Meshless Method for Non-Uniform Heat Transfer/Solidification Behavior of Continuous Casting Round Billet

doi:10.11900/0412.1961.2019.00433

Acta Metall Sin

2020, Vol. 56

Issue (8): 1165-1174 DOI: 10.11900/0412.1961.2019.00433

Current Issue | Archive | Adv Search

Meshless Method for Non-Uniform Heat Transfer/Solidification Behavior of Continuous Casting Round Billet

CAI Laiqiang¹^,², WANG Xudong¹^,²(

), YAO Man¹^,², LIU Yu³

1 School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China
2 Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), Dalian University of Technology, Dalian 116024, China
3 School of Mechanical Engineering, Northeast Electric Power University, Jilin 132012, China

Cite this article:

CAI Laiqiang, WANG Xudong, YAO Man, LIU Yu. Meshless Method for Non-Uniform Heat Transfer/Solidification Behavior of Continuous Casting Round Billet. Acta Metall Sin, 2020, 56(8): 1165-1174.

Download:

HTML

PDF(2907KB)
Export: BibTeX | EndNote (RIS)

Abstract

Compared with the mesh-based numerical calculation method, the meshless methods avoid the problems caused by geometric topology, nodal numbering and information transmission of discrete meshes or nodes, which shows significant advantages in solving the problems of complex computing domain boundaries, phase transformation, interface tracking, and crack propagation. Based on the moving least squares approximation and variational principles, a two-dimensional element-free Galerkin (EFG) model for heat transfer/solidification behavior of continuous casting round billets is derived and established in this work. Taking the measured heat flux as the boundary conditions, the non-uniform solidification behavior of the round billet is calculated and analyzed. The essential issues that affect the suitability and calculation accuracy of the meshless model are discussed, such as the nodal arrangement and the size of the supporting domain. The "concentric circle" nodal arrangement scheme in rectangular coordinate system is proposed, and the results show this scheme can conveniently deal with the problem of curve boundary and the solidified shell movement of round billet, showing great flexibility in node arrangement. When the supporting domain size is adopted to be 1.7 times of the average nodal spacing, the calculation accuracy is high under the regular and random nodal arrangement schemes. The results verify the feasibility and accuracy of EFG meshless model in the calculation of non-uniform heat transfer and solidification of billet. It shows a significant advantage in the phase transformation interface tracking, and provides a theoretical foundation for subsequent research on thermo-mechanical coupling and crack prediction analysis.

Key words: element-free Galerkin moving least squares approximation non-uniform solidification continuous casting round billet

Received: 16 December 2019

ZTFLH:

TF777.4

Fund: National Natural Science Foundation of China(51974056);National Natural Science Foundation of China(51474047);National Natural Science Foundation of China(51704073)

	Service

	E-mail this article
	Add to citation manager
	E-mail Alert
	RSS
	（）
	Articles by authors
	Laiqiang CAI
	Xudong WANG
	Man YAO
	Yu LIU

URL:

https://www.ams.org.cn/EN/10.11900/0412.1961.2019.00433 OR https://www.ams.org.cn/EN/Y2020/V56/I8/1165

Fig.1 Schematic of background cells, nodes and supporting domains around integration points adopted in the element-free Galerkin (EFG) method ( $X I$ and $X J$ are generic integration points in the calculation domain)

Fig.2 Schematics of the mold assembly (a) and structure of heat flux sensor (b) ( $T 1$ and $T 2$ are the temperatures measured by two thermocouples; $R 1$ and $R 2$ are the distances from the two thermocouples to the hot surface of the mold)

Table 1 Thermophysical properties of steel^[31]

Fig.3 Profiles of measured heat flux along the circumference at various mold heights
Color online

Fig.4 The regular nodal arrangement (a) and random nodal arrangement (b) adopted in EFG model

Fig.5 Comparison of EFG surface temperature calculated by regular and random nodal arrangements with finite element method (FEM) results
Color online

Fig.6 The comparisons of shell surface temperatures of different supporting domain sizes along the casting direction (α—scaling parameter)
Color online
(a) 120° from the inner arc(b) 180° from the inner arc

Fig.7 Effects of the supporting domain size on error

Fig.8 Temperature contours at the mold outlet
Color online

Fig.9 Position identification of liquid and solid phase interface at different heights under meniscus
Color online

Fig.10 Heat flux (a), predicted shell surface temperature (b) and shell thickness (c) along the casting direction at different angles

Fig.11 Comparisons of the circumferential heat flux with the shell thickness at mold height of 75 mm (a) and 285 mm (b), and mold outlet (c), and the comparison of averaged heat flux along the casting direction with the shell thickness (d)

[1]	Du F M, Wang X D, Liu Y, et al. Prediction of longitudinal cracks based on a full-scale finite-element model coupled inverse algorithm for a continuously cast slab [J]. Steel Res. Int., 2017, 88: 1700013 doi: 10.1002/srin.201700013
[2]	Wang X D, Kong L W, Yao M, et al. Novel approach for modeling of nonuniform slag layers and air gap in continuous casting mold [J]. Metall. Mater. Trans., 2017, 48B: 357
[3]	Hu P H, Wang X D, Wei J J, et al. Investigation of liquid/solid slag and air gap behavior inside the mold during continuous slab casting [J]. ISIJ Int., 2018, 58: 893
[4]	Jonayat A S M, Thomas B G. Transient thermo-fluid model of meniscus behavior and slag consumption in steel continuous casting [J]. Metall. Mater. Trans., 2014, 45B: 1842
[5]	Álvarez Hostos J C, Puchi Cabrera E S, Bencomo A D. Element-free Galerkin formulation by moving least squares for internal energy balance in a continuous casting process [J]. Steel Res. Int., 2015, 86: 1403 doi: 10.1002/srin.v86.11
[6]	Cheng H, Peng M J, Cheng Y M. The dimension splitting and improved complex variable element-free Galerkin method for 3-dimensional transient heat conduction problems [J]. Int. J. Numer. Methods Eng., 2018, 114: 321 doi: 10.1002/nme.v114.3
[7]	Garg S, Pant M. Numerical simulation of adiabatic and isothermal cracks in functionally graded materials using optimized element-free Galerkin method [J]. J. Therm. Stresses, 2017, 40: 846 doi: 10.1080/01495739.2017.1287534
[8]	Garg S, Pant M. Meshfree methods: A comprehensive review of applications [J]. Int. J. Comput. Methods, 2018, 15: 1830001 doi: 10.1142/S0219876218300015
[9]	Zhang J P, Wang S S, Gong S G, et al. Thermo-mechanical coupling analysis of the orthotropic structures by using element-free Galerkin method [J]. Eng. Anal. Bound. Elem., 2019, 101: 198 doi: 10.1016/j.enganabound.2019.01.011
[10]	Alizadeh M, Jahromi S A J, Nasihatkon S B. Applying finite point method in solidification modeling during continuous casting process [J]. ISIJ Int., 2010, 50: 411 doi: 10.2355/isijinternational.50.411
[11]	Zhang L, Rong Y M, Shen H F, et al. Solidification modeling in continuous casting by finite point method [J]. J. Mater. Process. Technol., 2007, 192-193: 511 doi: 10.1016/j.jmatprotec.2007.04.092
[12]	Zhang L, Rong Y M, Shen H F, et al. A new solution of solidification problems in continuous casting based on meshless method [J]. Int. J. Intell. Syst. Technol. Appl., 2008, 4: 177
[13]	Zhang L. Numerical simulation on solidification and thermal stress of solid shell in continuous casting mold based on meshless method [D]. Beijing: Tsinghua University, 2005
	(张雷. 基于无网格法的连铸结晶器内坯壳凝固与热应力的数值模拟 [D]. 北京: 清华大学, 2005)
[14]	Vaghefi R, Nayebi A, Hematiyan M R. Investigating the effects of cooling rate and casting speed on continuous casting process using a 3D thermo-mechanical meshless approach [J]. Acta Mech., 2018, 229: 4375 doi: 10.1007/s00707-018-2240-1
[15]	Zhang L, Shen H F, Rong Y M, et al. Numerical simulation on solidification and thermal stress of continuous casting billet in mold based on meshless methods [J]. Mater. Sci. Eng., 2007, A466: 71
[16]	Vertnik R, Šarler B. Simulation of continuous casting of steel by a meshless technique [J]. Int. J. Cast Met. Res., 2009, 22: 311 doi: 10.1179/136404609X368064
[17]	Vertnik R, Šarler B. Solution of a continuous casting of steel benchmark test by a meshless method [J]. Eng. Anal. Bound. Elem., 2014, 45: 45 doi: 10.1016/j.enganabound.2014.01.017
[18]	Álvarez Hostos J C, Bencomo A D, Puchi Cabrera E S. Simple iterative procedure for the thermal-mechanical analysis of continuous casting processes, using the element-free Galerkin method [J]. J. Therm. Stresses, 2018, 41: 160 doi: 10.1080/01495739.2017.1389325
[19]	Liu G R. Mesh Free Methods: Moving Beyond the Finite Element Method [M]. Boca Raton FL: CRC Press, 2002: 53
[20]	Liu G R, Gu Y T. An Introduction to Meshfree Methods and Their Programming [M]. Dordrecht: Springer, 2005: 54
[21]	Pandey S S, Kasundra P K, Daxini S D. Introduction of meshfree methods and implementation of element free Galerkin (EFG) method to beam problem [J]. Int. J. Theor. Appl. Res. Mech. Eng., 2013, 2: 85
[22]	Wang N, Wang X D, Cai L Q, et al. Calculation of continuous casting billet solidification based on element-free Galerkin method [J]. Chin. J. Eng., 2020, 42: 186
	(王宁, 王旭东, 蔡来强等. 基于无网格伽辽金法的连铸坯凝固计算方法 [J]. 工程科学学报, 2020, 42: 186)
[23]	Belytschko T, Lu Y Y, Gu L. Crack propagation by element-free Galerkin methods [J]. Eng. Fract. Mech., 1995, 51: 295 doi: 10.1016/0013-7944(94)00153-9
[24]	Liu X. Meshless Method [M]. Beijing: Science Press, 2011: 17
	(刘欣. 无网格方法 [M]. 北京: 科学出版社, 2011: 17)
[25]	Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method [J]. Comput. Methods Appl. Mech. Eng., 1996, 139: 49 doi: 10.1016/S0045-7825(96)01079-1
[26]	Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods [J]. Int. J. Numer. Methods Eng., 1994, 37: 229 doi: 10.1002/(ISSN)1097-0207
[27]	Hughes T J R. Unconditionally stable algorithms for nonlinear heat conduction [J]. Comput. Methods Appl. Mech. Eng., 1977, 10: 135 doi: 10.1016/0045-7825(77)90001-9
[28]	Bathe K J, Khoshgoftaar M R. Finite element formulation and solution of nonlinear heat transfer [J]. Nucl. Eng. Des., 1979, 51: 389 doi: 10.1016/0029-5493(79)90126-2
[29]	Won Y M, Yeo T J, Oh K H, et al. Analysis of mold wear during continuous casting of slab [J]. ISIJ Int., 1998, 38: 53 doi: 10.2355/isijinternational.38.53
[30]	Lally B, Biegler L, Henein H. Finite difference heat-transfer modeling for continuous casting [J]. Metall. Mater. Trans., 1990, 21B: 761
[31]	Yin H B, Yao M, Fang D C. 3-D inverse problem continuous model for thermal behavior of mould process based on the temperature measurements in plant trial [J]. ISIJ Int., 2006, 46: 539 doi: 10.2355/isijinternational.46.539
[32]	Álvarez Hostos J C, Bencomo A D, Puchi Cabrera E S, et al. A pseudo-transient heat transfer simulation of a continuous casting process, employing the element-free Galerkin method [J]. Int. J. Cast Met. Res., 2018, 31: 47 doi: 10.1080/13640461.2017.1366002

[1]	. [J]. 金属学报, 2001, 37(4): 429-433 .

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed