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Disturbance energy transport and sound production in gaseous combustion

Published online by Cambridge University Press:  12 July 2012

Michael J. Brear ,
Frank Nicoud ,
Mohsen Talei ,
Alexis Giauque  and
Evatt R. Hawkes
Michael J. Brear*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville 3010, Australia
Frank Nicoud
Affiliation:
Université Montpellier II, I3M, Place E. Bataillon, 34095 Montpellier, France Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), 42 Avenue Gaspard Coriolis, 31057 Toulouse CEDEX 01, France
Mohsen Talei
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville 3010, Australia
Alexis Giauque
Affiliation:
Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), 42 Avenue Gaspard Coriolis, 31057 Toulouse CEDEX 01, France Office National d’Etudes et de Recherches Aerospatiales (ONERA), 29 av. de la Div. Leclerc, F-92322 Châtillon, France
Evatt R. Hawkes
Affiliation:
School of Photovoltaic and Renewable Energy Engineering / School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052, Australia
*
†Email address for correspondence: [email protected]
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Abstract

This paper presents an analysis of the energy transported by disturbances in gaseous combustion. It extends the previous work of Myers (J. Fluid Mech., vol. 226, 1991, 383–400) and so includes non-zero mean-flow quantities, large-amplitude disturbances, varying specific heats and chemical non-equilibrium. This extended form of Myers’ ‘disturbance energy’ then enables complete identification of the conditions under which the famous Rayleigh source term can be derived from the equations governing combusting gas motion. These are: small disturbances in an irrotational, homentropic, non-diffusive (in terms of species, momentum and energy) and stationary mean flow at chemical equilibrium. Under these assumptions, the Rayleigh source term becomes the sole source term in a conservation equation for the classical acoustic energy. It is also argued that the exact disturbance energy flux should become an acoustic energy flux in the far-field surrounding a (reacting or non-reacting) jet. In this case, the volume integral of the disturbance energy source terms are then directly related to the area-averaged far-field sound produced by the jet. This is demonstrated by closing the disturbance energy budget over a set of aeroacoustic, direct numerical simulations of a forced, low-Mach-number, laminar, premixed flame. These budgets show that several source terms are significant, including those involving the mean-flow and entropy fields. This demonstrates that the energetics of sound generation cannot be examined by considering the Rayleigh source term alone.

JFM classification

Reacting Flows: Combustion Compressible Flows: Gas dynamics Acoustics: Jet noise
Type
Papers
Information
Journal of Fluid Mechanics , Volume 707 , 25 September 2012 , pp. 53 - 73
Copyright
Copyright © Cambridge University Press 2012

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References

1. Baum, M. 1994 Etude de l’allumage et de la structure des flammes turbulentes. PhD thesis, Ecole Centrale Paris.Google Scholar
2. Bloxsidge, G. J., Dowling, A. P., Hooper, N. & Langhorne, P. J. 1988 Active control of reheat buzz. AIAA J. 26 (7), 783–790.Google Scholar
3. Bourlioux, A., Cuenot, B. & Poinsot, T. 2000 Asymptotic and numerical study of the stabilization of diffusion flames by hot gas. Combust. Flame 120 (1–2), 143–159.CrossRefGoogle Scholar
4. Candel, S. 2002 Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 29, 1–28.Google Scholar
5. Cantrell, R. H. & Hart, R. W. 1964 Interaction between sound and flow in acoustic cavities: mass, momentum and energy considerations. J. Acoust. Soc. Amer. 36, 697–706.Google Scholar
6. Chu, B. T. 1956 Stability of systems containing a heat source: the Rayleigh criterion. In NACA Research memorandum (NACA RM 56D27).Google Scholar
7. Chu, B. T. 1965 On the energy transfer to small disturbances in fluid flow. Part 1. Acta Mechanica 1, 215–234.CrossRefGoogle Scholar
8. Colonius, T., Lele, S. K. & Moin, P. 1997 Sound generation in a mixing layer. J. Fluid Mech. 330, 375–409.CrossRefGoogle Scholar
9. Corjon, A. & Poinsot, T. 1995 A model to define aircraft separations due to wake vortex encounter. In 13th AIAA Applied Aerodynamics Conference, AIAA paper 95-1776, pp. 117–124. American Institute of Aeronautics and Astronautics (AIAA).Google Scholar
10. Corjon, A. & Poinsot, T. 1997 Behavior of wake vortices near ground. AIAA J. 35 (5), 849–855.Google Scholar
11. Cuenot, B., Bedet, B. & Corjon, A. 1997 NTMIX3D user’s guide manual, Preliminary Version 1.0.Google Scholar
12. Culick, F. E. C. 2001 Dynamics of combustion systems: fundamentals, acoustics and control. In Active Control of Engine Dynamics, pp. 89–206. NATO/Von Kármán Institute.Google Scholar
13. Doak, P. E. 1989 Momentum potential-theory of energy flux carried by momentum fluctuations. J. Sound Vib. 131 (1), 67–90.Google Scholar
14. Dowling, A. P. 1997 Acoustics of unstable flows. Theor. Appl. Mech. X, 171–186.Google Scholar
15. Dowling, A. P. & Stow, S. R. 2003 Acoustic analysis of gas turbine combustors. AIAA J. Propul. Power 19 (5), 751–764.Google Scholar
16. Flandro, G. A. 1985 Energy balance analysis of nonlinear combustion instability. AIAA J. Propul. Power 1 (3), 210–221.Google Scholar
17. Goldstein, M. E. 2005 On identifying the true sources of aerodynamic sound. J. Fluid Mech. 526, 337–347.Google Scholar
18. Karimi, N., Brear, M. J., Jin, S. H. & Monty, J. P. 2009 Linear and nonlinear forced response of a conical, ducted, laminar premixed flame. Combust. Flame 156, 2201–2212.Google Scholar
19. Karimi, N., Brear, M. J. & Moase, W. H. 2008 Acoustic and disturbance energy analysis of a flow with heat communication. J. Fluid Mech. 597, 67–89.Google Scholar
20. Karimi, N., Brear, M. J. & Moase, W. H. 2010 On the interaction of sound with steady heat communicating flows. J. Sound Vib. 329, 4705–4718.CrossRefGoogle Scholar
21. 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
22. Lord Rayleigh, 1878 The explanation of certain acoustical phenomena. Nature 18, 319–321.Google Scholar
23. Morfey, C. L. 1971 Acoustic energy in non-uniform flows. J. Sound Vib. 14 (2), 159–170.Google Scholar
24. Myers, M. K. 1991 Transport of energy by disturbances in arbitrary steady flows. J. Fluid Mech. 226, 383–400.Google Scholar
25. Nicoud, F. & Poinsot, T. 2005 Thermoacoustic instabilities: should the Rayleigh criterion be extended to include entropy changes? Combust. Flame 142, 153–159.Google Scholar
26. Nicoud, F. & Wieczorek, K. 2009 About the zero Mach number assumption in the calculation of thermoacoustic instabilities. Intl J. Spray Combust. Dyn. 1 (1), 67–111.Google Scholar
27. Pierce, A. D. 1981 Acoustics: An Introduction to its Physical Principles and Applications. McGraw-Hill.Google Scholar
28. Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104–129.CrossRefGoogle Scholar
29. Poinsot, T. J. & Veynante, D. 2001 Theoretical and Numerical Combustion. R. T. Edwards.Google Scholar
30. Putnam, A. A. 1971 Combustion-Driven Oscillations in Industry. American Elsevier.Google Scholar
31. Schuller, T., Durox, D. & Candel, S. 2003 A unified model for the prediction of laminar flame transfer functions: comparisons between conical and v-flame dynamics. Combust. Flame 134, 21–34.Google Scholar
32. Schwarz, A. & Janicka, J. 2009 Combustion Noise. Springer.Google Scholar
33. Talei, M., Brear, M. J. & Hawkes, E. R. 2011 Sound generation by laminar premixed flame annihilation. J. Fluid Mech. 679, 194–218.Google Scholar
34. Talei, M., Brear, M. J. & Hawkes, E. R. 2012 A parametric study of sound generation by laminar premixed flame annihilation. Combust. Flame 159, 757–769.Google Scholar
35. Williams, F. A. 1985 Combustion Theory: The Fundamental Theory of Chemically Reacting Flow Systems. Addison-Wesley.Google Scholar
36. Yoo, C., Wang, Y., Trouve, A. & Im, H. 2005 Characteristic boundary conditions for direct simulations of turbulent counterflow flames. Combust. Theor. Model. 9 (4), 617–646.Google Scholar