Scattering of acoustic duct modes by axial liner splices

Tam, Christopher K. W.; Huang, Ju; Chien, Eugene

doi:10.1016/j.jsv.2007.08.027

Cited by 20 publications

(34 citation statements)

References 15 publications

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“…Several other schemes have been investigated, including those based on trigonometric interpolation by Tang & Baeder 21 , and similar results to those presented here are seen in all cases considered. In all cases, and for any resolution ∆x, the optimized schemes are seen to give worse phase accuracy than the maximum-order schemes for the parameters simulated by Tam, Ju & Chien 20 . The same is true when the relative group velocity error is considered.…”

Section: B Comparison Of Optimized and Maximal-order Schemes For Nonmentioning

confidence: 90%

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DRP schemes perform poorly for decaying or growing oscillations

Brambley

2015

21st AIAA/CEAS Aeroacoustics Conference

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Computational aeroacoustics often uses high-order finite difference schemes optimized to require relatively few points per wavelength; such optimized schemes are often called Dispersion Relation Preserving (DRP). Here we ask the question: what is the equivalent of points per wavelength for growing or decaying waves, and how well are such waves resolved numerically? This paper shows that DRP optimized spatial derivatives perform poorly for waves that are not of constant amplitude, under performing maximal-order schemes. Such non-constant-amplitude waves are common in aeroacoustics, whether owing to the O(1/r) decay of an expanding spherical wave, due to exponential decay caused by acoustic linings, or because of the decay of high-azimuthal-order modes in the radial direction towards the centre of a cylindrical duct. An equivalent criterion to points per wavelength is proposed for non-constant-amplitude oscillations, reducing to the standard definition for constant-amplitude oscillations and valid even for pure growth or decay with no oscillation. Using this definition, coherent statements about points per wavelength necessary for a given accuracy can be made for maximum-order schemes applied to non-constant-amplitude oscillations. These features are illustrated through a numerical example.

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Section: B Comparison Of Optimized and Maximal-order Schemes For Nonmentioning

confidence: 90%

“…|dᾱ/dα − 1| > 0.01). Short and long dashed lines correspond to α∆x for varying ∆x with and without flow respectively for the axial wavenumbers investigated by Tam, Ju & Chien20 . the interval [0, 1] with N + 1 equally spaced points, and write our 2N + 2 degrees of freedom as…”

mentioning

confidence: 99%

DRP schemes perform poorly for decaying or growing oscillations

Brambley

2015

21st AIAA/CEAS Aeroacoustics Conference

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“…When numerically simulating such a system, it is found that for fine meshes the numerics are unstable at the grid scale, with finer meshes becoming unstable more rapidly, and these instabilities are therefore routinely filtered out. 3,7,13 However, since this instability can now be seen as the numerics attempting to accurately simulate the underlying mathematical differential equation, which has no regular mathematical solution, once part of the numerical solution is filtered out there is no justification that what is left is of any relevance to the physical problem being modelled. We have seen above that the illposedness causes problems with stability analysis, and it also causes problems for mode-matching 1, 5 and scattering.…”

Section: Illposednessmentioning

confidence: 99%

“…To force their stability, such numerical simulations always include an artificial damping term to filter out the instability. 3,7,13 This is connected with illposedness. In §IV we show that any model for which the Briggs-Bers criterion is inapplicable is illposed, and demonstrate what this means from a practical (computational and analytical) perspective.…”

Section: Introductionmentioning

confidence: 99%

“…For an acoustically lined duct wall, rather than modelling the physics of the lining, a simplified model of a linear and locally-reacting lining is usually assumed. [1][2][3][4][5] The response of the lining is then characterized by its impedance, Z(ω) = p/v, where a time-harmonic pressure forcing p exp{iωt} produces a time-harmonic fluid velocity v exp{iωt} normal to the lining. With nonzero mean flow, the duct boundary is considered to be an infinitely-thin vortex sheet separating the moving fluid on one side and the fluid on the lining surface on the other.…”

Section: Introductionmentioning

confidence: 99%

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Models for Acoustically-Lined Turbofan Ducts

Brambley

2008

14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference)

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Several models have recently been proposed for the impedance response of an acoustic lining; most recently, Rienstra's Enhanced Helmholtz Resonator model. All of these models have stability issues with nonzero mean flow, and there has been some debate over the existence of hydrodynamic instability waves over the surface of such acoustic linings. Mathematically, the standard proven Briggs-Bers stability analysis is not applicable. Computationally, the hydrodynamic modes are routinely ignored (in the frequency domain) and instabilities filtered out (in the time domain). This ambiguity causes significant problems for mode-matching and for scattering analysis. The inadequacies of the recently-proposed "Crighton-Leppington" stability criterion are demonstrated through a number of counterexamples. It is then shown that any impedance lining model not capable of being analysed using the Briggs-Bers criterion is illposed, in the true mathematical sense, and an explanation is given as to why such models should not be used in practice. Some commonly-used locally-reacting impedance boundaries (namely the mass-springdamper, three-parameter, Helmholtz Resonator, and Enhanced Helmholtz Resonator models) are shown to be illposed, and an empirical impedance model is suggested that is wellposed and stable, whilst maintaining mass-spring-damper-like behaviour for the propagating and first few cutoff modes. It is suggested that this model may well resolve the ambiguity caused by surface modes in scattering and mode-matching problems. A suggestion is also made for an additional fifth condition to be added to Rienstra's four conditions necessary for a locally-reacting impedance to be admissible.

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