An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined, circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. A computer program was developed. The mean flow model consists of a one dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows.

/pdf/transmission-of-sound-through-nonuniform-circular-ducts-with-1xwfto1kbu.pdf

Transmission of sound through nonuniform circular ducts with compressible mean flows

This paper describes the application of the finite-element method in combination with Galerkin's method in the determination of the acoustic properties of turbofan inlets containing high subsonic Mach number steady flows. An approximate solution for the steady inviscid f Ion field is obtained using an integral method for calculating the potential flowfield in the inlet with a correction to account for compressibility effects. The accuracy of the finite element technique in predicting the acoustic properties of annular ducts has been checked by comparison with available analytical solutions for the problems of plane and spinning wave propagation through a hard-walled annular duct with a constant mean flow. Results are presented comparing low-frequency plane wave propagation through a hard-walled turbofan inlet containing a one-dimensional steady flow with the same inlet containing a fully two-dimensional axisymmetric steady flow. It is shown that when one-dimensional steady flow is assumed to exist in the duct, the plane wave propagates with relatively little distortion. However, propagation of a plane wave through the fully two-dimensional flowfield in the inlet produces severe distortion due to the excitation of higher order modes.

Determination of Turbofan Inlet Acoustics Using Finite Elements

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.

/pdf/time-dependent-difference-theory-for-noise-propagation-in-a-4wow7r2dut.pdf

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

Acoustic transmission in non-uniform ducts with mean flow, part I: The method of weighted residuals

A comparison of experiment and theory for sound propagation in variable area ducts

The Method of Weighted Residuals (MWR) and the Finite Element Method (FEM) are considered as computational schemes in the problem of acoustic transmission in nonuniform ducts. MWR is presented in an improved form which includes the interaction of acoustic modes (irrotational) and hydrodynamic modes (rotational). FEM is based on a weighted residuals formulation using eight noded isoparametric elements. Both are applicable to two-dimensional and axially symmetric problems. Calculations are made for several sample problems to demonstrate accuracy and relative efficiency. One test case has implications in the phenomenon of subsonic acoustic choking and it is found that a large transmission loss is not an automatic consequence of propagation against a high subsonic mean flow.

Transmission in nonuniform ducts - A comparative evaluation of finite element and weighted residuals computational schemes

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Transmission in nonuniform ducts - A comparative evaluation of finite element and weighted residuals computational schemes