 Go to the P3 Under Poro

associated fi

Mesh 1

Because the geextruded meshretaining the dModel Example: Absorptive Muffler | 29

lection list, choose Inlet.ent Pressure Field in the p0 0.

specified the plane wave ition to be active on both the t boundaries, but with an on the inlet. The remaining default use the sound hard

cond pressure acoustics model tive liner domain. You will domain when configuring the first study step.

tics

sics toolbar, click Domains and choose Poroacoustics . oroacoustics settings window. Select Domain 2 only.us Matrix Properties, from the Rf list, choose User defined. In the eld, enter R_f.

ometry is long and slender and it has constant cross sections, an is used. This reduces the number of mesh elements while still esired mesh resolution of the acoustic field.

30 | Model Exa

Free Triangular 11 In the Model Builder window, under Component 1 right-click Mesh 1 and

choose More Operations>Free Triangular . 2 To more easily locate and select a boundary, click the Wireframe Rendering

button on the Graphics window toolbar.3 Select Boundaries 6, 9, and 16 only.

Size1 In the Mod

Component2 Go to the S

Element Siz3 Under Elem

Maximum e343[m/s]/

The global equal to theby 5, that isthe speed ofmple: Absorptive Muffler

el Builder under 1>Mesh 1, click Size .ize settings window. Under e click the Custom button.ent Size Parameters in the lement size field, enter 1500[Hz]/5.maximum element size is set minimal wavelength divided , /5 = c0/fmax/5, where c0 is sound.

4 Click the Build All button .

Swept 11 On the Mes2 Now, simply

detect sourc3 Click the ZoModel Example: Absorptive Muffler | 31

h toolbar, click Swept . push the Build All button and the mesher will automatically e and destination boundaries for the swept mesh.om Extents button on the Graphics toolbar.

32 | Model Exa

Study 1

Step 1: Frequency Domain1 In the Model Builder, expand the Study 1 node, then click Step 1: Frequency

Domain .2 Go to the Frequency Domain settings window. Under Study Settings in the

Frequencies field, enter range(50,25,1500).3 Locate the P

Selection sephysics treestep check b

4 In the tree, ComponentFrequency DAcoustics M

5 Click the Dthe table.

6 On the HomCompute

Results

The first defauthe highest freyou can plot t

Acoustic Pres1 In the Mod

then click Smple: Absorptive Muffler

hysics and Variables ction. Select the Modify and variables for study ox.under 1>Pressure Acoustics, omain, click Pressure

odel 2.isable button under

e toolbar, click .

lt plot shows the pressure distribution on the walls of the muffler at quency, 1500 Hz. To get a better view of the standing wave pattern, he norm of the pressure instead of the real part of the pressure.

sure (acpr)el Builder under Results, expand the Acoustic Pressure (acpr) node urface 1 .

2 Go to the Surface settings window. In the upper-right corner of the Expression section, click Replace Expression .

3 From the menu, choose Pressure Acoustics, Frequency Domain>Absolute pressure (acpr.absp) (or enter acpr.absp in the Expression field).

4 On the 3D plot group toolbar, click the Plot button .

The pattern is at 1250 Hz.1 In the Mod2 Go to the 3

value (freq) 3 On the 3D Model Example: Absorptive Muffler | 33

very different at different frequencies. See for example what happens

el Builder under Results, click Acoustic Pressure (acpr) .D Plot Group settings window. Under Data from the Parameter list, choose 1250.plot group toolbar, click the Plot button .

34 | Model Exa

At 1250 Hz, tx-coordinate. the first symma separate analfor the EigenThe two othersurface and th

Acoustic PresIn the Model the Isosurfacemple: Absorptive Muffler

he absolute value of the pressure does not vary much with the The reason is that this is just higher than the cutoff frequency for etric propagating mode, which is excited by the incoming wave. For ysis of the propagating modes in the chamber, see the description modes in a Muffler model starting on page 43. default plot groups show the sound pressure level on the wall e pressure inside the muffler as isosurfaces.

sure, Isosurfaces (acpr)Builder, under Results>Acoustic Pressure, Isosurfaces (acpr), click node to display the plot in the next figure.

1D Plot Grou1 On the Hom2 On the 1D 3 Go to the G

y-Axis Datafollowing se- In the Ex10*log10

- In the Deliner.

4 On the 1D preproductioModel Example: Absorptive Muffler | 35

p 4e toolbar, click Add Plot Group and choose 1D Plot Group .

plot group toolbar, click Global .lobal settings window. Under in the table, enter the ttings: pression column, enter (w_in/w_out)

scription column, enter No

lot group toolbar, click the Plot button . Your plot should be a n of the blue curve in Figure 11 on page 19.

36 | Model Exa

Model Wi

In this, the secabsorptive glasmake the folloexisting result1 On the Hom2 Go to the A

Domain mple: Absorptive Muffler

zard

ond version of the model, the muffler is lined with a layer of s wool. Continue working with the model developed so far and wing changes. The first task is to add a second study to keep the s intact.

e toolbar, click Add Study . dd Study window. Under Studies>Preset Studies click Frequency .

3 Click Add Study . A Study 2 node is added to the Model Builder.

Study 2

1 In the Mod2 In the Study

the Generat

Step 1: Frequ1 In the Mod2 In the FrequModel Example: Absorptive Muffler | 37

el Builder, click Study 2 . settings window, under the Study Settings section, click to clear

e default plots check box.

ency Domainel Builder under Study 2, click Step 1: Frequency Domain .ency Domain settings window, locate the Study Settings section.

38 | Model Exa

3 In the Frequencies field, enter range(50,25,1500).

4 On the Home toolbar, click Compute .

Results

You chose notfinished you chow the damp

Acoustic Pres1 In the Mod

(acpr) n

2 In the 3D Pchoose Solu

3 On the 3D mple: Absorptive Muffler

to have new default plots generated. Once the solution process is an use the existing plot groups and just switch the data set to see ing material affects the solution.

sure, Isosurfaces (acpr)el Builder under Results, click the Acoustic Pressure, Isosurfaces ode.

lot Group settings window under Data, from the Data set list tion 2.

plot group toolbar, click the Plot button .

At 1500 Hz, tstudy how the

1D Plot Grou1 On the 1D 2 Go to the G

Under Datachoose Solu

3 Under y-Axsettings in t- In the Ex10*log10

- In the DeAbsorpti

4 On the 1D the Plot but

5 In the Modsettings win

6 From the PoModel Example: Absorptive Muffler | 39

he pressure in the chamber is much lower than before. Continue to transmission has changed.

p 4plot group toolbar, click Global .lobal settings window. from the Data set list, tion 2. is Data enter these he table:pression column, enter (w_in/w_out).scription column, enter ve liner.

plot group toolbar, click ton .el Builder, click 1D Plot Group 4 . Go to the 1D Plot Group dow. Click to expand the Legend section.sition list, choose Upper left.

40 | Model Exa

7 Right-click 1D Plot Group 4 and choose Rename. Go to the Rename 1D Plot Group dialog box and type Transmission Loss in the New name edit field.

8 Click OK.

Now, create aUse streamlinemuffler). You the muffler's s

3D Plot G

1 On the Hom2 Click 3D Pl

box enter I3 Click OK.

Intensity1 Click Intensmple: Absorptive Muffler

plot that represents the intensity flux through the muffler system. s that follow the intensity vector (flux of energy through the

can change between solutions and frequencies to study and visualize ound-absorbing properties.

roup 5

e toolbar, click Add Plot Group and choose 3D Plot Group .ot Group 5 and press F2. In the Rename 3D Plot Group dialog ntensity as the New name.

ity and from the toolbar, click Streamline .

2 In the Streamline settings window, click the Replace Expression button. From the menu, choose Pressure Acoustics, Frequency Domain>Intensity (RMS) (acpr.Ix,acpr.Iy,acpr.Iz).

3 Under Selection, select Boundary 1 only.4 Under Coloring and Style:

- From the Line type list, choose Tube.- In the Tube radius expression field, enter 2.

5 Under Inten6 In the Colo

button Domain>In

7 On the 3D Model Example: Absorptive Muffler | 41

sity, right-click Streamline 1 and choose Color Expression .r Expression settings window, click the Replace Expression

. From the menu, choose Pressure Acoustics, Frequency tensity magnitude (RMS) (acpr.I_rms).plot group toolbar, click the Plot button .

42 | Model Exa

As a final step, pick one of the plots to use as a model thumbnail.1 In the Model Builder under Results click Acoustic Pressure, Isosurfaces .2 Click the Root node (the first node in the model tree). On the Root settings

window under Model Thumbnail, click Set Model Thumbnail.

Make adjustments to the image in the Graphics window using the toolbar buttons until the image is one that is suitable to your purposes.mple: Absorptive Muffler

Additional Examples from the Model Library

The Acoustics Module model library has other tutorial models available as well as advanced industrial and verification models. Short explanations and examples are given below for a cross-section of these models. Go to The Model Libraries Window to learn how to access these model files from COMSOL Multiphysics.

Gaussian ExplosionThis model intproblems. In pcontent in the

Figure 12: Represe

Eigenmodes In this model,are computed.Absorptive MuThe purpose ofind the cut-ofof the modes sAdditional Examples from the Model Library | 43

roduces important concepts to remember when solving transient articular, it examines the relationship between the frequency

sources driving the model, the mesh resolution, and the time step.

ntation of the pulse at time t=0.0315s.

in a Muffler the propagating modes in the chamber of an automotive muffler The geometry is a cross-section of the chamber as described in the ffler example in this guide.f the model is to study the shape of the propagating modes and to f frequencies. As discussed in the Absorptive Muffler tutorial, some ignificantly affect the damping of the muffler at frequencies above

44 | Additional

the cut-off. In the Eigenmodes in Muffler model, modes with cut-off frequencies up to 1500 Hz are studied.

Figure 13: First fulplot shows the ab

PiezoacoustiA piezoelectricacoustic pressuacoustic field. generation of phased array mtransducers, anacousto-bioth Examples from the Model Library

ly symmetric propagation mode of the muffler chamber (with no absorbing liner). The solute value of the pressure.

c Transducer transducer can be used either to transform an electric current to an re field or, the opposite, to produce an electric current from an These devices are generally useful for applications that require the sound in air and liquids. Examples of such applications include icrophones, ultrasound equipment, inkjet droplet actuators, sonar d devices for drug discovery, bioimaging, and

erapeutics.

Figure 14: SurfacekHz.

LoudspeakerAn important electro-mechathat often in aelectromagnetanother are mThis model ofextract the resfrequency. ThLoudspeaker DAdditional Examples from the Model Library | 45

and height plot of the pressure distribution created by the piezoactuator at f = 100

Driver in a Vented Enclosureclass of acoustic models are transducers, that is, nic-acoustic transducers. Transducers are true multiphysics models ddition to acoustics necessitate a structural mechanic and an ic physics added. One such class are loudspeakers (presented here), icrophones presented below. a boxed loudspeaker lets you apply a nominal driving voltage and ulting sound pressure level in the outside room as a function of the e electromagnetic properties of the driver are supplied from the river model (available with the AC/DC Module). The model uses

46 | Additional

the Acoustic-Shell Interaction interface and therefore requires the Structural Mechanics Module.

Figure 15: Iso-pres

The Brel &Another type Kjr 4134 conthose of the mmeasurementsThe membran Examples from the Model Library

sure contours (in gray scale) and deformation of the speaker cone (colors).

Kjr 4134 Condenser Microphoneof transducer is the microphone. This is a model of the Brel and denser microphone. The geometry and material parameters are icrophone. The modeled sensitivity level is compared to performed on an actual microphone and shows good agreement. e deformation, pressure, velocity, and electric field are also

determined. The model requires the Acoustics Module, the AC/DC Module, and the Structural Mechanics Module.

Figure 16: Deformof Brel & Kjr.

This concludeAdditional Examples from the Model Library | 47

ation of the microphone membrane (diaphragm) at 20 kHz. The geometry is courtesy

s this introduction.

48 | Additional Examples from the Model Library

IntroductionThe Acoustics Module Physics InterfacesThe Physics Interface List by Space Dimension and Study Type

The Model Libraries WindowBasics of AcousticsGoverning EquationsLength and Time ScalesBoundary ConditionsElastic WavesModels with Losses

Model Example: Absorptive MufflerModel DefinitionDomain EquationsBoundary ConditionsResults and DiscussionReferencesModel WizardGlobal DefinitionsGeometry 1DefinitionsMaterialsPressure Acoustics, Frequency DomainPoroacousticsMesh 1Study 1ResultsModel WizardStudy 2Results3D Plot Group 5

Additional Examples from the Model LibraryGaussian ExplosionEigenmodes in a MufflerPiezoacoustic TransducerLoudspeaker Driver in a Vented EnclosureThe Brel & Kjr 4134 Condenser Microphone

Introduction to Acoustics Module

Documents

Transcript of Introduction to Acoustics Module