Some aspects of “sound” attenuation in lined ducts containing inviscid mean flows with boundary layers

Tester, Brian J.

doi:10.1016/s0022-460x(73)80104-x

Cited by 69 publications

(42 citation statements)

References 14 publications

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“…Although a straight duct with uniform velocity profile and impedance wall is a simplification, it is an important model of the lined duct of a real turbofan engine [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A classification of duct modes based on surface waves

Rienstra

2001

7th AIAA/CEAS Aeroacoustics Conference and Exhibit

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For the relatively high frequencies relevant in a turbofan engine duct, the modes of a lined section may be classified in two categories: genuine acoustic 3D duct modes resulting from the finiteness of the duct geometry, and 2D surface waves that exist only near the wall surface in a way essentially independent of the rest of the duct. Per frequency and circumferential order there are at most four surface waves. They occur in two kinds: two acoustic surface waves that exist with and without mean flow, and two hydrodynamic surface waves that exist only with mean flow. The number and location of the surface waves depends on the wall impedance Z and mean flow Mach number. When Z is varied, an acoustic mode may change via small transition zones into a surface waves and vice versa.Compared to the acoustic modes, the surface waves behave-for example as a function of the wall impedance-rather differently as they have their own dynamics. They are therefore more difficult to find. A method is described to trace all modes by continuation in Z from the hard-wall values, by starting in an area of the complex Z-plane without surface waves.

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Section: Introductionmentioning

confidence: 99%

A classification of duct modes based on surface waves

Rienstra

2001

7th AIAA/CEAS Aeroacoustics Conference and Exhibit

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“…For describing the instantaneous acoustic perturbation propagation in a gas flowing through a lined duct, the authors of [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] consider the nonlinear Euler equations governing the gas flow and the solution of these equations describing the gas flow. After that, the…”

Section: Motivation Of the Mathematical Considerationsmentioning

confidence: 99%

Linear Stability with Respect to the Initial Value Perturbations in the Presence of Solutions of the Linearized Equation Having Strictly Positive Exponential Growth Rate

Bálint

Pârvan³

2016

INCAS BULLETIN

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“…This condition assumes an infinitely thin boundary layer, and effectively uses a vortex sheet model where the continuity of pressure and normal displacement is applied [16,39,15]. In the limit of an infinitely small source (w → 0) the present test case is equivalent to the benchmark problem proposed in reference [8] and for which a complete analytical solution has been made available.…”

Section: Problem Descriptionmentioning

confidence: 99%

A full discrete dispersion analysis of time-domain simulations of acoustic liners with flow

Gabard

2014

Journal of Computational Physics

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The effect of flow over an acoustic liner is generally described by the Myers impedance condition. The use of this impedance condition in time-domain numerical simulations has been plagued by stability issues, and various ad hoc techniques based on artificial damping or filtering have been used to stabilise the solution. The theoretical issue leading to the ill-posedness of this impedance condition in the time domain is now well understood. For computational models, some trends have been identified, but no detailed investigation of the cause of the instabilities in numerical simulations has been undertaken to date. This paper presents a dispersion analysis of the complete numerical model, based on finite-difference approximations, for a twodimensional model of a uniform flow above an impedance surface. It provides insight into the properties of the instability in the numerical model and clarifies the parameters that influence its presence. The dispersion analysis is also used to give useful information about the accuracy of the acoustic solution.Comparison between the dispersion analysis and numerical simulations shows that the instability associated with the Myers condition can be identified in the numerical model, but its properties differ significantly from that of the continuous model. The unbounded growth of the instability in the continuous model is not present in the numerical model due to the wavenumber aliasing inherent to numerical approximations. Instead, the numerical instability includes a wavenumber component behaving as an absolute instability. The trend previously reported that the instability is more likely to appear with fine grids is explained. While the instability in the numerical model is heavily dependent on the spatial resolution, it is well resolved in time and is not sensitive to the time step. In addition filtering techniques to stabilise the solutions are considered and it is found that, while they can reduce the instability in some cases, they do not represent a systematic or robust solution in general.

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Some aspects of “sound” attenuation in lined ducts containing inviscid mean flows with boundary layers

Cited by 69 publications

References 14 publications

A classification of duct modes based on surface waves

A classification of duct modes based on surface waves

Linear Stability with Respect to the Initial Value Perturbations in the Presence of Solutions of the Linearized Equation Having Strictly Positive Exponential Growth Rate

A full discrete dispersion analysis of time-domain simulations of acoustic liners with flow

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