水庫異重流運移過程之數值模擬

Numerical Simulation on the Propagation of Turbidity Currents in a Reservoir

曾仁彥(Ren-Yan Tzeng)

指導教授 ： 曾志民

長榮大學/管理學院/土地管理與開發研究所/碩士(2008年)

摘要

本論文研究目的在於探討水庫異重流運移過程之相關影響因素，並結合前人研究與經驗公式，建構平面二維的異重流數值模式，合理模擬水庫異重流運移過程，藉此了解發展過程中流速、厚度及濃度之沿程變化。研究方法乃修改前人研究之平面二維水庫沖淤模式，配合相關異重流經驗公式，建立平面二維異重流數值模式。本模式之數值方法，是以顯示有限差分法，配合分離演算法，將水流連續方程式與動量方程式、懸浮載泥沙對流擴散方程式及地形沖淤守恆方程式以差分方式處理，共同聯立求解，藉以描述異重流運移過程的現象。本研究並針對模式本身進行安定性、收斂性及連續性分析，以確保數值模式計算的合理性與正確性。
由前人研究得知，異重流之形成與入流流量、濃度及地形坡度關係密切，因此將其設定為模式主要控制條件進行異重流數值模擬。在模式檢驗方向，模式須符合C.F.L.之安定條件，求出本模式之最大可蘭數約為0.1；接著測試流場的收斂性分析，並計算水流入流與出流之體積以檢驗連續性分析，以及進行模式中格網大小之敏感性分析，結果皆能符合模式檢驗之要求標準，由此得知本數值模式具備合理性與正確性。本研究利用徐小微(2002)之實驗結果進行參數率定以及模式驗證，參數率定結果顯示，當坡度為0.006接近異重流臨界坡度，入流濃度固定為10.26(g/L)，入流量介於0.16(l/sec)∼0.24(l/sec)時，無因次捲入係數(Ew)範圍介於0.002123至0.0159，而Richardson number(Ri)的範圍介於0.063287至1.307725之間，數值模式可保持穩定計算。數值模式於模擬異重流運移的過程中，能正確反應出異重流沿程之速度、厚度及濃度變化趨勢，藉由模擬計算結果得知，在固定入流濃度下，當入流量愈大，相對其異重流運行速度愈快，而在固定入流量時，發現當入流濃度愈大時，其運行速度亦比入流濃度小時快。異重流的濃度變化首先隨著流動距離而降低，但是隨著時間的增長，上游持續的提供入流，濃度慢慢上升趨於一個定值。而在單一入流濃度的情況下，當入流量設定越大，則同一斷面的異重流厚度越厚，模式計算與試驗結果大致相符。

關鍵字

平面二維 ； 異重流 ； 濁流 ； 數值模式

並列摘要

This study aims to modify the existed two-dimensional numerical model for density current simulation, reasonably simulating the movement of density current in order to understand the changes of flow rate, thickness and concentration in the development processes. The numerical model composed of shallow water equations, suspended load convection-diffusion equation and sediment continuity equation. This study adopts explicit finite-difference scheme differentiating the governing equations and deals with computational mesh using leap-frog scheme. In terms of the correlation between flow field and topographical evolution, an uncoupled computation is adopted. Besides, This syudy also carry out the analysis of stability, convergence and continuity to ensure the rationality and correction for numerical model.
According to the past studies, the form of density current is highly related to the inflow rate, concentration and bottom slope. Therefore, they are set to be as the control conditions to proceed numerical simulation for density current. The numerical model has to satisfy the stable conditions created by C.F.L. and get the maximum courant number (0.1), examine the convergence of flow field, calculate the volume of inflow and outlet for checking the continuity, and analyze the sensitivity of mesh size. Consequently, the results can be achieved to the requirement for the numerical model. Experimental results (Hsu, 2002) were adopted for the model’s valibration and verification. The result for parameter calibration reveals that when slope value approach critical slope value (0.006,) inflow concentration value equals 10.26(g/L), and inflow rate is set between 0.16(l/sec) to 0.24(l/sec), it represents the dimensionless entrainment coefficient (Ew) ranges from 0.002123 to 0.0159, and Richardson number (Ri) ranges from 0.063287 to 1.307725, which numerical model can be calculated steadily.
Simulation results show that the more volume of inflow gets, the faster speed density current proceed, when the concentration of inflow is fixed. Moreover, when volume of inflow is fixed, the inflow concentration is getting more, its speed is faster than that of little concentration of inflow. However, the changes of density current will decrease with moving distance. With the time become long, if the headstream keeps flowing, the concentration will climb up to a fixed value. Under the circumstance of unique concentration of inflow, when volume of inflow is set a lot, the thickness of density current will become thicker in the same section. Calculation for the model and experimental consequence are quite same.

並列關鍵字

two-dimension ； turbidity current ； density current ； numerical model

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