Duct Acoustics: Fundamentals and Applications to Mufflers and Silencers

608 Pages·2021·20.799 MB·English

by  Erkan Dokumacı

Duct Acoustics
Usingahands-onapproach,thisself-containedtoolkitcoverstopicsrangingfromthe
foundationsofductacousticstotheacousticdesignofductsystems,throughpractical
modeling, optimization and measurement techniques. Discover in-depth analyses of
one-andthree-dimensionalmodelsofsoundgeneration,propagationandradiation,as
techniquesforassemblingacousticmodelsofductsystemsfromsimplercomponents
are described. Identify the weaknesses of mathematical models in use and improve
them by measurement when needed. Cope with challenges in acoustic design, and
improve understanding of the underlying physics, by using the tools described. An
essential reference for engineers and researchers who work on the acoustics of fluid
machineryductworks.
Erkan Dokumacı is Professor Emeritus of Mechanical Engineering at Dokuz Eylül
University (İzmir, Turkey). He is currently on the Editorial Advisory Board for the
JournalofSoundandVibrationandistheauthorofsoftwareusedforacousticdesign
of mufflers and silencers, aswell asmany scientific papers on duct acoustics.

Duct Acoustics
fl
Fundamentals and Applications to Muf ers
and Silencers
ERKAN DOKUMACI
DokuzEylülUniversity
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108840750
DOI:10.1017/9781108887656
©CambridgeUniversityPress2021
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Firstpublished2021
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Dokumaci,Erkan,1942–author.
Title:Ductacoustics:fundamentalsandapplicationstomufflersandsilencers/ErkanDokumaci,
DokuzEylülUniversity.
Description:Cambridge,UK;NewYork,NY:CambridgeUniversityPress,2021.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2020042217(print)|LCCN2020042218(ebook)|ISBN9781108840750(hardback)|
ISBN9781108887656(epub)
Subjects:LCSH:Gastubing–Soundproofing.|Airducts–Acousticproperties–Mathematicalmodels.|
Fluids–Acousticproperties–Mathematicalmodels.|Hydraulicmachinery–Noise.|Gas-machines–Noise.|
Acousticalengineering.
Classification:LCCTP757.D652021(print)|LCCTP757(ebook)|DDC620.2/3–dc23
LCrecordavailableathttps://lccn.loc.gov/2020042217
LCebookrecordavailableathttps://lccn.loc.gov/2020042218
ISBN978-1-108-84075-0Hardback
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To Figen and Pınar

Contents
Preface page xvii
1 Some Preliminaries 1
1.1 Introduction tothe Linear Theory ofSoundWave Motion 1
1.1.1 Linearization Hypothesis 1
1.1.2 Partitioning TurbulentFluctuations 2
1.1.3 Linearization of Inviscid Fluid Flow 4
1.1.4 Evolution ofNon-Linear Waves 7
1.2 Representationof Acoustic Waves in theFrequency Domain 8
1.2.1 Fourier Transform 8
1.2.2 Periodic Functions 10
1.2.3 Impulse Sampling 11
1.2.4 Power SpectralDensity 12
1.3 Representationof Waves inthe WavenumberDomain 14
1.3.1 Spatial Fourier Transform 14
1.3.2 Briggs’ Criterion 15
1.4 Intensity and Power of Sound Waves 15
1.5 Introduction tothe Linear System View of Duct Acoustics 19
References 21
2 Introduction toAcoustic Block Diagrams 23
2.1 Introduction 23
2.2 Classification of AcousticModels ofDucts 25
2.2.1 Classificationby Number of Ports 25
2.2.2 Classificationby Typeof Port 26
2.2.2.1 One-DimensionalElements 27
2.2.2.2 Modal Elements 27
2.3 Mathematical Models ofAcoustic Elements 29
2.3.1 One-Port Elements 29
2.3.2 Two-Port Elements 31
2.3.3 Multi-Port Elements 32
2.4 Assembly ofBlocks 33
2.4.1 Assembly ofTwo-Ports 34
2.4.2 Assembly ofMulti-Ports 36
vii
viii Contents
2.4.3 Optimization of Global MatrixSize 41
2.4.4 Contraction ofAssembled Modal Two-Ports 42
2.5 Acoustic Elements Based on Numerical Methods 44
2.5.1 The Finite Element Method 45
2.5.2 The Boundary ElementMethod 49
2.6 Programming Considerations 51
References 58
3 Transmissionof Low-FrequencySoundWavesin Ducts 59
3.1 Introduction 59
3.2 One-Dimensional Theory ofSoundPropagation inDucts 60
3.2.1 Unsteady Flow Equations 60
3.2.2 Equations Governing Acoustic WaveMotion 63
3.3 Solutionof LinearizedAcoustic Equations 65
3.3.1 Homogeneous Ducts (ε0 ¼0) 66
3.3.1.1 Uniform Ducts 67
3.3.1.2 Homogeneous Non-Uniform Ducts 68
3.3.2 Inhomogeneous Ducts (ε0 6¼0) 68
3.3.3 Numerical Matrizant Method 69
3.4 Time-Averaged Power ofOne-Dimensional AcousticWaves 72
3.5 Hard-Walled Uniform Ducts 73
3.5.1 WaveTransfer Matrix 74
3.5.2 Traveling Waves andDirection ofPropagation 75
3.5.3 Reflection Coefficient and Standing Waves 77
3.5.4 LumpedAcoustic Elements 79
3.6 Hard-Walled Homogeneous Ducts with Non-Uniform
Cross Section 80
3.6.1 WaveTransfer Matrix 81
3.6.2 HighFrequency Approximation 84
3.7 Ducts Packed with Porous Material 85
3.8 Acoustic Boundary Conditions on Duct Walls 87
3.8.1 ImpermeableWalls 87
3.8.1.1 No-Slip Model 87
3.8.1.2 Full-Slip Model 88
3.8.1.3 Partial-SlipModel 88
3.8.1.4 Rough-Wall Model 89
3.8.1.5 Unified Boundary Condition 90
3.8.2 Permeable Walls 91
3.9 Homogeneous Ductswith Impermeable Finite Impedance Walls 92
3.9.1 Non-Uniform Duct 93
3.9.2 Uniform Duct 95
3.9.2.1 Direction of Propagation 97
3.9.2.2 Wave Equation 98
3.9.2.3 Impedance Eduction Formula 98
3.9.2.4 Peripherally Non-Uniform Wall Impedance 98