Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T17:35:21.829Z Has data issue: false hasContentIssue false
  • English
  • Français

Shocks and singularities in the pressure field of a supersonically rotating propeller

Published online by Cambridge University Press:  21 April 2006

C. J. Chapman
C. J. Chapman
Affiliation:
Institute of Sound and Vibration Research, University of Southampton, Southampton S09 5NH, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

When linear acoustic theory is applied to the thickness noise problem of a supersonic propeller, it can give rise to a surface on which the pressure is discontinuous or singular. A method is described for obtaining the equation of this surface (when it exists), and the pressure field nearby; jumps, logarithms and inverse square roots occur, and their coefficients may be calculated exactly. The special case of a blade with a straight radial edge gives a cusped cone, whose sheets, each with a different type of discontinuity or singularity in pressure, are separated by lines of cusps; the coefficients in formulae for the pressure near the surface tend to infinity as a cusp line is approached, in proportion to the inverse quarter power of distance from the line. These results determine regions of space where nonlinear effects are important, and they suggest a strong analogy with sonic boom.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 192 , July 1988 , pp. 1 - 16
Copyright
© 1988 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

Blackburn H. W. 1984 Sound sources on high-speed surfaces. PhD thesis, University of Cambridge.
Caradonna, F. X. & Isom M. P. 1972 Subsonic and transonic potential flow over helicopter rotor blades. AIAA J. 10, 1606–1612.Google Scholar
Cramer, M. S. & Seebass A. R. 1978 Focusing of weak shock waves at an areCte. J. Fluid Mech. 88, 209–222.Google Scholar
Farassat F. 1975 Theory of noise generation from moving bodies with an application to helicopter rotors. NASA TR R-451.Google Scholar
Friedlander F. G. 1958 Sound Pulses. Cambridge University Press.
Gill, P. M. & Seebass A. R. 1975 Nonlinear acoustic behaviour at a caustic: an approximate analytical solution. Prog. Astronaut. Aeronaut. 38, 353–386.Google Scholar
Guiraud J.-P. 1965 Acoustique géométrique, bruit balistique des avions supersoniques et focalisation. J. Méc. 4, 215–267.Google Scholar
Hanson D. B. 1976 Near field noise of high tip speed propellers in forward flight. AIAA paper 76–565, presented at 3rd AIAA aeroacoustics conference, Palo Alto.Google Scholar
Hawkings D. 1979 Noise generation by transonic open rotors. Res. Paper 599, Westland Helicopters Ltd, Yeovil, England.Google Scholar
Hawkings, D. L. & Lowson M. V. 1974 Theory of open supersonic rotor noise. J. Sound Vib. 36, 1–20.Google Scholar
Hayes W. D. 1971 Sonic Boom. Ann. Rev. Fluid Mech. 3, 269–290.Google Scholar
Lilley G. M., Westley R., Yates, A. H. & Busing J. R. 1953 Some aspects of noise from supersonic aircraft. J. R. Aero. Soc. 57, 396–414.Google Scholar
Lowson, M. V. & Jupe R. J. 1974 Wave forms for a supersonic rotor. J. Sound Vib. 37, 475–489.Google Scholar
Obermeier F. 1983 On the propagation of weak and moderately strong, curved shock waves. J. Fluid Mech. 129, 123–136.Google Scholar
Rao P. S. 1956 Supersonic bangs, parts I and II Aero. Q. 7, 21–44 and 135–155.Google Scholar
Schwartz, I. R. (ed.) 1968 Second conference on sonic boom research. NASA SP-180.
Schwartz, I. R. (ed.) 1971 Third conference on sonic boom research. NASA SP-255.
Seebass, A. R. (ed.) 1967 Sonic boom research. NASA SP-147.
Sturtevant, B. & Kulkarny V. A. 1976 The focusing of weak shock waves. J. Fluid Mech. 73, 651–671.Google Scholar
Tam C. K. W. 1983 On linear acoustic solutions of high speed helicopter impulsive noise problems. J. Sound Vib. 89, 119–134.Google Scholar
Tam, C. K. W. & Salikuddin M. 1986 Weakly nonlinear acoustic and shock-wave theory of the noise of advanced high-speed turbopropellers. J. Fluid Mech. 164, 127–154.Google Scholar
Wanner J.-C. L., Vallee J., Vivier, C. & Thery C. 1972 Theoretical and experimental studies of the focus of sonic booms. J. Acoust. Soc. Am. 52, 13–32.Google Scholar
Warren C. H. E. 1968 Sonic bangs. In Noise and Acoustic Fatigue in Aeronautics (ed. E. J. Richards & D. J. Mead), pp. 266–284. Wiley.
Whitham G. B. 1956 On the propagation of weak shock waves. J. Fluid Mech. 1, 290–318.Google Scholar