18. - 20. 5. 2011, Brno, Czech Republic, EU
TESTING OF NUMERICAL MODEL SETTINGS FOR SIMULATION OF STEEL INGOT CASTING
AND SOLIDIFICATION
Markéta TKADLEČKOVÁ
a,b
, Karel MICHALEK a,b, Petr KLUS a,b, Karel GRYC a,b,
Vojtěch SIKORA a,b & Marek KOVÁČ c
a) VŠB – Technical University of Ostrava, Faculty of Metallurgy and Materials Engineering, Department of
Metallurgy, 17.listopadu 15, 708 33 Ostrava-Poruba, Czech Republic, [email protected]
b) VŠB – Technical University of Ostrava, Faculty of Metallurgy and Materials Engineering, RMTVC,
17.listopadu 15, 708 33 Ostrava-Poruba, Czech Republic, [email protected]
c) MECAS ESI s.r.o., Technická 2, 619 69 Brno, [email protected]
Abstract
The knowledge of existing casting parameters like casting speed, casting temperature of steel or the H/D
ingot ratio is the main precondition to minimize the well-known defects of steel ingots. Especially in
demanding metallurgical conditions, it is appropriate to apply the method of numerical modelling using some
of the available simulation software. Within the project named the Regional Materials Science and
Technology Centre, the technical background of the Department of Metallurgy and Department of Physical
Chemistry and Theory of Technological Processes at the Faculty of Metallurgy and Materials Engineering
(FMME) VSB - Technical University of Ostrava was extended by the workplace "Laboratory of Modelling of
Processes in the Liquid and Solid Phases”. The laboratory is equipped by new commercial simulation
software intended for 3D numerical simulation of molten steel flow during the filling of a metal mould and the
subsequent steel solidification with the prediction of macrosegregation and residual stress leading to cracks.
A correct parameter setting of calculation, from the preparation of geometry until the input values of heat
transfer coefficients, material properties or the definition of filling time, is a necessary condition for obtaining
relevant results from numerical modelling. The paper deals with testing and optimizing the conditions of
numerical model settings for simulation of steel ingot casting and solidification in an environment of newly
acquired commercial simulation software ProCAST. The conclusion summarizes the obtained knowledge
and listed the fields of research, which should contribute to deepening the long-term beneficial cooperation
between the commercial sphere and FMME.
Keywords: steel ingot, casting, solidification, ingot defects, numerical modelling
1.
INTRODUCTION
Despite the ever-increasing volume of steel continuous casting, production of steel ingots for forgings and
machine components is irreplaceable. Steel casting into the ingots allows even for the production of
oversized components weighing up to several hundred tons. The main precondition of the competitiveness of
any steel plant, not only in Europe, is production of a consistently high quality. However, despite significant
advances in technology of production of steel ingots, we can observe the defects in the final forgings that
may be caused due to the non-uniform cast macrostructure of an ingot as well as the macrostructure, which
is the result of plastic deformation during the subsequent process of the forming.
The solution to material weaknesses of forgings, or the final machine components, consists from a complex
optimization of the steel casting process as well as of subsequent heat treatment up to the actual process of
forming. One of the ways to monitor and optimize the production steps from the casting up to the process of
forming is the use of methods of numerical modelling. Within the framework of the "Regional Materials
Science and Technology Centre" (RMSTC) project in whose solution the Department of Metallurgy is
involved, the team managed to obtain commercial and teaching licenses of the program of excellence
designed primarily for a 3D, fully dimensional numerical calculation and simulation of steel melt flow
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dynamics during the filling of a cast iron mould and during the subsequent solidification of steel with the
possibility of the prediction of ingot defects, as well as the residual stresses leading to cracks and rupture.
The paper deals with the principle of numerical modelling in the purchased program, the characteristics of
individual software modules, which enable the complex study of material behaviour from the casting up to
heat treatment before the actual process of forming.
2.
PRINCIPLE OF NUMERICAL SIMULATION
Generally, the numerical solution of each task is divided into three stages: 1.Pre-processing: includes the
geometry modelling and the computational grid generation process, and definition of calculation.
2. Processing: involves the computation in the solver. 3. Post-processing: focuses on evaluation of the results.
2.1
Geometry modelling and computational grid generation
The geometry creation and computational grid generation anticipates the solution of numerical simulation of
steel casting and solidification. For testing purposes of the new software, the model of 1.9-ton steel ingot,
cast through the bottom, was used. The ingot geometry shown in Fig. 1a was created in CAD software. The
height of the ingot without the hot top was 1,450 mm; a mean diameter of the ingot reached 480 mm.
The CAD geometry of an ingot was then
loaded in the module of generation of the
computational grid of the simulation software,
and subjected to a topology analysis.
Topology is a field of mathematics concerned
with examining the properties of geometric
shapes, which are maintained in reciprocally
unique double-sided continuous images. The
individual components of the geometry of the
cast system are loaded into the preprocessor of grid generation gradually.
Before the loading of the next geometry
element, it is necessary for the previous
components to stay aligned and connected
Fig. 1. (a) 3D Geometry of casting system and ingot
(b) Cross-section through volume grid of the ingot
with only one surface. The contact of two
parts through one surface is necessary for a correct calculation of heat transfer.
After an inspectio of the loaded machine components, first the surface and then the volume grid of finite
elements were created. The volume grid was formed by 463,124 tetrahedrons. The cut through the grid is
shown in Fig.1b. Tools of the grid modelu enable its densification in an arbitrarily chosen point of the
geometry, the correction of the size and shape of a computing cell, and other useful operations. The
balanced distribution of computing sells throughout the computational volemu of the whole calculated system
and their refinement proportionally compared to the volume in small part sis a prerequisite for obtaining the
relevant results of the calculation.
2.2
Entering the calculation conditions
The completed geometrical grid is saved in *. mesh format and loaded in the solver module. There is a need
to define the material properties of individual parts of the cast system, the heat transfers at the interface of
individual geometric elements and boundary conditions, such as temperature, steel casting speed or the
conditions of heat transfer. The simulation of steel ingot casting and solidification was carried out for tool
steel. Type of steel grade was selected from the extensive material database of cast materials, metal and
sand moulds, filters and exothermic linings, which is part of the basic module of the program. The database
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is fully accessible to the end user, who may edit the data on the basis of validation. The current configuration
of the purchased software also includes a unique thermodynamic database, which allows the user to
calculate thermodynamic parameters according to the definition of the chemical composition of any new
material or to monitor changes in thermo-physical data during the changes in chemical composition [1].
In connection with entering the required data, it is appropriate to mention the fact that within the framework of
the RMSTC project the high-temperature device for direct measurement of thermo-physical properties,
especially the solidus and liquidus temperatures of steel and ferro-alloy samples (if necessary oxide
mixtures) using the thermal analysis within the working temperature range from ambient temperature to
2000 ° C at a controlled mode of heating and cooling was purchased, too. The device is also designed to
measure temperatures and other thermal phase transitions, specific heat and mass changes in the sample.
Output of the experimental measurements of thermodynamic parameters for a specific steel grade may be
used to refine the molten material parameters of numerical model, and thus the final result of numerical
calculation [2, 3]. The boundary conditions may not be represented only by constant quantities, but they can
reach the values defined by the function, table, etc. The most important boundary conditions for the
calculation of filling and solidification of steel ingots with the predictions of size of volume defects include the
temperature of cast melt, casting speed and the definition of the heat transfer method through the mould
wall. To describe the appropriate temperature distribution on the mould, most authors [4, 5] use for individual
interface (e.g., mould wall-ingot body, mould mat-ingot, etc.) the different coefficients of heat transfer.
Depending on the materials that are in contact, they range from 100 to 1000 W.m-2.K-1. The calculations
must include the influence of heat loss through walls of mould and through the hot top, and also the thermal
effect of exothermic and insulating powders. The calculation of the size of the central shrinkage, or the
central porosity is also influenced by the calculation of the formation of the air gap between the mould wall
and ingot body during the solidification and cooling due to the shrinkage [6]. This software, due to its special
module, automatically calculates with the modification of the heat transfer coefficient on the ingot / mould
interface as soon as the air gap begins to form, which is given by equations [2]:
h
1
1
; Rgap 
1
k
 Rgap
 hrad
gap
h0
(1)
where k is the air conductivity, gap is the width of air gap and the hrad is the radiation equivalent coefficient of
heat transfer. The calculation for the filling and solidification of steel ingots is made by the above-mentioned
method of finite elements. A continuous flow-thermal-mechanical model solves the complete Navier-Stokes
equations of the flow of molten metal, if required, including the influence of spontaneous convection.
Commonly, a k-epsilon model is used to calculate the turbulent flow. In the phase of filling and solidification,
the distribution of the temperature and velocity fields, pressure ratios during filling, the trace of metal
particles, vector fields, the proportion of blanks filling, the time-variable percentage of the solid fraction during
the flow, the trapped air in the mould cavity, and erosion of the mould, solidification time, heat flux, the local
cooling rate, prediction of macro- and micro- porosity and / or loose structure are analysed. To predict the
porosity, well-known Niyama criterion and DAS criterion (distance calculation of secondary dendrite axes Dendrite Arm Spacing) is used. The software also allows the calculation of thermal stress of metal moulds
using cycling analysis. This phase considers the full cycle with emphasis on filling, solidification and cooling
of ingot, its stripping and mould re-filling with liquid metal. The calculation of filling and solidification of steel
can also be supplemented with the calculation of residual stresses, plastic deformations and total ingot
deformation, further with the prediction of initiation of cracks and rupture in the ingot. The calculation predicts
the thermal and mechanical contact, deformations and dimensional changes of ingot and mould, the stress
in ingot and mould (tension, pressure), residual stresses, initiation of cracks and ruptures, the life of mould or
the initiation of air gaps (separation of the body of ingot from mould wall). Special module allows using multiprocessor computing stations, and therefore reducing the computational time required for each simulation.
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2.3
Post-processing
An integral and very significant phase of numerical modelling is the processing and the correct interpretation
of results. Both graphic and data results can be obtained through numerical simulation. The use of
animation, which is the projection of individual profiles as a continuous process of change from baseline to
final value over time is an effective means of illustration of the temperature, pressure, flow character profiles,
etc. The program allows automatic generation of PowerPoint presentations, export of videos and images, as
well as exports of computational grid deformations resulting from stress analyses. The user can also save
the individual steps of the evaluation that can be subsequently used for further study, which minimizes the
time required to evaluate the simulation results. The advantage is that after the analyses are performed, the
temperature, velocity, or heat flow curves, etc. can be "pulled" from any computing node.
3.
DISCUSSION OF RESULTS
The simulation results can be divided into the results obtained from the calculation of filling (Fig. 4, 5 and 6)
and results obtained by the calculation of solidification (Fig. 7, 8, 9). The results of mould filling rate from 50,
70 and 90% are shown in Fig. 3. The last image (d) shows the 90% mould filling including a suggestion of
the flow during the filling using the velocity vectors. The images below show that a number of small
recirculating vortices are produced in the volume of melt during filling.
Fig. 3. The velocity character scheme during the mould filling with a molten steel
and) 50% b) 70% c) 90% d) the flow image using velocity vectors
Fig. 4 shows the example of the temperature field after full ingot filling, including the hot top. It is obvious that
near the bottom of the mould the decrease in the temperature between the range of the solidus and liquidus
temperatures already started occurring. The more rapid decline in the steel melt temperature near the
bottom of the mould is probably caused due to heat dissipation, or heat capacity of the mould pad, which is
evident from Fig. 5. For the development of solid fraction at the time of the full filling of the ingot see Fig.5, in
which the creation of a thin solid layer in the lower part can be also viewed. The calculations also include the
recorded total heat flux between the mould wall and the ingot body (Fig. 6).
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Fig. 4. Division of
temperatures after ingot
casting
Fig. 5. Ratio of solid fraction at the moment
of full filling and the method of ingot
solidification from the mould wall at the time
of full filling of the ingot
Fig. 6. Total heat flux between
mould and ingot in approx.70%
filling: a) incl. the mould; b) ingot
surface after mould opening
The temperature change of steel during the solidification is shown in Fig. 7. The temperature fields suggest
that during the solidification the enclosure of the thermal node in the central area of ingot body occurs. It
appears that in this critical area micro- and possibly macro- porosity will arise due to prevention of the molten
steel filling from the hot top of the ingot. Closing of the liquid core in the volume of the ingot body was
confirmed by displaying the solid fraction ratio - see Fig. 8. The origination of micro- and macro- porosity is
then captured in Fig. 9.
25%
50%
75%
Fig. 7. Change in the temperature of steel during solidification
100%
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4.
CONCLUSION
The first simulation results of casting and
solidification of steel in the environment of the
newly purchased simulation software within
the framework of the RMSTC project clearly
demonstrated the power of the numerical tool
in the design and optimization of processes
occurring during casting and solidification of
steel. With the numerical calculation, it is
possible to determine the distribution of
temperature, pressure and velocity fields in
the cast system, to predict the size of central
shrinkage, porosity, cavities etc. The
indisputable
advantage
of
numerical
simulation is a relatively easy change of the
Fig. 8. Solid fraction ratio - the Fig. 9. Image of the final
boundary conditions. To be able to transfer
enclosure of the liquid core in extent of the micro- and
the practicable results into a real operational
the volume of ingot body
macro- porosity in the
system, it is inter alia necessary to have the
volume of the ingot body
most accurate information about the physical
properties of substances involved in the production process. The RMSTC project research creates a
workplace which is able to carry out an analysis of the key physical properties of concrete metal and oxide
systems, to find their temperature and other required dependencies, and additionally to implement the
physical properties to the numerical and physical modelling system.
This paper was created in the project No. CZ.1.05/2.1.00/01.0040 "Regional Materials Science and
Technology Centre" within the frame of the operation programme "Research and Development for
Innovations" financed by the Structural Funds and from the state budget of the Czech Republic
This paper was created as a part of the grant project solution No. SP2011/44 under the financial
support of Ministry of Education.
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