Numerical Simulation of the In-Mold Electromagnetic Stirring of Slabs in a Continuous Casting Process

本研究主要目的乃為利用計算流體軟體FIDAP，應用有限元素之數值方法，針對中國鋼鐵公司實際鑄造機器尺寸，探討含有電磁攪拌之連續鑄造扁鋼胚鑄模內流場及溫度場的數值解析。電磁攪拌主要目的在於減少鑄造缺陷，提升鋼胚品質。本研究針對含電磁攪拌之高紊流現象，則以高雷諾數的標準Κ-ε紊流模式進行模擬。 本研究對於具有相同管徑變化以及向下出口角度為5∘，15∘及25∘(分別為noz5d、noz15d and noz25d)三種注嘴設計進行注嘴內流場計算，並以其結果作為鑄模之入口條件。本研究探討無電磁攪拌設備、以及最大磁通量分別為0.13T以及0.07T之三種情況下，對應三種不同注嘴出口角度時，鋼液流場、溫度場及模液面性質之模擬結果。 本研究結果顯示：(1)在無電磁力作用下，撞擊點的位置隨著注嘴向下出口角度的增加而距模液面愈遠，模液面之鋼液平均速度為10cm/s，平均溫度為1528℃，平均波動振幅則為0.1mm。而noz15d之注嘴設計可產生較小的F值及較高的模液面平均溫度，是較佳的注嘴設計。(2)在電磁攪拌作用下，模液面之流場與溫度場均形成環流的分佈情形，三個注嘴出口角度下所得到撞擊點位置皆相同，平均為模液面下22.5公分，模液面之平均溫度較未加電磁力時低2~3℃。(3)當最大磁通量為0.13T時，模液面之最大鋼液流速增大八倍，平均波動振幅為10mm；當最大磁通量為0.07T時，模液面之最大鋼液流速增大四倍，平均波動振幅為2mm。(4)利用F值之分析，可知最大磁通量為0.13T及最大磁通量為0.07T兩條件下得到相似的結果，noz25d之設計可得到最小的F值，且具優良的對稱性，故在加入電磁攪拌設備後，向下25度之注嘴設計為較佳的選擇。A three-dimensional numerical simulation for the steel continuous casting process with the in-mold electromagnetic stirring (MEMS) of slabs was investigated using the commercial FIDAP code. Electromagnetic stirring is used to reduce the defects and to improve the quality of the final products. In this study, a simplified model for the electromagnetic force was used to simplify the electromagnetic force (EMF) problem. Three port angles for the SEN design and two intensities of magnetic forces were simulated. The results show that: (1) In EMS off operation, maximum velocities at the meniscus are all about 10cm/s while average fluctuation levels at the meniscus are about 0.1mm, and average temperatures at meniscus are about 1528℃. Furthermore, the case mold15d has smaller F-factor, lower impingement point, and higher average temperature at meniscus. The results show the mold with noz15d could be a better design. (2) In EMS on operation, the velocity profiles and temperature distribution are distinct from those without EMS. The impingement points have been lifted up to almost same position about 22~23cm below the meniscus at two narrow sides. Average temperature at meniscus is decreased by 2~3℃. It is seen that regular circulations of velocity pattern and temperature pattern at meniscus. Since the velocity at meniscus has increased, the temperature profiles at same narrow position became uniform. (3) For cases with 0.13T maximum magnetic density, the maximum velocity has increased by a factor 8 and average fluctuation level increased to be 10mm. For cases with 0.07T maximum magnetic density, the maximum velocity has increased by a factor 4 and average fluctuation level increased to be 2mm. (4) Comparisons of the results of F-factors for molds with EMS show that similar results are obtained. Molds with noz25d have smallest values of F-factor and better in symmetry for the two maximum magnetic flux densities. The results show that noz25d could be a better design for molds with EMS.中文摘要 I 英文摘要 III 目錄 V 圖目錄 VIII 表目錄 XIII 第一章 緒論 1 1.1 電磁攪拌之定義 3 1.2 文獻回顧 4 第二章 理論模式 8 2.1 數學理論模式 8 2.1.1 理論假設 8 2.1.2 統御方程式 9 2.1.3 K-ε紊流模式 10 2.1.4 電磁力之數學計算 11 2.2 邊界條件 15 2.2.1 三維注嘴邊界條件 15 2.2.2 三維注嘴出口平均特性參數計算方式 16 2.2.3 三維鑄模邊界條件 17 2.3 模液面波動振幅轉換方程式 19 2.4 無因次法 20 第三章 計算軟體與數值解程序 23 3.1 FIDAP簡介 24 3.2 FIDAP處理問題步驟 25 3.2.1 前處理 25 3.2.2 計算處理 28 3.2.3 後處理 28 3.3 單向流體流動之分類 29 3.4 數值解法 30 3.4.1 空間離散與係數矩陣 30 3.4.2 三維元素與其微分及積分 32 第四章 結果與討論 35 4.1 注嘴之流場分析 36 4.1.1 noz5d之模擬結果 37 4.1.2 noz15d之模擬結果 38 4.1.3 noz25d之模擬結果 38 4.1.4 noz5d、noz15d以及noz25d之比較 39 4.2 鑄模之流場及溫度場之分析 40 4.2.1 未加電磁力之模擬分析：mold5d、mold15d及mold25d 41 4.2.2 最大磁通量為0.13T下之模擬分析：mtbf5d、mtbf15d及mtbf25d 44 4.2.3 最大磁通量為0.07T下之模擬分析：mtbf5d、mtbf15d及mtbf25d 49 4.2.4 討論與比較 52 第五章 結論 57 符號說明 59 參考文獻 6