Mechanics of Flow-Induced Sound and Vibration Volume 1_ General Concepts and Elementary Sources

Cover......Page 3
Copyright......Page 4
Dedication......Page 5
Contents......Page 6
Preface to the Second Edition......Page 12
Preface to the First Edition......Page 16
List of Symbols......Page 20
1.1 Occurrences of Noise Induced by Flow......Page 24
1.2 Fluid–Body Interactions for Sound Production......Page 26
1.3 Dimensional Analysis of Sound Generation......Page 29
1.4 Signal Analysis Tools of Vibration and Sound......Page 33
1.4.1 A Simple Example of an Acoustic Radiator......Page 34
1.4.2.1 A Simple Example of Classical Correlation Analysis......Page 35
1.4.2.2.1 Periodic Signals......Page 38
1.4.2.2.2 Random Signals......Page 39
1.4.3.1 Periodic Signals......Page 42
1.4.3.2 Random Signals......Page 44
1.4.4.1 Descriptions of Linear Bandpass Filters......Page 48
1.4.4.2 Spatial Filtering and Wave Number Transformations......Page 51
1.4.4.3 Notes on Error Analysis......Page 55
1.5.1.1 Sound Pressure Level......Page 57
1.5.1.3 The Use of Transfer Functions......Page 58
1.5.2 An Example of the Use of Nondimensional Spectrum Levels for Scaling......Page 60
1.6 Mathematical Refresher......Page 62
1.6.2 Differential Operators......Page 64
1.6.3 Integral Theorems......Page 65
1.6.4 Dirac Delta Function......Page 66
References......Page 67
2.1.1 The Wave Equation......Page 70
2.1.2 Acoustic Plane Waves and Intensity......Page 72
2.1.3.1 Monopole Sources......Page 76
2.1.3.2 Dipole Sources......Page 79
2.1.3.3 Quadrupole Sources......Page 85
2.1.3.4 Average Acoustic Intensity......Page 87
2.2 Sommerfeld’s Radiation Condition......Page 89
2.3.1 The Wave Equation......Page 90
2.3.2 Kirchhoff’s Integral Equation and the Retarded Potential......Page 92
2.3.3 Acoustic Radiation From a Compact Region of Free Turbulence......Page 98
2.4.1 Curle’s Development of Lighthill’s Wave Equation......Page 101
2.4.2 Illustration I of Curle’s Equation: Radiation from a Concentrated Hydrodynamic Force......Page 104
2.4.3 Illustration II of Curle’s Equation: Radiation from a Heaving Sphere......Page 105
2.4.4 Powell’s Reflection Theorem......Page 107
2.5 Effects of Source Motion on Flow-Induced Noise......Page 113
2.6.1 General Implications......Page 117
2.6.2 Derivation of the Wave Equation With Vortical Sources......Page 119
2.6.3 The Physical Significance of the Vorticity Source......Page 121
2.6.4 The Effect of Solid Boundaries on Vortex Sound......Page 126
2.6.5 Relationships Between the Powell and the Lighthill–Curle Theories......Page 127
2.7.1 The Helmholtz Integral Equation......Page 131
2.7.2 Generalized Transforms and Stochastic Variables......Page 135
2.7.3 Equivalent Integral Representation for the Acoustic Pressure......Page 141
2.8 Sources in Ducts and Pipes......Page 145
2.8.1 Elementary Duct Acoustics......Page 146
2.8.2 Radiation From Multipoles in an Infinitely Long Pipe......Page 150
2.8.3 Radiation From the Opening of a Semi-Infinite Duct......Page 152
References......Page 156
3.1 Introduction......Page 160
3.2 Shear Flow Instabilities and the Generation of Vorticity......Page 161
3.3.1 General Considerations......Page 168
3.3.2 The Flow in the Opening and the Strouhal Numbers of Tones......Page 170
3.3.3.1 General Considerations......Page 177
3.3.3.2 Monopole Sources With an Acoustically-Compact Cavity Width......Page 179
3.3.3.3 Mitigation of Sound and Cavity Pressure......Page 181
3.4.1 The Essentials of Jet Tone Generation......Page 182
3.4.2 Dimensionless Frequencies of Jet Tones......Page 185
3.4.3 Hole, Ring, and Edge Tones......Page 189
3.4.4 Tones in Supersonic Jets......Page 197
3.5.1 Introduction......Page 202
3.5.2 Correlation Functions of Random Variables......Page 203
3.6.1 Acoustically-Useful Representations for Homogeneous Turbulence......Page 206
3.6.2 Spectrum Models for Homogeneous Turbulence......Page 209
3.6.3 Anisotropic Turbulence: Spectral Models Based on Stretched Coordinates......Page 212
3.6.4 Measured Turbulence in Plane Mixing Layers......Page 214
3.7 Fundamentals of Noise From Subsonic Turbulent Jets......Page 218
3.7.1.1 Discussion of the Source Term......Page 219
3.7.1.2 Formal Analytical Relationships for Including Source Convection......Page 221
3.7.2.1 Flow Development in Turbulent Jets......Page 225
3.7.2.2 Space–Time Statistical Properties of the Turbulence in Circular Jets; the Second-Order Correlation Tensor......Page 227
3.7.2.3 Methods of Approximating the Fourth-Order Correlation Tensor......Page 235
3.7.3 Expressions and Scaling law for Jet Noise......Page 239
3.7.3.1 The Role of Specific Turbulent Structures in Jet Noise......Page 246
3.7.4.1 Enablers for Computational Methods in Parametric Studies......Page 247
3.7.4.2 Noise Suppression......Page 254
3.8.1 Sound From Efflux Inhomogeneities......Page 256
3.8.2 Inhomogeneities in the Free-Turbulent Field......Page 261
References......Page 262
4.1 Introduction: History and General Description of Vortex Flow, Lift Fluctuation, and Sound......Page 274
4.2.1 A General Description of the Wake Structure and Vortex Generation......Page 276
4.2.2 Analysis of Vortex Production......Page 278
4.3.1 Mean Drag and Vortex-Shedding Frequencies......Page 283
4.3.2 Oscillatory Lift and Drag Circular Cylinders......Page 291
4.3.3 Representations of Axial Phase Uniformity: Correlation Lengths......Page 296
4.3.4 Other Influences on Vortex Shedding......Page 298
4.4 Estimations of Wake-Induced Forces in Two-Dimensional Flow......Page 303
4.5.1 The General Equations......Page 307
4.5.2 Sound From a Rigid Cylinder in a Cross-Flow......Page 309
4.5.3 Review of Measured Acoustic Intensities......Page 312
4.6 Radiation From Rotating Rods......Page 317
4.7 Other Topics in Vortex-Induced Noise......Page 323
4.7.1 Cylinders With Noncircular Cross Sections......Page 324
4.7.2 Unsteadiness in Tube Bundles......Page 327
4.7.3 Methods of Reducing Vortex-Induced Forces......Page 332
4.7.4 Sounds From Ducted Elements......Page 333
4.8 Appendix: The Sound Field of a Two-Dimensional Dipole......Page 337
References......Page 339
5.1 Introduction......Page 346
5.2 Response of Single-Degree-of-Freedom Systems to Temporally Random Excitation......Page 349
5.3.1 Modal Velocities and Excitation Functions......Page 353
5.3.2 Response Estimates for Structures of Many Modes......Page 365
5.4 Modal Shape Functions for Simple Structures......Page 374
5.5.1 Acoustic Radiation From a Simply Supported Panel......Page 379
5.5.2 The Fluid Impedance of a Simply Supported Panel......Page 384
5.5.3 Radiated Acoustic Power......Page 387
5.5.4 Radiation Efficiencies of Simple Structures......Page 390
5.5.5 Relationships for Estimating Total Acoustic Power......Page 392
5.5.6 Added Masses of Simple Structures......Page 398
5.6.1 Vibration of the Point-Driven Plate......Page 399
5.6.2 Sound From the Locally-Driven Fluid-Loaded Plate......Page 403
5.7.1 General Formulation for a One-Dimensional Structure......Page 407
5.7.2 Expressions for the Cylinder Vibration and Net Sound Pressure (k0L≪1)......Page 410
5.7.3 Self-Excited Vibration......Page 412
5.7.4 Semiempirical Modeling as a Nonlinear Oscillator......Page 416
5.7.5 Randomly Driven One-Dimensional Structures......Page 418
5.8 Summary and Principles of Noise Control......Page 424
5.8.2 Reductions in Noise by Structural Modifications......Page 425
5.8.3 Damping and Mass Loading......Page 426
5.8.4 Estimation of Radiation Efficiency and Added Mass......Page 427
References......Page 430
Further Reading......Page 433
6.1.1 Linear Bubble Motions......Page 434
6.1.2 Sound Propagation in Bubbly Liquids......Page 442
6.2.1 The Onset of Nonlinear Oscillations......Page 451
6.2.2 The Critical Pressure for Vaporous Cavitation......Page 452
6.2.3 The Importance of Diffusion......Page 457
6.3.1 Spherical Vapor-Filled Bubbles......Page 458
6.3.2 Spherical Bubbles With Internal Gas......Page 461
6.4.1 Dependence of Sound on Stages of Bubble History......Page 468
6.4.2 Spherical Collapses in Compressible Liquids......Page 474
6.4.3 Features of Noise in Developing Cavitation......Page 478
Appendix: Derivation of Approximate Spectral Functions......Page 484
References......Page 486
Index......Page 492