Instability of Elliptic Liquid Jets (original) (raw)
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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.
Axis-switching and breakup of low-speed elliptic liquid jets
International Journal of Multiphase Flow, 2012
Theoretical and experimental investigations are conducted to analyze the instability of a low-speed liquid jet emerging from an elliptic nozzle. The complexity of viscous free surface flow analysis for an asymmetric geometry is simplified using an approach based on the Cosserat theory (also called director theory) which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This work is mainly focused on the spatial instability analysis to examine the key characteristics of an elliptic jet such as jet profile, axis-switching and breakup length. In the experimental part, both natural (free) and excited (forced) breakup behaviors are studied. In the natural breakup, the effects of nozzle's ellipticity and length to diameter ratio are examined. In the forced breakup case, disturbances are applied to the jet, by modulating the jet exit velocity using a piezoelectric actuator with given sinusoidal perturbations. The spatial evolution of the jet shape is captured with a high speed camera. Liquid jet instability is studied for various nozzle geometries over a specific range of jet velocities and excitation frequencies. Results are compared with conventional circular nozzles which can be considered as a special case of an elliptic jet.
Effect of liquid properties on the oscillation of elliptical liquid jets
Understanding the interfacial oscillation characteristics of liquid jets discharging from orifices is essential to describe their breakup mechanism and subsequent spray formation. The present work deals with an experimental study on the interfacial oscillation of elliptical liquid jets. The experiments are conducted with an elliptical orifice of equivalent diameter 4.93 mm with major and minor axis lengths 7.12 mm and 3.45 mm respectively. The results are obtained for three different liquids: pure water, water-glycerol mixture, and Jet A-1 fuel. The liquid jets are visualized using backlight shadow-graphy technique involving a high intensity strobe lamp and a digital camera. The interfacial oscillation of liquid jets is characterized by measuring the wavelength and amplitude of jet oscillation from recorded digital images. The wavelength of jet oscillation (λ) of elliptical liquid jet increases linearly with increase in liquid jet velocity (U o ). The jets of Jet A-1, owing to its significantly lower surface tension compared to the other two liquids, display higher value of wavelength for a given U o . The experimental measurements of λ recorded at different flow conditions exhibit good agreement with the theoretical predictions obtained using mathematical model proposed by Rayleigh (1879) to describe capillary phenomena of liquid jet exhibiting undulations in its cross section. For a given liquid jet Weber number (We), the elliptical jets of Jet A-1 undergo a larger increase in λ compared to the jets of other two liquids. Further the variation of maximum and minimum amplitudes (D max and D min ) of jet oscillation of elliptical liquid jets with We is discussed.
Fluid Dynamics Research, 2001
A study has been made of the behaviour of a disturbed semi-inÿnite liquid jet using a spatial instability method. A sinusoidal disturbance in the axial component of jet velocity at the nozzle is considered which resulted in an elliptic free surface boundary value problem with two non-linear boundary conditions. The system is linearised using perturbation techniques and the ÿrst order solution resulted in the dispersion relation. The jet stability is found to depend explicitly on the frequency of the disturbance and the Weber number. The second and third order solutions have been derived analytically which are used to predict on jet break-up and satellite formation.
Experimental Investigation of Flow and Coherent Properties of Excited Non-Circular Liquid Jets
Journal of Applied Fluid Mechanics, 2019
Non-circular jet is identified as an efficient passive flow-control technique that attracts many research topics. The existence of twine-vortexes is the main reason for dissimilarity between circular and non-circular jets. Which also influences the production of droplets and satellites as well as the jet instability. This investigation presents instability analysis of liquid-gas interface as an applicable conception in free-jet flows. We experiment different jet geometries within a gas ambient in order to study their hydrodynamic behavior. These studies give an appropriate perception about contributing forces that play essential roles in fluid instability. We focus on varying viscosity and surface tension as our excitation techniques. These methods are vital to examine the key properties of non-circular jets such as breakup and decay length, axis-switching wavelength as well as produced droplets and satellites characteristics. First, instabilities of charged liquid jets are investigated by considering the interaction between electric and inertial forces. Also, the viscosity effect was studied for its interaction with the inertial and surface tension forces. In each case, liquid jet instability for various nozzle geometries over a specific range of jet velocity is examined. The obtained results illustrate that the geometry of nozzle has an important effect on jet instability. In addition, by increment of We number, the breakup and decay length as well as the axis-switching wavelength are raising. However, by the rise of twin-vortex number, the breakup length increases but the decay length and axis-switching wavelength decrease.
Capillary instability of an annular liquid jet
Journal of Fluid Mechanics, 1987
An analytical investigation of the stability of a viscous, annular liquid jet moving in an inviscid medium is presented. This problem is a generalization of the well-known cases of a round cylindrical jet (obtained here when the ratio of internal to external radii tends to zero) and the flat thin liquid sheet (when the ratio above tends to unity).
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.
This work presents an experimental study on the oscillation behavior of liquid jets discharging from elliptical, triangular, and square shaped non-circular orifices. The measurements of wavelength and amplitude of jet oscillation are extracted from digital images of the liquid jets captured via still photography technique at different flow conditions using three different liquids (pure water, water-glycerol mixture, and Jet A-1 fuel). The measured wavelength of jet oscillation ( λ), irrespective of the shape geometry of the tested non-circular orifices, increases linearly with increase in liquid jet velocity ( U o ) and scales with the liquid jet Weber number ( We ) as λ/ D eq ∝ We 0.5 . The experimental measurements of λ recorded at different flow conditions exhibit good agreement with the theoretical predictions obtained using the mathematical model proposed by Rayleigh (1879) for liquid jet undulating in its cross section. For a given U o , the liquid jet of Jet A-1 displays higher value of λ and undergoes a larger increase in λ along the axis of the jet compared to the jets of other two liquids. Further the trends on the variation of maximum and minimum amplitudes of the first wave segment of liquid jets discharging from the elliptical and square orifices with U o are discussed.
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.