RESED 3D k-ε 模式在明渠急彎水流之應用研究

Abstract

本研究發展靜水壓三維水理模式依黏滯係數計算，其中紊流模式採用雙方程模式之標準k-ε紊流模式，探討明渠流於急彎段之紊流流場現象。座標系統上，為使模式能便利處理不規則的渠道與底床邊界，水平方向與垂直方向分別採用正交曲線座標與σ座標系統。水理模式之架構先由深度平均之控制方程式求解水平二維每個計算格點之水平面高程以及水深平均流速，並將之帶入流速差異量方程式，求得三維各計算格點相對於水深平均流速之流速差異量，即可求出三維空間上每個計算格點之流速分佈。本研究採用K. Blanckaert (2009)之193°急彎渠道案例，針對12、8.2、6.3等三種不同寬深比進行模擬，並將模擬結果與試驗值比較，探討k-ε模式於二次流效應顯著之應用性。

Using a 3D hydrostatic model developed by a vertical horizontal splitting (VHS) algorithm along with the turbulent model in which the standard k-ε model, a two-equation turbulent model to calculate eddy viscosity, this study discuss the turbulent phenomenon in a sharp bend of an open channel flow. The orthogonal curvilinear and the sigma coordinate systems are used in horizontal and vertical directions, respectively to deal with the irregularity of channel geometry. The water elevation and the depth-averaged velocity are solved by the 2D depth-averaged model; and then the velocity profile along the vertical direction is solved by the velocity defect model. The developed model is appied to simulate the flow pattern in a 193° sharp bend flume (K. Blanckaert, 2009). Three width-depth ratios including 12, 8.2 and 6.3 are considered. The simulated flow patterns are compared with those obtained from experiment, to evaluate the applicability of k-ε model in flow simulation under strong secondary current.