Aeroacoustics of Low Mach Number Flows: Fundamentals, Analysis and Measurement

555 Pages·2017·12.502 MB·English

by  Stewart Glegg, William Devenport

Aeroacoustics of Low Mach Number Flows
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Aeroacoustics of Low
Mach Number Flows
Fundamentals, Analysis, and
Measurement
Stewart Glegg and William Devenport
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Dedication
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Contents
Preface xi
Part 1 Fundamentals 1
1 Introduction 3
1.1 Aeroacoustics of low Mach number flows 3
1.2 Sound waves and turbulence 4
1.3 Quantifying soundlevelsandannoyance 5
1.4 Symboland analysis conventions used inthis book 7
References 8
2 The equationsof fluid motion 9
2.1 Tensor notation 9
2.2 The equationof continuity 11
2.3 The momentum equation 14
2.4 Thermodynamic quantities 17
2.5 The role ofvorticity 21
2.6 Energy andacoustic intensity 24
2.7 Some relevantfluiddynamic concepts and methods 29
References 48
3 Linear acoustics 49
3.1 The acousticwaveequation 49
3.2 Plane wavesand spherical waves 51
3.3 Harmonic time dependence 52
3.4 Sound generation by a small sphere 53
3.5 Sound scattering bya small sphere 56
3.6 Superposition and far field approximations 58
3.7 Monopole, dipole, and quadrupolesources 59
3.8 Acoustic intensity andsound power output 62
3.9 Solution tothe wave equation using Green’sfunctions 64
3.10 Frequencydomainsolutions and Fourier transforms 70
References 72
4 Lighthill’s acoustic analogy 73
4.1 Lighthill’s analogy 73
4.2 Limitations ofthe acoustic analogy 75
viii Contents
4.3 Curle’stheorem 78
4.4 Monopole, dipole, and quadrupole sources 82
4.5 Tailored Green’s functions 86
4.6 Integralformulasfor tailored Green’sfunctions 89
4.7 Wavenumber andFourier transforms 90
References 93
5 The FfowcsWilliams and Hawkingsequation 95
5.1 Generalized derivatives 95
5.2 The Ffowcs Williams and Hawkings equation 99
5.3 Movingsources 104
5.4 Sourcesin afreestream 108
5.5 FfowcsWilliams and Hawkings surfaces 110
5.6 Incompressibleflow estimatesofacoustic source terms 112
References 114
6 The linearized Euler equations 115
6.1 Goldstein’s equation 115
6.2 Driftcoordinates 120
6.3 Rapid distortion theory 124
6.4 Acoustically compact thinairfoils andthe Kutta condition 130
6.5 The Prantl–Glauert transformation 134
References 136
7 Vortex sound 137
7.1 Theory ofvortex sound 137
7.2 Sound from two linevortices in free space 139
7.3 Surface forces inincompressible flow 142
7.4 Aeolian tones 146
7.5 Blade vortex interactions in incompressible flow 148
7.6 The effect of angle ofattackand bladethickness
on unsteady loads 154
References 162
8 Turbulence and stochastic processes 163
8.1 The nature ofturbulence 163
8.2 Averaging andthe expected value 165
8.3 Averagingofthegoverningequationsandcomputationalapproaches 167
8.4 Descriptionsof turbulence for aeroacoustic analysis 170
References 184
9 Turbulent flows 185
9.1 Homogeneous isotropic turbulence 185
9.2 Inhomogeneous turbulentflows 195
References 219