Phase-Field Modeling of Steel Scrap Melting in a Liquid Steel Bath

Jianghua Li, McMaster University

1 280 Main Street West Hamilton, Ontario, Canada, LSS 4L7

Tel.: 905-525-9140 Ext. 23317 Fax: 905528-9295

Email: lij8@McMaster.ca,

Geoffery A. Brooks CSIRO Minerals

Box 312 Clayton South Victoria, Australia, 3169 Tel.: Oil 61 3 9545 8544 Fax. 011 61 3 9562 8919

Entail: geoff.brooks@csiro.au

Nikolas Provatas McMaster University

1280 Main Street West Hamilton, Ontario, Canada, L8S 4L7

Tel.: 905-525-9140 Ext. 26897 Fax: 905528-9295

Email :provata@mcmaster.ca

Key words: Scrap melting, Molten steel bath, Electric arc furnace, Solidified shell, Phase field model

INTRODUCTION

The kinetics of scrap melting is an important aspect of EAF steelmaking and has been the subject of several studies 11-81• In EAF steelmaking, there are two distinct melting mechanisms; (i) the melting of scrap by the arc through a combination of radiant and convective heat transfer and (ii) the melting of scrap immersed in a molten steel bath without direct heating from the arc. In traditional EAF steelmaking, the first mechanism dominated the melting process but with the increasing usc of "hot heel" operation and a general trend to utilization of the liquid bath as the melting medium, the second mechanism has become more important.

Previous studies have focused on investigating the melting behaviour of single scrap pieces with regular shapes (1-MJ, though Gaye et at. (71 did consider the physics of multi-piece scrap melting. One of the most important aspects of scrap melting in a bath that has received little attention is the agglomeration of scrap pieces even though industrial experience suggests that this is a critical aspect of understanding the kinetics of scrap melting. The effect of preheating scrap, including the form<ttion of oxide layer, on scrap melting kinetics is another area worthy of future attention.

This study is focused on investigating multi-piece scrap melting in liquid steel by both mathematical modeling and high temperature experimentation. The study emphasizes the formation and agglomeration of solidified shells and investigates the effect of size, shape, oxidation and initial scrap temperature on melting behaviour. A new approach for modeling melting behaviour has been developed, the phase field techniqueLI0-171, to model convective heat transfer in the case of scrap melting in a bath. The phase field model is able to deal more easily with complex geometry compared to traditional "sharp intetface" heat transfer equations where tracking the intetfaccs and their interactions is complex. It is expected that from this study a better understanding of scrap melting can be developed and provide insight into how to improve the melting process in an EAF.

AISTech 2004 Proceedings- Volume I 833

THEORETICAL CONSIDERATIONS

Melting is a dissolution phenomenon in which heat and mass transfer between liquid and solid phases take place. The melting rate may be controlled by heat transfer, mass transfer or coupled heat and mass transfer depending on chemical composition of solid and liquid phases. For scrap melting in EAF, the most important solute is carbon, so that the global phenomenon can be comprehended, without Joss of generality, by looking at the coupling of heat and carbon transfeti7l. lf the carbon content in the solid scrap is different from that of the liquid steel and the heat transfer is much faster than mass transfer of carbon, only the mass transfer process needs to be considered. [fthe carbon content in the solid is equal to that in the liquid steel, only the heat transfer needs to be considered. In general, both transfer processes should be considered simultaneously. In the case of scrap melting in EAF, the carbon content of steel scrap is similar to that in liquid bath. Therefore, it was assumed in our study that the melting is controlled by heat transfer.

Let us consider the interface between liquid and solid steel at any time during the melting process. Figure 1 shows the temperature profile for melting of solid steel into a liquid steel bath. The bath has the temperature TL prior to immersion, the temperature of the solid steel is unifmm at T0, and after immersion, the interface acquires the temperature T, lower than the bath temperature. Thw;, heat transfer takes place through the boundary layer 8r, depending on fluid flow conditions in the system. Or is typically

defined as the distance between interface to the temperature point of 99 % Tl. . The thickness and characteristics of this boundary layer determines the heat flow from the liquid to solid phase. Inside the solid, heat will be transported from the cxtctior towards interior sections of the solid so I ely by heat conduction. The following two equations have traditionally been used to describe the melting process:

Where:

k is the thermal conductivity in the solid steel p and Cp are mass density and specific heat in the solid steel

h is heat transfer coefficient between liquid and solid llH 1 is latent heat of melting

vis the moving velocity of the interface (melting rate)

X;:, is the interface on the solid side

(1)

(2)

Equation (l) represents the heat balance at the interface and Equation (2) describes the heat conduction in solid steel. The melting rate can in principle be solved through Equations (I) and (2) by specifying boundary and initial conditions.

834

LiqUid steel

Figure I Schematic diagram of temperature profiles.

Argon

Unit: (mm)

Figure 2 - Schematic diagram of induction furnace cross section.

AISTech 2004 Proceedings - Volume I

EXPERIMENTS

.Experimental Design Experiments were designed to measure the melting rate of steel bar(s) in liquid steel bath. The effects of scrap size, shape and initial temperature on melting behaviour were investigated. The reason for using steel bars is that the heat transfer and melting can be controlled in two dimensions and the experiments are easy to perform.

The main experimental equipment consists of an electrical resistance furnace for preheating sample and an inducti011 furnace for melting sample. A MgO crucible, capable of holding 70 kg of molten steel, was fixed in the induction furnace box to contain Jiqwd steel bath which was formed by melting the same grade of steel as the samples (1080 steel). It was assumed that the chemistry or the steel was unchanged by the melting process, some oxidation of minor elements may have occurred during melting but this effect was assumed to be minor.

Figure 2 shows the schematic diagram of the induction furnace cross secti011. The sample was fixed on a horizontal bar and then immersed in liquid steel, whose temperature was set to be 1650± 5 °C. The immersed length was set as 170 nun. The induction furnace was off during immersion period to make sure there was no forced convection in liquid steel. After a given immersion time, the sample was pulled out quickly and quenched in water. In this way, the instantaneous dimension of the sample was kept and thus the change of dimension can be used to characterize tlte melting rate of the sample. To avoid oxidation of samples and liquid steel, the argon was injected from the top of the crucible.

The experiments started from single bar melting and then went to two-bar melting. The melting of multi-piece scrap with irregular shape will be the subject of future work.

Single Bar Melting In tltese experiments, the melting of single bars with various sizes and initial temperatures were perf01med.

The photograph of samples shown in Figure 3 shows how the diameter of round bar typically changes with immersion time. As seen, after immersion, a solidified shell was inunediately fonned around original bar and grew to its maximum thickness at approximately 20 seconds and then it began to melt back. The original bar began to melt after 40 seconds and eventually melted completely after 75 seconds. Since the diameters were not uniform, the middle sections of the samples (the sections between the two black lines in Figure 3) were cut off and an effective diameter calculated from the weight of this section. The melting processes of all other samples are very similar to that of samples shown in Figure 3. The melting rate was thereafter characterized by diameter changes over immersion time.

Figure 4 shows the diameter changes over immersion time for round bars with different initial sizes. The curves were obtained by fining

lJ4 l

·� Ai· . , � . . : � ·r

·iq l•ij -... 'I

�. 1 .• \ . ,. < ' j ··� � , "'.-.. ' • 'h: .... :-:. ,:.,.,. \ t - .. �� �·. '

tr• i. I ... . /;· m ·· .

... �-... . . .. : ,- ;." ..

; ti!l � m Ei!l m!1 flil 1 ' Immersion Time (s)

Figure 3 - Samples {38.1 mm, initial temp. 25°C) after immersion in liquid bath for given times (the time

interval between each sample is 10 seconds).

experimental points with polynomial curves for a guide to the eye. Note that the Y axis is RJ�, the instantaneous diameter divided by initial diameter. The initial diameters for three types of samples are 25.4 mm, 31.1! mm and 38.1 mm respectively with

0

m

1.4 .------------------,

1.2

o ..

o.t

1>.4

u 25.4ITII!I "·•mm ll8.1mm

0

0 10 10 *0 •o '0 eo 70 ee 81

lmm.nk>l\ Ttmll (e)

Figure 4 Diameter changes with immersion times for samples with various initial sizes.

24 26 28 30 32 34 ss $8 40

Sample Size (mm)

Figure 5 Melting times as a function of initi al sample sizes.

AISTech 2004 Proceedings- Volume I 835

vOrresponding melting timc.s of38 s, 54 s and 75 s, respectively. The relationship between initial size and melting time is shown in figure 5.

'"fhe region above R!R0=1 in Figure 4 represents the time period for formation and re-melting of a solidified shell and the peaks represent the relative maximum thickness of solidified shell (R/Ro). The peaks show that the relative maximum thicknesses of the solidified sheJis (Rmax/R0) for the three samples are similar but obviously, Rmax increases with increasing initial diameter of sample Rt. One important feature of the curves is that there is a plll.tcau region on each curve showing during which the interface stays at t11aximum thickness of solidified shell without changing much during this period. This phenomenon is believed to be related to an air gap between solidified layer and original bar and will be discussed later.

Figure 6 shows the diameter changes over immersion time for steel bars with three different preheating temperatures. The initial temperatures for three curves arc 25 °C, 400 °C and 800 °C with corresponding final melting times of 3 8 s, 29 s and 21 s respectively. Figure 7 reveals that the melting time decreases with increasing preheat temperature.

The results prcl!cnted in Figure 6 reveal that the maximum thickness of solidified shell decreases with increasing initial temperatures (1.06, 1 .04 and 1.01 for 25 °C, 400 °C and 800 °C, respectively). The time period for fonnation and re-fusion of solidified shell also decreases with increasing preheat temperalli.re (60 %, 45% and 20% of total melting time for 25 °C, 400 °C and 800 °C, respectively). Again, there is a plateau on each curve that decreases with initial temperature.

0 0:: ii!

0.8

0.6

0.4

o.�

0

0

soo •c 400 •c 25 •c

& 1 a n 20 26 30 35 40 4&

lmme..-sion Time (s)

Figure 6 - Diameter changes with immersion times for various preheated temperatures.

Effect of Oxidation Layer

4S

••

�H � j; %0

I!' �zs

ze

11

a

Figure 7- Effect of preheated temperatures on the melting times.

The steel scrap is usually heavily oxidized either when it is exposed to the air and moisture before charged into the furnace or when it is oxidized inside the furnace by the hot offgas. Therefore, the melting of oxidized steel bars in liquid steel was carried out to investigate the effect of oxidation layer of steel scrap on melting behaviour in l iquid steel. Also the melting of polished samples was performed for comparison. The oxidized samples were prepared by keeping the steel bars in the preheating furnace for 8 hours at 800 °C in air without injecting argon (exposed to the air). The thickness of oxidized layer was calculated to be 5-10 microns from the overall weight increase.

1t is noticed that there are many bubble }Joles embedded in the solidified layer of quenched oxidized sample. It reveals that some gases released during the solidification/melting processes, which was probably caused by the reduction reactions between the oxides of iron and the carbon in the liquid steel.

The experimental results reveal that the oxidized layer docs not have significant effect on the solidification/melting process. The oxidized samples melt only slightly faster than polished samples. The possible reasons arc: (a) the released gases cause the stirring of boundary layer between liquid metal and solidified layer, which will increase the heat transfer coefficient between solid and liquid metal and thus improve the melting rate; (b) the contact heat resistance between solidified layer and original bar, which wiU be discussed later, becomes larger due to the bad wettability between liquid steel and oxidized layer and the release of gases.

Two Bar Melting Two bar melting experiments were carried out to investigate the interaction between the two bars during solidification/melting. Two bars were jointed on the top part (Figure 8) but the spacing (L) between two bars was set as a variable.

836 AISTech 2004 Proceedings- Volume I

� Two -·

bondlngs ( By two bars )

Spacing L (rum)

Figure 8 Schematic diagram of two bar sp cciman used in two bar m elting experiments

Immersion Tlm61s) Figure 9 The melting process of two bar specimens

The photograph of samples shown in F igu re 9 show that the solidified steel shells formed and agglomerated at the early stage of immersion, leading to the formation of the compo sit e piece which melted as a whole. The r ight side of Figure 9 shows the cross section of the bars during immersion. We note that near the central region betvveen the two bars, the m erg ed solidified shell may pinch-off during the final stage of melting.

Using the mass change M/MO (M, instantaneous mass; MO, initial mass) over immersion time to characterize the melting rate {Figure 10), we can see that compared to curves for singl e bar melting (figure 6), tlte trends of the curves are similar but the peaks are much higher, which means that there is more solidified material formed per unit mass of original bars. This phenomenon can be ex plain ed by the interaction of two bars. The liquid steel in an area between the bars was solidified because it was cooled by both bars, leadi ng to a greater solidified mass than for single bar immersion. Exp erimental results reveal that the melting time of two bar specimen decreases with i ncreasing initial temperature of the bars.

1.4.

i.2

1

0 E

o.e

� o.t

G.4

0.2

l�'==p;rso�oc 4000C 260C

D I 10 15 20 25 30 31 40 .. 10 II .0 lmm•rston Tlme(s)

Figure I 0 Mass changes with immersion times for the m el ting of two bar specimens with various preheated temperatures

60.0

50.0 I s 40.0

j: 01 30.0 c: :.; 1 20.0 �

10.0

0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Spacing (mm)

Figure 11 Melting time of two bar specim en changes as a fun ction of sp aci ng between two bars

It was found that the as the spacing between two bars (L) increases, the final m elting time deceases as shown in Figure II, which makes sense because the interaction between two bars becomes weaker as spaci ng increases. In Figu re 11, the points with error bars are experimental results while the solid lines are predictions of our model, discussed blow. Experimental melting times arc consistent with our simulations, although more experimental points are currently bei ng obtained to verify the prediction of a jump in melting time at some critical spacing.

DISCUSSIONS OF EXPERIMENTAL RESULTS

As described earlier, the induction furnace was off during immersion period. Therefore, the heat transfer was dominated by natural convection in liquid steel bath. In reality, the heat transfer coefficient between liquid and solid steel is a function of shape and size of thc bar and v elocity of the interface. Since it is not very sensitive to the radius o f round bars in the case of2D natural convective flow, the effects of the changing shape and size during solidification/melting were neglected but the heat t ransfer coefficient is set as a fu nction of moving interface velocity according to Gayel7l

AISTech 2004 Proceedings- Volume I 837

pCP v h = __ __:______.!:..._ __ _

exp(pC P v I h.,1111 ) -1

where h31111 is the heat transfer coefficient for still interface and can be calculated by the following empirical equation[181:

Nu,., = h,1111 • H = 0.686( Gr · Pr)114

k

(3)

{4)

In Equation 4, His a characteristic length. In our case, it is the length of steel bar(s) inunersed in the liquid steel (170 mm). The physical properties in Equation 4 were taken at the temperature: T r = T"' + T, = 1520 + 1650

= 1585 ° C . The values 2 2

are listed in Table 1(191. Substituting these values into Equation 4, h _,,111 = 12500 WI m 2 • K . The heat transfer coefficient for

moving interface can be calculated from Equation 3. h is slightly larger than 1151;11 in the case of solidification and slightly

smaller in the case of melting.

Physical p

Properties (kglm3)

Value 6900

Table I Physical properties of liquid steel at l585°C'19l

cp J1 v /3

(Jikg.K) (N.Sim2) (m%) (Kl)

580 0.0045 6.52xl0-7 0.000062

k Tm (W/m.K) (]()

32 1520

The solidification/melting processes can be understood by considering the heat balance at the interface characterized by Equation (l) during the solidification/melting process. Physically, Equation ( l ) can also be written as:

Heat flux supplied by the liquid (HF1) = heat flux consumed for melting (HF 2) + heat flux dissipated in the solid (HF1)

When tlte cold bar(s) are immersed in the liquid steel, the temperature gradient oTI at the solid side of interface is very large Ox int

and hence HF3 (k BT l ) is much larger than HF1 ( h(�. - T8)) which is assumed only to vary with time slightly. This implies ax im

that the heat flux supplied by the liquid is smaller than that going into the scrap. According to the heat balance, the latent heat term must be negative (heat release) to balance Equation (1). This explains why solidification occurs in the early stage. As time

increases, arl becomes smaller rapidly but HFI ( h(TL - Ts)) changes only slightly. When HF, becomes equal to HFJ, the OX int

solidified layer reaches its maximum thickness. After that, HF1 becomes larger than HF, and melting begins. This explains the peaks in the melting curves (Figures 4, 6, 10).

In the late stage of melting, the change of temperature gradient becomes negligible and so the difference between HF, int

and HF1 becomes almost constant. The melting rate thus becomes nearly constant, which explains nearly-linear curves in Figure 4, 6 and 10 at this stage.

838 AISTcch 2004 Proceedings - Volume I

During the "plateau" in R/R11 the interface almost stops, which means HF1 almost equals HF3• The reason is an air gap formed between solidified layer and original bar during solidification/melting. It is well known that during strip casting process, when the liquid metal is rapidly solidified on the chill substrate to produce a metal strip, an air gap between the melt and the chill substrate develops. In our case, the formation of solidified layer in the early stage of our solidification/melting is quite similar to that in strip casting. The air gap leads to nonperfect contact between solidified layer and the substrate (in our case, the original steel bar). iherefore, the heat flux going into the original bar is limited by the thermal resistance of the air gap which leads to a heat accumulation in the solidification layer and subsequent slow-down of solidification, which is manifested as a plateau-like region. Since the temperature gradient inside solidified layer is always decreasing during this process (but very slowly) the balance between HF1 andHF3 is eventually reversed (HFJ >HF1) and the melting process begins.

The experimental results show that the final melting time decrease with increasing initial temperature of steel bar. When steel bar has a higher initial temperature, less heat is required to reach the melting temperature. Correspondingly, more heat is retained in

the solidified layer and the temperature gradient oTI decrease more rapidly, which also explain why the maximum thickness of OX int

the layer is reduced and the "plateau period" becomes shorter.

PHASE-FIELD MODEL

Jn previous studies, Equations (l) and (2}, along with boundary and initial conditions, were used to simulate melting processes. This type of model is called a sharp interface model because it treats the solid-liquid interface as a sharp dividing line. Because of the difficulty of using sharp-interface models to track free interfaces when complex geometry involved, previous models simulate Equations (I) and (2) for melting of single-piece scrap with simple geometry such as a plate, cylinder or sphere.

In our study, we introduce a new phase-field model of melting in the presence of convection. As shown below, the phase field model has several advantages over the sharp interface model and is a powerful method for simulating melting processes involving complex scrap geometry and agglomeration of different scrap pieces due to the merging of solidified shells.

Introduction to Phase Field Model The phase field method has been used by many researchers to describe solidification phenomena[l().171• The model replaces the need to track the explicit dynamics of the boundary by an equation of motion of a continuum phase field ¢ which describes the

phases in a solid-liquid system. The phase field (or the order parameter} ¢ takes on a constant value in each bulk phase, e.g. ¢ =-

1 in the liquid and ¢ = l in the solid. lt interpolates continuously from -I to I at the interface. In this way, the ¢ field naturally distinguishes the solid and liquid phases and converts the problem of simulating the advance of a sharp boundary to the simpler one of solving a partial differential equation that governs the evolution of the phase field rP. On a practical level, the widely recognized appeal of this model is that it avoids tracking of moving, sharp phase boundaries and very easily handles any number of topologically complex geometries. h also handles interface merging and pinching-off.

The governing phase field model describing solidification or melting of a pure material consists of the following two equations:

(5)

(6}

\Vhcre -T, w, and It arc free parameters and chosen such as to map Equations (5) and (6) onto a sharp interface modeJP11,

T-T"' ("' ) u = is dimensionless temperature (T,11 is the melting temperature) andD 'f'> u is the thermal diffusivity.

M/1 /Cp

Equation 5 governs the evolution of phase field r), and equation 6 describes the evolution of temperature field. As they stand, these equations describe solidification or melting of a pure substance in the absence of convection.

Phase Field Model for Convective Melting The phase field model is rapidly developing as a method of choice for simulating dendritic growth and other solidification microstructure in two dimensions or three dimensions and has enjoyed great success in elucidating microstmcture selection in

AISTech 2004 Proceedings - Volume I 839

solidification[IO-J?l_ However, as a reversed physical phenomenon, melting has not yet been adequately examined using the phase­field method. In this section we extend the above phase field model to include the effects of thetmal convection in melting.

The phase field model above does not consider convective heat transfer in the liquid. The heat Equation (7) involves only heat diffusion and latent heat production or absorption. In reality, convective heat transfer may dominate the solidification or melting process. The hciit equation is modified to take into account the convective heat transfer at the interface by "borrowing" a

convective heat transfer term h (u � - uint )j'V ¢J from the sharp interface model and adding it into the heat equation:

where,

au 1 a� -

I AJ - = V(D(¢,u)Vu) +--+h(u� - ui nt)VI"I ar 2 at

(7)

- h , heat transfer coefficient in phase field model , proportional to h , the heat transfer coefficient in sharp interface model

- u � is dimensionless temperature in liquid far from interface

- uint is the dimensionless temperature at interface

- Jv ¢j "activates" thermal convection at the solid/liquid interface

The relationship between h and h was obtained to be h = 3,.fi .....!!.!.._ for two dimensional simulation when making the 4 wpCp

convective heat transfer tenn in the phase field model equivalent to that in sharp interface modeJl23l_

In our simulations the parameters w and 't were chosen small enough so that the convective phase-field model gave results that were in close agreement witlt the sharp interface model of Equation (1) and (2)1231_

A detailed description of phase field model for convective melting and its derivation can be found in Reference (23).

A numerical solution of two coupled equations (Equations 5 and 7) is carried out by developing finite-<lifference equations (2D) by using standard lowest-order discretization1211l_ The thermal properties of solid and liquid steel, C P and k were taken as

temperature-dependent but density p and latent heat M 1 were assumed to be constant and taken as 7750 (solid steel), 6900

(liquid steel) kg I m 3 and 272000 J I kg [211_

An important issue in our simulations is tlte heat resistance of an air gap between the initial steel bar and solidified layer. In the model we used an effective heat conductivity k,ff for the air gap of the form:

(8)

where k0 is initial effective heat conductivity. t1,u, is the transition time point from solidification to the plateau period (stagnation of solidification). The exponent m varies from -0. 7- -0.5. We simulated the air gap by coupling Equation 8 to the initiiil state of

phase field ¢0- The form of lc�o· is motivated from Guowei Li and G. Thomas's study on interfacial heat conduction in strip casting1221. It is empirical and IL�ed merely to illustrate a form of conductivity that leads to a physical mechanism for the plateau in FiguJ"c 4, 6 and 10. The precise form of this function is not well known.

MODEL RESULTS

Simulations were run on solidification/melting of the bar(s) for the experimental conditions described above. The model results were validated by comparing with experimental results.

840 AISTech 2004 Proceedings- Volume I

Single Bar Melting Modeling Results Figure 12 and 13 show that phase field model produces curves (dotted lines) having the same trends as those obtained from experiments (solid lines) including peak heights and similar melting times. For instance, as the preheated temperature increases, the final melting time decreases and the height of the peaks of the curves decreases. Also, our simulations predict a plateau period at maximum thickness of solidified shell on each modeling curve.

Two Bar Melting Modeling Results Model results on two bar melting reveal that the final melting times predicted by phase field model (curves in Figure II) are quite close to those obtained from experimental results (points in Figure II). There is a critical spacing smaller than which the final melting time decreases with increasing spacing monotonically but beyond which the final melting time decreases dramatically and finally goes to the melting time of single bar. This transition occurs because when the spacing between two bars is smaller than critical spacing, two bars agglomerate due to the merging of solidified shells and then finally melt down as one piece. However, if the spacing is sufficiently larger than the critical spacing, the two bars agglomerate, then separate and finally melt down as two pieces. The final melting time decreases rapidly because separation greatly increases the surface of the solid steel exposed to liquid steel, which accelerates the heat transfer from liquid steel to solid steel.

0.8

� o.cs

ii! 0.4

0.2

0 6 10 16 20 26 30 36 40 46 Immersion Time (s)

Figure 12 Diameter changes as a fimction of immersion time for 25.4 mm sample for three preheated temperatures given by model and experimental results.

1.4 r------------------,

1.2 - Exp.Rtrults

--- Mod•lllng Rtsult.t

o o.e �

0.6

0.4

0.2

Immersion Time lsl

figure 13 Diameter changes as a function of immersion time for samples with various sizes (diameters) given by model and experimental results.

The phenomenon of solidified shell agglomeration and then separating was observed in our experiments, which provides solid validation of model prediction, although more experimental data will be obtained to validate our model more rigorously.

Multi-piece Scrap Melting Simulation Thus far we have only used phase field model to simulate the melting processes of individual scrap pieces. The true advantage of the phase field model lies in its ability to simulate the melting processes of multiple scrap pieces with complex geometry. The purpose of this paper is to demonstrate the validity of our approach to simple geometry before extending the technique to multi­piece scrap melting. The experimental and modeling results for multi-piece melting are under way and will be presented in an upcoming publication.

Discussions The model results indicate that the phase field model can be used successfully to simulate the melting processes on a large scale with reasonable accuracy. The comparison between our model results and experimental results shows some differences. The possible reasons for these differences are:

(I) It was assumed that heat transfer coefficient h (h) was not a function of the samples' shape and sizes, which would lead to

systematic error in the model. For example, we probably overestimated the value of h (h) for large sample (38.1 mm) while underestimate it for small sample (25.4 mm), which is a good reason to explain the systematic difference of final melting time between experiments and model.

(2) It is very difficult to find a scientific basis to determine the accurate contact heat conduction of air gap between solidified shell and original bar and its evolution with time.

(3) In experiments, the heat lost from liquid bath and steel samples is hard to calculate; the effect of the size and geometry of the crucible on natural convection flow pattern is out of our consideration; the dripping of solidified shell when it was pulled out from liquid steel may result in the inaccurate measurement of the radius of samples. All these factors will cause the inaccuracy of experimental results.

AISTech 2004 Proceedings- Volume I 841

CONCLUSIONS

The following results and conclusions were obtained from the melting experiments and phase field model: (1) A solidified layer will be formed in the early stage of the solidification/melting process when the steel bar(s) is imm ersed

in the liquid steel. If two bars are close enough during immersion, their solidified shells will agglomerate, which h as significant effect on the melting processes.

(2) The final melting time of single bar and two bars decreases with increasing initial temperature of steel bars approximately linearly.

(3) The oxidized layer of steel bar seems has only a s light effect on the solidification/melting process. (4) The air gap between the solidified shell and original bar has significant effect on the melting process. The direct effects

are (a) dccrca!!ing the maximum thickness of solidified layer and (b) creating a "plateau period" stagnation at the max.imum thickness of the solidified layer.

(5) The phase field model was used to simulate convective melting for the first time and predicted the similar results as experiments. Compared to the sharp interface model, the phase field model can handle the problems of irregular scrap shapes, which is a significant breakthrough in this research field. And we believe it is a powerful method to simulate multiple piece scrap melting.

ACKNOWLEGEMENT

This research was supported by McMaster Steel Research Center at McMaster University. The authors thank Dr. G. Irons for his valuable suggestions and 0. Kelly, G. Bishop and Dr. F. Z. Ji for their valuable help with melting experiments.

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