河道三維高含砂水流沉滓運移模式發展與應用

Abstract

為能探討高含砂水流運移現象並提供實際規劃應用參考，本研究採水平正交曲線、垂向sigma座標系統之靜水壓淺水波方程式，發展一三維高含砂水流沉滓運移數值模式。控制方程式以水平垂直分離概念，分為水深平均二維方程式與流速差異量方程式，搭配三維連續方程式求解三維流場。沉滓運移控制方程式分為三維質量傳輸方程式、作用層連續方程式與底床連續方程式。高含砂效應考量二次式流變關係反應非牛頓流體特性，以狀態函數反應含砂濃度對密度之影響，並採用考慮高含砂效應之懸浮載與底床載經驗式，反應高含砂水流沉滓運移與濃度變化。 高含砂水流及沉滓運移模式應用上需率定之相關參數甚多，因此首先進行模式參數敏感度分析，探討影響水理、濃度與底床沖淤模擬結果重要參數之權重。另研選數組高含砂水流實驗案例進行模式測試，探討水理及沉滓運移特性。探討重點包含：流變關係之阻力使潰壩湧波移動一段距離後發生停止運移之現象；彎道水位超高變化受流變關係之影響；流變關係與密度對底床載運移量之影響；並釐清落淤速度與剪力速度之比值，可判斷兩種紊流擴散係數分布於模擬三維懸浮載濃度分布之適用性。最後以實際應用角度，建立高含砂水流效應下，定床水深、流速與底床剪力相對於清水流之增量及以動床觀點探討底床載對底床沖淤之影響，以簡易關係式之型式供工程規劃設計應用之參考。

To investigate the transport behavior of hyper-concentrated flow and as a result to provide as a reference for engineering planning of practical cases, a hydrostatic three-dimensional model for hyper-concentrated flow and sediment transport in alluvial channels was developed in this study. By following the vertical and horizontal splitting concept (VHS), the shallow water flow governing equations were split into two parts including the depth-averaged two-dimensional equations and velocity defect equation in vertical direction. The former one was transformed into orthogonal curvilinear coordinate system; the latter one was derived as the form of sigma coordinate. Incorporated with continuity equation, the three-dimensional velocity field can therefore be solved. Sediment transport governing equations include three-dimensional mass transport equation, active-layer continuity equation, and bed-layer continuity equation. The effects of hyper-concentrated flow were treated as follows: a quadratic rheological relation was used to reflect the characteristics of non-Newtonian fluid; a state function was used to reflect the influence of concentration to density; the empirical suspended- and bed-load formulae with hyper-concentrated flow effect were used for the sediment transport computation. Sensitivity analysis was performed first to identify the weighting of parameters to be calibrated in the model. The influence extent induced by the parameters on water flow, suspended sediment concentration, and bed evolution, thereafter were examined and justified. To further investigate the characteristics of hyper-concentrated flow and sediment transport, several sets of experimental cases collected from the literatures were simulated. The case of dam-break wave propagation of non-Newtonian fluid was simulated to demonstrate the limit of traveling distance of hyper-concentrated flow. A channel bend flow experiment with 40% volume concentration of sediment was studied to investigate the effect of hyper-concentrated flow on super-elevation of water surface. A criterion of ratio of falling velocity and shear velocity was numerically examined and justified based on experimental data as a baseline for choosing the proper distribution type of turbulent diffusivity for simulation of suspended-load movement. At last, simple and concise regression relations for the increments of water depth, velocity, bed shear stress, and bed change caused by the hyper-concentrated flow were established for application of engineering planning and design.