Acoustics of Ducts and Muffler (Hardcover, 2, Updated)

Preface xiii

1 Propagation of Waves in Ducts 1

1.1 Plane Waves in an Inviscid Stationary Medium 2

1.2 Three-Dimensional Waves in an Inviscid Stationary Medium 5

1.3 Waves in a Viscous Stationary Medium 12

1.4 Plane Waves in an Inviscid Moving Medium 16

1.5 Three-Dimensional Waves in an Inviscid Moving Medium 18

1.6 One-Dimensional Waves in a Viscous Moving Medium 20

1.7 Waves in Ducts with Compliant Walls (Dissipative Ducts) 23

1.8 Three-Dimensional Waves along Elliptical Ducts 34

References 39

2 Theory of Acoustic Filters 41

2.1 Units for the Measurement of Sound 41

2.2 Uniform Tube 43

2.3 Radiation Impedance 46

2.4 Reflection Coefficient at an Open End 48

2.5 A Lumped Inertance 49

2.6 A Lumped Compliance 50

2.7 End Correction 51

2.8 Electroacoustic Analogies 51

2.9 Electrical Circuit Representation of an Acoustic System 52

2.10 Acoustical Filter Performance Parameters 53

2.11 Lumped-Element Representations of a Tube 58

2.12 Simple Area Discontinuities 60

2.13 Gradual Area Changes 62

2.14 Extended-Tube Resonators 67

2.15 Helmholtz Resonator 69

2.16 Concentric Hole-Cavity Resonator 70

2.17 An Illustration of the Classical Method of Filter Evaluation 71

2.18 The Transfer Matrix Method 74

2.19 TL of a Simple Expansion Chamber Muffler 85

2.20 An Algebraic Algorithm for Tubular Mufflers 88

2.21 Synthesis Criteria for Low-Pass Acoustic Filters 91

References 94

3 Flow-Acoustic Analysis of Cascaded-Element Mufflers 97

3.1 The Exhaust Process 97

3.2 Finite Amplitude Wave Effects 101

3.3 Mean Flow and Acoustic Energy Flux 102

3.4 Aeroacoustic State Variables 105

3.5 Aeroacoustic Radiation 108

3.6 Insertion Loss 111

3.7 Transfer Matrices for Tubular Elements 112

3.8 Perforated Elements with Two Interacting Ducts 119

3.9 Acoustic Impedance of Perforates 126

3.10 Matrizant Approach 129

3.11 Perforated Elements with Three Interacting Ducts 131

3.12 Other Elements Constituting Cascaded-Element Mufflers 137

References 143

4 Flow-Acoustic Analysis of Multiply-Connected Perforated Element Mufflers 147

4.1 Herschel-Quincke Tube Phenomenon 147

4.2 Perforated Element with Several Interacting Ducts 151

4.3 Three-Pass Double-Reversal Muffler 154

4.4 Flow-Reversal End Chambers 158

4.5 Meanflow Lumped Resistance Network Theory 163

4.6 Meanflow Distribution and Back Pressure Estimation 169

4.7 Integrated Transfer Matrix Approach 175

References 186

5 Flow-Acoustic Measurements 187

5.1 Impedance of a Passive Subsystem or Termination 187

5.2 Four-Pole Parameters of a Flow-Acoustic Element or Subsystem 203

5.3 An Active Termination – Aeroacoustic Characteristics of a Source 210

References 229

6 Dissipative Ducts and Parallel Baffle Mufflers 233

6.1 Acoustically Lined Rectangular Duct with Moving Medium 234

6.2 Acoustically Lined Circular Duct with Moving Medium 239

6.3 Transfer Matrix Relation for a Dissipative Duct 241

6.4 Transverse Wave Numbers for a Stationary Medium 244

6.5 Normal Impedance of the Lining 245

6.6 Transmission Loss 249

6.7 Effect of Protective Layer 251

6.8 Parallel Baffle Muffler 257

6.9 The Effect of Mean Flow 259

6.10 The Effect of Terminations on the Performance of Dissipative Ducts 260

6.11 Lined Bends 261

6.12 Plenum Chambers 261

6.13 Flow-Generated Noise 262

6.14 Insertion Loss of Parallel Baffle Mufflers 263

References 264

7 Three-Dimensional Analysis of Mufflers 267

7.1 Collocation Method for Simple Expansion Chambers 268

7.2 Finite Element Methods for Mufflers 275

7.3 Green’s Function Method for a Rectangular Cavity 292

7.4 Green’s Function Method for Circular Cylindrical Chambers 301

7.5 Green’s Function Method for Elliptical Cylindrical Chambers 303

7.6 Breakout Noise 306

References 316

8 Design of Mufflers 321

8.1 Requirements of an Engine Exhaust Muffler 321

8.2 Simple Expansion Chamber 322

8.3 Double-Tuned Extended-Tube Expansion Chamber 324

8.4 Tuned Concentric Tube Resonator 326

8.5 Plug Mufflers 327

8.6 Side-Inlet Side-Outlet Mufflers 329

8.7 Designing for Insertion Loss 331

8.8 Three-Pass Double-Reversal Chamber Mufflers 338

8.9 Perforated Baffle Muffler 347

8.10 Forked Dual Muffler System 349

8.11 Design of Short Elliptical and Circular Chambers 353

8.12 Back-Pressure Considerations 362

8.13 Practical Considerations 365

8.14 Design of Mufflers for Ventilation Systems 367

8.15 Active Sound Attenuation 369

References 375

Appendix A: Bessel Functions and Some of Their Properties 377

Appendix B: Entropy Changes in Adiabatic Flows 381

B.1 Stagnation Pressure and Entropy 381

B.2 Pressure, Density, and Entropy 382

Appendix C: Nomenclature 385

Index 389