Problems in flow acoustics

Möhring, W.; Muller, E; Obermeier, F.

doi:10.1103/revmodphys.55.707

Cited by 59 publications

(33 citation statements)

References 76 publications

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“…So to ensure potential vorticity conservation, the imposed purely acoustic perturbation (curl-free) acquires a rotational part by driving the vorticity mode; we recover the well-known fact that acoustic perturbation cannot be curl-free in shear flow [27]. From a more technical point of view, it is in fact a non-uniformity of the WKB method with an amplitude c H ∼ ετ i .…”

Section: Wkb Approachsupporting

confidence: 57%

“…We introduce a WKB method for which the two acoustic modes and the vorticity mode naturally come out from the equations as eigenvectors of an eigenvalue problem. An order 1 approximation is used instead of the classical order 0 WKB to improve the description and to take into account the well-known inherent rotational part of the acoustic mode which is due to potential vorticity conservation [27]. The plan of this paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

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Acoustic–vorticity coupling in linearly varying shear flows using the WKB method

Favraud

Pagneux

2013

Proc. R. Soc. A.

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The evolution of acoustic and vorticity perturbations in a two-dimensional incompressible linear flow is investigated. A weighted decomposition of the flow into a hyperbolic part and a rotation part allows continuous spanning of all linear flows such as hyperbolic flow, plane Couette flow and rigid rotation for instance. Using the Kelvin non-modal approach, the equations governing the time evolution of plane wave perturbations are reduced into a system of three first-order ordinary differential equations. This system is analysed using a WKB method where the small parameter ε is the ratio of the shear rate of the flow over the typical frequency of the perturbations. With this method, a basis of three modes naturally appears: two acoustic modes and one vorticity mode. At finite but small ε, couplings between the modes appear when the length of the wavenumber is minimal. For hyperbolic flow, incident vorticity mode generates the two acoustic modes, and an incident acoustic mode generates the other acoustic mode. More generally, for all flows, the hyperbolic part of the flow is responsible of the coupling between acoustic and vorticity modes, but also of the coupling between the two acoustic modes. These phenomena are illustrated by displaying wavepacket evolutions.

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Section: Wkb Approachsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Acoustic–vorticity coupling in linearly varying shear flows using the WKB method

Favraud

Pagneux

2013

Proc. R. Soc. A.

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“…The first three terms on the l.h.s of (2.25) specify the acoustic-vortical wave equation in a unidirectional shear flow [2][3][4][5]18,19] in the absence of cross flow. The generalization to include a uniform cross flow adds the fourth term on the l.h.s of (2.25) and restricts the shear flow to the linear velocity profile (2.24a).…”

Section: (A) Linear Unidirectional Shear With Uniform Cross Flowmentioning

confidence: 99%

On the acoustics of an impedance liner with shear and cross flow

Campos¹,

Legendre²,

Sambuc³

2014

Proc. R. Soc. A.

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The acoustic-vortical wave equation is derived describing the propagation of sound in (i) a unidirectional shear flow with a linear velocity profile upon which is superimposed (ii) a uniform cross flow; together with an impedance wall boundary condition representing the effect of a locally reacting acoustic liner in the presence of bias and shear flow. This leads to a third-order differential equation in the presence of cross flow, and in its absence simplifies to the Pridmore-Brown equation (second-order); also the singularity of the Pridmore-Brown equation for zero Doppler-shifted frequency is removed by the cross flow. Because the third-order wave equation has no singularities (except at the sonic condition), its general solution is a linear combination of three linearly independent MacLaurin series in powers of the distance from the wall. The acoustic field in the boundary layer is matched through the pressure and horizontal and vertical velocity components to the acoustic field in a uniform free stream consisting of incident and reflected waves. The scattering coefficients are plotted for several values of the five parameters of the problem, namely the angle of incidence, free stream and cross-flow Mach numbers, specific wall impedance and Helmholtz number using the boundary layer thickness.

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“…Flow acoustics concerns three different processes: propagation of sound through flow, generation of sound by flow, and generation of flow by sound [24], [26]. Correspondingly, there are three main effects: scattering (and refraction), acoustic radiation, and absorption.…”

Section: Introductionmentioning

confidence: 99%