Skip to main content
SpringerLink
Log in

Dynamic Systems Approach for Laminar Ducted Flames

  • Chapter
  • First Online:
Energy for Propulsion

Part of the book series: Green Energy and Technology ((GREEN))

  • 927 Accesses

Abstract

Combustion in physical systems is always affected by dynamic instabilities, most of them being of thermoacoustic origin. The interaction of the acoustics of the flame enclosure and the unsteady heat release from the flame are responsible for such instabilities. During such unstable operation, the flame often changes its dynamic state, with transition across several dynamic states being also quite common. The present chapter presents a brief review on the recent developments of dynamic systems approach applied to laminar ducted flames. The different tools of nonlinear time series analysis that are commonly used for this purpose have been described. Representative case studies of the technique applied to ducted non-premixed, premixed, and inverse diffusion flames have been presented. Finally, the promising nature of the complex networks-based approach for dynamic characterization of combustion systems has been highlighted.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. H.C. Mongia, T.J. Held, G.C. Hsiao, R.P. Pandalai, Challenges and progress in controlling dynamics in gas turbine combustors. J. Propul. Power 19(5), 822–829 (2003)

    Article  Google Scholar 

  2. F. Giuliani, P. Gajan, O. Diers, M. Ledoux, Influence of pulsed entries on a spray generated by an air-blast injection device: an experimental analysis on combustion instability processes in aeroengines. Proc. Combust. Inst. 29, 91–98 (2002)

    Article  Google Scholar 

  3. G.A. Richards, M.C. Janus, Characterization of oscillations during premix gas turbine combustion. J. Eng. Gas Turb. Power 120, 294–302 (1998)

    Article  Google Scholar 

  4. P.J. Langhorne, Reheat buzz: an acoustically coupled combustion instability. Part 1. Experiment. J. Fluid Mech. 193, 417–443 (1988)

    Article  Google Scholar 

  5. G.J. Bloxsidge, A.P. Dowling, P.J. Langhorne, Reheat buzz: an acousitcally coupled combustion instability. Part 2. Theory. J. Fluid Mech. 193, 445–473 (1988)

    Article  Google Scholar 

  6. A.P. Dowling, A.S. Morgans, Feedback control of combustion oscillations. Annu. Rev. Fluid Mech. 37, 151–182 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. K.H. Yu, A. Trouvé, J.W. Daily, Low-frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 47–72 (1991)

    Article  Google Scholar 

  8. J.W.S. Rayleigh, The explanation of certain acoustical phenomena. Nature 18, 319–321 (1878)

    Article  Google Scholar 

  9. T.J. Poinsot, A.C. Trouvé, D.P. Veynante, S.M. Candel, E.J. Esposito, Vortex-driven acoustically coupled combustion instabilities. J. Fluid Mech. 177, 265–292 (1987)

    Article  Google Scholar 

  10. P.-H. Renard, D. Thévenin, J.C. Rolon, S. Candel, Dynamics of flame/vortex interactions. Prog. Energy Combust. Sci. 26, 225–282 (2000)

    Article  Google Scholar 

  11. F.E.C. Culick, Unsteady motions in combustion chambers for propulsion systems. AGARDograph RTO-AG-AVT-039, 2006

    Google Scholar 

  12. K.R. McManus, T. Poinsot, S.M. Candel, A review of active control of combustion instabilities. Prog. Energy Combust. Sci. 19, 1–29 (1993)

    Article  Google Scholar 

  13. X. Wu, M. Wang, P. Moin, N. Peters, Combustion instability due to the nonlinear interaction between sound and flame. J. Fluid Mech. 497, 23–53 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. S.R. Turns, An Introduction to Combustion: Concepts and Applications (McGraw-Hill Book Co., Singapore, 2000)

    Google Scholar 

  15. N. Karimi, M.J. Brear, S.H. Jin, J.P. Monty, Linear and non-linear forced response of a conical, ducted, laminar premixed flame. Combust. Flame 156, 2201–2212 (2009)

    Article  Google Scholar 

  16. L. Kabiraj, R.I. Sujith, Nonlinear self-excited thermoacoustic oscillations: intermittency and flame blowout. J. Fluid Mech. 713, 376–397 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Gotoda, H. Nikimoto, T. Miyano, S. Tachibana, Dynamic properties of combustion instability in a lean-premixed gas turbine combustor. Chaos 21, 013124 (2011)

    Article  Google Scholar 

  18. S. Domen, H. Gotoda, T. Kuriyama, Y. Okuno, S. Tachibana, Detection and prevention of blowout in a lean premixed gas-turbine model combustor using the concept of dynamical system theory. Proc. Combust. Inst. 35, 3245–3253 (2015)

    Article  Google Scholar 

  19. S.A. Pawar, R. Vishnu, M. Vadivukkarasan, M.V. Panchagnula, R.I. Sujith, Intermittency route to combustion instability in a laboratory spray combustor. J. Eng. Gas Turb. Power 138, 041505 (2016)

    Article  Google Scholar 

  20. S. Datta, S. Mondal, A. Mukhopadhyay, D. Sanyal, S. Sen, An investigation of nonlinear dynamics of a thermal pulse combustor. Combust. Theor. Model. 13(1), 17–38 (2009)

    Article  MATH  Google Scholar 

  21. C.S. Daw, J.F. Thomas, G.A. Richards, L.L. Narayanaswami, Chaos in thermal pulse combustion. Chaos 5(4), 662–670 (1995)

    Article  Google Scholar 

  22. H.D. Ng, A.J. Higgins, C.B. Kiyanda, M.I. Radulescu, J.H.S. Lee, K.R. Bates, N. Nikiforakis, Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations. Combust. Theor. Model. 9, 159–170 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. K. Balasubramanian, R.I. Sujith, Non-normality and nonlinearity in combustion-acoustic interaction in diffusion flames. J. Fluid Mech. 594, 29–57 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  24. M. Tyagi, S.R. Chakravarthy, R.I. Sujith, Unsteady combustion response of a ducted non-premixed flame and acoustic coupling. Combust. Theor. Model. 11(2), 205–226 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. T.C. Lieuwen, Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor. J. Propul. Power 18(1), 61–67 (2002)

    Article  Google Scholar 

  26. S. Mondal, A. Mukhopadhyay, S. Sen, Dynamic characterization of a laboratory-scale pulse combustor. Combust. Sci. Technol. 186, 139–152 (2014)

    Article  Google Scholar 

  27. S. Balusamy, L.K.B. Li, Z. Han, M.P. Juniper, S. Hochgreb, Nonlinear dynamics of self-excited thermoacoustic system subjected to acoustic forcing. Proc. Combust. Inst. 35, 3229–3236 (2015)

    Article  Google Scholar 

  28. S. Candel, Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 29, 1–28 (2002)

    Article  Google Scholar 

  29. S. Ducruix, T. Schuller, D. Durox, S. Candel, Combustion dynamics and instabilities: elementary coupling and driving mechanisms. J. Propul. Power 19(5), 722–734 (2003)

    Article  Google Scholar 

  30. W.A. Sirignano, Driving mechanisms for combustion instability. Combust. Sci. Technol. 162–205, 2015 (1887)

    Google Scholar 

  31. E. Bradley, H. Kantz, Nonlinear time-series analysis revisited. Chaos 25, 097610 (2015)

    Article  MATH  Google Scholar 

  32. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J.D. Farmer, Testing for nonlinearity in time series: the method of surrogate data. Physica D 58, 77–94 (1992)

    Article  MATH  Google Scholar 

  33. R.C. Hilborn, Chaos and Nonlinear Dynamics, 2nd edn. (Oxford University Press, New York, 2000)

    Book  MATH  Google Scholar 

  34. F. Takens, Detecting strange attractors in turbulence, in Dynamical Systems and Turbulence (Lecture Notes in Mathematics), ed. by D.A. Rand, L.S. Young (Springer, Berlin, 1981)

    Google Scholar 

  35. H.D.I. Abarbanel, R. Brown, J.J. Sidorowich, L.S. Tsimring, The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 65(4), 1331–1392 (1993)

    Article  MathSciNet  Google Scholar 

  36. A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33(2), 1134–1140 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  37. P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractors. Physica D 9, 189–208 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  38. M.B. Kennel, R. Brown, H.D.I. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45(6), 3403–3411 (1992)

    Article  Google Scholar 

  39. L. Kabiraj, A. Saurabh, P. Wahi, R.I. Sujith, Route to chaos for combustion instability in ducted laminar premixed flames. Chaos 22, 023129 (2012)

    Article  Google Scholar 

  40. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  41. H. Kantz, A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A 185, 77–87 (1994)

    Article  Google Scholar 

  42. G.A. Gottwald, I. Melbourne, A new test for chaos in deterministic systems. Proc. R. Soc. Lond. A 460, 603–611 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  43. I. Falconer, G.A. Gottwald, I. Melbourne, K. Wormnes, Application of the 0–1 test for chaos to experimental data. SIAM J. Appl. Dyn. Syst. 6(2), 395–402 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  44. G.A. Gottwald, I. Melbourne, On the implementation of the 0–1 test for chaos. SIAM J. Appl. Dyn. Syst. 8(1), 129–145 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  45. J.P. Eckmann, S.O. Kamphorst, D. Ruelle, Recurrence plots of dynamical systems. Europhys. Lett. 4(9), 973–977 (1987)

    Article  Google Scholar 

  46. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329 (2007)

    Article  MathSciNet  Google Scholar 

  47. Y. Zou, Exploring recurrences in quasiperiodic dynamical systems. Ph.D. thesis, University of Potsdam, 2007

    Google Scholar 

  48. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, 1993)

    Google Scholar 

  49. G. Górski, G. Litak, R. Mosdorf, A. Rysak, Two phase flow bifurcation due to turbulence: transition from slugs to bubbles. Eur. Phys. J. B. 88, 239 (2015)

    Article  Google Scholar 

  50. R. Mosdorf, G. Górski, Detection of two-phase flow patterns using the recurrence network analysis of pressure fluctuations. Int. Commun. Heat Mass Transf. 64, 14–20 (2015)

    Article  Google Scholar 

  51. M.F. Llop, N. Gascons, F.X. Llauró, Recurrence plots to characterize gas-solid fluidization regimes. Int. J. Mult. Flow 73, 43–56 (2015)

    Article  Google Scholar 

  52. J.A. Bastos, J. Caiado, Recurrence quantification analysis of global stock markets. Physica A 390, 1315–1325 (2011)

    Article  Google Scholar 

  53. S. Nakano, Y. Hirata, K. Iwayama, K. Aihara, Intra-day response of foreign exchange markets after the Tohoku-Oki earthquake. Physica A 419, 203–214 (2015)

    Article  Google Scholar 

  54. J. Yan, Y. Wang, G. Ouyang, T. Yu, X. Li, Using max entropy ratio of recurrence plot to measure electrocorticogram changes in epilepsy patients. Physica A 443, 109–116 (2016)

    Article  MathSciNet  Google Scholar 

  55. J. Schlenker, V. Socha, L. Riedlbauchová, T. Nedělka, A. Schlenker, V. Potočková, Š. Malá, P. Kutílek, Recurrence plot of heart rate variability signal in patients with vasovagal syncopes. Biomed. Signal Process. Control 25, 1–11 (2016)

    Article  Google Scholar 

  56. M. Stöckl, D. Plück, M. Lames, Modeling game sports as complex systems—application of recurrence analysis to golf and soccer. Math. Comput. Model. Dyn. Syst. 23(4), 399–415 (2017)

    Article  Google Scholar 

  57. L.-P. Yang, S.-L. Ding, G. Litak, E.-Z. Song, X.-Z. Ma, Identification and quantification analysis of nonlinear dynamics properties of combustion instability in a diesel engine. Chaos 25, 013105 (2015)

    Article  Google Scholar 

  58. L. Kabiraj, A. Saurabh, H. Nawroth, C.O. Paschereit, Recurrence analysis of combustion noise. AIAA J. 53(5), 1199–1210 (2015)

    Article  Google Scholar 

  59. H. Gotoda, Y. Okuno, K. Hayashi, S. Tachibana, Characterization of degeneration process in combustion instability based on dynamical systems theory. Phys. Rev. E 92, 025906 (2015)

    Article  Google Scholar 

  60. V. Nair, R.I. Sujith, A reduced-order model for the onset of combustion instability: physical mechanisms for intermittency and precursors. Proc. Combust. Inst. 35, 3193–3200 (2015)

    Article  Google Scholar 

  61. H. Kinugawa, K. Ueda, H. Gotoda, Chaos of radiative heat-loss-induced flame front instability. Chaos 26, 033104 (2016)

    Article  MathSciNet  Google Scholar 

  62. L. Christodoulou, L. Kabiraj, A. Saurabh, N. Karimi, Characterizing the signature of flame flashback precursor through recurrence analysis. Chaos 26, 013110 (2016)

    Article  Google Scholar 

  63. L.-P. Yang, E.-Z. Song, S.-L. Ding, R.J. Brown, N. Marwan, X.-Z. Ma, Analysis of the dynamic characteristics of combustion instabilities in a pre-mixed lean-burn natural gas engine. Appl. Energy 183, 746–759 (2016)

    Article  Google Scholar 

  64. U. Sen, T. Gangopadhyay, C. Bhattacharya, A. Misra, S. Karmakar, P. Sengupta, A. Mukhopadhyay, S. Sen, Investigation of ducted inverse nonpremixed flames using dynamic systems approach, in Proceedings of ASME Turbo Expo, p. V04BT04A059, 2016

    Google Scholar 

  65. M. Tyagi, N. Jamadar, S.R. Chakravarthy, Oscillatory response of an idealized two-dimensional diffusion flame: analytical and numerical study. Combust. Flame 149, 271–285 (2007)

    Article  Google Scholar 

  66. S.J. Illingworth, I.C. Waugh, M.P. Juniper, Finding thermoacoustic limit cycles for a ducted Burke-Schumann flame. Proc. Combust. Inst. 34, 911–920 (2013)

    Article  Google Scholar 

  67. S.H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Books, Reading, MA, 1994)

    Google Scholar 

  68. V.N. Kurdyumov, M. Matalon, Dynamics of an edge flame in a mixing layer. Combust. Flame 139, 329–339 (2004)

    Article  Google Scholar 

  69. S.C. Reddy, L.N. Trefethen, Pseudospectra of the convection-diffusion operator. SIAM J. Appl. Math. 54(6), 1634–1649 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  70. L.N. Trefethen, Pseudospectra of linear operators. SIAM Rev. 39(3), 383–406 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  71. P.J. Schmid, D.S. Henningson, Stability and Transition in Shear Flows (Springer, New York, 2001)

    Book  MATH  Google Scholar 

  72. L.N. Trefethen, A.E. Trefethen, S.C. Reddy, T.A. Driscoll, Hydrodynamic stability without eigenvalues. Science 261, 578–584 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  73. J.S. Baggett, T.A. Driscoll, L.N. Trefethen, A mostly linear model of transition to turbulence. Phys. Fluids 7(4), 833–838 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  74. W. Kerner, Large-scale complex eigenvalue problems. J. Comput. Phys. 85, 1–85 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  75. B.F. Farrell, Optimal excitation of baroclinic waves. J. Atmos. Sci. 46(9), 1193–1206 (1989)

    Article  Google Scholar 

  76. A.P. Dowling, The calculation of thermoacoustic oscillations. J. Sound Vib. 180(4), 557–581 (1995)

    Article  Google Scholar 

  77. A. Fichera, C. Losenno, A. Pagano, Clustering of chaotic dynamics of a lean gas-turbine combustor. Appl. Energy 69, 101–117 (2001)

    Article  Google Scholar 

  78. T. Gebhardt, S. Grossmann, Chaos transition despite linear stability. Phys. Rev. E 50(5), 3705–3711 (1994)

    Article  Google Scholar 

  79. K. Matveev, Thermoacoustic instabilities in the Rijke tube: experiments and modeling, Ph.D. thesis, California Institute of Technology, 2003

    Google Scholar 

  80. V. Jegadeesan, R.I. Sujith, Experimental investigation of noise induced triggering in thermoacoustic systems. Proc. Combust. Inst. 34, 3175–3183 (2013)

    Article  Google Scholar 

  81. K.T. Kim, S. Hochgreb, Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor. Combust. Flame 159, 1215–1227 (2012)

    Article  Google Scholar 

  82. N. Noiray, D. Durox, T. Schuller, S. Candel, A unified framework for nonlinear combustion instability analysis based on the flame describing function. J. Fluid Mech. 615, 139–167 (2008)

    Article  MATH  Google Scholar 

  83. M.P. Juniper, Triggering in the horizontal Rijke tube: non-normality, transient growth, and bypass transition. J. Fluid Mech. 667, 272–308 (2011)

    Article  MATH  Google Scholar 

  84. S. Fedotov, I. Bashkirtseva, L. Ryashko, Stochastic analysis of a non-normal dynamical system mimicking a laminar-to-turbulent subcritical transition. Phys. Rev. E 66, 066310 (2002)

    Article  Google Scholar 

  85. V.S. Burnley, F.E.C. Culick, Influence of random excitations on acoustic instabilities in combustion chambers. AIAA J. 38(8), 1403–1410 (2000)

    Article  Google Scholar 

  86. I.C. Waugh, M.P. Juniper, Triggering in a thermoacoustic system with stochastic noise. Int. J. Spray Combust. Dyn. 3(3), 225–242 (2011)

    Article  Google Scholar 

  87. T. Lieuwen, A. Banaszuk, Background noise effects on combustor stability. J. Propul. Power 21(1), 25–31 (2005)

    Article  Google Scholar 

  88. Y. Duguet, A.P. Willis, R.R. Kerswell, Transition in pipe flow: the saddle structure on the boundary of turbulence. J. Fluid Mech. 613, 255–274 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  89. S. Nair, T. Lieuwen, Acoustic detection of blowout in premixed flames. J. Propul. Power 21(1), 32–39 (2005)

    Article  Google Scholar 

  90. S.J. Shanbhogue, S. Husain, T. Lieuwen, Lean blowoff of bluff body stabilized flames: scaling and dynamics. Prog. Energy Combust. Sci. 35, 98–120 (2009)

    Article  Google Scholar 

  91. A.H. Nayfeh, B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2004)

    MATH  Google Scholar 

  92. O. Batiste, E. Knobloch, I. Mercader, M. Net, Simulations of oscillatory binary fluid convection in large aspect ratio containers. Phys. Rev. E 65, 016303 (2001)

    Article  MathSciNet  Google Scholar 

  93. L. Holden, T. Erneux, Understanding bursting oscillations as periodic slow passages through bifurcation and limit points. J. Math. Biol. 31, 351–365 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  94. S.K. Han, D.E. Postnov, Chaotic bursting as chaotic itinerancy in coupled neural oscillators. Chaos 13(3), 1105–1109 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  95. R. Straube, D. Flockerzi, M.J.B. Hauser, Sub-Hopf/fold-cycle bursting and its relation to (quasi-)periodic oscillations. J. Phys.: Conf. Ser. 55, 214–231 (2006)

    Google Scholar 

  96. V. Nair, G. Thampi, R.I. Sujith, Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756, 470–487 (2014)

    Article  Google Scholar 

  97. V. Nair, R.I. Sujith, Intermittency as a transition state in combustor dynamics: an explanation for flame dynamics near lean blowout. Combust. Sci. Technol. 187, 1821–1835 (2015)

    Article  Google Scholar 

  98. U. Sen, T. Gangopadhyay, C. Bhattacharya, A. Mukhopadhyay, S. Sen, Dynamic characterization of a ducted inverse diffusion flame using recurrence analysis. Combust. Sci. Technol. 190(1), 32–56 (2018)

    Article  Google Scholar 

  99. Y. Pomeau, P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys. 74, 189–197 (1980)

    Article  MathSciNet  Google Scholar 

  100. H. Okamoto, N. Tanaka, M. Naito, Intermittencies and related phenomena in the oxidation of formaldehyde at a constant current. J. Phys. Chem. A 102, 7353–7361 (1998)

    Article  Google Scholar 

  101. K. Klimaszewska, J.J. Żebrowski, Detection of the type of intermittency using characteristic patterns in recurrence plots. Phys. Rev. E 80, 026214 (2009)

    Article  Google Scholar 

  102. L. Kabiraj, R.I. Sujith, P. Wahi, Bifurcations of self-excited ducted laminar premixed flames. J. Eng. Gas Turbines Power 134, 031502 (2012)

    Article  Google Scholar 

  103. Y. Matsui, An experimental study on pyro-acoustic amplification of premixed laminar flames. Combust. Flame 43, 199–209 (1981)

    Article  Google Scholar 

  104. D. Ruelle, F. Takens, On the nature of turbulence. Commun. Math. Phys. 20, 167–192 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  105. K. Kashinath, I.C. Waugh, M.P. Juniper, Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcation and routes to chaos. J. Fluid Mech. 761, 399–430 (2014)

    Article  Google Scholar 

  106. G.-S. Jiang, D. Peng, Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21(6), 2126–2143 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  107. S. Gottlieb, C.-W. Shu, Total variation diminishing Runge-Kutta schemes. Math. Comput. 67(221), 73–85 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  108. A. Sobiesiak, S. Rahbar, H.A. Becker, Performance characteristics of the novel low-NOx CGRI burner for use with high air preheat. Combust. Flame 115, 93–125 (1988)

    Article  Google Scholar 

  109. J. Miao, C.W. Leung, C.S. Cheung, Z. Huang, W. Jin, Effect of H\(_{2}\) addition on OH distribution of LPG/air circumferential inverse diffusion flame. Int. J. Hydrog. Energy 41, 9653–9663 (2016)

    Article  Google Scholar 

  110. L.K. Sze, C.S. Cheung, C.W. Leung, Appearance, temperature, and NOx emission of two inverse diffusion flames with different port design. Combust. Flame 144, 237–248 (2006)

    Article  Google Scholar 

  111. C.R. Kaplan, K. Kailasanath, Flow-field effects on soot formation in normal and inverse methane-air diffusion flames. Combust. Flame 124, 275–294 (2001)

    Article  Google Scholar 

  112. S.R. Stow, A.P. Dowling, Thermoacoustic oscillations in an annular combustor, in Proceedings of ASME Turbo Expo, p. V002T02A004, 2001

    Google Scholar 

  113. H. Herzel, P. Plath, P. Svensson, Experimental evidence of homoclinic chaos and type-II intermittency during the oxidation of methanol. Physica D 48, 340–352 (1991)

    Article  MATH  Google Scholar 

  114. D. Parthimos, D.H. Edwards, T.M. Griffith, Shil’nikov chaos is intimately related to type-III intermittency in isolated rabbit arteries: Role of nitric oxide. Phys. Rev. E 67, 051922 (2003)

    Article  Google Scholar 

  115. V. Nair, R.I. Sujith, Identifying homoclinic orbits in the dynamics of intermittent signals through recurrence quantification. Chaos 23, 033136 (2013)

    Article  Google Scholar 

  116. P. Holmes, Can dynamical systems approach turbulence? In J. Lumley, editor, Whither Turbulence? Turbulence at the Crossroads, (Springer, 1990), pp. 195–249

    Google Scholar 

  117. E. Stone, M. Gorman, M. el Hamdi, K.A. Robbins, Identification of ordered patterns as heteroclinic connections. Phys. Rev. Lett. 76(12), 2061–2064 (1996)

    Article  Google Scholar 

  118. E. Stone, P. Holmes, Unstable fixed points, heteroclinic cycles and exponential tails in turbulence production. Phys. Lett. A 155(1), 29–42 (1991)

    Article  MathSciNet  Google Scholar 

  119. P.W. Hammer, N. Platt, S.M. Hammel, J.F. Heagy, B.D. Lee, Experimental observation of on-off intermittency. Phys. Rev. Lett. 73(8), 1095–1098 (1994)

    Article  Google Scholar 

  120. M. Frank, M. Schmidt, Time series investigations on an experimental system driven by phase transitions. Phys. Rev. E 56(3), 2423–2428 (1997)

    Article  Google Scholar 

  121. H.G. Schuster, W. Just, Deterministic Chaos: An Introduction, 4th edn. (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2005)

    Book  MATH  Google Scholar 

  122. D.L. Feng, J. Zheng, W. Huang, C.X. Yu, W.X. Ding, Type-I-like intermittent chaos in multicomponent plasmas with negative ions. Phys. Rev. E 54(3), 2839–2843 (1996)

    Article  Google Scholar 

  123. A.-L. Barabási, The network takeover. Nat. Phys. 8, 14–16 (2011)

    Article  Google Scholar 

  124. E. Alm, A.P. Arkin, Biological networks. Curr. Opin. Struct. Biol. 13, 193–202 (2003)

    Article  Google Scholar 

  125. A.-L. Barabáasi, Z.N. Oltvai, Network biology: undersanding the cell’s functional organization. Nat. Rev. Genet. 5, 101–113 (2004)

    Article  Google Scholar 

  126. R. Albert, H. Jeong, A.-L. Barabási, Diameter of the World-Wide Web. Nature 401, 130–131 (1999)

    Article  Google Scholar 

  127. R. Albert, H. Jeong, A.-L. Barabási, Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)

    Article  Google Scholar 

  128. G.A. Pagani, M. Aiello, The power grid as a complex network: a survey. Physica A 392, 2688–2700 (2013

    Article  MathSciNet  Google Scholar 

  129. S. Arianos, E. Bompard, A. Carbone, F. Xue, Power grid vulnerability: a complex network approach. Chaos 19, 013119 (2009)

    Article  Google Scholar 

  130. A.K. Charakopoulos, T.E. Karakasidis, P.N. Papanicolaou, A. Liakopoulos, The application of complex network time seris analysis in turbulent heated jets. Chaos 24, 024408 (2014)

    Article  MATH  Google Scholar 

  131. C. Liu, W.-X. Zhou, W.-K. Yuan, Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence. Physica A 389, 2675–2681 (2010)

    Article  Google Scholar 

  132. R. Jacob, K.P. Harikrishnan, R. Misra, G. Ambika, Characterization of chaotic attractors under noise: a recurrence network perspective. Commun. Nonlinear Sci. Numer. Simulat. 41, 32–47 (2016)

    Article  MathSciNet  Google Scholar 

  133. Y. Okuno, M. Small, H. Gotoda, Dynamics of self-excited thermoacoustic instability in a combustion system: pseudo-periodic and high-dimensional nature. Chaos 25, 043107 (2015)

    Article  Google Scholar 

  134. M. Murugesan, R.I. Sujith, Combustion noise is scale-free: transition from scale-free to order at the onset of thermoacoustic instability. J. Fluid Mech. 772, 225–245 (2015)

    Article  Google Scholar 

  135. M. Murugesan, R.I. Sujith, Detecting the onset of an impending thermoacoustic instability using complex networks. J. Propul. Power 32(3), 707–712 (2016)

    Article  Google Scholar 

  136. H. Gotoda, H. Kinugawa, R. Tsujimoto, S. Domen, Y. Okuno, Characterization of combustion dynamics, detection, and prevention of an unstable combustion state based on a complex-network theory. Phys. Rev. Appl. 7, 044027 (2017)

    Article  Google Scholar 

  137. V. Godavarthi, V.R. Unni, E.A. Gopalakrishnan, R.I. Sujith, Recurrence networks to study dynamical transitions in a turbulent combustor. Chaos 27, 063113 (2017)

    Article  Google Scholar 

  138. J. Singh, R.B. Vishwanath, S. Chaudhuri, R.I. Sujith, Network structure of turbulent premixed flames. Chaos 27, 043107 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Uddalok Sen

  2. Mechanical Engineering Department, Jadavpur University, Kolkata, 700032, India

    Achintya Mukhopadhyay & Swarnendu Sen

Authors
  1. Uddalok Sen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Achintya Mukhopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Swarnendu Sen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Achintya Mukhopadhyay .

Editor information

Editors and Affiliations

  1. ACRI, The CFD Innovators, Los Angeles, California, USA

    Akshai K. Runchal

  2. Department of Mechanical Engineering, University of Maryland, Department of Mechanical Engineering, College Park, Maryland, USA

    Ashwani K. Gupta

  3. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Abhijit Kushari

  4. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Department of Aerospace Engineering, Kanpur, Uttar Pradesh, India

    Ashoke De

  5. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Department of Mechanical Engineering, Chicago, Illinois, USA

    Suresh K. Aggarwal

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sen, U., Mukhopadhyay, A., Sen, S. (2018). Dynamic Systems Approach for Laminar Ducted Flames. In: Runchal, A., Gupta, A., Kushari, A., De, A., Aggarwal, S. (eds) Energy for Propulsion . Green Energy and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-7473-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-7473-8_5

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-7472-1

  • Online ISBN: 978-981-10-7473-8

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics

Search

Navigation