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A coupled time-reversal/complex differentiation method for aeroacoustic sensitivity analysis: towards a source detection procedure

Published online by Cambridge University Press:  02 December 2009

ARIANE DENEUVE ,
PHILIPPE DRUAULT ,
RÉGIS MARCHIANO  and
PIERRE SAGAUT
ARIANE DENEUVE
Affiliation:
Institut Jean Le Rond d'Alembert, Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, case 162, 75252 Paris Cedex 05, France
PHILIPPE DRUAULT*
Affiliation:
Institut Jean Le Rond d'Alembert, Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, case 162, 75252 Paris Cedex 05, France
RÉGIS MARCHIANO
Affiliation:
Institut Jean Le Rond d'Alembert, Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, case 162, 75252 Paris Cedex 05, France
PIERRE SAGAUT
Affiliation:
Institut Jean Le Rond d'Alembert, Université Pierre et Marie Curie-Paris 6, 4 place Jussieu, case 162, 75252 Paris Cedex 05, France
*
†Email address for correspondence: [email protected]
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Abstract

Defining and identifying the aeroacoustic sources in a turbulent flow is a great challenge especially for noise control strategy. The purpose of the present study consists in proposing a new methodology to localize regions associated with sound generation. These regions are associated, in the present work, with those of high sensitivity of the acoustic field, using the heuristic argument that modifying the flow in these regions would lead to a very significant change in the radiated noise. The proposed method relies on the efficient coupling between the time-reversal theory applied to the Euler equations and the complex differentiation method to compute the sensitivity variable. To the knowledge of the authors, this is the first time that the time-reversal technique is applied to vectorial hydrodynamic equations, in place of the classical scalar wave equation. Subsequently, regions associated with sound generation are related to spatiotemporal events which exhibit the maximum of sensitivity to acoustical disturbances measured in far field. The proposed methodology is then successively tested on three cases for which the nature of the source is different: injection of mass, vibrating surfaces and flow instabilities arising in a plane mixing layer flow. For each test case, the two-dimensional Euler equations are solved using a numerical solver based on a pseudo-characteristics formulation. During these computations flow, variables are stored only at the computational boundaries. These variables are time reversed and relevant information concerning the acoustical disturbances is tagged using complex differentiation in order to lead the sensitivity analysis. The same numerical solver is used to access the evolution of the time-reversed variables. In each test case, the proposed methodology allows to localize successfully zones associated with noise generation.

JFM classification

Acoustics: Aeroacoustics Boundary Layers: Free shear layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 181 - 212
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Anderson, W. K., Newman, J. C., Whitfield, D. L. & Nielsen, E. J. 2001 Sensitivity analysis for the Navier–Stokes equations on unstructured meshes using complex variables. AIAA J. 1, 56–63.CrossRefGoogle Scholar
Barone, M. F. & Lele, S. K. 2005 Receptivity of the compressible mixing layer. J. Fluid Mech. 540, 301–335.CrossRefGoogle Scholar
Bogey, C. & Bailly, C. 2007 An analysis of the correlations between the turbulent flow and the sound pressure fields of subsonic jets. J. Fluid Mech. 583, 71–91.CrossRefGoogle Scholar
Bogey, C., Bailly, C. & Juve, D. 2000 Numerical simulation of sound generated by vortex pairing in a mixing layer. AIAA J. 40 (2), 235–243.CrossRefGoogle Scholar
Cassereau, D. & Fink, M. 1992 Time-reversal of ultrasonic fields. III. Theory of the closed time-reversal cavity. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39 (5), 579–592.CrossRefGoogle ScholarPubMed
Colonius, T. & Lele, S. K. 2004 Computational aeroacoustics: progress on nonlinear problems of sound generation. Prog. Aerosp. Sci. 40 (6), 345–416.CrossRefGoogle Scholar
Colonius, T., Lele, S. K. & Moin, P. 1994 The scattering of sound waves by a vortex numerical simulations and analytical solutions. J. Fluid Mech. 260, 271–298.CrossRefGoogle Scholar
Colonius, T., Lele, S. K. & Moin, P. 1997 Sound generation in a mixing layer. J. Fluid Mech. 330, 375–409.CrossRefGoogle Scholar
Dowling, A. P. & Ffwocs Williams, J. E. 2000 Sound and Sources of Sound. Ellis Horwood.Google Scholar
Druault, Ph., Yu, M. & Sagaut, P. 2009 Quadratic stochastic estimation of far field acoustic pressure with coherent structure events in a 2D compressible plane mixing layer. Intl J. Numer. Methods Fluids, doi:10.1002/fld.2047 (in press).CrossRefGoogle Scholar
Fink, M., Cassereau, D., Derode, A., Prada, C., Roux, P., Tanter, M., Thomas, J.-L. & Wu, F. 2000 Time-reversed acoustics. Prog. Rep. Phys. 63, 1933–1995.CrossRefGoogle Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.Google Scholar
Goldstein, M. E. 2003 A generalized acoustic analogy. J. Fluid Mech. 488, 315–333.CrossRefGoogle Scholar
Goldstein, M. E. & Leib, S. J. 2008 The aeroacoustics of slowly diverging supersonic jets. J. Fluid Mech. 600, 291–337.CrossRefGoogle Scholar
Howe, M. S. 2003 Theory of Vortex Sound. Cambridge Texts in Applied Mathematics, vol. 33. Cambridge University Press.Google Scholar
Jameson, A., Martinelli, L. & Pierce, N. 1998 Optimum aerodynamic design using the Navier–Stokes equations. J. Theor. Comput. Fluid Dyn. 10, 213–237.CrossRefGoogle Scholar
Jordan, P. & Gervais, Y. 2008 Subsonic jet aeroacoustics: associating experiment, modelling and simulation. Exp. Fluids 44 (1), 1–21.CrossRefGoogle Scholar
Kleinman, R. R. & Freund, J. B. 2008 The sound from mixing layers simulated with different ranges of turbulence scales. Phys. Fluids 20, 101503.CrossRefGoogle Scholar
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aeronaut. Soc. 20 (10), 657–682.CrossRefGoogle Scholar
Leclerc, E., Sagaut, P. & Mohammadi, B. 2006 On the use of incomplete sensitivities for feedback control of laminar vortex shedding. Comput. Fluids 35 (10), 1432–1443.CrossRefGoogle Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically: I. General theory. Proc. R. Soc. Lond. 211, 564–587.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Lilley, G. M. 1974 On the noise from jets. AGARD CP-131, 13.1–13.12.Google Scholar
Lu, S. Y. & Sagaut, P. 2007 a Direct sensitivity analysis for smooth unsteady compressible flows using complex differentiation. Intl J. Numer. Methods Fluids 53, 1863–1886.CrossRefGoogle Scholar
Lu, S. Y. & Sagaut, P. 2007 b Pseudo-characteristic formulation and dynamic boundary conditions for computational aeroacoustics. Intl J. Numer. Methods Fluids 53, 201–227.CrossRefGoogle Scholar
Lund, F. & Rojas, C. 1989 Ultrasound as probe of turbulence. Physica D 37, 508–514.CrossRefGoogle Scholar
Lyness, J. N. & Moler, C. B. 1967 Numerical differentiation of analytic functions. SIAM J. Numer. Anal. 4, 202–210.CrossRefGoogle Scholar
Peake, N. 2004 A note on “Computational aeroacoustics examples showing the failure of the acoustic analogy theory to identify the correct noise sources” by CKW Tam. J. Comput. Acoust. 12 (4), 631–634.CrossRefGoogle Scholar
Pierce, A. D. 1989 Acoustics, an Introduction to Its Physical Principles and Applications. Acoustical Society of America.Google Scholar
Roux, P. & Fink, M. 1995 Experimental evidence in acoustics of the violiation of time-reversal invariance induced by vorticity. Europhys. Lett. 32, 25–29.CrossRefGoogle Scholar
Roux, P., de Rosny, J., Tanter, M. & Fink, M. 1997 The Aharonov–Bohm effect revisited by an acoustic time reversal mirror. Phys. Rev. Lett. 79, 3170–3173.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Sesterhenn, J. 2001 A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes. Comput. Fluids 30, 37–67.CrossRefGoogle Scholar
Shu, C. W. & Osher, S. 1989 Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 83, 32–78.CrossRefGoogle Scholar
Spagnoli, B. & Airiau, C. 2008 Adjoint analysis for noise control in a two-dimensional compressible mixing layer. Comput. Fluids 37, 475–486.CrossRefGoogle Scholar
Spalart, R. P. 2007 Application of full and simplified acoustic analogies to an elementary problem. J. Fluid Mech. 578, 113–118.CrossRefGoogle Scholar
Squire, W. & Trapp, G. 1998 Using complex variables to estimate derivatives of real functions. SIAM Rev. 10 (1), 110–112.CrossRefGoogle Scholar
Tam, C. K. W. 2002 Computational aeroacoustics examples showing the failure of the acoustic analogy theory to identify the correct noise sources. J. Comput. Acoust. 10 (4), 387–405.CrossRefGoogle Scholar
Tam, C. K. W. & Auriault, L. 1998 Mean flow refraction effects on sound radiated from localized sources in a jet. J. Fluid Mech. 370, 149–170.CrossRefGoogle Scholar
Vatsa, V. N. 2000 Computation of sensitivity derivatives of Navier–Stokes equations using complex variables. Adv. Engng Softw. 31 (8-9), 655–659.CrossRefGoogle Scholar
Wagner, C., Hüttl, T. & Sagaut, P. (ed.) 2007 Large-Eddy Simulation for Acoustics. Cambridge University Press.CrossRefGoogle Scholar
Wang, M., Freund, J. B. & Lele, S. K. 2006 Computational prediction of flow-generated sound. Annu. Rev. Fluid Mech. 38, 483–512.CrossRefGoogle Scholar
Wei, M. J. & Freund, J. B. 2006 A noise-controlled free shear flow. J. Fluid Mech. 546, 123–152.CrossRefGoogle Scholar