scholarly journals On the deflection of a liquid jet by an air-cushioning layer

2018 ◽  
Vol 846 ◽  
pp. 711-751 ◽  
Author(s):  
M. R. Moore ◽  
J. P. Whiteley ◽  
J. M. Oliver
Keyword(s):  
Surface Tension ◽  
Equations Of Motion ◽  
Constant Thickness ◽  
Liquid Jet ◽  
Pressure Jump ◽  
Length Scales ◽  
Small Surface ◽  
Numerical Studies ◽  
Impact Problems ◽  
Systematic Derivation

A hierarchy of models is formulated for the deflection of a thin two-dimensional liquid jet as it passes over a thin air-cushioning layer above a rigid flat impermeable substrate. We perform a systematic derivation of the leading-order equations of motion for the jet in the distinguished limit in which the air pressure jump, surface tension and gravity affect the displacement of the centreline of the jet, but not its thickness or velocity. We identify thereby the axial length scales for centreline deflection in regimes in which the air layer is dominated by viscous or inertial effects. The derived length scales and reduced equations aim to expand the suite of tools available for future analyses of the evolution of lamellae and ejecta in impact problems. Assuming that the jet is sufficiently long that tip and entry effects can be neglected, we demonstrate that the centreline of a constant-thickness jet moving with constant axial speed is destabilised by the air layer for sufficiently small surface tension. Expressions for the fastest-growing modes are obtained in both the viscous-dominated air and inertia-dominated air regimes. For a finite-length jet emanating from a nozzle, we show that, in one particular asymptotic limit, the evolution of the jet centreline is akin to the flapping of an unfurling flag above a thin air layer. We discuss the distinguished limit in which tip retraction can be neglected and perform numerical investigations into the resulting model. We show that the cushioning layer causes the jet centreline to bend, leading to rupture of the air layer. We discuss how our toolbox of models can be adapted and utilised in the context of recent experimental and numerical studies of splash dynamics.

Investigation of the Linear Stability Problem of Electrified Jets, Inviscid Analysis

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Serkan Özgen ◽  
Oguz Uzol
Keyword(s):  
Surface Tension ◽  
Dispersion Relation ◽  
Linear Stability ◽  
Equations Of Motion ◽  
Density Ratio ◽  
Linear Stability Theory ◽  
Wave Number ◽  
Liquid Jet ◽  
Liquid Density ◽  
Electrified Jets

The instability characteristics of a liquid jet discharging from a nozzle into a stagnant gas are investigated using the linear stability theory. Starting with the equations of motion for incompressible, inviscid, axisymmetric flows in cylindrical coordinates, a dispersion relation is obtained, where the amplification factor of the disturbance is related to its wave number. The parameters of the problem are the laminar velocity profile shape parameter, surface tension, fluid densities, and electrical charge of the liquid jet. The dispersion relation is numerically solved as a function of the wave number. The growth of instabilities occurs in two modes, the Rayleigh and atomization modes. For rWe<1 (where We represents the Weber number and r represents the gas-to-liquid density ratio) corresponds to a Rayleigh or long wave instability, where atomization does not occur. On the contrary, for rWe>>1 the waves at the liquid-gas interface are shorter and when they reach a threshold amplitude the jet breaks down or atomizes. The surface tension stabilizes the flow in the atomization regime, while the density stratification and electric charges destabilize it. Additionally, a fully developed flow is more stable compared to an underdeveloped one. For the Rayleigh regime, both the surface tension and electric charges destabilize the flow.

RELATIONSHIP OF MAXIMUM DEFLECTIONS AND NATURAL FREQUENCIES VIBRATIONS OF ISOTROPIC CIRCULAR PLATES WITH INHOMOGENEOUS RESISTANCE CONDITIONS ON THE OUTER AND INNER CONTOUR

2021 ◽  
Vol 98 (6) ◽  
pp. 36-42
Author(s):  
A.V. TURKOV ◽  
◽  
S.I. POLESHKO ◽  
E.A. FINADEEVA ◽  
K.V. MARFIN ◽  
...  
Keyword(s):  
Variable Thickness ◽  
Constant Thickness ◽  
Circular Plates ◽  
Outer Contour ◽  
Numerical Studies ◽  
The Difference ◽  
Relationship Of ◽  
The Relationship ◽  
Hinged Support ◽  
Natural Transverse

The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

scholarly journals Shear instability of an axisymmetric air–water coaxial jet

2018 ◽  
Vol 843 ◽  
pp. 575-600 ◽  
Author(s):  
Jean-Philippe Matas ◽  
Antoine Delon ◽  
Alain Cartellier
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Scaling Laws ◽  
Shear Instability ◽  
Liquid Jet ◽  
Absolute Instability ◽  
Instability Waves

We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension and an absolute instability driven by confinement. We compare the predictions of this analysis with experimental results, and propose scaling laws for wave frequency in each regime. We finally introduce criteria to predict the boundaries between these three regimes.

scholarly journals Solution selection of axisymmetric Taylor bubbles

2018 ◽  
Vol 843 ◽  
pp. 518-535 ◽  
Author(s):  
A. Doak ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Constant Velocity ◽  
Numerical Scheme ◽  
Solution Space ◽  
Selection Mechanism ◽  
Small Surface ◽  
Taylor Bubble ◽  
Solution Selection ◽  
Selection Of ◽  
Taylor Bubbles

A finite difference scheme is proposed to solve the problem of axisymmetric Taylor bubbles rising at a constant velocity in a tube. A method to remove singularities from the numerical scheme is presented, allowing accurate computation of the bubbles with the inclusion of both gravity and surface tension. This paper confirms the long-held belief that the solution space of the axisymmetric Taylor bubble for small surface tension is qualitatively similar to that of the plane Taylor bubble. Furthermore, evidence suggesting that the solution selection mechanism associated with plane bubbles also occurs in the axisymmetric case is presented.

An Efficient Method for a Category of Contact/Impact Problems in Multibody Systems: Tree Topologies

2005 ◽  
Author(s):  
Michael J. Sadowski ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Momentum Balance ◽  
Unilateral Constraints ◽  
Constraint Forces ◽  
Rigid Body Dynamic ◽  
Tree Topologies ◽  
Contact Impact ◽  
Impact Problems

This paper presents an algorithm for the efficient numerical analysis and simulation of a category of contact/impact problems in multi-rigid-body dynamic systems with tree topologies. The algorithm can accommodate the jumps in structure which occur in the equations of motion of general multi-rigid-body systems due to a contact/impact event between bodies, or due to the locking of joints as long as the resulting system is a tree topology. The presented method uses a generalized momentum balance approach to determine the velocity jumps which take place across impacts in such multibody dynamic systems where event constraint forces are of the “non-working” category. The presented method does not suffer from the performance (speed) penalty encountered by most other momentum balance methods given its O(n) overall cost, and exact direct embedded consideration of all the constraints. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and potentially many unilateral constraints.

scholarly journals Droplet spreading and permeating on the hybrid-wettability porous substrates: a lattice Boltzmann method study

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 483-491 ◽  
Author(s):  
Wen-Kai Ge ◽  
Gui Lu ◽  
Xin Xu ◽  
Xiao-Dong Wang
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Droplet Spreading ◽  
Small Surface ◽  
Pore Sizes ◽  
Fluid Properties ◽  
Boltzmann Method ◽  
Porous Substrates

AbstractThe spreading and permeation of droplets on porous substrates is a fundamental process in a variety of applications, such as coating, dyeing, and printing. The spreading and permeating usually occur synchronously but play different roles in the practical applications. The mechanisms of the competition between spreading and permeation is significant but still unclear. A lattice Boltzmann method is used to study the spreading and permeation of droplets on hybrid-wettability porous substrates, with different wettability on the surface and the inside pores. The competition between the spreading and the permeation processes is studied in this work from the effects of the substrate and the fluid properties, including the substrate wettability, the porous parameters, as well as the fluid surface tension and viscosity. The results show that increasing the surfacewettability and the porosity contact angle both inhibit the spreading and the permeation processes. When the inside porosity contact angle is larger than 90° (hydrophobic), the permeation process does not occur. The droplets suspend on substrates with Cassie state. The droplets are more easily to permeate into substrates with a small inside porosity contact angle (hydrophilic), as well as large pore sizes. Otherwise, the droplets are more easily to spread on substrate surfaces with small surface contact angle (hydrophilic) and smaller pore sizes. The competition between droplet spreading and permeation is also related to the fluid properties. The permeation process is enhanced by increasing of surface tension, leading to a smaller droplet lifetime. The goals of this study are to provide methods to manipulate the spreading and permeation separately, which are of practical interest in many industrial applications.

Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions

2009 ◽  
Vol 465 (2109) ◽  
pp. 2725-2749 ◽  
Author(s):  
M. J. Ablowitz ◽  
T. S. Haut
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Asymptotic Series ◽  
High Order ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Small Surface ◽  
Petviashvili Equation ◽  
Dimensional Series

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech 2 solution of the Korteweg–de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev–Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes’ extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney–Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

Pattern Formation in Directional Solidification

2003 ◽  
Vol 782 ◽  
Author(s):  
Mike Greenwood ◽  
Mikko Haataja ◽  
Nikolas Provatas
Keyword(s):  
Surface Tension ◽  
Directional Solidification ◽  
Thermal Gradient ◽  
Adaptive Mesh Refinement ◽  
Interface Velocity ◽  
Adaptive Mesh ◽  
Field Method ◽  
Phase Field Method ◽  
Dendrite Morphology ◽  
Small Surface

We simulate directional solidification using the phase field method solved with adaptive mesh refinement. We examine length scale selection for two cases. For small surface tension anisotropy directed at forty five degrees relative to the pulling direction, we observe a transition from a seaweed to dendrite morphology as the thermal gradient is lowered, consistent with recent experimental findings. We show that the morphology of crystal structures can be unambiguously characterized through the local interface velocity distribution. We derive semi-empirically a phase diagram for the transition from seaweed to dendrites as a function of thermal gradient and pulling speed. As surface tension anisotropy is increased and aligned with the pulling direction we observe cellular and dendritic arrays directed in the pulling direction. We characterize wavelength selection and obtain a new universal scaling of the wavelength that differs from previous theories.

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