ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Casting and Solidification
Influence of Large-Scale Vortex Movement in Lower Recirculation Zone on Instable Flow Field in the Mold
Xiaowei ZhuDewei LiChunlei WuTretiak OleksandrQiang Wang
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2018 Volume 58 Issue 9 Pages 1687-1694

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Abstract

During continuous casting of slab, the flow field in the mold is unstable, which will lead to defects in final products. To investigate the instability of molten steel in the mold, an unsteady Reynolds-average (URAN) method is used to study the unstable flow of molten steel in the mold. The results show that the large-scale vortex movement in the lower recirculation zone is a major factor causing the instability of flow field. These vortexes change the outflow of molten steel in the lower recirculation zone. Molten steel discharging from one side of the nozzle outlet reaches a certain depth, it refluxes to the bottom of nozzle, while it discharging from the other outlet flows deep into the liquid pool. This will cause an asymmetric distribution of internal defects in the casting productions. These vortexes also affect the meniscus level fluctuations of molten steel. They change the reverse flow direction and pressure field in the lower recirculation zone, which affect the position and the angle of stream impinging on the narrow face. The paper could provide a basis for stabilizing the flow field in the mold.

1. Introduction

Flow field in the slab mold plays a decisive role in the quality of final products because it affects the meniscus level fluctuations, the flow velocity on the top face, the growth of shell and the distribution of bubbles and inclusions. Molten steel flows from nozzle to the interior of mold. After discharging from nozzle, the stream impinges on the narrow face of mold and divides into two parts. The stream flowing upward along the narrow face forms an upper recirculation zone, while the other flowing down along the narrow face forms a lower recirculation zone. It is generally recognized that the mold geometry is symmetrical, so the corresponding flow field is also symmetrical.1,2) However, same water model experiments and numerical simulations show that the flow field of molten steel in the slab mold is asymmetric and unstable.3) The unstable flow field and the slab quality are closely related. The unstable flow field can cause meniscus level fluctuations and affect the powder flowing steady into the gap between the mold and shell, which will vary heat transfer, resulting in longitudinal cracks.4) The unstable flow field also affects the flow velocity on the top surface of molten steel. Excessive surface velocity will share off liquid slag into molten steel, causing defects in rolled products.5) It also has effect on the floating of inclusions and bubbles. These inclusions and bubbles which can’t float up to the top surface will be captured by the shell, forming internal defects in final products.6) Therefore, studying the instability of flow field in the mold is of importance to improve the slab quality.

Because molten steel is a high temperature fluid, it is difficult to investigate the flow field by direct measurement. Therefore, there are two methods of analyzing the flow field in the mold. The first one is the water model experiment. Gupta et al.7,8) studied the oscillation of molten steel flow field in the mold by a series of water model experiments. It was found that the flow field of molten steel in the mold was time average symmetric, but it was mostly asymmetrical about the central plane and oscillating, and the frequency of flow fluctuation was proportional to the nozzle outlet angle and flow rate. Shen et al.9,10) studied the flow field distribution in a water model experiment by particle image velocimetry. The study found that the flow field in the mold was composed of two large vortexes, and these two vortexes were not symmetrical. Although the water model experiments can simulate the flow field of molten steel in the mold, the continuous casting process contains complicated heat and mass transfer and the influence of electromagnetic field on the flow of molten steel is hard to be simulated accurately by water model experiment as molten steel is conductive and water is non-conductive. The second method is numerical simulation. The conventional method to study the instability of molten steel in the mold is large eddy simulation. Quan et al.11,12) studied the fluid flow by large eddy simulation. It was found that there was long-term asymmetric in the mold and the flow velocity on the top surface of molten steel showed a wide range of fluctuations. Although the large eddy simulation can accurately calculate the fluid flow, its computational cost is relatively high, and simulating a long-time instability flow field of molten steel costs too much. Some scholars used the steady Reynolds average method to study the flow of molten steel in the mold13) and the calculation results were in good agreement with the experimental time-averaged results. However, the steady Reynolds averaged method cannot calculate the variation of the flow field. Schwarze et al.14,15) calculated the unstable flow field in the mold by an unsteady Reynolds average method. He compared his results with those of large eddy simulation and water model experiment. The two results are consistent with the water modeling experiment, and the computational resources of the unsteady Reynolds average method is far less than that of the large eddy simulation.

In this paper, the unsteady Reynolds average method is used to study the cause and influence factors of the instability of molten steel in the mold.

2. Model Description

2.1. Governing Equations

Three-dimensional incompressible Reynolds-averaged N–S equations of flow field are described as follows:   

u i x i =0
  
D u i Dt =- 1 ρ p x i + x j [ (μ+ μ t )( u i x j + u j x i - 2 3 ρk δ ij ) ]

There are two vortex structures in the turbulent flow. The first one has the characteristic of larger size and lower oscillation frequency. The second one has the characteristic of smaller size and higher oscillation frequency. The large-size vortexes play a leading role in the flow. During the large-scale vortex movement process, they will gradually break into small-scale vortices. While studying the low frequency vibration of the molten steel flow field in the mold, solving the small-scale vortex cost a lot of computational resources. Therefore, the turbulence model can be used to solve the large-size vortex movement in the mold.

In this paper, the standard k–ε turbulent model is used to solve the eddy viscosity μt, turbulent kinetic energy k and turbulent dissipation rate ε. The formulas are as follows:   

t ( ρk ) + x i ( ρk u i ) = x j [ ( μ+ μ t σ k ) k x j ]+ G k -ρε
  
t ( ρε ) + x i ( ρε u i ) = x j [ ( μ+ μ t σ k ) ε x j ]           + C 1ε ε k G k - C 2ε ρ ε 2 k

Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients.   

G k =-ρ u i u j ¯ u j x i

The eddy viscosity μt is computed by combining k and ε as follow:   

u t =ρ C μ k 2 ε

The model constants C1ε, C2ε, Cμ, σk, and σε have the following default values:

C1ε =1.44, C2ε=1.95, Cu =0.06, σk=1.0, σε =1.316)

The meniscus height can be calculated by the pressure distribution on the top surface of molten steel:17)   

h= P staic - P static ¯ ( ρ- ρ slag ) ×g

Where, Pstatic is static pressure at each point, P static ¯ is the average static pressure on the top surface, and ρslag is slag density.

2.2. Boundary Conditions

(1) Inlet: inlet velocity is 2 m/s, corresponding casting speed is 1.56 m/min.

(2) Outlet: a pressure boundary condition is imposed at the computational domain outlet.

(3) Top surface: a no shear boundary condition is applied.

(4) Other wall: a no slip boundary condition is applied. The velocity and turbulent quantities near the wall are computed by non-equilibrium wall functions.

2.3. Geometry and Mesh

These required parameters for calculation are shown in Table 1. Six points are selected to investigate the variation of flow field. The origin of the geometry is located at the top surface center, as shown in Fig. 1(a). The mesh of the computational domain is hexahedral structured, and the number of meshes is 937332, as shown in Figs. 1(b) and 1(c).

Table 1. Simulation parameters.
Process ParametersValue
Casting speed1.56 m/min
Domain width1320 mm
Domain thickness230 mm
Domain length3000 mm
SEN depth170 mm
ρ7020 kg/m3
ρslag3000 kg/m3
μ0.0062 Pa·s
Fig. 1.

Geometry, investigated points and mesh: (a) geometry and investigated points; (b) mesh of fluid in the mold; (c) mesh of fluid in nozzle.

3. Result and Discussion

To verify the accuracy of calculation, the water model experiment made by Gupta7) is selected as a basis to establish a numerical simulation model under the same conditions. The experimental results and calculation results are shown in Fig. 2. Figure 2(a) displays the experimental results obtained by Gupta et al. The flow field is not symmetrical. At the position about 1500 mm below the meniscus, the fluid from the left half moves across the entire mold width. Figure 2(b) is a schematic view of the results. Figure 2(c) is the calculation results. The calculated flow field is also asymmetric. The left stream reaches a certain depth and then migrates to the right, while the right one forms a large vortex. The experimental results and the calculation results are in good agreement, which verify the accuracy of numerical calculation.

Fig. 2.

Results of water model experiment and numerical simulation: (a) results of water model experiment; (b) schematic of flow field; (c) results of simulation.

3.1. Causes of Unstable Flow Field

Figure 3 shows the velocity distribution near nozzle outlets. After discharging from nozzle, the stream is divided into two parts, and concentrates mainly on the lower edge of outlets. Some scholars believe that the bias flow of molten steel may result from the instability of nozzle outflow.18,19) To verify this opinion, two points are selected at the lower edge of outlets. Figure 4 shows the time-varying values of the flow velocities at these two points. The velocities of these two points changes smoothly and the value is the same.

Fig. 3.

Flow field near nozzle outlets.

Fig. 4.

Time variation of velocities at two points near nozzle outlets.

Figure 5 shows the variation of flow field from 2 s to 12 s. After discharging from the nozzle, the stream continuously involves the fluid around it because of the turbulent effect. Therefore, two vortices form below the stream. At 2 s, the sizes of these two vortices are relatively small and vortices distribute symmetrically. From 2 s to 6 s, these vortexes on both sides gradually become bigger, and the heights of vortex center are basically the same. At 8 s, the left vortex center moves down while the height of right vortex remains unchanged. From 10 s to 12 s, the left vortex continues moving down, and the right vortex becomes larger. The balance of two vortexes is broken.

Fig. 5.

Variation of the flow field from 2 s to 12 s.

Figure 6 shows the vertical velocities variation of two points at 2.5 m below the meniscus. The vertical velocity at point 4 is always faster than that at point 3 before 100 s. The vertical velocities at points 3 and 4 appear as periodic oscillations when the time exceeds 100 s. Meanwhile, the peak values of vertical velocities of point 3 and point 4 do not appear at the same time. When the velocity of one-point increases, the velocity of the other point decreases. Therefore, the bias flow of molten steel always exists, no matter whether the stream discharging from nozzle is stable or not.

Fig. 6.

Vertical velocities variation of two points at 2.5 m below meniscus.

Figure 7 displays the variation of flow field in the period from 339 s to 359 s. The upper recirculation zone is composed of two large-scale vortexes on the both sides of nozzle, but the vortexes in the lower recirculation zone are more complex. The vortex generates at the corner of stream impinging on the narrow face. From 341 s to 347 s, the vortex on the left side becomes larger, and the right vortex moves downward. At 349 s, a new vortex generates near the right narrow face. From 349 s to 357 s, the new generated vortex grows and moves down.

Fig. 7.

Variation of flow field from 339 s to 359 s.

At the initial stage of flow, the flow field in the mold is symmetrical, the fluid instability occurs when the vortexes in lower recirculation zone are big enough. This unstable flow of vortexes is not caused by numerical errors but by the flow itself. In fluid mechanics, there are many unstable flows, such as the Karman vortex street. When the Reynolds number is greater than a certain value, a periodic vortex street will be formed behind the cylinder. There is also such a fluid flow as a turbulent plane jet with a rectangular cavity.20) Figure 8(a) shows the three-dimensional streamline of molten steel and Fig. 8(b) displays the vertical velocity distribution of 3 m below the meniscus at 349 s. Molten steel from the left nozzle outlet flows a certain depth along the narrow face and flows back to the bottom of the stream discharging from nozzle, while the molten steel from the right outlet flows directly out of the calculation domain. During continuous casting, argon is usually used to prevent nozzle clogging. Therefore, when molten steel flows out of the nozzle, a large number of bubbles are contained in the stream. Since the bubble density is smaller than molten steel density, most of bubbles escape from the top surface of molten steel to the atmosphere, but some bubbles still follow molten steel into liquid pool. Due to the asymmetry flow field, the trajectories of bubbles on the two sides of nozzle are different. At 349 s, the bubbles discharging from the left nozzle outlet can mostly float up to the top surface. However, a part of the bubbles discharging from right nozzle outlet are brought into the liquid pool. These bubbles will be captured by the solidified shell and form internal defects eventually.

Fig. 8.

Flow field in 349 s: (a) streamline of molten steel; (b)vertical velocity distribution of 3 m below the meniscus.

3.2. Influence of Vortex Movement to the Meniscus Level Fluctuations

Meniscus level fluctuations have crucial effects on the slab quality. The factors affecting the meniscus level fluctuations are casting speed, collision velocity of stream, collision angle of stream and distance of collision point from meniscus.21) Figure 9 shows the variation of flow field, pressure distribution and meniscus height from 304 s to 324 s. To distinguish the pressure changes in the lower recirculation zone, the pressure scale used in this paper is 0 Pa – −300 Pa. There are mainly four negative pressure zones in the mold, which are in the upper and lower recirculation zones, respectively. The lowest pressure zone is at the center of these vortexes. The high-pressure areas are mainly located inside the nozzle, the meniscus and the collision point between stream and narrow face. At 304 s, the left collision position of stream on the narrow face is higher than the right position, so the left meniscus height is higher than the right one. From 304 s to 324 s, the reverse flow in lower recirculation zone moves from the left side to the right. So, the left collision position of stream on the narrow face moves down, and the right one moves up. Eventually the right meniscus height increases.

Fig. 9.

Variation of flow field, pressure field and meniscus height from 304 s to 324 s: (a) flow and pressure field; (b) meniscus height.

The direction of reverse flow in the lower recirculation zone affects the collision position of stream. However, the reverse flow impacted the right stream, the height of the right impinging position is higher than the left one at 324 s. The angle of left stream impinging on the narrow face (α1) is larger than right (α2), as shown in Fig. 10. The impact angle of the stream on the narrow face of the mold can also be represented by the pressure distribution on the narrow face. The higher the pressure distributes on the narrow face, the greater the impact angle is. Figure 11 shows the variation of pressure field on narrow face from 304 s to 324 s. At 304 s, the pressure on the right side of the narrow face is high, while the pressure on the right narrow face is low. From 304 s – 324 s, the pressure on the left narrow face gradually increases, while the pressure on the right narrow face gradually decreases. Meanwhile, the position of the highest pressure point on the left side gradually moves downward, while that on the right side changes little. From 312 s to 324 s, the pressure on the left side of the lower recirculation zone is lower than that on the right one. The lower pressure zone will attract the nearby liquid. When the vortex moves down, it will bend the stream and change the collision angle of stream, so more liquid flows to the meniscus and affects the meniscus height.

Fig. 10.

Flow field and pressure distribution in narrow face at 324 s.

Fig. 11.

Variation of pressure on narrow face from 304 s to 324 s.

The influence of vortex movement in the lower recirculation zone on the meniscus height is mainly divided into two parts. These vortexes change the reverse flow direction and pressure field in the lower recirculation zone, which affect the position and the angle of stream impinging on the narrow face. Figure 12 shows the meniscus height variation of the both left and right sides after 100 s and their average values. The meniscus height variation is more irregular, but the average values of meniscus height are approximately identical, and they are consistent with the results of previous works.7,8)

Fig. 12.

Variation of meniscus height and their average value.

Figure 13 shows the meniscus height, the velocity on the top surface and the flow field at 376 s and 386 s. At 376 s, because the left meniscus is higher than the right one, the velocity of molten steel on the left side of the nozzle is faster than the right one. Molten steel with faster velocity will flow toward the slower side. The meniscus height and flow rate on both sides of the nozzle tend to be stable, as shown at 386 s. When molten steel flows across the nozzle, two vortexes are generated near the nozzle, as shown in Fig. 14. If these vortexes are large enough, slag will be entrained and defects will be formed.

Fig. 13.

Meniscus height, top surface velocity and streamline at 376 s and 386 s: (a) meniscus height; (b) top surface velocity; (c) streamlines.

Fig. 14.

Schematic of vortexes generated near the nozzle.

4. Conclusion

In this paper, the unsteady Reynolds averaged method is used to analyze the cause and influence factors of instable flow in the mold. The results obtained are as follows:

(1) Large-scale vortex movement in the lower recirculation zone is the major factor causing the instability of the flow field in the mold rather than the instability of the nozzle outflow.

(2) Large-scale vortex movement in the lower recirculation zone changes the outflow of molten steel in the lower recirculation zone. When molten steel discharging from one side of the nozzle outlet reaches to a certain depth, it refluxes to the bottom of the stream outflow from nozzle, while the other discharges deep into the liquid pool. This affects the floating of inclusions and bubbles and causes the asymmetric distribution of internal defects in casting productions.

(3) Large-scale vortex movement in the lower recirculation zone varies the collision angel of stream and distance between the collision point and meniscus. It will cause meniscus level fluctuations and lead to slab defects.

To stabilize the flow field of molten steel in the mold and improve the quality of slabs, the flow filed in the lower recirculation zone needs to be stable. At present, electromagnetic brake technology and electromagnetic swirling flow in nozzle technology can be applied to stabilize the flow field in slab continuous casting, but these technologies must be used rationally to suppress vortex movement in the lower recirculation zone.

Acknowledgments

Authors are grateful to the financial support from the National Natural Science Foundation of China (Nos. U1560207 and U51504057), the National Key R&D Program of China: Upgrading and Industrialization of Key Basic Material Technology (No. 2017YFB0304400).

References
 
© 2018 by The Iron and Steel Institute of Japan
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