Алгоритм расчета плавления утяжеленного комбинированного алюмосодержащего раскислителя цилиндрической формы в защитной оболочке
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 2
Abstract
ALGORITHM FOR MELTING CALCULATION OF THE WEIGHTED COMBINED ALUMINUM-CONTAINING DEOXIDIZER OF CYLINDRICAL FORM IN THE PROTECTIVE COVER Voloshyn R.V., Babenko M.V., Zhulkovski O.A., Zhulkovska I.I., Degtyarenko Ya.O. Abstract One of the problem solutions of resource saving in steel deoxidizing steel with aluminum is the density increasing of the aluminum ingot by adding a weighting agent and with the simultaneous surface insulation from the effects of slag oxidation. This problem relates to the thermal conductivity problems with moving boundaries of phase separation. The aim of the article is the development and improvement of algorithms for solving mathematical models of the melting kinetics of lump materials in cylindrical form in the melt at asymmetric boundary conditions. We apply the control volume approach. The half of the cylinder cross-section has been chosen as the rated operating conditions. To solve the problem, we form a square grid. As a result, we got control volumes with coordinates i, j. The values of the temperatures are determined in the center of the control volumes. The explicit difference scheme is used in the proposed calculating algorithm. The time step is chosen from the conditions of the explicit difference scheme stability. In the calculations we also tried to get the outer boundary of melting (solidification) not to change more than one step of the grid for one step time. This was achieved by reducing the time step with respect to those selected from the stability condition. The proposed calculation algorithm includes two stages of ingot melting: 1. The freezing of the melt cover during the period when the ingot is fully immersed in the metal melt. Thus, the algorithm describes the process of one-dimensional problem solution of the ingot melting. 2. Ingot melting, located on the border slag-metal, i.e, two-dimensional problem solution of ingot melting is described. Conclusions. This article presents the algorithms for calculation of one- and two-dimensional melting mathematical models of weighted combined aluminum-containing deoxidizer of cylindrical form in the protective cover in the melt and under asymmetric boundary conditions on the slag-metal interphase boundary, as well as the results of computational experiments and analysis of the calculated data that allows to establish rational modes of ingots input, ensuring the most favorable conditions for the melt in the casting ladle during metal tapping from the oxygen steel-making converter. References [1] Babenko M. V., Pavlyuchenkov I. A. Raskislenie metala s ispolzovaniem alyuminievyih sterzhney s zaschitnyim pokryitiem pri vnepechnoy dovodke stali. // A.Yasaui atyindyigyi Halyikaralyik kazakturIk universitetInIn habarshyisyi. # 1. 2008. S. 61—65. [2] R. V. Voloshin, M. V. Babenko. Matematicheskaya model plavleniya utyazhelennogo kombinirovannogo alyumosoderzhaschego raskislitelya tsilindricheskoy formyi v zaschitnoy obolochke // Matematichne modelyuvannya. – 2015. – #1(32). – S. 33 – 35. [3] Pavlyuchenkov I. A. Chislennoe modelirovanie (na osnove metoda Dyuzimbera) protsessov plavleniya tel v rasplave // Matematichne modelyuvannya. – 1997. – #2 S. 37 – 43. [4] Babenko M. V. Algoritm rascheta (na osnove metoda Dyuzimbera) dvuhmernoy zadachi plavleniya tsilindra v rasplave / M. V. Babenko, I.A. Pavlyuchenkov // Metalurgiyna teplotehnika: Zb. nauk. Prats Natsionalnoyi metalurgiynoyi akademiyi Ukrayini. – Dnipropetrovsk: PP Grek O.S., 2006.S. 3–7. [5] Algoritmicheskoe i programmnoe obespechenie protsessa plavleniya tugoplavkih materialov tsilindricheskoy formyi na granitse shlak-metall. Pavlyuchenkov I.A., Salo E.V., Voloshin R.V., Ovcharenko T.N. Sbornik tehnicheskie nauki, DGTU, 2010 g.
Authors and Affiliations
Р. В. Волошин, М. В. Бабенко, О. А. Жульковский, И. И. Жульковская, Я. О. Дегтяренко
Keywords
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