Zastosowanie metody kratowego równania Boltzmanna do modelowania w metalurgii i inżynierii materiałowej

• Autorzy: Svyetlichnyy D. , Straka R. , Łach Ł.

Identyfikatory

DOI

10.15199/24.2018.4.9

Warianty tytułu

EN

Application of Lattice Boltzmann Method for modeling in metallurgy and material science

• Języki publikacji: PL

Abstrakty

PL

W pracy przedstawiono podstawowe wiadomości o metodzie do modelowania matematycznego procesów i zjawisk zawierających przepływ gazu i cieczy nazywanej Lattice Boltzmann Method (LBM - Metoda kratowego równania Boltzmanna). Trzema głównymi kierunkami stosowania LBM w opracowaniach autorów są: przepływ cieczy o swobodnej powierzchni z uwzględnieniem wymiany ciepła i przemiany stanu skupienia; ciągły przepływ cieczy i gazu; przemiany fazowe. W pracy przedstawiono wyniki modelowania oraz zastosowania metody do modelowania procesów przemysłowych i jej wykorzystanie w procesie dydaktycznym. Zwrócono uwagę na przewagi opisywanej metody oraz duże możliwości przyspieszenia obliczeń poprzez ich zrównoleglenie na współczesnych procesorach graficznych (GPU - graphics processing unit) .

EN

The basic information about the Lattice Boltzmann Method (LBM), used for numerical modeling of the processes and phenomena contained fluid flow, is presented in the paper. Three main direction of application of the LBM developed and described by the authors are: fluid flow with free surface, taking into account conductive heat transfer and changes of state of matter; continuous fluid flow; and phase transformations. Results of simulations by LBM as well as its application to industrial processes and for teaching are presented in the paper. Attention is paid to advantages of the method and possibility to accelerate its calculations through their parallelization on modern graphics processing units (GPUs).

Słowa kluczowe

PL

metody obliczeniowe dynamiki cieczy; metoda kratowego równania Boltzmanna; automat komórkowy; przepływy wielofazowe; warunki brzegowe; swobodna powierzchnia

EN

computational fluid dynamics; lattice Boltzmann method; cellular automata; multiphase flow; boundary condition; free surface

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Hutnik, Wiadomości Hutnicze
• Rocznik: 2018
• Tom: Vol. 85, nr 4
• Strony: 141--151
• Opis fizyczny: Bibliogr. 35 poz., rys.

Twórcy

autor

Svyetlichnyy D.

• AGH Akademia Górniczo-Hutnicza Wydział Inżynierii Metali i Informatyki Przemysłowej, al. A. Mickiewicza 30, 30-059 Kraków

autor

Straka R.

• AGH Akademia Górniczo-Hutnicza Wydział Inżynierii Metali i Informatyki Przemysłowej, al. A. Mickiewicza 30, 30-059 Kraków

autor

Łach Ł.

• AGH Akademia Górniczo-Hutnicza Wydział Inżynierii Metali i Informatyki Przemysłowej, al. A. Mickiewicza 30, 30-059 Kraków

Bibliografia

• [1] An Dong, Shiyan Pan, Li Huang, Ting Dai, Bruce Krakauer, Mingfang Zhu. 2014. “Modeling of Ferrite-Austenite Phase Transformation Using a Cellular Automaton Model”. ISIJ International 54: 422– 429. doi: 10.2355/isijinternational.54.422.
• [2] Avrami Melvin. 1941. “Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III”. Journal of Chemical Physics 9: 177–184. doi:10.1063/1.1750872.
• [3] Bösch Fabian, Shyam S. Chikatamarla, Ilya V Karlin. 2015. „Entropic multirelaxation lattice Boltzmann models for turbulent flows”. Physical Review E 92 (4): 043309. doi: 10.1103/PhysRevE.92.043309.
• [4] Chikatamarla Shyam S., Santosh Ansumali, Ilya V Karlin. 2006. „Entropic lattice Boltzmann models for hydrodynamics in three dimensions”. Physical Review Letters 97 (1): 010201. doi: 10.1103/ PhysRevLett.97.010201.
• [5] Domingos Marco, Federica Chiellini, Antonio Gloria, Luigi Ambrosio, Paulo Bartolo, Emo Chiellini. 2012. “Effect of process parameters on the morphological and mechanical properties of 3D Bioextruded poly(ε‐caprolactone) scaffolds”. Rapid Prototyping Journal 18 (1): 56 – 67. doi: 10.1108/13552541211193502.
• [6] Eshraghi Shaun, Suman Das. 2012. “Micromechanical finite- element modelling and experimental characterisation of the compressive mechanical properties of polycaprolactone-hydroxyapatite composite scaffolds prepared by selective laser sintering for bone tissue engineering”. Acta Biomaterialia 8: 3138-3143. doi: 10.1016/j.actbio. 2012.04.022.
• [7] Frisch Uriel, Brosl Hasslacher, Yves Pomeau. 1986. “Lattice- Gas Automata for the Navier-Stokes Equation”. Physical Review Letters 56 (14): 1505-1508. doi: 10.1103/PhysRevLett.56.1505.
• [8] Frisch Uriel, Dominique d’Humieres, Brosl Hasslacher, Pierre Lallemand, Yves Pomeau, Jean-Pierre Rivet. 1987. “Lattice Gas Hydrodynamics in Two and Three Dimensions”. Complex Systems 1 (4): 649-707.
• [9] Geier Martin, Andreas Greiner, Jan G. Korvink. 2006. “Cascaded digital lattice Boltzmann automata for high Reynolds number flow”. Physical Review E 73 (6): 066705. doi: 10.1103/Phys- RevE.73.066705.
• [10] Geier Martin, Martin Schönherr, Andrea Pasquali, Manfred Krafczyk. 2015. “The cumulant lattice Boltzmann equation in three dimensions: Theory and validation”. Computers & Mathematics with Applications 70 (4): 507-547. doi: 10.1016/j.camwa.2015.05.001.
• [11] Higuera Francisco, Javier Jiménez. 1989. “Boltzmann Approach to Lattice Gas Simulations”. Europhysics Letters 9 (7): 663-668.
• [12] d’Humières Dominique. 2002. “Multiple–relaxation–time lattice Boltzmann models in three dimensions”. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 360 (1792): 437-451. doi: 10.1098/rsta.2001.0955.
• [13] Iba Yukito, Yasuhiro Akutsu, Kunihiko Kaneko. 1986. „Phase Transitions in 2-dimensional Stochastic Cellular Automata” in: S. Ishizaka gen. ed., “Science on Form: Proceeding of the First International Symposium for Science on Form” (KTK Scientific Publisher, Tokyo): 103-111.
• [14] Johnson William A., Robert F. Mehl. 1939. “Reaction Kinetics in Processes of Nucleation and Growth”. Transactions of the American Institute of Mining and Metallurgical Engineers 135: 416–442.
• [15] Koelman Johannes. 1991. “A simple lattice Boltzmann scheme for Navier-Stokes fluid flow”. Europhysics Letters 15 (6): 603- 607.
• [16] Kolmogorov Andriej N. 1937. “On the Statistical Theory of Crystallization of Metals”. Izv. Akad. Nauk SSSR, Ser. Mat. 3: 355–359 (in Russian).
• [17] Krzyzanowski Michal, Dmytro Svyetlichnyy, Grace Stevenson, W. Mark Rainforth. 2016. “Powder bed generation in integrated modelling of additive layer manufacturing of orthopaedic implants”, International Journal of Advanced Manufacturing Technology 87 (1-4): 519-530. doi: 10.1007/s00170-016-8491-x.
• [18] Ladd Anthony J. C. 1994. “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation”. Journal of Fluid Mechanics 271: 285-309. doi: 10.1017/ S0022112094001771.
• [19] Lam Christopher X. F., Swee Hin Teoh, Dietmar W. Hutmacher. 2007. “Comparison of the degradation of polycaprolactone and polycaprolactone-(β-tricalcium phosphate) scaffolds in alkaline medium”. Polymer International 56 (6): 718–728. doi: 10.1002/pi.2195.
• [20] Lan Yongjun, Dianzhong Li, Chang-Jen Huang, Ying Li. 2004. “A cellular automaton model for austenite to ferrite transformation in carbon steel under non-equilibrium interface conditions”. Modelling Simul. Mater. Sci. Eng. 12: 719–729. doi:10.1088/0965-0393/12/4/012.
• [21] Machalska A. 2017. „Symulacja przepływu spalin i wymiany ciepła w piecu grzewczym” Praca inżynierska, Akademia Górniczo Hutnicza im. Stanisława Staszica w Krakowie, Kraków.
• [22] Malik Amer, Gustav Amberg, Annika Borgenstam, John Ågren. 2013. “Phase-field modelling of martensitic transformation: the effects of grain and twin boundaries”. Modeling and Simulation in Materials Science Engineering 21 (8): 085003. doi:10.1088/0965- 0393/21/8/085003.
• [23] Matsumoto Mitsuhiro, Shiomi Masahiro, Kozo Osakada, Fumie Abe. 2002. „Finite element analysis of single layer forming on metallic powder bed in rapid prototyping by selective laser processing”, International Journal of Machine Tools and Manufacture 42 (1): 61-67. doi: 10.1016/S0890-6955(01)00093-1.
• [24] McNamara Guy R., Gianluigi Zanetti. 1988. „Use of the Boltzmann Equation to Simulate Lattice-Gas Automata”. Physical Review Letters 61: 2332-2335. doi: 10.1103/PhysRevLett.61.2332.
• [25] Mercuri Louis G., Larry M. Wolford, Bruce Sanders, R. Dean White, Anita Hurder, William Henderson. 1995. “Custom CAD/CAM total temporomandibular joint reconstruction system: preliminary multicenter report”. Journal of Oral and Maxillofacial Surgery 53 (2): 106- 115. doi: 10.1016/0278-2391(95)90381-X.
• [26] Qian Yuehong, Dominique D’Humières, Pierre Lallemand. 1992. “Lattice BGK Models for the Navier-Stokes Equations”. EPL (Europhysics Letters) 17 (6): 479–484. doi: 10.1209/0295-5075/17/6/001.
• [27] Singh Nitin. 2015. “Finite difference modeling of the conversion of beta-Titanium to its another allotropic form alpha-Titanium by the high temperature oxidation of the former”. doi:10.13140/ RG.2.1.3625.6483.
• [28] Straka Robert, Tadeusz Telejko. 2017. “Numerical model of a shaft furnace operation”, International Journal of Numerical Methods for Heat & Fluid Flow 27 (5): 1172-1184. doi: 10.1108/HFF-04-2016-0157.
• [29] Svyetlichnyy Dmytro S., Alexandr I. Mikhalyov. 2014. “Three-dimensional frontal cellular automata model of microstructure evolution – phase transformation module”, ISIJ International 54 (6): 1386-1395. doi: 10.2355/isijinternational.54.1386.
• [30] Svyetlichnyy Dmytro, Michal Krzyzanowski, Robert Straka, Łukasz Łach, W. Mark Rainforth. 2018. “Application of Cellular Automata and Lattice Boltzmann of Numerical Methods for modelling of Additive Layer Manufacturing”. International Journal of Numerical Methods for Heat & Fluid Flow 28 (1). doi: 10.1108/HFF-10-2016-0418.
• [31] Wang Guang W., Zhen Liu, Jun Zhang. 2013. “The Finite Difference Method for Two Models of Phase Transitions Driven by Configurational Force”. Advanced Materials Research 753–755: 932–938. doi:10.4028/www.scientific.net/AMR.753-755.932.
• [32] Williams Jessica M., Adebisi Adewunmi, Rachel M. Schek, Colleen L. Flanagan, Paul H. Krebsbach, Stephen E. Feinberg, Scott J. Hollister, Suman Das. 2005. “Bone tissue engineering using polycaprolactone scaffolds fabricated via selective laser sintering”. Biomaterials 26 (23): 4817-4827. doi: 10.1016/j.biomaterials.2004.11.057.
• [33] Wolfram Stephen. 1986. “Cellular Automaton Fluids 1: Basic Theory”. Journal of Statistical Physics 45 (3-4): 471-526. doi: 10.1007/ BF01021083.
• [34] Wu Guofeng, Bing Zhou, Yunpeng Bi, Yimin Zhao. 2008. “Selective laser sintering technology for customized fabrication of facial prostheses”. Journal of Prosthetic Dentistry 100 (1): 56–60. doi: 10.1016/S0022-3913(08)60138-9.
• [35] Zhu Benqiang, Hao Chen, Matthias Militzer. 2015. “Phase-field modeling of cyclic phase transformations in low-carbon steels”. Computational Materials Science 108: 333–341. doi:10.1016/J.COMMATSCI. 2015.01.023.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).