A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection

Rojas, Roberto; Takaki, Tomohiro; Ohno, Munekazu

doi:10.1016/j.jcp.2015.05.045

Cited by 125 publications

(62 citation statements)

References 53 publications

(75 reference statements)

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“…Computational models have been proposed that consist of explicitly tracking the location of the solid-liquid interface (see, e.g., [26][27][28]). Alleviating the high computational cost of explicit interface tracking, most computational studies over the past couple of decades have used the phase-field method [18,[29][30][31][32][33][34]. Still, even combining the most advanced state-of-the-art numerical methods and hardware, simulations remain limited to the scale of a handful of dendritic grains [35,36].…”

Section: Introductionmentioning

confidence: 99%

Multiscale dendritic needle network model of alloy solidification with fluid flow

Tourret

François

Clarke

2019

Computational Materials Science

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We present a mathematical formulation of a multiscale model for solidification with convective flow in the liquid phase. The model is an extension of the dendritic needle network approach for crystal growth in a binary alloy. We propose a simple numerical implementation based on finite differences and step-wise approximations of parabolic dendritic branches of arbitrary orientation. Results of the two-dimensional model are verified against reference benchmark solutions for steady, unsteady, and buoyant flow, as well as steady-state dendritic growth in the diffusive regime. Simulations of equiaxed growth under forced flow yield dendrite tip velocities within 10% of quantitative phase-field results from the literature. Finally, we perform illustrative simulations of polycrystalline solidification using physical parameters for an aluminum-10wt% copper alloy. Resulting microstructures show notable differences when taking into account natural buoyancy in comparison to a purely diffusive transport regime. The resulting model opens new avenues for computationally and quantitatively investigating the influence of fluid flow and gravity-induced buoyancy upon the selection of dendritic microstructures. Further ongoing developments include an equivalent formulation for directional solidification conditions and the implementation of the model in three dimensions, which is critical for quantitative comparison to experimental measurements.

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Section: Introductionmentioning

confidence: 99%

Multiscale dendritic needle network model of alloy solidification with fluid flow

Tourret

François

Clarke

2019

Computational Materials Science

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“…Most of the existing thermal LB models for solid-liquid phase change can be generally classified into two major categories: the phase-field method [221][222][223][224][225][226][227][228] and the enthalpy-based method [54][55][56][57][58][75][76][77][78][79][80][81]194,[229][230][231][232][233][234][235][236][237][238][239][240][241][242][243][244][245][246]. Besides, a couple of LB models were recently developed based on some interface-tracking methods [180,247].…”

Section: The Lb Methods For Solid-liquid Phase-change Heat Transfermentioning

confidence: 99%

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

Liu

et al. 2019

International Journal of Heat and Mass Transfer

181

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Since its introduction 30 years ago, the lattice Boltzmann (LB) method has achieved great success in simulating fluid flows and modeling physics in fluids. Owing to its kinetic nature, the LB method has the capability to incorporate the essential microscopic or mesoscopic physics, and it is particularly successful in modeling transport phenomena involving complex boundaries and interfacial dynamics.The LB method can be considered to be an efficient numerical tool for fluid flow and heat transfer in porous media. Moreover, since the LB method is inherently transient, it is especially useful for investigating transient solid-liquid phase-change processes wherein the interfacial behaviors are very important. In this article, a comprehensive review of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media at both the pore scale and representative elementary volume (REV) scale. The review first introduces the fundamentals of the LB method for fluid flow and heat transfer. Then the REV-scale LB method for fluid flow and single-phase heat transfer in porous media, and the LB method for solid-liquid phase-change heat transfer, are described. Some applications 2 of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media are provided. In addition, applications of the LB method to predict effective thermal conductivity of porous materials are also provided. Finally, further developments of the LB method in the related areas are discussed. Keyword: Lattice Boltzmann method; Single-phase heat transfer; Solid-liquid phase change; Porous media proposed the RLBE model with an enhanced collision operator, which was shown to be linearly stable. Based on the Bhatnagar-Gross-Krook (BGK) collision operator [104], the LB model using a single relaxation time, referred to as the BGK-LB model, has been independently proposed by Chen et al. [14], Koelman [15], and Qian et al. [16]. In the BGK-LB model, the equilibrium distribution function is chosen to recover the incompressible N-S equations in the incompressible limit. Due to its high efficiency and extreme simplicity, the BGK-LB model has become the most popular LB model, in spite of some well-known deficiencies (e.g., numerical instability, viscosity dependence of boundary 9 locations). Almost at the same time when the BGK-LB method was developed, d'Humières [17] proposed the multiple-relaxation-time (MRT) LB method. The MRT-LB equation (also referred to as generalized lattice Boltzmann equation (GLBE)) is an important extension of the RLBE proposed by Higuera et al. [12,13]. This work is significant because, in addition to it overcomes some deficiencies of the BGK-LB model, it facilitates the extension of the LB method, expanding the applications to a much wider range of phenomena and processes.In 1997, a direct connection between the LB equation and the continuous Boltzmann equation in kinetic theory was rigorously established by He and Luo [19,20]. In particular, it has been demonstrated that the LB equation c...

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“…The successful work of Kobayashi to simulate the complicated and beautiful dendrite growth during solidification opened the phase-field study area (Kobayashi, 1993;Kobayashi, 1994). Since then, in the solidification field (Asta et al, 2009;Steinbach, 2009;Takaki, 2014), the phase-field model has been applied to binary alloys (Warren and Boettinger, 1995;Wheeler et al, 1992), polycrystals (Miyoshi and Takaki, 2016;Steinbach and Pezzolla, 1999), quantitative models (Karma and Rappel, 1996;Ohno and Matsuura, 2009), multi-component alloys (Ohno et al, 2012), coupled models with convection (Beckermann et al, 1999;Rojas et al, 2015;Takaki et al, 2015b), and large-scale computations (Sakane et al, 2015;Shibuta et al, 2015;Takaki et al, 2014;Takaki et al, 2013;Yamanaka et al, 2011). The great success of the phase-field method in material science is due to the advantages of the phase-field method: tracking the interface position is not necessary, the curvature effects are included in the model, the evolution equations can be derived from the free-energy functional based on the second law of thermodynamics, the discretization of the time evolution equations is easy, and so on.…”

Section: Introductionmentioning

confidence: 99%

Phase-field topology optimization model that removes the curvature effects

Takaki

Kato

2017

Mechanical Engineering Journal

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The conventional phase-field topology optimization (PFTO) models minimize not only the objective function but also the interface energy. In the present study, a new PFTO model, which minimizes only the objective function, is developed by removing the curvature effect from the conventional PFTO model. Simulations of elastic strain energy minimization under a constant-volume constraint condition of a cantilever are performed using the developed and conventional PFTO models. From the simulation results, we confirm that the developed PFTO model that removes the curvature effects can efficiently optimize only the objective function.

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A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection

Cited by 125 publications

References 53 publications

Multiscale dendritic needle network model of alloy solidification with fluid flow

Multiscale dendritic needle network model of alloy solidification with fluid flow

Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review

Phase-field topology optimization model that removes the curvature effects

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