Transcription
Acoustics ModuleUser’s Guide
Acoustics Module User’s Guide 1998–2017 COMSOLProtected by U.S. Patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474;7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patentspending.This Documentation and the Programs described herein are furnished under the COMSOL Software LicenseAgreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the termsof the license agreement.COMSOL, the COMSOL logo, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop,LiveLink, and COMSOL Server are either registered trademarks or trademarks of COMSOL AB. All othertrademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and productsare not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of suchtrademark owners, see www.comsol.com/trademarks.Version: COMSOL 5.3Contact InformationVisit the Contact COMSOL page at www.comsol.com/contact to submit generalinquiries, contact Technical Support, or search for an address and phone number. You canalso visit the Worldwide Sales Offices page at www.comsol.com/contact/offices foraddress and contact information.If you need to contact Support, an online request form is located at the COMSOL Accesspage at www.comsol.com/support/case. Other useful links include: Support Center: www.comsol.com/support Product Download: www.comsol.com/product-download Product Updates: www.comsol.com/support/updates COMSOL Blog: www.comsol.com/blogs Discussion Forum: www.comsol.com/community Events: www.comsol.com/events COMSOL Video Gallery: www.comsol.com/video Support Knowledge Base: www.comsol.com/support/knowledgebasePart number: CM020201
C o n t e n t sChapter 1: IntroductionAcoustics Module Capabilities21What Can the Acoustics Module Do? . . . . . . . . . . . . . . . 21What are the Application Areas? . . . . . . . . . . . . . . . . . 23Which Problems Can You Solve? . . . . . . . . . . . . . . . . . 25Fundamental of Acoustics27Acoustics Explained . . . . . . . . . . . . . . . . . . . . . . 27Mathematical Models for Acoustic Analysis . . . . . . . . . . . . . 28Damping . . . . . . . . . . . . . . . . . . . . . . . . . . 30Artificial Boundaries. . . . . . . . . . . . . . . . . . . . . 32Acoustics Module Study Types33Stationary Study . . . . . . . . . . . . . . . . . . . . . . . 33Frequency Domain Study . . . . . . . . . . . . . . . . . . . . 34Eigenfrequency Study . . . . . . . . . . . . . . . . . . . . . 35Mode Analysis Study . . . . . . . . . . . . . . . . . . . . . 36Time Dependent Study . . . . . . . . . . . . . . . . . . . . 37Frequency Domain Modal and Time-Dependent Modal Studies . . . . . 38Modal Reduced Order Model . . . . . . . . . . . . . . . . . . 38Additional Analysis Capabilities . . . . . . . . . . . . . . . . . 38Acoustics Module Physics Interface Guide39Common Physics Interface and Feature Settings and Nodes. . . . . . . 44Where Do I Access the Documentation and Application Libraries? . . . . 44CONTENTS 3
Overview of the User’s Guide48Chapter 2: Pressure Acoustics InterfacesThe Pressure Acoustics, Frequency Domain Interface54Domain, Boundary, Edge, Point, and Pair Nodes for the PressureAcoustics, Frequency Domain Interface . . . . . . . . . . . . . 59Sound Hard Boundary (Wall) . . . . . . . . . . . . . . . . . . 61Initial Values. . . . . . . . . . . . . . . . . . . . . . . . . 61Monopole Domain Source . . . . . . . . . . . . . . . . . . . 61Dipole Domain Source. . . . . . . . . . . . . . . . . . . . 62Heat Source. . . . . . . . . . . . . . . . . . . . . . . . . 62Normal Acceleration . . . . . . . . . . . . . . . . . . . . . 63Normal Velocity . . . . . . . . . . . . . . . . . . . . . . . 63Normal Displacement . . . . . . . . . . . . . . . . . . . . . 64Sound Soft Boundary . . . . . . . . . . . . . . . . . . . . . 65Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 65Impedance . . . . . . . . . . . . . . . . . . . . . . . . . 65Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 69Plane Wave Radiation . . . . . . . . . . . . . . . . . . . . . 69Spherical Wave Radiation. . . . . . . . . . . . . . . . . . . . 70Cylindrical Wave Radiation . . . . . . . . . . . . . . . . . . . 71Incident Pressure Field. . . . . . . . . . . . . . . . . . . . . 71Interior Sound Hard Boundary (Wall) . . . . . . . . . . . . . . . 73Periodic Condition . . . . . . . . . . . . . . . . . . . . . . 74Axial Symmetry . . . . . . . . . . . . . . . . . . . . . . . 75Continuity . . . . . . . . . . . . . . . . . . . . . . . . . 75Pressure Acoustics . . . . . . . . . . . . . . . . . . . . . . 76Poroacoustics . . . . . . . . . . . . . . . . . . . . . . . . 81Narrow Region Acoustics . . . . . . . . . . . . . . . . . . . 88Background Pressure Field . . . . . . . . . . . . . . . . . . . 90Matched Boundary . . . . . . . . . . . . . . . . . . . . . . 92Far-Field Calculation. . . . . . . . . . . . . . . . . . . . . 93Interior Normal Acceleration . . . . . . . . . . . . . . . . . . 95Interior Normal Velocity . . . . . . . . . . . . . . . . . . . . 96Interior Normal Displacement. . . . . . . . . . . . . . . . . . 964 CONTENTS
Interior Impedance/Pair Impedance . . . . . . . . . . . . . . . . 97Interior Perforated Plate/Pair Perforated Plate . . . . . . . . . . . . 98Line Source . . . . . . . . . . . . . . . . . . . . . . . .100Line Source on Axis. . . . . . . . . . . . . . . . . . . . .102Monopole Point Source . . . . . . . . . . . . . . . . . . .103Dipole Point Source. . . . . . . . . . . . . . . . . . . . .105Quadrupole Point Source107. . . . . . . . . . . . . . . . . .Point Sources for 2D Components . . . . . . . . . . . . . . .109Circular Source (for 2D axisymmetric components) . . . . . . . .111The Pressure Acoustics, Transient Interface113Domain, Boundary, Edge, and Point Nodes for the PressureAcoustics, Transient Interface . . . . . . . . . . . . . . . .115Transient Pressure Acoustics Model. . . . . . . . . . . . . . .115The Gaussian Pulse Source Type Settings . . . . . . . . . . . . .116Normal Acceleration . . . . . . . . . . . . . . . . . . . .117Normal Velocity . . . . . . . . . . . . . . . . . . . . . .118Normal Displacement . . . . . . . . . . . . . . . . . . . .118Interior Normal Acceleration . . . . . . . . . . . . . . . . .119Interior Normal Velocity . . . . . . . . . . . . . . . . . . .120Interior Normal Displacement. . . . . . . . . . . . . . . . .120The Pressure Acoustics, Boundary Mode Interface122Initial Values. . . . . . . . . . . . . . . . . . . . . . . .123Boundary, Edge, Point, and Pair Nodes for the Pressure Acoustics,Boundary Mode Interface . . . . . . . . . . . . . . . . .124Modeling with the Pressure Acoustics Branch125Meshing (Resolving the Waves) . . . . . . . . . . . . . . . .125Lagrange and Serendipity Shape Functions . . . . . . . . . . . .127Time Stepping in Transient Models . . . . . . . . . . . . . . .128Frequency-Domain Modal and AWE . . . . . . . . . . . . . .130Solving Large Acoustics Problems Using Iterative Solvers. . . . . . .131Perfectly Matched Layers (PMLs) . . . . . . . . . . . . . . . .134Postprocessing Variables . . . . . . . . . . . . . . . . . . .137Evaluating the Acoustic Field in the Far-Field Region . . . . . . . .142Dedicated Acoustics Plots for Postprocessing . . . . . . . . . . .144About the Material Databases for the Acoustics Module . . . . . . .148CONTENTS 5
Specifying Frequencies: Logarithmic and ISO Preferred. . . . . . .Theory Background for the Pressure Acoustics Branch149150The Governing Equations. . . . . . . . . . . . . . . . . . .150Pressure Acoustics, Frequency Domain Equations . . . . . . . . .154Pressure Acoustics, Transient Equations . . . . . . . . . . . . .157Pressure Acoustics, Boundary Mode Equations . . . . . . . . . .157Theory for the Plane, Spherical, and Cylindrical Radiation BoundaryConditions . . . . . . . . . . . . . . . . . . . . . . .159Theory for the Far-Field Calculation: The Helmholtz-Kirchhoff Integral .161Theory for the Boundary Impedance Models165Impedance Conditions . . . . . . . . . . . . . . . . . . . .165RCL Models. . . . . . . . . . . . . . . . . . . . . . . .166Physiological Models . . . . . . . . . . . . . . . . . . . .168Waveguide End Impedance Models . . . . . . . . . . . . . . .176Porous Layer Models . . . . . . . . . . . . . . . . . . . .177Characteristic Specific Impedance Models . . . . . . . . . . . .178Theory for the Interior Impedance Models180Interior Perforated Plate Models . . . . . . . . . . . . . . . .180Theory for the Equivalent Fluid Models186Introduction to the Equivalent Fluid Models. . . . . . . . . . . .186About the Pressure Acoustics Fluid Models . . . . . . . . . . . .188About the Poroacoustics Models . . . . . . . . . . . . . . . .190About the Narrow Region Acoustics Models . . . . . . . . . . .204Theory for the Perfectly Matched Layers in the TimeDomain6 CONTENTS210Introduction to Perfectly Matched Layers. . . . . . . . . . . . .210Perfectly Matched Layers in the Time Domain . . . . . . . . . . .211
References for the Pressure Acoustics Branch212Chapter 3: Acoustic-Structure Interaction InterfacesThe Acoustic-Solid Interaction, Frequency Domain Interface216The Acoustic-Solid Interaction, Transient Interface219The Acoustic-Piezoelectric Interaction, Frequency DomainInterface222The Acoustic-Piezoelectric Interaction, Transient Interface225The Solid Mechanics (Elastic Waves) Interface228The Poroelastic Waves Interface229Domain, Boundary, and Pair Nodes for the Poroelastic WavesInterfaces . . . . . . . . . . . . . . . . . . . . . . .231Poroelastic Material . . . . . . . . . . . . . . . . . . . . .231Porous, Free . . . . . . . . . . . . . . . . . . . . . . .238Initial Values. . . . . . . . . . . . . . . . . . . . . . . .238Fixed Constraint . . . . . . . . . . . . . . . . . . . . . .239Periodic Condition . . . . . . . . . . . . . . . . . . . . .239Porous, Pressure . . . . . . . . . . . . . . . . . . . . . .239Prescribed Displacement . . . . . . . . . . . . . . . . . . .240Prescribed Velocity . . . . . . . . . . . . . . . . . . . . .241Prescribed Acceleration . . . . . . . . . . . . . . . . . . .242Roller . . . . . . . . . . . . . . . . . . . . . . . . . .243Septum Boundary Load . . . . . . . . . . . . . . . . . . .243Symmetry . . . . . . . . . . . . . . . . . . . . . . . .243CONTENTS 7
The Acoustic-Poroelastic Waves Interaction Interface244The Acoustic-Solid-Poroelastic Waves Interaction Interface247Theory for the Poroelastic Waves Interfaces250Elastic Waves Introduction . . . . . . . . . . . . . . . . . .250Poroelastic Waves Theory . . . . . . . . . . . . . . . . . .251Boundary Conditions for Poroelastic Waves . . . . . . . . . . .256Postprocessing Variables . . . . . . . . . . . . . . . . . . .259References for the Poroelastic Waves Interfaces . . . . . . . . . .260The Acoustic-Shell Interaction, Frequency Domain Interface262The Acoustic-Shell Interaction, Transient Interface265Modeling with the Acoustic-Structure Interaction Branch268Prestressed Acoustic-Structure Interaction . . . . . . . . . . . .268Solving Large Acoustic-Structure Interaction Models . . . . . . . .269Configuration of Perfectly Matched Layers (PMLs) forAcoustic-Structure Interaction Models . . . . . . . . . . . .270The Pipe Acoustics Interfaces272The Pipe Acoustics, Frequency Domain Interface. . . . . . . . . .272The Pipe Acoustics, Transient Interface . . . . . . . . . . . . .274Edge, Boundary, Point, and Pair Nodes for the Pipe AcousticsInterfaces . . . . . . . . . . . . . . . . . . . . . . .275Initial Values. . . . . . . . . . . . . . . . . . . . . . . .276Fluid Properties . . . . . . . . . . . . . . . . . . . . . .276Pipe Properties . . . . . . . . . . . . . . . . . . . . . .277Closed. . . . . . . . . . . . . . . . . . . . . . . . . .278Pressure . . . . . . . . . . . . . . . . . . . . . . . . .278Velocity . . . . . . . . . . . . . . . . . . . . . . . . .279End Impedance279. . . . . . . . . . . . . . . . . . . . . .Theory for the Pipe Acoustics Interfaces8 CONTENTS282Governing Equations . . . . . . . . . . . . . . . . . . . .282Theory for the Pipe Acoustics Boundary Conditions . . . . . . . .286Solving Transient Problems . . . . . . . . . . . . . . . . . .289
Cut-off Frequency . . . . . . . . . . . . . . . . . . . . .290Flow Profile Correction Factor β . . . . . . . . . . . . . . . . . 290References for the Pipe Acoustics Interfaces . . . . . . . . . . .291Chapter 4: Aeroacoustics InterfacesThe Linearized Potential Flow, Frequency Domain Interface295Domain, Boundary, Edge, Point, and Pair Nodes for the LinearizedPotential Flow, Frequency Domain Interface . . . . . . . . . .297Linearized Potential Flow Model . . . . . . . . . . . . . . . .298Initial Values. . . . . . . . . . . . . . . . . . . . . . . .299Sound Hard Boundary (Wall) . . . . . . . . . . . . . . . . .299Velocity Potential . . . . . . . . . . . . . . . . . . . . . .299Normal Mass Flow . . . . . . . . . . . . . . . . . . . . .300Plane Wave Radiation . . . . . . . . . . . . . . . . . . . .300Incident Velocity Potential . . . . . . . . . . . . . . . . . .301Sound Soft Boundary . . . . . . . . . . . . . . . . . . . .302Periodic Condition . . . . . . . . . . . . . . . . . . . . .302Normal Velocity . . . . . . . . . . . . . . . . . . . . . .302Impedance, Interior Impedance, and Pair Impedance . . . . . . . .303Vortex Sheet . . . . . . . . . . . . . . . . . . . . . . .303Interior Sound Hard Boundary (Wall) . . . . . . . . . . . . . .304Continuity . . . . . . . . . . . . . . . . . . . . . . . .304Mass Flow Edge Source . . . . . . . . . . . . . . . . . . .304Mass Flow Point Source . . . . . . . . . . . . . . . . . . .305Mass Flow Circular Source . . . . . . . . . . . . . . . . . .305Mass Flow Line Source on Axis . . . . . . . . . . . . . . . .306Axial Symmetry . . . . . . . . . . . . . . . . . . . . . .306The Linearized Potential Flow, Transient Interface307Domain, Boundary, Edge, Point, and Pair Nodes for the LinearizedPotential Flow, Transient Interface . . . . . . . . . . . . . .The Linearized Potential Flow, Boundary Mode Interface308310Boundary, Edge, Point, and Pair Nodes for the Linearized PotentialFlow, Boundary Mode Interface . . . . . . . . . . . . . . .312CONTENTS 9
The Compressible Potential Flow Interface313Domain, Boundary, and Pair Nodes for the Compressible Potential. . . . . . . . . . . . . . . . . . . . .314Compressible Potential Flow Model. . . . . . . . . . . . . . .Flow Interface315Initial Values. . . . . . . . . . . . . . . . . . . . . . . .316Slip Velocity . . . . . . . . . . . . . . . . . . . . . . . .316Symmetry . . . . . . . . . . . . . . . . . . . . . . . .316Normal Flow . . . . . . . . . . . . . . . . . . . . . . .316Mass Flow . . . . . . . . . . . . . . . . . . . . . . . .317Mean Flow Velocity Potential . . . . . . . . . . . . . . . . .317Periodic Condition . . . . . . . . . . . . . . . . . . . . .317Interior Wall (Slip Velocity) . . . . . . . . . . . . . . . . . .317The Linearized Euler, Frequency Domain Interface319Domain, Boundary, and Pair Nodes for the Linearized Euler,Frequency Domain Interface . . . . . . . . . . . . . . . .Linearized Euler Model. . . . . . . . . . . . . . . . . . .321322Rigid Wall . . . . . . . . . . . . . . . . . . . . . . . .325Initial Values. . . . . . . . . . . . . . . . . . . . . . . .325Axial Symmetry . . . . . . . . . . . . . . . . . . . . . .325Domain Sources . . . . . . . . . . . . . . . . . . . . . .325Background Acoustic Fields . . . . . . . . . . . . . . . . . .326Prescribed Acoustic Fields . . . . . . . . . . . . . . . . . .327Pressure (Isentropic) . . . . . . . . . . . . . . . . . . . .328Symmetry . . . . . . . . . . . . . . . . . . . . . . . .328Impedance and Interior Impedance . . . . . . . . . . . . . . .328Moving Wall. . . . . . . . . . . . . . . . . . . . . . . .329Interior Wall . . . . . . . . . . . . . . . . . . . . . . .329Asymptotic Far-Field Radiation. . . . . . . . . . . . . . . . .329Outflow Boundary . . . . . . . . . . . . . . . . . . . . .330Continuity . . . . . . . . . . . . . . . . . . . . . . . .331The Linearized Euler, Transient Interface332Domain, Boundary, and Pair Nodes for the Linearized Euler,10 C O N T E N T STransient Interface . . . . . . . . . . . . . . . . . . . .334Initial Values. . . . . . . . . . . . . . . . . . . . . . . .334Moving Wall. . . . . . . . . . . . . . . . . . . . . . . .335
The Linearized Navier-Stokes, Frequency Domain Interface336Domain, Boundary, and Pair Nodes for the Linearized Navier-Stokes,Frequency Domain and Transient Interfaces . . . . . . . . . .339Linearized Navier-Stokes Model . . . . . . . . . . . . . . . .340Wall. . . . . . . . . . . . . . . . . . . . . . . . . . .343Axial Symmetry . . . . . . . . . . . . . . . . . . . . . .344Interior Wall . . . . . . . . . . . . . . . . . . . . . . .344No Slip. . . . . . . . . . . . . . . . . . . . . . . . .344Isothermal . . . . . . . . . . . . . . . . . . . . . . . .345Initial Values. . . . . . . . . . . . . . . . . . . . . . . .345Interior Normal Impedance . . . . . . . . . . . . . . . . . .345First-Order Material Parameters . . . . . . . . . . . . . . . .346Domain Sources . . . . . . . . . . . . . . . . . . . . . .347Background Acoustic Fields . . . . . . . . . . . . . . . . . .347Pressure (Adiabatic). . . . . . . . . . . . . . . . . . . . .347Slip . . . . . . . . . . . . . . . . . . . . . . . . . . .348Prescribed Velocity . . . . . . . . . . . . . . . . . . . . .348Prescribed Pressure . . . . . . . . . . . . . . . . . . . . .349Normal Stress . . . . . . . . . . . . . . . . . . . . . . .349No Stress. . . . . . . . . . . . . . . . . . . . . . . .349Normal Impedance . . . . . . . . . . . . . . . . . . . . .349Stress . . . . . . . . . . . . . . . . . . . . . . . . . .350Adiabatic . . . . . . . . . . . . . . . . . . . . . . . . .350Prescribed Temperature . . . . . . . . . . . . . . . . . . .350Heat Flux. . . . . . . . . . . . . . . . . . . . . . . . .350Continuity . . . . . . . . . . . . . . . . . . . . . . . .351The Linearized Navier-Stokes, Transient Interface352Modeling with the Aeroacoustics Branch354Selecting an Aeroacoustics Interface . . . . . . . . . . . . . .354Meshing . . . . . . . . . . . . . . . . . . . . . . . . .355Stabilization . . . . . . . . . . . . . . . . . . . . . . . .356Solver Suggestions for Large Aeroacoustic Models . . . . . . . . .358Lagrange and Serendipity Shape Functions . . . . . . . . . . . .358Time Stepping in Transient Models . . . . . . . . . . . . . . .359Mapping Between CFD and Acoustics Mesh. . . . . . . . . . .359Coupling to Turbulent Flows (Eddy Viscosity) . . . . . . . . . . .361CONTENTS 11
Eigenfrequency Studies. . . . . . . . . . . . . . . . . . . .362Postprocessing Variables . . . . . . . . . . . . . . . . . . .362Theory Background for the Aeroacoustics Branch365General Governing Equations . . . . . . . . . . . . . . . . .366Linearized Potential Flow . . . . . . . . . . . . . . . . . . .368Compressible Potential Flow . . . . . . . . . . . . . . . . .372Linearized Euler . . . . . . . . . . . . . . . . . . . . . .374Linearized Navier-Stokes . . . . . . . . . . . . . . . . . . .377Scattered Field Formulation for LE and LNS. . . . . . . . . . . .378References for the Aeroacoustics Branch Interfaces380Chapter 5: Thermoviscous Acoustics InterfacesThe Thermoviscous Acoustics, Frequency Domain Interface384Domain, Boundary, and Pair Nodes for the Thermoviscous Acoustics,Frequency Domain Interface . . . . . . . . . . . . . . . .390Background Acoustic Fields . . . . . . . . . . . . . . . . . .394Wall. . . . . . . . . . . . . . . . . . . . . . . . . . .395Initial Values. . . . . . . . . . . . . . . . . . . . . . . .396Axial Symmetry . . . . . . . . . . . . . . . . . . . . . .396Interior Wall . . . . . . . . . . . . . . . . . . . . . . .396Interior Normal Impedance . . . . . . . . . . . . . . . . . .397Interior Velocity . . . . . . . . . . . . . . . . . . . . . .397Interior Temperature Variation . . . . . . . . . . . . . . . .398No Slip12 C O N T E N T S389Thermoviscous Acoustics Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .399Isothermal . . . . . . . . . . . . . . . . . . . . . . . .399Heat Source. . . . . . . . . . . . . . . . . . . . . . . .399Pressure (Adiabatic). . . . . . . . . . . . . . . . . . . . .399Symmetry . . . . . . . . . . . . . . . . . . . . . . . .400Velocity . . . . . . . . . . . . . . . . . . . . . . . . .400Slip . . . . . . . . . . . . . . . . . . . . . . . . . . .401Stress . . . . . . . . . . . . . . . . . . . . . . . . . .401No Stress402. . . . . . . . . . . . . . . . . . . . . . . .
Normal Stress . . . . . . . . . . . . . . . . . . . . . . .402Normal Impedance . . . . . . . . . . . . . . . . . . . . .402Adiabatic . . . . . . . . . . . . . . . . . . . . . . . . .403Temperature Variation . . . . . . . . . . . . . . . . . . . .403Heat Flux. . . . . . . . . . . . . . . . . . . . . . . . .403The Thermoviscous Acoustics, Transient Interface404Domain, Boundary, and Pair Nodes for the Thermoviscous Acoustics,Boundary Mode Interface . . . . . . . . . . . . . . . . .407Thermoviscous Acoustics Model . . . . . . . . . . . . . . . .408Background Acoustic Fields . . . . . . . . . . . . . . . . . .409The Thermoviscous Acoustics, Boundary Mode Interface410Domain, Boundary, and Pair Nodes for the Thermoviscous Acoustics,Boundary Mode Interface . . . . . . . . . . . . . . . . .412Thermoviscous Acoustics Model . . . . . . . . . . . . . . . .414The Acoustic-Thermoviscous Acoustic Interaction, FrequencyDomain Interface415The Thermoviscous Acoustic-Solid Interaction, FrequencyDomain Interface418The Thermoviscous Acoustic-Shell Interaction, FrequencyDomain InterfaceModeling with the Thermoviscous Acoustics Branch421424Meshing the Boundary Layer . . . . . . . . . . . . . . . . .424Solver Suggestions for Large Thermoviscous Acoustics Models . . . .425Lagrange and Serendipity Shape Functions . . . . . . . . . . . .428Transient Solver Settings . . . . . . . . . . . . . . . . . . .428Postprocessing Variables . . . . . . . . . . . . . . . . . . .429Theory Background for the Thermoviscous Acoustics Branch433The Viscous and Thermal Boundary Layers . . . . . . . . . . . .434General Linearized Compressible Flow Equations . . . . . . . . .435Acoustic Perturbation and Linearization . . . . . . . . . . . . .436Scattered Field Formulation and Background Acoustic Fields . . . . .441CONTENTS 13
Formulation for Eigenfrequency Studies . . . . . . . . . . . . .442Formulation for Mode Analysis in 2D and 1D axisymmetric . . . . . .443Formulation for the Boundary Mode Interface . . . . . . . . . . .444References for the Thermoviscous Acoustics, Frequency DomainInterface. . . . . . . . . . . . . . . . . . . . . . . .445Chapter 6: Ultrasound InterfacesThe Convected Wave Equation, Time Explicit Interface448Domain, Boundary, Edge, Point, and Pair Nodes for the ConvectedWave Equation Interface. . . . . . . . . . . . . . . . . .450Convected Wave Equation Model . . . . . . . . . . . . . . .451Domain Sources . . . . . . . . . . . . . . . . . . . . . .453Sound Hard Wall . . . . . . . . . . . . . . . . . . . . . .454Initial Values. . . . . . . . . . . . . . . . . . . . . . . .454Normal Velocity . . . . . . . . . . . . . . . . . . . . . .454Pressure . . . . . . . . . . . . . . . . . . . . . . . . .455Symmetry . . . . . . . . . . . . . . . . . . . . . . . .455Acoustic Impedance. . . . . . . . . . . . . . . . . . . . .455General Flux/Source . . . . . . . . . . . . . . . . . . . .456General Interior Flux . . . . . . . . . . . . . . . . . . . .457Modeling with the Convected Wave Equation Interface458Meshing, Discretization, and Solvers14 C O N T E N T S. . . . . . . . . . . . . .458Postprocessing: Variables and Quality . . . . . . . . . . . . . .459Absorbing Layers . . . . . . . . . . . . . . . . . . . . . .460Stabilizing Physical Instabilities (Filtering) . . . . . . . . . . . . .461Storing Solution on Selections for Large Models . . . . . . . . . .462Theory for the Convected Wave Equation Interface463Governing Equations of the Convected Wave Equation . . . . . . .463Boundary Conditions . . . . . . . . . . . . . . . . . . . .465The Lax-Friedrichs Flux . . . . . . . . . . . . . . . . . . .466References for the Convected Wave Equation Interface . . . . . . .466
Chapter 7: Geometrical Acoustics InterfacesThe Ray Acoustics Interface470Domain, Boundary, and Global Nodes for the Ray AcousticsInterface. . . . . . . . . . . . . . . . . . . . . . . .476Medium Properties . . . . . . . . . . . . . . . . . . . . .477Wall. . . . . . . . . . . . . . . . . . . . . . . . . . .479Axial Symmetry . . . . . . . . . . . . . . . . . . . . . .484Accumulator (Boundary) . . . . . . . . . . . . . . . . . . .485Material Discontinuity . . . . . . . . . . . . . . . . . . . .486Ray Properties . . . . . . . . . . . . . . . . . . . . . . .488Release . . . . . . . . . . . . . . . . . . . . . . . . .488Sound Pressure Level Calculation. . . . . . . . . . . . . . . .494Accumulator (Domain) . . . . . . . . . . . . . . . . . . .495Nonlocal Accumulator. . . . . . . . . . . . . . . . . . . .496Inlet . . . . . . . . . . . . . . . . . . . . . . . . . . .497Inlet on Axis . . . . . . . . . . . . . . . . . . . . . . .501Background Velocity . . . . . . . . . . . . . . . . . . . .504Auxiliary Dependent Variable . . . . . . . . . . . . . . . . .504Release from Edge . . . . . . . . . . . . . . . . . . . . .505Release from Point . . . . . . . . . . . . . . . . . . . . .505Release from Point on Axis . . . . . . . . . . . . . . . . . .505Release from Grid . . . . . . . . . . . . . . . . . . . . .505Release from Grid on Axis . . . . . . . . . . . . . . . . . .506Release from Data File. . . . . . . . . . . . . . . . . . . .506Ray Continuity . . . . . . . . . . . . . . . . . . . . . . .508Ray Termination . . . . . . . . . . . . . . . . . . . . . .509Ray Detector . . . . . . . . . . . . . . . . . . . . . . .510Modeling with the Ray Acoustics Interface511Mixed Diffuse and Specular Wall Conditions . . . . . . . . . . .511Assigning Directivity to a Source . . . . . . . . . . . . . . . .512Stopping Rays for a Given Conditions . . . . . . . . . . . . . .512Mesh Guidelines . . . . . . . . . . . . . . . . . . . . . .512Component Couplings. . . . . . . . . . . . . . . . . . . .515Using Ray Detectors . . . . . . . . . . . . . . . . . . . .517Impulse Response, Results Plots, Data Sets, and Derived Values . . . .517CONTENTS 15
Theory for the Ray Acoustics Interface520Introduction to Ray Acoustics . . . . . . . . . . . . . . . . .520Initial Conditions — Direction. . . . . . . . . . . . . . . . .521Material Discontinuity Theory . . . . . . . . . . . . . . . . .523Intensity and Wavefront Curvature . . . . . . . . . . . . . . .524Intensity and Phase Reinitialization . . . . . . . . . . . . . . .528Wavefront Curvature Calculation in Graded Media . . . . . . . . .531Attenuation Within Domains . . . . . . . . . . . . . . . . .536Ray Termination Theory . . . . . . . . . . . . . . . . . . .537Accumulator Theory: Domains . . . . . . . . . . . . . . . .539Accumulator Theory: Boundaries . . . . . . . . . . . . . . .540Sound Pressure Level Calculation Theory . . . . . . . . . . . .542References for the Ray Acoustics Interface . . . . . . . . . . . .543The Acoustic Diffusion Equation Interface544Domain, Boundary, and Global Nodes for the Acoustic Diffusion16 C O N T E N T SEquation Interface . . . . . . . . . . . . . . . . . . . .547Acoustic Diffusion Model. . . . . . . . . . . . . . . . . . .547Room . . . . . . . . . . . . . . . . . . . . . . . . . .548Wall. . . . . . . . . . . . . . . . . . . . . . . . . . .549Inward Energy Flux . . . . . . . . . . . . . . . . . . . . .550Initial Values. . . . . . . . . . . . . . . . . . . . . . . .550Fitted Domain . . . . . . . . . . . . . . . . . . . . . . .550Domain Source . . . . . . . . . . . . . . . . . . . . . .551Room Coupling . . . . . . . . . . . . . . . . . . . . . .551Mapped Room Coupling . . . . . . . . . . . . . . . . . . .552Destination Selection . . . . . . . . . . . . . . . . . . . .553Point Source . . . . . . . . . . . . . . . . . . . . . . .553Modeling with the Acoustic Diffusion Equation Interface554The Eigenvalue Study Type . . . . . . . . . . . . . . . . . .554Combined Stationary and Time Dependent Study . . . . . . . . .554Theory for the Acoustic Diffusion Equation Interface555Statistical Model of Reverberation Time . . . . . . . . . . . . .555The Acoustic Diffusion Equation . . . . . . . . . . . . . . . .556References for the Acoustic Diffusion Equation Interface. . . . . . .562
Chapter 8: Multiphysics CouplingsCoupling Features566Acoustic-Structure Boundary . . . . . . . . . . . . . . . . .566Thermoviscous Acoustic-Structure Boundary . . . . . . . . . . .568Aeroacoustic-Structure Boundary . . . . . . . . . . . . . . .569Acoustic-Thermoviscous Acoustic Boundary . . . . . . . . . . .570Acoustic-Porous Boundary . . . . . . . . . . . . . . . . . .571Porous-Structure Boundary . . . . . . . . . . . . . . . . . .572Background Potential Flow . . . . . . . . . . . . . . . . . .573Predefined Multiphysics Interfaces574Modeling with Multiphysics Couplings575Use Selections . . . . . . . . . . . . . . . . . . . . . . .575The Override Behavior . . . . . . . . . . . . . . . . . . .576The Solvers . . . . . . . . . . . . . . . . . . . . . . . .576Perfectly Matched Layers (PMLs) . . . . . . . . . . . . . . . .577Chapter 9: Structural Mechanics with the AcousticsModuleVibroacoustic Applications . . . . . . . . . . . . . . . . . .580The Solid Mechanics Interface . . . . . . . . . . . . . . . . .580The Piezoelectric Devices Interface . . . . . . . . . . . . . . .581Acoustic-Structure Multiphysics Interaction . . . . . . . . . . . .581Chapter 10: GlossaryGlossary of Terms584CONTENTS 17
18 C O N T E N T S
1Introduction
4 CONTENTS Overview of the User's Guide 48 Chapter 2: Pressure Acoustics Interfaces The Pressure Acoustics, Frequency Domain Interface 54 Domain, Boundary, Edge, Point, and Pair Nodes for the Pressure
