Nonlinear Instability Analysis of an Annular Swirling Viscous Liquid Sheet

2012 ◽  
Author(s):  
Kai Yan ◽  
Milind A. Jog ◽  
Zhi Ning
Keyword(s):  
Viscous Liquid ◽  
Velocity Ratio ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Perturbation Parameter ◽  
Liquid Sheet ◽  
Liquid Viscosity ◽  
Instability Analysis ◽  
Breakup Length ◽  
Sheet Breakup

A nonlinear spatial instability analysis of an annular swirling viscous liquid sheet has been carried out by a perturbation expansion method with the initial amplitude of the disturbance as the perturbation parameter. The viscous liquid sheet is considered to move axially and azimuthally and is exposed to co-flowing inner and outer gas streams. The effects of liquid swirl strength and liquid viscosity on the sheet instability and breakup length have been studied. The results show that except at very low values of swirl to axial velocity ratio of the liquid sheet, the liquid swirl destabilizes the sheet. The sheet breakup length increases slightly and then decreases rapidly with an increase in liquid swirl strength. Viscosity has a stabilizing effect on the sheet breakup. The sheet breakup length increases with an increase in liquid viscosity.

Weakly Nonlinear Instability of an Annular Liquid Sheet Subjected to Unequal Inner and Outer Gas Streams

2005 ◽  
Author(s):  
Ashraf A. Ibrahim ◽  
Milind A. Jog
Keyword(s):  
Liquid Velocity ◽  
Perturbation Expansion ◽  
Perturbation Parameter ◽  
Liquid Sheet ◽  
Nonlinear Stability Analysis ◽  
Fuel Injectors ◽  
Weakly Nonlinear ◽  
Gas Streams ◽  
Breakup Length ◽  
Air Stream

Instability and breakup of annular liquid sheet are encountered in fuel injectors used in gas turbine engines. A weakly nonlinear stability analysis has been carried out for annular liquid fuel sheet subjected to unequal inner and outer gas velocities by a perturbation expansion technique with the initial amplitude of the disturbance as the perturbation parameter. The liquid sheet is considered to move at a uniform axial velocity and is subjected to inner and outer gas streams of differing axial velocities. The breakup length is calculated, and the effect of the various flow parameters is investigated. It is found that the breakup length is reduced by an increase in the liquid velocity and the gas velocities. The inner air stream is more effective in disintegrating the sheet than the outer air stream.

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.

On the temporal instability of a two-dimensional viscous liquid sheet

1991 ◽  
Vol 226 ◽  
pp. 425-443 ◽  
Author(s):  
Xianguo Li ◽  
R. S. Tankin
Keyword(s):  
Growth Rate ◽  
Viscous Liquid ◽  
Local Maximum ◽  
Liquid Sheet ◽  
Rate Curve ◽  
Liquid Viscosity ◽  
Number Range ◽  
Liquid Sheets ◽  
Temporal Instability ◽  
Aerodynamic Instability

This paper reports a temporal instability analysis of a moving thin viscous liquid sheet in an inviscid gas medium. The results show that surface tension always opposes, while surrounding gas and relative velocity between the sheet and gas favour, the onset and development of instability. It is found that there exist two modes of instability for viscous liquid sheets – aerodynamic and viscosity-enhanced instability – in contrast to inviscid liquid sheets for which the only mode of instability is aerodynamic. It is also found that axisymmetrical disturbances control the instability process for small Weber numbers, while antisymmetrical disturbances dominate for large Weber numbers. For antisymmetrical disturbances, liquid viscosity, through the Ohnesorge number, enhances instability at small Weber numbers, while liquid viscosity reduces the growth rate and the dominant wavenumber at large Weber numbers. At the intermediate Weber-number range, Liquid viscosity has complicated effects due to the interaction of viscosity-enhanced and aerodynamic instabilities. In this range, the growth rate curve exhibits two local maxima, one corresponding to aerodynamic instability, for which liquid viscosity has a negligible effect, and the other due to viscosity-enhanced instability, which is influenced by the presence and variation of liquid viscosity. For axisymmetrical disturbances, liquid viscosity always reduces the growth rate and the dominant wavenumber, aerodynamic instability always prevails, and although the regime of viscosity-enhanced instability is always present, its growth rate curve does not possess a local maximum.

scholarly journals Longitudinal instabilities in an air-blasted liquid sheet

2001 ◽  
Vol 437 ◽  
pp. 143-173 ◽  
Author(s):  
ANTONIO LOZANO ◽  
FÉLIX BARRERAS ◽  
GUILLERMO HAUKE ◽  
CÉSAR DOPAZO
Keyword(s):  
Boundary Layer ◽  
Oscillation Frequency ◽  
Numerical Study ◽  
Near Field ◽  
Interface Velocity ◽  
Liquid Sheet ◽  
Linear Instability ◽  
Air Velocity ◽  
Instability Analysis ◽  
Sheet Breakup

An experimental and numerical study has been performed to improve the understanding of the air/liquid interaction in an air-blasted breaking water sheet. This research is focused in the near field close to the exit slit, because it is in this region where instabilities develop and grow, leading to the sheet breakup. In the experiments, several relevant parameters were measured including the sheet oscillation frequency and wavelength, as well as the droplet size distribution and the amplification growth rate. The flow was also investigated using linear instability theory. In the context of existing papers on instability analysis, the numerical part of this work presents two unique features. First, the air boundary layer is taken into account, and the effects of air and liquid viscosity are revealed. Second, the equations are solved for the same parameter values as those in the experiments, enabling a direct comparison between calculations and measurements; although qualitatively the behaviour of the measured variables is properly described, quantitative agreement is not satisfactory. Limitations of the instability analysis in describing this problem are discussed. From all the collected data, it is confirmed that the oscillation frequency strongly depends on the air speed due to the near-nozzle air/water interaction. The wave propagates with accelerating interface velocity which in our study ranges between the velocity of the water and twice that value, depending on the air velocity. For a fixed water velocity, the oscillation frequency varies linearly with the air velocity. This behaviour can only be explained if the air boundary layer is considered.

A non-linear model for impinging jets atomization

2008 ◽  
Vol 222 (2) ◽  
pp. 213-224 ◽  
Author(s):  
E A Ibrahim ◽  
B E Outland
Keyword(s):  
Linear Model ◽  
Weber Number ◽  
Drop Size ◽  
Impinging Jets ◽  
Liquid Sheet ◽  
Linear Perturbation ◽  
Breakup Length ◽  
Half Wavelength ◽  
Non Linear ◽  
Sheet Breakup

The problem considered is predicting the characteristics of the spray produced by atomization of an attenuating liquid sheet formed by the impingement of two liquid jets of equal diameters and momenta. A second-order non-linear perturbation analysis is employed to model the evolution of harmonic instability waves that lead to sheet distortion and fragmentation. The onset of atomization occurs when the uneven surface modulations of the thinning sheet bring its upper and lower interfaces in contact. It is found that the sheet is torn into ligaments at each half wavelength. The instability of the ligaments causes their eventual disintegration into drops. The results indicate that sheet breakup length, time, and resultant drop size decrease as Weber number is increased. A higher Weber number induces a greater sheet breakup thickness. The breakup length, thickness, time, and drop size are diminished at larger impingement angles. The theoretical predictions of the present non-linear model are in good agreement with available experimental data and empirical correlations for sheet breakup length and drop size.

Nonlinear Breakup Model for a Liquid Sheet Emanating From a Pressure-Swirl Atomizer

2007 ◽  
Vol 129 (4) ◽  
pp. 945-953 ◽  
Author(s):  
Ashraf A. Ibrahim ◽  
Milind A. Jog
Keyword(s):  
Flow Field ◽  
Ambient Pressure ◽  
Internal Flow ◽  
Liquid Sheet ◽  
Nonlinear Instability ◽  
Breakup Length ◽  
Sheet Breakup ◽  
Swirl Atomizer ◽  
Pressure Swirl ◽  
Pressure Swirl Atomizer

Predictions of breakup length of a liquid sheet emanating from a pressure-swirl (simplex) fuel atomizer have been carried out by computationally modeling the two-phase flow in the atomizer coupled with a nonlinear analysis of instability of the liquid sheet. The volume-of-fluid (VOF) method has been employed to study the flow field inside the pressure-swirl atomizer. A nonlinear instability model has been developed using a perturbation expansion technique with the initial amplitude of the disturbance as the perturbation parameter to determine the sheet instability and breakup. The results for sheet thickness and velocities from the internal flow solutions are used as input in the nonlinear instability model. Computational results for internal flow are validated by comparing film thickness at exit, spray angle, and discharge coefficient with available experimental data. The predictions of breakup length show a good agreement with semiempirical correlations and available experimental measurements. The effect of elevated ambient pressure on the atomizer internal flow field and sheet breakup is investigated. A decrease in air core diameter is obtained at higher ambient pressure due to increased liquid-air momentum transport. Shorter breakup lengths are obtained at elevated air pressure. The coupled internal flow simulation and sheet instability analysis provides a comprehensive approach to modeling sheet breakup from a pressure-swirl atomizer.

Breakup Model for Annular Liquid Sheets

2006 ◽  
Author(s):  
Ashraf A. Ibrahim ◽  
Milind A. Jog
Keyword(s):  
Fuel Injection ◽  
Surface Deformation ◽  
Perturbation Expansion ◽  
Perturbation Parameter ◽  
Liquid Sheet ◽  
Gas Streams ◽  
Liquid Sheets ◽  
Expansion Technique ◽  
Axially Moving ◽  
Breakup Model

The instability and breakup of annular liquid sheet is encountered in liquid atomization process used in numerous applications including liquid fuel injection in combustion engines and spray drying of foods. A nonlinear breakup model for annular liquid sheet exposed to both inner and outer air streams by a perturbation expansion technique with the initial amplitude of the disturbance as the perturbation parameter has been developed. The liquid sheet moves at a uniform axial velocity and subjects to axially moving inner and outer gas streams. The temporal evolution of the dimensionless surface deformation at the inner and outer liquid-gas interface has been evaluated until the point of breakup. The breakup length predictions show good agreement with the available experimental data.

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.

Modeling of Gas Turbine Fuel Nozzle Spray

1997 ◽  
Vol 119 (1) ◽  
pp. 34-44 ◽  
Author(s):  
N. K. Rizk ◽  
J. S. Chin ◽  
M. K. Razdan
Keyword(s):  
Gas Turbine ◽  
Fuel Injection ◽  
Near Field ◽  
Continuous Phase ◽  
Liquid Sheet ◽  
Vapor Concentration ◽  
Fuel Vapor ◽  
Fuel Injector ◽  
Gas Temperature ◽  
Sheet Breakup

Satisfactory performance of the gas turbine combustor relies on the careful design of various components, particularly the fuel injector. It is, therefore, essential to establish a fundamental basis for fuel injection modeling that involves various atomization processes. A two-dimensional fuel injection model has been formulated to simulate the airflow within and downstream of the atomizer and address the formation and breakup of the liquid sheet formed at the atomizer exit. The sheet breakup under the effects of airblast, fuel pressure, or the combined atomization mode of the airassist type is considered in the calculation. The model accounts for secondary breakup of drops and the stochastic Lagrangian treatment of spray. The calculation of spray evaporation addresses both droplet heat-up and steady-state mechanisms, and fuel vapor concentration is based on the partial pressure concept. An enhanced evaporation model has been developed that accounts for multicomponent, finite mass diffusivity and conductivity effects, and addresses near-critical evaporation. The presents investigation involved predictions of flow and spray characteristics of two distinctively different fuel atomizers under both nonreacting and reacting conditions. The predictions of the continuous phase velocity components and the spray mean drop sizes agree well with the detailed measurements obtained for the two atomizers, which indicates the model accounts for key aspects of atomization. The model also provides insight into ligament formation and breakup at the atomizer exit and the initial drop sizes formed in the atomizer near field region where measurements are difficult to obtain. The calculations of the reacting spray show the fuel-rich region occupied most of the spray volume with two-peak radial gas temperature profiles. The results also provided local concentrations of unburned hydrocarbon (UHC) and carbon monoxide (CO) in atomizer flowfield, information that could support the effort to reduce emission levels of gas turbine combustors.

Sign in / Sign up

Export Citation Format

Share Document