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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 楊照彥 | |
| dc.contributor.author | Ping-Hsue Tsai | en |
| dc.contributor.author | 蔡秉學 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:12:26Z | - |
| dc.date.available | 2009-08-12 | |
| dc.date.copyright | 2009-08-12 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-30 | |
| dc.identifier.citation | [1] Jamison, A. J., Ketsdever , A. D. & Muntz, E. P. 2002 Gas Dynamic Calibration of a Nano-Newton Thrust Stand, Review of Scientific Instruments Vol. 73, No. 10, pp. 3629-3673.
[2] Aktas, O., Aluru, N. R. & Ravaioli, U. 2001 Application of a Parallel DSMC Technique to Predict Flow Characteristics in Microfluidic Filters, Journal of Microelectromechanical Systems Vol. 10, No. 4, pp. 538-549. [3] Szwemin, P., Szymanski, K. H. & Jousten, S. 1999 Monte Carlo Study of a New PTB Primary Standard for Very Low Pressures, Metrologia, Vol. 36, No. 1, pp. 562-564. [4] Liepmann, H.W. 1961 Gaskinetics and Gasdynamics of Orifice Flow, Journal of Fluid Mechanics, Vol.10, No. 1, pp. 65-79. [5] Narasimha, R. 1961 Orifice Flow of High Knudsen Number, Journal of Fluid Mechanics, Vol.10, October, pp.371-384. [6] Narasimha, R. 1961 Some Flow Problems in Rarefied Gas Dynamics, Ph.D. thesis, California Institute of Technology, Pasadena, CA. [7] Narasimha, R. 1962 Collisionless Expansion of Gases into Vacuum, Journal of Fluid Mechanics, Vol. 12, No. 3, pp. 294-308. [8] Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, New York. [9] Gombosi, T. I. 1994 Gaskinetic Theory, Cambridge University Press, New York. [10] Shen, C. 2005 Rarefied Gas Dynamics-Fundamentals, Simulations, and Micro Flows, Springer. [11] Chen, X. 1996 Gaskinetics and Its Applications in Heat Transfer and Flows, Tsinghua University Press, Beijing. [12] Sharipov, F. 2004 Numerical Simulation of Rarefied Gas Flow Through a Thin Orifice, Journal of Fluid Mechanics, Vol.518, pp.35-60. [13] Cai, C. 2005 Theoretical and Numerical Studies Of Plume Flows in Vacuum Chambers, Ph.D. Dissertation, Department of Aerospace Engineering, Univercity of Michigan, Ann Arbor, Michigan. [14] Cai C. & Boyd, I. D. 2006 Collisionless Gas Expanding into Vacuum, Journal of Spacecraft and Rocket, Vol.44 No.6, pp.1326-1330. [15] Cai, C. 2007 Theoretical and Numerical Study of Free-Molecular Flow Problems, Journal of Spacecraft and Rockets, Vol.44, No.2, pp.619-624. [16] Pathria, R. K. 1996 Statistical Mechanics, 2nd Ed., Butterworth Heinemann Publications, Washington, DC. [17] Huang, K. 1987 Statistical Mechanics, 2nd Ed., Wiley, New York. [18] Shi, Y. S. 2008 Kinetic Numerical Methods for the Semiclassical Boltzmann Equation, Ph.D. thesis, Institute of Applied Mechanics, National Taiwan University. [19] J. J. Kelly 1996 Ideal Quantum Gas, Lecture Note. [20] K. Nanbu, 1996 Stochastic Solution Method of the Boltzmann Equation, The Report of the Institute of Fluid Science Tohoku University, Sendai Japan, Vol.8. [21] Charles, R.L. & Macrossan, M. N. 2003 Methods for Implementing the Stream Boundary Condition in DSMC Computations, International Journal for Numerical Methods in Fluid. Vol. 44, pp.1363-1371. [22] Oran, E.S., Oh, C.K. & Cybyk, B.Z. 1998 Direct Simulation Monte Carlo:Recent Advances and Applications, Annual Review of Fluid Mechanics. [23] Patterson, G. N. 1956 Molecular Flow of Gases, Wiley, New York. [24] Chen, G. 2005 Nanoscale Energy Transport and Conversion, Oxford University press, New York. [25] Rao, S. S. 2001 Applied Numerical Methods for Engineers and Scientists, 1st Ed., Prentice Hall Professional Technical Reference. [26] Burden, R. L. and Faires, J. D. 1989 Numerical Analysis, 8th Ed., PWS-KENT Publishing Company, Boston, USA. [27] Hsieh, T. Y. 2007 High Resolution Schemes for Phonon Heat Transfer and Ideal Quantum Gas Dynamics, Ph.D. thesis, Institute of Applied Mechanics, National Taiwan University. [28] 吳大猷，2003，「熱力學，氣體運動論，統計力學」，聯經出版。 [29] 鄭以禎，2003，「巨觀與統計熱力學」，偉明圖書公司出版。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42347 | - |
| dc.description.abstract | 本文內容探討數個量子氣體自由分子流問題，主要為流體從熱平衡的容器中擴張到真空當中；從物理空間與速度空間的關係中，以統計力學的觀點對粒子的分佈函數做積分後，得到數密度(number density)與分子平均速度在流場的分佈。粒子的分佈函數使用了三種不同的分佈函數：費米-迪拉克(Fermi-Dirac)、玻色-愛因思坦(Bose-Einstein)、馬克士威爾-波茲曼(Maxwell-Boltzmann)分佈函數，分別代表了三種表現不同的粒子：費米子(Fermions)、玻色子(Bosons)幾及古典粒子；前兩種量子分佈函數在得到的解析解中表現出了量子效應，產生與古典粒子完全不同之行為；透過改變分佈函數中的逸度(fugacity)，我們觀察到不同程度的量子效應，而在系統趨近於古典極限，也就是逸度遠小於1時，兩種量子統計將會回復到古典統計，解析的結果顯示古典粒子的表現介於兩種量子粒子之間。
在數值模擬方面採用直接模擬蒙地卡羅法(direct simulation Monte Carlo)模擬稀薄氣體的流場，將粒子間假設為沒有碰撞，試著驗證自由分子流解析解的正確性，可以看出兩者的結果非常相近。 | zh_TW |
| dc.description.abstract | This paper concentrates on several collisionless quantum gas flow problems . The problems concern collisionless flow expanding into vacuum. From a relationship between particle position and velocity, we obtain the corresponding exact solutions for the number density and velocity distributions for the problems. We obtain the exact solutions with 3 distribution functions, which are Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann distribution function, which represent 3 kinds of particles, fermions, bosons and classical particles. Solutions obtained from quantum distribution functions show the differences with classical particles, the quantum effects are found by changing the fugacity of the quantum distribution. In the classical limit, the fugacity is less than 1, three distribution functions converge in the limit. In general the classical particles behave between two quantum particles. Numerical solution results obtained with the direct simulation Monte Carlo method in agreement with the analytical solutions. In general the comparisons between the exact solution and the numerical solutions are virtually identical. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:12:26Z (GMT). No. of bitstreams: 1 ntu-98-R96543029-1.pdf: 936134 bytes, checksum: f76e59741b15ed902251cf6a186026e5 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 摘要 I
Abstract II 目錄 III 圖目錄 V 第一章、 緒論 1 1.1 引言 1 1.2 本文目的 2 1.3 本文內容 3 第二章、 量子統計下的平衡態分佈函數 4 2.1 粒子的可分辨性 4 2.2 大正則系綜(Grand Canonical)下的量子統計 5 2.3 三種統計的性質 6 2.4 古典極限 7 第三章、 直接模擬蒙地卡羅法 9 3.1 原理介紹 9 3.2 統馭方程式 10 3.3 碰撞條件 11 3.4 邊界條件 13 第四章、 自由分子流問題之解析解 16 4.1 自由分子流問題與解題方法 16 4.2 二維狹縫出口，出口高度為 ，分子流平均速度為０ 17 4.3 矩形狹縫出口，出口高度為 ，寬度為 ，分子流平均速度為０ 20 4.4 出口為兩個同心矩形之間的狹縫，矩形大小為 、 以及 、 ，分子流平均速度為０ 23 4.5 圓形半徑為 的出口，分子流平均速度為０ 26 4.6 出口為兩個同心圓之間的狹縫，半徑分別為 、 ，分子流平均速度等於０ 28 第五章、 結果與展望 33 5.1 結論 33 5.2 未來展望 34 參考文獻 35 圖表 38 附錄A. 自由分子流問題之推導 80 | |
| dc.language.iso | zh-TW | |
| dc.subject | 理想量子氣體 | zh_TW |
| dc.subject | 蒙地卡羅法 | zh_TW |
| dc.subject | 自由分子流 | zh_TW |
| dc.subject | 解析解 | zh_TW |
| dc.subject | 量子效應 | zh_TW |
| dc.subject | Free molecular flow | en |
| dc.subject | DSMC | en |
| dc.subject | analytical solutions | en |
| dc.subject | ideal quantum gas | en |
| dc.subject | quantum effect | en |
| dc.subject | collisionless flow | en |
| dc.title | 理想量子氣體自由分子流噴流問題之解析解 | zh_TW |
| dc.title | Analytical Solutions of Several Ideal Quantum Gas Effusion Flow Problems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃美嬌,黃俊誠,石育炘 | |
| dc.subject.keyword | 自由分子流,量子效應,理想量子氣體,解析解,蒙地卡羅法, | zh_TW |
| dc.subject.keyword | Free molecular flow,collisionless flow,quantum effect,ideal quantum gas,analytical solutions,DSMC, | en |
| dc.relation.page | 84 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-30 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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