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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊照彥(Jaw-Yen Yang) | |
dc.contributor.author | Cheng-Han Tsai | en |
dc.contributor.author | 蔡承翰 | zh_TW |
dc.date.accessioned | 2021-06-16T07:08:56Z | - |
dc.date.available | 2018-08-31 | |
dc.date.copyright | 2014-07-16 | |
dc.date.issued | 2014 | |
dc.date.submitted | 2014-07-08 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57875 | - |
dc.description.abstract | 在連體模型中,主要的統御方程式是透過歐拉或納維爾方程式來求解。然而在氣體稀薄程度提升時,將不再適用,此時方程式為波茲曼方程式。在相關的研究中,對波茲曼方程式作空間及速度離散,即可推導出格子波茲曼法 (Lattice Boltzmann Method, LBM)。
在本文中,根據Uehling-Uhlenbeck Boltzmann-BGK方程(Uehling-Uhlenbeck Boltzmann Bhatnagar-Gross-Krook Equation)及橢圓統計BGK方程(Ellipsoidal Statistical BGK equation, ESBGK)所發展出的半古典橢圓統計格子波茲曼法,透過這個方法,我們可以有效利用其主導的分布函數來計算出所需之宏觀量。利用此法以及D2Q9速度格子模型為基礎,模擬在三種不同粒子統計下,流體流過使用沉浸邊界速度修正法(Immersed Boundary Velocity Correction Method, IBVCM)的圓柱所產生的渦漩、渦度、壓力以及阻力係數之比較。由模擬結果顯示,ESBGK模型之間三種不同的粒子統計差異(Bose-Einstein統計、Fermi-Dirac統計和Maxwell-Boltzmann統計),並且隨著雷諾數的增加,流線出現了馮卡門漩渦現象。除此之外,還可運用半古典格子波茲曼可還原成古典格子波茲曼法的特性(MB統計),與其相關研究作驗證。當圓柱在流道中持續的移動,此時模擬比較而觀察出尾流渦漩在三種統計中有明顯不同的差異結果。 | zh_TW |
dc.description.abstract | Modeling gases in the continuum level is traditionally achieved with macroscopic level by using Euler or Navier-Stokes equations. However, as the degree of rarefaction of a gas increses, the governing equation becomes Boltzmann Equation. The Lattice Boltzmann method is derived by discretizing Boltzmann equation in physical and velocity space.
In the study, the development of a semiclassical lattice Boltzmann–Ellipsoidal Statistical method is based on the Uehling-Uhlenbeck Boltzmann-BGK equation. According to the method, we can effectively link its dominant distribution function to calculate the quantities of macroscopic properties. Here, we present simulations of the flow over cylinder for several Reynolds numbers based on D2Q9 lattice model and the semiclassical lattice Boltzmann–Ellipsoidal Statistical method. In this work, the Immerse Boundary Velocity Correction method (IBVCM) has been used to model the boundary of the cylinder. We compare the results of vortices, pressure, drag coefficient for different particle statistics : Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics. By studying the streamlines, we observed von Karman vortex street phenomenon as the Reynolds number increases. In addition, the movement of the cylinder boundary is not stationary in the flow channel by taking advantage of the boundary using IBVCM. We observed the wake and found differences in the results of the three statistics. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T07:08:56Z (GMT). No. of bitstreams: 1 ntu-103-R01543013-1.pdf: 15148023 bytes, checksum: c476fb4e5fb544c72d5cd75a0ca0ae9b (MD5) Previous issue date: 2014 | en |
dc.description.tableofcontents | 致謝……………………………………………………………………………………I
中文摘要…………………………………………………………………………II Abstract……………………………………………………………………III 目錄…………………………………………………………………………………IV 圖目錄………………………………………………………………………………VI 符號表………………………………………………………………………………IX 第一章 緒論 1 1-1 計算流體力學 1 1-2 格子Boltzmann法簡介 2 1-3 量子理論簡介 3 1-4 文獻回顧 4 1-5 本文目的 6 第二章 波茲曼傳輸方程式 7 2-1 氣體運動理論 7 2-2 分布函數 9 2-3 波茲曼傳輸方程式 11 2-4 Boltzmann H定理 15 2-5 馬克斯威爾分布 18 2-6 Boltzmann BGK 方程 21 2-7 格子Boltzmann方程 22 2-8 單鬆弛時間離散速度模型 24 2-9 Hermite展開平衡態分布函數 26 第三章 半古典格子波茲曼方程式 30 3-1 量子統計 30 3-2 半古典格子Boltzmann-BGK方程式 32 3-3 單鬆弛時間Chapman-Enskog分析 38 第四章 半古典橢圓統計格子波茲曼方程式 42 4-1 半古典格子Boltzmann-ESBGK方程式 42 4-2 宏觀物理量之求法 47 4-3 格子Boltzmann-ESBGK方程之Chapman-Enskog分析 47 第五章 基本模型與邊界處理方法 52 5-1 格子Boltzmann-ESBGK方程式 52 5-2 邊界條件 53 5-2-1 沉浸邊界速度修正法 53 5-2-2 標準反彈邊界 55 5-3 模擬參數定義及收斂條件 56 第六章 模擬結果與討論 58 6-1 圓柱繞流(Flow Over Cylinder) 58 6-2 模擬問題描述 59 6-3 模擬結果分析與探討 61 第七章 結論與未來展望 99 7-1 結論 99 7-2 未來展望 100 文獻回顧 101 | |
dc.language.iso | zh-TW | |
dc.title | 結合沉浸邊界速度修正法之半古典橢圓統計格子波茲曼流場模擬 | zh_TW |
dc.title | Hydrodynamic Flow Simulation Using Semiclassical Lattice Boltzmann-Elliposidal Statistical Method with Immersed Boundary Velocity Correction Method | en |
dc.type | Thesis | |
dc.date.schoolyear | 102-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳朝光(Chao-Kuang Chen),楊玉姿(Yue-Tzu Yang),何正榮(Jeng-Rong Ho) | |
dc.subject.keyword | 半古典格子波茲曼方法,半古典橢圓統計格子波茲曼法,D2Q9模型,圓柱繞流,沉浸邊界速度修正法, | zh_TW |
dc.subject.keyword | Semiclassical lattice Boltzmann method,Semiclassical lattice Boltzmann–Ellipsoidal Statistical method,D2Q9 lattice model,flow over circular cylinder,Immersed Boundary Velocity Correction Method, | en |
dc.relation.page | 103 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2014-07-09 | |
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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