Vysoká škola báňská – Technical University of Ostrava Faculty of Metallurgy and Materials Engineering

Department of Metallurgy and Foundry

ADVANCED METHODS OF THE NUMERICAL SIMULATION OF METALLURGICAL PROCESSES

ADVANCED METHODS OF NUMERICAL SIMULATIONS OF METALLURGICAL PROCESSES Didactic Text

doc. Ing. Markéta Tkadlečková, Ph.D. prof. Ing. Karel Michalek, CSC.

doc. Ing. Karel Gryc, Ph.D. doc. Ing. Ladislav Socha, Ph.D.

Ostrava 2016

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Description: ADVANCED METHODS OF THE NUMERICAL SIMULATION OF METALLURGICAL PROCESSES Authors: Markéta Tkadlečková, Karel Michalek, Karel Gryc, Ladislav Socha Edition: first, 2016 Pages: 62 Academic materials for the Metallurgy Engineering study program at the Faculty of Metallurgy and Materials Engineering. Proofreading: none. Project designation: Operation Program of Education toward Competitive Strength Description: ModIn - Modular innovation of bachelor and subsequent master programs at The Faculty of Metallurgy and Materials Engineering of VŠB - Technical University of Ostrava Ref. No.: CZ.1.07/2.2.00/28.0304 Realisation: VŠB - Technical University of Ostrava © Markéta Tkadlečková, Karel Michalek, Karel Gryc, Ladislav Socha

© VŠB – Technical University of Ostrava

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STUDY GUIDE

Academic materials for the Modern Metallurgical Technologies study programme at the Faculty of Metallurgy and Materials Engineering.

1. Prerequisites

This subject builds on the curriculum intended for the Modelling and Visualization of Metallurgical Processes and deepens the theoretical knowledge and practical skills in the area of Numerical Modelling of Metallurgical Processes. Attention is drawn primarily to the study of flows in metallurgical flow reactors using numerical simulations in the environment of the ANSYS FLUENT solver and a study of steel solidification in the simulation environment of QuikCAST software.

The aim of the subject and the outputs from learning

A student will be able to characterize the significance and use of numerical modelling in technical practice

A student will be able to determine the type of task, determine the appropriate solver and to define the conditions of calculation

Skills gained:

A student will be able to modelling an 3D geometry, to create a computational mesh of finite volumes and to numerical modelling in the CFD program ANSYS FLUENT

A student will understand the foundations of the modelling of filling and the solidification of steel in the QuikCAST program, including generating the computational mesh method of finite differences

A student will be able to process independently and propose technology for steel metallurgy

Who is the subject designed for?

The subject is included in the Master study programme for the Modern Metallurgical Technologies, but it may be studied by any candidate from another field of study, if he/she meets the required prerequisites.

This learning material is divided into chapters that correspond to the logical division of the studied subject = the first three thematic blocks are dedicated to the modelling of flow in flow reactors, used in steel metallurgy, in particular using SW ANSYS FLUENT, another four thematic chapters are then dedicated to the modelling of metal systems solidification. The estimated time to study this chapter may significantly differ, and therefore the chapters are further divided into subsections.

Method of communication with teachers:

During the teaching you will be required:

1. to work out a semester project on the assigned subject: The project will include a literary analysis of the foreign contribution from the area of 3D modelling concerning metallurgical processes, and the issue of steel casting optimisation and the experimental model study of the selected process from the metallurgy steel industry. Within the range of

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5 standard pages (5x1800 characters), relevant pictures, charts, tables (in doc. format). This project will be reviewed by a lecturer within 14 days after its submission, and the results shall be sent to students by emails.

2. Completing the credit test - the results of the credit test will be announced to students within 14 days after the test.

Within the scope of subject it is possible to use the individual consultations with a teacher, always after a written agreement by email.

The teacher can be contacted at this address: marketa.tkadleckova@vsb.cz, by phone at +420 59 732 5183, or personally at office number G326 (after a preliminary agreed date).

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TABLE OF CONTENT/ THEMATIC BLOCKS

PREFACE

THEMATIC BLOCK 1: Modelling flow in flow metallurgical reactors – examples of the modelling of steel flow in the tundish, of steel flow in subentry nozzles, in the initial stages of the filling of the bottom casting into ingots. Identification of the nature of the flow. Steady and unsteady flow conditions. The modelling of turbulent flow.

THEMATIC BLOCK 2: Description of the simulated area - the geometry of symmetric and asymmetric objects. The selection of the density and type of computational mesh. Boundary Conditions - Flow Boundary Conditions (velocity inlet, pressure inlet, mass flow inlet, pressure outlet, outflow). Determination of the parameters of turbulence.

THEMATIC BLOCK 3: Definitions and modification of the material properties. Using the definition of physical properties such as a temperature-dependent function. Thermal analysis - the determination of the heat capacity of metallic systems. Determination of the viscosity of material.

THEMATIC BLOCK 4: Modelling of the solidification of metallic systems. The equation of heat conduction.

THEMATIC BLOCK 5: Microsegregation models. Macrosegregation models. Porosity prediction models. Niyam criterion.

THEMATIC BLOCK 6: Identification of the modelled area. The calculation and selection of heat transfer coefficients.

THEMATIC BLOCK 7: Definition of the boundary conditions of the simulation of solidification. Determination of the material properties of a modelled system - identification of phase change temperatures, enthalpy vs. heat capacity, the dependence of thermodynamic properties on temperature.

Preface

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PREFACE

The Department of Metallurgy and Foundry at the Faculty of Metallurgy and Material Engineering at Vysoká škola báňská - Technical University of Ostrava belongs among the key workplaces in the Czech Republic. This university department ensures the preparation of new bachelors, masters, and doctors in the field of steel production and processing, in the bachelors and following study programmes concerning the Modern metallurgical technology and the Foundry technology, and at a doctoral level for the Metallurgical technology study programme.

Since the 1980s, the Department members of metallurgy and foundry operations in the framework of scientific and research activities, as well as during their extensive applied research have been focusing also on the methods of metallurgical processes modelling. The aim of each model study is to optimize the technology of steel production. The foundations of metallurgical processes modelling at the Department of Metallurgy was introduced by prof. Ing. Karel Michalek, CSc., especially in the area of physical modelling focused on the flows of steel in metallurgic reactors. The modelling of metallurgical processes in the laboratory conditions is invaluable, as a verification e.g. of the nature of steel flow or steel crystallization belongs to the most demanding methods of examination in operating conditions. Very often some processes may be in direct operating practice even almost insoluble.

Thanks to the robust development of computational technology and the software availability of simulation programs it is possible to use them for solving the issues of metallurgy, and so-called numerical modelling, which can be illustrated by a series of publications and conferences purely dedicated to the modelling of metallurgical processes. For this purpose today there are available efficient CFD (Computational Fluid Dynamics) software systems, which are the programs designed to calculate fluid dynamics (or any running medium). There are also softwares which allow the calculation of the solidification point, not only for steel. However, the use of such software is dependent on the extension of knowledge from the field of flow processes, numerical methods, computing technology, or on physical-chemical material sciences.

There is a large number of simulation softwares on the market at the moment, and it is not always easy to select the most suitable one to verify and optimize the process. The result of numerical modelling is also highly dependent on the selected parameters of calculation from the determination of the modelled area, through the generation of a computational mesh, up to the very definition of a mathematical model, the selected type of flow or set thermodynamic conditions of materials, which often require interdisciplinary cooperation with other workplaces. In particular during the verification of thermodynamic properties in materials thermal analysis comes into play that allows you to obtain information on the thermal capacity or temperatures of phase steel transformation. Setting the coefficients of the heat transfer in the processes of simulating the solidification point requires e.g. direct operating temperature measurements using pyrometers or contactless measuring using thermovision cameras. An integral part of numerical modelling is also the way of interpreting the results achieved. Here plays its role the experts' experience on the relevant issues.

Preface

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The main objective of the subject matter of the Advanced Numerical Simulations of Metallurgical Processes is therefore particularly a study of findings from the theory and practice of numerical modelling of metallurgical processes, and the creative development of student skills by introducing practical exercises on numerical modelling in an environment of the CFD program ANSYS FLUENT and QuikCAST used in lectures.

The authors:

Thematic block 1

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Thematic block 1

Flow modelling in the flow of metallurgical reactors - examples of modelling flow in the tundish, in the area of submerge entry nozzles, a mould, in the initial stages of filling during the bottom casting of steel into ingots. Character identification of steel flow. Stationary and non-stationary flow conditions. The modelling of turbulent flow.

Time for study: individual

Objective After studying this section you will be able to:

define the production of steel

describe the partial phases of steel production, identify and verify the metallurgical processes

identify the steel flow

Lecture

The process of steel production has recorded significant progress, particularly in the area of energy consumption and the quality of steel produced. Modern steel production usually involves phases which can be divided into the primary metallurgy of steel, the secondary metallurgy of steel, and the casting of steel.

Primary metallurgy is used to produce "raw" steel which is subsequently treated on various devices of secondary metallurgy before being cast. The main objective of primary metallurgy is the melting of a burden, the oxidation of accompanying elements such as silicon and manganese, decarbonisation, then dephosphoration and to a certain extent desulphurization. The finishing operation of the steel production is then carried out on secondary metallurgy equipment, whose aim is to further reduce the presence of undesirable elements, such as sulphur, oxygen, nitrogen, hydrogen, the modification of inclusions, the chemical composition modification of steel by alloying, thermal and chemical homogenization, and last but not least heating it up to reach the tapping temperature, which must ensure the continuous casting of steel.

Currently primary metallurgy is represented by two dominating technologies. Steel is produced either by the processing of liquid raw iron and steel scrap in an oxygen converter (BOF) or by processing only the steel scrap in electric arc furnaces (EAF). Steel from the primary aggregates is then cast into a ladle (L), which is typically moved by cranes or on wagons towards secondary metallurgy devices. Once the steel achieves the desired chemical composition and tapping temperature, it is cast either on a continuous steel casting () machine (CCM) or in a traditional way into ingots (I).

Thematic block 1

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The continuous casting of steel

Steel processed using the procedures of secondary metallurgy is further cast. With the continuous casting of steel the ladle is placed on the rotated casting stand of a casting machine. Thence the steel is cast through the shrouding tube into the tundish. Then the steel is taken through the submerge entry nozzle to the oscillating moulds (primary cooling zone), where the "controlled" solidification of steel is ensured. Under a mould there is a system of guiding and supportive rollers (secondary cooling zone) including refrigerating nozzles, which ensure the drawing, transforming and cooling the casting current of steel. The layout of ladles, the tundish and mould of five-strand machine for the continuous casting of steel is illustrated in Fig. 1.

Fig. 1 Diagram showing the foundry ladle, tundish, and moulds of five-lane equipment for the continuous casting of steel [1]

Tundish is one of the most important technology nodes of a continuous steel casting machine. It primarily ensures [1, 2]:

the liquid alloy is divided during the casting into individual casting strands, it regulates the steel mass flow into moulds, it reduces ferrostatic pressure of the liquid steel, it homogenizes temperature of the melt, it helps in the separation of inclusions, it provides a supply of steel in sequential casting during the exchange of ladles, it eliminates the turbulence of from ladle etc.

LADLE

TUNDISH

MOULDS

Thematic block 1

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From the tundish the steel is cast with an submerge entry nozzle into moulds. Entry nozzles protect a steel before so-called secondary oxidation (also reoxidation) because with this nozzle they reach into the liquid steel in a mould. Often by the flow through the nozzle the steel strand is protected also with the blasting of an inert gas (argon).

An important role in the continuous casting of steel is also played by mouldss that determine the final shape of a blank. Moulds of the continuous casting machine consist of a steel casing and a copper liner, which thanks to its high heat conductivity ensures a fast heat losses and the emergence of the shell of the continuously cast steel blank. At the point of steel solidification between the inner wall of a mould and the shell of a continuously cast blank an gas gap appears, which prevents the intense cooling of the blank. For this reason the mould is usually slightly tapered in its lower part. The usual reduction represents 1% per meter of a mould length (representing in a blank of quadrate 100 x 100 mm tapering of 1 mm per 1 meter of a mould length). Drawing of the blank is ensured thanks to the oscillation of a mould and adequate lubrication using casting powders, which among other things also protect the surface of the steel in a mould against secondary oxidation. Today a greater extent of the hydraulic ensuring of oscillation is promoted, which has several advantages, such as the size accuracy of the blank, a reduction of surface defects, and less friction force between a mould and a blank [3].

Despite the systematic improvement of continuous steel casting technologies we can record incidences of various defects in continuously cast blanks. The most common include so-called oscillation wrinkles, centre porosity, macrosegregation elements, and the occurrence of surface cracks. The defects are resulting from improperly set casting conditions (casting speed vs. casting temperature), the method of the heat losses, the type of casting powder used, the oscillation speed of a mould or the cooling method in the so-called secondary cooling zone.

Casting of steel into ingots The second method is the casting of steel into ingots. The manufacture of steel

ingots intended for forgings and machine components is irreplaceable, despite the increasing volume of steel production done by continuous casting [4, 5, and 6]. Especially in today's competitive environment, it is necessary to offer something special. That is why the ingot method is used to cast good quality steels and ingots of high weight and volume.

Currently in the Czech Republic the casting and production of steel ingots is done in the steelworks VÍTKOVICE HEAVY MACHINERY a.s., Pilsen Steel a.s., ŽĎAS a.s., and complementarily in TŘINECKÉ ŽELEZÁRNY, a.s. (the main preferred technology in TŘINECKÉ ŽELEZÁRNY is the continuous casting of steel). The first two mentioned companies focus, among other things, also on the production of heavy forged ingots designed especially for demanding machine components used in the power industry. It is most likely that these ingots will require excellent internal quality. However, despite the considerable progress in the field of technologies for the production of steel ingots, we can find defects on final forgings which may result from the inconsistent casting macrostructure of an ingot and a macrostructure, resulting from plastic deformation during subsequent forming processes.

Thematic block 1

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A scheme of the lay-out for bottom casting of steel ingot is shown in Fig. 2. In the following Fig. 3 there are the various components of a casting system [7, 8]. In Fig. 4 there is the view of the resulting semi-finished steel cast into a mould, ingot [9].

Fig. 2 Scheme of the casting system of steel ingot [7]

Fig. 3 View of a casting assembly in the cross-section and a description of individual components [8]

Fig. 4 A heavy forged ingot produced in a steelworks

in Sheffield in Great Britain [9]

As a result of changes in the volume of metal during the solidification mainly in the top

and central part of ingot porosities and precipitations occur. Thanks to the contraction of metal during solidification a gap between the body of an ingot and the mould wall appears. The tensions in the body of an ingot can initiate the emergence of cracks. In these cracks, which were filled with molten material enriched with non-metallic inclusions and elements with a tendency to segregate, then the so-called "V segregations" form. In an ingot from

Thematic block 1

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deoxidized steel we can encounter other types of exudations, mostly with segregations of the "A" type, or central segregation [10]. A cut of a typical macrostructure profile of a steel forging ingot is shown in Fig. 5 [10].

Fig. 5 Typical cross-section of a heavy forging ingot macrostructure profile by [10]

The methods of metallurgical process verification

It is obvious that steel production represents a complex process which is accompanied by a series of physical-chemical processes from melting, through the multiphase flow of steel and chemical reactions (processes taking place between the slag, metal and an inert gas) after solidification. A frequent problem in steel production is the setting the correct conditions e.g. in blowing argon for the steel processing in a ladle, the vacuum degassing of steel, optimising the nature of flow in individual reactors (ladle, tundish, nozzles), or the conditions for casting and the solidification of steel. Understanding these mechanisms requires knowledge on the technology of steel production, metallurgical thermodynamics, and kinetics. The other two mutually dependent requirements, which help to understand the production of steel, are experimental measurements and the modelling of processes. Especially in demanding metallurgical conditions, where it is very difficult to obtain information on how the steel flows in the metallurgical plants, or on the solidification point and the macrostructure of solidified metal, the method of numerical modelling plays an irreplaceable role.

Thematic block 1

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The numerical modelling of steel flow in flow metallurgical reactors. The identification of flow character. Stationary and non-stationary flow conditions. The modelling of turbulent flow.

The numerical modelling of many physical transport phenomena in fluids, i.e. the transport of mass, the moment (of momentum), heat, components etc. is closely linked to modelling a certain form of movement using mathematical methods. The condition for the compilation of a model is knowledge of an internal system structure, i.e. knowledge of the natural relations in the processes involved and the device designs, in which the processes take place. When drawing up an analytical mathematical model it is necessary to define individual elemental processes in the system, and describe them mathematically, mostly in the form of a differential equations system, supplemented by the equations of an empirical nature [1, 11, 12, and 13].

It is known that the amount of fluid in a flow reactor can be divided into three parts [1, 11, and 12]: a mixed volume, a volume with the "piston" flow, and a dead volume. The mixed volume closely is associated in particular with the gate part in which the kinetic energy of the entering strand provides an intensive agitation of liquid. This mixed volume is followed by the flow area of the so-called piston flow. A characteristic feature of piston flow is the even flow in a bath, in which no element of melt jumps the queue of another element. In reactors these are also areas in which the fluid flows very slowly. These areas represent the so-called dead volume, which is defined as an area in which the molten material spends more time than twice the average retention time.

From the flow classification point of view the area of a mixed volume can be assumed to have a turbulent character of flow, and the area of piston flow a laminar flow of steel. In relation to the time a constant-stationary flow is then defined, which is time independent, and the flow of non-stable - non-stationary, in which the variables changes over time.

The Navier - Stokes equation together with the continuity equation describes both modes of flow. In the case of non-stationary non-compressible isothermal flow they take the following form [21]:

The equation of continuity:

0

z

v

y

v

x

v zyx

(1)

The Navier-Stokes equations [21, 23]:

xxxxx

zx

yx

xx f

z

v

y

v

x

vv

x

p

z

vv

y

vv

x

vv

t

v

2

2

2

2

2

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(2)

y

yyyy

z

y

y

y

x

yf

z

v

y

v

x

vv

y

p

z

vv

y

vv

x

vv

t

v

2

2

2

2

2

21

(3)

zzzzz

zz

yz

xz f

z

v

y

v

x

vv

z

p

z

vv

y

vv

x

vv

t

v

2

2

2

2

2

21

(4)

Thematic block 1

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where

x,y,z - are coordinates, [1] vx, vy, vz - velocity components, [1] p - pressure, [Pa]

- density, [kg.m-3] f - components of external volume force, [1].

So we have four equations for the four unknowns, and as these equations are valid for laminar and turbulent flow, it seems that the problem of flow shape identification can be resolved using a mathematical expression. However, Navier-Stokes equations are difficult to solve (for its non-linearity) and for the majority of applications it is necessary to use a simplified numerical solution. Moreover, turbulent flow that is characterised by pressure and speed fluctuations even in the case of stationary flow, cannot be solved only based on Navier-Stokes equations, because the time and spatial scales of turbulent fluctuations is beyond the possibility of numerical methods. These problems can be avoided by introducing the so-called turbulent models. These are based on the time averaging of Navier-Stokes equations or on the elimination of negligible fluctuations, and they give us the equation for the medium speed and pressure (the fluctuations of turbulent flow are removed) [22].

Models of turbulence can be divided into several groups. It is clear that a number of turbulence models are available. The basic division of models is given by the flow nature, other subgroup is characterized by the method of mathematical model formation (direct method DNS - The Direct Numerical Simulation Method, the method of the time centring of turbulent flow quantities RANS - The Raynolds- Averaged Navier-Stokes Method, the method of large eddies LES - The Large Eddy Simulation Method, in which the small eddies of turbulent flow are filtered using subgrid models). In addition to the Reynolds voltage (RSM model - The Reynolds Stress Model) and the Bussinesq hypothesis (The Boussineq Approach) with the turbulent viscosity.

The selection of a turbulent model depends on the consideration and knowledge of the flow nature, an established practice for the given area of a solution, the required accuracy of the solution, the available computing capabilities, the amount of time needed for the simulation, and the possibilities and limits of the selected model [24, 25].

Thematic block 1

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Examples of flow modelling in a tundish, in the area of an ladle, a mould, in the initial stages of filling during the bottom casting of steel into ingots.

The issue of steel flow in a tundish At VSB-Technical University of Ostrava, the Department of Metallurgy and Foundry

from 2003 to 2005 a large GAČR project was implemented Reg. No 106/03/0266 "Prediction and minimising the transition zone areas in continuously cast blanks using modelling methods and project TTÚ-412/A8 " Research of steel flow in tundish ZPO no. 2 in TŽ, design and the verification of operating variants". One of steps in completing the projects was also numerical modelling to learn about the influence of boundary conditions in casting on the final range of mixed area for continuously casted steel blanks in conditions ZPO no. 2 operated at TŘINECKÉ ŽELEZÁRNY, a. s. Numerical modelling has been performed using the CFD FLUENT program.

The outputs of numerical modelling in the form of data file monitoring, and the concentration and temperature change at the time for each casting current at the outputs of a tundish for the relevant variants have been processed into the transitional dimensionless characteristics (see Fig. 6) of the dependence of the dimensionless concentration of time, and the changes of the dimensionless concentration of the length of blanks, on the basis of which it is possible to predict the extent of a mixed area. The concentration change in the shading tube is captured in jump shift curve at the time of entry into a tundish. The extent and location of the mixed area were evaluated for the 'strict' dimensionless specification 0.1 to 0.9. The beginning, the end, the length, and the weight of the individual casting currents of the given versions were read from the data files personally; recorded in the tables, and processed in the form of bar charts (see Fig. 7) [14].

Fig. 6 Transition characteristics of changes in the concentration for individual casting strands of a tundish for 8 tons of steel and the isothermal conditions of flow gained using numerical modelling techniques [14, 15]

Fig. 7 Range and the location of the mixed area under isothermal conditions in casting using all casting currents and 8 t weight of steel in a tundish [14, 15]

Thematic block 1

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The concentration change in time is captured by the current field of the FLUENT postprocessor for versions with 8 and 15 tonnes of steel in the tundish in Fig. 8 [15].

8 t

50 s

15 t

48 s

130 s 128 s

170 s 176 s

210 208 s

410 s 416 s

Fig. 8 Course changes of the concentration 0,2 m above the bottom of a tundish for a variant with 8 and 15 tonnes of steel in a tundish and in izothermal conditions of flow [15]

Numerical modelling of non-stationary steel flow through the subentry shroud with inner metering nozzle

The current experience of the researchers at the Department of Metallurgy and Foundry in the area of flow steel simulation in a tundish and on a ladle were also used in the physical and numerical modelling of non-stationary steel flow through the subentry shroud with inner metering nozzle in the contract research with TŘINECKÉ ŽELEZÁRNY, a.s. The numerical modelling of steel flow through the subentry shroud with inner metering nozzle was carried out using simulation package ANSYS WORKBENCH which has a 3D model maker DesignModeler, a generator of a computational mesh, and the CFD FLUENT program. The geometry of nozzles was modelled on a scale of 1:1. The 3D CAD geometry of the nozzle, including a detailed view of the area of the metering nozzle is shown in Fig. 9. The results were monitored for the influence of nozzle geometry on the flow rate through the nozzle. Attention was also paid to the nature of the speed and the pressure field inside the nozzle. The results have been completed with the distribution of shear stress on the nozzle walls, which makes it possible to forecast the risk of material erosion on the nozzle.

Thematic block 1

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3D CAD model of nozzle The character of steel flow in the

nozzle described using the vectors of speed in the cross-section of a nozzle - at the batcher place (a) and detail just below the batcher (b)

The distribution of the shear stress profile (risk of erosion) on the walls of the nozzle for individual averages of batchers

Fig. 9

Simulation of the steel flow in the initial stage of ingot mould filling in casting a steel ingot

The aim of simulation is mainly to capture the shape (behaviour) of free surface of the phase interface of steel and air. The simulation was performed in the software ANSYS Fluent 14.5.7. The solution includes only part of the filling from the inflow of meltage to the gating system, up to filling the bottom part of the ingot mould (Fig.10 and Fig. 11). Therefore, the model includes part of the inflow channel, the stool, and the lower section of the mould.

Fig.10 Side view of computing domain

Thematic block 1

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Fig. 11 The view on the charachter of the steel flow during the first period of the filling of the cast iron mould of steel of ingot casting

Questions for the subject studied

1. What is the difference between mathematical and numerical modelling techniques?

2. Do you know other simulation programs than the ANSYS Fluent for the verification of metallurgical processes?

Thematic block 2

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Thematic block 2 Description of the area - the geometry of symmetrical and asymmetrical objects. The choice of density and the type of computational mesh. Boundary conditions - Flow Boundary Conditions (velocity inlet, pressure inlet, mass flow inlet, pressure outlet, outflow). The determination of turbulence parameters.

Time for study: individual

Objective After studying this section you will be able to:

define the principle of numerical modelling

describe the process of numerical modelling in ANSYS Fluent

decide which type of computational mesh and boundary conditions for a specific task to use

Lecture

From the previous chapter it is clear that a significant disadvantage of numerical modelling is the complexity of model building and the design program, in particular for complex systems and actions. To solve the various processes of mass transfer, momentum, and energy there are today special and often universal software products available that contain the mathematical models of flow and solidification, and algorithms to resolve them. In general the numerical modelling of each task using commercial software is divided into three stages: 1) Pre-processing:

• definition of objectives • defining modelled area • creating geometry (in a CAD system) • preparation and creation of a computational mesh • specifications of the inputs, outputs and boundaries of modelled area • importing the calculation area in the CFD program • selection of a physical model • physical characteristic specification of the flowing medium • specifications of boundary conditions

2) Processing-Solving (phase of solutions): • proper numerical solutions

3) Post-processing (analytical phase): • the visualization of the calculation area and mesh • creating vector images • the visualization of scalar variables • creating graphs • qualitative numerical calculations • creating animations

Thematic block 2

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Programming systems intended in particular for the calculation of flow are known as Computational Fluid Dynamics programs (CFD), which can be interpreted as programs to calculate the fluid dynamics (or any flowing medium). The second group may be represented by the programming systems that enable not only the calculation of flow, but also the solidification of not only steel. With regard to the present wide range of programs we will now focus in detail on the programs available at VŠB - Technical University of Ostrava, namely the CFD program ANSYS FLUENT ( thematic block 2 to 3) and the program ProCAST/QuikCAST, which allow the calculation of flow dynamics and of steel solidification ( thematic block 4 to 7).

CFD program ANSYS FLUENT and its pre-processors

The CFD program ANSYS FLUENT is a part of software package ANSYS Academic Research CFD available from the university supercomputer centre at VSB - Technical University of Ostrava. This program package contains, apart from the CFD ANSYS FLUENT, also applications that allow for dealing with questions from the elastic solid mechanics, mechanics of fluids, aerodynamics, or chemical technology. The workspace of the software package is called the ANSYS WORKBENCH and it is used to run individual programs (creating geometry and meshes, CFD program FLUENT), and enables to organize project structures.

Design Modeler, hidden in this WORKBENCH under the name of Geometry, is a CAD system used for the 3D geometry modelling of solved areas. Apart from the design of the geometry itself it allows even loading geometry from other CAD systems, as well as their export.

To compile a calculation mesh the SW Meshing is available - combining the power of previous generators for computational mesh ICEM CFD, T-GRID, CFX-Mesh or Gambit. It allows you to generate meshes for different solving tools, such as FLUENT, CFX, POLYFLOW, and others, but also to export the readymade meshes into the desired format.

ANSYS FLUENT is a program that contains the physical models covering many options necessary for the modelling of flow, turbulence, heat transfer, and the reactions for industrial applications. ANSYS FLUENT uses the technologies of an unstructured mesh. The mesh can be created from the elements in the shapes of tetrahedrons and triangles in the case of 2D simulations; and in hexahedrons, tetrahedrons, polyhedrons, prism and pyramid cells for the 3D simulation. For the calculation it uses the finite volumes method.

The solving tools of ANSYS FLUENT run sturdily and effectively with all physical models and types of flows - stationary and non-stationary, incompressible, and also hypersonic. The ANSYS FLUENT program offers a unique range of turbulence models, such as

various versions of centred - models, k-omega models, and models with the Reynolds stress solution (RSM). It enables running parallelly and calculating almost in any platform (Windows, Linux, and Unix). The run is allowed on both the multicore and multiprocessor machines, or on computer clusters. Utilization of full 64-bit technology allows parallel calculation using the ANSYS FLUENT program on a mesh, with more than a billion computational cells. The advanced dynamic distribution of performance automatically redistributes the calculation to individual processors for achieving the highest efficiency [16, 17].

Thematic block 2

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The definition of a modelled area to model flows in reactors

Before dealing with the studied system using the numerical modelling in SW ANSYS FLUENT it is necessary to define the modelled area. When defining the geometry we shall take account of:

1) the desired objectives (What do I really want to find?),

2) the shape of studied system (symmetrical or asymmetrical area, details)

3) the complexity of a mathematical model (which partial differential equations will be addressed)

4) set-up options in the solving software

5) the performance of a computational system

The advantage of flow modelling in flow reactors using SW ANSYS FLUENT is to be able to limit the geometry only on the internal study system volume = this means that there is no need to model the geometry of flow reactor walls and the conditions on the wall (heat transfer, roughness, the entry of blown internal gas, etc.) are defined by values or features.

Examples of asymmetric geometry and symmetric flow reactors used in metallurgy

The asymmetrical five lane tundish with impact place and the partitions

Symmetrical ladle, in which one half of the geometry can be substituted with a condition of symmetry, and openings for a 3-point nozzle for blowing the internal gas defined in the software using a series of points - thus we can freely change the position of the "immersion" of that nozzle

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22

The geometry of a circular annulus in the nozzle estuary, which are used in the steel casting from ladles to inject argon and therefore to protect the casting srand against secondary oxidation.

The internal profile of an subentry shroud with inner metering nozzle used for casting from the tundish into a mould

Computational mesh

As it has already been mentioned in the subject of the Modelling and Visualization of Metallurgical Processes in numerical modelling the differential equations of flow and heat-transfer or substance redistribution, etc. are solved using the numerical methods. In the numerical solution of equations describing the flow and solidification of liquids there is some development. The oldest classical method is the finite differences method, for partial differential equations the finite volumes method can be used, or the finite elements method.

The principle of differential equation solutions lies in the geometry coverage of the solved areas by mesh (dividing the whole area into partial successive 2D cells in a two-dimensional area, or 3D cells in a three-dimensional area) and the search for discrete solutions in these sufficiently small sub-areas of the basic geometry using the so-called differential (algebraic) equations. The difference between the differential and the difference equation is defined as discretization error e.

The mesh applied on the geometry for the solved areas may be either a structured or unstructured. In the first case it concerns the creation of discrete non-overlapping elements, where the element boundaries are adjacent to the single boundary of the adjacent element, and this mesh cannot therefore be thickened. At present the unstructured mesh is starting to be supported, which is used in particular by the numerical method of finite elements. Both types of meshes can be developed in the Cartesian orthogonal system (the resultant region has the shape of a rectangle or cuboid) and in the curvilinear one. (Suitable for the area bounded by the curves, circles, etc.) [11].

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23

A distinction shall be made between:

surface meshing = a surface mesh made of rectangle or triangle elements on your desktop

An example of 2D elements mesh [18]

volume meshing = allows you to use hexahedral, tetrahedral, sphenoid and pyramid elements in different combinations.

The basic 3D elements [18]

An example of finished computational mesh ladle

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24

An example of a calculation mesh for an asymmetric four strands tundish

Setting of the boundary conditions

After setting up the mesh, it is necessary to define the boundary conditions of the area - input, output. Because in the previous step - in DesignModeler creation of the geometry- we have identified the body as a Fluid, it is not necessary in the Mesh to determine the wall elements- automatically outer surfaces of the body are considered to be walls (wall characteristics are then entered in the solver - ANSYS FLUENT software).

When modelling the turbulence flow using the standard k- model, it is necessary to specify any boundary conditions for both the kinetic turbulent energy and the speed of its dissipation (the conversion to heat). Normally, these parameters are dependent on the choice of the boundary conditions on the input. The flow on the input can be defined using [19]:

Speed (velocity inlet), which is determined by the scalar quantities; Pressure condition (pressure inlet), which is defined by the total pressure on the

input; Mass flow (mass flow inlet) in the case of compressible flow. In the case of the non-

compressible flow of liquids it is not necessary to define the intake of fluid using the mass flow rate, as the constant density of fluid and thus the input speed is assumed to have a stable mass flow rate.

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In addition to the boundary conditions on the intake into the flow reactor it is necessary to define the conditions at the outlet of the reactor correctly. Once again it is possible to define the flow at the outlet using [19]:

Pressure conditions (pressure outlet, pressure far-field), which is defined by the static pressure at the outlet;

The flow conditions (outflow), which provide for the free effluent of liquid from the reactor at the preservation of the mass equation. Such a condition is applied in the case when we do not know the speed and pressure at the outlet of a reactor. However, this condition is not suitable for the modelling of compressible liquids.

An example of boundary condition preparation at the border of the studied system in the workspace of Mesh pre-processor, which is a part of the software package ANSYS Academic Research Workbench.

1. STEP Indicate the area which represents an input. Click the right mouse button and select the Create Named Selection. Then define the entry condition - in our case the velocity-inlet.

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26

2. STEP Similarly proceed to define the output of the area. Once again choose the surface of the body that has the output function, click with the right button and from the menu select the Create Named Selection. Then define the output (Pressure-outlet, Outflow) depending on the selected condition on the input.

The resolution of input and output are in the software - ANSYS Fluent

Questions for the subject studied

1. What does pre-processing in the numerical modelling mean?

2. What do we evaluate in the post-processing stage?

3. What types of computational meshes do you know?

4. Is it possible to define the input marginal condition using another quantity than speed or temperature?

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Thematic block 3 The definition and modification of material properties. The use of physical properties definition as a temperature-dependent function. Thermal analysis - the determination of heat capacity for metal systems. The determination of material viscosity.

Time to study: individual

Objective After studying this section you will be able to:

Define the important material properties for numerical modelling of steel flow

Describe the principle of definition of material properties depending on the temperature or time.

Lecture

In the previous two thematic blocks we have learnt something about the conditions of the modelled area preparation and computational mesh of the studied system. Once we have finished these phases in the pre-processing, the finished computational mesh shall be imported into the environment of the ANSYS Fluent software, where it is necessary to:

define the type of flow

select the appropriate flow model

enter the operating conditions (the pressure and ambient temperature)

specify the values of boundary conditions (velocity/pressure/temperature at the inlet, the heat transfer/surface roughness/movement/symmetry of walls, conditions at the outlet from the modelled area, etc.)

determine material characteristics

The determination of some boundary, operating, or initial conditions for numerical simulation is not usually much of a problem. The definition of velocity and or the casting temperature of steel are determined according to the actual conditions of steel production.

However, the quality of the numerical simulation results is primarily determined by the quality of the thermodynamic parameters for steel and material reactor/forms, hence the used conditions of heat transfer among the different parts of the studied system, and the way of heat losses. And here we can find the first difficulties.

Thermodynamic properties, as the name suggests, are dependent on temperature (they change with temperature - they are dynamic). Among the most important thermodynamic properties of steels belong:

density,

thermal conductivity

thermal capacity or enthalpy,

kinematic viscosity

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28

in the event of changes in the state of the solidification curve (or the range of a two-phase zone between the temperature of liquid and solid).

A part of the simulation software is usually some material database that contains a whole series of materials including thermodynamic properties. Not always it contains our modelled material. In the case of the steel or material of walls in reactors/forms and the case of different chemical material composition, which is not a part of this database, it is necessary to define the new material. For this purpose we can use literary knowledge, or calculations in some available thermodynamic database or an experimental method, among which we include e.g. thermal analysis [20].

Material characteristics entered in the ANSYS Fluent using the Materials panel.

The temperature dependence of material characteristics can be defined in the ANSYS Fluent but also via the three possible types of polynomials [19]:

1) polynomial

2) Piecewise - linear:

where and is a number of segments

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29

3) Piecewise-polynomial:

where is defined characteristics.

If we use the definition of the temperature dependence characteristics on one of the above stated functions, the temperature must be defined in Kelvin to the best result. An example of a panel to define the characteristics by a polynomial is shown below [19]:

The density of steel in the liquid state can for example be obtained by calculation according to the equation (5) [21]:

WMnCCFeL %05,0%0035,0%069,0%128,0 (5)

where TFe 16000008,06980 (6)

The conductivity and density thermal capacity of steel in the solid form can be obtained according to the equations (7) and (8):

225 %83104,2%586,75%323,60555,079,45 MnTMnCTS (7) 2%130%103192,0955,487 CCTcS (8)

Thermal capacity may also be theoretically determined according to the well-known Neumann-Kopp rule [22].

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Questions for the subject studied

1. What does the "thermodynamic" or "thermophysical" feature of steel mean?

2. What possibilities for the identification of the material properties of steel do you know? Identify and describe at least three.

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Thematic block 4 Modelling processes of metal systems solidification. The equation of heat conduction.

Time to study: individual

Objective After studying this section you will be able to:

describe the methods for solving of processes related with the heat conductions..

define the equations of heat conduction during the solidification of steel ingot

Lecture

In the framework of the project "Regional Material Technological Research Centre (RMTVC), in which the Department of Metallurgy and Foundry is involved, they have managed to obtain a comprehensive commercial license of the ProCAST program, and the QuikCAST training program licence, intended for the numerical modelling of processes during the casting and solidification of not only steel.

The configuration of ProCAST software allows you to perform a comprehensive analysis of the filling, solidification, and stress states not only of the steel ingots, but also continuously cast blanks, with predictions of the defects and residual stresses. The comprehensive solution is provided through modules for the calculation of filling and solidification, and through the prediction module of macrosegregation, then the module for calculation of the residual stresses, and last but not least, for the continuous casting module.

The ProCAST program operates on the principle of finite elements method. The continuous current-heat-mechanical model addresses the complete Navier-Stokes equation of the molten metal flow, in the event of a request it includes the influence of spontaneous convection. For the calculation of turbulent flow the k-epsilon model is generally used. In the phase of calculating the filling and solidification we analyse the distribution of thermal and speed areas, the pressure relations during filling, the trace metal particles, the vector field, the ratio of blank filling, the time-variable percentage of the hardening phase during the flow, the closure of the air in the mould cavity or the erosion of the matrix, the time of solidification, heat flux, the local speed of cooling, the prediction of macro and micro porosity or sags. To predict porosity we use the familiar Niyam's criterion and DAS criterion (the distance calculation of the secondary dendrites axes - Dendrite Arm Spacing) [37, 38].

For the purposes of training the QuikCAST program is used, which operates on the principle of the finite difference method.

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The equation of heat conduction The numerical solutions of the metal system solidification are governed by the basic Fourier equation. In the three-dimensional system it has the shape of [23]:

z

t

zy

t

yx

t

x

tc

(9)

where c - is thermal capacity, [J.K-1]

- density, [kg.m-3]

- thermal conductivity, [W.m-1.K-1] t - temperature, [°C]

- time, [s] x, y, z - system coordinates. In the solidification process of the steel ingots, in addition to the basic Fourier equation for heat conduction, it is necessary to consider the calculation of the heat transfer:

between the surface of the insulating charge and surrounding areas, from the surface of the ingot into the gap between the ingot and the mould, from the ingot into the washer, from the ingot into the insulating plate, from the ingot at the isolation charge, from the outer surface of the mould to the surrounding area by the external surface of the insulating layer from the preheated metal into the solidified steel.

During the solidification of the metal alloy there is a change from the liquid phase to the solid phase taking place, in a certain range of liquid and solid temperatures. In the course of steel solidification the heat of solidification is released, which represents an internal heat source and is necessary to include in the solution of Fourier equation. In the case of steel the width depends on a two-stage band, on the shape of liquid and solid curves, and on the relevant phase diagram. In the equation of heat balance, the solidification boundary takes into account the time development of heat of solidification L. The differential equations contains the entity /SfL , which respects this physical quantity.

Then applies [23]:

x

t

x

fL

tc S

(10)

where fS is the proportion of the solidified phase during a given time step. This share is a function of temperature and it can be determined either theoretically from liquid and solid curves, or experimentally. With this advantage we include the mentioned ratio into the

value of measurement of the specific melting heat c. Overall heat c is given by the equation (11):

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33

C

tft

Lstfc (11)

where t is the solidification interval. If we are evaluating the solidification development in a view of enthalpy, then the equation has the following shape:

ttf

t

Lc

qtc

t

Hs

(12)

Questions for the subject studied

1. Do you remember from the Modelling and Visualization of Metallurgical Processes the difference between the solution with the finite differences method, the finite volumes method, and the finite elements method? Please describe the principles of solution for partial differential equations using these three numerical methods.

2. What is possible to solve (while verifying the steel production processes) using ProCAST or QuikCast softwares?

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34

Thematic block 5 Microsegregation models. Macrosegregation models. Porosity prediction models. Niyam criterion.

Time for study: individual

Objective After studying this section you will be able to:

describe the microsegregation and macrosegregation in steel

describe the theory of evolution of the porosity during solidification of steel

Lecture

Apart from the release of latent heat (the heat of solidification) it is necessary when calculating the volume defects of metal steel ingots to consider the redistribution of the solute. Most alloying elements show less solubility in the solid phase than in the liquid phase. For this reason the dissolved substances, which we generally call segregations, are redirected into the liquid phase, which leads to the continuous enrichment of the liquid phase, and the lower concentration of substances in the primary solid phase. This segregation is observed in a microstructural scale. The macrostructure typically consists of dendrite axes remote in the range between 10 and 100 micrometres. That is why this phenomenon is called microsegregation [24].

Consider now a small volume element, which contains several arms (axes) of dendrites and the liquid between them is the so-called mushy zone (the transitional area - soft). In the absence of any transport to or from the volume element the average content of the mixture remains unchained within the volume element, and at the level of nominal composition. However, if a liquid or solid phase with a concentration of solute different from the liquid or solid phase of internal volume flows into the volume element, the average compound of the mixture in the volume will differ from the nominal composition. If we follow the flow of a substance for long distances, then we are talking about the so-called macrosegregation. During the solidification (crystallisation) of large steel ingots we can find the positive or negative deviation of element content from the fluxing chemical analysis that are distributed at different heights and cross sections of the ingot. This chemical diversity negatively affects the consequent behaviour and characteristics of the ingot [10, 23, 24, 25] There are many causes of liquid flow and solid phase movement during the process of casting and the solidification in steel [24]:

The flow, which complements the participates during solidification and the contraction of liquid and solid phase during cooling;

Induced buoyant flow caused by temperature and the solvent gradient in the liquid phase. These buoyant and thermal forces may influence each other depending on the direction of the temperature gradient and on the change of liquid phase density;

The flow caused by capillary forces at the interphase liquid-gas interface; The residual flow from the filling;

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35

Flows induced by gas bubbles; The movement of small equiaxed crystals or solid fragments, incurred by

heterogeneous nucleation, or by separating from the walls of mould, or from the free surface or melted dendrites;

The solid phase can also float or become sediment, depending on its relative density in relation to the liquid phase.

The fundamental cause of segregation is therefore the movement of segregated liquid or solid phase during the process of solidification, as well as the fact that the molten material during its solidification rejects the solutes (because, as has already been mentioned above, most alloying elements have lower solubility in the solid phase than in the liquid phase), as can be seen from the partial equilibrium diagram Fig. 12 [26, 23, 24]. The enrichment of meltage often leads to the secondary reactions, e.g. the formation of metal carbides, sulphides, etc. Such a secondary reaction may significantly affect the scope of finite segregation. If the enriched molten material is

in contact with the solid phase for a longer period, a balance is achieved between them from the perspective of the solute according to the equation (12) in [26, 24]:

(12)

where CS and CL are the concentrations of a certain solute in the solid and liquid phases, K - equilibrium partition coefficient.

Diffusion and transfer of mass concentration of i-th constituent Ci per unit volume is given in (g.mol.cm-3) or in (g.cm-3). However for the dissolved substance in the dilute solution it is g.cm -

3 proportional to the mass % of the constituent w i. Therefore, in the solidification point C i refers mostly to W i [24, 26].

The equilibrium partition coefficient is valid for the coexistence of a crystal and meltage at a certain temperature, i.e. that the crystallization speed is equal to 0. Under these conditions the concentration of admixture ingredients in the meltage and crystal is given by the relevant binary graph, and their ratio is stable and determined by the value of a partition coefficient.

From a strictly thermodynamical point of view is k= as/aL, where as and aL are activities of the solute, in which the segregations are expected. The solutes in the diluted binary solution shall be governed by the Henry´s Law where as~Cs and al~Cl. Again, it applies that k is a temperature function and the lower the value of k, the greater the element inclination to segregation - see tab. 1 [26]. As it is clear from the Tab. 1, the stated equilibrium distribution

Fig. 12 Schematic of partial equilibrium graph for binary alloys [24]

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36

coefficients in certain elements may according to various authors, e.g. [24, 26], differ. This concerns in particular elements such as S, P, H, N, Ti, Al and Si, as their differences can achieve more than 100%.

Tab. 1 Binary equilibrium distribution coefficients of the most common elements in iron [23, 26]

Element Distribution coefficient according to [23]

Distribution coefficient according to [26]

Name Symbol Fe Fe

Oxygen O 0.02 0.02 0.02

Boron B 0.03 - -

Sulphur S 0.04,-0.05 0.02 0.02

Phosphorus P 0.15 0.13 0.06

Carbon C 0.20 (Fe) and 0.35 (Fe) 0.13 0.36

Hydrogen H 0.27 0.32 0.45

Nitrogen N 0.38 0.28 0.54

Zircon Zr 0.50 - -

Titanium Ti 0.60 0.14 0.07

Aluminium Al 0.60 0.92

Molybdenum Mo 0.70 0.80 0.60

Silicon Si 0.84 0.66 0.50

Manganese Mn 0.80,-0.90 0.84 0.95

Chromium Cr 0.97 0.95 0.85

Nickel Ni - 0.80 0.95

Vanadium V - 0.90 -

The greatest tendency for segregation are shown by S and O and then also C and P. For the balance of the solidification the following applies:

Cs.fs+CL.fL=C0 (13)

Where fs and fL determine the share of the solid and liquid phase, and C 0 is the total amount of the specific solute. However, in the case of steel it is necessary to take into account the interaction with other dissolved substances, because the equilibrium coefficient applies only under equilibrium conditions, which in the dendritical crystallization of steel are not met [24, 26]. Different types of macrosegregations on steel ingots are derived from the common mechanism of liquid alloy flow enriched with admixtures of the inter phase interface to the places, where heat-shrink and solidification take place. Such segregation can best be understood in the sense of the local solute redistribution equation (LSRE) derived by Flemings et al. [23, 24]:

(14)

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37

Where is the differential change of the meltage ratio in the volume element to the

differential change in the admixture concentration in the melted alloy of volume element (which corresponds to the differential temperature change),

- volume shrinkage factor, k - partition coefficient,

- the relative speed of the inter dendritical movement of meltage against the solid phase of a volume element,

- Hamilton operator, - the pace of izothermal progress in a volume element.

Fig. 13 shows the calculated segregation of phosphorus in δ-iron according to Flemings. The dashed line shows the concentration at the interface and the solid line shows the final composition. The difference is due to diffusion in the solid phase [26].

Fig. 13 Calculated segregation of phosphorus in delta iron as in Flemings in 1990 [26]

Fig. 14 The schematic flow of the liquid phase through a small volume inside the transition area. Blue rings represent cuts through the dendrite arm [24]

Equation (14) is based on a small volume element inside the transition area, as was

mentioned above and is shown in Fig. 14. The Flemings equation assumes that during the solidification point any solid phase does not enter into the element, nor is removed, an admixture enters or leaves the element only in the meltage which compensates for the contraction.

According to Sheil´s analysis [24] similarly diffusion inside the element is neglected, as well as the diffuse flow from the element, and it is expected to mix completely in the liquid phase of a volume element. Then the concentration of dissolved admixture in the liquid phase CL, which is according to the equilibrium phase diagram of temperature functions given by:

m

TTC mL

(15)

where T is the temperature of iron melting, Tm is the melting point of a pure ingredient, and m is the curve inclination of admixture liquid. If we include in the assumption the heat transfer from the flowing dissolved substances in the liquid phase into or out of a volume

Thematic block 5

38

element, and take into account the different densities of solid and liquid phases, then the final LSRE will be as follows:

T

n

L

S

L

S u

kC

f

dC

df

1

1

11 (16)

where fS is the volume of solid fraction, k the partition coefficient, un is the velocity flow of the liquid phase in the direction of the normal to the isotherm, vT is the speed of isotherms proceeding, and where

S

LS

(17)

where is the contraction during solidification, S and L is the density of the solid and liquid phase. In the case of one-dimensional solidification the speed of the liquid phase when compensating the contraction during solidification is given by

11 T

L

STshrinkn

u (18)

It is necessary to note that the direction of flow topping up the contraction takes place is in the opposite direction to the speed of the isotherm. In Fig. 15 the flow of the liquid phase through the transition area is shown schematically.

Fig. 15 Schematic diagram of liquid phase flow through the transition area during steel solidification [24]

From Fig. 15 it is seen that as long as the concentration of dissolved substances in the liquid phase along the isotherm is uniform, the flowing liquid phase from or into a volume element in the direction of an isotherm has the same concentration of solute as the liquid phase within the volume element. For this reason the flow parallel to a plan does not cause

macrosegregation in the transition area. Flow factor can be defined as:

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T

nu

11

(19)

then the equation (20) can be adjusted according to [24, 26]:

(20)

where CL is a concentration of a certain solute in the liquid phase, C0 the total amount of solute, f s the proportion of solid phase,

the factor flow k the equilibrium partition coefficient. This relationship is known as the Scheil equation. Ohnaka made changes to Scheil equations and incorporated into them the effects of mass flow for macrosegregation and proposed the following relationship:

/1

0 1/ K

SL efCCr (21)

where r is the coefficient of segregation in [26]. A much more realistic assumption is incomplete mixing in meltage. On the basis of the material balance for dissolved elements along the thickness interface dx parallel to the plane of interface there can be derived:

xCRxCDtC LLL /// 22 (22)

Where x´ is the distance from the solid phase/liquid phase interface, which itself is in motion. R is the linear speed, at which the interface moves (the linear velocity of solidification) and t is the time from the beginning of solidification. R is the time function, therefore the equation (22) requires to be solved using numerical methods. However Burton et al. resolved it analytically so that R is a constant. Enriched molten material based on the Burton equation may be described as follows:

1

0 1/

effK

SL fCC (23)

where:

meeeeff kRKKKK /exp1/ (24)

where is km is the coefficient of mass transmission. For the slow solidification the ratio R/k m <<1, for a strong mixing Keff≈Ke applies (Scheil equation). But if R/km>>1, Keff≈1 and Cl≈C0, then there are almost no segregations. This is the situation in very rapid solidification. However, Brody, Merton, and Flemings took into account the diffusion in solid dendrites and adjusted the Scheil equation as follows [16]:

1

0 1/1* K

eSeLeS eKfCKCKC (25)

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40

where: 2/4 dtD fS (26)

and where Ds is the diffusion coefficient of the solute in the solid phase, t f is the time of solidification, d distance of dendrites axes. The analysis is approximate and is only valid for small values of α. The segregation is also influenced by the dispersion of the dendritic structure. If the primary dendrites are defined as axially symmetrical ellipsoids, then their spacing can be expressed [27, 28]:

2/14/14/12/1

1 /3,4 GRkTDT mm (27)

where ∆Tm is the temperature difference between the liquid and solid phase, D is the diffusion coefficient of carbon, Г Gibbs-Thomson parameter, k the partition coefficient of carbon, R is the speed of solidification, and G is the temperature gradient. This Osvald's mechanism is mostly used for the theoretical analysis of the formation and the growth of secondary dendrites. On the basis of this mechanism Imagumbai gives the general relationship for the secondary unfolding of dendrites arms [27, 28]:

nn

m

nRkTRD

8/2

2/11

2 (28)

where the θ is a local time of solidification, which can be determined:

GRTm / (29)

The above stated relations show that among the dominant factors influencing the extent of dendrites arms, hence the extent of segregation (the distribution of admixtures in a solid phase and meltage), the ratio between the diffusion and changes in temperature during solidification (the speed of solidification) belong to ingot (for real ingots the natural and forced convection of meltage will have an effect on the value of the distribution coefficient) and the characteristics of a material. The speed of solidification depends on the dimensions and shape of the ingot, as well as on its chemical composition and casting temperature [27, 28]. Niyam criterion Using Niyam criterion we can predict the porosity of emerging at the end of solidification casting. It is the relationship of temperature gradient and the rate of the cooling [29, 30].

(30) N... Niyam criterion [K1/2 cm-1 s1/2] G … local temperature gradient [K cm-1) R... the rate of cooling [K s-1]

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If the calculated value of Niyam criterion (equation (30)) for the cast will be lower than the critical value, i.e. N ≤ Nkr, in a given point of the cast the likelihood of porosity, i.e. sags, is increased. The critical value of Niyam criterion according to [29] is independent from the size of the casting. Thanks to this we can use this criterion with a sufficient accuracy of results in the simulation programs [29, 30].

Questions for the subject studied

1. What is the difference between microsegregation and macrosegregation?

2. What characterises the equilibrium partition coefficient?

3. What microsegregation models do you know?

4. What is the Niyam criterion?

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42

Thematic block 6 Identification of the modelled area. Calculation and selection of the heat transfer coefficients.

Time for study: xx hours

Objective After studying this section you will be able to:

make a decision for construction of the computational mesh

describe the differences among the mesh of finite elements and of finite differences

processes the data from thermography measurement and implemented them to the setting of numerical model

Lecture

Identification of the modelled area

The start of the verification process for the casting and the solidification of steel is once again linked to the definition of a modelled area. In comparison with the definition of a modelled area on the flow reactors, where it is possible to restrict the analysis only to the internal volume of a studied system, it is usually necessary for the calculation of flow and the solidification of metal alloys to create a complete geometry of the casting system (if we do not know exactly the mathematical function that could describe the heat losses from the surface of the ingot/blank/casting):

In the case of steel ingot modelling it is a system of an ingot - matrix (head = hot top, mould, stool, gating system, insulation).

In the case of modelling continuously cast blanks you can define a whole radial/vertical geometry including a simple mould, or limit only to the blank and the heat losses on the whole length of a blank defined using custom functions.

Before the modelling it is also appropriate to consider whether or not to restrict the geometry only on its symmetrical part and thus simplify and speed up the whole calculation. Preparation of the computational mesh in ProCAST SW

The ProCAST program is equipped with the pre-processor Visual Mesh for the creation of a simple geometry and for the generation of a finite elements mesh (tetrahedrons).

Visual Mesh includes a 3D automatic generator for the surface and volume tetrahedron meshes, it ensures the link between the CAD interface and the formation of calculation meshes, and it allows you to perform operations on the assemblies and boolean. You can generate both continuous and discontinuous computational meshes. The generated meshes can be exported to other software that are built on the finite elements method. Thanks to the finite element method this software can be very precise and in particular describe very accurately the geometry shapes of ingots [31].

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43

The module tools of a mesh enable its densification in any chosen location of its geometry, to repair the size and shape of any computational cell, and other useful operations. The even distribution of computational cells throughout the entire volume of a calculated system and their refining in proportional to the volume of small parts is a prerequisite for obtaining the relevant calculation results.

When loading the geometry into the module of a mesh computational (Visual Mesh) in the simulation software ProCAST the topology is analysed.

Topology is a field of mathematics examining the properties of geometric shapes that are maintained in reciprocally definite mutually connected views. The individual components of casting system geometry are loaded to the mesh creation pre-processor gradually. Before loading the next geometry element it is necessary for the previous component to be aligned and linked by only one surface. Contact between the two components through one surface is required for the correct calculation of heat transfer. After checking the loaded bodies a first surface and then the specific volume mesh of finite elements is created [5].

Before generating a mesh, it is necessary to consider whether not to divide the

calculation at the stage of filling and the stage of solidification. This division of calculation allows a much more accurate assessment of results for each stage of ingot production. Usually rougher meshes are recommended in the calculations of filling, and finer mesh at the stage of solidification. The number of computational cells also affects not only the quality of the displayed results, but also the computational time.

In the calculation phase it is also necessary to take into account the significant

temperature gradient between the molten steel and the walls of a mould, especially in the early stages of cooling. To obtain more accurate results of the temperature changes in the course of the filling, it is advisable during mesh generation to create a layer of several centimetres between the mould and an ingot, which can ensure the possibility of identifying the forces of solidified steel fraction during the filling process. The volume mesh section for the calculation of the filling phase is displayed in Fig. 16. The violet volume mesh of ingot was formed using 50 mm cells, the ochre thin layer between the ingot body and the wall of mould was the mesh created by 30 mm cells.

The change of mesh during the solidification phase enables a better prediction of stress

states, the size of air gap between the body of ingot and the walls of a mould, or the scope of porosity. Concerning the accuracy of calculation it is possible to neglect in simulations eventually even the inflow system. That is why for making the calculation mesh more accurate for the calculation of solidification we can limit the geometry of casting configuration only to the washer, the mould, the casting head and insulation. The size of volume cells in the whole body of the ingot was 30 mm.

In Fig. 17 there is the difference in the size of a displayed defect - porosity - depending on the size of computational cells and the scale setting.

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44

mold ingot

Fine mesh Rough mesh

Fig. 16 Volume mesh for a) the calculation of the filling phase b) the calculation of the solidification

phase in a cross-section for a casting configuration of a 90 ton heavy steel ingot [32]

a)

b)

c)

Fig. 17 The character of porosity displayed in the original mesh a) using the same scale as the finer mesh b) in a more appropriate scale setting for a given type of coarser mesh c) the character of porosity using finer meshs throughout the whole volume of an ingot [32]

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On the contrary, considering in the calculation the macrosegregation, it is appropriate to restrict the calculation to only one type of mesh, and solve the entire filling process and solidification process as one. If we take into account the filling and solidification separately, as in the calculation of porosity, it is important to realize that during the casting between the contact of meltage and steel with some metal form a shell appears on the surface of casting. Because the subsequent calculation of solidification only the thermal arrays (not the concentration) are counted, the development of macrosegregation in this solidified fraction would be not calculated and it would appear as a zero.

The calculation time of macrosegregation is also greatly extended, because it is necessary in the course of the solidification to count not only the distribution of components depending on their solubility in their liquid and solid phases, but also with the incidence of natural meltage convection (or with the occurrence of an air gap between the ingot body and the wall of a mould, which was at the existing simulations a neglected sector).

The preparation of a computational mesh in the QuikCAST SW

The computational mesh generator is a part of the program. The geometry is however necessary to be prepared in one of the available external CAD systems and import it into the environment of QuikCAST in *.stl format. Each part of the foundry system is imported gradually and the automatic fusing of the surface mesh is carried out. After loading the entire geometry we proceed to the creation of volume mesh. Building the mesh in this program is done automatically after you enter the maximum and minimum sizes of the cells, and it is fully on the user what size he/she chooses with regard to the entire geometry of this model.

A comparison of the volume mesh for the casting assembly of 1.7-tonne ingot, created by the method of finite elements in the Visual Mesh and the method and the final differences in QuikCAST is illustrated in Fig. 18. The volume mesh of finite elements for the casting assembly was formed by 463,124 tetrahedrons. The volume mesh of final differences in the same casting assembly was then made up of cells shaped of rectangular hexahedrons, and their number scheme reached 957,790 which is twice the amount.

As it is clear from Fig. 18 the method of finite differences allows for a relatively simple calculation in the orthogonal system. On the other hand the differential mesh copies the complexity of rounded or chamfered shapes with difficulties, leading to the necessity of using a mesh with a greater density of nodes. So if we want to densify this mesh in a specific place, this densification takes place across the entire height/width of the casting assembly (an increase in the number of computational cells), which complicates the calculation because of inaccuracies in thermal boundary conditions, time, and demand on the processing unit.

After setting up the mesh it is possible in the postprocessor QuikCAST to display the so-called "volume correction factor' and in accordance with the scale from 0 - 100 % it can be seen how the individual cells of this mesh copy the original shape of casting system ( Fig. 19), or how the original shape is copied. The red colour corresponds to the cell fully describing the original shape and the conditions of calculation (i.e. from 100° %) [33].

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Fig. 18 The comparison of volume mesh for casting of a 1.7-tonne ingot created by the method of finite elements (left) and the method of finite differences (right) [33]

Fig. 19 The correction factor of finite differences volume mesh [33]

The determination of transfer conditions and the heat losses of modelled system

The quality of numerical simulation results depends not only on the used thermodynamic parameters of materials, but also on the conditions used for the heat transfer between the individual parts of a casting system, as well as on the definition of heat losses [34].

The methods of verification used for the thermodynamic quantities of steel or casting metal system will be described in the next chapter. We will now look at the issue of identifying coefficients for the heat transfer between the individual components of a studied system, the heat losses on a system surface, and the determination of ambient temperature. In the case of modelling of the flow and solidification of steel the heat of the molten metal is absorbed into the walls of flow reactors or moulded in three ways [23]:

1. by conduction in solid units, or in the case of thin immovable layers of liquids or gases; 2. by convection in moving liquids or gases, and loose materials; 3. by radiation i.e. by electromagnetic waves from one body to another by an interjacent

environment.

During the heat transfer between the solid body and the fluid (or gas) we are talking about

the transfer of heat. The quantity of heat (Q) that passes in time through the surface S of the substance with temperature t 1 into the wall of temperature t 2 (respectively which passes from the surface of a body into the surrounding area), can be expressed using the so-called Newton's relationship:

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47

SttQ 21 (35)

where is the coefficient of the heat transfers, [W.m -2.K -1 ] t1 – the temperature of the substance (or the surface temperature of the

body) [°C] t2 – the wall temperature (or ambient temperature), [°C] S – cooled area, [m2] Q – amount of heat, [J ]

– time, [s ]

Heat passing through the area determines the so-called heat flux [W.m-2]:

Sn

t

(36)

where is thermal conductivity, [W.m-1.K-1]

t

n

– temperature gradient,

S – area, [m2].

The heat flux depends on the thermal conductivity of bodies. The quantity of heat Q, which

passes through the area S in time , is known as the density of heat flow q:

S

Qq (37)

If the temperature of the individual body points changes in time, it is an unsettled heat transfer. In the theory of the non-stationary management of heat the Fourier equation for the heat transformation is often used.

Heat losses by radiation is described by the Stefan - Boltzmann law in the shape of [35]:

W =ε⋅σ T4 (38) where W is the intensity of radiation, [W⋅m-2] ε - emissivity, [1] σ - Stefan – Boltzmann constant, [W·m-2·K-4] T - thermodynamic temperature, [K].

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48

The definition of a mathematical flow model requires knowledge of the heat flux through the walls of flow reactors and the ambient temperature. In the case of a mathematical model definition for the flow and solidification of steel it is necessary to define both the ambient temperature and the heat flux through the walls, including the heat losses using radiation, and also the coefficients of the heat transfer between the individual components of a casting assembly.

The definition of heat transfer coefficients (HTC) between the individual components

of a casting assembly in modelling solidification is not so simple. In the literature there are usually constant values mentioned, ranging from 100 to 1,000 W.m -2.K -1. In fact, the value will vary depending on the temperature and time.

In determining the heat losses and the HTC it is therefore, in addition to data in the literature or theoretical calculations, appropriate to use some of the available experimental temperature measurements or thermal flow measurements. The results of experimental measurements can then be used either directly for the parameter settings of a mathematical model, or indirectly to compare the results of thermal fields with the numerical modelling results [34].

For the measurement of high temperatures, over 1,500°C, it is possible to use thermocouples. The lifetime of thermocouples and their long-term stability is often very low, so it is more suited to a one-time measurement. Much better at high temperatures is the use of proximity pyrometrical temperature measurements [36].

Both these methods can provide information on the temperature size in one particular point of a measured surface or object. In order to obtain an image on temperature distribution over the entire surface of measurement including the heat flux, it is beneficial to use thermovision cameras.

The results of thermovision measurement can be processed in a software that allows to display the thermal field distribution, profiles, histograms, and flow charts. It also offers the possibility of generating trends, the detection of hot or cold areas, etc. In Fig. 20 is the view of a desktop with the SW GORATEC Thermography Studio [37].

The temperature scale on the evaluated image indicates the range of measured temperatures. On the temperature scale (see Fig. 21) it is possible to select from the temperature ranges obtained directly by the own experimental measurements, or adjust the range according to the needs. The maximum graduation of scale is typically limited. The colour scale offers up to 256 colours. This information is essential in terms of being able to compare the results from the subsequent numerical modelling, where you can set the scale in the display of the thermal array for experimental results, and also the temperature scale for the numerical modelling results, so that they were comparable.

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Fig. 20 View on the work surface of the SW GORATEC Thermography Studio [37] 1 - Main toolbar, 2 - Navigation Panel containing icons that allow you to change easily all activated characteristics of the studied point on the thermal image or to perform various operations, 3 - Panel with the statistical data of all analysed objects (e.g., it is possible to detect the average values, minimum, maximum, etc.), 4 - Panel of analysed figure 5 - Temperature scale that indicates the relationship between the selected colour and temperature. SW allows you to change any colour range 6 - Panel of displayed graphs - displayed profiles, etc. for the selected object to be analysed

The correct temperature of an evaluated surface can be calculated using the SW only if the emissivity is correctly determined. It is necessary to take into account that in the monitored area during the experimental measurements there are different materials that may have a completely different emissivity. The calculation is also dependent on the defined ambient temperature. The panel used to define the emissivity and ambient temperature is shown in Fig. 22.

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Fig. 21 View on the tool bar on the temperature scale [37]

Fig. 22 The panel to determine emissivity and ambient temperature [37]

For example SW Thermography Studio offers the possibility to analyse a point, line, or selected area, as is evident from the thermal field image of a mould surface Fig. 23 [34]. As can be seen in Fig. 23, the temperature scale is modified with regard to the extent of measured values. This means in a way to be able to find out the specific temperature on the analysed surface. The smaller the selected range of temperatures, the more accurately determined temperature in the selected location.

Even more precise information about the temperatures on a surface, we should find out after adjusting the scale from the RAINBOW mode to the sharp transition mode, the so-called CONTRAST mode (see fig. 24). The advantage of displaying the temperature in sharp contours, and modifying the minimum and maximum values, is the possibility of obtaining accurate information on a temperature at the selected point of geometry.

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Fig. 23 The thermal field image of a mould surface in the Rainbow mode with marked points, lines and areas including the table with statistical data (picture size, the date of acquisition, the time of acquisition, the minimum and maximum temperature measured, emissivity used on the camera, ambient temperature and the measurement sensitivity) [34]

Fig. 24 The image of thermal field on the mould surface in the Contrast mode using a range of 16 (left) and 32 colours (right) As Fig. 23 shows, when analysing temperature using a point we can evaluate the estimated temperature of surface in a particular place. The determined temperatures in the individual points are then, in addition to the information directly displayed in the figure, always recorded in the table (see. Tab. 2).

Tab. 2 Temperatures measured in the selected points on the surface of a mould shell are marked in Fig. 23 [34]

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If we choose the surface temperature evaluation using a line, then we can obtain a thermal profile in the selected horizontal (or even the vertical) plane. An example of such a temperature profile for the selected plane 1 and 2 (see Fig. 23, note: the plane 1 is closer to the washer) is captured in Fig. 25. From Fig. 25 we can read the maximum and minimum temperatures on the horizontal plane.

Fig. 25 Thermal profile on the horizontal plane 1 and 2 (see Fig. 23) on the surface of the mould [34] Another possibility is the thermal analysis of selected area surface. Once again, as in the two previous cases, in the analysis we can individually set the emissivity and the ambient temperature. In Fig. 23 two rectangular fields were selected (left area 1 and then 2), identified in Tab. 3 as Area 1 and Area 2. The selected area is then transferred to the forms of a histogram (see Fig. 26). In the Tab. 3 there are for individual fields listed the minimum and maximum temperature values, average temperature, the emissivity used, ambient temperature, analysed area dimension and the heat flow of radiation (P2) and the heat

radiation flux of a particular selected area ( P2). Tab. 3 Summary of thermal information on selected areas on the mould surface [34]

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Fig. 26 Histograms of the selected area 2 (see fig. 23) on the surface of the mould From the histogram in Fig. 26 we can obtain information on the distribution of heat flux density (or heat flow) in the selected area. It can be seen that the histogram has the similar structure as the graph with a temperature profile. In the left information column we can interpret individual letters as follows:

Rectangle 1 - area 1

E: 0.85 - - selected emissivity of the reference object

S: - size of the selected area

P2 - heat flow of radiation, which is defined by the following

equation:

(39)

where is the Stephan Boltzmann constant, [W·m -2 ·K-4]

– emissivity, [1] T – found temperature at the analysed surface, [K] T0 – ambient temperature, [K]

S – selected area, [m2]

P2 - heat flow [W.m-2] radiation of the selected area, which is defined as

P2 = S. P2 (40) Information received on the thermal flows can be used to refine the coefficients settings of heat transfer for the numerical model for filling and the solidification of the steel [34, 38].

Questions for the subject studied

1. Can be used in the calculation of filling and the solidification in ProCAST SW two different types of computational meshs, or can we use for the calculation of the filling one and for calculating the solidification another type of mesh? If so, why and where?

2. What is emissivity?

3. What is the difference between the heat flux and heat-transfer coefficient?

Thematic block 7

54

Thematic block 7 The definition of boundary conditions of the solidification process simulation. The determination of material properties for the modelled system - the identification of the phase changes temperatures, enthalpy vs. heat capacity, and the dependency of thermodynamic characteristics on the temperature.

Time to study: individual

Objective After studying this section you will be able to:

define the input data for setting of numerical modelling of casting and solidification of steel ingot.

decide about the type of interface among the individual parts of the modelled area

define and solve the processes related with solidification of steel.

Lecture

In the case of filling and the solidification of steel ingots among the most important and most easily influenced technological boundary conditions belongs the casting temperature and casting speed. On the other hand the conditions of heat transfer are determined by the thermal properties of a defined material. The quality of a cast steel is typically determined by a customer's requirements and by technology specifications. The material and shape of a casting system is generally chosen on the basis of the experience in a steelworks. It therefore cannot be freely and simply changed. Interface setting

It is then necessary to define the so-called INTERFACE (or the conditions of the heat

transfer on the interface of two different domains), which is governed by the value of heat transfer coefficients between the individual components of a casting system. For an interface definition we should choose between coincident, non-coincident, and equivalent conditions.

The choice of this interface condition is related to the method of calculating the heat transfer and generating the computational mesh. As it has already been stated in the section dedicated to mesh generation, when loading the bodies into the computational mesh generator the so-called topology must be carried out, in which it is necessary to have the various components connected with one surface. In the subsequent generation of the computational mesh there is then usually at the interface e.g. between the mould and the ingot one common compute node. But it is in fact in the calculation of filling and solidification between the meltage temperature of an ingot and a mould there is a significant difference (usually the mould temperature is significantly lower than the melt temperature of steel - in Fig. 27 illustrated using green spots). In this case it would be good to have two nodes to distinguish between the two domains. The choice of coincident condition ensures the modification of the interface and the duplication of a computed node, as shown in yellow in Fig. 27. But in fact the thickness of the modified interface is zero [39].

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Fig. 27 The graphical representation of coincident condition use for the relevant calculation of heat transfer at the interface of two different domains (e.g. ingot- mould) [39]

If in the generation of a computational mesh a difference between the computational nodes on the interface of the two domains (Fig. 28) occurred, it is possible to select the so-called non-coincident condition. A non-coincidental condition shall ensure the creation of a "new" nodes.

Fig. 28 The graphical illustration of non-coincident condition use for the relevant calculation of heat transfer at the interface of two different domains (e.g. ingot- mould) [39]

The equivalent condition in the interface is chosen ( Fig. 29), if the two adjacent domains are parts of the same subject, but to create their geometry they were used separately for an easier subsequent individual display and the evaluation of results (e.g. the ingot was divided into its upper and lower part, the body and head of ingot). The equivalent condition at the interface then ensures a continuous calculation of the temperature profile and the speed profile [39].

Fig. 29 A graphical illustration of equivalent conditions use for the relevant calculation of heat transfer at the interface of the two identical domains in the same material (e.g. ingot-casting head) [39]

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At the interface between the ingot and other parts of the foundry set a coincident condition was used. The view of interface between the ingot and the mould, or ingot and the washer, is displayed in Fig. 30.

In addition to the type of interface it is necessary to define on any interface the size of the coefficient for the heat transfer (HTC - Heat Transfer Coefficient). The coefficient of heat transfer between the lining and casting stake (see fig. 31a) and its wall should be very low, in the range from 0 to 5 W.m -2.K -1. The reason is the geometry of the casting stake. The entry of steel is too long, and if there is not a detailed mesh, a small number of elements can lead to the faster solidification of steel in the casting stake - thus for solidifying and interrupting the calculation.

Also at the interface between the wall of a mould and the body of an ingot (see Fig. 31b) is in the stage of filling recommended to have a low heat transfer, in the range from 5 to 100 W.m -2.K -1. The reason for the low value of the coefficient was similarly as for the casting stake facing the danger of metal solidification in the course of filling. At the stage of solidification the coefficients between the elements of the casting assembly can be increased up to the values of 750 to 1,000 W.m -2.K -1[31].

a) b)

Fig. 30 Demonstration of individual component selection for the casting assembly when defining the conditions of heat transfer. In this case the coincidental condition of heat transfer was used

Fig. 31 a) Displayed area between the casting stake wall and the lining of the casting stake, where the value of heat transfer coefficient was only 5 W.m -2.K -1

b) Displayed contacts between the inner mould wall and ingot body, where the coefficient of heat transfer during the filling phase was in the range from 5 to 100 W.m -2.K -1 [31]

Setting the conditions of heat losses over the surface of a simulated system In the phase of pre-processing it is also necessary to define the conditions for the heat

losses over the surface of a simulating system (Fig. 32). The heat losses through the surface of a simulating system are typically determined by emissivity, ambient temperature, and the coefficients of heat transfers. The ambient temperature can be constant or vary depending on time.

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Fig. 32 The view of selected areas in mould, the level in the casting head and bottom washer defining the conditions of the heat losses in the ProCAST pre-processor [40]

Setting of the casting speed and temperature

The casting speed and casting temperature are typically chosen as parameters dependent on time, which means that it changes over time.

The determination of material properties

Today a number of commercial thermodynamic databases are available (CompuTherm, Thermo-Calc, IDS, etc.) which already have an integrated system to calculate thermodynamic properties. From the user's point of view it is a black box - a user is not fully aware of the calculation principles. For this reason it is then appropriate to verify the obtained results e.g. with the values reported in the literature by other authors, or eventually supplement this verification using experimental methods.

The thermodynamic databases allow to provide calculations for metallic materials based on Al, Fe, Ni, Mg, Cu, or possibly other elements. The calculation of the thermodynamic properties for steel is done based on the Fe and can be further defined for the following alloying components: Al, B, C, Co, Cr, Cu, Mg, Mn, Mo, N, Nb, Ni, P, S, Si, Ti, V, W. Other alloying elements, which are not mentioned in the manual for the relevant thermodynamic database, usually do not influence the results of calculation (and are not taken into account for calculation).

For these calculation e.g. at the thermodynamic database CompuTherm microsegregation models are used: Scheil and Lever (Lever Rule). The lever rule presupposes a very good diffusion in a solid form. It is possible to choose the third alternative calculation using the Back Diffusion function, which is defined as the rate of cooling (Cooling Rate). For the calculation of steel liquid and solid temperature it is recommended to use the lever rule [39].

The view of a desktop displaying the thermodynamic CompuTherm database, which is an integrated part of the ProCAST simulation software, depicted in Fig. 33.

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Fig. 33 The view on the desktop with ProCAST, which includes an integrated thermodynamic CompuTherm database that can be activated selecting the Material (in basic bar at the top)

The determination of material properties via thermal analysis

As has already been mentioned in the previous section, the theoretically calculated thermodynamic properties of metallic materials (steel, cast-iron etc.) is appropriate to verify them using the experimental studies or compare them with data in literature. In a more detailed study however we find that the experimental data of these complex systems are still insufficient and the thermo-physical and thermodynamic properties of steels are the subject of intensive research. Very important data such as the temperature and the latent heat of phase transformations, heat capacity, surface tension. For casting steel technology knowledge of a solid temperature is very important, and the temperature of a liquid is particularly crucial. The determination of phase temperatures in such complex polycomponent systems, e.g. steels, is very demanding [33].

Among the most known methods of thermal analysis belong e.g. [41]:

Differential thermal analysis (DTA)

This method is based on the measurement of the temperature differences between the actual temperature of the sample and the temperature defined in the selected temperature program.

Differential sensing or scanning thermal analysis (DSC) The sample is subjected to linear heat and the speed of the heat flow in a sample, proportional to the immediate specific melting heat, is continuously measured.

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59

Thermogravimetric analysis (TGA) A sample (milligrams to grams) is exposed to heat stress, and its change in weight is monitored using sensitive micro scales. Therefore, using thermogravimetry we can easily and quickly determine the thermal or thermal-oxidation stability of the sample (i.e. what temperature the material can "withstand"). By analysing the steps of material degradation it is then possible to deduce its composition, moisture content, organic matter content, and inorganic substance [42].

Combination of methods TGA/DTA, simultaneous TGA/DSC, etc.

In Fig. 34 there is an illustrative figure of a high temperature device for the thermal analysis of heat-physical properties in metals and slags STA449 F3 Jupiter from Netzsch Gerätebau GmbH [43]. In Fig. 35 there is a detailed view of a measuring rod with crucibles using the DTA method [44].

Fig. 34 A high-temperature device for thermal analysis of heat-physical properties for metals and slags STA449 F3 Jupiter from Netzsch Gerätebau GmbH [43]

Fig. 35 Detailed view of a measuring rod with crucibles when using the DTA method [44]

Questions for the subject studied

1. What is an interface?

2. Can we use the equivalent condition for an "alloy-form" interface? If not, why?

Literature

60

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