運用數值模擬於均勻混合河口懸浮載之運移特性探討

Abstract

在臺灣，水庫清淤是維持用水安全的重要工作，含砂水到達下游時，因為流速及雷諾數降低，河水垂直混和能力大幅下降，會在感潮河段至河口處與密度不同的大陸棚海水形成河口密度流現象，此密度流之料源以粒徑極小的水庫底泥為主，其為凝聚性沉滓，顆粒容易互相絮凝，以致增加吸收重金屬和其他汙染物及營養鹽的表面積，這些污染嚴重的泥砂停留過久，可能會對人口密集且生態多樣的河口地區造成威脅，因此，本研究希望透過數值模擬方法，了解河口密度流的運移特性，希冀能找出影響其流動特性較為關鍵的因子，這將可能有助於減少清淤所造成的汙染和破壞，在達到水庫永續經營目標的同時，保障河口生態及下游居民的生活品質，創造雙贏的局面。 本研究所建立的數值模型主要分成水理部分與質量傳輸部分。水理部分係基於保守形式的淺水波方程式，在空間離散中以有限體積法，搭配Roe近似求解數值通量，並採用三階精度的全差變遞減格式(total variation diminishing scheme)的龍格－庫塔法(Runge–Kutta method)進行時間離散；質量傳輸部分的控制方程式，係基於考慮流體對流及延散作用對質量傳輸造成的影響所建立，為提升模式的穩定性，本研究質量傳輸部分之模型，是以有限差分法中的一階精度之隱式尤拉法進行時間離散，空間離散部分則在對流項採用一階精度迎風格式，延散項使用二階精度的中央差分法進行建模。而本研究所建立的數值模型在水理方面通過一維潰壩問題、長波問題，及駐波問題的驗證，而質量傳輸部分則分別測試了延散項的準確性，及對流項和延散項間的相互關係之驗證。 在完成模式驗證後，本研究分別模擬並討論了河川及泥砂入流條件、潮汐，和延散係數對懸浮載在大陸棚運移模式之影響，結果顯示，潮汐有助於增加質量傳輸能力，另外，河川的入流條件對於泥砂是否能順利向大陸棚方向運移，扮演著重要的角色。最後，本研究模擬不同水庫排砂情境對河口懸浮載運移之影響，在河川出流量不大的情況下，濃度歷線峰值的偏移對河口泥砂運移的影響非常有限。

In Taiwan, the desilting of reservoirs is an important task to ensure sufficient water resources. When suspend load reaches downstream, the flow velocity and Reynolds number decrease, and the vertical mixing of river water will decrease. The sediment-water flow will form estuary density flow with shelf seawater with different density, which occurs from the tidal river reach to the estuary. The source of this density flow is mainly reservoir sediments with small particle sizes, which may carry more heavy metals and other pollutants. These pollutions could pose a threat to densely populated and ecologically diverse estuaries. Therefore, this study would discuss the estuary density flow through numerical simulation methods. This study aims to identify key factors affecting estuary flow characteristics, which may help reduce pollution and damage from dredging. The purpose of this study is to maintain the sustainability of the reservoir while protecting the ecology of the estuary and the quality of life of downstream residents, creating a win-win situation. The numerical model established in this research is mainly divided into the hydraulic model and sediment mass transport model. The hydraulic model is based on the conservative form of the shallow water equation and applies the finite volume method and the Roe approximation method to solve the numerical flux in spatial discretization. Besides, total variation diminishing (TVD) Runge–Kutta method with third-order accuracy is used for time discretization. The governing equation for the mass transport part is based on the effects of fluid convection and dispersion on mass transportation. In order to improve the stability of the model, the first-order precision implicit Euler method in the finite difference method is used for time discretization. In addition, in the part of spatial discretization, the first-order accuracy is adopted for the convection term, and the central difference method of the second-order accuracy is applied for the dispersion term. The numerical model established in this research has verified the one-dimensional dam-break problem, long-wave problem, and standing-wave problem in the aspect of hydraulics. In the mass transport model, we tested the consistency of the dispersion term and the interrelationship between the dispersion term and advection term respectively. After completing the model verification, we simulated and discussed the effects of the river and sediment inflow conditions, tidal conditions, and dispersion coefficients on the transport model of suspended loads on the shelf. The results show that the tide can increase mass transport. Also, river inflow condition is a key factor in the intensity of sediment movement to the ocean. At the end of the study, we attempted to simulate the effects of different reservoir dredging schemes on estuary suspended load transport. In the case of small river inflows, the migration of concentration peaks has very limited effects on the transportation of estuarine sediments.