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A finite element method for a weakly nonlinear dynamic analysis and bifurcation tracking of thermo-acoustic instability in longitudinal and annular combustors

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  • Laera, D.
  • Campa, G.
  • Camporeale, S.M.

Abstract

The aim of this paper is to investigate how nonlinear flame models influence the bifurcation process that characterize the transition to self-sustained thermo-acoustic pressure oscillations in gas turbine combustors. The analysis is carried out by means of a Finite Element Method solver able to treat complex combustor systems with multiple burners. The heat release fluctuations are coupled to the velocity fluctuations in the burner by means of nonlinear dependence. Two polynomial expressions of the third and of the fifth order are respectively considered. At first the proposed numerical procedure is validated in a longitudinal configuration against analytical results obtained in a low-order framework. Then, the ability of the proposed numerical approach to treat combustion systems with multiple independent flames is verified on an annular configuration equipped with twelve burners. In both configurations, in order to track bifurcation diagrams, the amplitudes of velocity fluctuations at limit cycles are plotted against the acoustic-combustion interaction index n considered as a control parameter. Regardless of the configuration, supercritical and subcritical bifurcations are obtained depending of the chosen flame model. The influence of time delay and acoustic damping is also investigated.

Suggested Citation

  • Laera, D. & Campa, G. & Camporeale, S.M., 2017. "A finite element method for a weakly nonlinear dynamic analysis and bifurcation tracking of thermo-acoustic instability in longitudinal and annular combustors," Applied Energy, Elsevier, vol. 187(C), pages 216-227.
    • Handle: RePEc:eee:appene:v:187:y:2017:i:c:p:216-227
    DOI: 10.1016/j.apenergy.2016.10.124
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    References listed on IDEAS

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    1. Zhao, Dan & Li, Shihuai & Yang, Wenming & Zhang, Zhiguo, 2015. "Numerical investigation of the effect of distributed heat sources on heat-to-sound conversion in a T-shaped thermoacoustic system," Applied Energy, Elsevier, vol. 144(C), pages 204-213.
    2. Zhao, Dan & Li, Lei, 2015. "Effect of choked outlet on transient energy growth analysis of a thermoacoustic system," Applied Energy, Elsevier, vol. 160(C), pages 502-510.
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    4. Fichera, A. & Losenno, C. & Pagano, A., 2001. "Experimental analysis of thermo-acoustic combustion instability," Applied Energy, Elsevier, vol. 70(2), pages 179-191, October.
    5. Zhang, Zhiguo & Zhao, Dan & Dobriyal, R. & Zheng, Youqu & Yang, Wenming, 2015. "Theoretical and experimental investigation of thermoacoustics transfer function," Applied Energy, Elsevier, vol. 154(C), pages 131-142.
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    Cited by:

    1. Li, Xinyan & Huang, Yong & Zhao, Dan & Yang, Wenming & Yang, Xinglin & Wen, Huabing, 2017. "Stability study of a nonlinear thermoacoustic combustor: Effects of time delay, acoustic loss and combustion-flow interaction index," Applied Energy, Elsevier, vol. 199(C), pages 217-224.
    2. Wang, L.X. & Zheng, J.H. & Li, M.S. & Lin, X. & Jing, Z.X. & Wu, P.Z. & Wu, Q.H. & Zhou, X.X., 2019. "Multi-time scale dynamic analysis of integrated energy systems: An individual-based model," Applied Energy, Elsevier, vol. 237(C), pages 848-861.
    3. Fang, Guochang & Tian, Lixin & Liu, Menghe & Fu, Min & Sun, Mei, 2018. "How to optimize the development of carbon trading in China—Enlightenment from evolution rules of the EU carbon price," Applied Energy, Elsevier, vol. 211(C), pages 1039-1049.
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    5. Sun, Yuze & Zhao, Dan & Ni, Siliang & David, Tim & Zhang, Yang, 2020. "Entropy and flame transfer function analysis of a hydrogen-fueled diffusion flame in a longitudinal combustor," Energy, Elsevier, vol. 194(C).
    6. Wu, Gang & Lu, Zhengli & Pan, Weichen & Guan, Yiheng & Li, Shihuai & Ji, C.Z., 2019. "Experimental demonstration of mitigating self-excited combustion oscillations using an electrical heater," Applied Energy, Elsevier, vol. 239(C), pages 331-342.

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