Numerical Modeling of Electron Beam Cold Hearth Melting for the Cold Hearth

Abstract

The electron beam cold hearth melting (EBCHM) process is one of the key processes for titanium alloy production. The unique characteristic of this pyrometallurgy process is the application of the cold hearth, which is responsible for controlling the Low-Density Inclusions (LDIs) and High-Density Inclusions (HDIs) in the melt. As a key process of inclusion removal, the information such as melt residence time in the cold hearth is directly related to the control of metallurgical defects in the ingot, and may also affect the composition distribution of the ingot. In this paper, the details for the physical phenomena, namely the evolution of the pool, the evolution of the flow, and the evolution of the component in the cold hearth during EBCHM are investigated using a modified multi-physical numerical model. The effects of melting temperature and melting speed on these phenomena were investigated. The purpose is to provide more fundamental knowledge and to further enhance the applications of EBCHM for more titanium alloys.

1. Introduction

Titanium alloys are one of the potential materials which have multiple advantages including low density, high tensile strength, and decent toughness [1]. Nowadays, the development tendency for the preparation of titanium alloys is to use the electron beam cold hearth melting (EBCHM) process as an alternative to the traditional Vacuum Arc Melting (VAR) to reduce the cost of the alloy [2,3]. The trait of EBCHM is that the technique introduced a horizontal water-cooled copper hearth and separated the melting, refining, and casting process. Compared to VAR, this concept is more effective in removing undesired impurities and inclusions, namely N, O, C, Low-Density Inclusions (LDIs) as well as High-Density Inclusions (HDIs). This outstanding advantage makes EBCHM able to effectively consolidate both sponge and scrap material [4]. Thus, single-melt EBCHM ingot became a possible solution for producing low-cost titanium alloy plates with significant cost savings. Also, EBCHM can produce long-length ingots (>10 m), which accelerates the implementation time for titanium plate production [5].

The efficacy of the EBCHM purification process is attributed to the meticulous regulation of thermal and mass transfer within the cold hearth, as depicted in Figure 1. Optimal fluid dynamics ensure that HDIs settle at the base of the copper hearth, while LDIs are afforded sufficient time for thermal decomposition. Concurrently, impurities are progressively volatilized from the molten pool’s surface, driven by elevated saturated vapor pressures.

However, EBCHM utilizes a high-energy-density electron beam as a heat source, and the lack of elaborate control during EBCHM can lead to serious consequences, including interruptible flow and composition segregation caused by element evaporation [6]. Thus, a robust understanding of the metaphysical phenomena both in the cold hearth and the mold should be carefully studied to reduce defects in the final products caused by extensive operation [7]. Even so, observing the EBCHM process requires overcoming many technical difficulties. The flow regime tracking equipment needs to outlive extreme temperature and pressure conditions since the titanium alloy needs to be heated up to over 1800 °C, and the pressure in the chamber is around 0.001–0.1 Pa to prevent contaminant of nitrogen and oxygen [8]. Also, temperature tracking equipment like two two-color pyrometers will be disturbed by the emitting light with the spectral line of 500 nm in the titanium vapor when the vacuum pressure of the chamber is above 0.04 Pa [9]. Although the Al evaporation behavior can be suspected from the chemical analysis of the titanium alloy ingot [10], the response system of components exchange is still fuzzy, since it is influenced by complicated evaporation and convection.

To confirm the melt-flow evolution during the EBCHM process, an effective option is to employ mathematical modeling based on thermal dynamic calculation [11]. With assumptions of uniform temperature distribution on the melt surface, Akhonin et al. developed a mathematical model to describe the kinetics of aluminum evaporation during EBCHM process [12]. Powell combined mathematical modeling with thermal dynamic calculation to predict titanium evaporation rate and aluminum activity [13]. A series of works related to the mold using numerical modeling were provided [14,15,16,17].

However, only a few attempts are focused on metaphysical phenomena in the cold hearth. Bellot has built a comprehensive model of the cold hearth to understand the EBCHM process [18]. Simulations of a pilot furnace and an industrial-type furnace have shown that the metal flow is reduced to a thin film of liquid representing on average only 15 to 20 pct of the total depth of metal in the crucible. This attempt provides valuable knowledge for further understanding the melting and solidification process in the cold hearth. In our previous work, we established a three-dimensional transient multi-physics field numerical simulation model to comprehend the evolution of the melt pool morphology during the melting process of large-scale Ti-6 wt%Al-4 wt%V (Ti64) ingots (slab/round), the flow state within the melt pool, and its influence on the homogenization of composition. We summarized the theoretical mechanisms for controlling compositional homogenization within the crystallizer [19,20,21]. Building upon this foundation, the present manuscript conducts a further trace-back investigation into the melting and refining processes that titanium metal melt undergoes before entering the crystallizer, namely the flow/evaporation/solidification process within the cold hearth. The purity and elemental composition of the cold hearth melt are directly inherited by the crystallizer, making its design critical in the EBCHM process. However, the majority of existing studies focus predominantly on the crystallizer, with scant discussion on key issues such as the flow state of the melt in the cold hearth, the residence time of inclusions, and the homogenization of chemical composition.

Therefore, to further our understanding of the electron beam cold hearth process, this paper establishes a validated three-dimensional transient multi-physics field-coupled numerical model of cold hearth melting for the first time. It explores the effects of melting temperature and melting speed on the flow, solidification, element evaporation, and homogenization processes within the cold hearth container. The aim is to provide recommendations for the precise control of macro-segregation during the EBCHM process of large-scale Ti64 ingots.

2. Model Description

To further understand the physical and chemical phenomena that occur during the electron beam cold hearth melting process, this paper established the melting process models of Ti64 titanium alloy for the cold hearth (500 mm × 1800 mm) and studied the element loss control and homogenization behavior of Ti64 titanium alloy melt under high temperature and high vacuum conditions.

2.1. Physical Phenomenon Model Equation

The physical phenomena in EBCHM mainly include metal melting and solidification, mass and heat transfer under flow influence, and continuous element volatilization on the melt pool surface. The numerical model established in this paper uses the solidification/melting model and the species transport model to calculate the solidification and mass transfer phenomena during the continuous casting process, respectively. The surface reaction is activated on the melt surface to study the influence of volatilization on the composition distribution of the melt pool and solidified part. User-defined function programming model implements some specific parameter changes.

A three-dimensional transient multi-field coupled mathematical model of the cold hearth necessitates the consideration of mass, momentum, and energy conservation equations within the melt pool of the cold hearth. The mathematical intricacies of these equations are comprehensively delineated in references [19,20,21], as detailed in

Table 1. Physical phenomenon model equation.

Physical Phenomenon Model Equation
Mass conservation	$\frac{\partial \rho }{\partial t}+\nabla \cdot \left(\rho \overrightarrow{\nu }\right)=0$
Momentum conservation	$\frac{\partial }{\partial t}\left(\rho \overrightarrow{v}\right)+\nabla \cdot \left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla p+\nabla \cdot \left(\overline{\stackrel{‾}{\tau }}\right)+\rho g+{\mathcal{S}}_{i,P}+{\mathcal{S}}_{i,m}$
	$S_{i,P}=\rho g{\beta }_T(T-T_{liq})+{\sum }_i\rho g{\beta }_{c,i}(Y_{i,liq}-Y_0)$
Energy equations	$\begin{array}{c}\begin{array}{c}\frac{\partial }{\partial t}\left(\rho H\right)+\nabla \cdot \left(\rho \overrightarrow{v}H\right)=\nabla \cdot \left(k\nabla T\right)+Q_r\end{array}\\ H=h+∆H=h_{ref}+{\int }_{T_{ref}}^T{c}_{p}dT+\beta ∆H_f\end{array}$
Supporting relations	${\beta }^{n+1}={\beta }^n-\lambda \frac{a_p(T_c-T^{*})∆t}{\rho V_c{L}_c-a_p∆t{L}_c\frac{\partial T^{*}}{\partial \beta }}$
	$T^{*}=T_{melt}+{\sum }_{i=0}^{N_t-1}{m}_i{Y}_i{\beta }^{K_i-1}$

. Notably, the model employs the enthalpy/porosity technique recommended by ANSYS Fluent to track the liquid/solid interface. The mushy zone, where the liquid/solid phase coexists, is treated as a porous medium with porosity equating to the liquid fraction. This approach incorporates appropriate momentum sink terms in the momentum equation to account for the pressure drop induced by the presence of solid material. The porosity of each cell is set equal to the liquid fraction within that cell. In fully solidified regions, the porosity is zero, rendering the velocity in these zones negligible.

To simulate the evaporation, mixing, and transport of aluminum during EBCHM, a convection/diffusion equation was added to predict the local mass fraction of each species, $Y_{i,liq}$, namely Al and Ti in the present case. This conservation equation has the following general form:

$$\begin{gathered} \begin{array}{c}\frac{\partial }{\partial t}\left(\rho Y_{i,liq}\right)+\nabla \cdot \left(\rho \left[\beta {\overrightarrow{v}}_{liq}{Y}_{i,liq}+\left(1-\beta \right){\overrightarrow{v}}_p{Y}_{i,sol}\right]\right)\end{array} \\ =R_i+\nabla \cdot \left(\rho \beta D_{i,m,liq}\nabla Y_{i,liq}\right)-K_i{Y}_{i,liq}\frac{\partial }{\partial t}\left(\rho \left(1-\beta \right)\right)+\frac{\partial }{\partial t}(\rho (1-\beta )Y_{i,liq}) \end{gathered}$$

(1)

The molar rate of evaporation of Al ($R_i$) can be calculated by the forward rate constant for the reaction $k_{f,r}$ with data provided in Refs. [6,21] using the following equation, $T^{\mathrm{*}}$ is the interface temperature. In the current study, $T^{\mathrm{*}}$ is selected from the literature [22,23].

2.2. Computational Domain and Boundary Conditions

The numerical simulation model involved in this article was established using the ANSYS Fluent 17.0 software. The geometry of the cold hearth is based on the 1:1 cold hearth, the size of which is provided by the cooperative enterprise in Yunnan province, China. The schematic diagram of the EBCHM is shown in Figure 2a, where the high-energy intensity electron beam is used as the heat source for melting feedstocks and maintaining the fluidity of molten alloy. The cold hearth’s geometric model and boundary conditions are shown in Figure 2b. The modeling area includes velocity inlet, molten pool surface, and outlet. The total length is 1800 mm, and the width is 500 mm. The inlet uses the speed inlet (m/s). There is an inclined design near the overflow inlet to capture high-density inclusions. A half-symmetric geometric structure is selected as the computational domain to save computation time. The inlet is set as a long and thin area in the middle of the melt pool, and the molten Ti64 melt continuously enters the computational domain at a constant speed from the inlet and leaves at the outlet at the overflow inlet. The surface of the cold hearth is a free surface boundary condition, and the sidewall of the cold hearth is a no-slip wall. After grid independence calculation and optimization, the described computational domain consists of 1.24 million hexahedral grids.

Some assumptions we made for the model are as follows: (1) In our previous research [19], we discovered that as long as the scanning frequency of the electron beam heat source is sufficiently high and the scanning gaps are sufficiently short, it can be considered a uniform surface heat source. Therefore, we assume the electron beam heat source to be a uniform surface heat source. (2) It is assumed that mass transfer within the solid phase follows the Scheil rule model, which presupposes no diffusion. (3) It is assumed that the influence of Marangoni Forces (thermal and compositionally) on the model is ignored.

In the EBCHM melting process, the cold hearth has a water-cooling environment, and the corresponding heat transfer coefficient is taken as 2000 W/(m²·K) according to the literature suggestion [24]. The liquid and solid temperatures of Ti64 are taken from the literature [24], which are 1928 K and 1878 K, respectively. The thermal conductivity k, specific heat Cp, liquid fraction $\beta$, and density $\rho$ of Ti64 are taken from the literature [24], and the results are shown in Figure 2c. The diffusivity of aluminum in molten Ti64 was provided in reference [21]. Pressure/velocity coupling is used as the coupling algorithm, discrete model selection is PRESTO, based on Green/Gauss cell and third-order MUSCL.

2.3. Model Validation

The actual electron EBCHM of Ti64 titanium alloy takes a long time, and it is difficult to precisely control the pulling speed, temperature, and vacuum degree. However, due to the objective qualitative relationship between various parameters in the casting process, the collected data can be used to indirectly infer the accuracy of the model. The verification of the cold hearth model is shown in Figure 3a–c. Figure 3a shows the morphology of the cold hearth shell after the casting process collected from a cooperative industry. Different cold hearth melting pool morphologies exist for different alloy compositions and casting conditions. To qualitatively verify the accuracy of the coupled model, this study used the established multi-physics coupling model to calculate the flow state of the melt body in the cold hearth, and compared the obtained results with the actual shape of the cold hearth melt pool after large-scale cold hearth casting, as shown in Figure 3b. The flow path line in the Ti64 cold hearth melt pool depicted by the model is consistent with the actual situation. In addition to flow, elemental segregation is also caused by surface volatilization in the cold hearth (Figure 3c). Based on the Bernoulli effect, the fluid accelerates at the outlet, and the aluminum elements lost due to volatilization on the melt surface can be replenished quickly, resulting in a more uniform composition at the outlet position. However, since the diffusion coefficient of elements in the solid phase can be almost neglected compared with that in the liquid phase, this segregation should not affect the elemental composition of the unmelted part at the bottom of the cold hearth. The numerical simulation results are consistent with the above description, laying a good foundation for subsequent models.

3. Results and Discussion

Electron beam cold hearth melting is a pivotal process in the production of titanium alloys, significantly enhancing the quality and efficiency of ingot casting. However, the casting of aluminum-containing titanium alloys, such as Ti64, is prone to elemental evaporation leading to compositional segregation, which compromises the quality of the titanium alloy. Previous research on the location of aluminum loss in Ti64 has primarily centered around two theories. One posits that aluminum loss pre-dominantly occurs at the surface of the melt pool of the crystallizer. Conversely, some researchers argue that the evaporation within the cold hearth melt pool, which is also exposed to vacuum conditions for extended periods, is non-negligible. While studies have been conducted on aluminum segregation within the crystallizer, this paper focuses on whether aluminum evaporation during the cold hearth melting process impacts the compositional segregation of Ti64. To this end, we have established, for the first time, a model of the EBCHM process for the cold hearth and simulated the Ti64 process, incorporating material flow and theoretical evaporation rates, as well as solidification cooling and mass and heat transfer. Notably, the electron beam heat source is treated as a uniform surface heat source, based on the assumption from previous studies [19,20,21] that an electron beam can be considered a uniform surface heat source provided its scanning frequency is sufficiently high and the scanning gaps are sufficiently short, and this assumption aids in reducing computational complexity.

3.1. Formation Process of the Pool in the Cold Hearth during EBCHM

To evaluate the effect of melting speed and melting temperature on the pool profile, the cases of EBCHM with a melting temperature range from 2073 to 2273 K and melting speeds of 250, 500, 750, and 1000 kg/h were investigated. The values for these melting speeds are derived from industrial field data provided by the partners. The predicted pool evolutionary tendency is shown in Figure 4. The results indicate that the pool is very shallow and is unwelcome in the aspects of the reduction of HDI. Increasing the melting temperature will improve the depth of the pool, especially in the center of the inlet. Thus, a “V” shape is noticed in Figure 4 with the increase in the melting speed. Considering the symmetrical condition, the pool of the cold hearth shows an evolutionary tendency of a “W” shape. Additionally, the increase in melting speed will also cause an enhancement in the “W” shape. Both the pool depth near the inlet and the outlet will develop, creating a gradient that is beneficial for capturing the HDI, and preventing these HDI enter into the ingot.

To further explain the evolutionary tendency of the pool depth, a coordinate system is built with an X-axis started from the outlet as shown in Figure 4. The pool depth change on the intersection slices along the X-axis is presented at X = 0, 210, 390, 640, 890, 1140, and 1390 mm. The H value and h1 value, namely the pool depth on the symmetrical plan and center of the inlet were calculated, respectively. The results are shown in Figure 5. In Figure 5a,b, the evolution of H value and h1 value achieved at a melting speed of 500 kg/h and melting temperatures of 2073 K, 2173 K, and 2273 K are presented, respectively. The results indicating a positive ΔH = 5 mm appears in the region where X = 210 mm to 1390 mm with the increase of melting temperature from 2073 K to 2223 K, and the peak of ΔH is 10 mm appears in the region where X = 0 mm to 210 mm with a melting temperature of 2223 K. However, the evolutionary tendency of h1 shows a significant difference with H. For all the cases, the peak value of pool depth appears in the region where 640 mm to 890 mm, and the maximum Δh1 = 10 mm. Additionally, the gradient of the pool depth near the outlet, namely the region where X = 0 mm to 210 mm, is increased to 11 mm with a melting temperature of 2223 K.

In Figure 5c,d, the evolution of the H value and h1 value achieved at a melting temperature of 2273 K and melting speeds of 250 kg/h, 500 kg/h, 750 kg/h, and 1000 kg/h are presented, respectively. With a low melting speed (250–500 kg/h), the peak value for H disappears at X = 390 mm, whilst at a high melting speed (750–1000 kg/h), the peak value for H disappears at X = 210 mm. The pool depth reduces on both sides from the location of X, and the peak of ΔH is 15.5 mm near the outlet. Influenced by the continuous washing from the inlet, the h1 value at high melting speed shows a significant difference compared to the H value at the same condition. With melting speeds of 750 kg/h and 1000 kg/h, the h1 value increased significantly in the region of X = 390 mm to 1390 mm and continuously increased along the X-axis. The corresponding h1 value is 33.4 mm and 36.1 mm for X = 390 mm and 1390 mm, respectively. It is worth noting that for Figure 5d, when X = 400 mm, h1 of 750 and 1000 kg/h is lower than h1 of 250 and 500 kg/h, which is because the shape of the melt pool in the cold furnace will also change with the continuous increase of melt flow rate, especially at h1 position, the increase of melt flow rate will lead to the formation of melt pit. It gradually develops vertically near the entrance (about 500–1400 mm). In addition, the longitudinal development of the molten pit will change the flow dynamics of the fluid and promote the development of longitudinal reflux, which will lead to lower h1.

3.2. The Evolution of the Flow in the Cold Hearth during EBCHM

The evolution of pool shape will also cause the revision of the flow which is the key to the reduction of the inclusions and the homogenization of the pool component. In this section, the flow evolutionary tendency for the cases of EBCHM with a melting temperature range from 2073 to 2273 K and melting speeds of 250, 500, 750, and 1000 kg/h were investigated, and the results are shown in Figure 6. The streamline in the figure is the trace of the massless particle trajectory with velocity distribution. The purpose is to understand the effect of melting temperature and melting speed on the flow pattern. In the studied range, the pool shape evolutionary tendency caused by increasing melting speed has a slight influence on the flow streamline. The flow is concentrated near the outlet because of the mold design and reaches the peak velocity. For the cases at a melting speed of 500 kg/h and a melting temperature of 2073 K, 2173 K, and 2223 K, the peak values of the outlet velocity are 0.23 m/s, 0.16 m/s, and 0.14 m/s, respectively. For the cases at a melting temperature of 2273 K and a melting speed of 250 kg/h, 500 kg/h, 750 kg/h, and 1000 kg/h, the peak values of the outlet velocity are 0.06 m/s, 0.12 m/s, 0.19 m/s, and 0.21 m/s, respectively.

Employing the maximum velocity at the overflow as the characteristic velocity, and the average depth of the liquid phase at the overflow location (the mean of H and h1) as the characteristic length, the Reynolds number is calculated. This defines the fluid state near the outlet, as illustrated in Figure 7a,b. Within the studied range, the Reynolds numbers near the outlet exceed 3000, indicating that the flow state of the melt is turbulent.

3.3. The Evolution of the Aluminum Component in the Cold Hearth during EBCHM

Because of the high temperature and vacuum environment, the component distribution control of the EBCHM process is important. The previous experimental data shows that the component distribution along the X-axis is uniform. However, the mechanism of the component homogenization is still unclear, which may provide useful information for the control of the subsequent process.

In this section, the component distribution in the cold hearth was presented for the cases of EBCHM with a melting temperature range from 2073 to 2273 K and melting speeds of 250, 500, 750, and 1000 kg/h, where the initial Al concentrations in these cases are 9 wt.%. The results are shown in Figure 8. For the case with a melting temperature of 2273 K and a melting speed of 250 kg/h, the results indicate that the Al component distributions near the flow death zone in the corner and the sidewall are less uniform than the pool center. An obvious component gradient is noticed on the outlet which may lead to component control problems for the subsequent processes. The formation of this composition gradient is caused by the continuous evaporation of Al and insufficient mass transformation in the pool. The numerical data of the cases indicate that this component gradient can be improved by reducing the melting temperature or increasing the melting speed.

To quantify the homogenization degree of the melt flowing from the cold hearth into the crystallizer, we extracted the Al concentration data at the outlet of the cold hearth in Figure 9 and Figure 10, to understand the influence of melting temperature and melting speed on the Al concentrations at the cold hearth outlet, respectively. The flow-induced mass transfer makes the composition of the melt relatively uniform, but the increase in melting temperature slightly reduces the homogenization degree of the melt at the outlet. However, at the outlet of the overflow inlet, the Al content of the melt entering the crystallizer decreases by 2%–4% compared with the raw material composition, as shown in Figure 9. When the melting speed increases, the homogenization of the melt body in both the main body of the melt pool and the outlet of the overflow inlet is significantly improved, as shown in Figure 10.

We exported the element concentration distribution data of the melt body at the outlet of the overflow inlet and sorted them in descending order. The horizontal axis is the percentage of the selected data in the data set. The obtained area chart represents the homogenization situation at the outlet of the cold hearth under different melting temperatures and different melting speeds, as shown in Figure 11a,b. The lower the slope of the surface feature line on the area chart, the better the homogenization degree; the higher the slope, the more unevenness of the melt body. Quantitatively, the segregation degree Φ of the Al element concentration data at the outlet is defined as the ratio of the sum of the mixture concentrations to the sum of the initial concentrations, using Equation (3):

$$\mathsf{\Phi }=\frac{\mathrm{sum} \mathrm{of} Al \mathrm{concentrations} \mathrm{of} \mathrm{the} \mathrm{melt} \mathrm{at} \mathrm{the} \mathrm{outlet}}{\mathrm{sum} \mathrm{of} \mathrm{initial} Al \mathrm{concentrations}}$$

(2)

Studies have shown that as the melting temperature increases, the uniformity of the cold hearth outlet decreases from 0.9508 to 0.8500. On the contrary, as the melting speed increases, the homogenization within the outlet of the cold hearth increases from 0.5862 to 0.9352. This indicates that lower temperature combined with higher casting speed can enhance the homogenization of Al element at the outlet of the cold hearth. Within the studied range, increasing the melting speed can effectively increase the homogenization degree at the overflow inlet. On the one hand, increasing melting speed will reduce the residence time of the melt body in the cold hearth, thereby reducing volatilization loss; On the other hand, increasing melting speed will significantly increase Al element content replenished into the cold hearth, and a better balance between volatilization/replenishment loss is achieved in the melt pool. When melting speed is above 500 kg/h, a good element homogenization degree can be achieved near the overflow inlet within a temperature range of 2073–2273 K.

The above discussion shows that macro-segregation within the cold hearth can be effectively controlled through appropriate melting conditions. The values of H, h1, Re, and $\mathsf{\Phi }$ obtained under different smelting conditions are listed in

Table 2. The values of H, h1, Re, and $\mathsf{\Phi }$ with different casting conditions during the EBCHM process.

Melting Temperature (K)	Melting Speed (kg/h)	H (mm)	h1 (mm)	Re	$\mathsf{\Phi }$
2073	500	8.43	11.71	4982	0.9508
2173	500	11.79	17.21	4951	0.8874
2223	500	13	19.57	4765	0.0855
2273	250	19.96	18.94	3193	0.5862
2273	500	15.39	22.01	5347	0.8087
2273	750	12.99	24.57	9171	0.9205
2273	1000	11.02	25.91	8837	0.9352

.

4. Conclusions

To reduce the cost, the electron beam cold hearth melting (EBCHM) process has emerged as a key process in producing high-quality titanium alloy ingots and electrodes. One of the keys to this unique pyrometallurgy process is the application of the cold hearth, which is responsible for controlling the HDI in the melt. In this paper, the details of the physical phenomena in the cold hearth during EBCHM are investigated. The main occlusions are listed as follows:

(1)

The pool presents a shallow “V” shape with a low melting speed and melting temperature. The depth gradient for the pool is limited and unwelcome for collecting HDI. Increasing the melting temperature of melting speed will turn this pool into a “W” shape because of the continuous rushing of the melt near the inlet.

(2)

Due to the design of the cold hearth, the flow pattern in the pool in the studied range has slight changes. For the flow patterns presented, turbulence-characteristic Reynolds numbers were noticed.

(3)

The results for the case with a melting temperature of 2273 K and a melting speed of 250 kg/h indicate that the Al component distributions near the flow death zone in the corner and the sidewall are less uniform than the pool center. This component gradient can be improved by reducing the melting temperature or increasing the melting speed.

In conclusion, the cold hearth melting process is not the predominant factor influencing the segregation of Al elements. Rather, the segregation primarily originates from the transfer phenomena within the crystallizer. It is noteworthy that our numerical model overlooked the shielding effect of the feedstock blocks on the electron beam during the hydraulic propulsion process in the feeding of the melt pool when considering the surface temperature of the melt pool. This has led to a certain degree of deviation in the results. We plan to optimize this aspect in our future research.