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AEE548 FUNDAMENTALS OF AERODYNAMIC NOISE

Course Objectives

 The course starts with making the students aware of the existence of international regulations that limit noise emissions from aircraft. Noise is described really as unwanted sound which to some level always exists due to interactions of the system elements or the system itself with the working fluid environment. Therefore, the course continues with the defition of sound, the basic equations that govern its propagation, concepts of frequency, amplitude, sound pressure levels, frequency-time domain relations. It is then shown that the basic equation governing sound propagation can be obtained from the fundamental flow equations. Inhomogenous wave equation is also introduced with analytical solutions in free-space. Lighthill's theory of sound generation is described with its application to estimate the scales of sound based on the relevant parameters of the source region. The 8th-power law is obtained that explains the success of reducing the jet noise over the years by introduction of turbofan engines. Effects of source convection is discussed. A similar analogy for sound generation by moving bodies is also given in relation to moving helicopter blades, and the sources of sound on such a configuration are explained. Interaction of rotor-stator blades on turbomachines causes tonal noise and its physics is discussed. The mathematical relation that describes the interaction mechanism is given. The sound propagation through constant cross-sectional ducts is discussed that leads to understanding of propagation and radiation mechanisms for generated sound internally in engines. The cut-off ratio is described. By advent of very capable computers as well as advanced numerical algorithms noise generation and propagation problems started being treated computationally. The area that deals with this is called computational aeroacoustics. Important points one must be aware of in computational aeroacoustics are also discussed. The commonly used Kirchhoff's method for extrapolating nearfield acoustic solution to far-field microphone locations is derived for quiescent medium, and points about which one must be careful in applications are explained. Also the numerical errors associated with numerical algorithms are described and principles of good algorith design are given. Analytical treatment of jet noise radiation from literature is discussed briefly with emphasis on understanding of the generation mechanisms and flight effects on radiation.

Course Content

Basic equations of fluid dynamics, linearized Euler equations, speed of sound. Classical acoustics: the wave equation, solutions in Cartesian, cylindrical, and spherical coordinates. Fourier transform and convolution integrals, Green's function for the wave equation. Compact, noncompact sources. Lighthill's theory of aerodynamic noise: acoustic analogy, jet noise, scaling laws. Turbomachinery noise: duct acoustics, mode generation mechanisms, sound attenuation. Noise from moving bodies: helicopter noise, propeller noise, airframe noise. Computational aeroacoustics: high-resolution numerical algorithms, boundary conditions.

Course Learning Outcomes

 By this course the students will be able to

• be aware of importance of quitening aircraft for meeting international noise regulations

• appreciate the fact that in noise studies sound waves are of really small amplitude and usually diverse frequencies

• linearize the fundamental flow equations and obtain equations governing wave propagation

• derive an inhomogenouse wave equation from the full non-linear Navier-Stokes equations and identify the sources of sound due to the flow

• use Green's function for developing an analytical solution to the inhomogenous wave equation given its source, and perform scale analysis towards the radiated sound levels

• understand physics of sound propagation through circular and rectangular ducts, and determine the frequencies and modal numbers of the propagating waves

• analyze the pattern of rotor-stator interactional modes that result in turbomachines

• understand the generation of sound by moving rotor blades, and propagation patterns of sound from these sources

• understand the points one must always be aware of in using numerical approaches to solving aeroacoustics problems

• appreciate basic jet noise generation mechanisms, and flight effects in jet noise radiation