PIV and LDV evidence of hydrodynamic instability over a liner in a duct with flow

Marx, David; Aurégan, Yves; Bailliet, Hélène; Valière, Jean-Christophe

doi:10.1016/j.jsv.2010.03.025

Cited by 71 publications

(64 citation statements)

References 20 publications

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“…In contrast, most modern computational aeroacoustics simulations assume stability, either explicitly or implicitly, and then tune the artificial numerical filtering they apply in order to achieve this, irrespective of whether the equations being solved support an instability. One has only to think of the flapping of a flag in the wind [32] to realize that flow over non-rigid surfaces may be physically unstable, and there is growing experimental evidence that flows over acoustic linings also exhibit an instability [30,31]. Incorporating viscosity into the boundary layer over acoustic linings affects the stability of the flow, and can completely stabilize the flow provided viscosity is strong enough [36].…”

Section: Resultsmentioning

confidence: 99%

“…It should be noted that flow past a non-rigid boundary is often unstable, both in theory [28,29] and in practice [30,31], as can be appreciated by considering the flapping of a flag in the wind [32]. While the modified boundary conditions mentioned above remove the illposedness of arbitrarily fast exponential growth caused by overly simple modelling assumptions, they should therefore still be expected to result in most cases in a convectively unstable system [26,33].…”

Section: Introductionmentioning

confidence: 99%

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Time-domain implementation of an impedance boundary condition with boundary layer correction

Gabard

2016

Journal of Computational Physics

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A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley [ , AIAA J. 49(6), pp. 1272[ -1282. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time-domain implementation of an impedance boundary condition with boundary layer correction

Gabard

2016

Journal of Computational Physics

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“…However, for specific liners and under particular flow conditions, some experiments have shown that a convective hydrodynamic instability may grow on the liner and is likely to lead to sound amplification [1,2,3,4,5,6]. Evidence of such instabilities have been shown as well numerically [7,8].…”

Section: Introductionmentioning

confidence: 99%

Global linear stability analysis of flow in a lined duct

Pascal

Piot

Casalis

2017

Journal of Sound and Vibration

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Eigenmodes of the linearised Euler equations are computed in order to study lined flow duct global stability. A simplified configuration is considered and the governing equations are discretised by means of the discontinuous Galerkin method. A biorthogonal technique is used to decompose the global eigenfunctions into local eigenmodes. The system dynamics switches from noise amplifier to resonator as the length of the liner is increased. The global mode in the liner region is shown to be mainly composed of a hydrodynamic unstable wave and a left-running acoustic mode.

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“…Moreover, use of this filtering implicitly assumes that flow over acoustic linings is stable, which may not reflect reality [11,1,26]. This paper investigates the numerical instability of time-domain simulations using the Myers boundary condition by performing a dispersion analysis of the discretised problem.…”

Section: Introductionmentioning

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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PIV and LDV evidence of hydrodynamic instability over a liner in a duct with flow

Cited by 71 publications

References 20 publications

Time-domain implementation of an impedance boundary condition with boundary layer correction

Time-domain implementation of an impedance boundary condition with boundary layer correction

Global linear stability analysis of flow in a lined duct

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

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