二相流模式應用於恆溫冶金流體之流場模擬與分析

Simulation of two-phase metallurgical flows in isothermal condition

李峴禕(Hsien-Yi Li)

中原大學/工學院/土木工程研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200089

摘要

本文是利用二相流 (Two-Phase Flows) 數值模式探討在恆溫冶金流體相關應用之現象，內容採用最小平方有限元素法 (LSFEM) 之數值模式求解無因次三維不可壓縮流體動量與質量守恆方程式，配以尤拉慣性座標描述自由液面動力與運動邊界條件，對具自由液面之流體運動問題作完整描述，再以流體體積法為基礎配以一連續函數在此稱之“Color Function”；將密度ρ與黏度μ視為一連續函數的變化關係對自由液面氣液接觸之二相流動問題進行數值模擬。
文中將模擬有關恆溫冶金流體應用在四種不同的模式並進行定性驗證及比較，另外和水體找出其差異性作比較。首先是將 3-D 鐵合金熔爐裡Tapping 模式與 Johansen (2002) 2-D 模擬之現象做比較及驗證，發現利用最小平方有限元素法所得的結果與其文獻符合，且為定性相似的；驗證三維冶金流體應用於潰壩模式，並與Martin J .C and Moyce W. J. (1952)的實驗數據及水體潰壩模擬的數值作比較；冶金流體應用於潰壩波撞擊下游柱狀體之模擬，並觀察冶金流體在撞擊柱體後產生的自由液面變化；三維圓球型液滴 (liquid drop) 球體受重力影響變形現象之模擬，得到不同時間的冶金流體液滴波前的位置變化，並探討模式底部分別為滑動邊界和非滑動邊界表現出自由液面及波前形狀的變化情形。從這些案例中可以明確的以三維模式顯示比較出冶金流體在不同的表面張力，其自由液面的變化情形。

關鍵字

冶金流 ； 潰壩 ； 自由液面 ； 二相流 ； 最小平方有限元素法 ； 液滴 ； 數值模擬

並列摘要

This research studied the two-phase flow models to investigate the metallurgical flows phenomena in isothermal condition. The least-square finite element method (LSFEM) is adopted for the numerical simulation of the three-dimensional incompressible fluid represented by conservation form of mass and momentum equations. For a complete description of the free-surface motion, a volume of fluid (VOF) method with fixed Euler inertia coordinate is adopted. “Color function” is expressed by a continuous function to express the interface of two-phase fluid.
This paper simulates the metallurgical flows in isothermal condition of four different setups. First the simulation of tapping phenomena in ferro-alloy furnaces and is compared with numerical simulation of Johansen (2002) in 2-D phenomena, next the three-dimensional dam break the metallurgical flows in isothermal condition will be compared with experimental data of Martin J. C. and Moyce W. J. (1952) also with numerical simulation of water dam break. The same as above setup, the third case is about a long cylindrical body set in the channel to observe the metallurgical flows, free surface variations after the collision of flow on the cylinder. Simulation of three-dimensional spherical liquid drop deformation under the influence of gravity is the last case, changes in wave position in front of the metallurgical droplet at different times is presented by assuming that the bottom of the model with free slip or no slip boundary conditions, respectively. From these cases, we can apply the three-dimensional model in the simulation of metallurgical flows.

並列關鍵字

Metal Flow ； Two-Phase Flow ； Free-Surface ； Dam-Berak ； Least-Square Finite Element Method ； Numerical Simulation ； Liquid Drop

參考文獻

25. 陳昭昇(2010) “三維自由液面水流撞擊物體之流場模擬與分析”，

24. 宋詠程(2003) “液滴掉落現象之數值模擬”，私立中原大學土木工程學系碩士學位論文。

23. 鄭雅允(2003)“二相流模式探討明渠流在不規則底床運行之現象”,

Transformation Technologies. Vol.32,pp.128-236.

of California : Los Alamos, NM.