Nonlinear instability of liquid jets with thermocapillarity

1995 ◽  
Vol 283 ◽  
pp. 97-123 ◽  
Author(s):  
F. Mashayek ◽  
N. Ashgriz
Keyword(s):  
Ambient Temperature ◽  
Liquid Jets ◽  
Stable Configuration ◽  
Initial Surface ◽  
Breakup Mechanism ◽  
Capillary Flows ◽  
First Case ◽  
Satellite Drops ◽  
Thermal Disturbance ◽  
Surface Disturbance

The breakup mechanism of a capillary jet with thermocapillarity is investigated. Effects of the heat transfer from the liquid to the surrounding ambient, the liquid thermal conductivity, and the temperature-dependent surface tension coefficient on the jet instability and the formation of satellite drops are considered. Two different disturbances are imposed on the jet. In the first case, the jet is exposed to a spatially periodic ambient temperature. In addition to the thermal boundary condition, an initial surface disturbance with the same wavenumber as the thermal disturbance is also imposed on the jet. Both in-phase and out-of-phase thermal disturbances with respect to surface disturbances are considered. For the in-phase thermal disturbances, a parameter set is obtained at which capillary and thermocapillary effects can cancel each other and the jet attains a stable configuration. No such parameter set can be obtained when the thermocapillary flows are in the same direction as the capillary flows, as in the out-of-phase thermal disturbances. In the second case, only an initial thermal disturbance is imposed on the surface of the liquid while the ambient temperature is kept spatially and temporally uniform.

Temporal analysis of capillary jet breakup

1995 ◽  
Vol 291 ◽  
pp. 163-190 ◽  
Author(s):  
N. Ashgriz ◽  
F. Mashayek
Keyword(s):  
Linear Theory ◽  
Large Range ◽  
Reynolds Numbers ◽  
Temporal Analysis ◽  
Liquid Jets ◽  
Breakup Mechanism ◽  
Jet Breakup ◽  
Satellite Drops ◽  
Wide Range ◽  
Breakup Time

The temporal instability of a cylindrical capillary jet is analysed numerically for different liquid Reynolds numbers Re, disturbance wavenumbers k, and amplitudes ε0. The breakup mechanism of viscous liquid jets and the formation of satellite drops are described. The results show that the satellite size decreases with decreasing Re, and increasing k and ε0. Marginal Reynolds numbers below which no satellite drops are formed are obtained for a large range of wavenumbers. The growth rates of the disturbances are calculated and compared with those from the linear theory. These results match for low-Re jets, however as Re is increased the results from the linear theory slightly overpredict those from the nonlinear analysis. (At the wavenumber of k = 0.9, the linear theory underpredicts the nonlinear results.) The breakup time is shown to decrease exponentially with increasing the amplitude of the disturbance. The cut-off wavenumber is shown to be strongly dependent on the amplitude of the initial disturbance for amplitudes larger than approximately $\frac13$ of the initial jet radius. The stable oscillations of liquid jets are also investigated. The results indicate that liquid jets with Re ∼ O(1) do not oscillate, and the disturbances are overdamped. However, liquid jets with higher Re oscillate with a period which depends on Re and ε0. The period of the oscillation decreases with increasing Re at small ε0; however, it increases with increasing Re at large ε0. Marginal Reynolds numbers below which the disturbances are overdamped are obtained for a wide range of wavenumbers and ε0 = 0.05.

scholarly journals THE NUMERICAL MODELLING OF THE EFFECT OF OCCURRENCE DURATION ON THE WATER LEVEL DIFFERENCE FOR THE BOSPHORUS STRAIT

2011 ◽  
Vol 1 (32) ◽  
pp. 28
Author(s):  
Mehmet Nuri Ozturk ◽  
Yalçın Yüksel
Keyword(s):  
Water Level ◽  
Black Sea ◽  
Surface Elevation ◽  
The Black Sea ◽  
Solution Technique ◽  
Initial Surface ◽  
Sea Of Marmara ◽  
Level Difference ◽  
First Case ◽  
Layered Flow

The straits connecting two large water bodies show highly strong and stratified currents related to meteorological, morphological and hydrodynamic conditions. The Bosphorus is a long sea strait connecting the Black Sea and the Sea of Marmara. There is a two layer current system in the Bosphorus, which is largely determined by conditions at the Black Sea. The upper layer flows from the Black Sea to the Sea of Marmara caused by decline in surface elevation between the Black Sea and Sea of Marmara. The lower layer flows in opposite direction caused by the density difference which is due to the difference in salinities. In this study the effect of occurrence duration of water level difference (Δh) on the Bosphorus current structure was modelled using a three dimensional hydrodynamic modelling approach. The approach is based on an unstructured flexible mesh and uses a finite volume solution technique, which provides an optimal flexibility while retaining an efficient numerical solution. The meshes are based on linear triangular elements. An uniform rectangular channel which has simple geometry compare with Bosphorus was used for modelling. The channel has Bosphorus average values in dimensions. It is 900 m in width, 32,000 m in length and 64 m in depth. The constant salinty bondary conditions were described at the open bondaries corresponding Marmara and Black Sea boundaries and no water level difference as initial surface elevation. Using k-ε turbulence choice and hydrostatic pressure assumption, the two different occurrence duration for the same increase at the water level difference were modelled. In the first case the increasing of the duration for the water level difference described shorter than the second case. The model results show that, in the first case one-layered flow becomes dominated whole the channel flow, on the other hand in the second case two-layered flow persisted.

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.

Surface Disturbance Evolution and the Splattering of Turbulent Liquid Jets

1994 ◽  
Vol 116 (4) ◽  
pp. 721-727 ◽  
Author(s):  
Sourav K. Bhunia ◽  
John H. Lienhard
Keyword(s):  
Power Spectra ◽  
Liquid Jets ◽  
Surface Roughening ◽  
Water Mixture ◽  
Damping Effect ◽  
Turbulent Pressure ◽  
Surface Disturbance ◽  
Free Surface Turbulence ◽  
Rms Amplitude ◽  
Surface Disturbances

In this study, we investigate the growth of surface disturbances on turbulent liquid jets in air and its relation to the amount of splattering when the jet strikes a target. A laser-based optical technique is used to measure the instantaneous local amplitude of fluctuations on jets produced by fully-turbulent tube nozzles. Measurements were made over the portion of the jet between 0.2 and 45 nozzle diameters downstream of the nozzle. Jets of water, an isopropanol-water mixture, and water with a surfactant were studied. The local rms amplitude of surface disturbances scales with the jet Weber number and the dimensionless distance from the target. The measurements show a nonexponential growth of the rms amplitude as the liquid moves downstream. Power spectra of the disturbance amplitudes show broadband turbulent disturbances to be dominant over any single wavenumber Rayleigh-type instability. The measured rms amplitude of roughness on the jet surface correlates well with the fraction of impinging liquid splattered, as hypothesized in previous models of splattering. A mathematical model of the free-surface/turbulence interaction is also given. The spectrum of surface disturbances is calculated based on the pressure spectrum of isotropic, homogeneous turbulence. Both the theoretical model and the experiments show that the high-wavenumber portion of the spectrum decays as k−19/3 owing to the damping effect of capillary forces on the turbulent pressure spectrum that drives surface roughening.

scholarly journals Effect of Steel Surface Roughness and Expanded Graphite Condition on Sliding Layer Formation

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2960
Author(s):  
Aleksandra Rewolińska ◽  
Karolina Perz ◽  
Grzegorz Kinal
Keyword(s):  
Surface Roughness ◽  
Steel Surface ◽  
Friction Pair ◽  
Expanded Graphite ◽  
Initial Surface ◽  
Layer Formation ◽  
Material Transfer ◽  
Surface Geometry ◽  
First Case ◽  
Ring Pin

The aim of the research was to evaluate the influence of the initial roughness of a steel pin cooperating with a graphite ring—dry and wet—on the mechanism of sliding layer formation. A ring–pin friction pair was used for the study, where the rings were made of expanded graphite, while the pins were made of acid-resistant steel. In the first case, the steel pin interacted with a dry graphite ring, and in the second case, the graphite rings were moist. To determine the effect of initial surface roughness, the pins were divided into three roughness groups. To determine changes in surface geometry due to material transfer, the Ra and Rz parameters were measured. This project investigated how the initial roughness value of the steel surface pin cooperating with expanded graphite influences the formation of the sliding layer. Increasing the initial roughness of the steel surface interacting with the graphite contributes to faster layer formation and reduced roughness. The state of the expanded graphite—dry and wet—influences the formation of the sliding layer of graphite—a wet graphite component causes a faster smoothing of the steel surface. The running time of the wear apparatus has an effect on the resulting layer. The highest roughness group is the most favorable from the viewpoint of sliding layer formation.

scholarly journals Generation of Surface Waves Due to Initial Axisymmetric Surface Disturbance in Water with a Porous Bottom

2019 ◽  
Vol 24 (3) ◽  
pp. 625-644 ◽  
Author(s):  
P. Kundu ◽  
B.N. Mandal
Keyword(s):  
Free Surface ◽  
Asymptotic Form ◽  
Velocity Potential ◽  
Hankel Transform ◽  
Initial Surface ◽  
Initial Value ◽  
Poisson Problem ◽  
Different Types ◽  
Surface Disturbance ◽  
Infinite Integral

Abstract A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.

Drop Formation in Non-Newtonian Jets at Low Reynolds Number

2006 ◽  
Author(s):  
Vineet Dravid ◽  
Ping Bu Loke ◽  
Carlos M. Corvalan ◽  
Paul E. Sojka
Keyword(s):  
Reynolds Number ◽  
High Speed ◽  
Computational Models ◽  
Shear Thinning ◽  
Liquid Jets ◽  
Initial Increase ◽  
Element Analysis ◽  
Subsequent Decrease ◽  
Satellite Drops ◽  
Moderate Reynolds Number

The major objective of this work is to develop accurate computational models to predict evolution of shear thinning liquid jets. A secondary objective is to investigate the formation of satellite drops, and to determine the conditions under which their diameter can be controlled. The theoretical approach of Galerkin-finite element analysis is used solve the complete two-dimensional set of axisymmetric governing equations and the kinematic and dynamic boundary conditions at the free surface. The effect of shear thinning behavior on break-up is studied in detail, in the case of an infinitely long non-Newtonian jet. It is found that the shear thinning behavior may be useful in controlling satellite drop sizes. (We observe that increasing the shear thinning behavior at moderate Reynolds number (Re = 5) leads to an initial increase in the satellite drop size, followed by a subsequent decrease.) Experimental validation for the theory is then presented for the case of a shear thinning non-Newtonian jet. The experimental fluid is pumped through a capillary and drop shapes are obtained using a high speed camera. The experimentally obtained shapes are compared to those predicted by theory with results found to be in good agreement.

Drop Formation in Non-Newtonian Jets at Low Reynolds Numbers

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
V. Dravid ◽  
P. B. Loke ◽  
C. M. Corvalan ◽  
P. E. Sojka
Keyword(s):  
High Speed ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Liquid Jets ◽  
Initial Increase ◽  
Low Reynolds Numbers ◽  
Subsequent Decrease ◽  
Satellite Drops ◽  
Element Approach ◽  
Secondary Objective

The objective of this study was to develop an experimentally verified computational model that accurately predicts evolution of shear-thinning liquid jets. A secondary objective was to investigate the formation of satellite drops and to determine conditions under which their diameter can be controlled. The model employs the Galerkin finite/element approach to solve the complete two-dimensional set of axisymmetric governing equations and the corresponding kinematic and dynamic boundary conditions at the free surface. The effect of shear-thinning behavior on breakup was studied in detail for the case of an infinitely long non-Newtonian jet. It was found that shear-thinning behavior may be useful in controlling satellite drop sizes. (We observe that increasing the shear-thinning behavior at Re∼5 leads to an initial increase in the satellite drop size, followed by a subsequent decrease.) Comparison of model predictions with experimental data is presented for the case of a shear-thinning non-Newtonian jet. The experimental liquid was pumped through a capillary and drop shapes obtained using a high speed camera. The experimentally obtained shapes were compared to those predicted by the model and found to be in good agreement.

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