Numerical Methods for Tracking Interfaces With Surface Tension in 3-D Mold Filling Processes

2002 ◽  
Author(s):  
Matthew W. Williams ◽  
Doug Kothe ◽  
Deniece Korzekwa ◽  
Phil Tubesing
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Three Dimensional ◽  
Surface Force ◽  
Qualitative Behavior ◽  
Force Model ◽  
Simulation Tool ◽  
Software Simulation ◽  
Number Problem ◽  
Asymmetric Top

Gravity-pour casting processes are simulated for both low and high Weber number flows. The validation problems examined are a symmetric side-fill problem and a more complex asymmetric top-fill problem with flow over and obstacle. A recently developed continuum surface force model was implemented within a transient three-dimensional software simulation tool and applied to the low Weber number problem. The resulting simulations are compared with experiments that were conducted in order to validate current and future gravity-pour casting simulations. The simulations are found to capture much of the qualitative behavior of the complex three-dimensional flows.

Interactions Between High-Viscosity Droplets Deposited on a Surface: Experiments and Simulations

2012 ◽  
Author(s):  
J. Esmaeelpanah ◽  
A. Dalili ◽  
S. Chandra ◽  
J. Mostaghimi ◽  
H. C. Fan ◽  
...  
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Surface Force ◽  
Line Length ◽  
High Viscosity ◽  
Droplet Shape ◽  
Viscous Liquids ◽  
Straight Lines

A combined numerical and experimental investigation of coalescence of droplets of highly viscous liquids dropped on a surface has been carried out. Droplets of 87 wt% glycerin-in-water solutions with viscosity 110 centistokes were deposited sequentially in straight lines onto a flat, solid steel plate and droplet impact photographed. Impacting droplets spread on the surface until liquid surface tension and viscosity overcame inertial forces and the droplets recoiled, eventually reaching equilibrium. Droplet center-to-center distance was varied and droplet line length was measured from photographs. As droplet spacing was increased there was less interaction between the droplets. A three dimensional parallel code has been developed to simulate fluid flow and free surface interaction by solving the continuity, momentum and volume-of-fluid (VOF) equations. The two-step projection method was employed to solve the governing equations for the whole domain including both liquid and air phases. The continuum-surface-force (CSF) scheme was applied to model surface tension and the piecewise-linear-interface-construction (PLIC) technique used to reconstruct the free surface. Computer generated images of impacting droplets modeled droplet shape evolution correctly and compared well with photographs taken during experiments. Accurate predictions were obtained for droplet line length during spreading and at equilibrium.

Surface Tension Capability Within an Adaptively Refined Compressible Flow Code

2017 ◽  
Author(s):  
Z. Jibben ◽  
J. Velechovsky ◽  
T. Masser ◽  
M. Francois
Keyword(s):  
Surface Tension ◽  
Compressible Flow ◽  
Piecewise Linear ◽  
Surface Force ◽  
Force Model ◽  
Material Interface ◽  
Flow Solver ◽  
Interface Reconstruction ◽  
Volume Method ◽  
Inviscid Compressible Flow

We present a method to simulate surface tension between immiscible materials within an inviscid compressible flow solver. The material interface is represented using the volume of fluid technique with piecewise-linear interface reconstruction. We employ the continuum surface force model for surface tension, implemented in the context of the MUSCL-Hancock finite volume method for the Euler equations on an adaptively refined Eulerian mesh. We show results for droplet verification test cases.

scholarly journals Relaxation and breakup of a cylindrical liquid column

1970 ◽  
Vol 39 (2) ◽  
pp. 57-64 ◽  
Author(s):  
Mohammad Ali ◽  
Akira Umemura
Keyword(s):  
Surface Tension ◽  
Stokes Equations ◽  
Capillary Wave ◽  
Three Dimensional ◽  
Surface Tension Force ◽  
Surface Force ◽  
Computer Code ◽  
Vof Method ◽  
Liquid Column ◽  
Navier Stokes

Instability of capillary wave and breakup of a square cylindrical liquid column during its relaxation have been investigated numerically by simulating three-dimensional Navier-Stokes equations. For this investigation a computer code based on volume-of-fluid (VOF) method has been developed and validated with published experimental results. The result shows that the agreement of numerical simulation is quite well with the experimental data. The code is then used to study the capillary wave and breakup phenomena of the liquid column. The investigation shows the underlying physics during relaxation of the square cylindrical liquid column, illustrates the formation and propagation of capillary wave, and breakup processes. The breakup behavior for the present configuration of the liquid column shows some significant differences from those predicted by conventional jet atomization theories. The formation of capillary wave is initiated by the surface tension on the sharp edge of the square end of the cylinder and the propagation of the wave occurs due to the effect of surface tension force on the motion of the fluid. The propagation of capillary wave to the end of liquid column causes a disturbance in the system and makes the waves unstable which initiates the breakup of the liquid column. The characteristics of the capillary wave show that the amplitude of the swell grows faster than the neck of the wave and that of the tip wave grows much faster than the other waves. The velocity of the liquid particle is dominated by the pressure in the liquid column. Keywords: Instability; Continuum surface force; Liquid disintegration; Capillary wave; Surface tension; VOF method doi:10.3329/jme.v39i2.1847 Journal of Mechanical Engineering, Vol. ME39, No. 2, Dec. 2008 57-64

Surface Tension Model for Particle Method Using Inter-Particle Force Derived From Potential Energy

2012 ◽  
Author(s):  
Eiji Ishii ◽  
Taisuke Sugii
Keyword(s):  
Surface Tension ◽  
Fluid Flow ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Particle Method ◽  
Surface Force ◽  
Continuous Surface ◽  
Particle Force ◽  
Surface Tension Model

Fluid-flow simulation within micro/nano spaces is essential for designing micro/nano devices, such as those in micro-electro-mechanical systems and nanoimprint processes. Surface tension is a dominant force in the fluid flow within micro/nano spaces. Surface-tension models can be classified into two groups: models based on continuous surface force in immiscible phases, and models based on inter-particle force in miscible phases. The surface-tension model based on inter-particle force for modeling interactions between materials would fit fluid-flow simulation within micro/nano spaces better than the surface-tension model based on continuous surface force. We developed a surface tension model using inter-particle force for use with a particle method in a past study. However, workings of inter-particle forces in miscible phases were not verified. Furthermore, accuracy in three-dimensional simulation needed to be verified. These subjects were verified in this study using simple benchmark tests. First, cohesion based on potential energy was validated to qualitatively check the workings of inter-particle force. The phase separation from the mixed two-phase flow due to inter-particle force was simulated. Next, the inter-particle force at the gas-liquid interface was quantitatively verified using the theory of the Young-Laplace equation; the pressure in a droplet was compared in two- and three-dimensional simulations, and the predicted pressures in a droplet agreed well with this theory. The inter-particle force at the gas-liquid-solid interface for the wall adhesion of a droplet was also verified; the results for wall adhesion in three-dimensional space agreed much better than that in two-dimensional space. We found that our surface tension model was useful for simulating the fluid flow within micro/nano spaces.

The Study of Hybrid Method in the Onset of Droplet Escaping From the Film

2009 ◽  
Author(s):  
Yun Guo ◽  
Yuki Ishiwatari ◽  
Satoshi Ikejiri ◽  
Yoshiaki Oka
Keyword(s):  
Surface Tension ◽  
Gas Phase ◽  
Hybrid Method ◽  
Surface Force ◽  
Force Model ◽  
Phase Density ◽  
Droplet Entrainment ◽  
Liquid Phases ◽  
Good Agreement ◽  
The Continuum

A particle-grid hybrid method for simulating the onset of droplet entrainment is described. The air and liquid phases are expressed by grid and particle separately. The effects of surface tension and wall adhesion are calculated by the continuum surface force model. The fluid film variation and the droplet disengaging procedure are analyzed. The onset of entrainment criterion is obtained and it has a good agreement with Ishii’s correlation. The influences of surface tension and gas phase density on the criterion are also studied. Several simulation flow fields are given for illustrating the efficiency of the method.

Numerical Studies of Double Emulsions in a Coaxial Flow-Focusing Microfluidic Device

2017 ◽  
Author(s):  
Zhenyu Zhao ◽  
Bo Dong ◽  
Cong Chen ◽  
Weizhong Li
Keyword(s):  
Surface Tension ◽  
Droplet Size ◽  
Microfluidic Device ◽  
Outer Surface ◽  
Surface Force ◽  
Force Model ◽  
Flow Focusing ◽  
Geometry Model ◽  
Droplet Sizes ◽  
Size And Morphology

A simplified two dimensional coaxial flow-focusing geometry model was developed for computation domain, and then a volume of fluid based on continuum surface force model was carried out to study the influence of flow parameters on the droplet formation in a coaxial flow-focusing microfluidic device. The effects of flow rates, viscosities and the surface tensions of the three phases which are called the outer fluid, middle fluid and inner fluid on the size and morphology of the droplets were investigated. The results reveal that if the velocity and viscosity of the outer fluid are increased, the sizes of outer and inner droplets become smaller. By increasing the velocity of the middle fluid, the outer droplets become bigger, while the inner droplet size decreases. As the velocity of inner fluid increases, more inner fluid is injected, which leads to an increment with both outer and inner droplet size. Both of the outer and inner droplet sizes become bigger as the outer surface tension coefficients increase, and for the same reason, the increment with the outer surface tension result in an increase with the outer droplet size, but has no effect on the inner droplet size. Similarly, the droplets morphology almost does not vary with the viscosity of both middle and inner fluid. In fact, the principles revealed above are related with the interaction between the viscosity shear stress and the surface tension.

scholarly journals On sharp surface force model: Effect of sharpening coefficient

2020 ◽  
Vol 3 (3) ◽  
pp. 226-232 ◽  
Author(s):  
Kurian J. Vachaparambil ◽  
Kristian Etienne Einarsrud
Keyword(s):  
Surface Tension ◽  
Capillary Rise ◽  
Surface Tension Force ◽  
Surface Force ◽  
Volume Of Fluid ◽  
Tension Force ◽  
Force Model ◽  
Relative Ease

Abstract Amongst the multitude of approaches available in literature to reduce spurious velocities in Volume of Fluid approach, the Sharp Surface Force (SSF) model is increasingly being used due to its relative ease to implement. The SSF approach relies on a user-defined parameter, the sharpening coefficient, which determines the extent of the smeared nature of interface used to determine the surface tension force. In this paper, we use the SSF model implemented in OpenFOAM® to investigate the effect of this sharpening coefficient on spurious velocities and accuracy of dynamic, i.e., capillary rise, and static bubble simulations. Results show that increasing the sharpening coefficient generally reduces the spurious velocities in both static and dynamic cases. Although static millimeter sized bubbles were simulated with the whole range of sharpening coefficients, sub-millimeter sized bubbles show nonphysical behavior for values larger than 0.3. The accuracy of the capillary rise simulations has been observed to change non-linearly with the sharpening coefficient. This work illustrates the importance of using an optimized value of the sharpening coefficient with respect to spurious velocities and accuracy of the simulation.

Numerical Analysis of Heat Transfer of a Flow Confined by Wire Screen in Lithium Bromide Absorption Process

2014 ◽  
Vol 348 ◽  
pp. 40-50 ◽  
Author(s):  
Herbert Obame Mve ◽  
Romuald Rullière ◽  
Rémi Goulet ◽  
Phillippe Haberschill
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Numerical Analysis ◽  
Lithium Bromide ◽  
Surface Tension Force ◽  
Surface Force ◽  
Geometrical Parameters ◽  
Force Model ◽  
Vof Model ◽  
Static Contact

The present study deals with the numerical analysis of heat transfer inside a lithium bromide solution flowing down between finely meshed plastic wire screens. These screens confine the flow through capillary action while allowing the water vapor transfer inside an innovative absorber technology. The complex menisci shape formed on the confinement grid level, where the surface tension forces are of first importance, are reconstructed by a volume of fluid (VOF) model. A continuum surface force model is used to account for the surface tension force. A static contact angle is used to define the wall adhesion. A new algorithm, consisting to set an unique constant temperature at the liquid/vapour interface and to determine the evolution of heat transfer characteristics over the simulation domain, has been implemented and validated by analytical solutions. A parametric study has been conducted to determine the effect of the inlet velocity and the geometrical parameters (wire diameter and the number of divisions).

Optimum Design for the Frame of Open Type Abrasive Flow Polish Machine

2012 ◽  
Vol 497 ◽  
pp. 89-93
Author(s):  
Liang Liang Yuan ◽  
Ke Hua Zhang ◽  
Li Min
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Finite Element Methods ◽  
Optimization Design ◽  
Low Cost ◽  
Three Dimensional ◽  
Force Model ◽  
Optimization Analysis ◽  
Open Type ◽  
Set Up

In order to process heterotype hole of workpiece precisely, an open abrasive flow polish machine is designed, and the optimization design of machine frame is done for low cost. Firstly, basing on the parameters designed with traditional ways, three-dimensional force model is set up with the soft of SolidWorks. Secondly, the statics and modal analysis for machine body have been done in Finite element methods (FEM), and then the optimization analysis of machine frame has been done. At last, the model of rebuild machine frame has been built. Result shows that the deformation angle value of machine frame increased from 0.72′ to 1.001′, the natural frequency of the machine decreased from 75.549 Hz to 62.262 Hz, the weight of machine decreased by 74.178 Kg after optimization. It meets the strength, stiffness and angel stiffness requirement of machine, reduces the weight and cost of machine.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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