陡坡渠道水流不穩定性之理論與試驗分析

Theoretical and Experimental Analyses of Flow Instability in High Gradient Channels

10.29417/JCSWC.202303_54(1).0003

詹勳全(Hsun-Chuan Chan)；林柏瑋(Po-Wei Lin)；謝東原(Tung-Yuan Hsieh)；鍾亦婷(Yi-Ting Chung)；簡以達(Yi-Da Chien)

陡坡 ； 不穩定現象 ； 維德尼可夫數 ； Steep slopes ； Instability ； Vedernikov number

中華水土保持學報

54卷1期（2023 / 03 / 01）

27 - 37

繁體中文;英文

水流於陡坡流動時，因重力、表面摩擦、黏滯力及流體內部紊流應力間之作用，當水體受到擾動無法維持均勻流的流況，自由表面開始出現不穩定現象並隨流動距離逐漸發展，最後擴大形成一系列之滾波。不穩定現象會對水利構造物會產生不利之影響，如產生的壓力變化或水流週期性衝擊會導致渠道發生結構性破壞，渠道內水深急遽上升會導致溢流發生，甚至引起水流噴濺而沖蝕渠道周圍土壤。本研究透過理論與試驗，針對不穩定現象進行探討，利用維德尼可夫數 （Vedernikov number）推導不穩定現象的理論判別條件，過程考慮坡度對於福祿數的影響，找出不穩定現象在不同渠道型式發生的臨界條件及影響之水理因子。研究結果顯示，影響矩形以及梯形穩定性之水理因子，包括：坡度、曼寧粗糙係數、水深及渠底寬；影響拋物線形斷面以及半圓形斷面穩定性之水理因子為：坡度、曼寧粗糙係數、渠頂寬及自由水面寬；就不同斷面形狀而言，以矩形渠道較易維持穩定之水流。另外，本研究選擇矩形斷面進行渠槽試驗，針對推導之理論判別結果與試驗結果進行比較，結果顯示當水流條件鄰近於臨界值時，本研究所推導的穩定判別條件可以成功判別不穩定現象發生與否。

Water flow on steep slopes is not uniform because of the effects of the gravity, surface friction, viscous force, and turbulent stress of the fluid. Instabilities appear and gradually develop over the flow distance on free surfaces affected by disturbances, which finally expand to form a series of roll waves. The instability phenomenon has negative consequences for water conservancy structures. For example, pressure changes and periodic impacts of water flow cause structural damage to the channel, rapid rise of water depth in the channel and overflow, and even cause water splash to introduce soil erosion around the channel. Therefore, this study explores the instability phenomenon both theoretically and empirically. The theoretical derivation uses the Vedernikov number to distinguish instability phenomena. In addition, the derivation processing of critical conditions considers the influence of the slope on the Froude number, and the critical conditions for the occurrence of instability phenomena in different channels were determined. The rectangular and trapezoidal shape, slope, Manning roughness coefficient, water depth, and channel width were the influencing factors. For the parabolic cross-section and semicircular cross-sections, the influencing factors were the slope, Manning roughness coefficient, water surface width, and water depth. It was the easiest to maintain the stability of flow in different sections of the rectangular channel. In the experiments, the rectangular channel was selected for testing. On the basis of the comparison between the test and judgment results of the theory in this study, when the water flow conditions are close to the critical value, the conditions could successfully be determined.

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