- 學位論文
以拉格朗日結構變化探討滾筒中穩態顆粒流之動態行為
Investigation of the Dynamics of Steady Granular Flow in a Rotating Drum by Lagrangian Coherent Structure Evolution
摘要
本研究藉系統性實驗探討滾筒乾顆粒以及完全沉浸水的濕顆粒流之拉格朗日相干結構(Lagrangian coherent structure, LCS)，以期望在傳統尤拉場觀點之外提供不同的資訊。本研究藉由控制滾筒轉速(w = 0.135~0.4654rad/s)達到福祿數(Fr)為6.28*10^-4~7.5*10^-3的乾濕穩態顆粒流，所對應的流動型態為滾動(rolling)。顆粒運動以高速攝影機記錄，利用實驗顆粒(聚甲醛樹酯polyoxymethylene)表面的紋理特性發展出”影像索引值相似度法”來定位影像中的顆粒質心，並搭配最近鄰居法作時間上之顆粒配對以計算顆粒的瞬時速度，進一步求出顆粒流尤拉觀點下的速度場，搭配虛擬質點的追蹤求出有限時間Lyapunov指數(Finite-Time Lyapunov Exponent, FTLE)分布，並以其背脊形狀(ridge)定義流場中的LCS結構。實驗結果發現需要追蹤5~7個滾筒旋轉週期才能完整地呈現LCS結構。流動層區域有較大的FTLE值，因為顆粒運動較快所致，而固體層區域的顆粒與滾筒進行剛體運動，其FTLE值不會隨時間變化。若比較乾濕顆粒流的FTLE場，後者的LCS結構資訊較為混亂，歸因為流體潤滑而引發顆粒運動的微小擾動。此外，乾濕顆粒流的FTLE場皆會產生相交的排斥物質線(rLCS)及吸引物質線(aLCS)，只是乾顆粒流的aLCS封閉迴路形成在rLCS封閉迴路之外圈，而濕顆粒流的結果相反。本研究更進一步利用真實顆粒以及隨理論速度場模型運動之虛擬質點軌跡求出相似的LCS結構。最後於軌跡的追蹤下發現顆粒流三維運動的模式，並以統計顆粒運動的方法加以證明。
並列摘要
This thesis studies the Lagrangian coherent structures (LCS) for a dry or a fully immersed steady granular flow in a rotating drum by systematic experiments to complement the information based on Eulerian description. In this thesis, LCS is located by the Finite-Time Lyapunov Exponent (FTLE) field. We drove the drum at various constant speeds (w = 0.135~0.4654rad/s) so that the Froude numbers are 6.28*10^-4~7.5*10^-3 giving flows in the rolling regime. The granulate motion was monitored by high speed digital camera and we developed a method of index similarity to locate particle centers exploiting the fact that identical spheres poly possess similar surface texture. The same sphere was paired in two consecutive images by the method of the nearest neighbor to achieve particle traking velocimetry (PTV) to obtain its instantaneous velocity. A mean Eulerian velocity field was then interpolated and averaged from these particle velocities.The obtained velocity field was employed to advect virtual particles in time so their trajectories can be used to compute FTLE and the corresponding LCS. Higher FTLE value was measured in the flowing layer due to the faster bulk motion therein. In contrast, the value in the packed bed in solid body rotation remained a nearly constant small value. It took about 5-7 rotation cycles to extract LCS structure and LCS for the immersed bulk seemed more smeared out since the lubricated particles could move more easily and hence randomly than dry ones. In addition, attracting LCS (aLCS) was found to intersect with repelling LCS (rLCS) and aLCS was observed to encompass rLCS for the dry flow but the opposite was found for the immersed flow. We also tried to calculate FTLE using real particle trajectories and virtual trajectories as advected by a theoretical model. Dynamically similar results were found. Lastly, the long-time virtual particle trajectories merged onto a limit cycle suggesting longitudinal velocity component in the current thin drum flows and such three dimensional flow was confirmed by simple visualization experiments.