Influence of Vertical Vibration on Surface Velocity of a Liquid Bridge

2014 ◽  
Vol 580-583 ◽  
pp. 2890-2893
Author(s):  
Ru Quan Liang ◽  
Zhi Hui Zhang ◽  
Tai Yin Gao ◽  
Fu Sheng Yan
Keyword(s):  
Liquid Bridge ◽  
Stokes Equations ◽  
Silicone Oil ◽  
Conservation Equation ◽  
Vertical Vibration ◽  
Surface Velocity ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Two Phase ◽  
Energy Conservation Equation

In this paper, the vertical vibration influence on the surface velocity of a 5cSt silicone oil liquid bridge has been investigated numerically. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the two-phase surface is captured by using the mass conserving level set method. The present results indicate that the axial and radial surface velocities of the liquid bridge are suppressed by the external vertical vibration.

Flow of High Prandtl Number Fluid under Varying Axial Magnetic Field

2012 ◽  
Vol 256-259 ◽  
pp. 2412-2415
Author(s):  
Ru Quan Liang ◽  
Shuo Yang ◽  
Jun Hong Ji ◽  
Ji Cheng He
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Internal Flow ◽  
Conservation Equation ◽  
Staggered Grid ◽  
Zone Method ◽  
Two Phase ◽  
Energy Conservation Equation ◽  
Structure Of Flow

From engineering actual conditions of single crystal grown by floating zone method, Navier-Stokes equations coupled with the energy conservation equation were solved on a staggered grid based on the half floating area physical model. The two-phase surface was captured by using the mass conserving level set method. The internal flow structure of flow field of high Pr number liquid bridge was studied under uniform magnetic field environment in microgravity, which is important to optimize the process of the crystal growth.

Thermocapillary Convection of Low Prandtl Number Fluids under Uniform Magnetic Fields

2014 ◽  
Vol 580-583 ◽  
pp. 2970-2973 ◽  
Author(s):  
Ru Quan Liang ◽  
Di Bei ◽  
Fu Sheng Yan ◽  
Dian Qiao Geng
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Thermocapillary Convection ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Conservation Equation ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Constant Frequency ◽  
Energy Conservation Equation

Numerical simulations on thermocapillary convection of low Pr number molten tin under uniform magnetic field have been conducted under microgravity. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the free surface is captured by using the level set method. The present results show that the transverse uniform magnetic field can restrain the thermocapillary convection, and the fluid velocity at the hot corner fluctuates with a constant frequency at the steady state.

Flow Characteristics for High Prandtl Number Fluid under Zero Gravity

2013 ◽  
Vol 353-356 ◽  
pp. 3611-3614
Author(s):  
Ru Quan Liang ◽  
Shuo Yang ◽  
Jun Hong Ji ◽  
Ji Cheng He
Keyword(s):  
Free Surface ◽  
Flow Velocity ◽  
Liquid Bridge ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Conservation Equation ◽  
Staggered Grid ◽  
Vortex Center ◽  
Zero Gravity ◽  
Two Phase

This paper investigated the flow structure in liquid bridge of high Pr Number fluid under zero gravity condition. The free surface deformation and the effects of gas phase around liquid bridge were considered. Navier-Stokes equations coupled with the energy conservation equation were solved on a staggered grid. The two-phase surface was captured by using the mass conserving level set method. The results indicated that location of vortex center move gradually toward the free surface due to thermocapillary convection. The flow velocity nearby the surface of liquid bridge is faster than the internal flow velocity, and the overall velocity level tends to decline with time evolution.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

Temperature Distribution of High Prandtl Number Liquid Bridge under Zero Gravity

2013 ◽  
Vol 712-715 ◽  
pp. 1638-1641
Author(s):  
Ru Quan Liang ◽  
Shuo Yang ◽  
Jun Hong Ji ◽  
Fu Sheng Yan ◽  
Ji Cheng He
Keyword(s):  
Temperature Field ◽  
Prandtl Number ◽  
Liquid Bridge ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Ambient Air ◽  
Conservation Equation ◽  
Staggered Grid ◽  
Zero Gravity ◽  
High Prandtl Number

A numerical model has been developed to investigate temperature field of high prandtl number liquid bridge under zero-gravity condition, and numerical simulations have been carried out. The Navier-Stokes equations coupled with the energy conservation equation on a staggered grid. In numerical calculations, we considered not only the free surface deformation but also the effects of ambient air. Overall numerical analysis of liquid bridge was carried out by level set method of mass conservation to capture two phase interfaces. Simultaneously, results of temperature field in liquid bridge and ambient gas-phase were given.

Numerical Simulation of Transient Three-Dimensional Temperature and Kerf Formation in Laser Fusion Cutting

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Karim Kheloufi ◽  
El Hachemi Amara ◽  
Ahmed Benzaoui
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Front Surface ◽  
Conservation Equation ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Laser Fusion ◽  
Current Case ◽  
Energy Conservation Equation ◽  
Laser Fusion Cutting

In the present study, a three-dimensional transient numerical model was developed to study the temperature field and cutting kerf shape during laser fusion cutting. The finite volume model has been constructed, based on the Navier–Stokes equations and energy conservation equation for the description of momentum and heat transport phenomena, and the volume of fluid (VOF) method for free surface tracking. The Fresnel absorption model is used to handle the absorption of the incident wave by the surface of the liquid metal, and the enthalpy-porosity technique is employed to account for the latent heat during melting and solidification of the material. To model the physical phenomena occurring at the liquid film/gas interface, including momentum/heat transfer, a new approach is proposed which consists of treating friction force, pressure force applied by the gas jet, and the heat absorbed by the cutting front surface as source terms incorporated into the governing equations. All these physics are coupled and solved simultaneously in fluent CFD®. The main objective of using a transient phase change model in the current case is to simulate the dynamics and geometry of a growing laser-cutting generated kerf until it becomes fully developed. The model is used to investigate the effect of some process parameters on temperature fields and the formed kerf geometry.

Modeling and Simulation of Resin Filling and Cure Processes in Molds Partially Filled with Porous Media

2007 ◽  
Vol 553 ◽  
pp. 33-38
Author(s):  
Vítor A.F. Costa
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Control Volume ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Clear Fluid ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation ◽  
Real Process

The complete and simultaneous simulation of the overall filling and curing processes is presented. Fluid flow in the porous medium is described by the Brinkman-Forchheimer flow model, and fluid flow in the clear fluid domain is described by the Navier-Stokes equations. The flow front is captured using the volume fraction concept and a compressive convective scheme. Energy conservation equation and resin conversion equation give the equations to obtain the temperature and degree of cure, respectively. The physical model is solved using a control volume based finite element method. A limited set of results is presented, showing the usefulness of the information obtained from the complete and simultaneous simulation of the overall real process.

Thermocapillary Convection in a Floating Half Zone

2012 ◽  
Vol 248 ◽  
pp. 218-223
Author(s):  
Ru Quan Liang ◽  
Wen Jun Duan ◽  
Guang Dong Duan ◽  
Ja Ba
Keyword(s):  
Free Surface ◽  
Liquid Bridge ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Ambient Air ◽  
Conservation Equation ◽  
Staggered Grid ◽  
Relative Pressure ◽  
External Vibration ◽  
Free Surface Deformation

A numerical simulation has been conducted to investigate the effect of the external vibration referred to as g-jitter on the marangoni convection in liquid bridge of high Pr number fluid by taking both the dynamic free surface deformation and ambient air effects into consideration. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the free surface deformation is captured by introducing the mass conserving level set approach. The pressure distributions within the liquid bridge under external vibrations were investigated, and the results show that the pressure in liquid bridge presents periodic oscillation under external vibration. The closer to the hot disk, the greater the relative pressure value is. Moreover, the surface deformation and the surface amplitude under external vibration were investigated as well.

An Implementation of MAC Grid-Based IIM-Stokes Solver for Incompressible Two-Phase Flows

2011 ◽  
Vol 10 (5) ◽  
pp. 1333-1362 ◽  
Author(s):  
Zhijun Tan ◽  
K. M. Lim ◽  
B. C. Khoo
Keyword(s):  
Stokes Equations ◽  
Second Order ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Two Phase ◽  
Immersed Interface Method ◽  
Type Method ◽  
Pressure Poisson Equation ◽  
Correction Terms ◽  
Derivatives Of

AbstractIn this paper, a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces. The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method. The augmented variables and /or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines and are then applied to the fluid through the jump conditions. The Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient Uzawa-type method. The numerical results show that the overall scheme is second order accurate. The major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary conditions. The proposed method avoids solution of the pressure Poisson equation, and comparisons are made to show the advantages of time savings by the present method. The generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

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