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研究生:劉芳谷
研究生(外文):Fang-Ku Liu
論文名稱:具攻角平板流場數值模擬分析及其動態網格建立
論文名稱(外文):Numerical simulation of flow past flat plate with angle of attack And adaptive mesh refinement
指導教授:許立傑
指導教授(外文):Li-Chieh Hsu
學位類別:碩士
校院名稱:國立雲林科技大學
系所名稱:機械工程系碩士班
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:2009
畢業學年度:97
語文別:中文
論文頁數:131
中文關鍵詞:渦漩剝離適應性網格史卓赫數
外文關鍵詞:Strouhal Numberadaptive meshvortex shedding
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本文利用頻譜元素法數值模擬不同攻角平板於二維不可壓縮黏滯性流場中所引發的物理現象,在本研究中,為了避免在真實流場中,因平板厚度或尖端楔型角所引發其他的物理現象所引響,故平板厚度設1×10-5,為一近似直線的二維物理模型。在流場參數設定方面,以Re=140, 200兩種不同雷諾數模擬α=20°, 30°, 40°, 50°四種不同攻角的平板流場,其目的主要是將流場可視化觀測,觀察平板表面壓力變化、史卓赫數、升阻力係數計算、以及渦漩剝離(Vortex Shedding)行為等流場的特性分析。並且以加入適應性網格所得結果與一致性網格相比。
在Re=140, α=20°的平板流場中,並未有渦漩剝離的行為發生,流場現象為四種攻角最為單純的一種,而當攻角角度增加至30°開始有渦漩週期剝離現象產生。在相同雷諾數中,隨著攻角角度的增加,所計算出的史卓赫數也隨之下降。在升阻力係數計算上,阻力係數會隨攻角角度增加而上升;升力係數在α=20°~ 40°之間會隨攻角角度增加而上升,但α=50°時則會有突降的情形。
在適應性網格加密部分,由總體誤差(global error)與加密次數關係曲線中可發現,雖然在前三次分割加密時誤差有上升情形,但隨著分割加密次數的增加,誤差也隨之下降,直到分割加密第72次之後,誤差則呈現收歛趨勢,其總誤差率也從原0.006%下降到0.002%以下。並由不同加密次數之U速度、V速度、渦度結果相比較下,發現網格隨加密次數增其解加更加平滑(smooth)。
Numerical simulation of flow past a two-dimensional flat plate in various angle of attack by spectral element method. In this study, particularly, we use a very thin flat plate with thickness t/c=1×10-5, to let it be similar to a straight line model and to reduce the effect of leading edge. The angle of attack of flat plate are simulated with α = 20 °, 30 °, 40 °, 50 °, in two inlet flow condition, Re=140, 200, respectively. The purpose of this research is using the spectral element method to obtain the flow field detail of the process of vortex formation, breakdown and also the vortex shedding phenomena in downstream. The vortex shedding frequency, Strouhal number, lift coefficient and drag coefficient are calculated as time goes on.
In the flow field, Re = 140, α = 20 °, of the flat plate, there was no occurrence of vortex shedding. The calculated Strouhal number declined as the degree of angle of attack increased. The drag coefficient would increase as the angle of attack increase. The lift coefficient would increase as the angle of attack increase in the range of α = 20 ° ~ 40 ° ,but drop suddenly in α = 50 °.
Global error in the relations with the adaptive mesh can be found. Although the global error are upward in the first three cycle. However, with the increase in the number of cycle error also decreased, until after 72 of cycle the error was convergence, the .006 of percent global error rate dropped to below 0.002%. Comparison of different adaptive mesh Results of U velocity, V velocity, vorticity contour.
摘 要 i
ABSTRACT ii
誌 謝 iii
目 錄 iv
表 目 錄 vi
圖 目 錄 vii
符號說明 vii
第一章 緒 論 1
1.1 研究背景與動機 1
1.2 文獻回顧 2
1.2.1 平板流 2
1.2.2 頻譜元素法 3
1.3 研究目的與論文撰寫順序 4
第二章 數值方法 6
2.1 頻譜元素法(Spectral Element Method) 6
2.2 數學模式 10
2.3 數值方法 10
2.3.1 時間離散 (Temporal Discretization) 10
2.2.1 空間離散 (Spatial Discretization) 12
第三章 具攻角平板模擬 13
3.1 邊界條件 13
3.1.1物理模型 13
3.1.2 流場模擬條件 14
3.2 具攻角平板渦漩行為 15
3.2.1 平板攻角α=20°,Re=140, 200 23
3.2.2 平板攻角α=30°,Re=140, 200 33
3.2.3 平板攻角α=40°,Re=140, 200 44
3.2.4 平板攻角α=50°,Re=140 55
3.3 渦漩剝離長度與頻率 61
3.4 史卓赫數計算 65
3.5 升力與阻力係數計算 67
3.6 小結 73
第四章 適應性網格 (adaptive mesh) 75
4.1 前言 75
4.2 適應性網格策略 78
4.3 誤差估算原理 82
4.4 網格分割策略 87
4.4 適應性迴圈(adaptive loop) 88
4.5 適應性網格應用 90
4.5.1 適應性加密過程 93
4.5.2 結果比較 93
第五章 結論與未來展望 111
5.1 具攻角平板流場 111
5.2 適應性網格應用 112
5.3 未來展望 112
參考文獻 113
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