Oscillation Mark Formation in Continuous Casting Processes
by Jessica Elfsberg
Casting of Metals Royal Institute of Technology SE-100 44 Stockholm, Sweden
Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan framlägges till offentlig granskning för avläggande av
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Oscillation Mark Formation in Continuous Casting Processes
by Jessica Elfsberg Casting of Metals Royal Institute of Technology
S-100 44 Stockholm, Sweden
Abstract
Oscillation marks are ripples formed on the surface of continuously cast material.
They may cause cracking and decrease the yield of the process since some material must be grinded away to avoid crack growth. A study of break-out shells, a full- scale water model study and full-scale experiments in four different plants have been performed to analyse the formation of oscillation marks. The hypothesis initiating the studies was that there is an optimal oscillation frequency. Material cast at the optimal frequency will have smaller oscillation marks and fewer cracks and, maybe most important, all marks are of the same character and depth. The optimal oscillation frequency is determined by its relation to casting velocity and interfacial tension between metal and protective medium, e.g. slag:
a 2 f v
= ⋅ where ( metal surrounding)
g surroundin / metal
g a 2
ρ
− ρ
⋅ σ
= ⋅
The results from the experiments indicate that there is an optimal frequency at which the surface quality gets better. A theoretical analysis has been worked out.
The suggestion is that the marks form as the surface tension balance controlling the meniscus shape collapses. The collapses occur when the meniscus grows too high and bulges out towards the mould wall.
Calculations were performed to analyse the influence of interfacial tension on the oscillation marks. The results show that the higher the interfacial tension gets the deeper and wider will the marks get. Instead of analysing the friction forces acting in the meniscus region, it was assumed that the oscillation cause a variation of the interfacial tension. In some of the calculations, the interfacial tension was changed from one value to another at some point. The mark shape then becomes a combination of the different cases.
Oscillationsmärkesbildning vid kontinuerliga gjutprocesser
av Jessica Elfsberg Metallernas gjutning Kungliga Tekniska Högskolan
100 44 Stockholm, Sverige
Sammanfattning
Oscillationsmärken är tvärgående ”räfflor” som bildas på ytan av kontinuerligt gjutet material. Märkena kan orsaka sprickbildning samt minska utbytet av processen eftersom man måste slipa ämnena för att undvika spricktillväxt. En undersökning av genombrottsskal, en fullskalig vattenmodellstudie och fullskaliga experiments vid fyra olika gjutningsanläggningar har genomförts för att analysera bildningen av oscillationsmärken. Hypotesen som initierade arbetet var att det finns en optimal oscillationsfrekvens. Material som gjuts vid den optimala frekvensen får mindre oscillationsmärken och färre sprickor och, kanske viktigast, alla märken kommer att vara av samma typ och vara lika djupa. Den optimala oscillationsfrekvensen bestäms av dess relation till gjuthastighet och gränsytspänningen mellan smälta och omgivande medium, till exempel slagg:
a 2 f v
= ⋅ där ( metal surrounding)
g surroundin / metal
g a 2
ρ
− ρ
⋅ σ
= ⋅
Resultaten från experimenten indikerar att det finns en optimal frekvens vid vilken ytkvaliteten blir bättre. En teoretisk analys har utarbetats och föreslår att oscillationsmärkena bildas när ytspänningsbalansen som bestämmer meniskens form kollapsar. Kollapsen inträffar när menisken blir för hög och bular ut mot kokillväggen.
Inverkan av gränsytspänningen på märkenas profil har analyserats med hjälp av beräkningar. Resultaten visar att högre gränsytspänning ger djupare, och bredare märken. Istället för att analysera de friktionskrafter som uppkommer mellan smälta och slagg i meniskområdet, antogs det att oscillationen orsakar en variation av gränsytspänningen. I några beräkningar ändrades gränsytspänningen från ett värde till ett annat vid en viss tidpunkt. Märkets form förändrades till en kombination av formerna för de olika gränsytspänningarna.
The thesis includes the following supplements:
Supplement 1
Thoughts about the Initial Solidification Process during Continuous Casting of Steel
Fredriksson, H. and Elfsberg, J.
Scandinavian Journal of Metallurgy 2002, Vol. 31, pp. 292-297
I prepared samples and performed microscopy studies. I also took part in writing the report.
Supplement 2
Experimental Study of the Formation of Oscillation Marks in Continuous Casting of Steel Billets
Elfsberg, J., Widell, B., Fredriksson, H.
4th European Continuous Casting Conference, Oct 14-15 2002, Birmingham, England.
I performed the experiments, most of the evaluations and report writing.
Supplement 3
Oscillation Mark Formation on Continuously Cast Copper Elfsberg, J., Fredriksson, H.
ISRN:KTH:MG-INR-03:02 SE TRITA-MG-2003:02
I performed the experiments, most of the evaluations and report writing.
Supplement 4
Oscillation Mark Formation on Continuously Cast Stainless Steel and Carbon Steel Slabs
Elfsberg J., Fredriksson H.
ISRN:KTH:MG-INR-03:03 SE TRITA-MG-2003:03
I performed the experiments, most of the evaluations and report writing.
Supplement 5
Theoretical Study of Oscillation Mark Formation in Continuous Casting Processes Elfsberg J., Fredriksson H.
ISRN:KTH:MG-INR-03:04 SE TRITA-MG-2003:04
I did the calculations and the report writing.
Contents
1. Introduction………... 1
2. History and Principles of Continuous Casting……….. 1
History 1 The Principles of Conventional Continuous Casting 3
Casting Powder 4
Oscillation Parameters 5
3. Review on the Formation of Oscillation marks………. 6 4. Experimental work……….. 10
Study of break-out shells 10
DDS- Steel Slabs 11
Fundia Special Bar AB – Steel Billets 11
Fundia Armeringsstål A/S – Steel Billets 11
Outokumpu Copper AB – Copper Strips 12
Outokumpu Copper AB – Water Model 12
Why modelling liquid metal flow using water 12
Avesta Polarit AB – Stainless Steel Slabs 13
5. Experimental Results……….. 14
Study of break-out shells 14
DDS- Steel Slabs 16
Fundia Special Bar AB – Steel Billets 17
Fundia Armeringsstål A/S – Steel Billets 19
Outokumpu Copper AB – Copper Strips 19
Outokumpu Copper AB – Water Model 20
Avesta Polarit AB – Stainless Steel Slabs 21
6. Theoretical background………... 24 6.1 Heat Transfer……….. 24
Conduction 24 Radiation 25
Convection 25
Heat transport in Continuous Casting 25
Heat transport in the Model for Oscillation Mark Formation 26 The Heat Transfer from the Melt to the Shell 27 The Heat Transfer from the Shell to the Mould 28 Determination of Solid Shell Growth Rate and Shell Tip Radius 28
Solidification in the z-direction 29
6.2 Surface Tension Balance and Angles between Phases……… 30 6.3 Pressure balance and Meniscus Shape………. 32
Derivation of the Laplace Capillary Constant 33 Pressure Balance and Angles between the Phases 35
7. Theoretical analysis……….. 36
7.1 The Model for the Oscillation Mark Formation………... 36
The First Approach 37 The Second Approach 37 Optimal Oscillation Frequency 38 7.2 Calculation of Oscillation Mark Profile……… 39
The First Approach 39 The Second Approach 40 8. Results of Calculations………. 40
The First Approach 40 The Second Approach 41 9. Discussion………. 44
10. Future Works………... 46
11. Acknowledgements………. 47
12. References………... 48 Supplements 1-5
1. Introduction
All metal manufacturing includes a solidification process. The metal is either atomised to a powder, or it is cast. There is several casting methods used today.
Many of the methods use the mould only once, for example sand mould casting, the lost-wax method and precision casting. For larger quantities of liquid metal, there are basically two methods: ingot casting and continuous casting. Ingot casting normally uses a permanent mould made by cast iron isolated by ceramic material. There are limitations with the ingot casting methods. The structure in the centre of the ingot will get coarse which decreases the strength of the metal and when casting larger quantities of metal the handling of the ingots gets very complex. To be able to increase the manufacturing capacity without decreasing the quality, the development of a continuous casting process started in 1856. Since then continuous casting has grown to be the major technique for casting steel.
Copper is today continuously cast using a similar design as for steel casting.
The heart of a continuous casting machine is the mould. The mould is an open- ended tube in which the metal is poured. The liquid metal is protected by either a gas, inert or reductive, or some melted compound. For steel the most common protection media are casting powder, i.e. an oxide mixture, or rape-seed oil. In the mould the liquid metal starts to solidify and during the solidification, surface defects called oscillation marks are formed. The oscillation marks appears as grooves perpendicular to the casting direction. They are typically 0.1-1 mm deep.
The oscillation marks may work as initiation point for cracks and beneath them there is a zone with higher risk for inclusions, pores and segregation. There may also be cracks on the cast surface formed in the mould. It is clear that the surface quality of the cast material is mainly determined by the process in the mould.
The formation of oscillation marks has been extensively examined by many authors and there are several models describing the formation of oscillation marks in continuous casting. To be able to control the formation of marks, the mechanism of the formation must be fully known. This work suggests that there is an optimal oscillation frequency. At the optimal oscillation frequency, it is suggested that no, or very small, oscillation marks form.
2. History and Principles of continuous casting History
To be able to increase the casting capacity without decreasing the quality, the development of a continuous casting process started in 1856. Henri Bessemer suggested a model in which liquid metal was poured between to water-cooled rolls.
Figure 1. The twin-roll caster suggested by Bessemer [1]
The process was by then hard to control and the cast material was of very poor quality. In 1887 R M Daelen suggested a process using a vertical water-cooled mould open in its top and bottom. In this process problems with sticking occurred when casting steel and not until 1933, when Siegfried Junghans introduced the concept of mould oscillation, a functional continuous casting process for steel could be developed. In Junghans development the mould was moved downward at a velocity equal to the casting speed for approximately three- quarters of each cycle followed by a rapid return to the starting position. There were therefore no relative motion between the mould and the strand shell during the down-stroke. In 1954 there was a major break-through in continuous casting steel processes. A new oscillation profile, suggested by Concast/Halliday, produced a condition called negative strip. Negative strip is when the down-stroke velocity in each cycle exceeds the casting speed. Sinusoidal oscillation was first used on two Russian slab casters installed in 1959. Presently, sinusoidal is essentially the standard mode of oscillation worldwide. It is relatively simple to design and has the advantage of lower moments of inertia and smaller jerk (the rate of change of acceleration with respect to time). If the jerk is too high, problems related to vibration, noise and wear of moving parts and bearings can occur. However, non-sinusoidal oscillation has received renewed attention and with sophisticated hydraulic oscillators, a wide variety of profiles may come in use.
The benefits of continuous casting compared to ingot casting are:
● Higher yield
● Smaller number of necessary manufacturing steps
● More mechanised casting process
● More even composition
● Better surface finish.
A lot of development of the continuous casting processes has taken place the last decades. For example different electromagnetic devices have been introduced.
Electromagnetic fields can be used for braking and for stirring the liquid metal in the mould. It is also possible to press the melt away from the mould walls with a strong electromagnetic field.
Today conventional continuous casting, described in figure 2, is the dominant casting process for steel. In the future, electromagnetic casting may get in common use as well as the twin-roll caster suggested by Bessemer in 1856. Many of the problems can today be handled, but the process is still very expensive [1].
The Principles of Conventional Continuous Casting
Figure 2 shows the principal design of a conventional continuous casting machine:
Figure 2. A continuous casting machine [1]. Melt flows from a ladle to a tundish and further to a mould. Between the ladle and the tundish, and from tundish to mould, ceramic tubes protect the melt. Beneath the mould there are a secondary cooling zone and a straightening zone.
From a ladle, the liquid metal flows down into a tundish. The tundish acts as distributor if there is more than one mould, it evens the temperature and the composition of the melt and it makes it possible for inclusions to leave the melt.
From the tundish the melt flows to the mould/moulds. A mould for steel casting is normally made by copper which is water-cooled; the surface towards the liquid metal is often covered with a protective layer by for example chromium. To avoid sticking in the mould it is oscillated. The casting process is started with the help of a dummy bar on which the metal freezes, so when it is moved downwards a strand can be drawn out from the mould. The velocity of the strand and the cooling must be controlled so that the solid shell is strong enough when the
strand leaves the mould. Beneath the mould there is a secondary cooling zone in which water is sprayed on the surface of the strand. Further down in the machine, the strand is bent so it gets horizontal and then straightened. When the strand is solid throughout the whole cross section it can be cut to proper lengths, often with an oxy-gas torch.
The casting can be protected or not protected. In protected casting, the melt is not in contact with air at any time before it leaves the mould. In the ladle, a slag layer on the top of the melt protects it. The melt flows through a ceramic tube from the ladle to the tundish, the outlet of the ceramic tube is beneath the surface in the tundish, i.e. the tube is submerged. The melt surface is covered with some oxide mixture in the ladle and flows through one or more nozzles from the tundish to the mould/moulds. These nozzles are submerged in the melt in the mould. In the mould, casting powder, i.e. an oxide mixture, covers the melt surface. The casting powder protects the metal from contact with the air and may act as a lubricant in the meniscus region. In unprotected casting of steel rape-seed oil is often used as protective media. The oil burns and cracks, forming a reducing atmosphere in the mould.
In continuous casting of thin copper strips either a salt mixture or a controlled, inert or reducing, atmosphere is used as protection from oxygen.
As the melt fills the mould, the following occurs: in the upper part of the mould, a meniscus forms. The meniscus is the melt forming a convex upper surface just at the mould wall. The meniscus is curved because there is an interfacial tension between liquid metal and protective media [2]. Beneath this meniscus, a solid shell forms as the metal gets close to the wall. The solidified shell is continuously pulled downwards, at the same time new melt is poured down into the mould. The moving shell grows and shrinks when it is strong enough to withstand the metallostatic pressure. Then an air gap forms between the shell and the mould.
Casting Powder
The casting powder can either be a mechanical mixture of fine grain oxides or a pre-melted and granuled mixture. Granuled powders are preferable since they do not get packed and may thus be fed by automatic feeders. The properties considered important are viscosity, basicity, melt temperature, melting rate and degree of crystallisation. These properties can be connected to the composition of the powder. Another important factor is the particle size distribution. Particles of the same size will always have empty space in between. If there are particles of a wide range of sizes, the particles will pack tighter and air passage gets more difficult.
The main ingredients of casting powders are CaO, SiO2, Al2O3, MgO, Na2O and CaF2. The acidic oxide SiO2 forms SiO42- which forms a silicate network. This network will bind up and contain the other oxides. Al2O3, which is an amphoteric
oxide, can replace the SiO42- in the network. The Al2O3 molecule can form two negative ions, AlO4-, and will thus increase the viscosity strongly if there is excess oxygen present. The following oxides are basic and decrease the viscosity since they break the silicate network: CaO, MgO, BaO, SrO, Na2O, Li2O, K2O. Also fluoride ions lower the viscosity [4], [5]. Graphite is also included (3-6 %) to control the melt rate.
The casting powder has several functions [6], [7], [8], [9], [10], [11], [12]:
● Protect the metal from oxidation
● Thermally isolate the upper surface to prevent meniscus solidification
● Absorb inclusions from the melt and dissolve them
● Lubricate the surface between mould and shell
● Create a homogeneous heat transport
● Determine the meniscus shape by determining the metal/slag interfacial tension.
The composition of the casting powder may change throughout the casting due to reactions between steel and slag. As the composition changes, the essential properties of the slag will also change. Reactions between the metal and the slag will result in major mass transport between them. Mass transport across the interface will decrease the surface tension of the liquid metal.
Oscillation Parameters
The formation of the oscillation marks is regarded to be influenced by the mould oscillation. There are a number of parameters describing the oscillation, for example:
Instantaneous mould velocity
v s f f t
m= ⋅ ⋅ ⋅ ⋅ ⋅
2 2
π cos π 60 [m/min] Equation 1
where s is the stroke length [mm], f is the oscillation frequency [1/min] and t is the cycle time [s].
Average mould velocity f
s 2
vaverage = ⋅ ⋅ [m/min] Equation 2
Total cycle time
tc =60f
[s] Equation 3
The negative strip time, tN, is the time during which the velocity of the down- going mould is higher than the casting velocity. For the sinusoidal mode of oscillation, tN is calculated by the equation [13]:
⋅ π
=π
sf arccos V f
tN 60 c [s] Equation 4
where VC is the casting velocity [m/min].
The oscillation parameters should be chosen so that the negative strip time is large enough for avoiding sticking. Typical values are 0.2-0.3 seconds [1].
The distance between oscillation marks has been assumed to follow the
expression:
p V
f
= G [mm] Equation 5
[3], [6], [13], [14].
3. Review on the Formation of Oscillation Marks
There is a lot of work done in the field of formation of oscillation marks. Some of the suggestions on formation mechanisms are here reviewed.
Sato presented in 1979 [15] the idea of the formation on a “secondary” meniscus formed due to pressure variations caused by the oscillation. He suggests that the marks are formed in two steps, first the solid meniscus shell is lifted by the upward moving mould. This lift causes the formation of two convex surfaces, ab and bc in figure 3b. Then, as the mould turns, the two convex surfaces are forged together and the mark is formed. Figure 3 shows the formation of a mark during casting operation without the use of casting powder. Figure 4 shows the conditions for casting with the use of casting powder. The mechanisms for the two cases are the same, but the presence of the slag will cause a different pressure term [15].
Figure 3. The oscillation mark formation during continuous casting without the use of slag. The mark forms during the upstroke. The solid meniscus us lifted by the mould movement [15].
Figure 4. The formation of oscillation marks in continuous casting with the use of casting powder [15].
In 1980 Saucedo et al. [16] performed work from which they deduce that the oscillation marks, or ripples, form because the meniscus solidifies. They suggest
that no marks will form if the rate of heat extraction is lowered. In a paper from 1991 Saucedo [17] present the theory more detailed. The oscillation marks are suggested to form when the oscillation forces the liquid metal to regain contact with the mould wall. This can happen in two ways, either an overflow occurs, or the shell is bent towards the mould by the metallostatic pressure. It is also possible that the two processes combine [17]. Figure 5 shows the different ways the liquid metal can get in contact with the mould wall above the frozen meniscus. The left mark is usually termed folding mark, and the mark in the middle is called an overflow mark.
Figure 5. The mark formation starts with solidification of the meniscus. Then the metal can get in contact with the mould wall in different ways: i. the rising liquid pushes the solid shell towards the wall, ii. the liquid overflows the shell or iii. The first two combines.
In 1980 Tomono et al. [18] performed experiments with organic substances. They could observe the formation and concluded that the two mark types, i.e. folding marks and overflow marks, are formed of different reasons. They suggest that oscillation marks form when the meniscus is submitted to compressive force by particles sticking to the wall, and that folding marks form independently of the oscillation. They used the Bikerman equation for calculating the meniscus shape and connected the oscillation mark properties to the discrepancy between observed meniscus shape and calculated [18].
In 1984 Takeuchi and Brimacombe [3] described how the pressure in the liquid slag channel varies and draws the meniscus back towards the mould wall during the negative strip. The difference between marks with and without hooks is assumed to be caused by the difference in strength of the meniscus skin. If the skin is strong, an overflow will occur, and a hook forms. If the skin is weaker, the
shell is purely pressed against the wall and no overflow is needed, and no hook forms. They describe how the meniscus follows the oscillation [3], [19], [20].
Figure 7. The fluctuation of the meniscus with mould oscillation [3]
In 1986 Suzuki et al. [21] presented a theory for the oscillation mark formation.
Their model assume that an over-lap mechanism control the formation. The meniscus in surface tension balance with the shell moves upwards as the solid shell grows inwards, see figure 8.
Figure 8. Suzuki et al. suggested in 1986 that the meniscus moves inwards and upwards according to a surface tension balance.
Delhalle et al. [22] described, in a work from 1989, three different formation mechanisms for oscillation marks, see figure 9. The three mechanisms are based upon meniscus solidification. The liquid metal may overflow the solid shell or first the liquid metal overflow the shell and then the shell is remelted or the solid shell may be bent back by metallostatic pressure. Solidification of the curved part results in hook formation. The size and shape of the oscillation marks is said to depend on the heat extraction, the oscillation and the interfacial properties [22].
Figure 9. A. Mould oscillation and product withdrawal cause liquid steel to overflow the solid hook. The overflowing liquid freezes against the mould wall and a new shell tip forms. B. as A, but here partial or total remelting of the solid shell tip is assumed. C. the metallostatic pressure bends the solid shell back against the mould [22].
Lainez and Busturia [23] performed work to determine exactly when the oscillation marks form. They suggest that solidification do not start at the meniscus, but further down in the mould, namely at the lower part of the solid slag rim. They connect the oscillation mark formation to this region and say that they form at the point where the mould downward speed is at maximum [23].
4. Experimental Work
Experiments have been performed in industrial scale at Danish Steel Works Ltd.
(DDS), Fundia Smedjebacken, Fundia Mo-i-Rana, Outokumpu Copper Västerås and AvestaPolarit, Avesta. A surface profilometer was used to get information about the surface topography of the steel slabs and the steel billets. We also performed some metallographic analysis of the materials. In the copper casting case, the flow pattern in the mould has been studied using a water model. We also studied the surface appearance of the cast copper strips for different oscillation frequencies and protective medium. In our first work we studied shell tips from break-out-shells from continuous casting plants in Sweden. A break-out is when the solidifying shell breaks and the liquid metal flows out from it, leaving an empty shell in the mould.
Study of Break-Out Shells
A number of break-outs from steel casting machines have been analysed. The shape of the marks, the shape of the tip and the microstructure were analysed.
DDS – Steel Slabs
A steel with 0.119%C, 0.127%Mn, 0.036%Si, 0.013%P and 0.008%S were studied.
During this experiment the oscillation frequency was varied, the velocity was kept constant, but the stroke length was varied to keep the negative strip time constant.
Later the velocity was varied together with the stroke length while the oscillation frequency was constant. 11 different oscillation frequencies between 74 and 134 min-1 and 5 different velocities, in the range of 0.7-1.1 m/min, were tested.
Casting powder was used at the casting. The surface topography was measured with the surface profilometer and the surfaces were photographed, using a digital camera. Some samples were studied in a light optical microscope. The numbers of transversal cracks on the 200 mm long specimens were counted.
Fundia Special Bar AB – Steel Billets
In Smedjebacken experiments on 5 different heats, A-E, were performed. The alloys used in the four heats A-D contains about 0.16% C, 0.3% Si, 1.2% Mn. The sulphur content were varied between 0,004 and 0,033% and as the sulphur content varied, the Ca and Al contents also varied. The fifth heat, E, was studied because the steel grade shows extremely shallow oscillation marks. The composition of E is 0.55% C, 1.86% Si, 0.85% Mn and 0.017% S.
In these castings, casting powders were used. During the experiments 5 different frequencies, in the range of 90-240 min-1, were tested. The stroke length was constant ±3 mm and the casting velocity was 1.6 m/min.
The surface profile of one of the narrow sides of the cast strand was measured using the surface profilometer and from heat A, B and E samples from the regions of different oscillation frequency were cut out. In each region one could find deep marks, and more shallow marks. Both types were cut out and metallographically prepared and studied in a light optical microscope. Some of the regions on the billets were photographed using a digital camera.
Fundia Armeringsstål A/S – Steel Billets
In Mo-i-Rana 3 different heats, M-O, were studied. Two of them were quite similar in composition while the third had considerably lower carbon content. The compositions of M and N were 0.18% C, 0.2% Si, 0.75% Mn. Sulphur contents were 0.023 and 0.036 respectively. The third heat, O, was a steel grade with considerably lower carbon content. The composition was 0.08% C, 0.18% Si, 0.65% Mn and 0.034% S.
In these trials rapeseed oil was used as lubricant. The velocity could not be varied, only the oscillation frequency. The stroke length was ±5.2 mm. For the different charges the oscillation 5 frequencies between 90 and 180 1/min were tested.
The surface topography was measured with the surface profilometer and the surfaces were photographed, using a digital camera.
Outokumpu Copper AB – Copper Strips
In the copper experiment two different protective media were used, the oscillation frequency and the velocity, by varying the number of down-lets in the nozzle.
Normally the protective media is a carbon carrying gas, but we also used a salt mixture, with the major ingredient Na2B4O7 (borax). The composition of the copper alloy was Cu-0.03%Sn. On these samples we studied the shape of the oscillation mark along the broad side of the strip. The waviness of the oscillation marks was compared to the down-let arrangement. The heat transport to the mould cooling water was registered.
Outokumpu Copper AB- Water Model
A full-scale water model was used to study how the free surface shape varied with the nozzle arrangement. The nozzle design was not exactly equal to the one in the casting machine, but they were similar enough to give sufficient information about the upper surface. The number and the positions of closed nozzles were varied and the flow pattern was photographed.
Why Modelling Liquid Metal Flow using Water?
It is common to use water modelling of continuous casting to get information about flow patterns. To compare two systems the following demands are needed:
● Dynamic similarity
● Geometrical similarity
● Kinematic similarity
● Thermally similarity
When we use water as a model material, it is of course impossible to achieve thermal similarity but for steel flow the thermal similarity is not so important since there are small temperature differences and the natural convection can be neglected. Geometrical similarity is reached if the model is proper scaled.
Kinematic similarity will be reached if geometrical and dynamic similarity can be reached. For dynamic similarity the following dimensionless numbers must be equal in the steel process and in the water model:
Froudes number gL
Fr v
2
= Equation 6
Reynolds number.
=vLν
Re Equation 7
Webers number.
σ
=ρv L W
2 Equation 8
v is the velocity of the fluid and L is a characteristic length for the process, ν is the kinematic viscosity for the fluid, ρ is the density of the fluid and σ is the surface tension for the fluid. The dimensionless numbers are tools used in fluid mechanics to compare systems. According to fluid mechanics, two systems with identical dimensionless numbers satisfy the Navier-Stokes equation. The systems are therefore comparable. Data for the different fluids are given in Table 1.
Table 1. Data for water, steel and copper [24], [25].
Media Density [kg/m3] Viscosity [Pa·s] Surface tension [J/m2] Water 1000 0.001 0.073
Liquid steel 7000 0.007 1.8
Liquid copper 8000 0.004 1.3
This means that the kinematic viscosity, ν, are in the cases of water and steel about 1E-6 m2/s and for copper it is 2E-6 m2/s. Reynolds number are thus easy to get equal. Froude’s number is controlled by the scaling. Both the length and the velocity must be chosen correctly. The choice of water to simulate steel makes it impossible to get all the three numbers equal for the two cases. In bulk flow in the mould it is possible to neglect the surface tension and thereby the Weber number [26]
Avesta Polarit AB – Stainless Steel Slabs
In this experiment the oscillation frequency was varied while the velocity and the stroke length were kept constant. The steel studied was 316L with the composition 11%Ni, 17%Cr, 4.5%Mo and 0.002%S. The sulphur is of interest because it decreases the surface tension of the alloy. According to the literature, the surface tension of this alloy is about 1.7 J/m2 for sulphur contents about 0.002 wt% [27]. The sulphur content of the studied charges is lower than that, so the surface tension will be somewhat higher than 1.7 J/m2.
Casting powder was used. 4 different oscillation frequencies between 100 and 180 min-1 were tested. The surface topography was measured with the surface
profilometer and the surfaces were photographed, using a digital camera. The purpose of this campaign was to study the appearance of hooks beneath the surface. Samples with a length of 300 mm´s were cut out and on these the marks were very carefully studied. The samples cast at 120 min-1 and at 160 min-1 were studied in a light optical microscope. The dendrite arm spacing and the content of Mo, Ni and Cr was measured in a microprobe around marks from these samples.
5. Experimental Results
Study of Break-Out Shells
Two different types of oscillation marks were observed on the break-out shells. In the literature these marks are termed overflow marks and folding marks. It was also observed that the top shell does not form a continuous even line around the mould shell and that the shell growth occurs in steps, as shown in figure 10 a and b. The white arrows indicate oscillation marks found just at the level where the shell thickness starts to change.
Figure 10 a. The upper surface does not behave as an even line during the casting. The white arrow points at an oscillation mark.
Figure 10 b. The same sample as in figure 10 a seen from the perpendicular direction. The growth of the shell has occurred in steps.
We examined a number of break-out shells. The shapes of seven shell tips are shown in figure 11.
Figure 11. Seven observed shell tips from break-outs.
One shell tip was studied more carefully. Figure 12 shows the microstructure of that tip. We can identify two different regions, one fine grained on the top and a coarser below.
Figure 12. The microstructure of a shell tip from a break-out. We can see two different regions, a fine-grained to the left, and a coarser grained to the right.
DDS – Steel Slabs
From the experiment on steel slabs at DDS, data on the oscillation mark distances for different frequencies were achieved. The fraction of oscillation marks with cracks on the wide side of the slab could be determined, see figure 13. There is a minimum for 83 min-1. The minimum at 134 min-1 is probably not reliable since the evaluation was harder on that sample. As the surface profiles on both the narrow sides were measured, it is possible to observe that the oscillation marks do not form at the same level around the slab, see figure 14. Figure 14 also shows periods of shallow marks followed by a deep mark; see especially on the higher curve between 6400 and 6600 mm. Figure 15 shows the oscillation mark distance for different frequencies. The curve has a maximum for f=83 min-1.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
70 80 90 100 110 120 130 140
Oscillation frequency [1/min]
Fraction of oscillation marks with cracks
Figure 13. Diagram showing the fraction of oscillation marks with cracks as a function of oscillation frequency.
0 5 10 15 20 25
6400 6600 6800 7000 7200
Distance from start [mm]
Surface profile [mm]
Figure 14. The oscillation marks on the both narrow sides of the slab, are not identical. The solid line at about 6850 mm is caused by a signal disturbance.
7 8 9 10 11 12 13
70 80 90 100 110 120 130 140
Oscillation frequency [1/min]
Oscillation mark distance [mm]
Figure 15. Diagram showing the oscillation mark distance at different oscillation frequencies.
Fundia Special Bar AB – Steel Billets
In these experiments it was clearly seen that the oscillation mark pattern changes immediately as the oscillation frequency is changed, see figure 17. Further it was observed that the oscillation mark distance decrease when the frequency increases.
Figure 17. The oscillation marks change appearance immediately when the oscillation frequency is changed. The frequency is changed from 100 min-1 to 240 min-1.
The diagram in figure 18 shows the fraction of deeper marks as a function of oscillation frequency for the two heats C and D. The sulphur content was lower for C than for D. Thereby C had a higher interfacial tension. For C a minimum is
f=100 min-1 f=240 min-1
seen at 137 min-1 and for D a very clear minimum is present at f=150 min-1. When the fraction of deeper marks is zero, all the marks have the same appearance.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
80 90 100 110 120 130 140 150 160
Oscillation frequency [1/min]
Fraction of deeper marks
C D
Figure 18. Diagram of the fraction of deep marks as a function of frequency for steel cast with casting powder.
Figure 19 shows the distances between the oscillation marks for the two heats A and B who are low in sulphur and high in sulphur respectively. The higher sulphur content reduces the interfacial tension and decreases the distance.
0 2 4 6 8 10 12 14 16 18 20
100 120 140 160 180 200 220 240
Oscillation frequency [1/min]
Distance [mm]
low sulfur high sulfur
Figure 19. The oscillation mark distances for two heats of the same steel with different sulphur contents.
Fundia Armeringsstål A/S – Steel Billets
In this study, the oscillation marks formed during casting with rape-seed oil as protection have been examined. It was deduced that oscillation marks are formed in the same way as on materials cast with casting powder. Between the marks, a ripple pattern can be seen, with the mark distance of about 1 mm. The ripples are assumed to form due to vibrations in the machine and are not further analysed.
The diagram in figure 20 shows the fraction of deeper marks as a function of frequency. There are maxima at approximately 125 min-1 and 150 min-1 respectively.
Figure 20. Diagram of the fraction of deeper oscillation marks as a function of frequency for steel cast without casting powder, but with rape-seed oil.
Outokumpu Copper AB – Copper Strips
On the cast copper strips, there are patterns of different types of oscillation marks.
The marks on the narrow sides are deeper than the ones on the wide sides. This fact may be due to the deformation of the strip caused by the rolls in the machine, or due to the difference in heat extraction between the narrow and the wide sides.
Deeper marks are also found on the strips cast with the use of salt. The salt addition caused a decrease by approximately 10% of the heat extraction from the mould (measured as difference in temperature of mould cooling water), see figure 21.
The surface appearances of the copper strips were studied. Figure 22 shows a strip cast with the use of salt, v=1.1m/min and f=150 min-1. A waviness of the
0 0.1 0.2 0.3 0.4 0.5 0.6
0 50 100 150 200
Oscillation frequency [1/min]
Low sulphur High sulphur Fraction of deeper marks
oscillation marks is clear. The waviness can be connected to the nozzle arrangement in the down-let system. The ridges in the waves, corresponds to open nozzles and the upwards convex bulge is formed beneath closed nozzles.
v=1,1 m/min
0 50 100 150 200 250 300 350 400
0 100 200 300 400 500 600 700 800 900 1000 Time [s]
Heat transport [kW]
0 10 20 30 40 50 60 70 80 90 100
Mould level [%]
Front
Back
Figure 21. The heat transported to the mould cooling water is shown as a function of time for the two wide sides of the mould. The lowest curve shows the liquid metal level in the mould, in % of some reference.
Figure 22. Photo of the surface of the copper strip cast at v=1.1 m/min and f=150 min-1 and salt used as protection. The marks are wavy as given by the down-let system.
Outokumpu Copper AB – Water Model
In the water model study it could be seen that the water forms a concave bulge right beneath the closed nozzles. The streams from the nozzles on each side of the closed one/ones will interrupt the bulging when they press the surface downwards. When the profile of the water surface was compared with the oscillation marks on the cast strips, it seemed clear that the same thing happens in the mould. There is one exception, close to the narrow side of the strip there are a recirculation bulge on the cast strip. This one is not so strong in the water model – because there is no shell moving downwards in the water model.
Salt addition
Figure 23. Photo of half the water model. We can see how the water forms an upwards convex bulge beneath the closed nozzles and is pressed downwards by the streams from the open nozzles.
Avesta Polarit AB – Stainless Steel Slabs
On the sample cast with the frequency 120 min-1 marks both with and without hooks were found. On the samples cast at the other frequencies, no hooks were found. The marks with hooks often showed some cracks which the marks without hook did not. The Mo, Ni and Cr content around the oscillation marks with hooks were measured using a microprobe. Figure 24 shows the fraction of deeper oscillation marks and the depth of the deep marks as a function of oscillation frequency. There is a clear minima of the depth for f=160 min-1.
Figure 25 shows the microstructure of the material around the oscillation mark. A
“hook” which has been flown over by another liquid can clearly be seen. There are some cracks in the bottom of the mark. The structure close to the surface is very fine-grained while it gets coarser further from the surface.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0 50 100 150 200
Frequency [1/min]
Fraction deep marks
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Depth of deep marks [mm]
Fraction deep marks Depth of deep marks [mm]
Measurements from 500 mm for each frequency
Figure 24. Diagram of the fraction of deeper marks and depth of deeper marks as a function of oscillation frequency. We see that the fraction of deeper marks decreases as the frequency increases and that the depth shows a minimum for f=160 min-1.
During the casting process, the temperature of the mould cooling water was logged. The temperature difference between inlet and outlet water can be used for determining the heat extraction. The differences in mould water temperatures are between 3.25 and 4.25 K and shown in figure 25. To determine the heat extraction, we also need the volume of water flowing through the mould per time unit. These numbers are: for both the narrow sides, 400 l and for the wide sides 5300 and 5400 l respectively.
3 3.2 3.4 3.6 3.8 4 4.2 4.4
50 60 70 80 90 100
Cast length [m]
Water temperature [°C]
difftemp ÖK difftemp ytter difftemp inner difftemp VK
f=180 /min f=160 /min f=120/min f=100/min
Figure 25. The mould cooling water temperature difference as a function of cast length. The plus signs represent changed oscillation frequency.
Figure 6 shows an oscillation mark with a hook and some cracks in the overflow material.
Figure 26. Photo of oscillation mark with a hook and cracks (indicated by white arrows). The structure close to the surface is much more fine-grained than the structure more far from the surface. The oscillation frequency was 120 min-1.
6. Theoretical background
Our model of oscillation mark formation is based on a heat balance, a surface tension balance and a pressure balance. A heat balance gives us the growth rate, the surface tension balance gives us the angles between the phases and a pressure balance gives us the shape of the liquid metal meniscus during the process. Below the physical principles needed are described.
6.1 Heat transfer
Heat can be transported by conduction, by radiation and by convection.
Conduction
Conduction is when energy is transported through the material by propagation of vibrations of the atoms. Conductive heat transport is described by Fourier´s first law:
dx kdT dt
dq =− Equation 9
q is amount of heat per unit area, t is time, k is heat conductivity [W/mK], T is temperature and x is thickness of layer heat travels through.
Heat transfer across an interface is described by the following relation:
(T2 T1)
dt h
dq=− ⋅ − Equation 10
If the heat must travel through several layers, we can treat the layers as connected in series and L/kA as a resistance, the total resistance is:
A ...
k x A k
x A k
x A k
x
3 3
3 2 2
2 1 1
1
+ ⋅ + ⋅
= ⋅
⋅ Equation 11
and
(T2 T1)
L A k dt
dQ=− ⋅ ⋅ − Equation 12
can be used to calculate the heat flown through the system. Q is q times A.
A more general relation than the ones above is the general heat conduction equation
2 2
Dx T D Dt
DT =α Equation 13
α is the thermal diffusivity which can be determined as:
Cp
k
⋅
=ρ
α [m2/s] Equation 14
where k is the heat conduction coefficient of the material with the unit [J/m⋅s⋅K], ρ is the density of the material in [kg/m2] and Cp is the heat capacity in [J/kg⋅K].
Radiation
The heat radiation can be determined by:
(T T )dt
A
dW=ε⋅σ⋅ ⋅ 4− 04 Equation 15
where W is energy [J], ε is emissivity, which is a dimensionless, material dependant factor, σ is the Stefan-Boltzmann constant =5 67 10, ⋅ −8 [W/m2⋅K4], A is the area, T is the temperature of the body, T0 is the temperature of the surrounding and t is the time.
Convection
Convection is energy transport caused by movement of the surrounding matter.
Natural convection is when media moves because of differences in heat content.
Forced convection is when material, e.g. water or air, is forced to pass a body. If the body is warmer it will be cooled by the flowing fluid and vice versa.
Convection can be described by the following equation:
( − ∞)
⋅
⋅
=h A T T
dt dQ
0
kon Equation 16
hkon is the convective heat transfer coefficient, [J/m2⋅s⋅K].
Heat Transport in Continuous Casting
In the mould, zone 1, the dominant heat transport mechanism is conduction through several layers. The layers are mushy zone, solid metal, air gap, liquid slag, solid slag, chromium layer on mould wall, copper in mould wall and mould
cooling water. The conduction through several layers can be treated as heat transfer across a boundary. The heat transported from the steel in the mould can be calculated by using the temperature difference of the mould cooling water.
A
T C
Q V water
water p water
water⋅ρ ⋅ ⋅∆
= Equation 17
Here Vwater is the water flow, ρwater is the density of the water (assumed to be constant and =1 kg/m3, Cpwateris the heat capacity of water (=4.184 [kJ/kg⋅K]), ∆T is monitored and A is the contact area between cast material and mould, [m2].
( ⋅ + ⋅ )⋅
= 2 b 2 d
A (length of contact in the mould) Equation 18 Beneath the mould, in zone 2, the metal is cooled mainly by forced convection when water is sprayed on the surface. In this the radiation and conduction through support rolls dominates the process. The 3rd zone can be said to start as the strand is solid across the entire cross-section. Here in this zone, the heat transfers through radiation, natural convection and through conduction to the support rolls.
Heat Transport in the Model for Oscillation Mark Formation In the analysis of the oscillation mark formation, we consider convective heat transfer to be the controlling one in the mould. We further assume that there are two convective steps, heat transfer from the superheated melt, across a laminar boundary layer, to the surface of the solidifying strand and heat transfer across a gap between strand and mould. A conductive component is also include in our analysis but we do not consider radiation apart from the fact that the convective heat transfer coefficient for heat flow across the gap between shell and mould wall, may include radiative transfer.
Figure 27. The main heat transfer mechanisms at the meniscus are convective heat transfer from the bulk liquid to the shell and convective heat transfer from the shell to the mould.
Mould wall
Air gap
Solid shell
Laminar boundary layer
