Numerical Simulation of Dendritic Solidification with Convection: Two-Dimensional Geometry

Al-Rawahi, Nabeel; Tryggvason, Grétar

doi:10.1006/jcph.2002.7092

Cited by 126 publications

(79 citation statements)

References 32 publications

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“…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%

“…In [26], the no-slip condition between the melt and the solid was realized via a drag resistivity in the diffused interface region. In [2], the NavierStokes equations are solved in two steps (with the first step considering only the advection and viscous terms and a trial pressure, and the second step considering only the pressure gradient). In these two steps, the unprojected velocity and the pressure gradient are multiplied by an index function to set the velocity in the solid to zero.…”

Section: Incorporating Melt Convectionmentioning

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%

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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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Section: Incorporating Melt Convectionmentioning

confidence: 99%

Section: Incorporating Melt Convectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…The continuity and momentum equations, Eqs. (1) and (2), were solved by the modified projection method based on the staggered grids [20] . An explicit finite difference scheme was employed for solving the time-dependent terms of Navier-Stokes equation, Eq.…”

Section: Solution Scheme Of Numerical Modelmentioning

confidence: 99%

Simulation of dendritic growth of magnesium alloys with fluid flow

Guo

Xiong

2017

China Foundry

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A s the lightest known structural metals, magnesium alloys are treated as the green engineering materials of the 21st century due to their superior properties such as low density, high specific strength, excellent castability, good machinability and recyclability [1] . Magnesium alloys have been widely used in automotive, aerospace and 3C (computer, communication and consumer electronics) industries to replace steel, cast iron and even aluminum alloy. Such components and parts include steering wheels, gear boxes, notebook shells and mobile phone frames, etc. [2] . The performance of magnesium alloy parts is strongly influenced by the microstructure formed during solidification. Since the fluid flow has a significant impact on the structure formation of alloys during solidification [3] , and dendritic structure is probably the most commonly observed structure of magnesium alloys [4] , studying the effect of Abstract: Fluid flow has a significant impact on the microstructure evolution of alloys during solidification. Based on the previous work relating simulation of the dendritic growth of magnesium alloys with hcp (hexagonal closepacked) structure, an extension was made to the formerly established CA (cellular automaton) model with the purpose of studying the effect of fluid flow on the dendritic growth of magnesium alloys. The modified projection method was used to solve the transport equations of flow field. By coupling the flow field with the solute field, simulation results of equiaxed and columnar dendritic growth of magnesium alloys with fluid flow were achieved. The simulated results were quantitatively compared with those without fluid flow. Moreover, a comparison was also made between the present work and previous works conducted by others. It can be concluded that a deep understanding of the dendritic growth of magnesium alloys with fluid flow can be obtained by applying the present numerical model.

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“…The approach developed by Singh 35 uses the line integral form and computes the local normal and tangent vectors along the triangle edges using the simple approach of Al-Rawahi 42,43 shown in Eq. (27) following Fig.…”

Section: Surface Tensionmentioning

confidence: 99%

Marker-Based, 3-D Adaptive Cartesian Grid Method for Multiphase Flow around Irregular Geometries

Uzgoren

Sim

Shyy

2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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Computational simulations of multiphase flow are challenging because many practical applications require adequate resolution of not only interfacial physics associated with moving boundaries with possible topological changes, but also around three-dimensional, irregular solid geometries. In this paper, we focus on the simulations of fluid/fluid dynamics around complex geometries, based on an Eulerian-Lagrangian framework. The approach uses two independent but related grid layouts to track the interfacial and solid boundary conditions, and is capable of capturing interfacial as well as multiphase dynamics. In particular, the stationary Cartesian grid with time dependent, local adaptive refinement is utilized to handle the computation of the transport equations, while the interface shape and movement are treated by marker-based triangulated surface meshes which freely move and interact with the Cartesian grid. The markers are also used to identify the location of solid boundaries and enforce the no-slip condition there. Issues related to the contact line treatment, topological changes of multiphase fronts during merger or breakup of objects, and necessary data structures and solution techniques are also highlighted. Selected test cases including spacecraft fuel tank flow management, and movement and rupture of interfaces associated with liquid plug flow are presented.

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Numerical Simulation of Dendritic Solidification with Convection: Two-Dimensional Geometry

Cited by 126 publications

References 32 publications

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

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

Simulation of dendritic growth of magnesium alloys with fluid flow

Marker-Based, 3-D Adaptive Cartesian Grid Method for Multiphase Flow around Irregular Geometries

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