On the acoustics of an exponential boundary layer

Campos, L. M. B. C.; Serrão, P. G. T. A.

doi:10.1098/rsta.1998.0277

Cited by 36 publications

(43 citation statements)

References 78 publications

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“…The effect of vorticity on the sound is represented in the present model by a boundary layer with a linear velocity profile; the velocity profile would be different in a viscous turbulent boundary layer. The acoustic of shear flows has been considered for the other shear velocity profiles namely exponential [13], hyperbolic tangent [14] and parabolic [15]; there are both fundamental qualitative similarities (existence of critical layer and continuous spectrum) and moderate quantitative changes (pressure fields and scattering coefficients). Viscosity can absorb sound in a boundary layer [25] but this is mostly high-frequency effect.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…Mungur & Plumblee 1969), which neglects temperature variation and viscous and thermal dissipation (Eversman 1971;Mariano 1971;Goldstein & Rice 1973;Jones 1977;Nagel & Brand 1982;Campos & Serrão 1998;Vilenski & Rienstra 2007). These dissipative terms were included by Nayfeh (1973) when considering viscous flow over a permeable boundary, although gradients of the mean flow at the wall were assumed to be O(1), and so this analysis is not applicable to thin boundary layers.…”

Section: Introductionmentioning

confidence: 99%

Acoustic implications of a thin viscous boundary layer over a compliant surface or permeable liner

BRAMBLEY

2011

J. Fluid Mech.

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This paper considers the implications of a high-Reynolds-number thin parallel boundary layer on fluid-solid interaction. Two types of boundaries are considered: a compliant boundary which is flexible but impermeable, such as an elastic sheet or elastic solid, and a permeable boundary which is rigidly fixed, such as a perforated rigid sheet. The fluid flow consists of a steady flow along the boundary and a small time-dependent perturbation, with the boundary reacting to the perturbation. The fluid displacement due to the perturbation is assumed to be much smaller than the boundary-layer thickness. The analysis is equally valid for compressible and incompressible fluids. Numerical examples are given for compressible flow along a cylindrical duct, for both permeable and compliant cylinder walls. The difference between compliant and permeable walls is shown to be dramatic in some cases. High-and low-frequency asymptotics are derived, and shown to compare well to the numerics. When used with a mass-spring-damper boundary, this model is shown to lead to similar, but not identical, temporal instability with unbounded growth rate to that seen for slipping flow using the Myers boundary condition. It is therefore suggested that a regularization of the Myers boundary condition removing the unbounded growth rate may lead to, or at least inform, a regularization of the model presented here.

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“…The acoustic wave equation in an unidirectional shear flow is known as the Pridmore-Brown (1958) or Lilley (1973) equation although it dates further back to Haurwitz (1934). Four exact solutions have been published, for a linear velocity profile homentropic [28] or homenergetic [29] and exponential [30] and hyperbolic tangent [31] velocity profiles. A fifth exact solution has been obtained for a parabolic velocity profile, relevant to the acoustics of ducted flows [32].…”

Section: Acoustic Modes In a Duct Containing A Parabolic Shear Flowmentioning

confidence: 99%