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研究生:陳鳴諭
研究生(外文):Ming-Yu Chen
論文名稱:曼德爾問題於鋰電池隔離膜之數值模擬
指導教授:周鼎贏
學位類別:碩士
校院名稱:國立中央大學
系所名稱:能源工程研究所
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:54
中文關鍵詞:多孔介質鋰電池多孔彈性力學
外文關鍵詞:Porous mediaLithium-ion batteryPoroelasticity
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本文針對鋰離子電池內部的多孔介質因受到電極膨脹而被壓縮的現象進行探討。文獻回顧中提到,多孔介質基於不同的假設,會使用不同的力學模型,像是多孔彈性力學或黏彈性力學,來分析多孔介質的受力。為了探討鋰電池內部的多孔介質在受壓行為下的力學行為,與多孔材質受壓後對電池表現可能造成的影響,我們使用多孔彈性力學中的Mandel問題模型,模擬多孔介質受壓下的變化。
本文利用PETSc函式庫進行有限元素法模擬,探討多孔介質的性能。根據不同的曲線圖得出孔壓與位移在二維區域內的曲線分布變化。其中多孔介質的孔隙度、楊氏模數、泊松比、滲透率與體積模數,還有電解質液體的黏度與體積模數都設定為已知值。假定頂部和底部邊界是不透水層、可視為液壓絕緣,而側面邊界則暴露在空氣中、壓力設定為0。對上下板子施加壓應力的狀況下,採用多孔彈性力學的經典二維Mandel問題,模擬矩形區域內多孔介質孔壓分布與位移隨時間的變化。結果顯示,中心的孔壓分布會隨時間遞進而溢散減小。
This paper analyzes the phenomenon that the internal porous media of a lithium-ion battery is compressed due to electrode expansion. It is mentioned in the literature review that the porous media is based on different assumptions and uses different mechanical models, such as poroelasticity or viscoelasticity, to analyze the stress of porous materials. In order to explore the mechanical behavior of the internal porous media of a lithium-ion battery under compression and the possible impact on battery performance after the porous media is compressed, we use the Mandel problem model in poromechanics to simulate the change of porous materials under compression.
We use the PETSc (Portable, Extensible Toolkit for Scientific Computation) function library to perform the finite element method simulation to discuss the performance of the porous media. According to different graphs, the curve distribution changes of pore pressure and displacement in a two-dimensional area are obtained. The porosity, Young's modulus, Poisson's ratio, permeability, and bulk modulus of the porous media, as well as the viscosity and bulk modulus of the electrolyte liquid, are all set to known values. Assume that the top and bottom boundaries are impervious and can be considered as hydraulic insulation, while the side boundaries are exposed to air and the pressure is set to zero. Under the condition of applying compressive stress to the upper and lower plates, the classical two-dimensional Mandel's problem of porous elasticity is used to simulate the change in the pore pressure distribution and displacement of the porous media with time in a rectangular region. The results show that the pore pressure distribution in the center decreases with time and then the pressure release.
摘要 i
Abstract ii
致謝 iii
圖目錄 v
表目錄 vi
符號說明 vii
第一章、 前言 1
1.1 研究背景與動機 1
1.2 研究目的 1
1.3 多孔彈性力學介紹 1
1.4 電池內部結構的膨脹壓縮與Mandel問題 2
1.5 重要專有名詞介紹 3
第二章、 文獻回顧 4
2.1 電池發展史與鋰離子電池的開發 4
2.2 鋰離子電池結構與電化學原理 6
2.3 隔離膜功能原理與性能 7
2.4 隔離膜的機械性質 9
2.4.1 隔離膜的正交各向異性 10
2.4.2 彈黏塑性和溫度依賴性 12
2.4.3 隔離膜機械性質實驗 13
2.5 多孔彈性力學 15
第三章、 研究方法與理論模型 17
3.1 有限元素法簡介 17
3.2 理論模型 Mandel’s Problem 20
3.3 統御方程式 21
3.4 數據結果 28
3.5 結果與討論 34
3.6 結論 35
參考文獻 36
附錄A 應力與應變公式與常用定理 41
附錄B Mandel問題的解析解公式 42
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