Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T21:08:59.222Z Has data issue: false hasContentIssue false
  • English
  • Français

Multifractality in combustion noise: predicting an impending combustion instability

Published online by Cambridge University Press:  23 April 2014

Vineeth Nair  and
R. I. Sujith
Vineeth Nair
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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Nonlinear Dynamical Systems: Fractals Reacting Flows: Turbulent reacting flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 635 - 655
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bassingthwaighte, J. B., Liebovitch, L. S. & West, B. J. 1994 Fractal Physiology. Oxford University Press.Google Scholar
Burnley, V. S. & Culick, F. E. C. 2000 Influence of random excitations on acoustic instabilities in combustion chambers. AIAA J. 38, 1403–1410.Google Scholar
Candel, S. 2002 Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 29, 1–28.Google Scholar
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, 1–56.Google Scholar
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, 120–127.Google Scholar
Chakravarthy, S. R., Sivakumar, R. & Shreenivasan, O. J. 2007 Vortex-acoustic lock-on in bluff-body and backward-facing step combustors. Sadhana 32, 145–154.CrossRefGoogle Scholar
Clavin, P., Kim, J. S. & Williams, F. A. 1994 Turbulence-induced noise effects on high-frequency combustion instabilities. Combust. Sci. Technol. 96, 61–84.Google Scholar
Coats, C. M. 1996 Coherent structures in combustion. Prog. Energy Combust. Sci. 22, 427–509.Google Scholar
Culick, F. E. C.2006 Unsteady motions in combustion chambers for propulsion systems. Vol. AG-AVT-039. RTO AGARDograph.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. p. 66. Cambridge University Press.CrossRefGoogle Scholar
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. 84–88. North-Holland.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.Google 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
Gouldin, F. C. 1987 An application of fractals to modeling premixed turbulent flames. Combust. Flame 68, 249–266.Google Scholar
Gouldin, F. C., Bray, K. N. C. & Chen, J. Y. 1989 Chemical closure model for fractal flamelets. Combust. Flame 77, 241–259.Google Scholar
Gouldin, F. C., Hilton, S. M. & Lamb, T. 1988 Experimental evaluation of the fractal geometry of flamelets. Twenty-Second International Symp. on Combustion 541–550.Google Scholar
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, 125–138.Google Scholar
Hurst, H. E. 1951 Long-term storage capacity of reservoirs. Trans. Am. Soc. Civil Engrs 116, 770–808.Google Scholar
Ihlen, E. A. 2012 Introduction to multifractal detrended fluctuation analysis in Matlab. Front. Physiol. 3.Google Scholar
Jegadeesan, V. & Sujith, R. I. 2013 Experimental investigation of noise induced triggering in thermoacoustic systems. Proc. Combust. Inst. 34, 3175–3183.Google Scholar
Kantelhardt, J. W. 2011 Fractal and multifractal time series. In Mathematics of Complexity and Dynamical Systems, pp. 463–487. Springer.Google Scholar
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, 441–454.Google Scholar
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, 87–114.Google Scholar
Kaplan, D. T. & Glass, L. 1992 Direct test for determinism in a time series. Phys. Rev. Lett. 68, 427–430.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18 (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.Google Scholar
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.Google Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.Google Scholar
Lieuwen, T. C. 2001 Phase drift characteristics of self-excited, combustion driven oscillations. J. Sound Vib. 242, 893–905.Google Scholar
Lieuwen, T. C. 2002 Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor. J. Propul. Power 18, 61–67.Google Scholar
Lieuwen, T. C. 2003 Statistical characteristics of pressure oscillations in a premixed combustor. J. Sound Vib. 260, 3–17.Google Scholar
Lieuwen, T. 2005 Online combustor stability margin assessment using dynamic pressure data. J. Engg. Gas Turbines Power 127, 478–482.Google Scholar
Lieuwen, T. & Banaszuk, A. 2005 Background noise effects on combustor stability. J. Propul. Power 21, 25–31.Google Scholar
Lieuwen, T. C. & Yang, V.(ed.) 2005 Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling, vol. 210, AIAA Inc.Google Scholar
Mandelbrot, B. B. 1974 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331–358.Google Scholar
Mandelbrot, B. B. 1982 The Fractal Geometry of Nature. W. H. Freeman and Company.Google Scholar
Massey, F. J. 1951 The Kolmogorov–Smirnov test for goodness of fit. J. Am. Stat. Assoc. 46, 68–78.Google Scholar
McManus, K. R., Poinsot, T. & Candel, S. M. 1993 A review of active control of combustion instabilities. Prog. Energy Combust. Sci. 16, 1–29.Google Scholar
Meneveau, C. & Sreenivasan, K. R. 1987 The multifractal spectrum of the dissipation field in turbulent flows. Nucl. Phys. B Proc. Suppl. 2, 49–76.Google Scholar
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, 103–112.CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.Google Scholar
Montroll, E. W. & Schlesinger, M. F. 1982 On $1/f$ noise and other distributions with long tails. Proc. Natl Acad. Sci. USA 79, 3380–3383.Google Scholar
Nair, V. & Sujith, R. I. 2013 Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification. Chaos 23, 033136.Google Scholar
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, 273–290.Google Scholar
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.Google Scholar
Noiray, N. & Schuermans, B. 2013 Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors. Intl J. Non-Linear Mech. 50, 152–163.Google Scholar
Paladin, G. & Vulpiani, A. 1987 Anomalous scaling laws in multifractal objects. Phys. Rep. 156, 147–225.Google Scholar
Parker, L. J., Sawyer, R. F. & Ganji, A. R. 1979 Measurement of vortex frequencies in a lean, premixed prevaporized combustor. Combust. Sci. Technol. 20, 235–241.Google Scholar
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, 1685–1689.Google Scholar
Pikovsky, A., Rosenblum, M. & Kurths, J. 2001 Synchronization: A Universal Concept in Nonlinear Sciences. p. 38. Cambridge University Press.Google Scholar
Pitz, R. W. & Daily, J. W. 1983 Combustion in a turbulent mixing layer formed at a rearward-facing step. AIAA J. 21, 1565–1570.Google Scholar
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
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, 74–77.Google Scholar
Rayleigh, J. W. S. 1878 The explanation of certain acoustical phenomena. Nature 18, 319–321.Google Scholar
Richardson, L. F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Rogers, D. E. & Marble, F. E. 1956 A mechanism for high-frequency oscillation in ramjet combustors and afterburners. Jet Propul. 26, 456–462.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, 117–132.CrossRefGoogle Scholar
Schlesinger, M. F. 1987 Fractal time and $1/f$ noise in complex systems. Ann. N.Y. Acad. Sci. 504, 214–228.Google Scholar
Schwarz, A. & Janicka, J.(ed.) 2009 Combustion Noise. Springer.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. Monterey, California.Google Scholar
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23, 539–604.Google Scholar
Sreenivasan, K. R. & Meneveau, C. 1986 The fractal facets of turbulence. J. Fluid Mech. 173, 357–386.Google Scholar
Sreenivasan, K. R. & Meneveau, C. 1988 Singularities of the equations of fluid motion. Phys. Rev. A 38, 6287–6295.Google Scholar
Strahle, W. C. 1978 Combustion noise. Prog. Energy Combust. Sci. 4, 157–176.Google Scholar
Strahle, W. C. & Jagoda, J. I. 1988 Fractal geometry applications in turbulent combustion data analysis. Twenty-Second Symp. on Combustion 561–568.Google Scholar
Surovyatkina, E. 2005 Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems. Nonlinear Process. Geophys. 12, 25–29.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490.CrossRefGoogle Scholar
West, B. J. 2006 Where Medicine Went Wrong: Rediscovering the Path to Complexity. p. 55. World Scientific.CrossRefGoogle Scholar
West, B. J. & Goldberger, A. L. 1987 Physiology in fractal dimensions. Am. Sci. 75, 354–365.Google Scholar
West, B. J., Latka, M., Glaubic-Latka, M. & Latka, D. 2003 Multifractality of cerebral blood flow. Physica A 318, 453–460.Google Scholar
Wiesenfeld, K. 1985 Noisy precursors of nonlinear instabilities. J. Stat. Phys. 38, 1071–1097.Google Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517–519.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds numbers. J. Fluid Mech. 63, 237–255.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.Google Scholar
Zank, G. P. & Matthaeus, W. H. 1990 Nearly incompressible hydrodynamics and heat conduction. Phys. Rev. Lett. 64, 1243–1246.Google Scholar
Zia, R. K., Redish, E. F. & McKay, S. R. 2009 Making sense of the Legendre transform. Am. J. Phys. 77, 614–622.Google Scholar