Skip to main content
SpringerLink
Log in

Critical transitions and their early warning signals in thermoacoustic systems

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Many complex systems undergo critical transitions. A thermoacoustic system is one such system which exhibits a catastrophic transition to a state of oscillatory instability known as thermoacoustic instability. So far, several early warning signals have been devised to detect the transition from stable operation to thermoacoustic instability in both laminar and turbulent systems. We focus on these early warning signals, and the challenges faced while detecting oscillatory instabilities in practical systems. In contrast to the transition from a fixed point to limit cycle oscillations in laminar systems, turbulent systems exhibit a transition from a chaotic state to limit cycle via a state of intermittency. In this review, we highlight the importance of the inherent fluctuations in the system in providing early warning signals for critical transitions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 15
Fig. 16

Reproduced with permission from Gopalakrishnan et al. [25]

Fig. 17

Reproduced with permission from Kabiraj et al. [29]

Fig. 18

Reproduced with permission from George et al. [11]

Fig. 19

Reproduced with permission from Nair et al. [41]

Fig. 20
Fig. 21

Reproduced with permission from Bury et al. [67]

Fig. 22
Fig. 23

Redrawn with permission from Nair et al. [40] and Pavithran et al. [45]

Fig. 24

Reproduced with permission from Nair et al. [41]

Fig. 25

Reproduced with permission from Murugesan and Sujith [99]

Fig. 26

Reproduced with permission from Gotoda et al. [101]

Fig. 27

Reproduced from Pavithran et al. [46]

Fig. 28

Reproduced with permission from Mukhophadhyay et al. [105]

Similar content being viewed by others

References

  1. M.P. Juniper, R.I. Sujith, Annu. Rev. Fluid Mech. 50, 661 (2018)

    Article  ADS  Google Scholar 

  2. T.C. Lieuwen, V. Yang, Combustion instabilities in gas turbine engines: operational experience, fundamental mechanisms, and modeling (American Institute of Aeronautics and Astronautics, 2005)

  3. S.C. Fisher, S.A. Rahman, J. Center, Remembering the Giants (NASA History Division, Washington, DC, 2009)

  4. J.W.S. Rayleigh, Nature 18(455), 319 (1878)

    Article  ADS  Google Scholar 

  5. T.J. Poinsot, A.C. Trouve, D.P. Veynante, S.M. Candel, E.J. Esposito, J. Fluid Mech. 177, 265 (1987)

    Article  ADS  Google Scholar 

  6. F. Güthe, B. Schuermans, Meas. Sci. Technol. 18(9), 3036 (2007)

    Article  ADS  Google Scholar 

  7. S.A. Pawar, A. Seshadri, V.R. Unni, R.I. Sujith, J. Fluid Mech. 827, 664 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  8. K. McManus, T. Poinsot, S.M. Candel, Prog. Energy Combust. Sci. 19(1), 1 (1993)

    Article  Google Scholar 

  9. S. Mondal, V.R. Unni, R.I. Sujith, J. Fluid Mech. 811, 659 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  10. R.I. Sujith, V.R. Unni, Phys. Fluids 32(6), 061401 (2020)

    Article  ADS  Google Scholar 

  11. N.B. George, V.R. Unni, M. Raghunathan, R.I. Sujith, J. Fluid Mech. 849, 615 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Scheffer, J. Bascompte, W.A. Brock, V. Brovkin, S.R. Carpenter, V. Dakos, H. Held, E.H. van Nes, M. Rietkerk, G. Sugihara, Nature 461(7260), 53 (2009)

    Article  ADS  Google Scholar 

  13. M. Scheffer, S.R. Carpenter, T.M. Lenton, J. Bascompte, W. Brock, V. Dakos, J. van de Koppel, I.A. van de Leemput, S.A. Levin, E.H. van Nes et al., Science 338(6105), 344 (2012)

    Article  ADS  Google Scholar 

  14. D. Angeli, J.E. Ferrell, E.D. Sontag, Proc. Natl. Acad. Sci. 101(7), 1822 (2004)

    Article  ADS  Google Scholar 

  15. E.A. Gopalakrishnan, Y. Sharma, T. John, P.S. Dutta, R.I. Sujith, Sci. Rep. 6(1), 1 (2016)

    Article  Google Scholar 

  16. S.J. Shanbhogue, S. Husain, T. Lieuwen, Prog. Energy Combust. Sci. 35(1), 98 (2009)

    Article  Google Scholar 

  17. R.I. Sujith, V.R. Unni, Proc. Combust. Inst. 38(3), 3445–3462 (2021)

  18. V. Nair, G. Thampi, S. Karuppusamy, S. Gopalan, R.I. Sujith, Int. J. Spray Combust. Dyn. 5(4), 273 (2013)

    Article  Google Scholar 

  19. J. Tony, E.A. Gopalakrishnan, E. Sreelekha, R.I. Sujith, Phys. Rev. E 92(6), 062902 (2015)

    Article  ADS  Google Scholar 

  20. T.C. Lieuwen, J. Propul. Power 18(1), 61 (2002)

    Article  Google Scholar 

  21. N. Ananthkrishnan, S. Deo, F.E. Culick, Combust. Sci. Technol. 177(2), 221 (2005)

    Article  Google Scholar 

  22. S. Etikyala, R.I. Sujith, Chaos: Interdiscipl. J. Nonlinear Sci. 27(2), 023106 (2017)

    Article  Google Scholar 

  23. P. Subramanian, S. Mariappan, R.I. Sujith, P. Wahi, Int. J. Spray Combust. Dyn. 2(4), 325 (2010)

    Article  Google Scholar 

  24. E.A. Gopalakrishnan, J. Tony, E. Sreelekha, R.I. Sujith, Phys. Rev. E 94(2), 022203 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  25. E.A. Gopalakrishnan, R.I. Sujith, Int. J. Spray Combust. Dyn. 6(3), 293 (2014)

    Article  Google Scholar 

  26. C.C. Jahnke, F.E. Culick, J. Propul. Power 10(4), 508 (1994)

    Article  Google Scholar 

  27. S. Lei, A. Turan, Combust. Theor. Model. 13(3), 541 (2009)

    Article  ADS  Google Scholar 

  28. J.D. Sterling, Combust. Sci. Technol. 89(1–4), 167 (1993)

    Article  Google Scholar 

  29. L. Kabiraj, A. Saurabh, P. Wahi, R.I. Sujith, Chaos Interdiscipl. J. Nonlinear Sci. 22(2), 023129 (2012)

    Article  Google Scholar 

  30. A.H. Nayfeh, B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods (Wiley, Hoboken, 2008)

    MATH  Google Scholar 

  31. D. Premraj, S.A. Pawar, L. Kabiraj, R.I. Sujith, EPL (Europhys. Lett.) 128(5), 54005 (2020)

    Article  Google Scholar 

  32. L. Kabiraj, R.I. Sujith, J. Fluid Mech. 713(376–397), 13 (2012)

    Google Scholar 

  33. Y. Guan, V. Gupta, L.K.B. Li, J. Fluid Mech. 894, 52 (2020)

    Article  Google Scholar 

  34. N. Ananthkrishnan, K. Sudhakar, S. Sudershan, A. Agarwal, J. Sound Vib. 1(215), 183 (1998)

    Article  ADS  Google Scholar 

  35. N. Mukherjee, M. Heckl, A. Bigongiari, R. Vishnu, S.A. Pawar, R.I. Sujith, in Proceedings of the 22nd International Congress on Sound and Vibration (2015)

  36. S. Singh, A. Roy, K.V. Reeja, A. Nair, S. Chaudhuri, R.I. Sujith, J. Eng. Gas Turbines Power 143, 051028 (2020)

    Article  Google Scholar 

  37. P. Subramanian, R.I. Sujith, P. Wahi, J. Fluid Mech. 715, 210 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  38. K. Kashinath, I.C. Waugh, M.P. Juniper, J. Fluid Mech. 761, 399 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  39. Y. Weng, V.R. Unni, R.I. Sujith, A. Saha, Nonlinear Dyn. 2020, 1–12 (2020)

    Google Scholar 

  40. V. Nair, R.I. Sujith, J. Fluid Mech. 747, 635 (2014)

    Article  ADS  Google Scholar 

  41. V. Nair, G. Thampi, R.I. Sujith, J. Fluid Mech. 756, 470 (2014)

    Article  ADS  Google Scholar 

  42. V. Nair, R.I. Sujith, Int. J. Aeroacoust. 15(3), 312 (2016)

    Article  Google Scholar 

  43. J. Venkatramani, V. Nair, R.I. Sujith, S. Gupta, S. Sarkar, J. Fluids Struct. 61, 376 (2016)

    Article  ADS  Google Scholar 

  44. Y. Pomeau, P. Manneville, Commun. Math. Phys. 74(2), 189 (1980)

    Article  ADS  Google Scholar 

  45. I. Pavithran, V.R. Unni, A.J. Varghese, R.I. Sujith, A. Saha, N. Marwan, J. Kurths, EPL (Europhys. Lett.) 129(2), 24004 (2020)

    Article  ADS  Google Scholar 

  46. I. Pavithran, V.R. Unni, A.J. Varghese, D. Premraj, R.I. Sujith, C. Vijayan, A. Saha, N. Marwan, J. Kurths, Sci. Rep. 10, 17405 (2020)

    Article  ADS  Google Scholar 

  47. E.H. van Nes, M. Scheffer, Am. Nat. 169(6), 738 (2007)

    Article  Google Scholar 

  48. V. Dakos, J. Bascompte, Proc. Natl. Acad. Sci. 111(49), 17546 (2014)

    Article  ADS  Google Scholar 

  49. T.M. Lenton, V.N. Livina, V. Dakos, E.H. van Nes, M. Scheffer, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 370(1962), 1185 (2012)

    Article  ADS  Google Scholar 

  50. M. Scheffer, S. Carpenter, J.A. Foley, C. Folke, B. Walker, Nature 413(6856), 591 (2001)

    Article  ADS  Google Scholar 

  51. V. Guttal, C. Jayaprakash, Ecol. Lett. 11(5), 450 (2008)

    Article  Google Scholar 

  52. V. Guttal, C. Jayaprakash, Theor. Ecol. 2(1), 3 (2009)

    Article  Google Scholar 

  53. V. Dakos, E.H. van Nes, P. D’Odorico, M. Scheffer, Ecology 93(2), 264 (2012)

    Article  Google Scholar 

  54. D.A. Seekell, S.R. Carpenter, M.L. Pace, Am. Nat. 178(4), 442 (2011)

    Article  Google Scholar 

  55. Q. An, A.M. Steinberg, S. Jella, G. Bourque, M. Füri, J. Eng. Gas Turbines Power 141, 5 (2019)

    Article  Google Scholar 

  56. J. Lee, D. Santavicca, J. Propul. Power 19(5), 735 (2003)

    Article  Google Scholar 

  57. G.A. Richards, D.L. Straub, E.H. Robey, J. Propul. Power 19(5), 795 (2003)

    Article  Google Scholar 

  58. T. Lieuwen, J. Eng. Gas Turbines Power 127(3), 478 (2005)

    Article  Google Scholar 

  59. C. Boettiger, A. Hastings, Proc. R. Soc. B Biol. Sci. 279(1748), 4734 (2012)

    Article  Google Scholar 

  60. V. Livina, P. Ditlevsen, T. Lenton, Phys. A 391(3), 485 (2012)

    Article  Google Scholar 

  61. P. Ritchie, J. Sieber, Chaos Interdiscipl. J. Nonlinear Sci. 26(9), 093116 (2016)

    Article  Google Scholar 

  62. C. Boettiger, A. Hastings, J. R. Soc. Interface 9(75), 2527 (2012)

    Article  Google Scholar 

  63. P.S. Dutta, Y. Sharma, K.C. Abbott, Oikos 127(9), 1251 (2018)

    Article  Google Scholar 

  64. S.R. Carpenter, J.J. Cole, M.L. Pace, R. Batt, W. Brock, T. Cline, J. Coloso, J.R. Hodgson, J.F. Kitchell, D.A. Seekell et al., Science 332(6033), 1079 (2011)

    Article  ADS  Google Scholar 

  65. V. Dakos, M. Scheffer, E.H. van Nes, V. Brovkin, V. Petoukhov, H. Held, Proc. Natl. Acad. Sci. 105(38), 14308 (2008)

    Article  ADS  Google Scholar 

  66. C.F. Clements, J.M. Drake, J.I. Griffiths, A. Ozgul, Am. Nat. 186(1), 50 (2015)

    Article  Google Scholar 

  67. T.M. Bury, C.T. Bauch, M. Anand, J. R. Soc. Interface 17(170), 20200482 (2020)

    Article  Google Scholar 

  68. I. Pavithran, R.I. Sujith, Chaos Interdiscipl. J. Nonlinear Sci. 31(1), 013116 (2021)

    Article  Google Scholar 

  69. B.B. Mandelbrot, The Fractal Geometry of Nature, vol. 173 (WH freeman, New York, 1983)

  70. B.J. West, M. Latka, M. Glaubic-Latka, D. Latka, Phys. A 318(3–4), 453 (2003)

    Article  MathSciNet  Google Scholar 

  71. J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H.E. Stanley, Phys. A 316(1–4), 87 (2002)

    Article  Google Scholar 

  72. E.A.F.E. Ihlen, Front. Physiol. 3, 141 (2012)

    Article  ADS  Google Scholar 

  73. B.B. Mandelbrot, J.R. Wallis, Water Resour. Res. 5(5), 967 (1969)

    Article  ADS  Google Scholar 

  74. A. Carbone, G. Castelli, H. Stanley, Phys. Rev. E 69(2), 026105 (2004)

    Article  ADS  Google Scholar 

  75. H. Gotoda, M. Amano, T. Miyano, T. Ikawa, K. Maki, S. Tachibana, Chaos Interdiscipl. J. Nonlinear Sci. 22(4), 043128 (2012)

    Article  Google Scholar 

  76. V. Nair, G. Thampi, S. Karuppusamy, S. Gopalan, S.R.P.I. Nair, System and method for predetermining the onset of impending oscillatory instabilities in practical devices (2017). US Patent 9,804,054

  77. B. Kerres, V. Nair, A. Cronhjort, M. Mihaescu, SAE Int. J. Engines 9(3), 1795 (2016)

    Article  Google Scholar 

  78. V.R. Unni, R.I. Sujith, J. Fluid Mech. 784, 30 (2015)

    Article  ADS  Google Scholar 

  79. V.R. Unni, V.N. Vinod, S.R.P.I. Nair, System and method for detecting precursors to control blowout in combustion systems (2019). US Patent 10,267,519

  80. J. Eckmann, S.O. Kamphorst, D. Ruelle et al., World Sci. Ser. Nonlinear Sci. Ser. A 16, 441 (1995)

    Google Scholar 

  81. C. Webber, N. Marwan, Recurrence Quantification Analysis (Springer, Berlin, 2015)

    Book  Google Scholar 

  82. F. Takens, in Dynamical Systems and Turbulence, Warwick 1980 (Springer, Berlin, 1981), pp. 366–381

  83. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438(5–6), 237 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  84. V. Nair, G. Thampi, R.I. Sujith, in Turbo Expo: Power for Land, Sea, and Air, vol. 45691 (American Society of Mechanical Engineers, 2014), vol. 45691, p. V04BT04A005

  85. H. Gotoda, Y. Shinoda, M. Kobayashi, Y. Okuno, S. Tachibana, Phys. Rev. E 89(2), 022910 (2014)

    Article  ADS  Google Scholar 

  86. V.R. Unni, R.I. Sujith, in 52nd AIAA/SAE/ASEE Joint Propulsion Conference (2016), p. 4649

  87. V. Godavarthi, V.R. Unni, E.A. Gopalakrishnan, R.I. Sujith, Chaos Interdiscipl. J. Nonlinear Sci. 27(6), 063113 (2017)

    Article  Google Scholar 

  88. R. Jacob, K. Harikrishnan, R. Misra, G. Ambika, Phys. Rev. E 93(1), 012202 (2016)

    Article  ADS  Google Scholar 

  89. V. Godavarthi, S.A. Pawar, V.R. Unni, R.I. Sujith, N. Marwan, J. Kurths, Chaos Interdiscipl. J. Nonlinear Sci. 28(11), 113111 (2018)

    Article  Google Scholar 

  90. J.P. Zbilut, J.M. Zaldivar-Comenges, F. Strozzi, Phys. Lett. A 297(3–4), 173 (2002)

    Article  ADS  Google Scholar 

  91. K.H. Kraemer, R.V. Donner, J. Heitzig, N. Marwan, Chaos Interdiscipl. J. Nonlinear Sci. 28(8), 085720 (2018)

    Article  Google Scholar 

  92. S. Chiocchini, T. Pagliaroli, R. Camussi, E. Giacomazzi, J. Propul. Power 34(1), 15 (2018)

    Article  Google Scholar 

  93. P. Kasthuri, I. Pavithran, S.A. Pawar, R.I. Sujith, R. Gejji, W. Anderson, Chaos Interdiscipl. J. Nonlinear Sci. 29(10), 103115 (2019)

    Article  Google Scholar 

  94. T. Braun, V.R. Unni, R.I. Sujith, J. Kurths, N. Marwan, Nonlinear Dyn. 2021, 1–19 (2021)

    Google Scholar 

  95. D. Premraj, S. Kumarasamy, S.A. Pawar, L. Kabiraj, A. Prasad, R.I. Sujith, Europhys. Lett. 134(3), 34006 (2021)

  96. LdF Costa, O.N. Oliveira Jr, G. Travieso, F.A. Rodrigues, P.R. Villas Boas, L. Antiqueira, M.P. Viana, L.E. Correa Rocha, Adv. Phys. 60(3), 329 (2011)

    Article  ADS  Google Scholar 

  97. Y. Zou, R.V. Donner, N. Marwan, J.F. Donges, J. Kurths, Phys. Rep. 787, 1 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  98. M. Murugesan, R.I. Sujith, J. Fluid Mech. 772, 225 (2015)

    Article  ADS  Google Scholar 

  99. M. Murugesan, R.I. Sujith, J. Propul. Power 32(3), 707 (2016)

    Article  Google Scholar 

  100. M. Murugesan, R.U. Vishnu, V.N. VINOD, S.R.P.I. Nair, Devices and methods for early prediction of impending instabilities of a system (2019). US Patent 10,337,414

  101. H. Gotoda, H. Kinugawa, R. Tsujimoto, S. Domen, Y. Okuno, Phys. Rev. Appl. 7(4), 044027 (2017)

    Article  ADS  Google Scholar 

  102. S. Tandon, R.I. Sujith, Chaos Interdiscipl. J. Nonlinear Sci. 31(4), 043126 (2021)

    Article  Google Scholar 

  103. A. Ray, Signal Process. 84(7), 1115 (2004)

    Article  ADS  Google Scholar 

  104. C.S. Daw, C.E.A. Finney, E.R. Tracy, Rev. Sci. Instrum. 74(2), 915 (2003)

    Article  ADS  Google Scholar 

  105. A. Mukhopadhyay, R.R. Chaudhari, T. Paul, S. Sen, A. Ray, J. Propul. Power 29(4), 950 (2013)

    Article  Google Scholar 

  106. S. Gupta, A. Ray, A. Mukhopadhyay, Proc. Inst. Mech. Engineers Part I J. Syst. Control Eng. 220(5), 339 (2006)

    Google Scholar 

  107. S. Chakraborty, S. Gupta, A. Ray, A. Mukhopadhyay, Proc. Inst. Mech. Engineers Part G J. Aerospace Eng. 222(8), 1097 (2008)

    Article  Google Scholar 

  108. S. Datta, A. Mukhopadhyay, D. Sanyal, in ASME International Mechanical Engineering Congress and Exposition (2006), vol. 47853, pp. 127–135

  109. V.R. Unni, A. Mukhopadhyay, R.I. Sujith, Int. J. Spray Combust. Dyn. 7(3), 243 (2015)

    Article  Google Scholar 

  110. V.R. Unni, V.N. Vinod, S.R.P.I. Nair, A. Mukhopadhyay, System and method for controlling oscillatory instabilities in a device (2018). US Patent 10,095,247

  111. S. Sarkar, K.G. Lore, S. Sarkar, V. Ramanan, S.R. Chakravarthy, S. Phoha, A. Ray, in Annual Conf. of the Prognostics and Health Management (2015)

  112. S. Sarkar, K.G. Lore, S. Sarkar, in CoCo@ NIPS (2015)

  113. N.F. Ghalyan, S. Mondal, D.J. Miller, A. Ray, J. Dyn. Syst. Meas. Contr. 141, 10 (2019)

    Article  Google Scholar 

  114. I. Pavithran, V.R. Unni, A.J. Varghese, P. Kasthuri, R.P.I.N. Sujith, System and method for determining the amplitude of oscillatory instabilities in fluid mechanical devices (2021). US Patent App. 16/633,657

  115. T. Kobayashi, S. Murayama, T. Hachijo, H. Gotoda, Phys. Rev. Appl. 11(6), 064034 (2019)

    Article  ADS  Google Scholar 

  116. V.N. Vapnik, IEEE Trans. Neural Netw. 10(5), 988 (1999)

    Article  Google Scholar 

  117. T. Hachijo, S. Masuda, T. Kurosaka, H. Gotoda, Chaos Interdiscipl. J. Nonlinear Sci. 29(10), 103123 (2019)

    Article  Google Scholar 

  118. S. Domen, H. Gotoda, T. Kuriyama, Y. Okuno, S. Tachibana, Proc. Combust. Inst. 35(3), 3245 (2015)

    Article  Google Scholar 

  119. P. Chattopadhyay, S. Mondal, C. Bhattacharya, A. Mukhopadhyay, A. Ray, J. Mech. Des. 139, 11 (2017)

    Article  Google Scholar 

  120. E. Aguilar-Ruiz, V. Rajasekharan-Unni, R.I. Sujith, A. Saha, Bull. Am. Phys. Soc. 2020, 65 (2020)

    Google Scholar 

  121. S. Mondal, A. Chattopadhyay, A. Mukhopadhyay, A. Ray, Energy AI 2020, 100085 (2021)

    Article  Google Scholar 

  122. J. Dhadphale, V.R. Unni, A. Saha, R.I. Sujith, arXiv:2106.12758 (2021)

  123. G. Waxenegger-Wilfing, U. Sengupta, J. Martin, W. Armbruster, J. Hardi, M. Juniper, M. Oschwald, Chaos Interdiscipl. J. Nonlinear Sci. 31(6), 063128 (2021)

    Article  Google Scholar 

  124. S. Xiong, S. Mondal, A. Ray, J. Dyn. Syst. Meas. Control 140, 2 (2018)

    Article  Google Scholar 

  125. C. Bhattacharya, J. O’Connor, A. Ray, Combust. Sci. Technol. 2020, 1–32 (2020)

    Google Scholar 

  126. C. Bhattacharya, A. Ray, J. Dyn. Syst. Meas. Control 142, 11 (2020)

    Article  Google Scholar 

  127. S. Mondal, N.F. Ghalyan, A. Ray, A. Mukhopadhyay, Combust. Sci. Technol. 2018, 65 (2018)

    Google Scholar 

  128. U. Sengupta, C.E. Rasmussen, M.P. Juniper, in ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition (American Society of Mechanical Engineers Digital Collection, 2020)

  129. T. Hashimoto, H. Shibuya, H. Gotoda, Y. Ohmichi, S. Matsuyama, Phys. Rev. E 99(3), 032208 (2019)

    Article  ADS  Google Scholar 

  130. S. Mondal, S. De, A. Mukhopadhyay, S. Sen, A. Ray, Combust. Sci. Technol. 2020, 1–28 (2020)

    Google Scholar 

  131. U. Sengupta, C.E. Rasmussen, M.P. Juniper, J. Eng. Gas Turbines Power 143(7), 071001 (2021)

    Article  Google Scholar 

  132. M. Lee, K.T. Kim, V. Gupta, L.K.B. Li, Proc. Combust. Inst. 2020, 5 (2020)

    Google Scholar 

  133. D. Rouwenhorst, J. Hermann, W. Polifke, J. Eng. Gas Turbines Power 139, 2 (2017)

    Article  Google Scholar 

  134. D. Tonon, A. Hirschberg, J. Golliard, S. Ziada, Int. J. Aeroacoust. 10(2–3), 201 (2011)

    Article  Google Scholar 

  135. A. Larsen, J.H. Walther, J. Wind Eng. Ind. Aerodyn. 67, 253 (1997)

    Article  Google Scholar 

  136. J. Venkatramani, S. Sarkar, S. Gupta, J. Sound Vib. 419, 318 (2018)

    Article  ADS  Google Scholar 

  137. T. Hachijo, H. Gotoda, T. Nishizawa, J. Kazawa, Phys. Rev. Appl. 14(1), 014093 (2020)

    Article  ADS  Google Scholar 

  138. T. Hachijo, H. Gotoda, T. Nishizawa, J. Kazawa, J. Appl. Phys. 127(23), 234901 (2020)

    Article  ADS  Google Scholar 

  139. A. Raaj, J. Venkatramani, S. Mondal, Chaos Interdiscipl. J. Nonlinear Sci. 29(4), 043129 (2019)

    Article  Google Scholar 

  140. I. Pavithran, V.R. Unni, A.J. Varghese, R.I. Sujith, A. Saha, N. Marwan, J. Kuths, in ASME Turbo Expo 2021 (American Society of Mechanical Engineers Digital Collection, 2021)

  141. I. Pavithran, V.R. Unni, R.P.I.N. Sujith, System and method for predetermining the onset of impending oscillatory instabilities in practical devices (2021). US Patent App. 16/633,650

  142. N. Noiray, B. Schuermans, Int. J. Non-Linear Mech. 50, 152 (2013)

    Article  ADS  Google Scholar 

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

  144. V. Nair, R.I. Sujith, Proc. Combust. Inst. 35(3), 3193 (2015)

    Article  Google Scholar 

  145. A. Seshadri, V. Nair, R.I. Sujith, Combust. Theor. Model. 20(3), 441 (2016)

    Article  ADS  Google Scholar 

  146. A. Seshadri, I. Pavithran, V.R. Unni, R.I. Sujith, AIAA J. 56(9), 3507 (2018)

    Article  ADS  Google Scholar 

  147. S.R.P.I. Nair, A. Seshadri, I. Pavithran, Apparatus to estimate the root means square value or the amplitude of limit cycle oscillations in systems that encounter oscillatory instabilities and methods thereof (2021). US Patent App. 16/605,054

  148. G. Bonciolini, A. Faure-Beaulieu, C. Bourquard, N. Noiray, Combust. Flame 226, 396 (2021)

    Article  Google Scholar 

  149. A.K. Dutta, G. Ramachandran, S. Chaudhuri, Phys. Rev. E 99(3), 032215 (2019)

    Article  ADS  Google Scholar 

  150. V. Godavarthi, P. Kasthuri, S. Mondal, R.I. Sujith, N. Marwan, J. Kurths, Chaos Interdiscipl. J. Nonlinear Sci. 30(3), 033121 (2020)

    Article  Google Scholar 

  151. S.M. Baer, T. Erneux, J. Rinzel, SIAM J. Appl. Math. 49(1), 55 (1989)

    Article  MathSciNet  Google Scholar 

  152. P. Ashwin, S. Wieczorek, R. Vitolo, P. Cox, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 370(1962), 1166 (2012)

    Article  ADS  Google Scholar 

  153. J. Tony, S. Subarna, K.S. Syamkumar, G. Sudha, S. Akshay, E.A. Gopalakrishnan, E. Surovyatkina, R.I. Sujith, Sci. Rep. 7(1), 1 (2017)

    Article  Google Scholar 

  154. G. Bonciolini, D. Ebi, E. Boujo, N. Noiray, R. Soc. Open Sci. 5(3), 172078 (2018)

    Article  ADS  Google Scholar 

  155. G. Bonciolini, N. Noiray, Nonlinear Dyn. 96(1), 703 (2019)

    Article  Google Scholar 

  156. S. Manikandan, R.I. Sujith, Exp. Therm. Fluid Sci. 114, 110046 (2020)

    Article  Google Scholar 

  157. X. Zhang, Y. Xu, Q. Liu, J. Kurths, Sci. China Technol. Sci. 63(11), 2315 (2020)

    Article  ADS  Google Scholar 

  158. X. Zhang, Y. Xu, Q. Liu, J. Kurths, C. Grebogi, Nonlinear Dyn. 104(3), 2733 (2021)

    Article  Google Scholar 

  159. V.R. Unni, E.A. Gopalakrishnan, K.S. Syamkumar, R.I. Sujith, E. Surovyatkina, J. Kurths, Chaos Interdiscipl. J. Nonlinear Sci. 29(3), 031102 (2019)

    Article  Google Scholar 

  160. V.R. Unni, A. Krishnan, R. Manikandan, N.B. George, R.I. Sujith, N. Marwan, J. Kurths, Chaos Interdiscipl. J. Nonlinear Sci. 28(6), 063125 (2018)

    Article  Google Scholar 

  161. A. Krishnan, R. Manikandan, P. Midhun, K.V. Reeja, V.R. Unni, R.I. Sujith, N. Marwan, J. Kurths, EPL (Europhys. Lett.) 128(1), 14003 (2019)

    Article  ADS  Google Scholar 

  162. A. Krishnan, R.I. Sujith, N. Marwan, J. Kurths, J. Fluid Mech. 916, 5 (2021)

    Article  Google Scholar 

  163. A. Roy, C. Premchand, M. Raghunathan, A. Krishnan, V. Nair, R.I. Sujith, Combust. Flame 226, 274 (2020)

    Article  Google Scholar 

  164. V.R. Unni, R.I. Sujith, Proc. Combust. Inst. 36(3), 3791 (2017)

    Article  Google Scholar 

  165. M. Raghunathan, N.B. George, V.R. Unni, P. Midhun, K.V. Reeja, R.I. Sujith, J. Fluid Mech. 888, 8 (2020)

    Article  Google Scholar 

  166. V. Stolbova, E. Surovyatkina, B. Bookhagen, J. Kurths, Geophys. Res. Lett. 43(8), 3982 (2016)

    Article  ADS  Google Scholar 

  167. V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, J. Kurths, Nonlinear Process. Geophys. 21(4), 901 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank A. Roy, S. Tandon, P. Kasthuri, and A. Sahay for their comments/suggestions for the manuscript. We acknowledge the help from Mr. P R., Midhun and S. Anand in conducting the experiments for the data used in Sect. 4.1.2. R.I.S. thanks the SERB, Department of Science and Technology for founding this work through the Swarnajayanti, and JC Bose fellowships and the Office of Naval Research Global (ONRG). I. P. is grateful to the Ministry of Human Resource Development, India and the Indian Institute of Technology Madras for providing research assistantship. We thank Dr. Ramesh Kolar (ONRG) for his strong support.

Author information

Authors and Affiliations

  1. Department of Physics, IIT Madras, Chennai, 600036, India

    Induja Pavithran

  2. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, 08540, USA

    Vishnu R. Unni

  3. Department of Aerospace Engineering, IIT Madras, Chennai, 600036, India

    R. I. Sujith

Authors
  1. Induja Pavithran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vishnu R. Unni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. I. Sujith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Induja Pavithran.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pavithran, I., Unni, V.R. & Sujith, R.I. Critical transitions and their early warning signals in thermoacoustic systems. Eur. Phys. J. Spec. Top. 230, 3411–3432 (2021). https://doi.org/10.1140/epjs/s11734-021-00214-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00214-w

Search

Navigation