Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-05T09:07:02.068Z Has data issue: false hasContentIssue false
  • English
  • Français

Lighthill quadrupole radiation in supersonic propeller acoustics

Published online by Cambridge University Press:  26 April 2006

N. Peake  and
D. G. Crighton
N. Peake
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
D. G. Crighton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Sound generation by the Lighthill quadrupole is an important mechanism in the noise of supersonic and transonic propellers. Full numerical calculation of the quadrupole radiation must, however, require knowledge of the flow at all points exterior to the blades (involving transonic aerodynamics) and the evaluation of special functions. We describe how these difficulties may be largely avoided, using an asymptotic approximation that the number of blades, B, is large, and prove that to leading order the problem of the radiation in a given direction reduces to one of determining the (two-dimensional) flow field at just one radial station, legitimately achieved by linearized supersonic analysis. Simple formulae are derived for the far-field acoustic pressure generated by unswept blades, from which absolute level predictions can be made accurately and quickly. These formulae predict a significantly greater intensity, over broad angular ranges, than is predicted by the linear theory for thickness noise sources.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 363 - 382
Copyright
© 1991 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. A., 1968 Handbook of Mathematical Functions. Dover.
Blackburn, H. W.: 1982 Quadrupoles in potential flow. J. Fluid Mech. 116, 507–530.Google Scholar
Caughey, D. A.: 1969 Second-order wave structure in supersonic flows. NASA Contract Rep. CR-1438.Google Scholar
Chapman, C. J.: 1988 Shocks and singularities in the pressure field of a supersonically rotating propeller. J. Fluid Mech. 192, 1–16.Google Scholar
Crighton, D. G. & Parry, A. B., 1990a Asymptotic theory of propeller noise – Part 2: Supersonic single-rotation propeller AIAA J. (submitted).Google Scholar
Crighton, D. G. & Parry, A. B., 1990b Higher approximations in the asymptotic theory of propeller noise AIAA J. (submitted).Google Scholar
Deming, A. F.: 1937 Noise from propellers with symmetrical sections at zero blade angle. NACA TN 605.Google Scholar
Deming, A. F.: 1938 Noise from propellers with symmetrical sections at zero blade angle, II. NACA TN 679.Google Scholar
Farassat, F.: 1981 Linear acoustic formulae for calculation of rotating blade noise. AIAA J. 19, 1122–1130.Google Scholar
Williams, J. E. Ffowcs 1979 On the role of quadrupole source terms generated by moving bodies. AIAA Paper 79–0576.Google Scholar
Williams, J. E. Ffowcs & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. R. Soc. Lond. A 264, 321–342.Google Scholar
Garrick, I. E. & Watkins, C. E., 1954 A theoretical study of the effect of forward speed on the free-space sound-pressure field around propellers. NACA Rep. 1198.Google Scholar
Gutin, L.: 1936 On the sound field of a rotating airscrew. NACA TM 1195.Google Scholar
Hanson, D. B.: 1980 Helicoidal surface theory for harmonic noise of propellers in the far field. AIAA J. 18, 1213–1220.Google Scholar
Hanson, D. B.: 1983 Compressible helicoidal surface theory for propeller aerodynamics and noise. AIAA J. 1, 881–889.Google Scholar
Hanson, D. B. & Fink, M. R., 1979 The importance of quadrupole sources in prediction of transonic tip speed propeller noise. J. Sound Vib. 62, 19–38.Google Scholar
Hawkings, D. L. & Lowson, M. V., 1974 Theory of open supersonic rotor noise. J. Sound Vib. 36, 1–20.Google Scholar
Jones, D. S.: 1966 Generalized Functions. McGraw-Hill.
Lighthill, M. J.: 1952 On sound generated aerodynamically. T. General theory. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Lighthill, M. J.: 1958 An Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press.
Lilley, G. M., Westley, R., Yates, A. H. & Busing, J. R., 1953 Some aspects of noise from supersonic aircraft. J. R. Aeronaut. Soc. 57, 396–414.Google Scholar
Lynam, E. J. H. & Webb, H. A. 1919 The emission of sound by airscrews. Advisory Committee for Aeronautics 624.Google Scholar
Parry, A. B. & Crighton, D. G., 1989a Asymptotic theory of propeller noise - Part 1: Subsonic single-rotation propeller. AIAA J. 27, 1184–1190.Google Scholar
Parry, A. B. & Crighton, D. G., 1989b Prediction of counter-rotation propeller noise. AIAA Paper 89–1141.Google Scholar
Parry, A. B. & Crighton, D. G., 1990 Spanwise interference effects in the asymptotic theory of propeller noise. AIAA J. (to be submitted).Google Scholar
Peake, N. & Crighton, D. G., 1991 Frequency domain radiation integrals for the Lighthill quadrupole radiation. J. Fluid Mech. (to be submitted).Google Scholar
Schmitz, F. H. & Yu, Y. H., 1979 Theoretical modelling of high-speed helicopter impulsive noise. J. Am. Helicopter Soc. 24, 10–19.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.