Based on the obtained thermodynamic data, we built the model and package of equilibrium calculation of multi-reactions including the liquid inclusions generation. The computed results are shown in Figure 5. As presented in Figure 5a, the liquid inclusions were stable in the region surrounded by the red dashed line as the mass fractions of aluminum and cerium were feasible. When the mass fraction of cerium was 0.02%, the inclusions in the 253MA steel transferred from Ce2Si2O7 to liquid phases as the increase of aluminum addition, and cerium aluminates were formed as the aluminum content excess 0.017%, shown in Figure 5b. When the mass fraction of cerium was 0.03%, the inclusions first transferred from cerium silicates to liquid phase, and the amount of liquid inclusions began to decline as CeAlO3 appeared, shown in Figure 5c. When the mass fraction of cerium increased to 0.04%, the liquid inclusions precipitated first and then disappeared as the aluminum addition reached 0.015%, Figure 5d. Considering the required cerium content of 0.03–0.04% in 253MA steel, the aluminum addition should be the key factor of restricting the inclusions to liquid, which was about 0.01%.

According to the above thermodynamic calculations, only 0.01% aluminum was needed to transfer the solid inclusions to liquid phases, then the Si-Al alloy, the chemical compositions are listed in Table 1, and were chosen as the deoxidant. The SEM observation and EDS analysis results of sampled inclusions from equilibrium experiments at steelmaking and casting temperature are present in Figure 6. It can be seen that, the inclusions were almost Al-Si-O system after Si-Al alloy was added for 60 min. The inclusions were mainly Ce2O3/Ce2O2S after cerium was added for 5 min. The morphologies and compositions changed during the following 25 min, and finally the spherical and liquid inclusions were formed at 1500 ◦C (the casting temperature). Altogether, the results showed that the solid inclusions were modified to liquid ones after aluminum was first added in the form of Si-Al alloy and then cerium was added. Nevertheless, it should take more than 30 min to finish the modifying process after cerium addition. The mechanism of the modifying process can be explained as: (1) the inclusions of Al-Si-O system are formed after Si-Al alloy is added; (2) a number of Ce2O3/Ce2O2S are formed immediately after cerium is added owing to the strong chemical reaction between cerium and oxygen solutes, and the oxygen activity in molten steel is sharply declined; (3) the early generated Al-Si-O inclusions decomposed to solutes of aluminum, silicon, and oxygen since the decline of oxygen activity; (4) the reactions between Ce2O3/Ce2O2S and silicon, aluminum, oxygen keep going on as the continuous diffusion of solutes in molten steel; and (5) the liquid inclusions are ultimately formed as the schematic diagram shown in Figure 6.

**Figure 5.** Calculation results by developed thermodynamic package. (**a**) Liquid regions of inclusions; (**b**) Effect of aluminum addition on inclusions, *w*Ce = 0.02%; (**c**) Effect of aluminum addition on inclusions, *w*Ce = 0.03%; (**d**) Effect of aluminum addition on inclusions, *w*Ce = 0.04%.

**Figure 6.** Inclusions evolution in 253MA steel after Al addition.

### **4. Conclusions**

The liquid region is near the SiO2 corner in the phase diagram of Al2O3-SiO2-Ce2O3 systems optimized by the CALPHAD technique, implying the possibility of modifying Ce2O3/Ce2O2S to liquid phases. Then the thermodynamic model coded in the user defined package computes the appropriate aluminum addition, about 0.01%, to control the inclusion compositions' inner boundaries of liquid region. The spherical liquid inclusions are found after 30 min of cerium addition when Si-Al alloys are chosen as the deoxidant instead of pure silicon. The thermodynamic and experimental results can support the theory and data groundwork to remit the nozzle clogging of 253MA steel in the future.

**Author Contributions:** Conceptualization, methodology Y.L. and C.L.; Validation, T.Z.; Writing—review and editing, Y.L.; Supervision, C.L.; Funding acquisition, T.Z. and M.J.

**Funding:** This research was funded by Natural Science Foundation of Chongqing (cstc2018jcyjAX0792), Open Project from Key Laboratory of Ecological Utilization of Multi-metallic Mineral of Education Ministry (NEMM2018003), Research Project from Chongqing Committee of Education (KJQN201801408, KJZD-M201801401) and the Introduce Talents Research Start-up Fund in Central South University of China.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Investigation on the Slag-Steel Reaction of Mold Fluxes Used for Casting Al-TRIP Steel**

**Kaitian Zhang 1,2, Jianhua Liu 2 and Heng Cui 1,\***

Received: 14 March 2019; Accepted: 29 March 2019; Published: 1 April 2019

**Abstract:** The reaction between [Al] in molten steel and (SiO2) in the liquid slag layer was one of the restrictive factors in the quality control for high Al-TRIP steel continuous casting. In this work, the composition and property variations of two slags during a slag-steel reaction were analyzed. Accordingly, the crystalline morphologies of slag were discussed and the solid layer lubrication performance was evaluated by Jackson α factors. In addition, a simple kinetics equilibrium model was established to analyze the factors which affected SiO2 consumption. The results reflected that slag-steel reacted rapidly in the first 20 minutes, resulting in the variation of viscosity and the melting temperature of slags. The slag-steel reaction also affected the crystal morphology significantly. Slag was precipitated as crystals with a higher melting temperature, a higher Jackson α factor, and a rougher boundary with the consumption of SiO2 and the generation of Al2O3. In other words, although generated Al2O3 acted as a network modifier to decrease the viscosity of the liquid slag layer adjacent slab shell, the consumption of SiO2 led to the deterioration of the lubrication performance in the solid slag layer adjacent copper, which was detrimental to the quality control for high Al-TRIP steel. Finally, a kinetics equilibrium model indicated that it is possible to reduce a slag-steel reaction by adjusting factors, such as the diffusion coefficient k, *c*SiO2 , ρ*f* and *Lf* , during the actual continuous casting process.

**Keywords:** Al-TRIP steel; slag; slag-steel reaction; crystalline morphology; equilibrium model

### **1. Introduction**

While the "environmentally friendly, safety, long-life and low-cost" have become an international consensus of the automobile industry, attention for developing advanced automobile strength steel have been paid to high Al-TRIP (Transformation Induced Plasticity), which had a good combination of high strength and high toughness [1–4]. However, 1.35% Al-TRIP steel, currently in industrial production, is a kind of typical peritectic steel with volume shrinkage during peritectic reaction L + δ → γ [5]. As a result, the inhomogeneous growth of the solidification shell increases the incidence risk of the slab surface defects [6]. During the continuous casting process, slag plays an important role in counteracting this phenomenon. It controls the quality of slab through the properties of non-metallic inclusions absorption, lubrication, thermal transmission, etc. Therefore, a system of slag with suitable functions, such as the chemical composition, viscosity, and crystallization morphology, was greatly befitting for a continuous casting process [7,8]. Study on the behavior of slag, especially for the physicochemical characteristics of liquid slag film cling to the slab shell and the crystallization properties of solid slag film attaching to copper, will provide profound guidance for enhancing the slab surface quality of high Al-TRIP steel.

Many investigations on slag used for continuous casting of high Al content steel have been carried out. Conventional slags were mainly based on the CaO-SiO2-CaF2 system. However, because of Equation (1), which would take place during the continuous casting of high Al steel, the chemical composition of slag would change rapidly into an obvious increase in Al2O3 and decrease in SiO2, leading to the deterioration of slag physicochemical properties and casting [9].

$$\text{4[Al]} + \text{3(SiO}\_2\text{)} \rightarrow \text{2(Al}\_2\text{O}\_3) + \text{3[Si]} \tag{1}$$

Yu et al. [10] tried to use a high SiO2 with a low basicity flux to counteract the increase in basicity caused by the (SiO2)-[Al] reaction, and the casting experiments showed that the slab had a good surface quality. Zhang et al. [11] also studied the variation in viscosity and crystallization properties by adjusting Al2O3/SiO2, however, the improvement effect on continuous casting was not significant. Some researchers have tried to suppress the deterioration in the performance of slag by adding fluxing agents [12,13]. Park et al. [13] studied the addition of CaF2 that was beneficial to the reduction of the viscosity of high Al steel slag, but because of the high basicity of Na2O, when the content of CaF2 exceeds 8%, the viscosity-reducing effect was weakened significantly.

Primarily, it was the drastic slag-steel reaction during the continuous casting process that led to slag performance deterioration. Many attempts based on conventional slag still find it difficult to avoid the slag-steel reaction effectively. Therefore, some researchers began to explore the study of non-reactive or weakly reactive slag [6,14–21]. Among them, Wang et al. [16,17] studied the effect of various oxide additions on the crystallization behavior and heat transfer properties of the CaO-Al2O3 system continuous casting slag and provided some guidelines for the design of a reasonable CaO-Al2O3 system slag. Cho et al. [18] designed the CaO-Al2O3 based slag for continuous casting of 1.45% Al steel and found that the reactivity of Equation (1) was reduced significantly, resulting in a certain improvement of the slab quality. Seo et al. [19,20] focused on the lubrication of a solid layer of slag used for high Al-AHSS (Advanced High Strength Steel) steel and proposed to control the crystalline morphology by Jackson α factors. It was found that the crystallization at the slag film was too strong to affect the lubrication, which ultimately led to defects in the slab.

In summary, the current design schemes of slag still could not continuously cast high Al-TRIP steel perfectly caused by exorbitant Al2O3 and free of SiO2 content in slag after the reaction. And the additions of fluxing agents, such as Li2O and Na2O, would also lead to cost problems for industrial production. As a result, Cho et al. [21] proposed a slag feeding technology to improve the castability and surface quality of a continuous cast TWIP (Twinning-induced plasticity) steel. Therefore, low-reactive slag, rather than non-reactive slag, might be a suitable and economic method for the continuous casting of high Al-TRIP steel. The influence of consuming SiO2 during continuous cast Al-TRIP steel slab still requires further study.

Based on the investigation of the composition variation of CaO-SiO2 system slag in an actual Al-TRIP steel continuous casting process, a kind of low-reactive slag based on CaO-SiO2-Al2O3 system was adopted in this work. The initial low-reactive slag and corresponding slag samples after 10 min, 20 min, and 120 min of slag-steel high-temperature reaction were analyzed to determine their compositions and properties variation. Next, the crystalline morphologies were investigated by BSE (Back Scattering Electron) and Jackson α factors were adopted to evaluate solid layer lubrication performance. Finally, a kinetics equilibrium model of (SiO2) in liquid slag was established to analyze the factors that affected SiO2 consumption.

### **2. Experiments**

### *2.1. Materials Preparation*

The chemical composition of high Al-TRIP steel is listed in Table 1, samples were cut with a weight of 300 g from an industrial slab. The initial compositions of two types of industrial slag were tested by XRF (X-Ray Fluorescence) shown in Table 2. Among them, *S*/*A* was the content ratio of SiO2 and Al2O3, which represented the reactivity of slag samples; *R* was the basicity of slag samples, which was represented by the content ratio of CaO and SiO2; η represented the viscosity of slag samples at 1300 ◦C; and *T*m represented the melting temperature of slag samples. It is worth mentioning that sample A was used as the control group in the actual Al-TRIP steel continuous casting production. And sample B was used to high-temperature static balance experiment.

**Table 1.** Main chemical composition of Al-TRIP (Transformation Induced Plasticity) steel, wt.%.

**Table 2.** Main chemical compositions and properties of initial slag samples, wt.%.

1,2 Calculated by Factsage software 7.2, and η were calculated at 1300 ◦C.

### *2.2. Experimental Method*

Figure 1 shows the schematic diagram of the high-temperature static balance experimental apparatus. 300 g steel was put into Si-Mo high-temperature furnace with zirconia crucible. The steel was heated to 1550 ◦C by 10 ◦C /min and then stayed the temperature with argon at the rate of 5 L/min to prevent the oxidation of steel. To simulate the situation of a continuous addition of slag in the industry casting process, excess 60 g pre-melted slag was added on the surface of molten steel and taken out of the furnace after continuing heat preservation for 10 min, 20 min, and 120 min. Finally, after crushing and grinding, the slag chemical compositions were measured by XRF. The viscosities of 1300 ◦C and melting temperature for samples were calculated by Factsage software 7.2 (GTT-Technologies, Aachen, Germany). In addition, part of the slag sample was embedded in the epoxy resin and sprayed with gold, and then, the microstructure and crystal composition of slag sample B during the high-temperature static experiment were observed by Scanning Electron microscopy (Zeiss, Heidenheim, Germany) in Back Scattering Electron mode.

**Figure 1.** Schematic of the experimental apparatus.

### **3. Results**

### *3.1. Compositions Variation of Slag during the Slag-Steel Reaction*

The main compositions of slag sample A and B in different reaction time (10 min, 20 min, and 120 min) with 1.35% Al-TRIP steel are shown in Figure 2. In the first 10 min, the content of SiO2 decreased sharply while the content of Al2O3 increased sharply. This means that because of the strong reaction driving force, which resulted in a low content of Al2O3 and high content of SiO2 in initial

slag samples, both sample A and B reacted rapidly with steel. In the following 10 min, the reaction (1) continued, however, the reactive rates of both samples gradually calmed down by the reason of the actual content ratio of Al2O3/SiO2 in slag being increased. In other words, the reaction driving force was weakened. After 20 min, there was no obvious change in the tendency of compositions for sample A and sample B, indicating that the reaction had reached a kinetics equilibrium, and the equilibrium compositions were nearly 20 min after the beginning of the slag-steel reaction. Eventually, there was only 5.69% SiO2 content in slag sample B and its composition had moved from the CaO-SiO2-Al2O3 system to CaO-Al2O3 system. On the other hand, the final content of SiO2 was 19.84% in sample A, which kept sample A in the CaO-SiO2-Al2O3 system. In addition, because of the evaporation, no Na2O was detected in sample B after the reaction.

**Figure 2.** Variation of main compositions for slag sample: (**a**) Sample A; (**b**) sample B.

#### *3.2. Properties Variation of Slag during the Slag-Steel Reaction*

The viscosity at 1300 ◦C and melting temperature of slag samples before and after the reaction were calculated by Factsage software, shown in Figure 3. It was apparent that the melting temperature increased significantly and then gradually stabilized during the reaction. This was almost consistent with the composition of Al2O3 with a high melting temperature. The viscosity increased rapidly in the first 10 min of the reaction, and then decreased and gradually stabilized. In general, the variation of the composition and properties of sample A were consistent with that of sample B, indicating that the slag-steel reaction during the actual continuous casting process can be simulated through the high-temperature static balance experiment, so as to analyze the influence of the change of (SiO2)/(Al2O3) content on the properties of slag.

**Figure 3.** Variation of viscosity and melting temperature for slag sample A and B.

### *3.3. Revolution of Crystalline Morphology for Slag during the Slag-Steel Reaction*

Figure 4 was the morphology of the original slag sample B. The distribution of slag components for industrial slag was mainly composed of three parts unevenly. Part I was only blocked Al2O3 with a high melting temperature. It precipitated prematurely during the continuous casting process, and it performed as amphoteric oxide depending on the basicity of slag. Part II was mainly composed of C, which was a matrix of slag and played a role in assisting melting. Part III was more complex, the main compositions were P1 (Al2O3·4SiO2), P2 (2CaSiO3·CaAl2O4·BaO) and a small amount of P3 (CaF2). Among them, P1 existed alone, while P3 existed around P2.

**Figure 4.** Morphology of original slag: (**a**) full view; (**b**) details of Part III.

The crystal morphology for slag sample B after the slag-steel reaction experiment (10 min, 20 min and 120 min respectively) are shown in Figure 5. The significant difference in the microstructure of the crystal morphology of the slag with different extent of slag-steel can be clearly observed. As shown in Figure 5a, after the slag-steel reaction lasted for 10 min, the slag matrix was smooth, with a dendritic crystalline phase on the surface but without large crystalline phase. After the slag-steel reacted for 20 min, as shown in Figure 5b, the slag became rough, and there were few large-size planar granular crystalline phases with smooth boundaries on the surface. After the reaction lasted for 120 min, as shown in Figure 5c, the crystalline phase size further increased and the boundary was rougher.

**Figure 5.** Crystals morphology of slag after reaction: (**a**) 10 min; (**b**) 20 min; (**c**) 120 min.

Specifically, Figure 6 shows the details of the slag morphology after the slag-steel reaction for 10 min. The dendritic crystalline phase was CaF2, which was a benefit to lubrication. The matrix of slag crystallized uniformly along the CaF2 dendritic, and the composition was 3CaO·3SiO2·2Al2O3·BaO. No cuspidine (3CaO·2SiO2·CaF2) with high melting temperature was observed, indicating the slag had good performance on the uniform thermal transmission and melting characteristic so far.

**Figure 6.** Details of crystals morphology after reaction lasted for 10 min.

After the reaction lasted for 20 min, as shown in Figure 7, the morphology of CaF2 (P1) was a granular structure with a smooth boundary, which was favorable for the lubrication performance. The slag crystallized with P1 as the core, and is surrounded by P2 (CaAl2O4) and few CaF2 dendrites. The main component of a boundary (P3) was aluminosilicates of Ca and Ba, and Ba had a tendency to make up for the formation of fluoride by Ca. The matrix of the slag was CaAl2O4 and a small amount of CaSiO3, resulting from the large consumption of SiO2.

**Figure 7.** Details of crystals morphology after reaction lasted for 20 min.

As the reaction progressed to 120 min (Figure 8), the morphology was similar to that in Figure 6. However, the distribution was dense and uneven with the larger size and sharp boundary, leading to an unfavorable lubrication performance. With the growth of the CaF2 boundary, the surrounding Ba was constantly absorbed into the core, forming BaF2 and Ba-containing calcium aluminate (P2) eventually. The dendritic CaF2 (P3) still existed between the CaF2 core and the boundary. Compared with Figures 6 and 7, the crystal composition in Figure 8 was more complicated. There were Ba-containing CaAl2O4 and CaAl4O7 with high melting temperature.

**Figure 8.** Details of crystals morphology after reaction lasted for 120 min.

In addition, Figure 9 was the crystalline morphology at the slag-steel interface after reaction for 120 min. The crystal was dominated by gehlenite and alumina with less fluoride. There were P1 ((Ba, Ca)F2), P2 (Ca2SiO4), P3 (3CaAl4O7·BaO), and P4 (Al2O3). Since the Ba2+ electrostatic potential was smaller than Ca2+, P1 was mainly composed of BaF2. P2 was 2CaO·SiO2, which was converted from wollastonite (CaSiO3) with a large consumption of SiO2. In addition, the duration of the slag-steel reaction was 120 min, which was close to the reaction equilibrium. Considering the kinetic conditions in the experimental furnace, the Al2O3 generated by the reaction was concentrated at the slag-steel interface and difficult to diffuse. Therefore, amounts of large-size crystals P3 and P4 could be observed, which had a significant effect on the heat transfer performance of slag-steel interface, and further affected the melting and consumption of slag.

**Figure 9.** Morphology of original slag: (**a**) full view; (**b**) details of Part III.

### **4. Discussion**

### *4.1. The Relationship between the Properties and Compositions Variation of Slag*

In an alkalescent melting system, according to previous researchers [16,22], the existential form of Al2O3 was [AlO4] 5− tetrahedron, which could incorporate into [SiO4] 4− tetrahedral units to act as the network former, resulting in the increase of viscosity. With the content of (CaO)/(Al2O3) having decreased, Al2O3 existed in the form of [AlO6] 9− octahedral, which could act as a network modifier, leading to a decrease of viscosity. Therefore, the viscosity of both slags was not decreased monotonically, it fluctuated slightly in the later period of reaction.

In summary, there were obvious differences in the crystalline phase in each part of the slag after the slag-steel reaction, mainly reflected in the content of SiO2. Different crystalline phase performed different lubrication effect. The Jackson α factor was adopted in this work to evaluate the roughness of the crystalline phase. The crystals tended to be more faceted and anisotropic when their Jackson α factor increased [20]. The main crystalline phases and their corresponding melting temperature and Jackson α factors were shown in Table 3. As the reaction progressed, the content of SiO2 was gradually reduced while Al2O3 increased significantly, resulting in a gradual replacement of CaSiO3 and CaAl2O4 (with lower Jackson α factors) by CaAl4O7 (with higher Jackson α factor). From the perspective of crystallography, crystals with higher Jackson α factor consisted of crystallographic planes with different orientations, which were distributed at different angles to the heat dissipation direction. This was favorable for the formation of crystals with regular geometrical shapes, and thus the anisotropy of crystals was increased, which resulted in the decrease of lubrication performance in solid slag layer adjacent to the copper. In general, although generated Al2O3 acted as network modifier to decrease the viscosity of liquid slag layer adjacent slab shell, the consumption of SiO2 led to the deterioration of lubrication performance in solid slag layer adjacent copper, which was detrimental to the quality control for high Al-TRIP steel.

**Table 3.** Typical crystals of slag sample B and corresponding Jackson α factors, wt.%.

1 Based on reference [20].

### *4.2. Kinetics Equilibrium Model of Slag during the Reaction*

Non-linear fitting of SiO2 content in both slags through Origin software is shown in Figure 10. These content variations had good agreement with function *ct* − *c*0 = *a* × [1 − exp (*b* × *t*)]. From the perspective of mathematics, coefficient a influenced the limit of the function, and *b* influenced the inflection time of the function.

**Figure 10.** Details of crystals morphology after reaction lasted for 120 min.

Therefore, the reactivity of the slag was closely related to coefficient *a* and *b*. Theoretically, during the casting of 1.35% Al-TRIP steel, a certain content of SiO2 in the powder slag was consumed because of reaction (1), and the rest of SiO2, accompanied by molten slag, was flowed into the gap between solidification shell and copper. Therefore, the kinetics equilibrium balance of SiO2 content in the liquid slag layer could be expressed as Figure 11.

**Figure 11.** Kinetics equilibrium balance of SiO2 content in liquid slag layer.

The *c0* was the content of SiO2 in the initial powder slag. At time *t*, the SiO2 content in the liquid slag decreased to *ct*. Thus, the SiO2 content flow into the gap between copper and slab shell at this time was also *ct*. The Rm was the consumption of SiO2 caused by the slag-steel interface reaction. Assuming that the supplementary of liquid slag from powder slag layer was equal to consumed slag from liquid slag layer during the continuous casting, and the SiO2 content in the liquid slag layer was uniform at time *t*. Thus, the mass balance of SiO2 in the liquid slag layer could be expressed as follows:

$$\frac{d[\text{SiO}\_2]\_t}{dt} = \frac{M[\text{SiO}\_2]\_0 - 100R\_m - M[\text{SiO}\_2]\_t}{N} \tag{2}$$

where, [SiO2]*t* was SiO2 content in the liquid slag layer at time *t*, %; [SiO2]0 was SiO2 content in initial powder slag, %; *M* was the consumed rate of liquid slag, kg/s; *N* was the mass of liquid slag layer, kg; *Rm* was the SiO2 consumption rate from slag-steel interface reaction, kg/s; and *t* was time, s.

The slag-steel reaction consumed SiO2 and produced Al2O3. In a constant temperature condition, the SiO2 consumption rate *Rm* was associated with [Al] content in steel and the initial SiO2 content in powder slag. If the reaction was adequate during the experiments, *Rm* could be expressed as follows:

$$R\_{\rm ll} = Ak \mathfrak{c}\_{\rm A1}^{\rm m} \mathfrak{c}\_0^{\rm n} \tag{3}$$

where, *A* was reaction area, cm2; *k* was diffusion coefficient related to flow velocity and viscosity. Thus, the Equation (1) could be rewritten as Equation (4) by an integral method.

$$c\_t - c\_0 = -\frac{100}{\rho\_s v\_s Q} \times A k c\_{\rm Al}^m c\_0^n \times \left[1 - \exp\left(\frac{\rho\_s v\_s Q}{\rho\_f L\_s}\right)\right] \tag{4}$$

where, *c*Al was the [Al] content in steel, %; ρ*s* was molten steel density, g/cm3; ρ*f* was slag density, g/cm3; *Q* was slag consumption for steel, g/g; *Vs* was equivalent casting speed, cm/s; *Lf* was thickness of liquid slag layer, cm. Combined with Figure 10, the coefficients a and b could be written as follows:

$$a = -\frac{100}{\rho\_s V\_s Q} \times (k(V\_s c\_{Al}) \, ^\text{m}c\_{SiO2}^\text{n} \tag{5}$$

$$b = -\frac{\rho\_s V\_s Q}{\rho\_f L\_f} \tag{6}$$

In this work, the temperature, *c*Al, ρ*s*, *Q*, *Lf* and *Vs* could be considered as constant, while ρ*f* , *Lf* , *c*SiO2 and *k* were different. Therefore, from the perspective of the slag-steel reactivity, *k* and *c*SiO2 influenced the limit SiO2 consumption of the reaction and ρ*f* and *Lf* influenced the SiO2 consumption rate of the reaction.

#### **5. Conclusions**

This work investigated the variations of slag components, properties, and crystalline phases during a slag-steel reaction. The following conclusions can be made:

**Author Contributions:** Investigation, K.Z. and H.C.; project administration, H.C. and J.L.; writing—original draft, K.Z.; writing—review & editing, K.Z. and H.C.

**Funding:** This research was funded by the National Natural Science Foundation of China (No. U1860106).

**Conflicts of Interest:** The authors declare no competing interests.

### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **High Quality Steel Casting by Using Advanced Mathematical Methods**

### **Tomas Mauder \* and Josef Stetina**

Energy Institute, Brno University of Technology, 616 69 Brno, Technicka 2, Czech Republic<EMAIL_ADDRESS>**\*** Correspondence<EMAIL_ADDRESS>Tel.: +420-541-14-3252

Received: 15 November 2018; Accepted: 30 November 2018; Published: 4 December 2018

**Abstract:** The main concept of this paper is to utilize advanced numerical modelling techniques with self-regulation algorithm in order to reach optimal casting conditions for real-time casting control. Fully 3-D macro-solidification model for the continuous casting (CC) process and an original fuzzy logic regulator are combined. The fuzzy logic (FL) regulator reacts on signals from two data inputs, the temperature field and the historical steel quality database. FL adjust the cooling intensity as a function of casting speed and pouring temperature. This approach was originally designed for the special high-quality high-additive steel grades such as higher strength grades, steel for acidic environments, steel for the offshore technology and so forth. However, mentioned approach can be also used for any arbitrary low-carbon steel grades. The usability and results of this approach are demonstrated for steel grade S355, were the real historical data from quality database contains approximately 2000 heats. The presented original solution together with the large steel quality databases can be used as an independent CC prediction control system.

**Keywords:** continuous casting; fuzzy logic; optimal cooling; steel quality prediction

### **1. Introduction**

The continuous casting technology is a well-known predominant process how the steel is produced in the world. CC is already fully-grown technology and successfully casting million tonnes of classic low-carbon and low-alloy steel grades per year. In spite of this fact, casting of special high-strength grades, steels for acidic environment, steels for the offshore technology, high alloyed tool steels, can be still challenging in order to ensure a constant steel quality through the whole casting process. Flick and Stoiber [1] described present issues and future trends in the CC technology. The quality of the steel is still a discussed topic. In CC the solid shell is permanently subjected to thermal and mechanical stresses and it can give rise to crack formation, see Birat et al. [2]. Figure 1 shows CC installation and mechanical tensile/compression stresses in specific locations. The rejected slabs, by the quality control system, which need to be scraped is very uneconomic. The breakdown situation caused by a low quality of these steels could have a catastrophic effect on material and human losses. This quality issue can be handled by using the advanced numerical modelling methods, optimization-regulation techniques and statistical evaluations of the real casting data.

Historically, there are many papers which combine the numerical modelling and optimizationregulation approaches, such as Santos et al. [3] who applied the genetic algorithm, Zhemping et al. [4] verified the usage of the ant colony algorithm, Zheng et al. [5] attempted to use the swarm optimization on 2-D solidification model, Mauder and Novotny [6] showed the possibility of using classical mathematical programming method and compared the results with simple Nelder-Mead algorithm, Ivanova [7] constructed basic predictive control algorithm for 2-D solidification model and so forth. Rao et al. [8] publish a comprehensive review dealing with parameters optimization of selected casting processes. Unfortunately, these works are far from the use on the real casting process,

because they often calculate very simplified solidification models (simple geometry, 2-D mesh, simple boundary conditions, contain a small steel database, etc.) and it is proven that the numerical results of these models in compare with the 3-D fine-mesh validated solidification models are poor, see Mosayebidorcheh and Bandpy [9]. Moreover, the optimization algorithms are often based on black-box approach that generally needs a large number of optimization iterations before the optimal solution is found. This is not a problem in the case of simple solidification models, which calculates the temperature field very fast. However, in the case of the complex 3D numerical simulations it is not possible to use these optimization algorithms for the real time control.

**Figure 1.** Scheme of the continuous casting and mechanical stresses during bending and straightening. 1—tundish; 2—mould; 3—nozzle; 4—cooling circuit; 5—roller.

This paper describes both, the original 3-D solidification model, the so-called Brno Dynamic Solidification Model® (BrDSM) and advanced optimal control algorithm based on the fuzzy logic (FL-BrDSM). This unique combination represents a tool for achievement of high steel quality products. Besides of the numerical and fuzzy regulation models, special attention must be concentrated to proper setting of thermophysical parameters of investigated steel grade, experimental measurement of boundary conditions and statistical evaluations of the real casting data.

Presented approach is demonstrated on the real radial slab caster with twelve cooling loops in the secondary cooling for the special grade of steel S355. This steel was selected expediently because it is mainly used for shipbuilding projects, marine mechanical systems and deep-water ocean offshore structural projects were the quality of steel S355 plates is essential. The mechanical properties for these grades of steel are specified by the European Standards.

### **2. Solidification Model—BrDSM**

The core of presented approach is the 3-D transient solidification model. The computing precision, accuracy, robustness and fast computational times are essential. In order to reach these specifications a suitable numerical scheme should be selected. Numerical mesh independence tests as well as tests of the calculation speed on different CPU/GPU and mainly a properly validation on the real casting data were made.

The transient 3-D solidification model is based on Fourier-Kirchhoff Equation [2] which can be expressed as:

$$\frac{\partial(h\rho)}{\partial \tau} + v\_{\text{cast}} \frac{\partial(h\rho)}{\partial z} = \nabla \cdot \left(k\_{eff} \nabla T\right),\tag{1}$$

with boundary conditions:

$$T(x,y,z)|\_{z=0} = T\_{pouring} \qquad\qquad\text{the meniscus}\tag{2}$$

$$-\lambda \frac{\partial T}{\partial \mathbf{n}} = 0 \tag{3}$$

$$
\dot{\lambda} - \lambda \frac{\partial T}{\partial n} = \frac{\dot{m}\_{\text{water}} c\_{\text{water}} (T\_{\text{out}} - T\_{\text{in}})}{S\_{\text{model}}} \tag{4}
$$

$$-\lambda \frac{\partial T}{\partial \mathbf{n}} = \frac{\pi (1/2) d\_{\text{rel}}}{S\_{\text{rel}}} \text{ltr} c\_{\text{rel}} (T\_{\text{rel}} - T\_{\text{amb}}) + \sigma \varepsilon \left( T\_{\text{rel}}^4 - T\_{\text{amb}}^4 \right) \qquad \text{beneath the rollerers},\tag{5}$$

$$-\lambda \frac{\partial T}{\partial n} = ht\varepsilon (T - T\_{\text{water}}) + \sigma \varepsilon \left(T^4 - T\_{\text{water}}^4\right) \qquad \text{because the spray cooling.} \tag{6}$$

$$\lambda \frac{\partial T}{\partial n} = 0.84 (T - T\_{\text{water}})^{4/3} + \sigma \varepsilon \left(T^4 - T^4\right) \qquad \text{within the solidification shell free surface} \tag{7}$$

$$
\lambda - \lambda \frac{\partial T}{\partial \mathbf{n}} = 0.84 (T - T\_{amb})^{4/3} + \sigma \varepsilon \left( T^4 - T\_{amb}^4 \right) \qquad \text{within the solidified shell free surface.} \tag{7}
$$

*keff* is the effective thermal conductivity (W/mK); *T* is the temperature (K); *Tpouring* is the pouring temperature (K); *h* is the specific enthalpy (J/kg); *ρ* is the density (kg/m3); *τ* is the time (s); *vcast* is the casting speed (m/min); *z* is the direction of casting (m), *Trol* is the roller temperature; *Twater* is the cooling water temperature; *Tamb* is the ambient temperature; . *mwater* is the mass water flow in the mould (kg/s); *cwater* is the specific heat capacity of water (J/kgK); *htc* is the heat transfer coefficient beneath spraying surface (W/m2K); *σ* is the Stefan-Boltzman constant (W/m2K4) and *ε* is the emissivity of the slab surface (-).

The latent heat released during the solidification in Equation (1) is substituted by the enthalpy *h* and can be expressed as:

$$h = \int\_0^T \left( \mathfrak{c}(\tilde{\xi}) - \Delta H \frac{\partial f\_s}{\partial \tilde{\xi}} \right) \mathrm{d}\tilde{\xi}\_{\prime\prime} \tag{8}$$

where Δ*H* is the latent heat (J/kg) and *fs* is the solid fraction (-). The Enthalpy method was used for modelling the solidification process, see Mauder et al. [10]. The Enthalpy method is robust method because it ensures energy conservation and there is no discontinuity at either the liquidus or the solidus temperatures because the solidification/melting path is characterized strictly by decreasing/increasing enthalpy. In the Equation (1) the enthalpy is calculated in the first step as the primary variable and the temperature is calculated from a defined enthalpy-temperature relationship in the second step Equation (8).

In the presented solidification model, Equation (8) is substituted by an enthalpy-temperature function obtained by the InterDendritic Solidification (IDS) package created by the Miettinen [11]. The IDS allows calculation of enthalpy, thermal conductivity, density and other thermophysical parameters as a function of temperature from 1600 ◦C–0 ◦C.

Fluid flow of the liquid steel can be calculated by the computational fluid dynamics (CFD) techniques. However, computational times are even with the use of new modern modelling approaches far from the real duration of the simulated process. The influence of heat transfer by the fluid flow is account in the effective thermal conductivity term *keff*. The thermal conductivity is increased by the flow of liquid steel at different distances from the meniscus, where *keff* is represented by Zhang et al. [12] as follows:

$$k\_{eff} = \begin{cases} k & T \le T\_{sol} \\ 4k + \frac{3k\left(T - T\_{liq}\right)}{\left(T\_{paving} - T\_{liq}\right)} & T \ge T\_{liq} \land 0 \le z \le 1 \text{ m} \\\ k + \frac{3k(T - T\_{sol})}{\left(T\_{liq} - T\_{sol}\right)} & T\_{sol} \ge T \ge T\_{liq} \land 0 \le z \le 1 \text{ m} \\\ k + \frac{k\left(T - T\_{liq}\right)}{\left(T\_{pwing} - T\_{liq}\right)} & T \ge T\_{liq} \land 1 \text{m} \le z \le 3 \text{ m} \\\ k & z \ge 3 \text{ m}\_{\prime} \end{cases} \tag{9}$$

where *k* is the thermal conductivity (W/mK); *Tsol* is the temperature of solidus (K); *Tliq* is the temperature of liquidus (K); and *z* is the distance from the meniscus (m).

The heat transfer in the mould region described by Equation (4) is calculated from the heat balance between heat removal from the mould walls and internal water cooling in-out temperature difference. The real data comes directly from the measurement of cooling water temperatures and flow rates, which are affected by the casting speed and steel carbon content.

The situation beneath the rollers Equation (5) also comes from the heat balance assumption. The removed heat from the slab surface is equal to the heat, which is radiated to the surroundings by the rollers. In the case of internal cooled rollers, Javurek et al. [13] published a paper on how to determine boundary conditions in the case of dry casting.

In the spraying area, the strand is cooled by the water or water–air mixture sprays. Nozzle parameters like air and water flow, nozzle position and impact angles have an effect on the cooling efficiency, the *htc* from the Equation (6) respectively. Totten et al. [14] showed several empirical formulas describing how to deal with the heat transfer coefficient beneath the nozzle. However, these empirical formulas include many constants and parameters and their correct determination for a particular cooling setup is difficult. Proper determination of boundary conditions is crucial in case to obtain a real results, see Lopez et al. [15].

The advantage of the model discussed in this paper is that it obtains its heat transfer coefficients from measurements of the spraying characteristics of all nozzles used by the caster on a so-called hot plate in the experimental laboratory, according to Raudensky et al. [16]. Thus, the model takes *htc* as a function of water flow, casting speed, surface temperature, air pressure and can be expressed mathematically as:

$$
\hbar \hbar t \mathbf{c} = f \left( \dot{m}\_{\text{water}}, v\_{\text{cast}}, \ T\_{\text{surface}}, p\_{\text{air}} \right). \tag{10}
$$

### **3. Numerical Formulation and Massive Parallelization**

There are several discretization schemes how to solve the Equations (1)–(7). After large-scale numerical studies two numerical schemes proved to be good candidates for solving the case of 3-D transient heat transfer problem with solidification phenomena, Simple Explicit (SE) and Alternating Direction Implicit (ADI), see Mauder et al. [10]. The ADI scheme proposed by Douglas and Gunn is unconditionally stable and retains the second-order accuracy when applied to 3-D problems. However, ADI scheme has very limited possibility of parallelization on multiple CPU and massive parallelization on GPU is out of question. In the case of complex 3-D solidification-optimization models, the requirement for the real time control can be reached only by the use of the massive parallelization techniques. In Table 1 there are computation times for ADI and SE schemes tested on three different types of meshes (coarse-mesh with 10 000 nodes, fine-mesh with 125,000 nodes and the very-fine mesh with 1,000,000 nodes) on Intel(R) Core(TM) i7-3770 CPU @ 3.4GHz 16GB RAM. More information about efficiency, robustness and accuracy of the examined numerical schemes can be found in Mauder et al. [10].

**Table 1.** Computation time for non-parallel and parallel solution (s).

This is the reason why the numerical core in presented solidification model is created by SE scheme. On the one hand, SE has its limitation in the form of stability condition, thus for fine meshes the time step has to be very small. However, due to the use of massive parallelization on GPU this issue is compensated. The calculation on GPU is more than 50 times faster for very-fine meshes. The SE scheme applied to Equation (1) can be in the form:

$$h\_{i,j,k}^{n+1} \rho\_{i,j,k}^{n+1} = h\_{i,j,k}^{n} \rho\_{i,j,k}^{n} + \Delta \tau \left[ \dot{Q} \mathbf{x} + \dot{Q} \mathbf{y} + \dot{Q} \mathbf{z} \right] - \Delta \tau \left. v\_{\text{cast}} \frac{h\_{i,j,k+1}^{n} \rho\_{i,j,k+1}^{n} - h\_{i,j,k}^{n} \rho\_{i,j,k}^{n}}{\Delta z\_{k-1}} \right. \tag{11}$$

where:

. *QΨ* = 2 0.5 *kn ξ*+1 + 0.5 *kn ξ* −1 *Tn ξ*+1−*Tn ξ* Δ*Ψξ* − 0.5 *kn ξ*−1 + 0.5 *kn ξ* −1 *Tn ξ* −*Tn ξ*−1 Δ*Ψξ*−1 Δ*Ψξ*+Δ*Ψξ*−1 *Ψ* ∈ {*x*, *y*, *z*} *ξ* ∈ {*i*, *j*, *k*}. (12)

The index *n* + 1 is associated to the future time; *n* is the index corresponding to the actual time; Δ*τ* is the increment of the time; *x*, *y* and *z* are the directions; Δ*Ψ* are increments in the directions and *ξ* are the positions. The time step Δ*τ* has to fulfil a well-known stability condition:

$$
\Delta \tau \le \frac{1}{\left(\frac{2k(T)}{\rho(T)\varepsilon(T)}\right)\left(\sum\_{\mathbf{Y}} \frac{1}{\Delta \mathbf{Y}^2}\right) + \frac{v\_{\text{out}}}{\Delta z}}. \qquad \Psi \in \{x, y, z\} \tag{13}
$$

The numerical model has a non-equidistant mesh in all directions. The reason for this is that the largest temperature gradients are near the surface. In axis *z* (direction of casting) the nodes are adapted to the real rollers and nozzles positions to get more accurate determination of boundary conditions in secondary cooling zone. Mesh independence test in Figure 2 indicates when the convergence is achieved. In *x* axis is the number of elements, in *y*-left axis is the temperature in several points on the top surface (distance from meniscus 1, 2, 4, 10, 15, 20 m) and in the *y*-right axis is the value of the metallurgical length. This study shows that the number of elements should be at least 2 500,000. Finer mesh do not affected the results significantly. These results with respect the results obtained in Table 1 show again the needs of SE GPU parallel scheme in order to calculate complex 3-D solidification model in the real time.

**Figure 2.** Temperatures and metallurgical length for different mesh densities.

The mesh decomposition is sketched out in Figure 3. The primary mesh is created on CPU, then is divided into many sub-meshes (regions). The boundary conditions and initial condition are set on CPU. Further, numerical regions are separately send to the GPU units where Equations (10) and (11) are calculated. After the temperatures in future time step are calculated, the values in separated regions are send back to CPU where boundary conditions are recalculated and again send to the GPU. This loop is repeated until final temperature field is reached.

**Figure 3.** Numerical mesh CPU-GPU decomposition.

### **4. Fuzzy Logic Regulator—FL-BrDSM**

The BrDSM can calculate the temperature distribution of the strand in real time for given casting parameters such as the initial temperature distribution, intensity of cooling, speed of casting and so forth. The problem is how to set input parameters in the optimal way to get a required (optimal) temperature distribution. This is referred to as an inverse problem. For this reason, supervision-system/optimal-regulator based on fuzzy logic has been created. The FL regulator treats the solidification model as a black-box and when the FL regulator changes input parameters such as casting speed and intensity of cooling, the black-box returns the final temperature field for new input parameters. Based on the temperature field the FL regulator adjusts input parameters and repeats the process in a closed-loop until the optimal solution is found.

Several regulation approaches have been tested in the past, such as PID regulation, FL regulation, Model Predictive Control (MPC) regulation and their combinations. The most promising regulation outcome for dynamic changes in process parameters was reached by using a combination of MPC and FL regulation, see Stetina et al. [17]. This approach generally requires a large number of iterations because several future scenarios are calculated. For the real time simulation, this is possible only with use of GPU solidification model.

The most important parameters for the MPC/FL regulator are so called optimal surface temperature intervals. These temperature intervals should guarantee smooth temperature (cooling) profiles and high quality of final steel with zero or minimum surface defects. The optimal cooling strategy is to keep the surface temperatures in these intervals, see Figure 4. These intervals are set by the user and they are distinct for different grades of steel. In Section 5 is discussed how to set these intervals.

**Figure 4.** Optimal temperature intervals.

FL regulator extracts temperatures in the regulation points from the computed result (output from BrDSM) and by compare them with the prescribed temperature values to determine their errors. With all the temperature information, the FL regulator infers modifications for each cooling circuits. The temperatures in the regulation points are influenced by all previous cooling circuits, which should be taken account. The closer cooling circuit has a bigger influence on the regulation point, thus artificial parameter so call impact parameter in the range from 0 to 10 is created. The regulator evaluates the errors and impacts by the fuzzy rules. These rules give the value of modification for each cooling circuit. One circuit can get several different modifications from following control points proportional to the impact. Some modifications can require increase of cooling, the other decrease of cooling. The algorithm uses the final value for modification of one cooling loop as a sum of these values.

Membership functions for all fuzzy statements are trapezoidal-shaped uniformly distributed through the corresponding interval. These intervals are professionally/expertly set based on caster geometry and another caster parameters. As a defuzzification method, the standard centre of gravity was chosen.

The combination of the FL regulator with the GPU solidification model can predict future temperature states and it works like the MPC system. The detailed description of the FL regulator including linguistic variables and linguistic rules, input and output data and so forth, is described in Mauder et al. [18].

### **5. Steel S355 and Real Casting Data**

A frequent occurrence of surface defects in slabs of the cast steel grade S355 was the reason for statistical and numerical investigation. The importance of high quality of the steel S355 was mentioned in the introduction. The chemical composition is listed in Table 2.

**Table 2.** Chemical composition of steel S355.

Three typical defects were found: transverse facial cracks, star cracks and longitudinal facial cracks. The most common defects were the star cracks. These defects primarily appear at the top surface of the strand and possible causes for these defects are hard cooling and tensile stresses at the straightening area [2]. Therefore, the top surface of the strand and the temperatures at the straightening area were investigated.

The real casting data were statistically evaluated from approximately 2000 heats cast in 2011 and 2012 in EVRAZ VITKOVICE STEEL machinery in the Czech Republic. The evaluation of the statistical hypothesis shows that the surface temperature in the unbending point significantly influences the surface quality of slabs. The heats were divided into two groups. Heats where surface defects were found and heats without surface defects. The surface temperature was measured by a pyrometer at the straightening area. The results in a form of histogram are shown in Figure 5. The heats without surface defects were fitted by the Gauss curve to obtain optimal temperature intervals at unbending point.

**Figure 5.** Surface temperatures in unbending point with and without defects.

Hypothesis tests show that we cannot reject the hypothesis on the 5% level of significance stating that the surface temperature at the straightening area influences the presence of surface defects. This leads back to the following idea: if we will keep the surface temperature in some range, the occurrence of surface defects would be minimized. The optimal temperature intervals at unbending point were set according to the statistical results from heats without defects 916.03 ± 6.89 ◦C.

There are three pyrometers distributed on the examined caster. First one at end of the mould, the second one at unbending point (Figure 5) and the last one at the end of tertiary cooling zone. The most significant area is at unbending point from the perspective of cracks. However, smooth decreasing of surface temperatures through the casting process has positive influence on the final steel quality. Thus, the optimal temperature intervals for the fuzzy regulator were obtained by the curve fitting of these three points using following function:

$$y = \text{x}a^b + c,\tag{14}$$

where *y* is the temperature, *x* is distance from the meniscus and constant *a*, *b* and *c* were found by using curve fitting tool. These constants have to be found for each grade of steel separately. Optimal temperature intervals obtained this way are used as the input parameters for FL-BrDSM. Thermophysical properties for the steel grade S355 as functions of the temperature were calculated using the InterDendritic Solidification (IDS) thermodynamic-kinetic package (version 1.3.1, Helsinki University of Technology, Helsinki, Finland). The results are presented in Figure 6a. The solidification model of the IDS is a so-called "grey box", that is, it combines empirical or semi-emprical submodels with physically conceived submodels. The IDS model has been created at Aalto University in Helsinki [11] and is further developed, see Louhenkilpi et al. [19]. The IDS model consists of two main submodels for the simulation of interdendritic solidification (solves solidification from liquidus temperature to 1000 ◦C, i.e., the formation of, for example, ferrite or austenite) and simulation of solid state austenability (solves solidification from 1000 ◦C to temperature, 25 ◦C, that is, the formation of proeutectoid ferrite, cementite, perlite, bainite and martensite. The model also supports basic calculations of properties that influence the strength behaviour of steel and can serve as a basis for predictive crack criteria, see Figure 6b).

**Figure 6.** Temperature dependent physical properties for the steel grade S355, (**a**) thermophysical properties; (**b**) Mechanical properties.

### **6. Results and Discussion**

The input parameters for the FL-BrDSM were: the thermophysical properties of steel grade S355 (from IDS); optimal surface temperature intervals (from statistical evaluation); speed of casting (set by the user); meniscus temperature (from historical/actual casting data in case of offline/online simulation); heat fluxes at the mould (from historical/actual casting data as a function of casting speed); and maximal and minimal water flows at the secondary cooling (from the caster specification). The output parameters for the FL-BrDSM were the temperature field (from BrDSM) and the optimal cooling intensity at the secondary cooling zone (from the FL regulator).

The geometry of the investigated CC machine is as follows: a mould length of 900 mm; a radius of 8000 mm; a length of secondary cooling after an unbending point of 8500 mm; length of tertiary cooling of 2000 mm. The secondary cooling zone is divided into 12 independent cooling loops according to Figure 7. For more detailed caster description see Mauder et al. [18].

**Figure 7.** Position of cooling loops.

Firstly, the FL regulator was tested for static process parameters. The optimal temperature field for the average casting speed 1.7 m/min is shown in Figure 8. The cross-section size of the slab was 1530 mm × 250 mm and the numerical mesh was created from over 1.5 million nodes. Because the CC is a dynamic process and the casting speed varies in time, it is necessary to keep surface temperatures at constant values in order to achieve a high steel quality. Thus, optimization was carried out for two different casting speeds in order to obtain the optimal relationship between cooling intensities and the casting speed, see Table 3. These results can be used for the real CC process in case of steel grade S355 casting.

The cooling intensity in loops 9 and 11 (last two loops at top surface) reaches its minimal allowed values for casting speed of 1.5 m/min. This means that for lower values of casting speed is even a better solution possibly exists. The last two cooling loops at top surface should therefore be replaced by smaller nozzles, which can operate smaller water flows (soft cooling). Moreover, significant savings of water consumption can be reached. In the case of casting speed 1.9 m/min, the maximal allowed cooling intensity values (physical limitations of pumps) were reached. This casting speed should not be exceeded, otherwise the surface temperature increases over the optimal temperature interval and the number of defects may rise.

**Figure 8.** Optimal temperature field after fuzzy regulation.

**Table 3.** Optimal cooling intensities for cooling loops and different casting speeds.

Another set of simulations were carried out for dynamic changes in process parameters such as casting speed or casting temperature. The following results show 1 h casting process where a drop of the casting speed from 1.9 to 1.2 m/min at time 30 min and the increase of the casting speed from 1.2 to 1.9 m/min occurs at time 40 min. The Figure 9 shows the response in cooling intensities for all 12 cooling loops on casting speed drop calculated by FL regulator. Because MPC were used, several future scenarios were calculated and optimal dynamic changes were found. The value of temperature errors after each regulation points (surface temperatures after each cooling loop) are shown in Figure 10. The maximal temperature error was approximately 20 ◦C but average temperature error was less than 10 ◦C. This can be consider as a very good regulation results.

Static and dynamic simulations proved regulation possibilities of the presented FL-BrDSM solution. The computation time without GPU was 27.25 min for static and 47.20 min for dynamic simulation. With GPU approach, the computation time was less than 1 min and 2 min in case of dynamic simulation respectively. This declares that there is no problem to solve complex fine-mesh (more than 3 million nodes) 3D transient solidification models and their optimal regulation in the real time on the real CC machine.

**Figure 10.** Surface temperature errors after each cooling loop.

### **7. Conclusions**

The FL-BrDSM was tested for many different fuzzy parameters, for different casting temperatures and casting speeds constraints, for different caster and slab geometries and for different steel grades. This paper is focused on the quality improvement of the steel grade S355 and demonstration of the FL-BrDSM. The first part of the work was focused on detail description of solidification model and its GPU version. Than FL regulator was described. Last part of the work was statistical evaluation of real historical casting data for steel grade S355. The influence of the surface temperature at the straightening area to the occurrence of surface defects was statistically evaluated as significant. From the statistic results the optimal (recommended) temperature field was obtained and used as the input to the FL-BrDSM. For different casting speeds the optimal cooling intensities were found. The control of the CC process using recommended cooling curves can decrease the number of surface defects. The dynamic simulation shows real time regulation possibilities in the case of casting speed drop. The same approach can be applied for any grade of steel. The main advantage of the presented approach is a small number of evaluations before the optimal solution is reached and its overall versatility. This also allows for the on-line real-time regulation of a real CC process.

**Author Contributions:** Conceptualization, T.M. and J.S.; Methodology, J.S.; Software, T.M.; Validation, T.M. and J.S.; Formal Analysis, J.S.; Investigation, T.M.; Resources, T.M.; Data Curation, J.S.; Writing-Original Draft Preparation, T.M.; Writing-Review & Editing, T.M.; Visualization, T.M.; Supervision, J.S.; Project Administration, J.S.; Funding Acquisition, J.S.

**Funding:** This research was funded by the project NETME+, LO1202, with the financial support from the Ministry of Education, Youth and Sports of the Czech Republic under the "National Sustainability Programme I and APC was funded by the Open Access fond Brno University of Technology.

**Acknowledgments:** The authors gratefully acknowledge funding from the Open Access fond Brno University of Technology and Specific research on BUT FSI-S-17-4444.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript and in the decision to publish the results.

### **References**

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Effect of Cooling Rate on the Formation of Nonmetallic Inclusions in X80 Pipeline Steel**

### **Xianguang Zhang, Wen Yang, Haikun Xu and Lifeng Zhang \***

School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China<EMAIL_ADDRESS>(X.Z<EMAIL_ADDRESS>(W.Y<EMAIL_ADDRESS>(H.X.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +86-10-62332267

Received: 5 March 2019; Accepted: 25 March 2019; Published: 29 March 2019

**Abstract:** Nonmetallic inclusions have a strong influence on the hydrogen-induced cracking (HIC) and sulfide stress cracking (SSC) in pipeline steels, which should be well controlled to improve the steel resistance to HIC and SSC. The effects of cooling rate on the formation of nonmetallic inclusions have been studied both experimentally and thermodynamically. It was found that the increasing cooling rate increased the number density and decreased the size of the inclusions, while the inverse results were obtained by decreasing the cooling rate. Furthermore, as the cooling rate decreased from 10 to 0.035 K/s, the inclusions were changed from Al2O3-CaO to Al2O3-CaO-MgO-CaS. At a high cooling rate, the reaction time is short and the inclusions cannot be completely transformed which should be mainly formed at high temperatures. While, at low cooling rate, the inclusions can be gradually transformed and tend to follow the equilibrium compositions.

**Keywords:** pipeline steel; inclusions; cooling rate; composition

### **1. Introduction**

High-grade pipeline steels have been widely used in the construction of long-distance oil and gas transportation systems, which requires good combination of high strength, toughness, corrosion resistance and weldability. Hydrogen-induced cracking (HIC) and sulfide stress cracking (SSC) have been recognized as the vital threats to the safety of the pipeline operation, and caused significant economic losses throughout the world [1–8]. It has been acknowledged [5,9] that nonmetallic inclusions are one of the dominant factors affecting the HIC and SSC in pipeline steels, especially the large inclusions with string shape. Therefore, it is crucial to control the inclusions in pipeline steels to improve the steel resistance to HIC and SSC.

There are several kinds of inclusions in pipeline steel due to its complex alloy elements. The inclusions are mainly identified as aluminum oxides, calcium oxides or calcium sulfide, magnesium oxides and manganese compounds [10]. It was reported that the calcium aluminate with low melting temperature can be elongated into string shape after rolling, which is harmful to the performance of pipeline steels [11–13]. Researchers proposed that the inclusions should be controlled to CaO-Al2O3-CaS, CaO-CaS type [11] or Al2O3-CaS type [14,15] to reduce their detrimental effects. Hence, the type and composition of the inclusions are important to pipeline steels which should be well controlled. Inclusions are usually controlled by adjusting compositions of slag or/and steel during steelmaking process [16–21]. In addition, the nonmetallic inclusions can transform even during and after solidification. It was reported that in stainless steel the inclusion of MnO-SiO2 can transform to MnO-Cr2O3 spinel during heat treatment and the transformation rate depended on both temperature and size of the inclusions [22]. Therefore, the evolution of the inclusions during the cooling process is also very important for the formation of inclusions in the final product.

Cooling rate is an important parameter during the continuous casting, which largely changes the temperature and time of the steels experienced during the solidification and subsequent solid-state cooling process. Hence, the cooling rate may have a strong influence on the precipitation and transformation behaviors of the inclusions in pipeline steels. However, the previous works were mainly focused on the influences of compositions of the slag or steels on the formation of the inclusions. Little attention has been paid to the evolution of inclusions at different cooling rates. Goto et al. [23,24] investigated the effects of cooling rate during solidification on the formation of oxides in plain low carbon steels. It was found that [23,24] the amount, size and compositions of the oxides are strongly influenced by the cooling rate. However, according to the best of the authors' knowledge, no systematic work has been reported regarding the effects of cooling rate on the formation of inclusions in high-grade pipeline steels, especially the type and composition of the inclusions, which requires a stricter control in inclusions. In the current work, the number, size distributions and compositions of inclusions in X80 pipeline steel formed at different cooling rates were studied systematically to clarify the effects of cooling rate on the precipitation, growth and transformation of the inclusions in pipeline steel.

### **2. Materials and Methods**

X80 pipeline steel was used in this study, the composition of which is shown in Table 1. The production procedure of X80 pipeline steel is "basic oxygen furnace (BOF)→ladle furnace (LF) refining→RH refining→Ca treatment→soft-blowing→continuous casting". Molten steel specimens were taken from the ladle furnace after the Ca treatment and soft-blowing for 600 s, and quenched into water immediately. Figure 1a shows a schematic of the thermal history for re-melting and cooling treatments of the specimens used in this study. The specimens were first re-melted at 1873 K for 600 s in a Si-Mo resistance furnace under an argon atmosphere in MgO crucibles, as schematically shown in Figure 1b. After that, the crucibles were taken out and cooled at three different cooling rates by employing water, air or furnace, respectively, as schematically shown in Figure 1a.

The cooling rate in air was evaluated from Equation (1) [25] which relates the secondary dendrite arm spacing with the cooling rate and it is valid for a carbon content below 0.53 mass%.

$$
\lambda = 148 C\_R^{-0.38} \text{ \textdegree} \tag{1}
$$

where, *λ* represents the secondary dendrite arm spacing (μm), and *CR* is the cooling rate (K/s). The average secondary dendrite arm spacing was measured to be around 191 μm, and thus the average cooling rate in air was estimated to be 0.51 K/s. The dendritic structure for the samples cooled in furnace and in water did hardly produce clear images. The cooling rates in furnace and in water were estimated to be 0.035 K/s [26] using a pyrometer and 10 K/s using thermocouples [27], respectively, from the temperature of 1873 to 983 K.

After cooling to room temperature, the samples were cut and polished for analyzing the distribution of the inclusions. The morphology, number, area and chemical composition of inclusions in the samples were detected by using an automated Scanning Electron Microscope-Energy Dispersive Spectrometer (SEM-EDS, FEI, Pittsburgh, PA, USA) inclusion analysis system (Aspex Explorer) operated at 15 kV. The minimum detectable inclusion was set as approximately 0.5 μm, and the maximum diameter was chosen as the size of inclusion. The area of around 17 mm2 were scanned for the of inclusions analyses for each sample.

**Table 1.** Chemical composition of the alloy used in this study (mass%).

**Figure 1.** Schematic illustrations of (**a**) the thermal history for re-melting and cooling treatments of the specimens and (**b**) the Si-Mo resistance furnace employed in this study.

Two statistical parameters, area fraction and number density, are defined as the following two equations to characterize nonmetallic inclusions.

$$AF = \frac{A\_{inclusion}}{A\_{total}},$$

where, *AF* is the area fraction of inclusions, ppm; *Ainclusion* is the total area of the detected inclusions, μm2; and *Atotal* is the area scanned, mm2.

$$ND = \frac{n}{A\_{total}} \,\prime \tag{3}$$

where, *ND* is the number density of inclusions, per mm2; and *n* is number of detected inclusions on the area of *Atotal*.

### **3. Results and Discussion**

#### *3.1. Characterization of the Inclusions Formed at Different Cooling Rates*

The element mapping of a typical inclusion formed at the cooling rate of 10 K/s (water cooling) is shown in Figure 2a. The morphology of the inclusion is spherical and it mainly contains the elements of Al, Ca, O, and a small amount of Mg. The composition and size distributions of inclusions were plotted in ternary phase diagrams, as shown in Figure 2b–c, where the scanning area and number of inclusions are presented and the black star indicates the average composition. Most of the inclusions are the Al2O3-CaO, with a very small amount of MgO and CaS. The diameters of the inclusions are mostly smaller than 3.5 μm. Figure 2d shows the variation in composition of the inclusions against its equivalent diameter. The contents of Al2O3 and CaO are almost stable regardless the size of the inclusions, and the contents of MgO and CaS are very low.

**Figure 2.** (**a**) Element mapping of a typical inclusions formed at the cooling rate of 10 K/s. Summary of the (**b**–**c**) composition and size distributions of inclusions and (**d**) variations in composition of inclusions against its diameter formed at the cooling rate of 10 K/s.

The element mapping of a typical inclusion formed at the cooling rate of 0.51 K/s (air cooling) is shown in Figure 3a. The morphology of the inclusion is spherical and it mainly contains the elements of Al, Ca, O. The content of Mg seems slightly higher than that of the water-cooled specimen shown in Figure 2a. The composition and size distributions of inclusions are shown in Figure 3b–c. Most of the inclusions are the Al2O3-MgO-CaO and Al2O3-CaO-CaS. In addition, the diameters of the inclusions are mostly smaller than 3 μm. The average composition of the inclusions is about 62% Al2O3-3% MgO-26% CaO-9% CaS. Figure 3d shows the variation in composition of the inclusions as a function of its diameter. With the increase in diameter of inclusions, the Al2O3 and CaO contents are increased, while the CaS content is decreased. Around 10% CaS was contained in inclusions with the diameter of 0.5 μm.

**Figure 3.** (**a**) Element mapping of a typical inclusions formed at the cooling rate of 0.51 K/s. Summary of the (**b**–**c**) composition and size distributions of inclusions and (**d**) variations in composition of inclusions against its diameter formed at the cooling rate of 0.51 K/s.

The element mapping of a typical inclusion at the cooling rate of 0.035 K/s (furnace cooling) is shown in Figure 4a. The morphology of the inclusion is spherical and it mainly contains the elements of Al, Ca, O, Mg and S. The contents of Mg and S are much higher than that of the high cooling rates as shown in Figures 2a and 3a. More importantly, it can be noticed that the inclusion is not as uniform as that of the inclusions formed at a high cooling rates (Figures 2a and 3a). According to the element distribution, the out-layer of the inclusion is CaS, while the core is composed by Al2O3-MgO-CaO. The composition and size distributions of the inclusions formed at the cooling rate of 0.035 K/s (furnace cooling) are shown in Figure 4b,c. Most of the inclusions were the Al2O3-MgO-CaO and Al2O3-CaO-CaS. The diameters of inclusions are mostly larger than 3 μm and the number of inclusions is low. The average composition of inclusions is about 76% Al2O3-7% MgO-3% CaO-14% CaS.

**Figure 4.** (**a**) Element mapping of a typical inclusions formed at the cooling rate of 0.035 K/s. Summary of the (**b**–**c**) composition and size distributions of inclusions and (**d**) variations in composition of inclusions against its diameter formed at the cooling rate of 0.035 K/s.

Figure 4d shows the variation in composition of inclusions against its diameter. The content of Al2O3 increases with the increase in diameter of the inclusions up to 4 μm, then it has a large fluctuation with the further increase in diameter. The content of CaO is slightly increased in the inclusions larger than 4 μm. The contents of CaS and MgO do not show strong dependence on the size of the inclusions.

Table 2 summarized the mean composition of the inclusions that were formed at different cooling rates. At a cooling rate of 10 K/s, the inclusions are mostly Al2O3-CaO with a very small amount of CaS and MgO. When the cooling rate is decreased to 0.51 K/s, the contents of CaO, CaS and MgO are increased. As the cooling rate is further decreased to 0.035 K/s, the contents of CaS and MgO are further increased, while the CaO content is decreased due to the transition of the CaO to CaS.

**Table 2.** Average composition of the inclusions formed at various cooling rates in X80 pipeline steel (mass%).

### *3.2. Effects of Cooling Rate on the Formation of the Inclusions*

Figure 5a,b shows the variation in number density and area fraction of inclusions as a function of its diameters formed at different cooling rates, respectively. The peak position of the number density appears at the diameter of around 1 μm for the cases of various cooling rates, then it gradually decreases with the increase in diameter of the inclusions. The low cooling rate of 0.035 K/s results in relatively uniform distributions in size and area fractions of the inclusions. The high cooling rates of 10 and 0.51 K/s are similar in number density and area fraction distributions. The total number density of the inclusions formed at various cooling rates is summarized in Figure 5c. The number density increases dramatically with the increase in cooling rate from 0.035 to 0.51 K/s, then it becomes almost constantwith the further increase in heating rate. The area fraction and average diameter of the inclusions formed at different cooling rates are shown in Figure 5d,e, respectively. With the increase in cooling rate from 0.035 to 0.51 K/s, the area fraction and average diameter are decreased, and then theybecome almost constant.

The number density of the inclusions should be related with the nucleation of the inclusions. According to the classical homogenous nucleation theory, as for a homogeneous nucleation of an inclusion in liquid steel, the activation energy for nucleation can be written as [28]

$$
\Delta G^\* = \frac{16\pi\sigma^3}{3\Delta G\_v^2} = \frac{16\pi}{3}\sigma^3 \frac{V\_m^2}{\left(RT\ln\eta\right)^2} \tag{4}
$$

where σ is the interfacial tension between the inclusion and liquid steel, Δ*Gv* the driving force for the inclusion nucleation, *Vm* the molar volume of the inclusion and *η* is the supersaturation, viz., the ratio of activities of precipitating elements to the solubility product.

The critical radius, r\*, for nucleation is given by

$$\mathbf{r}^\* = -2\sigma / \Delta \mathbf{G}\_{\upsilon} \tag{5}$$

The nucleation rate is written as [28]

$$I = K\_Z \Gamma\_A N\_A \exp\left(\frac{-\Delta G^\*}{kT}\right) \exp(-\tau/t),\tag{6}$$

where *KZ* is the Zeldovitch factor, the value for *KZ* is about 10−2. Γ*A* is the jump frequency of atom A on the nucleus surface and is proportional to its diffusion coefficient in the liquid phase. *NA* is the atomic concentration of atom A per unit volume. *k* is the Boltzmann's constant and *T* is the absolute temperature. *τ* is the incubation time, when the time *t* is larger than *τ*, the nucleation rate is stationary. Indeed, the pre-exponent factor is usually assumed to be constant and in the range of 1035–1045 (m−3·s−1). Therefore, according to Equation (6), the nucleation rate is inversely proportional to the activation energy ΔG\*.

**Figure 5.** Variation in (**a**) number density and (**b**) area fraction of inclusions against its diameter under different cooling rates. The effects of cooling rate on the (**c**) number density, (**d**) area fraction and (**e**) mean equivalent diameter of the inclusions.

At a high cooling rate, the supersaturation (driving force) for inclusion nucleation is larger, due to the increase in elements segregation [24], which decreased the activation energy (Δ*G*\*) and the critical radius (r\*) for nucleation, according to Equations (4) and (5). This indicates that the nucleation become easier at a high driving force. On the other hand, the increase in driving force promotes the nucleation rate according to Equation (6). This should result in the high number density of the inclusions at a high cooling rate. It needs to point out that the supersaturation may be not always increase with the increase in cooling rate, and it may have an upper limit above which the supersaturation may not change obviously. This can be the reason for the almost constant number density of inclusions above 0.51 K/s.Furthermore, because the driving force for nucleation is changing in the present work, which is difficult to be evaluated, qualitative analysis is carried out in this study.

The low cooling rate has a low driving force for nucleation results in low number density of inclusions. On the other hand, at a low cooling rate, the inclusions have longer time to grow, the Ostwald-ripening effect is pronounced which results in coarse and low number density of inclusions.

In order to understand the effects of cooling rate on the composition of the inclusions, the contents of the various inclusions against the temperature in the pipeline steel was calculated by Fact Sage, which is shown in Figure 6a. The steel was melted at 1873 K as indicated in by a broken line in the phase

diagram, at which all the inclusions were in liquid phase. With the decrease in temperature, the amount of liquid inclusions including CaO(l) and Al2O3(l) is increased at first and then it is decreased. During the solidification, the liquid inclusions gradually disappeared, and the solid inclusions including CaS, MgO-Al2O3 spinels and CaO-2Al2O3 are formed. The calculated average composition of the inclusions against the temperature obtained by combining the contents of each phase is shown in Figure 6b.

**Figure 6.** (**a**) Phase transformation and (**b**) average composition of inclusions during cooling of X80 pipeline steel. The CaO(l), Al2O3(l), SiO2(l), CaS(l) and MgO(l) are all belong to one slag phase in (**a**).

At the cooling rate of 10 K/s, the reaction time is very short, inclusions could not be completely transformed. The inclusions should be mostly formed in the liquid steel. Therefore, the Al2O3-CaO type inclusion was dominantly formed. However, at the slow cooling rate, there is longer time for inclusion to transform. The solid inclusions including CaS, MgO-Al2O3, CaO-2Al2O3 and CaO-2MgO-8Al2O3 can be formed. Therefore, the contents of CaS and MgO are increased with the decrease in cooling rate. Consequently, the CaO content is decreased due to the transformation of CaO into CaS.

It should be noticed that the thermodynamic prediction is based on the concept of equilibrium, which is useful to help understand the precipitation sequence of the inclusions during cooling, but it cannot be used directly to discuss the amount of inclusions formed. For example, the measured CaS content at the heating rate of 0.035 K/s is much lower than that of the thermodynamic prediction

in Figure 6b. This should be attributed to the slower precipitation kinetics of CaS, which can be apparently seen in Figure 4a, that only the out-layer of the inclusions was composed by CaS.

From the above discussion it can be concluded that, at the rapid cooling rate, the inclusions are mostly formed at high temperatures, which is retained to room temperature. While, at the slow cooling rate, the inclusions can be gradually transformed and tends to follow the equilibrium compositions at low temperature.

### **4. Conclusions**

In the current study, the effects of cooling rate on the formation of inclusions in X80 pipeline steel were investigated. The main results obtained were summarized as follows:

(1) High cooling rate resulted in large number density and fine inclusions, while, the inverse results were obtained at low cooling rate. At a high cooling rate the driving force for nucleation is larger, which increased the nucleation frequency of inclusions, thus resulted in high number density of inclusions. On the contrary, at low cooling rate, the nucleation frequency is lower and the Ostwald-ripening effect is pronounced, which caused the low number density and coarse inclusions.

(2) As the cooling rate decreased from 10 to 0.035 K/s, the inclusions were changed from Al2O3-CaO to Al2O3-CaO-MgO-CaS. At a high cooling rate, the reaction time is short and the inclusions cannot be completely formed, which should be mainly formed at high temperatures. At the low cooling rate, the inclusions can be gradually transformed and tends to follow the equilibrium compositions at low temperature.

**Author Contributions:** X.Z., W.Y. and L.Z., conceived and designed the experiments; X.Z., W.Y. and H.X. performed the experiments and collected the data; X.Z., and W.Y. analyzed the data; X.Z. and H.X. writing—original draft preparation; W.Y. and L.Z. discussed with the results and revised the manuscript. L.Z. supervised and project administration.

**Funding:** This research was financially supported by the National Key R&D Program of China (2017YFB0304001, 2016YFB0300102), National Science Foundation China (Grant No. 51874031, No. 51725402 and No. U1860206), the Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-15-067A1), Beijing Key Laboratory of Green Recycling and Extraction of Metals (GREM) and the High Quality Steel Consortium (HQSC) and Green Process Metallurgy and Modeling (GPM2) at the School of Metallurgical and Ecological Engineering at University of Science and Technology Beijing (USTB), China.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### **Comparison of Transverse Uniform and Non-Uniform Secondary Cooling Strategies on Heat Transfer and Solidification Structure of Continuous-Casting Billet**

### **Yanshen Han 1, Xingyu Wang 1, Jiangshan Zhang 1, Fanzheng Zeng 2, Jun Chen 2, Min Guan 3 and Qing Liu 1,\***

Received: 9 April 2019; Accepted: 8 May 2019; Published: 10 May 2019

**Abstract:** Water flux distribution largely influences the heat transfer and solidification of continuously-cast steel billets. In this paper, a secondary cooling strategy of transverse non-uniform water flux (i.e., higher flux density on billet center), was established and compared with the uniform cooling strategy using mathematical modeling. Specifically, a heat transfer model and a cellular automaton finite element coupling model were established to simulate the continuous casting of C80D steel billet. The water flux was measured using different nozzle configurations to assist the modeling. The mathematical results were validated by comparing the surface temperature and the solidification structure. It is shown that the non-uniform cooling strategy enables the increase of corner temperature and reduction in surface temperature difference, while a higher reheating rate is found on the surface center of the billet. Moreover, the non-uniform cooling strategy can enhance the cooling effect and refine the solidification structure. Accordingly, the liquid pool length is shortened, and the equiaxed crystal density is increased along with the decreased equiaxed crystal ratio. The uniform cooling strategy contributes to reducing internal cracks of billet, and the non-uniform one is beneficial for surface quality and central segregation. For C80D steel, the non-uniform cooling strategy outperforms the uniform one.

**Keywords:** numerical simulation; C80D steel; transverse water flux distribution; heat transfer; solidification structure

### **1. Introduction**

Continuous casting is the main method of steel production at present, and its cooling and solidification process largely influences the quality of blanks. During casting, the cooling of the blanks is realized in the mold, secondary cooling zone, and air-cooling zone. Since the cooling conditions in the mold and the air-cooling zone are relatively steady, the control of solidification mainly focuses on the secondary cooling zone. Secondary cooling is particularly important, as it is closely related to the heat transfer and solidification structure of the blank, and therefore influences the formation of defects, such as cracks [1–3], central pipe [4], and segregation [5–7]. To minimize the defects, water flux and its distribution were frequently resorted to as a means to improve the product quality through both numerical simulation and industrial trials [8–10].

Secondary cooling is achieved by spraying water on the blank using arranged nozzles and is directly influenced by the water flux distribution. The nozzle arrangement varies for different

cross-sectional casting blanks, such as slab, billet, and bloom. For a continuous casting slab, there is a wide range of water flux on the slab surface owing to its large section size, and the nozzle collocations are usually complex in the secondary cooling zone. Therefore, the water flux distribution needs to be taken into consideration along both the transverse direction and casting direction [10–13]. Moreover, the transverse water flux distribution can be used as a method to improve the quality of slab by the collocations of nozzles. Wang et al. [14] optimized the water flux distribution along slab width direction through the arrangement of spraying nozzles, and the centerline macro-segregation and transverse cracking were improved significantly. Long et al. [15] proposed that a uniform solidified shell in the transverse direction was beneficial to mitigating slab central macro-segregation, thanks to the optimized transverse water flux distribution.

As for small sectional blanks, typically including square billet and rectangular billet, there is usually only one spraying nozzle along the transverse direction on one side of the billet. The transverse water flux distribution is not as complicated as slab and normally assumed to be uniform in the literature [6–8,16–18]. Zeng et al. [6] investigated the solidification structure and macro-segregation of a rectangular billet under different secondary cooling conditions. Ma et al. [18] optimized secondary cooling water distribution to improve billet quality. Their works mainly focus on the total water flux and its distribution along the casting direction, and is not related to the uniformity of transverse water flux distribution, which depends on the nozzle type, installation parameter, and inevitable aging and clogging. The change of transverse water flux distribution obviously affects the solidification behavior of the billet. What is worth mentioning is that Assuncao et al. [19] compared uniform and non-uniform water flux distribution on the thermal behavior of a round billet in a recent work. They found that there is a big difference between them, and the thermal behavior of the billet is more accurate using the measured water flux distribution. However, round billet and square billet still differs greatly, especially at the corner of square billet, which is largely associated with corner defects. Until recently, the transverse water flux distributions of square billet under different nozzle collocations have drawn little attention, and the heat transfer behavior and solidification structure of the billet are still unclear under different transverse water flux distributions.

The present work shed lights on the transverse water flux distribution in the secondary cooling zone of square billet. Two similar continuous casters with different types and arrangements of spraying nozzles were studied. Transverse water flux distribution was measured using an apparatus, and two cooling strategies were obtained, including transverse uniform and non-uniform distribution of secondary cooling water. A heat transfer model and a cellular automaton finite element (CAFE) coupling model were used to analyze the heat transfer and solidification structure of the billet, respectively. The main differences between the two cooling strategies were compared on the solidification behavior of the billet, and the advantages of each cooling strategy were discussed.

### **2. Brief Description of the Studied Continuous Caster**

Two similar continuous casters are involved in the present study. Both casters are four-strand circular-arc casters with a curved mold that mainly produce billets with a small section size (150 mm × 150 mm). The two casters have their own features and produce different steel grades. At the mold, electromagnetic stirrer (EMS, Produced by Hunan Kemeida Electric Co., Ltd., Yueyang, China) is applied on each caster and the stirrer can generate a rotating magnetic field. The schematic diagrams of the casters and nozzle arrangements are shown in Figure 1. Caster 1 and Caster 2 have similar cooling zones, however, the length of each cooling zone and nozzle arrangement at the secondary cooling zone are different. For Caster 1, a full cone jet nozzle and flat jet nozzle (Produced by Jiangsu Boji Spraying Systems Co., Ltd., Yangzhou, China) are used in the foot-roller zone and the secondary cooling zone, respectively. Moreover, all the nozzles overspray on the billet surface and the flat jet nozzles deflect at an angle of 30◦. With regard to Caster 2, two full cone jet nozzles (Produced by Beijing Zhongye Metallurgical Equipment Manufacturing Co., Ltd., Beijing, China) are installed on the width direction

in the foot-roller zone, and one full cone jet nozzle is installed on the width direction that just fully covers the billet surface in the secondary cooling zone.

### **3. Spraying Nozzle Measurement of Water Flux Distribution**

The water flux distribution largely influences the local thermal behavior of billet during continuous casting [11,19]. It is essential to clarify the effect of water flux distribution on the secondary cooling. Under the practical installation conditions, transverse water flux distributions were measured in the secondary cooling zone of Caster 1 and Caster 2. The water flux distribution along the casting direction was not taken into consideration due to the limitation of the experimental set-up.

### *3.1. Experimental Apparatus*

Measurements were carried out using an experimental apparatus that can quantify the water flow rate, spraying angle, and water flux distribution of the spraying nozzle. Figure 2 shows the schematic diagram of the experimental apparatus. The apparatus includes water tank, gas tank, water-gas regulator, control system, and water collector. Water tank and gas tank supply sufficient water pressure and gas pressure, and the water-gas regulator is used to adjust the water pressure and the gas pressure to a desired value. The water collector consists of a row of grooves and one pressure sensor is installed under each groove. The width of each groove is 25 mm.

**Figure 2.** Schematic diagram of experimental apparatus.

### *3.2. Water Flux Distribution Measurement*

Six actual water spraying nozzles were adopted in the experiment. Among the nozzles, Nozzle A, Nozzle B, and Nozzle C were used in the foot-roller zone, secondary cooling zone A, and secondary cooling zone B of Caster 1, respectively. Nozzle D, Nozzle E, and Nozzle F were used in the foot-roller zone, secondary cooling zone A, and secondary cooling zone B of Caster 2, respectively. The type number and jet type of the nozzles were different. Nozzle A, Nozzle D, Nozzle E, and Nozzle F were full cone jet nozzles, while Nozzle B and Nozzle C were flat jet nozzles. In practical casting process, the water pressure and jet distance of nozzles are listed in Table 1. The spraying angle and water flux distribution were measured, as shown in Table 1 and Figure 3.

**Figure 3.** Water flux distributions of spraying nozzles under specific collocations.

In Figure 3, it can be seen that the water flux distribution is non-uniform and generally symmetric for each spraying nozzle, and there is more water on the spraying center and less water on the spraying edge. As the billet width is 150 mm, an effective range on the billet surface is counted from −75 mm to 75 mm. In the effective range, the water flux distributions of Nozzle A, Nozzle B, Nozzle C, and Nozzle D are generally uniform, while the water flux of Nozzle E and Nozzle F is unevenly distributed with a higher water flow rate on the center and a lower one around the corner. Corresponding to different cooling zones of the continuous casters, it can be found that the transverse water flux distributions are relatively uniform in the foot-roller zones of Caster 1 and Caster 2. In the secondary cooling zone, the transverse water flux distributions of Caster 1 and Caster 2 are uniform and non-uniform, respectively. It indicates that Caster 1 and Caster 2 have two different cooling strategies, namely transverse uniform and non-uniform secondary cooling strategies.

### **4. Numerical Modeling and Validation**

Caster 1 was chosen in the numerical model to study the solidification behaviors of the billet under different secondary cooling strategies. The water flux distribution in the secondary cooling zone of Caster 2 was applied on Caster 1 to compare with the original one, and two cooling modes were determined as follows.

Mode 1: Original water flux distribution in the secondary cooling zone was adopted on Caster 1, and the transverse water flux distribution was regarded as uniform on the billet surface, as shown in Figure 4a.

**Figure 4.** Schematic diagram of water flux distribution in the foot-roller zone and secondary cooling zone during continuous casting: (**a**) Mode 1; (**b**) Mode 2.

Mode 2: Water flux distribution in the secondary cooling zone of Caster 2 was applied on Caster 1. The transverse distribution of secondary cooling water is non-uniform, and there is more water on the surface center and less water on the surface edge of the billet, as shown in Figure 4b.

In the simulation, all the other parameters of Mode 1 and Mode 2 were the same except for the different transverse water cooling in the secondary cooling zone.

### *4.1. Model Development*

### 4.1.1. Heat Transfer Model

Some assumptions were made to simplify the mathematical model.

1. The heat transfer in casting direction and meniscus was neglected.

Based on the assumptions, a two-dimensional unsteady state heat transfer equation was expressed as follows:

$$
\rho \mathbb{C}\_{P,eff} \frac{\partial \mathbb{T}}{\partial \mathbf{x}} = \frac{\partial}{\partial \mathbf{x}} (\lambda\_{eff} \frac{\partial T}{\partial \mathbf{x}}) + \frac{\partial}{\partial y} (\lambda\_{eff} \frac{\partial T}{\partial y}) \tag{1}
$$

where ρ is the density of steel in kg/m3; *Cp,e*ff is the effective specific heat in J/(kg·K); *T* is the temperature of steel in K; τ is the calculation time in s; λ*e*ff is the effective thermal conductivity in W/(m2·K); *x* is the distance from the billet center along transverse direction in m, and *y* is the distance from billet center on the inner radius face in thickness direction in m.

The effect of latent heat on the solidification of steel at the mushy zone was incorporated into the effective specific heat, and represented by enthalpy, as shown in the Equations (2) and (3).

$$\mathcal{C}\_{p,eff} = \mathcal{C}\_P - L \cdot \frac{\partial f\_s}{\partial T} \tag{2}$$

$$H = \int\_0^T \mathbf{C}\_P \mathbf{d}T + L(\mathbf{1} - f\_5) \tag{3}$$

where *CP* is the actual specific heat in J/(kg·K); *L* is the latent heat in J/kg; *H* is the enthalpy in J/kg and *fs* is the solid fraction.

A slice moving method was applied in the simulation. To simplify the calculation, the geometric model of the slice adopted a quarter of the cross section of the billet with a thickness of 10 mm and the rounded corners were neglected, namely with a dimension of 75 mm × 75 mm × 10 mm. It was assumed the slice moved along the casting direction from the mold to the foot-roller zone, the secondary cooling zone, and finally the air-cooling zone. In the mold, the heat flux was obtained from a heat balance of the cooling water, and equalized to the empirical equation, as shown in Table 2. To consider the effect of the gap on the heat transfer, a decreasing heat flux was used from the billet center to the corner, and the heat flux at the corner decreased with the increase of distance from the meniscus [10]. In the foot-roller zone and the secondary cooling zone, the surface temperature of the billet is mostly above the Leidenfrost point. The heat flux was characterized by an integrated heat transfer coefficient, which was a function of water flux density. In the air-cooling zone, the radiation was the main heat transfer pattern and the heat extraction was obtained according to the Stefan–Boltzmann law.

**Table 2.** Water flow rates, boundary conditions, and calculated formulae of different cooling zones.

The water flow rates, boundary conditions, and calculated formulae [20–22] of different cooling zones are listed in Table 2. In Table 2, *qm*, *qf*, *qs*, and *qa* are the heat flux of the mold, the foot-roller zone, the secondary cooling zone, and the air-cooling zone, respectively, W/m2; *hf* and *hs* are the heat transfer coefficient of the foot-roller zone and the secondary cooling zone, respectively, W/(m2K); *T*, *Tf*, *Ts*, and *Ta* are the temperature of the billet surface, the water temperature of the foot-roller zone, the water temperature of the secondary cooling zone, and the environment temperature of the air-cooling zone, respectively, K; β is a coefficient between the shape of the mold and parameter of casting, W/(m2·s1/2); *t* is the holding time in the mold, s; σ is Stefan–Boltzmann constant, W/(m2·K4); ε is the radiation coefficient. The numerical values of *qm*, β, *hf*, and *hs* can be obtained by a calculation using casting parameters.

In the simulation, the boundary conditions of Mode 1 and Mode 2 were treated as the same in the mold, the foot-roller zone, and the air-cooling zone. As for the secondary cooling zone, the boundary condition of Mode 1 was uniform. For Mode 2, the billet surface was divided into three sections along the transverse direction, and the boundary condition of each section was separated according to local water flux density, as shown in Figure 4. Whether Mode 1 or Mode 2, the boundary condition along the casting direction was constant at each secondary cooling zone.

### 4.1.2. Nucleation Model

Procast software was used to establish the nucleation model and dendritic tip growth model. A continuous nucleation distribution function, *dn*/*d*(Δ*T*) was used to describe the grain density change [23], and *dn* is induced by the increase of undercooling, *d* (Δ*T*). The distribution function is expressed by Equation (4):

$$\frac{dn}{d(\Delta T)} = \frac{n\_{\text{max}}}{\sqrt{2\pi}\Delta T\_{\sigma}} \exp\left[-\frac{1}{2} (\frac{\Delta T - \Delta T\_{\text{max}}}{\Delta T\_{\sigma}})^2\right] \tag{4}$$

where Δ*T* is the calculated local undercooling in K; Δ*Tmax* is the mean undercooling in K; Δ*T*σ is the standard deviation in K, and *nmax* is the maximum nucleation density in m−3.

### 4.1.3. Dendritic Tip Growth Model

The KGT (Kurz, Giovanola, Trivedi) model [24,25] was used as the model of growth kinetics of a dendrite tip in the C80D steel. Based on the marginal stability criterion, Equation (5) is obtained.

$$V^2A + VB + \mathcal{C} = 0\tag{5}$$

where *V* is the growth velocity of a dendrite tip, and *A*, *B,* and *C* are expressed by Equations (6) to (8).

$$A = \frac{\pi^2 \Gamma}{p^2 D^2} \tag{6}$$

$$B = \frac{mC\_0(1 - k\_0)\xi\_C}{D[1 - (1 - k\_0)Iv(P)]} \tag{7}$$

$$\mathbf{C} = \mathbf{G} \tag{8}$$

where Г is the Gibbs–Thomson coefficient; *P* is the Peclet number for solute diffusion; *D* is the diffusion coefficient in the liquid; *m* is the liquidus slope; *C*0 is the initial concentration; *k*0 is the partition coefficient; *Iv*(*P*) is the Ivantsov function; ξ*c* = π2/(*k*0*P*) closes to unity at a low temperature gradient, and *G* is the temperature gradient. For the dendrite growth regime, *G* has little effect on the growth velocity *V* and can be regarded as zero.

Moreover, the undercooling at dendrite tip, Δ*T*, is expressed as Equation (9). The relationship between the undercooling Δ*T* and growth velocity *V* can be calculated by substituting an arbitral value of the Peclet number into Equations (5) and (9). The material properties [26,27] of C80D steel that were used in the simulation are given in Table 3. The partition coefficients and liquidus slopes were assumed to be constants from liquidus to solidus.

$$
\Delta T = mC\_0 \left[ 1 - \frac{1}{1 - (1 - k\_0)I\upsilon(P)} \right] + \frac{2\Gamma}{r} \tag{9}
$$

where *r* is the dendrite tip radius, *r* = (2*D*·*P*)/*V*.

**Table 3.** Chemical composition of C80D steel and related parameters.

To accelerate the computational speed, a set of values for the undercooling and growth velocity of the dendrite tip are calculated in Equations (5) and (9). Then the following Equation (10) is obtained.

$$V = a\sharp\Delta T^2 + a\sharp\Delta T^3\tag{10}$$

where *a*2 and *a*3 are the fitting coefficients of the multinomial of dendrite tip growth velocity. The values of *a*2 and *a*3 were calculated using the material properties shown in Table 3, and the specific values are 3.041 × 10−6 m/(s·K2) and 2.146 × 10−5 m/(s·K3), respectively.

### *4.2. Material Properties*

C80D steel was studied and its main chemical composition has been given in Table 3. Variations of solid fraction, enthalpy, thermal conductivity, and density with temperature were calculated using a thermodynamic database from JMatPro software according to the steel composition, as shown in Figure 5. The flow of liquid steel, which results from the initial flow from the submerged nozzle, natural convection, and external force of mold electromagnetic stirring (MEMS), can enhance the heat transfer during solidification. The thermal conductivities of the liquid and the mushy zone were enlarged to consider the effect of fluid flow [17,28]. The thermal conductivity of solid adopted calculated values, five times the thermal conductivity of solidus was adopted for the liquid phase, and the thermal conductivity of the mushy zone was assumed to change with temperature linearly.

**Figure 5.** Calculated thermo-physical properties of C80D steel, (**a**) solid fraction, (**b**) density and enthalpy, and (**c**) thermal conductivity.

### *4.3. Model Validation*

### 4.3.1. Casting Parameters

Industrial tests were conducted on Caster 1 to calibrate the heat transfer model and the CAFE coupling model. The main casting parameters of the tests are listed in Table 4.

**Table 4.** Casting parameters used for C80D steel billet.

### 4.3.2. Heat Transfer Model Validation

The surface temperature of the billet was measured using an infrared radiation pyrometer, the error range of which is ±1.5%. During the measurement, the pyrometer was perpendicular to the surface center of the side arc and peak values were adopted as the local temperature. The temperature of the billet was also calculated by the heat transfer model under practical casting parameters. Figure 6 shows the comparison between the calculated temperature and the measured temperature. A good agreement was obtained between the mathematical and the actual results within the error range. It can be concluded that the heat transfer model is generally reliable.

**Figure 6.** Temperature profiles of surface center.

### 4.3.3. CAFE Coupling Model Validation

The transverse billet sample was sliced, polished and etched by hydrochloric acid, and then the actual solidification structure was revealed. From the billet surface to the center, the solidification structure features with an outer chilled layer, a columnar crystal zone, a mixed crystal zone, and an equiaxed crystal zone. Moreover, the columnar crystal deflects on account of MEMS. The deflection was neglected in the simulation. MEMS can also enlarge the equiaxed crystal zone, which is considered by adjusting the maximum nucleation density. The solidification structure was simulated using the CAFE coupling model. The maximum nucleation density was adjusted to match the simulated solidification structure and the actual one, and finally was set as 2.5 × 109 m−3. Figure 7 shows the comparison of the actual solidification structure and the simulated one. Each zone of the actual solidification structure and the simulated one shares basically the equivalent area. This result indicates the selected nucleation parameters are reasonable and the CAFE coupling model is reliable to simulate the solidification structure of C80D steel.

**Figure 7.** Comparison of (**a**) actual solidification structure and (**b**) simulated solidification structure.

#### **5. Results and Discussion**

Following the casting parameters shown in Table 4, comparisons were made between transverse uniform and non-uniform distribution of secondary cooling water on the heat transfer behavior and solidification structure.

#### *5.1. Comparison of Surface Temperature*

Figure 8 comparatively presents the 3D topography of the surface temperature variation under the two cooling strategies. Their temperature variations generally show a similar and typical tendency. The surface temperature starts at around 1500 ◦C and rapidly drops to less than 800 ◦C caused by the intense cooling in the mold and foot-roller zone. Thereafter, the temperature fluctuates in different sections of the secondary cooling zone owing to the change of cooling intensity, and finally decreases slowly in the air-cooling zone. As the cooling condition in the mold and the foot-roller zone are the same, the surface temperature distributions of Mode 1 and Mode 2 exhibit no difference. In the secondary cooling zone of Mode 1, a wide range low-temperature zone (less than 700 ◦C) is observed near the billet corner, and the temperature difference between the corner and the center is large. For Mode 2, the cooling is strengthened at the center and weakened at the corner owing to more water on the surface center and less water on the surface edge. As a result, the low-temperature zone is narrowed and the temperature difference along the width direction becomes small. When billet enters into the air-cooling zone, the billet surface reheats and the temperature distribution tends to become uniform gradually.

**Figure 8.** Temperature variations of the billet surface during continuous casting: (**a**) Mode 1; (**b**) Mode 2.

To analyze the temperature variation quantitatively, the temperature variations of billet center, surface center, and billet corner are highlighted in Figure 9. It shows that the temperature of the billet center keeps nearly constant until a fast drop at the final stage of solidification, and there exists little difference between Mode 1 and Mode 2. The corner temperature in the secondary cooling zone of Mode 1 is below 600 ◦C mostly, while that of Mode 2 is all above 600 ◦C. For Mode 2, the temperature difference of the billet corner and surface center is 174 ◦C, much lower than that of Mode 1 with a value of 356 ◦C, which means a more uniform transverse temperature distribution of Mode 2, beneficial for surface quality [29].

**Figure 9.** Temperature variations of the billet center, surface center, and billet corner: (**a**) Mode 1; (**b**) Mode 2.

When the billet enters into the air-cooling zone, the reheating rates of the billet corner and surface center for Mode 1 are 114 ◦C/m and 95 ◦C/m, respectively. As for Mode 2, the reheating rate of the billet corner is decreased to 73 ◦C/m and that of surface center is increased to 138 ◦C/m. These effects may result in reheat-type internal cracks as the reheating rate exceeds 100 ◦C/m [30]. At the straightening point, the corner temperature of Mode 2 is 792 ◦C, which is 32 ◦C higher than that of Mode 1. The corner of the billet is a crack-prone area on account of the low temperature. The transverse non-uniform secondary cooling strategy is able to increase the corner temperature and contribute to avoiding the third temperature zone of low ductile for C80D steel, thus reducing the possibility of generating corner cracks [29].

### *5.2. Comparison of Internal Temperature*

The temperature distributions of a one-fourth cross section at various positions are exhibited in Figure 10. Except for the temperature near the billet corner, the difference of internal temperature between Mode 1 and Mode 2 is not as significant as the surface temperature. It indicates water flux distribution mainly affects the surface and subsurface temperature. At the end of the foot-roller zone, the liquid core shape is nearly square and no difference exists between Mode 1 and Mode 2. When billet reaches the end of the secondary cooling zone A, the liquid core shape becomes arc-shaped and the shell thickness of Mode 1 is slightly smaller than that of Mode 2. Moreover, the difference becomes more obvious at the end of secondary cooling zone B. When the billet arrives at the straightening point, the temperature distributions of Mode 1 and Mode 2 are nearly the same except for a low-temperature zone at the billet corner of Mode 1.

**Figure 10.** Temperature distributions of one-fourth cross section at various positions.

Figure 11 presents the internal temperature distribution from the meniscus to the air-cooling zone. The temperature near the billet surface between the two cooling modes has a big difference. It indicates that the surface and subsurface areas are more sensitive to water flux distribution. As the solidus temperature of C80D steel is 1359 ◦C, the shell thicknesses of billet are evaluated at the end of the secondary cooling zone for Mode 1 and Mode 2, which are 41.9 mm and 43.8 mm, respectively. Meanwhile, the liquid pool lengths of Mode 1 and Mode 2 can also be obtained, which are 10.60 m and 10.32 m, respectively. Compared with Mode 1, the shell thickness at the end of the secondary cooling zone is increased by 1.9 mm and the liquid pool length is decreased by 0.28 m for Mode 2. These effects mean that the transverse non-uniform secondary cooling strategy increases the cooling intensity on billet.

**Figure 11.** Internal temperature distribution from meniscus to air-cooling zone: (**a**) Mode 1; (**b**) Mode 2.

### *5.3. Comparison of Solidification Structure*

The solidification structures under the two cooling strategies were simulated using the CAFE coupling model and presented in Figure 12. Different kinds of structures are demarcated by solid lines. As seen from Figure 12, the columnar crystal zone and the mixed crystal zone of Mode 2 are longer than that of Mode 1, and the equiaxed crystal zone shows the opposite result. The columnar crystal is closely related to temperature gradient during solidification [31], and liable to grow at a big temperature gradient.

**Figure 12.** Simulated solidification structure of one-fourth cross section: (**a**) Mode 1; (**b**) Mode 2.

At the end of secondary cooling zone A, the temperature distribution and gradient from the billet center to surface center were calculated using the heat transfer model, as shown in Figure 13. It can be seen that there are differences between Mode 1 and Mode 2 on the temperature distribution and gradient, and the differences become unclear at the position of 30 mm from the billet center. Within the range of 30 mm to 50 mm from the billet center, where the solidification proceeds, the temperature distribution and gradient are highlighted. It can be seen that the temperature gradient of Mode 2 is bigger than that of Mode 1. Therefore, the growth of columnar crystal for Mode 2 is promoted. Consequently, the solidification structure of Mode 2 exhibits a relatively wider columnar crystal zone.

**Figure 13.** Calculated temperature (**a**) variation and (**b**) gradient from the billet center to surface center at the end of secondary cooling zone A.

According to the solidification structures shown in Figure 12, the equiaxed crystal ratio was calculated in light of areal percentage. Meanwhile, the number of equiaxed crystal was counted to calculate the equiaxed crystal density. Table 5 shows the equiaxed crystal ratio and density of different cooling strategies. The equiaxed crystal density of Mode 2 is increased and the equiaxed crystal ratio is decreased compared with Mode 1. It indicates that the transverse non-uniform secondary cooling strategy is able to increase the compactness of central equiaxed crystal and decrease the equiaxed crystal ratio. It has been documented that the equivalent effect can be acquired by increasing the secondary cooling intensity [6,7], and that intense secondary cooling is beneficial to reducing the central segregation of high carbon steel billet with a small section size [32]. Transverse non-uniform secondary cooling strategy enhances the cooling effect using the same amount of water, and therefore shows potential to minimize the central segregation of the billet.

**Table 5.** Equiaxed crystal ratio and density of different cooling strategies.

### *5.4. Summary*

Table 6 summarizes the main comparative factors between transverse uniform and non-uniform secondary cooling strategies according to the above findings. Compared with transverse uniform secondary cooling strategy, the non-uniform strategy features a higher corner temperature, smaller transverse temperature difference, shorter liquid pool length, narrower central equiaxed crystal zone, and finer central equiaxed crystal of billet. These effects are beneficial to improving the surface quality and central segregation of billet. Disadvantageously, the reheating rate of the surface center is increased and may lead to reheat-type internal cracks in billet when the transverse distribution of secondary cooling water is non-uniform. In a word, the uniform cooling strategy contributes to reducing internal cracks of billet, and the non-uniform one is beneficial for surface quality and central segregation. According to the demands of different steel grades, the continuous caster can adopt a proper cooling strategy, which is associated with nozzle collocations. C80D steel has a high demand for central segregation and surface quality, but a low demand for internal cracks as the cracks can be eliminated in the rolling process. Therefore, transverse non-uniform secondary cooling strategy is a better choice for the production of C80D steel.

### **6. Conclusions**

Water flux distributions of six spraying nozzles were measured using an apparatus. The nozzles were from two similar continuous casters. Two secondary cooling strategies were obtained, namely transverse uniform and non-uniform distribution secondary cooling strategies. A heat transfer model and a CAFE coupling model were established and assisted by the measured water flux distributions. The models were verified by comparing the surface temperature and the solidification structure to ensure their accuracy. The heat transfer and solidification structure of C80D steel billet were compared under the two cooling strategies. The following conclusions can be drawn:

**Author Contributions:** Conceptualization, Y.H. and Q.L.; data curation, Y.H. and X.W.; investigation, Y.H., X.W. and M.G.; project administration, Q.L.; validation, F.Z. and J.C.; writing—original draft, Y.H.; writing—review and editing, J.Z. and Q.L.

**Funding:** This research was funded by the Innovative and Entrepreneurial Talent Project in Jiangsu province, grant number 2016A426, and independent subject of State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, grant number 41617003.

**Acknowledgments:** The authors are grateful to the Innovative and Entrepreneurial Talent Project in Jiangsu province, and independent subject of State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, China, which enabled the research to be carried out successfully.

**Conflicts of Interest:** The authors declare no conflicts of interest.

### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Deformation Behavior of Internal Porosity in Continuous Casting Wide-Thick Slab during Heavy Reduction**

### **Chenhui Wu 1,2, Cheng Ji 1,2,\* and Miaoyong Zhu 1,2**

Received: 20 December 2018; Accepted: 23 January 2019; Published: 25 January 2019

**Abstract:** Heavy reduction (HR) is a novel technology that could effectively improve the internal porosities and other internal quality problems in continuously cast steel, during which a large reduction deformation is implemented at and after the strand solidification end. In the present paper, non-uniform solidification of the wide-thick slab was calculated with a two-dimensional (2D) heat transfer model. Based on the predicted temperature distribution at the solidification end of the casting strand, a three-dimensional (3D) thermal-mechanical coupled model was developed for investigating the deformation behavior of the internal porosities in wide-thick slab during HR. An Arrhenius-type constitutive model for the studied steel grade was derived based on the measured true stress-strain with single-pass thermosimulation compression experiments and applied to the 3D thermal-mechanical coupled model for improving the calculation accuracy. With the developed 3D thermal-mechanical coupled model, deformation behavior of the two artificial porosities located at the slab center of 1/2 width and 1/8 width during HR was investigated under different condition of HR deformation, HR start position, and HR reduction mode. Based on the calculated porosity closure degree (ηs) and the corresponding equivalent strain (εeq) under different HR conditions, a prediction model that describes the quantitative relationship between ηs and εeq was derived for directly and accurately evaluating the process effect of HR on improving the internal porosities in wide-thick slab.

**Keywords:** continuous casting; wide-thick slab; non-uniform solidification; heavy reduction; porosity; deformation

### **1. Introduction**

Due to solidification shrinkage and gas entrapment, internal porosity often occurs in casting steel. As one kind of the common internal defects, it seriously influences the mechanical properties of the final products, for example, decreasing the fatigue life and the yield strength, and should be eliminated in the subsequent rolling or forging process.

To provide theoretical guide for process design of rolling or forging, many investigations were carried out by previous researchers to clarify the closure mechanism of internal porosity in metal materials during the forging or rolling process. To quantitatively evaluate the porosity closure during forging process, Tanaka et al. [1] proposed the hydrostatic integration parameter, which was widely adopted as an indicator of the porosity closure degree by subsequent researchers [2–5]. In addition to the hydrostatic integration parameter, many other researchers [6–9] also adopted effective strain as the indicator of porosity closure degree during hot working process, and different threshold values mboxciteB7-metals-421132,B8-metals-421132,B9-metals-421132 of effective strain for eliminating the internal porosity were reported. Recently, a void aspect ratio evaluation index, defined as a function of

stress deviator, effective strain, and effective stress, was proposed by Chen et al. [10], which could give an accurate description of the porosity evolution during forging process. After carrying out full-scale hot-rolling experiments, Ståhlberg et al. [11] concluded that temperature gradient between the lower temperature on workpiece surface and the higher temperature in its internal region, as obtained by water cooling, was advantageous for the elimination of internal porosity with a relatively small rolling reduction. The effect of temperature gradient was further discussed in the later studies of forging [4,12] or rolling [3,13,14] with numerical or experimental methods, and all of these investigations confirmed the promotion effect of temperature gradient on the porosity closure. During forging process, die shape is another critical process parameter that influences the process effect on eliminating the internal porosities in workpiece, and in order to design an optimum die geometry, some studies were conducted by previous researchers to investigate the effect of die shapes on porosity closure during open die forging [6,15,16], upset process [4], and hot radial forging [17], et al.

Internal porosities in casting steel usually could be eliminated by rolling or forging process. However, due to the increased solidification time for casting steel with a large section size, its internal porosities become more serious with the presence of coarser cast structure [4,18]. Under condition of large components that were produced by rolling or forging with a relatively low compression ratio [11,19–21], the serious internal porosities in large section size casting steel could not be easily eliminated, which seriously influences the mechanical properties of the final products. Meanwhile, as one of the main counter measures of the internal porosities, the traditional mechanical soft reduction (SR) [22,23] was proved to be insufficient on significantly improving the serious internal porosities in the casting steel with a large section size. In order to improve the serious internal defects in continuous casting steel significantly, some earlier researchers [24–27] proposed heavy reduction (HR) technology. By implementing a large reduction deformation around the strand solidification end, the internal quality of continuous casting steel could be significantly improved by HR, which effectively contributes to the complete elimination of internal porosity in the subsequent rolling or forging process.

As an effective counter measure of internal defects in continuous casting steel, HR has attracted more and more researchers' attention with the rapidly increased demand for large components in the large equipment manufacturing industry in recent years. Some theoretical and experimental investigations were carried out recently for studying the improving effect of HR on porosity and other internal defects in continuous casting bloom [28,29], billet [30], or slab [19–21], and some new HR technologies were then proposed and applied. By establishing a three-dimensional (3D) thermal-mechanical coupled model, the present authors [28] studied the deformation behavior of continuous casting bloom during HR and developed the two-stage sequential heavy reduction technology. Industrial trials indicated that the homogeneity and compactness of the continuous casting bloom could be obviously improved after the application of two-stage sequential heavy reduction technology. Based on numerical simulation results, two kinds of new HR technologies, named as START and HRPISP, were respectively proposed by Xu et al. [19] and Zhao et al. [20,21] for simultaneously improving the internal porosity and macro-segregation in continuous casting wide-thick slab, and the effectiveness of START was proved by experimental results in plant.

To provide theoretical basis for the development of the HR process and thus improve the internal porosities in wide-thick slab more effectively, the porosity deformation behavior during HR in the wide-thick slab continuous casting process was systematically investigated mainly by the numerical simulation method in the present work. A two-dimensional (2D) heat transfer model was established to calculate the non-uniform solidification process of the wide-thick slab. Based on the predicted heat transfer results by the 2D heat transfer model and the derived constitutive model for the studied steel grade during HR, a 3D thermal-mechanical coupled model, containing two artificial spheroidal porosities, respectively, located the slab center of 1/8 width (P1/8) and 1/2 width (P1/2), was established. With this 3D thermal-mechanical coupled model, the deformation behavior of P1/8 and P1/2 during HR was numerically investigated under different HR conditions, including the HR deformation, HR start position, and HR mode. Based on the predicted porosity deformation results under different HR

conditions and the corresponding equivalent strain (εeq), a prediction model for the porosity closure behavior was derived to describe the quantitative relationship between the porosity closure degree (ηs) and εeq.

### **2. Finite Element Model**

### *2.1. 2D Heat Transfer Model*

During HR, the deformation behavior of the casting strand is closely related to its temperature distribution. In order to improve the calculation efficiency, a 2D heat-transfer model, as shown in Figure 1, was firstly developed with the commercial finite element software MSC.Marc (2013.0.0, MSC Software Corporation, Newport Beach, CA, USA) based on the practical casting conditions in Table 1 and some simplified conditions [31]. Heat transfer analysis was then carried out with this model, which determined the strand solidification end and the corresponding initial temperature field for the subsequent 3D thermal-mechanical coupled model in Section 2.2. Due to the symmetry of heat transfer behavior of the casting strand along its width direction, half of the wide-thick slab transverse section, as shown in Figure 1, was taken as the calculation domain. Four-nodes quadrilateral elements with a side length of 5 mm were applied to uniformly mesh the calculation domain, and the final 2D heat transfer model contains 11,200 elements and 11,457 nodes. Automatic time step with 0.1 s and 1 s taken as the minimum and maximum time step, respectively, was adopted during the calculation.

**Figure 1.** Schematic of the two-dimensional (2D) heat transfer model.