垂直二維水動力泥砂模式於水庫泥砂運移特性之運用分析

The Application of Two-dimensional Vertical Multilayer Hydrodynamic and Sediment Transport Modelling of Density Currents in a Reservoir

白楷伊(Kai-Yi Bai)

指導教授 ： 游景雲

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202002083

摘要

本研究建立了垂直二維水動力泥砂模式於水庫泥砂運移特性之運用分析。水庫中的異重流具有複雜的混合以及分層特性，它影響了水庫的水質且降低了其庫容。隨著頻繁的排砂操作使得異重流得以排出水庫，因此異重流於水庫運移特性之研究在台灣變得越來越重要。傳統上，利用求解三維Navier-Stokes方程可以獲得精準的答案，但其極高的計算成本始終是一個嚴重的問題，尤其是針對大尺度工程問題。在過去的幾年中，在靜水壓和Boussinesq近似的假設下，學者持續致力於發展有效率的準三維模型。因此，遵循相同的最新建模策略，本研究使用有限體積方法建立了多層水動力泥砂模型。在該模型中，由於對計算區域進行垂直劃分，除了可以更精準模擬地形變化，也能求出完整的垂直向流場變化。此外，我們的模型也已針對多個案例進行嚴格驗證，包括風驅動環流、地形變化流場驗證、潮汐波傳播和密度驅動環流，皆有通過網格收斂測試和準確性評估。在驗證完此模式後，該模型將用於研究在不同條件下之水庫泥砂運移特性分析，例如泥砂入流條件、底床坡度、初始水位高以及不同出流口位置。結果得到不同流動條件下與泥砂輸送之間的關係，可得知坡度、入流量、初始水位以及出流入口皆會使得泥砂運移情況改變。最後本研究模擬在不規則地形下的運移情況，不規則地形使得流場變化大，也影響泥砂運移的速度以及形狀。

關鍵字

淺水波方程 ； 泥砂傳輸 ； 有限體積法 ； 多層淺水波模式 ； 包辛尼斯克近似 ； 異重流

並列摘要

This study aims to develop a multilayer hydrodynamic and sediment transport model for simulating the morphology of density currents in a reservoir. The propagating density current in a reservoir essentially behaves the stratification causing the intense mixing, which also impacts reservoir water quality and reduces its capacity. This kind of issues become more important in Taiwan in line with the more and more frequent sediment flushing operation which lead to density currents flushing out of a reservoir. In some applications, three-dimensional (3D) models solving Navier-Stokes equations are used. However, the extremely high computational cost, especially for the large-scale environmental problems, is always a serious concern. In the past years, continuous efforts have been devoted to the development of efficient quasi-three-dimensional models based on the hydrostatic assumption and the Boussinesq approximation. Following the same state-of-the-art modelling strategy, this study develops a multilayer shallow-water and sediment transport model with a finite volume method. In this model, a terrain following coordinate with the high local resolution is used to vertically divide the computational domain into multiple layers to better address bottom topography and velocity profile. Our model is rigorously validated against several benchmark cases including wind-driven circulation, subcritical flow over a hump, tidal wave propagation, and density-driven circulation. Those cases passes convergence tests and the accuracy is also in good agreement with analytical solutions. Subsequently, the model is applied to investigate the reservoir dynamics and sediment transport under different conditions, e.g., flow discharge, bottom slope, concentration and initial water level. Overall, the results show the interaction between flow conditions and sediment transport. It can be investigated that the slope, inflow, initial water level and outflow inlet will all change the sediment transport. Finally, this study simulates sediment transport on irregular terrain. Irregular terrain makes the flow fields change greatly, and also affects the velocity and shape of density currents.

並列關鍵字

shallow-water equation ； sediment transport ； multilayer system ； hydrostatic ； Boussinesq approximation ； density current

參考文獻

1. Altinakar, S., Graf, W. H., Hopfinger, E. J. (1990). Weakly depositing turbidity current on a small slope. Journal of Hydraulic Research, 28(1), 55-80.

2. Audusse, E. (2005). A multilayer Saint-Venant model: derivation and numerical validation. Discrete Continuous Dynamical Systems-B, 5(2), 189.

3. Audusse, E., Benkhaldoun, F., Sari, S., Seaid, M., Tassi, P. (2014). A fast finite volume solver for multi-layered shallow water flows with mass exchange. Journal of Computational Physics, 272, 23-45.

4. Audusse, E., Bristeau, M. O., Pelanti, M., Sainte-Marie, J. (2011). Approximation of the hydrostatic Navier–Stokes system for density stratified flows by a multilayer model: kinetic interpretation and numerical solution. Journal of Computational Physics, 230(9), 3453-3478.

5. Audusse, E., Bristeau, M. O., Perthame, B., Sainte-Marie, J. (2011). A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. ESAIM: Mathematical Modelling and Numerical Analysis, 45(1), 169-200.