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Comparative Analysis of Fixed-Grid Methods in Addressing a Benchmark Problem Coupled Natural Convection and Melting 固定网格方法在解决自然对流与熔化耦合基准问题中的比较分析
Pub Date : 2024-07-12 DOI: 10.1007/s11663-024-03198-9
Jibai Kang, Weiling Wang, Sen Luo, Miaoyong Zhu

For decades, the fixed-grid method (FGM) has undergone extensive development and widespread application in addressing phase change problems. Nonetheless, comparative studies on various FGMs in convective regime are considerably scarce. Moreover, it has been proven that two-dimensional (2D) numerical simulations can cause large deviations from experimental observations. Therefore, this study, based on a reference experiment involving gallium melting, seeks to comprehensively and quantitatively compare three prevalent FGMs: enthalpy method (EM), total enthalpy method (TEM), and heat source method (HSM). The TEM validates overestimation of temperature at low Péclet numbers, as the heat dissipation induced by non-uniform thermal properties in solid and liquid phases is not accounted for. To address this issue, a revised TEM has been introduced. The three FGMs were implemented within the OpenFOAM software, with over 150 simulations conducted on 3D meshes. The comparison focused on evaluating the numerical robustness, accuracy and stability of these FGMs, along with exploring their similarities and differences in flow patterns and velocities. Results obtained reveal that EM offers accuracy but lacks robustness, TEM manifests relatively large errors and instability due to oscillation with variations in grid size and time step, while HSM excels in robustness, accuracy, and stability. Under an identical discretization scheme, all FGMs predict similar melt front shapes, vortex structures, and velocity magnitudes. However, with the upwind scheme, the velocity magnitude of the secondary flow is approximately 50 pct of that with high-order schemes, yet it tends to overestimate the melting rate. The reason lies in the limited capacity of the slow secondary flow to effectively disrupt the stable and persistent vortex in the primary flow direction, consequently enhancing heat transfer efficiency in this direction.

几十年来,固定网格法(FGM)在解决相变问题方面得到了广泛的发展和应用。然而,关于对流体系中各种定格网格法的比较研究却相当匮乏。此外,事实证明,二维(2D)数值模拟可能会导致与实验观测结果的巨大偏差。因此,本研究基于涉及镓熔化的参考实验,试图全面、定量地比较三种常用的 FGM:焓法(EM)、总焓法(TEM)和热源法(HSM)。TEM 验证了在低佩克莱特数时温度被高估的情况,因为固相和液相的非均匀热特性引起的散热没有考虑在内。为了解决这个问题,我们引入了一种经过修订的 TEM。在 OpenFOAM 软件中实现了三种 FGM,并在三维网格上进行了 150 多次模拟。比较的重点是评估这些 FGM 的数值稳健性、准确性和稳定性,同时探索它们在流动模式和速度方面的异同。比较结果表明,EM 具有较高的精度,但缺乏稳健性;TEM 的误差相对较大,而且随着网格大小和时间步长的变化会产生振荡,因而不稳定;而 HSM 在稳健性、精度和稳定性方面表现出色。在相同的离散化方案下,所有 FGM 预测的熔体前沿形状、涡旋结构和速度大小相似。然而,采用上风方案时,二次流的速度大小约为高阶方案的 50%,但它往往会高估熔化率。究其原因,在于缓慢的二次流有效扰乱一次流方向上稳定而持久的漩涡的能力有限,因此无法提高一次流方向上的传热效率。
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引用次数: 0
Distribution Behavior of Titanium Between Ferrosilicon Melt and CaO-SiO2-Al2O3 Slag: Thermochemical and Structural Assessments 钛在硅铁熔体和 CaO-SiO2-Al2O3 熔渣之间的分布行为:热化学和结构评估
Pub Date : 2024-07-10 DOI: 10.1007/s11663-024-03200-4
Min Joo Lee, Tae Sung Kim, Joo Hyun Park

The titanium distribution ratio (({L}_{Ti})) between ferrosilicon (FeSi) melt and the CaO-SiO2-Al2O3 slag was measured at 1773 K (1500 °C). FeSi-slag equilibration was carried out using various slag compositions. The ({L}_{Ti}) was presented against the Vee ratio (pct CaO/pct SiO2 = C/S) between 0.3 and 1.2, and Al2O3 content from 5 to 20 mass pct. The ({L}_{Ti}) exhibited minima at about C/S=0.7(±0.1) at a fixed Al2O3 content. In a C/S < 0.7 regime, i.e., relatively acidic melts, Ti4+ ions were considered as network forming [TiO4]-tetrahedron unit in the aluminosilicate framework. However, in a C/S > 0.7 regime, i.e., relatively basic melts, Ti4+ ions were considered to form the [TiO5]-pyramid structure unit compensated by Ca2+. When adding Al2O3 into the basic melts over 10 mass pct, [AlO4]-tetrahedrons take Ca2+ ions for charge compensation, resulting in a decrease of stability of [TiO5] unit because of Ca2+ depletion. At a greater than 10 mass pct Al2O3 content in the basic melts, Ti4+ replaced Al3+ to form the [TiO4]-tetrahedron unit, decreasing the activity coefficient of TiO2 in the slag.

硅铁(FeSi)熔体和 CaO-SiO2-Al2O3 熔渣之间的钛分布比(({L}_{Ti}))是在 1773 K(1500 °C)下测量的。使用不同的熔渣成分进行了硅铁-熔渣平衡。({L}_{Ti})与 0.3 至 1.2 之间的 Vee 比(CaO/SiO2 百分比 = C/S)以及 5 至 20 质量百分比的 Al2O3 含量相关。在固定的 Al2O3 含量下,({L}_{Ti}) 在 C/S=0.7(±0.1) 左右呈现出最小值。在 C/S < 0.7 条件下,即在相对酸性的熔体中,Ti4+ 离子被认为是铝硅酸盐框架中形成[TiO4]-四面体单元的网络。然而,在 C/S > 0.7 条件下,即在相对碱性的熔体中,Ti4+ 离子被认为在 Ca2+ 的补偿下形成 [TiO5]- 金字塔结构单元。当向超过 10 质量百分数的碱性熔体中添加 Al2O3 时,[AlO4]-四面体会吸收 Ca2+ 离子进行电荷补偿,导致[TiO5]单元的稳定性因 Ca2+ 耗竭而降低。当碱性熔体中 Al2O3 的含量大于 10 质量百分数时,Ti4+ 取代 Al3+ 形成 [TiO4]- 四面体单元,从而降低了熔渣中 TiO2 的活度系数。
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引用次数: 0
DDPM Simulation for Fluidization Behavior and Reduction of Iron Ore Fines with Hydrogen in the Fluidized Bed 流化床中铁矿粉的流化行为和氢气还原的 DDPM 模拟
Pub Date : 2024-07-10 DOI: 10.1007/s11663-024-03205-z
Wenlei Zhou, Fuyong Su, Likun Yang, Sizong Zhang, Hailong Huo

In this paper, the hydrogen direct reduction of iron ore fines is numerically studied by using the Dense Discrete Phase Model (DDPM) in the fluidized bed. The fluidization behavior at different inlet gas velocities (Ug) as well as the influence of Ug and hydrogen concentration on reduction degree (RD) are comprehensively investigated. The result indicates the increase of time-averaged solids volume fraction for the same cross-sectional heights with increasing Ug when the bed height (H) exceeds 0.06 m. Furthermore, the reduction rate of mineral powder increases with higher Ug value, and the RD reaches almost 100 pct after 4000 seconds of reduction time with Ug ranging from 0.35 to 0.65 m/s. The reduction rate increases noticeably with the increase of hydrogen concentration in the range of 10 to 100 pct, and Fe2O3 can be completely converted to Fe under condition of 65 pct H2 concentration after 4000 seconds. Moreover, higher H2 concentration leads to faster rate of Fe2O3 consumption and Fe production. The mass fraction peak values of Fe3O4 and FeO are in the range of 0.29 to 0.34 and 0.21 to 0.24 under different H2 concentrations, respectively.

本文利用流化床中的致密离散相模型(DDPM)对铁矿粉的氢气直接还原进行了数值研究。全面研究了不同入口气体速度(Ug)下的流化行为,以及 Ug 和氢浓度对还原度(RD)的影响。结果表明,当床高(H)超过 0.06 米时,相同截面高度下的时间平均固体体积分数随 Ug 的增加而增加。此外,矿粉的还原率随 Ug 值的增加而增加,在 Ug 为 0.35 至 0.65 m/s 时,还原时间为 4000 秒后,还原度几乎达到 100%。在 10 至 100 pct 的范围内,还原率随氢气浓度的增加而明显增加,在 65 pct 的氢气浓度条件下,4000 秒后 Fe2O3 可完全转化为 Fe。此外,氢气浓度越高,Fe2O3 的消耗和 Fe 的生成速度越快。在不同的 H2 浓度下,Fe3O4 和 FeO 的质量分数峰值范围分别为 0.29 至 0.34 和 0.21 至 0.24。
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引用次数: 0
Evolution of Inclusion Distribution in Continuous Casting Slabs During Strip Feeding 带材喂料过程中连铸坯中夹杂物分布的演变
Pub Date : 2024-07-10 DOI: 10.1007/s11663-024-03186-z
Rui Zhang, Hong-Chun Zhu, Hua-Bing Li, Zhou-Hua Jiang, Tao Pan, Shu-Cai Zhang, Hao Feng

Feeding strip significantly enhances continuous cast slab quality. To clarify its impact on inclusion distribution, a mathematical model coupling flow, solidification and inclusion motion have been developed. The upper recirculation, lower recirculation, and unformed recirculation flow occur during continuous casting. Under the resultant forces of drag, virtual mass, pressure gradient, Saffman, gravity, buoyancy, etc., the inclusion motion can be divided into two stages: Injection and Split flow. Feeding strip mainly affects inclusion motion by altering the drag, virtual mass, pressure gradient, and Saffman forces, which are closely related to the molten steel flow. After feeding strip, the lower recirculation on the strip feeding side is compressed, while it on the no-feeding side is expanded. The unformed recirculation flow on strip feeding side squeezes the flow below lower recirculation on no-feeding side. A higher strip feeding speed promotes downward inclusion motion, increasing the chance of being captured between the slab edge and strip. Unformed recirculation flow guides inclusions on the no-feeding side toward the slab edge, while expanded flow directs them toward the center. Consequently, inclusions on strip feeding side gradually gather between slab edge and quarter, while inclusions on no-feeding side first gather toward center and then toward edge of slab with increased strip feeding speed.

喂料带可大大提高连铸板坯的质量。为了阐明其对夹杂物分布的影响,我们建立了一个将流动、凝固和夹杂物运动耦合在一起的数学模型。连铸过程中会出现上部再循环、下部再循环和未成型再循环流动。在阻力、虚拟质量、压力梯度、萨夫曼力、重力、浮力等作用下,包体运动可分为两个阶段:注入和分流。带钢喂入主要通过改变与钢水流动密切相关的阻力、虚质量、压力梯度和 Saffman 力来影响夹杂运动。喂入钢带后,喂入钢带一侧的下部再循环流被压缩,而未喂入钢带一侧的下部再循环流则被扩张。带钢喂入侧未成形的再循环流挤压未喂入侧下再循环流。较高的板带喂料速度会促进夹杂物向下运动,增加夹杂在板坯边缘和板带之间的机会。未变形的再循环流将不进料侧的夹杂物引向板坯边缘,而膨胀流则将夹杂物引向板坯中心。因此,带钢喂料侧的夹杂物会逐渐聚集在板坯边缘和四分之一之间,而不喂料侧的夹杂物会随着带钢喂料速度的增加,先向板坯中心聚集,然后再向板坯边缘聚集。
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引用次数: 0
The Turbulence Length Scale as A Criterion to Evaluate the Performances of Tundish Inhibitors to Float Non-Metallic Inclusions 将湍流长度尺度作为评估水槽抑制剂浮起非金属夹杂物性能的标准
Pub Date : 2024-07-10 DOI: 10.1007/s11663-024-03192-1
A. Nájera-Bastida, R. D. Morales, J. Guarneros-Guarneros, J. Rodríguez-Ávila, R. Zárate-Gutiérrez

Five turbulence inhibitor (TI) designs are evaluated to define the highest performance to float non-metallic inclusions through the turbulence length scale analysis. The flow structures in the flow mushrooms, formed by the entry jet and its impact with a TI, generate coherent structures in the boundary layers’ walls of this device. The second invariant of the velocity gradient, Q, analyzes these structures. In the mushroom region, the inhibitor yielding the largest magnitudes of this second invariant has the most significant efficiency to float inclusions. Other criteria like the wall shear stress, the turbulent viscosity ratio, and the kinetic energy/friction velocity ratio are proved to be as valuable as the Q criterion to assess the performance of a given TI to float inclusions. This theory was tested numerically through the dynamics of amine particles in a tundish water model to simulate the dynamics of the non-metallic inclusions in steel and with amine powder injection experiments. The mass of powder escaping through the strand decreased as the absolute magnitudes of these criteria rose.

通过湍流长度尺度分析,评估了五种湍流抑制器(TI)设计,以确定浮动非金属夹杂物的最高性能。由入口射流及其与 TI 的撞击形成的流菇中的流动结构会在该装置的边界层壁上产生相干结构。速度梯度的第二个不变量 Q 分析了这些结构。在蘑菇区,产生该第二不变量最大值的抑制剂对夹杂物的浮动效率最高。事实证明,其他标准,如壁剪应力、湍流粘度比和动能/摩擦速度比,与 Q 标准一样有价值,可用于评估给定 TI 在浮动夹杂物方面的性能。该理论通过在外滩水模型中模拟钢中非金属夹杂物动态的胺颗粒动态以及胺粉末注入实验进行了数值测试。随着这些标准绝对值的增加,通过钢绞线逸出的粉末质量也随之减少。
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引用次数: 0
Dissolution of Oxide Particles in Multi-component Slags Governed by Diffusive and Convective Fluxes 多组分炉渣中氧化物颗粒的溶解受扩散和对流通量控制
Pub Date : 2024-07-08 DOI: 10.1007/s11663-024-03175-2
Daniel Marian Ogris, Susanne Michelic, Ernst Gamsjäger

The kinetics of the dissolution of oxide particles in metallurgical slags is simulated by means of a sharp-interface finite difference model where multi-component diffusion is considered. The effect of convective fluxes on the dissolution kinetics is being considered by a constrained boundary layer thickness. The thickness of this boundary layer can be estimated from theory and is used together with the interdiffusivity matrix to predict the dissolution kinetics of spherical alumina particles in various CaO–SiO2–Al2O3 slags. The numerical results are compared to experimental observations using High-Temperature Confocal Scanning Laser Microscopy (HT-CSLM). The results imply that the processes controlling the dissolution kinetics are multi-component diffusion with density-driven convective fluxes in the liquid slag gaining more influence in the later stages of the dissolution process

通过锐面有限差分模型模拟了冶金渣中氧化物颗粒的溶解动力学,其中考虑了多组分扩散。对流通量对溶解动力学的影响是通过限制边界层厚度来考虑的。该边界层的厚度可以从理论上估算出来,并与相互扩散矩阵一起用于预测球形氧化铝颗粒在各种 CaO-SiO2-Al2O3 矿渣中的溶解动力学。数值结果与使用高温共焦激光扫描显微镜(HT-CSLM)进行的实验观察结果进行了比较。结果表明,控制溶解动力学的过程是多组分扩散过程,在溶解过程的后期阶段,液渣中的密度驱动对流通量的影响更大。
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引用次数: 0
Thermodynamic Study of High-Purity TiSi2 Prepared by Directional Solidification 定向凝固法制备高纯 TiSi2 的热力学研究
Pub Date : 2024-07-08 DOI: 10.1007/s11663-024-03194-z
Yakun Zhang, Yun Lei, Yongsheng Ren, Wenhui Ma

The equilibrium segregation coefficient of impurities in materials is the theoretical basis for its purification. This study used the high-temperature chemical equilibration technique to determine the solid solubility and the approximate equilibrium segregation coefficients of Fe, Mn, Al, Cu, and Ni impurities in TiSi2. The results showed that the solid solubilities of Al, Fe, Mn, Ni, and Cu in TiSi2 were in the range of 1.0 to 1.5 wt pct, and their equilibrium segregation coefficients were less than 1.

材料中杂质的平衡偏析系数是材料提纯的理论基础。本研究采用高温化学平衡技术测定了 TiSi2 中铁、锰、铝、铜和镍杂质的固溶解度和近似平衡偏析系数。结果表明,Al、Fe、Mn、Ni 和 Cu 在 TiSi2 中的固溶度在 1.0 至 1.5 wt pct 之间,其平衡偏析系数小于 1。
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引用次数: 0
TiO2 and Reducing Gas: Intricate Relationships to Direct Reduction of Iron Oxide Pellets 二氧化钛和还原气体:氧化铁颗粒直接还原的复杂关系
Pub Date : 2024-07-08 DOI: 10.1007/s11663-024-03168-1
Pasquale Cavaliere, Behzad Sadeghi, Aleksandra Laska, Damian Koszelow

In response to the imperative for sustainable iron production with reduced CO2 emissions, this study delves into the intricate role of TiO2 in the direct reduction of iron oxide pellets. The TiO2-dependent reducibility of iron oxide pellets utilizing H2 and CO gas across varied temperatures and gas compositions is thoroughly investigated. Our findings unveil the nuanced nature of the TiO2 effect, underscored by its concentration-dependent behavior, revealing an optimal range between 1 and 1.5 pct TiO2, where a neutral or positive impact on reduction kinetics and diffusion coefficient is observed. Notably, the synergistic interplay of CO and H2 at 1000 °C emerges as particularly efficacious, suggesting complementary effects on the reduction process. The introduction of H2 into the reducing atmosphere regulated by CO not only extends the transition range but also markedly expedites the rate of reduction. Furthermore, our study highlights the temperature sensitivity of the TiO2 effect, with higher TiO2 content correlating with prolonged reduction time in a 100 pct H2 atmosphere at 900 °C. In a 100 pct H2 atmosphere, the non-contributory role of TiO2 stems from the water-gas shift reaction. Conversely, introducing H2 into a CO-controlled reducing atmosphere with TiO2 enhances the transition range and expedites the reduction rate. Additionally, our findings underscore the role of total iron content, revealing a direct correlation with the reduction process.

为了满足可持续铁生产和减少二氧化碳排放的需要,本研究深入探讨了二氧化钛在氧化铁球团直接还原过程中的复杂作用。我们深入研究了在不同温度和气体成分下,利用 H2 和 CO 气体还原氧化铁球团时 TiO2 的相关还原性。我们的研究结果揭示了二氧化钛效应的细微差别,其浓度依赖行为突出表明了在 1 至 1.5 pct TiO2 之间的最佳范围内,对还原动力学和扩散系数有中性或积极的影响。值得注意的是,CO 和 H2 在 1000 °C 时的协同作用尤其有效,这表明它们对还原过程具有互补作用。在由 CO 调节的还原气氛中引入 H2,不仅扩大了过渡范围,还明显加快了还原速度。此外,我们的研究还强调了二氧化钛效应的温度敏感性,在 900 °C 的 100 pct H2 大气中,二氧化钛含量越高,还原时间越长。在 100 pct H2 大气中,TiO2 的非贡献作用源于水-气转移反应。相反,在有 TiO2 的一氧化碳控制还原气氛中引入 H2,可提高过渡范围并加快还原速度。此外,我们的研究结果还强调了总铁含量的作用,揭示了与还原过程的直接关系。
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引用次数: 0
Optimization of the Evaluation Method for Bentonite Used in Iron Ore Pelletizing 优化铁矿石造粒所用膨润土的评价方法
Pub Date : 2024-07-08 DOI: 10.1007/s11663-024-03187-y
Wei Mo, Yuxin Feng, Zeping Wang, Jinlin Yang, Jinpeng Feng, Xiujuan Su

Bentonite is an essential binder in the iron ore pelletization process. However, limited research has been conducted on the correlation between the physical and chemical properties of bentonite and its pelletizing performances, while the evaluation criteria for pelletizing bentonite have not been standardized. To optimize the current evaluation methods, this study tested the physical and chemical properties of five representative bentonites, as well as their green balling performance after pelletizing. Additionally, a multiple regression model was constructed using R. Stepwise regression and relative weight analysis were used to optimize and evaluate the indicators of bentonite. The results showed that the raw ball performance was mainly affected by water absorption (WA), swelling index (SI), and swelling capacity (SC). The dry ball performance was mainly affected more by methylene blue index (MBI) and cation exchange capacity (CEC). The following stepwise regression analysis revealed that WA, CEC, and SC were significant predictors for green ball drop strength; WA and SI for green ball compressive strength; and WA, MBI, and SC for dry ball compressive strength. The multiple regression model developed in this study exhibits high goodness of fit and accuracy, making it a valuable way for assessing the impact of different quality bentonites on pelletizing performance as well as optimizing the evaluation methodology of bentonite’s performance in iron ore pelletization.

膨润土是铁矿石球团过程中必不可少的粘结剂。然而,关于膨润土的物理和化学性质与其球团性能之间的相关性的研究还很有限,而膨润土球团的评价标准也尚未统一。为了优化当前的评价方法,本研究测试了五种具有代表性的膨润土的物理和化学性质,以及它们在造粒后的绿球性能。此外,还利用 R 语言构建了多元回归模型,并采用逐步回归法和相对重量分析法对膨润土的各项指标进行了优化和评价。结果表明,生球性能主要受吸水率(WA)、膨胀指数(SI)和膨胀能力(SC)的影响。干球性能主要受亚甲基蓝指数(MBI)和阳离子交换容量(CEC)的影响较大。逐步回归分析表明,WA、CEC 和 SC 对绿球抗压强度有显著的预测作用;WA 和 SI 对绿球抗压强度有显著的预测作用;WA、MBI 和 SC 对干球抗压强度有显著的预测作用。本研究建立的多元回归模型具有很高的拟合度和准确性,因此是评估不同质量的膨润土对球团性能的影响以及优化膨润土在铁矿石球团中的性能评估方法的重要方法。
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引用次数: 0
Large Eddy Simulation of Molten Steel Flow and Inclusion Transport in a New Butterfly-Type Induction Heating Tundish 新型蝶形感应加热连铸机中钢水流动和夹杂物迁移的大涡流模拟
Pub Date : 2024-07-08 DOI: 10.1007/s11663-024-03201-3
Ning Wang, Zhongqiu Liu, Huang Cheng, Fengsheng Qi, Changjun Wang, Li Zhang, Baokuan Li

In addressing the retrofitting issues of conventional non-induction heating tundish, a novel butterfly-type induction heating tundish model was devised. A three-dimensional coupled mathematical model of magnetic, thermal, and fluid fields was established to investigate the temperature distribution, flow characteristics, and temperature rise curves within the butterfly-type tundish. The model for inclusion motion and removal, based on Large Eddy Simulation (LES), was devised, integrating factors such as normal critical velocity, coefficient of restitution, and critical incident angle at the wall boundary conditions to provide a more precise depiction of the reflection and adsorption processes of inclusions on the tundish wall. The findings suggest that induction heating can effectively offset the temperature loss of the molten steel and enhance the removal rate of inclusions, particularly those of large size. The outlet temperature increases by − 15 K, 7 K, 15 K, and 26 K, and the total removal rate of inclusions reaches 69.18, 83.37, 87.69, and 92.01 pct at 0, 600, 800, and 1000 kW, respectively. The channel serves as the primary site for inclusion removal when employing induction heating. Among these, the removal rates within the channel and at the slag layer exhibit a positive correlation with the inclusion diameter, while the remaining wall removal rates show a negative correlation. The implementation of induction heating technology leads to a notable decrease in the entry of large-sized inclusions into the mold.

为解决传统非感应加热外锅的改造问题,设计了一种新型蝶式感应加热外锅模型。建立了磁场、热场和流体场的三维耦合数学模型,以研究蝶形中间包内的温度分布、流动特性和温升曲线。以大涡流模拟(LES)为基础,设计了夹杂物运动和去除模型,综合了法向临界速度、恢复系数和壁面边界条件的临界入射角等因素,更精确地描述了夹杂物在中间包壁面上的反射和吸附过程。研究结果表明,感应加热可以有效抵消钢水的温度损失,提高夹杂物的去除率,尤其是大尺寸夹杂物的去除率。在 0、600、800 和 1000 kW 条件下,出口温度分别提高 - 15 K、7 K、15 K 和 26 K,夹杂物的总去除率分别达到 69.18、83.37、87.69 和 92.01 pct。在采用感应加热时,通道是去除夹杂物的主要部位。其中,通道内和熔渣层的去除率与夹杂物直径呈正相关,而其余壁面的去除率则呈负相关。采用感应加热技术后,大尺寸夹杂物进入模具的情况明显减少。
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引用次数: 0
期刊
Metallurgical and Materials Transactions B
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