Finite Element Modeling of Silicon Transport into Germanium Using a Simplified Crystal Growth Technique

2011 ◽  
Vol 312-315 ◽  
pp. 240-247
Author(s):  
Farid Mechighel ◽  
Mohammed El Ganaoui ◽  
Bernard Pateyron ◽  
Mahfoud Kadja ◽  
S. Dost
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Crystal Growth ◽  
Concentration Profile ◽  
Similar Material ◽  
Growth Technique ◽  
Vertical Bridgman ◽  
Growth Methods

A numerical simulation study, using finite element method, was carried out to examine the temperature and concentration fields in the dissolution process of silicon into germanium melt. This work utilized a simplified configuration which may be considered to be similar material configuration to that used in the Vertical Bridgman growth methods. The concentration profile for the Si-Ge sample processed using this technique shows increasing transport silicon into the melt with time, moreover, a flat stable interface is observed. The mass and momentum equations for fluid flow, the energy and the solute mass transport were numerically solved. Results showed good agreements with experiments.

The Meshfree Interface Finite Element Method for Numerical Simulation of Dendritic Solidification with Fluid Flow

2018 ◽  
Vol 15 (07) ◽  
pp. 1850057 ◽  
Author(s):  
Adam Yehudi Ghoneim
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Degrees Of Freedom ◽  
Mathematical Formulation ◽  
Solidification Process ◽  
Dirichlet Boundary Conditions ◽  
Dendritic Solidification ◽  
Element Method

In this paper, we use the newly proposed meshfree interface finite element method (MIFEM) for numerical simulation of dendritic solidification with fluid flow. In the MIFEM, meshfree points without connectivity are imposed directly at the zero-isocontour of an implicit function defining the interface which is allowed to arbitrarily intersect the finite elements. The MIFEM utilizes the constructed interface points for meshfree solution of a variational level set equation based on the Ginzburg–Landau energy functional minimization such that the reinitialization procedure is completely eliminated. To account for inter-element discontinuities, field variables at interface-embedded elements are computed by extending the approximation using the meshfree interface points as additional degrees of freedom directly corresponding to the interface. This is achieved by meshfree interpolation at the interface region via radial basis functions which inherently satisfies the Kronecker-delta and the partition of unity conditions allowing for precise and easy imposition of Dirichlet boundary conditions at the interface. We use the MIFEM for solving the interfacial evolution equation and the set of mass, momentum, and energy conservation equations describing the dendritic solidification process with fluid flow. Mathematical formulation and implementation to multiple case studies will be presented and discussed.

scholarly journals The plane-to-cellular-to-dendrite transition of the shape of the crystallization front during the crystallization of Al-Cu alloys

2006 ◽  
Vol 71 (3) ◽  
pp. 303-312
Author(s):  
Vesna Radojevic ◽  
Andreja Valcic ◽  
Slobodanka Nikolic ◽  
Aleksandar Golubovic
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Crystal Growth ◽  
Temperature Gradient ◽  
Crystallization Front ◽  
The Finite Element Method ◽  
Cu Alloys ◽  
Vertical Bridgman

The evolution of the crystallization front from a planar to a dendritic one as a function of the G L/(Rc 0) parameter was investigated during the crystallization of Al-Cu alloys by the vertical Bridgman method. Six series of alloys with different initial compositions of Cu were solidified at different growth rates. A mathematical model for the heat transfer during vertical Bridgmen crystal growth was developed. The model was solved using the finite element method. The temperature gradient in the melt at the beginning of crystal growth was calculated using the obtained model. Discrete stages of the crystallization front were identified in the experiments, as the ratio G L/(Rc 0) decreased.

scholarly journals Finite Element Method Using a Characteristic-Based Split for Numerical Simulation of a Carbonate Fracture-Cave Reservoir

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Liehui Zhang ◽  
Yuhui Zhou ◽  
Lei Zhao ◽  
Deliang Zhang
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Numerical Calculation ◽  
Network Model ◽  
Free Flow ◽  
Complex Flow ◽  
Fracture Systems ◽  
Characteristic Based Split

Fracture-cave carbonate reservoirs occur widely in source rocks and are prospects for exploitation worldwide. However, the presence of massive caves and multiscale fracture systems results in extremely complex fluid flow patterns. Therefore, in this paper, a discrete network model for fracture-cave reservoirs was established to study fluid flow characteristics and pressure distributions in complex flow regimes. In this study, the cave system was treated as a free-flow region, and the fluid flow in fracture systems followed the Navier-Stokes and Darcy equations, respectively. After discrete modeling, the Galerkin finite element method was used for numerical calculation of the single-phase free flow; the method maintains a high-precision result with low grid orientations during the simulation. In addition, because only one linear equation requires solving at each step, the solution is obtained quickly. Moreover, based on the proposed discrete media network model of fracture-cave reservoirs and the finite element numerical calculation method, a corresponding simulator was also developed. The finite element numerical simulation method based on the characteristic-based split (CBS) algorithm has proven to be applicable to complex flow problems in fracture-cave reservoirs.

The study of the elastic deformation of a flexible wheel by a cam wave generator

2020 ◽  
Vol 65 (1) ◽  
pp. 51-58
Author(s):  
Sava Ianici
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Deformation ◽  
Theoretical Study ◽  
Elastic Field ◽  
The Finite Element Method ◽  
Elastic Deformations ◽  
Wave Generator ◽  
Two Stages

The paper presents the results of research on the study of the elastic deformation of a flexible wheel from a double harmonic transmission, under the action of a cam wave generator. Knowing exactly how the flexible wheel is deformed is important in correctly establishing the geometric parameters of the wheels teeth, allowing a better understanding and appreciation of the specific conditions of harmonic gearings in the two stages of the transmission. The veracity of the results of this theoretical study on the calculation of elastic deformations and displacements of points located on the average fiber of the flexible wheel was subsequently verified and confirmed by numerical simulation of the flexible wheel, in the elastic field, using the finite element method from SolidWorks Simulation.

Sign in / Sign up

Export Citation Format

Share Document