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系統識別號 U0002-2808200806550400
中文論文名稱 以直接模擬蒙地卡羅法計算三維不同結構微管流場與熱傳特性探討
英文論文名稱 The Investigation of 3-D effects on Heat and Fluid Flow Characteristics of Mircochannels with Different Structure
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 96
學期 2
出版年 97
研究生中文姓名 陳昭雄
研究生英文姓名 Chau-Hsung Chen
學號 695370139
學位類別 碩士
語文別 中文
口試日期 2008-07-20
論文頁數 71頁
口試委員 指導教授-洪祖昌
委員-楊照彥
委員-王興華
委員-吳宗信
中文關鍵字 直接模擬蒙地卡羅法  結構  微管 
英文關鍵字 DSMC  Structure  Micro-channel 
學科別分類 學科別應用科學機械工程
中文摘要 本文以直接模擬蒙地卡羅法(Direct Simulation Monte Carlo Method)[2]來模擬三維微結構物微管與三維背向式梯度微管之流場,並且比較二維流場與三維流場模擬流場內部的性質與熱傳現象。其次是探討三維微管內center、medium、corner之差異性,而這是在二維模擬場是無法看到的結果,也是三維模擬微管存在的價值所在,並更趨近於真實。而在對於加大寬高比3倍、5倍的三維之流場來說,雖然邊界會越趨近於二維,但是對於所受的影響還是依然明顯而不同於二維微流場。而本文所使用的工作流體為氮氣(N2),分子模型則採用VHS分子模型。
模擬之結果發現,在三維與二維驗證與比較方面,三維模擬因為受到兩端壁的影響作用導致與二維模擬結果有些不同,但是當把寬高比加大成3倍時,此時兩端壁的效應影響變小,三維模擬結果已經跟二維模擬結果接近,而到5倍時結果又更為接近。在三維微結構物微管不管在剪應力或者熱通量上,center、medium、corner的差異性變化依舊明顯;而在三維背向式梯度微管裡,可以發現在剪應力的部份,前端的center、medium、corner變化來的比較大;而在熱通量的部份,在最一開始center、medium、corner呈現上升的狀態,不過隨之就沒在往上升,而是呈現穩定狀態。
英文摘要 This article direct simulates the 3-D Microstructure and the 3-D backward-facing step by the Direct Simulation Monte Carlo Method , and contrast to the 2-D flow field and the 3-D flow field simulation flow field the interior of Nature and Heat Transfer.Next is in the discussion the 3-D Microchannel difference of center, medium, the corner, but this is the result which is unable in the 2-D simulation to see, is also the 3-D simulation Microchannel existence value is, and really draws close. But in regarding enlarged beam-to-depth ratio 3 time, 5 time of the 3-D flow fields, although the boundary will more draw close in the 2-D, but regarding received the influence was still obvious and is different with the 2-D flow field. But this article uses the operating fluid for the nitrogen (N2), the molecular model uses the VHS model.
Result of the simulation discovered that in the 3-D and the 2-D confirmation and comparison aspect, because the 3-D simulation receives two end walls the influence functions to cause with the 2-D simulation result to be somewhat different, but when enlarges the beam-to-depth ratio 3 times, this time two end wall's effect influences change are small, the result of the 3-D simulation was already close with the 2-D simulation result, but to 5 time of time results is also closer. In the 3-D backward-facing step, to discover that in the shear stress part, front end center, medium, corner changes is quite big; But in the heat flux part, in center, medium, corner presents the rise most from the very beginning the condition, but along with it not in toward rise, but contrary to presents the steady state.
論文目次 目錄.....................................................IV
表目錄..................................................VII
圖目錄.................................................VIII
符號說明.................................................XI
第一章 緒 論...........................................1
1-1 前言 .................................................1
1-2 紐森數的定義..........................................2
1-3 波茲曼方程式(Boltzmann equation)......................3
1-4 波茲曼方程式的數值解..................................5
1-5文獻回顧...............................................6
第二章 直接模擬蒙地卡羅法................................12
2-1 DSMC 法.............................................12
2-2 假設與基本流程 .......................................13
2-2-1 DSMC法基本的假設...................................13
2-2-2 DSMC法的計算基本流程概述...........................13
2-2-3計算時須注意的項目..................................14
2-3 網格設置與計算時步...................................15
2-4 模擬加權因子與流場初始條件...........................16
2-5 流場邊界處理.........................................16
2-6 低速流之進出口條件設定方法...........................19
2-7排序與粒子碰撞........................................21
2-8 流場性質的取樣 .......................................23
2-9 流場性質的輸出 .......................................23
第三章 分子間的碰撞.....................................24
3-1 VHS分子模型.........................................24
3-2 單原子分子模型 .......................................25
3-3 雙原子分子模型 .......................................26
第四章 結果與討論........................................30
4-1 不同結構微管之二維模擬結果...........................30
4-2不同結構微管之三維模擬與二維模擬驗證比較..............32
4-3三維不同結構微管之Center、Medium、Corner的剪應力比較..33
4-4三維不同結構微管之Center、Medium、Corner的熱通量比較..34
第五章 結論與未來工作....................................36
5-1 結論.................................................36
5-2 未來工作.............................................37
參考文獻.................................................38


表目錄
表4-1 VHS 分子模型基本參數………………………………………43
表4-2二維之微結構物微管流場基本設定 …………………………43
表4-3三維之微結構物微管流場基本設定 …………………………44
表4-4二維之背向式梯度微管流場基本設定 ………………………45
表4-5三維之背向式梯度微管流場基本設定 ………………………46


圖目錄
圖1 Kn值與統御方程式間的關係圖 ………………………………46
圖2-1 DSMC流程圖……………………………………………………47
圖2-2碰撞示意圖 ……………………………………………………47
圖4-1 Liou與Fang二維微結構物微流場模型圖 …………………48
圖4-2三維微結構物微流場模型圖 …………………………………48
圖4-3三維微結構物微流場模型計算域圖 …………………………48
圖4-4 Hong Xue 與Bin Xu 二維背向式階梯微管物理模型圖……49
圖4-5三維背向式梯度微流場模型圖 ………………………………49
圖4- 6三維背向式梯度之DSMC 模擬計算域圖 ……………………49
圖4-7微結構物的取樣穩態變化驗證圖 ……………………………50
圖4-8 Pin/Pe=2.5 Liou & Fang(上圖)與本文模擬(下圖)之溫度場
........................................................51
圖4-9 Pin/Pe=4.0 Liou & Fang(上圖)與本文模擬(下圖)之溫度場……………51
圖4-10 Liou & Fang之溫度分佈圖 ………………………………………………52
圖4-11模擬Liou & Fang之溫度分佈圖 …………………………………………52
圖4-12背向式梯度的取樣穩態變化驗證圖 ……………………………………53
圖4-13 Hong Xue & Bin Xu之速度圖 ……………………………………………54
圖4-14模擬Hong Xue & Bin Xu之速度圖 ………………………………………54
圖4-15 Hong Xue & Bin Xu之壓力圖 ……………………………………………55
圖4-16模擬Hong Xue & Bin Xu之壓力圖 ………………………………………55
圖4-17 (微結構物)上壁面的不同管徑寬度與二維模擬之剪應力圖……………56
圖4-18 (微結構物)下壁面的不同管徑寬度與二維模擬之剪應力圖……………56
圖4-19 (微結構物)上壁面的不同管徑寬度與二維模擬之熱通量圖……………57
圖4-20 (微結構物)下壁面的不同管徑寬度與二維模擬之熱通量圖……………57
圖4-21 (背向梯度)上壁面的不同管徑寬度與二維模擬之剪應力圖……………58
圖4-22 (背向梯度)下壁面的不同管徑寬度與二維模擬之剪應力圖……………58
圖4-23 (背向梯度)上壁面的不同管徑寬度與二維模擬之熱通量圖……………59
圖4-24 (背向梯度)下壁面的不同管徑寬度與二維模擬之熱通量圖……………59
圖4-25(微結構物)上壁面三維寬高比1倍的管角、管壁中、兩者間的剪應力.60
圖4-26(微結構物)下壁面三維寬高比1倍的管角、管壁中、兩者間的剪應力.60
圖4-27(微結構物)上壁面三維寬高比3倍的管角、管壁中、兩者間的剪應力圖.61
圖4-28(微結構物)下壁面三維寬高比3倍的管角、管壁中、兩者間的剪應力圖.61
圖4-29(微結構物)上壁面三維寬高比5倍的管角、管壁中、兩者間的剪應力圖.62
圖4-30(微結構物)下壁面三維寬高比5倍的管角、管壁中、兩者間的剪應力圖.62
圖4-31(背向梯度)上壁面三維寬高比1倍的管角、管壁中、兩者間的剪應力圖.63
圖4-32(背向梯度)下壁面三維寬高比1倍的管角、管壁中、兩者間的剪應力圖.63
圖4-33(背向梯度)上壁面三維寬高比3倍的管角、管壁中、兩者間的剪應力圖.64
圖4-34(背向梯度)下壁面三維寬高比3倍的管角、管壁中、兩者間的剪應力圖.64
圖4-35(背向梯度)上壁面三維寬高比5倍的管角、管壁中、兩者間的剪應力圖.65
圖4-36(背向梯度)下壁面三維寬高比1倍的管角、管壁中、兩者間的剪應力圖.65
圖4-37(微結構物)上壁面三維寬高比1倍的管角、管壁中、兩者間的熱通量圖.66
圖4-38(微結構物)下壁面三維寬高比1倍的管角、管壁中、兩者間的熱通量圖.66
圖4-39(微結構物)上壁面三維寬高比3倍的管角、管壁中、兩者間的熱通量圖.67
圖4-40(微結構物)下壁面三維寬高比3倍的管角、管壁中、兩者間的熱通量圖.67
圖4-41(微結構物)上壁面三維寬高比5倍的管角、管壁中、兩者間的熱通量圖.68
圖4-42(微結構物)下壁面三維寬高比5倍的管角、管壁中、兩者間的熱通量圖.68
圖4-43(背向梯度)上壁面三維寬高比1倍的管角、管壁中、兩者間的熱通量圖.69
圖4-44(背向梯度)下壁面三維寬高比1倍的管角、管壁中、兩者間的熱通量圖.69
圖4-45(背向梯度)上壁面三維寬高比3倍的管角、管壁中、兩者間的熱通量圖.70
圖4-46(背向梯度)下壁面三維寬高比3倍的管角、管壁中、兩者間的熱通量圖.70
圖4-47(背向梯度)上壁面三維寬高比5倍的管角、管壁中、兩者間的熱通量圖.71
圖4-48(背向梯度)下壁面三維寬高比5倍的管角、管壁中、兩者間的熱通量圖.71



參考文獻 [1] Mohamed Gad-el-Hak, The MEMS Handbook, CRC Press, 2002.
[2] Bird, G. A., Molecular Gas Dynamics And The Direct Simulation of Gas Flows, Oxford University Press, 1994.
[3] Bird, G. A., “Approach to Translational Equilibrium in a Rigid Sphere Gas,” Phys. Fluids Vol. 6, pp. 1518-1519, 1963.
[4] Bird, G. A., “The Velocity Distribution Function Within a Shock Wave,” Journal of Fluid Mechanics, Vol. 30, part 3, pp. 479-487, 1967.
[5] Borgnakke, C., and Larsen, P. S., “Statistical Collision Model for Monte Carlo Simulation of Polyatomic Gas Mixture,” Journal of Computational Physics, Vol. 18, No. 4, pp. 405-420,1975.
[6] Bird, G. A., Molecular Gas Dynamics. Oxford,UK:Clarenden,1976
[7] Bird, G. A., “Perception of Numerical Method in Rarefied Gas Dynamics,” in Rarefied Gas Dynamics:Theoretical and Computational Techniques, Vol. 118 of Progress in Aeromautics and Astronautics, AIAA, Washington, DC, 1989.
[8] Muntz, E. P., “Rarefied gas dynamics,”Annu. Rev. Fluid Mech. 21,pp.387-417 ,1989.
[9] Cheng, H. K., “Perspectives on hypersonic viscous flow research” Annu. Rev. Fluid Mech. 25, pp.455–484, 1993.
[10] Cheng, H. K., and Emmanuel, G., “Perspectives on hypersonic nonequilibrium flow,” AIAA J. 33, pp.385–400, 1995.
[11] Bird, G. A., “Recent Advances and Current Challenges for DSMC,” Comput. Math. Appl., Vol. 35, pp. 1-14, 1998.
[12] Beskok, A., and Karniadakis, D. E., Modeling Separation in
Rarefied Gas Flows, 28th AIAA Shear Flow Control Conference,
Snowmass Village, CO, 1997.
[13] Arkilic, E. B., Breuer, K. S., and Schmidt, M. A., “Gaseous Flow
in Micro-channels,” Application of Microabrication to Fluid
Mechanics, ASME, FED-Vol. 197, p.57-66, 1994.
[14] Piekos, E. S., and Breuer, K. S., “Numerical Modeling of Micromechanical Devices Using the Direct Simulation Monte Carlo Method,” Journal of Fluids Engineering, Vol. 118, pp.464-469, 1996.
[15] Nance, R. P., Hash, D. B., and Hassan, H. A., “Role of Boundary Conditions in Monte Carlo Simulation of Microelectromechanical Systems,” Journal of Thermophysics and Heat Transfer, Vol. 12, No. 3, pp.447-449, 1998.
[16] Fan, J., and Shen, C., “Statistical Simulation of Low-speed Rarefied Gas Flows, ” Journal of computational physics, Vol. 167, pp. 393-412,2001.
[17] Liou, W. W., and Fang, Y.C., ”Implicit Boundary Conditions for Direct Simulation Monte Carlo Method in MEMS Flow Predictions,” CMES, Vol. 1, No. 4, pp.119-128, 2000.
[18] Liou, W. W., and Fang, Y.C., “Computation of the Flow and Heat Transfer in Microdevices Using DSMC With Implicit Boundary Conditions,” Journal of Heat Transfer, Vol. 124, pp.338-345, 2002.
[19] Wu, J. S., Lee, F., and Wong, S. C., “Pressure Boundary Treatment in Micromechanical Devices Using the Direct Simulation Monte Carlo Method, ” JSME International Journal, Vol. 44, pp. 439-450, 2001.
[20] Wang, M., and Li, Z., “Gas Mixing in Microchannels Using the Direct Simulation Monte Carlo Method, ”International Journal of Heat and Mass Transfer, Vol. 49, pp. 1696-1702, 2006.
[21] 羅文彬,”以直接模擬蒙地卡羅法模擬二維微管流場”,淡江大學機械與機電工程學系碩士論文,台北,2004.
[22] 賴怡利,”以直接模擬蒙地卡羅法分析微尺寸方管之流場現象”,成功大學 航空太空工程學系碩士論文,台南,1998.
[23] 潘建志,”流經靠近一平板的矩形柱體稀薄氣流的直接模擬蒙地卡羅法分析”,大同大學機械工程學系碩士論文,台北,2000.
[24] 林文榮,”利用DSMC方法分析微通道氣體流動特性與熱傳之研究”,國立雲林科技大學機械工程系碩士論文,雲林,2000.
[25] 王奕婷,”流體在微渠道流動之數值模擬”,國立中山大學機械與機電工程系碩士論文,高雄,2003.
[26] Sun, H., Faghri, M., ”Effects of Rarefaction and Compressibility of Gaseous Flow in Microchannels Using DSMC,” Numerical Heat Transfer, Part A, Vol. 38, pp. 153-168, 2000.
[27] Yan, F., Farouk, B., “Computations of Low Pressure Flow and Heat Transfer in Ducts Using the Direct Simulation Monte Carlo Method,” J. of Heat Transfer, Vol.124, pp. 609-616,2002.
[28] Xue, H., Chen, S., ”DSMC Simulation of Microscale
Backward-facing Step Flow,” Microscale Thermophysical Engineering, Vol. 7, pp. 69-86, 2003.
[29] 陳炳炫,“Knudsen區氣體微尺度流動之蒙地卡羅直接模擬”,
國防大學中正理工學院國防科學研究所碩士論文,桃園,2003.
[30] 蘇嘉南,”以三維蒙地卡羅法模擬分析高速微管流場”,國立成功大學航空太空工程研究所碩士論文,台南,2000.
[31] 沈青,”稀薄氣體動力學” 國防工業出版社,北京,2003.
[32] 洪念慈,”以直接模擬蒙地卡羅法計算三維微管流場”,淡江大學機械與機電工程學系碩士論文,台北,2004.
[33] Zhen, C. E., Hong, Z. C., Lin, Y. J., and Hong, N. T., “Comparison of 3-D and 2-D DSMC Heat Transfer Calculations of Low-Speed Short Microchannel Flows,” Numerical Heat Transfer, Part A, Vol. 52, No. 3, 2007,pp. 239-250.
[34] 邱昱中,“微結構三維流場及熱傳現象”,淡江大學機械與機電工程學系碩士論文,台北,2005.
[35] 黃盈翔,” 以直接模擬蒙地卡羅法計算三維背向式階梯微流場”, 淡江大學機械與機電工程學系碩士論文,台北,2006.
[36] Hong Xue, Bin Xu, Yao Wei, and Jian Wu, “Unique Behaviors of A Backward-facing Step Flow at Microscale,” Numerical Heat Transfer, Part A, Vol. 47, pp. 251-268, 2005.
[37] 林雅茹,” 以直接模擬蒙地卡羅法計算三維微管流場與熱傳特性探討”, 淡江大學機械與機電工程學系碩士論文,台北,2007.
[38] Bird G A. Direct Simulation of the Boltzmann equation. Phys. Fluids,13:2676,1970.
[39] Wagner,W. “A convergence proof for Bird’s direct simulation Monte Carlo method for the Boltzmann equation. ” J. Stat. Phys.,66:1011,1992.
[40] Pulvirenti ,M,Wagner, W and Zavelani, M B. Convergence of particle schemes for the Boltzmann equation. Euro.J. Mech.,B7:339,1994.
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