三維靜水壓k-ε明渠水流模式之發展

Abstract

本研究採垂直水平分離演算(VHS)之概念發展三維靜水壓水理模式，搭配紊流模式計算紊流黏滯係數，其中紊流模式分別採用雙方程模式之標準k-ε紊流模式及兩種零方程模式。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σ座標系統，使模式邊界能夠更貼近真實渠道之蜿蜒與底床起伏。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。數值方法方面，水平、垂直模式與k、ε方程式皆採隱式法求解。分別採用直渠道案例以及急彎彎道案例進行模擬分析，並比較三種模式之紊流黏滯係數表現以及模擬結果之差異性，以探討明渠流之紊流流場現象。

A 3D hydrostatic model based on a vertical horizontal splitting (VHS) concept is developed in this study. The standard k-ε model, a two-equation turbulent model, and two kinds of zero-equation models are adopted to calculate eddy viscosity. The orthogonal curvilinear coordinate system and the sigma coordinate system are used to cope with the irregularity of channel geometry. The water elevation and the depth-averaged velocity will be solved by the 2D depth-averaged model, and then the velocity profile along the vertical direction will be solved by the velocity defect model. The implicit numerical schemes are used to discrete all of the equations to preserve the model stability unconditionally. Two experimental cases including the flow in straight channel and sharp bend were simulated by the model. Through the comparison between the experimental data and simulation results, the eddy viscosity computed from two-equation and zero-equation turbulent models were examined and discussed in depth.