Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-21T06:41:26.607Z Has data issue: false hasContentIssue false
  • English
  • Français

A global analysis of tonal noise in flows around aerofoils

Published online by Cambridge University Press:  30 July 2014

Miguel Fosas de Pando Open the ORCID record for Miguel Fosas de Pando [Opens in a new window] ,
Peter J. Schmid  and
Denis Sipp
Miguel Fosas de Pando*
Affiliation:
LadHyX, CNRS–Ecole Polytechnique, 91128 Palaiseau, France
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Denis Sipp
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
*
†Present address: Departamento de Ingeniería Mecánica y Diseño Industrial, Escuela Superior de Ingeniería, Universidad de Cádiz, c/Chile 1, 11002 Cádiz, Spain. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The generation of discrete acoustic tones in the compressible flow around an aerofoil is addressed in this work by means of nonlinear numerical simulations and global stability analyses. The nonlinear simulations confirm the appearance of discrete tones in the acoustic spectrum and, for the chosen flow case, the global stability analyses of the mean-flow dynamics reveal that the linearized operator is stable. However, the flow response to incoming disturbances exhibits important transient growth effects that culminate in the onset of aeroacoustic feedback loops, involving instability processes on the suction- and pressure-surface boundary layers together with their cross-interaction by acoustic radiation at the trailing edge. The features of the aeroacoustic feedback loops and the appearance of discrete tones are then related to the features of the least-stable modes in the global spectrum: the spatial structure of the direct modes displays the coupled dynamics of hydrodynamic instabilities on the suction surface and in the near wake. Finally, different families of global modes will be identified and the dynamics that they represent will be discussed.

JFM classification

Acoustics: Aeroacoustics Instability: Instability Wakes/Jets: Separated flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 754 , 10 September 2014 , pp. 5 - 38
Copyright
© 2014 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

Adams, N. A. & Shariff, K. 1996 A high-resolution hybrid compact-ENO scheme for shock–turbulence interaction problems. J. Comput. Phys. 127 (1), 27–51.Google Scholar
Akbar, T.2010 Simulation of three-dimensional flows past infinite cylindrical bodies. PhD thesis, Université de Strasbourg.Google Scholar
Alizard, F., Cherubini, S. & Robinet, J.-C. 2009 Sensitivity and optimal forcing response in separated boundary layer flows. Phys. Fluids 21, 064108.Google Scholar
Arbey, H. & Bataille, J. 1983 Noise generated by aerofoil profiles placed in a uniform laminar flow. J. Fluid Mech. 134, 33–47.Google Scholar
Arcondoulis, E., Doolan, C. J. & Zander, A. C.2009 Aerofoil noise measurements at various angles of attack and low Reynolds number. In Proceedings of ACOUSTICS 2009 Adelaide, 23rd–25th November 2009. Australian Acoustics Society.Google Scholar
Barkley, D. 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75 (5), 750–756.Google Scholar
Bodony, D. J. 2006 Analysis of sponge zones for computational fluid mechanics. J. Comput. Phys. 212 (2), 681–702.Google Scholar
Brooks, T. F., Pope, D. S. & Marcolini, M. A.1989 Aerofoil self-noise and prediction. NASA Ref. Pub. 1218.Google Scholar
Cherubini, S., Robinet, J.-Ch. & De Palma, P. 2010 The effects of non-normality and nonlinearity of the Navier–Stokes operator on the dynamics of a large laminar separation bubble. Phys. Fluids 22, 014102.Google Scholar
Chong, T. P. & Joseph, P. 2012 ‘Ladder’ structure in tonal noise generated by laminar flow around an aerofoil. J. Acoust. Soc. Am. 131 (6), 461–467.Google Scholar
Chu, B. T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica 1 (3), 215–234.Google Scholar
Desquesnes, G., Terracol, M. & Sagaut, P. 2007 Numerical investigation of the tone noise mechanism over laminar aerofoils. J. Fluid Mech. 591, 155–182.Google Scholar
Dovgal, A. V., Kozlov, V. V. & Michalke, A. 1994 Laminar boundary layer separation: instability and associated phenomena. Prog. Aerosp. Sci. 30 (1), 61–94.CrossRefGoogle Scholar
Edwards, W. S., Tuckerman, L. S., Friesner, R. A. & Sorensen, D. C. 1994 Krylov methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 110 (1), 82–102.Google Scholar
Ehrenstein, U. & Gallaire, F. 2008 Two-dimensional global low-frequency oscillations in a separating boundary-layer flow. J. Fluid Mech. 614, 315–327.Google Scholar
Fink, M. R. 1975 Prediction of aerofoil tone frequencies. J. Aircraft 12 (2), 118–120.Google Scholar
Fosas de Pando, M., Sipp, D. & Schmid, P. J. 2012 Efficient evaluation of the direct and adjoint linearized dynamics from compressible flow solvers. J. Comput. Phys. 231 (23), 7739–7755.Google Scholar
Gallaire, F., Marquillie, M. & Ehrenstein, U. 2007 Three-dimensional transverse instabilities in detached boundary layers. J. Fluid Mech. 571, 221–233.Google Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013 Modal and transient dynamics of jet flows. Phys. Fluids 044103.Google Scholar
Le Garrec, T., Gloerfelt, X. & Corre, C. 2008 A numerical insight into the effect of confinement on trailing edge noise. J. Acoust. Soc. Am. 123 (5), 3022.CrossRefGoogle Scholar
Hammond, D. A. & Redekopp, L. G. 1998 Local and global instability properties of separation bubbles. Eur. J. Mech. (B/Fluids) 17 (2), 145–164.Google Scholar
Hanifi, A., Schmid, P. J. & Henningson, D. S. 1996 Transient growth in compressible boundary layer flow. Phys. Fluids 8, 826–837.CrossRefGoogle Scholar
Hernández, V., Román, J. E. & Vidal, V. 2005 SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31 (3), 351–362.Google Scholar
Jones, L. E. & Sandberg, R. D. 2011 Numerical analysis of tonal aerofoil self-noise and acoustic feedback-loops. J. Sound Vib. 330, 6137–6152.Google Scholar
Jones, L. E., Sandberg, R. D. & Sandham, N. D. 2008 Direct numerical simulations of forced and unforced separation bubbles on an aerofoil at incidence. J. Fluid Mech. 602, 175–207.Google Scholar
Jones, L. E., Sandberg, R. D. & Sandham, N. D. 2010 Stability and receptivity characteristics of a laminar separation bubble on an aerofoil. J. Fluid Mech. 648, 257–296.CrossRefGoogle Scholar
Kennedy, C. A., Carpenter, M. H. & Lewis, R. M. 2000 Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations. Appl. Numer. Maths 35 (3), 177–219.Google Scholar
Kingan, M. J. & Pearse, J. R. 2009 Laminar boundary layer instability noise produced by an aerofoil. J. Sound Vib. 322 (4–5), 808–828.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.Google Scholar
Lodato, G., Domingo, P. & Vervisch, L. 2008 Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows. J. Comput. Phys. 227 (10), 5105–5143.Google Scholar
Longhouse, R. E. 1977 Vortex shedding noise of low tip speed, axial flow fans. J. Sound Vib. 53 (1), 25–46.Google Scholar
Marquet, O., Lombardi, M., Chomaz, J.-M., Sipp, D. & Jacquin, L. 2009 Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities. J. Fluid Mech. 622, 1–21.Google Scholar
Marquet, O., Sipp, D., Chomaz, J.-M. & Jacquin, L. 2008 Amplifier and resonator dynamics of a low-Reynolds-number recirculation bubble in a global framework. J. Fluid Mech. 605, 429–443.Google Scholar
McAlpine, A., Nash, E. C. & Lowson, M. V. 1999 On the generation of discrete frequency tones by the flow around an aerofoil. J. Sound Vib. 222 (5), 753–779.Google Scholar
Nakano, T., Fujisawa, N. & Lee, S. 2006 Measurement of tonal-noise characteristics and periodic flow structure around NACA0018 aerofoil. Exp. Fluids 40 (3), 482–490.Google Scholar
Nash, E. C., Lowson, M. V. & McAlpine, A. 1999 Boundary-layer instability noise on aerofoils. J. Fluid Mech. 382, 27–61.Google Scholar
Paterson, R. W., Vogt, P. G., Fink, M. R. & Much, C. L. 1973 Vortex noise of isolated aerofoils. J. Aircraft 10 (5), 296–302.Google Scholar
Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104–129.Google Scholar
Sandberg, R. D., Jones, L. E., Sandham, N. D. & Joseph, P. F. 2009 Direct numerical simulations of tonal noise generated by laminar flow past aerofoils. J. Sound Vib. 320, 838–858.Google Scholar
Schmid, P. J. & Henningson, D. S. 2002 On the stability of a falling liquid curtain. J. Fluid Mech. 463, 163–171.CrossRefGoogle Scholar
Sesterhenn, J. 2000 A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes. Comput. Fluids 30 (1), 37–67.Google Scholar
Sidje, R. B. 1998 EXPOKIT: a software package for computing matrix exponentials. ACM Trans. Math. Softw. 24 (1), 130–156.Google Scholar
Stewart, G. W. 2002 A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Applics. 23 (3), 601–614.CrossRefGoogle Scholar
Takagi, Y., Fujisawa, N., Nakano, T. & Nashimoto, A. 2006 Cylinder wake influence on the tonal noise and aerodynamic characteristics of a NACA0018 aerofoil. J. Sound Vib. 297 (3–5), 563–577.CrossRefGoogle Scholar
Tam, C. K. W. 1974 Discrete tones of isolated aerofoils. J. Acoust. Soc. Am. 55 (6), 1173–1177.Google Scholar
Tam, C. K. W. & Ju, H. 2011 Aerofoil tones at moderate Reynolds number. J. Fluid Mech. 690, 536–570.Google Scholar
Trefethen, L. N. 1997 Pseudospectra of linear operators. SIAM Rev. 39 (3), 383–406.Google Scholar
Wright, S. E. 1976 The acoustic spectrum of axial flow machines. J. Sound Vib. 45 (2), 165–223.Google Scholar