Numerical simulation of shrinkage porosity defect in billet continuous casting

Xingjuan Wang; Yinxing Guo; Pengcheng Xiao; Zengxun Liu; Liguang Zhu

doi:10.1515/htmp-2022-0246

Article Open Access

Numerical simulation of shrinkage porosity defect in billet continuous casting

Xingjuan Wang , Yinxing Guo , Pengcheng Xiao , Zengxun Liu and Liguang Zhu

Published/Copyright: February 15, 2023

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From the journal High Temperature Materials and Processes Volume 42 Issue 1

Abstract

Shrinkage porosity is a typical internal defect in the continuous casting billet, which occurs frequently and is difficult to solve. To explore the influence factors of central shrinkage porosity, a novel unsteady thermomechanical coupling analysis algorithm is developed based on the billet solidification characteristics, and the central shrinkage behavior during the ending solidification process is simulated. Results show that when the casting speed increases from 1.6 to 2.8 m·min⁻¹ and the center outward displacement is reduced from 9.20 × 10⁻² mm to 5.8 × 10⁻² mm, it means casting speed has a significant effect on the formation of shrinkage porosity, and for this caster, the higher casting speed is more suitable for the secondary cooling zone. Without the changes in the solidification structure, when the superheat degree of molten steel increases from 10 to 40°C, the center outward displacement value decreases from 7.12 × 10⁻² mm to 6.91 × 10⁻² mm. In that case, the superheat degree has no obvious effect on the center displacement value.

Keywords: central shrinkage porosity; continuous casting; process parameters; solidification

1 Introduction

Central shrinkage porosity is a common internal defect of continuous casting billet. As porosity will be oxidized in the reheating furnace and difficult to be welded in the rolling process [1], it often causes hot-rolled steel defects. Therefore, the billet with shrinkage porosity is often degraded for use or judged as a waste product, which seriously restricts the product quality and production efficiency.

The shrinkage porosity locates inside the high-temperature billet [2], so it is difficult to be detected quickly online. In the past few decades, researchers have established a large number of mathematical models to analyze the formation mechanism of central shrinkage porosity. Yong et al. [3] reduced the center defect of the casting billet by reducing the primary cooling intensity and the water distribution in the mold and by optimizing the wide and narrow sides of the mold; Wang et al. [4] calculated the temperature distribution and shell thickness distribution of the continuous casting billet by establishing a casting billet heat transfer numerical model, studied the thermodynamic behavior of the solidified shell of the continuous casting billet, and analyzed the central shrinkage porosity; Cai et al. [5] directly numerically simulated the solidification shrinkage process of continuous casting billet by establishing the transient thermoelastic–viscoplastic finite element model [5] and the transient two-dimensional coupled finite element model [6], which could more thoroughly analyze the generation process of central shrinkage porosity.

At the same time, secondary cooling control is crucial to influence the quality of continuous casting billet [7], the technology of secondary cooling water distribution has been continuously improved, and the traditional water distribution method has moved toward intelligence. Before 2015, the traditional water distribution method was mostly adopted, and the purpose of water distribution was achieved by establishing a temperature compensation control model [8] and developing a spray secondary cooling system [9]. The calculation results obtained by the traditional secondary cooling control model [10] based on the change of continuous casting parameters were not accurate. In recent years, experts have begun to focus on the research of intelligent water distribution methods, which are concentrated on the continuous optimization of algorithms [11]. It has successively experienced genetic algorithm [12], neural network algorithm [13], finite volume algorithm [14], differential evolution algorithm [15], particle swarm optimization algorithm [16], and the more accurate improved artificial bee colony algorithm [17]. Based on the continuously optimized algorithm, more accurate secondary cooling water distribution data can be obtained. However, although experts have conducted in-depth research on central shrinkage porosity and secondary cooling water distribution, it is difficult to directly predict the central shrinkage porosity defects accurately and effectively.

Overall, the formation mechanism of defects is very complex and difficult to predict; therefore, traditional improvement measures usually go through a long trial-and-error cycle. It is closely related to the temperature drop rate and cooling condition, during the solidification process for the formation of the shrinkage porosity in the center of the casting billet, and is controlled by the shrinkage at the solidification front and the internal and external stress. However, it is difficult for traditional methods of section observation and detection to predict the existence of central shrinkage porosity in time cause of the changes in continuous casting working conditions. Therefore, numerical simulation research is carried out to investigate the formation mechanism of the central shrinkage porosity, and then the central quality of casting billet with different working conditions could be systematically predicted. It has important scientific research value and application significance. Based on the author’s tracking observation and theoretical analysis of the central quality of continuous casting billet over the years, a new simulation algorithm for central shrinkage porosity is established, which successfully predicts the occurrence conditions of the central shrinkage porosity, and the quality of billet with different casting parameters has been analyzed systematically.

2 Model establishment

2.1 Formation mechanism of central shrinkage porosity

According to the solidification principle of casting billet, the formation of the central shrinkage porosity originates from the uneven distribution of the temperature between the surface and inside of the casting billet. Thermal stress is triggered when the volume density of molten steel changed during the cooling and solidification process. Under the action of thermal stress, the volume contraction inside and outside of the casting billet occurs asynchronously. The specific process consists of the following two parts:

When the continuous casting billet is in the mold or secondary cooling zone, the surface temperature of the solidified shell is decreased, which leads to the shell surface shrinkage, so the central region of billet will bear compressive stress. At the same time, the central area will prevent surface shrinkage, causing the surface of the casting billet to be subjected to tensile stress [18]. At this stage, the central solid fraction of the casting billet is relatively low (<30%), overlapping of columnar crystals is not serious, so the molten steel can flow freely to supplement shrinkage.
When the casting billet leaves the secondary cooling zone and is no longer cooled by water spraying, the surface temperature of the billet shell rises and the center temperature continues to drop, making the surface temperature and the center temperature closer and closer. But the central part of the temperature drop rate is fast, and the shrinkage of the center is larger than the surface side, so that the center is subjected to tensile stress, and the surface is subjected to compressive stress, which leads to the generation of central shrinkage porosity of the continuous casting billet.

The traditional numerical models may lack the analysis of the second process mentioned earlier and only study the temperature drop process in the center area, resulting in the simulated results that show that the center area is in a state of contraction, and so it is difficult to predict the formation of the central shrinkage porosity.

Based on the aforementioned facts, a new algorithm is developed in this model. The specific process is as follows: (1) The temperature is used as the body load to complete the stress calculation, the appropriate temperature field range is selected, and the temperature calculation process within the range is divided into several equal parts to pave the way for the stress field calculation; (2) considering that the coefficient of thermal expansion is affected by temperature, the state of the casting billet at the intermediate time between adjacent time points divided into equal parts is used as the reference surface for calculating the range of adjacent time, and the reference surface is divided into different materials according to different temperature ranges; (3) on the basis of the aforementioned facts, the temperature field is retrieved based on how the temperature fluctuation affects the formation of the central shrinkage porosity, and the thermo-mechanical coupling calculation is completed. Finally, the displacement distribution caused by thermal stress is obtained; (4) the formation of the central shrinkage porosity is known by the displacement value of each node on the X-axis of the solidification end model. If the displacement value in the displacement cloud map scale is positive, namely, the center of the billet moves outward. It means that the result has a central shrinkage porosity; on the contrary, no shrinkage porosity appears when the center of the casting billet moves inward.

2.2 Simplification and hypothesis of the model

Referring to the previous numerical simulation methods [19], the following simplified assumptions are made for the mathematical model:

Ignore the heat transfer process in the casting direction and only consider the heat transfer process in the cross-section direction of the billet.
The effective thermal conductivity is applied in the solid–liquid two-phase region and the liquid phase region to simplify the heat transfer process of casting billet into a conduction heat transfer process.
The physical parameters of casting billet is only considered to be related to temperature.
It is assumed that the internal composition medium of the casting billet is continuous dense entity, which conforms to the characteristics of homogeneity in all directions.
Meet the requirements of small deformation theory.
Ignore the thermal stress generated in the casting direction and only consider the thermal stress in the cross-section direction.
Ignore the influence of the hydrostatic pressure of the molten steel in the casting direction and the bending straightening force in the vertical casting direction.

2.3 Meshing of mathematical models

Based on the law of solidification and heat transfer of the billet, the cross-section size of the selected casting billet was studied, and a 1/4 two-dimensional conduction heat transfer model was established. Making the center of the casting billet as the coordinate origin, the solid model was established, and then the mesh was divided by using ANSYS finite element software [20].

By using the PLANE two-dimensional four-node element in ANSYS software, the grid was divided according to the heat transfer characteristics of the casting billet during the continuous casting process, and the grid division method was uniform. The thickness spacing of the surface layer of the casting billet shell was 1 mm, the grid size at the corners was 1 mm, and the internal size of the casting billet was 2 mm × 2 mm. The central element was locally densified to help the temperature change in the central part of the casting billet. If the center mesh is rough, the actual displacement of the center cannot be well displayed as shown in Figure 1.

Figure 1

Two-dimensional heat transfer model.

2.4 Initial conditions and boundary conditions

Initial conditions

The initial temperature of molten steel is set as the tundish temperature:
(1) T = T c ,
where T _c is the casting temperature (°C).
Boundary conditions

As the casting billet model is symmetric, the adiabatic boundary condition is applied to the center symmetric boundary of the model.

When heat transfer is completed during the solidification of continuous casting billet in the mold, the boundary conditions of conduction and heat transfer are applied to the surface of the billet, and the heat transfer resistance on the surface of the casting billet is transformed into equivalent thermal resistance, and then the equivalent thermal resistance is transformed into the form of the thermal conductivity coefficient. Thus, the third type of boundary condition is applied to the surface of the casting billet, and the formula for calculating the equivalent heat transfer coefficient is as follows:

(2) 1 h = d m λ m + 1 h 0 + 1 h w ,

where h is the comprehensive equivalent heat transfer coefficient, W·(m⁻¹·°C⁻¹); d _m is thickness of copper plate, m; λ _m is thermal conductivity of copper wall, W·(m⁻¹·°C⁻¹); h ₀ is the equivalent heat transfer coefficient between the surface of casting billet and copper wall, W·(m⁻¹·°C⁻¹); and h _w is the heat transfer coefficient between copper wall and flowing water, W·(m⁻¹·°C⁻¹).

The monotonic method is used for the treatment of the boundary conditions in the heat transfer process of the casting billet in the secondary cooling zone, and the heat transfer between the billet and the roller table as well as the air radiation is ignored. It is considered that the secondary cold water is evenly distributed in the same cooling section of the secondary cooling zone [21].

Nozzles are arranged on each surface of the foot roller section in the secondary cooling zone, and each part is cooled by cooling water. The relationship between heat transfer coefficient and cooling water density is as follows:

(3) h = 0.581 ω 0.451 ( 1 − 0.0075 T w ) ,

where ω is the density of water flow, L·m⁻²·s⁻¹; T _w is the temperature of cooling water, °C.

Convective heat transfer and radiation heat transfer are applied to other parts of the secondary cooling zone at the same time. The formula for heat flow density of radiation heat transfer is as follows:

(4) q = ε σ [ ( T s + 273 ) 4 − ( T α + 273 ) 4 ] ,

where q is heat flux, W·m⁻²; ε is the radiation blackness coefficient value, 0.8; σ is the Stefan Boltzmann constant (5.67 × 10⁻⁸W·m⁻²·K⁻⁴); T _s is outer surface temperature of billet shell, °C; and T _α is the operating room temperature value, 35°C.

In the air-cooling section, radiation heat transfer is only considered without water spraying, and the boundary conditions of equation (4) are adopted in the air-cooling section.

2.5 Working conditions

Typical continuous casting process parameters required are presented in Table 1.

Table 1

Typical continuous casting process parameters

Project	Numerical	Unit
Cross-section size	165 × 165	mm
Cooling water velocity of mold	10	m·s⁻¹
Radius	6	mm
Effective length of mold	900	mm
Thickness of the copper tube	14	mm
Length of the zero segment	320	mm
Length of the first segment	1,600	mm
Length of the second segment	2,900	mm
Length of the third segment	2,900	mm
Length of the air cooling segment	7,490	mm

The water quantity of each segment of secondary cooling is presented in Table 2.

Table 2

Secondary cooling parameters under different casting speeds

Casting speed (m·min⁻¹)	Zero segment (t·h⁻¹)	First segment (t·h⁻¹)	Second segment (t·h⁻¹)
1.6	5.68	6.48	4.09
2.0	6.68	7.73	6.11
2.4	8.00	9.34	9.03
2.8	9.66	11.30	12.84

3 Results and discussion

3.1 The effect of casting speed

3.1.1 Temperature distribution under different casting speeds

The degree of superheat is 20°C, the specific water flow is 0.83 L·kg⁻¹, and the casting speed is 1.6, 2, 2.4, and 2.8 m·min⁻¹, respectively, and the temperature field of the 165 mm × 165 mm billet model is analyzed. The changes in central temperature, surface temperature, and corner temperature of the casting billet at different casting speeds is shown in Figure 2(a)–(d) were obtained through simulation calculation, and the yellow marked part is the temperature change distribution of the second cooling zone.

Figure 2

Variation of billet temperature under different casting speeds: (a) 1.6 m·min⁻¹, (b) 2 m·min⁻¹, (c) 2.4 m·min⁻¹, and (d) 2.8 m·min⁻¹.

It can be seen from the figure that the surface of the casting billet at four casting speeds of 1.6, 2, 2.4, and 2.8 m·min⁻¹ has a large temperature return phenomenon after the secondary cooling zone. At 1.6 m·min⁻¹ casting speed, 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the return temperature of the casting billet corner are 159.1, 174.4, and 302.9°C, respectively, in turn. At 2.0 m·min⁻¹ casting speed, 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the return temperature of the casting billet corner are 160.7, 162.8, and 292.8°C in turn. At 2.4 m·min⁻¹ casting speed, 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the return temperature of the casting billet corner are 160.7, 151.1, and 279.5°C, respectively, in turn. At 2.8 m·min⁻¹ casting speed, 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the return temperature of the casting billet corner are 159.3, 141.2, and 266°C in turn, respectively, and the center temperature of the casting billet continues to decrease during this process.

Without changing other process conditions, the residence time of billet in the cooling zone is shortened with the increase in the casting speed, and the flow of water sprayed onto the billet surface is reduced. For the aforementioned reasons (as shown in Figure 2), with the increase in the casting speed, the surface temperature of the billet decreases more and more slowly. Therefore, the reheating of billet shell is shifted to an earlier time, and the degree of temperature return is reduced.

3.1.2 Formation of central shrinkage porosity at different casting speeds

Under the premise of not changing other process parameters, only the casting speed is changed to carry out the thermal–mechanical coupling analysis, and the data analysis of the simulation results is carried out to obtain the law that the casting speed affects the formation of central shrinkage holes in the casting billet.

Figure 3(a)–(d) shows the cloud diagrams of the displacement distribution of the model along the X direction under the four casting speeds of 1.6, 2.0, 2.4, and 2.8 m·min⁻¹, respectively, in turn.

Figure 3

Cloud diagram of displacement distribution under different casting speeds: (a) 1.6 m·min⁻¹, (b) 2.0 m·min⁻¹, (c) 2.4 m·min⁻¹, and (d) 2.8 m·min⁻¹.

Under four casting speeds of 1.6, 2.0, 2.4, and 2.8 m·min⁻¹, Figure 4(a)–(d) shows the displacement changes of each node along the X-direction on the X-axis of the model when central solid fraction are 0.4, 0.5, 0.6, 0.7, and 0.8.

Figure 4

Displacement at different casting speeds: (a) 1.6 m·min⁻¹, (b) 2.0 m·min⁻¹, (c) 2.4 m·min⁻¹, and (d) 2.8 m·min⁻¹.

With the continuous solidification of the billet, the central solid fraction increases, and the solid part of the billet becomes more and more. In this process, the displacement of the center of the billet at the time of five kinds of central solid fraction is studied. Thus, the changing trend in the center shrinkage porosity can be obtained.

Figure 4 shows that at 1.6, 2.0, 2.4, and 2.8 m·min⁻¹ casting speeds, when the central solid fraction is 0.4, the central displacement values are 1.16 × 10⁻², 6.61 × 10⁻³, 4.9 × 10⁻³, and 3.3 × 10⁻³ mm, respectively; when the central solid fraction is 0.5, the central displacement values are 3.5 × 10⁻², 2.41 × 10⁻², 1.86 × 10⁻², and 1.52 × 10⁻² mm, respectively; when the central solid fraction is 0.6, the central displacement values are 5.55 × 10⁻², 4.07 × 10⁻², 3.36 × 10⁻², and 3.29 × 10⁻² mm, respectively; when the central solid fraction is 0.7, the central displacement values are 7.45 × 10⁻², 5.52 × 10⁻², 4.89 × 10⁻², and 4.52 × 10⁻² mm, respectively; when the central solid fraction is 0.8, the central displacement values are 9.20 × 10⁻², 6.94 × 10⁻², 6.14 × 10⁻², and 5.8 × 10⁻² mm, respectively.

With the increase in the casting speed, the central displacement value decreases. When the casting speed is 1.6 m·min⁻¹ under the four kinds of casting speeds, the maximum surface temperature recovery occurs in the section of the central solid fraction of 0.3–0.8, which is larger than that at the casting speed of 2.0 and 2.4 m·min⁻¹, so that the central displacement value of the casting billet is relatively large and the central shrinkage porosity formed by the casting billet is large.

With the continuous solidification of the casting billet, central solid fraction increases, and the solid ratio gradually expands. After billet leaves the spray zone of cooling water, the temperature of the billet shell gradually increases, while the center temperature gradually decreases (but still in the two-phase region), and the difference between the two temperature changes leads to the formation of shrinkage porosity in the center region. With the increase in the casting speed, the surface temperature increases, so that the temperature gradient of the billet section decreases, and the volume shrinkage caused by solidification decreases. Therefore, the size of the central shrinkage porosity decreases as the casting speed increases.

3.2 The effect of superheat degree

3.2.1 Temperature distribution under different superheat degrees

For the four conditions of 2.0 m·min⁻¹, specific water volume of 0.83 L·kg⁻¹, and molten steel superheat of 10, 20, 30, and 40°C, the changes of the temperature field of the casting billet are analyzed as follows (Figure 5), and the yellow marked part in the figure shows the temperature change distribution of the second cooling zone.

Figure 5

Variation of billet temperature under different superheat: (a) 10°C, (b) 20°C, (c) 30°C, and (d) 40°C.

Figure 5 shows that under the superheat of 10, 20, 30, and 40°C at 2.0 m·min⁻¹, there is a large temperature return phenomenon on the casting billet surface after the secondary cooling section. When the superheat degree is 10°C, the temperature return of 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the corner of the casting billet are 160.7, 163.2, and 292.9°C, respectively; when the superheat degree is 20°C, the temperature return of 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the corner of the casting billet are 160.7, 162.8, and 292.8°C, respectively; when the superheat degree is 30°C, the temperature return of 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the corner of the casting billet are 160.6, 162.4, and 292.6°C, respectively; when the superheat degree is 40°C, the temperature return of 1/2 of the casting billet surface, 1/4 of the casting billet surface, and the corner of the casting billet are 160.4, 162, and 292.3°C, respectively, and the central temperature of the casting billet decreases continuously in this process.

The results show that the temperature return interval of the center of the casting billet surface, 1/4 of the casting billet surface, and the corner of the casting billet is almost the same. Under the same other process conditions, the change in superheat has no significant effect on the temperature distribution of casting billet.

3.2.2 Formation of central shrinkage porosity at different superheat degree

Figure 6(a)–(d) shows the cloud diagrams of the displacement distribution of the model along the X direction under the conditions that the superheat degrees of molten steel are 10, 20, 30, and 40°C, respectively.

Figure 6

Cloud diagram of displacement distribution under different superheat: (a) 10°C, (b) 20°C, (c) 30°C, and (d) 40°C.

Under four superheat degree of 10, 20, 30, and 40°C, respectively, Figure 7(a)–(d) show the displacement changes of each node along the X-direction on the X-axis of the model when the central solid fraction are 0.4, 0.5, 0.6, 0.7, and 0.8.

Figure 7

Displacement under different superheat: (a) 10°C, (b) 20°C, (c) 30°C, and (d) 40°C.

Figure 7 shows that under the superheat of 10°C, 20°C, 30°C, and 40°C, when the central solid fraction is 0.4, the central displacement values are 7.29 × 10⁻³, 6.61 × 10⁻³, 6.52 × 10⁻³, and 6.17 × 10⁻³ mm, respectively; when the central solid fraction is 0.5, the central displacement values are 2.39 × 10⁻², 2.41 × 10⁻², 2.28 × 10⁻², and 2.23 × 10⁻² mm, respectively; when the central solid fraction is 0.6, the central displacement values are 4.11 × 10⁻², 4.07 × 10⁻², 4.08 × 10⁻², and 3.75 × 10⁻² mm, respectively; when the central solid fraction is 0.7, the central displacement values are 5.68 × 10⁻², 5.52 × 10⁻², 5.58 × 10⁻², and 5.41 × 10⁻² mm, respectively; when the central solid fraction is 0.8, the central displacement values are 7.12 × 10⁻², 6.94 × 10⁻², 6.92 × 10⁻², and 6.91 × 10⁻² mm.

By comparing the data of each group, it can be seen that with the change of superheat, the displacement value of each point of the casting billet is basically the same. As the influence of dendrite structure change on the central shrinkage porosity cannot be realized in ANSYS for simulation analysis, this model only considered the influence of casting temperature change. In the process of continuous casting, the temperature change of each node is almost the same under different superheat degrees. But what needs to be pointed out is when the superheat is high, the center of the molten steel becomes a columnar crystal structure, which easily leads to the quality defects such as central shrinkage porosity and central porosity. At low superheat, the center of molten steel forms the coarse equiaxed crystal structure, which is beneficial to restrain the formation of central shrinkage porosity.

3.2.3 Industrial test verification

Take the cross section of HRB500E billets at different casting speeds on site for macrostructure detection.

As shown in Figure 8, the detection diagrams of casting billet at 1.6 and 2.0 m·min⁻¹ casting speeds are shown.

Figure 8

Defect detection diagrams of billet at different casting speeds: (a) 1.6 m·min⁻¹ and (b) 2.0 m·min⁻¹.

According to YBT 4002-2013 macrostructure defect rating chart of continuous casting steel billet, the following ratings are made: at 1.6 m·min⁻¹, the rating results of the center shrinkage porosity of the billet are grade 2; at 2.0 m·min⁻¹, the rating results of the center shrinkage porosity of the billet are grade 1. The size of the central shrinkage porosity decreases as the casting speed increases. It verifies the model calculation results.

4 Conclusion

Based on the thermo-mechanical coupling analysis, the formation of the central shrinkage porosity and the influence of casting parameters have been studied. The results show that:

The thermal–mechanical coupling analysis of the finite element model under typical conditions can analyze the formation central shrinkage porosity process of the casting billet, which solves the problem that cannot be solved by the traditional method.
When the casting speed increases from 1.6 to 2.8 m·min⁻¹, the center–outward displacement value decreases from 9.20 × 10⁻² mm to 5.8 × 10⁻² mm. That means in this caster, the casting speed can weaken the surface temperature of billet, reduce the central displacement value, then the formation tendency of the central shrinkage porosity will be declined.
Without considering the central structure changes of the casting billet, when the superheat degree of molten steel increases from 10–40°C, the center–outward displacement decreases from 7.12 × 10⁻² to 6.91 × 10⁻² mm.

Acknowledgement

The authors would like to gratefully acknowledge the financial support of the National Natural Science Foundation of China Project (51904107, 51974133, and U21A20114). The authors also wish to thank the research supported by Natural Science Foundation of Hebei Province Project (E2019209543, E2020209005, and E2021209094), Hebei Province Higher Education Science and Technology Research Project (BJ2019041), Hebei Province Talents Project Funding Project A202102002, and Tangshan City Talent Funding Project (A202010004).

Funding information: National Natural Science Foundation of China Project (51904107, 51974133, and U21A20114); Hebei Natural Science Foundation Projects (E2019209543, E2020209005, and E2021209094); Hebei Provincial Colleges and Universities Science and Technology Wood Research Project (BJ2019041); Hebei Province “Three Three Three Talent Project” funded project (A202102002); and Tangshan City Talent funding project (A202010004).
Author contributions: Yin Xingguo conducted the study and results analysis under the guidance of Peng Chengxiao, Xing Juanwang, and Li Guangzhu, and participated in experimental design and morphological analysis in the research activities. Zeng Xunliu has contributed to image processing and data calculation. All authors have read and approved the manuscript for publication.
Conflict of interest: The authors state no conflict of interest.

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Received: 2022-07-28

Revised: 2022-10-02

Accepted: 2022-10-05

Published Online: 2023-02-15

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/htmp-2022-0246

Keywords for this article

central shrinkage porosity; continuous casting; process parameters; solidification

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BY 4.0