Mechanics of Flow-Induced Sound and Vibration Volume 2_ Complex Flow-Structure Interactions

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 Introductory Concepts: The Cavitation Index, and Cavitation Similitude......Page 24
1.2.1 Simple Rules of Similitude......Page 27
1.2.2.2 Semi-Empirical Formulas for Ki......Page 34
1.2.2.3 Importance of Nucleation......Page 48
1.3.1 Cavitating Jets......Page 50
1.3.2 Hydrofoil Cavitation......Page 52
1.3.3 Cavitation in the Wake of a Disk......Page 57
1.4.1 General Characteristics......Page 59
1.4.2 Noise at Blade Passage Frequency and Its Harmonics......Page 60
1.4.3 Blade Rate Pressures for Calculating Hull Vibration Induced by Cavitation......Page 62
1.4.4 Review of Attempts at Scaling Cavitation Noise......Page 65
1.4.5 Dependence of Cavitation Noise on the Velocity......Page 69
1.4.6 Procedures for Rough Estimation of Levels......Page 72
1.5.1 Response to a Continuous Pressure Field......Page 77
1.5.2 Transient Bubble Motion–Splitting and Formation......Page 79
1.5.3.1 Formation in Stagnant Liquids......Page 84
1.5.3.2 Formation in Moving Liquids......Page 85
1.6.1 General Observations......Page 86
1.6.2 Underwater Splash Noise......Page 89
1.6.3 Airborne Splash Noise......Page 92
1.6.4 Cooling Tower Noise......Page 94
References......Page 96
2.1 Introduction......Page 104
2.2.1 Development of Wall Flow......Page 106
2.2.2 Simple Prediction Methods for Turbulent Boundary Layers......Page 108
2.3.1 General Relationships......Page 114
2.3.2.1 Overview of the Spectrum......Page 123
2.3.2.2 Semi-Empirical Modeling Based on Dimensional Reasoning and Fundamental Statistical Properties......Page 126
2.3.2.3 Features of the Frequency Spectrum of Wall Pressures at a Point......Page 134
2.4.1 Magnitude and Frequency Dependence of Wall Pressure......Page 140
2.4.2 Space–Time Correlations......Page 146
2.4.3.1 The “Corcos” Result......Page 152
2.4.3.2 Spectrum Modeling Based on Comprehensive Theory......Page 154
2.4.3.3 Survey of Measured Pressures on Smooth Walls at Low Numbers, k1%3ckc and k3%3ckc......Page 166
2.4.4 Special Features of Rough-Wall Boundary Layer Pressures Related to Sound......Page 174
2.4.5 Pressure Fluctuations in Turbulent Pipe Flow......Page 179
2.5 Pressure Fluctuations Beneath Nonequilibrium Wall Layers......Page 180
2.5.1 Transitional Flow......Page 181
2.5.2 Flows With Adverse Pressure Gradient......Page 182
2.5.3 Separated Flows......Page 186
2.5.4 Ground Pressures Beneath Atmospheric Turbulence......Page 187
Appendix: Derivation of Eq. (2.25)......Page 189
References......Page 191
3.1.1 Techniques for Measuring Pressures at Low Wave Numbers Using Arrays......Page 202
3.1.2 Effects of Transducer Size and Shape: The Response Function......Page 209
3.2.1 Introduction and Review of Analytical Fundamentals......Page 215
3.2.2 Wave-Vector Filtering Action by Flexible Panels......Page 223
3.2.3 Effects of Hydrodynamic Coincidence on Single-Mode Structural Response......Page 225
3.2.4 Empirical Confirmation......Page 229
3.2.5 Average Response of Many Modes......Page 231
3.3 Sound From Flow-Induced Modal Vibration......Page 238
3.4 General Rules for Hydroacoustic Similarity and Noise Control......Page 242
3.5.1 General Analysis......Page 246
3.5.2 Acoustic Quadrupole Radiation From Turbulent Boundary Layers......Page 254
3.6 Sources of Dipole Sound at Shape Discontinuities......Page 257
3.6.1 General Relationships for Effectively Unbounded Rough Surfaces......Page 259
3.6.2 Diffraction of Quadrupole Sound By Distributed Wall Roughness......Page 264
3.6.3 Far Field Sound from Rough-Wall Turbulent Boundary Layers......Page 267
3.6.4.1 Dipole Strengths of Roughness Elements on Continuously Rough Surfaces......Page 269
3.6.4.2 Radiated Sound From Viscous Forces on Roughness Elements......Page 271
3.6.4.3 Vibration and Sound From Rough Elastic Surfaces......Page 275
3.6.4.4 Extensions to Force Dipoles From Walls With Step Discontinuities......Page 279
3.7 Filtering Action of Rubber Blankets......Page 284
3.8.1 Quantitative Estimates of Sound Generated By Various Mechanisms......Page 290
3.8.2 Experience With Noise Control in Aircraft......Page 294
3.9.1 The Wave Number Spectrum of Reverberant Sound......Page 296
3.9.2 Resonant Mode Response to Random Incidence Sound......Page 300
3.9.3 Transmission by Mass–Controlled Panel Vibration......Page 301
3.9.4 Comparison of Theory With Measured Transmission Losses......Page 303
Appendix: Elastomer Equations......Page 304
Transmission of Pressure Through a Fluid-Like Layer......Page 305
Transmission of Pressure Through an Elastomeric Layer......Page 306
References......Page 309
4 Sound Radiation From Pipe and Duct Systems......Page 320
4.1 Internal and External Acoustic Pressures on Cylindrical Surfaces......Page 321
4.1.1 Acoustic Radiation to the External Fluid......Page 322
4.1.2.1 Modal Expansion Green’s Function......Page 326
4.1.2.2 Integral Green’s Function......Page 330
4.1.2.3 Acoustic Pressure on the Rigid Wall: The Blocked Pressure......Page 332
4.1.3 The Coupling of Internal Pressure Field With Wall Motion......Page 334
4.2.2 The Equations of Motion......Page 337
4.2.3 Response of the Point-Driven Fluid-Loaded Cylindrical Shell......Page 339
4.2.4 Properties of Acoustical Coupling With the Inner and Outer Fluids......Page 342
4.2.5 Example: Airborne Acoustic Radiation From a Point-Driven Duct......Page 345
4.2.6 Example: Airborne Acoustic Radiation From a Duct Enclosing an Acoustic Dipole......Page 346
4.3 Noise From Turbulent Pipe Flow......Page 349
4.4 Sound Transmission Through Pipe and Duct Walls......Page 353
4.4.1 High-Frequency Sound Transmission by Resonant Shell Modes: General Analysis for ω%3eωco......Page 355
4.4.2 High-Frequency Sound Transmission by Resonant Wall Vibration: ω%3eωR, ω%3eωco......Page 359
4.4.3 High-Frequency Sound Transmission by Resonant Wall Vibration: ω%3eωco, ω%3cωR......Page 361
4.4.4 Mass-Controlled Transmission Loss......Page 363
4.4.5 Low-Frequency Sound Transmission......Page 365
4.4.6 Sound Transmission Through Rectangular Duct Walls......Page 366
4.4.7 Example of Calculations of Transmission Loss; Circular Ducts......Page 367
4.5.1.1 Compressible Flow Relationships......Page 369
4.5.1.2 Dimensional Expressions for the Radiated Sound Power......Page 375
4.5.1.3 Practical Formulas for Sound Generation by Valves......Page 377
4.5.2.2 Sound From Ventilation Systems......Page 385
4.5.2.3 Final Notes on Aerodynamic Noise Control......Page 388
4.6.1 Cavitation Inception......Page 391
4.6.2 Behavior of Cavitation Noise......Page 392
References......Page 395
5.1 Introduction......Page 400
5.2.1 Summary......Page 401
5.2.2.1 Fundamental Half-Plane Problem......Page 405
5.2.2.2 Sound Radiation From Turbulence Encountering a Half-Plane......Page 409
5.2.2.3 General Applicability of Eq. (5.6): The Kutta Condition......Page 412
5.3 Forces and Sound Due to Inflow Unsteadiness......Page 414
5.3.1.1 Outline of the General Theory......Page 415
5.3.1.2 Aerodynamic Influence Functions......Page 420
5.3.2 Oscillatory Lift Spectra From Ingested Turbulence......Page 424
5.3.3 Observations of Noise From Inflow Inhomogeneities......Page 432
5.3.4.1 Effect of Section Thickness on Turbulence Ingestion Noise......Page 437
5.3.4.2 Effect of Turbulence Anisotropy on Turbulence Ingestion Noise......Page 438
5.4.1 Introduction......Page 440
5.4.2 General Features of the Sound Spectrum......Page 441
5.4.3.1 Vortex Formation and Its Frequency......Page 446
5.4.4.1 Theoretical Modeling of the Two-Dimensional Wake......Page 453
5.4.4.2 Measurements of Surface Pressures of Vortex Street Wakes......Page 457
5.4.4.3 Spanwise Correlation and Lift Coefficients of Vortex Shedding......Page 460
5.5.1 Analytical Description......Page 463
5.5.2 Vortex Sound From Blunt Trailing Edges......Page 464
5.5.3 Tones From Laminar-Flow Airfoils......Page 465
5.6.1 Summary of Acoustic Scattering Theory......Page 467
5.6.2 Radiated Sound Pressure in Terms of the Surface Pressure......Page 472
5.6.3.1 Sound From Sharp-Edged Airfoils at Small Angle of Attack......Page 478
5.6.3.2 Sound From Airfoils With Shaped (Beveled) Trailing Edges......Page 479
5.6.4 Measurements of Broadband Noise From Turbulent Wall Jets and Blown Flaps......Page 488
5.6.5 Modifications of Aerodynamic Scattering Theory for Surfaces of Finite Thickness and Impedance......Page 493
5.7 Flow-Induced Vibration and Singing......Page 495
5.7.1.1 Modal Response and Excitation Force Spectra......Page 496
5.7.1.2 Hydrodynamic Damping......Page 499
5.7.1.3 Viscous Damping......Page 501
5.7.2.1 General Characteristics......Page 502
5.7.2.2 Model of Flow-Induced Vibration and Control by Hysteretic Damping......Page 507
5.7.2.3 Effects of Trailing Edge Vibration on the Vortex Shedding and Vortex-Induced Forces; Results of Measurements for Se.........Page 510
5.7.2.4 Semiempirical Modeling as a Nonlinear Oscillator......Page 513
References......Page 517
6.1 Introduction......Page 528
6.2.1 Sources of Noise......Page 530
6.2.2 Elementary Kinematics of Sound Radiation by Fan Rotors......Page 533
6.2.3 Features of Sound From Inhomogeneous Inflow......Page 537
6.3 Design Parameters of Rotors as Lifting Surfaces......Page 542
6.3.1 Similitude of Powering Performance of Turbomachines......Page 543
6.3.2 Propeller Blades as Lifting Surfaces......Page 547
6.4.1 Fundamental Analysis......Page 554
6.4.2 Acoustic Spectrum From Rotor Blade Forces Resulting From Inhomogeneous Inflow......Page 563
6.4.3 Hydrodynamic Limit of Interaction Tones: k0R→0......Page 572
6.5.1 Sounds From Steady Loading: Gutin Sound......Page 575
6.5.2 Laminar Flow Surfaces......Page 577
6.5.3 Turbulent Trailing-Edge Noise......Page 580
6.5.4 Broadband Noise Related to Steady Loading......Page 585
6.5.5 Propeller Singing......Page 593
6.5.6 Thickness Noise......Page 595
6.6.1.1 Single-Blade Element Analysis of Rotors First-Order Estimate of the Sound Pressure......Page 599
6.6.1.2 Blade-Vortex Interactions in Helicopter Noise......Page 607
6.6.1.3 Influence of Adjacent Blades; Incompressible Cascade Effects......Page 610
6.6.1.4 Acoustic Interference in Blade Rows......Page 612
6.6.1.5 Unsteady Lifting Surface Theory: Free-Field Rotors at Low Mach Number......Page 613
6.6.2 Turbulent Inflows......Page 616
6.6.3.1 Propeller Fan in Homogeneous Turbulence......Page 628
6.6.3.2 Interaction of Blade Rows in Turbulent Inflow......Page 632
6.6.3.3 The Case of an Automotive Fan Behind a Radiator......Page 637
6.6.4 Inversion of Leading-Edge Pressure on Rotor Blades to Infer Upwash......Page 642
6.6.5 Control of Sound Sources in Axial Flow Fans......Page 644
6.7.1 Propagation of Acoustic Modes of a Ducted Rotor......Page 648
6.7.2 Case Study: Sound From a High-Bypass Engine Compressor Fan......Page 653
6.7.3 Acoustic Characteristics of Centrifugal Fans......Page 658
6.7.4.1 Noise-Control Methods for Centrifugal Fans......Page 662
6.7.4.2 General Acoustic Fan Laws......Page 664
References......Page 668
Index......Page 682