Time-Dependent Difference Theory for Noise Propagation in a Two-Dimensional Duct

Baumeister, K. J.

doi:10.2514/3.50906

Cited by 26 publications

(10 citation statements)

References 18 publications

(1 reference statement)

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“…Recently, the attenuation of sound propagation in a circular duct with shear mean flow was treated by the authors [3]. Investigations [1,2,4,9] using various schemes to solve similar problems with different geometric shape were also found to have good results.…”

Section: Introductionmentioning

confidence: 97%

Theoretical prediction of sound propagation in an annular duct

Wang

Chen

Tse

1992

Journal of the Chinese Institute of Engineers

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In this paper, sound propagation in an annular duct with shear mean flow is studied using the Galerkin method. A simple polynomial which satisfies the boundary conditions is selected as the basis funciton. It not only can be used in the calculation of an annular duct, but also can be used for circular ducts. The refraction effect due to shear mean flow is observed in upstream and downstream propagation. It is more apparent in the upstream case. The sound attenuation due to acoustic liners is investigated and the optimum liner which causes the maximum attenuation is also demonstrated. ft Sm ' x*(tf®íiT^umMmmmmz¥¿m > msm&fSMcmzntimïï

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Section: Introductionmentioning

confidence: 97%

Theoretical prediction of sound propagation in an annular duct

Wang

Chen

Tse

1992

Journal of the Chinese Institute of Engineers

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“…For the numerical examples considered here, the grid system shown in Fig. 1 On the other hand, an explicit transient method generates no matrices, and is generally faster than a frequency domain approach (Baumeister, 1980a (Miller, 1988). Consequently, the method of choice in the present paper is a time dependent method.…”

Section: Problem Statementmentioning

confidence: 99%

“…However, a simple integration procedure resolves this problem. Baumeister (1980aBaumeister ( & 1980b gives precise details for generating the time difference equations at the boundaries. …”

Section: The Expressionsmentioning

confidence: 99%

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

Baumeister

Kreider

1996

Journal of Vibration and Acoustics

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An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

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“…It may therefore be assumed that if r,, is sufficiently large the radiated field will behave locally as a plane wave propagating outwards from the origin and normally incident on C,. This assumption yields the Sommerfeld condition -= -af ikf on Cm ar (7) and is equivalent to the specification of a 'pc' impedance in acoustical terminology. A useful physical interpretation of equation (7) and one which facilitates its extension to the case with mean flow is to regard it as a statement that at large distances from the inlet the sound field will behave as if it emanates from a single complex source located at the origin.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Wave envelope and infinite elements for acoustical radiation

Astley

1983

Numerical Methods in Fluids

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SUMMARYFinite element models are presented for the calculation of near and far field acoustical radiation. These models are applied to the specific problem of fan noise radiation from axisymmetric turbofan inlets. In all cases conventional acoustic finite elements are used within an inner region close to the inlet. The far field is represented by infinite elements or wave envelope elements. Theory and results are presented for the case with zero mean flow. Comparisons of computed data with analytic solutions and measured values establish the utility of both the infinite element and wave envelope element schemes in determining the near field values of acoustical pressure. The wave envelope scheme is shown to be effective also in the far field. Both schemes use meshes an order of magnitude more sparse that would be required in conventional numerical discretizations, and may consequently be applied at modest computational cost.

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Time-Dependent Difference Theory for Noise Propagation in a Two-Dimensional Duct

Cited by 26 publications

References 18 publications

Theoretical prediction of sound propagation in an annular duct

Theoretical prediction of sound propagation in an annular duct

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

Wave envelope and infinite elements for acoustical radiation

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