The propagation of sound in shear flows is relevant to the acoustics of wall and duct boundary layers, and to jet shear layers. The acoustic wave equation in a shear flow has been solved exactly only for a plane unidirectional homentropic mean shear flow, in the case of three velocity profiles: linear, exponential and hyperbolic tangent. The assumption of homentropic mean flow restricts application to isothermal shear flows. In the present paper the wave equation in an plane unidirectional shear flow with a linear velocity profile is solved in an isentropic non-homentropic case, which allows for the presence of transverse temperature gradients associated with the ***non-uniform sound speed. The sound speed profile is specified by the condition of constant enthalpy, i.e. homenergetic shear flow. In this case the acoustic wave equation has three singularities at finite distance (besides the point at infinity), viz. the critical layer where the Doppler shifted frequency vanishes, and the critical flow points where the sound speed vanishes. By matching pairs of solutions around the singular and regular points, the amplitude and phase of the acoustic pressure in calculated and plotted for several combinations of wavelength and wave frequency, mean flow vorticity and sound speed, demonstrating, among others, some cases of sound suppression at the critical layer.
Get full access to this article
View all access options for this article.
References
1.
AlmgrenM.1968Acoustic boundary layer influence in scale model simulation of sound propagation: theory and numerical examples. J. Sound Vib.105, 321–327.
2.
BalsaT.F.1976aThe far-field of high-frequency convected, singularities in sheared flows, with application to jet noise prediction. J. Fluid Mech.74, 193–208
3.
BalsaT.F.1976bReffraction and shielding of sound from a source in a jet. J. Fluid Mech.76, 443–456.
4.
BatchelorG.K.1967Fluid Dynamics, Cambridge U.P.
5.
BookerJ.R. & BrethertonF.P.1967A critical layer for internal gravity waves in a shear flow. J. Fluid Mech.27, 513–529.
6.
CamposL.M.B.C.1978aOn the spectral broadening of sound by turbulent shear layers. Part I: Scattering by moving interfaces and reffraction in turbulence. J. Fluid Mech.89, 723–749.
7.
CamposL.M.B.C.1978bOn the spectral broadening of sound by turbulent shear layers. Part II: Spectral broading of experimental and aircraft noise. J. Fluid Mech.89, 751–779.
8.
CamposL.M.B.C.1983aSur la propagation du sons dans les ecoulements non-uniformes et non-stationaires. Revue d'Acoustique67, 217–233.
9.
CamposL.M.B.C.1986aOn waves in gases. Part I: Acoustics of jets, turbulence and ducts. Rev. Mod. Phys.58, 117–182.
10.
CamposL.M.B.C.1992Effects on acoustic fatigue loads of multiple reflection between a plate and a turbulent wake. Acustica76, 109–117.
11.
CamposL.M.B.C.1996On the correlation of acoustic pressures induced by a turbulent wake on a nearby wall. Acta Acustica82, 9–17.
12.
CamposL.M.B.C.1997On the spectra of aerodynamic noise and aeroacoustic fatigue. Progr. Aerosp. Sci.33, 353–389.
13.
CamposL.M.B.C.2007On 36 forms of the acoustic wave equation in potential flows and inhomogeneous media. Rew. Appl. Mech.60, 149–171.
14.
CamposL.M.B.C. & KobayashiM.H.K.2000On the reflection and transmission of sound in a thick shear layer. J. Fluid Mech.424, 303–326.
15.
CamposL.M.B.C.OliveiraJ.M.G.S. & KobayashiM.H.1998On sound propagation in a linear shear flow. J. Sound Vib. (to appear).
16.
CamposL.M.B.C. & SerrãoP.G.T.A.1998On the acoustics of an exponential boundary layer. Phil. Trans. Roy. Soc.A356, 2335–2378.
17.
EvermanW.1971Effect of boundary layer on the transmission and attenuation of sound in an acoustically treated circular duct. J. Acoustic. Soc. Amer.39, 1372–1380.
18.
EvermanW. & BeckenmeyerR.J.1972Transmission of sound in ducts with thin shear layers: convergence to the uniform flow case. J. Acoust. Soc. Am.52, 216–225.
19.
GoldsteinM. E1979Scattering and distortion of the unsteady motion on transversely sheared mean flows. J. Sound Vib.91, 601–602.
20.
GoldsteinM. E.1982High-frequency sound emission from moving point multipole sources embedded in arbitrary transversely sheared mean flows. J. Sound Vib.80, 449–460.
21.
GoldsteinM.E.1986Aeroacoustics. Mc Graw-Hill.
22.
GoldsteinM. & RiceE.1973Effect of shear on duct wall impedance. J. Sound Vib.30, 79–84.
23.
GrahamE.W. & GrahamB.B.1969Effect of a shear layer on plane waves in a fluid. J. Acoust. Soc. Am.46, 169–175.
24.
HansonD.B.1984Shielding of propfan cabin noise by the fuselage boundary layer. J. Sound Vib.92, 591–598.
25.
HaurwitzB, 1931Zur Theorie der Wellenbewegungen in Luft and Wasser. Veroff. Geophys. Inst. Univ. Leipz.6, 324–364.
26.
HershA.S. & CattonI.1971Effects of shear flow on sound propagation in rectangular ducts. J. Acoust. Soc. Am.50, 992–1003.
27.
HoC.M. & KovasznayL.S.G.1976aPropagation of a coherent acoustic wave through a turbulent shear flow, J. Acoust. Soc. Am.60, 40–45
