The study of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method (original) (raw)

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

Physics of Fluids, 2014

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Instability of Elliptic Liquid Jets

Journal of Fluid Mechanics

INSTABILITY OF ELLIPTIC LIQUID JETS GHOBAD AMINI-BAZIANI The motion of liquid jets ejected from elliptical orifices is studied theoretically and experimentally. In the theoretical part of the study, the linear evolution of initially small disturbances on the inviscid jets is investigated using a three-dimensional analysis. In addition, to study the viscous free-surface flows, an approach based on the Cosserat theory (also called directed theory) is used. Temporal and spatial analyses are performed and the dispersion equations of waves on the jet column are derived to show the growth rate of disturbances for different modes under various conditions. An equation for the jet profile is suggested which describes the axis-switching phenomenon and breakup for various conditions. The equations are approximated for small and large ellipticities, and wellknown dispersion relations of circular and planar jets are retrieved. It is shown that in the xvi "The history of science teaches only too plainly the lesson that no single method is absolutely to be relied upon, that sources of error lurk where they are least expected, and that they may escape the notice of the most experienced and conscientious worker."

Weakly nonlinear instability of a viscous liquid jet

Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems, 2017

A weakly nonlinear stability analysis of an axisymmetric viscous liquid jet is performed. The calculation is based on a small-amplitude perturbation method and restricted to second order. Contrary to the inviscid jet and the planar viscous sheet cases studied by Yuen in 1968 [1] and Yang et al. in 2013 [2], respectively, a part of the solution results from a polynomial approximation of Bessel functions. Results on interface shapes for a small wave number and initial perturbation amplitude, four different Ohnesorge numbers, taking into account the approximate part or not, are used to predict the influence of liquid viscosity on satellite drop formation and evaluate the influence of the approximation. It is observed that the liquid viscosity has a retarding effect on satellite drop formation, in agreement with previous experimental and numerical work. In addition, it is found that the approximate terms can be reasonably ignored, providing a simpler viscous weakly nonlinear model for the description of the first nonlinearity growth in liquid jets. The present work replaces the ILASS 2016 paper [3] by the authors on the same subject.

The breakup and atomization of a viscous liquid jet

Acta Mechanica Sinica, 1996

Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet. With respect to the spatial growing disturbance mode, the numerical results obtained from the solution of the dispersion equation reveal that a dimensionless parameter Jr exists. As Jr > 1, the axisymmetric disturbance mode is most unstable; and when Jr < 1, the asymmetric disturbances come into being, their growth rate increases with the decrease of Jr, till one of them becomes the most unstable disturbance. The breakup of a low-speed liquid jet results from the developing of axisymmetric disturbances, whose instability is produced by the surface tension; while the atomization of a high-speed liquid jet is brought about by the evolution of nonaxisymmetric disturbance, whose instability is caused by the aerodynamic force on the interface between the jet and the ambient gas.

The instability of jets of arbitrary exit geometry

International Journal for Numerical Methods in Fluids, 1995

This paper describes a calculation technique to determine the linear instability characteristics of jets of arbitrary exit geometry. In particular, elliptic and rectangular jets are considered. The numerical procedure involves both a conformal transformation between the computational domain and the physical plane and a solution of the transformed stability equation in the computational domain. Modem, efficient, conformal mappings are used for both simply and doubly connected domains. The numerical solution is based on a hybrid finite difference/ pseudospectral discretization of the stability equation. The technique is validated by comparison with previous stability calculations for circular and elliptic jets. Calculations are performed for the stability characteristics of elliptic and rectangular jets of aspect ratio 2:l. Growth rates, phase velocities, and pressure eigenfunctions are presented.

The non-linear breakup of an inviscid liquid jet

Fluid Dynamics Research, 1989

A liquid jet originating from a nozzle with radius * ro breaks up into droplets in consequence of disturbances of certain frequencies, depending on the fluid properties and the nozzle geometry. A theoretical model is developed to describe the growth of these disturbances at the jet surface. The model is based on the inviscid and irrotational flow governed by the Laplace equation together with the kinematicat and dynamical conditions at the free surface of the jet. A comparison is made between the model and experimental data from literature. The model predicts a dependence on the disturbance amplitude of the breakoff mode. Contrary to other experimental results, the model predicts satellites (i.e. smaller droplets between the main larger ones) at wavelengths exceeding a critical value of s x 2~rn*. The disturbances grow at wavelengths more than the theoretical bound of 2nr$. Discrepancies with experimental data are possible because of the neglect of the effect of viscosity in the theory. It is shown that the effect of viscosity on the jet can be neglected under certain conditions.

An experimental investigation of the convective instability of a jet

Chemical Engineering Science, 2003

This paper is an experimental study of the convective instability of a jet. It is well known that a jet issuing forth from a nozzle is unstable due to surface tension forces that cause it to break downstream into drops. We apply a disturbance of a given frequency at the nozzle tip. This applied frequency determines the wavelength and the growth rate of the growing disturbances and, thereby, the drop size. We measure the wavelength and the growth rate by ÿtting the entire digitized image of a jet to the functional form suggested by the linear theory. Thus, it makes use of the entire proÿle instead of the small number of points used in previous studies. Also, in contrast to previous work, we independently measure the jet velocity and the wave speed. At high non-dimensional jet velocity, the experimental results for the growth rates and the wave numbers agree with the linear stability theory of an inÿnite jet in the absence of gravity. At very low velocity (low Froude number) gravity is important and the agreement is not good. ?

Study of instability of liquid jets under gravity

AIP Conference Proceedings, 2017

Breakup of water jets under gravity is a commonplace phenomenon. The role of surface tension in the instability of water jets was recognized by Rayleigh and the theory propounded goes by the name of Plateau-Rayleigh theory. The necks and bulges down along the jet-length that are created by perturbation waves of wavelengths larger than a certain value keep growing with time and ultimately cause the jet to breakup into drops. The effect of perturbation waves have been investigated experimentally and found to confirm the essentials of the theory. However, there is no unanimity about the origin of these perturbation waves. Recently, the idea of recoil capillary waves as an important source of the perturbation waves has been emphasized. The recoil of the end point of the remaining continuous jet at its breakup point is considered to travel upward as a recoil capillary wave which gets reflected at the mouth of the nozzle from which the jet originates. The reflected capillary wave travels along the jet downward with its Doppler shifted wavelength as a perturbation wave. We set up an experiment to directly verify the existence and effect of the recoil capillary waves and present some preliminary results of our experiment.

Weakly nonlinear instability of a Newtonian liquid jet

Journal of Fluid Mechanics, 2018

A weakly nonlinear stability analysis of an axisymmetric Newtonian liquid jet is presented. The calculation is based on a small-amplitude perturbation method and performed to second order in the perturbation parameter. The obtained solution includes terms derived from a polynomial approximation of a viscous contribution containing products of Bessel functions with different arguments. The use of such an approximation is not needed in the inviscid case and the planar case, since the equations of those problems can be solved in an exact form. The developed model depends on three dimensionless parameters: the initial perturbation amplitude, the perturbation wavenumber and the liquid Ohnesorge number, the latter being the dimensionless liquid viscosity. The influence of the approximate terms was shown to be relatively small for a large range of Ohnesorge numbers so that they can be ignored. This simplification provides a jet model as simple to use as the previous ones, but taking into a...