Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-16T06:14:56.618Z Has data issue: false hasContentIssue false

Acoustic resonances in a high-lift configuration

Published online by Cambridge University Press:  14 June 2007

STEFAN HEIN
Affiliation:
Institute of Aerodynamics and Flow Technology, DLR Göttingen, Germany
THORSTEN HOHAGE
Affiliation:
Institute for Numerical and Applied Mathematics, University of Göttingen, Germany
WERNER KOCH
Affiliation:
Institute of Aerodynamics and Flow Technology, DLR Göttingen, Germany
JOACHIM SCHÖBERL
Affiliation:
Centre for Computational Engineering Science, RWTH Aachen University, Germany

Abstract

Low- and high-frequency acoustic resonances are computed numerically via a high-order finite-element code for a generic two-dimensional high-lift configuration with a leading-edge slat. Zero mean flow is assumed, approximating the low-Mach-number situation at aircraft landing and approach. To avoid unphysical reflections at the boundaries of the truncated computational domain, perfectly matched layer absorbing boundary conditions are implemented in the form of the complex scaling method of atomic and molecular physics. It is shown that two types of resonance exist: resonances of surface waves which scale with the total airfoil length and longitudinal cavity-type resonances which scale with the slat cove length. Minima exist in the temporal decay rate which can be associated with the slat cove resonances and depend on the slat cove geometry. All resonances are damped owing to radiation losses. However, if coherent noise sources exist, as observed in low-Reynolds-number experiments, these sources can be enhanced acoustically by the above resonances if the source frequency is close to a resonant frequency.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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

REFERENCES

Agarwal, A. & Morris, P. 2002 Investigation of the physical mechanisms of tonal sound generation by slats. AIAA Paper 2002-2575.CrossRefGoogle Scholar
Andreou, C., Graham, W. & Shin, H.-C. 2006 Aeroacoustic study of airfoil leading edge high-lift devices. AIAA Paper 20062515.Google Scholar
Bérenger, J. 1994 A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185200.CrossRefGoogle Scholar
Chew, W. & Weedon, W. 1994 A 3-D perfectly matched medium from modified Maxwell's equation with stretched coordinates. Microwave Optical Technol. Lett. 7 (13), 599604.CrossRefGoogle Scholar
Chew, W., Jin, J. & Michielssen, E. 1997 Complex coordinate stretching as a generalized absorbing boundary condition. Microwave Optical Technol. Lett. 15 (3), 144147.3.0.CO;2-G>CrossRefGoogle Scholar
Choudhari, M. & Khorrami, M. 2006 Slat cove unsteadiness: effect of 3D flow structure. AIAA Paper 2006-0211.CrossRefGoogle Scholar
Collino, F. & Monk, P. 1998 The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19, 20612090.Google Scholar
Crighton, D. 1991 Airframe noise. In Aeroacoustics of Flight Vehicles: Theory and Practice. Vol. 1: Noise Sources (ed. Hubbard, H. H.), pp. 391447. NASA.Google Scholar
Czech, M., Crouch, J., Stoker, R., Strelets, M. & Garbaruk, A. 2006 Cavity noise generation for circular and rectangular vent holes. AIAA Paper 2006-2508.CrossRefGoogle Scholar
Davy, R., Moens, F. & Remy, H. 2002 Aeroacoustic behaviour of a 1/11 scale Airbus model in the open anechoic wind tunnel CEPRA 19. AIAA Paper 2002-2412.CrossRefGoogle Scholar
Deck, S. 2005 Zonal-detached-eddy simulation of the flow around a high-lift configuration. AIAA J. 43, 23722384.CrossRefGoogle Scholar
Dobrzynski, W. & Pott-Pollenske, M. 2001 Slat noise source studies for farfield noise prediction. AIAA Paper 2001-2158.CrossRefGoogle Scholar
Dobrzynski, W., Nagakura, K., Gehlhar, B. & Buschbaum, A. 1998 Airframe noise studies on wings with deployed high-lift devices. AIAA Paper 98-2337.Google Scholar
Dobrzynski, W., Gehlhar, B. & Buchholz, H. 2001 Model and full scale high-lift wing wind tunnel experiments dedicated to airframe noise reduction. Aerosp. Sci. Technol. 5, 2733.Google Scholar
Fischer, M., Friedel, H., Holthusen, H., Gölling, B. & Emunds, R. 2006 Low noise design trends derived from wind tunnel testing on advanced high-lift devices. AIAA Paper 2006-2562.CrossRefGoogle Scholar
Grosche, F.-R., Schneider, G. & Stiewitt, H. 1997 Wind tunnel experiments on airframe noise sources of transport aircraft. AIAA Paper 97-1642.CrossRefGoogle Scholar
Guo, Y. 1997 A model for slat noise generation. AIAA Paper 97-1647.CrossRefGoogle Scholar
Hayes, J., Horne, W., Soderman, P. & Bent, P. 1997 Airframe noise characteristics of a 4.7% scale DC-10 model. AIAA Paper 97-1594.CrossRefGoogle Scholar
Hein, S., Hohage, T. & Koch, W. 2004 On resonances in open systems. J. Fluid Mech. 506, 255284.CrossRefGoogle Scholar
Hein, S., Koch, W. & Schöberl, J. 2005 Acoustic resonances in a 2D high lift configuration and a 3D open cavity. AIAA Paper 200-2867.CrossRefGoogle Scholar
Helmholtz, H. 1954 On the Sensations of Tone, 2nd edn. Dover.Google Scholar
Heyman, E. & Felsen, L. 1983 Creeping waves and resonances in transient scattering by smooth convex objects. IEEE Trans. Antennas Propagat. 31, 426437.Google Scholar
Hislop, P. & Sigal, I. 1996 Introduction to Spectral Theory. Springer.Google Scholar
Hohage, T., Schmidt, F. & Zschiedrich, L. 2003a Solving time-harmonic scattering problems based on the pole condition. I: Theory. SIAM J. Math. Anal. 35, 183210.Google Scholar
Hohage, T., Schmidt, F. & Zschiedrich, L. 2003b Solving time-harmonic scattering problems based on the pole condition. II: Convergence of the PML method. SIAM J. Math. Anal. 35, 547560.Google Scholar
Horne, W., James, K., Arledge, T., Soderman, P., Burnside, N. & Jaeger, S. 2005 Measurements of 26%-scale 777 airframe noise in the NASA A mes 40 by 80 foot wind tunnel. AIAA Paper 2005-2810.CrossRefGoogle Scholar
Hu, F. 2004 Absorbing boundary conditions. Intl J. Comput. Fluid Dyn. 18, 513522.CrossRefGoogle Scholar
Jenkins, L., Khorrami, M. & Choudhari, M. 2004 Characterization of unsteady flow structures near leading-edge slat: Part I. PIV measurements. AIAA Paper 20042801.Google Scholar
Kaepernick, K., Koop, L. & Ehrenfried, K. 2005 Investigation of the unsteady flow field inside a leading edge slat cove. AIAA Paper 20052813.Google Scholar
Khorrami, M. 2003 Understanding slat noise sources. In Proc. EUROMECH Colloquium 449, Computational Aeroacoustics: From Acoustic Sources Modeling to Far-Field Radiated Noise Prediction, Chamonix, France.Google Scholar
Khorrami, M., Berkman, M. & Choudhari, M. 2000 Unsteady flow computations of a slat with a blunt trailing edge. AIAA J. 38, 20502058.CrossRefGoogle Scholar
Khorrami, M., Singer, B. & Berkman, M. 2002a Time-accurate simulations and acoustic analysis of slat free-shear layer. AIAA J. 40, 12841291.Google Scholar
Khorrami, M., Singer, B. & Lockard, D. 2002b Time-accurate simulations and acoustic analysis of slat free-shear layer: Part II. AIAA Paper 20022579.Google Scholar
Khorrami, M., Choudhari, M. & Jenkins, L. 2004 Characterization of unsteady flow structures near leading-edge slat: Part II. 2D computations. AIAA Paper 20042802.Google Scholar
Koch, W. 2005 Acoustic resonances in rectangular open cavities. AIAA J. 43, 23422349.CrossRefGoogle Scholar
Lassas, M. & Somersalo, E. 1998 On the existence and convergence of the solution of PML equations. Computing 60, 229241.CrossRefGoogle Scholar
Lax, P. & Phillips, R. 1967 Scattering Theory. Academic.Google Scholar
Michel, U., Barsikow, B., Helbig, J., Hellmig, M. & Schüttepelz, M. 1998 Flyover noise measurements on landing aircraft with a microphone array. AIAA Paper 982336.Google Scholar
Moiseyev, N. 1998 Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302, 211293.CrossRefGoogle Scholar
Morse, P. & Ingard, K. 1968 Theoretical Acoustics. McGraw-Hill.Google Scholar
Oerlemans, S. & Sijtsma, P. 2004 Acoustic array measurements of a 1:10.6 scaled Airbus A340 model. AIAA Paper 20042924.Google Scholar
Olson, S., Thomas, F. & Nelson, R. 2000 A preliminary investigation into slat noise production mechanisms in high-lift configuration. AIAA Paper 20004508.Google Scholar
Olson, S., Thomas, F. & Nelson, R. 2001 Mechanisms of slat noise production in a 2D multi-element airfoil configuration. AIAA Paper 20012156.Google Scholar
Piet, J., Michel, U. & Böhning, P. 2002 Localization of the acoustic sources of the A340 with a large phased microphone array during flight tests. AIAA Paper 20022506.Google Scholar
Pott-Pollenske, M., Alvarez-Gonzalez, J. & Dobrzynski, W. 2003 Effect of slat gap on farfield noise and correlation with local flow characteristics. AIAA Paper 20033228.Google Scholar
Reed, M. & Simon, B. 1978 Methods of Modern Mathematical Physics IV. Academic.Google Scholar
Roger, M. & Pèrennés, S. 2000 Low-frequency noise sources in two-dimensional high-lift devices. AIAA Paper 2000–1972.Google Scholar
Rossiter, J. 1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. ARC R.&M. 3438.Google Scholar
Schöberl, J. 1997 NETGEN An advancing front 2D/3D-mesh generator based on abstract rules. Comput. Visualiz. Sci. 1, 4152.Google Scholar
Singer, B., Lockard, D. & Brentner, K. 2000 Computational aeroacoustic analysis of slat trailing-edge flow. AIAA J. 38, 15581564.Google Scholar
Soderman, P., Kafyeke, F., Burnside, N., Chandrasekharan, R., Jaeger, S. & Boudreau, J. 2002 Aerodynamic noise induced by laminar and turbulent boundary layers over rectangular cavities. AIAA Paper 20022406.Google Scholar
Stoker, R., Guo, Y., Street, C. & Burnside, N. 2003 Airframe noise source locations of a 777 aircraft in flight and comparisons with past model scale tests. AIAA Paper 20033232.Google Scholar
Storms, B., Hayes, J., Moriarty, P. & Ross, J. 1999 Aeroacoustic measurements of slat noise on a three-dimensional high-lift system. AIAA Paper 991957.Google Scholar
Szabó, B. & Babuška, I. 1991 Finite Element Analysis. Wiley.Google Scholar
Takeda, K., Ashcroft, G., Zhang, X. & Nelson, P. 2001 Unsteady aerodynamics of slat cove flow in a high-lift device configuration. AIAA Paper 2001–0706.Google Scholar
Takeda, K., Zhang, X. & Nelson, P. 2002 Unsteady aerodynamics and aeroacoustics of a high-lift device configuration. AIAA Paper 2002–0570.Google Scholar
Takeda, K., Zhang, X. & Nelson, P. 2004 Computational aeroacoustic simulations of leading-edge slat flow. J. Sound Vib. 270, 559572.CrossRefGoogle Scholar
Tam, C. 1976 The acoustic modes of a two-dimensional rectangular cavity. J. Sound Vib. 49, 353364.Google Scholar
Tam, C. & Pastouchenko, N. 2001 Gap tones. AIAA J. 39, 14421448.Google Scholar
Taylor, M. 1996 Partial Differential Equations II, Springer.Google Scholar
Terracol, M., Labourasse, E., Manoha, E. & Sagaut, P. 2003 Simulation of the 3D unsteady flow in a slat cove for noise prediction. AIAA Paper 20033234.Google Scholar
Überall, H., Dragonette, L. & Flax, L. 1977 Relation between creeping waves and normal modes of vibration of a curved body. J. Acoust. Soc. Am. 61, 711715.Google Scholar
Zworski, M. 1999 Resonances in physics and geometry. Not. AMS 46, 319328.Google Scholar