Numerical simulation on multiple pouring
process for a 292 t steel ingot
* Shen Houfa
Male, born in 1964, Ph.D, Professor. Research interests: modeling and simulation of solidification process related to conventional casting, ingot casting and continuous casting.
E-mail: shen@tsinghua.edu.cn
Received: 2013-04-11 Accepted: 2013-09-26
Tu Wutao1, Zhang Xiong2, *Shen Houfa1 and Liu Baicheng1
1. Key Laboratory for Advanced Materials Processing Technology, Ministry of Education; School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
2. Sinotrans Ltd., Beijing 100044, China
T
he multiple pouring (MP) process [1-2], i.e., sequential pouring with different concentrations, is widely applied to suppress macrosegregation in large steel ingots, e.g., over 100 tonnages. During this process, the molten steel from several ladles with different carbon concentrations is fed successively in a tundish, and the steel is poured into the mould from the tundish after the bath level reaches a stable height in the tundish. It is believed that the primary carbon distribution in the mould at the end of a MP process is crucial for the forming of macrosegregation in the subsequent solidiication process. However, numerical or experimental studies on MP processes are rarely reported.Although the understanding of the whole MP process is limited, some critical issues related have been addressed. Numerical and water models were built to analyze the fluid flow characteristics in the ladle during the tapping process [3-4]. Investigations were conducted to analyze the melt low and heat transfer in the ladles both before and during the teeming to the tundish [5]. Vortex formation in the ladle was
Abstract:
A ladle-tundish-mould transportation model considering the entire multiple pouring (MP) process is proposed. Numerical simulation is carried out to study the carbon distribution and variation in both the tundishand the mould for making a 292 t steel ingot. Firstly, the luid low as well as the heat and mass transfer of
the molten steel in the tundish is simulated based on the multiphase transient turbulence model. Then, the carbon mixing in the mould is calculated by using the species concentration at the tundish outlet as the inlet
condition during the teeming process. The results show a high concentration of carbon at the bottom and a low concentration of carbon at the top of the mould after a MP process with carbon content high in the irst ladle and low in the last ladle. Such carbon concentration distribution would help reduce the negative segregation at the bottom and the positive segregation at the top of the solidiied ingot.
Key words:
multiple pouring; transportation; numerical simulation; large steel ingotCLC numbers: TG142/TP391.9 Document code: A Article ID: 1672-6421(2014)01-052-07
analyzed to optimize the critical bath level during the ladle teeming process [6-8]. Similarly, the fluid low phenomenon in the tundish has also been widely studied. The residence time distribution of the melt in a tundish was studied to characterize the melt low in the tundish by a combined model [9]. The tundish drainage process was analyzed by multiphase models to study thermo fluid dynamics of the steel [10]. The complete casting sequence in the tundish, including 1 min illing period, 46 min holding period, and 1 min empty period, was mathematically modeled [11]. Besides, the outlet concentration of the tundish was predicted from mathematical formulations [12-13]. However, there is still a lack of the studies on transient luid low coupling with concentration variation. Liu et al.[14] studied the macrosegregation phenomenon in an ingot during the solidiication process using a three-layer primary carbon distribution assumption, and the result shows that the primary carbon distribution in the mould should not be neglected in modeling macrosegregation.
Fig. 1: Schematic of multi-pouring process for a
292 t ingot (illing and holding stage)
Fig. 2: Time evolution of molten steel weight in the tundish
1 Multiple pouring process
Three ladles with different concentrations were used in the MP process for making a 292 t steel ingot (average Fe-0.362wt.% C). The irst ladle contained 150 t molten steel (0.38wt.% C), while the second one contained 90 t (0.36wt.% C) and the third one contained 60 t (0.32wt.% C). The schematic of this MP process is shown in Fig. 1. The whole process can be divided into three stages according to the melt level in the tundish, as shown in Fig. 2. The irst stage is called illing process (stage I in Fig. 2), during which the reined molten steel of the irst ladle is poured into the tundish through the inlet of the tundish until the bath level reaches a certain height. Then it comes to the second stage, or the holding stage (stage II in Fig. 2), where the molten steel in the second ladle is poured into the tundish and mixes with the melt poured from the irst stage, meanwhile the outlet of the tundish is kept open so the molten steel gets poured into the mould. During the holding stage, the bath level in the tundish is maintained at almost the same height. After the melt in the ladles has been totally drained, it comes to the draining process, the third stage (stage III in Fig. 2), when the bath level in the tundish begins to decrease. When it reaches a certain height, termed “the critical height”, the outlet of the tundish is closed and the MP process is over. It takes about 3,030 s for the molten steel to pour from all the three ladles through the tundish into the mould.
2 Mathematic model
According to the actual MP process, two CFD models have been utilized for the tundish and mould respectively. Both models consider transient, non-isothermal and two-phase lows of steel and gas. In the models, the Realizable k-ε model [15] was employed in the far-wall ield zones, which were believed to have superior performance for flows involving rotation, boundary layers under strong adverse pressure gradient, separation, and recirculation. For the near-wall field zones, the standard wall function (SWF) approach was adopted. The models were used in combination with the volume of fluid (VOF) multiphase model, which has been proved to be the most reliable and efficient one in regard to identifying the dynamic positions of the interfaces. The assumptions used in the models are: (1) two phases are defined: the liquid phase
m (molten steel) and the gas phase a (air gas for the tundish model, argon gas for the mould model). The corresponding volume fraction was given by αm and αa with the relationship αm + αa = 1; (2) only the low of the molten steel was considered and the solidification of the molten steel was neglected; (3) the motion of the molten steel affected by the blowing argon was not considered; (4) the slag layer on the top of the melt in tundish was not included in the model. The governing equations for both the tundish and mould are as follows:
Mass: Momentum: Energy: Species: Density: Viscosity:
In the equations, α is the volume fraction, u is the velocity, ρ is the density, p is the pressure, μ is the dynamic viscosity, g is the gravity vector, T is the temperature, λ is the
thermal conductivity, cp is the speciic heat, cs is the species concentration and Ds is the mass diffusivity. The subscripts of variables “m” and “a” refer to molten steel phase and gas phase, respectively.
The conservation equations were numerically solved using the control-volume based CFD software FLUENT, version 6.3. The pressure-velocity correction was done with the PISO procedure and the PRESTO scheme was used for pressure discretization. For the tundish (diameter: 2.4 m, height: 3 m), a 3D calculation was made. The entire tundish was meshed into (1) (3) (4) (5) (6) (2) 1# 0.38% Ladle Tundish 2# 0.36% 3# 0.32% Mould Critical height Molten steel in tundish (t)
Puringtime s( ) 60 50 40 30 20 10 0
Total amount of molten steel after pouring t( )
2 0 1 5 1 0 0 5 0 . . . . Height of bath level m( )
0 55 246 292
0 500 1000 1500 2000 2500 3000 Ⅰ
Ⅱ
Fig. 3: Fluid low during illing process in tundish: (a) 20 s, (b) 50 s, (c) 80 s 189,317 hexagonal volume elements. It should be noted that
the tundish has been partitioned into different blocks according to their different characters. On the other hand, for the mould (diameter: 3.4 m, height: 4.5 m), a 2D calculation was adopted considering the geometrical symmetry. The dynamics mesh method was used to generate the grid system, which consists
of 5,293 elements initially and 71,623 elements finally. The calculations were carried out on a workstation with maximum of 48 parallel processes. The time-step was set to be 10-3 s at the beginning and was later adjusted to 2×10-3 s. The total calculation takes about 15 days. The thermophysical properties of the materials are summarized in Table 1.
Table 1: Thermophysical properties of molten steel, air gas and argon gas used in CFD
Material ρ (kg·m-3
) λ (W·m-1
·K-1
) cp (J·kg-1
·K-1
) μ (kg·m-1
·s-1
) Ds (kg·m-1
·s-1 )
Molten steel 7300 30 840 0.006 1.46×10-8 Air gas 1.225 0.0242 1006.43 1.7894×10-5
0 Argon gas 1.6228 0.0158 520.64 2.125×10-4
0
The boundary conditions of the tundish and mould at the solid walls, the free surface, and the axis of symmetry are kept identical to those in an actual MP process. The velocity and pressure boundary conditions were used in both the tundish and the mould. As for the mould, an initial velocity proile was presumed right above the free surface as the velocity boundary condition. The mesh region was expanding and the boundaries were also moving with the pouring process. Meanwhile, since the shape of the inlet was changing during the pouring process, the magnitude of the velocity was also changing accordingly. Besides, all the initial ields are established to meet the actual industrial environment.
3 Results and discussions
The tundish is an important unit in the MP process. It provides
a buffer for the molten steel, which enables the steel ladle changing without interruption of the process low.
3.1 Filling process in tundish
The filling process in the vertical symmetric plane of the tundish is shown in Fig. 3. During the process, the molten steel from the nozzle at the bottom of the ladle lows into the tundish and the bath level increases as the outlet of the tundish beneath the stopper is kept closed. It takes about 80 s before the bath level reaches the highest height of 1.96 m. All the molten steel in this process is provided by the irst ladle (0.38wt. % C), so no carbon mixing happens. The low pattern is similar to the one in regular luid teeming process, which has been studied by many researchers [3-4]. In order to illustrate the low pattern clearly, the plotted vectorized velocities are all scaled uniformly in length in Fig. 3 as well as in all subsequent velocity plots.
3.2 Holding process in tundish
During the holding process, the bath level in the tundish is kept at the height of 1.96 m. This set height is controlled by the low rate balance between the inlet and outlet of the tundish. The melt from the second ladle is added at 890 s after the teeming while the melt from the third ladle is added at 1,800 s. Figure 4 shows the luid low during the holding process. The original transient flow pattern becomes dynamically stable at 105 s roughly. It should be noted that the low pattern is kept almost the same even though the carbon concentration changed after
The melt low is divided into two main streams, a right-oriented stream ⑴ and a left-oriented stream ⑵. The right-oriented stream
⑴ hits the wall and then divides into three streams ⑶, ⑷ and ⑸. Two of the streams move along the wall at the horizontal plane ⑶
and ⑷ and then meet at the stopper rod forming two recirculation loop with the left-oriented stream ⑵. Meanwhile, the third stream
⑸ descends along the wall in the vertical symmetric plane. At
the middle plane (height 2 in Fig. 5(a)), the extraction force acts as the main driving force. Under the effect of this force, the melt nearby lows towards the steel jet, as shown in Fig. 5(c) ⑹ and ⑺. In the vertical symmetric plane, the low is divided into two streams after they met the jet, one ascends to the top ⑻ forming a clockwise directional recirculation loop with the descending wall stream ⑸ while the other one descends to the bottom ⑼. When it comes to the horizontal plane near the bottom (height 1 in Fig. 5(a)), the steel jet impinges on the bottom wall of the tundish. The low pattern is similar to the pattern at height 3, with two streams ⑽ and ⑾ move along the wall horizontally and one stream ascends ⑿ to the surface. The two horizontal streams ⑽ and ⑾ meet at the outlet instead of the stopper rod, and merge at leaving the tundish outlet together with a left-oriented stream ⒀. As for the ascending stream, it forms an anti-clockwise recirculation loop with the descending stream ⑼. Under the extraction force of the outlet, the melt above the outlet descends to the outlet ⒁. It is concluded that four main streams ⑽, ⑾, ⒀, and ⒁ contribute to the outlow at the
outlet of the tundish.
During the holding process, the carbon mixing in the tundish develops in the manners of convection and diffusion. Owing to the violent flow induced by the impinging of the plunging steel jet, the mixing mainly develops in the manner of convection. The time evolution of carbon concentration is shown in Fig. 6.
Before 890 s, the carbon concentration in the tundish is Fig. 4: Fluid low during holding process in tundish: (a) 85 s, (b) 105 s, (c) 1,360 s, (d) 2,290 s
Fig. 6: Carbon concentration during holding process in tundish: (a) 910 s, (b) 1,360 s, (c) 1,800 s, (d) 2,290 s Fig. 5: Flow pattern in tundish at 1,360 s at different
planes: (a) vertical symmetric plane, (b) height 1 horizontal plane, (c) height 2 horizontal plane, (d) height 3 horizontal plane
(a) (b) (c) (d)
3
2
1
(a)
(b)
(c)
(d)
⑴
⑵ ⑶
⑹ ⑷
⑸
⑻
⑼
⑺
⑿ ⑽
⑾ ⒀
Fig. 7: Carbon concentration in tundish at 1,360 s of different planes: (a) vertical symmetric plane, (b) height 1 horizontal plane, (c) height 2 horizontal plane, (d) height 3 horizontal plane
Fig. 8: Fluid low during draining process in tundish: (a) 2,300 s, (b) 2,600 s, (c) 2,900 s homogenous at nearly 0.38 wt.%, i.e., the carbon concentration
in the irst ladle. As shown in Fig. 6, the carbon concentration is diluted and becomes more even because of mixing with each addition of fresh molten steel (Fig. 6(a) and (c)).
Similar to the analysis of the flow pattern above, a representative concentration distribution at 1,360s (Fig. 6(b)) is chosen for analyzing this mixing process. Figure 7 shows the carbon mixing in horizontal and vertical planes at 1,360s. As shown in Fig. 7, the carbon distribution in the tundish is a combination of several carbon concentration circulations, which is bound up with flow pattern (Fig. 5). As the flow pattern is analyzed above, the convection acts as the main mechanism for species mixing in the impinging area and outlet area while the diffusion does at the recirculation center. So the carbon concentration is high in the middle while it is low in the impinging and outlet regions, which is shown in Fig. 7. As analyzed above, four main streams ⑽, ⑾, ⒀, and ⒁ in Fig. 5 contribute to the outlet low. The irst three streams ⑽, ⑾ and
⒀ directly come from the jet with low carbon concentration while the other stream ⒁ carries high concentration carbon from the recirculation as shown in Fig. 7.
3.2 Draining process in tundish
During the draining process, the bath level in the tundish decreases from 1.96 m to 0.27 m. The lowest height of molten steel left in the tundish, defined as the critical height, is set so to avoid the slag entrainment and gas entrapment. Figures 8 and 9 show the luid low and carbon concentration during the draining process, respectively. As shown in Fig. 8, the flow pattern tends to be quiet with the disappearance of the plunging steel jet. The diffusion becomes a more important process for the carbon mixing. Without fresh steel added, the
carbon concentration shows a trend of homogenization as shown in Fig. 9, where the homogenized melt is lowing out of the tundish outlet.
Figure 10 demonstrates the carbon concentration at the tundish outlet during MP process. This concentration is averaged at the outlet cross section. It should be kept in mind that this concentration curve starts at 80 s when the outlet gets opened. Obviously, the concentration generally decreases after the fresh molten steel is added from the second ladle and third ladle, and the average concentration variation rate at a certain outlet flow amount depends on the concentration difference between the ladles. However, there are still some luctuations
Fig. 9: Carbon concentration during draining process in tundish: (a) 2,300 s, (b) 2,600 s, (c) 2,900 s
(a)
(b)
(c)
(d)
(a) (b) (c)
on the concentration variation curve. This may be explained by the competition of the different carbon concentration streams, as shown in Fig. 5. When the stream with high concentration prevails over the others, the concentration at the outlet will
Fig. 10: Carbon concentration variation at
tundish outlet during MP process
Fig. 11: Distribution of carbon concentrations in mould at different time: (a) 1,070 s, (b) 1,770 s, (c) 2,410 s, (d) 3,030 s
increase a little and vice versa.
3.3 Carbon distribution in mould
Figure 11 shows the carbon distribution in the mould during the pouring process. It should be noted that the filling into the mould starts at the time of 80 s when the illing process for the tundish ends. In Fig. 11(a), molten steel with different concentration begins to enter the mould and spread gradually, the mixing region is mainly determined by the impact action of the inlet velocity. Because the impact action tends to accumulate along the symmetric axis and this impact decreases along the axial and radial directions, the mixing region takes on a V-shape region in the upper mould. The bath level is increasing with the development of the MP process. In the impact region, the carbon mixing develops mainly in the manner of convection under the effect of limited impact depth. As for the rest region, the carbon mixing develops mainly in the manner of diffusion (Figs.11 (b)-(d)).
The inal carbon distribution at the end of the MP process is shown in Fig. 11(d). It can be found that the carbon concentration is delaminated. The concentration at bottom of ingot is higher while it is lower at the top with V shape contour. It could be indicated that this carbon delamination is helpful to restrain the conically shaped negative segregation at the bottom and the V shape positive segregation at the top of ingot. However, further investigation of concentration variation and macrosegregation during solidiication of ingot with experimental validation should be underway.
4 Conclusions
A ladle-tundish-mould model considering the entire MP process is developed and numerical simulation is carried out to study the flow characteristics and carbon distribution in both the tundish and the mould of a 292-ton steel ingot. The carbon concentration at the tundish outlet generally decreases with time as a result of the sequentially decreased carbon concentration in ladles. The outlet concentration is the competition result of streams with the low carbon concentration from plunging jet and the streams with high
carbon concentration from the recirculation. The main conclusions can be summarized as follows:
(1) During multiple pouring process for making steel ingot, the carbon distribution in the tundish is obtained from a combination of several carbon concentration circulations, which is closely bound up with the low pattern. Both diffusion and convection exist and the latter is predominant in carbon mixing.
(2) The carbon distribution in the mould at the end of MP process is in a delaminated pattern. A V-shaped low carbon concentration zone is formed in the upper region of the ingot which is favorable to restrain the positive segregation at the top, while a high carbon concentration zone is retained in the bottom region which is helpful to suppress the negative segregation at the bottom of the ingot.
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