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系統識別號 U0002-1507201311164100
中文論文名稱 高低密度差之非連續異重流在斜板上的運動
英文論文名稱 Gravity currents of different densities from instantaneous sources propagating on sloping boundaries
校院名稱 淡江大學
系所名稱(中) 水資源及環境工程學系碩士班
系所名稱(英) Department of Water Resources and Environmental Engineering
學年度 101
學期 2
出版年 102
研究生中文姓名 周書毓
研究生英文姓名 Shu-Yu Chou
學號 699480025
學位類別 碩士
語文別 中文
口試日期 2013-06-25
論文頁數 64頁
口試委員 指導教授-戴璽恆
委員-張麗秋
委員-黃名村
中文關鍵字 異重流  重力對流  熱理論  黏滯效應  減速階段 
英文關鍵字 Gravity currents  gravitational convections  thermal theory  viscous effects  deceleration phase 
學科別分類 學科別應用科學環境工程
中文摘要 本論文探討密度差異不同之流體,於多個傾斜邊界上流動模式,而密度差異之流體,我們稱之為異重流,也可稱作為密度流或重力流,其成因為兩種比重差且可以相混的流體(此指液相),受重力作用下,比重較大的流體潛入比重較小的流體,則稱之為異重流(gravity currents)。了解異重流於斜板上之運動特性,可有效利用於幫助水庫排砂,增加水庫壽命,而異重流於斜坡上運動之研究可分為連續入流與非連續入流兩類,並由數值模擬分析與實際實驗操作兩種方式執行,本論文採取的方法為實驗操作之非連續入流類型,研究範圍為 0°≤θ≤9° 斜板上所瞬時生成之異重流流動模式。
於先前的研究中,我們了解所有異重流皆遵守一個固定的流動模式,即異重流前端位置皆遵守3⁄2指數關係式。在此,我們選擇了不同密度差 ϵ≈0.02,0.05,0.10,0.17 溶液做實驗,並將 ϵ≈0.02 訂為低密度差,其餘訂為高密度差分開討論。由我們的研究結果發現,異重流前端位置於減速段末端會偏離3⁄2指數關係式標準。另外,由同密度差不同傾斜角度之異重流實驗結果中,我們發現動量關係式內的經驗常數 KM,其值與角度成正向關係,並於 θ≈6° 時達最大值;而由同角度不同密度差實驗結果,發現最大前端速度與密度差成正向關係,達最大前端速度所需時間則與密度差成反向關係。
英文摘要 This paper examines flow patterns of different fluid densities on multiple inclined boundaries, and the flows are called gravity currents. Gravity currents are generated because that the high density fluid penetrates into the low density fluid due to gravity effect. Understanding gravity current characteristics can effectively help utilize the reservoir desilting technique to increase the life of the reservoir. Gravity currents on sloping boundaries can be divided into two categories with non-continuous inflow by numerical simulation and actual experimental operation in two ways, the approach taken in this paper for the experimental operation of the non-continuous inflow type. Experiments for gravity currents generated from an instantaneous buoyancy source propagating on an inclined boundary in the slope angle range 0°≤θ≤9° are reported.
In previous studies, we know all the gravity current flows are to follow a fluid pattern, i.e. the gravity currents front position obeys with the power-relationship. In this study, four relative density differences were chosen, i.e. ϵ≈0.02,0.05,0.10,0.17. ϵ≈0.02 as low relative density difference, which the rest is set at a high relative density difference discussed separately. In our results, we found the front location data deviate from the power-relationship on the late deceleration phase. In addition, we found the experience of the momentum equation constants KM is proportional to the angle, and the maximum value is occurs at θ≈6°; By the same angle different density difference experimental results, the maximum front velocity is proportional to the density difference and t(max )is inversely proportional to the density difference.
論文目次 目錄
中文摘要 I
Abstract III
目錄 i
表目錄 iii
圖目錄 iv
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
第二章 文獻回顧 4
2.1 熱理論 5
第三章 研究方法 8
3.1 實驗方式與裝置 8
3.2 實驗步驟 11
第四章 結果與分析 12
4.1 θ=9° 之異重流 12
4.1.1 低密度差定性特徵 12
4.1.2 高密度差定性特徵 15
4.1.3 低密度差定量分析結果 18
4.1.4 低密度差定量分析討論 20
4.1.5 高密度差定量分析結果 24
4.1.6 高密度差定量分析討論 25
4.2 θ=6° 之異重流 28
4.2.1 低密度差分析 28
4.2.2 高密度差分析 31
4.3 θ=2° 之異重流 33
4.3.1 低密度差分析 33
4.3.2 高密度差分析 36
4.4 θ=0° 之異重流 39
4.4.1 低密度差分析 39
4.4.2 高密度差分析 43
第五章 結論與建議 48
5.1 低密度差異重流 48
5.2 高密度差異重流 51
5.3 總結 53
5.4 建議 54
參考文獻 57
附錄 59


表目錄
表1 相對密度差ϵ=0.02之異重流實驗結果參數 55
表2 不同相對密度差與角度之異重流實驗結果參數 55
表3 不同相對密度差與角度之異重流實驗結果參數 56
表4 相對密度差ϵ=0.02之異重流實驗結果參數 56

圖目錄
圖1.1 lock-exchange flows實驗示意圖 2
圖3.1 異重流實驗渠道剖面圖 10
圖4.1 密度差2%斜板角度9°之異重流於加速階段濃度影像 13
圖4.2 密度差2%斜板角度9°之異重流於減速階段濃度影像 14
圖4.3 密度差17%斜板角度9°之異重流於加速階段濃度影像 16
圖4.4 密度差17%斜板角度9°之異重流於減速階段濃度影像 17
圖4.5 密度差2%斜板角度9°異重流前端速度 u_f、前端位置 x_f 與時間之關係 19
圖4.6 密度差2%斜板角度9°之異重流(x_f+x_0)3⁄2與t之關係圖 19
圖4.7 密度差2%斜板角度9°之異重流頭部濃度影像放大圖、頭部內密度與總密度之比率關係圖 21
圖4.8 密度差2%斜板角度2°,6°,9°異重流頭部內密度與總密度比率和異重流前端位置與總密度的二分之一次方比率之關係圖 23
圖4.9 密度差17%斜板角度9°異重流前端速度、(x_f+x_0)3⁄2 與時間之關係圖 24
圖4.10 密度差10%、5%斜板角度9°之異重流(x_f+x_0)3⁄2 與t之關係圖 26
圖4.11 密度差17%斜板角度2°,6°,9°異重流頭部內密度與總密度比率和異重流前端位置與總密度的二分之一次方比率關係圖 27
圖4.12 密度差2%斜板角度6°之異重流濃度影像 29
圖4.13 密度差2%斜板角度6°之異重流前端速度、(x_f+x_0)3⁄2與時間的關係圖 30
圖4.14 密度差17%,5%斜板角度2°之(x_f+x_0)3⁄2與 t 的關係圖 32
圖4.15 密度差2%斜板角度2°之異重流濃度影像 34
圖4.16 密度差2%斜板角度2°異重流前端速度、(x_f+x_0)3⁄2與時間的關係圖 35
圖4.17 密度差17%斜板角度2°之異重流濃度影像 37
圖4.18 密度差17%,5%斜板角度2°之異重流(x_f+x_0)3⁄2與時間的關係圖 38
圖4.19 密度差2%斜板角度0°之異重流濃度影像 41
圖4.20 密度差2%斜板角度0°異重流前端速度與 t 關係圖 42
圖4.21 密度差2%斜板角度0°之異重流 x_f 3⁄2 與 t 關係圖 42
圖4.22 密度差17%斜板角度0°之異重流濃度影像 45
圖4.23 密度差17%斜板角度0°之異重流前端位置 x_f與時間t之關係圖 46
圖4.24 密度差17%,5%斜板角度0°之異重流x_f 3⁄2 與時間的關係圖 47
圖5.1 密度差2%異重流常數 K_M 與角度之關係統計圖 50
圖5.2 密度差5%,10%,17%異重流常數 K_M 與角度之關係統計圖 52


參考文獻 1. A. Dai and M. Garcia, “Gravity currents down a slope in deceleration phase,” Dyn. Atmos. Oceans 49, 75–82 (2010)
2. A. Dai, “Note on the generalized thermal theory for gravity currents in the deceleration phase,” Dyn. Atmos. Oceans 50, 424–431 (2010)
3. Allen, J. 1985 Principles of Physical Sedimentology. Allen & Unwin.
4. Baines, P. G. 2001 Mixing in flows down gentle slopes into stratified environments. J. Fluid Mech. 443, 237–270.
5. Baines, P. G. 2005 Mixing regimes for the flow of dense fluid down slopes into stratified environments. J. Fluid Mech. 538, 245–267.
6. Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
7. Beghin, P., Hopfinger, E. J. & Britter, R. E. 1981 Gravitational convection from instantaneous sources on inclined boundaries. J. Fluid Mech. 107, 407–422.
8. Birman, V. K., Battandier, B. A., Meiburg, E. & Linden, P. F. 2007 Lock-exchange flows in sloping channels. J. Fluid Mech. 577, 53–77.
9. Birman, V. K., Martin, J. E. & Meiburg, E. 2005 The non-boussinesq lock-exchange problem. Part 2. High-resolution simulations. J. Fluid Mech. 537, 125–144.
10. Britter, R. E. & Linden, P. F. 1980 The motion of the front of a gravity current travelling down an incline. J. Fluid Mech. 99, 531–543.
11. Cantero, M., Lee, J., Balachandar, S. & Garcia, M. 2007 On the front velocity of gravity currents. J. Fluid Mech. 586, 1–39.
12. Dade, W. B., Lister, J. R. & Huppert, H. E. 1994 Fine-sediment deposition from gravity surges on uniform slopes. J. Sed. Res. 64, 423–432.
13. Dalziel, S. B. 2012 DigiFlow User Guide. Dalziel Research Partners.
14. Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.
15. Fannelop, T. K. 1994 Fluid Mechanics for Industrial Safety and Environmental Protection. Elsevier.
16. Grobelbauer, H. P., Fannelop, T. K. & Britter, R. E. 1993 The propagation of intrusion fronts of high density ratios. J. Fluid Mech. 250, 669–687.
17. Hopfinger, E. J. 1983 Snow avalanche motion and related phenomena. Annu. Rev. Fluid Mech. 15, 47–76.
18. Huppert, H. & Simpson, J. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785–799.
19. Huppert, H. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal boundary surface. J. Fluid Mech. 121, 43–58.
20. Hoult, D. P. 1972 Oil spreading on the sea. Annu. Rev. Fluid Mech. 4, 341–368.
21. Keller, J. J. & Chyou, Y. P. 1991 On the hydraulic lock exchange problem. J. Appl. Math. Phys. 42, 874–909.
22. La Rocca, M., Adduce, C., Sciortino, G. & Pinzon, A. B. 2008 Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom. Physics of Fluids 20 (10), 106603.
23. Lowe, R. J., Rottman, J. W. & Linden, P. F. 2005 The non-boussinesq lock-exchange problem. Part 1. Theory and experiments. J. Fluid Mech. 537, 101–124.
24. Marino, B., Thomas, L. & Linden, P. 2005 The front condition for gravity currents. J. Fluid Mech. 536, 49–78.
25. Maxworthy, T. 2010 Experiments on gravity currents propagating down slopes. Part 2. The evolution of a fixed volume of fluid released from closed locks into a long, open channel. J. Fluid Mech. 647, 27–51.
26. Maxworthy, T. & Nokes, R. I. 2007 Experiments on gravity currents propagating down slopes. Part 1. The release of a fixed volume of heavy fluid from an enclosed lock into an open channel. J. Fluid Mech. 584, 433–453.
27. Monaghan, J. J., Cas, R. A. F., Kos, A. M. & Hallworth, M. 1999 Gravity currents descending a ramp in a stratified tank. J. Fluid Mech. 379, 39–69.
28. Rastello, M. & Hopfinger, E. J. 2004 Sediment-entraining suspension clouds: a model of powder-snow avalanches. J. Fluid Mech. 509, 181–206.
29. Ross, A. N., Dalziel, S. B. & Linden, P. F. 2006 Axisymmetric gravity currents on a cone. J. Fluid Mech. 565, 227–253.
30. Seon, T., Znaien, J., Perrin, B., Hinch, E. J., Salin, D. & Hulin, J. P. 2007 Front dynamics and macroscopic diffusion in buoyant mixing in tilted tubes. Phys. Fluids 19, 125105.
31. Shin, J., Dalziel, S. & Linden, P. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.
32. Simpson, J. 1997 Gravity Currents, 2nd edn. Cambridge University Press. Tickle, G. 1996 A model of the motion and dilution of a heavy gas cloud released on a uniform slope in calm conditions. J. Haz. Mat. 49, 29–47.
33. Webber, D., Jones, S. & Martin, D. 1993 A model of the motion of a heavy gas cloud released on a uniform slope. J. Haz. Mat. 33, 101–122.
34. Y. Chen, “Gravity currents from instantaneous sources propagating on sloping boundaries”, Department of Water Resources and Environmental Engineering
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