Advertisement

The European Physical Journal Special Topics

, Volume 228, Issue 9, pp 1891–1901 | Cite as

Devil’s staircases in a thermoacoustic system with sinusoidal excitations

  • Zhengyuan Zhang
  • Jiazhong ZhangEmail author
  • Pengyu Fan
  • Yongsen He
Regular Article Topical issue
  • 23 Downloads
Part of the following topical collections:
  1. Periodic Motions and Chaos in Nonlinear Dynamical Systems

Abstract

The influences of sinusoidal excitations on a Rijke tube system through the introduction of nonlinear dynamics are investigated in detail. The system is governed by one-dimensional partial differential equations, which are addressed by means of the Galerkin procedure and analysed from the viewpoint of nonlinear dynamics. The results show a rich variety of behaviours in the system, including subcritical bifurcation, hysteresis and phase locking. In certain parameter ranges, the solution switches between periodic and quasi-periodic. These ranges mainly depend on the intensity of the heat source in the tube. The phase-locking intervals that correspond to periodic solutions compose a devil’s staircase, whose Lebesgue measure increases as the amplitude of the excitation increases.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Veselya, T. Vit, EPJ Web Conf. 67, 02126 (2014)CrossRefGoogle Scholar
  2. 2.
    M. Vesely, P. Dancova, T. Vit, V. Lédl, EPJ Web Conf. 67, 02127 (2014)CrossRefGoogle Scholar
  3. 3.
    P. Novotny, S.S. Hsu, A.B. Wang, T. Vit, EPJ Web Conf. 67, 02086 (2014)CrossRefGoogle Scholar
  4. 4.
    P. Subramanian, R.I. Sujith, P. Wahi, J. Fluid Mech. 715, 210238 (2012)Google Scholar
  5. 5.
    P. Subramanian, R.I. Sujith, J. Fluid Mech. 679, 315342 (2011)CrossRefGoogle Scholar
  6. 6.
    S. Etikyala, R.I. Sujith, Chaos 27, 023106 (2017)ADSCrossRefGoogle Scholar
  7. 7.
    P. Subramanian, S. Mariappan, R.I. Sujith, P. Wahi, Int. J. Spray Combust. Dyn. 2, 325356 (2010)CrossRefGoogle Scholar
  8. 8.
    L. Kabiraj, R.I. Sujith, J. Fluid Mech. 713, 376397 (2012)CrossRefGoogle Scholar
  9. 9.
    K. Kashinath, I.C. Waugh, M.P. Juniper, J. Fluid Mech. 761, 399430 (2014)CrossRefGoogle Scholar
  10. 10.
    L. Kabiraj, A. Saurabh, P. Wahi, R.I. Sujith, Chaos 22, 023129 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    R. Delage, Y. Takayama, T. Biwa, Chaos 27, 043111 (2017)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Orchini, S.J. Illingworth, M.P. Juniper, J. Fluid Mech. 775, 387414 (2015)CrossRefGoogle Scholar
  13. 13.
    S. Mondal, S.A. Pawar, R.I. Sujith, Chaos 27, 103119 (2017)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Y. Okuno, M. Small, H. Gotoda, Chaos 25, 043107 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    A. Orchini, G. Rigas, M.P. Juniper, J. Fluid Mech. 805, 523550 (2016)CrossRefGoogle Scholar
  16. 16.
    H. Gotoda, H. Nikimoto, T. Miyano, S. Tachibana, Chaos 21, 013124 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    J. Sui, D. Zhao, B. Zhang, N. Gao, Exp. Therm. Fluid Sci. 81, 336 (2017)CrossRefGoogle Scholar
  18. 18.
    F. Selimefendigil, H.F. Öztop, Eur. J. Mech. B/Fluids 48, 135 (2014)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    I.C. Waugh, M.P. Juniper, Int. J. Spray Combust. Dyn. 3, 225 (2011)CrossRefGoogle Scholar
  20. 20.
    I. Waugh, M. Geu, M. Juniper, Proc. Combust. Inst. 33, 2945 (2011)CrossRefGoogle Scholar
  21. 21.
    E.A. Gopalakrishnan, R.I. Sujith, J. Fluid Mech. 776, 334353 (2015)CrossRefGoogle Scholar
  22. 22.
    E.A. Gopalakrishnan, J. Tony, E. Sreelekha, R.I. Sujith, Phys. Rev. E 94, 022203 (2016)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    V. Gupta, A. Saurabh, C.O. Paschereit, L. Kabiraj, J. Sound Vib. 390, 55 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    L.K.B. Li, M.P. Juniper, Proc. Combust. Inst. 34, 947 (2013)CrossRefGoogle Scholar
  25. 25.
    L.K.B. Li, M.P. Juniper, J. Fluid Mech. 735, R5 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    K. Kashinath, K.B. Larry, M.P. Juniper, J. Fluid Mech. 838, 690 (2018)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    V. Nebendahl, W. Dur, Phys. Rev. B 87, 075413 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    M. Takigawa, M. Horvati, T. Waki, S. Krämer, C. Berthier, F. Lévy-Bertrand, I. Sheikin, H. Kageyama, Y. Ueda, F. Mila, Phys. Rev. Lett. 110, 067210 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    YuM Shukrinov, A.E. Botha, SYu Medvedeva, M.R. Kolahchi, A. Irie, Chaos 24, 033115 (2014)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    K.I. Matveev, F.E.C. Culick, J. Sound Vib. 264, 689706 (2003)CrossRefGoogle Scholar
  31. 31.
    T. Sayadi, V. Le Chenadec, P.J. Schmid, F. Richecoeur, M. Massot, J. Fluid Mech. 753, 448471 (2014)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Zhengyuan Zhang
    • 1
  • Jiazhong Zhang
    • 1
    Email author
  • Pengyu Fan
    • 1
  • Yongsen He
    • 1
  1. 1.School of Energy and Power Engineering, Xi’an Jiaotong UniversityXi’anP.R. China

Personalised recommendations