- 學位論文
考量紊流間歇性及非均向性影響下之隨機泥砂運動行為模擬
Stochastic Sediment Transport Modeling under the Effects of Intermittency and Anisotropy of Turbulent Flow
摘要
明渠流中的泥砂傳輸模擬，該研究被廣泛運用在水利工程、河川底床形貌變化、相關水利政策的制定等範疇，其中泥砂顆粒在水體中的運動行為除了受平均水流的影響外，還受到紊流效應造成泥砂顆粒的不規則擴散行為，因此，為描述此隨機現象，本研究以力學的基礎下結合序率方法(stochastic method)來模擬泥砂顆粒在水流中的運動軌跡，以說明泥砂顆粒受紊流影響之隨機運動行為。 紊流由各種不同尺度的紊流結構物所組成，屬於極為複雜的流況。根據文獻資料顯示，靠近底床處因受到紊流結構物和底床粗糙度的影響，造成該區域呈現非均向性(anisotropy)的紊流流況，反之，隨著與底床間的距離增加，該效應對於整體流況的影響也越趨減緩，造成上部區域呈現均向性(isotropy)的紊流流況。底床沉積物的再懸浮運動是一間歇性(intermittency)的過程，即泥砂顆粒沉降至底床時，該顆粒會停滯於底床一段時間，當發生更強的流動時再將其挾帶起。此外，以流速擾動項之各分量進行象限分析，可將紊流突發事件(turbulent bursting event)區分成四個種類，各別為outward interactions (Q_1)、ejections (Q_2)、inward interactions (Q_3)、sweeps (Q_4)，其中又以ejection和sweep兩種事件對於整體流況及泥砂傳輸行為具有顯著影響，而各種事件在空間中具有不均勻的分布情形(inhomogeneous spatial distribution)，ejection傾向分布在上層流域中而sweep則較常在發生在靠近底床處。然多數文獻僅侷限於描述紊流特性，較少分析該效應對泥砂傳輸的影響，因此，本研究藉由隨機擴散粒子追蹤模型(Stochastic Diffusion Particle Tracking Model, SD-PTM)來模擬泥砂顆粒受到以上紊流效應影響之運動行為。 根據朗之萬方程式(Langevin equation)推導出的SD-PTM包含兩個元素，一為顆粒隨著整體流況移動的平均漂移項(mean drift term)，另一為顆粒受紊流影響所產生不規則運動的隨機項(random term)。本研究以SD-PTM為原型，並發展出兩種模型來討論紊流效應對粒子運動之作用，第一個模型為SD-PTM with SBM，結合偏斜布朗運動(skewed Brownian motion)和Mittag-Leffler厚尾分布(Mittag-Leffler heavy tailed distribution)來分別描述粒子在非均向性紊流下之偏好運動方向及沉降顆粒等待時間之分布情形；另一個模型為modified SD-PTM，將隨機項分成兩項來代表ejection和sweep兩種事件對粒子運動的影響。綜合上述，本研究預期透過粒子運動軌跡之統計值，分析紊流效應所產生的影響，並以流速剖面與泥砂濃度曲線來驗證模型的準確度。
並列摘要
Turbulent flow is a chaotic condition filled with vortex structures in the flow. Based on past studies, the flow region can be divided into two parts (the near-bed region and the upper flow region) by the spatial gradient of the flow velocity. The flow condition near the bed wall tends to be anisotropic because of the turbulent structures and the roughness effects. Furthermore, it is also found that the resuspension of the deposited sediment particle is an intermittent process and possesses a waiting time effect before being entrained up. Additionally, turbulent bursting events are composed of outward interactions (Q_1), ejections (Q_2), inward interactions (Q_3), and sweeps (Q_4). Among these events, ejections (Q_2) and sweeps (Q_4) significantly contribute to time occupied, momentum flux, and sediment flux. In addition, the occurrences of the turbulent coherent structures were assumed equivalent in the past. However, recent studies reveal that the occurrences of bursting events are inhomogeneous in different bed elevations. As mentioned above, these characteristics (inhomogeneous event occurrences, preferred movement of turbulent anisotropy, and intermittent process of the particle deposition) were focused on the details of the turbulence and seldom discussed their influences on sediment transport in past studies. This study proposes two Stochastic Diffusion Particle Tracking Models (SD-PTM), using the stochastic Lagrangian method to describe sediment particle movement. The proposed model integrates these turbulent characteristics determined from the Direct Numerical Simulation dataset to reveal more details of sediment particle motion in the turbulent flow. The first model, SDPTM with SBM, incorporates the skewed Brownian motion and the Mittag-Leffler heavy-tailed distribution to represent the turbulent anisotropy effects and the intermittent waiting time of the deposited particles. The second model, modified SDPTM, considers the inhomogeneous spatial distribution of ejection and sweep events and depicts the particle movement direction under the event's influence. We obtain the particle trajectories from the model and analyze the anomalous diffusion in sediment transport by calculating the variance of the particle trajectories. Validating the proposed models with the flow velocity and the sediment concentration profiles of past studies reveals the performance of the proposed models. Conclusively, when a detailed description of the turbulent flow can be made available, we can simulate sediment particle motion more comprehensively under these extreme flow conditions.