Dynamic Distributions of Mold Flux and Air Gap in Slab Continuous Casting Mold

Transcription

1 ISIJ International, Vol. 59 (2019), ISIJ International, No. 2 Vol. 59 (2019), No. 2, pp Dynamic Distributions of Mold Flux and Air Gap in Slab Continuous Casting Mold Zhenyu NIU, Zhaozhen CAI* and Miaoyong ZHU School of Metallurgy, Northeastern University, NO. 3-11, Wenhua Road, Heping District, Shenyang, P. R. China. (Received on September 5, 2018; accepted on September 20, 2018; J-STAGE Advance published date: November 20, 2018) The distributions of mold flux and air gap in shell/mold gap have significant influences on the shell heat transfer in slab continuous casting mold. To describe the dynamic distribution characteristics of the mold flux and air gap, a three-dimensional thermo-mechanical model coupling with a complex interfacial heat transfer model was developed, in consideration of the interactions between the thermo-mechanical behaviors of solidified shell and distributions of mold flux and air gap. Based on these, the contact and heat transfer behaviors between the shell and mold copper plates, as well as the influence of wide face mold taper on the distributions of mold flux and air gap during a peritectic steel continuous casting were studied. The results show that the temperatures of copper plate hot faces beneath the bolt columns are higher than those beneath the deeper channels, and the calculated temperatures of copper plates coincide well with the measured data by thermocouples. Due to the thermal contraction, the shell corners in mold shrink away from mold corners as the slab moving downward, which causes the thick mold flux film and air gap concentrate around the corners and off-corners. As a result, the hot spots form at the shell off-corners. With greater wide face tapers, the thicknesses of mold flux film and air gap at wide face corner decrease. When the wide face taper increases to 4 mm, the air gap on shell wide face corner disappears near the mold exit. KEY WORDS: slab continuous casting; heat transfer; air gap; mold flux film; simulation. 1. Introduction The homogeneity of shell heat transfer in mold is one of the most important key factors to ensure the slab high quality production. Due to the shell dynamic shrinkage in practical slab continuous casting, the distributions of mold flux film and air gap in mold are quite non-uniform. As a result, the shell solidification in mold becomes quite uneven, which would induce the slab surface and subsurface cracks, as well as longitudinal deprssion. 1 4) To homogenize the shell heat transfer in mold, deep investigation on the distribution behaviors of the mold flux film and air gap in mold during slab continuous casting is quite urgent for improving the casting process or optimizing mold structure. Since the distribution of mold flux film and air gap formation in mold are invisible and affected by many factors, such as the mold cooling structures and cooling processes, 5,6) physical properties of mold flux, 7 9) mold taper 10,11) etc., many previous works have been carried out to reveal the evolution laws of the thermal and mechanical behaviors of shell and mold copper plates during the continuous casting by mathematical simulations. In the early stage, most of the mathematical models 12 14) characterized the heat transfer between mold and solidi- * Corresponding author: caizz@smm.neu.edu.cn DOI: fied shell as heat transfer boundary conditions which were obtained by the regression analysis 15) of the measured temperature data by thermocouples in mold copper plates. In these models, the distributions of the heat transfer media infilling the shell/mold interfacial gap were ignored. In order to consider the influence of mold flux film distribution on the shell heat transfer, Thomas and his co-workers 16) proposed an interfacial heat transfer model, named CON1D, which took the mass conservation of mold flux in the shell/mold gap into account and described the mold flux film longitudinal distribution. The CON2D model proposed by Li and Thomas 17) took the mutual influence between thermal contraction of solidified shell and the size of interfacial gap into account. Both of the models were successfully applied to simulate the shell solidification behaviors, and the idea tapers for slab and billet molds and sub-mold bulging behaviors were predicted. 10,11,18 20) Nevertheless, the effect of the shell thermal contraction on the distributions of different mold flux film layers and air gap could not be described by the models. Based on the above investigations, Saraswat et al. 21) developed a two dimensional thermo-mechanical model, by which the distributions of various flux layers and air gap in a billet mold were predicted. In the recent research, Cai et al. 22,23) developed a two dimensional thermo-mechanical coupled finite element model, which could predict the shell shrinkage, air gap formation and mold flux film distribution 283

2 in shell/mold gap during slab continuous casting. However, the influences of the heat transfer and shrinkage of the solidifying shell along casting direction on the mold flux film distribution and air gap formation couldn t be described by the two dimensional slice models. Previous works have provided various modelling approaches to gain insights into the heat transfer and deformation behaviors of slab in continuous casting mold. 24) However, the distributions of the heat transfer media infilling the shell/mold gap and the 3-D contact behavior between mold and slab were partly or seldom involved which may greatly affect the simulated results in modelling the slab defect formation such as surface cracks and off-corner depression. 25) In order to describe the distribution characteristics of the mold flux films which include the liquid and solid flux film layers, and the formation process of air gap under the complex slab continuous casting conditions, a three dimensional finite element model coupling with an interfacial heat transfer model, in which the dynamic distributions of the mold flux film and air gap were considered, was developed in the present work. Based on these, the shell deformation and the temperature evolution of shell, as well as the non-uniform distributions of mold flux films and air gap formation during a peritectic steel solidifying in mm 300 mm mold were predicted. Moreover, the distribution characteristics of the mold flux film and air gap in shell/mold gap with the different wide face mold tapers were investigated. 2. Model Description 2.1. Mold Geometry Since the geometry of the practical slab continuous casting mold is symmetrical in the directions of its width and thickness as well as the heat transfer and deformation of solidified shell in it, a quarter of mold-slab system was selected as the computational domain for reducing the computation cost. The detailed geometric features of the mold copper plates are shown in Figs. 1 and 2. It should be noted that the gradient coating layers in the mold hot faces ranging from 0.5 mm to 1.5 mm from mold top to exit are coated there to protect the copper plates from wear. According to the research by Meng et al., 26) the mold temperature is affected by the coating layer to a certain extent, therefore, Fig. 1. Geometry of slab continuous casting mold. (Online version in color.) Fig. 2. Water channel structure of the mold copper plates. 284

3 a coating layer was set exactly as the practical one in the finite element model. Moreover, in most of practical thick slab continuous casting, the copper plate of mold narrow face is thicker than that of wide face. In the present work, the thickness of mold narrow face copper plate is 10 mm thicker than the wide face Mathematical Model Interfacial Heat Transfer Model The heat transfer between shell and model is quite complex. At the upper part of mold, shell surface temperature is higher than the mold flux crystallization temperature. The gap between mold and shell is filled with liquid flux and solid flux, where at the side near shell is liquid flux and near the mold side is solid flux. As the shell surface cools down, the liquid flux turns to the solid flux gradually. At this time, once the interfacial gap continuously grows due to the shell shrinkage, the air gap forms between mold and solid flux layer. Accordingly, the heat transfer model in shell/mold gap can be divided into two patterns, as shown in Fig. 3. According to the heat transfer patterns, the thermal resistances of different media in the gap can be expressed by Eqs. (1) (3). 4,27) For liquid flux: d Rliq c liq kliq E liq d liq 1 Rliq rad s f... (1) rf ( Tcry Ts )( Tcry Ts) Rliq Rliq c Rliq rad Where, R c liq, R rad liq and R liq are the conductive, radiative and total thermal resistances of liquid flux in m 2 K/W, respectively. d liq is the thickness of liquid flux film in m. k liq is the thermal conductivity of the liquid flux in W/(m K). E liq is the absorption coefficient of liquid flux in m 1. ε s and ε f are emissivities of shell and the flux, respectively. T cry and T s are the temperatures of mold flux crystallization and shell surface in K, respectively. δ is the Stefan-Boltzmann constant, the value is W/(m 2 K 4 ). r f is the refractive index of mold flux. For solid flux: c dsol Rsol ksol Esoldsol 1 rad f m Rsol rf ( Tcry Tb )( Tcry Tb) Esoldsol s m 1 = rf ( Tb Ts )( Tb Ts ) c rad Rsol Rsol Rsol (for T T ) s cry (for T T ) cry s... (2) Where, R c rad sol, R sol and R sol are the conductive, radiative and total thermal resistances of solid flux in m 2 K/W, respectively. d sol is thickness of solid flux film in m. k sol is the thermal conductivity of the flux in W/(m K). E sol is the absorption coefficient of solid flux in m 1. ε m is the emissivity of the mold copper plate. T b is the interface temperature at the solid flux side in K. For air gap: c dair Rair kair Eairdair 1 rad m f Rair... (3) rair ( Tm Ta )( Tm Ta) c rad Rair Rair Rair Where, R c air, R rad air and R air are the conductive, radiative Fig. 3. Schematic diagram of shell solidification in mold and the circuit diagram of the interfacial thermal resistance. (Online version in color.) 285

4 and total thermal resistances of air gap in m 2 K/W, respectively. d air is thickness of air gap in m. k air is the thermal conductivity of air gap in W/(m K). E air is the absorption coefficient of air gap in m 1. T a is the interface temperature at the air gap side in K. T m is the temperature of mold surface in K. r air is the refractive index of air. Since the heat flux passing through various layers is conserved, the thicknesses and thermal resistances of different layers can be obtained by solving the following equations. In the calculation, T s and T m were the current temperatures of slab and mold which were obtained from the finite element model. T cry was given as a constant. T a and T b were obtained by the Newton iteration method. For heat transfer pattern Ⅰ: Ts Tcry Tcry T Rliq Rsol dgap dliq dsol For heat transfer pattern Ⅱ: Ta Tm T T Rair Rint dgap dsol dair b Tb Tm Rint... (4) T T R b a s b sol... (5) Where, d gap is the total thickness of mold/slab gap in m. R int is the contact thermal resistance between mold copper plate and solid flux film formed by the mold flux film shrinkage during solidification. In the present work, the thermal resistance was defined as a function of the solid flux thickness. The value was assigned according to researches by Cho et al. 28,29) Therefore, the heat flux of the shell/mold interface, q t, can be expressed by Ts Tm qt... (6) Rint Rsol Rliq Rair During the practical casting process, the mold flux consumption increases with the casting speed, therefore, it is reasonable to assume that the move speed of mold flux film was in proportion to the casting speed. In the present work, the 0.25 mm initial thickness of the mold flux film was set according to the casting speed and the mold flux consumption. The thermal physical properties of the mold flux, air gap, mold copper plate, as well as shell used in the equations were listed in Table Heat Transfer of Mold and Slab The heat transfers in mold and slab are governed by the conservation of energy. According to the characteristics of the mold heat transfer, the heat transfer of the copper plates was governed by the following transient heat conduction equation: Tm m c m kmtm... (7) t Where, ρ m, c m, and k m are density, specific heat and conductivity of mold copper plates in kg/m 3, J/(kg K), W/ (m K), respectively. T m is the temperature of mold copper plates in K, t is the current time in s. Table 1. Thermal physical properties of mold flux, air gap, mold copper plate, as well as shell. 4,7,21) Heat transfer of the slab could be described by the following equation: HT ( s ) s ( T s ) ks( Ts) Ts t... (8) Where, ρ s (T s ), k s (T s ) and H(T s ) are the temperature dependent density, conductivity and enthalpy of the steel in kg/ m 3, W/(m K), J/kg, respectively. T s is the temperature of slab in K. The thermal boundary conditions on the symmetry planes of both slab and mold were expressed by the following equations. q k ( T )( T ) n 0... (9) s s s s qm km( Tm ) n 0... (10) Where q s and q m are the specified heat fluxes on the symmetry planes of slab and mold in W/m 2, n is the normal vector of the corresponding symmetry planes. Through solving the interfacial heat transfer model which has been described in chapter 2.2.1, heat transfer between mold and slab could be obtained. The detailed heat fluxes loading on both mold hot faces and slab surface were expressed as Eq. (6). Heat transfer between the water channel walls and the cooling water was expressed as following equation: q km( Tm) n hw( Tm Tw )... (11) Where, T w is the temperature of cooling water in K, whose values change linearly from inlet water temperature to outlet water temperature. h w is the heat transfer coefficient between cooling water and the water channel walls in W/(m 2 K), which can be given according to the following dimensionless correlation. 30) hd w k w w Items Unit Value Crystallization temperature, T cry K Thermal conductivity of liquid flux, k liq W/(m K) 1.8 Thermal conductivity of solid flux, k sol W/(m K) 1.63 Thermal conductivity of air, k air W/(m K) Emissivity of mold, ε m 0.4 Emissivity of flux, ε f 0.9 Emissivity of shell, ε s 0.8 Absorption coefficient of liquid flux, E liq m 1 51 Absorption coefficient of solid flux, E sol m Absorption coefficient of solid flux, E air m 1 0 Refractive index of flux, r f 1.6 Refractive index of air gap, r air 1.0 vd w w w w cww k w... (12) Where, ρ w, v w, k w, μ w and c w are density, velocity, conductivity, dynamic viscosity and specific heat of the cooling water in kg/m 3, m/s, W/(m K), Pa s, and J/(kg K), respec- 286

5 tively. d w is the hydraulic diameter of water channel in m. The initial temperature of the simulation steel at meniscus was assumed to be the pouring temperature Stress Model Deformation behaviors of solidified shell in mold were governed by the following equation: F 0... (13) Where, σ are stress in Pa. F is the mass force in N/m 3. In consideration of the creep behavior of solidified shell during practical continuous casting, an elasto-viscoplastic constitutive model 31) was applied in the present work, as shown in the following equations: Q n m C exp t T 2 C wc wc... (14) n Ts Ts m Ts Ts Where, ε and σ are the equivalent strain rate and equivalent stress in s 1 and MPa, respectively. C is pre-exponential factor whose value have relations with the carbon content of steel w c pct. n is the temperature dependent equivalent stress exponent. m is the temperature dependent time exponent. Q is the ratio of plastic deformation activation energy to the gas constant whose value is K 1. The displacement boundary of the slab nodes on the symmetric faces was set as follow: { u s } n 0... (15) And the displacement boundary of the slab nodes at the exit of mold was defined as the following equation: w Vc t... (16) Where, {Δu s } is the displacement vector increment of the slab nodes on the symmetric faces in m. w is the displacement along the casting direction in m. V c is casing speed in m/s. Ferrostatic pressure on the solidification front was calculated by the following equation: P moltengh... (17) Where ρ molten, g and h are the density of molten steel, gravity acceleration and metallic bath depth of the said location in kg/m 3, m/s 2 and m, respectively. The detailed application of the ferrostatic pressure can be found in the reference. 32) All the properties of the simulation steel mentioned above, such as phase transformation temperatures, conductivity, enthalpy and thermal linear expansion, etc. were given by a micro-segregation model shown in our previous work. 22) The properties of the cooling water and copper plates were listed in Table 2. To solve the above models, a finite element commercial software of MSC.Marc was applied with the method of direct coupled field. During the calculation, the activate/ deactivate element technique was used. The work mechanism is that once the slab moves into the mold working region (between the meniscus and the mold exit), the elements of the slab would be activated. Otherwise, the elements were deactivated. Detailed calculation flow chart of the models was shown in Fig Results and Discussion 3.1. Model Validation Since the shell heat transfer and deformation in moldslab system are invisible and in high temperature, it is difficult to validate the validity of the models by detecting the behaviors directly. However, in order to monitor the mold breakout, many thermocouples are often installed in mold copper plates to measure the temperatures. Therefore, the temperature distributions of the copper plates measured by the thermocouples were used to validate the validity indirectly in the present work. Figure 5(a) shows the calculated temperature fields of the copper plates under the casting conditions shown in Table 3. It could be seen that the maximum temperature of mold Table 2. Thermal properties of copper plates and cooling water. 14,23) Items Copper Water Nickel Thermal conductivity, W/(m K) 298 K K K 310 Fig. 4. Calculation flow chart of the models Specific heat, J/(kg K) Density, kg/m

6 Fig. 5. Temperatures of mold copper plates: (a) calculated temperatures, comparisons between calculated and measured temperatures at (b) wide face and (c) narrow face, (d) temperature evolutions measured by the thermocouples nearby the corner. Table 3. beneath the bolt columns are 10 K higher than those beneath the deeper channels. At the bottom of mold, temperatures rise up because no cooling water flows through there, the result is similar to the study of by Hibbeler.33) Figures 5(b) and 5(c) show the comparisons of the temperature distributions of mold wide and narrow faces at the positions of three-row thermocouple installations between the calculation and the measurement. It can be seen that the simulation temperatures coincide quite well with the measured temperatures. It should be noted that since the shell corner solidification in mold is more complex than those of wide and narrow faces center, the validation of the temperature conformity between simulation and measurement is quite necessary. Figure 5(d) shows the temperature evolutions of 3 thermocouples installed 50 mm nearby the slab corner under steady casting condition. The average temperatures of the thermocouples marked in Fig. 5(a) as A, B, and C are K, K, and K. That means the measurement temperatures of the copper plate nearby the corner are quite same to the simulation shown in Fig. 5(b). Therefore, the present models can be applied to well describe the mold-slab heat transfer and deformation behaviors during carbon steel casting. Typical casting conditions. Items Value Main chemical composition of steel 0.08C-0.3Si-1.5Mn-0.013P-0.003S (wt%) Size of slab cross section (mm mm) Casting speed (m/min) 0.85 Pouring temperature (K) Effective mold height (mm) 800 Mold narrow face taper (%) 1.05 Mold wide face taper (m) 2, 3, 4 Mold wide face water flow (L/min) Mold narrow face water flow (L/min) 670 Mold input water temperature (K) 305 Mold output water temperature (K) 310 Mold flux consumption (kg/ton steel) 0.45 hot face appears at the position of 20 mm below meniscus. The highest temperatures of the wide and narrow faces are about 519 K and 593 K, respectively. Because the thickness of the narrow face copper plate is 10 mm thicker than that of wide face, the heat transfer efficiency of the copper plate reduces. As a result, the hot face temperature of the narrow face is overall higher than the wide face at the same height. Moreover, because of the arrangement of the cooling water channels shown in Fig. 2, the temperatures of the areas 3.2. Shell Deformation The deformation behavior of shell solidifying in mold is the main factor to cause the uneven distribution of mold flux film and the air gap formation in shell/mold gap. Figure 6 shows the shell deformation at different positions of 100 mm, 300 mm, 500 mm and 800 mm below mold meniscus. At the initial solidification stage of 100 mm below meniscus, the shell corner begins to detach from copper plates 288

7 Fig. 6. Deformation of slab corner at (a) 100 mm, (b) 300 mm, (c) 500 mm, (d) 800 mm below meniscus. because of the thermal contraction. However, the gap size is quite small. As the shell moving down, the gaps between shell and mold at both of wide and narrow face corners grow continuously. When the shell moves down to 500 mm below meniscus, because the narrow face mold taper compensates continuously, the gap of shell narrow face corner turns to reduce. While, during the whole solidification process, the gap of wide face corner grows continuously because the mold taper of 2 mm of the wide face is too small for 300 mm thickness slab casting Distributions of Mold Fluxes and Air Gaps Figure 7 shows the liquid flux film distributions around the shell wide and narrow face corners caused by shell deformation mentioned above. For the wide face, the liquid flux film distributes homogeneously at the meniscus. The thickness is about 0.22 mm. With the shell moving downward, the thickness of the center area decreases. When the shell moves down to 252 mm below meniscus, the liquid flux solidifies completely. As to the thickness of the offcorner, the general distribution characteristic shows rapid increase first and decrease then for the evolutions of shell/ mold gap size and shell surface temperature. The maximum thickness of liquid flux film reaches 0.43 mm at the position 50 mm below meniscus and 10 mm away from the corner. Moreover, because the mold flux film of the off-corner is quite thicker than that of the center area, the off-corner liquid flux solidifies laggingly, it disappears at about 443 mm below meniscus. As to the shell corner, because of the high-efficiency heat transfer, its temperature decreases quickly. The liquid flux around shell corner correspondingly solidifies quickly. The liquid flux disappears at the height of 91 mm below meniscus. Figure 7(b) shows the shell narrow face liquid flux distribution. It can be seen that its general distribution trend is similar to that of wide face. The liquid flux films covering Fig Liquid flux distribution around shell corners: (a) wide face, (b) narrow face.

8 Fig. 8. Solid flux distribution around shell corners: (a) wide face, (b) narrow face. (Online version in color.) Fig. 9. Air gap formation around shell corners: (a) wide face, (b) narrow face. (Online version in color.) center area and off-corner disappear at 261 mm and 382 mm below meniscus. The maximum thickness of liquid fluxes reaches 0.42 mm at the position 43 mm below meniscus and 8 mm away from the corner. Figure 8 shows the solid flux film distributions around the shell wide and narrow face corners. For the wide face, the solid flux film evenly distributes at the meniscus, and the thickness is about 0.03 mm. As the shell moving down, the thickness of the center area begins to increase, which corresponds to the decrease of liquid flux film thickness. When the shell moves down to the 252 mm below meniscus, the thickness of center area reaches its maximum (about 0.25 mm) and stop grows. At the off-corner area, the thickness shows a faster growth rate with the evolution of shell/mold gap size. The maximum thickness is about 1.46 mm at the position of 352 mm below meniscus and 10 mm away from corner. As to the corner, the thickness is thinner than that of the off-corner because it solidifies in an earlier stage. Figure 8(b) shows the shell narrow face solid flux film distribution. The general distribution trend is similar to that of wide face. The solid flux film covering center area grows to its maximum thickness of 0.25 mm at 261 mm below meniscus, while, in the off-corner, the maximum thickness of 1.32 mm appears at the position of 322 mm below meniscus and 8 mm away from the shell corner. The air gap distributions around shell wide and narrow face corners are shown in Fig. 9. It can be seen that the air gap firstly forms at the shell corner 91 mm below meniscus. For the wide face, since the shell corner shrinks continuously and the compensation of the mold taper in the slab thickness direction is insufficient, the air gap grows continuously, where the maximum thickness reaches about 0.7 mm at the mold exit. Different from the wide face, the narrow face air gap increases first and then decreases. The maximum thickness is 0.48 mm at the position of 330 mm below meniscus. At the position of 66 mm above mold exit, the corner air gap completely disappears Shell Temperature Evolution Figure 10(a) shows the surface temperature distributions of shell wide and narrow faces under the above heat transfer conditions. At the meniscus, the shell temperature is the pouring temperature (1 814 K). With the shell moving downward, the shell surface temperature decreases sharply. When the shell moves down to 100 mm below meniscus, the temperatures of shell wide and narrow face off-corners 290

9 Fig. 10. Slab surface temperature (a) and the shell growth of wide face centerline (b) in mold. become higher than the face center areas because of the thick mold flux film distribution and air gap formation. When the shell moves to the exit of mold, temperatures of slab corner, wide face off-corner, narrow face off-corner, wide center and narrow center are K, K, K, K and K, respectively. The high temperatures of the off-corners would increase the probability of slab surface crack and longitudinal depression. Figure 10(b) shows the shell wide face centerline growth in the mold. At the positions of 700 mm and 800 mm below meniscus, the shell thicknesses are 16.7 mm and 18.2 mm. The thicknesses are quite close to the measurement values of 17.1 mm and 18.8 mm gotten from breakout shell Effect of Mold Wide Face Taper on Mold Flux and Air Gap Distributions As mentioned above in Chapter 3.2 that the current mold taper of wide face is too small to compensate the shell wide face shrinkage, increasing the mold taper by 1 mm and 2 mm were introduced to minimize the size of shell/mold gap of the wide face in the present work. Figure 11(a) shows the mold flux film distributions of shell wide face corner under different wide face tapers of 2 mm, 3 mm, and 4 mm. It could be seen that the maximum thickness of mold flux film at mold wide face corner decreases slightly with the increase of wide face taper. The mold flux film reduces about 0.03 mm as the mold wide face Fig. 11. Distributions of wide face mold flux film (a) and air gap (b) under different wide face tapers. taper increases 1 mm. Formations of the air gap at shell wide face corner under different wide face tapers are shown in Fig. 11(b). It could be seen that the air gaps under different wide face tapers form at the similar positions, where is about 91 mm below meniscus. However, the air gap distributions with different mold tapers show quite different tendency as the shell moving downward. When the mold taper increases to 3 mm, the air gap almost remains stable as the shell moves down to 300 mm below meniscus. Once the mold taper increases to 4 mm, the air gap greatly reduces when the shell moves down to 300 mm below meniscus, and it disappears when the shell moves to about 80 mm near the mold exit. At the mold exit, the thickness of wide face air gap decreases about 0.4 mm with the wide face taper increases per 1 mm. Figure 12(a) shows the mold flux film distributions of narrow face corner under different wide face tapers. It can be seen that the change of mold wide face taper has very small influence on the distribution of narrow face mold flux film. However, as to the air gap, it increases slightly with the wide face taper since the shell shrinkage increases with greater wide face tapers. 291

10 at mold exit. While, the air gap of narrow side increases first and then decreases. The maximum thickness of 0.48 mm appears at the height of 330 mm below meniscus, and disappears at the height of 66 mm above mold exit. (4) With the mold wide face taper increases per 1 mm, the maximum thicknesses of the wide face mold flux film and air gap decrease about 0.03 mm and 0.4 mm, respectively. Once the wide face taper increases to 4 mm, wide face air gap near the mold exit disappears. The change of mold wide face taper has small influence on narrow face mold flux film distribution, while, the narrow face air gap slightly increases with the wide face taper increases. Acknowledgements The present work is financially supported by the National Natural Science Foundation of China ( , ), Fundamental Research Funds for the Central Universities of China (N ). REFERENCES Fig. 12. Distributions of narrow face mold flux film (a) and air gap (b) under different mold wide face tapers. 4. Conclusion In this paper, a thermo-mechanical model coupling with an interfacial heat transfer model between shell and mold was developed to predict the distributions of mold fluxes and air gaps during a peritectic steel slab continuous casting. Some conclusions could be drawn as follow: (1) At the upper part of the mold, the shell corner detach from the mold after it completely solidified. As the solidified shell moves downward, the corner gap at shell wide face grows continuously, while the narrow face air gap grows quickly first and then reduces. (2) The liquid flux film distributes uniformly at the meniscus, while it became thicker around the corner and offcorner and shows a distribution trend of increase first and decrease then. The maximum thickness appears at 40 mm to 50 mm below meniscus and 8 mm to 10 mm away from the corner. As for the solid flux film, the thickness continuously increases before the liquid flux completely solidified, and the maximum thickness appears at 320 mm to 360 mm below meniscus and 8 mm to 10 mm away from the corner. (3) Air gap firstly forms at shell corner 91 mm below meniscus. At shell wide face corner, the air gap grows continuously, where the maximum thickness is about 0.7 mm 1) R. B. Mahapatra, J. K. Brimacombe and I. V. Samarasekera: Metall. Trans. B, 22 (1991), ) A. Yamauchi, K. Sorimachi, T. Sakuraya and T. Fujii: ISIJ Int., 33 (1993), ) K. C. Mills and A. B. Fox: ISIJ Int., 43 (2003), ) H. Nakada, M. Susa, Y. Seko, M. Hayashi and K. Nagata: ISIJ Int., 48 (2008), ) X. Jin, T. Ren and J. Guan: 2009 Int. Conf. on Measuring Technology and Mechatronics Automation, IEEE Computer Society, Washington, DC, (2009), ) D. Jing and K. Cai: Acta Metall. Sin., 36 (2000), ) A. Yamauchi, T. Emi and S. Seetharaman: ISIJ Int., 42 (2002), ) K. C. Mills: ISIJ Int., 56 (2016), 1. 9) K. C. Mills: ISIJ Int., 56 (2016), ) C. Li and B. Thomas: ISSTech Steelmaking Conf., ISS-AIME, Warrendale, PA, (2003), ) B. G. Thomas, M. Dziuba and G. D. Gresia: 14th IAS Steelmaking Conf., Instituto Argentino de Siderurgia, Buenos Aires, (2003), ) J. K. Park, I. V. Samarasekera, B. G. Thomas and U. S. Yoon: 83rd Steelmaking Conf., ISS/AIME, Warrendale, PA, (2000), 9. 13) Z. Yan, S. S. Cheng and Z. J. Cheng: Ironmaking Steelmaking, 41 (2014), ) X. Liu and M. Zhu: ISIJ Int., 46 (2006), ) C. A. M. Pinheiro, I. V. Samarasekera, J. K. Brimacomb and B. N. Walker: Ironmaking Steelmaking, 27 (2000), ) Y. Meng and B. G. Thomas: Metall. Mater. Trans. B, 34 (2003), ) C. Li and B. G. Thomas: Metall. Mater. Trans. B, 35 (2004), ) J. K. Park, C. Li, B. G. Thomas and I. V. Samarasekera: 60th Electric Furnace Conf., ISS, Warrendale, PA, (2002), ) Y. Meng, C. Li, J. Parkman and B. Thomas: Solidification Processes and Microstructure: A Symposium in Honor of Wilfried Kurz, TMS, Warrendale, PA, (2004), ) L. C. Hibbeler, B. G. Thomas, B. Santillana, A. Hamoen and A. Kamperman: Metall. Ital., 2 (2009), 1. 21) R. Saraswat, D. M. Maijer, P. D. Lee and K. C. Mills: ISIJ Int., 47 (2007), ) Z. Cai and M. Zhu: Acta Metall. Sin., 47 (2011), ) Z. Cai and M. Zhu: Acta Metall. Sin., 47 (2011), ) B. G. Thomas: Steel Res. Int., 89 (2018), ) P. E. Ramirez Lopez, P. N. Jalali, U. Sjöström, P. G. Jönsson, K. C. Mills and I. Sohn: ISIJ Int., 58 (2018), ) X. Meng and M. Zhu: ISIJ Int., 49 (2009), ) K. Gu, W. Wang, L. Zhou, F. Ma and D. Huang: Metall. Mater. Trans. B, 43 (2012), ) J. Cho, H. Shibata, T. Emi and M. Suzuki: ISIJ Int., 38 (1998), ) J. W. Cho, T. Emi, H. Shibata and M. Suzuki: ISIJ Int., 38 (1998), ) J. K. Park, I. V. Samarasekera, B. G. Thomas and U. S. Yoon: Metall. Mater. Trans. B, 33 (2002), ) P. F. Kozlowski, B. G. Thomas, J. A. Azzi and H. Wang: Metall. Trans. A, 23 (1992), ) K. Liu, Y.-h. Chang, Z.-g. Han and J.-q. Zhang: J. Iron Steel Res. Int., 20 (2013), ) L. C. Hibbeler, B. G. Thomas, R. C. Schimmel and G. Abbel: Metall. Mater. Trans. B, 43 (2012),