- 學位論文
方形溝槽中兩層牛頓流體之界面波與包覆現象特性分析
The Characterization of Interfacial Wave and Encapsulation Phenomenon for Two-layered Newtonian Fluids in a Rectangular Channel
摘要
本研究利用溝槽比12.5:1之方形溝槽探討兩層牛頓流體之界面波和包覆現象產生情形。因為我們想要探討密度差異對界面穩定度與包覆現象的影響，固為此流體對可在幾乎維持兩邊流體的黏度差異不變下，所以我們採用食鹽水及黏度較高的矽油流體對，藉著食鹽水濃度的調整，改變兩流體間密度差。 首先，以矽油-16.7wt%濃度鹽水，在分別逐漸提高個別流體的流量下，建構由界面不穩定和包覆發生時臨界雷諾數所形成之包覆/穩定圖。我們發現由三區域所構成之包覆/穩定圖分別為包覆/界面波不穩定區、包覆/界面波穩定區、不包覆/界面波穩定區，其中由包覆/界面波不穩定區域可發現，界面的不穩定會影響包覆程度且會產生與界面波成垂直的包覆波。接著再將鹽水濃度調高至24.8wt%，亦即在兩流體密度差異變大下，另一新區域不包覆/界面波不穩定區會形成， 同時我們發現要到達此區前要先經歷包覆/界面波不穩定。另外包覆/穩定圖顯示，當鹽水密度調高，其不包覆區域有提前發生的現象。之後接著我們探討厚度比、溝槽長寬比、流量對包覆現象之影響。 為瞭解波之特性針對包覆/界面波我們分別建構時間振幅曲線圖、頻譜圖，以及利用cross spectrum估算波速，並使用線性穩定度分析計算波時間成長速率，再利用Gaster Transformation將其轉換成波空間成長速率，據此與實驗結果作比較，以界定線性理論分析的有效範圍，進而瞭解不穩定界面波形成之原因。 經線性理論所求得的理論值與實驗值比較後，我們證實本系統波的行為應為線性理論可描述之長波系統，且此長波可由薄層效應(thin layer effect)穩定之。
並列摘要
In this study, the interfacial wave and encapsulation phenomenon of two-layered Newtonian fluids in a rectangular flow channel with aspect ratio 12.5 are investigated. A fluid pair of brine and high viscosity silicon oil is utilized because its density difference across fluids can be adjusted by the variation of brine concentration with little change in viscosity stratification between two fluids. Thus, the effect of density on the interfacial stability and encapsulation can be examined. First, by variation of flow rates of both silicon oil and 16.7wt% brine we constructed a diagram of encapsulation and stability. It demonstrated that the diagram is composed of three major regions, such as encapsulation / interfacial instablility, encapsulation / interfacial stability and non-encapsulation / interfacial stability. It was found that the encapsulation wave, manifesting itself as a vertical wave to the interfacial wave, is excited after the occurrence of interfacial waves. Subsequently, by adjusting the brine concentration to 24.8wt% a new region, non-encapsulation / interfacial instability, emerges in encapsulation/stability diagram. It comes after the non-encapsulation / interfacial instability. It shows the density different across the fluids can prevent two parallel fluids in a flow channel from the encapsulation. To investigate the characteristics of encapsulation and interfacial waves in terms of depth ratio, aspect ratio, and Reynolds number, the amplitude/time diagram and power density spectrum diagram are plotted. Cross spectrum is performed to determine wave speed and wavelength of each harmonics, of which interfacial wave is composed. Thus, the time-evolving growth rate, evaluated by linear stability theory, may be then converted to the spatial growth rate by Gaster Transformation. This theoretical linear growth rate based on the spatial travel, in turn, was compared with the experimentally measuring growth rate. Accordingly the valid range of linear stability theory prediction in terms of parameter space can be determined.