Aeroacoustics

AERE-583/483

Previous offerings

Fall 2024, '20, F'16, F'14, F '12

Course Objectives

Noise is a nuisance around airports, highways, railways, wind farms, etc. Aerodynamic noise (aeroacoustics) is a branch of fluid dynamics that deals with noise generated due to fluid flow and its interaction with solid bodies. Strict regulations are enforced by the government on how much noise an aircraft, powerplant, wind turbine can generate for it to safely operate. This course builds upon fundamentals of acoustics and aeroacoustics and delves deeper into noise generation, propagation, and modeling with the objective of familiarizing the student with the analytical and numerical methods available to understand and predict aerodynamically generated noise. Knowledge of aeroacoustics would make future graduates more employable at companies such as GE, P&W, R&R, Siemens, MHI, all of which produce equipment with a number of aerodynamic noise challenges to overcome.

Outcomes

On completion of the course the attentive student will understand:

• Solution of the linear wave equation in 1-, 2-, and 3-D using Generalized functions and Green’s functions.
• Principles and applications of duct acoustics.
• Analytical and numerical methods to compute noise from simple sources.
• Fundamentals of aerodynamic noise sources in airframes, turbomachines, and wind turbines.
• Overview of analytical/numerical methods available to predict engineering aerodynamic noise sources.

Syllabus

• The (linear) wave equation:
  • In Cartesian, cylindrical, and spherical coordinates
  • 1-D, 2-D, and 3-D sound waves
  • Extensive treatment of 1-D waves: reflection, transmission concepts
  • Solution of the linear wave equation
  • Use of Generalized and Green’s functions
  • Solutions for point and distributed sources; concepts of compact and non-compact sources
• Sound Propagation in waveguides: duct acoustics
  • Concepts of phase velocity, group velocity, and cut-off modes
  • Normal mode analyses
  • 2-D rectangular, 2-D thin annulus, and 3-D rectangular, cylindrical and annular waveguides Treatment without and with mean flow
• Ray/geometric theory of acoustics: Snell’s law, refraction of sound by temperature and wind gradients, etc.
  • Lighthill’s acoustic analogy, aerodynamic sounds sources - monopole, dipole, and quadrupole
  • Reciprocal theorem and Kirchoff’s theorem
  • Introduction to engineering aerodynamic noise sources and overview of numerical/analytical prediction methods:
• Jet noise:
  • Eighth-power law from Lighthill’s analogy
  • Jet screech, mixing noise and broadband shock noise
• Turbomachinery (propeller) noise sources and application of duct acoustics:
  • Sound propagation in cylindrical and annular ducts with mean flow; normal mode analysis
  • Tonal noise: rotor “self” noise (buzzsaw), and rotor-stator interaction tones
  • Broadband noise: rotor “self” noise (trailing edge), rotor-stator interaction, inlet turbulence
• Trailing edge noise: wind turbine, airframe
  • Scattering of noise from a sharp trailing edge
  • Noise prediction methods - semi-empirical, direct computations

Reading material

There is no text book for this course. The suggested reading materials include the following.

• Blackstock, D. T. (2000). Fundamentals of physical acoustics. John Wiley & Sons.
• Kinsler, L. E., Frey, A. R., Coppens, A. B., & Sanders, J. V. (1999). Fundamentals of acoustics (4th Edition).
• Pierce, A. D. (1981). Acoustics: an introduction to its physical principles and applications. McGraw-Hill.
• Howe, M. S. (1998). Acoustics of fluid-structure interactions. Cambridge university press.
• Wright, M. C. M. (2005). Lecture notes on the mathematics of acoustics. Imperial College Press.
• Morse, P. M., & Ingard, U. K. (1987). Theoretical Acoustics. Princeton University Press.
• Crighton, D. G., Dowling, A. P., Williams, J. E. F., Heckl, M., & Leppington, F. G. (1992). Modern Methods in analytical acoustics: Lecture Notes. Springer-Verlag.

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Lecture videos

Live lecture capture

• Playlist of all live lecture capture videos

Online meetings

• Week 0
  • A tutorial on Fourier transforms
• Week 1
  • Tutorial 1. Logistics; introduction to aeroacoustics
  • Tutorial 2. Simple sources of sound; spectrograms; windowing; spectral analysis of different instruments; linear wave equation/solution; x-t diagrams
• Week 2
  • Tutorial 3. Method of characteristics; Generalized functions; example problem
  • Tutorial 4.
• Week 3
  • Tutorial 5. Example problem (waves on a string); different initial and boundary conditions; impedance; linearized wave equation derived from conservation laws
  • Tutorial 6. Spherical waves; impedance as function of frequency; Fourier transforms and Helmholtz equation; intensity, sound pressure/power levels, intensity level
• Week 4
  • Tutorial 7. Helmholtz equation; effect of windowing on Fourier transforms; octave, 1/3rd octave, narrow bands in frequency
  • Tutorial 8. Parseval’s theorem; spectra computation using Python; power spectrum vs. power spectral density; coherent and incoherent sources
• Week 5
  • Tutorial 9. Plane waves: reflection and transmission; transmission loss; general solution
  • Tutorial 10. Spherical waves reflection and transmission; example problems
• Week 6
  • Tutorial 11. More normally-incident reflection/transmission problems
  • Tutorial 12. Characteristic and specific impedance; impedance tubes; phasors
  • Addendum to #12: Phasors
• Week 7
  • Tutorial 13. Oblique waves: reflection and transmission; critical angle for complete reflection
  • Tutorial 14. Oblique wave reflection/transmission example problems
• Week 8
  • Tutorial 15. No class.
  • Tutorial 16. Waveguides - duct acoustics
• Week 9
  • Tutorial 17. Modal analysis for rectangular ducts; example problems for duct acoustics
  • Tutorial 18. Rectangular ducts: mode cut-off phenomenon
• Week 10
  • Tutorial 19. Underwater waveguides: example problem; dispersion relation; modal analysis in Mathematica
  • Tutorial 20. Waves in a weighted chain; Bessel functions; vibration in a cylindrical diaphragm; Mathematica analysis
• Week 11
  • Tutorial 21. Waves on a annular diaphragm: example problems; acoustic wave propagation in a duct
  • Tutorial 22. Waveguides: wave propagation in ducts
• Week 12
  • Tutorial 23. Spherical waves: spherical Bessel functions; pulsating sphere problem
  • Tutorial 24. Spherical waves; multipole expansion; mono-,di-,quadrupoles
• Week 14
  • Tutorial 27. Lighthill’s acoustic analogy; silent flight of the owl
  • Tutorial 28. Generalized functions and their properties; problems; Green’s functions
  • Tutorial 29. Green’s functions and their properties; Lighthill’s acoustic analogy
• Week 14
  • Tutorial 30. Convolutions; Lighthill’s acoustic analogy; distributed sources; Curle’s analogy; Ffowcs Williams-Hawkings analogy
  • Tutorial 31. Noise sources and noise reduction ideas

Note: This course was formerly taught as Engineering Mechanics (EM-580)