Skip to main content Accessibility help

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

  • Meenatchidevi Murugesan (a1) and R. I. Sujith (a1)


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.


Corresponding author

Email address for correspondence:


Hide All
Abugov, D. I. & Obrezkov, O. I. 1978 Acoustic noise in turbulent flames. Combust. Explos. Shock Waves 14 (5), 606612.
Albert, R., Jeong, H. & Barabasi, A. L. 2000 Error and attack tolerance of complex networks. Nature 406 (6794), 378382.
Alm, E. & Arkin, A. P. 2003 Biological networks. Curr. Opin. Struct. Biol. 13 (2), 193202.
Arianos, S., Bompard, E., Carbone, A. & Xue, F. 2009 Power grid vulnerability: a complex network approach. Chaos 19, 013119.
Barabasi, A. L. 2011 The network takeover. Nat. Phys. 8 (1), 1416.
Barabási, A. L. & Albert, R. 1999 Emergence of scaling in random networks. Science 286 (5439), 509512.
Barabasi, A. L., Albert, R. & Jeong, H. 1999 Diameter of the world wide web. Nature 401 (9), 130131.
Barabasi, A. L. & Bonabeau, E. 2003 Scale-free networks. Sci. Am. 288 (5), 6069.
Barabasi, A. L. & Oltvai, Z. N. 2004 Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5 (2), 101113.
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.
Belliard, A.1997 Etude expérimentale de l’émission sonore des flammes turbulentes. PhD Dissertation, Universités d’Aix-Marseille, France.
Bragg, S. L. 1963 Combustion noise. J. Inst. Fuel 36 (1), 1216.
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), 120127.
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), 145154.
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.
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), 595603.
Chiu, H. H. & Summerfield, M. 1974 Theory of combustion noise. Acta Astronaut. 1 (7), 967984.
Clavin, P. 2000 Dynamics of combustion fronts in premixed gases: from flames to detonations. Proc. Combust. Inst. 28 (1), 569585.
Clavin, P. & Siggia, E. D. 1991 Turbulent premixed flames and sound generation. Combust. Sci. Technol. 78 (1–3), 147155.
Coats, C. M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22 (5), 427509.
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), 14571463.
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), 15381558.
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.
Dowling, A. P. & Mahmoudi, Y. 2015 Combustion noise. Proc. Combust. Inst. 35 (1), 65100.
Dowling, A. P. & Stow, S. R. 2003 Acoustic analysis of gas turbine combustors. J. Propul. Power 19 (5), 751764.
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.
Frisch, U. 1995 Turbulence: The Legacy of AN Kolmogorov. Cambridge University Press.
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.
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.
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.
Gotoda, H., Nikimoto, H., Miyano, T. & Tachibana, S. 2011 Dynamic properties of combustion instability in a lean premixed gas-turbine combustor. Chaos 21, 013124.
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.
Hegde, U. G., Reuter, D. & Zinn, B. T. 1988 Sound generation by ducted flames. AIAA J. 26 (5), 532537.
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.
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.
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), 49724975.
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), 15.
Lesne, A. & Laguës, M. 2011 Scale Invariance: From Phase Transitions to Turbulence. Springer.
Lieuwen, T. C. 2002 Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor. J. Propul. Power 18 (1), 6167.
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), 26752681.
Lovejoy, S. & Schertzer, D. 1986 Scale invariance, symmetries, fractals, and stochastic simulations of atmospheric phenomena. Bull. Am. Meteorol. Soc. 67 (1), 2132.
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.
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.
Nair, V. & Sujith, R. I. 2014 Multifractality in combustion noise: predicting an impending instability. J. Fluid Mech. 747, 635655.
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, 273290.
Nair, V., Thampi, G. & Sujith, R. I. 2014 Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756, 470487.
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), 38223826.
Noiray, N. & Schuermans, B. 2012 Theoretical and experimental investigations on damper performance for suppression of thermoacoustic oscillations. J. Sound Vib. 331 (12), 27532763.
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. 119152. InTech,; doi:10.5772/34810.
Pagani, G. A. & Aiello, M. 2014 Power grid complex network evolutions for the smart grid. Physica A 396, 248266.
Paret, J. & Tabeling, P. 1998 Intermittency in the two-dimensional inverse cascade of energy: experimental observations. Phys. Fluids 10 (12), 31263136.
Pocheau, A. 1994 Scale invariance in turbulent front propagation. Phys. Rev. E 49 (2), 11091122.
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, 265292.
Quenell, G. 1994 Spectral diameter estimates for $k$ -regular. Adv. Maths 106 (1), 122148.
Rajaram, R.2007 Characteristics of sound radiation from turbulent premixed flames, PhD thesis, Georgia Institute of Technology, USA.
Rajaram, R. & Lieuwen, T. 2009 Acoustic radiation from turbulent premixed flames. J. Fluid Mech. 637, 357385.
Rayleigh, J. W. S. 1878 The explanation of certain acoustical phenomena. Nature 18, 319321.
Rogers, D. E. 1956 A mechanism for high-frequency oscillation in ramjet combustors and afterburners. J. Jet Propul. 26 (6), 456462.
Rouhani, S. Z. & Sohal, M. S. 1983 Two-phase flow patterns: a review of research results. Prog. Nucl. Energy 11 (3), 219259.
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), 117132.
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), 167186.
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.
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.
Sommeria, J. 1986 Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139168.
Strahle, W. C. 1971 On combustion generated noise. J. Fluid Mech. 49 (02), 399414.
Strahle, W. C. 1978 Combustion noise. Prog. Energy Combust. Sci. 4 (3), 157176.
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.
Watts, D. J. & Strogatz, S. H. 1998 Collective dynamics of ‘small-world’ networks. Nature 393 (6684), 440442.
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, 144.
Yu, K. H., Trouve, A. & Daily, J. W. 1991 Low-frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 4772.
Zank, G. P. & Matthaeus, W. H. 1990 Nearly incompressible hydrodynamics and heat conduction. Phys. Rev. Lett. 64 (11), 12431246.
Zhang, J. & Small, M. 2006 Complex network from pseudo-periodic time series: topology versus dynamics. Phys. Rev. Lett. 96 (23), 238701.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed