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研究生:陳炳煌
研究生(外文):Ping-Huang Chen
論文名稱:不同紊流模式於迴流區域之分析與比較
論文名稱(外文):Assessment of Various Low-Reynolds Number Turbulence Models in Recirculation Flow
指導教授:楊一龍
指導教授(外文):Yi-Lung Yang
學位類別:碩士
校院名稱:中華大學
系所名稱:機械與航太工程研究所
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:2006
畢業學年度:94
語文別:中文
論文頁數:82
中文關鍵詞:小凸脊雷諾數迴流誤差現象
外文關鍵詞:κ-εκ-ωturbulence model
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本研究結合前人之紊流模式,並將其成果分為三類;第一類為Chien之κ-ε紊流模式與Nagano和Kim之κ-ε紊流模式,其阻尼函數直接與牆壁距離有關之探討,第二類為Fan,Lakshminarayana和Barnett之κ-ε紊流模式與兩種Yang和Shih之κ-ε紊流模式,其阻尼函數為牆壁距離與紊流動能組合之探討,而第三類為Wilcox之κ-ω低雷諾數和高雷諾數紊流模式、Jones和Launder之κ-ε紊流模式、Launder和Sharma之κ-ε紊流模式及Goldberg和Apsley之κ-ε紊流模式,做完全無牆壁距離效應之探討。首先透過完全發展之紊流圓管流場進行分析,配合不同紊流模式模擬比較,判斷何者與實驗數據最相近,結果以Chien之κ-ε紊流模式、Fan,Lakshminarayana和Barnett之κ-ε紊流模式及Wilcox之κ-ω低雷諾數紊流模式,與實驗數據有較佳之吻合,可以做為此三類之代表。在通過小凸脊之後方測量及另一45度傾斜面漸增管後方測量其迴流長度、速度斷面、黏滯係數及渦流剪應力等做比較,結果都是以Chien之κ-ε紊流模式較接近實驗結果,而Fan,Lakshminarayana和Barnett之κ-ε紊流模式與Chien之κ-ε紊流模式之結果接近,而Wilcox之κ-ω低雷諾數紊流模式誤差最大,雖然Chien之κ-ε紊流模式較接近實驗結果,但其自由區渦流黏滯係數過大,而迴流區又太小之現象仍需進一步改良。
In this research, turbulence models were divided into three categories. The first category uses wall distance in their damping function, such as κ-ε turbulence models of Chien and Nagano & Kim. The second category couples the wall distance with turbulence kinetic energy in their damping function, such as κ-ε turbulence models of Fan, and Yang & Shih. The last category is a wall-distance-free turbulence model. They are Wilcox’s κ-ω turbulence model, Jones & Launder κ-ε turbulence model、Launder & Sharma κ-ε turbulence model and Goldberg & Apsley κ-ε turbulence model. A fully developed turbulence pipe flow was used to examine the performance of these turbulence models. The results showed the κ-ε turbulence models of Chien and Fan, and κ-ω turbulence model of low Reynolds number perform better in terms of velocity distribution, turbulence kinetic energy distribution, and dissipative rate distribution. Two reversed flow problems were used to validate these turbulence models. The first case is the channel flow over a two-dimensional hump. The second problem is the flow over a slanted backward-facing step. In both cases, the Chien’s κ-ε turbulence model gives the best velocity distribution and eddy viscosity distribution among these three models. The κ-ε turbulence model of fan gives almost the same result of Chien’s. The low Reynolds number κ-ω turbulence model provides a much smaller eddy viscosity and lack of mixing in the region of reverse flows. The difference between the current turbulence calculation and experiment is still large. Further modification of the turbulence models is still required.
中文摘要 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥Ⅰ
英文摘要 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥Ⅱ
目錄 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥Ⅲ
圖表索引 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥Ⅴ
第一章 緒論
1-1 前言‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥01
1-2 文獻回顧‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥02
1-3 研究目的與方法‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥04
1-4 章節安排‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥05
第二章 網格的建立
2-1 網格之產生‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥06
2-2 網格分佈之影響‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥06
2-3 網格數目之影響‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥09
第三章 統御方程式
3-1 流場統御方程式‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥12
3-2 κ-ε紊流模式 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥14
3-2-1 Jones 和 Launder (JL)κ-ε紊流模式‥‥‥‥‥‥‥15
3-2-2 Launder和 Sharma (LS)κ-ε紊流模式‥‥‥‥‥‥‥16
3-2-3 Chien (CH) κ-ε紊流模式‥‥‥‥‥‥‥‥‥‥‥‥17
3-2-4 Nagano和Kim (NK)κ-ε紊流模式‥‥‥‥‥‥‥‥‥18
3-2-5 Yang和Shih (YS) κ-ε紊流模式‥‥‥‥‥‥‥‥‥19
3-2-6 Yang 和 Shih (YS2) κ-ε紊流模式‥‥‥‥‥‥‥‥20
3-2-7 Fan,Lakshminarayana和Barnett(FLB)κ-ε紊流模式 22
3-2-8 Goldberg 和 Apsley (GA)κ-ε紊流模式‥‥‥‥‥‥23
3-3 κ-ω紊流模式 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥24
3-3-1 Wilcox (KWH) 高雷諾數κ-ω紊流模式‥‥‥‥‥‥‥25
3-3-2 Wilcox (KW) 低雷諾數κ-ω紊流模式‥‥‥‥‥‥‥25
第四章 數值分析
4-1 圓管紊流分析比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥27
4-1-1 速度之分佈比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥27
4-1-2 渦流剪應力之分佈比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥32
4-1-3 近牆渦流剪應力之分佈比較 ‥‥‥‥‥‥‥‥‥‥‥‥36
4-1-4 紊流動能之分佈比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥40
4-1-5 近牆紊流動能之分佈比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥44
4-1-6 散逸率之分佈比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥48
4-1-7 近牆散逸率之分佈比較 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥52
4-1-8 紊流應力除以紊流動能之分佈比較 ‥‥‥‥‥‥‥‥‥56
4-1-9 近牆紊流應力除以紊流動能之分佈比較 ‥‥‥‥‥‥‥60
4-2 小凸脊後方迴流之分析 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥64
4-3 45∘傾斜面漸増管之分析 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥69
第五章 結論及未來展望
5-1 結論 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥77
5-2 未來展望 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥79
參考文獻 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥80
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[2] W.P. Jones and B.E. Launder, The prediction of laminarization with a two-equation model of turbulence, Int. J. Heat Mass Trans. 15 (1972) 301-314.
[3] B.E. Launder and B.I. Sharma, Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disk, Lett. Heat Mass Trans. 1 (1974) 131-138.
[4] K.Y. Chien, Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model, AIAA J. 20, (1982) 33-38.
[5]Y.Nagano and C.Kim. A two-equation model for heat transport shaer flows, J. Heat Trans. 110 (1988) 583-589.
[6] Wilcox,D.C.,“ Reassessment of the Scale Determining Equation for Advanced Turbulence Models,” AIAA Journal, Vol. 26, No. 11, Nov. 1988, pp. 1299-1310.
[7] Yang,Z.,and Shih,T.H., "A κ-ε Modeling of Near Wall Turbulence," Proceedings of 4th International Symposium on Computational Fluid Dynamics, UC Davis, 1991.
[8] Wilcox,D.C., “The Remarkable Ability of Turbulence Model Equations to Describe Transition,” Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, California state Univ., Long Beach, CA, Jan.13-15, 1992.
[9] Yang ,Z., and Shih,T.H.,“A New Time Scale Based κ-ε Model For Near-Wall Turbulence,”AIAA Journal, Vol.31, N0. 7, pp. 1191-1198. (1993)
[10]S.Fan,B.Lakshminarayana and M.Barnett, Low-Reynolds- number κ-ε Model for unsteady turbulent boundary-layer flows, AIAA J. 31 (1993) 1777-1784.
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[12]Launder,B.E., and Spalding,D.B., Mathematical Models of Turbulence, Academic Press 1972, London and New York.

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