铝电解槽多物理场数学建模及应用研究
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摘要
铝电解槽是炼铝的核心设备,其发展与进步代表了电解铝工艺的革新。多物理场在铝电解槽内产生、演变并相互作用,影响铝电解生产的能耗、效率、槽寿命等技术经济指标。因此,建立可靠、灵活、易用的铝电解槽多场耦合仿真模型对开发高效率、高产率、低能耗与长寿命的先进槽型具有重要意义。
铝电解槽的多场耦合仿真计算非常复杂。铝电解槽内外分布着形状各异的几十种媒质材料,这使得数值计算的前期准备工作如网格剖分、边界条件施加等非常繁杂。单个物理场或耦合场求解的实施步骤难易程度不同,耦合关系、接触现象、磁场开域及收敛性等问题进一步增加了计算的难度。
本文以铝电解槽内电、磁、热、流、力五个物理场为对象,在使用少量假设条件、合理分割场域、多场共享模型信息和结果的前提下,建立起了较为完整的铝电解槽多物理场仿真模型。在大型预焙槽、特大型预焙槽及导流槽等不同槽型上应用该模型进行了各种仿真研究。
论文主要创新点如下:
(1)从降低方法误差的角度出发,把接触方程引入至电磁场模型,消除水平电流及垂直磁场计算误差;建立了槽内导体与复杂母线系统组成的多槽电磁场模型及母线磁场转换模型。研究表明,接触模型的运用使电力线分布更平缓,水平电流明显降低;在电场分布较均匀的情况下降低垂直磁场计算误差的幅度较小,但在电场分布不均的情况下降低垂直磁场计算误差达0.6 mT;无论电场分布是否均匀,与单一面积常数母线模型相比,考虑母线截面变化可降低垂直磁场计算误差0.3～0.4 mT。
(2)基于VOF自由面跟踪法和自定义的电磁力离散插值函数建立了单一求解域内的电解质—铝液两相流模型,并进行稳态流场的求解。研究表明,在2 000～3 000次迭代后流场计算的最大残差水平低于1×10~(-4)。在河南某电解铝厂350 kA槽上进行了电—磁—流场模型的验证,结果说明了仿真模型的可行性和准确性。
(3)以现代大面进电铝电解槽为对象,深入研究了槽内导体及母线配置对电、磁、流场分布的影响,总结了磁场分布特征、母线设计思路,获得了场量分布的协调一致性规律,即电场分布越均匀,磁场分布亦越均匀,界面变形越小。
(4)针对垂直磁场数据多、分布离散的特点,建立了正交最小二乘法曲面拟合函数,突破了常量或线性函数给波动稳定性分析造成的应用局限,同时提高了计算精度。将不同长宽比下的磁场计算结果耦合到波动方程中,计算得到了槽稳定性随长宽比的变化趋势。研究表明,槽内导体产生的磁场分布规律相似,数值随长宽比增加而减小,从而槽子稳定性变好;附加母线产生的磁场后,槽子稳定性变差。
(5)开发了瞬态焙烧启动热场与应力场模型,对河南某电解铝试验厂300 kA槽上进行了热场及应力场计算。研究表明,设计的非均匀电阻率焦粒层铺设方法分别使内衬温差降低8.0%～30.0%、升温速度降低4.5%～12.5%,从而有效避免早期槽破损;根据线弹性理论,在热膨胀阶段采用半石墨质炭块时槽体位移与热应力最大,采用石墨化炭块时最小,而在随后30 d的热钠膨胀阶段,采用无烟煤炭块时槽体位移与应力最大,采用石墨化炭块时电解槽应力最小。
(6)针对导流槽和特大型槽开发必须解决的热平衡和磁场分布优化设计问题,获得了一种维持良好热平衡的导流槽结构与工艺方案,以及一种垂直磁场在3.5 mT以下的特大型槽及母线结构方案。
Aluminum reduction cell is the core equipment for industrial electrowinning of aluminum. Its developments and advancements represent up-to-date improvements of aluminum reduction technologies. In aluminum reduction cells multiple physical fields take place, develop and interact with each other inside the cell and affect economic indexes e.g. energy consumption, current efficiency and pot life time during production. Therefore to build up the liable, versatile and easy-to-use multiple physical coupled simulation models are of great significance to develop advanced reduction cells with higher current efficiency, higher labor productivity, lower energy cost and longer pot life.
The coupled simulations of aluminum reduction cells are very complicated. That tens of media materials with different shapes distribute inside and outside the cell makes some preparation work for numerical calculation so complex including grid meshing, boundary conditions applying and etc. Solution procedures or difficulties for individual field or coupled fields are quite different. Some problems such as coupled relations, contact phenomena, magnetic open boundary and convergence are much difficult to deal with.
The paper focuses on five physical fields in the aluminum reduction cell, which are the electric, magnetic, thermal, flow and stress fields respectively. The integrated simulation models for the multiple physical fields were set up based on less boundary condition, reasonable partitions of field domains and shared model data and result data between different physical fields. These models were employed in simulation researches on large-scale, super-scale and drained cells.
The main achievements are summarized as follows:
(1) From the point of view to decrease method errors, contact equations were incorporated into the electro-magnetic model to eliminate calculation errors of the horizontal current and vertical magnetic component. The multi-cell model including inside inductors and outside busbar circuits and the electro-to-magnetic transfer model for busbar circuits were built up. Results indicate that using the contact model makes electric fluxes distributed smoothly and horizontal current decreased greatly. With the use of contact equations calculation error of vertical magnetic component was decreased to a less extent for the case with the uniform distributions of the electric field, but by 0.6 mT for the case with the nonuniform distributions of the electric field. The changeable cross-section busbar model makes calculation error decreased by 0.3-0.4 mT than the constant one no matter how the electric field distributes.
(2) The single-domain electrolyte-aluminum two phase flow model was built up based on Volume of Fluid (VOF) interface tracking and user-defined interpolation functions for discrete electromagnetic forces to simulate the static flow filed. The model was observed to achieve convergence with the maximum residual level less than 1×10~(-4) after 2 000-3 000 iterations. The electro-magneto-flow model was applied on the 350 kA prebake cell of one plant located at Henan and well validated for feasibility and accuracy.
(3) As the modern prebake anode cell with side risers is concerned, impacts of inside conductors and outside busbars on distributions of the electric, magnetic and flow field were systematically studied. Characteristics of the magnetic distribution and methods to design busbar were summarized. The general relation was obtained that the distribution of one field coordinates with those of other fields. Namely if electric field distributes more smoothly, so does the magnetic field. The electrolyte-aluminum interface distortion also becomes much flatter.
(4) Surface fitting function based on orthogonal least square method was established to deal with thousands of discrete data of magnetic vertical component from the magnetic model. This function can make a breakthrough of the limits of the constant or linear expression in the wave stability analysis and improve accuracy. Magnetic results under a range of aspect ratio of pots were calculated and imported into the MHD model to find out how instability varies with the aspect ratio. The results show that magnetic fields distribute similarly for the cells with different aspect ratios and reduce with increasing aspect ratio, which therefore cause the pots more stable. Instability analysis also show that total magnetic field after appended by busbar circuits makes the pots become less stable.
(5) The transient heating-up thermal and stress models during bake-out and start-up periods were developed. They were used on 300 kA pot at one pilot smelter in Henan. It is found that the designed coke bed laying method with non-uniform resistivity reduces temperature difference by 8.0%-30.0% and heating-up rate by 4.5%-12.5% respectively in the lining, and decreases the risk of early failure of the cell effectively. Suppose all materials are linear elastic, pot displacement and thermal stress are the largest with semi-graphitic blocks as cathodes and the smallest with graphitized blocks as cathodes respectively at the end of the bake-out. Howerer after 30 d thermal and sodium expansion stage displacement and stress become largest with anthracitic blocks and smallest with graphitized blocks respectively.
(6) As required by the drained reduction cell and the super-scale reduction cell fundamental design issues are to keep thermal balance and design optimized magnetic field. One reasonable technical and structure scheme with good thermal balance for drained cells, and one structure and busbar design configuration with vertical magnetic component under 3.5 mT for super-scale cells were found out finally.
铝电解槽的多场耦合仿真计算非常复杂。铝电解槽内外分布着形状各异的几十种媒质材料,这使得数值计算的前期准备工作如网格剖分、边界条件施加等非常繁杂。单个物理场或耦合场求解的实施步骤难易程度不同,耦合关系、接触现象、磁场开域及收敛性等问题进一步增加了计算的难度。
本文以铝电解槽内电、磁、热、流、力五个物理场为对象,在使用少量假设条件、合理分割场域、多场共享模型信息和结果的前提下,建立起了较为完整的铝电解槽多物理场仿真模型。在大型预焙槽、特大型预焙槽及导流槽等不同槽型上应用该模型进行了各种仿真研究。
论文主要创新点如下:
(1)从降低方法误差的角度出发,把接触方程引入至电磁场模型,消除水平电流及垂直磁场计算误差;建立了槽内导体与复杂母线系统组成的多槽电磁场模型及母线磁场转换模型。研究表明,接触模型的运用使电力线分布更平缓,水平电流明显降低;在电场分布较均匀的情况下降低垂直磁场计算误差的幅度较小,但在电场分布不均的情况下降低垂直磁场计算误差达0.6 mT;无论电场分布是否均匀,与单一面积常数母线模型相比,考虑母线截面变化可降低垂直磁场计算误差0.3～0.4 mT。
(2)基于VOF自由面跟踪法和自定义的电磁力离散插值函数建立了单一求解域内的电解质—铝液两相流模型,并进行稳态流场的求解。研究表明,在2 000～3 000次迭代后流场计算的最大残差水平低于1×10~(-4)。在河南某电解铝厂350 kA槽上进行了电—磁—流场模型的验证,结果说明了仿真模型的可行性和准确性。
(3)以现代大面进电铝电解槽为对象,深入研究了槽内导体及母线配置对电、磁、流场分布的影响,总结了磁场分布特征、母线设计思路,获得了场量分布的协调一致性规律,即电场分布越均匀,磁场分布亦越均匀,界面变形越小。
(4)针对垂直磁场数据多、分布离散的特点,建立了正交最小二乘法曲面拟合函数,突破了常量或线性函数给波动稳定性分析造成的应用局限,同时提高了计算精度。将不同长宽比下的磁场计算结果耦合到波动方程中,计算得到了槽稳定性随长宽比的变化趋势。研究表明,槽内导体产生的磁场分布规律相似,数值随长宽比增加而减小,从而槽子稳定性变好;附加母线产生的磁场后,槽子稳定性变差。
(5)开发了瞬态焙烧启动热场与应力场模型,对河南某电解铝试验厂300 kA槽上进行了热场及应力场计算。研究表明,设计的非均匀电阻率焦粒层铺设方法分别使内衬温差降低8.0%～30.0%、升温速度降低4.5%～12.5%,从而有效避免早期槽破损;根据线弹性理论,在热膨胀阶段采用半石墨质炭块时槽体位移与热应力最大,采用石墨化炭块时最小,而在随后30 d的热钠膨胀阶段,采用无烟煤炭块时槽体位移与应力最大,采用石墨化炭块时电解槽应力最小。
(6)针对导流槽和特大型槽开发必须解决的热平衡和磁场分布优化设计问题,获得了一种维持良好热平衡的导流槽结构与工艺方案,以及一种垂直磁场在3.5 mT以下的特大型槽及母线结构方案。
Aluminum reduction cell is the core equipment for industrial electrowinning of aluminum. Its developments and advancements represent up-to-date improvements of aluminum reduction technologies. In aluminum reduction cells multiple physical fields take place, develop and interact with each other inside the cell and affect economic indexes e.g. energy consumption, current efficiency and pot life time during production. Therefore to build up the liable, versatile and easy-to-use multiple physical coupled simulation models are of great significance to develop advanced reduction cells with higher current efficiency, higher labor productivity, lower energy cost and longer pot life.
The coupled simulations of aluminum reduction cells are very complicated. That tens of media materials with different shapes distribute inside and outside the cell makes some preparation work for numerical calculation so complex including grid meshing, boundary conditions applying and etc. Solution procedures or difficulties for individual field or coupled fields are quite different. Some problems such as coupled relations, contact phenomena, magnetic open boundary and convergence are much difficult to deal with.
The paper focuses on five physical fields in the aluminum reduction cell, which are the electric, magnetic, thermal, flow and stress fields respectively. The integrated simulation models for the multiple physical fields were set up based on less boundary condition, reasonable partitions of field domains and shared model data and result data between different physical fields. These models were employed in simulation researches on large-scale, super-scale and drained cells.
The main achievements are summarized as follows:
(1) From the point of view to decrease method errors, contact equations were incorporated into the electro-magnetic model to eliminate calculation errors of the horizontal current and vertical magnetic component. The multi-cell model including inside inductors and outside busbar circuits and the electro-to-magnetic transfer model for busbar circuits were built up. Results indicate that using the contact model makes electric fluxes distributed smoothly and horizontal current decreased greatly. With the use of contact equations calculation error of vertical magnetic component was decreased to a less extent for the case with the uniform distributions of the electric field, but by 0.6 mT for the case with the nonuniform distributions of the electric field. The changeable cross-section busbar model makes calculation error decreased by 0.3-0.4 mT than the constant one no matter how the electric field distributes.
(2) The single-domain electrolyte-aluminum two phase flow model was built up based on Volume of Fluid (VOF) interface tracking and user-defined interpolation functions for discrete electromagnetic forces to simulate the static flow filed. The model was observed to achieve convergence with the maximum residual level less than 1×10~(-4) after 2 000-3 000 iterations. The electro-magneto-flow model was applied on the 350 kA prebake cell of one plant located at Henan and well validated for feasibility and accuracy.
(3) As the modern prebake anode cell with side risers is concerned, impacts of inside conductors and outside busbars on distributions of the electric, magnetic and flow field were systematically studied. Characteristics of the magnetic distribution and methods to design busbar were summarized. The general relation was obtained that the distribution of one field coordinates with those of other fields. Namely if electric field distributes more smoothly, so does the magnetic field. The electrolyte-aluminum interface distortion also becomes much flatter.
(4) Surface fitting function based on orthogonal least square method was established to deal with thousands of discrete data of magnetic vertical component from the magnetic model. This function can make a breakthrough of the limits of the constant or linear expression in the wave stability analysis and improve accuracy. Magnetic results under a range of aspect ratio of pots were calculated and imported into the MHD model to find out how instability varies with the aspect ratio. The results show that magnetic fields distribute similarly for the cells with different aspect ratios and reduce with increasing aspect ratio, which therefore cause the pots more stable. Instability analysis also show that total magnetic field after appended by busbar circuits makes the pots become less stable.
(5) The transient heating-up thermal and stress models during bake-out and start-up periods were developed. They were used on 300 kA pot at one pilot smelter in Henan. It is found that the designed coke bed laying method with non-uniform resistivity reduces temperature difference by 8.0%-30.0% and heating-up rate by 4.5%-12.5% respectively in the lining, and decreases the risk of early failure of the cell effectively. Suppose all materials are linear elastic, pot displacement and thermal stress are the largest with semi-graphitic blocks as cathodes and the smallest with graphitized blocks as cathodes respectively at the end of the bake-out. Howerer after 30 d thermal and sodium expansion stage displacement and stress become largest with anthracitic blocks and smallest with graphitized blocks respectively.
(6) As required by the drained reduction cell and the super-scale reduction cell fundamental design issues are to keep thermal balance and design optimized magnetic field. One reasonable technical and structure scheme with good thermal balance for drained cells, and one structure and busbar design configuration with vertical magnetic component under 3.5 mT for super-scale cells were found out finally.
引文
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