運用二維模式於靜水池消能效率之探討

Abstract

在水利工程中，靜水池作為一種水力消能設施，主要透過水躍和紊流作用，將溢洪道排出的大量動能與位能轉化並消散。水躍是在消能池內影響消能的重要因素。傳統上，儘管水躍為三維(3D)現象，研究卻多採一維(1D)或3D模型。3D模型精度高但計算成本高，1D模型則無法捕捉水躍的渦流與側向流動。考量計算效率與準確性，二維(2D)模型提供了一個有潛力的替代方案。本研究旨在評估2D水力模型在模擬突擴、漸擴式消能靜水池實驗中的應用能力及局限性。研究核心為透過模擬不同上下游寬度比、入流擴張角度和入流偏心率等幾何設計參數組合，以找出能最大化能量消散效率的最佳設計。入流擴張角度和入流偏心率與水躍後水深(h2)的模擬與實驗數據的誤差率呈正比，而與上下游寬度比呈反比。上下游寬度比對消能效率有顯著影響，但當寬度比達到一定值後，消能效率存在極限，不再顯著提升。擴張角度未在消能效率上呈現明確趨勢，其特性隨尾水條件變化而異。偏心率在消能效率的特性上與擴張角度類似，其特性同樣隨尾水條件變化而變化，但當入流的側牆與擴張後的側牆重合時，消能效率會降低，這可能與其「與h2誤差率呈正相關」的驗證結果有關。最後進行了混合幾何因子之設計，確認會有疊加效應，但疊加後的因子特性會有些許改變。

In hydraulic engineering, stilling basins serve as crucial energy dissipators, primarily transforming and dissipating the significant kinetic and potential energy discharged from spillways through hydraulic jumps and turbulent action. Hydraulic jumps are a key factor influencing energy dissipation within these basins. Traditionally, despite hydraulic jumps being a three-dimensional (3D) phenomenon, most research has employed one-dimensional (1D) or 3D models. While 3D models offer high accuracy, they come with substantial computational costs. Conversely, 1D models fail to capture the complex vortex and lateral flows inherent in hydraulic jumps. Considering both computational efficiency and accuracy, two-dimensional (2D) models present a promising alternative. This study aims to evaluate the applicability and limitations of 2D hydraulic models in simulating experimental cases of abrupt and gradual expansion stilling basins. The core of this research revolves around identifying optimal geometric design parameters, including various expansion width ratios, expansion angles, and inflow eccentricities, to maximize energy dissipation efficiency. Our findings indicate that the error rate between simulated and experimental data for the tailwater depth (h2) after a hydraulic jump is directly proportional to the expansion angle and inflow eccentricity, but inversely proportional to the expansion width ratio. The expansion width ratio significantly impacts energy dissipation efficiency; however, there's a limit to this enhancement, beyond which further increases in the ratio do not lead to substantial improvements in efficiency. The expansion angle did not show a clear trend in energy dissipation efficiency, with its characteristics varying depending on tailwater conditions. Similarly, eccentricity exhibited characteristics in energy dissipation efficiency akin to the expansion angle, also changing with tailwater conditions. Notably, when the inflow's sidewall aligns with the expanded sidewall, energy dissipation efficiency decreases, which may be related to its positive correlation with the h2error rate. Finally, a design incorporating mixed geometric factors was implemented, confirming a superposition effect, though the characteristics of the superimposed factors exhibited slight alterations.