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Transient acoustic processes in a low-Mach-number shear flow

Published online by Cambridge University Press:  26 April 2006

Meng Wang  and
D. R. Kassoy
Meng Wang
Affiliation:
Department of Mechanical Engineering and Center for Combustion Research. University of Colorado, Boulder, CO 80309, USA
D. R. Kassoy
Affiliation:
Department of Mechanical Engineering and Center for Combustion Research. University of Colorado, Boulder, CO 80309, USA
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Abstract

A systematic perturbation procedure, based on a small mean flow Mach number and large duct Reynolds number, is employed to formulate and solve an initial-boundary-value problem for acoustic processes in a shear flow contained within a rigid-walled parallel duct. The results describe the general transient evolution of acoustic waves driven by a plane source located at a given duct cross-section. Forced bulk oscillations near the source and oblique wave generation are shown to result from refraction of the basic planar axial disturbance by the shear flow. Refraction also causes the axial waves to exhibit higher-order amplitude variations in the transverse direction. As the source frequency approaches certain critical values, specific refraction-induced oblique waves evolve into amplifying purely transverse waves. As a result, the magnitude of the refraction effect increases with time, and quasi-steady solutions do not exist. The analysis is extended to the thin acoustic boundary layer adjacent to the solid walls to examine the shear-layer structure induced by the variety of acoustic waves in the core flow. Nonlinear effects and acoustic streaming are shown to be negligibly small on the scale of a few axial wavelengths.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 509 - 536
Copyright
© 1992 Cambridge University Press

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References

Barnett, D. O. 1970 An analytical investigation of heat transfer in pulsating turbulent flow in a tube. Ph.D. dissertation, Auburn University.
Barnett, D. O. 1981 The effect of pressure pulsations and vibrations in fully developed pipe flow. Re. AEDC-TR-80–31. Arnold Engineering Development Center.Google Scholar
Baum, J. D. & Levine, J. N. 1987 Numerical investigation of acoustic refraction. AIAA J. 25, 1577–1586.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1980 Table of Integrals, Series, and Products, Corrected and Enlarged Edn. Academic.
Hersh, A. S. & Catton, I. 1971 Effect of shear flow on sound propagation in rectangular ducts. J. Acoust. Soc. Am. 50, 992–1003.Google Scholar
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Springer.
Lighthill, M. J. 1978 Acoustic streaming. J. Sound Vib. 61, 391–418.Google Scholar
Morse, P. M. & Ingard, K. U. 1968 Theoretical Acoustics. McGraw-Hill.
Mungur, P. & Gladwell, G. M. L. 1969 Acoustic wave propagation in a sheared fluid contained in a duct. J. Sound Vib. 9, 28–48.Google Scholar
Oberhettinger, F. & Badil, L. 1973 Tables of Laplace Transforms. Springer.
Pridmore-Brown, D. C. 1958 Sound propagation in a fluid flowing through an attenuating duct. J. Fluid Mech. 4, 393–406.Google Scholar
Richardson, E. G. & Tyler, E. 1929 The transverse velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established. Proc. Phys. Soc. Lond. 42, 1–15.Google Scholar
Romie, F. E. 1956 Heat transfer to fluids flowing with velocity pulsations in a pipe. Ph.D. dissertation, University of California, Los Angeles.
Rott, N. 1964 Theory of time-dependent laminar flows. In High Speed Aerodynamics and Jet Propulsion, vol. IV, pp. 395–438. Princeton University Press.
Rott, N. 1980 Thermoacoustics. Adv. Appl. Mech. 20, 135–175.Google Scholar
Schlichting, H. 1979 Boundary Layer Theory, Seventh Edn. McGraw-Hill.
Sexl, T. 1930 Annular effect in resonators observed by E. G. Richardson. Z. Phys. 61, 349–362.Google Scholar
Stokes, G. G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9 (II), 8–106.Google Scholar
Uchida, S. 1956 The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe. Z. Angew. Math. Phys. 7, 403–422.Google Scholar
Wang, M. & Kassoy, D. R. 1990 Evolution of weakly nonlinear waves in a cylinder with a movable piston. J. Fluid Mech. 221, 27–52.Google Scholar