Empirical Correlation of the Primary Stability Variable of Liquid Jet and Liquid Sheet Under Acoustic Field

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
V. Sivadas ◽  
K. Balaji ◽  
M. Sampathkumar ◽  
M. M. Hassan ◽  
K. M. Karthik ◽  
...  
Keyword(s):  
Weber Number ◽  
Liquid Velocity ◽  
Primary Stability ◽  
Surface Tension Force ◽  
Liquid Sheet ◽  
Acoustic Energy ◽  
Inertia Force ◽  
Liquid Jet ◽  
Pipe Length ◽  
Stability Functions

The investigation focuses on optimizing the length of wind-pipe that transmits acoustic energy from the compression driver to the cavity of twin-fluid atomizers. To accomplish this objective, the primary variable of stability, that is, the breakup length of liquid jet and sheet under acoustic perturbations has been experimentally characterized for a range of wind-pipe length and liquid velocity. The analysis considers liquid phase Weber number in the range of 0.7–8, and the results are compared with primary breakup data without acoustic perturbations. The range of Weber number tested belongs to Rayleigh breakup zone, so that inertia force is negligible compared to surface tension force. It shows the existence of unique stability functions based on dimensionless products up to an optimum wind-pipe length, which extends greater for liquid sheet configuration. The present results may find relevance in atomizer design that utilizes acoustic source to enhance liquid column breakup processes.

Absolute and convective instability of a liquid sheet

1990 ◽  
Vol 220 ◽  
pp. 673-689 ◽  
Author(s):  
S. P. Lin ◽  
Z. W. Lian ◽  
B. J. Creighton
Keyword(s):  
Weber Number ◽  
Convective Instability ◽  
Density Ratio ◽  
Sheet Thickness ◽  
Surface Tension Force ◽  
Liquid Sheet ◽  
Inertia Force ◽  
Liquid Density ◽  
Gas To Liquid ◽  
Density Ratios

The linear stability of a viscous liquid sheet in the presence of ambient gas is investigated. It is shown that there are two independent modes of instability, sinuous and varicose. The large-time asymptotic amplitude of sinuous disturbances is found to be bounded but non-vanishing for all calculated values of Reynolds numbers and the gas-to-liquid density ratios when the Weber number is greater than one half. The Weber numberWeis defined as the ratio of the surface tension force to the inertia force per unit area of the gas–liquid interface. WhenWeis smaller than one half, the sinuous mode is stable if the gas-to-liquid density ratio is zero, otherwise it is convectively unstable. The varicose mode is always convectively unstable unless the density ratio,Q, is zero. Then it is asymptotically stable. The spatial growth rate of the varicose mode is smaller than that of the sinuous mode for the same flow parameters. The wavelength of the most amplified waves in both modes is found to scale with the product of the sheet thickness andQ/We. It is shown, by use of the energy equation, that the mechanism of instability is a capillary rupture whenWe[ges ] 0.5, and the convective instability is due to the interfacial pressure fluctuation whenWe< 0.5.

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 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.

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.

Nonlinear instability of plane liquid sheets

2000 ◽  
Vol 406 ◽  
pp. 281-308 ◽  
Author(s):  
SEYED A. JAZAYERI ◽  
XIANGUO LI
Keyword(s):  
Weber Number ◽  
Density Ratio ◽  
Perturbation Expansion ◽  
Liquid Sheet ◽  
Fundamental Wave ◽  
Liquid Density ◽  
Initial Amplitude ◽  
Nonlinear Stability Analysis ◽  
Liquid Sheets ◽  
Breakup Time

A nonlinear stability analysis has been carried out for plane liquid sheets moving in a gas medium at rest by a perturbation expansion technique with the initial amplitude of the disturbance as the perturbation parameter. The first, second and third order governing equations have been derived along with appropriate initial and boundary conditions which describe the characteristics of the fundamental, and the first and second harmonics. The results indicate that for an initially sinusoidal sinuous surface disturbance, the thinning and subsequent breakup of the liquid sheet is due to nonlinear effects with the generation of higher harmonics as well as feedback into the fundamental. In particular, the first harmonic of the fundamental sinuous mode is varicose, which causes the eventual breakup of the liquid sheet at the half-wavelength interval of the fundamental wave. The breakup time (or length) of the liquid sheet is calculated, and the effect of the various flow parameters is investigated. It is found that the breakup time (or length) is reduced by an increase in the initial amplitude of disturbance, the Weber number and the gas-to-liquid density ratio, and it becomes asymptotically insensitive to the variations of the Weber number and the density ratio when their values become very large. It is also found that the breakup time (or length) is a very weak function of the wavenumber unless it is close to the cut-off wavenumbers.

Dynamics of Liquid Sheet Breakup in Splash Plate Atomization

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
G. Thunivumani ◽  
Hrishikesh Gadgil
Keyword(s):  
Solid Surface ◽  
Weber Number ◽  
Jet Impingement ◽  
Liquid Sheet ◽  
Force Balance ◽  
Impingement Angle ◽  
Wide Range ◽  
Perforated Sheet ◽  
Sheet Breakup ◽  
Regime Map

An experimental study was conducted to investigate the breakup of a liquid sheet produced by oblique impingement of a liquid jet on a plane solid surface. Experiments are carried out over a wide range of jet Weber number (80–6300) and various jet impingement angles (30 deg, 45 deg, and 60 deg) are employed to study the sheet dynamics. The breakup of a liquid sheet takes place in three modes, closed rim, open rim, and perforated sheet, depending upon the Weber number. The transitions across the modes are also influenced by the impingement angle with the transition Weber number reducing with increase in impingement angle. A modified regime map is proposed to illustrate the role of impingement angle in breakup transitions. A theoretical model based on force balance at the sheet edge is developed to predict the sheet parameters by taking the shear interaction between the sheet and the solid surface into account. The sheet shape predicted by the model fairly matches with the experimentally measured sheet shape. The breakup length and width of the sheet are measured and comparisons with the model predictions show good agreement in closed rim mode of breakup.

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.

Parametric Study of the Coupling Power Factor for the Statistical Energy Analysis of Piping Acoustic Vibration

2013 ◽  
Author(s):  
Ahmed H. Dweib
Keyword(s):  
Energy Analysis ◽  
Element Model ◽  
Coupling Factor ◽  
Acoustic Energy ◽  
Piping System ◽  
Statistical Energy Analysis ◽  
Multiple Sources ◽  
Pipe Length ◽  
Flow Equations ◽  
System Parameters

Energy-based finite element model is utilized for the evaluation of the Statistical Energy Analysis (SEA) coupling factor and the dependence of the coupling factor on the different system parameters is studied. Previous research has shown that the coupling factor is largely dependent on the modal densities of the fluid and pipe subsystems, which depend on the pipe dimensional parameters. The coupling factor depends also on the spectrum of the acoustic power generated, which in turn depends on the mass flow rate, the pressure reduction ratio and the characteristics of the pressure-reducing device. This study is concerned with the piping system parameters, downstream of the pressure-reducing valve. The system parameters selected for consideration are the pipe diameter to thickness ratio D/T and the pipe length to diameter ratio L/D. The study presents the effect of the variation in these two dimensionless parameters on the coupling factor. The results of the analysis can be used directly in the formulation of SEA power flow equations for large piping systems with multiple sources of acoustic energy as part of the fatigue life evaluation in critical services.

scholarly journals Breakup of the Water Sheet Formed by Two Liquid Impinging Jets

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Yakang Xia ◽  
Lyes Khezzar ◽  
Shrinivas Bojanampati ◽  
Arman Molki
Keyword(s):  
Weber Number ◽  
Reynolds Numbers ◽  
Impinging Jets ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Impingement Angle ◽  
Number Range ◽  
Breakup Length ◽  
Sheet Breakup ◽  
Visualization Experiments

Flow visualization experiments are carried out to study the flow regimes and breakup length of the water sheet generated by two impinging liquid jets from an atomizer made of two identical tubes 0.686 mm in diameter. These experiments cover liquid jet Reynolds numbers based on the pipe diameter in the range of 1541 to 5394. The effects of the jet velocities and impingement angle between the two jets on the breakup performance are studied. Four spray patterns are recognized, which are presheet formation, smooth sheet, ruffled sheet, and open-rim sheet regimes. Water sheet breakup length is found to be consistent with previous experimental and theoretical results in the lower Weber number (based on water jet diameter and velocity) range. In the relatively high Weber number range, the breakup length tends to a constant value with increasing Weber number, and some discrepancies between experimental and theoretical predictions do exist. Measured water sheet area increases with increasing liquid jet Reynolds numbers and impingement angle within the range of the current study.

Stabilizing effect of surrounding gas flow on a plane liquid sheet

2011 ◽  
Vol 672 ◽  
pp. 5-32 ◽  
Author(s):  
OUTI TAMMISOLA ◽  
ATSUSHI SASAKI ◽  
FREDRIK LUNDELL ◽  
MASAHARU MATSUBARA ◽  
L. DANIEL SÖDERBERG
Keyword(s):  
Growth Rate ◽  
Gas Flow ◽  
Liquid Velocity ◽  
Air Flow ◽  
Liquid Sheet ◽  
Mean Velocity ◽  
Order Of Magnitude ◽  
The Stability ◽  
The Waves ◽  
Half Thickness

The stability of a plane liquid sheet is studied experimentally and theoretically, with an emphasis on the effect of the surrounding gas. Co-blowing with a gas velocity of the same order of magnitude as the liquid velocity is studied, in order to quantify its effect on the stability of the sheet. Experimental results are obtained for a water sheet in air at Reynolds number Rel = 3000 and Weber number We = 300, based on the half-thickness of the sheet at the inlet, water mean velocity at the inlet, the surface tension between water and air and water density and viscosity. The sheet is excited with different frequencies at the inlet and the growth of the waves in the streamwise direction is measured. The growth rate curves of the disturbances for all air flow velocities under study are found to be within 20% of the values obtained from a local spatial stability analysis, where water and air viscosities are taken into account, while previous results from literature assuming inviscid air overpredict the most unstable wavelength with a factor 3 and the growth rate with a factor 2. The effect of the air flow on the stability of the sheet is scrutinized numerically and it is concluded that the predicted disturbance growth scales with (i) the absolute velocity difference between water and air (inviscid effect) and (ii) the square root of the shear from air on the water surface (viscous effect).

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