The capillary interactions, including the capillary force and capillary suction, between two unequal-sized particles with a fixed liquid volume are investigated. The cap- illary interaction model is used within the Yo...The capillary interactions, including the capillary force and capillary suction, between two unequal-sized particles with a fixed liquid volume are investigated. The cap- illary interaction model is used within the Young-Laplace framework. With the profile of the meridian of the liquid bridge, the capillary suction, and the liquid volume as state variables, the governing equations with two-fixed-point boundary axe first derived using a variable substitution technique, in which the gravity effects are neglected. The capillary suction and geometry of the liquid bridge with a fixed volume are solved with a shooting method. In modeling the capillary force, the Gorge method is applied. The effects of var- ious parameters including the distance between two particles, the ratio of particle radii, and the liquid-solid contact angles are discussed.展开更多
The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. An...The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. And the basis for establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper firstly utilizes the ‘0-1' combined BEM to separate the boundary by means of discretization of Green's integral equation based on the Laplace equation, then separates the free surface of wave with FEM and derives the FEM equation of wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height could be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode is established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode is of high accuracy.展开更多
SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equ...SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.展开更多
On the basis of the Young-Laplace Equation that describes the pressure difference between each side of a curved liquid surface, a static equilibrium model is established to describe the surface shape of the weld bead....On the basis of the Young-Laplace Equation that describes the pressure difference between each side of a curved liquid surface, a static equilibrium model is established to describe the surface shape of the weld bead. The geometrical model for the molten pool is included, which is essential to explain the undercut phenomenon during high speed bead-on-plate welding. The results got from an iteration algorithm show that it is the force balance on the liquid mixture of the deposited metal and the molten base metal that causes the undercut. Some factors and their effects are also analyzed.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.51368038 and11162008)the Alumni Foundation of Civil Engineering of Lanzhou University of Technology(No.TM-QK-0701)the Environmental Protection Department of Gansu Province of China(No.GSEP-2014-23)
文摘The capillary interactions, including the capillary force and capillary suction, between two unequal-sized particles with a fixed liquid volume are investigated. The cap- illary interaction model is used within the Young-Laplace framework. With the profile of the meridian of the liquid bridge, the capillary suction, and the liquid volume as state variables, the governing equations with two-fixed-point boundary axe first derived using a variable substitution technique, in which the gravity effects are neglected. The capillary suction and geometry of the liquid bridge with a fixed volume are solved with a shooting method. In modeling the capillary force, the Gorge method is applied. The effects of var- ious parameters including the distance between two particles, the ratio of particle radii, and the liquid-solid contact angles are discussed.
文摘The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. And the basis for establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper firstly utilizes the ‘0-1' combined BEM to separate the boundary by means of discretization of Green's integral equation based on the Laplace equation, then separates the free surface of wave with FEM and derives the FEM equation of wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height could be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode is established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode is of high accuracy.
基金supported by the National Natural Science Foundation of China (Grant No. 50921001)
文摘SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.
文摘On the basis of the Young-Laplace Equation that describes the pressure difference between each side of a curved liquid surface, a static equilibrium model is established to describe the surface shape of the weld bead. The geometrical model for the molten pool is included, which is essential to explain the undercut phenomenon during high speed bead-on-plate welding. The results got from an iteration algorithm show that it is the force balance on the liquid mixture of the deposited metal and the molten base metal that causes the undercut. Some factors and their effects are also analyzed.
