跳到主要內容

臺灣博碩士論文加值系統

(44.211.31.134) 您好!臺灣時間:2024/07/13 00:43
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:陳澤興
研究生(外文):Chen, Tzer Shing
論文名稱:波茲曼方程式在流體粒子/電子/聲子傳播現象模擬
論文名稱(外文):Simulation of Boltzon/Electron/Phonon Flow Phenomena Using Boltzmann Transport Equation
指導教授:洪哲文洪哲文引用關係
指導教授(外文):Hong, Che-Wun
學位類別:博士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
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:2016
畢業學年度:104
語文別:中文
論文頁數:95
中文關鍵詞:波茲曼方程式
外文關鍵詞:Boltzmann Transport Equation
相關次數:
  • 被引用被引用:0
  • 點閱點閱:245
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
本論文主要以波茲曼傳播方程式(Boltzmann Transport Equation, BTE),藉由模擬非連體粒子(non-continuum particles)的實際運動行為來分析:
(1) 流體粒子(boltzons)在微米流道之二相流;
(2) 電子(electrons)在奈米線內之熱、電傳導現象;
(3) 聲子(phonons)在奈米及微米尺度下之熱傳導現象。
對於微流道二相流,將波茲曼傳播方程式離散化成晶格波茲曼模式(Lattice Boltzmann Modeling, LBM),並加入能量守恆成為熱晶格波茲曼法(TLBM),在穩態平衡時設定為波茲曼-馬克斯威爾分佈(Boltzmann-Maxwell Distribution),可用來分析微流道氣泡在二相流移動現象,及溫度邊界對其影響,大大減少計算流體力學(Computational Fluid Dynamics, CFD)二相流計算時間並維持計算精準度。
波茲曼傳播方程式亦可應用於波粒雙重性(paricle-wave duality)之電子傳播分析,在計算量子力學(Computational Quantum Mechanics, CQM)提供電子態密度與能量關係圖後,可再設定平衡時電子能量為費米-狄拉克分佈(Fermi-Dirac Distribution),運用波茲曼傳播方程式推導其電子傳導率、電子熱傳導率、以及席貝克係數(Seebeck Coefficient)與奈米結構之關係,本論文計算矽塊(bulk Silicon)及1nm直徑矽鍺超晶格奈米線(Si-Ge superlattice nanowire)的電子傳輸現象。模擬結果顯示,其計算精準度大致合理,唯同樣方法應用於非連續能量之聲子熱傳導率計算,則誤差極大且計算時間超過目前超級電腦允許容量。
針對此問題,本論文另行發展聲子波茲曼模擬,將聲子強度(phonon intensity)分布取代速度分布,並以統計物理之波西-愛因斯坦分佈(Bose-Einstein Distribution),結合離散座標法(discrete ordinate method, DOM)來分析線徑1 nm至1μm矽鍺奈米線的聲子傳輸現象,並獲致與實驗結果相符之熱傳導率。

This thesis mainly employs the Boltzmann Transport Equation (BTE), which is based on the non-continuum particle collision dynamics, to analyze the transport phenomena as below: (1) two-phase boltzon (fluid particle) flow in a micro-channel; (2) electric and thermal conductivities of electron flow in a nanowire; (3) thermal conductivity of phonon flow in micro and nanowires.
The Boltzmann Transport Equation has been discretized to transform into a lattice Boltzmann model (LBM) and energy conservation is further considered to derive into a thermal lattice Boltzmann scheme (TLBM). The Boltzmann-Maxwell distribution is assumed for the equilibrium velocity distribution function. This thesis takes a microchannel two-phase flow as an example to verify the scheme for checking the thermal effect on the bubble transportation.
The BTE is also employed to analyze an electron flow in a nanowire, assuming the Fermi-Dirac distribution is valid. Since electrons are inherent in particle-wave duality, a computational quantum mechanics (CQM) platform has to be employed to provide the relationship between the density of state versus energy level. A 1nm diameter Si-Ge superlattice nanowire has been taken as an example to calculate the electron conductivity, electron thermal conductivity, as well as the Seebeck coefficient.
Since the same computational quantum technique is too time-consuming to calculate the phonon flow in the nanowires, a modified phonon Boltzann scheme, using discrete ordinate method (DOM), has been derived. The phonon intensity is used to replace the velocity function and the Bose-Einstein distribution was assumed. The new scheme is able to perform more efficient computation and reasonable accuracy on thermal conductivity evaluation in both nano-scale nanowires and micro-scale microwires.

摘要 1
Abstract 2
誌謝 3
目錄 4
表目錄 7
圖目錄 8
符號說明 11
縮寫說明 16
第一章 緒論 17
1.1前言 17
1.2液體冷卻熱電晶片與微型直接甲醇燃料電池 18
1.3矽與矽鍺奈米線熱電材料 20
1.4氣泡流動與熱毛細現象文獻回顧 22
1.5矽鍺奈米線熱電材料文獻回顧 24
1.6研究動機與目標 26
第二章 粒子傳輸理論 27
2.1 波茲曼傳輸方程式 28
2.2 晶格波茲曼方程式與熱晶格波茲曼方程式 30
2.2.1晶格波茲曼方程式 30
2.2.2 標準D2Q9模型 32
2.2.3流場的熱晶格波茲曼法 33
2.2.4流場的邊界條件 35
2.2.5 溫度場的熱晶格波茲曼法 38
2.2.6 溫度場的邊界條件 40
2.3計算量子力學 42
2.3.1密度泛函理論 43
2.3.2電子波茲曼傳輸方程式 45
2.4聲子波茲曼傳輸方程式 49
2.4.2單層二維熱傳分析 54
2.4.3雙層二維熱傳分析 56
第三章 系統模式建構與模擬方法 59
3.1 模擬計算流程 59
3.2 模式建立 62
3.2.1微流道二相流 62
3.2.2矽鍺超晶格奈米線電子傳播模式 65
3.2.3矽鍺超晶格奈米線聲子傳播模式 67
第四章 結果與討論 74
4.1微流道二相流 74
4.2矽鍺超晶格奈米線電子傳播分析 81
4.3矽鍺超晶格奈米線聲子傳播分析 86
第五章 結論 93
5.1結論 93
參考文獻 94



[1] Á.G. Miranda, T.S. Chen, C.W. Hong, Feasibility study of a green energy powered thermoelectric chip based air conditioner for electric vehicles. Energy, 59, p.633-641, 2013.
[2] W.S. Liu, X. Yan, G. Chen and Z.F. Ren, Recent advances in thermoelectric nanocomposites. Nano Energy, 1(1): p. 42-56, 2012.
[3] Mildred S. Dresselhaus, Gang Chen, Ming Y. Tang, Ronggui Yang, Hohyun Lee, Dezhi Wang, Zhifeng Ren, Jean-Pierre Fleurial and Pawan Gogna, New directions for low-dimensional thermoelectric materials. Advanced Materials, 19, p.1043-1053, 2007.
[4] G. J. Snyder and E. S. Toberer, Complex thermoelectric materials. Nature Materials, 7, p.105-114, 2008.
[5] Allon I. Hochbaum, Renkun Chen, Rau Diaz Delgado, Wenjie Liang, Erik C. Garnett, Mark Najarian, Arun Majumdar and Peidong Yang, Enhanced thermoelectric performance of rough silicon nanowires. Nature, 451, p.163-167, 2008.
[6] Akram I. Boukai, Yuri Bunimovich, Jamil Tahir-Kheli, Jen-Kan Yu, William A. Goddard III and James R. Heath, Silicon nanowires as efficient thermoelectric materials. Nature, 451, p.168-171, 2008.
[7] Li-Dong Zhao, Shih-Han Lo, Yongsheng Zhang, Hui Sun, Gangjian Tan, Ctirad Uher, C. Wolverton, Vinayak P. Dravid and Mercouri G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature, 508, p.373-377, 2014.
[8] Lu, G. Q., and Wang, C. Y., “Electrochemical and flow characterization of a direct methanol fuel cell,” Journal of Power Sources, Vol. 134, No. 1, pp. 33-40, 2004.
[9] Yang, H., Zhao, T. S., and Te, Q., “In situ visualization study of CO2 gas bubble behavior in DMFC anode flow fields,” Journal of Power Sources, Vol. 139, No. 1-2, pp. 79-90, 2005.
[10] Yang, H., and Zhao, T. S., “Effect of anode flow field design on the performance of liquid feed direct methanol fuel cells,” Electrochimica Acta, Vol. 50, No. 16-17, pp. 3243-3252, 2005.
[11] Wong, C. W., Zhao, T. S., Ye, Q., and Liu, J. G., “Transient Capillary Blocking in the Flow Field of a Micro-DMFC and Its Effect on Cell Performance,” Journal of The Electrochemical Society, Vol. 152, No. 8, pp. A1600-A1605, 2005.
[12] Litterst, C., Eccarius, S., Hebling, C., Zengerle, R., and Koltay, P., “Increasing μDMFC efficiency by passive CO2 bubble removal and discontinuous operation,” Journal of Micromechanics and Microengineering, Vol. 16, No. 9, pp. S248-S253, 2006.
[13] Young, N. O., Goldstein, J. S., and Block, M. J., “The motion of bubbles in a vertical temperature gradient,” Journal of Fluid Mechanics, Vol. 6, No. 3, pp. 350-356, 1959.
[14] Jun, K. T., and Kim, C. J. “Microscale pumping with traversing bubbles in microchannels,” in Proc. IEEE Solid-State Sensor Actuator Workshop, Hilton Head Island, SC, pp. 144–147, 1996.
[15] Bratukhin, Y. K., Kostarev, K. G., Viviani, A., and Zuev, A. L., “Experimental study of Marangoni bubble migration in normal gravity,” Experiments in Fluids, Vol. 38, No. 5, pp. 594-605, 2005.
[16] Steele, M.C. and Rosi, F.D., Thermal Conductivity and Thermoelectric Power of Germanium-Silicon Alloys. Journal of Applied Physics, 1958. 29(11): p. 1517-1520.
[17] Abeles, B., Beers, D.S., Dismukes, J.P., and Cody, G.D., Thermal Conductivity of Ge-Si Alloys at High Temperatures. Physical Review, 1962. 125(1): p. 44-&.
[18] Slack, G.A. and Hussain, M.A., The Maximum Possible Conversion Efficiency of Silicon-Germanium Thermoelectric Generators. Journal of Applied Physics, 1991. 70(5): p. 2694-2718.
[19] Hicks, L.D. and Dresselhaus, M.S., Effect of Quantum-Well Structures on the Thermoelectric Figure of Merit. Physical Review B, 1993. 47(19): p. 12727-12731.
[20] Hicks, L.D. and Dresselhaus, M.S., Thermoelectric Figure of Merit of a One-Dimensional Conductor. Physical Review B, 1993. 47(24): p. 16631-16634.
[21] Hicks, L.D., Harman, T.C., Sun, X., and Dresselhaus, M.S., Experimental study of the effect of quantum-well structures on the thermoelectric figure of merit. Physical Review B, 1996. 53(16): p. 10493-10496.
[22] Lin Y. and Dresselhaus M.S., “Thermoelectric Properties of Superlattice Nanowires,” Physical Review B, Vol. 68, pp. 075304-075318, 2003.
[23] Dames C. and Chen G., “Theoretical Phonon Thermal Conductivity of Si/Ge Superlattice Nanowires,” Journal of Applied Physics, Vol. 95, pp. 682-693, 2004.
[24] Kittle C., Introduction to Solid State Physics, Wiley, New York, 1986.
[25] Akram I. Boukai, Yuri Bunimovich, Jamil Tahir-Kheli, Jen-Kan Yu, William A. Goddard III and James R. Heath, Silicon nanowires as efficient thermoelectric materials. Nature, 451, p.168-171, 2008.
[26] Hochbaum, A.I., Chen, R.K., Delgado, R.D., Liang, W.J., Garnett, E.C., Najarian, M., Majumdar, A., and Yang, P.D., Enhanced thermoelectric performance of rough silicon nanowires. Nature, 2008. 451(7175): p. 163-U5.
[27] Boukai, A.I., Bunimovich, Y., Tahir-Kheli, J., Yu, J.K., Goddard, W.A., and Heath, J.R., Silicon nanowires as efficient thermoelectric materials. Nature, 2008. 451(7175): p. 168-171.
[28] Zhu, G.H., Lee, H., Lan, Y.C., Wang, X.W., Joshi, G., Wang, D.Z., Yang, J., Vashaee, D., Guilbert, H., Pillitteri, A., Dresselhaus, M.S., Chen, G., and Ren, Z.F., Increased Phonon Scattering by Nanograins and Point Defects in Nanostructured Silicon with a Low Concentration of Germanium. Physical Review Letters, 2009. 102(19).
[29] Eun Kyung Lee, Liang Yin, Yongjin Lee, Jong Woon Lee, Sang Jin Lee, Junho Lee, Seung Nam Cha, Dongmok Whang, Gyeong S. Hwang, Kedar Hippalgaonkar, Arun Majumdar, Choongho Yu, Byoung Lyong Choi, Jong Min Kim, and Kinam Kim, Large Thermoelectric Figure-of-Merits from SiGe Nanowires by Simultaneously Measuring Electrical and Thermal Transport Properties. Nano Lett., 12, p.2918−2923, 2012.
[30] Paul A. Tipler, Ralph A. Llewellyn ,"Modern Physics" sixth Edition ,Fig 8.16 .
[31] D. A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models, Springer-Verlag Berlin Heidelberg, 2000 (Chapter5)
[32] Fei, K., Cheng, C. H., and Hong, C. W., “Lattice Boltzmann simulations of CO2 bubble dynamics at the anode of a DMFC,” ASME Journal of Fuel Cell Science and Technology, Vol. 3, No. 2, pp. 180-187, 2006.
[33] Zou, Q., and He, X., “On pressure and velocity boundary conditions for the lattice Boltzmann BGK model,” Physics of Fluids, Vol. 9, No. 6, pp. 1591-1598, 1997.
[34] Shi, Y., Zhao, T. S., and Guo, Z. L., “Thermal lattice Bhatnagar-Gross-Krook model for flows with viscous heat dissipation in the incompressible limit,” Physical Review E, Vol. 70, No. 62, pp. 066310, 2004.
[35] Inamuro, T., Yoshino, M., Inoue, H., Mizuno, R., and Ogino, F., “A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heat-transfer problem,” Journal of Computational Physics, Vol. 179, No. 1, pp. 201-215, 2002.
[36] Levine, I.N., Quantum chemistry. 6. ed. 2009, Upper Saddle River, N.J.: Pearson Education. 2 bd.
[37] W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects,” Physical Review, 140, p.1133-&, 1965.
[38] A. Majumdar,“Microscale heat conduction in dielectric thin films,” ASME Journal ofHeat Transfer, Vol. 115, pp.7-16, 1993.
[39] G.Chen, "Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices." Physical Review B 57.23 ,1998.
[40] Chen G., “Thermal Conductivity and Ballistic-phonon Transport in the Cross-plane Direction of Superlattices,” Physical Review B, Vol. 57, pp. 14958-14973, 1998.
[41] Lu X., Shen W. Z. and Chu J. H., “Size Effect on the Thermal Conductivity of Nanowires,” Journal of Applied Physics, Vol. 91, pp. 1542-1552, 2002.
[42] Rey, Guillem Colomer. Numerical methods for radiative heat transfer. Universitat Politècnica de Catalunya, 2007.
[43] Majumdar A., “Microscale Heat Conduction in Dielectric Thin Films,” ASME Journal of Heat Transfer, Vol. 115, pp. 7-16, 1993.
[44] K. Fei, T. S. Chen and C. W. Hong,” Direct Methanol Fuel Cell Bubble Transport Simulations via Thermal Lattice Boltzmann and Volume of Fluid Methods” Journal of Power Sources, vol. 195, pp. 1940-1945, 2010.
[45] P. D. Desai, Thermodynamic Properties of Iron and Silicon. Journal of Physical and Chemical Reference Data, 15, p.967-983, 1986.
[46] H. R. Shanks, P. D. Maycock, P. H. Sidles and G. C. Danielson, Thermal conductivity of silicon from 300 to 1400 K. Physical Review, 130, p.1743-1748, 1963.
[47] R. A. Serway, Principles of physics. 2nd ed. Saunders golden sunburst series, Fort Worth: Saunders College Pub. Xxxii, p.954, 1998.
[48] Li D., Wu T., Kim P., Shi L., Yang P. and Majumdar A., “Thermal Conductivity of Individual Silicon Nanowires,” Applied Physics Letters, Vol. 83, pp. 2934-2936, 2003.
[49] Hsiao, T. K. et al. Thermal Conductivity Phase Diagram of SiGe Nanowires. Nano Communications. Vol. 19 No.2 , pp.38-42 , 2012/06/01.
[50] T. K. Hsiao et al. Observation of room temperature ballistic thermal conduction persisting over 8.3μm in SiGe nanowires. Nature Nanotech. 8, 534, 2013.


連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top