應用沉浸邊界法與移動網格模擬紊流流況下之結構物沖刷現象

Abstract

本研究使用大渦流模式結合沉浸邊界法與移動網格法，模擬流體經過一結構物對底部泥沙所造成沖刷堆積的影響，大渦流模式(Large eddy simulation)為三維的水動力模式，較能捕捉到在高雷諾數下的紊流現象，在高雷諾數的流場中特別重要。結構物表面的複雜邊界主要使用沉浸邊界法(Immersed boundary method)來處理，與傳統的貼體法(body-fitting)相比，沉浸邊界法假想力的形式寫進統御方程式使其滿足邊界條件，在卡氏座標即可很有效率的處理複雜幾何或是移動網格的問題，另外再底床網格的部分則使用移動網格法(Arbitrary Lagrangian-Eulerian scheme) 計算網格座標速度使其滿足泥沙傳輸，並且模擬紊流邊界層中的底床形貌變化。 本研究一開始使用沉浸邊界法模擬流體流經一圓柱，改變雷諾數由潛變流模擬至紊流，觀察其尾流的變化，確認邊界與流場符合現實情況後，我們再依照Roulund, et al.(2005)所做的實驗配置，設定邊界條件進行模擬，並且分別討論圓柱前緣沖刷與圓柱下游沙漣(sand ripples)的形成過程，以及紊流動能在沖刷過程中所扮演的腳色，結果發現沖刷最強的區域通常都受到一個持續穩定的上升流場給帶動，如前緣的馬蹄形渦流(horseshoe vortex)。一開始前緣掏刷出來的泥沙會在圓柱後方低壓區域產生堆積，堆積丘的下游處容易產生分離流動使得沙漣更加明顯。而紊流動能大的區域通常為流場交界處，該區域由於其動能消散(disspation rate)十分強，故會使部分懸浮泥沙失去動能而在此沉積。

In this study, we apply the large eddy simulation (LES) code that combines the immersed boundary method (IBM) and the arbitrary Lagrangian-Eulerian method (ALE) to simulate the evolution of the erodible bed around a structure. This code is a three dimensional computational fluid dynamics simulator, which is capable of resolving the detailed turbulent flow field. This is particularly important in the high Reynolds number flow. We employ the IBM to model the surface of the structure. Compared to traditional body-fitting methods, IBM applies the body force to satisfy the desired boundary condition. It can efficiently handle the complex geometry and moving grids in Cartesian coordinate system. In addition, we apply the ALE method in our grid. It can calculate the grid velocity to guarantee conservation of sediment mass and simulate bed form dynamics in a turbulent boundary layer. We simulate flow over a cylinder as a test case for IBM. Cases ranging from the regimes of creeping flow to turbulent flow are investigated. The present numerical model is then validated against the experimental results by Roulund et al.(2005), who investigated erosion around a cylinder in a laboratory setting. We discuss erosion in front of the cylinder, the development of sand ripples behind the cylinder, and turbulence kinetic energy (TKE). The numerical results show that the most dramatic erosion region is affected by the steady upflow associated with the horseshoe vortex. Moreover, we observe that sediments in front of the edge pile up in the lower pressure area. Flow separation easily occurs behind the ripples, leading to the growth of the ripple amplitude. We found that high TKE occurs at regions of flow convergence, which is usually associated with strong dissipation, leading to the deposition of suspended sediments.