Sound-Flow Interactions

By: Y. Auregan, A. Maurel, V. Pagneux

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Hardcover | 1 October 2002

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Thenheintroducesveryclearlythescatteringofsoundbecauseofvorticity andgivesthemostrecentresultsonultrasoundpropagationthroughadis- dered?ow. V. Ostashevpresentsgeometricalacousticsinmovingmediaand theimportantpracticalproblemofsoundpropagationinturbulence(at- sphere,ocean). A. Fabrikantexaminestheplasma-hydrodynamicsanalogies includingtheresonantwave-?owinteractioninshear?ows,wavesofnegative VI Preface energyandover-re?ectionandacousticoscillatorsin?uid?ows. P. J. Mor- sondescribesthedynamicsofthecontinuousspectrumwhichoccursinshear ?ow. Theresultsareinterpretedinthecontextofin?nitedimensionalHam- toniansystemstheory. G. Chagelishvilipresentsnewlinearmechanismsof acousticwavegenerationinsmoothshear?owsusinganon-modalstudy. N. Peakepresents?uid-structureinteractionsinthepresenceofmean?ows, includingtheproblemsofinstabilityandcausality. Finally,W. Lauterborn presentsnonlinearacousticswithapplicationstosonoluminescenceandto acousticchaos. InthisCarg`eseSummerSchool,54studentsfrom12nations,and11l- turersfrom7nationsparticipated. Aknowledgements. TheSummerSchoolandthispublicationwouldnot havebeenpossiblewithout: ?nancialsupportfromtheEuropeanUnion,theCentreNationaldela RechercheScienti?que,theMinist`eredesA?airesEtrang`eres,theM- ist`eredel'EducationNationale,delaRechercheetdelaTechnologieand theGroupementdeRecherche"Turbulence"; the guidance of Elisabeth Dubois-Violette, director of the Institut d'EtudesScienti?quesdeCarg`ese; thehelpofChantalAriano,NathalieBedjai,BrigitteCassegrain,Pierre- EricGrossiandthewholeteaminpreparingandhostingofthisschool. Finally,wewishtothankthelecturersforgivingsomuchtimeinprep- ingthelecturesandwritingthemup,aswellasmakingthemselvesavailable fordiscussionsduringtheschool. 1 LeMans,Paris,Lyon YvesAur´egan , 2 September2001 Agn`esMaurel , 1 VincentPagneux , 3 Jean-Fran¸coisPinton . 1 Laboratoired'Acoustiquedel'Universit´eduMaine,UMRCNRS6613, Av. OMessiaen,72085LeMansCedex9,France 2 LaboratoireOndesetAcoustique,UMRCNRS7587, ESPCI,10rueVauquelin,75005Paris,France 3 LaboratoiredePhysique,UMRCNRS1325, EcoleNormaleSup´erieuredeLyon,46all´eed'Italie,69007Lyon,France Preface VII SomeofthelecturersoftheCarg`eseSchool,fromlefttoright:M. S. Howe,A. Hirschberg,P. Morrison,W. Lauterborn,V. Ostashev,A. Fabrikant,N. Peake, T. Colonius(PhotoC. Schram) SomeoftheparticipantsoftheCarg`eseSchool(PhotoC. Schram) TableofContents APrimitiveApproachtoAeroacoustics AvrahamHirschberg,ChristopheSchram. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 FluidDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 Lighthill'sAnalogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 JetNoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 Thermo-Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 AcousticalEnergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 7 Rijke-Tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 8 Vortex-SoundTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 9 ChoiceoftheGreen'sFunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 10 Howe'sEnergyCorollary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 11 TheOpenPipeTerminationofanUn?angedPipe . . . . . . . . . . . . . . 21 12 Whistler-NozzleandHumanWhistling . . . . . . . . . . . . . . . . . . . . . . . . 25 13 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 LecturesontheTheoryofVortex-Sound MichaelS. Howe. .

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Kids & Children's Books Educational Material Science Educational Material Physics Educational Material Non-Fiction Science Physics Classical Mathematics Wave Mechanics including Vibration & Acoustics Medicine Medicine in General Fluid Mechanics

Mathematics Applied Mathematics Engineering & Technology Mechanical Engineering & Materials Mechanical Engineering Mathematical Physics Thermodynamics & Heat

A Primitive Approach to Aeroacoustics	p. 1
Introduction	p. 1
Fluid Dynamics	p. 2
Lighthill's Analogy	p. 4
Jet Noise	p. 7
Thermo-Acoustics	p. 9
Acoustical Energy	p. 10
Rijke-Tube	p. 11
Vortex-Sound Theory	p. 14
Choice of the Green's Function	p. 17
Howe's Energy Corollary	p. 20
The Open Pipe Termination of an Unflanged Pipe	p. 21
Whistler-Nozzle and Human Whistling	p. 25
Conclusion	p. 27
References	p. 28
Lectures on the Theory of Vortex-Sound	p. 31
Aerodynamic Sound	p. 31
Lighthill's Acoustic Analogy (1952)	p. 31
Aerodynamic Sound from Low-Mach-Number Turbulence of Uniform Mean Density	p. 34
Aerodynamic Sound from Low-Mach-Number Turbulence of Variable Mean Density	p. 35
Vorticity and Entropy Fluctuations as Sources of Sound	p. 37
The Rôle of Vorticity in Lighthill's Theory	p. 37
Acoustic Analogy in Terms of the Total Enthalpy	p. 39
Vorticity and Entropy Sources	p. 40
Fundamental Solutions of the Wave Equation	p. 43
The Helmholtz Equation	p. 43
The Wave Equation	p. 46
General Solution of the Inhomogeneous Wave Equation	p. 47
General Solution in the Frequency-Domain	p. 47
General Solution in the Time-Domain	p. 49
Compact Green's Functions	p. 49
Time-Harmonic Problems	p. 50
Time-Domain Problems	p. 52
Influence of Solid Bodies on the Generation of Aerodynamic Sound	p. 58
Integral Representation of Aerodynamic Sound	p. 58
Curle's Theory Applied to Compact Bodies	p. 60
Vortex Sound	p. 61
Influence of Vortex Shedding	p. 62
Vortex-Airfoil Interaction Noise	p. 66
Blade-Vortex Interactions in Two-Dimensions	p. 67
Three-Dimensional Interactions	p. 70
Blade-Vortex Interactions in Three Dimensions	p. 71
Vorticity Production by Sound	p. 74
Interaction of Sound with a Solid Surface	p. 75
Interactions at a Trailing Edge	p. 78
Leading Edge Interactions	p. 80
Application to Resonant Oscillations	p. 83
Perforated Screens	p. 85
Rayleigh Conductivity	p. 85
The Bias Flow Aperture	p. 87
Reflection and Transmission of Sound by a Perforated Screen	p. 91
Compression Wave Generated when a Train Enters a Tunnel	p. 94
The Governing Equations	p. 96
Linear Theory	p. 98
Contribution from the Surface Dipoles	p. 102
Contribution from the Exit Flow Vorticity	p. 103
The Flared Portal	p. 104
Suppression of the Micro-pressure Wave	p. 104
The Function ϕ*	p. 105
Optimal Flaring	p. 106
Comparison with Measurements	p. 107
References	p. 110
Sound-Vortex Interaction in Infinite Media	p. 112
Introduction	p. 112
The Basics - Vortex Sound	p. 113
Incompressible Flow	p. 113
Slightly Compressible Flow	p. 115
Incompressible Vortex Dynamics	p. 117
Vortex Sound	p. 119
Bibliographical Notes	p. 121
Scattering of Sound by Vorticity	p. 122
Kelvin's Theorem	p. 122
Scattering to Order M	p. 125
Bibliographical Notes	p. 129
Two Dimensions	p. 131
Vanishing Circulation	p. 131
Surface Waves	p. 132
Shallow Water	p. 135
Deeper Water	p. 139
Experimental Results	p. 140
Bibliographical Notes	p. 141
Multiple Scattering	p. 143
Equations to Order M²	p. 144
Appendix	p. 148
Example: a "Gas" of Vortices	p. 151
Two Dimensions	p. 152
Three Dimensions	p. 154
Bibliographical Notes	p. 154
Loose Ends	p. 156
Optical Theorem	p. 156
Validity of the Born Approximation	p. 158
Geometrical Acoustics in Moving Media	p. 160
Introduction	p. 160
Linearized Equations of Fluid Dynamics	p. 161
Solution of Linearized Equations of Fluid Dynamics	p. 162
Debye Series	p. 162
Eikonal Equation	p. 163
Dispersion Equation	p. 163
Transport Equation	p. 163
Conservation of Acoustic Energy	p. 163
Geometrical Acoustics in a Three-Dimensional Inhomogeneous Medium	p. 164
Group and Phase Velocities	p. 164
Ray Path	p. 165
Eikonal and Time of Sound Propagation	p. 165
Amplitude of the Sound Pressure	p. 166
Geometrical Acoustics in a Stratified Medium	p. 166
Refraction Law for the Unit Vector n	p. 166
Refraction Law for the Unit Vector s	p. 167
The Ray Path	p. 168
Eikonal	p. 168
References	p. 168
Sound Propagation and Scattering in Random Moving Media	p. 169
Introduction	p. 169
Equations for a Sound Wave in a Random Moving Medium	p. 170
Helmholtz-Type Equation	p. 170
Parabolic Equation	p. 171
Parabolic Equation in a Refractive Medium	p. 172
Statistical Description of Random Inhomogeneities	p. 172
Correlation Functions and Spectral Densities	p. 172
Energy, Inertial, and Dissipation Subranges	p. 173
Kolmogorov Spectrum	p. 173
Gaussian Spectrum	p. 174
von Kármán Spectrum	p. 174
Scattering of Sound	p. 177
Sound Scattering Cross-Section	p. 177
von Kármán Spectrum	p. 178
Line-of-Sight Sound Propagation in a Random Moving Medium	p. 178
Statistical Moments of a Sound Field	p. 179
Effective Correlation Function and Spectral Density	p. 180
Markov Approximation	p. 180
Rytov Method	p. 180
Formulas for Statistical Moments of a Sound Field	p. 181
Coherence Function	p. 183
Interference of the Direct and Ground-Reflected Waves	p. 184
Mean Squared Sound Pressure	p. 185
Comparison with Experimental Data	p. 186
Sound Propagation Near Impedance Ground in a Refractive, Turbulent Atmosphere	p. 187
Mean Sound Field	p. 188
Coherence Function	p. 188
References	p. 190
Plasma-Hydrodynamic Analogy for Waves and Vortices in Shear Flows	p. 192
Research Philosophy	p. 192
Resonant Wave-Flow Interactions	p. 194
Negative Wave Energy and Over-Reflection	p. 199
Acoustic Analogues of Microwave Devices: Monotron and Klystron	p. 201
Wave-Vortex Interactions	p. 206
Analogies Table	p. 208
New Linear Mechanisms of Acoustic Wave Generation in Smooth Shear Flows (Nonmodal Study)	p. 210
Introduction	p. 210
Basic Problems in Shear Flows	p. 210
Essence of the Difficulties of the Modal Approach	p. 211
Onto Nonmodal Approach	p. 211
Mathematics of the Study	p. 213
Types of Disturbances	p. 216
Onto the Value of Shear Rate	p. 217
The Dynamics of SFH of Acoustic Waves	p. 217
Velocity Field of SFH of Acoustic Waves	p. 218
The Dynamics of SFH of Acoustic Waves: Low Shear Rates	p. 220
The Dynamics of SFH of Acoustic Waves: Moderate Shear Rates	p. 222
The Dynamics of the SFH of Vortices	p. 223
Conversion of Vortices to Waves	p. 224
The Nature of the Conversion Phenomenon	p. 226
Onto the Amplitude of the Generated Wave SFH at Conversion	p. 227
Demonstration of the Conversion Phenomenon by Direct Numerical Calculation	p. 227
Onto the Vortex-Wave Interaction	p. 230
Mutual Transformation of Waves	p. 230
Mechanical Analogy	p. 231
Qualitative Description of the Resonance Transformation of Waves	p. 231
Conclusion	p. 234
References	p. 235
Singular Eigenfunctions and an Integral Transform for Shear Flow	p. 238
Introduction	p. 238
Shear Flow	p. 238
Equilibrium and Linearization	p. 239
Singular Eigenmodes and the Continuous Spectrum	p. 240
The Integral Transform-Coordinate Change	p. 243
Integral Transform Pair	p. 243
Solution	p. 245
Hamiltonian Interpretation	p. 245
References	p. 246
Structural Acoustics with Mean Flow	p. 248
Basic Problem	p. 248
Solution Technique	p. 250
Solution for Fluid-Loaded Plate with Mean Flow	p. 253
Wave Energy	p. 254
Modifications to the Basic Model	p. 257
Plate Curvature	p. 257
Nonlinear Motion	p. 259
Effects of a Boundary Layer	p. 262
Conclusion	p. 263
References	p. 264
Nonlinear Acoustics and Acoustic Chaos	p. 265
Introduction	p. 265
Origin of Nonlinearity	p. 266
Equation of State	p. 266
Simple Nonlinear Waves	p. 268
Shock Waves	p. 270
Sonoluminescence	p. 272
Chaos Physics	p. 276
Acoustic Chaos	p. 280
References	p. 283
Subject Index	p. 285
Table of Contents provided by Publisher. All Rights Reserved.

Sound-Flow Interactions

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