MATHEMATICAL MODELING OF METAL FLOW IN CRYSTALLIZER AT ITS SUPPLY FROM SUBMERSIBLE NOZZLE WITH ECCENTRIC HOLES

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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Mathematical modeling of filling the CCM mold with liquid metal during its supply from a rotating submersible nozzle

Izvestiya Ferrous Metallurgy ◽

10.17073/0368-0797-2021-4-302-310 ◽

2021 ◽

Vol 64 (4) ◽

pp. 302-310

Author(s):

V. I. Odinokov ◽

A. I. Evstigneev ◽

E. A. Dmitriev ◽

S. Yu. Alexandrov ◽

G. I. Usanov

Keyword(s):

Mathematical Modeling ◽

Liquid Metal ◽

Steel Casting ◽

Theoretical Calculations ◽

Rectangular Cross Section ◽

New Technology ◽

Metal Flow ◽

Experimental Studies ◽

Equations Of Mathematical Physics ◽

Difference Form

Experimental studies of the flow of liquid metal in CCM mold are long, complex and labor consuming process. Therefore, mathematical modeling by numerical methods is increasingly used for this purpose. The article considers a new technology for liquid metal supply into a mold. The authors present original patented design of the device, consisting of direct-flow and rotating bottom nozzles. The main results of investigations of the melt flow in the mold are considered. The objects of research were hydrodynamic and heat flows of liquid metal at new process of steel casting into a CCM mold of rectangular section. The result is spatial mathematical model describing flows and temperatures of liquid metal in the mold. To simulate the processes occurring during metal flow in the mold, special software was designed. Theoretical calculations are based on fundamental equations of hydrodynamics, equations of mathematical physics (equation of heat conduction taking into account mass transfer) and proven numerical method. The area under study was divided into elements of finite dimensions; for each element, resulting system of equations was written in difference form. The results are fields of velocities and temperatures of metal flow in the mold volume. A calculation program was compiled based on developed numerical schemes and algorithms. An example of calculation of steel casting into a mold of rectangular cross-section, and flow diagrams of liquid metal along various sections of the mold are given. Vector flows of liquid metal in different sections of the mold are clearly presented at different angles of rotation of the deep-bottom nozzle. The authors have identified the areas of intense turbulence. Metal flows of the described technological process were compared with traditional metal supply through a fixed bottom nozzle.

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Mathematical Model of Thermal Physics of the Dual-Cycle Cooling System of the Tool for Pieces Nanostructuring Burnishing

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.770.449 ◽

2015 ◽

Vol 770 ◽

pp. 449-455 ◽

Cited By ~ 1

Author(s):

Viktor P. Kuznetsov ◽

Andrei S. Skorobogatov ◽

V.G. Gorgots

Keyword(s):

Mathematical Modeling ◽

Heat Transfer ◽

Mathematical Model ◽

Cooling System ◽

Heat Removal ◽

System Of Equations ◽

Thermal Physics ◽

Nanostructuring Burnishing ◽

Dual Cycle ◽

The Mathematical Model

The article considers the problems of the mathematical modeling of thermal physics of the tool for nanostructuring burnishing. Physical and equivalent heat diagram of the system are developed. On the basis of the equivalent heat transfer diagram, the equivalent circuit and the system of equations of the mathematical model are created. The dependence of the tool indenter tip temperature on cooling system thermal parameters is obtained. The comparison of efficiency of heat removal from the tool indenter when using the developed two-circuit cooling system and the system supplying lubricant cooling liquid through the lathe centre spindle, as well as when applying nanostructuring burnishing without cooling is carried out.

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EVALUATION OF RISKS EMERGENCIES BY MODELLING THE FUNCTIONAL STATUS OF THE OBJECTS

Visnyk of Taras Shevchenko National University of Kyiv Geology ◽

10.17721/1728-2713.83.13 ◽

2018 ◽

pp. 91-97

Author(s):

V. Zatserkovnyy ◽

M. Bogoslovskyi

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Decision Making ◽

Risk Analysis ◽

Information Technologies ◽

Economic Systems ◽

System Of Equations ◽

Complete State ◽

Physical And Mathematical Modeling ◽

Main Components

Here one can find the approach to develop a model of functional state of researched object for the assessment of the risks emergencies appearance. The analysis of the causes of appearance and development of natural and anthropogenic emergencies is conducted and the most indicative causes are defined. Emergency risk analysis is part of a system-wide approach to decision-making in the process of managing territories, procedures and practical measures to address the challenges of managing a security process. The basis of risk analysis is the physical and mathematical modeling of natural and socio-economic systems and processes occurring in them, which involves the interaction of the main components of the system with the environment in regular and extra-ordinary situations. Since dangerous phenomena (emergencies) occur in a certain area with specific coordinates, it is quite clear that geo-information systems (GIS) and geo-information technologies (GIS) are most appropriate for assessing the risk of emergencies. To describe the functioning of the monitoring object it is necessary to construct its mathematical model. The most complete state of the object of the study is characterized by its mathematical functional and statistical model (a system of equations that describes the dependence of the parameters of the monitoring object, its systems and subsystems on external and internal effects in the process of its functioning). Based on the analysis of this model, it becomes possible to formulate the main tasks that are solved by GIS in monitoring of natural or socio-economic systems, and synthesize the optimal structure of GIS.

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Experimental Investigation of Heat Transfer in Liquid Metal Flow in a Horizontal Tube in Longitudinal and Transverse Magnetic Fields under the Conditions of Nonuniform Heating around the Perimeter

Heat Transfer Research ◽

10.1615/heattransres.v35.i12.90 ◽

2004 ◽

Vol 35 (1-2) ◽

pp. 67-75

Author(s):

L. G. Genin ◽

V. G. Sviridov ◽

O. N. Ivanova ◽

V. G. Zhilin ◽

Yu. P. Ivochkin ◽

...

Keyword(s):

Heat Transfer ◽

Experimental Investigation ◽

Magnetic Fields ◽

Liquid Metal ◽

Metal Flow ◽

Horizontal Tube ◽

Transverse Magnetic ◽

Nonuniform Heating ◽

Liquid Metal Flow

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Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

SCIENCE & TECHNOLOGIES OIL AND OIL PRODUCTS PIPELINE TRANSPORTATION ◽

10.28999/2541-9595-2020-10-6-599-609 ◽

2020 ◽

Vol 10 (6) ◽

pp. 599-609

Author(s):

Valery А. Gruzdev ◽

◽

Georgy V. Mosolov ◽

Ekaterina A. Sabayda ◽

◽

...

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Roughness Coefficient ◽

Computational Domain ◽

Channel Deformations ◽

Geological Surveys ◽

Kuban River ◽

The Stability ◽

Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

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The effect of pressure on the compressibility of aluminum alloys

Automation. Modern Techologies ◽

10.36652/0869-4931-2020-74-3-102-107 ◽

2020 ◽

pp. 102-107

Keyword(s):

Mechanical Properties ◽

Mathematical Model ◽

Liquid Metal ◽

Control Systems ◽

Physical And Mechanical Properties ◽

Reliable Data ◽

Output Process ◽

Automated Control ◽

Input And Output ◽

Crystallization Under Pressure

To obtain reliable data on the properties of liquid metal and create automated control systems, the technological process of molding with crystallization under pressure is studied. A mathematical model of the input and output process parameters is developed. It is established that the compressibility of the melt can represent the main controlled parameter influencing on the physical-mechanical properties of the final products. The obtained castings using this technology are not inferior in their physical and mechanical properties to those produced by forging or stamping.

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