Chapter
2.3. The momentum equation
2.3.1. General considerations
2.4. Thermodynamic quantities
2.5. The role of vorticity
2.5.2. The vorticity equation
2.5.3. The speed of sound in ideal flow
2.6. Energy and acoustic intensity
2.6.1. The energy equation
2.7. Some relevant fluid dynamic concepts and methods
2.7.1. Streamlines and vorticity
2.7.4. Vortex filaments and the Biot Savart law
Chapter 3: Linear acoustics
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
Chapter 4: Lighthill's acoustic analogy
4.2. Limitations of the acoustic analogy
4.2.1. Nearly incompressible flow
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
Chapter 5: The Ffowcs Williams and Hawkings equation
5.1. Generalized derivatives
5.2. The Ffowcs Williams and Hawkings equation
5.4. Sources in a free stream
5.5. Ffowcs Williams and Hawkings surfaces
5.6. Incompressible flow estimates of acoustic source terms
Chapter 6: The linearized Euler equations
6.1. Goldstein's equation
6.3. Rapid distortion theory
6.4. Acoustically compact thin airfoils and the Kutta condition
6.5. The Prantl-Glauert transformation
7.1. Theory of vortex sound
7.2. Sound from two line vortices in free space
7.3. Surface forces in incompressible flow
7.5. Blade vortex interactions in incompressible flow
7.6. The effect of angle of attack and blade thickness on unsteady loads
7.6.1. The effect of angle of attack
7.6.2. The effect of airfoil thickness
Chapter 8: Turbulence and stochastic processes
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
8.4.1. Time correlations and frequency spectra of a single variable
8.4.2. Time correlations and frequency spectra of two variables
8.4.3. Spatial correlation and the wavenumber spectrum
Chapter 9: Turbulent flows
9.1. Homogeneous isotropic turbulence
9.1.1. Mathematical description
9.1.2. The von Kármán spectrum
9.1.3. The Liepmann spectrum
9.2. Inhomogeneous turbulent flows
9.2.1. The fully developed plane wake
9.2.2. The zero pressure gradient turbulent boundary layer
9.2.3. The turbulent boundary layer wall-pressure spectrum
Part 2: Experimental approaches
Chapter 10: Aeroacoustic testing and instrumentation
10.1. Aeroacoustic wind tunnels
10.2. Wind tunnel acoustic corrections
10.2.1. Shear layer refraction
10.2.2. Corrections for a two-dimensional planar jet
10.2.3. Effects of shear layer thickness and curvature
10.2.4. Considerations for hybrid anechoic tunnels
10.4. The measurement of turbulent pressure fluctuations
10.5. Velocity measurement
Chapter 11: Measurement, signal processing, and uncertainty
11.1. Limitations of measured data
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
11.6.1. Calculating spectra
11.6.2. Uncertainty estimates
11.6.4. Correlation functions
11.7. Wavenumber spectra and spatial correlations
Chapter 12: Phased arrays
12.1. Basic delay and sum processing
12.1.1. Basic principles, resolution, and spatial aliasing
12.1.3. Acoustic images and source levels
12.1.5. Broadband noise sources
12.2. General approach to array processing
12.2.2. The definition of source strength
12.2.3. Source images and the point spread function
12.2.5. Signal-to-noise ratio
12.2.7. Array-processing algorithms
12.3. Deconvolution methods
12.3.3. The CLEAN algorithm
12.3.4. Integrated source maps
12.4. Correlated sources and directionality
Part 3: Edge and boundary layer noise
Chapter 13: The theory of edge scattering
13.1. The importance of edge scattering
13.2. The Schwartzschild problem and its solution based on the Weiner Hopf method
13.2.1. The boundary value problem
13.2.2. Obtaining the Schwartzschild solution using the Weiner Hopf method
13.2.3. The radiation condition and the Weiner Hopf separation
13.2.4. Generalized Fourier transforms and Laplace transforms
13.3. The effect of uniform flow
13.4. The leading edge scattering problem
13.4.1. The leading edge response
13.4.2. The trailing edge correction
Chapter 14: Leading edge noise
14.1. The compressible flow blade response function
14.1.1. The compressible and incompressible flow blade response to a step gust
14.1.2. Leading and trailing edge solutions
14.1.3. The first-order solution for the surface pressure
14.1.4. The unsteady lift in compressible flow
14.1.5. An arbitrary gust
14.2. The acoustic far field
14.2.1. The acoustic far field from the leading edge interaction
14.2.2. The far-field directionality and scaling
14.2.3. Impulsive gusts of finite span
14.3. An airfoil in a turbulent stream
14.4. Blade vortex interactions in compressible flow
14.4.1. The upwash velocity spectrum from a blade vortex interaction
Chapter 15: Trailing edge and roughness noise
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]
Part 4: Rotating blades and duct acoustics
Chapter 16: Open rotor noise
16.1. Tone and broadband noise
16.2. Time domain prediction methods for tone noise
16.2.3. Supersonic tip speeds
16.3. Frequency domain prediction methods for tone noise
16.3.1. Harmonic analysis of loading and thickness noise
16.4. Broadband noise from open rotors
16.5. Haystacking of broadband noise
16.5.1. Amplitude modulation
16.5.2. Blade-to-blade correlation
16.6. Blade vortex interactions
Chapter 17: Duct acoustics
17.2. The sound in a cylindrical duct
17.2.1. General formulation
17.2.2. Hard-walled ducts
17.2.3. Modal propagation
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
18.1. Sources of sound in ducted fans
18.2. Duct mode amplitudes
18.2.1. Thickness noise for a ducted fan
18.2.2. Blade loading noise
18.2.4. In duct sound power
18.3. The cascade blade response function
18.3.1. The rectilinear cascade model
18.3.2. The acoustic duct modes
18.3.3. The acoustic modes from an arbitrary gust
18.3.4. The sound power spectrum
18.4. The rectilinear model of a rotor or stator in a cylindrical duct
18.4.2. An axial dipole example
18.5. Wake evolution in swirling flows
18.6.1. The upwash coefficients
18.6.2. Unskewed self-similar wakes
18.7. Broadband fan noise
A.1. Symbol conventions, symbol modifiers, and Fourier transforms
Appendix C: The cascade blade response function
Aeroacoustics of Low Mach Number Flows
：Fundamentals, Analysis, and Measurement
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