May 22 – 25, 2023
Europe/London timezone

3D modeling of macro-segregation and formation of freckles in solidification based on the fully decoupled enthalpy-porosity method

May 25, 2023, 10:30 AM
Oral Presentation (MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes MS07


Mr Xiaoyu Feng (Computational Transport Phenomena Laboratory (CTPL), Division of Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST))


The problem of solidification with macro-segregation and the formation of freckles is usually a complicated one that involves mass, momentum, heat, and species transfers between the solid, mushy, and liquid phase regions [1]. In several natural and industrial applications, the quantitative description of phase change, chemical heterogeneities, and multi-phase and multi-component flows serve an essential role in this process. In the aerospace industries and civil engineering, where materials with high strength, heat-treatable capacity, and fatigue resistance are in high demand, this naturally sets very strict requirements for internal compositions and their distribution in parts and workpieces [2]. For the petroleum industry, the efficient and economical recovery of natural gas hydrate from the subsurface and the safe operation of natural gas pipelines to prevent hydrate or wax blockage are also based on a deeper understanding of solidification and phase change [3,4]. Even on an interstellar scale, the deposition of planetary components during cooling constitutes a kind of separation [5]. Nonlinearities and interactive multi-physical fields are the major challenges in modeling this topic, and they raise the high computational costs associated with its 3D simulations. Our work proposes an operator-splitting and matrix-oriented method based on the enthalpy-porosity model to avoid non-linear systems. Also, the combination of vectorization and forward techniques to assemble the matrix of the linear system enhances the implementability of extensions to 3D applications. Finally, a number of 2D and 3D benchmark cases are presented to validate the accuracy and effectiveness of this scheme [6-8]. This numerical method also shows its ability to capture physical processes, such as channel segregation and freckle formation, caused by solutely and thermally driven flow.


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[2] JC Beddoes, W Wallace, and MC De Malherbe. The technology of titanium aluminides for aerospace applications. Materials and Manufacturing Processes, 7(4):527–559, 1992.

[3] Rui Song, Xiaoyu Feng, Yao Wang, Shuyu Sun, and Jianjun Liu. Dissociation and transport modeling of methane hydrate in core-scale sandy sediments: A comparative study. Energy, 221: 119890,2021.

[4] Guojun Yu, Bo Yu, Yongtu Liang, Min Wang, Yogendra Joshi, and Dongliang Sun. A new general model for phase-change heat transfer of waxy crude oil during the ambient-induced cooling process. Numerical Heat Transfer, Part A: Applications, 71(5):511-527, 2017.

[5] Takeshi Kuritani. Magmatic differentiation examined with a numerical model considering multicomponent thermodynamics and momentum, energy and species transport. Lithos, 74(3-4):117-130, 2004.

[6] Michel Bellet, H Combeau, Y Fautrelle, D Gobin, M Rady, E Arquis, O Budenkova, B Dussoubs, Y Duterrail, A Kumar, et al. Call for contributions to a numerical benchmark problem for 2d columnar solidification of binary alloys. International Journal of Thermal Sciences, 48(11):2013-2016, 2009.

[7] Kangxin Chen and Houfa Shen. Modeling of macrosegregation benchmarks using a stabilized finite element algorithm based on a semi-implicit pressure correction scheme. International Journal of Numerical Methods for Heat & Fluid Flow, 2019.

[8] DJ Hebditch and JD Hunt. Observations of ingot macrosegregation on model systems. Metallurgical and Materials Transactions B, 5(7):1557-1564, 1974.

Participation In-Person
Country Saudi Arabia
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Primary author

Mr Xiaoyu Feng (Computational Transport Phenomena Laboratory (CTPL), Division of Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST))


Prof. Huangxin Chen (School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University) Prof. Shuyu Sun (Computational Transport Phenomena Laboratory (CTPL), Division of Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST))

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