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研究生:紀富謦
研究生(外文):Chi, Fu-Ching
論文名稱:非均溫微通道滑移流之數值模擬
論文名稱(外文):Numerical simulation of slip flow through micro-channel with non-uniform temperature
指導教授:曾培元
指導教授(外文):Tzeng Pei-Yuan
口試委員:曾培元宋齊有劉中和
口試委員(外文):Tzeng Pei-YuanSoong Chyi-YeouLiu Chung-Ho
口試日期:100.7.15
學位類別:碩士
校院名稱:國防大學理工學院
系所名稱:機械工程碩士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:69
中文關鍵詞:微通道滑移速度熱蠕變直接模擬蒙地卡羅法
外文關鍵詞:Micro ChannelSlip VelocityThermal CreepDSMC
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本研究旨在針對微通道中,因非均溫所造成的溫度梯度,而導致稀薄氣體所產生的熱蠕變效應,將此效應作模擬分析。研究環境為常溫常壓下,流場氣體的平均自由路徑與微通道的特徵長度比值Kn數(Kundsen number)約介於滑移流區。由於尺度效應,流場的高Kn數使得傳統的計算流體力學(Computational Fluid Dynamics, CFD)已經不敷使用。故採用直接模擬蒙地卡羅(Direct Simulation Monte Carlo, DSMC)法,透過模擬分子的運動和碰撞,直接實現真實流動的過程。並在流動邊界中,利用傳統計算流體動力學的特徵化理論,加入改良式壓力邊界條件,取代原先的通量法邊界,並且以更接近真實的新計算方式求出壁面滑移速度。將模擬出微通道中因壁面非均溫所造成的溫度梯度,探討因壁面溫度梯度對滑移速度之影響,最後模擬因進、出口溫差所形成流場溫度梯度,進而驅動流體之熱蠕變驅動流,且隨不同壁面性質、切向溫度梯度大小等因素,探討熱蠕變驅動流及熱蠕變效應對滑移速度的影響關係。
This study simulated rarefied gas flows in the micro-channels, with non-uniform temperature caused by tangential temperature gradients along the channel walls, leading to thermal creep phenomenon. Research environment for the standard temperature and pressure, the mean free path of the fluid, , is of the same order as the characteristic channel size, . A ratio of the two length scales, , is commonly referred to as Knudsen number, . The value of Knudsen number in the range of 0.01 to 0.1, is called slip flow. Because of the scale effect, the flow field of high Knudsen number caused the traditional Computational Fluid Dynamics inadequate for use. By using the direct simulation Monte Carlo method, through simulation of molecular movement and collision for achieving true mobility. In the stream boundary, using improved pressure boundary condition with computational fluid dynamics characteristics theory, to replace the original boundary flux method, and developed a new way to calculate more realistic slip velocity. Wall temperature gradient effects on slip velocity, are studied by simulating the micro-channel with non-uniform wall temperature resulting from difference between inlet and outlet temperatures. In addition, the influences of different reflection rules for wall boundary conditions are also examined.
誌謝 ii
目錄 v
圖目錄 vi
符號說明 viii
1. 前言 1
1.1 研究動機 1
1.2 研究方法分析 1
1.3 文獻回顧與探討 3
1.3.1 壓力邊界文獻 3
1.3.2 滑移速度文獻 5
1.3.3 熱蠕變效應文獻 6
1.4 論文架構 7
2. 基礎分子氣體動力論 9
2.1 前言 9
2.2 速度分布函數 10
2.3 碰撞理論及分子模型 13
2.4 分子碰撞理論與分子碰撞模型 17
2.4.1 碰撞截面積 17
2.4.2 硬球分子模型(Hard Sphere, HS) 19
2.4.3 可變硬球分子模型(Variable Hard Sphere, VHS) 20
2.5 Boltzmann方程式 21
2.6 Maxwell分布 22
3. DSMC之數值方法 23
3.1 DSMC原理 23
3.2 數值模擬的流程 24
3.3 邊界條件設定 27
3.3.1 流動邊界 27
3.3.2 固體邊界 32
4. 二維流場模擬結果與討論 38
4.1 程式驗證 38
4.1.1 問題說明 38
4.1.2 文獻驗證比較 39
4.2 滑移速度模擬 42
4.2.1 滑移速度簡介 42
4.2.2 滑移速度驗證 43
4.3 滑移速度取法 44
4.3.1 取法簡介 44
4.3.2 滑移速度取法比較 47
4.4 壁面溫度梯度 50
4.4.1 壁面溫度梯度簡介 50
4.4.2 壁面溫度梯度模擬 50
4.5 熱蠕變現象 51
4.5.1 熱蠕變效應簡介 51
4.5.2 模擬熱蠕變效應之壁面條件 53
4.5.3 熱蠕變效應對壓力驅動流體之影響 58
5. 結論與建議 63
5.1 結論 63
5.2 未來方向 64
參考文獻 65
自傳 69
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