耦合輸砂模式之研究

Abstract

就物理觀點而言，泥砂運動與水流間，的確有著密不可分的相關性，就數 學觀點而言，當底床及粒徑百分組成變化足以嚴重影響流況時，分離演算 法便不再適用，而此時則需以耦合演算法來模擬河川變量流沖淤之現象。 本研究之目的在應用普立斯曼四點有限差分法，採用Zhang & Xie (1992)提出一新的輸砂公式(Shamov 公式)，和Karim & Kennedy(1982)發 展之"IALLUVIAL"模式中模擬混合層及甲護現象的方法，發展一耦合演算 輸砂模式。耦合演算水流連續方程式、動量方程式、泥砂連續方程式及粒 徑百分組成連續條件式，分離演算混合層厚度及甲護現象關係式。同時引 入一加權因子 β1，以處理上游邊界之河床質百分組成。應用台大水工試 驗所之非均勻質輸砂資料(顏氏，1987)為依據，針對數值參數中之ΔX、 Δt、θ、φs、β1及輸砂物理參數中混合層厚度、粒徑級配的分類及甲 護作用的與否，進行模式之測試及檢定分析。最後以較穩定或較佳的參數 進行模擬，與台大水工試驗所之實驗資料作比較分析，對於實驗中之平衡 試驗、超載試驗、減載試驗及清水沖刷試驗，探討沖刷及淤積情況下，水 面高程及底床高程的變動，及水力篩選的現象。從結果分析中可知，耦合 模式相當穩定，不受ΔX、θ及φs的影響；模式中考慮混合層厚度隨著時 間及空間演變的方式，對底床沖淤量及水力篩選之模擬頗有助益。而模式 對於底床坡度、福祿數、水深、平均流速、摩擦坡度及水力篩分，數值結 果與實驗資料頗為接近。 The purpose of this study is to develope a coupled mobile-bed model which is capable of simulating the bed evolution in an all- uvial channel. This model attempts to couple the water continuity equation, water momentum equation, sediment continuity equation, and hydraulic sorting equation, but decouple the computation of the mixed-layer thickness and armoring relation. The governing equations are discretized by the use of the pressimann's four- point scheme. The sediment predictor proposed by Zhang & Xie (1992) was used to compute the sediment transport capacity for each computational point. The mathematical formulations of hydr- aulic sorting and armoring coded in IALLUVIAL model (Karim & Kennedy, 1982) are used in this model. This new coupled model was examined through the test simulation with the use of experimental data set which were conducted in the Hydraulic Research Labor- atory of National Taiwan University (1988). The influence of numerical and physical parameters to the model's stability was studied through the sensitivity test. The numerical parameters considered here include space interval ΔX,time interval Δt, temparal weighting factor θ, spatial weighting factor φs,and the sediment-inflow weighting factor β1. The physical parametars include the mixed-layer thickness, size classes, and the armoring factor. From the test results, it can be concluded that the parameters ΔX, θ, and φs have little effect on the simulation results.Among the parameters tested, the variation of mixed-layer thickness seems to be the most important factor which seriouly influences the model's stability.With the various input sediment discharge, the phenomena of bed evolution and hydraulic sorting are analyzed in details. Again, from the results, one can find that this newly proposed model can reasonably simulate the bed evolution, the change of size fraction, and the water flow under the underloading, overloading, and equilibrium conditions.