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

Processes ◽  
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.

The effect of air swirl profile on the instability of a viscous liquid jet

2000 ◽  
Vol 424 ◽  
pp. 1-20 ◽  
Author(s):  
Y. LIAO ◽  
S. M. JENG ◽  
M. A. JOG ◽  
M. A. BENJAMIN
Keyword(s):  
Viscous Liquid ◽  
Growth Rates ◽  
Axial Velocity ◽  
Weber Number ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Three Dimensional ◽  
Interfacial Instability ◽  
Liquid Jet ◽  
Axisymmetric Mode

A temporal linear stability analysis has been carried out to predict the instability of a viscous liquid jet surrounded by a swirling air stream with three-dimensional disturbances. The effects of flow conditions and fluid properties on the instability of the liquid jet are investigated via a parametric study by varying axial Weber number axial velocity ratio of the gas to liquid phase, swirl Weber numbers, density ratio and the Ohnesorge number. It is observed that the relative axial velocity between the liquid and gas phases promotes the interfacial instability. As the axial Weber number increases, the growth rates of unstable waves, the most unstable wavenumber and the unstable range of wavenumbers increase. Meanwhile, the increasing importance of helical modes compared to the axisymmetric mode switches the breakup regime from the Rayleigh regime to the first wind-induced regime and on to the second wind-induced regime. The predicted range of wavenumbers in which the first helical mode has higher growth rates than the axisymmetric mode agrees very well with experimental data. Results show that the destabilizing effects of the density ratio and the axial Weber number are nearly the same. Liquid viscosity inhibits the disintegration process of the liquid jet by reducing the growth rate of disturbances and by shifting the most unstable wavenumber to a lower value. Moreover, it damps higher helical modes more significantly than the axisymmetric mode. Air swirl has a stabilizing effect on the liquid jet. As air swirl strength increases, the growth rates of helical modes are reduced more significantly than that of the axisymmetric mode. The air swirl profile is found to have a significant effect on the instability of the liquid jet. The global, as well as local, effects of the swirl profile are examined in detail.

Linear Instability Analysis of an Annular Swirling Viscous Liquid Jet

2011 ◽  
Vol 66-68 ◽  
pp. 1556-1561 ◽  
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.

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

Energies ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1854 ◽  
Author(s):  
Jin-Peng Guo ◽  
Yi-Bo Wang ◽  
Fu-Qiang Bai ◽  
Fan Zhang ◽  
Qing Du
Keyword(s):  
Power Law ◽  
Liquid Velocity ◽  
Linear Instability ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Critical Curves ◽  
Jet Breakup ◽  
Plane Jets ◽  
Gas Space ◽  
Aerodynamic Asymmetry

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.

Two-dimensional modeling of viscous liquid jet breakup

2012 ◽  
Vol 224 (3) ◽  
pp. 499-512 ◽  
Author(s):  
M. Ahmed ◽  
M. Youssef ◽  
M. Abou-Al-Sood
Keyword(s):  
Viscous Liquid ◽  
Liquid Jet ◽  
Two Dimensional ◽  
Dimensional Modeling ◽  
Jet Breakup

Jet Breakup and Mixing Throat Lengths for the Liquid Jet Gas Pump

1974 ◽  
Vol 96 (3) ◽  
pp. 216-226 ◽  
Author(s):  
R. G. Cunningham ◽  
R. J. Dopkin
Keyword(s):  
Work Performance ◽  
Velocity Ratio ◽  
Area Ratio ◽  
Liquid Jet ◽  
Pump Efficiency ◽  
One Dimensional ◽  
Jet Breakup ◽  
Nozzle Contour ◽  
The One ◽  
The Impact

Gas compression with a liquid jet occurs isothermally and hence with minimum work. Performance characteristics of the liquid jet gas pump (efficiency and compression ratio versus inlet volumetric flow ratio) are predicted accurately by a one-dimensional analysis providing the mixing zone remains in the throat. Jet breakup was investigated to enable prediction of required throat length and to improve efficiency. Effects of throat length, nozzle contour and spacing, nozzle-throat area ratio (0.15 to 0.45), jet velocity and suction pressure were investigated. Optimum throat lengths were found; corresponding efficiencies exceed 40 percent. Two jet breakup flow regimes were found: impact and jet disintegration. For the impact regime, jet breakup length-depends on inlet velocity ratio, jet Reynolds number and nozzle-to-throat area ratio. Optimum throat lengths were found to be an empirical function of nozzle-to-throat area ratio and ranged from 12 to 32 throat dia. These results, coupled with the one-dimensional model, permit design of efficient liquid jet gas pumps.

A non-linear model for the atomization of a swirling viscous liquid jet

2008 ◽  
Vol 222 (11) ◽  
pp. 2137-2145
Author(s):  
E A Ibrahim ◽  
T L Williams
Keyword(s):  
Viscous Liquid ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Wave Number ◽  
Liquid Jet ◽  
Jet Instability ◽  
Viscous Forces ◽  
Swirl Injectors ◽  
Satellite Drops ◽  
Surface Disturbances

The instability and consequent atomization of a swirling viscous liquid jet emanated into gaseous surroundings and subjected to periodical surface disturbances is modelled and investigated. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative forms. Numerical solutions of the governing equations along with appropriate initial and boundary conditions are obtained through a robust finite-difference scheme. The computations yield real-time evolution of the interfacial profile and subsequent breakup characteristics of the liquid jet. It is found that the jet disintegrates into main and satellite drops, under all the conditions considered in the present study. The swirl enhances the instability of the jet and causes radial stretching of the main drops, whereas the satellite drops exhibit axial elongation. Increasing viscosity hinders jet instability and leads to main and satellite drop deformations that are similar to those produced by the swirl. The sizes of both main and satellite drops are diminished at higher disturbance wave numbers. A greater swirl strength induces a higher dominant wave number, and hence a reduced size of resultant main and satellite drops. Larger satellite drops and smaller main drops are produced as viscous forces are increased. The present model could be used as a guide for designing swirl injectors.

scholarly journals On the thermal instability of supercavitating liquid jet surrounded by coaxial rotary gas

2021 ◽  
Vol 37 ◽  
pp. 551-565
Author(s):  
Ming Lü ◽  
Zhi Ning
Keyword(s):  
Mathematical Model ◽  
Temperature Gradient ◽  
Thermal Instability ◽  
Dominant Frequency ◽  
Liquid Jet ◽  
Liquid Temperature ◽  
Jet Instability ◽  
Jet Stability ◽  
Effects Of Temperature ◽  
The Mathematical Model

Abstract Based on the jet stability theory, under the conditions of gas rotation, fluid compressibility and supercavitation, this paper gives the mathematical model describing the thermal instability of supercavitating liquid jet surrounded by a coaxial rotary gas, and the corresponding numerical method for solving the mathematical model is proposed and verified by the data in reference. Then, this paper analyzes the effects of gas–liquid temperature differences and temperature gradients on jet instability, and studies the thermal stability of supercavitating jet. The results show that the maximum disturbance growth rate, the dominant frequency and the maximum disturbance wave numbers increase linearly with the increase of gas–liquid temperature differences. The existence of temperature gradient inside the jet makes the effects of temperature differences on jet instability more obvious. The temperature gradient will inhibit the effect of supercavitation on jet instability, while gas–liquid temperature difference will promote the effect of supercavitation on jet instability.

scholarly journals Flapping Instability of an Atomized Liquid Jet

2010 ◽  
Author(s):  
Jean-Philippe Matas ◽  
Alain Cartellier
Keyword(s):  
Experimental Study ◽  
Large Amplitude ◽  
Liquid Velocity ◽  
Velocity Ratio ◽  
Liquid Jet ◽  
Liquid Droplets ◽  
Typical Size ◽  
Coaxial Jets ◽  
Break Up ◽  
Large Wavelength

We present an experimental study of the flapping instability which appears when a coaxial liquid jet is atomized by a cocurrent fast gas stream. When primary atomization does not lead to a total break-up of the liquid jet, it undergoes a large-wavelength instability, characterized by very large amplitude oscillations, and can break into large liquid fragments whose typical size is the jet diameter. These large liquid fragments, and consequently the flapping instability, are to be avoided in applications related to combustion where liquid droplets need to be as small as possible. We carried out experiments with air and water coaxial jets, with a gas/liquid velocity ratio of order 50. We studied the consequence of the flapping instability on the break-up of the liquid jet. Measurements of the frequency of the instability were carried out. We suggest a mechanism where the flapping instability could be triggered by non axisymmetrical KH modes.

scholarly journals Vorticity dynamics in a spatially developing liquid jet inside a co-flowing gas

2019 ◽  
Vol 877 ◽  
pp. 429-470
Author(s):  
A. Zandian ◽  
W. A. Sirignano ◽  
F. Hussain
Keyword(s):  
Liquid Velocity ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Three Dimensional ◽  
Upstream Region ◽  
Inertia Force ◽  
Liquid Jet ◽  
Viscous Forces ◽  
Surface Deformations ◽  
Axial Acceleration

A three-dimensional transient round liquid jet within a low-speed coaxial outer gas flow is numerically simulated and analysed via vortex dynamics ($\unicode[STIX]{x1D706}_{2}$ analysis). Two types of surface deformations are distinguished, which are separated by a large indentation on the jet stem. First, there are those inside the recirculation zone behind the leading cap – directly affecting the cap dynamics and well explained by the local vortices. Second, deformations upstream of the cap are mainly driven by the Kelvin–Helmholtz (KH) instability, unaffected by the vortices in the behind-the-cap region (BCR), and are important in the eventual atomization process. Different atomization mechanisms are identified and are delineated on a gas Weber number ($We_{g}$) versus liquid Reynolds number ($Re_{l}$) map based on the relative gas–liquid velocity. In a frame moving with the liquid velocity, this result is consistent with prior temporal studies. A simpler and clearer portrait of similarity of the atomization domains is shown by using the relative gas–liquid axial velocity, i.e. $We_{r}$ and $Re_{r}$, and avoiding the widely used velocity ratio as a third key parameter. A detailed comparison of vorticity along the axis in an Eulerian frame versus a frame fixed to a surface wave reveals that the vortex development and surface deformations are periodic in the upstream region, but this periodicity is lost closer to the BCR. In the practical range of the density ratio and for early times in the process, axial vorticity is mainly generated by baroclinicity while streamwise vortex stretching becomes more important at later times and only at lower relative velocities when pressure gradients are reduced. The inertia, vortex, pressure, viscous and surface tension forces are analysed to delineate the dominant causes of the three-dimensional instability of the axisymmetric KH structure due to surface acceleration in the axial, radial and azimuthal directions. The inertia force related to the axial gradient of kinetic energy is the main cause of the axial acceleration of the waves, while the azimuthal acceleration is mainly caused by the pressure and viscous forces. The viscous forces are negligible in the radial direction and away from the nozzle exit in the axial direction. It is interesting to note that azimuthal viscous forces are important even at high $Re_{l}$, indicating that inertia is not totally dominant in this instability occurring early in the atomization cascade.

NONLINEAR SIMULATION OF A HIGH-SPEED, VISCOUS LIQUID JET

1998 ◽  
Vol 8 (2) ◽  
pp. 155-178 ◽  
Author(s):  
J. H. Hilbing ◽  
Stephen D. Heister
Keyword(s):  
Viscous Liquid ◽  
High Speed ◽  
Liquid Jet ◽  
Nonlinear Simulation
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