Aeroacoustics of Low Mach Number Flows

Part 1: Fundamentals

1: Introduction

• Abstract
• 1.1 Aeroacoustics of low Mach number flows
• 1.2 Sound waves and turbulence
• 1.3 Quantifying sound levels and annoyance
• 1.4 Symbol and analysis conventions used in this book

2: The equations of fluid motion

• Abstract
• 2.1 Tensor notation
• 2.2 The equation of continuity
• 2.3 The momentum equation
• 2.4 Thermodynamic quantities
• 2.5 The role of vorticity
• 2.6 Energy and acoustic intensity
• 2.7 Some relevant fluid dynamic concepts and methods

3: Linear acoustics

• Abstract
• 3.1 The acoustic wave equation
• 3.2 Plane waves and spherical waves
• 3.3 Harmonic time dependence
• 3.4 Sound generation by a small sphere
• 3.5 Sound scattering by a small sphere
• 3.6 Superposition and far field approximations
• 3.7 Monopole, dipole, and quadrupole sources
• 3.8 Acoustic intensity and sound power output
• 3.9 Solution to the wave equation using Green's functions
• 3.10 Frequency domain solutions and Fourier transforms

4: Lighthill's acoustic analogy

• Abstract
• 4.1 Lighthill's analogy
• 4.2 Limitations of the acoustic analogy
• 4.3 Curle's theorem
• 4.4 Monopole, dipole, and quadrupole sources
• 4.5 Tailored Green's functions
• 4.6 Integral formulas for tailored Green's functions
• 4.7 Wavenumber and Fourier transforms

5: The Ffowcs Williams and Hawkings equation

• Abstract
• 5.1 Generalized derivatives
• 5.2 The Ffowcs Williams and Hawkings equation
• 5.3 Moving sources
• 5.4 Sources in a free stream
• 5.5 Ffowcs Williams and Hawkings surfaces
• 5.6 Incompressible flow estimates of acoustic source terms

6: The linearized Euler equations

• Abstract
• 6.1 Goldstein's equation
• 6.2 Drift coordinates
• 6.3 Rapid distortion theory
• 6.4 Acoustically compact thin airfoils and the Kutta condition
• 6.5 The Prantl–Glauert transformation

7: Vortex sound

• Abstract
• 7.1 Theory of vortex sound
• 7.2 Sound from two line vortices in free space
• 7.3 Surface forces in incompressible flow
• 7.4 Aeolian tones
• 7.5 Blade vortex interactions in incompressible flow
• 7.6 The effect of angle of attack and blade thickness on unsteady loads

8: Turbulence and stochastic processes

• Abstract
• 8.1 The nature of turbulence
• 8.2 Averaging and the expected value
• 8.3 Averaging of the governing equations and computational approaches
• 8.4 Descriptions of turbulence for aeroacoustic analysis

9: Turbulent flows

• Abstract
• 9.1 Homogeneous isotropic turbulence
• 9.2 Inhomogeneous turbulent flows

Part 2: Experimental approaches

10: Aeroacoustic testing and instrumentation

• Abstract
• 10.1 Aeroacoustic wind tunnels
• 10.2 Wind tunnel acoustic corrections
• 10.3 Sound measurement
• 10.4 The measurement of turbulent pressure fluctuations
• 10.5 Velocity measurement

11: Measurement, signal processing, and uncertainty

• Abstract
• 11.1 Limitations of measured data
• 11.2 Uncertainty
• 11.3 Averaging and convergence
• 11.4 Numerically estimating fourier transforms
• 11.5 Measurement as seen from the frequency domain
• 11.6 Calculating time spectra and correlations
• 11.7 Wavenumber spectra and spatial correlations

12: Phased arrays

• Abstract
• 12.1 Basic delay and sum processing
• 12.2 General approach to array processing
• 12.3 Deconvolution methods
• 12.4 Correlated sources and directionality

Part 3: Edge and boundary layer noise

13: The theory of edge scattering

• Abstract
• 13.1 The importance of edge scattering
• 13.2 The Schwartzschild problem and its solution based on the Weiner Hopf method
• 13.3 The effect of uniform flow
• 13.4 The leading edge scattering problem

14: Leading edge noise

• Abstract
• 14.1 The compressible flow blade response function
• 14.2 The acoustic far field
• 14.3 An airfoil in a turbulent stream
• 14.4 Blade vortex interactions in compressible flow

15: Trailing edge and roughness noise

• Abstract
• 15.1 The origin and scaling of trailing edge noise
• 15.2 Amiet's trailing edge noise theory
• 15.3 The method of Brooks, Pope, and Marcolini [8]
• 15.4 Roughness noise

Part 4: Rotating blades and duct acoustics

16: Open rotor noise

• Abstract
• 16.1 Tone and broadband noise
• 16.2 Time domain prediction methods for tone noise
• 16.3 Frequency domain prediction methods for tone noise
• 16.4 Broadband noise from open rotors
• 16.5 Haystacking of broadband noise
• 16.6 Blade vortex interactions

17: Duct acoustics

• Abstract
• 17.1 Introduction
• 17.2 The sound in a cylindrical duct
• 17.3 Duct liners
• 17.4 The Green's function for a source in a cylindrical duct
• 17.5 Sound power in ducts
• 17.6 Nonuniform mean flow
• 17.7 The radiation from duct inlets and exits

18: Fan noise

• Abstract
• 18.1 Sources of sound in ducted fans
• 18.2 Duct mode amplitudes
• 18.3 The cascade blade response function
• 18.4 The rectilinear model of a rotor or stator in a cylindrical duct
• 18.5 Wake evolution in swirling flows
• 18.6 Fan tone noise
• 18.7 Broadband fan noise

Appendix A: Nomenclature

A.1 Symbol conventions, symbol modifiers, and Fourier transforms

A.2 Symbols used

Appendix B: Branch cuts

Appendix C: The cascade blade response function

Index