Aeroacoustics of Low Mach Number Flows

Aeroacoustics of Low Mach Number Flows: Fundamentals, Analysis, and Measurement provides a comprehensive treatment of sound radiation from subsonic flow over moving surfaces, which is the most widespread cause of flow noise in engineering systems. This includes fan noise, rotor noise, wind turbine noise, boundary layer noise, and aircraft noise.

Beginning with fluid dynamics, the fundamental equations of aeroacoustics are derived and the key methods of solution are explained, focusing both on the necessary mathematics and physics. Fundamentals of turbulence and turbulent flows, experimental methods and numerous applications are also covered.

The book is an ideal source of information on aeroacoustics for researchers and graduate students in engineering, physics, or applied math, as well as for engineers working in this field.

Supplementary material for this book is provided by the authors on the website www.aeroacoustics.net. The website provides educational content designed to help students and researchers in understanding some of the principles and applications of aeroacoustics, and includes example problems, data, sample codes, course plans and errata. The website is continuously being reviewed and added to.

• Explains the key theoretical tools of aeroacoustics, from Lighthill’s analogy to the Ffowcs Williams and Hawkings equation
• Provides detailed coverage of sound from lifting surfaces, boundary layers, rotating blades, ducted fans and more
• Presents the fundamentals of sound measurement and aeroacoustic wind tunnel testing

Researchers and grad students in engineering, physics or applied math with an interest in hydro or aeroacoustics. Also engineers working in aeroacoustics and fluid dynamics

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