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Contents Intr on The Acoustics Module Physics Interfaces The Physics Interface List by Space Dimension and Study Type.. 7 The Model Libraries Window Basics of acoustics np EC Length and Time Scales 3 Boundary Conditions Models with Lo 15 Model Example: Absorptive MuffI Mocel definition Domain equations 6 Boundary Conditi d di References 20 Additional Examples from the Model Library 43 aussian Explo Eigenmodes in a Muffler Piezoacoustic transducer speaker Driver in a Vente The Bruel Kjaer 4134 Condenser Microphone ntroduction The Acoustics Module consists of a sct of physics interfaces, which cnablc you to simulate the propagation of sound in fluids and in solids. The interface pplications include pressure acoustics, acoustic-solid interactiOn, aeroacoustics, and thermoacoustics Figure /: COMSOL model of the sound pressure level distribution in a muffler system Acoustic simulations using this module can easily model classical problems such as scattering, diffraction, emission, radiation, and transmission of sound. These problems arc relevant to muffler dcsign, loudspcakcr construction, sound insulation for absorbers and diffusers the evaluation of directional acoustic patterns like directivity, noise radiation problems, and much more. The acoustic-structure interaction features can model problems involving structure and fluid-born sound and their interaction. For example, acoustic-structure interaction is simulated for detailed muffler design, ultrasound piezo-actuators sonar technology, and noise and vibration analysis of machinery in the automotive industry. Using thc Comsol, multiphysics capabilities enables thc analysis and design of electroacoustic transducers such as loudspeakers, sensors, microphones, anld receivers Aeroacosutic problems can be analyzed and modeled by solving either the linearized potential flow equations or the linearized Euler equations. These are used to model the one way interaction between an external flow and an acoustic field, applications range from jet-engine noise analysis to simulating acoustic flow sensors and mufflers with flow 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 arc shown in figurc 2 and are available under the Acoustics branch in the model wizard. The next section The Acoustics Module Physics Interfaces" provides you with an overview of the interface functionality O) Pressure Acoust (D Pressure Acoustics, Frequency Comain(acpr) uD Pressure Acoustics,TIarsienz(actd Qu Boundary Mace Acoust cs (acbm) uP Acoustic.So id Interaction, Frequency Domain(acs) MA Acoustic-So id Interaction, Transient(astd Cou Pipe aLuuslis Tidllaitr L(pcLd a ALuusliL-Shell I: 1. Liun, Fieyuenl y Durdin(dush n ALuslit-SlellInleldtLiun T:dnsiuiL(dLshLd mR ALuuslit-PezueleLLrit Inlerdliunl, Freyuenty durnldini (dlpa) MR ALuusliL-PecttletLrit InlerdtLiun T Idrisienl aLpa O Eldslit Wave(ewi He Puruelaslit Wdve (uww m) Linearized Euler Frecuency Domain (lef) D) Linearized Potential Flow, Frequen=y Domain(ae) wu))Linearized potential Flow T I Linearized Potential Flow, Bur dary Mode(aebm A )) Thermoacoustics ))Thermoacoustics, Frequercy Dcmain(ta A Thermoaccustic-Sclid Interaction, Frequency Domain(tas) i Thermoaccustic-ShelI ' nters:ior, frequency Domain(tash Figure 2: The Acoustics Moduie physics interfaces. Some interfaces require additional modules-both of the Acoustic Shell Interaction interfaces and the Thermoacoustic Shell Interaction interface require the Structural Mechanics Module. The Pipe Acoustics, Transient intcrface requires the Pipe Flow Moduilc Thcrc arc many application arcas whcrc thcsc interfaces arc uscd-from modeling simple pressure waves in air to examining complex interactions between elastic waves and pressure waves in porous materials. For a brief introduction to the basic concepts and theory of acoustics see the "Basics of Acoustics"starting on page 12 The Acoustics Module model library has many examples of applications ranging from modeling sound insulation lining, modeling loudspeakers, microphones, and roduction mufflers. These examples show, among other things, how to simulate acoustic osses. 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 ll for own model by golng to the tutorial "Model Example: Absorptive Muffler>hr information about accessing thesc modcls. you can also gct started with yo starting on Page 16 The acoustics Module physics Interfaces There are four main branches--Pressure Acoustics. Acoustic-Structure Interaction, Aeroacoustics, and Thermoacoustics--and each of the physics interfaces are briefly described here, followed by a table on page 7 listing th physics interface availability by space dimension and preset study types PRESSURE AC○UST|CS The Pressure Acoustics branch(() has physics interfaces where the sound field is described and solved by the pressure p. The pressure represents the acoustic variations on top of the aMbient stationary pressure. The ambient pressure is, in the absence of flow, simply the static absolute pressure The interfaces enable solving the acoustic problem both in the frequency domain using the Pressure Acoustics, Frequency Domain interface((), where the Helmholtz cquation is solved, and as a transient systcm using the Pressure Acoustics, Transient interface(())), where the classical wave equation is solved The boundary Mode Acoustics interface((ym) is used to study propagating modes in waveguides and ducts (only a finite set of shapes, or modes can propagate over a long distance) a large variety of boundary conditions are available, include hard walls and impedance conditions, radiation, symmetry, and periodic conditions for modeling open boundaries, and conditions for applying sources. The interfaces also have several fluid models, which, in a homogenized way, mimic the behavior of sound propagation in more complex nedia. This includes the propagation in porous or fibrous materials(the poroacoustics domain feature ), the propagation in narrow structures of constant cross section(the Narrow Region Acoustics domain feature), and fluid models for defining bulk absorption behavior. So-called perfectly matched layers(PMi s) arc also availablc to truncate the computational domain. Finally, the far-field feature can be used to determine the pressure in any Introduction point outside the computational domain. Dedicated results and analysis capabilities exist for visualizing the far-field in polar 2D, 2D, and 3D plots re 3: A 3D far-field polar blot of at 3000 Hz From the vented Loudspeaker Enclosure mode! found in the model library ACOUSTIC-STRUCTURE INTERACTION The Acoustic Structure Interaction branch(p)has interfaces that apply to a multiphysics phcnomcnon wherc thc fluids prcssurc causcs a fluid load on the solid domain and the structural acceleration affects the fluid domain as normal acceleration across the fluid-solid boundary. The interfaces under this branch are the Acoustic-Solid Interaction, Frequency Domain (Mp); the Acoustic-Solid Interaction, Transient (p); the Acoustic-Shell Interaction, Frequency Domain(i); the Acoustic-Shell Interaction, Transient())); the Acoustic-Piezoelectric Interaction, Frequency Domain(ik); and the Acoustic-Piezoelectric Interaction, Transient(MN)interfaces Acoustic-Piczoclcctric Intcraction interfaces also support solving and modeling the electric field in a piezoelectric material. The piezoelectric coupling can be in stress-Charge or stralnl-charge fornl The Pipe Acoustics, Transient(VDm )and the Pipe Acoustics, Frequency Domain(Oml )interfaces are available with the addition of the Pipe Flow Module These interfaces are used for modeling the propagation of sound waves in ID flexible pipc systcms. The cquations arc formulated in a gcncral way to include the effects of the pipe wall compliance and allow the possibility of a stationary background flow roduction Two more physics interfaces are available under this branch- Elastic Waves(i), for modeling elastic waves in solids, and Poroelastic Waves(i), 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 Biot's eq uations in the freyuency domain With these interfaces you can model frequency domain and transient problems involving pressure acoustics and solid mechanics, with 3D, 2D, and 2D axisymmetric gcomctrics AEROACOUSTICS The one way interaction of a background fluid flow with an acoustic field (so called flow borne noise/sound is modeled using the interfaces found under the Aeroacoustics branch())). The coupling between the fluid mechanics and the acoustics is bascd on solving thc sct of lincarizcd governing cquations. In this way for the acoustic variations of the dependent variables on top of a stationary background mean-flow. Different interfaces exist that solve the governing equations under various physical approximations The linearized potential Flow, Frequency Domain(m)))and the linearized Potential Flow, Transient( w)))interfaces model the interaction of a stationary background potential flow with an acoustic field This interface is only suited for cascs wherc the flow is inviscid and, bcing irrotational has no vorticity tI background flow is typically solved for using the Compressible Potential Flow interface(≡) The Linearized Potential Flow, Boundary Mode interface ((m)is used to study boundary mode acoustic problems in a background flow field. It is typically used to define sources at the inlet of ducts The Iincarizcd Eulcr, Frcqucncy Domain interface(m))and the The Lincarizcd Euler, Transient interface(wnl )solve the Linearized Euler equations. They are used to compute the acoustic variations in density, velocity, and pressure in the presence of a stationary background mean-flow that is well approximated by an Ideal gas flow THERMOACOUSTICS The interfaces under the Thermoacoustics branch()))are used to accurately model acoustics in geometries with small dimensions. Near walls, viscosity and thernal conduction become important because a viscous and a therinal boundary layer are created, resulting in significant losses. This makes it necessary to include thermal conduction effects and viscous losses explicitly in the governing 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(m))), the governing equations are implemented in the time harmonic formulation and solved in the frequency domain. Both mechanical and thermal boundary conditions exist ling the thermoacoustic domain to a prcssurc acoustic domain is also straightforward, with a predefined boundary condition A Thernoacoustic-Solid Interaction, Frequency Domain interface (n)is available to solve coupled vibro-acoustic problems. This can, for example, be used to model small electroacoustic transducers or damping in MEMS devices Predefined boundary conditions exist between solid domains and fluid domains The Thcrmoacoustic-Shcll Intcraction, Frcqucncy Domain interface(i)is uscd for modeling the interactions between shells and acoustics in small dimensions This can, for example, be used to analyze the danped vibrations of shells in hearing aids and prevent feedback problems Figure 4: Deformation of the diaphrag:n (or membra: e) at /2 kHz in the Axisymrret Microphone mcdel found in the mode! library 6 Intr roduction


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