Nine decades of rocket engine and gas turbine development have shown that thermoacoustic oscillations are difficult to predict but can usually be eliminated with relatively small ad hoc design changes. These changes can, however, be ruinously expensive to devise. This review explains why linear and nonlinear thermoacoustic behavior is so sensitive to parameters such as operating point, fuel composition, and injector geometry. It shows how nonperiodic behavior arises in experiments and simulations and discusses how fluctuations in thermoacoustic systems with turbulent reacting flow, which are usually filtered or averaged out as noise, can reveal useful information. Finally, it proposes tools to exploit this sensitivity in the future: adjoint-based sensitivity analysis to optimize passive control designs and complex systems theory to warn of impending thermoacoustic oscillations and to identify the most sensitive elements of a thermoacoustic system.


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Literature Cited

  1. Abrams DM, Strogatz SH. 2004. Chimera states for coupled oscillators. Phys. Rev. Lett. 93:174102 [Google Scholar]
  2. Ananthakrishnan N, Deo S, Culick FEC. 2005. Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber. Combust. Sci. Technol. 177:221–48 [Google Scholar]
  3. Armitage C, Balachandran R, Mastorakos E, Cant R. 2006. Investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations. Combust. Flame 146:419–36 [Google Scholar]
  4. Bade S, Wagner M, Hirsch C, Sattelmayer T, Schuermans B. 2013. Design for thermo-acoustic stability: procedure and database. J. Eng. Gas Turbines Power 135:121507 [Google Scholar]
  5. Balachandran R, Ayoola BO, Kaminski CF, Dowling AP, Mastorakos E. 2005. Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations. Combust. Flame 143:37–55 [Google Scholar]
  6. Balasubramanian K, Sujith RI. 2008. Thermoacoustic instability in a Rijke tube: non-normality and nonlinearity. Phys. Fluids 20:044103 [Google Scholar]
  7. Barabási Al, R Albert. 1999. Emergence of scaling in random networks. Science 286:509–12 [Google Scholar]
  8. Bauerheim M, Nicoud F, Poinsot T. 2016. Progress in analytical methods to predict and control azimuthal combustion instability modes in annular chambers. Phys. Fluids 28:021303 [Google Scholar]
  9. Bellows BD, Bobba MK, Forte A, Seitzman JM, Lieuwen T. 2007. Flame transfer function saturation mechanisms in a swirl-stabilized combustor. Proc. Combust. Inst. 31:3081–88 [Google Scholar]
  10. Bellucci V, Flohr P, Paschereit CO, Magni F. 2004. On the use of Helmholtz resonators for damping acoustic pulsations in industrial gas turbines. J. Eng. Gas Turbines Power 126:271–75 [Google Scholar]
  11. Boujo E, Denisov A, Schuermans B, Noiray N. 2016. Quantifying acoustic damping using flame chemiluminescence. J. Fluid Mech. 808:245–57 [Google Scholar]
  12. Bourgouin JF, Durox D, Moeck J, Schuller T, Candel SM. 2015. Characterization and modeling of a spinning thermoacoustic instability in an annular combustor equipped with multiple matrix injectors. J. Eng. Gas Turbines Power 137:021503 [Google Scholar]
  13. Burnley VS, Culick FEC. 2000. Influence of random excitations on acoustic instabilities in combustion chambers. AIAA J 38:1403–10 [Google Scholar]
  14. Candel SM. 1992. Combustion instabilities coupled by pressure waves and their active control. Symp. Int. Combust. 24:1277–96 [Google Scholar]
  15. Candel SM. 2002. Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 29:1–28 [Google Scholar]
  16. Candel SM, Durox D, Schuller T, Bourgouin JF, Moeck JP. 2014. Dynamics of swirling flames. Annu. Rev. Fluid Mech. 46:147–73 [Google Scholar]
  17. Chomaz JM. 1993. Linear and non-linear, local and global stability analysis of open flows. Turbulence in Spatially Extended Systems R Benzi, C Basdevant, S Ciliberto 245–57 Commack, NY: Nova Sci. Publ. [Google Scholar]
  18. Chomaz JM. 2005. Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37:357–92 [Google Scholar]
  19. Chu BT. 1965. On the energy transfer to small disturbances in fluid flow (part I). Acta Mech 1:215–34 [Google Scholar]
  20. Clavin P, Kim JS, Williams FA. 1994. Turbulence-induced noise effects on high frequency combustion instabilities. Combust. Sci. Technol. 96:61–84 [Google Scholar]
  21. Ćosić B, Moeck JP, Paschereit CO. 2014. Nonlinear instability analysis for partially premixed swirl flames. Combust. Sci. Technol. 186:713–36 [Google Scholar]
  22. Crocco L. 1951. Aspects of combustion stability in liquid propellant rocket motors, part I: fundamentals. Low frequency instability with monopropellants. J. Am. Rocket Soc. 8:163–78 [Google Scholar]
  23. Crocco L. 1969. Research on combustion instability in liquid propellant rockets. Symp. Int. Combust. 12:85–99 [Google Scholar]
  24. Crocco L, Cheng SI. 1956. Theory of Combustion Instability in Liquid Propellant Rocket Motors London: Butterworths [Google Scholar]
  25. Culick FEC. 1971. Non-linear growth and limiting amplitude of acoustic oscillations in combustion chambers. Combust. Sci. Technol. 3:1–16 [Google Scholar]
  26. Culick FEC. 2006. Unsteady motions in combustion chambers for propulsion systems RTO AGARDograph AG-AVT-039, Res. Technol. Organ., North Atl. Treaty Organ. Washington, DC: [Google Scholar]
  27. Donner RV, Zou Y, Donges JF, Marwan N, Kurths J. 2010. Recurrence networks—a novel paradigm for nonlinear time series analysis. New J. Phys. 12:033025 [Google Scholar]
  28. Dowling AP. 1997. Nonlinear self-excited oscillations of a ducted flame. J. Fluid Mech. 346:271–90 [Google Scholar]
  29. Dowling AP. 1999. A kinematic model of a ducted flame. J. Fluid Mech. 394:51–72 [Google Scholar]
  30. Dowling AP, Morgans AS. 2005. Feedback control of combustion oscillations. Annu. Rev. Fluid Mech. 37:151–82 [Google Scholar]
  31. Dranovsky ML. 2007. Combustion Instabilities in Liquid Rocket Engines: Testing and Development Practices in Russia Reston, VA: AIAA [Google Scholar]
  32. Ducruix S, Schuller T, Durox D, Candel S. 2003. Combustion dynamics and instabilities: elementary coupling and driving mechanisms. J. Propuls. Power 19:722–34 [Google Scholar]
  33. Durox D, Schuller T, Noiray N, Candel S. 2009. Experimental analysis of nonlinear flame transfer functions for different flame geometries. Proc. Combust. Inst. 32:1391–98 [Google Scholar]
  34. Eldredge JD, Dowling AP. 2003. The absorption of axial acoustic waves by a perforated liner with bias flow. J. Fluid Mech. 485:307–35 [Google Scholar]
  35. Gelb A, Vander Velde WE. 1968. Multiple-Input Describing Functions and Nonlinear System Design New York: McGraw-Hill [Google Scholar]
  36. Gopalakrishnan EA, Sujith RI. 2015. Effect of external noise on the hysteresis characteristics of a thermoacoustic system. J. Fluid Mech. 776:334–53 [Google Scholar]
  37. 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]
  38. Gotoda H, Nikimoto H, Miyano T, Tachibana S. 2011. Dynamic properties of combustion instability in a lean premixed gas-turbine combustor. Chaos 21:013124 [Google Scholar]
  39. 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 Scholar]
  40. Gotoda H, Shinoda Y, Kobayashi M, Okuno Y, Tachibana S. 2014. Detection and control of combustion instability based on the concept of dynamical system theory. Phys. Rev. E 89:022910 [Google Scholar]
  41. Gysling DL, Copeland GS, McCormick DC, Proscia WM. 2000. Combustion system damping augmentation with Helmholtz resonators. J. Eng. Gas Turbines Power 122:269–74 [Google Scholar]
  42. Han X, Li J, Morgans AS. 2015. Prediction of combustion instability limit cycle oscillations by combining flame describing function simulations with a thermoacoustic network model. Combust. Flame 162:3632–47 [Google Scholar]
  43. Harrje DT, Reardon FH. 1972. Liquid propellant rocket combustion instability Tech. Rep. NASA-SP-194, Natl. Aeronaut. Space Admin. Washington, DC: [Google Scholar]
  44. Heckl M. 1990. Non-linear acoustic effect in the Rijke tube. Acoustica 72:63–71 [Google Scholar]
  45. Hemchandra S. 2012. Premixed flame response to equivalence ratio fluctuations: comparison between reduced order modeling and detailed computations. Combust. Flame 159:3530–43 [Google Scholar]
  46. Higgins B. 1802. On the sound produced by a current of hydrogen gas passing through a tube. J. Nat. Philos. Chem. Arts 1:129–31 [Google Scholar]
  47. Hill DC. 1992. A theoretical approach for analyzing the restabilization of wakes Tech. Rep. 103858, Natl. Aeronaut. Space Admin. Washington, DC: [Google Scholar]
  48. Hill DC. 1995. Adjoint systems and their role in the receptivity problem for boundary layers. J. Fluid Mech. 292:183–204 [Google Scholar]
  49. Huang Y. 2015. Advanced methods for validating combustion instability predictions using pressure measurements PhD Thesis, Purdue Univ., West Lafayette, IN [Google Scholar]
  50. Huang Y, Yang V. 2009. Dynamics and stability of lean-premixed swirl-stabilized combustion. Prog. Energy Combust. Sci. 35:293–364 [Google Scholar]
  51. Jahnke CC, Culick FEC. 1994. Application of dynamical systems theory to nonlinear combustion instabilities. J. Propuls. Power 10:508–17 [Google Scholar]
  52. Jegadeesan V, Sujith RI. 2013. Experimental investigation of noise induced triggering in thermoacoustic systems. Proc. Combust. Inst. 34:3175–83 [Google Scholar]
  53. Juniper MP. 2011. Triggering in the Rijke tube: non-normality, transient growth and bypass transition. J. Fluid Mech. 667:272–308 [Google Scholar]
  54. Juniper MP. 2012. Triggering in thermoacoustics. Int. J. Spray Combust. Dyn. 4:217–38 [Google Scholar]
  55. Kabiraj L, Saurabh A, Karimi N, Sailor A, Mastorakos E. et al. 2015a. Chaos in an imperfectly premixed model combustor. Chaos 25:023101 [Google Scholar]
  56. Kabiraj L, Saurabh A, Wahi P, Sujith RI. 2012a. Route to chaos for combustion instability in ducted laminar premixed flames. Chaos 22:023129 [Google Scholar]
  57. Kabiraj L, Steinert R, Saurabh A, Paschereit CO. 2015b. Coherence resonance in a thermoacoustic system. Phys. Rev. E 92:042909 [Google Scholar]
  58. Kabiraj L, Sujith RI. 2012. Nonlinear self-excited thermoacoustic oscillations: intermittency and flame blowout. J. Fluid Mech. 713:376–97 [Google Scholar]
  59. Kabiraj L, Sujith RI, Wahi P. 2012b. Bifurcations of self-excited ducted laminar premixed flames. J. Eng. Gas Turbines Power 134:31502 [Google Scholar]
  60. Kantelhardt JW. 2012. Fractal and multifractal time series. Mathematics of Complexity and Dynamical Systems RA Meyers 463–87 Berlin: Springer [Google Scholar]
  61. Karimi N, Brear MJ, Jin SH, Monty JP. 2009. Linear and non-linear forced response of a conical, ducted, laminar premixed flame. Combust. Flame 156:2201–12 [Google Scholar]
  62. Kashinath K, Waugh IC, Juniper MP. 2014. Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: bifurcations and routes to chaos. J. Fluid Mech. 761:399–430 [Google Scholar]
  63. Kerswell RR. 2018 Nonlinear nonmodal stability theory. Annu. Rev. Fluid Mech 50:319–45 [Google Scholar]
  64. Kim KT, Lee JG, Quay BD, Santavicca DA. 2010a. Response of partially premixed flames to acoustic velocity and equivalence ratio perturbations. Combust. Flame 157:1731–44 [Google Scholar]
  65. Kim KT, Lee JG, Quay BD, Santavicca DA. 2010b. Spatially distributed flame transfer functions for predicting combustion dynamics in lean premixed gas turbine combustors. Combust. Flame 157:1718–30 [Google Scholar]
  66. Komarek T, Polifke W. 2010. Impact of swirl fluctuations on the flame response of a perfectly premixed swirl burner. J. Eng. Gas Turbines Power 132:061503 [Google Scholar]
  67. Krediet HJ, Beck CH, Krebs W, Schimek S, Paschereit CO, Kok JBW. 2012. Identification of the flame describing function of a premixed swirl flame from LES. Combust. Sci. Technol. 184:888–900 [Google Scholar]
  68. Lacasa L, Luque B, Ballesteros F, Luque J, Nun JC. 2008. From time series to complex networks: the visibility graph. PNAS 105:4972–75 [Google Scholar]
  69. Landau LD. 1944. On the problem of turbulence. C. R. Acad. Sci. URSS 44:387–91 [Google Scholar]
  70. Lesne A, Lagues M. 2011. Scale Invariance: From Phase Transitions to Turbulence Berlin: Springer [Google Scholar]
  71. Lieuwen TC. 2002. Experimental investigation of limit-cycle oscillations in an unstable gas turbine combustor. J. Propuls. Power 18:61–67 [Google Scholar]
  72. Lieuwen TC. 2012. Unsteady Combustor Physics Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  73. Lieuwen TC, Banaszuk A. 2005. Background noise effects on combustor stability. J. Propuls. Power 21:25–31 [Google Scholar]
  74. Lieuwen TC, McManus KR. 2003. Introduction: combustion dynamics in lean-premixed prevaporized (LPP) gas turbines. J. Propuls. Power 19:721 [Google Scholar]
  75. Lieuwen TC, Yang V. 2005. Combustion Instabilities in Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling Reston, VA: AIAA [Google Scholar]
  76. Luchini P, Bottaro A. 2014. Adjoint equations in stability analysis. Annu. Rev. Fluid Mech. 46:493–517 [Google Scholar]
  77. Macquisten MA, Whiteman M, Stow SR, Moran AJ. 2014. Exploitation of measured flame transfer functions for a two-phase lean fuel injector to predict thermoacoustic modes in full annular combustors. Proc. ASME Turbo Expo, Düsseldorf, Ger., June 16–20 Pap. GT2014-25036 New York: Am. Soc. Mech. Eng. [Google Scholar]
  78. Magri L, Bauerheim M, Juniper MP. 2016a. Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity. J. Comput. Phys. 325:395–410 [Google Scholar]
  79. Magri L, Bauerheim M, Nicoud F, Juniper MP. 2016b. Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part II. Uncertainty quantification. J. Comput. Phys. 325:411–21 [Google Scholar]
  80. Magri L, Juniper MP. 2013. Sensitivity analysis of a time-delayed thermo-acoustic system via an adjoint-based approach. J. Fluid Mech. 719:183–202 [Google Scholar]
  81. Magri L, Juniper MP. 2014. Global modes, receptivity, and sensitivity analysis of diffusion flames coupled with duct acoustics. J. Fluid Mech. 752:237–65 [Google Scholar]
  82. Mandelbrot BB. 1999. Multifractals and Noise: Wild Self-Affinity in Physics Berlin: Springer [Google Scholar]
  83. Matveev KI. 2003a. Energy consideration of the nonlinear effects in a Rijke tube. J. Fluids Struct. 18:783–94 [Google Scholar]
  84. Matveev KI. 2003b. Thermoacoustic instabilities in the Rijke tube: experiments and modeling PhD Thesis, Calif. Inst. Technol., Pasadena [Google Scholar]
  85. McManus KR, Poinsot T, Candel SM. 1993. A review of active control of combustion instabilities. Prog. Energy Combust. Sci. 19:1–29 [Google Scholar]
  86. Mensah GA, Moeck JP. 2017. Acoustic damper placement and tuning for annular combustors: an adjoint-based optimization study. J. Eng. Gas Turbines Power 139:061501 [Google Scholar]
  87. Moeck JP, Bothein MR, Schimek S, Lacarelle A, Paschereit CO. 2008. Subcritical thermoacoustic instabilities in a premixed combustor Presented at 14th AIAA/CEAS Aeroacoust. Conf., May 5–7, Vancouver, AIAA Pap 2008–2946 [Google Scholar]
  88. Mondal S, Unni VR, Sujith RI. 2017. Onset of thermoacoustic instability in turbulent combustors: an emergence of synchronized periodicity through formation of chimera-like states. J. Fluid Mech. 811:659–81 [Google Scholar]
  89. Mongia HC, Held TJ, Hsiao GC, Pandalai RP. 2003. Challenges and progress in controlling dynamics in gas turbine combustors. J. Propuls. Power 19:822–29 [Google Scholar]
  90. Murugesan M, Sujith RI. 2015. Combustion noise is scale-free: transition from scale-free to order at the onset of thermoacoustic instability. J. Fluid Mech. 772:225–45 [Google Scholar]
  91. Murugesan M, Sujith RI. 2016. Detecting the onset of an impending thermoacoustic instability using complex networks. J. Propuls. Power 32:707–12 [Google Scholar]
  92. Nair V, Sujith RI. 2014. Multifractality in combustion noise: predicting an impending combustion instability. J. Fluid Mech. 747:635–55 [Google Scholar]
  93. Nair V, Sujith RI. 2015. A reduced-order model for the onset of combustion instability: physical mechanisms for intermittency and precursors. Proc. Combust. Inst. 35:3193–200 [Google Scholar]
  94. Nair V, Thampi G, Karuppusamy S, Gopalan S, Sujith RI. 2013. Loss of chaos in combustion noise as a precursor of impending combustion instability. Int. J. Spray Combust. Dyn. 5:273–90 [Google Scholar]
  95. Nair V, Thampi G, Sujith RI. 2014. Intermittency route to thermoacoustic instability in turbulent combustors. J. Fluid Mech. 756:470–87 [Google Scholar]
  96. Nicoud F, Benoit L, Sensiau C, Poinsot T. 2007. Acoustic modes in combustors with complex impedances and multidimensional active flames. AIAA J 45:426–41 [Google Scholar]
  97. Nicoud F, Wieczorek K. 2009. About the zero Mach number assumption in the calculation of thermoacoustic instabilities. Int. J. Spray Combust. Dyn. 1:67–111 [Google Scholar]
  98. Noiray N. 2017. Linear growth rate estimation from dynamics and statistics of acoustic signal envelope in turbulent combustors. J. Eng. Gas Turbines Power 139:041503 [Google Scholar]
  99. Noiray N, Denisov A. 2017. A method to identify thermoacoustic growth rates in combustion chambers from dynamic pressure time series. Proc. Combust. Inst. 36:3843–50 [Google Scholar]
  100. Noiray N, Durox D, Schuller T, Candel S. 2008. A unified framework for nonlinear combustion instability analysis based on the flame describing function. J. Fluid Mech. 615:139–67 [Google Scholar]
  101. Noiray N, Durox D, Schuller T, Candel S. 2009. Dynamic phase converter for passive control of combustion instabilities. Proc. Combust. Inst. 32:3163–70 [Google Scholar]
  102. Noiray N, Schuermans B. 2013a. Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors. Int. J. Non-Linear Mech. 50:152–63 [Google Scholar]
  103. Noiray N, Schuermans B. 2013b. On the dynamic nature of azimuthal thermoacoustic modes in annular gas turbine combustion chambers. Proc. R. Soc. Lond. 469:20120535 [Google Scholar]
  104. Oberleithner K, Schimek S, Paschereit CO. 2015. Shear flow instabilities in swirl-stabilized combustors and their impact on the amplitude dependent flame response: a linear stability analysis. Combust. Flame 162:86–99 [Google Scholar]
  105. O'Connor J, Acharya V, Lieuwen T. 2015. Transverse combustion instabilities: acoustic, fluid mechanic, and flame processes. Prog. Energy Combust. Sci. 49:1–39 [Google Scholar]
  106. Oefelein JC, Yang V. 1993. Comprehensive review of liquid-propellant combustion instabilities in F-1 engines. J. Propuls. Power 9:657–77 [Google Scholar]
  107. Okuno Y, Small M, Gotoda H. 2015. Dynamics of self-excited thermoacoustic instability in a combustion system: pseudo-periodic and high-dimensional nature. Chaos 25:043107 [Google Scholar]
  108. Orchini A, Rigas G, Juniper MP. 2016. Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube. J. Fluid Mech. 805:523–50 [Google Scholar]
  109. Palies P, Durox D, Schuller T, Candel S. 2011. Nonlinear combustion instability analysis based on the flame describing function applied to turbulent premixed swirling flames. Combust. Flame 158:1980–91 [Google Scholar]
  110. Paschereit CO, Schuermans B, Polifke W, Mattson O. 2002. Measurement of transfer matrices and source terms of premixed flames. J. Eng. Gas Turbines Power 124:239–47 [Google Scholar]
  111. Pawar SA, Vishnu R, Vadivukkarasan M, Panchagnula MV, Sujith RI. 2016. Intermittency route to combustion instability in a laboratory spray combustor. J. Eng. Gas Turbines Power 138:041505 [Google Scholar]
  112. Pikovsky AS, Kurths J. 1997. Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 78:775–78 [Google Scholar]
  113. Poinsot T. 2017. Prediction and control of combustion instabilities in real engines. Proc. Combust. Inst. 36:1–28 [Google Scholar]
  114. Poinsot TJ, Trouvé AC, Veynante DP, Candel SM. 1987. Vortex-driven acoustically coupled combustion instabilities. J. Fluid Mech. 177:265–92 [Google Scholar]
  115. Prieur K, Durox D, Schuller T, Candel S. 2016. The describing function of swirled spray flames Presented at 24th Int. Congr. Theor. Appl. Mech., Aug. 21–26, Montreal [Google Scholar]
  116. Provansal M, Mathis C, Boyer L. 1987. Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182:1–22 [Google Scholar]
  117. Rankine WJM. 1870. On the thermodynamic theory of waves of finite longitudinal disturbance. Proc. R. Soc. Lond. 18:80–83 [Google Scholar]
  118. Rayleigh JWSB. 1878. The explanation of certain acoustical phenomena. Nature 18:319–21 [Google Scholar]
  119. Rayleigh JWSB. 1896. The Theory of Sound 2 New York: Dover [Google Scholar]
  120. Reynolds WC, Hussain AKMF. 1972. The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54:263–88 [Google Scholar]
  121. Richards G, Straub DL, Robey EH. 2003. Passive control of combustion dynamics in stationary gas turbines. J. Propuls. Power 19:795–810 [Google Scholar]
  122. Rigas G, Jamieson NP, Li LKB, Juniper MP. 2016. Experimental sensitivity analysis and control of thermoacoustic systems. J. Fluid Mech. 787:R1 [Google Scholar]
  123. Sampath R, Chakravarthy SR. 2016. Investigation of intermittent oscillations in a premixed dump combustor using time-resolved particle image velocimetry. Combust. Flame 172:309–25 [Google Scholar]
  124. Schimek S, Moeck JP, Paschereit CO. 2011. An experimental investigation of the nonlinear response of an atmospheric swirl-stabilized premixed flame. J. Eng. Gas Turbines Power 133:101502 [Google Scholar]
  125. Schmid PJ. 2007. Nonmodal stability theory. Annu. Rev. Fluid Mech. 39:129–62 [Google Scholar]
  126. Schmid PJ, Henningson D. 2001. Stability and Transition in Shear Flows Berlin: Springer [Google Scholar]
  127. Shreekrishna, Hemchandra S, Lieuwen TC. 2010. Premixed flame response to equivalence ratio perturbations. Combust. Theory Model. 14:681–714 [Google Scholar]
  128. Sipp D, Lebedev A. 2007. Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593:333–58 [Google Scholar]
  129. Sirignano WA. 2016. Driving mechanisms for combustion instability. Combust. Sci. Technol. 187:162–205 [Google Scholar]
  130. Sondhauss C. 1850. Über die Schallschwingungen der Luft in erhitzten Glasröhren und in gedeckten Pfeifen von ungleicher Weite. Ann. Phys. Chem. 79:1–34 [Google Scholar]
  131. Steele RC, Cowell LH, Cannon SM, Smith CE. 2000. Passive control of combustion instability in lean premixed combustors. J. Eng. Gas Turbines Power 122:412–19 [Google Scholar]
  132. Sterling JD, Zukoski EE. 1991. Nonlinear dynamics of laboratory combustor pressure oscillations. Combust. Sci. Technol. 77:225–38 [Google Scholar]
  133. Strogatz S. 1994. Nonlinear Dynamics and Chaos Boulder, CO: Westview Press [Google Scholar]
  134. Subramanian P, Mariappan S, Sujith RI, Wahi P. 2010. Bifurcation analysis of thermoacoustic instability in a horizontal Rijke tube. Int. J. Spray Combust. Dyn. 2:325–55 [Google Scholar]
  135. Subramanian P, Sujith RI, Wahi P. 2013. Subcritical bifurcation and bistability in thermoacoustic systems. J. Fluid Mech. 715:210–38 [Google Scholar]
  136. Suchorsky MK, Sah SM, Rand RH. 2010. Using delay to quench undesirable vibrations. Nonlinear Dyn 62:407–16 [Google Scholar]
  137. Summerfield M. 1951. A theory of unstable combustion in liquid propellant rocket systems. J. Am. Rocket Soc. 21:108–14 [Google Scholar]
  138. Tammisola O, Juniper MP. 2016. Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes. J. Fluid Mech. 792:620–57 [Google Scholar]
  139. Tony J, Gopalakrishnan EA, Sreelekha E, Sujith RI. 2015. Detecting deterministic nature of pressure measurements from a turbulent combustor. Phys. Rev. E 92:062902 [Google Scholar]
  140. Truffin K, Poinsot T. 2005. Comparison and extension of methods for acoustic identification of burners. Combust. Flame 142:388–400 [Google Scholar]
  141. Unni VR. 2016. A unified approach to study lean blowout and thermoacoustic instability PhD Thesis, Indian Inst. Technol. Madras, Chennai, India [Google Scholar]
  142. Unni VR, Sujith RI. 2015. Multifractal characteristics of combustor dynamics close to lean blowout. J. Fluid Mech. 784:30–50 [Google Scholar]
  143. Unni VR, Sujith RI. 2017. Flame dynamics during intermittency in a turbulent combustor. Proc. Combust. Inst. 36:3791–98 [Google Scholar]
  144. Vishnu R, Sujith RI, Aghalayam P. 2015. Role of flame dynamics on the bifurcation characteristics of a ducted V-flame. Combust. Sci. Technol. 187:894–905 [Google Scholar]
  145. Waugh I, Illingworth S, Juniper MP. 2013. Matrix-free continuation of limit cycles for bifurcation analysis of large thermoacoustic systems. J. Comput. Phys. 240:225–47 [Google Scholar]
  146. Waugh IC, Juniper MP. 2011. Triggering in a thermoacoustic system with stochastic noise. Int. J. Spray Combust. Dyn. 3:225–42 [Google Scholar]
  147. Waugh IC, Kashinath K, Juniper MP. 2014. Matrix-free continuation of limit cycles and their bifurcations for a ducted premixed flame. J. Fluid Mech. 759:1–27 [Google Scholar]
  148. West BJ, Latka M, Glaubic-Latka M, Latka D. 2003. Multifractality of cerebral blood flow. Physica A 318:453–60 [Google Scholar]
  149. Wilhite J, Dolan B, Villalva Gomez R, Kabiraj L, Paschereit CO, Gutmark E. 2016. Analysis of combustion oscillations in a staged MLDI burner using decomposition methods and recurrence analysis Presented at AIAA SciTech Forum Expo., Jan. 8–12, Gaylord Palms, FL, AIAA Pap 2016–1156 [Google Scholar]
  150. Worth NA, Dawson JR. 2013. Modal dynamics of self-excited azimuthal instabilities in an annular combustion chamber. Combust. Flame 160:2476–89 [Google Scholar]
  151. Yi T, Santavicca DA. 2010. Flame transfer functions for liquid-fueled swirl-stabilized turbulent lean direct fuel injection combustion. J. Eng. Gas Turbines Power 132:021506 [Google Scholar]
  152. Yu W, Chen G, J. 2009. On pinning synchronization of complex dynamical networks. Automatica 45:429–35 [Google Scholar]
  153. Zhu M, Dowling AP, Bray KNC. 2002. Forced oscillations in combustors with spray atomizers. J. Eng. Gas Turbines Power 124:20–30 [Google Scholar]
  154. Zinn B. 1970. A theoretical study of non-linear damping by Helmholtz resonators. J. Sound Vib. 13:347–56 [Google Scholar]
  155. Zinn BT, Lores ME. 1971. Application of the Galerkin method in the solution of non-linear axial combustion instability problems in liquid rockets. Combust. Sci. Technol. 4:269–78 [Google Scholar]

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