Upscaling mesoscopic simulation results to develop constitutive relations for macroscopic modeling of equiaxed dendritic solidification

Rad, Mahdi; Založnik, Miha; Combeau, Hervé; Beckermann, C.

doi:10.1016/j.mtla.2019.100231

Cited by 12 publications

(5 citation statements)

References 32 publications

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“…The model was shown to be capable of quantitatively predicting grain envelope shapes, growth velocities, and internal solid fraction for a single grain growing into an infinite melt [34,36,37] and for transient interactions among several grains [35,38]. The envelope model has been successfully used for simulations of in situ synchrotron X-ray imaging experiments [38][39][40], for modeling spacing adjustments and growth competition in columnar growth [37,41], and for characterizing grain shapes and growth kinetics under the influence of solutal interactions used in upscaling to macroscopic models [42]. The model was also extended to include fluid flow and solute advection [40,43].…”

Section: Mesoscopic Grain Envelope Methodsmentioning

confidence: 99%

Comparing mesoscopic models for dendritic growth

Tourret,

Sturz,

Viardin

et al. 2020

Preprint

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We present a quantitative benchmark of multiscale models for dendritic growth simulations. We focus on approaches based on phase-field, dendritic needle network, and grain envelope dynamics. As a first step, we focus on isothermal growth of an equiaxed grain in a supersaturated liquid in three dimensions. A quantitative phase-field formulation for solidification of a dilute binary alloy is used as the reference benchmark. We study the effect of numerical and modeling parameters in both needle-based and envelope-based approaches, in terms of their capacity to quantitatively reproduce phase-field reference results. In light of this benchmark, we discuss the capabilities and limitations of each approach in quantitatively and efficiently predicting transient and steady states of dendritic growth. We identify parameters that yield a good compromise between accuracy and computational efficiency in both needle-based and envelope-based models. We expect that these results will guide further developments and utilization of these models, and ultimately pave the way to a quantitative bridging of the dendrite tip scale with that of entire experiments and solidification processes.

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Section: Mesoscopic Grain Envelope Methodsmentioning

confidence: 99%

Comparing mesoscopic models for dendritic growth

Tourret,

Sturz,

Viardin

et al. 2020

Preprint

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“…The second mean-field model, referred to as the "Upscaled model", was proposed by Torabi Rad et al [9]. The main concepts are the same as in the Classical model: volume-averaged description, three phases, interface balances.…”

Section: Comparison With Mean-field Modelsmentioning

confidence: 99%

“…The key difference is that in the Upscaled IOP Publishing doi:10.1088/1757-899X/1281/1/012054 10 model the constitutive relations were obtained by upscaling from full-field GEM simulations. The upscaling was done by averaging over a simulated ensemble of equiaxed grains arranged periodically on a BCC lattice [9]. The upscaled constitutive relations describe: (i) the variation of the envelope sphericity during growth, (ii) a diffusion flux fitted to the full-field simulations, (iii) the dependence of the envelope velocity on an effective concentration, different from the extragranular concentration.…”

Section: Comparison With Mean-field Modelsmentioning

confidence: 99%

Investigation of diffusive grain interactions during equiaxed dendritic solidification

Chirouf,

Appolaire,

Finel

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

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Grain growth during the solidification of an alloy is accompanied by the enrichment of the surrounding liquid phase in chemical species. The resulting diffusion fields induce interactions between the grains that are strongly dependent on their spatial arrangement. The influence of these diffusive interactions is not limited to the shapes and sizes of grains but also controls the overall kinetics of the transformation. In this study we investigate the role of the spatial arrangement of equiaxed grains in the average growth kinetics of an ensemble of grains. We perform full-field simulations of different grain ensembles using the mesoscopic grain envelope model (GEM). We show that the growth kinetics of randomly arranged ensembles is fundamentally different from that of periodic arrangements. We provide an explanation of this difference through analyses of the behaviour of individual grains in their local neighbourhood, defined by a Voronoi tessellation. Finally, we compare the full-field GEM simulations to state-of-the-art mean-field models and we point out the limitations of the latter in the prediction of dendritic growth.

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“…This model was later incorporated into the multiphase volume-averaged solidification model by Wang and Beckermann [75][76][77][78]. More recently, it was extended by Wu and Ludwig [81,82,84,85] and many other research groups [26,[137][138][139][140][141], to enhance the model's accuracy.…”

Section: Envelope Descriptionmentioning

confidence: 99%

Volume-Averaged Modeling of Multiphase Flow Phenomena during Alloy Solidification

Ludwig

Kharicha

2019

Metals

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The most recent developments and applications in volume-averaged modeling of solidification processes have been reviewed. Since the last reviews of this topic by Beckermann and co-workers [Applied Mech. Rev. 1993, p. 1; Annual Rev. Heat Transfer 1995, p. 115], major progress in this area has included i) the development of a mixed columnar-equiaxed solidification model; ii) further consideration of moving crystals and crystal dendritic morphology; and iii) the model applications to analyze the formation mechanisms of macrosegregation, as-cast structure, shrinkage cavity and porosity in different casting processes. The capacity of computer hardware is still a limiting factor. However, many calculation examples, as verified by the laboratory casting experiments, or even by the casting processes at a small industrial scale, show great application potential. Following the trend of developments in computer hardware (projection according to Moore’s law), a full 3D calculation of casting at the industry scale with the multiphase volume-averaged solidification models will become practically feasible in the foreseeable future.

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Upscaling mesoscopic simulation results to develop constitutive relations for macroscopic modeling of equiaxed dendritic solidification

Cited by 12 publications

References 32 publications

Comparing mesoscopic models for dendritic growth

Comparing mesoscopic models for dendritic growth

Investigation of diffusive grain interactions during equiaxed dendritic solidification

Volume-Averaged Modeling of Multiphase Flow Phenomena during Alloy Solidification

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