Capillary Instability of Liquid Jets Issuing From Elliptic Nozzles

2010 ◽  
Author(s):  
Ghobad Amini ◽  
Ali Dolatabadi
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Aspect Ratio ◽  
Stokes Equations ◽  
Practical Importance ◽  
Nozzle Geometry ◽  
Navier Stokes ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Breakup Mechanism

Breakup of a liquid jet issuing from an orifice is one of the classical problems in fluid dynamics due to its theoretical and practical importance. The main application of the process is in spray and droplet formation, which is of interest in the combustion in liquid-fuelled engines, ink-jet printers, coating systems, medical equipment, and irrigation device. The complexity of the breakup mechanism is due to the large number of parameters involved such as the design of injection nozzle, and thermodynamic states of both liquid and gas. In addition, different combinations of surface tension, inertia, and aerodynamic forces acting on the jet, define main breakup regimes. Effects of nozzle geometry on the behavior of liquid jets have been overlooked in the literature. Elliptic jets have never been investigated theoretically since mostly circular jets or liquid sheets have been analyzed; while experiments have shown that by using elliptical nozzles, entrainment and air mixing of fuel in combustion will be increased. In this article, instability of an elliptic liquid jet under the effect of inertia, viscous, and surface tension forces has been studied using temporal linear analyses. The effects of the gravity and the surrounding gas have been neglected. 1-D Cosserat equation (directed curve) has been used which can be considered as simplified form of Navier-Stokes equations. Results are comparable with classical Rayleigh mode of circular jet when the aspect ratio (ratio of major to minor axis) is one. Growth rate of instability on an elliptic liquid jet under various conditions has been compared with those of a circular jet. Results show that in comparison with a circular jet, the elliptic jet is more unstable and by increasing the aspect ratio the instability grows faster. In addition, similar to the circular case, the effect of viscosity is diminishing the growth rate for the elliptic jet.

Impingement Heat Transfer of Free-Surface Liquid Jets

2002 ◽  
Author(s):  
Albert Y. Tong
Keyword(s):  
Heat Transfer ◽  
Free Surface ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Stagnation Region ◽  
Navier Stokes Equations ◽  
Impingement Heat Transfer

The problem of convective heat transfer of a circular liquid jet impinging onto a substrate is studied numerically. The objective of the study is to understand the hydrodynamics and heat transfer of the impingement process. The Navier-Stokes equations are solved using a finite-volume formulation. The free surface of the jet is tracked by the volume-of-fluid method. The energy equation is modeled by using an enthalpy-based formulation. Detailed flow fields as well as free surface contours and pressure distributions on the substrate have been obtained. Local Nusselt number variations along the solid surface have also been calculated. The effects of several key parameters on the hydrodynamics and heat transfer of an impinging liquid jet have been examined. It has been found that the jet-inlet velocity profile and jet elevation have a significant effect on the hydrodynamics and heat transfer, particularly in the stagnation region, of an impinging jet. The numerical results have been compared with experimental data obtained from the literature. The close agreement supports the validity of the numerical study.

Numerical and Experimental Studies of Air Bubbles Coalescence in a Quiescent Water Column

2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Jean-Michel Martinez ◽  
Xavier Chesneau ◽  
Belkacem Zeghmati
Keyword(s):  
Surface Tension ◽  
Water Column ◽  
Stokes Equations ◽  
Experimental Studies ◽  
Numerical Results ◽  
Navier Stokes ◽  
Liquid Jet ◽  
Air Bubbles ◽  
Navier Stokes Equations ◽  
Effect Of Surface

Numerical and experimental studies of the dynamics of bubbles coalescence is reported. The numerical method based on the PLIC-VOF method and our advection and surface tension algorithms has been applied to analyse the effect of surface tension and convective terms of the Navier-Stokes equations on air bubbles' coalescence in a quiescent water column. Experimental and numerical results show a mechanical attraction between both bubbles' interface before the coalescence. We analyse the effect of the type of discretization of the convective terms of the Navier-Stokes equations on the shape of bubble after the coalescence phenomenon. Numerical results are in agreement with the images of bubbles' coalescence of our experimental device recorded by a camera. Somes images show obviousness bubbles' coalescence caracterized by an intense liquid jet within the following bubble.

scholarly journals Numerical stability analysis of a vortex ring with swirl

2019 ◽  
Vol 878 ◽  
pp. 5-36 ◽  
Author(s):  
Yuji Hattori ◽  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès
Keyword(s):  
Numerical Simulation ◽  
Growth Rate ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Base Flow ◽  
Critical Layer ◽  
Navier Stokes ◽  
Instability Mode ◽  
Navier Stokes Equations

The linear instability of a vortex ring with swirl with Gaussian distributions of azimuthal vorticity and velocity in its core is studied by direct numerical simulation. The numerical study is carried out in two steps: first, an axisymmetric simulation of the Navier–Stokes equations is performed to obtain the quasi-steady state that forms a base flow; then, the equations are linearized around this base flow and integrated for a sufficiently long time to obtain the characteristics of the most unstable mode. It is shown that the vortex rings are subjected to curvature instability as predicted analytically by Blanco-Rodríguez & Le Dizès (J. Fluid Mech., vol. 814, 2017, pp. 397–415). Both the structure and the growth rate of the unstable modes obtained numerically are in good agreement with the analytical results. However, a small overestimation (e.g. 22 % for a curvature instability mode) by the theory of the numerical growth rate is found for some instability modes. This is most likely due to evaluation of the critical layer damping which is performed for the waves on axisymmetric line vortices in the analysis. The actual position of the critical layer is affected by deformation of the core due to the curvature effect; as a result, the damping rate changes since it is sensitive to the position of the critical layer. Competition between the curvature and elliptic instabilities is also investigated. Without swirl, only the elliptic instability is observed in agreement with previous numerical and experimental results. In the presence of swirl, sharp bands of both curvature and elliptic instabilities are obtained for $\unicode[STIX]{x1D700}=a/R=0.1$, where $a$ is the vortex core radius and $R$ the ring radius, while the elliptic instability dominates for $\unicode[STIX]{x1D700}=0.18$. New types of instability mode are also obtained: a special curvature mode composed of three waves is observed and spiral modes that do not seem to be related to any wave resonance. The curvature instability is also confirmed by direct numerical simulation of the full Navier–Stokes equations. Weakly nonlinear saturation and subsequent decay of the curvature instability are also observed.

Effect of intermediate fluid layer on Kelvin–Helmholtz instability

2018 ◽  
Vol 96 (10) ◽  
pp. 1145-1154 ◽  
Author(s):  
Ying Zhang ◽  
Wenqiang Shang ◽  
Mengjun Yao ◽  
Boheng Dong ◽  
Peisheng Li
Keyword(s):  
Growth Rate ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Immiscible Fluids ◽  
Navier Stokes ◽  
Helmholtz Instability ◽  
Flow Configuration ◽  
Front Tracking Method ◽  
Internal Disturbance ◽  
Over Time

Two-dimensional K-H (Kelvin–Helmholtz) instability of the three-component immiscible fluids with an intermediate fluid layer is numerically studied using the front-tracking method (FTM). The instability is governed by the Navier–Stokes equations and the conservation of mass equation for incompressible flow. A finite difference method is used to discretize the governing system. This study focuses on the influence of flow configuration, the thickness of intermediate fluid layer and the distribution of intermediate fluid layer on K-H instability. It is shown that the larger the initial horizontal velocity difference is, the faster the internal disturbance increases, and the characteristic form of K-H instability becomes more obvious for different flow configuration. It is also observed that the thickness of the intermediate fluid layer is negatively correlated to the billow height and the numerical growth rate. In addition, when the intermediate fluid layer is thicker than 0.4 times the disturbance wavelength, the billow height and the numerical growth rate for the K-H instability of the upper and lower interfaces change over time synchronously. The higher the initial height of the lower interface is, the greater the growth rate and billow height of the upper interface are. Besides, the upper and lower interfaces are rolled up synchronously over time when the intermediate fluid layer is symmetrically distributed with y = 0.5 in the fluid system.

Comparative study on interfacial oscillations of rectangular and elliptical liquid jets

2020 ◽  
Vol 234 (7) ◽  
pp. 1272-1286 ◽  
Author(s):  
Amin Jaberi ◽  
Mehran Tadjfar
Keyword(s):  
Aspect Ratio ◽  
Weber Number ◽  
High Speed ◽  
Nozzle Geometry ◽  
Liquid Jets ◽  
High Speed Photography ◽  
Aspect Ratios ◽  
Water Jets ◽  
Switching Phenomenon ◽  
Axis Switching

The instability characteristics and flow structures of water jets injected from rectangular and elliptical nozzles with aspect ratios varying from 2 to 6 were experimentally studied and compared. Shadowgraph technique was employed for flow visualization, and structures on the liquid jet surface were captured using high speed photography. It was found that disturbances originating from the nozzle geometry initially perturbed the liquid column, and then, at high jet velocities, disturbances generated within the flow dominated the jet surface. It was also found that rectangular nozzles introduced more disturbances into the flow than the elliptical ones. The characteristic parameters of axis-switching phenomenon including wavelength, frequency, and amplitude were measured and compared. Axis-switching wavelength was found to increase linearly with Weber number. Also, the wavelengths of rectangular jets were longer than the elliptical jets. Further, the frequency of axis-switching was shown to be reduced with increase of both Weber number and aspect ratio. It was observed that the axis-switching amplitude increased monotonically, reached a peak, and then decreased gradually. It was also found that the axis-switching amplitude varied with Weber number. At lower values of Weber number, the rectangular nozzles had higher amplitude than the elliptical nozzles. However, at higher values of Weber number, this relation was reversed, and the elliptical nozzles had the higher axis-switching amplitudes. This reversal Weber number decreased with the orifice aspect ratio. The reversal Weber number for aspect ratio of 4 was about 289, and it had decreased to 144 for the aspect ratio of 6.

Level Set Based Modeling of Electrowetting on Dielectrics Droplet

2012 ◽  
Vol 461 ◽  
pp. 138-141
Author(s):  
Yin Xia Chang ◽  
Si Xiang Zhang ◽  
Wei Zhou ◽  
Bao Liu
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Level Set ◽  
Stokes Equations ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Navier Stokes ◽  
Electric Force ◽  
Electrowetting On Dielectric ◽  
Static Contact

This paper discusses the modeling of Electrowetting On Dielectric (EWOD) device that moves fluid droplets through surface tension effects and electric force. Instead of using a static contact angle as most papers did, we take the dynamic contact angle into count by using expression proposed by Voinov and Tanner. Firstly, the level set model and its initial values is present. Then the governing equations are discussed, and the diffused format is adopted for density and viscosity varies to smooth over the interface. The detailed expression for surface tension and electric force are also described for Navier–Stokes equations. After presenting the boundary conditions, the steps of numerical implementation are detailed.

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