A numerical evaluation of the temperature of a solidification point in ingot casting processes

Simple item page
dc.citation.epage420
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage410
dc.contributor.affiliationНаціональний університет Барранки
dc.contributor.affiliationUniversidad Nacional de Barranca
dc.contributor.authorЗамбрано, М.
dc.contributor.authorZambrano, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T10:28:08Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractАналіз для чисельного обчислення температури біля точки затвердіння рідкої сталі або розплаву, що міститься у формі, здійснюється через взаємодію рівнянь збереження маси, імпульсу та теплопередачі. За допомогою асимптотичних методів проаналізовано процес охолодження рідкої сталі за рахунок відведення тепла через стінки форми та отримано звичайне диференціальне рівняння, яке описує температуру межі розплав–повітря. Крім того, температура розплаву у формі навколо точки затвердіння обчислюється чисельно за допомогою програмного забезпечення OpenFOAM.
dc.description.abstractAn analysis for the numerical computing of the temperature around a solidification point of liquid steel or melt contained in a mould is performed via the interaction of the conservation equations of mass, momentum and heat transfer. A cooling process of liquid steel due to the extraction of heat through the walls of the mould is analyzed using asymptotic methods and an ordinary differential equation that describes the temperature of interface melt-air is obtained. Also, the temperature of the melt in the mould around the solidification point is computed numerically using the OpenFOAM software.
dc.format.extent410-420
dc.format.pages11
dc.identifier.citationZambrano M. A numerical evaluation of the temperature of a solidification point in ingot casting processes / M. Zambrano // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 410–420.
dc.identifier.citationenZambrano M. A numerical evaluation of the temperature of a solidification point in ingot casting processes / M. Zambrano // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 410–420.
dc.identifier.doi10.23939/mmc2023.02.410
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63403
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 2 (10), 2023
dc.relation.references[1] Vynnycky M., Zambrano M., Cuminato J. A. On the avoidance of ripple-marks on cast metal surfaces. International Journal of Heat and Mass Transfer. 86, 43–54 (2015).
dc.relation.references[2] Wray P. J. Geometric features of chill-cast surfaces. Metallurgical Transactions B. 12, 167–176 (1981).
dc.relation.references[3] Tomono H., Kurz W., Heinemann W. The liquid steel meniscus in molds and its relevance to the surface quality of casting. Metallurgical Transactions B. 12, 409–411 (1981).
dc.relation.references[4] Jacobi H., Schwerdfeger K. Ripple marks on cast steel surfaces. ISIJ International. 53 (7), 1180–1196 (2013).
dc.relation.references[5] Fredriksson H., Elfsberg J. Thoughts about the initial solidification process during continuous casting of steel. Scandinavian Journal of Metallurgy. 31 (5), 292–297 (2002).
dc.relation.references[6] Takeuchi E., Brimacombe J. K. The formation of oscillation marks in the continuous casting of steel slabs. Metallurgical Transactions B. 15, 493–509 (1984).
dc.relation.references[7] Steinr¨uck H., Rudisher C., Schneider W. Modelling of continuous casting process. Nonlinear Analysis: Theory, Methods & Applications. 30 (8), 4915–4925 (1997).
dc.relation.references[8] Schwerdtfeger K., Sha H. Depth of oscillation marks forming in continuous casting of steel. Metallurgical and Materials Transactions B. 31, 813–826 (2000).
dc.relation.references[9] Vynnycky M., Zambrano M. Towards a “moving-point” formulation for the modelling of oscillation-mark formation in the continuous casting of steel. Applied Mathematical Modelling. 63, 243–265 (2018).
dc.relation.references[10] Bikerman J. Physical Surfaces. Elsevier Science (2012).
dc.relation.references[11] Pletcher R. Computational Fluid Mechanics and Heat Transfer. CRC Press (1997).
dc.relation.references[12] Dantzig J., Tucker C. Modeling in Material Processing. Cambridge University Press (2012).
dc.relation.references[13] Crank J. Free and Moving Boundary Problems. Oxford University Press (1975).
dc.relation.references[14] Elsevier Science. OpenFOAM — Field Operation and Manipulation. OpenFOAM foundation (2012).
dc.relation.references[15] Leveque J. R. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press (2002).
dc.relation.references[16] Mitchell S. L., Vynnycky M. On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions. Journal of Computational and Applied Mathematics. 264, 49–64 (2014).
dc.relation.references[17] Mitchell S. L., Vynnycky M. Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems. Applied Mathematics and Computation. 215 (4), 1609–1621 (2009).
dc.relation.references[18] Prosperetti A., Tryggvason G. Computational Methods in Multiphase Flow. Cambridge University Press (2009).
dc.relation.references[19] Burden R., Faires J. Numerical Analysis. Brooks/Cole (2012).
dc.relation.references[20] Leveque R. J. Finite Difference Methods for Ordinary and Partial Differential Equations. Society for Industrial and Applied Mathematics (SIAM) (2007).
dc.relation.references[21] Chen G., Xiong Q., Morris P., Paterson E., Sergeev A., Wang Y. OpenFOAM for Computational Fluid Dynamics. Notices of the AMS. 61 (4), 354–363 (2014).
dc.relation.references[22] Eaton J., Bateman D., Hauberg S., Wehbring R. GNU Octave, version 5.2.0 manual: a high-level interactive language for numerical computations. https://www.gnu.org/software/octave/doc/v5.2.0 (2020).
dc.relation.references[23] Caldwell J., Kwan Y. Y. Numerical methods for one-dimensional Stefan problems. Communications in Numerical Methods in Engineering. 20 (7), 535–545 (2004).
dc.relation.references[24] Voller V. R. Fast Implicit Finite-Difference Method for the Analysis of Phase Change Problems. Numerical Heat Transfer, Part B: Fundamentals. 17 (2), 155–169 (1990).
dc.relation.references[25] Voller V. R., Prakash C. A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems. International Journal of Heat and Mass Transfer. 30 (8), 1709–1719 (1987).
dc.relation.referencesen[1] Vynnycky M., Zambrano M., Cuminato J. A. On the avoidance of ripple-marks on cast metal surfaces. International Journal of Heat and Mass Transfer. 86, 43–54 (2015).
dc.relation.referencesen[2] Wray P. J. Geometric features of chill-cast surfaces. Metallurgical Transactions B. 12, 167–176 (1981).
dc.relation.referencesen[3] Tomono H., Kurz W., Heinemann W. The liquid steel meniscus in molds and its relevance to the surface quality of casting. Metallurgical Transactions B. 12, 409–411 (1981).
dc.relation.referencesen[4] Jacobi H., Schwerdfeger K. Ripple marks on cast steel surfaces. ISIJ International. 53 (7), 1180–1196 (2013).
dc.relation.referencesen[5] Fredriksson H., Elfsberg J. Thoughts about the initial solidification process during continuous casting of steel. Scandinavian Journal of Metallurgy. 31 (5), 292–297 (2002).
dc.relation.referencesen[6] Takeuchi E., Brimacombe J. K. The formation of oscillation marks in the continuous casting of steel slabs. Metallurgical Transactions B. 15, 493–509 (1984).
dc.relation.referencesen[7] Steinr¨uck H., Rudisher C., Schneider W. Modelling of continuous casting process. Nonlinear Analysis: Theory, Methods & Applications. 30 (8), 4915–4925 (1997).
dc.relation.referencesen[8] Schwerdtfeger K., Sha H. Depth of oscillation marks forming in continuous casting of steel. Metallurgical and Materials Transactions B. 31, 813–826 (2000).
dc.relation.referencesen[9] Vynnycky M., Zambrano M. Towards a "moving-point" formulation for the modelling of oscillation-mark formation in the continuous casting of steel. Applied Mathematical Modelling. 63, 243–265 (2018).
dc.relation.referencesen[10] Bikerman J. Physical Surfaces. Elsevier Science (2012).
dc.relation.referencesen[11] Pletcher R. Computational Fluid Mechanics and Heat Transfer. CRC Press (1997).
dc.relation.referencesen[12] Dantzig J., Tucker C. Modeling in Material Processing. Cambridge University Press (2012).
dc.relation.referencesen[13] Crank J. Free and Moving Boundary Problems. Oxford University Press (1975).
dc.relation.referencesen[14] Elsevier Science. OpenFOAM - Field Operation and Manipulation. OpenFOAM foundation (2012).
dc.relation.referencesen[15] Leveque J. R. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press (2002).
dc.relation.referencesen[16] Mitchell S. L., Vynnycky M. On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions. Journal of Computational and Applied Mathematics. 264, 49–64 (2014).
dc.relation.referencesen[17] Mitchell S. L., Vynnycky M. Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems. Applied Mathematics and Computation. 215 (4), 1609–1621 (2009).
dc.relation.referencesen[18] Prosperetti A., Tryggvason G. Computational Methods in Multiphase Flow. Cambridge University Press (2009).
dc.relation.referencesen[19] Burden R., Faires J. Numerical Analysis. Brooks/Cole (2012).
dc.relation.referencesen[20] Leveque R. J. Finite Difference Methods for Ordinary and Partial Differential Equations. Society for Industrial and Applied Mathematics (SIAM) (2007).
dc.relation.referencesen[21] Chen G., Xiong Q., Morris P., Paterson E., Sergeev A., Wang Y. OpenFOAM for Computational Fluid Dynamics. Notices of the AMS. 61 (4), 354–363 (2014).
dc.relation.referencesen[22] Eaton J., Bateman D., Hauberg S., Wehbring R. GNU Octave, version 5.2.0 manual: a high-level interactive language for numerical computations. https://www.gnu.org/software/octave/doc/v5.2.0 (2020).
dc.relation.referencesen[23] Caldwell J., Kwan Y. Y. Numerical methods for one-dimensional Stefan problems. Communications in Numerical Methods in Engineering. 20 (7), 535–545 (2004).
dc.relation.referencesen[24] Voller V. R. Fast Implicit Finite-Difference Method for the Analysis of Phase Change Problems. Numerical Heat Transfer, Part B: Fundamentals. 17 (2), 155–169 (1990).
dc.relation.referencesen[25] Voller V. R., Prakash C. A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems. International Journal of Heat and Mass Transfer. 30 (8), 1709–1719 (1987).
dc.relation.urihttps://www.gnu.org/software/octave/doc/v5.2.0
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectточка затвердіння
dc.subjectпроцес охолодження
dc.subjectасимптотичні методи
dc.subjectзвичайне диференціальне рівняння
dc.subjectsolidification point
dc.subjectcooling process
dc.subjectasymptotic methods
dc.subjectordinary differential equation
dc.titleA numerical evaluation of the temperature of a solidification point in ingot casting processes
dc.title.alternativeЧисельна оцінка температури точки затвердіння в процесах лиття зливків
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 2