冶金熔体中夹杂物一般动力学的理论研究及其应用
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摘要
夹杂物的动力学一直是一个引起广泛兴趣的研究课题，其涉及的内容很广，基本的物理过程大致包括：形核、生长、聚合、传递等，夹杂物去除可以视为传递过程的结果。弄清冶金熔体中夹杂物动力学的一般规律，开展夹杂物去除技术的基础和应用研究，对于纯净钢生产、提高冶金企业的技术水平和市场竞争力具有重要的理论意义和现实意义。
本文第一部分，对夹杂物动力学的若干方面进行了理论和实验研究。
采用聚苯乙烯颗粒，对夹杂物颗粒运动阻力的形状修正系数进行了水模型实验。发现，在相同体积下，不同颗粒的形状修正系数的大小满足如下规律：棒状颗粒沿长轴方向＜球形颗粒＜十字形颗粒沿平面方向＜簇状颗粒＜十字形颗粒沿平面的法向＜棒状颗粒沿横向；一般地，夹杂物的形状修正系数，可取1.5～2.8。
对夹杂物在冶金容器壁面上吸附的稳定性进行了力学分析，结合已有的实验结果，提出了夹杂物吸附效率的一个预测关系，进而给出了夹杂物的壁面传质系数。结果表明，传质系数是流体壁面剪力的函数，随着壁面剪力的增大，传质系数呈现先增后减的规律，在某个临界剪力出现极大值，这个临界剪力大约是使夹杂物颗粒在壁面发生滚动的临界剪力的5倍。
对夹杂物生长的两种主要形式“扩散长大”和“碰撞聚合”，进行适当的物理简化和数学建模，推导了夹杂物生长速率的解析关系，建立了夹杂物生长的动力学理论。本文获得的扩散长大率，得到前人实验结果的检验。理论分析显示，夹杂物的早期生长依赖于扩散长大和布朗运动碰撞，前者作用是主要的，后期生长依赖于湍流碰撞和Stokes碰撞，湍流碰撞占主导地位。在冶炼过程，碰撞聚合比较迅速，而在连铸过程，碰撞聚合作用并不明显，精炼过程则处于一个过渡状况。对夹杂物碰撞聚合的微观形态进行了Monte-Carlo模拟，结果与文献报道的实验观察一致。尝试用分形理论解释夹杂物的凝聚结构，发现夹杂物的分形维数约等于2.25。
基于上述研究，把形核、生长、聚合和传递等基本物理过程耦合在一起，建立了一个有普适性的夹杂物通用动力学模型，为深入研究冶金反应器中夹杂物的动力学行为奠定了基础。
论文第二部分，基于前面的研究，在Euler(流场)-Lagrange(颗粒运动)框架
上海大学博士学位论文
下，提出了一个夹杂物运动、聚合和去除祸合的统计模型。应用这个模型，对某
工业中间包中夹杂物的传递和去除进行了数学模拟。结果发现，通过浮力上浮，
是中间包中夹杂物去除的主要方式，壁面吸附、碰撞聚合增进了夹杂物的去除效
果。半径10卿、20“m、30林m夹杂物的总去除效率接近20%、42%和75%，其
中壁面吸附的贡献占1/6一1/4。碰撞长大对夹杂物去除的贡献<5%，表明中间包
中夹杂物的碰撞长大并不显著，这个结论与传统的观点明显不同。
论文第三部分，基于前面的研究，对新型金属液纯净技术—单电流电磁
分离夹杂物技术进行了系统的理论和实验研究，以期提供了一种经济、实用的钢
液净化手段。
解析了直流和交流激励下，金属液在圆管、扁平管中的磁场分布，提出了相
对电磁浮力、净化效率、净化时间的概念和理论关系，建立了单电流电磁分离夹
杂物技术的基本框架。理论分析和数值计算表明，工频交流电产生的电磁力分布
逼近直流电，使用直流电看上去没有必要;夹杂物的电磁净化效率是电流密度、
颗粒半径及其在分离管中停留时间的函数，圆管和扁管的净化效率接近;矩形电
磁净化管会在截面诱发二次流，二次流的出现扰乱了夹杂物的正常迁移，延滞了
颗粒的迁移时间，对夹杂物的去除不利。
利用AI一22%si和Al一5%Mg一2%Sic合金，采用工频电流进行了电磁分离夹
杂物的静态实验。结果发现，通电305、电流密度保持4x106刀衬，初晶si在
各种管道中都能完全偏聚，而半径大于50林m的siC颗粒，完全偏聚只要不到105
的时间，SIC颗粒的偏聚比初晶Si快。电磁分离技术可望移植到表面增强梯度功
能材料具的制备，从而提供一种经济、实用的新方法。
利用AI一8%Mg一2%A12O3合金，采用工频电流进行了电磁分离夹杂物的连续
实验。结果发现，在铝液流速2.3一2.9。而s，电流密度0.8一1 .4 xl护刀mZ的条件
下，出口温度比入口温度提高了15一25℃，加热效果可以满足对金属液加热的需
要。通电密度1.4x 107 A/mZ，金属液在管道中的停留时间保持105，A1203颗粒
的去除效率可达95%。在净化处理后的铝液中，发现大于20林m的夹杂物都能成
功去除。实验结果与理论预测基本吻合。
论文第最后部分，研究了材料电磁制备过程中，晶粒磁取向的微观机制，提
出了晶粒取向的一个动力学模型，获得了取向时间的一个分析解。对Bi一3%合金，
在300℃下和已3T的磁场中进行了淬火实验，得到了有取向的BIMn织构。发现
铁磁性的BIMn晶粒的磁取向时间小于l秒，与理论预测吻合。在BIMn织构的
形成过程中，取向不是控制性环节。
With the increasing demands for the quality of steel product, much attention has been drawn to the production of pure steel in metallurgical enterprises throughout the world. It is key to how to control the level of impurity, especially the inclusion, which mainly responsible for the defect of most steel products. Therefore, it is of significance to investigate the law of dynamics, such as growth, transfer and removal of inclusions in molten melts, and further improve the conventional process or develop new techniques regarding pure steel.
The paper is divided into four parts. In the first part, the experimental and theoretical studies are carried out from several aspects involving the dynamics of inclusions as follows:
The modification coefficients of motion resistance, Cs, of inclusion particles of different shape to the ideal spherical particle are measured by model experiments using polystyrene particle of radius 1-2.6mm. It is found that the order of increasing Cs is the rod-like particle oriented its long axis, the spherical particle, the flake-like particle oriented its plane, the cluster-type particle, the flake-like particle oriented the normal to its plane, and the rod-like particles oriented its radial axis. Commonly, Cs=1.5-2.8 for real inclusion particles.
The mechanical condition that an inclusion adheres stably to the rough wall of vessel exposed to a shear flow is analyzed theoretically, then a relationship of the adhesion efficiency is formulated, and the mass transfer coefficient, , of inclusion to the wall due to turbulence fluctuation and field force effect is obtained which is the function of wall friction force of fluid. It indicates that there exists a peak for the mass transfer coefficient over the wall friction force, and in most cases, the turbulence promotes the transfer of inclusion to wall.
A theory on inclusion growth of single particle in molten melts is developed. Two main growth modes, diffusion-reaction-precipitation and collision-coalescence, of inclusion are simplified physically and modeled mathematically, and some analytic
solutions or relationships for the growth rate of inclusion are derived, which give an general physical picture of inclusion growth. The theoretical growth rate of diffusion is supported by the experimental results early reported by Japanese scholar. This theory shows that the early growth of inclusion depends on diffusion-reaction-precipitation and Braunian motion collision, and the former is decisive, while the latter growth depends on turbulence shear collision and Stokes' collision, and the former is dominant; The collision and coalescence proceeds quickly during smelting process, and is negligible in continuous casting process, moreover, a transition state exists in the refining process. Further, the micro- structure of inclusion aggregate is simulated by methods of Monte-Carlo, the resultant aggregates agree with the cluster inclusions reported in literatures. The Fractal theory is introduced to interpret the structure of the aggregate, the simulation shows that the cluster inclusion has a Fractal dimension of 2.25.
Based on above studies, a general dynamic model of inclusion coupling the nucleation, growth, coalescence and transfer has been developed firstly, which is expected to lay a foundation to further investigate widely and profoundly the basic behavior of inclusion in metallurgical vessels.
In the second part, foregoing theory has been utilized to build a comprehensive mathematical model within the Lagrangian framework to study the transport of inclusion in some continuous casting tundish. The results demonstrate that the floatout by buoyancy is the main path of removal of inclusion, and the coalescence and adhesion to wall provide a secondary aid. In present tundish, a removal efficiency of 20%-75% can be obtained for inclusion of radius from 10m to 30m. The coalescence helps the removal of inclusion, but seems not notable, restricted by the practical condition of tundish.
In the third part, as another application, the only-by-current ele
本文第一部分，对夹杂物动力学的若干方面进行了理论和实验研究。
采用聚苯乙烯颗粒，对夹杂物颗粒运动阻力的形状修正系数进行了水模型实验。发现，在相同体积下，不同颗粒的形状修正系数的大小满足如下规律：棒状颗粒沿长轴方向＜球形颗粒＜十字形颗粒沿平面方向＜簇状颗粒＜十字形颗粒沿平面的法向＜棒状颗粒沿横向；一般地，夹杂物的形状修正系数，可取1.5～2.8。
对夹杂物在冶金容器壁面上吸附的稳定性进行了力学分析，结合已有的实验结果，提出了夹杂物吸附效率的一个预测关系，进而给出了夹杂物的壁面传质系数。结果表明，传质系数是流体壁面剪力的函数，随着壁面剪力的增大，传质系数呈现先增后减的规律，在某个临界剪力出现极大值，这个临界剪力大约是使夹杂物颗粒在壁面发生滚动的临界剪力的5倍。
对夹杂物生长的两种主要形式“扩散长大”和“碰撞聚合”，进行适当的物理简化和数学建模，推导了夹杂物生长速率的解析关系，建立了夹杂物生长的动力学理论。本文获得的扩散长大率，得到前人实验结果的检验。理论分析显示，夹杂物的早期生长依赖于扩散长大和布朗运动碰撞，前者作用是主要的，后期生长依赖于湍流碰撞和Stokes碰撞，湍流碰撞占主导地位。在冶炼过程，碰撞聚合比较迅速，而在连铸过程，碰撞聚合作用并不明显，精炼过程则处于一个过渡状况。对夹杂物碰撞聚合的微观形态进行了Monte-Carlo模拟，结果与文献报道的实验观察一致。尝试用分形理论解释夹杂物的凝聚结构，发现夹杂物的分形维数约等于2.25。
基于上述研究，把形核、生长、聚合和传递等基本物理过程耦合在一起，建立了一个有普适性的夹杂物通用动力学模型，为深入研究冶金反应器中夹杂物的动力学行为奠定了基础。
论文第二部分，基于前面的研究，在Euler(流场)-Lagrange(颗粒运动)框架
上海大学博士学位论文
下，提出了一个夹杂物运动、聚合和去除祸合的统计模型。应用这个模型，对某
工业中间包中夹杂物的传递和去除进行了数学模拟。结果发现，通过浮力上浮，
是中间包中夹杂物去除的主要方式，壁面吸附、碰撞聚合增进了夹杂物的去除效
果。半径10卿、20“m、30林m夹杂物的总去除效率接近20%、42%和75%，其
中壁面吸附的贡献占1/6一1/4。碰撞长大对夹杂物去除的贡献<5%，表明中间包
中夹杂物的碰撞长大并不显著，这个结论与传统的观点明显不同。
论文第三部分，基于前面的研究，对新型金属液纯净技术—单电流电磁
分离夹杂物技术进行了系统的理论和实验研究，以期提供了一种经济、实用的钢
液净化手段。
解析了直流和交流激励下，金属液在圆管、扁平管中的磁场分布，提出了相
对电磁浮力、净化效率、净化时间的概念和理论关系，建立了单电流电磁分离夹
杂物技术的基本框架。理论分析和数值计算表明，工频交流电产生的电磁力分布
逼近直流电，使用直流电看上去没有必要;夹杂物的电磁净化效率是电流密度、
颗粒半径及其在分离管中停留时间的函数，圆管和扁管的净化效率接近;矩形电
磁净化管会在截面诱发二次流，二次流的出现扰乱了夹杂物的正常迁移，延滞了
颗粒的迁移时间，对夹杂物的去除不利。
利用AI一22%si和Al一5%Mg一2%Sic合金，采用工频电流进行了电磁分离夹
杂物的静态实验。结果发现，通电305、电流密度保持4x106刀衬，初晶si在
各种管道中都能完全偏聚，而半径大于50林m的siC颗粒，完全偏聚只要不到105
的时间，SIC颗粒的偏聚比初晶Si快。电磁分离技术可望移植到表面增强梯度功
能材料具的制备，从而提供一种经济、实用的新方法。
利用AI一8%Mg一2%A12O3合金，采用工频电流进行了电磁分离夹杂物的连续
实验。结果发现，在铝液流速2.3一2.9。而s，电流密度0.8一1 .4 xl护刀mZ的条件
下，出口温度比入口温度提高了15一25℃，加热效果可以满足对金属液加热的需
要。通电密度1.4x 107 A/mZ，金属液在管道中的停留时间保持105，A1203颗粒
的去除效率可达95%。在净化处理后的铝液中，发现大于20林m的夹杂物都能成
功去除。实验结果与理论预测基本吻合。
论文第最后部分，研究了材料电磁制备过程中，晶粒磁取向的微观机制，提
出了晶粒取向的一个动力学模型，获得了取向时间的一个分析解。对Bi一3%合金，
在300℃下和已3T的磁场中进行了淬火实验，得到了有取向的BIMn织构。发现
铁磁性的BIMn晶粒的磁取向时间小于l秒，与理论预测吻合。在BIMn织构的
形成过程中，取向不是控制性环节。
With the increasing demands for the quality of steel product, much attention has been drawn to the production of pure steel in metallurgical enterprises throughout the world. It is key to how to control the level of impurity, especially the inclusion, which mainly responsible for the defect of most steel products. Therefore, it is of significance to investigate the law of dynamics, such as growth, transfer and removal of inclusions in molten melts, and further improve the conventional process or develop new techniques regarding pure steel.
The paper is divided into four parts. In the first part, the experimental and theoretical studies are carried out from several aspects involving the dynamics of inclusions as follows:
The modification coefficients of motion resistance, Cs, of inclusion particles of different shape to the ideal spherical particle are measured by model experiments using polystyrene particle of radius 1-2.6mm. It is found that the order of increasing Cs is the rod-like particle oriented its long axis, the spherical particle, the flake-like particle oriented its plane, the cluster-type particle, the flake-like particle oriented the normal to its plane, and the rod-like particles oriented its radial axis. Commonly, Cs=1.5-2.8 for real inclusion particles.
The mechanical condition that an inclusion adheres stably to the rough wall of vessel exposed to a shear flow is analyzed theoretically, then a relationship of the adhesion efficiency is formulated, and the mass transfer coefficient, , of inclusion to the wall due to turbulence fluctuation and field force effect is obtained which is the function of wall friction force of fluid. It indicates that there exists a peak for the mass transfer coefficient over the wall friction force, and in most cases, the turbulence promotes the transfer of inclusion to wall.
A theory on inclusion growth of single particle in molten melts is developed. Two main growth modes, diffusion-reaction-precipitation and collision-coalescence, of inclusion are simplified physically and modeled mathematically, and some analytic
solutions or relationships for the growth rate of inclusion are derived, which give an general physical picture of inclusion growth. The theoretical growth rate of diffusion is supported by the experimental results early reported by Japanese scholar. This theory shows that the early growth of inclusion depends on diffusion-reaction-precipitation and Braunian motion collision, and the former is decisive, while the latter growth depends on turbulence shear collision and Stokes' collision, and the former is dominant; The collision and coalescence proceeds quickly during smelting process, and is negligible in continuous casting process, moreover, a transition state exists in the refining process. Further, the micro- structure of inclusion aggregate is simulated by methods of Monte-Carlo, the resultant aggregates agree with the cluster inclusions reported in literatures. The Fractal theory is introduced to interpret the structure of the aggregate, the simulation shows that the cluster inclusion has a Fractal dimension of 2.25.
Based on above studies, a general dynamic model of inclusion coupling the nucleation, growth, coalescence and transfer has been developed firstly, which is expected to lay a foundation to further investigate widely and profoundly the basic behavior of inclusion in metallurgical vessels.
In the second part, foregoing theory has been utilized to build a comprehensive mathematical model within the Lagrangian framework to study the transport of inclusion in some continuous casting tundish. The results demonstrate that the floatout by buoyancy is the main path of removal of inclusion, and the coalescence and adhesion to wall provide a secondary aid. In present tundish, a removal efficiency of 20%-75% can be obtained for inclusion of radius from 10m to 30m. The coalescence helps the removal of inclusion, but seems not notable, restricted by the practical condition of tundish.
In the third part, as another application, the only-by-current ele
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