高低密度差之非連續異重流在斜板上的運動

Gravity currents of different densities from instantaneous sources propagating on sloping boundaries

周書毓(Shu-Yu Chou)

指導教授 ： 戴璽恆

淡江大學/工學院/水資源及環境工程學系碩士班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.00425

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。

關鍵字

異重流 ； 重力對流 ； 熱理論 ； 黏滯效應 ； 減速階段

並列摘要

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.

並列關鍵字

Gravity currents ； gravitational convections ； thermal theory ； viscous effects ； deceleration phase

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)

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.

7. Beghin, P., Hopfinger, E. J. & Britter, R. E. 1981 Gravitational convection from instantaneous sources on inclined boundaries. J. Fluid Mech. 107, 407–422.