Finite element simulation of single crystal growth process using GSMAC method

Kohno, Haruhiko; Tanahashi, Takahiko

doi:10.1016/s0377-0427(02)00543-5

Cited by 8 publications

(4 citation statements)

References 7 publications

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“…Logically, if we would like to avoid developing of empirical parameter set in order to adjust our 2D model for particular flow case, using of 3D modeling approach is obligatory. The large eddy simulation (LES) method, which is receiving growing attention at the present time and is actually being used for practical applications (Thomas et al, 2001;Horvat et al, 2001;Kohno and Tanahashi, 2002), was chosen for our numerical studies of cold crucible melting process. Our model experiments in crucible induction furnace have shown applicability of LES to the discussed flow category, not only providing good agreement in terms of calculated flow pattern, but also confirming experimentally determined characteristics of flow oscillations (Umbrashko et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Numerical studies of the melting process in the induction furnace with cold crucible

Umbrasko¹,

Baake²,

Nacke³

et al. 2008

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose-Aims to present recent activities in numerical modeling of cold crucible melting process. Design/methodology/approach-3D numerical analysis was used for electromagnetic problem and 3D large eddy simulation (LES) method was applied for fluid flow modeling. Findings-The comparative modeling shows, that higher H/D ratio of the melt is more efficient when total power consumption is considered, but this advantage is held back by higher heat losses through the crucible walls. Also, calculations reveal that lower frequencies, which are energetically less effective, provide better mixing of the melt. Originality/value-3D electromagnetic model, which allows to take into account non-symmetrical distribution of Joule heat sources, together with transient LES fluid flow simulation gives the opportunity of accurate prediction of temperature distribution in the melt.

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Section: Introductionmentioning

confidence: 99%

Numerical studies of the melting process in the induction furnace with cold crucible

Umbrasko¹,

Baake²,

Nacke³

et al. 2008

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…The fluid flow calculations are required for complete understanding how process parameters influence thermal pattern. The Large Eddy Simulation (LES) method, which is receiving growing attention at the present time [4][5][6], was chosen to accompany more common 2D RANS models for our numerical studies of cold crucible melting process. Model experiments in crucible induction furnace have shown applicability of LES to the discussed flow category, not only providing good agreement in terms of calculated flow pattern, but also confirming experimentally determined characteristics of flow oscillations [7].…”

Section: Introductionmentioning

confidence: 99%

Thermal and Hydrodynamic Analysis of the Melting Process in the Cold Crucible Using 3D Modeling

Umbrasko¹,

Baake

Nacke

et al. 2008

Heat Trans Res

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The experimental and numerical investigations of the turbulent melt flow are carried out in various laboratory and industrial sized induction furnaces, like induction crucible furnace and induction furnace with cold crucible (IFCC). The results of the transient 3D LES simulation of the turbulent melt flow revealed the large scale periodic flow instabilities and the temperature distribution in the melt, which both are in good agreement with the expectations based on the data from the experiments. The studies, presented in this paper, contain the numerical simulation of turbulent melt flow of experimental and industrial size induction furnaces and demonstrate the possibility of using the three-dimensional transient LES approach for successful simulation of heat and mass transfer processes in metallurgical applications.

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“…[2]. In a wide class of problems one has to consider the pure convective transport, for instance, convection of level set [3,4] or volumeof-fluid function [5,6] in free boundary problems, convection of mass fraction in multiphase or multicomponent flows [7,8] and convection of some auxiliary function in the k-turbulent 657 In spite of the different concepts underlying the Eulerian and Lagrangian schemes, all numerical methods for convection problems can be equally judged with respect to the capability of accurate capturing the discontinuities of the exact solution while retaining the solution monotonicity. There are quite a few works on the numerical schemes possessing this property.…”

Section: Introductionmentioning

confidence: 99%

A fast high‐resolution algorithm for linear convection problems: particle transport method

Smolianski

Shipilova

Haario

2006

Numerical Meth Engineering

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The paper is devoted to a novel explicit technique, the particle transport method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high-resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one-and two-dimensional benchmark problems. The numerical results confirm that the method has the 2nd-order spatial accuracy and can be significantly faster than the grid-based methods of the same order. AbstractThe paper is devoted to a novel explicit technique, the Particle Transport Method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high-resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one-and two-dimensional benchmark problems. The numerical results confirm that the method has the 2nd-order spatial accuracy and can be significantly faster than the grid-based methods of the same order.

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Finite element simulation of single crystal growth process using GSMAC method

Cited by 8 publications

References 7 publications

Numerical studies of the melting process in the induction furnace with cold crucible

Numerical studies of the melting process in the induction furnace with cold crucible

Thermal and Hydrodynamic Analysis of the Melting Process in the Cold Crucible Using 3D Modeling

A fast high‐resolution algorithm for linear convection problems: particle transport method

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