Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-02T22:04:37.906Z Has data issue: false hasContentIssue false
  • English
  • Français

The aerodynamic noise of small-perturbation subsonic flows

Published online by Cambridge University Press:  29 March 2006

Roy Amiet  and
W. R. Sears
Roy Amiet
Affiliation:
Cornell University
W. R. Sears
Affiliation:
Cornell University
Get access Rights & Permissions [Opens in a new window]

Abstract

The method of matched asymptotic expansions is used to simplify calculations of noise produced by aerodynamic flows involving small perturbations of a stream of non-negligible subsonic Mach number. This technique is restricted to problems for which the dimensionless frequency ε, defined as ωb/a0, is small, ω being the circular frequency, b the typical body dimension, and a0 the speed of sound. By combining Lorentz and Galilean transformations, the problem is transformed to a space in which the approximation appropriate to the inner region is found to be incompressible flow and that appropriate to the outer, classical acoustics. This approximation for the inner region is the unsteady counterpart of the Prandtl-Glauert transformation, but is not identical to use of that transformation in a straightforward quasi-steady manner. For wings in oscillatory motion, it is the same approximation as was given by Miles (1950).

To illustrate the technique, two examples are treated, one involving a pulsating cylinder in a stream, the other the impinging of plane sound waves upon an elliptical wing in a stream.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 44 , Issue 2 , 11 November 1970 , pp. 227 - 235
Copyright
© 1970 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

Küssner, H. G. 1940 Allgemeine Tragflächentheorie. Luftfahrtforschung, 17, 370–378.Google Scholar
Küssner, H. G. 1941 General airfoil theory. NACA Tech. Memo. no. 979.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Lighthill, M. J. 1962 Sound generated aerodynamically. Proc. Roy. Soc. A 267, 147–182.Google Scholar
Miles, J. M. 1950 On the compressibility correction for subsonic unsteady flow. J. Aero. Sci. 17, 181–182.Google Scholar
Müller, E. A. & Obermeier, F. 1967 Das tanzende Wirbelpaar als Schallquelle. Vortrag auf der Sitzung des Fachausschusses ‘Akustik’ der Deutschen Physikalischen Gesellschaft, Freudenstadt.
Obermeier, F. 1967a Berechnung aerodynamisch erzeugter Schallfelder mittels der Methode der ‘Matched Asymptotic Expansions’. Acustica, 18, 238–239.Google Scholar
Obermeier, F. 1967b The spinning vortices as a source of sound. AGARD C.P. no. 22, pp. 22–1–22–8.Google Scholar
Schade, T. & Krienes, S. 1947 The oscillating circular airfoil on the basis of potential theory. NACA Tech. Memo. no. 1098.Google Scholar
Sears, W. R. 1954 Small-perturbation theory. In General Theory of High-Speed Aerodynamics. Princeton University Press.Google Scholar
Sears, W. R. 1960 Small-Perturbation Theory. Princeton Aero. Paperbacks.
Shen, S. F. & Crimi, P. 1965 The theory for an oscillating thin airfoil as derived from the Oseen equations. J. Fluid Mech. 23, 585–609.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.