臺灣博碩士論文加值系統

近年來極低軌道衛星(VLEO Satellites)因其應用潛力，而成為太空發展重點，當中應用較為廣泛的便是立方衛星(CubeSat)，設計上其個別單位(U)體積、重量和一公升的水相同(10×10×10cm3)，並具有成本低廉，可單次進行多顆部署，與星群運作等優點；但受限於尺寸與軌道高度，其使用壽限較傳統衛星短少，故研究其影響因子，便是十分重要的工作。
本研究應用一種基於C++語言發展而來的直接模擬蒙地卡羅法(DSMC)，即「平行直接模擬蒙地卡羅法(PDSC++)」；由於PDSC++應用平行計算技術，故相較於傳統DSMC，可藉由更快的運算效率完成模擬；而經與其他DSMC程式相互驗證，其模擬結果具有一定之可信度。
透過結果分析可發現，在攻角效應上，其流場特性分布情況，會隨衛星攻角姿態改變，且在45°攻角下，所受到之應力為本研究攻角條件下之最小值；而在軌道高度效應上，則發現軌道高度愈高，流場會愈加稀薄，此時衛星所受到之應力值也越小；而在構型效應上，則發現衛星所受應力大小，與其尺寸大小成正比；除此之外，在太陽能板效應研究上，則發現在太陽能板展開後，因其與流場之碰撞面增加，故增大其所受應力，亦影響其流場特性分布情況；透過前述研究成果，本論文可供後續立方衛星任務規劃、軌道設計、操控姿態等研究做為參考。

The application of very-low earth orbit (VLEO) satellite has become a popular issue in space development lately. And the CubeSat is one of its kind, that has been widely used. With the equivalent scale in size and weight per unit as 1-liter water, it needs less budget than conventional satellites do. Also, this characteristic makes it could be multiple deployed, and work in constellation. On the other hand, its life time is shorter than those conventional satellites do. Thus the aerothermodynamics researches become an important issue in this topic.
In this study we use a parallel DSMC code called PDSC++. Compare to traditional DSMC, it could complete simulation in higher efficiency with parallelizing computing techniques. Through benchmarks with other codes, results of PDSC++ show high fidelity with them, thus founded its credibility.
Our researches tempt to simulate the hypersonic rarefied flow of VLEO CubeSat. Through those results, we found out that as angle of attack changed, posture changed either, which would influence flow properties distribution. And its orbit altitude is disproportionate to the flow particle density, which influences the value of stress. Also, the size configuration is proportional to the stress. At last, as solar panels deployed, cubesat got more surfaces to react with flow particles, thus stress may increase as flow interacting with cubesat. With those results, it would be helpful in future cubesat mission deign.

目錄

誌謝 ii
摘要 iii
Abstract iv
目錄 v
表目錄 viii
圖目錄 ix
符號說明 xii
1. 前言 1
1.1 研究動機 1
1.2 研究方法分析 3
1.3 文獻回顧 6
1.4 研究目的 13
2.分子動力學 14
2.1 基本原理 14
2.2 平均自由徑 14
2.3 速度分布函數 15
2.4 波茲曼方程式 18
2.5 麥斯威爾分布 22
2.6 分子間碰撞原理 24
2.7 分子碰撞模式 26
3. 直接模擬蒙地卡羅法 31
3.1 基本原理 31
3.2 數值模擬流程 32
3.3 模擬條件設定 35
3.3.1 狀態設定 35
3.3.2 邊界設定 36
3.3.2.1 流動邊界 36
3.3.2.2 固體邊界 38
3.4 分子碰撞模擬 43
3.4.1 碰撞對估算 43
3.4.2 碰撞對選擇 44
3.4.3 碰撞結果 45
3.5 研究方法 46
3.5.1 平行化蒙地卡羅法(PDSC++) 46
3.5.2 程式驗證 48
3.5.3 立方衛星模擬驗證 50
3.5.3.1 模擬設定 51
3.5.3.2 結果比較 52
4. 立方衛星流場模擬 55
4.1 研究模型建置 55
4.2 模擬條件設定 58
4.3 攻角對流場之效應探討 60
4.4 軌道高度對流場之效應探討 68
4.5 尺寸構型對流場之效應探討 79
4.5.1 長度影響效益 80
4.5.2 寬度影響效益 81
4.6 太陽能板對流場之效應探討 96
5. 結論 118
5.1 總結 118
5.2 未來研究與應用方向 119
參考文獻 120
自傳 127

[1]https://en.wikipedia.org/wiki/Russian_Aerospace_Defence_Forces
[2]https://en.wikipedia.org/wiki/Air_Force_Space_Command
[3]https://en.wikipedia.org/wiki/Strategic_Defense_Initiative
[4]https://abcnews.go.com/Politics/trump-signs-memo-establishing-us-space-command-combatant/story?id=59884940
[5]https://spacewatch.global/2019/05/japanese-military-space-mod-to-allocate-100-personnel-for-space-domain-mission-unit-by-fy2022-seeks-replacement-for-lost-worldview-4/
[6]https://www.reuters.com/article/us-france-nationalday-defence/france-to-create-space-command-within-air-force-macron-idUSKCN1U80LE
[7]Heidt, H., Puig-Suari, J., Moore, A.S., Nakasuka, S., and Twiggs, R.J., 2000, “CubeSat: A New Generation of Picosatellite for Education and Industry Low-Cost Space Experimentation,” Small Satellite Conference Paper, no.32.
[8]Llop, J. V., Roberts, P. C.E., Hao, Z., Tomas, L. R., Beauplet, V., 2014, “2014-Very Low Earth Orbit mission concepts for Earth Observation. Benefits and challenges.,” Proceedings of the 12th Reinventing Space Conference.
[9]https://edition.cnn.com/videos/politics/2016/11/21/space-wars-cubesat-origwx-jm.cnn
[10]Ethiraj, V., 2013, “Modern Advances in Ablative TPS, Descent, and Landing Systems Short Course”, NASA, California, pp. 4.
[11]Tsien, H. S., 1946, “Super-Aerodynamics, Mechanics of Rarefied Gases,” Journal of the Aeronautical Sciences, 13(12), pp. 653-664.
[12]Chapman, S. and Cowling, T. G., 1970, The Mathematical Theory of Non-Uniform Gases, Cambridge Univ. Press, Cambridge.
[13]Bhatnagar, P. L., Gross, E. P. and Krook, M., 1954, “A Model for Collision Processes in Gases, I. Small Amplitude Processes in Charged and Neural One-Component Systems,” Physical Review, Vol. 94, No. 3, pp. 511-524.
[14]Alder, B. J., and Wainwright, T. E., 1959, “Studies in Molecular Dynamics. I. General Method,” The Journal of Chemical Physics, 31(2), pp. 459–466.
[15]Havilan, J. K. and Lavin, M. L., 1962, “Applications of the Monte Carlo Method to Heat Transfer in a Rarefied Gas,” Physics of Fluid, Vol. 5, pp. 1399-1405.
[16]Bird, G. A., 1976, Molecular Gas Dynamics, New York, Oxford: Clarendon Press.
[17]Bird, G. A., 1994, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, New York, Oxford: Clarendon Press.
[18]1976, “US Standard Atmosphere, 1976”, NOAA,NASA,USAF, U.S. Government Printing Office.
[19]Bird, G. A., 1963, “Approach to Translational Equilibrium in a Rigid Sphere Gas”, Physics of Fluids, No. 6, pp. 1518.
[20]Leeuw, J. H., 1965, Rarefied Gas Dynamics, New York, Academic Press, Vol. 1, pp. 216.
[21]Kogan, M. N., 1969, Rarefied Gas Dynamics, New York, Plenum Press.
[22]Karamcheti, K., 1974, Rarefied Gas Dynamics, New York, Academic Press.
[23]Bird, G. A., 1990, “Application of the Direct Simulation Monte Carlo to the Full Shuttle Geometry,” AIAA/ASME 5th Joint Thermophysics and Heat Transfer Conference, Washington, D.C.
[24]Rault, D. F. G. and Woronowicz, M. S., 1995, “Application of direct simulation Monte Carlo to satellite contamination studies,” Journal of Spacecraft and Rockets, Vol. 32, No. 3.
[25]Ivanov, M. S. and Gimelshein, S. F., 1998, “Computational Hypersonic Rarefied Flows”, Journal of Fluid Mechanics, Vol. 30, pp.469–505.
[26]Garcia, A. L., Bell, J. B., Crutchfield, W. Y., and Alder, B. J., 1999, “Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo”, Journal of Computational Physics, Vol.154, pp.134–155.
[27]Hank, H., Jordi, P.-S., Augustus, S. M., Shinichi, N., Robert, J. T., 2000 ,“CubeSat: A new Generation of Picosatellite for Education and Industry Low-Cost Space Experimentation”, 14TH Annual/USU Conference on Small Satellites, Logan City.
[28]Riabov, V. V., 2002, “Aerodynamics of Two Side-by-Side Plates in Hypersonic Rarefied-Gas Flows”, 32nd AIAA Fluid Dynamics Conference and Exhibit, Washington, D.C..
[29]Wu, J.-S., Tseng, K.-C., and Yang, T.-J., 2003, “Parallel Implementation of DSMC Using Unstructured Mesh,” International Journal of Computational Fluid Dynamics, Vol. 17(5), pp. 405–422.
[30]Kenneth, M., and Mildred, M. M., 2005, “Gas–surface interactions and satellite drag coefficients,” Planetary and Space Science, Vol. 53, pp. 793–801.
[31]Padilla, J. F., 2008, “Atmospheric Interactions with Spacecraft,” Ph.D. Dissertation, Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan.
[32]David, F., 2010, “Assessment of Gas-Surface Interaction Models for Computation of Rarefied Hypersonic Flows,” Encyclopedia of Aerospace Engineering, New Jersey, John Wiley & Sons, Ltd.
[33]Várhegyi, Z., 2011, “Trajectory Analysis and Preliminary Mission Design for QB50”, Master's Thesis, Budapest University of Technology and Economics, Budapest.
[34]李學東、魏傳鋒，2013，“高超聲速氣流非結構化網格DSMC算法研究”，航天器環境工程，第30卷，第四期，第375-379頁。
[35]羅明忠，2015，“利用平行直接模擬蒙地卡羅法模擬具反應與非高速稀薄氣體熱流場之研究”，博士論文，國立交通大學機械工程研究所，新竹。
[36]James, P. M., Bret, L., and Thomas, N. W., 2018, “CubeSat On-Orbit Temperature Comparison to Thermal-Balance-Tuned-Model Predictions,” Journal of Thermophysics and Heat Transfer, Vol. 32, No. 1, pp. 237-255, 2018.
[37]Palharini, R. C., and Azevedo, J. L. F., 2017, “Thermochemical Nonequilibrium Computations of a Brazilian Reentry Satellite,” Journal of Spacecraft and Rockets, Vol. 54, No. 4, pp. 961-966, 2017.
[38]Pikus, A., Berger, A., Bolliger, M., Parkos, D., and Alexeenko, A., 2017, “DSMC Aerothermal Study for 3U CubeSat Probes in LEO,” 47th AIAA Thermophysics Conference, Washington, D.C.
[39]http://foundation.nmns.edu.tw/writing/past.php?v=1&id=192
[40]Bird, G. A., 1977, “Direct Simulation of the Incompressible Kramers Problem,” Progress in Astronautics and Aeronautics, Vol. 51, pp. 323-333.
[41]Moss, J. N., and Bird, G. A., 1985, “Direct Simulation of Transitional Flow for Hypersonic Reentry Conditions,” Progress in Astronautics and Aeronautics, Vol. 96, pp. 113-139.
[42]Alexander, F. J., Garcia, A. L. and Alder, B. J., 1998, “Cell Size Dependence of Transport Coefficients in Stochastic Particle Algorithms,” Physics of Fluids, Vol. 10, No. 6, pp. 1540-1542.
[43]陳炳炫，2004， “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兵研所，桃園。
[44]Pardilla, J. F., 2007, “Assessment of Gas-Surface Interaction Models in DSMC Analysis of Rarefied Hypersonic Flows,” AIAA Paper 3891.
[45]Cercignani, C. and Lampis, M., 1971, “Kinetic Models for Gas-Surface Interactions,” Transport Theory and Statistical Physics, Vol. 1, pp. 101-114.
[46]李延愷，1992，“極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。
[47]Tzeng, P. Y., Chou, I. W., Liu, C. H., and Li, W. K., 2011, “Improvement of the Gas-Surface Collision Rule for Adiabatic Walls in DSMC Modeling of Rarefied Gas Convection in a Micro Enclosure,” Journal of Aeronautics Astronautics and Aviation, pp. 147-158.
[48]Logan, R. M. and Stickney, R. E., 1966, “Simple Classical Model for the Scattering of Gas Atoms from the Surfaces,” The Journal of Chemical Physics, Vol. 44, pp. 195-201.
[49]Tzeng, P. Y., Soong, C. Y., Liu, M. H., and Yen, T. H., 2008, “Atomistic Simulation of Rarefied Gas Natural Convection in a Finite Enclosure Using a Novel Wall-Fluid Molecular Collision Rule for Adiabatic Solid Walls,” International Journal of Heat and Mass Transfer, Vol.51, pp. 445-456.
[50]Su, C. C., 2013, “Parallel Direct Simulation Monte Carlo (DSMC) Methods for Modeling Rarefied Gas Dynamics,” Ph.D. Dissertation, Department of Mechanical Engineering, National Chiao Tung University, Hsinchu.
[51]Wu, J.S., Tseng, K.C., and Wu, F.Y. , 2004, “Parallel three-dimensional DSMC method using mesh refinement and variable time-step scheme,” Journal of Computer Physics Communications, 162, pp. 166-187.
[52]Kannenberg, K.C., and Boyd, I.D., 2000, “Strategies for Efficient Particle Resolution in the Direct Simulation Monte Carlo Method”, Journal of Computational Physics, 157.2, pp. 727-745.
[53]Su, C.C., Tseng, K.C., Cave, H.M., Wu, J.S., Lian, Y.Y., Kuo, T.C., and Jermy, M.C. , 2010 “Implementation of a transient adaptive sub-cell module for the parallel-DSMC code using unstructured grids,” Computers & Fluids, 39 , pp. 1136-1145.
[54]Bird, G. A., 2005 “The DS2V/3V Program Suite for DSMC Calculations, in Rarefied Gas Dynamics: Proceedings of the 24th International Symposium on Rarefied Gas Dynamics,” AIP Conference Proceedings, New York, pp. 541-546.
[55]Wu, J.S., and Lian, Y.Y., 2003,“Parallel three-dimensional direct simulation Monte Carlo method and its applications, ” Computers & Fluids, 32, pp. 1133-1160.
[56]Wu, J.S., and Tseng, K.C., 2005, “Parallel DSMC Method Using Dynamic Domain Decomposition,” International Journal for Numerical Methods in Engineering, 63, pp. 37-76.
[57]Holden, M.S., Wadhams, T.P., Harvey, J.K., and Candler, G.V., 2006, “Comparisons between Measurements in Regions of Laminar Shock Wave Boundary Layer Interaction in Hypersonic Flows with Navier-Stokes and DSMC Solutions,” DTIC Paper.
[58]https://cceres.psl.eu/spip.php?rubrique21&lang=en
[59]Moss, J.N., and Bird, G.A., 2004, “DSMC Simulations of Hypersonic Flows With Shock Interactions and Validation With Experimentss,”37th AIAA Thermophysics Conference, Portland.