The effect of natural convection on the dendritic tip stability during directional solidification: insights from phase-field-lattice Boltzmann simulations

Abstract

In this paper, the effect of natural convection on the stability of the dendritic tip during directional solidification under various gravitational field conditions is numerically investigated using the phase-field lattice-Boltzmann method. The coupled equations were implemented for parallel computing on multi-graphics processing units using in-house code written in modular Compute Unified Device Architecture. In the single-crystal case, downward buoyancy transports solute from the dendrite roots toward the tips, leading to solute enrichment near the tips. This enrichment reduces the local undercooling, slows dendrite growth, and eventually triggers tip splitting at high convection intensities. In contrast, the upward buoyancy moves rejected solutes from tips to interdendritic regions, barely affecting solute distribution along the crystal symmetry axis and stabilizing tips. In bi-crystalline systems, downward convection induces tip splitting and plume formation in converging grain boundaries, and drives solute flow to promote sidebranching in diverging grain boundaries, while upward convection has a negligible impact on grain boundaries. This work offers quantitative insights into the dynamic mechanism by which natural convection regulates dendritic tip stability, thereby elucidating the role of natural convection in microstructure evolution during directional solidification.

Keywords

Phase-field / lattice-Boltzmann / dendrite growth / solutal convection / tip splitting

References

[1] Behera A.,Sahoo A. K.,Mahapatra S. S.. Electrical discharge machining of Ni-based superalloy and its applications in aero turbine parts: a comprehensive review Adv. Mater. Proc. Technol. 2024 11 1085 121

[2] Al-nafeay R. H.,Al-Roubaiy A. O.,Omidvar H.. Overview of joining and repairing techniques of Ni-based superalloy for industrial gas turbine applications IOP Conf. Ser. Mater. Sci. Eng. 2021 1094 012141

[3] Yang L.,Ren N.,Li J..et al. Thermal-solutal convection-induced low-angle grain boundaries in single-crystal nickel-based superalloy solidification J. Mater. Sci. Technol. 2025 208 214 29

[4] Chen Y.,Yao Z.,Dong J..et al. Microstructural deterioration mechanism of directionally solidified Ni-based superalloy used in first-stage industrial gas turbine blades after ultra long-term service Mater. Charact. 2024 213 114000

[5] Yan X.,Xu Q.,Tian G.,Liu Q.,Hou J.,Liu B.. Multi-scale modeling of liquid-metal cooling directional solidification and solidification behavior of nickel-based superalloy casting J. Mater. Sci. Technol. 2021 67 36 49

[6] Guo C.,Zha H.,Wang J..et al. Coupled PF and LB simulation study of morphology evolution in columnar dendrite growth induced by natural convection Results. Phys. 2025 77 108452

[7] Ren N.,Li J.,Panwisawas C.,Xia M.,Dong H.,Li J.. Insight into the sensitivities of freckles in the directional solidification of single-crystal turbine blades J. Manuf. Proc. 2022 77 219 28

[8] Zhang H.,Zhao Y.,Xiong W..et al. Modelling freckles and spurious grain formation in directionally solidified superalloy castings Commun. Mater. 2024 5 232 PMC11489085

[9] Yang L.,Ren N.,Xia M.,Li J.,Li J.. Multiphysics modeling of dendritic thermomechanical deformation during the directional solidification of nickel-based single-crystal superalloys Int. J. Miner. Metall. Mater. 2025 32 2510 22

[10] Liu Y.,Shang Y.,Wang F..et al. A novel model of the cross-section variation effect induced by contraction convection on freckle defects in directional solidification J. Mater. Res. Technol. 2025 35 570 80

[11] Reinhart G.,Browne D. J.,Kargl F..et al. In-situ X-ray monitoring of solidification and related processes of metal alloys NPJ Microgravity 2023 9 70 PMC10482908

[12] Zhang Z.,Wang C.,Koe B.,Schlepütz C. M.,Irvine S.,Mi J.. Synchrotron X-ray imaging and ultrafast tomography in situ study of the fragmentation and growth dynamics of dendritic microstructures in solidification under ultrasound Acta Mater. 2021 209 116796

[13] Nagira T.,Kitano H.,Kimura T..et al. In-situ observation of solidification behaviors of Fe-Mn-Cr-Ni-Si alloy during TIG melt-run welding using synchrotron radiation X-ray Mater. Charact. 2024 214 114093

[14] Wu F.,Mullen J.,Deng Y..et al. Probing dendrite growth under microgravity via machine learning-aided multi-scale characterisation Acta Mater. 2026 302 121659

[15] Shevchenko N.,Budenkova O.,Chichignoud G.,Eckert S.. Formation of varying dendritic morphologies in a directionally solidifying Ga-In-Bi alloy Acta Mater. 2025 288 120818

[16] Neumann-heyme H.,Shevchenko N.,Grenzer J.,Eckert K.,Beckermann C.,Eckert S.. In-situ measurements of dendrite tip shape selection in a metallic alloy Phys. Rev. Mater. 2022 6 063401

[17] Ruvalcaba D.,Mathiesen R.,Eskin D.,Arnberg L.,Katgerman L.. In situ observations of dendritic fragmentation due to local solute-enrichment during directional solidification of an aluminum alloy Acta Mater. 2007 55 4287 92

[18] Reinhart G.,Grange D.,Abou-Khalil L..et al. Impact of solute flow during directional solidification of a Ni-based alloy: in-situ and real-time X-radiography Acta Mater. 2020 194 68 79

[19] Xie L.,Sun H.,Wen Y.,Hua L.,Zhang L.. Electromagnetic treatment enhancing performance of metal materials: a review Prog. Mater. Sci. 2025 153 101488

[20] Hu Z.,Huang C.,Xie L.,Hua L.,Yuan Y.,Zhang L.. Machine learning assisted quality control in metal additive manufacturing: a review Adv. Powder Mater. 2025 4 100342

[21] Wang B.,Tong X.,Yu P.,Tian J.,Ouyang H.. An immersed boundary finite-volume method based on the wall shear stress model for incompressible Navier-Stokes equations Ocean Eng. 2026 343 123182

[22] Dobravec T.,Mavrič B.,Zahoor R.,Šarler B.. A coupled domain-boundary type meshless method for phase-field modelling of dendritic solidification with the fluid flow Int. J. Numer. Methods Heat Fluid Flow. 2023 33 2963 81

[23] Xia Q.,Lai S.,Kim J.,Li Y.. Phase field modeling of melting and solidification dynamics in metallic powders during the bed fusion process Commun. Nonlinear Sci. Numer. Simul. 2025 146 108762

[24] Shankar B.,Shivakumara I.. Stability of natural convection in a vertical layer of Navier-Stokes-Voigt fluid Int. Commun. Heat Mass Transfer 2023 144 106783

[25] Zhang X.,Kang J.,Guo Z.,Xiong S.,Han Q.. Development of a Para-AMR algorithm for simulating dendrite growth under convection using a phase-field-lattice Boltzmann method Comput. Phys. Commun. 2018 223 18 27

[26] Miller W.. The lattice Boltzmann method: a new tool for numerical simulation of the interaction of growth kinetics and melt flow J. Cryst. Growth 2001 230 263 9

[27] Miller W.,Succi S.,Mansutti D.. Lattice Boltzmann model for anisotropic liquid-solid phase transition Phys. Rev. Lett. 2001 86 3578 81

[28] Rojas R.,Takaki T.,Ohno M.. A phase-field-lattice Boltzmann method for modeling motion and growth of a dendrite for binary alloy solidification in the presence of melt convection J. Comput. Phys. 2015 298 29 40

[29] Yang Q.,Zhang A.,Jiang B..et al. Numerical investigation of eutectic growth dynamics under convection by 3D phase-field method Comput. Math. Appl. 2022 114 83 94

[30] Sun D.,Pan S.,Han Q.,Sun B.. Numerical simulation of dendritic growth in directional solidification of binary alloys using a lattice Boltzmann scheme Int. J. Heat Mass Transfer 2016 103 821 31

[31] Sun D.,Zhu M.,Wang J.,Sun B.. Lattice Boltzmann modeling of bubble formation and dendritic growth in solidification of binary alloys Int. J. Heat Mass Transfer 2016 94 474 87

[32] Zhang A.,Du J.,Guo Z.,Wang Q.,Xiong S.. Evolution of specific interface area during solidification: a three-dimensional thermosolutal phase-field study Comput. Phys. Commun. 2021 267 108042

[33] Zhang A.,Meng S.,Guo Z.,Du J.,Wang Q.,Xiong S.. Dendritic growth under natural and forced convection in Al-Cu alloys: from equiaxed to columnar dendrites and from 2D to 3D phase-field simulations Metall. Mater. Trans. B. 2019 50 1514 26

[34] Qiu Y.,Wu M.,Qin X.,Xiong S.. Phase-field lattice-Boltzmann study on fully coupled thermal-solute-convection dendrite growth of Al-Cu alloy China Foundry 2024 21 125 36

[35] Zhang Y.,Zhou J.,Yin Y.,Ji X.,Shen X.,Guo Z.. Study on the solutal convection during dendrite growth of superalloy under directional solidification condition J. Mater. Res. Technol. 2023 23 3916 27

[36] Yang C.,Xu Q. Y.,Liu B. C.. Phase‐field-lattice Boltzmann simulation of dendrite growth under natural convection in multicomponent superalloy solidification Rare Metals 2019 39 147 55

[37] Lee J.,Ohno M.,Shibuta Y.,Takaki T.. Uniquely selected primary dendrite arm spacing during competitive growth of columnar grains in Al-Cu alloy J. Cryst. Growth 2021 558 126014

[38] Takaki T.,Sakane S.,Ohno M.,Shibuta Y.,Aoki T.. Large-scale phase-field lattice Boltzmann study on the effects of natural convection on dendrite morphology formed during directional solidification of a binary alloy Comput. Mater. Sci. 2020 171 109209

[39] Takaki T.,Sakane S.,Aoki T.. Natural convection on dendrite morphology: a high-performance phase-field Lattice Boltzmann Study ISIJ Int. 2023 63 83 90

[40] Ma C.,Zhang R.,Li Z..et al. Solidification shrinkage and shrinkage-induced melt convection and their relation with solute segregation in binary alloys Comput. Mater. Sci. 2022 215 111815

[41] Yang L.,Dong Z.,Wang L.,Provatas N.. Improved multi-order parameter and multi-component model of polycrystalline solidification J. Mater. Sci. Technol. 2022 101 217 25

[42] Ma D.,Wu Q.,Bührig-Polaczek A.. Some new observations on freckle formation in directionally solidified superalloy components Metall. Mater. Trans. B. 2011 43 344 53

[43] Ren N.,Panwisawas C.,Li J.,Xia M.,Dong H.,Li J.. Solute enrichment induced dendritic fragmentation in directional solidification of nickel-based superalloys Acta Mater. 2021 215 117043

[44] Felicelli S. D.,Poirier D. R.,Heinrich J. C.. Modeling freckle formation in three dimensions during solidification of multicomponent alloys Metall. Mater. Trans. B. 1998 29 847 55

[45] Felicelli S. D.,Sung P. K.,Poirier D. R.,Heinrich J. C.. Transport properties and transport phenomena in casting nickel superalloys Int. J. Thermophys. 2014 19 1657 69

[46] Sun Q. Y.,Ren Y.,Liu D.. Numerical investigations of freckles in directionally solidified nickel-based superalloy casting with abrupt contraction in cross section Results Phys. 2019 12 1547 58

[47] Matache G.,Stefanescu D. M.,Puscasu C.,Alexandrescu E.. Dendritic segregation and arm spacing in directionally solidified CMSX-4 superalloy Int. J. Cast Metals Res. 2016 29 303 16

[48] Schneider M. C.,Gu J. P.,Beckermann C.,Boettinger W. J.,Kattner U. R.. Modeling of micro- and macrosegregation and freckle formation in single-crystal nickel-base superalloy directional solidification Metall. Mater. Trans. A. 1997 28 1517 31

[49] Sung P. K.,Poirier D. R.,Felicelli S. D.. Simulating the initiation of a channel during directional solidification of a superalloy Metall. Mater. Trans. A. 2001 32 202 7

[50] Hobbs R. A.,Tin S.,Rae C. M. F.. A castability model based on elemental solid-liquid partitioning in advanced nickel-base single-crystal superalloys Metall. Mater. Trans. A. 2005 36 2761 73

[51] Chen S.,Doolen G. D.. Lattice Boltzmann method for fluid flows Annu. Rev. Fluid Mech. 1998 30 329 64

[52] Qian Y. H.,D'humières D.,Lallemand P.. Lattice BGK models for navier-stokes equation Europhys. Lett. 1992 17 479 84

[53] Beckermann C.,Diepers H.,Steinbach I.,Karma A.,Tong X.. Modeling melt convection in phase-field simulations of solidification J. Comput. Phys. 1999 154 468 96

[54] Medvedev D.,Kassner K.. Lattice Boltzmann scheme for crystal growth in external flows Phys. Rev. E. Stat. Nonlin. Soft Matter Phys. 2005 72 056703

[55] Zhang H.,Xu Q.,Shi Z.,Liu B.. Numerical simulation of dendrite grain growth of dd6 superalloy during directional solidification process Acta. Metall. Sin. 2014 ; 50, 345-54.