Acoustic Transmission in Non-Uniform Ducts with Mean Flow, Part II: The Finite Element Method

A time dependent numerical formulation was derived for sound propagation in a two dimensional straight soft-walled duct in the absence of mean flow. The time dependent governing acoustic-difference equations and boundary conditions were developed along with the maximum stable time increment. Example calculations were presented for sound attenuation in hard and soft wall ducts. The time dependent analysis were found to be superior to the conventional steady numerical analysis because of much shorter solution times and the elimination of matrix storage requirements.

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Time-dependent difference theory for noise propagation in a two-dimensional duct

We study the application of a B-splines Finite Element Method (FEM) to time-harmonic scattering acoustic problems. The infinite space is truncated by a fictitious boundary and second-order Absorbin...

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B-Spline FEM for Time-Harmonic Acoustic Scattering and Propagation

A critical examination is presented of the use of optimized axially segmented acoustic liners to increase the attenuation of a liner. New calculations show that segmenting is most efficient at high frequencies with relatively long duct lengths where the attenuation is low for both uniform and segmented liners. Statistical considerations indicate little advantage in using optimized liners with more than two segments, while the bandwidth of an optimized two-segment liner is shown to be nearly equal to that of a uniform liner. Multielement liner calculations show a large degradation in performance, due to changes in assumed input model structure. Finally, in order to substantiate previous and future analytical results, in-house (finite difference) and contractor (mode matching) programs are used to generate theoretical attenuations for a number of liner configurations for liners in a rectangular duct with no mean flow. Overall, the use of optimized multisectioned liners (sometimes called phased liners) fails to offer sufficient advantage over a uniform liner to warrant their use, except in lowfrequency, single-mode application. AdB F f* H* / M m p pA x x* y y* 6 Nomenclature speed of sound sound attenuation function frequency channel height length of duct Mach number transverse mode number dimensionless Fourier coefficient of pressure, p(x,y),p*/pA amplitude of pressure fluctuation or p JcJ 2 dimensionless axial coordinate, x* /H* axial coordiante dimensionless transverse coordinate, y*/H* transverse coordinate fractional impedance variation specific acoustic impedance dimensionless frequency/*//*/cJ or co*//*/27rcJ

Evaluation of Optimized Multisectioned Acoustic Liners

Wave envelope elements for acoustical radiation in inhomogeneous media

Finite difference equations are derived for sound propagation in a two dimensional, straight, soft wall duct with a uniform flow by using the wave envelope concept. This concept reduces the required number of finite difference grid points by one to two orders of magnitude depending on the length of the duct and the frequency of the sound. The governing acoustic difference equations in complex notation are derived. An exit condition is developed that allows a duct of finite length to simulate the wave propagation in an infinitely long duct. Sample calculations presented for a plane wave incident upon the acoustic liner show the numerical theory to be in good agreement with closed form analytical theory. Complete pressure and velocity printouts are given to some sample problems and can be used to debug and check future computer programs.

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K. J. Baumeister

Papers

Finite-difference theory for sound propagation in a lined duct with uniform flow using the wave envelope concept