本研究以數值模型探討碳溶解於鋼液中的影響因子。碳溶解速率快慢主要受到碳在鋼液中擴散速度的影響，吾人假設碳粒溶解於鐵水中之速率為準穩態(quasi-steady)過程，因此以穩態模型模擬不同狀態下的碳粒溶解速率。由模擬結果中可發現顆粒表面上的質量溶解速率分佈明顯受到回流區分佈的影響並與流場流速相關。研究中將穩態模擬結果之Sherwood數與流場有關之Reynolds, Schmidt數利用曲線適性法建構一lump系統，其可預測不同狀態下碳粒溶解時間，文中建立之關於質傳與熱傳之回歸式如下:
Sh=2.81+0.52 Re^0.52 Sc^0.38
Nu=0.53+0.27 〖Re〗^034 Pr^0.16
本研究也建立了動態縮減模型，並比較兩者溶解時間之差異。以作為Lump系統修正之參考。另外，本研究亦建立一二維噴吹模型以驗證二維噴吹模型、動態縮減模型以及lump系統預估之溶解時間，確認系統之可靠性。

In this study, a numerical model is built to investigate the factors on carbon dissolution rate and develop a lump system for carbon particle dissolution in hot liquid metal. We assume the carbon particles dissolve in the molten iron is a quasi-steady process. Therefore, the steady state model has been developed.
The simulation data shows the distribution of mass dissolution rate at the particle surface is significantly affected by the flow circulation behind a particle as a relative flow velocity is applied. The lump system has been developed by the correlation of Reynolds number and Schmidt number, which can predict the carbon particles dissolve at times of different state. The correlation of mass/heat transfer are as following:
Sh=2.81+0.52 Re^0.52 Sc^0.38
Nu=0.53+0.27 〖Re〗^034 Pr^0.16
The study also established a transient model, and compare the time of dissolution between two models. Simulation results of transient model show that when the Reynolds number is smaller, the dissolution rate of carbon particles goes to be slightly longer.in addition this study also building a two dimension injection model through the simulation result of different model confirm the reliability of lump system

論文審定書 i
誌謝 ii
摘要 v
Abstract vi
目錄 vii
圖目錄 x
表目錄 xii
符號說明 xiii
第1 章 序論 1
1.1 前言 1
1.2 文獻回顧 3
1.3 研究目的 11
1.4 本文架構 12
第2 章 研究方法與理論分析 13
2.1 碳溶解理論 13
2.2 影響因子 15
viii
2.2.1 鐵水溫度 15
2.2.2 液體攪拌 15
2.2.3 碳粒尺寸 16
2.3 研究方法 17
2.3.1 暫態單顆碳粒模擬 17
2.3.2 穩態單顆碳粒模擬 18
2.3.3 二維噴吹模型 18
第3 章 第三章 數值模型 19
3.1 模型介紹 19
3.2 數值模型與統御方程式 23
3.2.1 統御方程式 23
3.2.2 數學模型 27
3.2.3 數值方法 31
3.2.4 格點測試 31
第4 章 結果與討論 33
4.1 穩態模擬結果與建立之lump 系統. 33
4.1.1 穩態模擬結果 33
4.1.2 lump 系統中的質傳 36
4.1.3 lump 系統中的熱傳 37
4.1.4 不同工作條件下之lump 系統結果的整合 38
4.2 二維與三維暫態模擬結果 48
4.2.1 二維單顆碳粒模擬結果 48
4.2.2 三維單顆碳粒模擬結果 52
4.3 暫態模擬與lump 系統 的比較 56
4.4 二維與三維噴吹模型 59
4.4.1 二維噴吹模型 59
第5 章 結論與未來展望 62
第6 章 參考文獻 64

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