異重流在無渠槽斜坡之運動

Gravity currents generated by constant inflow on a lateral unconfined slope

徐立中(Li-Chung Hsu)

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/碩士(2017年)

https://doi.org/10.6342/NTU201703429

摘要

本論文探討異重流於坡度下進行三維運動之實驗。透過系統性的反覆實驗操作，發現異重流之流動型態在坡度角越高時，流域為越細長的楔形形狀，前端頭部提升越高、混合捲氣越劇烈，並且有較大主流流速，在低角度則反之。經實驗理論及因次分析後，角度的提升有使特徵參數K_1、K_5下降，K_2、K_3、α_v1、α_v2上升的趨勢。而前端位置與時間應符合〖x_(v,f)〗^(4/3)~t(W_p)^(1/3)f(θ)，前端密度差也有(∆ρ/ρ)〖(x_(v,f)〗^(-5/3)g~(W_p)^(2/3)f(θ)之關係，惟有0^°、3^°異重流流動情況在本研究分析後發現與理論模型差異甚大，此時可能另須考慮黏滯力之影響，故本研究不適用。另外，過去文獻中此類異重流流動形態被假設為非穩定成長區段與穩定成長區段兩部分，穩定成長區段像是可預測的線性成長，非穩定成長區段則視為不可預測的半圓盤狀成長。經過量化穩定成長區段特徵參數，由各種具物理特性的參數值大小也可以發現提升角度，會使異重流幅員變細長、頭部成長變大、前端速度上升、密度差下降之變化。此外，觀察實驗影像後發現非穩定成長區段並非所有情況都為半圓盤狀，為了使半圓盤能有更大的彈性變化成半橢圓盤，在半圓盤加入非穩定成長區段之比例係數k，如此更符合實際流況量化出非穩定成長區段特徵參數，結果發現k之大小隨著流量的增加而下降。

關鍵字：異重流；坡度；定流量；密度差；特徵參數。

關鍵字

異重流 ； 坡度 ； 定流量 ； 密度差 ； 特徵參數

並列摘要

This thesis examines gravity currents generated by the constant inflow on a lateral unconfined slope. The slope angle and input discharge are the controlling factors to determine the configuration of gravity currents. From the experimental results of gravity currents, as increasing the slope of inclined bottom, the evolving structures become more slender and thinner in current width and depth, respectively. In dimensional analysis, the front position of gravity currents associated with the power-law relation,〖(x_(v,f)〗^(4/3)~t(W_p)^(1/3)f(θ) and (∆ρ/ρ)〖(x_(v,f)〗^(-5/3)g~(W_p)^(2/3)f(θ), is derived, except for the small angle 0^°、3^°. In addition, the flow pattern is categorized as two regions, namely steady region (body of gravity current) and unsteady region (the current head). By quantifying characteristic parameters of these two region, we found K_2、K_3、α_v1、α_v2 increase and K_1、K_5 decrease as slope increases. Also, Gravity currents front velocity increases and density difference decreases as slope increases. Finally, we observe shape ratio coefficient k decreases as the discharges increases.

Keywords: gravity currents, unconfined slope, constant inflows, density difference, characteristic parameters.

並列關鍵字

gravity currents ； unconfined slope ； constant inflows ； density difference ； characteristic parameters

參考文獻

2. Adduce, C., Sciortino, G., Proietti, S.,2012.Gravity currents produced by lock-exchanges experiments and simulations with a two layer shallow-water model with entrainment. J. Hydraul. Eng. 138(2),111-121.

3. Beghin, P., Hopfinger, E.J., Britter, R.E.,1981.Gravitaional convection from instantaneous sources on inclined boundaries. J. Fluid Mech. 107, 407-422.

4. Britter, R.E.,1979.The spread of a negatively buoyant plume in a calm Environment. Atomspheric Environment. 13, 1241-1247.

5. Britter, R.E., Linden, P.F.,1980.The motion of the front of a gravity current travelling down an incline. J. Fluid Mech. 586, 1-39.

6. Cantero, M., Lee, J., Balachandar, S., Garcia, M.,2007.On the front velocity of gravity currents. J. Fluid Mech. 586, 1-39.