二維彎道動床模式之發展研究

Abstract

本研究旨在發展一水深平均水平二維之彎道動床模式。模式在發展過程中，通盤考量二次流之效應，水理演算不忽略延散剪應力項；懸浮載之運算包含環流傳輸項；底床載的演算，則將其運移之修正角度納入考量，包含流速、底床坡降及曲率半徑之影響。在數值處理上，水理採用雙階分割操作趨近法，將水理控制方程分割成延散步驟和傳播步驟求解，數值差分則是採用隱式法，使模式可採用較大之演算間距；沉滓運移則是採用耦合演算法(同時求解所有沉滓運移控制方程式)，利用Newton-Raphson疊代聯立求解。藉由模擬Struiksma(1983) DHL-T2之彎道實驗，發現在固定參數下，模式並無法適切模擬出彎道入口段過度沖淤(overshoot)之現象。經由模式彎道二次流效應之敏感度分析，發現底床載二次流效應對底床沖淤之影響最大。因此，透過調整底床載二次流效應之程度，可檢定彎道模擬時之合適底床載參數。最後，將此參數檢定架構應用於DHL-T1及DLFM實驗之模擬，驗證此架構之合宜性。

The purpose of this study is to develop a 2-D depth-averaged mobile-bed model for channel bends. To the model, the secondary current effect is thoroughly considered for the water and sediment movements, which include the dispersion stress term in the flow momentum equation, the circulatory transport term in the suspension transport equation, and the angle of sediment transport in the bed load transport equation. The angle of sediment transport includes the effects of the flow velocity, the bed slope, and the radius of channel bend. As for the numerical solution procedure, the split-operator approach is used to solve the flow equations. Based on the decomposition of the momentum equations, the split-operator procedure involves two steps in which one is the dispersion step, and the other one is propagation step includes the pressure and bed friction terms. Implicit discretized method is adopted to relax the time step restriction to allow large time steps. The direct coupling, i.e. simultaneous solution of the sediment equations and Newton-Raphson methods, is used to solve the sediment governing equations. By using the uniform parameters in the DHL-T2 case of Struiksma’s(1983) experiment, the simulated results can’t demonstrate the overshoot phenomenon near the entrance of channel bend. The sensitive analysis indicates that the secondary-current effect in the bed-load transport equation has significant effect on the bed evolution. Hence, the nonuniform parameters of the secondary-current effect in the bed load transport equation are the key for the model calibration. Finally, the calibration process is applied to DHL-T1and DLFM cases to assess its rationality.