異重流前端葉及裂口的分裂與聚合

Abstract

當異重流隨時間向前流動時，在異重流前端位置可明顯觀測到由頻繁聚合及分裂行為所產生的凹凸不規則結構，在此不規則結構當中，我們將凸起結構稱為葉(Lobe)、凹陷結構稱為裂口(Cleft)，葉及裂口(Lobe-and-Cleft)結構為對異重流前端形貌造成變化的重要因素之一。 本研究主要目的有二，第一在過往研究當中亦有針對異重流之流動行為進行分析，然而大部分皆為低雷諾數部分，因此於本研究中我們將針對高雷諾數的部分進行分析，並比較高低雷諾數可能之差異性。第二則是過往文獻中亦較缺乏分析的異重流前端分裂聚合產生葉及裂口結構之原因，在本研究中我們將使用異重流內部渦度場分析分裂聚合行為時渦旋之變化，並將以渦旋解釋造成分裂聚合之起因。 研究之方法我們則使用數值方法求解統御方程式模擬重流體在一長形水槽中與環境流體混合而形成之雷諾數分別為1788、3450、8950、13000、17000之三維異重流，並求解包含濃度場、速度場、渦度場等三維流場中之相關重要參數進行分析比對。 本研究所針對五組不同雷諾數案例結果則顯示，我們除了成功拓展高雷諾數方面之研究資料，在各項雷諾數前端流場資料分析也都符合過往研究中之趨勢。此外，我們也能夠合理的利用渦度強度標準λ_ci呈現齒狀(Tooth-like)結構分裂聚合過程中之行為。而藉由解析有關渦度時變率變化之渦度方程式，包含方程式中對於總體時變率變化最具貢獻之傾斜項分析，以及子母渦旋(Parent and offspring vortex)之交互作用行為皆能有效針對裂口之生成及分裂前進之方向進行合理之解釋。 在我們的研究貢獻當中，除了成功拓展異重流由低雷諾數至高雷諾數下之流動行為分析，並能解釋不穩定渦度場變化對於異重流前端形貌之影響作用。

While the gravity current flows, it splits and merges frequently at the leading edge of the gravity current, leading to some protrusion and depression structure. In these irregular structures, the protrusion part is called lobe and the depression one is called cleft, both of which are the key points affecting the topology of gravity current. There were two main objectives in our study, the first one was to explore the high-Reynolds-number regime, which was analysed insufficiently in previous studies, and this provided us the access to compare the difference of gravity currents at high and low Reynolds numbers. The other was to determine the causes influencing the splits and merges, both of which lead to the generation and dissipation of lobe-and-cleft structure. The analysis of splits and merges was also relatively lacking in the previous research. In our research, we analysed the variation of vorticity field in the gravity current and concluded the generation and dissipation of lobe-and-cleft structure with the variation of the vortex. The Numerical methods were conducted to solve the governing equations in order to simulate the three-dimensional gravity current, which happens between the interface of high-concentration fluid and ambient fluid, at Reynolds number of 1788, 3450, 8950, 13000, 17000, respectively. Some important parameters such as concentration, velocity, vorticity, and so forth were analysed. Results revealed that we successfully expanded the information from low-Reynolds number to high-Reynolds number, and the tendency of the statistical results at different Reynolds number were also similar to the results in the previous study. Furthermore, the swirling parameter of λ_ci was used to represent the variation of vortex when the lobe-and-cleft structure split and merged. Both the analysis of vorticity equation, including the observation of tilting term whose contribution was greatest in the equation, and the analysis of the interactions between the parent and offspring vortex, all provided the physical supports that the vortex has great influence on the generation and the evolution of the new cleft. It provides the evidence that the study can help us to compare the difference of gravity current from low to high Reynolds number, and the unstable turbulence structure has influence on the topology of gravity current.