Numerical simulation on flow and heat transfer in twin roll strip casting and rolling molten pool with side dams vibrating

A three-demensional numerical model is established to predict the free surface, the temperature field, the flow field, the turbulent kinectic energy, the outlet temperature, and the liquid fraction in the twin roll strip casting and rolling molten pool with side dams vibrating. The numerical simulations are also conducted to compare the flow and heat transfer characteristics under different vibration frequencies and different casting temperatures. The results show that the heat transfer is enhanced, the mixing of solutes is optimized, the strip outlet temperatures are homogeniazed, the kiss lines are higher, and the rolling intervals are extended as the frequency increased. Excessive casting temperature leads some unexpected problems such as liquid steel leakage and unformed strips. It also makes the height of kiss line uneven. Lower casting temperature leads the strip outlet temperature more uniform. It also leads the kiss lines higher. Finally, a new approach to advancing the development of twin roll strip casting and rolling is proposed through these analyses.


Introduction
Twin roll thin strip casting and rolling technology (TRSC) is considered to be a very promising steel manufacturing technology [1]. Molten metal flows into the molten pool consisted of side dams and casting rolls from a tundish. Then, it solidifies into steel shell on the surface of casting rolls. Subsequently, the solidified shell is plastically deformed at kiss point and finally rolled into thin strip [2,3]. Twin roll strip casting and rolling technology has received extensive attention for the production of steel because of the distinguishing feature of low casting cost, low emission and rapid solidification [4,5]. Side dam is the leakage proof device on the side of molten pool. Its main function is to restrict the liquid metal and ensure that the strip with high-quality edge can be obtained [6][7][8]. Solid [9][10][11], electromagnetic [12][13][14], and gas [15] side sealing technologies are widely studied and developed [9]. Among them, the solid side dams are the most widely used in practice.
In the production process, the vibration of side dam is found to optimize the flow and heat transfer characteristics in the molten pool. Vibration was first added to the casting process by Chernov. He found that vibration optimized solidification [16]. Since then, the role of mechanical [17], ultrasonic [18], and electromagnetic [19] vibration in solidification have been continuously explored. The effect of vibration is divided into micro and macro aspects. Microscopically, vibration can refine grains, homogenize atomic diffusion, accelerate solidification speed, etc. [19][20][21][22]. Kudryashova et al. [23] found the optimal frequency 50 Hz and amplitude 0.5 mm of metal vibration solidification through numerical simulations and experiments. Yao et al. [24] studied the solidification process of Mg-8Li-3Al under ultrasonic vibration. They found that ultrasonic vibration can change the α phase to better structure. Lyubinmov et al. [25] studied the effect of vibration on motion stability of solidification front. They found that vibration perpendicular to the front had a destructive effect, while the parallel vibration was the opposite. Niu et al. [26] predicted the microstructure evolution of molten steel and obtained the optimal vibration parameters experimentally. Macroscopically, vibration also makes differences. It can improve strip surface defects and fracture ripple. It 1 3 optimizes solidification shrinkage cavity. It helps to obtain good lubrication conditions for inner wall of mold. It also prevents the adhesion between molten steel and the inner wall [27,28]. Lankford et al. [29] believed that the shell would be subjected to the stress caused by vibration in the solidification process. They studied the effect of this stress on the strength and ductility of strip. Zang et al. [28] studied the effect of periodic stress in vibrating casting roll on solidification quality. Schwerdtfeger et al. [30] established a mathematical model to predict the depth of surface defects of billet produced by the vibration.
Some reserachers performed numerical simulation on TRSC [31]. Miyazawa and Szekely [32] first established a mathematical model for TRSC. They found that casting roll spacing, rotating speed and feed speed would acquire great influence. Santos et al. [33] proposed and verified the numerical model of 2D finite difference method for solidification in TRSC. Hwang et al. [34] used finite element method, volume of fluid (VOF), and equivalent specific enthalpy method in the simulation of molten pool. They obtained the growth law of the solidified layer thickness. They also got the position of the free surface, solidification front and kiss point. Xu et al. [35] studied the characteristics of free surface of the molten pool, boundary layer fluctuation, and circumfluence stability by using large eddy simulation. A full-scale water model experiment was conducted for model validation. Pelss et al. [36] numerically simulated the flow and solidification in the molten pool by using enthalpy porosity model and VOF model. Jiang et al. [37] simulated different parameters of TRSC lead making process such as casting temperature, molten pool depth, and casting speed. Finally, they obtained the optimum process parameters.
Overall, vibration shows many advantages in metal solidification such as better strip quality and faster solidification speed. On the one hand, the influence of side dam vibration on flow and heat transfer in TRSC molten pool is rarely mentioned in the previous literature. On the other hand, numerical simulation has been widely used but the mathamatical model on a TRSC molten pool with side dam vibrating has not been proposed yet. In the present work, a 3D numerical model for TRSC molten pool with side dams vibrating is proposed to study the flow and heat transfer in molten pool, optimize the quality of strip, and further promote the development of TRSC technology. The fundamental characteristics of flow and heat transfer are studied. The comparison of fundamental characteristics under different vibration frequencies and casting temperatures are also analyzed.

Model parameters
The parameters of the model are listed in Table 1. Figure 1 shows the physical model of the molten pool. In order to see the parameters in details, we have enlarged the distributor on the right of Fig. 1.
Numerical simulations are based on about 1 million cells to obtain a grid-independent result. The quality distribution of the grid is above 0.5. Finally, 372,728 grids of 3.12 mm are used in numerical simulations based on the computing resources and computing load. Global grid division of the molten pool is shown in Fig. 2.

Governing equations
Flow and heat transfer in molten pool is obtained by solving the following equations [38] within a finite control volume.
where t is the time; μ is the dynamic viscosity; λ is the viscosity coefficient; p is the pressure; F i is the physical force of unit volume, H is the enthalpy of unit mass; q v is the heat generation rate of unit volume, Φ is the mechanical or dissipation coefficient, and q r is the radiation heat flux.
SST k-ω model is adopted to solve the steel flow field because of the high velocity rotating shear flow. The influence of turbulent shear stress is considered in the model [39].
where ρ m is the density, v m is the fluid velocity, μ m is the mixture viscosity, μ t,m is the mixture turbulent viscosity, σ k is the turbulent Prandtl number of k equation, σ ω is the turbulent  [40] is used to deal with the solidification of liquid metal in the molten pool. In this model, the mushy zone is treated as porous medium, the volume of liquid metal in each unit is defined as porosity. The momentum of liquid metal in the porous medium area should meet the following equation.
where S ′ is the momentum in mushy zone, S is the momentum in liquid phase, β is the liquid phase volume fraction, � ⃗ v is the liquid phase velocity, � ⃗ v p is the solid phase velocity, and A mush is the mushy zone constant.
where T solidus is the solidus temperature, T liquidus is liquidus temperature.
There are usually gas-liquid-solid three phases in the multiphase flow of molten pool, but the solidified shell is treated as porous medium in the calculation. Consequently, the multiphase flow in the molten pool is simplified as twophase flow.
VOF model [41] is used for two-phase flow in molten pool. VOF model is a multiphase flow surface tracking method based on Euler method. In this model, each group of fluids shares one set of momentum equations. The volume fraction of each fluid in the calculation domain is tracked on each unit by introducing phase volume fraction. All variables and their properties in each control volume are shared too. The volume fraction sum of all fluid phases is 1. α p represent the volume fraction of the p-phase fluid.
According to α p , the physical parameters and variable values will be weighted into the control volume. The multiphase interface tracking in each unit is obtained by solving the continuity equation. The equation is written as follows for the p-phase fluid.  where ρ p is the density of phase p, v p is the phase p velocity, m qp is the mass transfer from phase q to phase p, m pq is the mass transfer from phase p to phase q, and S ap is the quality source term.

Boundary conditions
In this paper, the initial temperature of the molten metal is the inlet temperature T in of the distributor. The initial temperature of the air on the upper surface is 573 K. The initial casting velocity meets the following equations, which are calculated by the physical model.
where v pull is the pull velocity at casting roll outlet, R A is the solid zone radius from roll center, v z is the solid phase zone z-direction linear velocity, and v y is the solid phase zone y-direction linear velocity.
As shown in Fig. 3, the inlet type is velocity inlet, the inlet temperature is T in . The inlet velocity v in , inlet turbulent kinetic energy k in , and inlet turbulent energy dissipation rate ε in satisfy the following equations [42]. The velocities in other directions are 0 m·s −1 . The inlet fluid is all set as liquid.
where ρ s is the solid density, ρ l is the molten metal density, and I is the turbulence intensity.
Outflow is set as outlet condition. The molten metal is completely solidified. The outlet velocity v out should be equal to 0.9 to 1 times of the casting roll speed. The temperature gradient along the z direction is 0.
The actual casting velocity is set in the numerical simulations. The wall velocity adopts the moving boundary condition. The matching relationship between the roll velocity and the pull velocity is shown in Eq. (15) and Eq. (16).
where θ is the included angle between contact arc of roll surface and connecting line of casting roll.
where α is the cladding angle of molten pool, β is the contact angle of molten pool, K is the deformation resistance of metal, ω is the rotation angular speed of crystallization roll, c is the correction factor, k m is the harmonic average thermal conductivity, σ is the root mean square surface roughness, and H is the microhardness of soft contact materials.
The air outlet pressure is 101.325 kPa. Air temperature is 573 K. A symmetrical interface is used to central area of the molten pool. The other boundaries are set as wall type.
The accurate heat flux q under different vibration conditions between the side dams and the molten pool under vibration conditions are measured experimentally. They were given as Eq. (18) to Eq. (21) when the vibration frequencies were 7 Hz, 13 Hz, 25 Hz, and 30 Hz, represently. We analyzed the chemical composition of the materials used as shown in Table 2. All the parameters are calculated according to the composition of materials. In this paper, all these parameters are set as constants according to the previous literature [35]. The thermodynamic parameters used in this paper are given in Table 3. All the material parameters are used in current simulations.

Model verification
The molecular kinematic viscosity of molten steel at 1850 K is similar to that of water at room temperature. The correctness of the numerical model can be proved by verifying that the free surface fluctuation of the water model is consistent with that in the numerical simulations. In this paper, a 1:1 water model experiment is carried out to verify the numerical model. Many pictures are taken to show the free surface fluctuation. The outlet velocity are also calculated by monitoring the flow. As shown in 1536848.1T − 974.2T 2 + 0.20749T 3 − 8.097 × 10 6 1518.9 < T Fig. 4, the fluctuation trend of the free surface obtained experimentally by taking photos. The fluctuations are compared with that obtained numerically in Fig. 5. The results obtained experimentally is similar to that obtained from the numerical simulations, both of which are in the range of 4 to 8 mm. Moreover, the outlet velocity measured experimentally is 0.84 m·s −1 and that monitored in simulation is 0.8234 m·s −1 , with a relative error of 2.016%. Finally, it can be believed that the results of the numerical simulation are reliable.

Simulation results
The numerical simulation schemes are given in Table 4. All the parameters comes from factory. The parameters applied in engineering are used in simulations. Different vibration frequencies and casting temperatures are simulated. The fundamental flow and heat transfer characteristics with side dams vibrating are studied by using the results under 7 Hz vibration frequency and 1840 K casting temperature. Faces 1-5 and lines 1-5 in Fig. 6 are selected to demonstrate the steel flow and temperature distribution. Faces 1-5 and lines 1-5 are very representative because they are located in some special positions in the molten pool. Face 1 is the side dam plane. It can directly show the influence of side dam vibration on the flow streamlines, heat transfer and solidification of the surrounding molten metal. Face 2 is located 1/2 between the side dam and the transverse distributor nozzle. It is affected by both the side dam vibration and the transverse distributor nozzle. Face 3 is located in the center of the second distributor nozzle from the side dam. The influence of distributor nozzle is studied here. Face 4 is located in the center of the second nozzle and the third. It represents the characteristics of non-nozzle position. Face 5

Steel flow path with side dams vibrating
In this paper, the microvibration amplitude and frequency determine that vibration has little influence on the flow streamline in the molten pool. In fact, the influence of vibration on flow is far less than the fluctuation of the free surface. This section is mainly to show the basic characteristics of the flow streamlines. Similarly, the influence of casting temperature is also not obvious. Figure 7 shows the streamline diagrams on each section of the molten pool under steady state. The black lines represent the flow streamline. The dark background near the top is the gas phase. The light background area below is the liquid phase. As shown in Fig. 7a, the flow direction is divided into upper and lower. Vortex 1 and vortex 2 are formed near the free surface because of the molten metal inertia and roll rotation in upward area. Vortex 1 is close to meniscus and vortex 2 is near the distributor wall. Inclusions near the meniscus and roll surface may be drawn into the molten metal so that the molten metal cleanliness and the strip quality may be deteriorated. The heat transfer between roller surface and molten metal is enhanced, which leads the roll surface shell to be cut off and difficult to form. A long elliptical vortex 3 exists above the kiss point. Its generation because of highspeed rotation of the casting roll. The molten metal near the kiss line flows back to upper part because of vortex 3. Vortex 3 also lead the molten metal near the kiss piont to be mixed with the higher-temperature molten metal. By this way, the solidification segregation is reduced and the steel internal quality is improved. Vortex 3 also fuses the growth of primary dendrites caused by uneven temperature. It conduces to core nucleation and equiaxed crystal growth of strip. Figure 7b shows that the vortex distribution at non-distributor nozzle is quite different from that at distributor nozzle. There is only vortex 4 under free surface. Vortex 6 is formed because the moleten metal flow is blocked by the distributor outer wall. Vortex 7 is similar to vortex 3 in shape but significantly smaller. Furthermore, there is no vortex on Face 2 as shown in Fig. 7c

Interface phenomena with side dams vibrating
The interface phenomena near meniscus is important. To analyze the free surface fluctuation in the molten pool, free surface fluctuations at different times are shown in Fig. 8. The free surface near the casting roll decreases when t = 0.02 s leads to free surface fluctuation along y direction. The fluctuation is transmitted to the distributor wall when t = 0.08 s. It is believed that the fluctuation along y direction is caused by the rotation of the casting roll. Two different fluctuations are formed on the free surface due to the distributor nozzle jet at 0.2 s. Next, they move towards to the casting roll surface. They are also considered to be the reason for the free surface fluctuation along x direction.
The velocity distributions along z direction on line 3 and line 5 are shown in Fig. 9. The fluctuation range of free surface velocity along x direction is 0 to 0.24 m·s −1 . The wave distance range is 20 to 50 mm. The velocity sharply decreases and the peak value of velocity wave increases at x = 225 mm near the side dam because of the enhancement of heat transfer near the side dam, the faster solidification at the bottom of the molten pool and the increase of the molten metal downward flow velocity. There are also two areas with large amplitude between x = 35 to 75 mm and x = 120 to 240 mm because of the upward distributor nozzle jet. Figure 9b also indicates that z direction velocity fluctuation range of free surface along y direction is 0 to 0.15 m·s −1 . The wave distance range is 20 to 40 mm.
Overall, a comprehensive comparison of the fluctuation in x and y directions is made. The results show that the velocity fluctuation amplitude in x direction is twice than that in y direction. The velocity fluctuation is larger near the side dam.  Figure 10 shows the turbulent kinetic energy distribution in molten pool. It indicates that the lower area of the molten pool has higher turbulent kinetic energy due to the vortex at the bottom of casting roll. The peak value can reach 0.0232 m 2 ·s −2 on line 4 and 0.0356 m 2 ·s −2 on line 5. It suggests the mixing degree of solute in the central molten pool is smaller but the distribution range of mixing area is wider. The peak on line 5 is greater than that on line 4. The turbulent kinetic energy on line 5 increases near the free surface, resulting in a small peak. This phenomenon is due to the higher kiss line near the side dam.
The molten metal flow in the molten pool will affect the uniformity of heat transfer. Consequently, it ultimately affect the quality of the strip. The free surface fluctuation of the molten pool is critical to whether the free surface is crusted and whether the strip has longitudinal cracks [44]. In Figs. 8, 9, and 10, we find that the free surface fluctuation has little change after adding vibration. It is not caused by vibration but the distributor nozzle jet and the rotation of the crystallization roller. The free surface fluctuation is still acceptable after the vibration is added. It will not lead to the deterioration of strip quality. The vibration only plays a certain role near the side dam because of the enhanced heat transfer. This further proves that the vibration has a small effect on flow but mainly affect the thermal boundary conditions at the side dam. Figure 11a, b, and c are the temperature feilds on face 3, face 4, and face 2, respectively. The basic laws of the temperature field at these three sections are consistent. Figure 11d is the temperature field of the y symmetry plane. The figure indicates that the temperature of the lower half of the molten pool will be 100 to 200 K lower than that of the upper half because of the high circumfluence velocity and the high contact pressure between rollers. Fujita et al. [45] verified that experimetally.

Solidification and temperature distribution with side dams vibrating
In this paper, 0.3 is selected as the liquid fraction of the actual kiss point, which is consistent with Raza's [46] results. The intersection of kiss point line and each curve is the solidified kiss point. Figure 12 shows that kiss point is located at 15 mm to 30 mm away from outlet. The liquid fraction on face 3 is lower than that on Face 2 and face 4 at 55 mm away from the center line of the molten pool bottom. The reason is that this area is located at the y direction distributor nozzle. The casting roll rotates and brings the molten steel with excessive superheat to the lower side when it flows into the molten pool, resulting in a lower kiss point. The liquid fraction on the center line of side dam decreases within 75 to 125 mm. The circumfluence velocity in this area is high because of the x direction distributor nozzle jet. This leads the heat transfer between the molten pool and the side dam to be enhanced and the liquid fraction here will first decrease and then increase.
It is worth pointing out that too high or too low kiss point is undesirable. Too high kiss point leads to excessive rolling force, increased tendency of strip cracking and even roll  jamming. By contraries, too low kiss point leads to reduction of plastic deformation range, formation of shrinkage and cavity and even melt leakage. This shows that it is very important to selected appropriate vibration parameters. Vibration did not significantly change the temperature field in the molten pool. The temperature field information we obtained is basically similar to that obtained by predecessors [47]. It also indicates that vibration only changes the thermal boundary conditions near the side dam again. The main factors affecting the temperature field are the casting parameters of the molten pool, the parameters of the crystallization roll and the structure of the distributor. Figure 13 shows the liquid phase distribution on side dam surface under different vibration frequencies. The area between 0.3 and 0.6 isoline is the mushy zone of the molten pool. That between 0.6 and 1 is the molten area. The molten steel near the side dam is in a semi-molten state at 0 Hz. The liquid fraction begins to rise when it is vibrating because the interfacial heat flux between the side dam and the molten pool decreases. The kiss point declines significantly because the vibration introduced causes the separation between the side dam and shell on its surface. Comparing the liquid fraction distribution under different frequencies, it is found the area of the erosion pit decreases significantly and the kiss point increases as the vibration frequency increases because the heat transfer between the side dam and the molten pool is enhanced as the frequency increases.

Influence of vibration frequency
As shown in Fig. 14. The area of mushy zone at the lower part near the side dam without vibration is significantly larger than that under vibration conditions. The kiss line rises from left to right along the x direction because of the high interfacial heat flux without vibration and the increase of solidification velocity at the lower part near the side dam. With the increase of vibration frequecy, the kiss line obviously increases, the mushy zone area increases, the rolling interval extends, and the strip forming is optimized. This is more conductive to the formation of high quality strips. Figure 15a indicates that the turbulent kinetic energy near the side dam under vibration is greater than that without vibration. The peak is located at the center of the molten pool. The solidification zone at 7 Hz is located at the lowest part of the molten pool because the kiss line is close to the outlet. The distance from the fluid mixing zone in the molten pool to the outlet increases with the increase of the vibration frequency. This also indicates the kiss line is much higher. The mixing zone is wider. This optimize the mixing of solute in the molten pool. This also optimize the distribution of crystal nucleus. In this way, the strip crystal structure is refined. Then denser and better quality strips are obtained. From Fig. 15b, the turbulent kinetic energy near the side dam increases as a whole with the increase of the vibration frequency. Specifically, the turbulent kinetic energy increases first and then decreases. It changes circularly in x direction. The turbulent kinetic energy reaches the peak value in x direction within 15 to 20 mm. It reaches the peak value again within 45 to 55 mm. The turbulent kinetic energy increases with vibration frequency increase before 45 and 55 mm. However, it changes by contratries after that. It is believed that vibration still improves the turbulent kinectic energy of molten steel, which will also optimize the mixing of solutes. Figure 16 indicates that the temperature near the side dam without vibration is significantly lower than that under vibration conditions. The temperature of the strip edge decreases within 5 mm away from the side dam. The decrease reaches 176 K. Moreover, the strip outlet temperature decreases with vibration frequency increase. There is little difference between the strip edge temperature at 13 Hz and 30 Hz but that at 7 Hz is 100 K higher than 30 Hz. More uniform strip outlet temperature will reduce the thermal stress and help obtain better-quality strips. The area of erosion pit becomes larger and the position of kiss line decreases when low-frequency vibration is added. The reason is that there is an air gap between the side dam and the molten pool. The air gap destroys the heat transfer. The increase of the erosion pit put forward higher requirements for the side dams. That requires us to reasonably design the upper water channel of the side dam. However, the erosion pit shrinks and the kiss line rises with the frequency increase. The vibration starts to optimize the heat transfer. The rise of the kiss line extends the casting rolling interval, which is more conducive to the strip forming. The shell formed at the upper part of the side dam also breaks away. This prevents the occurrence of edge defects of the strip. Turbulence kinetic energy in the molten pool is generally improved under vibration. This indicates that vibration disturbs the flow. Research shows that this disturbance effect increases the nucleation rate and refine grains [48,49]. Research by Lu et al. [50] shows that the problem of central segregation is mainly caused by the enrichment of alloy elements at kiss point. The disturbance effect will stir the molten pool, homogenize the solute field distribution in the molten pool, inhibit the local enrichment of alloy elements, and effectively improve the central segregation of cast rolling strip. Figure 17 shows that the area of erosion pit when the casting temperature is 1820 K is larger than that under other casting temperatures. The area of erosion pit increases obviously with the casting temperature increase when it exceeds 1840 K. It is found that the solidification distribution law in the mushy zone on the side dam surface is similar under different casting temperature in Fig. 17. This shows the casting temperature does not play a decisive role in the solidification distribution on the side dam. Figure 18 indicates that the solidification distribution on the y symmetry plane when the casting temperature is 1820 K is completely different from that under other casting temperatures. The main two differences are that the kiss line in the lower right area of the molten pool is not increased and the mushy zone area distribution is reduced. Comparing  Fig. 18a, b, c, and d, the kiss line decreases with the casting temperature increase. Excessive casting temperature is unacceptable. This will cause the liquid steel leakage. Higher casting temperatures also make the kiss lines near the side dam significantly higher than that far away from the side dam, which will make the strip edge quality worse. Figure 19a shows that the turbulent kinetic energy distribution is within the range of 44 to 104 mm in x direction. The peaks value on the center line of the molten pool near the side dam reachs 0.0047 m 2 ·s −2 when the casting temperatures are 1820 K and 1840 K. And it reaches 0.0163 m 2 ·s −2 when 1860 K and 1880 K, which is 3 to 4 times than that at lower casting temperatures. Turbulent kinetic energy at the outlet when 1880 K is not zero, indicating that the molten steel at the outlet has not completely solidified. This will lead to problems such as steel leakage and strip not forming. Figure 19b shows that the turbulent kinetic energy near the side dam decreases with the increase of temperature. The   Figure 20 indicates that there are three peaks in the temperature distribution. They are exactly the position of distributor nozzle. Obviously, this is because of the distributor nozzle jet. The strip outlet temperature fluctuation becomes more uniform under lower casting temperature because of the extension of the rolling interval. The difference between strip outlet temperature and solidus temperature is only 75 K when the casting temperature is 1800 K. This is disadvantageous to the formation of strip. The strip temperature increases with the casting temperature increase.

Influence of casting temperature
For the side dam surface, the casting temperature does not play a decisive role in the solidification distribution. However, it is also found that the size of the erosion pit decreases first and then increases with the temperature increase. Therefore, selecting a good casting temperature is important. Proper casting temperature and vibration parameters effectively prevent the excessive erosion of side dam and prolong its service life. High casting temperature makes the kiss line decrease obviously. It worsens the strip quality. At the same time, high temperature makes the temperature distribution near the kiss line uneven and height of the kiss line uneven. Uneven temperature and the uneven kiss line lead to defects in the strip. Moreover, that In x direction also directly leads strip to bear greater thermal stress and be easy to crack. High casting temperature also leads to the incomplete solidification, which leads extremely dangerous breakout. The turbulent kinetic energy is small when the casting temperature is too low. The solute cannot be fully mixed so that segregation and other problems occur. The excessive rise of kiss line also leads to roller sticking. Therefore, in this paper, the casting temperature of 1840 to 1860 K is relatively appropriate.

Conclusions
In this paper, numerical simulations are carried out to obtain the basic laws of flow, heat transfer, and solidification in the molten pool of TRSC with the side dam vibrating. The conclusions are summarized as follows.
1. The fundamental flow and heat transfer characteristics under 7 Hz, 1840 K is obtained. The free surface fluctuations is larger near the side dams. The velocity fluctuation amplitude in x direction is twice than that in y direction. The turbulent kinectic energy near the side dam reachs 0.0356 m 2 ·s −2 . However, the turbulent kinectic energy in the center of the molten pool is only 0.0232 m 2 ·s −2 . The temperature in the lower part of molten pool is 100 to 200 K higher than that in the upper part. The kiss lines is located at 15 to 30 mm away from the outlet. It is higher than that without vibration. 2. The vibration introduced does optimize the TRSC process. As the frequency increase, the heat transfer is enhanced and the kiss line is higher, the mushy zone area is larger, the rolling interveal is longer. These are beneficial to strip formation. The fluid mixing zone becomes wider. This is not only good for the mixing of solues but the crystal nucleus distribution. Also, the vibration makes the strip outlet temperature more uniform to reduce the thermal stress. The difference in temperature is reduced from 176 to 75 K because of the vibration. Thirteen hertz is considered to be the optimal frequency. 3. The casting temperatures also make some differences.
Higer casting temperature leads to lower and more uneven kiss lines. The turbulent kinectic energy under higher casting temperature is 3 to 4 times higher than that under lower temperature. At 1880 K, the turbulent kinectic energy is not 0 at the outlet, indicating the molten steel has not completely solidified. Also higher casting temperatures make the strip outlet temperature more uneven. At 1880 K, the difference in temperature is bigger than 70 K. However, that is smaller than 30 K at 1820 K. One thousand eight hundred forty to 1860 K is considered to be the best casting temperature.
Funding This work was supported by the National Natural Science Foundation of China (No. 51706037).