Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T17:20:48.414Z Has data issue: false hasContentIssue false
  • English
  • Français

Multifractal analysis of flame dynamics during transition to thermoacoustic instability in a turbulent combustor

Published online by Cambridge University Press:  06 February 2020

Manikandan Raghunathan Open the ORCID record for Manikandan Raghunathan [Opens in a new window] ,
Nitin B. George Open the ORCID record for Nitin B. George [Opens in a new window] ,
Vishnu R. Unni ,
P. R. Midhun ,
K. V. Reeja  and
R. I. Sujith
Manikandan Raghunathan*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Madras600 036, India
Nitin B. George
Affiliation:
Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412Potsdam, Germany
Vishnu R. Unni
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, California92093, USA
P. R. Midhun
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Madras600 036, India
K. V. Reeja
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Madras600 036, India
R. I. Sujith
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Madras600 036, India
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Gas turbine combustors are susceptible to thermoacoustic instability, which manifests as large amplitude periodic oscillations in acoustic pressure and heat release rate. The transition from a stable operation characterized by combustion noise to thermoacoustic instability in turbulent combustors has been described as an emergence of order (periodicity) from chaos in the temporal dynamics. This emergence of order in the acoustic pressure oscillations corresponds to a loss of multifractality in the pressure signal. In this study, we investigate the spatiotemporal dynamics of a turbulent flame in a bluff-body stabilized combustor during the transition from combustion noise to thermoacoustic instability. During the occurrence of combustion noise, the flame wrinkles due to the presence of small-scale vortices in the turbulent flow. On the other hand, during thermoacoustic instability, large-scale coherent structures emerge periodically. These large-scale coherent structures roll up the wrinkled flame surface further and introduce additional complexity in the flame topology. We perform multifractal analysis on the flame contours detected from high-speed planar Mie scattering images of the reactive flow seeded with non-reactive tracer particles. We find that multifractality exists in the flame topology for all the dynamical states during the transition to thermoacoustic instability. We discuss the variation of multifractal parameters for the different states. We find that the multifractal spectrum oscillates periodically during the occurrence of thermoacoustic instability at the time scale of the acoustic pressure oscillations. The loss of multifractality in the temporal dynamics and the oscillation of the multifractal spectrum of the spatial dynamics go hand in hand.

JFM classification

Nonlinear Dynamical Systems: Fractals Reacting Flows: Turbulent reacting flows Vortex Flows: Vortex shedding
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A14
Copyright
© The Author(s), 2020. Published by 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

Aref, H. 1983 Integrable, chaotic, and turbulent vortex motion in two-dimensional flows. Annu. Rev. Fluid Mech. 15 (1), 345–389.CrossRefGoogle Scholar
Ball, P. 1999 The Self-Made Tapestry: Pattern Formation in Nature. Oxford University Press.Google Scholar
Beauvais, A. A. & Montgomery, D. R. 1997 Are channel networks statistically self-similar? Geology 25 (12), 1063–1066.2.3.CO;2>CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48, R29–R32.Google ScholarPubMed
Camazine, S., Deneubourg, J. L., Franks, N. R., Sneyd, J., Bonabeau, E. & Theraula, G. 2003 Self-Organization in Biological Systems. Princeton University Press.Google Scholar
Candel, S. M. 1992 Combustion instabilities coupled by pressure waves and their active control. In Symposium (International) on Combustion, vol. 24, pp. 1277–1296. Elsevier.Google Scholar
Cheng, Q. 2014 Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions. Nonlinear Process. Geophys. 21 (2), 477–487.CrossRefGoogle Scholar
Chhabra, A. & Jensen, R. V. 1989 Direct determination of the f (𝛼) singularity spectrum. Phys. Rev. Lett. 62, 1327–1330.CrossRefGoogle Scholar
Ciotti, L., Budroni, M. A., Masia, M., Marchettini, N. & Rustici, M. 2011 Competition between transport phenomena in a reaction–diffusion–convection system. Chem. Phys. Lett. 512 (4-6), 290–296.CrossRefGoogle Scholar
Coleman, H. W. & Steele, W. G. 2018 Experimentation, Validation, and Uncertainty Analysis for Engineers. Wiley.CrossRefGoogle Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.CrossRefGoogle Scholar
Dauphiné, A. 2013 From the Fractal Dimension to Multifractal Spectrums, chap. 3, pp. 39–57. Wiley Online Library.Google Scholar
Davidson, P. 2015 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.CrossRefGoogle Scholar
Engelking, R. 1978 Dimension Theory. North-Holland.Google Scholar
Foroutan-pour, K., Dutilleul, P. & Smith, D. L. 1999 Advances in the implementation of the box-counting method of fractal dimension estimation. Appl. Maths Comput. 105 (2–3), 195–210.CrossRefGoogle Scholar
Frisch, U. & Kolmogorov, A. N. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Fung, Y. C. 1955 An Introduction to the Theory of Aeroelasticity. Wiley.Google Scholar
George, N. B., Unni, V. R., Raghunathan, M. & Sujith, R. I. 2018 Pattern formation during transition from combustion noise to thermoacoustic instability via intermittency. J. Fluid Mech. 849, 615–644.CrossRefGoogle Scholar
Giri, A., Tarafdar, S., Gouze, P. & Dutta, T. 2014 Multifractal analysis of the pore space of real and simulated sedimentary rocks. Geophys. J. Intl 200 (2), 1108–1117.CrossRefGoogle Scholar
Goltz, C. 1996 Multifractal and entropic properties of landslides in Japan. Geol. Rundsch. 85 (1), 71–84.CrossRefGoogle Scholar
Gonzalez, R. C., Woods, R. E. & Eddins, S. L. 2004 Digital Image Processing Using MATLAB. pp. 349–438. Pearson.Google Scholar
Górski, A. Z., Drozdz, S., Mokrzycka, A. & Pawlik, J. 2012 Accuracy analysis of the box-counting algorithm. In Proceedings of the 5th Symposium on Physics in Economics and Social Sciences, Warszawa, Poland, November 25–27, 2010. APP.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 (4), 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 (1), 013124.CrossRefGoogle Scholar
Gotoda, H., Okuno, Y., Hayashi, K. & Tachibana, S. 2015 Characterization of degeneration process in combustion instability based on dynamical systems theory. Phys. Rev. E 92, 052906.Google ScholarPubMed
Gülder, Ö. L., Smallwood, G. J., Wong, R., Snelling, D. R., Smith, R., Deschamps, B. M. & Sautet, J. C. 2000 Flame front surface characteristics in turbulent premixed propane/air combustion. Combust. Flame 120 (4), 407–416.CrossRefGoogle Scholar
Hardalupas, Y. & Orain, M. 2004 Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame. Combust. Flame 139 (3), 188–207.CrossRefGoogle Scholar
Ho, C. M. & Nosseir, N. S. 1981 Dynamics of an impinging jet. Part 1. The feedback phenomenon. J. Fluid Mech. 105, 119–142.CrossRefGoogle Scholar
Holman, J. P. 1989 Heat Transfer. McGraw-Hill.Google Scholar
Hong, S., Speth, R. L., Shanbhogue, S. J. & Ghoniem, A. F. 2013 Examining flow-flame interaction and the characteristic stretch rate in vortex-driven combustion dynamics using PIV and numerical simulation. Combust. Flame 160 (8), 1381–1397.CrossRefGoogle Scholar
Ihlen, E. A. & Vereijken, B. 2013 Multifractal formalisms of human behavior. Human Movement Sci. 32 (4), 633–651.CrossRefGoogle ScholarPubMed
Ivanov, P. Ch., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Rosenblum, M. G., Struzik, Z. R. & Stanley, H. E. 1999 Multifractality in human heartbeat dynamics. Sensors Actuators A 399, 461.Google ScholarPubMed
Juniper, M. P. & Sujith, R. I. 2018 Sensitivity and nonlinearity of thermoacoustic oscillations. Annu. Rev. Fluid Mech. 50 (1), 661–689.CrossRefGoogle Scholar
Keller, J. O., Vaneveld, L., Korschelt, D., Hubbard, G. L., Ghoniem, A. F., Daily, J. W. & Oppenheim, A. K. 1982 Mechanism of instabilities in turbulent combustion leading to flashback. AIAA J. 20 (2), 254–262.CrossRefGoogle Scholar
Ken, H. Y., Trouve, A. & Daily, J. W. 1991 Low-frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 47–72.Google Scholar
Kim, M., Choi, Y., Oh, J. & Yoon, Y. 2009 Flame–vortex interaction and mixing behaviors of turbulent non-premixed jet flames under acoustic forcing. Combust. Flame 156 (12), 2252–2263.CrossRefGoogle Scholar
Lam, L., Lee, S.-W. & Suen, C. Y. 1992 Thinning methodologies – a comprehensive survey. IEEE Trans. Pattern Anal. Mach. Intell. 14 (9), 869–885.CrossRefGoogle Scholar
Lieuwen, T. C. 2012 Unsteady Combustor Physics. Cambridge University Press.CrossRefGoogle Scholar
Lopes, R. & Betrouni, N. 2009 Fractal and multifractal analysis: a review. Med. Image Anal. 13 (4), 634–649.CrossRefGoogle ScholarPubMed
Lovejoy, S. & Schertzer, D. 1991 Multifractal Analysis Techniques and the Rain and Cloud Fields, pp. 111–144. Springer.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 (2), 331–358.CrossRefGoogle Scholar
Mandelbrot, B. B. 1983 The Fractal Geometry of Nature. W. H. Freeman.CrossRefGoogle Scholar
Mandelbrot, B. B. 1989 Multifractal measures, especially for the geophysicist. Pure Appl. Geophys. 131, 5–42.CrossRefGoogle Scholar
Martínez, V. J., Jones, B. J., Domínguez-Tenreiro, R. & Weygaert, R. 1990 Clustering paradigms and multifractal measures. Astrophys. J. 357, 50.CrossRefGoogle Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K. R. 1986 The fractal facets of turbulence. J. Fluid Mech. 173, 357–386.Google Scholar
Meneveau, C. & Sreenivasan, K. R. 1987 Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59 (13), 1424.CrossRefGoogle ScholarPubMed
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.CrossRefGoogle Scholar
Mondal, S., Unni, V. R. & Sujith, R. I. 2017 Onset of thermoacoustic instability in turbulent combustors: an emergence of synchronized periodicity through formation of chimera-like states. J. Fluid Mech. 811, 659–681.CrossRefGoogle Scholar
Murcio, R., Masucci, A. P., Arcaute, E. & Batty, M. 2015 Multifractal to monofractal evolution of the London street network. Phys. Rev. E 92, 062130.Google ScholarPubMed
Nair, S. & Lieuwen, T. C. 2007 Near-blowoff dynamics of a bluff-body stabilized flame. J. Propul. Power 23 (2), 421–427.CrossRefGoogle Scholar
Nair, V. & Sujith, R. I. 2014 Multifractality in combustion noise: predicting an impending combustion instability. J. Fluid Mech. 747, 635–655.CrossRefGoogle Scholar
Nair, V., Thampi, G. & Sujith, R. I. 2014 Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756, 470–487.CrossRefGoogle Scholar
Normant, F. & Tricot, C. 1991 Method for evaluating the fractal dimension of curves using convex hulls. Phys. Rev. A 43 (12), 6518.CrossRefGoogle ScholarPubMed
North, G. L. & Santavicca, D. A. 1990 The fractal nature of premixed turbulent flames. Combust. Sci. Technol. 72 (4-6), 215–232.CrossRefGoogle Scholar
Ostu, N. 1979 A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9 (1), 62–66.Google Scholar
Pawar, S. A., Seshadri, A., Unni, V. R. & Sujith, R. I. 2017 Thermoacoustic instability as mutual synchronization between the acoustic field of the confinement and turbulent reactive flow. J. Fluid Mech. 827, 664–693.CrossRefGoogle Scholar
Pesin, Y. B. 2008 Dimension Theory in Dynamical Systems: Contemporary Views and Applications. University of Chicago Press.Google Scholar
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.CrossRefGoogle 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.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Premchand, C. P., George, N. B., Raghunathan, M., Unni, V. R., Sujith, R. I. & Nair, V. 2019 Lagrangian analysis of intermittent sound sources in the flow-field of a bluff-body stabilized combustor. Phys. Fluids 31 (2), 025115.CrossRefGoogle Scholar
Puthenveettil, B. A., Ananthakrishna, G. & Arakeri, J. H. 2005 The multifractal nature of plume structure in high-Rayleigh-number convection. J. Fluid Mech. 526, 245–256.CrossRefGoogle Scholar
Renard, P. H., Rolon, J. C., Thévenin, D. & Candel, S. 1999 Investigations of heat release, extinction, and time evolution of the flame surface, for a nonpremixed flame interacting with a vortex. Combust. Flame 117 (1–2), 189–205.CrossRefGoogle Scholar
Richardson, L. F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Rockwell, D. 1983 Oscillations of impinging shear layers. AIAA J. 21 (5), 645–664.CrossRefGoogle Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Annu. Rev. Fluid Mech. 11 (1), 67–94.CrossRefGoogle Scholar
Salat, H., Murcio, R. & Arcaute, E. 2017 Multifractal methodology. Physica A 473, 467–487.CrossRefGoogle Scholar
Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y. & Marsan, D. 1997 Multifractal cascade dynamics and turbulent intermittency. Sensors Actuators A 5 (03), 427–471.Google Scholar
Shanbhogue, S., Shin, D. H., Hemchandra, S., Plaks, D. & Lieuwen, T. C. 2009 Flame-sheet dynamics of bluff-body stabilized flames during longitudinal acoustic forcing. Proc. Combust. Inst. 32 (2), 1787–1794.CrossRefGoogle Scholar
Shepherd, I. G., Cheng, R. K. & Talbot, L. 1992 Experimental criteria for the determination of fractal parameters of premixed turbulent flames. Exp. Fluids 13 (6), 386–392.CrossRefGoogle Scholar
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23 (1), 539–604.CrossRefGoogle Scholar
Stella, A., Guj, G., Kompenhans, J., Richard, H. & Raffel, M. 2001 Three-components particle image velocimetry measurements in premixed flames. Aerosp. Sci. Technol. 5 (5), 357–364.CrossRefGoogle Scholar
Strahle, W. C. 1978 Combustion noise. Prog. Energy Combust. Sci. 4 (3), 157–176.CrossRefGoogle Scholar
Tanner, B. R., Perfect, E. & Kelley, J. T. 2006 Fractal analysis of Maine’s glaciated shoreline tests established coastal classification scheme. J. Coast. Res. 1300–1304.CrossRefGoogle Scholar
Telesca, L., Colangelo, G., Lapenna, V. & Macchiato, M. 2003 Monofractal and multifractal characterization of geoelectrical signals measured in southern Italy. Chaos Solitons Fractals 18 (2), 385–399.CrossRefGoogle Scholar
Telesca, L., Lovallo, M., Molist, J. M., Moreno, C. L. & Meléndez, R. A. 2015 Multifractal investigation of continuous seismic signal recorded at El Hierro volcano (Canary Islands) during the 2011–2012 pre- and eruptive phases. Tectonophysics 642, 71–77.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Tiezzi, E. B. P., Pulselli, R. M., Marchettini, N. & Tiezzi, E. 2008 Dissipative structures in nature and human systems. In Design and Nature IV, p. 293. WIT Press.Google Scholar
Unni, V. R., Krishnan, A., Manikandan, R., George, N. B., Sujith, R. I., Marwan, N. & Kurths, J. 2018 On the emergence of critical regions at the onset of thermoacoustic instability in a turbulent combustor. Chaos 28 (6), 063125.CrossRefGoogle Scholar
Unni, V. R. & Sujith, R. I. 2015 Multifractal characteristics of combustor dynamics close to lean blowout. J. Fluid Mech. 784, 30–50.CrossRefGoogle Scholar
Unni, V. R. & Sujith, R. I. 2017 Flame dynamics during intermittency in a turbulent combustor. Proc. Combust. Inst. 36 (3), 3791–3798.CrossRefGoogle Scholar
Veneziano, D., Moglen, G. E. & Bras, R. L. 1995 Multifractal analysis: pitfalls of standard procedures and alternatives. Phys. Rev. E 52 (2), 1387.Google ScholarPubMed
Wagon, S. 2010 Mathematica® in Action: Problem Solving Through Visualization and Computation. Springer.CrossRefGoogle Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4), 517–519.CrossRefGoogle Scholar
Zukoski, E. 1985 Combustion instability sustained by unsteady vortex combustion. In 21st Joint Propulsion Conference, p. 1248. AIAA.Google Scholar