Journal articles: 'Continuous casting Mathematical models'

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Vynnycky, Michael. "Applied Mathematical Modelling of Continuous Casting Processes: A Review." Metals 8, no. 11 (November 9, 2018): 928. http://dx.doi.org/10.3390/met8110928.

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With readily available and ever-increasing computational resources, the modelling of continuous casting processes—mainly for steel, but also for copper and aluminium alloys—has predominantly focused on large-scale numerical simulation. Whilst there is certainly a need for this type of modelling, this paper highlights an alternative approach more grounded in applied mathematics, which lies between overly simplified analytical models and multi-dimensional simulations. In this approach, the governing equations are nondimensionalized and systematically simplified to obtain a formulation which is numerically much cheaper to compute, yet does not sacrifice any of the physics that was present in the original problem; in addition, the results should agree also quantitatively with those of the original model. This approach is well-suited to the modelling of continuous casting processes, which often involve the interaction of complex multiphysics. Recent examples involving mould taper, oscillation-mark formation, solidification shrinkage-induced macrosegregation and electromagnetic stirring are considered, as are the possibilities for the modelling of exudation, columnar-to-equiaxed transition, V-segregation, centreline porosity and mechanical soft reduction.

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Doroshenko, Volodymyr, Volodymyr Kravchenko, Olena Mul, and Olena Tokova. "Continuous-Discrete Boundary Problems in the Concepts of the Construction of Foundry Rotary-Conveyor Lines." Boundary Field Problems and Computer Simulation 57 (January 18, 2019): 29–34. http://dx.doi.org/10.7250/bfpcs.2018.004.

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The problem of mathematical construction for the process of the control of the metal casting crystallization and cooling in a foundry mold is considered. The casting is surrounded by a layer of sand mixture, which is a porous dispersed medium that conducts heat, in terms of the concepts of the construction of foundry rotary-conveyor lines (RCL). The problem of developing an interval model for determining the speed of the conveyor line from the production of metal castings is studied. Herewith, continuous processes of the transport and technological movement of the processed materials, equipment, tools, energy carriers, and final production output are combined with inevitable stops of this continuity, which lead to discreteness, and a combination with a number of accompanying continuous, discrete or reciprocating processes. The adequacy of the model for the given technological parameters is justified. The mathematical description and agreement of the values of technological parameters for regulation and finding the optimal speed of the conveyor line at the interaction of its component rotational systems, as well as the mathematical models for program control and remote monitoring of technological modes in order to obtain the casting of the given quality are considered. The possibility of selecting the corrective parameters for the change of the conveyor line speed is shown. Tiek skatīta matemātiskās konstrukcijas problēma metāla liešanas kristalizācijas un dzesēšanas kontroles procesam liešanas veidnē. Lējumu ieskauj smilšu maisījuma slānis, kas ir poraini izkliedēts materiāls, kas vada siltumu. Lietojot lietuves rotācijas konveijeru līniju (RCL) koncepciju, tiek pētīta intervāla modeļa izveides problēma konveijera līnijas ātruma noteikšanai metāla lējumu ražošanai. Tajā pašā laikā nepārtraukti apstrādājamo materiālu, iekārtu, rīku, enerģijas nesēju un gala produkcijas transportēšanas un tehnoloģiskās kustības procesi tiek apvienoti ar šīs nepārtrauktības neizbēgamajiem apstāšanās gadījumiem, kas noved pie kombinācijas ar vairākiem nepārtrauktiem, diskrētiem vai pārvietošanās procesiem. Ir pierādīta modeļa piemērotība attiecīgajiem tehnoloģiskajiem parametriem. Tiek parādīta iespēja izvēlēties koriģējošos parametrus konveijera līnijas ātruma maiņai.

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Mazur, Igor, and Tanya I. Cherkashina. "Mathematical and Physical Modeling of Soft Cobbing Process of Hot Rolling Steels." Materials Science Forum 704-705 (December 2011): 160–64. http://dx.doi.org/10.4028/www.scientific.net/msf.704-705.160.

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The soft cobbing, used in steel’s continuous casting, is widely applying in technologies of rolled metal manufacturing. It is important to know ingot’s stress-strain state and dynamics of ingot’s changes while cobbing, when there is a liquid metal in the centre of section. The complex questions of numerical modeling of soft cobbing process and experimental investigation on physics plasticine models are considered in presented work. The analysis of findings is presented in the article.

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Miłkowska‐Piszczek, Katarzyna, and Jan Falkus. "Control and Design of the Steel Continuous Casting Process Based on Advanced Numerical Models." Metals 8, no. 8 (July 30, 2018): 591. http://dx.doi.org/10.3390/met8080591.

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The process of continuous casting of steel is a complex technological task, including issues related to heat transfer, the steel solidification process, liquid metal flow and phase transitions in the solid state. This involves considerable difficulty in creating the optimal process control system, which would include the influence of all the physico‐chemical phenomena which may occur. In parallel, there is an intensive development of new mathematical models and an increase in computer performance, therefore complex numerical simulations requiring substantial computing time can be conducted. This paper presents a review of currently applied numerical methods allowing the phenomena accompanying the process of continuous casting of steel to be accurately represented. Special attention was paid to the selection of appropriate methods to solve the technological problem selected. The possibilities of applying selected numerical models were analysed in order to modify and improve the existing process or to design a new one linked to the implementation of new steel grades in the current production. The description of the method of defining the boundary conditions, initial conditions and material parameters as vital components ensuring that numerical calculations based upon them in the finite element method, which is that most frequently applied, are correct is an important element of the paper. The possibility of reliably defining the values of boundary parameters on the basis of information on the intensity of cooling in individual zones of the continuous casting machine was analysed.

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Vapalahti, Sami, Seppo Louhenkilpi, and Tuomo Räisänen. "The Effect of Fluid Flow on Heat Transfer and Shell Growth in Continuous Casting of Copper." Materials Science Forum 508 (March 2006): 503–8. http://dx.doi.org/10.4028/www.scientific.net/msf.508.503.

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Molten metal is cooled in a continuous casting mould forming initially a thin shell that grows thicker. The main phenomena in the mould are: fluid flow, heat transfer and solidification. A lot of mathematical models have been developed to simulate these phenomenons in continuous casting machines but most of the models developed are not calculating the fluid flow at all. In these models, it is assumed that the strand (solid and liquid) is withdrawn through the machine with a constant velocity field (= casting speed) and the convective heat transfer generated by the fluid flow is taken into account by using an effective thermal conductivity method. Also at the Helsinki University of Technology, these kinds of heat transfer models have been developed (TEMPSIMU for steels and CTEMP3D for coppers). The flow in the mould is three-dimensional and turbulent. Coupled models calculate the fluid flow, heat transfer and solidification simultaneously. The fluid flow is affected by many things: inlet flow rate, design of the inlet nozzle (SEN), immersion depth of the SEN, movement of the solid shell, natural convection, solidification shrinkage, etc. and the fully coupled, turbulent fluid flow and heat transfer models are generally subjected to convergence difficulties and they need a lot of computing time. Due to these reasons, these kinds of models are not so much used in industry so far. In the present study, a commercial FLOW-3D package is used to make coupled simulations of heat transfer, turbulent fluid flow and solidification in a copper continuous casting machine. The effect of thermophysical material data are also studied and presented. The material data are calculated by a model developed at the Helsinki University of Technology, called CASBOA.

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Moro, L., J. Srnec Novak, D. Benasciutti, and F. de Bona. "Copper Mold for Continuous Casting of Steel: Modelling Strategies to Assess Thermal Distortion and Durability." Key Engineering Materials 754 (September 2017): 287–90. http://dx.doi.org/10.4028/www.scientific.net/kem.754.287.

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In this work the durability assessment and the permanent deformation of a copper mold for continuous casting of steel have been investigated using mathematical models based on the Finite Element method. The cyclic plasticity behavior of the material is represented by a combined kinematic-isotropic model experimentally validated. Results from thermo-mechanical analysis are in good agreement with measurements. In particular, creep effects included into the model permit the evolution of bulging near the meniscus area to be correctly predicted. A life estimation is performed considering strain-life and stress-rupture time curves according to a cumulative damage law.

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Jędrzejczyk, D., M. Hojny, and M. Głowacki. "Development of Software for the Simulation of Rolling Steel Under the Coexistence of Liquid and Solid State / Rozwój Oprogramowania Do Symulacji Walcowania Stali W Warunkach Współistnienia Fazy Ciekłej I Stałej." Archives of Metallurgy and Materials 60, no. 4 (December 1, 2015): 2783–90. http://dx.doi.org/10.1515/amm-2015-0447.

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The paper presents the results of the application simulating the rolling process of steel in terms of coexistence of liquid and solid phases. The created mathematical models can be the basis for creation of systems that simulate the final phase of the continuous casting process relying on using a roller burnishing machine for continuous casting of steel. For a complete description of the performance of the material during deformation in these conditions, the constructed mathematical model is a fully three-dimensional model and consists of three parts: thermal, mechanical, and density variation submodels. The thermal model allows the prediction of temperature changes during plastic deformation of solidifying material. The mechanical model determines the kinetics of plastic continuum flow in the solid and semi-solid states, and the resulting deformation field. The temperature of the process forces supplementing the description of the performance of the material with a density variation model that allows the prediction of changes in the density of the material during the final phase of solidification with simultaneous plastic deformation. For the purpose built model, experimental studies were performed using a physical simulator Gleeble 3800®. They allowed the determination of the necessary physical properties of the metal within the temperature of change state. In addition to presenting the developed models the work also includes the description of the author’s application that uses the above mathematical models. The application was written in the fully object-oriented language C++ and is based on the finite element method. The developed application beside the module data input, also consist of a module of three-dimensional visualization of the calculations results. Thanks to it, the analysis of the distribution of the particular rolling parameters in any cross-section of the rolled strip will be possible. The paper presents the results of the authors’ research in the area of the advanced computer simulation.

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Ramírez-López, Adán, Omar Dávila-Maldonado, Alfonso Nájera-Bastida, Rodolfo Dávila Morales, Carlos Rodrigo Muñiz-Valdés, and Jafeth Rodríguez-Ávila. "Computer Modeling of Grain Structure Formation during Quenching including Algorithms with Pre- and Post-Solidification." Metals 12, no. 4 (April 4, 2022): 623. http://dx.doi.org/10.3390/met12040623.

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Simulation of the grain growth process, as a function of steel heat transfer conditions, is helpful for predicting grain structures of continuous cast steel products. Many authors have developed models based on numerical methods to simulate grain growth during metal solidification. Nevertheless, the anisotropic nature of grain structures makes necessary the employment of new mathematical methods such as chaos theory, fractals, and probabilistic and stochastic theories of simulation. The problem is significant for steelmakers to avoid defects in products and to control the steel microstructure during the continuous casting process. This work discusses the influence of nodal solidification times and computer algorithms on the dynamic formation of the chill, columnar, and equiaxed zones including physical phenomena such as nucleation and grain growth. Moreover, the model incorporates pre-nucleation and pre-growth routines in the original algorithm. There is a description of the influence of the mathematical parameter criteria and probabilities over the grain morphology obtained after solidification. Finally, an analysis of these algorithms elucidates the differences between these structures and those obtained from models considering only the solidification.

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Vaghefi, Reza, MR Hematiyan, and Ali Nayebi. "Three-dimensional thermo-mechanical analysis of continuous casting and comparison with two-dimensional models." Journal of Strain Analysis for Engineering Design 53, no. 6 (June 4, 2018): 421–34. http://dx.doi.org/10.1177/0309324718780131.

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In this study, a three-dimensional thermo-elasto-plastic model is developed for simulating a continuous casting process. The obtained results are compared with those from different two-dimensional analyses, which are based on plane stress, plane strain, and generalized plane strain assumptions. All analyses are carried out using the meshless local Petrov–Galerkin method. The effective heat capacity method is employed to simulate the phase change process. The von Mises yield criterion and elastic–perfectly-plastic model are used to simulate the stress state during the casting process; while, material parameters are assumed to be temperature-dependent. Based on the three-dimensional and two-dimensional models, numerical results are provided to determine the stress, displacement, and temperature fields induced in the cast material. It is observed that the present meshless local Petrov–Galerkin method is accurate in three-dimensional thermo-mechanical analysis of highly nonlinear phase change problems. Reasonable agreements are observed between the results obtained from the three-dimensional analysis with those retrieved by the generalized plane strain assumption. However, it is observed that the results obtained under plane stress/strain conditions have some significant differences with the results obtained from three-dimensional modeling of continuous casting.

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Krasnikov, Kyrylo Serhiiovych. "MATHEMATICAL MODELING OF THE DISTRIBUTION OF ARGON IN A TUNDISH WITH A MOLTEN METAL DURING FILLING." Modern Problems of Metalurgy, no. 23 (March 27, 2020): 130–35. http://dx.doi.org/10.34185/1991-7848.2020.01.13.

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The article is devoted to the mathematical description of the process of filling an intermediate ladle (tundish) with argon, which is blown into the melt stream falling from the steel casting ladle, which is common at metallurgical plants. Metallurgical plants use an intermediate ladle to reliably supply a continuous casting machine for the melt. Also important for the tundish is the removal of non-metallic inclusions using argon. The good distribution of argon bubbles in the tundish significantly influences the removal of unwanted melt components such as hydrogen and nitrogen. Given the need for gas to escape, the melt speed in the intermediate ladle should be sufficiently low, especially near outflow holes, where melt needs to be homogeneous and slow for a high–quality casting. Conducting experiments during the operation of a metallurgical plant is undesirable, costly and is accompanied by difficulties associated with high temperature and opacity of the melt. Therefore, the experiments are often carried out in laboratories on the so-called cold models, where the melt is replaced by water, argon – by air, and the tundish – by the transparent container of the rectangular shape under the conditions of similarity. Despite the obvious advantages of such cold modeling, today most experiments are still conducted on mathematical models, which are a much cheaper and low-erroneous way of predicting the development of a given process under different conditions. Mathematical modeling of melt motion helps to select the optimal geometry of the tundish, as well as the required amount of argon and usefulness of barriers on a way of melt streams. The article proposes to use the convection-diffusion equation for the argon field and the Navier-Stokes equations – for the velocity field. The numerical solution using finite volume method is well tested and provides sufficient accuracy. In addition, this method is easily parallelized to speed up computing on modern multi-core processors. A graphical user interface software application allows you to display the status of the system on the screen for further review and adoption decisions.

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Pieprzyca, J., and J. Jowsa. "Method for Determining the Time Constants Characterizing the Intensity of Steel Mixing in Continuous Casting Tundish." Archives of Metallurgy and Materials 60, no. 1 (April 1, 2015): 245–49. http://dx.doi.org/10.1515/amm-2015-0039.

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AbstractA common method used in identification of hydrodynamics phenomena occurring in Continuous Casting (CC) device's tundish is to determine the RTD curves of time. These curves allows to determine the way of the liquid steel flowing and mixing in the tundish. These can be identified either as the result of numerical simulation or by the experiments - as the result of researching the physical models. Special problem is to objectify it while conducting physical research. It is necessary to precisely determine the time constants which characterize researched phenomena basing on the data acquired in the measured change of the concentration of the tracer in model liquid's volume. The mathematical description of determined curves is based on the approximate differential equations formulated in the theory of fluid mechanics. Solving these equations to calculate the time constants requires a special software and it is very time-consuming. To improve the process a method was created to calculate the time constants with use of automation elements. It allows to solve problems using algebraic method, which improves interpretation of the research results of physical modeling.

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Khan, Muhammad A. A., and Anwar K. Sheikh. "Virtual Casting: State of the Art in Metal Casting Simulation Tools." Journal of Engineering Research [TJER] 15, no. 2 (November 7, 2018): 142. http://dx.doi.org/10.24200/tjer.vol15iss2pp142-154.

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The demands on the productivity and robustness of metal casting processes for high quality components are continuously increasing. Moreover, the financial considerations necessitate meticulous and reliable planning of the entire casting process before it is actually put into practice. A holistic approach to perform cradle to grave analysis of cast products is simulation-based metal casting. This method allows engineers to model, verify, and validate the process followed by its optimization and performance prediction in virtual reality. This paper provides insights on state of the art in simulation-based metal casting with reference to some case studies. Casting simulations software, mathematical models and solution methods, and casting process simulation together with the results obtained are clearly explained. The current practices revealed extensive utilization of simulation packages for defect minimization, yield maximization, and improved quality. The ongoing research on integration of casting simulations with mechanical performance simulations makes it possible to analyze the serviceability of cast parts. The reliability of cast part in service with dynamic loading of varying thermal and mechanical load cycles can be predicted through this integration. However, more rigorous work is needed in this area, particularly by developing the reliability prediction modules embedded in advanced simulation tools.

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Khan, Muhammad A. A., and Anwar K. Sheikh. "Virtual Casting: State of the Art in Metal Casting Simulation Tools." Journal of Engineering Research [TJER] 15, no. 2 (November 7, 2018): 42. http://dx.doi.org/10.24200/tjer.vol15iss2pp42-54.

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The demands on the productivity and robustness of metal casting processes for high quality components are continuously increasing. Moreover, the financial considerations necessitate meticulous and reliable planning of the entire casting process before it is actually put into practice. A holistic approach to perform cradle to grave analysis of cast products is simulation-based metal casting. This method allows engineers to model, verify, and validate the process followed by its optimization and performance prediction in virtual reality. This paper provides insights on state of the art in simulation-based metal casting with reference to some case studies. Casting simulations software, mathematical models and solution methods, and casting process simulation together with the results obtained are clearly explained. The current practices revealed extensive utilization of simulation packages for defect minimization, yield maximization, and improved quality. The ongoing research on integration of casting simulations with mechanical performance simulations makes it possible to analyze the serviceability of cast parts. The reliability of cast part in service with dynamic loading of varying thermal and mechanical load cycles can be predicted through this integration. However, more rigorous work is needed in this area, particularly by developing the reliability prediction modules embedded in advanced simulation tools.

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Zhao, Jiangbo, Xiaodong Sun, Liang Zhao, and Junzheng Wang. "Robust backstepping control of double-rod cylinder for motion synchronization of mold oscillator." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 232, no. 1 (October 14, 2017): 29–38. http://dx.doi.org/10.1177/0959651817733588.

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High-performance synchronization control of two double-rod cylinders used to oscillate the mold of a continuous casting machine is considered in this article. Friction between strand shell and mold plays an important role to achieve high-precision control of mold oscillator. A new friction model is proposed for exact system modeling and is proved useful. Using a force-distribution method to consider the coupling effect between two cylinders, mathematical models of each cylinder are presented and a simple robust backstepping control strategy is proposed, which can reduce the influences of time-varying system parameters and unmodeled uncertainties. The transient performance and stability of the proposed controller are rigorously proved. Simulation and experimental results show that proposed synchronization control method can achieve good performance for given tracking task.

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Odinokov, V. I., E. A. Dmitriev, and A. I. Evstigneev. "MATHEMATICAL MODELING OF METAL FLOW IN CRYSTALLIZER AT ITS SUPPLY FROM SUBMERSIBLE NOZZLE WITH ECCENTRIC HOLES." Izvestiya Visshikh Uchebnykh Zavedenii. Chernaya Metallurgiya = Izvestiya. Ferrous Metallurgy 61, no. 8 (October 24, 2018): 606–12. http://dx.doi.org/10.17073/0368-0797-2018-8-606-612.

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Flow of liquid melt in the crystallizer is a little-studied process. Analytical solutions of melt flow in general case refer to complex mathematical problems, therefore numerical methods are used to model it. The purpose of this work is to use numerical method proposed by Professor V.I. Odinokov, based on finite-difference representation of the initial system of equations. This method has been successfully used in mechanics of continuous media, in foundry industry in mathematical modeling of strained deformed state of shell molds on investment models,as well as in other technological works, which indicates its universality. In the present study, the object of research is hydrodynamic flows of liquid metal during steel casting into a rectangular section mold when fed from a submerged nozzle with eccentric holes, and the result is a spatial mathematical model describing the flows of liquid metal in the crystallizer. To simulate the processes occurring in the crystallizer, the software complex “Odyssey” was used. The theoretical calculation is based on fundamental equations of hydrodynamics and approved numericalmethod. Solution of differential equations system formulatedin the work was carried out numerically. Investigated area was divided into elements of finite dimensions, for each element the resulting system of equations was written in the difference form. The result of the solution is velocity field of metal flow in crystallizer volume. To solve the system of algebraic equations obtained, a numerical scheme and a calculation algorithm were developed. Based on developed numerical scheme and algorithm, a computation program was compiled in Fortran-4. Mathematical model makes it possible to vary geometric dimensions of the crystallizer and cross-section of metal exit openings from the immersion nozzle, and it can also help to understand the flow pattern of the cast metal that affects heat dissipation of crystallizer walls and to find the optimal parameters for liquid metal outlet from the gravy glass at various casting modes. As an example it is given calculation of steel casting into a rectangular mold with a height of 100 cm and a section of 2000×40 (cm) in plan. Casting was carried out from immersion nozzle eccentrically in both sides in a horizontal plane. The calculation results are presented in graphical form. The movement of liquid metal flows is shown, their magnitudes and intensity are determined.

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Dobrovská, Jana, Hana Francová, Bedřich Smetana, Karel Stránský, Věra Dobrovská, and František Kavička. "Experimental Analysis on the Causes of the Breakout of Continuous Cast Steel Slab." Materials Science Forum 782 (April 2014): 67–72. http://dx.doi.org/10.4028/www.scientific.net/msf.782.67.

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The paper deals with investigation into segregation behavior of selected elements in longitudinal cut of continuous steel slab, in the breakout area. The breakout occurred after a flying change of tundish in order to begin casting of another steel grade. Altogether 11 samples were taken from the part of a solidified slab. Concentrations of selected elements (Al, Si, P, S, Cr, Mn, Ni and Mo) were measured in these samples using scanning electron microscope and energy dispersive spectroscopy. Using the original mathematical models the basic micro-segregation characteristics and the parameter of macro-heterogeneity were further determined for each analyzed element. Then a quantitative measurement of inclusions ("micro-purity") in the samples was performed using a metallographic microscope. Then method of differential thermal analysis was used for the measurements of temperatures of phase transformations. The following main results were found: - magnitude of micro-segregation of the analyzed elements in the measured sections of 1000 μm is approximately the same in all the analyzed samples, - chemical macro-heterogeneity is very high across the analyzed slab section, - very uneven mixing of melts of both steels was probably one of the main causes of formation of the breakout.

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Bielnicki, Marcin, and Jan Jowsa. "Physical and numerical modeling of liquid slag entrainment in mould during slabs casting." Metallurgical Research & Technology 117, no. 5 (2020): 509. http://dx.doi.org/10.1051/metal/2020055.

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The paper presents results of physical and numerical modeling of liquid slag entrainment during continuous casting of steel slabs process. The main aim of this work was to determine the critical casting speed and also to specify, which entrainment mechanism is most responsible for transport of slag droplets into steel volume. Physical modeling was based on water-oil model of mould, made on reduced linear scale of Sl = 0.4. In mathematical modeling, Realizable k-ε and LES WALE models were used to describe turbulent motion of water and oil, whereas Volume of Fluid model was used to take into account interactions between phases. It was found, that the main cause of slag entrainment is the formation of von Karman vortex in the vicinity of submerged entry nozzle. The results of laboratory experiments and numerical simulations were compared each other. Both method are a useful tools for modeling of slag entrainment. Great agreement was found between laboratory experiments and numerical simulation carried out using LES WALE model, regarding the shape of the oil and oil entrainment as a result of vortex structures formation. However, in the simulation case using Realizable k-ε model, the oil entrainment hasn’t been modeled for the conditions under consideration.

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Gonzalez-Trejo, Jesus, Cesar Augusto Real-Ramirez, Ignacio Carvajal-Mariscal, Florencio Sanchez-Silva, Francisco Cervantes-De-La-Torre, Raul Miranda-Tello, and Ruslan Gabbasov. "Hydrodynamic Analysis of the Flow inside the Submerged Entry Nozzle." Mathematical Problems in Engineering 2020 (October 20, 2020): 1–14. http://dx.doi.org/10.1155/2020/6267472.

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The quality of steel produced by continuous casting depends mainly on the characteristics of the liquid steel flow pattern within the mold. This pattern depends on the flow dynamics of the nozzle that is immersed in liquid steel. This work characterizes the fluid dynamics within two separate submerged entry nozzle models with a square cross section bore. The Froude similarity criterion and water as working fluid have been used. The models consist of a square-shaped tube with one inlet and two lateral squared exits at the bottom. To enhance the flow visualization, the models do not have exit ports. Moreover, one of the models has a “pool,” a volume at the bottom, and the other prescinds of it. The geometrical parameters and operational conditions of physical experiments were reproduced in the numerical simulations. The turbulence model used in this work is large eddy simulation (LES) with dynamic k-equation filtering. It was found that transient numerical simulations reproduce the dynamic nature of the internal flow pattern seen in physical experiments. The results show that the flow pattern within the pool nozzle is defined by only one large vortex; on the other hand, in the nozzle, without the pool, the flow pattern achieves a complex behavior characterized by two small vortexes. This study will allow to build nozzles that produce a symmetric, regular fluid flow pattern inside the mold, which leads to improvements on the process such as low energy consumption and finally in cost reductions.

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Haas, Tim, Christian Schubert, Moritz Eickhoff, and Herbert Pfeifer. "Numerical Modeling of the Ladle Flow by a LES-Based Eulerian–Lagrange Approach: A Systematic Survey." Metallurgical and Materials Transactions B 52, no. 2 (February 16, 2021): 903–21. http://dx.doi.org/10.1007/s11663-021-02064-2.

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AbstractTo account for increasing economic and ecological pressure, the steel industry is obligated to continuously optimize all processes. An important optimization approach is numerical modeling although its potential is limited by the accuracy of the mathematical models. In a previous work, a validation database was created and a validation score was derived from this data which allows a comprehensive qualitative accuracy assessment for those models. Here, this system is employed for a systematic optimization of the isothermal flow in the casting ladle. For that, different submodels, namely the turbulence models, subgrid turbulence models, bubble-induced turbulence and interfacial closure models as well as influencing factors, such as the grid resolution or the initial bubble size, are analyzed. It is shown that the large eddy turbulence model is more accurate than the Reynolds-average approach because it is able to reproduce the anisotropy of turbulence in the bubble region. In accordance with the literature, a grid dependency of the lift force is found which can be reduced using an averaged shear field as an additional variable. For the interfacial closure models, the combination of the Tomiyama drag model for fully contaminated systems and the Tomiyama lift correlation showed the best agreement with the experimental data. The results of the survey are summarized to a best-practice guideline with which the validation score can be increased from 38.7 with the Reynolds-average approach to 85.1 on a coarse grid respectively, and 87.8 on a fine grid. However, some upscaling problems of the numerical system from the water model to the real ladle are revealed. There is a need to find accurate yet efficient grid resolutions which make the large eddy turbulence model affordable with the current computational resources. Furthermore, alloying elements or non-metallic inclusions might alter the interfacial forces considerably. However, no studies on their effect have been published yet.

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Forzan, Michele, Fabrizio Dughiero, Mattia Guglielmi, and Antonio Marconi. "Investigation on the induction stirring effect in a laboratory scale crucible with the variation of electrical supply parameters." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 1 (December 9, 2019): 177–84. http://dx.doi.org/10.1108/compel-06-2019-0231.

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Purpose This paper aims to study the possibility of controlling the electromagnetic stirrer (EMS) is fundamental in a continuous casting line to achieve the desired properties of homogeneity and mechanical strength in the solidified cast. Design/methodology/approach Coupled electromagnetic (EM) and fluid dynamic (FD) simulations allow to predict the mixing effect on molten metal, in terms of velocity amplitude and shape of the flow. This paper describes the numerical results of EMS effect within a cylindrical crucible, surrounded by a solenoidal inductor, filled with a low melting temperature alloy, i.e. GalInStan. Findings Induced forces and resulting velocity distribution of the flow of the liquid metal have been calculated depending on varying amplitude and frequency of the supplied current. As expected, at a given amplitude of the current supply, the velocity distribution shows a maximum at a certain frequency while the intensity of electrodynamic forces monotonically increase as the frequency increases Originality/value The paper deals with simply models and experiments applied to coupled EM and FD problem, to assess the applied methodology.

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Wang, Yi, and Xin Jian Ma. "Technology Research and Application of Dynamic Secondary Cooling of Continuous Casting." Advanced Materials Research 457-458 (January 2012): 142–45. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.142.

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Secondary cooling is one of the important techniques of continuous casting. A mathematical model for heat transfer during solidification in continuous casting was established in researching on influence of the solidifying process on slab quality. The dynamic secondary cooling system has been analyzed with consideration of the principles, nozzles arrangement method and mathematical model of solidification process. The model was applied on some continuous casting machines. It indicates that the dynamic cooling model is better than conventional ones.

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22

Uljanov, Vladimir A., and Viacheslav N. Guschin. "MATHEMATICAL AND PHYSICAL MODELING OF SECTIONS IN CONTINUOUS CASTING." Scholarly Notes of Komsomolsk-na-Amure State Technical University 1, no. 3 (September 30, 2010): 89–95. http://dx.doi.org/10.17084/2010.iii-1(3).13.

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Yang, Hyunjin, Surya P. Vanka, and Brian G. Thomas. "Mathematical Modeling of Multiphase Flow in Steel Continuous Casting." ISIJ International 59, no. 6 (June 15, 2019): 956–72. http://dx.doi.org/10.2355/isijinternational.isijint-2018-743.

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24

Liu, Qing, Liangzhou Wang, Liqiang Zhang, Liguo Cao, Xiuzhong Ding, Mei Liang, and Yongge Qi. "Mathematical model of heat transfer for bloom continuous casting." Journal of University of Science and Technology Beijing, Mineral, Metallurgy, Material 15, no. 1 (February 2008): 17–23. http://dx.doi.org/10.1016/s1005-8850(08)60004-3.

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25

Chen, Shou Dong, Jing Chao Chen, and Lian Hao Lv. "Simulation of Microstructures in Solidification of Continuous Casting Aluminum Alloy Thin Strip." Advanced Materials Research 399-401 (November 2011): 1750–54. http://dx.doi.org/10.4028/www.scientific.net/amr.399-401.1750.

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Based on the research on the solidification of twin-roll continuous casting aluminum alloy thin strip, the analytical model of heterogeneous nucleation, the growth kinetics of tip (KGT) of twin-roll continuous casting aluminum alloy thin strip solidification are established by means of the principle of metal solidification, meantime based on the cellular automaton, the emulational model of twin-roll continuous casting aluminum alloy thin strip solidification is established. The foundation for the emulational simulation of twin-roll continuous casting thin strip solidification structure is laid. Meanwhile has confirmed the mathematical simulation feasibility by using the solidification process of twin-roll continuous casting aluminum alloy Thin Strip.

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26

Netto, Pedro Q., Roberto P. Tavares, and Roderick I. L. Guthrie. "Mathematical Models for Near Net Shape Casting Processes." ISIJ International 36, Suppl (1996): S175—S178. http://dx.doi.org/10.2355/isijinternational.36.suppl_s175.

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27

D. Fachinotti, Vı́ctor, and Alberto Cardona. "Constitutive models of steel under continuous casting conditions." Journal of Materials Processing Technology 135, no. 1 (April 2003): 30–43. http://dx.doi.org/10.1016/s0924-0136(02)00955-x.

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28

Sholomitskii, Andrei, and Aleksey Sotnikov. "Position Control and Alignment of the CCM Equipment." Materials Science Forum 946 (February 2019): 644–49. http://dx.doi.org/10.4028/www.scientific.net/msf.946.644.

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The improved technology of position control and alignment of the continuous casting machine (CCM) equipment based on high-precision online geodetic measurements is considered. The mathematical model for the technological axis of the continuous casting machine, the technique of the rational alignment of the machine’s equipment and the software implementing this technique are proposed. The application experience of the developed technique for control and aligning the equipment of continuous casting machines of different types is shown. The data on the efficiency of the technique for continuous casting machine equipment and its impact on the quality of a continuously cast ingot are presented.

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29

He, Dong Feng, Ai Jun Xu, Gang Yu, and Nai Yuan Tian. "Dynamic Scheduling Method for Steelmaking-Continuous Casting." Applied Mechanics and Materials 44-47 (December 2010): 2162–67. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.2162.

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A method of dynamic scheduling of steelmaking-continuous casting is proposed, which includes static scheduling based on genetic algorithm and dynamic scheduling based on scheduling rules, mathematical model and complete rescheduling utilizing genetic algorithm. The simulation with eight hours’ production data in S steel plant showed that the method could draw quickly a high quality and performable dynamic scheduling plan according to random production disturbance. The average utilization rate of converter could reach 95% and the generation period of initial scheduling is less than 3 minutes. The max dynamic scheduling adjustment period did not exceed 1 minute.

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Zhang, Qi, La Dao Yang, and Heng Wen. "A Mathematical Modeling of Heat Transfer in Continuous Casting Slab." Applied Mechanics and Materials 44-47 (December 2010): 33–37. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.33.

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A two-dimensional (2-D) heat transfer and solidification model has been established and applied to calculate the temperature distribution and solid shell thickness profile of a continuous casting slab in a steel plant. A finite difference method was used for the numerical simulation. For thermal analysis, the 2-D slice unsteady-state heat conduction equation with enthalpy convention was used. Meanwhile, non-linear material properties of specific heat and thermal conductivity as well as phase changes during solidification were considered in the model. The temperature distribution and solid shell thickness calculated by mathematical model agree with those predicted by industrial and experimental measurements. The model could also be used to predict the optimum process parameters on casting speed, heat removal rates and the water distribution of secondary cooling zone.

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31

Choudhary, S. K., and D. Mazumdar. "Mathematical Modelling of Transport Phenomena in Continuous Casting of Steel." ISIJ International 34, no. 7 (1994): 584–92. http://dx.doi.org/10.2355/isijinternational.34.584.

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32

Mazumdar, Dipak, and Roderick I. L. Guthrie. "The Physical and Mathematical Modelling of Continuous Casting Tundish System." ISIJ International 39, no. 6 (1999): 524–47. http://dx.doi.org/10.2355/isijinternational.39.524.

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Falkus, Jan, and Katarzyna Miłkowska-Piszczek. "Developing continuous-casting-process control based on advanced mathematical modelling." Materiali in tehnologije 49, no. 6 (November 18, 2015): 903–12. http://dx.doi.org/10.17222/mit.2014.176.

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34

Tang, Lixin, Jiyin Liu, Aiying Rong, and Zihou Yang. "A mathematical programming model for scheduling steelmaking-continuous casting production." European Journal of Operational Research 120, no. 2 (January 2000): 423–35. http://dx.doi.org/10.1016/s0377-2217(99)00041-7.

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35

Tieu, A. K., and I. S. Kim. "Simulation of the continuous casting process by a mathematical model." International Journal of Mechanical Sciences 39, no. 2 (February 1997): 185–92. http://dx.doi.org/10.1016/0020-7403(96)00052-5.

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36

Ivanova, A. A. "Calculation of Phase-Change Boundary Position in Continuous Casting." Archives of Foundry Engineering 13, no. 4 (December 1, 2013): 57–62. http://dx.doi.org/10.2478/afe-2013-0082.

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Abstract The problem of determination of the phase-change boundary position at the mathematical modeling of continuous ingot temperature field is considered. The description of the heat transfer process takes into account the dependence of the thermal physical characteristics on the temperature, so that the mathematical model is based on the nonlinear partial differential equations. The boundary position between liquid and solid phase is given by the temperatures equality condition and the Stefan condition for the two-dimensional case. The new method of calculation of the phase-change boundary position is proposed. This method based on the finite-differences with using explicit schemes and on the iteration method of solving of non-linear system equations. The proposed method of calculation is many times faster than the real time. So that it amenable to be used for model predictive control of continuous semifinished product solidification.

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37

Wang, Yi, and Xin Jian Ma. "Optimal Design of Dynamic Secondary Cooling of Continuous Casting." Advanced Materials Research 472-475 (February 2012): 1907–10. http://dx.doi.org/10.4028/www.scientific.net/amr.472-475.1907.

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Numerical simulation of the secondary cooling is applied to the design of continuous casting. The mathematical model for solidification process of the strand under air-mist was established and calculated with the finite element model. The model is used to calculate the feasible operating range of the continuous casting machines. The dynamic secondary cooling system has been analyzed with consideration of the thermo mechanical principles and numerical model. The adequacy of the model has been confirmed with experimental results.

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38

Sinha, Asish Kumar, and Yogeshwar Sahai. "Mathematical Modeling of Inclusion Transport and Removal in Continuous Casting Tundishes." ISIJ International 33, no. 5 (1993): 556–66. http://dx.doi.org/10.2355/isijinternational.33.556.

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39

Choudhary, S. K., D. Mazumdar, and A. Ghosh. "Mathematical Modelling of Heat Transfer Phenomena in Continuous Casting of Steel." ISIJ International 33, no. 7 (1993): 764–74. http://dx.doi.org/10.2355/isijinternational.33.764.

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40

PAN, Hongwei, and Shusen CHENG. "Mathematical model of flow characteristic in multi-strand continuous casting tundishes." Acta Metallurgica Sinica (English Letters) 22, no. 4 (August 2009): 297–307. http://dx.doi.org/10.1016/s1006-7191(08)60102-7.

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41

Liu, Li Jun, Zhi Wen, Fu Yong Su, Rui Feng Dou, Xun Liang Liu, and Guo Feng Lou. "Research and Application of Integrated Scheduling Management System of Steelmaking-Casting-Rolling Based on Heat Process Model." Advanced Materials Research 760-762 (September 2013): 1017–22. http://dx.doi.org/10.4028/www.scientific.net/amr.760-762.1017.

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by studying steelmaking-casting-rolling production process, a mathematical model of integrated batch planning is established innovatively to minimize processing costs of whole line and computed by an intelligent optimization ant algorithm. On the premise of utilizing and coordinating capacity of steelmaking and rolling, the mathematical model of integrated batch planning can create integrated batch planning to combine steelmaking-casting-rolling closely according to each process constraint conditions and optimization objective. Furthermore, another mathematical model of job scheduling based on heat process model is proposed to not only guarantee the logistics balance between continuous casting and hot rolling, but also acquire the highest ratio of DHCR and lowest energy consumption.

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42

Bruch, Christian, and Peter Valentin. "Mathematical Modelling of Fluid Flow in a Continuous Casting Tundish with regard to Extraordinary Casting Conditions." steel research international 75, no. 10 (October 2004): 659–65. http://dx.doi.org/10.1002/srin.200405825.

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43

Louhenkilpi, Seppo, Jukka Laine, Jyrki Miettinen, and Risto Vesanen. "New Continuous Casting and Slab Tracking Simulators for Steel Industry." Materials Science Forum 762 (July 2013): 691–98. http://dx.doi.org/10.4028/www.scientific.net/msf.762.691.

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Research group of Metallurgy at Aalto University has been developing simulation models and tools for continuous casting since from the early 80s. The main models developed are the heat transfer model, DYN3D, and the solidification and microstructure model IDS. The models have been further developed and integrated to a continuous casting simulator and to a slab simulator. The continuous casting simulator calculates the important phenomena taking place in the strand during casting and the slab simulator calculates the phenomena taking place in the slabs when they are transferred from caster to reheating furnace. The numerical solution algorithms in the simulators are so fast that they can be used in on-line applications. The simulators have today many new options as hydrogen removal and quality prediction modules. In this paper, the simulators and their modules are presented.

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44

Thomas, B. G., and B. Ho. "Spread Sheet Model of Continuous Casting." Journal of Engineering for Industry 118, no. 1 (February 1, 1996): 37–44. http://dx.doi.org/10.1115/1.2803646.

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Spreadsheet programs, such as Microsoft Excel, Informix WINGZ, and Lotus 123, provide a framework for very fast and easy development of simple engineering models. The present paper describes a model of the continuous casting process that has been developed using a spreadsheet program, Microsoft Excel, running on a Macintosh II personal computer. The model consists of two-dimensional (2-D) steady-state finite-difference heat conduction calculations within a continuous casting mold coupled to a one-dimensional (1-D) transient solidification heat transfer model of the solidifying shell. The model structure and equations are described and the model predictions are compared with previous solutions. Practical examples using the model are discussed and sample results are provided. Spreadsheet programs running on personal computers are capable of relatively complex calculations that would require extensive effort using conventional programming languages.

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45

Liu, Guoliang, Haibiao Lu, Bin Li, Chenxi Ji, Jiangshan Zhang, Qing Liu, and Zuosheng Lei. "Influence of M-EMS on Fluid Flow and Initial Solidification in Slab Continuous Casting." Materials 14, no. 13 (July 1, 2021): 3681. http://dx.doi.org/10.3390/ma14133681.

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A mathematical model coupled with electromagnetic field has been developed to simulate the transient turbulence flow and initial solidification in a slab continuous casting mold under different electromagnetic stirring (EMS) currents and casting speeds. Through comparing the magnetic flux density, flow field with measured results, the reliability of the mathematical model is proved. The uniform index of solidified shell thickness has been introduced to judge the uniformity of the solidified shell. The results show that a horizonal recirculation flow has been generated when EMS is applied, and either accelerated or decelerated regions of flow field are formed in the liquid pool. Large EMS current and low casting speed may cause the plug flow near the mold narrow face and a suitable EMS current can benefit to the uniform growth of solidified shell. Meanwhile, an industrial test exhibits that EMS can weaken the level fluctuation and number density of inclusion. Overall, a rational EMS current range is gained, when the casting speed is 1.2 m/min, the rational EMS current is 500–600 A.

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Odinokov, V. I., A. I. Evstigneev, E. A. Dmitriev, S. Yu Aleksandrov, and G. I. Usanov. "Modeling of Molten Metal Flows in a Continuous-Casting Machine Mold at Free Rotation of the Floating Closed-Bottom Nozzle." Key Engineering Materials 910 (February 15, 2022): 24–29. http://dx.doi.org/10.4028/p-soh58m.

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Currently, mathematical modeling applying numerical methods is widely used in the study of metallurgical processes, including metal casting processes in continuous-casting machines. The authors developed a new technology and device for casting metal into a continuous-casting machine mold and metal mixing using the effect of a rotating closed-bottom submerged nozzle with eccentric holes. The theoretical study of processes of mold filling with molten metal was carried out applying a proven numerical method and a special software package. A calculation program was developed based on the numerical schemes and algorithms. The results of calculating metal casting into a rectangular mold are presented as an example. The calculation results are provided in the form of molten metal flow patterns in various sections of the mold.

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Assunção Jr, M. O., and M. Vynnycky. "MATHEMATICAL MODELLING OF MACROSEGREGATION IN INGOT CASTING." Revista de Engenharia Térmica 17, no. 2 (December 28, 2018): 74. http://dx.doi.org/10.5380/reterm.v17i2.64133.

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The occurrence of macrosegregation in alloys produced by ingot casting can adversely affect the quality of the final product. Macrosegregation can be described as a severe variation on the macroscopic scale of the chemical species that compose the alloy, and the ability of computational simulations to predict such defects remains far from perfect. Therefore, this research focuses on the development of a two-dimensional mathematical model that - through computational simulations - could be applied to study and predict the formation of macrosegregation in the ingot casting of binary alloys. Once accomplished, this work can establish the framework to new studies that will tackle more advanced problems, e.g., for actual ingot geometries, three-dimensional models and industrially-important ternary alloys.

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Li, Yang, Yan Jin, Hui Yu, Kang Yang, Fan Ai, Jun Wang, and Hong Bin Huang. "Numerical Calculation of Fluid Flow in a Continuous Casting Tundish." Advanced Materials Research 774-776 (September 2013): 316–20. http://dx.doi.org/10.4028/www.scientific.net/amr.774-776.316.

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Placement in the middle retaining wall package, aimed at controlling the flow of liquid steel forms, so that movement of a reasonable level remained stable, while reducing interference from turbulence and dead zones, molten steel in order to extend the average stay of removal in favor of inclusion to improve the cleanliness of molten steel. Keywords:Tundish; Retaining Wall; Flow field; Mathematical Modeling; Inclusion;Optimization setting

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Huang, Bang-fu, Nai-yuan Tian, Zhe Shi, and Zhi-wei Ma. "Steel ladle exchange models during steelmaking and continuous casting process." Journal of Iron and Steel Research International 24, no. 6 (June 2017): 617–24. http://dx.doi.org/10.1016/s1006-706x(17)30093-6.

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Mauder, Tomas, and Josef Stetina. "High Quality Steel Casting by Using Advanced Mathematical Methods." Metals 8, no. 12 (December 4, 2018): 1019. http://dx.doi.org/10.3390/met8121019.

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The main concept of this paper is to utilize advanced numerical modelling techniques with self-regulation algorithm in order to reach optimal casting conditions for real-time casting control. Fully 3-D macro-solidification model for the continuous casting (CC) process and an original fuzzy logic regulator are combined. The fuzzy logic (FL) regulator reacts on signals from two data inputs, the temperature field and the historical steel quality database. FL adjust the cooling intensity as a function of casting speed and pouring temperature. This approach was originally designed for the special high-quality high-additive steel grades such as higher strength grades, steel for acidic environments, steel for the offshore technology and so forth. However, mentioned approach can be also used for any arbitrary low-carbon steel grades. The usability and results of this approach are demonstrated for steel grade S355, were the real historical data from quality database contains approximately 2000 heats. The presented original solution together with the large steel quality databases can be used as an independent CC prediction control system.

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Journal articles on the topic 'Continuous casting Mathematical models'

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