Effects of Asymmetric Gas Distribution on the Instability of a Plane Power-Law Liquid Jet

As a kind of non-Newtonian fluid with special rheological features, the study of the breakup of power-law liquid jets has drawn more interest due to its extensive engineering applications. This paper investigated the effect of gas media confinement and asymmetry on the instability of power-law plane jets by linear instability analysis. The gas asymmetric conditions mainly result from unequal gas media thickness and aerodynamic forces on both sides of a liquid jet. The results show a limited gas space will strengthen the interaction between gas and liquid and destabilize the power-law liquid jet. Power-law fluid is easier to disintegrate into droplets in asymmetric gas medium than that in the symmetric case. The aerodynamic asymmetry destabilizes para-sinuous mode, whereas stabilizes para-varicose mode. For a large Weber number, the aerodynamic asymmetry plays a more significant role on jet instability compared with boundary asymmetry. The para-sinuous mode is always responsible for the jet breakup in the asymmetric gas media. With a larger gas density or higher liquid velocity, the aerodynamic asymmetry could dramatically promote liquid disintegration. Finally, the influence of two asymmetry distributions on the unstable range was analyzed and the critical curves were obtained to distinguish unstable regimes and stable regimes.

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Simulation of Laminar Liquid Jets in Gaseous Crossflow Before the Onset of Primary Breakup

Volume 6: Fluids and Thermal Systems; Advances for Process Industries, Parts A and B ◽

10.1115/imece2011-65338 ◽

2011 ◽

Cited By ~ 1

Author(s):

C.-L. Ng ◽

K. A. Sallam

Keyword(s):

Experimental Data ◽

Fuel Injection ◽

Liquid Jets ◽

Liquid Jet ◽

Jet Breakup ◽

Primary Breakup ◽

Density Ratios ◽

First Time ◽

Two Sides ◽

Reduced Pressures

The deformation of laminar liquid jets in gaseous crossflow before the onset of primary breakup is studied motivated by its application to fuel injection in jet afterburners and agricultural sprays, among others. Three crossflow Weber numbers that represent three different liquid jet breakup regimes; column, bag, and shear breakup regimes, were studied at large liquid/gas density ratios and small Ohnesorge numbers. In each case the liquid jet was simulated from the jet exit and ended before the location where the experimental data indicated the onset of breakup. The results show that in column and bag breakup, the reduced pressures along the sides of the jet cause the liquid to move to the sides of the jet and enhance the jet deformation. In shear breakup, the flattened upwind surface pushes the liquid towards the two sides of the jet and causing the gaseous crossflow to separate near the edges of the liquid jet thus preventing further deformation before the onset of breakup. It was also found out that in shear breakup regime, the liquid phase velocity inside the liquid jet was large enough to cause onset of ligament formation along the jet side, which was not the case in the column and bag breakup regimes. In bag breakup, downwind surface waves were observed to grow along the sides of the liquid jet triggered a complimentary experimental study that confirmed the existence of those waves for the first time.

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Stability of a Viscous Liquid Jet in a Coaxial Twisting Compressible Airflow

Processes ◽

10.3390/pr9060918 ◽

2021 ◽

Vol 9 (6) ◽

pp. 918

Author(s):

Li-Mei Guo ◽

Ming Lü ◽

Zhi Ning

Keyword(s):

Viscous Liquid ◽

Axial Velocity ◽

Liquid Velocity ◽

Velocity Ratio ◽

Dominant Mode ◽

Liquid Jet ◽

Axisymmetric Mode ◽

Jet Instability ◽

Jet Stability ◽

Jet Breakup

Based on the linear stability analysis, a mathematical model for the stability of a viscous liquid jet in a coaxial twisting compressible airflow has been developed. It takes into account the twist and compressibility of the surrounding airflow, the viscosity of the liquid jet, and the cavitation bubbles within the liquid jet. Then, the effects of aerodynamics caused by the gas–liquid velocity difference on the jet stability are analyzed. The results show that under the airflow ejecting effect, the jet instability decreases first and then increases with the increase of the airflow axial velocity. When the gas–liquid velocity ratio A = 1, the jet is the most stable. When the gas–liquid velocity ratio A > 2, this is meaningful for the jet breakup compared with A = 0 (no air axial velocity). When the surrounding airflow swirls, the airflow rotation strength E will change the jet dominant mode. E has a stabilizing effect on the liquid jet under the axisymmetric mode, while E is conducive to jet instability under the asymmetry mode. The maximum disturbance growth rate of the liquid jet also decreases first and then increases with the increase of E. The liquid jet is the most stable when E = 0.65, and the jet starts to become more easier to breakup when E = 0.8425 compared with E = 0 (no swirling air). When the surrounding airflow twists (air moves in both axial and circumferential directions), given the axial velocity to change the circumferential velocity of the surrounding airflow, it is not conducive to the jet breakup, regardless of the axisymmetric disturbance or asymmetry disturbance.

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Linear Instability Analysis of an Annular Swirling Viscous Liquid Jet

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.66-68.1556 ◽

2011 ◽

Vol 66-68 ◽

pp. 1556-1561 ◽

Cited By ~ 1

Author(s):

Kai Yan ◽

Ming Lv ◽

Zhi Ning ◽

Yun Chao Song

Keyword(s):

Viscous Liquid ◽

Liquid Velocity ◽

Aerodynamic Force ◽

Numerical Procedure ◽

Liquid Sheet ◽

Linear Instability ◽

Viscous Force ◽

Liquid Jet ◽

Instability Analysis ◽

Linear Instability Analysis

A three-dimensional linear instability analysis was carried out for an annular swirling viscous liquid jet with solid vortex swirl velocity profile. An analytical form of dispersion relation was derived and then solved by a direct numerical procedure. A parametric study was performed to explore the instability mechanisms that affect the maximum spatial growth rate. It is observed that the liquid swirl enhances the breakup of liquid sheet. The surface tension stabilizes the jet in the low velocity regime. The aerodynamic force intensifies the developing of disturbance and makes the jet unstable. Liquid viscous force holds back the growing of disturbance and the makes the jet stable, especially in high liquid velocity regime.

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Curved Non-Newtonian Liquid Jets With Surfactants

Journal of Fluids Engineering ◽

10.1115/1.3203202 ◽

2009 ◽

Vol 131 (9) ◽

Cited By ~ 9

Author(s):

Jamal Uddin ◽

Stephen P. Decent

Keyword(s):

Free Surface ◽

Shear Thickening ◽

Linear Instability ◽

Liquid Jets ◽

Liquid Jet ◽

Long Wavelength ◽

Droplet Sizes ◽

Wavelength Approximation ◽

Steady Solutions ◽

Linear Instability Analysis

Applications of the breakup of a liquid jet into droplets are common in a variety of different industrial and engineering processes. One such process is industrial prilling, where small spherical pellets and beads are generated from the rupture of a liquid thread. In such a process, curved liquid jets produced by rotating a perforated cylindrical drum are utilized to control drop sizes and breakup lengths. In general, smaller droplets are observed as the rotation rate is increased. The addition of surfactants along the free surface of the liquid jet as it emerges from the orifice provides a possibility of further manipulating breakup lengths and droplet sizes. In this paper, we build on the work of Uddin et al. (2006, “The Instability of Shear Thinning and Shear Thickening Liquid Jets: Linear Theory,” ASME J. Fluids Eng., 128, pp. 968–975) and investigate the instability of a rotating liquid jet (having a power law rheology) with a layer of surfactants along its free surface. Using a long wavelength approximation we reduce the governing equations into a set of one-dimensional equations. We use an asymptotic theory to find steady solutions and then carry out a linear instability analysis on these solutions.

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Influence of Jet Velocity on Jet Breakup in Immiscible Liquid-Liquid Systems

Chemical Product and Process Modeling ◽

10.2202/1934-2659.1347 ◽

2009 ◽

Vol 4 (3) ◽

Author(s):

Chi M Phan ◽

Geoffrey M Evans

Keyword(s):

Droplet Size ◽

High Speed ◽

Immiscible Liquid ◽

Linear Instability ◽

Liquid Jets ◽

Instability Analysis ◽

Jet Breakup ◽

Liquid Systems ◽

Jet Velocity ◽

Simplified Solution

The breakup of a laminar liquid jet is the underling phenomena used to generate emulsions in micro-scale devices. Jet breakup is induced by the most unstable disturbance growing on the jet surface, and linear instability analysis can be utilized to predict the resultant droplet size. Previously, instability analysis has been applied to stationary jets at intermediate Re only. This study investigates the influence of the jet velocity on the jet breakup at low Re number. The breakups of moving liquid jets were monitored using a high speed camera. The jet diameter, jet breakup length and resultant droplet sizes were strongly influenced by jet velocity. In addition to a simplified solution, a linear analysis for a moving jet was developed to determine the resultant droplet size. It was found that the full analysis is required to correctly predict the droplet size at low Re number.

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Theoretical Analysis of Surface Waves on Liquid Jets in Crossflows with Deformation

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.681.152 ◽

2013 ◽

Vol 681 ◽

pp. 152-157

Author(s):

Shao Lin Wang ◽

Yong Huang ◽

Fang Wang ◽

Zhi Lin Liu

Keyword(s):

Growth Rate ◽

Theoretical Analysis ◽

Surface Waves ◽

Cross Section ◽

Aerodynamic Force ◽

Linear Instability ◽

Wave Number ◽

Liquid Jets ◽

Liquid Jet ◽

The Cross

Liquid jets in cross air flows are widely used and play an important role in propulsion systems, such as ramjet combustors. Surface waves on the liquid jets in gaseous crossflows have been observed in numerous experiments. Especially for lower gas Webber number, liquid jets breaks up due to the surface waves. However compared with injecting into gas coaxial flow, liquid jet will be deformed in crossflow due to the transverse aerodynamic force. Deformation of jet is investigated by analyzing stress force equilibrium of the cross-section. Though linear instability analysis, dispersion relation and growth rate of surface waves of liquid jet with deformation were derived. According to the present theoretical analysis, the cross-section shape can be deformed to stable ellipse only if the gas velocity was lower than 9m/s for 1mm diameter jet. The maximum growth rate of disturbances takes place at wave number 0.7 approximately, and it will decrease with increasing the jet diameter. The range of instable wave number will expand and the most instable wave number will grow for the deformed jets.

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Liquid jet primary breakup in a turbulent cross-airflow at low Weber number

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.704 ◽

2019 ◽

Vol 879 ◽

pp. 775-792 ◽

Cited By ~ 1

Author(s):

M. Broumand ◽

M. Birouk ◽

S. Vahid Mahmoodi J.

Keyword(s):

Power Law ◽

Turbulence Intensity ◽

Weber Number ◽

Travelling Waves ◽

Perforated Plate ◽

Liquid Jet ◽

Mean Velocity ◽

Jet Breakup ◽

Jet Trajectory ◽

Primary Breakup

The influence of turbulence characteristics of a cross-airflow including its velocity fluctuations and integral length and time scales on the primary breakup regime, trajectory and breakup height and time of a transversely injected liquid jet was investigated experimentally. Turbulence intensity of the incoming airflow was varied from $u_{rms}/u_{g}=1.5\,\%$ to 5.5 % (where $u_{g}$ is cross-airflow streamwise mean velocity and $u_{rms}$ is the r.m.s. of the corresponding cross-airflow streamwise mean velocity fluctuation) by placing at the inlet of the test section a perforated plate/grid with a solidity ratio of $S=50\,\%$. Over the range of gas Weber number, $3.1<We_{g}<7.14$, the ensuing liquid jet exhibited more fluctuations and late breakup transitional behaviour under turbulent airflow conditions than in a uniform cross-airflow. Proper orthogonal decomposition of the liquid jet dynamics revealed that the use of grid caused a rise in the wavelength of travelling waves along the liquid jet, which hindered the transition of the liquid jet primary breakup regime from enhanced capillary breakup to the bag breakup mode. The quantitative results demonstrated that, at a constant airflow mean velocity, turbulent cross-airflow caused the liquid jet to bend earlier compared with its uniform counterpart. A power-law empirical correlation was proposed for the prediction of the liquid jet trajectory which takes into account the effect of turbulent Reynolds number. The liquid jet breakup height (in the $y$-axis direction) normalized by the jet diameter, and accordingly the liquid jet breakup time normalized by the airflow integral time scale, were found to decrease with increasing the airflow turbulence intensity. Two power-law empirical correlations were proposed to predict the liquid jet breakup height and time.

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Formation and Breakup of Liquid Jets Curved by Gravity

Volume 7: Fluids Engineering ◽

10.1115/imece2017-71608 ◽

2017 ◽

Cited By ~ 1

Author(s):

Manash Pratim Borthakur ◽

Binita Nath ◽

Gautam Biswas ◽

Dipankar Bandyopadhyay

Keyword(s):

Weber Number ◽

Droplet Size Distribution ◽

Bond Number ◽

Liquid Jets ◽

Liquid Jet ◽

Horizontal Distance ◽

Ohnesorge Number ◽

Jet Breakup ◽

Jet Trajectory ◽

Vertical Height

The formation and breakup of a liquid jet in air with gravity acting perpendicular to the direction of the jet is studied computationally. The liquid jet follows a parabolic path due to the influence of gravity which curves the jet trajectory. Both symmetric and asymmetric perturbations develop on the liquid surface which lead to jet breakup with varying droplet size distribution. The limiting length of the jet at breakup increases with increase in the Weber number and Ohnesorge number. At higher value of Weber number, the liquid jet traverses a longer horizontal distance when released from the same vertical height. Increasing the Bond number leads to a significant increase in the curvature of the jet trajectory. The volume of drops produced varies temporally for a given Weber number and decreases with the increasing value of Weber number. The detached drops undergo rolling motion as well as shape oscillations as they continue to fall on their trajectories.

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