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On the use of the method of matched asymptotic expansions in propeller aerodynamics and acoustics

Published online by Cambridge University Press:  26 April 2006

H. H. Brouwer
H. H. Brouwer
Affiliation:
National Aerospace Laboratory NLR, 1006 BM Amsterdam. The Netherlands
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Abstract

The applicability of the method of matched asymptotic expansions to both propeller aerodynamics and acoustics is investigated. The method is applied to a propeller with blades of high aspect ratio, in a uniform axial flow. The first two terms of the inner expansion and the first three terms of the outer expansion are considered. The matching yields an expression for the spanwise distribution of the downwash velocity. A numerical application shows that the first two terms of the inner solution do not yield an acceptable approximation for the downwash velocity. However, recasting the analytical expressions into an integral equation, similar to Prandtl's lifting line equation for wings, yields results for both aerodynamic and acoustic quantities, which agree well with experimental results. The method thus constitutes a practical analysis method for conventional propellers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 242 , September 1992 , pp. 117 - 143
Copyright
© 1992 Cambridge University Press

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References

Brouwer, H. H. 1989 A lifting line model for propeller noise. AIAA Paper 89–1079.Google Scholar
Crighton, D. G. & Leppington, F. G. 1973 Singular perturbation methods in acoustics: diffraction by a plate of finite thickness. Proc. R. Soc. Lond. A 335. 313–339.Google Scholar
Dahlquist, G. & Björck, A. 1974 Numerical Methods. Prentice-Hall.
Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion.. Phil. Trans. R. Soc. Lond. A 264, 321–342.Google Scholar
Glauert, H. 1959 The Elements of Aerofoil and Airscrew Theory, 2nd Edn (reprinted). Cambridge University Press.
Goldstein, S. 1929 On the vortex theory of screw propellers.. Proc. R. Soc. Lond. A 123, 440–465.Google Scholar
Gutin, L. 1948 On the sound field of a rotating propeller. NACA TM 1195.Google Scholar
Hanson, D. B. 1985 Near-field frequency-domain theory for propeller noise. AIAA J. 13, 449–504.Google Scholar
Hanson, D. B. 1986 Propeller noise caused by blade tip radial forces. AIAA Paper 86–1892.Google Scholar
Hanson, D. B. 1991 Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise, Volume I — Development of theory for blade loading, wakes, and noise. NASA CR 4329.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
Johnson, W. 1986 Recent developments in rotary-wing aerodynamic theory. AIAA J. 24, 1219–1244.Google Scholar
Kooi, J. W. & De Wolf, W. B. 1988 Aerodynamic measurements on a 1/5 scale model of the Fokker 50 propeller and comparison with theoretical predictions In Advanced Propellers & Their Installation on Aircraft. Cranfield Institute of Technology, UK.
Liepmann, H. W. & Puckett, A. E. 1947 Introduction to Aerodynamics of a Compressible Fluid. John Wiley.
Lordi, J. A. & Homicz, G. F. 1981 Linearized analysis of the three-dimensional compressible flow through a rotating annular blade row. J. Fluid Mech. 103, 413–442.Google Scholar
Milne-Thomson, L. M. 1958 Theoretical Aeordynamics. Dover.
Pierce, G. A. & Vaidyanathan, A. R. 1981 Helicopter rotor loads using a matched asymptotic expansions technique. NASA CR 165748.Google Scholar
Prandtl, L. & Tietjens, O. G. 1957 Applied Hydro- and Aerodynamics. Dover.
Reissner, H. 1937 On the vortex theory of the screw propeller. J. Aero. Sci. 5. 1–7.Google Scholar
Schulten, J. B. H. M. 1984 Aerodynamics of wide-chord propellers in non-axisymmetric flow. AGARD Symp. on Aerodynamics and Acoustics of Propellers, Toronto, Paper 7.
Schulten, J. B. H. M. 1988 Frequency-domain method for the computation of propeller acoustics. AIAA J. 26, 1027–1035.Google Scholar
Sparenberg, J. A. 1984 Elements of Hydrodynamic Propulsion. Martinus Nijhoff.
Van Dyke, M. D. 1964 Lifting-line theory as a singular perturbation problem. Appl. Maths Mech. 28, 90–102.Google Scholar
Van Dyke, M. D. 1975 Perturbation Methods in Fluid Mechanics. Stanford: The Parabolic Press.
Van Holten, Th. 1975 The computation of aerodynamic loads on helicopter blades in forward flight, using the method of the acceleration potential. Thesis, Delft University of Technology.
Van Holten, Th. 1976 Some notes on unsteady lifting line theory. J. Fluid Mech. 77, 561–579.Google Scholar
Vavra, M. H. 1960 Aero-thermodynamics and Flow in Turbomachines. John Wiley.
Wilmott, P. 1988 Unsteady lifting-line theory by the method of matched asymptotic expansions. J. Fluid Mech. 186, 303–320.Google Scholar