臺灣博碩士論文加值系統

本研究以直接模擬蒙地卡羅(DSMC)法且應用梯形網格進行二微收縮式微噴嘴流場特性模擬，探討在微米及奈米尺度下稀薄氣體對於流場特性的影響並進行分析。先將真實三維微噴嘴流場模擬簡化成二維收縮式微噴嘴進行模擬。應用修正型非時間計數器(M-NTC)法則，估算出每個網胞在一個時歩內所需執行的碰撞次數，且使用不同的壁面反射條件如鏡反射、散反射與等向性散射作為壁面邊界條件設定。使用梯形網格之DSMC法，研究背壓(Back Pressure)、反射條件、與稀薄程度在收二維縮式微噴嘴內其對流場的影響。

In this study, it uses Direct Simulation Monte Carlo (DSMC) method with trapezoidal meshes to simulate characteristics of flows field for two-dimensional convergent micronozzle. The influence of the micro/nanoscale rarefied gas effects on flow characteristics were investigated and analyzed. First, real three-dimensional micronozzle flow field use simplified to a two–dimensional convergent micronozzle. Modified no time counter (M-NTC) rule is applied on the selection of representative collision pairs. Different reflect boundary conditions, such as specular/diffuse/isotropic reflection an adopted as wall boundary conditions. Finally the effects of back pressure, reflection conditions, and rarefaction on the flow field characteristics in two-dimensional convergent micronozzle are studied.

誌謝 ii
摘要 iii
ABSTRACT iv
表目錄 viii
圖目錄 ix
符號說明 xii
1. 緒論 1
1.1 研究背景與動機 1
1.2 文獻回顧 2
1.3 研究方法 5
1.3.1 以Knudsen 數作為流區的分類 5
1.3.2 分析與選定 6
1.4 研究內容與論文架構 7
2. 氣體分子動力理論 9
2.1 前言 9
2.2 速度分布函數 9
2.3 微觀與巨觀性質 12
2.4 Boltzmann 方程式 15
2.5 矩方程式(Moment Equation) 18
2.6 H定理 21
2.7 Maxwell─Boltzmann 分布 22
2.8 分子間作用力 24
2.9 雙體彈性碰撞力學 25
2.9.1 碰撞截面與分子模式 29
2.9.2 平均自由路徑 37
2.9.3 平均碰撞時間 37
2.9.4 分子移動時步 38
3. DSMC數值方法 39
3.1 基本原理 39
3.2 DSMC之應用 40
3.2.1 初始狀態 40
3.2.2 碰撞過程模擬 41
3.3 邊界條件設定 44
3.3.1 流動邊界(Stream Boundary)設定 45
3.3.2 固體邊界的設定 52
3.4 模擬程序 58
4. 收縮式噴嘴流場模擬 60
4.1 程式驗證 60
4.1.1 研究模型建置 60
4.1.2 模擬條件設定 62
4.1.3 模型簡化與網格建置 66
4.1.4 驗證結果 68
4.2 稀薄效應對噴嘴流場影響 79
4.2.1 問題之描述與規劃 79
4.2.2 模擬結果與分析 81
4.3 反射條件對噴嘴流場影響 86
4.3.1 問題之描述與規劃 86
4.3.2 模擬結果與分析 88
4.4 背壓對噴嘴流場影響 93
4.4.1 問題之描述與規劃 93
4.4.2 模擬結果與分析 95
5. 總結 100
5.1 總結 100
5.2 未來研究方向 102
參考文獻 103
自傳 108

[1]Petersen, K. E., “Silicon as a Mechanical Material,” Proceedings of the IEEE, Vol. 70, pp. 420-457, 1982.
[2]http://www.csa.com/discoveryguides/mems/overview.
[3]李汶墾， “微流耦合機制之理論研究及在微流系統上之應用”，博士論文，國防大學中正理工學院，桃園，2010。
[4]宋齊有， “微機電系統技術之軍事航太應用”，微機電系統技術與應用，國科會精密儀器發展中心出版，台北，第13.4.1節，pp. 1202-1212，2003。
[5]Milligan, M., “Nozzle Characteristics in the Transition Regime Between Continuum and Free Molecular Flow,” AIAA journal, Vol. 2, pp. 1088-1092, 1964.
[6]Rae, W., “Some Numerical Results on Viscous Low-Density Nozzle Flows in the Slender-Channel Approximation,” AIAA journal, Vol. 9, pp. 811-821, 1971.
[7]Rothe, D., “Electron-Beam Studies of Viscous Flow in Supersonic Nozzles,” AIAA journal, Vol. 9,pp. 804-811, 1971.
[8]Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, New York, 1994.
[9]Xie C., “Characteristics of Micronozzle Gas Flows,” Physics of Fluids, Vol. 19, pp. 037120-1-6, 2007.
[10]Boyd, I., Penko, P., Meissner, D., and Dewitt, K., “Experimental and Numerical Investigations of Low-Density Nozzle and Plume Flows of Nitrogen,” AIAA journal, Vol. 30, pp. 2453-2461, 1992.
[11]Boyd, I., Vangilder, D., and Edward, J., “Computational and Experimental Investigations of Rarefied Flows in Small Nozzles,” AIAA journal, Vol. 34, pp. 2320-2326, 1996.
[12]Bayt, R., Ayon, A., and Breuer, K., “A Performance Evaluation of MEMS-Based Micronozzles,” in 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Vol. 97, pp. 3169-3179, 1997.
[13]Ivanov, M. S., Markelov, G. N., Ketsdever, A. D., and Wadsworth, D. C., “Numerical Study of Cold Gas Micronozzle Flows.” AIAA journal, Vol. 52, pp. 1-15, 1999.
[14]Ketsdever, A., Clabough, M., Gimelshein, S., and Alexeenko, A., “Experimental and Numerical Determination of Micropropulsion Device Efficiencies at Low Reynolds Numbers,” AIAA journal, Vol. 43, pp. 1191-1201, 2005.
[15]Sun, J. W., Liu, M. H., Zhang, G. X., Zhang, X. F., and Chen, Y. L., “Effect of Slip Boundary Condition on Numerical Results of 2D Micro Thruster,” Department of thermal Science and Energy Engineering, Vol. 26, pp. 1000-1328, 2005.
[16]Xie C., “Subsonic Choked Flow in the Microchannel,” Physics of Fluids, Vol. 18, pp. 127104-1-5, 2006.
[17]Alexeenko, A.,Fedosov, D.,Gimelshein, S.,Levin, D., and Collins, R., "Transient heat transfer and gas flow in a MEMS-based thruster," Microelectromechanical Systems, Journal of, Vol. 15, pp. 181-194, 2006.
[18]Yang, H. W., and Zhao, Y., “On Micro Nozzle Transition Area Flow by DSMC Method ,” Journal of Harb in Institute of Technology, Vol. 30, pp. 106-111, 2007.
[19]Yang, H. W., and Zhao, Y., “Simulation on Performance of Laval Micronozzle by Means of DSMC,” Journal of Solid Rocket Technology, Vol. 30, pp. 106-111, 2007.
[20]Hagiwara, S., Sawada, F., Horisawa, H., and Funaki, I., “Experimental and Numerical Investigation on Thrust Performance Improvement of Micro-Single-Nozzle Thrusters,” Transactions of Space Technology Japan, Vol. 7, pp. 19-24, 2008.
[21]Zhang, X. F., Liu, M. H., Li, L., Wang, D. and Chen, Y. L., “Effect of Temperature Boundary Conditions on Micronozzle Performance,” Journal of University of Science and Technology of China, Vol. 38, pp. 394-399, 2008.
[22]Liu, Z. M., and Zhang, T., “Numerical Investigation on Gas Flow in Laval Micronozzle,” Journal of Aerospace Power, Vol. 24, pp. 1556-1564, 2008.
[23]Lin, C., and Gadepalli, V., "A computational study of gas flow in a De-Laval micronozzle at different throat diameters," International Journal for Numerical Methods in Fluids, Vol. 59, pp. 1203-1216, 2009.
[24]Sun, Z.,Li, Z.,He, Y., and Tao, W., "Coupled solid (FVM)Luid (DSMC) Simulation of Micro-Nozzle with Unstructured-Grid," Microfluidics and Nanofluidics, pp. 1-11, 2009.
[25]Darbandi, M., and Roohi, E., "Study of Subsonic-Supersonic Gas Flow Through Micro/Nanoscale Nozzles Using Unstructured DSMC Solver," Microfluidics and Nanofluidics, pp. 1-15, 2010.
[26]Vincenti, W. G., and Kruger, C. H., Jr., Introduction to Physical Gas Dynamics, Wiley, New York, 1965.
[27]沈清，稀薄氣體動力學，國防工業出版社，北京，2003。
[28]Koura, K. and Matsumoto, H., “Variable Soft Sphere Molecular Model for Inverse-Power-Law or Lennard-Jones Potential,” Physics of Fluids, Vol. 3, pp. 2459-2465, 1991.
[29]Koura, K. and Matsumoto, H., “Variable Soft Sphere Molecular Model for Air Species,” Physics of Fluids, Vol . 4, pp. 1083-1085, 1992.
[30]羅仲禹， “微通道氣體流動與熱傳之蒙地卡羅直接模擬”， 碩士論文，國防大學中正理工學院，桃園，第41-116頁，2001。
[31]李延愷，“極超音速流中具噴流之刻槽圓錐體的流場及熱傳數值分析”，碩士論文，國防大學中正理工學院，桃園，1992。
[32]Bird, G. A., “Sophisticated DSMC,” Notes prepared for a short course at the DSMC07 meeting, SantaFe, Sep. 30, 2007.
[33]羅明忠，“蒙地卡羅法應用於高速氣流通過淺槽光窗之流場模擬”，碩士論文，國防大學中正理工學院，桃園，2009。
[34]劉峙佑，“微奈米流道分子氣動力模擬的邊界處理研究”，碩士論文，國防大學中正理工學院，桃園，第36-53頁，2008。
[35]陳炳炫， “Knudsen區氣體微尺度流動之蒙地卡羅直接模擬”，博士論文，國防大學中正理工學院，桃園，第34-48頁，2004。
[36]呂景琳，“微通道分子動力模擬的絕熱壁面邊界處理研究”，碩士論文，國防大學中正理工學院，桃園，第39-53頁，2008。
[37]Nance, R.P., and Hassan, H., "Role of boundary conditions in Monte Carlo simulation of MEMS devices," Journal of thermophysics and heat transfer, Vol. 12, pp. 447-449, 1998.
[38]王沫然、王金庫、李志信，“DSMC方法的壓力邊界條件實現”，計算物理，第二十一卷，第四期，第316-320頁，2004。
[39]Liou, W., and Fang, Y., "Implicit boundary conditions for direct simulation Monte Carlo method in MEMS flow predictions," In other words, Vol. 2, pp. 7, 2000.
[40]Wang, M., and Li, Z., "Simulations for Gas Flows in Microgeometries Using the Direct Simulation Monte Carlo Method," International Journal of Heat and Fluid Flow, Vol. 25, pp. 975-985, 2004.
[41]劉明和， “應用蒙地卡羅直接分子模擬法於差溫加熱之微區間系統自然對流研究” ，博士論文，國防大學中正理工學院，桃園，第19-25頁，2005。
[42]Tzeng, P. Y., Chou, I. W., Lo, M. L., Liu, C. H., “The improvement of gas surface collision rule for adiabatic walls in DSMC modeling of rarefied gas convection in micro-enclosure,” 16th National Computational Fluid Dynamics Conference, 2009.
[43]Janson, S. W., Helvajian, H., Breuer, K. “MEMS Microengineering and Aerospace Systems,” AIAA paper, Vol. 99, pp. 3802-3813, 1999.
[44]http://exploration.grc.nasa.gov
[45]邱士恆, "微噴嘴流之蒙地卡羅直接模擬" ，碩士論文，國立台灣大應用力學研究所，台北， 2000。
[46]胡大文，氣體動力學，復文書局，台南，1977。