三維異重流於寬廣無渠道斜坡運動

Three dimensional gravity currents propagating on different unbounded slopes

黃友麟(Yu-Lin Huang)

指導教授 ： 戴璽恆

國立臺灣大學/工學院/工程科學及海洋工程學研究所/博士(2021年)

https://doi.org/10.6342/NTU202103495

摘要

本研究利用理論模型、因次分析以及水槽實驗，觀察異重流於不同平面斜坡運動。水槽斜坡及異重流密度差異是影響異重流運動的主要關鍵，因此研究主要探討坡度及密度對於異重流的影響。其中實驗坡度介於0◦ ≤ θ ≤ 12◦，相對密度差ϵ = (ρ1 − ρ0)/ρ0 介於0.02 ≤ ϵ ≤ 0.15 ，當中ρ1 為重流體密度，ρ0 為環境流體密度。透過理論模型及實驗結果，可進一步的求得不同坡度及相對密度差的異重流增捲係數α (entrainment coefficient )。其中發現增捲係數會隨著相對密度變大而變小，原因是當相對密度差變大的時候，重流體比較不容易與環境流體混合。此外，由結果發現此理論模型在小角度案例中並不適用。由因次分析以及實驗結果可發現，異重流在減速運動中會有兩種不同的運動型態，分別是重力與慣性力平衡的慣性段，以及重力與黏滯力平衡的黏滯段。受斜坡的影響，異重流運動形貌上有明顯的差異性，這樣的差異可進一步將異重流分為高角度(12◦、9◦、6◦) 與低角度（3◦、0◦）兩類。由於形貌上的差異，會影響異重流在後減速黏滯段的運動中，邊界層間黏滯力的作用面積不同而有不同的因次關係。受密度差異影響，異重流也可分為高相對密度差(ϵ = 0.15、0.10、0.05) 及低相對密度差(ϵ = 0.02) 兩類。在後減速黏滯段，因為前面運動強烈的混合下，發現高密度差的異重流在黏滯段與低密度差異重流運動型態相似。

關鍵字

異重流 ； 密度流 ； 斜坡 ； 相對密度差

並列摘要

The study is about three dimensional gravity currents propagating on different unbounded slopes. Theoretical model, dimensional analysis and experimental observations are performed in this research. Slopes and density differences are two typical factors that influence gravity currents’ flow. In the experiment, the slopes are in the range between 0◦ ≤ θ ≤ 12◦ and the relative density difference ϵ = (ρ1 −ρ0)/ρ0 are in the range 0.02 ≤ ϵ ≤ 0.15, where ρ1 and ρ0 are the densities of the heavy and light ambient fluids, respectively. The entrainment coefficient can be found by theoretical model and experiment results. It shows that, the entrainment coefficient increases as the relative density difference decreases. By dimensional analysis, the deceleration phase of gravity currents can be divided into two different stages. In the early stage of deceleration phase, the force balance is between the buoyancy force and the inertial force. In the late stage of the deceleration phase, the force balance is between the buoyancy force and the viscous force. Besides, the morphology can be classified more detail into two cases, including high angle cases (12◦、9◦、6◦) and low angle cases（3◦、0◦). The morphology differences affect the active area region in boundary layer thickness that leads to the power-law relationships with different types. Gravity currents also can be divided into two cases by density differences, including high-density contrast cases (ϵ = 0.15、0.10、0.05) and low-density difference case(ϵ = 0.02). With violent mixing between heavy fluid and ambient fluid in the inertial phase, the density difference is similar in the late deceleration phase.

並列關鍵字

gravity currents ； density currents ； unbounded slopes ； density difference

參考文獻

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