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Multifractality in combustion noise: predicting an impending combustion instability

  • Vineeth Nair (a1) and R. I. Sujith (a1)
Abstract

The transition in dynamics from low-amplitude, aperiodic, combustion noise to high-amplitude, periodic, combustion instability in confined, combustion environments was studied experimentally in a laboratory-scale combustor with two different flameholding devices in a turbulent flow field. We show that the low-amplitude, irregular pressure fluctuations acquired during stable regimes, termed ‘combustion noise’, display scale invariance and have a multifractal signature that disappears at the onset of combustion instability. Traditional analysis often treats combustion noise and combustion instability as acoustic problems wherein the irregular fluctuations observed in experiments are often considered as a stochastic background to the dynamics. We demonstrate that the irregular fluctuations contain useful information of prognostic value by defining representative measures such as Hurst exponents that can act as early warning signals to impending instability in fielded combustors.

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Corresponding author
Email address for correspondence: sujith@iitm.ac.in
References
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Bassingthwaighte, J. B., Liebovitch, L. S. & West, B. J. 1994 Fractal Physiology. Oxford University Press.
Burnley, V. S. & Culick, F. E. C. 2000 Influence of random excitations on acoustic instabilities in combustion chambers. AIAA J. 38, 14031410.
Candel, S. 2002 Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 29, 128.
Candel, S., Durox, D., Ducruix, S., Birbaud, A.-L., Noiray, N. & Schuller, T. 2009 Flame dynamics and combustion noise: progress and challenges. Intl J. Aeroacoust. 8, 156.
Chakravarthy, S. R., Shreenivasan, O. J., Boehm, B., Dreizler, A. & Janicka, J. 2007 Experimental characterization of onset of acoustic instability in a nonpremixed half-dump combustor. J. Acoust. Soc. Am. 122, 120127.
Chakravarthy, S. R., Sivakumar, R. & Shreenivasan, O. J. 2007 Vortex-acoustic lock-on in bluff-body and backward-facing step combustors. Sadhana 32, 145154.
Clavin, P., Kim, J. S. & Williams, F. A. 1994 Turbulence-induced noise effects on high-frequency combustion instabilities. Combust. Sci. Technol. 96, 6184.
Coats, C. M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22, 427509.
Culick, F. E. C.2006 Unsteady motions in combustion chambers for propulsion systems. Vol. AG-AVT-039. RTO AGARDograph.
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. p. 66. Cambridge University Press.
Frisch, U. & Parisi, G. 1985 On the singularity structure of fully developed turbulence. In Turbulence and Predictability in Geophysical Fluid Dynamics (ed. Gil., M., Benzi, R. & Parisi, G.), pp. 8488. North-Holland.
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.
Gouldin, F. C. 1987 An application of fractals to modeling premixed turbulent flames. Combust. Flame 68, 249266.
Gouldin, F. C., Bray, K. N. C. & Chen, J. Y. 1989 Chemical closure model for fractal flamelets. Combust. Flame 77, 241259.
Gouldin, F. C., Hilton, S. M. & Lamb, T. 1988 Experimental evaluation of the fractal geometry of flamelets. Twenty-Second International Symp. on Combustion 541550.
Hegde, U. G., Reuter, D., Daniel, B. R. & Zinn, B. T. 1987 Flame driving of longitudinal instabilities in dump type ramjet combustors. Combust. Sci. Technol. 55, 125138.
Hurst, H. E. 1951 Long-term storage capacity of reservoirs. Trans. Am. Soc. Civil Engrs 116, 770808.
Ihlen, E. A. 2012 Introduction to multifractal detrended fluctuation analysis in Matlab. Front. Physiol. 3.
Jegadeesan, V. & Sujith, R. I. 2013 Experimental investigation of noise induced triggering in thermoacoustic systems. Proc. Combust. Inst. 34, 31753183.
Kantelhardt, J. W. 2011 Fractal and multifractal time series. In Mathematics of Complexity and Dynamical Systems, pp. 463487. Springer.
Kantelhardt, J. W., Koscielny-Bunde, E., Rego, H. H. A., Havlin, S. & Bunde, A. 2001 Detecting long-range correlations with detrended fluctuation analysis. Physica A 295, 441454.
Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A. & Stanley, H. E. 2002 Multifractal detrended fluctuation analysis of nonstationary time series. Physica A 316, 87114.
Kaplan, D. T. & Glass, L. 1992 Direct test for determinism in a time series. Phys. Rev. Lett. 68, 427430.
Kolmogorov, A. N. 1941 Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 1618 (in Russian). Translated into English by Kolmogorov, A. N. Proceedings: Mathematical and Physical Sciences Vol. 434, No. 1890, Turbulence and Stochastic Process: Kolmogorov’s Ideas 50 Years On (Jul. 8, 1991) , pp. 15–17.
Komarek, T. & Polifke, W. 2010 Impact of swirl fluctuations on the flame response of a perfectly premixed swirl burner. Trans. ASME: J. Engng Gas Turbines Power 132, 061503.
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.
Lieuwen, T. C. 2001 Phase drift characteristics of self-excited, combustion driven oscillations. J. Sound Vib. 242, 893905.
Lieuwen, T. C. 2002 Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor. J. Propul. Power 18, 6167.
Lieuwen, T. C. 2003 Statistical characteristics of pressure oscillations in a premixed combustor. J. Sound Vib. 260, 317.
Lieuwen, T. 2005 Online combustor stability margin assessment using dynamic pressure data. J. Engg. Gas Turbines Power 127, 478482.
Lieuwen, T. & Banaszuk, A. 2005 Background noise effects on combustor stability. J. Propul. Power 21, 2531.
Lieuwen, T. C. & Yang, V.(ed.) 2005 Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling, vol. 210, AIAA Inc.
Mandelbrot, B. B. 1974 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331358.
Mandelbrot, B. B. 1982 The Fractal Geometry of Nature. W. H. Freeman and Company.
Massey, F. J. 1951 The Kolmogorov–Smirnov test for goodness of fit. J. Am. Stat. Assoc. 46, 6878.
McManus, K. R., Poinsot, T. & Candel, S. M. 1993 A review of active control of combustion instabilities. Prog. Energy Combust. Sci. 16, 129.
Meneveau, C. & Sreenivasan, K. R. 1987 The multifractal spectrum of the dissipation field in turbulent flows. Nucl. Phys. B Proc. Suppl. 2, 4976.
Meneveau, C. & Sreenivasan, K. R. 1989 Measurement of $f(\alpha )$ from scaling of histograms and applications to dynamical systems and fully developed turbulence. Phys. Lett. A 137, 103112.
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429484.
Montroll, E. W. & Schlesinger, M. F. 1982 On $1/f$ noise and other distributions with long tails. Proc. Natl Acad. Sci. USA 79, 33803383.
Nair, V. & Sujith, R. I. 2013 Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification. Chaos 23, 033136.
Nair, V., Thampi, G., Karuppusamy, S., Gopalan, S. & Sujith, R. I. 2013 Loss of chaos in combustion noise as a precursor of impending combustion instability. Intl J. Spray Combust. Dyn. 5, 273290.
Nair, V., Thampi, G., Sulochana, K., Saravanan, G. & Sujith, R. I.2012 System and method for predetermining the onset of impending oscillatory instabilities in practical devices, Provisional Patent, Filed October 26.
Noiray, N. & Schuermans, B. 2013 Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors. Intl J. Non-Linear Mech. 50, 152163.
Paladin, G. & Vulpiani, A. 1987 Anomalous scaling laws in multifractal objects. Phys. Rep. 156, 147225.
Parker, L. J., Sawyer, R. F. & Ganji, A. R. 1979 Measurement of vortex frequencies in a lean, premixed prevaporized combustor. Combust. Sci. Technol. 20, 235241.
Peng, C.-K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E. & Goldberger, A. L. 1994 Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 16851689.
Pikovsky, A., Rosenblum, M. & Kurths, J. 2001 Synchronization: A Universal Concept in Nonlinear Sciences. p. 38. Cambridge University Press.
Pitz, R. W. & Daily, J. W. 1983 Combustion in a turbulent mixing layer formed at a rearward-facing step. AIAA J. 21, 15651570.
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.
Prasad, R. R., Meneveau, C. & Sreenivasan, K. R. 1988 The multifractal nature of the dissipation field of passive scalars in fully turbulent flows. Phys. Rev. Lett. 61, 7477.
Rayleigh, J. W. S. 1878 The explanation of certain acoustical phenomena. Nature 18, 319321.
Richardson, L. F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.
Rogers, D. E. & Marble, F. E. 1956 A mechanism for high-frequency oscillation in ramjet combustors and afterburners. Jet Propul. 26, 456462.
Schadow, K. C. & Gutmark, E. 1992 Combustion instability related to vortex shedding in dump combustors and their passive control. Prog. Energy Combust. Sci. 18, 117132.
Schlesinger, M. F. 1987 Fractal time and $1/f$ noise in complex systems. Ann. N.Y. Acad. Sci. 504, 214228.
Schwarz, A. & Janicka, J.(ed.) 2009 Combustion Noise. Springer.
Smith, D. A. & Zukoski, E. E.1985 Combustion instability sustained by unsteady vortex combustion. In AIAA/SAE/ASME/ASEE 21st Joint Propulsion Conference. Monterey, California.
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23, 539604.
Sreenivasan, K. R. & Meneveau, C. 1986 The fractal facets of turbulence. J. Fluid Mech. 173, 357386.
Sreenivasan, K. R. & Meneveau, C. 1988 Singularities of the equations of fluid motion. Phys. Rev. A 38, 62876295.
Strahle, W. C. 1978 Combustion noise. Prog. Energy Combust. Sci. 4, 157176.
Strahle, W. C. & Jagoda, J. I. 1988 Fractal geometry applications in turbulent combustion data analysis. Twenty-Second Symp. on Combustion 561568.
Surovyatkina, E. 2005 Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems. Nonlinear Process. Geophys. 12, 2529.
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476490.
West, B. J. 2006 Where Medicine Went Wrong: Rediscovering the Path to Complexity. p. 55. World Scientific.
West, B. J. & Goldberger, A. L. 1987 Physiology in fractal dimensions. Am. Sci. 75, 354365.
West, B. J., Latka, M., Glaubic-Latka, M. & Latka, D. 2003 Multifractality of cerebral blood flow. Physica A 318, 453460.
Wiesenfeld, K. 1985 Noisy precursors of nonlinear instabilities. J. Stat. Phys. 38, 10711097.
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517519.
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds numbers. J. Fluid Mech. 63, 237255.
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, 12431246.
Zia, R. K., Redish, E. F. & McKay, S. R. 2009 Making sense of the Legendre transform. Am. J. Phys. 77, 614622.
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