Global linear stability analysis of flow in a lined duct

Pascal, Lucas; Piot, Estelle; Casalis, Grégoire

doi:10.1016/j.jsv.2017.08.007

Cited by 7 publications

(5 citation statements)

References 45 publications

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“…It should also be noted that the upstreampropagating acoustic wave identified by k − B0 is strongly attenuated when the instability occurs (k − B0 = −17.56 + 100.8i at frequency ω = 0.4310). This means that the global instability that consists of the unstable hydrodynamic wave and the first left-running acoustic mode described in lined duct by Pascal et al (2017) does not occur in our system. Figure 6(a) and (b) show the periodic fields for ω = 0.4310 when the unstable Bloch wave propagates through the lined duct with the maximum amplification.…”

Section: Instability Near the Acoustic Resonancementioning

confidence: 89%

A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow

Dai

Aurégan

2018

J. Fluid Mech.

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This paper presents a two-dimensional (2-D) cavity-by-cavity description of a convective instability near a lined wall with low dissipation due to the coupling of hydrodynamic modes with resonance of the wall. For a liner consisting of an array of deep cavities periodically placed along a duct containing a mean shear flow, the acoustic and hydrodynamic disturbances are described by the linearized Euler equations. The Bloch modes and the scattering matrix of periodic cells are used to examine the instability over the liner. The unstable Bloch mode is due to the coupling of a hydrodynamic mode in the shear flow with the cavity resonance. It is demonstrated that even when all the transverse modes are stable in the duct–cavity system, i.e. when the Kelvin–Helmholtz instability of the shear flow over the cavities does not occur, such an instability over the liner can still exist. The unstable Bloch wave, excited by the incident sound wave at the upstream part of the liner, convectively grows along the liner, and regenerates sound near the downstream edge of the liner with a sound level higher than the incident sound level. It is shown that a homogenized approach, where the wall effect is described by a homogeneous impedance, can also explain the unstable behaviour above the liner. It reveals that a small wall resistance and a small and positive reactance are two necessary conditions for such an instability.

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Section: Instability Near the Acoustic Resonancementioning

confidence: 89%

A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow

Dai

Aurégan

2018

J. Fluid Mech.

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“…The existence of instabilities above acoustic materials in the presence of a grazing flow has been experimentally proven [3][4][5]. Sometimes, it is difficult in computations to distinguish between real and numerical instabilities [6][7][8][9][10][11]. An analysis of the different types of instability that can occur above a material is therefore of importance for a better understanding of the results of experiments or computations.…”

Section: Introductionmentioning

confidence: 99%

Slow sound laser in lined flow ducts

Coutant

Aurégan

Pagneux

2019

The Journal of the Acoustical Society of America

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This work considers the propagation of sound in a waveguide with an impedance wall. In the low frequency regime, the first effect of the impedance is to decrease the propagation speed of acoustic waves. Therefore, a flow in the duct can exceed the wave propagation speed at low Mach numbers, making it effectively supersonic. This work analyzes a setup where the impedance along the wall varies such that the duct is supersonic then subsonic in a finite region and supersonic again. In this specific configuration, the subsonic region act as a resonant cavity, and triggers a laser-like instability. This work shows that the instability is highly subwavelength. Besides, if the subsonic region is small enough, the instability is static. This worl also analyzes the effect of a shear flow layer near the impedance wall. Although its presence significantly alter the instability, its main properties are maintained. This work points out the analogy between the present instability and a similar one in fluid analogues of black holes known as the black hole laser.

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“…Also, it should be mentioned that global stability analyses have been performed recently by Pascal et al [56] and Rahbari and Scalo [58]. In the following, the spectrum of standard canonical flows are first considered briefly to show how a MSD wall can lead to instability before the method is applied to the numerical simulation.…”

Section: Stability Analysismentioning

confidence: 99%

Numerical simulation of a turbulent channel flow with an acoustic liner

Sebastian

Marx

Fortuné

2019

Journal of Sound and Vibration

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Numerical simulations of a compressible turbulent channel flow with an acoustic impedance boundary condition are performed to assess how the flow is modified compared with a channel flow with rigid walls. When the liner resonance frequency is not too large and the resistance sufficiently small, turbulent statistics deviate from those obtained with rigid walls and surface waves are found traveling along the liner surface. For small resonance frequencies these waves are two-dimensional, they have a large wavelength compared to the turbulent structures and modulate these structures. As a result, they transport momentum toward the impedance wall, causing a drag increase. When the resonance frequency increases, the waves along the liner surface progressively lose their spanwise coherence while their streamwise wavelength decreases to get close to the flow typical length scales, which may also result in a drag increase when the resistance is sufficiently small. In the cases in which the surface waves are twodimensional, a connection is established between them and the unstable modes computed by using a linear stability analysis. Given the streamwise periodicity of the channel, a temporal stability analysis is performed rather than a spatial analysis, the latter being more frequently encountered in acoustic mode computations. This temporal analysis shows that the unstable mode in the vicinity of an acoustic liner arises from the A-branch of wall modes.

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Global linear stability analysis of flow in a lined duct

Cited by 7 publications

References 45 publications

A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow

A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow

Slow sound laser in lined flow ducts

Numerical simulation of a turbulent channel flow with an acoustic liner

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