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

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