三維大渦模式在明渠水流之應用

Abstract

本研究基於垂直水平分離演算(VHS)之概念，利用大渦模擬(large-eddy simulation, LES)發展一三維大渦模式，其中紊流黏滯係數採用Smagorinsky次網格模式計算，並以雷諾平均假設下之兩種零方程紊流模式相互比較，探討明渠流之紊流流場現象。在座標系統上，水平方向與垂直方向分別採用正交曲線座標系統與 座標系統，使模式能便利處理不規則的渠道與底床邊界。水理模式之架構係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面高程以及水深平均流速，並將之代入流速差異量方程式，求得三維每個計算格點相對於水深平均流速之流速差異量，即可求解出三維空間上每個計算格點之流速分佈。最後，本研究分別採用突擴渠道流速場案例以及直渠道渦度場案例來模擬紊流流場，探討不同計算網格大小對不同型態紊流模式模擬結果之影響。

To investigate the turbulence of open-channel flow, a hydrostatic three-dimensional model based on a vertical-horizontal splitting (VHS) method with large-eddy simulation was used in this study. The eddy viscosity was treated by Smagorinsky sub-grid model. The results were compared with two commonly used Reynolds-averaged zero-equation models. By following the vertical and horizontal splitting concept, the shallow water flow governing equations were split into two parts including the depth-averaged 2D equations and velocity defect equation in vertical direction. The depth-averaged 2D equations were transformed into orthogonal curvilinear coordinate system, to solve the elevation of every water column and depth-averaged velocities. The velocity defect equations can be derived by subtracting the 2D depth-averaged equations from the 3D Navier-Stokes equations. The sigma coordinate was used to fit the complex geometry in channel bed. Incorporating with the continuity equation, the three-dimensional velocity field can therefore be solved. Two experimental cases including sudden expansion and straight channel were simulated to investigate the effect of computational grid size on the model’s accuracy.