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Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

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Abstract

We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the unsteady heat release rate as the flame’s response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos, can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al. (Chaos (Woodbury, N Y) 22:023129, 2012). By analyzing the temporal variation of phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.

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Acknowledgements

We thank Dr. Lipika Kabiraj for sharing the experimental data with us to validate our model. The research at UC San Diego was supported by internal grants. RIS acknowledges the support of ONRG (Grant No. N62909-18-1-2061, contract monitor, Dr. R. Kolar).

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, 92093, USA

    Yue Weng, Vishnu R. Unni & Abhishek Saha

  2. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    R. I. Sujith

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  1. Yue Weng
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  2. Vishnu R. Unni
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  3. R. I. Sujith
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Correspondence to Vishnu R. Unni or Abhishek Saha.

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Weng, Y., Unni, V.R., Sujith, R.I. et al. Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors. Nonlinear Dyn 100, 3295–3306 (2020). https://doi.org/10.1007/s11071-020-05706-3

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