Skip to main content
SpringerLink
Log in

Floquet instability of a large density ratio liquid-gas coaxial jet with periodic fluctuation

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

By numerical simulation of basic flow, this paper extends Floquet stability analysis of interfacial flow with periodic fluctuation into large density ratio range. Stability of a liquid aluminum jet in a coaxial nitrogen stream with velocity fluctuation is investigated by Chebyshev collocation method and the Floquet theory. Parametric resonance of the jet and the influences of different physical parameters on the instability are discussed. The results show qualitative agreement with the available experimental data.

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

Similar content being viewed by others

References

  1. Plateau J. Statique experimentale et theorique des liquids soumle sux sseule forces[J]. Moleculaire Gauthier Villars, 1873, 1(1):2–10.

    Google Scholar 

  2. Rayleigh Lord. On the instability of jets[J]. Proc London Math Soc, 1879, 10(1):4–13.

    Article  Google Scholar 

  3. Weber C Z. Zum zerfall eines flussigkeitsstrahles[J]. Math Mech, 1931, 11(36):136–154.

    Google Scholar 

  4. Chandrasekhar S. Hydrodynamic and hydromagnetic stability[M]. Oxford: Oxford University Press, 1961, p537.

    Google Scholar 

  5. Keller J B, Rubinow S I, Tu Y O. Spatial instability of a jet[J]. Phys Fluids, 1973, 16:2052–2055.

    Article  Google Scholar 

  6. Lin S P, Lian Z W. Mechnisms of the breakup of liquid jet[J]. AIAA Journal, 1990, 28(1):120–126.

    Article  Google Scholar 

  7. Lin S P, Ibrahim E A. Instability of a viscous liquid jet surrounded by a viscous gas in a vertical pipe[J]. J Fluid Mech, 1990, 218:641–58.

    Article  MathSciNet  Google Scholar 

  8. Lin S P, Chen J N. Role played by the interfacial shear in the instability mechanism of a viscous liquid jet surrounded by a viscous gas in a pipe[J]. J Fluid Mech, 1998, 376:37–51.

    Article  MATH  Google Scholar 

  9. Grant NJ. Rapid solidification of metallic particulates[J]. Journal of Metals, 1983, 35(1):20–27.

    Google Scholar 

  10. Rai G, Lavernia E J, Grant N J. Powder size and distribution in ultrasonic gas atomization[J]. Journal of Metals, 1985, 37(8):22–26.

    Google Scholar 

  11. Rai G, Lavernia E J, Grant N J. Effect of the atomisation variable on the powder characteristics in the USGA process[C]. In: Proceedings of the Fifth International Powder Metallurgy Conference, Princeton, N J, USA, 1986.

  12. Zhou Z W, Tang X D. The effect of the pulsation in gas flow on the stability of melted metal jet[C]. In: Fourth International Conference on Spray Forming, 1999.

  13. Wang Y X, Hu G H, Zhou Z W. Floquet stability analysis of two-layer flows in vertical pipe with periodic fluctuation[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(8):1011–1019. DOI 10.1007/s10483-006-0801-1

    Article  Google Scholar 

  14. Woods D R, Lin S P. Instability of a liquid film flow over a vibrating inclined plane[J]. J Fluid Mech, 1995, 294:391–407.

    Article  MATH  MathSciNet  Google Scholar 

  15. Burya A G, Shkadov V Y. Stability of a liquid film flowing down an oscillating inclined surface[J]. Fluid Dynamics, 2001, 36(5):671.

    Article  MATH  MathSciNet  Google Scholar 

  16. Li X J, Hu G H, Zhou Z W. Variation of velocity profile of jet and its effect on interfacial stability[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(1):1–6. DOI 10.1007/BF02438358

    Article  Google Scholar 

  17. Xinmin X. Numerical analysis of spectral method[M]. Beijing: Science Press, 2000 (in Chinese).

    Google Scholar 

  18. He J, Wang Z. Ordinary differential equations[M]. Volume I, II, III. Hunan: Hunan Science and Technology Press, 1979 (in Chinese).

    Google Scholar 

  19. Zhu J, Ru C Q, Mioduchowski A. High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators[J]. Eur Phys J B, 2007, 58:411–421.

    Article  Google Scholar 

  20. Veistinen M K, Lavernia E J, Baram J C, Grant N J. Jet behavior in ultrasonic gas atomization[J]. The International Journal of Powder Metallurgy, 1989, 25(2):89–92.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, Shanghai University, Shanghai, 200072, P. R. China

    Zhen Li  (李振), Guo-hui Hu  (胡国辉) & Zhe-wei Zhou  (周哲玮)

Authors
  1. Zhen Li  (李振)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guo-hui Hu  (胡国辉)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhe-wei Zhou  (周哲玮)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhe-wei Zhou  (周哲玮).

Additional information

Contributed by ZHOU Zhe-wei

Project supported by the National Natural Science Foundation of China (No. 10772107) and the Program of Science and Technology Commission of Shanghai Municipality of China (No. 071605102)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Z., Hu, Gh. & Zhou, Zw. Floquet instability of a large density ratio liquid-gas coaxial jet with periodic fluctuation. Appl. Math. Mech.-Engl. Ed. 29, 975–984 (2008). https://doi.org/10.1007/s10483-008-0801-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-008-0801-y

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation