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系統識別號 U0002-2107200911075300
中文論文名稱 以直接模擬蒙地卡羅法模擬微流道之氣體流場與熱傳特性分析探討
英文論文名稱 The Investigation of Fluid Dynamics and Heat Transfer of Micro-channel Flows using DSMC Simulation
校院名稱 淡江大學
系所名稱(中) 機械與機電工程學系碩士班
系所名稱(英) Department of Mechanical and Electro-Mechanical Engineering
學年度 97
學期 2
出版年 98
研究生中文姓名 潘穎哲
研究生英文姓名 Ying-Jhe Pan
學號 696371029
學位類別 碩士
語文別 中文
口試日期 2009-06-18
論文頁數 82頁
口試委員 指導教授-洪祖昌
委員-楊照彥
委員-洪祖昌
委員-李宗翰
委員-黃俊誠
中文關鍵字 直接模擬蒙地卡羅法  微機電系統  微管 
英文關鍵字 DSMC  MEMS  microchannel 
學科別分類 學科別應用科學機械工程
中文摘要 近年來由於工業的發展及半導體工業的成熟,相關領域的產品與物件都具有低成本、高精確度與運作快速等特性。微機電系統(Micro-Electro-Mechanical Systems, MEMS)的尺寸都與分子平均自由徑同等級甚至更小。在稀薄度氣體流場得分析中數值模型須考慮分子觀點。直接模擬蒙地卡羅(Direct simulation Monte Carlo, DSMC)法是目前被認為較精確且使用最廣泛的方法。
本文以DSMC法分析在微機電系統中十分重要的幾何微管。首先利用DSMC法模擬一簡單二維矩形微管,將其結果與Navier-Stokes方程搭配滑移(Slip)邊界條件的分析之結果做比較,以探討氣體稀薄(Rarefaction)效應對流場性質所造成之影響。當流場稀薄度較高時,可觀察到DSMC模擬結果與Navier-Stokes方程的解有明顯的差異,故在分析稀薄度較高之流場時,應使用DSMC法會有較準確之結果。
為減少計算時間與記憶體,常會以二維模擬做為代表。在實際工程應用中應以三維分析作為研發參考,故本文探討三維以及二維之矩形維管、微結構管與背向式階梯管流場,比較二維與三維結果,由比較結果可知寬高比大於五時,其流場性質趨近二維結果比率有98%,當寬高比小於五時,三維流場與熱傳性質會與二維結果產生較大差距,故在近壁面流場或寬高比小於5之三維流場模擬會偏離二維結果。
英文摘要 Due to the development and maturation of the semiconductor industry in recent year, the products of related fields are low-cost, high-accurate and high-speed. The characteristic size of Micro-Electro-Mechanical Systems (MEMS) is in the same order as or even smaller than the mean free path (MFP) of gas molecules. In rarefied-gas flow, a mathematical model, which bases on the molecular point of view, has to be considered in the predictions of flow dynamics. The direct simulation Monte Carlo (DSMC) method is a popular and accurate simulation technique for rarefied-gas flows.
In this thesis, the DSMC method was applied to analyze microchannels which are the most important elements of MEMS. At first, we simulate a 2-D straight rectangular cross-section microchannel using the DSMC method. To study the influence of rarefaction effects on the flow properties, the DSMC results are compared with the numerical solutions of Navier-Stokes equations with slip boundary conditions. The discrepancy between the DSMC results and the Navier-Stokes solutions becomes more obvious when the degree of rarefaction increases. The results show that we must use the DSMC method in rarefied-gas flows to get more accurate results.
In order to reduce the computation time and memory requirement, the 2-D simplification of a 3-D flow problem is often used in the DSMC simulation. In practical engineering applications, this simplification, however, is inappropriate as the cross-section aspect ratio of the 3-D structure decreases. We simulated the 3-D straight rectangular cross-section microchannels, the 3-D microchannels with microstructures and the 3-D microchannels with backward-facing steps. The results of the 3-D structures are compared with those of 2-D simplifications. It is found that the approaching level of the 3-D results to those of the 2-D simplification is over 98 % when the cross-section aspect ratio is greater than 5. When the cross aspect ratio is less than 5, the influence of 3-D effect can no longer be ignored and it is necessary to use a full 3-D simulation in the analysis of microchannel flows.
論文目次 目錄
誌謝.............................................I
中文摘要.............................................II
英文摘要.............................................III
目錄.............................................V
表目錄.............................................VIII
圖目錄.............................................IX
符號說明.............................................XII

第一章 緒 論.............................................1
1-1研究動機...............................................1
1-2紐森數的定義...........................................1
1-3波茲曼方程式及其解法...................................4
1-4文獻回顧...............................................8
第二章 直接模擬蒙地卡羅法...............................13
2-1 DSMC法...............................................13
2-2網格設置與計算時步....................................16
2-3流場初始條件..........................................16
2-4流場邊界處理..........................................18
2-5碰撞對(Collision Pair)的選擇..........................19
2-6低速流之進出口條件設定方法............................20
2-6-1隱性邊界法..............................21
2-6-2粒子控制邊界法..........................22
2-7流場性質的取樣........................................23
2-8 流場性質的輸出.......................................24
第三章 分子模型的選擇...................................25
3-1硬球模型(HS)..........................................25
3-2可變硬球模型(VHS).....................................25
3-3可變軟球模型(VSS).....................................26
3-4雙原子分子模型........................................27
3-5流場性質之計算........................................29
第四章 結果與討論........................................32
4-1模擬模型..............................................32
4-2二維模擬結果..........................................32
4-2-1矩形微管程式驗證與取樣..................32
4-2-2微結構微管程式驗證與取樣收斂............33
4-2-3背向式階梯微管程式驗證與取樣收斂........33
4-3 DSMC法與Navier-stokes方程式模擬結果比較..............34
4-4二維與三維微結構微管流場與熱傳特性分析................37
4-5二維與三維背向式階梯微管流場與熱傳特性分析............39
4-6 三維微管流場模擬結果.........................43
第五章 結論與建議........................................45
5-1結論..................................................45
5-2未來工作..............................................46
參考文獻.................................................47


表目錄

表 4-1 VHS 分子模型基本參數 51
表 4-2 二維矩形微管微流場基初始設定 51
表 4-3三維矩形微管微流場初始設定 51
表 4-4二維微結構微管流場初始設定 52
表 4-5三維微結構微管流場初始設定 52
表 4-6二維背向式階梯微管流場初始設定 53
表 4-7三維背向式階梯微管流場初始設定 53



圖目錄
圖1-1 Kn值與統御方程式間的關係圖 54
圖2-1 稀薄度與密度之關係………….……………….………………54
圖2-2 DSMC流程圖 55
圖2-2分子碰撞面積示意圖 56
圖3-1硬球模型碰撞示意圖 56
圖4-1矩形微流場模型示意圖(a)二維模型 (b)三維模型 57
圖4-2微結構微管流場模型示意圖(a)二維模型 (b)三維模型 57
圖4-3背向式階梯微管流場模型示意圖(a)二維模型 (b)三維模型 58
圖4-4 滑移速度模擬驗證圖 58
圖4-5流體與壁面溫差模擬驗證圖 59
圖4-6熱通量模擬驗證圖 59
圖4-7溫度模擬驗證圖 59
圖4-8流體與壁面溫差模擬驗證圖 60
圖4-9熱通量模擬驗證圖 60
圖4-10 不同截面速度模擬驗證圖 60
圖4-11空管微管流場性質穩態圖 61
圖4-12微結構微管流場性質穩態圖 61
圖4-13背向式階梯微管流場性質穩態圖 61
圖4-14流場中心線Kn值 62
圖4-15微管之密度分布 62
圖4-16微管之速度分布 63
圖4-17微管之溫度分布 63
圖4-18中心線密度比較圖 64
圖4-19中心線速度比較圖 65
圖4-20滑移速度比較圖 66
圖4-21中心線溫度比較圖 67
圖4-22壁面溫度比較圖 68
圖4-23熱通量比較圖 69
圖4-24二維與三維流場中心速度 70
圖4-25二維與三維流場溫度(微結構上方) 70
圖4-26二維與三維上壁面摩擦係數 71
圖4-27二維與三維下壁面摩擦係數 71
圖4-28二維與三維上壁面壓力係數 72
圖4-29二維與三維下壁面壓力係數 72
圖4-30二維與三維上壁面熱通量 73
圖4-31二維與三維下壁面熱通量 73
圖4-32三維趨近二維流場比率關係圖 74
圖4-33上壁面滑移速度比較圖 74
圖4-34入口流場中心線速度比較圖(H=0.75μm) 75
圖4-35下壁面滑移速度比較圖(底部) 75
圖4-36上壁面熱通量比較圖 76
圖4-37下壁面熱通量比較圖 76
圖4-38上壁面摩擦係數比較圖 77
圖4-39下壁面摩擦係數比較圖 77
圖4-40流場速度分布圖(Kn=0.04) 78
圖4-41流場速度向量圖(Kn=0.04) 78
圖4-42二維流場速度分布圖. 79
圖4-43三維流場速度分布圖(Y/H=1) 79
圖4-44三維空管流場速度模擬結果 80
圖4-45三維空管流場溫度模擬結果 80
圖4-46三維微結構微管流場速度模擬結果 81
圖4-47三維微結構微管流場溫度模擬結果 81
圖4-48三維背向式階梯微管流場速度模擬結果 82
圖4-49三維背向式階梯微管流場溫度模擬結果 82




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