, Volume 53, Issue 8, pp 2067–2078 | Cite as

Temporal analysis of breakup for a power law liquid jet in a swirling gas

  • Xin-Tao Wang
  • Zhi Ning
  • Ming Lü
  • Chun-Hua Sun


The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.


Breakup mechanisms Power law liquid jet Temporal mode Disturbances Gas swirling 

List of symbols


Nozzle radius, m


Power law index


Dimensionless rotational strength

\( k_{r} \)

Dimensionless wave numbers in the jet direction


Dimensionless temporal disturbance growth rate


Dimensionless maximum unstable growth rate


Generalized Reynolds number

\( \bar{p}_{1} \)

Jet pressure, Pa

\( \bar{p}_{2} \)

Gas pressure, Pa


Gas–liquid density ratio


Initial jet velocity, m/s


Gas rotational strength, m2/s


Weber number


Dimensionless frequency of oscillation


Dimensionless dominant characteristic wave frequency


Consistency coefficient, Pa sn


Initial disturbance amplitude


Jet density, kg/m3


Gas density, kg/m3


Surface tension factor, N/m



Project supported by the National Natural Science Foundation of China (Grant Nos. 51776016 and 51606006), Beijing Natural Science Foundation (Grant No. 3172025), the China Postdoctoral Science Foundation (Grant No. 2016M591061), and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 2016JBM049).


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Mechanical, Electronic and Control EngineeringBeijing Jiaotong UniversityBeijingChina

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