方坯连铸宏观传输现象复合数值模拟的研究
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摘要
连铸钢液的凝固过程中伴随着液相流动、固相移动、固液相及两相区传热以及溶质传输等复杂的物理现象,它们是影响连铸生产的重要环节。采用计算机数值仿真技术对其加以研究,已成为研究连铸工艺和铸坯质量的重要手段。
本论文针对连铸过程中发生的各种宏观传输现象,首次提出了复合数值模拟研究方法。在拉坯方向上将整个铸机空间划分为两个独立的计算区域,即上部计算域和下部计算域,前者作为三维稳态流动、传热及溶质传输耦合数学模型的计算域空间,后者则作为二维非稳态凝固传热数学模型的计算域空间,在数值计算过程中对两者进行了有机地统一。通过整个铸机空间内的复合数值模拟,为二冷制度的合理设计提供了必要的理论依据和实现手段。该研究方法应用范围较广,不仅适用于方坯连铸,对于板坯、薄板坯连铸也同样适用。
在连铸二冷制度的设计中,考虑到中间包浇铸温度在实际连铸生产中的波动以及不同季节内二冷水温度的变化,提出了一种形式新颖的二次冷却控制模型框架。除通常的模型框架中所采用的拉坯速度外,还引入了两个新的控制变量,即:
在该模型框架中,为水量,为拉速,为过热度,、和为与拉速有关的系数,为与过热度有关的系数,为与二冷水温有关的系数。
采用热分析仪和高温热模拟机,分别测试了方坯试样的高温热物理性能和机械力学性能,并进行了扫描电镜分析,为数值仿真过程中相关热物理性质及冶金限制准则的合理确定提供了实验依据。另外,还测试了二冷喷嘴的冷态及热态性能,为二冷区传热边界条件的准确定义提供了必要的依据。
对影响宏观传输模型精度的三个最重要的钢种热物理性质(即密度、导热系数和溶质分配系数),采用了新的、考虑更为全面的取值方法。局部混合密度取为各相密度的调和平均值,详细考虑了各相密度随温度和溶质浓度的变化关系;局部有效导热系数取为串联型和并联型导热系数的算术平均值,通过引入对流影响系数来描述了流动对传热的影响效果;对于二元合金,溶质分配系数在平衡凝固条件下由二元相图直接读取,在非平衡凝固条件下则取为与温度有关的值。
根据典型微观凝固单元体内的溶质质量守恒,并经严格的推导,建立了二元包晶/共晶合金微观偏析半解析数学模型。模型中,详细考虑了反向扩散和粗化对液相浓度的稀释效果。对于Q235钢,该微观偏析模型的求解过程相当繁琐、费时。本文首次按两种不同模式(对应于包晶点前后的两个凝固温度区间)对凝固路径进行了回归分析,为宏观传输模型中非平衡凝固路径的确定提供了理论根据。
在复合数值模拟研究中,首先基于单区域连续介质理论和固定网格方法,建立了方坯连铸凝固过程三维稳态钢液流动、凝固传热及溶质传输耦合数学模型;
然后基于有限厚度薄片层思想和微观单元体的进出热量平衡关系,建立了方坯连铸过程二维非稳态传热模型。在三维耦合模型中,依据临界固相分数将两相区分别视为非牛顿半固相流体和多孔介质,在等轴晶区和柱状晶区分别采用各向同性和各向异性渗透率来描述多孔介质的渗透特性,在能量方程中首次考虑了速度粘性耗散项;在二维传热模型中,没有耦合钢液流动和溶质传输的计算,而是根据浇铸温度、拉坯距离和局部固相分数来近似描述了钢液流动对传热的影响效果。
综合应用三维耦合模型和二维传热模型,针对涟钢1号方坯铸机进行了复合数值模拟研究,获得了优化的二冷控制模型以及铸坯相应的流场、温度场和溶质浓度场。仿真结果表明:入流钢液形成向上和向下两个流股,随着拉坯距离的增加,钢液流股由强烈的湍流形式逐渐演变成充分发展的平推型流动;拉坯方向上,铸坯表面温度的总体波动相对较小,表面温度范围及其变化速率均满足冶金限制准则的要求;铸坯断面上会发生溶质元素的宏观偏析,中心偏析程度随着拉坯距离和拉速的增加而相应增大。另外为便于对比分析,还应用单纯的二维传热模型对整个连铸过程进行了数值仿真运算。结合已有的实际生产数据可知,复合数值模拟方法较之单纯二维模拟方法,具有更好的仿真精度和实用价值。
相关的仿真研究成果已经应用于涟钢的实际生产中。从铸机改造后的生产状况来看,铸坯质量得到了明显的改善,铸机拉速有了显著提高,其最高拉速在3.8~4.0m/min左右,连铸生产稳定,在投产后的四个月内获得的经济总效益相对头年同期为750余万元。生产数据表明,连铸机的二冷优化改造取得了非常可观的经济效益,达到了改造的预期目的。说明本文在进行二冷优化设计和连铸过程仿真时,所采用的复合数值模拟方法具有较好的合理性和实用性。
综上所述,本文所建立的复合数值模拟研究方法,兼顾了两种数学模型的优势,既可充分地保证数值仿真运算的精度,又可大幅度降低仿真运算的成本,促进了仿真精度和计算成本的有机统一。该研究方法适用于各种连铸工艺的过程仿真及二冷设计,具有较高的理论及实用价值。
Solidification process of continuous casting (CC) steel liquid involves complex physical phenomena, such as liquid flow, solid movement, heat transfer in solid phase, liquid phase & mushy zone and solute transport, etc., which are important influencing factors for CC process. It has become a significant research instrument on CC process and slab quality to make study on the mentioned solidification process based on numerical simulation techniques.
A hybrid numerical simulation approach has been put forward firstly in this thesis, according to the various macro-transport phenomena in CC process, in which, the whole length of caster is divided into two independent calculation domains along withdrawing direction, viz., the upper domain which is specially for the 3-D steady conjugated flow, heat transfer & solute transport mathematical model of billet CC and the lower domain which is for the 2-D unsteady heat transfer mathematical model of billet CC, and there is an organic unity of them during numerical calculation. The necessary theoretical foundation & implemental means have been provided for reasonable design of secondary cooling system, by the hybrid numerical simulation within range of whole length of caster. This method can be used in a wide range, which adapts not only to billet CC, but also to slab & thin slab CC.
By consideration of fluctuations of casting temperature in tundish in actual CC process and changes of temperature of secondary cooling water in different seasons, an original frame of secondary cooling control model has been developed for the design of secondary cooling system. Besides casting speed used in normal frame of control model, two new control variable have been imported into this new model frame, as described as below:
in which, refers to water flowrate, refers to casting speed, refers to superheat, , & are coefficients related to casting speed, is coefficient related to superheat, is coefficient related to temperature of cooling water.
Thermal physical properties and mechanical properties of the billet samples have been measured by thermo-analyzer and thermo-simulator respectively, and scanning electron microscope analysis has also been executed for the samples, which provide the experimental gists for reasonable determining of thermo-physical properties and
metallurgical rules in numerical simulation, In addition, the normal temperature performance and high temperature performance of the spraying nozzles have been tested to provide the necessary basis for accurate defining of heat transfer conditions in secondary cooling zone.
Three thermo-physical properties, which are most important for accuracy of macroscale transport model, have been determined by new & more considerate methods, which include density, thermal conductivity and solute partition coefficient. Local mixing density is set to be the harmonic average of density of each phase, in which, evolution of phase density with temperature & solute concentration has been considered detailedly. Local effective thermal conductivity equals to the arithmetic average of series-wound thermal conductivity and shunt-wound thermal conductivity, in which a convection affecting coefficient is imported to depict the effect of steel liquid flow to heat transfer. For binary alloy system, in condition of equilibrium solidification, solute partition coefficient is decided directly from phase diagram, but in nonequilibrium condition, it’s changing with temperature.
A semi-analytic microsegreation mathematical model for binary peritectic/eutectic alloy system has been erected by strict derivation, in terms of mass balance pricinple of solute in the typical micro-solidification volume element, in which, the dilution effects of back diffusion & coarsening to solute concentration in liquid phase have been considered detailedly. For Q235 carbon steel, numerical solution of the microsegregation model will be very difficult and take a long time. A regressive analysis has been executed firstly according to two different modes (
本论文针对连铸过程中发生的各种宏观传输现象,首次提出了复合数值模拟研究方法。在拉坯方向上将整个铸机空间划分为两个独立的计算区域,即上部计算域和下部计算域,前者作为三维稳态流动、传热及溶质传输耦合数学模型的计算域空间,后者则作为二维非稳态凝固传热数学模型的计算域空间,在数值计算过程中对两者进行了有机地统一。通过整个铸机空间内的复合数值模拟,为二冷制度的合理设计提供了必要的理论依据和实现手段。该研究方法应用范围较广,不仅适用于方坯连铸,对于板坯、薄板坯连铸也同样适用。
在连铸二冷制度的设计中,考虑到中间包浇铸温度在实际连铸生产中的波动以及不同季节内二冷水温度的变化,提出了一种形式新颖的二次冷却控制模型框架。除通常的模型框架中所采用的拉坯速度外,还引入了两个新的控制变量,即:
在该模型框架中,为水量,为拉速,为过热度,、和为与拉速有关的系数,为与过热度有关的系数,为与二冷水温有关的系数。
采用热分析仪和高温热模拟机,分别测试了方坯试样的高温热物理性能和机械力学性能,并进行了扫描电镜分析,为数值仿真过程中相关热物理性质及冶金限制准则的合理确定提供了实验依据。另外,还测试了二冷喷嘴的冷态及热态性能,为二冷区传热边界条件的准确定义提供了必要的依据。
对影响宏观传输模型精度的三个最重要的钢种热物理性质(即密度、导热系数和溶质分配系数),采用了新的、考虑更为全面的取值方法。局部混合密度取为各相密度的调和平均值,详细考虑了各相密度随温度和溶质浓度的变化关系;局部有效导热系数取为串联型和并联型导热系数的算术平均值,通过引入对流影响系数来描述了流动对传热的影响效果;对于二元合金,溶质分配系数在平衡凝固条件下由二元相图直接读取,在非平衡凝固条件下则取为与温度有关的值。
根据典型微观凝固单元体内的溶质质量守恒,并经严格的推导,建立了二元包晶/共晶合金微观偏析半解析数学模型。模型中,详细考虑了反向扩散和粗化对液相浓度的稀释效果。对于Q235钢,该微观偏析模型的求解过程相当繁琐、费时。本文首次按两种不同模式(对应于包晶点前后的两个凝固温度区间)对凝固路径进行了回归分析,为宏观传输模型中非平衡凝固路径的确定提供了理论根据。
在复合数值模拟研究中,首先基于单区域连续介质理论和固定网格方法,建立了方坯连铸凝固过程三维稳态钢液流动、凝固传热及溶质传输耦合数学模型;
然后基于有限厚度薄片层思想和微观单元体的进出热量平衡关系,建立了方坯连铸过程二维非稳态传热模型。在三维耦合模型中,依据临界固相分数将两相区分别视为非牛顿半固相流体和多孔介质,在等轴晶区和柱状晶区分别采用各向同性和各向异性渗透率来描述多孔介质的渗透特性,在能量方程中首次考虑了速度粘性耗散项;在二维传热模型中,没有耦合钢液流动和溶质传输的计算,而是根据浇铸温度、拉坯距离和局部固相分数来近似描述了钢液流动对传热的影响效果。
综合应用三维耦合模型和二维传热模型,针对涟钢1号方坯铸机进行了复合数值模拟研究,获得了优化的二冷控制模型以及铸坯相应的流场、温度场和溶质浓度场。仿真结果表明:入流钢液形成向上和向下两个流股,随着拉坯距离的增加,钢液流股由强烈的湍流形式逐渐演变成充分发展的平推型流动;拉坯方向上,铸坯表面温度的总体波动相对较小,表面温度范围及其变化速率均满足冶金限制准则的要求;铸坯断面上会发生溶质元素的宏观偏析,中心偏析程度随着拉坯距离和拉速的增加而相应增大。另外为便于对比分析,还应用单纯的二维传热模型对整个连铸过程进行了数值仿真运算。结合已有的实际生产数据可知,复合数值模拟方法较之单纯二维模拟方法,具有更好的仿真精度和实用价值。
相关的仿真研究成果已经应用于涟钢的实际生产中。从铸机改造后的生产状况来看,铸坯质量得到了明显的改善,铸机拉速有了显著提高,其最高拉速在3.8~4.0m/min左右,连铸生产稳定,在投产后的四个月内获得的经济总效益相对头年同期为750余万元。生产数据表明,连铸机的二冷优化改造取得了非常可观的经济效益,达到了改造的预期目的。说明本文在进行二冷优化设计和连铸过程仿真时,所采用的复合数值模拟方法具有较好的合理性和实用性。
综上所述,本文所建立的复合数值模拟研究方法,兼顾了两种数学模型的优势,既可充分地保证数值仿真运算的精度,又可大幅度降低仿真运算的成本,促进了仿真精度和计算成本的有机统一。该研究方法适用于各种连铸工艺的过程仿真及二冷设计,具有较高的理论及实用价值。
Solidification process of continuous casting (CC) steel liquid involves complex physical phenomena, such as liquid flow, solid movement, heat transfer in solid phase, liquid phase & mushy zone and solute transport, etc., which are important influencing factors for CC process. It has become a significant research instrument on CC process and slab quality to make study on the mentioned solidification process based on numerical simulation techniques.
A hybrid numerical simulation approach has been put forward firstly in this thesis, according to the various macro-transport phenomena in CC process, in which, the whole length of caster is divided into two independent calculation domains along withdrawing direction, viz., the upper domain which is specially for the 3-D steady conjugated flow, heat transfer & solute transport mathematical model of billet CC and the lower domain which is for the 2-D unsteady heat transfer mathematical model of billet CC, and there is an organic unity of them during numerical calculation. The necessary theoretical foundation & implemental means have been provided for reasonable design of secondary cooling system, by the hybrid numerical simulation within range of whole length of caster. This method can be used in a wide range, which adapts not only to billet CC, but also to slab & thin slab CC.
By consideration of fluctuations of casting temperature in tundish in actual CC process and changes of temperature of secondary cooling water in different seasons, an original frame of secondary cooling control model has been developed for the design of secondary cooling system. Besides casting speed used in normal frame of control model, two new control variable have been imported into this new model frame, as described as below:
in which, refers to water flowrate, refers to casting speed, refers to superheat, , & are coefficients related to casting speed, is coefficient related to superheat, is coefficient related to temperature of cooling water.
Thermal physical properties and mechanical properties of the billet samples have been measured by thermo-analyzer and thermo-simulator respectively, and scanning electron microscope analysis has also been executed for the samples, which provide the experimental gists for reasonable determining of thermo-physical properties and
metallurgical rules in numerical simulation, In addition, the normal temperature performance and high temperature performance of the spraying nozzles have been tested to provide the necessary basis for accurate defining of heat transfer conditions in secondary cooling zone.
Three thermo-physical properties, which are most important for accuracy of macroscale transport model, have been determined by new & more considerate methods, which include density, thermal conductivity and solute partition coefficient. Local mixing density is set to be the harmonic average of density of each phase, in which, evolution of phase density with temperature & solute concentration has been considered detailedly. Local effective thermal conductivity equals to the arithmetic average of series-wound thermal conductivity and shunt-wound thermal conductivity, in which a convection affecting coefficient is imported to depict the effect of steel liquid flow to heat transfer. For binary alloy system, in condition of equilibrium solidification, solute partition coefficient is decided directly from phase diagram, but in nonequilibrium condition, it’s changing with temperature.
A semi-analytic microsegreation mathematical model for binary peritectic/eutectic alloy system has been erected by strict derivation, in terms of mass balance pricinple of solute in the typical micro-solidification volume element, in which, the dilution effects of back diffusion & coarsening to solute concentration in liquid phase have been considered detailedly. For Q235 carbon steel, numerical solution of the microsegregation model will be very difficult and take a long time. A regressive analysis has been executed firstly according to two different modes (
引文
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