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研究生：	林鴻昇 Lin, Hung-sheng
論文名稱：	以COMSOL有限元素軟體分析凝固問題 Analysis Of Solidification Problems By Using Finite Element Package COMSOL Multiphysics
指導教授：	趙隆山 Chao, Long-Sun
學位類別：	碩士 Master
系所名稱：	工學院 - 工程科學系 Department of Engineering Science
論文出版年：	2010
畢業學年度：	98
語文別：	中文
論文頁數：	57
中文關鍵詞：	相變化、有限元素法、等效比熱法、熱焓法、COMSOL Multiphtsics
外文關鍵詞：	Phase Change, Finite Element Method, Enthalpy Method, COMSOL Multiphtsics, Effective Specific Heat Method
相關次數：	點閱：159 下載：10
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在材料的製造過程當中，液體與固體的相變化是相當重要的物理現象，有效模擬出相變化情況以及增加準確度能夠幫助了解材料相變化過程的情形。本文使用多重物理量有限元素套裝軟體COMSOL Multiphysics進行相變化問題之模擬探討。相變化問題有正解解析解的一維史蒂芬問題、紐曼問題和二維Rathjen問題。本研究先針對這些問題，搭配不同處理潛熱效應的方法，進行凝固熱傳行為之模擬，最後將數值解與解析解進行準確度比較分析。然後再進一步對二維凝固問題，考慮自然對流效應，模擬矩形容器右側受到一個鑄模熱傳效應時，其內部溫度與流場分布及凝固情形。經由分析的結果可以得到求解史蒂芬問題相變化熱傳遞問題時，使用熱焓法可獲得較好的準確度。求解相變化問題時運用有限元素套裝軟體進行模擬可得到不錯的準確度，本文之研究可提供一個有效模擬相變化熱傳遞問題的方法，並且期望可作為進一步研究之參考。

In the manufacturing process of material, the liquid and solid phase change is an important physical phenomenon. An effective and accurate simulation is helpful to understand the phase-change process. In the thesis, the finite element package COMSOL Multiphysics is used to investigate the process simulation. The phase change problems with exact solutions are studied, which include the one-dimensional Stefan and Neumann problems and the two-dimensional Rathjen problem. The study utilizes two different methods of handling latent heat, enthalpy and effective specific heat methods, to simulate the solidification behavior of those problems. The numerical solutions are compared with the exact ones. Furthermore, in the research, a two-dimensional solidification problem with the natural convection effect is simulated, in which the computing domain is square and the right boundary is subjected to the heat extraction caused by the mold influence. From the analysis, the enthalpy method could have the better results than the effective specific scheme. It could obtain considerably accurate numerical solutions to use the finite element package to solve solidification problems. The results of the study offer an effective way to simulate the heat transfer problem of a solidification process and it is expected that the results can be an important reference for the further study using the package.

摘要.................................................................................................................Ⅰ
致謝.................................................................................................................Ⅲ
目錄.................................................................................................................Ⅳ
表目錄.............................................................................................................Ⅵ
圖目錄.............................................................................................................Ⅶ
符號說明........................................................................................................Χ
第一章	緒論....................................................................................................1
    1.1 前言..................................................................................................1
1.2文獻回顧...........................................................................................2
1.3研究方法與目的...............................................................................4
第二章 理論分析............................................................................................5
2.1有限元素法基本概念.......................................................................5
       2.1.1有限元素法之加勒金法(Galerkin method) ...................6
2.2 有限元素法的分析過程..................................................................8
2.3 COMSOL 有限元素分析軟................................................................9
第三章 相變化熱傳問題數值方法與分析...............................................14
    3.1一維高低溫熱傳問題....................................................................14
3.2 史蒂芬問題（Stefan Problem）..................................................15
3.3 求解史蒂芬問題之數值方法.......................................................16
       3.3.1 等效比熱法（Effective specific heat method）........16
       3.3.2 熱焓法（Enthalpy method）..............................................18
3.4紐曼問題（Neumann Problem）.......................................................20
3.5求解紐曼問題之數值方法............................................................ 22
   	   3.5.1等效比熱法（Effective specific heat method）...........22
   3.5.2 熱焓法（Enthalpy method）...............................................22
3.6 Rathjen問題...................................................................................23
3.7二維矩形溫度場與流場效應........................................................24
      3.7.1矩形自然對流問題................................................................24
      3.7.2二維矩形凝固問題................................................................26
第四章 結果與討論.....................................................................................33
4.1史蒂芬問題(Stefan Problem) ................................................... 33
4.2紐曼問題(Neumann Problem) ......................................................34
4.3 Rathjen問題...................................................................................35
4.4 二維矩形問題................................................................................35
4.5二維矩形純鋁凝固問題.................................................................36
第五章 結論..................................................................................................50
參考文獻.........................................................................................................52

                                    

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2015-08-27公開

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