optimization design of wide face water slots for medium ... · medium-thick slab casting mold;...

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Vol.13 No. 5 September 2016Research & Development CHINA FOUNDRY

Optimization design of wide face water slots for medium-thick slab casting mold

*Tong-min Wang Male, born in 1971, Ph. D, Professor. His main research fields cover the numerical simulation of metal solidification and in-situ observation on grain growth by synchrotron radiation imaging.

E-mail: [email protected]

Received: 2016-01-11; Accepted: 2016-08-09

Xue-lin Yin 1, Li Wu 1, Jun-jia Zhang 1, Hui-jun Kang 2, Zong-ning Chen 2, Jin-song Chen 3, Zhi-qiang Cao 1, Ting-ju Li 1, *Tong-min Wang 1

1. Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China

2. Laboratory of Special Processing of Raw Materials, Dalian University of Technology, Dalian 116024, China3. Dalian Dashan Heavy Machinery Co., Ltd., Dalian 116024, China

C ontinuous casting is the most widely used casting method due to its significant superiority in the

processing of steels, such as high productivity, good quality and associated savings in capital cost, energy and man power [1, 2]. The mold is the most critical component of a continuous casting. It is known that during the continuous casting process, a large amount of sensible and latent heat of molten steel dissipates in the primary cooling zone, thus, a large temperature gradient develops across the copper plates, which causes thermal stresses and distortions [3]. Therefore, the temperature distribution is very important to mold life and the quality of casting slabs.

Abstract: A three-dimensional finite-element model has been established to investigate the thermal behavior of the medium-thick slab copper casting mold with different cooling water slot designs. The mold wall temperatures measured using thermocouples buried in different positions of the mold with the original designed cooling system were analyzed to determine the corresponding heat flux profile. This profile was then used for simulation to predict the temperature distribution and the thermal stress distribution of the molds. The predicted temperatures during operation matched the plant measurements. The results showed that the maximum temperature, about 635 K in the wide hot surface, was found about 60 mm below the meniscus and 226 mm from the center of the mold. For the mold with the type I modified design, there was an insignificant decrease in temperature of about 5 K, and for the mold with the type II modified design, the maximum temperature was decreased by about 15 K and the temperature of the hot surface was distributed more uniformly along the length of the mold. The corresponding maximum thermal stress at the hot surface of the mold was reduced from 408 MPa to 386 MPa with the type II modified design. The results indicated that the modified design II is beneficial to the increase of mold life and the quality of casting slabs.

Key words: medium-thick slab casting mold; water slots design; heat flux profile; thermal behavior; finite-element analysis

CLC numbers: TG146.1+1 Document code: A Article ID: 1672-6421(2016)05-327-08

Many studies have been carried out to shed light on the thermal behavior of copper molds during the continuous casting process over past years. In order to assess the role of various process parameters impacting mold life, O’Connor and Dantzig developed a finite-element model to calculate the thermo-mechanical state in the mold and casting slab [4]. Thomas and Park et al. applied a three-dimensional finite-element model to predict temperature, thermal distortion, thermal stress and hot face cracks in a funnel shaped mold for casting thin-slab [1, 5-7]. Santillana et al. applied a one-dimensional finite-element model to modify the 3D model, and predict temperatures for copper plates with different thicknesses [8, 9]. Meng and Zhu established a three-dimensional finite-element heat-transfer model to predict temperature, distortion and thermal stress of hot copper plates and simulate the effect of casting speed on thermal behavior in a thin-slab continuous casting mold [10]. Z. Yan et al. established a three-dimensional finite-element heat-transfer model to predict temperature and simulate the effect of copper plate thickness on temperature in the mold of thin-slab

DOI: 10.1007/s41230-016-5113-z

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Vol.13 No. 5 September 2016Research & DevelopmentCHINA FOUNDRY

Fig. 1: Back view of mold’s wide face showing slot geometry and thermocouple locations

continuous casters [11].The above-mentioned works have analyzed the effect of many

operating parameters on the temperature distribution such as casting speed, copper plate thickness and so on, and the research objects are almost all thin slabs. At present, less attention has been paid to the design of cooling water slots of copper plates, especially for the medium-thick slab casting mold. For the purpose of achieving a lower and more uniform distribution of temperature, temperature distribution in three kinds of casting mold copper plates were investigated in this work, using three-dimensional finite-element models and operating conditions which came from Dalian Dashan Heavy Machinery Co. Ltd. Meanwhile, the mold plate temperatures measured in the plant were used to determine the corresponding heat-flux profile in medium-slab casting molds. Simulations were carried out for both the mold with original design and with two types of modified designs of cooling systems, and a comparison of the results corresponding to the three designs can be used as a useful reference for the optimization of continuous casting molds design.

1 Simulation model1.1 Geometry model

The wide copper plate is shown in Fig. 1, which is of dimensions 1,700×1,100×39.5 (mm). There are some cooling water slots on the outer side of the plate as shown in the figure. To obtain the mold temperatures, ten rows of thermocouples were buried in the mold every 100 mm from the mold top to the end. The wide face contained nine columns of thermocouples: one of the columns was located along the centerline of the face and the others were situated every 226 mm from the centerline in addition to the most left and the right two columns as shown in Fig. 1. Therefore, a total of 90 thermocouples were symmetrically buried in the copper plate, with the distance from the hot face to the tip of thermocouples being 25 mm.

Three kinds of half-plate model (the model is symmetrical) with different water slot arrangements were established using commercial modeling software UG NX®, including one original designed plate and two plates with modified design (I and II) based on variations from the original by changing the cooling water slots. The three models and corresponding cross sections are shown in Fig. 2a-2c.

In the original designed copper plate, five water slots as shown in Fig. 2(d) were arranged evenly between the thermocouple's bolts, including two deep slots and three center shallow slots. The water slots of the type I modified design had the same shape as the original design. However, there were four center shallow slots in three groups of water slots on the right side of the copper plate. Comparing the type II modified design and the original design, the shape of water slots changed as shown in Fig. 2(e), and among the three groups of water slots on the right side of copper plate, the center shallow slots were replaced by five deep slots. The representative different distribution and geometry of cooling water slots are shown in Fig. 3, and other detailed geometrical parameters are listed in Table 1.

Fig. 2: Three kinds of half-plate model with different water slot arrangements: (a) original design; (b) modified design (I); (c) modified design (II); and shape of water slots: (d) original design and modified design (I); (e) modified design (II)

1700

1100

ThermocoupleWater slot

-791 -678 -452 -226 0 226 452 678 791

0

100

200

300

400

500

600

700

800

900

1000

(a) (b) (c) (d) (e)

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Table 1: Geometrical parameters of cooling water slots

Copper plates Original design

Modified design (I)

Modified design (II)

Distance between bolts (mm) 113 113 113

Length of water slots (mm) 1,050 1,050 1,050

Number of shallow water slots 42 48 24

Number of deep water slots 28 28 58

Distance between water slots (mm) 20 20/16 20/13

Shallow water slots depth (mm) 15 15 15

Deep water slots depth (mm) 21 21 21

Water slots width (mm) 5 5 5

(1)

Fig. 3: Different distribution and geometry of cooling water slots: (a) original design; (b) modified design (I); (c) modified design (II)

Table 2: Thermal properties of copper and water

Property Copper WaterThermal conductivity

(W·m-1·K-1) 377 0.597

Density (Kg·m-3) 8,978 1,000

Specific heat (J·Kg-1·K-1) 381 4,187

relevant boundary conditions can be expressed as follows:(i) top and bottom of mold

where ha is the convection exchange coefficient of air, and Ta is the temperature of the ambient air.

(ii) cold face of mold contacting the cooling water tank

where hc is the effective heat transfer coefficient, which is 8,000 W·m-2·K-1 in this study, and T0 is the initial temperature of the water tank.

(iii) cooling water slot of mold

where Tw is the temperature of cooling water, which is imposed as linear functions based on the inlet and outlet temperatures given in Table 3. The water slot heat transfer coefficient, hw, is determined from the following dimensionless correlation:

where dw is hydraulic diameter of water slot, λw is thermal conductivity, μw is viscosity, ρw is density and Cw is specific heat of cooling water.

where A and L are the area of the cross-section and the perimeter of the cross-section of the cooling water in a slot, respectively.

(2)

1.2 Heat transfer model and boundary condition

In order to simulate the temperature distribution of copper plates with different water slot arrangements, the following assumptions were made: (1) heat transfer between the cooling water and the mold copper plate is at steady state; (2) thermal properties of copper plate and cooling water are isotropic, and density and heat capacity are constant; (3) water in the cooling channel is in plug flow and nuclear boiling of the cooling water is negligible; (4) heat absorption by the mold powder above the meniscus is negligible.

During the continuous casting process, the temperature distribution can be described with the three-dimensional heat conduction equation expressed as:

with initial condition

where T is the temperature, ρ, λ and Cp are the density, thermal conductivity and specific heat, respectively, which can be obtained in Table 2, and ω is the source of heat [1], which is 0 in this study. The axes of x, y and z in the coordinate system are parallel to the length, the height and the width of copper plate, respectively, and their coordinate origin is at the midpoint of the symmetry plane in the half copper plate.

Assuming a steady-state continuous casting process, the

(3)

(4)

(5)

(6)

Table 3: Operation conditions of continuous casting

Conditions Value

Meniscus level (below mold top) (mm) 100

Casting speed (m·min-1) 1.8

Input water temperature (K) 298

Output water temperature (K) 311

Water flow (l·min-1) 3,417

(7)

113 113 113

1100

1100

1100

1050

1050

1050

a=20 a=16 a=13

(a) (c)(b)

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(iv) heat flux of the symmetry plane

(v) hot face of mold below meniscusTo compare the original and the two modified cooling systems,

the three designs were subjected to identical boundary conditions. The heat exchange between the casting slab and the hot surface of the mold can be simplified to a heat flux function of different point coordinates on the hot mold face. The previous studies usually obtained the distribution of heat flux from empirical relations [12-14], however, in this study, the coefficients of the heat flux function are determined using an inverse algorithm.

To determine the heat flux distribution on the mold hot face, arbitrary heat flux distributions were first applied as boundary conditions using the 3-D finite-element model. Then, these arbitrary values were adjusted until the temperatures calculated by the finite-element model at the thermocouple locations match well with the measured ones. Figure 5 shows the heat-flux distribution over the wide face based on linear interpolation and extrapolation of the heat flux values at the thermocouple positions.

1.3 Stress model and boundary conditionThermal stresses are calculated by solving the constitutive equation using the finite element method. For a thin-slab casting mold, the copper plate was considered to be thermo elastic-plastic. The isotropic stress-strain relation can be expressed by the constitutive equation as follows:

where λ and G are Lamé coefficients, α is the coefficient of thermal expansion, ∆T is temperature change, i, j, k are the coordinate directions, and δij is Kronecker’s delta, the value of the delta is 1 when i=j, or the value is 0. The value of εij can be obtained from the following formula:

where εije is the elastic strain, εij

p is the plastic strain, and εijT is

the thermal strain.In order to calculate the thermal stress distribution of copper

plate, boundary conditions are loaded on the mold as follows:(i) Temperature load is imported from the results of

temperature calculation;(ii) Rigid body motion is prevented by constraining the

symmetry plane and the copper plate from normal displacement.

2 Results and discussion2.1 Model availabilityThe temperature distributions in the mold copper plate for the original design and two modified designs were computed with the commercial finite-element analysis package ANSYS Workbench®, and the temperature contours are shown in Fig. 6. For the three kinds of mold designs, all of the conditions were identical as mentioned in Section 1.Fig. 5: Heat flux profiles of hot face along mold length

at different positions from centerline

Fig. 6: Temperature contours of half-plate with different cooling systems: (a) original design; (b) modified design (I); (c) modified design (II)

(8)

(10)

(9)

The calculated temperatures of the copper plate with original design at positions of thermocouples based on the heat flux function in Fig. 5 have been compared with in-plant measurements to verify the precision of the above-mentioned models, and the results are shown in Fig. 7. As it can be seen from this figure, although there is some difference

between the measured and calculated values, on the whole, the model predictions agree reasonably well with the measured temperatures. This comparison confirms that the heat flux curves in Fig. 5 are calibrated properly. It is worth pointing out that the real temperature of thermocouples has a great fluctuation during production which is caused by periodic contact between the

Temperature (K) Temperature (K) Temperature (K)

(a) (b) (c)

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Fig. 7: Comparison of measured and calculated temperatures at thermocouple positions: (a) 0 mm; (b) 226 mm; (c) 452 mm; (d) 678 mm (the distance from centerline of copper plate)

mold wall and the slab surface originating from mold oscillation, shell shrinkage and ferrostatic pressure.

2.2 Longitudinal distribution of temperatureFigure 8 shows the hot surface temperature distribution along the mold length at different positions across the wide face of the copper plate with the original design. As seen from this figure, the temperature at the hot surface of the mold copper plate increases sharply from a lower level to the maximum, and then decreases gradually with the increase of the distance below the top surface of the mold. The maximum temperature of the wide face is found about 60 mm below the meniscus and is 635 K at the location of 226 mm from the centerline of the mold. It is noted that within about 50 mm from the mold exit, the model predicts an increase in hot surface temperature of almost 40 K. Such an effect is due to the end of the water slots being 25 mm above the mold exit,

and the lesser cooling makes the temperature rise to a certain degree.

The longitudinal distributions of temperature in the mold for the type I and II modified design during the steady continuous casting processes are shown in Fig. 9. The calculation results show that the hot surface temperature distributions of the mold with different water slots arrangement are almost similar. However, the extreme temperature varies with cooling structure. The maximum temperature of the wide face is 630 K and 620 K for the type I and the type II modified design, respectively, as shown in Fig. 9. Comparing with the original design, the copper plate with the type II modified design gains more than 15 K reduction in the highest temperature on the hot surface of the wide plate. And the temperature reduction of the part with higher temperature is larger than that of the part with lower temperature as shown in Fig. 10, which shows the temperature distributions at different positions of the original design and the type I and the type II modified designs. Accordingly, it is concluded that the temperature distributes more uniformly down the length of the mold.

2.3 Transverse distribution of temperatureAccording to the location of the maximum temperature and the shape characteristics of mold, the hot face temperatures of the mold with original design at four different heights are compared, which are 940, 700, 460 and 220 mm from the mold exit, respectively. The results are shown in Fig. 11. It is noted that high and low temperatures are located at the positions of bolts and water slots respectively, because water slots often have a larger spacing across bolt locations. Thus, deeper water

Fig. 8: Hot surface temperature distributions down the length of mold with original design

(a) (b)

(c) (d)

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slots adjacent to bolts were often made to avoid temperature increases. Figure 11 also shows that near the edge of the wide face, temperature decreases with increasing distance from centerline due to no heat flux transferred across the copper plate.

The transverse distributions of temperature at 700 mm from the mold exit on the hot surface with the original design and the type I and II modified designs are shown in Fig. 12. It can be seen that, the type II modified design of the cooling system secured a marked reduction in the highest temperature especially in the area from the distance of 450 mm to 700 mm from the centerline, where most of the cracks form according to data from the plant.

Based on the above results, it can be seen that the temperature distribution of the wide copper plate with the type II modified

Fig. 9: Longitudinal distribution of temperature: (a) modified design (I); (b) modified design (II)

Fig. 10: Comparison between original design and type I and type II modified design in temperature distribution at positions thermocouples located: (a) 0 mm; (b) 226 mm; (c) 452 mm; (d) 678 mm (distance from centerline of copper plate)

Fig. 11: Temperature distribution of hot surface with original design at different heights from mold exit

(a) (b)

(a) (b)

(c) (d)

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design is the most reasonable among these three designs. This is because the cooling area is increased and the effective copper plate area is decreased, especially for constant water flow in this study.

2.4 Thermal stress distributionFigure 13 shows the distribution of calculated thermal Von Mises stress on the hot copper surface with original design and the type I and II modified designs. Thermal stress depends mainly on the temperature gradient and the coefficient of thermal expansion. As can be seen from the figure, thermal stress distribution is basically in proportion to the temperature gradient on both the original design and the two modified designs.

Fig. 13: Distribution of calculated thermal stress on hot copper surface: (a) original design; (b) modified design (I); and (c) modified design (II)

Fig. 12: Transverse distributions of hot surface temperature at 700 mm from the mold exit

The peak thermal stress is about 408 MPa on the hot surface with the original design, which occurs about 60 mm below the meniscus where temperature is the highest and the temperature gradient between the hot and the cold surface of copper plate is the largest. It can be seen that the type II modified design of the cooling system not only reduces the peak value of thermal stress but also the possibility of maximum thermal stress appears, which may further help to reduce the casting force and improve the quality of the casting slab during the continuous casting process.

3 ConclusionsThe thermal behaviors of a medium-thick slab casting mold with original and modified cooling water slot systems have been investigated using measurements in the plant and a three-dimensional heat transfer model with ANSYS Workbench®. From this investigation, the following conclusions can be drawn:

(1) The model predictions of temperature based on the heat flux profile during the continuous casting process matched the plant observations.

(2) For the mold with the original designed cooling system, the hot surface temperature reached 635 K and was the highest 60 mm below the meniscus and 226 mm from

the centerline of the mold. Within about 50 mm from the mold exit, the temperature of the hot surface increased by about 40 K because the terminals of the cooling water slots could not completely reach the mold exit. The temperature distributions of the hot surface along the length of the mold with different cooling systems were similar. However, the type II modified design cooling system resulted in lowering the extreme temperature to 620 K and improving the uniformity of the temperature distribution along the length of the mold.

(3) The temperature at bolt positions was higher than that of water slot positions for the transverse distributions of different heights of the mold. However, this characteristic was decided by the heat flux and the cooling system. The type II modified design cooling system gained a reduction in the highest temperature especially at the height of 450 to 700 mm, where most of the cracks formed according to the data from the plant.

(4) The distribution of thermal stress was basically in proportion to the temperature distribution, and the peak value was about 408 MPa, which occurred about 60 mm below the meniscus. The magnitude of thermal stress at the hot surface of the mold with type II modified design cooling system was reduced to 386 MPa and the possibility of the peak thermal stress’s appearance was also reduced.

(b)(a) (c)

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References[1] Park J K, Thomas B G, Samarasekera I V, et al. Thermal and

mechanical behavior of copper molds during thin-slab casting (I): Plant trial and mathematical modeling. Metallurgical and Materials Transactions B, 2002, 33: 425-436.

[2] Thomas B G. Modeling of the continuous casting of steel-past, present, and future. Metallurgical and Materials Transactions B, 2002, 33: 795-812.

[3] Meng Xiangning, Zhu Miaoyong. Thermal behavior of hot copper plates for slab continuous casting mold with high casting speed. ISIJ International, 2009, 49: 1356-1361.

[4] Oconnor T G, Dantzig J A. Modeling the thin-slab continuous-casting mold. Metallurgical and Materials Transactions B, 1994, 25: 443-457.

[5] Park J K, Thomas B G, Samarasekera I V, et al. Thermal and mechanical behavior of copper molds during thin-slab casting (II): Mold crack formation. Metallurgical and Materials Transactions B, 2002, 33: 437-449.

[6] Park J K, Samarasekera I V, Thomas B G, et al. Analysis of thermal and mechanical behavior of copper mould during thin slab casting. In: Proc. 83rd Steelmaking Conference, Pittsburgh, PA, 2000, 83: 9-21.

[7] Yoon U S, Park J K, Thomas B G, et al. Mold crack formation of

the funnel shaped mold during thin slab casting. In: Proc. 85th Steelmaking Conference, Warrendale, PA, 2002: 245-260.

[8] Santillana B, Hibbeler L C, Thomas B G, et al. Heat transfer in funnel-mould casting: Effect of plate thickness. ISIJ International, 2008, 48: 1380-1388.

[9] Hibbeler L C, Thomas B G, Santillana B, et al. Longitudinal face crack prediction with thermo-mechanical models of thin slabs in funnel moulds. La Metallurgia Italiana, 2009: 1-10.

[10] Liu Xudong, Zhu Miaoyong. Finite element analysis of thermal and mechanical behavior in a slab continuous casting mold. ISIJ International, 2006, 46: 1652-1659.

[11] Yan Z, Cheng S S, Cheng Z J. Study on temperature field for copper plate funnel shape mould. Ironmaking and Steelmaking, 2014, 41: 206-212.

[12] Shamsi M R R I, Ajmani S K. Three dimensional turbulent fluid flow and heat transfer mathematical model for the analysis of a continuous slab caster. ISIJ International, 2007, 47: 433-442.

[13] Thomas B G, Ho B, Li Guowei. Heat flow model of the continuous slab casting mold, interface, and shell. Mclean Symposium Proceedings, Urbana, 1998: 177-193.

[14] Liu Heping, Yang Chunzheng, Zhang Hui, et al. Numerical simulation of fluid flow and thermal characteristics of thin slab in the funnel-type molds of two casters. ISIJ International, 2011, 51: 392-401.

This research was financially supported by the National Natural Science Foundation of China (Nos. 51525401, 51274054, U1332115, 51401044), the Science and Technology Planning Project of Dalian (No. 2013A16GX110), the China Postdoctoral Science Foundation (2015M581331), and the Fundamental Research Funds for the Central Universities.

optimization design of wide face water slots for medium ... · medium-thick slab casting mold;...

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