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Combustion noise is scale-free: transition from scale-free to order at the onset of thermoacoustic instability

Published online by Cambridge University Press:  30 April 2015

Meenatchidevi Murugesan  and
R. I. Sujith
Meenatchidevi Murugesan*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
R. I. Sujith
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
*
†Email address for correspondence: mena.murugesan90@gmail.com
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Abstract

We investigate the scale invariance of combustion noise generated from turbulent reacting flows in a confined environment using complex networks. The time series data of unsteady pressure, which is the indicative of spatiotemporal changes happening in the combustor, is converted into complex networks using the visibility algorithm. We show that the complex networks obtained from the low-amplitude, aperiodic pressure fluctuations during combustion noise have scale-free structure. The power-law distributions of connections in the scale-free network are related to the scale invariance of combustion noise. We also show that the scale-free feature of combustion noise disappears and order emerges in the complex network topology during the transition from combustion noise to combustion instability. The use of complex networks enables us to formalize the identification of the pattern (i.e. scale-free to order) during the transition from combustion noise to thermoacoustic instability as a structural change in topology of the network.

JFM classification

Nonlinear Dynamical Systems: Pattern formation Reacting Flows: Turbulent reacting flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 225 - 245
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Copyright
© 2015 Cambridge University Press 

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References

Abugov, D. I. & Obrezkov, O. I. 1978 Acoustic noise in turbulent flames. Combust. Explos. Shock Waves 14 (5), 606–612.Google Scholar
Albert, R., Jeong, H. & Barabasi, A. L. 2000 Error and attack tolerance of complex networks. Nature 406 (6794), 378–382.CrossRefGoogle ScholarPubMed
Alm, E. & Arkin, A. P. 2003 Biological networks. Curr. Opin. Struct. Biol. 13 (2), 193–202.Google Scholar
Arianos, S., Bompard, E., Carbone, A. & Xue, F. 2009 Power grid vulnerability: a complex network approach. Chaos 19, 013119.Google Scholar
Barabasi, A. L. 2011 The network takeover. Nat. Phys. 8 (1), 14–16.CrossRefGoogle Scholar
Barabási, A. L. & Albert, R. 1999 Emergence of scaling in random networks. Science 286 (5439), 509–512.CrossRefGoogle ScholarPubMed
Barabasi, A. L., Albert, R. & Jeong, H. 1999 Diameter of the world wide web. Nature 401 (9), 130–131.Google Scholar
Barabasi, A. L. & Bonabeau, E. 2003 Scale-free networks. Sci. Am. 288 (5), 60–69.Google Scholar
Barabasi, A. L. & Oltvai, Z. N. 2004 Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5 (2), 101–113.Google Scholar
Bastian, M., Heymann, S. & Jacomy, M.2009 Gephi: an open source software for exploring and manipulating networks. In Proceedings of the 3rd International ICWSM Conference, pp. 361–362.Google Scholar
Belliard, A.1997 Etude expérimentale de l’émission sonore des flammes turbulentes. PhD Dissertation, Universités d’Aix-Marseille, France.Google Scholar
Bragg, S. L. 1963 Combustion noise. J. Inst. Fuel 36 (1), 12–16.Google Scholar
Chakravarthy, S. R., Shreenivasan, O. J., Boehm, B., Dreizler, A. & Janicka, J. 2007a Experimental characterization of onset of acoustic instability in a nonpremixed half-dump combustor. J. Acoust. Soc. Am. 122 (1), 120–127.CrossRefGoogle Scholar
Chakravarthy, S. R., Sivakumar, R. & Shreenivasan, O. J. 2007b Vortex-acoustic lock-on in bluff-body and backward-facing step combustors. Sadhana 32 (1–2), 145–154.Google Scholar
Charakopoulos, A. K., Karakasidis, T. E., Papanicolaou, P. N. & Liakopoulos, A. 2014 The application of complex network time series analysis in turbulent heated jets. Chaos 24, 024408.Google Scholar
Chen, G., Dong, Z. Y., Hill, D. J., Zhang, G. H. & Hua, K. Q. 2010 Attack structural vulnerability of power grids: a hybrid approach based on complex networks. Physica A 389 (3), 595–603.Google Scholar
Chiu, H. H. & Summerfield, M. 1974 Theory of combustion noise. Acta Astronaut. 1 (7), 967–984.CrossRefGoogle Scholar
Clavin, P. 2000 Dynamics of combustion fronts in premixed gases: from flames to detonations. Proc. Combust. Inst. 28 (1), 569–585.Google Scholar
Clavin, P. & Siggia, E. D. 1991 Turbulent premixed flames and sound generation. Combust. Sci. Technol. 78 (1–3), 147–155.Google Scholar
Coats, C. M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22 (5), 427–509.CrossRefGoogle Scholar
Das, R. K. & Pattanayak, S. 1993 Electrical impedance method for flow regime identification in vertical upward gas–liquid two-phase flow. Meas. Sci. Technol. 4 (12), 1457–1463.CrossRefGoogle Scholar
Davis, A., Marshak, A., Wiscombe, W. & Cahalan, R. 1996 Scale invariance of liquid water distributions in marine stratocumulus. Part I: spectral properties and stationarity issues. J. Atmos. Sci. 53 (11), 1538–1558.Google Scholar
Donner, R. V., Zou, Y., Donges, J. F., Marwan, N. & Kurths, J. 2010 Recurrence networks – a novel paradigm for nonlinear time series analysis. New J. Phys. 12, 033025.Google Scholar
Dowling, A. P. & Mahmoudi, Y. 2015 Combustion noise. Proc. Combust. Inst. 35 (1), 65–100.Google Scholar
Dowling, A. P. & Stow, S. R. 2003 Acoustic analysis of gas turbine combustors. J. Propul. Power 19 (5), 751–764.CrossRefGoogle Scholar
Dubos, T., Babiano, A., Paret, J. & Tabeling, P. 2001 Intermittency and coherent structures in the two-dimensional inverse energy cascade: comparing numerical and laboratory experiments. Phys. Rev. E 64, 036302.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of AN Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gao, Z. & Jin, N. 2009 Flow-pattern identification and nonlinear dynamics of gas–liquid two-phase flow in complex networks. Phys. Rev. E 79 (6), 066303.Google Scholar
Gao, Z. K., Jin, N. D., Wang, W. X. & Lai, Y. C. 2010 Motif distributions in phase-space networks for characterizing experimental two-phase flow patterns with chaotic features. Phys. Rev. E 82 (1), 016210.Google Scholar
Gotoda, H., Amano, M., Miyano, T., Ikawa, T., Maki, K. & Tachibana, S. 2012 Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor. Chaos 22, 043128.CrossRefGoogle Scholar
Gotoda, H., Nikimoto, H., Miyano, T. & Tachibana, S. 2011 Dynamic properties of combustion instability in a lean premixed gas-turbine combustor. Chaos 21, 013124.CrossRefGoogle Scholar
Gotoda, H., Shinoda, Y., Kobayashi, M. & Okuno, Y. 2014 Detection and control of combustion instability based on the concept of dynamical system theory. Phys. Rev. E 89, 022910.Google ScholarPubMed
Hegde, U. G., Reuter, D. & Zinn, B. T. 1988 Sound generation by ducted flames. AIAA J. 26 (5), 532–537.Google Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.Google Scholar
Kumar, R. N.1975 Further experimental results on the structure and acoustics of turbulent jet flames. In AIAA 2nd Aero-Acoustics Conference, AIAA 75-523, pp. 24–26.Google Scholar
Lacasa, L., Luque, B., Ballesteros, F., Luque, J. & Nuno, J. C. 2008 From time series to complex networks: the visibility graph. Proc. Natl Acad. Sci. USA 105 (13), 4972–4975.Google Scholar
Lacasa, L., Luque, B., Luque, J. & Nuno, J. C. 2009 The visibility graph: a new method for estimating the Hurst exponent of fractional Brownian motion. Eur. Phys. Lett. 86 (3), 1–5.Google Scholar
Lesne, A. & Laguës, M. 2011 Scale Invariance: From Phase Transitions to Turbulence. Springer.Google Scholar
Lieuwen, T. C. 2002 Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor. J. Propul. Power 18 (1), 61–67.CrossRefGoogle Scholar
Liu, C., Zhou, W. X. & Yuan, W. K. 2010 Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence. Physica A 389 (13), 2675–2681.Google Scholar
Lovejoy, S. & Schertzer, D. 1986 Scale invariance, symmetries, fractals, and stochastic simulations of atmospheric phenomena. Bull. Am. Meteorol. Soc. 67 (1), 21–32.Google Scholar
Murugesan, M., Nair, V. & Sujith, R. I.2014 System and method for early detection of onset of instabilities using complex networks, Provisional Patent, Filed on 29 April 2014.Google Scholar
Nair, V. & Sujith, R. I. 2013 Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification. Chaos: Interdiscip. J. Nonlinear Sci. 23, 033136.Google Scholar
Nair, V. & Sujith, R. I. 2014 Multifractality in combustion noise: predicting an impending instability. J. Fluid Mech. 747, 635–655.Google Scholar
Nair, V., Thampi, G., Karuppasamy, S., Gopalan, S. & Sujith, R. I. 2013 Loss of chaos in combustion noise as a precursor for impending instability. Intl J. Spray Combust. Diag. 5, 273–290.Google Scholar
Nair, V., Thampi, G. & Sujith, R. I. 2014 Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756, 470–487.Google Scholar
Ni, X. H., Jiang, Z. Q. & Zhou, W. X. 2009 Degree distributions of the visibility graphs mapped from fractional Brownian motions and multifractal random walks. Phys. Lett. A 373 (42), 3822–3826.Google Scholar
Noiray, N. & Schuermans, B. 2012 Theoretical and experimental investigations on damper performance for suppression of thermoacoustic oscillations. J. Sound Vib. 331 (12), 2753–2763.Google Scholar
Nunez, A. M., Lacasa, L., Gomez, J. P. & Luque, B. 2012 Visibility algorithms: a short review. In New Frontiers in Graph Theory (ed. Zhang, Y.), pp. 119–152. InTech,; doi:10.5772/34810.Google Scholar
Pagani, G. A. & Aiello, M. 2014 Power grid complex network evolutions for the smart grid. Physica A 396, 248–266.CrossRefGoogle Scholar
Paret, J. & Tabeling, P. 1998 Intermittency in the two-dimensional inverse cascade of energy: experimental observations. Phys. Fluids 10 (12), 3126–3136.Google Scholar
Pocheau, A. 1994 Scale invariance in turbulent front propagation. Phys. Rev. E 49 (2), 1109–1122.CrossRefGoogle ScholarPubMed
Poinsot, T. J., Trouve, A. C., Veynante, D. P., Candel, S. M. & Esposito, E. J. 1987 Vortex-driven acoustically coupled combustion instabilities. J. Fluid Mech. 177, 265–292.Google Scholar
Quenell, G. 1994 Spectral diameter estimates for $k$ -regular. Adv. Maths 106 (1), 122–148.Google Scholar
Rajaram, R.2007 Characteristics of sound radiation from turbulent premixed flames, PhD thesis, Georgia Institute of Technology, USA.Google Scholar
Rajaram, R. & Lieuwen, T. 2009 Acoustic radiation from turbulent premixed flames. J. Fluid Mech. 637, 357–385.Google Scholar
Rayleigh, J. W. S. 1878 The explanation of certain acoustical phenomena. Nature 18, 319–321.CrossRefGoogle Scholar
Rogers, D. E. 1956 A mechanism for high-frequency oscillation in ramjet combustors and afterburners. J. Jet Propul. 26 (6), 456–462.CrossRefGoogle Scholar
Rouhani, S. Z. & Sohal, M. S. 1983 Two-phase flow patterns: a review of research results. Prog. Nucl. Energy 11 (3), 219–259.Google Scholar
Schadow, K. C. & Gutmark, E. 1992 Combustion instability related to vortex shedding in dump combustors and their passive control. Prog. Energy Combust. Sci. 18 (2), 117–132.CrossRefGoogle Scholar
Schadow, K. C., Gutmark, E., Parr, T. P., Parr, D. M., Wilson, K. J. & Crump, J. E. 1989 Large-scale coherent structures as drivers of combustion instability. Combust. Sci. Technol. 64 (4–6), 167–186.Google Scholar
Shats, M. G., Xia, H. & Punzmann, H. 2005 Spectral condensation of turbulence in plasmas and fluids and its role in low-to-high phase transitions in toroidal plasma. Phys. Rev. E 71, 046409.Google Scholar
Smith, D. A. & Zukoski, E. E.1985 Combustion instability sustained by unsteady vortex combustion. In AIAA/SAE/ASME/ASEE 21st Joint Propulsion Conference, AIAA-85-1248.Google Scholar
Sommeria, J. 1986 Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139–168.Google Scholar
Strahle, W. C. 1971 On combustion generated noise. J. Fluid Mech. 49 (02), 399–414.Google Scholar
Strahle, W. C. 1978 Combustion noise. Prog. Energy Combust. Sci. 4 (3), 157–176.Google Scholar
Strozzi, F., Zaldívar, J. M., Poljansek, K., Bono, F. & Gutiérrez, E. 2009 From Complex Networks to Time Series Analysis and Vice versa: Application to Metabolic Networks. Office for Official Publications of the European Communities.Google Scholar
Watts, D. J. & Strogatz, S. H. 1998 Collective dynamics of ‘small-world’ networks. Nature 393 (6684), 440–442.CrossRefGoogle ScholarPubMed
Xiao, Z., Wan, M., Chen, S. & Eyink, G. L. 2009 Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation. J. Fluid Mech. 619, 1–44.Google Scholar
Yu, K. H., Trouve, A. & Daily, J. W. 1991 Low-frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 47–72.CrossRefGoogle Scholar
Zank, G. P. & Matthaeus, W. H. 1990 Nearly incompressible hydrodynamics and heat conduction. Phys. Rev. Lett. 64 (11), 1243–1246.Google Scholar
Zhang, J. & Small, M. 2006 Complex network from pseudo-periodic time series: topology versus dynamics. Phys. Rev. Lett. 96 (23), 238701.Google Scholar