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Study on the breakup of liquid jet in a coaxial swirling compressible gas flow

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Abstract

The breakup length and position of liquid jet are the important parameters to determine the atomization quality. The nonlinear dispersion equation is used to study the breakup length and position of liquid jet with cavitation bubbles in a coaxial swirling compressible gas flow. First, the comparison of the jet breakup characteristics under linear and nonlinear stability theories is made, and then the effects of swirling gas, fluid compressibility and cavitation bubbles on jet breakup length are analyzed. The results show that the second-order perturbation may accelerate the breakup of liquid jet and may also inhibit the jet breakup when nonlinear stability theory is taken. In addition, the breakup position of liquid jet may appear after the main droplet and also appear after the satellite droplet. With the increase in gas rotational strengths, fluid compressibility and bubble volume fractions, the breakup length decreases, which indicates that swirling gas, fluid compressibility and cavitation bubbles can accelerate the jet breakup to a certain extent. In general, the effect of fluid compressibility on jet breakup length is the most obvious.

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References

  1. Krishna, M.V.G., Lin, S.P.: Nonlinear stability of a viscous film with respect to three dimensional side-band disturbances. Phys. Fluids 20(20), 1039–1044 (1977)

    Article  MATH  Google Scholar 

  2. Wang, T., Zhang, X., Zhang, J.B., et al.: Numerical analysis of the influence of the fuel injection timing and ignition position in a direct-injection natural gas engine. Energy Convers. Manag. 149, 748–759 (2017)

    Article  Google Scholar 

  3. Ozgen, S., Uzol, O.: Investigation of the linear stability problem of electrified jets, inviscid analysis. J. Fluids Eng. 134(9), 1–9 (2012)

    Article  Google Scholar 

  4. Turner, M.R., Sazhin, S.S., Healey, J.J., et al.: A breakup model for transient diesel fuel sprays. Fuel 97, 288–305 (2012)

    Article  Google Scholar 

  5. Liang, X., Deng, D.S., Nave, J.C., et al.: Linear stability analysis of capillary instabilities for concentric cylindrical shells. J. Fluid Mech. 683, 235–262 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cao, J.M.: Theoretical investigation evolvement of surface waves in liquid jet sprays. Adv. New Renew. Energy 2(3), 165–172 (2014)

    Google Scholar 

  7. Jazayeri, S.A., Li, X.G.: Nonlinear instability of plane liquid sheets. J. Fluid Mech. 406(3), 281–308 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Yang, L.J., Wang, C., Fu, Q.F., et al.: Weakly nonlinear instability of planar viscous sheets. J. Fluid Mech. 735, 249–287 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Yuen, M.C.: Nonlinear capillary instability of a liquid jet. J. Fluid Mech. 33(1), 151–163 (1968)

    Article  MATH  Google Scholar 

  10. Gao, Y.Q., Wei, M.R., Yan, F.W., Chen, L.F., et al.: Effects of cavitation flow and stagnant bubbles on the initial temporal evolution of diesel spray. Exp. Therm. Fluid Sci. 87, 69–79 (2017)

    Article  Google Scholar 

  11. Lafrance, P.: Nonlinear breakup of a laminar liquid jet. Phys. Fluids 18(4), 428–432 (1975)

    Article  MATH  Google Scholar 

  12. Ibrahim, A.A., Jog, M.A.: Nonlinear breakup of a coaxial liquid jet in a swirling gas stream. Phys. Fluids 18(11), 114101-1-114101-11 (2006)

    Article  MATH  Google Scholar 

  13. Ibrahim, A.A., Jog, M.A.: Nonlinear instability of an annular liquid sheet exposed to gas flow. Int. J. Multiph. Flow 34(7), 647–664 (2008)

    Article  Google Scholar 

  14. Rangel, R.H., Sirignano, W.A.: Nonlinear growth of Kelvin–Helmholtz instability: effect of surface view tension and density ratio. Phys. Fluids 31(7), 1845–1855 (1988)

    Article  Google Scholar 

  15. Chen, L.F., Liu, Z.X., Lin, Y.Z., et al.: Different spray droplet evaporation models for non-ideal multi-component fuels with experimental validation. Int. J. Heat Mass Transf. 94, 292–300 (2016)

    Article  Google Scholar 

  16. Ibrahim, E.A., Lin, S.P.: Weakly nonlinear instability of a liquid jet in a viscous gas. J. Appl. Mech. 59, 291–296 (1992)

    Article  Google Scholar 

  17. Tharakan, T.J., Ramamurthi, K., Balakrishnan, M.: Nonlinear breakup of thin liquid sheets. Acta Mech. 156(1–2), 29–46 (2002)

    Article  MATH  Google Scholar 

  18. Ibrahim, A.A.: Comprehensive Study of Internal Flow Field and Linear and Nonlinear Instability of an Annular Liquid Sheet Emanating from an Atomize. University of Cincinnati, Cincinnati (2006)

    Google Scholar 

  19. Yan, K., Jog, M.A., Ning, Z.: Nonlinear spatial instability of an annular swirling viscous liquid sheet. Acta Mech. 224(12), 3071–3090 (2013)

    Article  MathSciNet  Google Scholar 

  20. Lü, M., Ning, Z., Yan, K., et al.: Temporal and spatial stability of liquid jet containing cavitation bubbles in coaxial swirling compressible flow. Meccanica 51(9), 2121–2133 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hadji, L., Schreiber, W.: The stability of an inviscid liquid sheet containing vapor bubbles. J. Phys. Nat. Sci. 1(2), 1–11 (2007)

    Google Scholar 

  22. Gao, Z.Y.: A study of the propagation velocity of pressure wave in gas–liquid two phase mixtures. J. Eng. Thermophys. 5(2), 200–205 (1984)

    Google Scholar 

  23. Lin, S.P.: Breakup of Liquid Sheets and Jets. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  24. Zhou, H., Zhao, G.F.: Hydrodynamic Stability. National Defense Industry Press, Beijing (2004)

    Google Scholar 

  25. Zhou, G.J., Yan, Z.Y., Xu, S.X., et al.: Fluid Mechanics. Higher Education Press, Beijing (2000)

    Google Scholar 

  26. Mulemane, A., Subramaniyam, S., Lu, P.H., et al.: Comparing cavitation in diesel injectors based on different modeling approaches. SAE Paper, 2004-01-0027

  27. Sallam, K.A., Dai, Z., Faeth, G.M.: Liquid breakup at the surface of turbulent round liquid jets in still gases. Int. J. Multiph. Flow 28, 427–449 (2002)

    Article  MATH  Google Scholar 

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Acknowledgements

This project was supported by the National Natural Science Foundation of China (Grant Nos. 51606006, 51776016), Beijing Natural Science Foundation (Grant Nos. 3172025, 3182030), National Engineering Laboratory for Mobile Source Emission Control Technology (Grant No. NELMS2017A10) and the Talents Foundation of Beijing Jiaotong University (Grant No. 2018RC017).

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Correspondence to Zhi Ning.

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Lü, M., Ning, Z. & Yan, K. Study on the breakup of liquid jet in a coaxial swirling compressible gas flow. Nonlinear Dyn 97, 1263–1273 (2019). https://doi.org/10.1007/s11071-019-05046-x

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