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金属学报  2017, Vol. 53 Issue (4): 494-504    DOI: 10.11900/0412.1961.2016.00386
  本期目录 | 过刊浏览 |
电渣重熔全过程的数学模型开发及过程模拟研究
李青(),王资兴,谢树元
宝山钢铁股份有限公司研究院 上海 201900
Research on the Development of Mathematical Model of the Whole Process of Electroslag Remelting and the Process Simulation
Qing LI(),Zixing WANG,Shuyuan XIE
Research Institute, Baoshan Iron & Steel Co., Ltd., Shanghai 201900, China
引用本文:

李青,王资兴,谢树元. 电渣重熔全过程的数学模型开发及过程模拟研究[J]. 金属学报, 2017, 53(4): 494-504.
Qing LI, Zixing WANG, Shuyuan XIE. Research on the Development of Mathematical Model of the Whole Process of Electroslag Remelting and the Process Simulation[J]. Acta Metall Sin, 2017, 53(4): 494-504.

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摘要: 

基于多物理场耦合计算,结合电渣重熔(ESR)工艺,开发了应用于ESR全过程数值模拟的数学模型。模型涵盖了熔炼过程的电磁场、流动、传热、熔化及凝固多个物理过程,给出了熔炼过程温度及液相体积分数分布、熔池及糊状区形状尺寸等过程控制所相关的特征信息。利用铸锭温度分布历史,该模型可以计算与铸锭质量密切关联的多种凝固参数信息。该模型可以实现对未知ESR过程的稳态模拟预测,也可以针对实际过程进行熔炼全程(包括模冷阶段)的瞬态模拟分析。模型计算的熔池形状及深度与剖锭分析的结果接近,预测的二次枝晶臂间距分布与枝晶组织分析照片相符合。本模型可应用于过程分析及优化,并为新产品和工艺研发提供重要的技术支撑。

关键词 电渣重熔数值模拟多物理场二次枝晶间距    
Abstract

Electroslag remelting (ESR) is duly an important process for the production of high quality special steels and superalloys. Conventional ESR research has long been known as trial and error approach, which is excessively expensive and time-consuming, due to the complex process mechanism involving interactions of multiple physical fields, simultaneous phase transformations and chemical reactions. As the alternative way of study, ESR numerical simulation has been profoundly developed. Till now, systematically formulated model could demonstrate so many aspects of the process including electromagnetic field, fluid flow, heat and mass transfer, electrode melting, ingot solidification, slag/metal interface phenomenon, solidification structure parameters, ingot elements distribution, etc. There is a trend of multi-scale combined simulation, trying to bridge the gap between macro- and micro-scopes, thus could realize the control of solidified structure. Numerical modeling and simulation of ESR process have been widely accepted for its superiority of low cost, high speed, flexible adaptability and systematic results. Through combination of simulation and experiment, the ESR R&D process can be significantly promoted. Further, with the newly developed control technology supported by theoretical models, high precision and perfect quality control are expected to achieve. In this work, a mathematical model and the calculating code for the simulation of practical ESR process were developed based on multi-physics coupling calculation. The model considers many features of the process including the heat of the dropping liquid metal from the electrode, the naturally formed melt pool and the growing of the ingot, the cooling shrinkage of the solidified ingot away from the mould boundary, the changed slag skull thickness along the ingot growing direction, the matching between melt rate and input melting parameters, the specific boundary conditions, etc. The model covers physics of electromagnetic field, fluid flow, heat transfer, and melting and solidification during the remelting process, giving the characteristic information about distributions of temperature and liquid phase volume fraction, shape and size of melt pool and mushy zone, etc. highly concerned with the process control. Using history of temperature distributions and evolution, the model can compute various solidification parameters closely related to the ingot quality. The model realizes predictions for the unknown ESR process with steady state mode calculation and also analysis in transient mode of the whole ESR process from the melting start point of electrode to the end of cooling stage of ingot within the mould. Electromagnetic fields and steady and transient process simulations were carried out and discussed here for the practical IN718 alloy ESR process. The simulated melt pool profile and its depth size approximate to the experimental result of the ingot dissection analysis, and the predicted secondary dendrite spacing distribution coincides with the pictures of dendrite structure analysis fairly well. The model could be applied to the process analysis and optimization, and provide important technical support for the R&D of new product and technology.

Key wordselectroslag remelting    numerical simulation    multi-physics field    secondary dendrite arm spacing
收稿日期: 2016-08-26     
图1  电磁场计算涉及的几何区域及边界示意图
No. A˙x A˙r ?˙
?A˙x?x=0 0 ?˙0
- - Medium boundary condition
- - Medium boundary condition
- - Medium boundary condition
- - Medium boundary condition
- - Medium boundary condition
- - Medium boundary condition
0 0 -
?A˙x?x=0 0 0
?A˙x?r=0 ?A˙r?r=0 ??˙?r=0
表1  图1中电磁场计算方程的边界条件
图2  流场、温度场计算设计的几何区域及边界示意图
No. u v k ε T
u=0 v=0 ?k?x=0 Boundary node value calculated with k Tm*
u=0 v=0 ?k?r=0 Boundary node value calculated with k Tm*
u=0 ?v?x=0 ?k?x=0 ?ε?x=0 Radiation boundary
u=0 v=0 ?k?r=0 Boundary node value calculated with k Ts*
u=0 - - - -
u=0 v=0 ?k?x=0 Boundary node value calculated with k -
- - - - Tb,1
- - - - Tb,2
?u?r=0 v=0 ?k?r=0 ?ε?r=0 ?T?r=0
表2  图2中传输方程计算的边界条件
图3  计算的磁场强度幅值和电流密度分布
图4  计算的Joule焦耳热和电磁力分布
图5  不同熔速条件下模拟的流场、温度及液相体积分数分布
图6  随熔速变化的熔池深度、糊状区间距以及渣池最高温度的模拟结果
图7  模型计算的实验条件下ESR全程的流场、温度及液相体积分数分布变化
图8  随铸锭高度变化的熔池深度、糊状区间距以及渣池最高温度的模拟结果
图9  铸锭沿轴向剖面的熔池形状分析照片
图10  模型计算的二次枝晶臂间距在铸锭的分布
图11  铸锭剖面的枝晶组织形貌
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