Nonlinear Instability and Breakup of a Viscous Compound Liquid Jet

Yoshinaga, Takao; Yamamoto, Kentaro

doi:10.1299/jfst.6.477

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…Moreover, a two-step finite difference scheme was used to study the effects of key parameters on breakup and drop formation. Other related studies are reported by Radev and Gospodinov [17], Yoshinaga and Maeda [24] and Yoshinaga and Yamamoto [25].…”

Section: Introductionsupporting

confidence: 56%

Effects of gravity on the breakup and instability of a viscous compound jet

Afzaal

Uddin

Decent

et al. 2015

J. Phys. A: Math. Theor.

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Encapsulated droplet formation resulting from the rupture and breakup of a compound liquid thread has numerous applications in industry. Understanding the process through which a compound thread will breakup and form droplets of a desired size is thus of great relevance and may help in developing refined experimental techniques. In this paper, we investigate the breakup and the instability of a viscous compound thread falling under gravity. The governing equations are formulated and a reduced one-dimensional set of equations is obtained using an asymptotic approach. The steady-state solutions, which are dependent on the axial distance along the thread, are determined using a modified Newton's method. Thereafter, we present a linear temporal instability analysis to study the effects of how key parameters affect the structure and onset of rupture. Finally, we investigate the nonlinear behaviour of waves along the free surface through using a finite difference scheme based on the Lax-Wendroff method and we obtain the breakup times and the sizes of main and satellite droplets.

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Section: Introductionsupporting

confidence: 56%

Effects of gravity on the breakup and instability of a viscous compound jet

Afzaal

Uddin

Decent

et al. 2015

J. Phys. A: Math. Theor.

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“…On the other hand, in the series expansion (12) for the annular phase, the expansion is considered around a mid-plane of the annular phase r = R in terms of the thickness |r − R|. Mehring and Sirignano (1999) adopted this sort of expansion ( 12) for the analysis of sinuous (antisymmetric) deformations in a planar liquid sheet and later Yoshinaga and coworkers Maeda 2008, Yoshinaga andYamamoto 2011) applied this to the annular liquid phase in a compound liquid jet. Instead of this series expansion (12), averaged quantities of velocity and pressure over the thickness could be used for the annular phase Sirignano 2000, Sano andFunakoshi 2008).…”

Section: Long Wave Approximation and Non-linear Reduced Equationsmentioning

confidence: 99%

Instabilities of a liquid column jet in a surrounding gas flowing through a coaxial cylindrical sheath

Yoshinaga¹

2020

Fluid Dyn. Res.

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In this paper, instabilities and breakup phenomena of a viscous liquid column jet in an inviscid stationary surrounding gas are analytically investigated, when the jet flows through a coaxial cylindrical sheath. Under a long wave approximation, axisymmetric non-linear evolution equations of the jet and surrounding gas are derived and numerically solved under a spatially periodic boundary condition. Validity and limitation of the approximation are examined in the linear regime in comparison with exact three-dimensional instabilities. It is shown in the non-linear analysis that there exist three types of breakup modes: the Rayleigh mode in which the surface tension instability is dominant and the breakup is caused by pinching, the first wind-induced mode in which blobs connected by threads are produced by increased aerodynamic instability and the second wind-induced mode in which the jet surface deforms to be spiked like a cusp without pinching and droplets are to be produced from a tip of the cusp. The existing regions of these modes are examined in the parameter space of the Weber number and the sheath radius for different Reynolds numbers and density ratios.

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“…Nath et al [6] conducted a temporal stability analysis of a plane liquid sheet that is subjected to different gas velocities on both sides. Yoshinaga [7] examined the breakup and encapsulation phenomena of a gas-cored compound liquid jet, which consists of an inviscid and incompressible core gas and surrounding annular liquid.…”

Section: Introductionmentioning

confidence: 99%

Linear Stability Analysis of a Conical Liquid Sheet

Yang

et al. 2010

Journal of Propulsion and Power

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A linear instability analysis method has been used to investigate the breakup of a conical liquid sheet under the combined influence of sinuous and varicose modes of disturbances at the liquid-gas interfaces. The maximum disturbance wave growth rate of two disturbance modes has been worked out by solving the dispersion equation of a conical liquid sheet, and the corresponding angular frequencies and dominant wave numbers have been obtained. A modified model to predict the breakup length of the conical liquid sheet was adopted. Furthermore, the surface deformation curves, which can estimate how long time the breakup process will take, have been plotted by solving the surface deformation equation. For both modes, the maximum disturbances growth rate and the dominant wave number increase as the pressure drop increase, while the breakup length and breakup time decrease with the increase of the pressure drop. Although the whole conical liquid sheet presents the varicose shape when the breakup takes place, the sinuous mode dominates the breakup process. With the increase of the geometrical characteristic parameter, the breakup length and breakup time decrease. The phase angle between the two modes affects the breakup slightly. To validate the conical sheet breakup model, the experiments were performed with the injectors of different geometry characteristics parameters and a high-speed dynamic measurement system was used to grab the detailed information of the liquid sheet breakup process. Comparison with experimental results shows that the calculation results coincide with the experiments, and the present analysis provides a good starting point for predicting unstable, wave-type behavior of the conical liquid sheet.

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Nonlinear Instability and Breakup of a Viscous Compound Liquid Jet

Cited by 4 publications

References 10 publications

Effects of gravity on the breakup and instability of a viscous compound jet

Effects of gravity on the breakup and instability of a viscous compound jet

Instabilities of a liquid column jet in a surrounding gas flowing through a coaxial cylindrical sheath

Linear Stability Analysis of a Conical Liquid Sheet

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