Reflection of sound by a boundary layer

Brand, R. S.; Nagel, Robert T.

doi:10.1016/0022-460x(82)90468-0

Cited by 16 publications

(6 citation statements)

References 3 publications

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“…This trend starts to become evident at ever-smaller angles of incidence as the Mach number increases. According to Brand & Nagel (1982), as one approaches the acoustic waves are refracted away from the wall and hence the acoustic-field boundary layer signature is weakened. This effect is all the more pronounced as the Mach number increases and explains the decreasing receptivity levels at high angles of incidence.…”

Section: Numerical Results and Comparison With Literaturementioning

confidence: 99%

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An adjoint compressible linearised Navier–Stokes approach to model generation of Tollmien–Schlichting waves by sound

2019

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The generation of the first-mode instability through scattering of an acoustic wave by localised surface roughness, suction or heating is studied with a time-harmonic compressible adjoint linearised Navier–Stokes (AHLNS) approach for subsonic flow conditions. High Strouhal number analytical solutions to the compressible Stokes layer problem are deduced and shown to be in better agreement with numerical solutions compared to previous works. The adjoint methodology of Hill in the context of acoustic receptivity is extended to the compressible flow regime and an alternative formulation to predict sensitivity to the angle of incidence of an acoustic wave is proposed. Good agreement of the acoustic AHLNS receptivity model is found with published direct numerical simulations and the simpler finite Reynolds number approach. Parametric investigations of the influence of the acoustic wave angle on receptivity amplitudes reveal that the linearised unsteady boundary layer equations are a valid model of the acoustic signature for a large range of acoustic wave obliqueness values, failing only where the wave is highly oblique and travels upstream. An extensive parametric study of the influence of frequency, spanwise wavenumber, local Reynolds number and free-stream Mach number over the efficiency function for the different types of wall perturbation mechanisms is undertaken.

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Section: Numerical Results and Comparison With Literaturementioning

confidence: 99%

“…This trend starts to become evident at ever-smaller angles of incidence as the Mach number increases. According to Brand & Nagel (1982), as one approaches Θ = 180 • the acoustic waves are refracted away from the wall…”

Section: Adjoint Hlns Comparison With Finite Reynolds Number Theory (mentioning

confidence: 99%

An adjoint compressible linearised Navier–Stokes approach to model generation of Tollmien–Schlichting waves by sound

2019

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“…Several authors [1][2][3][4][5][6][7][8] have addressed the problem of propagation in lined flow ducts for adiabatic, inviscid sound propagation. In these cases, they have assumed continuity of displacement at the wall since it seems to be the more appropriate.…”

Section: Introductionmentioning

confidence: 99%

Influence of grazing flow and dissipation effects on the acoustic boundary conditions at a lined wall

Aurégan

Starobinski

Pagneux

2001

The Journal of the Acoustical Society of America

113

112

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The problem of sound propagation near a lined wall taking into account mean shear flow effects and viscous and thermal dissipation is investigated. The method of composite expansion is used to separate the inviscid part, in the core of the flow, from the boundary layer part, near the wall. Two diffusion equations for the shear stress and the heat flux are obtained in the boundary layer. The matching of the solutions of these equations with the inviscid part leads to a modified specific acoustic admittance in the core flow. Depending on the ratio of the acoustic and stationary boundary layer thicknesses, the kinematic wall condition changes gradually from continuity of normal acoustic displacement to continuity of normal acoustic mass velocity. This wall condition can be applied in dissipative silencers and in aircraft engine-duct systems.

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“…Firstly, we study the inviscid limit of the governing equations. This analysis is similar to that of [Duck, 1990], however the technique to derive the acoustic reflection coefficient is based on the work of [Brand and Nagel, 1982]. A complete disturbance profile is obtained by introducing an inner viscous layer that satisfies the no-slip condition and deriving composite solutions.…”

Section: Introductionmentioning

confidence: 99%

IUTAM Laminar-Turbulent Transition

2022

IUTAM Bookseries

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The study of acoustic receptivity in quiet disturbance environments can be decomposed into several sub-problems. One such problem consists of determining the response of the unsteady boundary layer to acoustic forcing in the freestream. In this paper, we describe two methods to characterize the acoustic boundary layer response based on the linear stability equations. In their inviscid form, we first show how to determine the reflection coefficient. The sum of the incident and reflected waves then drives the unsteady Stokes motion within the boundary layer, for which a double-layer high Strouhal number asymptotic solution is obtained. The outer layer solution is calculated numerically whereas the inner layer solution, introduced to satisfy the no-slip condition, is determined analytically. The full linear stability equations can also be integrated numerically to directly obtain a complete disturbance profile accounting for the effects of viscosity. A comparison between these models and the linearised unsteady boundary layer equation (LUBLE) model shows good agreement at high Strouhal number, low Mach number and for downstream-travelling waves. However, for near sonic Mach numbers and for upstream-travelling waves, the LUBLE are shown to be not valid because the assumption that the acoustic wavelength is long compared to the boundary layer thickness no longer holds.

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Reflection of sound by a boundary layer

Cited by 16 publications

References 3 publications

An adjoint compressible linearised Navier–Stokes approach to model generation of Tollmien–Schlichting waves by sound

An adjoint compressible linearised Navier–Stokes approach to model generation of Tollmien–Schlichting waves by sound

Influence of grazing flow and dissipation effects on the acoustic boundary conditions at a lined wall

IUTAM Laminar-Turbulent Transition

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