Двовимірна математична модель теплофізичних процесів, які протікають при отриманні листової заготовки за допомогою валків-кристалізаторів
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 1
Abstract
THE TWO-DIMENSIONAL MATHEMATICAL MODEL OF THERMAL PROCESSES THAT OCCUR DURING ROTATION OF THE ROLL-MOLD IN A CONTINUOUS CASTING PROCESS Sokol A.M. Abstract Formulation of the problem The priority of Ukrainian metallurgy is implementing modern energy saving technologies. The most promising technology of the metal sheet production is the twin-roll casting process. Analysis of recent research and publications Analysis of recent publications shows that more should explore the following questions: ways to ensure uniform heat distribution in the flow of melt along the crystallizer rollers; ensure the required metal sheet quality (requirements for metal structure and its temperature at the outlet of the installation); increasing defect-free performance of the installation; search rational and optimal modes of equipment usage, creation the teaching materials to operators, automation of the production process. Solving these problems depends on the knowledge of hydrodynamic characteristics of the metal movement and associated heat transfer processes. Experimental results are few, so researchers are widely used computer modeling methods. Formulation of research objectives This paper studies thermal processes occurring in the twin-roll casting process. It is proposed to create a mathematical model. It should describe the thermal processes and consider the crystallization and melting metal. Mathematical model can be customized for various modifications of the casting process by changing thermal parameters of installation and metal. Presenting main material When constructing a mathematical model made some assumptions: heat flow along the rolls small, it does not take into account; mixing the liquid phase does not take into account; the width of ingots at any installation height are constant; rolls is a body which is not deformed; possible presence of air gap and friction between the surfaces of ingot and crystallizer rollers not taken into account. To describe these processes can use standard heat equation, which takes into account the diffusion and convective heat transfer mechanisms. The crystallization and melting considered by introducing the effective heat capacity. We confine ourselves to two dimensions Cartesian coordinate plane because of the symmetry. As the calculation area we choose half-section along the plane of symmetry, and divide it into 3 separate zones: melt zone; rolls zone; environment zone. We approximate additions of the heat transfer differential equation by using central finite differences in two-dimensional Cartesian coordinates on a uniform grid (xOz). Convection counted using macroscopic transport. We have created software that implements the mathematical model. The software allows you to perform computational experiments with different process parameters. Programming language was the Object Pascal. Using the developed software allows to efficiently manage the crust formation process, crimping zone temperature and temperature at the installation outlet (by selecting the casting temperature conditions, cooling mode, extraction speed). This will affect the quality of products. In the future planned development of the proposed mathematical model. Solving the heat equation in three-dimensional setting will take into account the width of the preform and the corresponding difference in the thermal state of the center band and near-boundary zone. Construction conjugate heat and hydrodynamic mathematical model is seen as complex and significant step in the process for consideration of important roll casting-rolling factors. References 1. Matsushita T. Development and commercialization of twin roll strip caster / T. Matsushita, K. Nakayama, H. Fukase, S. Osada // IHI Engineering Review. – 2009. – Vol. 42. – № 1. – P. 1–9. 2. Barekar N. S. Twin Roll Casting of Aluminum Alloys – An Overview / N. S. Barekar, B. K. Dhindaw // Materials and Manufacturing Processes. – Published online: 28 Apr 2014. – http://www.tandfonline.com/doi/full/10.1080/10426914.2014.912307 #.U3IBU6K4rmU. 3. Cook R. Development of the twin-roll casting process / R. Cook, P. G. Grocock, P. M. Thomas, D. V. Edmonds, J. D. Hunt // Journal of Materials Processing Technology. – 2010. – Vol. 55, Is. 2. – P. 76–84. 4. Haga T. Development of a twin roll caster for light metals / T. Haga // Journal of of Achievements in Materials and Manufacturing Engineering. – 2010. – Vol. 43, Is. 1. – P. 393–402. 5. Wang B. Modelling of melt flow and solidification in the twin-roll strip casting process / B. Wang, J. Y. Zhang, J. F. Fan,S. L. Zhao, S. B. Ren, K. C. Chou // Steel Research International. – 2009. – Vol. 80, Is. 3. – P. 218–222. 6. Santos C. A. Modeling of solidification on twin-roll strip casting / C. A. Santos, J. A. Spim, A. Garcia // Journal of Materials Processing Technology. – 2000. – Vol 102. – P. 33–39. 7. Gridin A. Yu. Matematicheskoe modelirovanie temperaturnogo polya metalla i valkov v processe valkovoj razli-vki-prokatki / A. Yu. Gridin // Obrabotka materialov davleniem. – 2009. – №1 (20). – S. 75– 83. 8. Zeng J. Numerical simulation of the twin-roll casting process of magnesium alloy strip / J. Zeng, R. Koitzsch, H. Preifer, B. Friedrich // Journal of Materials processing Technology. – 2009. – Vol. 209. – P. 2321–2328. 9. Saxena A. Modeling of fluid flow and heat transfer in twin-roll casting of aluminum alloys / A. Saxena, Y. Sahai // Material Transactions. – The Japan Institute of Metals. – 2002. – Vol. 43, №. 2. – P. 206–213. 10. Miehe A. Modelling of heat transfer and solidification processes in horizontal twin-roll casting of magnesium AZ31 / A. Miehe,U. Gross // OP Conference Series: Materials Science and Engineering. – 2012. – Vol. 33, Is. 1. – P. 12–17. 11. Kloss W. Duenbandgiessen mit variable Giasspalt. Umformtechnische Schriften / W. Kloss.– Aachemn: Shaker Verlag, 2005. Band 144. – 180p. 12. Santos C. A. Modelling of solidification in twin-roll strip casting / C. A. Santos, J. A. Spim, A. Garcia // Journal of Materials Processing Technology. – 2000. – №102(1–3). – P. 33–39. 13. Zgang X. M. Modelling of the micro-segregation of twin-roll thin strip casting / X. M. Zgang, Z. Y. Jiang, X. H. Liu, G. D. Wang // Journal of Materials Processing Technology. – 2005. №162–163. – P. 591–595. 14. Zinov'ev A. V. Modelirovanie processa neprery'vnogo lit'ya tonkix polos v valkovom kristallizatore / A. V. Zinov'ev, V. S. Savchenko, A. A. Bondarenko. – Dnіpropetrovs'k: «Sistemnі texnologії», 2005. – T.8: Suchasnі problemi metalurgії. Naukovі vіstі. Plastichna deformacіyametalіv. – C. 32–36. 15. Nogovicy'n A. V. Chislennoe modelirovanie gidrodinamicheskix i teplovy'x processov pri neprery'vnoj dvuxvalkovoj razlivke stali / A. V. Nogovicy'n,A. D. Podol'cev, I. N. Kucheryavaya // Metall i lit'yo Ukrainy' – 2015. – № 3 (262) – Kiev : Izdatel'stvo FTIMS NAN Ukrainy'.– C. 15–20. 16. Guthrie R.I.L. Mathematical and physical modeling of steel flow and solidification in twin roll (horizontal belt thin strip casting machines) / R.I.L. Guthrie, R.P. Tavares // Inter Conf on CFD in Mineral & Metal Processing and Power Generation. CSIRO. – 1997. – P. 41–54.
Authors and Affiliations
А. М. Сокол
Keywords
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