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Numerical Investigation of the Coupled Effect of H/D Ratio and Effective Volume on Optimized Blast Furnace Profile 高/低比和有效容积对优化高炉炉型的耦合效应的数值研究
Pub Date : 2024-08-02 DOI: 10.1007/s11663-024-03218-8
Junjie Li, Lulu Jiao, Shibo Kuang, Ruiping Zou, Wenqi Zhong, Aibing Yu

The design and optimization of blast furnace (BF) profiles generally rely on limited empirical knowledge and experience. Such exercise can now be improved by means of process modeling and optimization. In this work, the effect of furnace profile on BF performance is numerically investigated across a wide range of furnace volumes (500 to 6000 m3), focusing on the ratio of effective height to belly diameter (H/D ratio). This is done based on the recently developed 3D multi-fluid BF process model. The results indicate that the optimized H/D ratio under different furnace volumes can be determined by minimizing the total energy consumption, namely, the summation of chemical and physical energy consumptions. Comparative analysis indicates that the industrial data on the variation of H/D ratio with furnace volume, collected over years, can be reproduced quantitatively by the current model. The increase in BF size or volume results in high thermal energy efficiency and low coke rate, primarily attributed to the reduced heat dissipation from the top gas and furnace wall. But there exists a size threshold between small and large BFs, approximately 2000 m3 under the conditions considered. Beyond this threshold, the BF performance and in-furnace states do not change significantly. Optimum BF profile needs to consider the coupled effect of H/D ratio and effective furnace volume.

高炉(BF)炉型的设计和优化通常依赖于有限的经验知识和经验。现在可以通过工艺建模和优化来改进这种做法。在这项工作中,我们对高炉炉型对高炉性能的影响进行了数值研究,研究范围涵盖高炉容积(500 至 6000 立方米),重点关注有效高度与炉腹直径之比(H/D 比)。这项研究是基于最近开发的三维多流体 BF 工艺模型进行的。结果表明,在不同炉子容积下的优化 H/D 比可以通过最小化总能耗来确定,即化学能耗和物理能耗的总和。对比分析表明,目前的模型可以定量再现多年来收集的有关 H/D 比率随炉容积变化的工业数据。BF 尺寸或体积的增加会导致热能效率高和焦炭率低,这主要归因于炉顶煤气和炉壁的散热量减少。但在小型和大型 BF 之间存在一个尺寸阈值,在考虑的条件下约为 2000 立方米。超过这个临界值后,BF 的性能和炉内状态不会发生显著变化。最佳 BF 曲线需要考虑 H/D 比和有效炉体积的耦合效应。
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引用次数: 0
Numerical Simulation of Multi-physics Characteristics in Tundish with Channel Induction Heating 带通道感应加热装置的外容器中多物理特性的数值模拟
Pub Date : 2024-07-31 DOI: 10.1007/s11663-024-03211-1
Bin Yang, Shifu Chen, Hong Lei, Dazhao Gou

To investigate the qualitative and quantitative effects of flow rate on fluid dynamics within a tundish using channel induction heating, a mathematical model was developed to reflect the macroscopic transport phenomena. The simulation results show that as inlet velocities increased from 0.3 to 0.9, the ratios of plug zone volume to total volume, dead zone volume to total volume, plug zone to dead zone, and plug zone to mixed zone consistently fell within the ranges of 0.257 to 0.263, 0.118 to 0.119, 2.152 to 2.231, and 0.412 to 0.427. Concurrently, the inclusion removal rate in the tundish's dead zone under channel induction heating increased with the inlet velocity. Additionally, analysis of the mean characteristics in the tundish system reveals that the mean residence time linearly decreases with increasing mean flow temperature and linearly increases with the inlet velocity. Furthermore, the inclusion removal rate linearly increases with the inlet velocity. This work enables precise quantitative and qualitative predictions and analyses of physical parameters in the electromagnetic induction heating tundish at various casting speeds, providing an efficient method for evaluating and optimizing the multi-physical fields within the metallurgical container.

为了研究流速对使用通道感应加热的中间包内流体动力学的定性和定量影响,我们建立了一个数学模型来反映宏观传输现象。模拟结果表明,当入口速度从 0.3 增加到 0.9 时,塞区体积与总体积之比、死区体积与总体积之比、塞区与死区之比以及塞区与混合区之比始终保持在 0.257 至 0.263、0.118 至 0.119、2.152 至 2.231 和 0.412 至 0.427 的范围内。同时,在通道感应加热条件下,熔池死区的夹杂物去除率随入口速度的增加而增加。此外,对中间包系统平均特性的分析表明,平均停留时间随平均流动温度的增加而线性减少,随入口速度的增加而线性增加。此外,夹杂物去除率随入口速度的增加而线性增加。这项工作能够在各种铸造速度下对电磁感应加热中间包中的物理参数进行精确的定量和定性预测和分析,为评估和优化冶金容器内的多物理场提供了一种有效方法。
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引用次数: 0
Effect of Mold Oscillation on Multiphase Flow and Slag Entrainment in a Slab Continuous Casting Mold 模具摆动对板坯连铸模中多相流和熔渣夹带的影响
Pub Date : 2024-07-29 DOI: 10.1007/s11663-024-03219-7
Fu Zheng, Wei Chen, Lifeng Zhang

In the current study, a three-dimensional mathematical model that integrated the large eddy simulation (LES) turbulent model, volume of fluid (VOF) multiphase model, and the dynamic mesh model, was developed to investigate the influence of the mold oscillation on the steel, slag, and air multiphase flow and the slag entrainment in a slab continuous casting mold. The results indicated that the mold oscillation led to an increase of about 0.35 m/s in the speed of molten steel at the impact point of the upper and lower circulation on the narrow surface. However, it reduced about 0.047 m/s in the maximum speed of the meniscus at 1/4 width of the mold. The Fast Fourier Transform (FFT) analysis revealed that the characteristic frequency of the speed fluctuation in the gravity direction of the meniscus near the narrow surface was 1.27 Hz without the consideration of the mold oscillation. Upon the application of the mold oscillation, a new characteristic frequency of 3 Hz, matching the mold oscillation frequency, emerged with twice the intensity of the original 1.27 Hz frequency. Moreover, the mold oscillation had little effect on the characteristic frequency of the speed fluctuation on the meniscus far away from the narrow surface. A user-defined function (UDF) was employed to quantify the number, size, and spatial distribution of entrained slag droplets. The net slag entrainment rate was reduced from 0.0152 to 0.0113 kg/s after the consideration of the mold oscillation, and the number of entrained slag droplets was also decreased. The effect of mold oscillation on the size distribution of entrained slag droplets and the occurrence location of the slag entrainment on the meniscus were not significant.

本研究建立了一个集大涡模拟(LES)湍流模型、流体体积(VOF)多相模型和动态网格模型于一体的三维数学模型,以研究结晶器振荡对板坯连铸结晶器中钢、渣、空气多相流和夹渣的影响。结果表明,结晶器摆动导致狭窄表面上的上下循环冲击点处的钢水速度增加了约 0.35 m/s。但是,在模具 1/4 宽度处,半月板的最大速度降低了约 0.047 m/s。快速傅立叶变换(FFT)分析表明,在不考虑模具振荡的情况下,窄表面附近的半月板重力方向速度波动的特征频率为 1.27 Hz。在加入模具振荡后,出现了与模具振荡频率相匹配的 3 赫兹的新特征频率,其强度是原来 1.27 赫兹频率的两倍。此外,模具振荡对远离狭窄表面的半月板上的速度波动特征频率影响很小。采用用户自定义函数(UDF)来量化夹渣液滴的数量、大小和空间分布。考虑到模具振荡后,净夹渣率从 0.0152 kg/s 降至 0.0113 kg/s,夹渣液滴的数量也有所减少。模具摆动对夹渣液滴的大小分布以及夹渣在半月板上的出现位置的影响并不显著。
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引用次数: 0
Effect of the Al2O3 Content and MgO/Al2O3 Ratio on the Viscosity and Structure of CaO–SiO2–MgO–Al2O3-Based Furnace Slag with CaO/SiO2 = 1.2 Al2O3 含量和 MgO/Al2O3 比对 CaO-SiO2-MgO-Al2O3 基 CaO/SiO2 = 1.2 炉渣粘度和结构的影响
Pub Date : 2024-07-29 DOI: 10.1007/s11663-024-03220-0
Jianwei Song, Lei He, Tu Hu, Tingting Lv, Li Gao

The effects of the Al2O3 content and MgO/Al2O3 ratios on the structure and viscosity of CaO–SiO2–MgO–Al2O3 silicate-based slag were studied by the rotating cylinder method. The evolution of the silicate structure was analyzed by Fourier transform infrared spectroscopy. The results show that when the CaO/SiO2 ratio is 1.20 and the MgO content is 10 mass pct, the Si–O–Al structure and [AlO4]5− tetrahedron structure of the slag increase with increasing Al2O3 content (17 to 22 pct), which increases the viscosity, break-point temperature, and activation energy of the slag. In addition, when the CaO/SiO2 ratio is 1.20 and the Al2O3 content is 18, 20, and 22 mass pct, respectively, with the increase of MgO/Al2O3 ratio in the range of 0.4 to 0.7, the viscosity, break-point temperature, and activation energy of slag decrease. The analysis of the Raman spectra in the 800 to 1200 cm−1 range indicates that complex silicate structures ([Si2O5]2−, [Si2O6]4−) disaggregate into simpler structures ([Si2O7]6− and [SiO4]4−) with the MgO/Al2O3 ratio increase. The proportion of structural units Q3 and Q2 decreases, the proportion of Q1 and Q0 increases, and the proportion of silicate structural units (Q0 + Q1)/(Q2 + Q3) increases, which indicates that the non-bridging oxygen content in the slag increases, resulting in a decrease in slag polymerization.

采用转筒法研究了 Al2O3 含量和 MgO/Al2O3 比率对 CaO-SiO2-MgO-Al2O3 硅酸盐炉渣结构和粘度的影响。傅里叶变换红外光谱分析了硅酸盐结构的演变。结果表明,当 CaO/SiO2 比为 1.20、MgO 含量为 10 质量百分数时,炉渣的 Si-O-Al 结构和 [AlO4]5- 四面体结构随着 Al2O3 含量(17 至 22 质量百分数)的增加而增加,从而增加了炉渣的粘度、断点温度和活化能。此外,当 CaO/SiO2 比为 1.20,Al2O3 含量分别为 18、20 和 22 质量百分点时,随着 MgO/Al2O3 比在 0.4 至 0.7 范围内的增加,炉渣的粘度、断点温度和活化能均降低。对 800 至 1200 cm-1 范围内的拉曼光谱的分析表明,随着 MgO/Al2O3 比率的增加,复杂的硅酸盐结构([Si2O5]2-、[Si2O6]4-)分解为较简单的结构([Si2O7]6- 和 [SiO4]4-)。结构单元 Q3 和 Q2 的比例减少,Q1 和 Q0 的比例增加,硅酸盐结构单元(Q0 + Q1)/(Q2 + Q3)的比例增加,这表明炉渣中的非桥氧含量增加,导致炉渣聚合度降低。
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引用次数: 0
Sticking in Shaft Furnace and Fluidized Bed Ironmaking Processes: A Comprehensive Review Focusing on the Effect of Coating Materials 竖炉和流化床炼铁工艺中的粘结现象:以涂层材料的影响为重点的综合评述
Pub Date : 2024-07-26 DOI: 10.1007/s11663-024-03188-x
Rou Wang, Suneeti Purohit, Khadijeh Paymooni, Tom Honeyands

Production of direct reduced iron (DRI), particularly with green hydrogen, is a key pathway to the decarbonization of the iron and steel industry. However, the sticking tendency during the production of DRI creates serious operational issues and limits production outputs. Coating inert materials on the surface of iron ores can act as a barrier to effectively prevent the bonding between newly formed iron surfaces, and can interfere with the formation of iron whiskers. However, the principle of coating has not been systematically studied. This review covers the mechanism of sticking in both shaft furnaces and fluidized bed-based gaseous DRI production. The factors that influence the reduction kinetics and morphology, including physical and chemical ore properties, pellet induration conditions, and reduction conditions are summarized as well. Understanding the relationship between these factors and morphology change is critical to eliminating the sticking issues of DRI. Findings from this study suggest that coating with inert additives (e.g., metal oxides) can successfully prevent sticking in both shaft furnaces and fluidized bed processes. The types of additives and coating methods, the stage of reduction where the coating is applied, and reduction temperature will dramatically affect the coating performance. The outlook is discussed as well given the need for further work to improve the performance of coating (methods, timing, and cheaper alternatives), to further de-risk DRI technologies.

生产直接还原铁(DRI),特别是使用绿色氢气生产直接还原铁(DRI),是钢铁工业实现脱碳的关键途径。然而,直接还原铁生产过程中的粘连倾向造成了严重的操作问题,并限制了产量。在铁矿石表面涂覆惰性材料可以起到屏障的作用,有效防止新形成的铁表面之间的粘结,并能干扰铁须的形成。然而,涂层的原理尚未得到系统研究。本综述涉及竖炉和基于流化床的气态 DRI 生产中的粘附机理。还总结了影响还原动力学和形态的因素,包括矿石的物理和化学性质、球团压制条件和还原条件。了解这些因素与形态变化之间的关系对于消除 DRI 的粘结问题至关重要。本研究的结果表明,使用惰性添加剂(如金属氧化物)涂覆可成功防止竖炉和流化床工艺中的粘结。添加剂和涂层方法的类型、应用涂层的还原阶段以及还原温度都会极大地影响涂层性能。鉴于需要进一步改进涂层性能(方法、时间安排和更便宜的替代品)以进一步降低 DRI 技术的风险,我们还对前景进行了讨论。
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引用次数: 0
Study on Behavior of Slag Rim and Shell Initial Solidification at Meniscus in Continuous Casting Slab Mold 连铸板模中渣边和壳体在半月板处的初始凝固行为研究
Pub Date : 2024-07-25 DOI: 10.1007/s11663-024-03195-y
Zijian Wei, Zhihao Wang, Di Zhang, Yu Liu, Xudong Wang, Man Yao

Understanding the formation of a slag rim on the mold meniscus is crucial for controlling surface defects in the initial shell. However, there is a scarcity of quantitative studies on this matter. This study has developed a comprehensive three-dimensional (3D) numerical model for analyzing the meniscus multi-phase flow, heat transfer, and solidification, considering mold oscillation. The 3D morphology of the solidifying shell and the slag rim in the meniscus region were accurately reproduced. The solidification depth (DIS), solidification length (LIS) and oscillation mark depth (DOM) of the initial shell were used to quantify the morphological characteristics of the initial shell. The results confirmed that the formation position difference of the slag rim along the circumferential direction of the mold significantly affects the initial solidification and uniform growth of the shell. In the corner of the mold, the deeper overflow makes the oscillation mark extend 2.8 to 3.2 mm in the direction of casting. In addition, in order to quantitatively investigate the influence of the slag rim, a two-dimensional (2D) model is established with phenomena and parameters considered the same as those of the 3D model. According to the slag rim morphology obtained by the 3D model, in the 2D model, it is proposed to construct three slag rims with the same maximum thickness of 6 mm at 10, 20 and 35 mm above the meniscus (HRim). The simulation of initial shell morphology revealed that a lower formation position of the slag rim led to more severe overflow of molten steel from the meniscus, resulting in non-uniform continuous growth of the initial shell. This increases the likelihood of potential blockage in the liquid slag flow towards the slag channel between solidified shell and mold.

了解模具半月板上熔渣边缘的形成对于控制初始型壳的表面缺陷至关重要。然而,这方面的定量研究却很少。本研究建立了一个全面的三维(3D)数值模型,用于分析半月板多相流、传热和凝固,并考虑了模具振荡。该模型精确再现了凝固壳体和半月板区域熔渣边缘的三维形态。利用初始壳体的凝固深度(DIS)、凝固长度(LIS)和振荡标记深度(DOM)来量化初始壳体的形态特征。结果证实,渣缘沿模具圆周方向的形成位置差异显著影响了壳体的初始凝固和均匀生长。在结晶器的拐角处,较深的溢流使得振痕在浇铸方向上延伸了 2.8 至 3.2 毫米。此外,为了定量研究渣边的影响,建立了一个二维(2D)模型,其现象和参数与三维模型相同。根据三维模型得到的渣边形态,在二维模型中,建议在半月板(HRim)上方 10 毫米、20 毫米和 35 毫米处构建三个最大厚度相同(6 毫米)的渣边。对初始炉壳形态的模拟显示,炉渣边缘的形成位置越低,钢水从半月板溢出的情况越严重,导致初始炉壳的连续生长不均匀。这增加了液态熔渣流向凝固型壳和模具之间熔渣通道的潜在阻塞可能性。
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引用次数: 0
Modeling and Comparison Study of Industrial AC-Arcs 工业交流电弧的建模和比较研究
Pub Date : 2024-07-24 DOI: 10.1007/s11663-024-03214-y
Hákon Valur Haraldsson, Halldór Traustason, Yonatan A. Tesfahunegn, Merete Tangstad, Gudrun Saevarsdottir

Electric arcs are a necessary heat source in many industrial processes that take place in Submerged Arc Furnaces (SAFs). Arcs exhibit non-linear electrical characteristics and behave in a complex manner. Therefore, an improved understanding of their behavior enables better control of furnace operation. Modeling of industrial arcs is a multiphysics process that involves simultaneously solving several coupled physical phenomena, such as electromagnetics, fluid dynamics, and heat transfer, including a radiative heat transfer from the plasma arc. Coupling fluid dynamics and electromagnetics is known as Magnetohydrodynamics (MHD). For practical applications, however, there are also simpler approaches to arc modeling, either based on simplified physical principles or empirical behavior. In this paper, a combined Cassie–Mayr model (CMM) and a channel arc model (CAM) are implemented and coupled with a submerged arc furnace electrical circuit model. The complete circuit model parameters such as resistances and inductances are estimated using modeling of a full size furnace, and then, actual measurements from a SAF are used to validate the models by comparing current and voltage waveform. Both models are then used to estimate harmonic distortion in a SAF for different arc current ratios, which should help operators to estimate the arc current in real time thus be able to lower and raise the electrode to keep operating conditions constant.

电弧是在埋弧炉(SAF)中进行的许多工业流程所必需的热源。电弧具有非线性电气特性,行为复杂。因此,加深对其行为的了解有助于更好地控制熔炉的运行。工业电弧建模是一个多物理过程,涉及同时求解多个耦合物理现象,如电磁学、流体动力学和热传递,包括等离子体电弧的辐射热传递。流体动力学和电磁学的耦合被称为磁流体动力学(MHD)。不过,在实际应用中,也有基于简化物理原理或经验行为的更简单的电弧建模方法。本文实施了卡西-迈尔模型(CMM)和槽弧模型(CAM)的组合,并将其与埋弧炉电路模型相结合。利用全尺寸电弧炉建模估算电阻和电感等完整电路模型参数,然后通过比较电流和电压波形,利用电弧炉的实际测量结果验证模型。然后,这两种模型都可用于估算不同电弧电流比下 SAF 中的谐波失真,这将有助于操作人员实时估算电弧电流,从而能够降低或升高电极以保持操作条件不变。
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引用次数: 0
Research on Mathematical Model and Process Parameter Optimization of Rotary Hearth Furnace Process Toward Energy and Cost Saving 以节约能源和成本为目标的转炉工艺数学模型和工艺参数优化研究
Pub Date : 2024-07-24 DOI: 10.1007/s11663-024-03190-3
Yingpeng Dong, Yanbing Zong, Runsheng Xu, Yuancheng Huang, Jianliang Zhang, Rongrong Wang, Jinpeng Shi, Yongsheng Yang

To explore the solutions of saving energy and cost of the rotary hearth furnace (RHF) direct reduction process, this paper constructed an energy consumption model, an economic evaluation model, and a carbon emission calculation model of the RHF direct reduction process. According to the actual production conditions of a steel plant, the influence of combustion air temperature and oxygen enrichment rate on the energy consumption, cost, and carbon emission of the RHF direct reduction process were studied. The calculation results show that for every 50 °C increase in the combustion air temperature, the process energy consumption, comprehensive cost, and carbon emission reduce by about 11 kgce, 42 CHY, and 44 kg, respectively. For every 2 pct increase in the oxygen enrichment rate of the combustion air, the corresponding values are about 10 kgce, 26 CHY, and 37 kg, respectively. In addition, the mathematical model established in this paper can be used to calculate the process energy consumption, cost, and carbon emissions under different raw material and fuel conditions, which is of great theoretical significance for the green and low-carbon transformation of the RHF direct reduction process.

为探索转底炉(RHF)直接还原工艺的节能降耗方案,本文构建了 RHF 直接还原工艺的能耗模型、经济评价模型和碳排放计算模型。根据某钢铁厂的实际生产条件,研究了燃烧空气温度和富氧率对 RHF 直接还原工艺的能耗、成本和碳排放的影响。计算结果表明,燃烧空气温度每升高 50 °C,工艺能耗、综合成本和碳排放量分别降低约 11 kgce、42 CHY 和 44 kg。助燃空气富氧率每增加 2 个百分点,相应的数值分别为 10 kgce、26 CHY 和 37 kg。此外,本文建立的数学模型可用于计算不同原料和燃料条件下的工艺能耗、成本和碳排放,对 RHF 直接还原工艺的绿色低碳改造具有重要的理论意义。
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引用次数: 0
Ultrasounds Induced Microstructure Transition and Improved Mechanical Property of Directionally Solidified Ternary Cu–Al–Ni Alloy 超声诱导定向凝固三元铜-铝-镍合金的微结构转变并改善其力学性能
Pub Date : 2024-07-24 DOI: 10.1007/s11663-024-03213-z
Y. J. Hu, J. Y. Wang, W. Zhai, B. Wei

Two ultrasonic modes, i.e., continuous and pulsed ultrasounds, were introduced into the directional solidification process of Cu68.3Al27.6Ni4.1 alloy. A columnar-to-equiaxed structure transition occurred to primary β(Cu3Al) phase within continuous ultrasonic field, which was accompanied with a grain size reduction by 7.5 times. Under pulsed ultrasound, β phase maintained the fine columnar structures with a similar grain size. In the former case, numerous β phase nucleation sites formed ahead of solid/liquid (S/L) interface because of the large local undercoolings induced by transient cavitation. Meanwhile, intensive acoustic streaming suppressed the liquid temperature gradient from 120 to 85 K/cm, which interrupted the solute transportation along heat flow direction and resulted in equiaxed microstructures. Under the intermittent ultrasonic action in the latter case, fewer nucleation sites were generated near S/L interface but small columnar β grains were split from the original ones under stable cavitation. Since no steady convection was driven, the liquid temperature gradient of 110 K/cm remained almost constant, making those grains grow into refined columnar structures. Under the action of pulsed ultrasound, the yield strength was enhanced by a factor of 1.5 because of grain refinement strengthening, together with 94 pct shape recovery rate due to columnar grain structures.

在 Cu68.3Al27.6Ni4.1 合金的定向凝固过程中引入了两种超声模式,即连续超声和脉冲超声。在连续超声场中,主β(Cu3Al)相发生了柱状到方形结构的转变,同时晶粒尺寸缩小了 7.5 倍。在脉冲超声下,β 相保持细柱状结构,晶粒大小相似。在前一种情况下,由于瞬态空化引起的大量局部过冷,在固/液(S/L)界面前形成了大量的 β 相成核点。同时,密集的声流将液体温度梯度从 120 K/cm 抑制到 85 K/cm,从而中断了溶质沿热流方向的迁移,形成了等轴微结构。在后一种情况下,在间歇性超声波作用下,S/L 接口附近产生的成核点较少,但在稳定的空化作用下,小的柱状 β 晶粒从原来的晶粒中分裂出来。由于没有驱动稳定的对流,110 K/cm 的液体温度梯度几乎保持不变,使得这些晶粒成长为精致的柱状结构。在脉冲超声的作用下,由于晶粒细化强化,屈服强度提高了 1.5 倍,同时由于柱状晶粒结构,形状恢复率达到 94%。
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引用次数: 0
Model for Surface Tension of Pure Liquid Metals: Revisit to Iida’s Model 纯液体金属的表面张力模型:重温饭田模型
Pub Date : 2024-07-22 DOI: 10.1007/s11663-024-03209-9
Yoongu Kang, In-Ho Jung

In the present study, a well-known Iida’s equation for surface tension was modified to improve the predictivity of the surface tension of pure liquid metals. A semi-empirical equation for the surface tensions (({sigma }_{m})) of liquid metal at its melting temperature proposed by Iida et al. uses a generalized (alpha ) value of 0.51 to represent the ratio of the distance required to separate one atomic pair from its equilibrium distance. This study improved the predictability of the equation by refining the (alpha ) value using the equilibrium interatomic distance (({r}_{e})) and atomic radius (({r}_{a})). Assigning an accurate (alpha ) value for each element greatly improves the prediction accuracy of the surface tension for liquid metals. Furthermore, the critical temperature (({T}_{c})) was calculated based on the interatomic distance (({r}_{c})) at ({T}_{c}) and temperature coefficient of density ((d{rho }_{T})/(dT)) and used to predict the temperature dependence coefficient of surface tension ((d{sigma }_{T})/(dT)). As results, more accurate surface tensions of 42 liquid metals were predicted over the entire liquid state temperature.

Graphical Abstract

本研究对著名的饭田表面张力方程进行了修改,以提高纯液态金属表面张力的预测能力。饭田等人提出的液态金属在其熔化温度下的表面张力(({sigma }_{m}))半经验方程使用 0.51 的广义 (alpha )值来表示分离一个原子对所需的距离与其平衡距离之比。这项研究通过使用平衡原子间距离(({r}_{e}))和原子半径(({r}_{a}))来改进 (α )值,从而提高了方程的可预测性。为每种元素指定精确的 (α ) 值可以大大提高液态金属表面张力的预测精度。此外,临界温度(({T}_{c}))是根据原子间距离(({r}_{c}))在({T}_{c})和密度温度系数((d{rho }_{T})/(dT))计算出来的,并用于预测表面张力的温度依赖系数((d{sigma }_{T})/(dT))。结果,42 种液态金属在整个液态温度下的表面张力都得到了更精确的预测。
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引用次数: 0
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Metallurgical and Materials Transactions B
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