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Acoustic theory of the many-bladed contra-rotating propeller: analysis of the effects of blade sweep on wake interaction noise

Published online by Cambridge University Press:  11 April 2019

M. J. Kingan Open the ORCID record for M. J. Kingan [Opens in a new window]  and
A. B. Parry Open the ORCID record for A. B. Parry [Opens in a new window]
M. J. Kingan
Affiliation:
Department of Mechanical Engineering, University of Auckland, Auckland 1010, New Zealand
A. B. Parry*
Affiliation:
30 Ypres Road, Allestree, Derby DE22 2LZ, UK
*
†Email address for correspondence: anthony.parry.pig@gmail.com
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Abstract

An analytical model is presented for the wake interaction tones produced by a contra-rotating propeller. We re-cast the usual far-field radiation formulae as a double integral over a nominal propeller source annulus. Assuming that the number of blades on both propellers is large, we evaluate the integral asymptotically in terms of its leading-order contributions from interior stationary or boundary critical points which represent the specific locations on the propeller annulus that dominate the sound radiation. The asymptotic approach is powerful producing results in the form of one-line algebraic formulae that contain no integrals or special functions yet remain accurate. The asymptotics show that sweep is not necessarily beneficial and can cause the blade design to become critical for particular tones and directions in terms of a continuum of interior points distributed along a line on the propeller source annulus producing a higher-order result and thus an enhanced radiated sound field. The paper also shows how the interior points are completely consistent with the sub- or super-critical gust response of a swept blade. Tones with low and zero azimuthal mode order are treated as special cases and the asymptotics show that, as the mode order reduces, the radiated sound becomes concentrated around the flight axis where even higher-order solutions are possible, including rings and annuli of stationary points around the propeller annulus. Full numerical calculations confirm the accuracy of the asymptotic approach.

JFM classification

Acoustics: Aeroacoustics Wakes/Jets: Wakes

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 385 - 427
Copyright
© 2019 Cambridge University Press 

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References

Adamczyk, J. J. 1974 Passage of a swept airfoil through an oblique gust. J. Aircraft 11, 281–287.Google Scholar
Bleistein, N. & Handelsman, R. A. 1969 Uniform asymptotic expansions of double integrals. J. Math. Analysis Applics. 27, 434–453.Google Scholar
Brady, C. W. 1951 Propellers for high powers and transonic speeds. In Proceedings of the 3rd Anglo-American Aeronautical Conference, Brighton, UK, 4–7 September, pp. 613–668.Google Scholar
Brandvik, T., Hall, C. A. & Parry, A. B. 2012 Angle-of-attack effects on counter-rotating propellers at take-off. In ASME Turbo Expo 2012, Copenhagen, Denmark, 11–15 June. ASME Paper GT2012-69901.Google Scholar
Bryan, G. H.1920 The acoustics of moving sources with application to airscrews. British ARC R & M No. 584.Google Scholar
Carazo, A., Roger, M. & Omais, M. 2011 Analytical prediction of wake-interaction noise in counterrotation open rotors. In 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), Portland, OR, 5–8 June. AIAA Paper 2011-2758.Google Scholar
Chako, N. 1965 Asymptotic expansions of double and multiple integrals occurring in diffraction theory. J. Inst. Maths Applics. 1, 372–422.Google Scholar
Colin, Y., Blanc, F., Caruelle, B., Barrois, F. & Djordjevic, N. 2012b Computational strategy for predicting CROR noise at low-speed. Part II. Investigation of the noise sources computation with the chorochronic method. In 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Colorado Springs, CO, 4–6 June. AIAA Paper 2012-2222.Google Scholar
Colin, Y., Caruelle, B., Node-Langlois, T., Omais, M. & Parry, A. B. 2012a Computational strategy for predicting CROR noise at low-speed. Part I. Review of the numerical methods. In 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Colorado Springs, CO, 4–6 June. AIAA Paper 2012-2221.Google Scholar
Colin, Y., Caruelle, B. & Parry, A. B. 2012c Computational strategy for predicting CROR noise at low-speed. Part III. Investigation of noise radiation with the Ffowcs-Williams Hawkings analogy. In 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Colorado Springs, CO, 4–6 June. AIAA Paper 2012-2223.Google Scholar
Cooke, J. C. 1982 Stationary phase in two dimensions. IMA J. Appl. Maths 29, 25–37.Google Scholar
Cooper, A. & Peake, N. 2005 Upstream-radiated rotor–stator interaction noise in mean swirling flow. J. Fluid Mech. 523, 219–250.Google Scholar
Cooper, A. & Peake, N. 2006 Rotor-stator interaction noise in swirling flow: stator sweep and lean effects. AIAA J. 44, 981–991.Google Scholar
Crighton, D. G. & Parry, A. B. 1991 Asymptotic theory of propeller noise. Part II. Supersonic single-rotation propeller. AIAA J. 29, 2031–2037.Google Scholar
Crighton, D. G. & Parry, A. B. 1992 Higher approximations in the asymptotic theory of propeller noise. AIAA J. 30, 3023–3039.Google Scholar
Daly, B. B. 1958 Noise level in fans. J. Inst. Heating Ventilating Engng 25, 29–45.Google Scholar
Delattre, G. & Falissard, F. 2015 Influence of torque ratio on counter-rotating open-rotor interaction noise. AIAA J. 53, 2726–2738.Google Scholar
De Laborderie, J. & Moreau, S. 2016 Prediction of tonal ducted fan noise. J. Sound Vib. 372, 105–132.Google Scholar
Envia, E. 1994 Asymptotic theory of supersonic propeller noise. AIAA J. 32 (2), 239–246.Google Scholar
Envia, E. 2015 Aeroacoustic analysis of a high-speed open rotor. Intl J. Aeroacoust. 14 (3 & 4), 569–606.Google Scholar
Envia, E. & Kerschen, E. J. 1984 Noise produced by the interaction of a rotor wake with a swept stator blade. In 9th AIAA Aeroacoustics Conference, Williamsburg, VA, 10–15 October. AIAA Paper No. 84-2326.Google Scholar
Envia, E. & Kerschen, E. J. 1986 Noise generated by convected gusts interacting with swept airfoil cascades. In 10th AIAA Aeroacoustics Conference, Seattle, WA, 9–11 July. AIAA Paper No. 86-1872.Google Scholar
Envia, E. & Kerschen, E. J.1990 Influence of vane sweep on rotor–stator interaction noise. NASA CR 187052.Google Scholar
Falissard, F. & Delattre, G. 2014 Investigation of counter rotating open rotor orthogonal blade/vortex interaction noise. In 20th AIAA/CEAS Aeroacoustics Conference, AIAA Aviation forum, Atlanta, GA, 16–20 June. AIAA Paper 2014-2748.Google Scholar
Fuss, U. & Parry, A. B. 2011 SAGE1 demonstrator: enabling open rotor technologies. In 20th ISABE Conference, Gothenburg, Sweden, 12–16 September. ISABE Paper 2011-1305.Google Scholar
Gautschi, G. 1970 Error function and Fresnel integrals. In Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (9th Printing) (ed. Abramowitz, M. & Stegun, I. A.). Dover.Google Scholar
Glegg, S. A. L. 1999 The response of a swept blade row to a three-dimensional gust. J. Sound Vib. 227 (1), 29–64.Google Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 2014 Table of Integrals, Series, and Products, 8th edn. (ed. Zwillinger, D. & Moll, V.). Academic.Google Scholar
Graham, J. M. R. 1970 Lifting surface theory for the problem of an arbitrarily yawed sinuosoidal gust incident on a thin aerofoil in incompressible flow. Aeronaut. Q. 21, 182–198.Google Scholar
Grasso, G., Christophe, J., Schram, C. F. & Verstraete, T. 2014 Influence of the noise prediction model on the aeroacoustic optimization of a contra-rotating fan. In 20th AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, 16–20 June. AIAA Paper 2014-2611.Google Scholar
Gutin, L. 1936 On the sound field of a rotating propeller. Physik. Zeitschr. der Sowjetunion 9 (1), 57–71; (translated as 1948 NACA Tech. Memo. 1195).Google Scholar
Hanson, D. B. 1983 Compressible helicoidal surface theory for propeller aerodynamics and noise. AIAA J. 21 (6), 881–889.Google Scholar
Hanson, D. B. 1985 Noise of counter-rotation propellers. J. Aircraft 22 (7), 609–617.Google Scholar
Hanson, D. B.2001 Theory for broadband noise of rotor and stator cascades with inhomogeneous inflow turbulence including effects of lean and sweep. NASA CR-2001-210762.Google Scholar
Hanson, D. B. & Parzych, D. J.1993 Theory for noise of propellers in angular inflow with parametric studies and experimental verification. NASA CR-4499.Google Scholar
Harris, R. & Cuthbertson, R. D. 1987 UDF/727 flight test program. In 23rd AIAA/SAE/ASME/ASEE Joint Propulsion Conference, San Diego, CA, 29 June–2 July. AIAA Paper 1987-1733.Google Scholar
Hubbard, H. H.1948. Sound from dual-rotating and multiple single-rotating propellers. NACA Tech. Note 1654.Google Scholar
Jaouani, N., Roger, M., Thomas Node-Langlois, T. & Serre, G. 2016 Effect of a model leading-edge vortex on the blade aerodynamic response for application to CROR tonal noise predictions. In 22nd AIAA/CEAS Aeroacoustics Conference, Lyon, France, 30 May–1 June. AIAA Paper 2016-2744.Google Scholar
Jones, D. S. & Kline, N. 1958 Asymptotic expansion of multiple integrals and the method of stationary phase. J. Math. Phys. 37, 1–28.Google Scholar
Kingan, M. J. 2014 Advanced open rotor noise prediction. Aeronaut. J. 118 (1208), 1125–1135.Google Scholar
Kingan, M. J., Ekoule, C. E., Parry, A. B. & Britchford, K. 2014 Analysis of advanced open rotor noise measurements. In 20th AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, 16–20 June. AIAA Paper 2014-2745.Google Scholar
Kingan, M. J. & Self, R. 2009 Counter-rotation propeller tip vortex interaction noise. In 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Miami, FL, 11–13 May. AIAA Paper 2009-3135.Google Scholar
Lynam, E. J. H. & Webb, H. A.1919 The emission of sound by airscrews. British ARC R & M No. 624.Google Scholar
Metzger, F. B. & Rohrbach, C. 1979 Aeroacoustic design of the propfan. In 5th Aeroacoustics Conference, Seattle, WA, 12–14 March. AIAA Paper 1979-0610.Google Scholar
Moreau, S., Quaglia, M. E. & Fernando, R. 2015 A 3D analytical approach for open rotor blade vortex interaction (bvi) tonal noise. In 21st AIAA/CEAS Aeroacoustics Conference, Dallas, TX, 22–26 June. AIAA Paper 2015-2984.Google Scholar
Parker, R. & Lathoud, M. 2010 Green aeroengines: technology to mitigate aviation impact on environment. Proc. Inst. Mech. Engng, Part C: J. Mech. Engng Sci. 224 (3), 529–538.Google Scholar
Parry, A. B.1988 Theoretical prediction of counter-rotating propeller noise. PhD thesis, Department of Applied Mathematical Studies, University of Leeds.Google Scholar
Parry, A. B. 1995 The effect of blade sweep on the reduction and enhancement of supersonic propeller noise. J. Fluid Mech. 293, 181–206.Google Scholar
Parry, A. B. 1997 Modular prediction scheme for blade row interaction noise. J. Propul. Power 13 (3), 334–341.Google Scholar
Parry, A. B., Britchford, K. M., Kingan, M. J. & Sureshkumar, P. 2012 Aeroacoustic tests of isolated open rotors at high speed. In 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Colorado Springs, CO, 4–6 June. AIAA Paper 2012-2220.Google Scholar
Parry, A. B. & Crighton, D. G. 1989a Prediction of counter-rotation propeller noise. In 12th Aeroacoustics Conference, San Antonio, TX, April 10–12. AIAA Paper 89-1141.Google Scholar
Parry, A. B. & Crighton, D. G. 1989b Asymptotic theory of propeller noise. I. Subsonic single-rotation propeller. AIAA J. 27, 1184–1190.Google Scholar
Parry, A. B., Kingan, M. & Tester, B. J. 2011 Relative importance of open rotor tone and broadband noise sources. In 17th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Portland, OR, 5–8 June. AIAA Paper 2011-2763.Google Scholar
Parry, A. B. & Vianello, S. 2012 A project study of open rotor noise. Intl J. Aeroacoust. 11, 247–258.Google Scholar
Peake, N. & Boyd, W. K. 1993 Approximate method for the prediction of propeller noise near-field effects. J. Aircraft 30 (5), 603–610.Google Scholar
Peake, N. & Crighton, D. G. 1991a Lighthill quadrupole radiation in supersonic propeller acoustics. J. Fluid Mech. 223, 363–382.Google Scholar
Peake, N. & Crighton, D. G. 1991b An asymptotic theory of nearfield propeller acoustics. J. Fluid Mech. 232, 285–301.Google Scholar
Peters, A. & Spakovszky, Z. S. 2010 Rotor interaction noise in counter-rotating propfan propulsion systems. In ASME Turbo Expo 2010, Glasgow, UK, 14–18 June. ASME Paper GT2010-22554.Google Scholar
Quaglia, M. E., Léonard, T., Moreau, S. & Roger, M. 2017 3D analytical model for orthogonal blade–vortex interaction noise. J. Sound Vib. 399, 104–123.Google Scholar
Quaglia, M. E., Moreau, S., Roger, M. & Fernando, R. 2016 A preliminary semi-empirical approach for CROR noise modelling. In 22nd AIAA/CEAS Aeroacoustics Conference. AIAA Paper 2016-2743.Google Scholar
Roger, M. & Carazo, A. 2010 Blade-geometry considerations in analytical gust-airfoil interaction noise models. In 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7–9 June. AIAA Paper 2010-3799.Google Scholar
Roger, M., Schram, C. & Moreau, S. 2012 On open rotor blade–vortex interaction noise. In 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Colorado Springs, CO, 4–6 June. AIAA Paper 2012-2216.Google Scholar
Roger, M., Schram, C. & Moreau, S. 2014 On vortex-airfoil interaction noise including span-end effects, with application to open-rotor aeroacoustics. J. Sound Vib. 333, 283–306.Google Scholar
Rohrbach, C. & Metzger, F. B. 1975 The Prop-Fan – a new look in propulsors. In 2nd Aeroacoustics Conference, Hampton, VA, 24–26 March. AIAA Paper 75-1208.Google Scholar
Sharma, A. & Chen, H. 2013 Prediction of aerodynamic tonal noise from open rotors. J. Sound Vib. 332, 3832–3845.Google Scholar
Sohoni, N. G., Hall, C. A., Brandvik, T. & Parry, A. B. 2015 Prediction and measurement of unsteady blade surface pressures on an open rotor. In ASME Turbo Expo 2015, Montreal, Canada, 15–19 June. ASME Paper GT2012-42334.Google Scholar
Soulat, L., Kernemp, I., Sanjose, M., Moreau, S. & Fernando, R. 2013 Assessment and comparison of tonal noise models for counter-rotating open rotors. In 19th AIAA/CEAS Aeroacoustics Conference, Berlin, Germany, 27–29 May. AIAA Paper 2013-2201.Google Scholar
Soulat, L., Kernemp, I., Sanjose, M., Moreau, S. & Fernando, R. 2016 Numerical assessment of the tonal noise of counter-rotating open rotors at approach. Intl J. Aeroacoust. 15, 23–40.Google Scholar
Stürmer, A. & Yin, J. 2009 Low-speed aerodynamics and aeroacoustics of CROR propulsion systems. In 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Miami, FL, 11–13 May. AIAA Paper 2009-3134.Google Scholar
Stürmer, A., Marquez Gutierrez, C. O., Roosenboom, E. W. M., Schröder, A., Geisler, R., Pallek, D., Agoc, J. & Neitzke, K. 2012 Experimental and numerical investigation of a contra rotating open-rotor flowfield. J. Aircraft 49 (6), 1868–1877.Google Scholar
Van Zante, D. E. & Envia, E. 2014 Prediction of the aero-acoustic performance of open rotors. In ASME Turbo Expo, Dusseldorf, Germany, 16–20 June. ASME Paper No. GT2014–26413.Google Scholar
Whitfield, C. E., Mani, R. & Gliebe, P. R.1990a High speed turboprop: aeroacoustic study (counterrotation). Volume I: model development. NASA CR185241.Google Scholar
Whitfield, C. E., Mani, R. & Gliebe, P. R.1990b High speed turboprop: aeroacoustic study (counterrotation). Volume II: computer programs. NASA CR185242.Google Scholar
Young, R. H. 1951 Contra-rotating axial flow fans. J. Inst. Heating Ventilating Engng 18 (187), 448–477.Google Scholar
Zachariadis, A., Hall, C. A. & Parry, A. B. 2011 Contra-rotating open rotor operation for improved aerodynamics and noise at takeoff. In ASME Turbo Expo 2011, Vancouver, Canada, 6–10 June. ASME Paper GT2011-45205.Google Scholar
Zhang, W., Wang, X., Jing, X., Liang, A. & Sun, X. 2017 Three-dimensional analysis of vane sweep effects on fan interaction noise. J. Sound Vib. 391, 73–94.Google Scholar