Hostname: page-component-84b7d79bbc-g7rbq Total loading time: 0 Render date: 2024-07-30T16:40:56.666Z Has data issue: false hasContentIssue false
  • English
  • Français

Weakly nonlinear acoustic and shock-wave theory of the noise of advanced high-speed turbopropellers

Published online by Cambridge University Press:  21 April 2006

Christopher K. W. Tam  and
M. Salikuddin
Christopher K. W. Tam
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306
M. Salikuddin
Affiliation:
Lockheed-Georgia Company, Marietta, Georgia 30063
Get access Rights & Permissions [Opens in a new window]

Abstract

An acoustic and shock-wave theory of the noise generated by advanced turbo-propellers operating at supersonic tip helical velocity and high-subsonic cruise Mach number is developed. The theory includes the thickness and loading noise of the highly swept propeller blades. When operating at their design conditions these propellers radiate extremely intense sound waves. Because of the weakly nonlinear propagation effects these high-intensity acoustic disturbances steepen up quickly to form shock waves. In the present theory advantage is taken of the fact that in the blade fixed-rotating-coordinate system the acoustic and shock-wave fields are time independent. The problem is formulated in this coordinate system as a boundary-value problem. Weakly nonlinear propagation effects are incorporated into the solution following Whitham's nonlinearization procedure (Whitham 1974). The change in the disturbance-propagation velocity due to fluid-particle motion as well as the change in the speed of sound resulting from compression and rarefaction are all taken into account. It is found that the equal-area rule of Whitham's shock-fitting method is also applicable to the present problem. This method permits easy construction of the three-dimensional shock surfaces associated with the acoustic disturbances of these high-speed turbopropellers. Numerical results of the present theory are compared with the measurements of the JETSTAr flight experiment and the United Technology Research Center low-cruise Mach number open-wind-tunnel data. Very favourable overall agreements are found. The comparisons indicate clearly that, when these supersonic turbopropellers are operated at their high subsonic design-cruise Mach number, weakly nonlinear propagation effects must be included in the theory if an accurate prediction of the waveform of the sound wave incident on the design aircraft fuselage is to be obtained. This is especially true for noise radiated in the upstream or forward directions. In the forward directions the effective propagation velocity of the acoustic disturbances is greatly reduced by the convection velocity of the ambient flow. This allows more time for the cumulative nonlinear propagation effects to exert their influence, leading to severe distortion of the waveform and the formation of shock waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 164 , March 1986 , pp. 127 - 154
Copyright
© 1986 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

Barger, R. L. 1980 Theoretical prediction of nonlinear propagation effects on noise signatures generated by subsonic or supersonic propellers or rotor blade tips. NASA TP 1660.
Brooks, B. M. 1980 Acoustic measurements of three propfan models. AIAA paper 80–0995.Google Scholar
Brooks, B. M. 1983 Analysis of JETSTAR propfan acoustic flight test data. Hamilton Standard Engineering Report HSER 8882.
Brooks, B. M. & Metzger, F. B. 1980 Acoustic test and analysis of three advanced turboprop models. NASA CR-159667.
Dugan, J. F., Miller, B. A., Graber, E. & Sagerser, D. A. 1980 The NASA high-speed turboprop program. NASA TM 81561.
Farassat, F. 1975 Theory of noise generation from moving bodies with an application to helicopter rotors. NASA TR R-451.
Farassat, F. 1981 Linear acoustic formulas for calculation of rotating blade noise. AIAA J. 19, 1122–1130.Google Scholar
Farassat, F. & Succi, G. P. 1980 A review of propeller discrete frequency noise prediction technology with emphasis on two current methods for time domain Calculations. J. Sound Vib. 71, 399–419.Google Scholar
Ffowcs Williams, J. E. & Ha Wkings, D. L. 1969 Sound generated by turbulence and surfaces in arbitrary motion. Phil. Trans. Soc. Lond. A 264, 321–342.Google Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw Hill, New York.
Hanson, D. B. 1980a Helicoidal surface theory for harmonic noise of propellers in the far field. AIAA J. 18, 1213–1220.Google Scholar
Hanson, D. B. 1980b Influence of propeller design parameters on far field harmonic noise in forward flight. AIAA J. 18, 1313–1319.Google Scholar
Hanson, D. B. 1985 Near-field frequency-domain theory for propeller noise. AIAA J. 23,499–504.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
Jou, W. H. 1979 Supersonic propeller noise in a uniform flow. AIAA paper 79–0348.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically I — General theory. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Metzger, F. B. & Rohrbach, C. 1979 Aeroacoustic design of the propfan. AIAA paper 79–0610.Google Scholar
Nystrom, P. A. & Farassat, F. 1980 A numerical technique for calculation of the noise of high speed propellers with advanced geometry. NASA TP 1662.
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. & Burton, D. E. 1984 Sound generated by instability waves of supersonic flows. Part I. Two dimensional mixing layers. Part II. Axisymmetric jets. J. Fluid Mech. 138, 249–295.Google Scholar
Whitham, G. B. 1974 Linear and nonlinear waves. Wiley-Interscience, New York.
Woan, C. J. & Gregorek, G. M. 1978 The exact numerical calculation of propeller noise. AIAA paper 78–1122.Google Scholar