Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-30T10:19:37.971Z Has data issue: false hasContentIssue false
  • English
  • Français

Scattering and distortion of the unsteady motion on transversely sheared mean flows

Published online by Cambridge University Press:  19 April 2006

M. E. Goldstein
M. E. Goldstein
Affiliation:
NASA Lewis Research Center, Cleveland, Ohio 44135
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that the pressure and velocity fluctuations of the unsteady motion on a transversely sheared mean flow can be expressed entirely in terms of the derivatives of two potential functions. One of these is a convected quantity (i.e. it is frozen in the flow) that can be specified as a boundary condition and is related to a transverse component of the upstream velocity field. The other can be determined by solving an inhomogeneous wave equation whose source term is also a convected quantity that can be specified as a boundary condition in any given problem. The latter is related to the curl of the upstream vorticity field. The results are used to obtain an explicit representation of the three-dimensional gust-like or hydrodynamic motion on a transversely sheared mean flow. It is thereby shown that this motion is ‘driven’ entirely by the two convected quantities alluded to above.

The general theory is used to study the interaction of an unsteady flow with a scmi-infinite plate embedded in a shear layer. The acoustic field produced by this interaction is calculated in the limits of low and high frequency. The results are compared with experimental one-third octave sound pressure level radiation patterns. The agreement is found to be excellent, especially in the low frequency range, where the mean-flow and convective effects are shown to have a strong influence on the directivity of the sound.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 4 , 27 April 1979 , pp. 601 - 632
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Davies, P. O. A. L., Fisher, M. J. & Barratt, M. J. 1968 The characteristics of the turbulence in the mixing region on a round jet. J. Fluid Mech. 15, 337.Google Scholar
Bowling, A. P., Ffowcs Williams, J. E. & Goldstein, M. E. 1978 Sound production in a moving stream. Phil. Trans. Roy. Soc. A 288, 321.Google Scholar
Durbin, P. 1979 Rapid distortion for turbulence distorted by a constant shear-layer adjacent to a wall. Submitted to J. Fluid Mech.Google Scholar
Ffowcs Williams, J. E. & Hall, H. H. 1970 Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane. J. Fluid Mech. 40, 657.Google Scholar
Goldstein, M. E. 1975 The low frequency sound from multiple sources in axisymmetric shear flows, with application to jet noise. J. Fluid Mech. 70, 595.Google Scholar
Goldstein, M. E. 1976 Aeroacoastics. McGraw-Hill.
Goldstein, M. E. 1978 Characteristics of the unsteady motion on transversely sheared mean flows. J. Fluid Mech. 84, 305.Google Scholar
Hunt, J. C. R. 1977 A review of the theory of rapidly distorted flows and its applications. 13th Biennial Fluid Dyn. Symp., Poland. (To be published in Fluid Dyn. Trans., Polish Acad. Sci.)Google Scholar
Kovásznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aero Sci. 20, 657.Google Scholar
Liefmann, H. W. 1952 On the application of statistical concepts to the buffeting problem. J. Aero. Sci. 19, 793.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory. Proc. Roy. Soc. A 211, 564.Google Scholar
Mani, R. 1976 The influence of jet flow on jet noise. Part 1. The noise of unheated jets. J. Fluid Mech. 73, 753.Google Scholar
Moffatt, H. K. 1965 The interaction of turbulence with strong wind shear. Proc. URSI—IDGG Int. Coll. Atmos. Turb. Radio Wave Propagation, Moscow.Google Scholar
Möhring, W. 1976 Über Schallwellen in Scherströmungen, Fortschritte der Akustik. DAGA 76, VDI, pp. 543–546.Google Scholar
Mörse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Olsen, W. A. 1976 Noise generated by impingement of turbulent flow on airfoils of varied chord, cylinders and other flow obstructions. N.A.S.A. Tech. Memo. X-73644. (See also 3rd A.I.A.A. Aero-Acoustics Conf. A.I.A.A. Paper no. 76–504.)Google Scholar
Sears, W. R. 1941 Some aspects of non-stationary airfoil theory and its practical applications. J. Aero. Sci. 83, 104.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20, 417.Google Scholar