明渠超臨界流交波現象模擬之分析

Abstract

本研究旨在發展一超臨界流二維水理模式，以分析交波之流況。延續謝(2003)所發展之水深平均二維模式，增加不同流況邊界條件設定的功能，使模式能進行超臨界流、亞臨界流、混合流況的模擬。在數值處理上，採用雙階分割操作趨近法，將控制方程式分割成延散步驟和傳播步驟兩個步驟進行求解；在數值差分上則採用隱式法，使模式可以採用較大的演算間距。為驗證模式的合理性與正確性，分別採用直線道的水躍與潰壩案例，彎道的亞臨界流、超臨界流、混合流等案例，進行模式功能展示與模擬正確性的驗證工作。 本研究在交波現象模擬過程中，直線道部分採用Ippen等(1951)的束縮渠道，彎道部分採用Reinauer等(1997)所做的實驗進行分析。模擬參數之敏感度分析顯示，格網數目與格網正交性會對模擬結果產生影響；此外，在採用de Vriend(1977)的流速剖面下，不考慮二次流效應的彎道交波之模擬結果更為接近實驗值。最後擇用較適當之參數進行交波現象模擬與分析。

The purpose of this study is to develop a 2D depth-averaged flow model to analyze the cross-wave phenomenon in supercritical flow condition. The model developed herein extends Hsieh’s (2003) 2D depth-averaged model with the capability of dealing with various types of boundary condition to handle the supercritical, subcritical and mixed flow problems. The split-operator procedure involves two steps, in which one is the dispersion step, and the other one is propagation step including the pressure and bed friction terms, is used to solve the flow equations. Implicit scheme is adopted to relax the time interval restriction. The hydraulic jump and dam break cases in straight channels and subcritical, supercritical and mixed flow cases in curved channels have been studied to demonstrate the capability and accuracy of the proposed model. The experimental data of Ippen et al. (1951) in straight channel, and Reinauer and Hager (1997) in curved channel are adopted and simulated by the proposed model to analyze the cross-wave phenomenon. The sensitivity analysis is performed to analyze the effect level of numerical parameters and the results indicate that the cross-wave simulation is influenced significantly by grid numbers and grid orthogonalaity. Based on the velocity profile proposed by de Vriend (1977), the simulation results without considering the secondary effect shows better agreement in comparison with experimental data. Finally, the appropriate numerical parameters mentioned previously are adopted；and the comparison of simulation results with the experimental data is quite convincing.