Numerical simulation of dendritic solidification with convection: Three-dimensional flow

Al-Rawahi, Nabeel; Tryggvason, Grétar

doi:10.1016/j.jcp.2003.09.020

Cited by 82 publications

(59 citation statements)

References 24 publications

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“…The dendrite tip velocity differs by an order of about 10 2 for the two undercoolings considered. These results compare very well with those reported in [4,34].…”

Section: Three-dimensional Crystal Growth With Convectionsupporting

confidence: 92%

“…It has been shown from numerical simulations [2,4,[26][27][28] and experiments [29] that fluid flow has an important effect on crystal growth. There are a variety of ways to incorporate convection using the phase-field method or front-tracking methods.…”

Section: Incorporating Melt Convectionmentioning

confidence: 99%

“…An implementation of dendritic growth with fluid flow using a front- tracking method is given in [4]. The 2D case studied here is from [26].…”

Section: Two-dimensional Crystal Growth With Convectionmentioning

confidence: 99%

“…To incorporate anisotropy in this 3D solidification growth example, we consider the following equilibrium temperature [4]:…”

Section: High-undercooling Casementioning

confidence: 99%

“…Front-tracking techniques have been widely used for such sharp front solidification processes. Recently these techniques have been used successfully to reproduce the complex dendritic structure in crystal growth in undercooled melts including effects such as liquid trapping, tip-splitting, side branching and coarsening [1][2][3] Successful three-dimensional front-tracking implementations including the effects of melt flow have been presented [4]. The advantages of front-tracking methodologies lie in their ability to directly enforce the freezing interface temperature (Gibbs-Thomson) relation and energy balance (Stefan condition).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods

Tan

Zabaras

2006

Journal of Computational Physics

111

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A method combining features of front tracking methods and fixed domain methods is presented to model dendritic solidification of pure materials. To explicitly track the interface growth and shape of the solidifying crystals, a front tracking approach based on the level set method is implemented. To easily model the heat and momentum transport, a fixed domain method is implemented assuming a diffused freezing front where the liquid fraction is defined in terms of the level set function. The fixed domain approach, by avoiding the explicit application of essential boundary conditions on the freezing front, leads to an energy conserving methodology that is not sensitive to the mesh size. To compute the freezing front morphology, an extended Stefan condition is considered. Applications to several classical Stefan problems and two-and three-dimensional crystal growth of pure materials in an undercooled melt including the effects of melt flow are considered. The computed results agree very well with available analytical solutions as well as with results obtained using front-tracking techniques and the phase field method.

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“…The dendrite tip velocity differs by an order of about 10 2 for the two undercoolings considered. These results compare very well with those reported in [4,34].…”

Section: Three-dimensional Crystal Growth With Convectionsupporting

confidence: 92%