泛用性三維計算流體力學模式應用於明渠流之研究

Abstract

由於計算機運算速度之提昇與數值方法之進步，使得三維計算流體力學（CFD）模式已能廣泛應用於可壓縮及不可壓縮流場、層流與亂流、暫態與穩態流、多相流、自由液面流等問題，對於工業設計與分析上有很大的助益。另一方面，由於計算流體力學與傳統明渠水流計算之基本假設不同，如明渠水力計算的底床糙度多採用曼寧係數，然計算流體力學模式則採用壁函數（wall function）近似之。因此，本文係以三維計算流體力學的觀點出發，進行明渠水流之模擬。本文採用商業版流體力學模式STAR-CD進行平床渠流流場及水躍流場之數值模擬，並針對模式所採用之壁函數及流體體積函數法（VOF）等參數進行討論，以了解模擬結果對自由液面變動之影響。 根據平床渠流之模擬結果，本模式目前所能應用之曼寧值範圍為0.0111至0.0135間；而由水躍流場之模擬結果顯示，在福祿數6.65及2.9之流場須分別取體積濃度值0.7與0.5以決定自由液面位置，方可顯示較佳之水躍曲線；此外，本模式對於不連續之自由液面流具有良好之模擬結果。

Owing to the high performance computation and improvement of the numerical method, the three-dimensional computational fluid dynamics models have been applied for compressible and incompressible flows, laminar and turbulent flows, transient and steady-state flows, multi-phase flows and free surface flows,etc. are useful for industrial analysis and design. On the other hand, due to the difference of the basic assumptions in the computational fluid dynamics and the computational hydraulics, i.e., Manning’s roughness formula used in the computational hydraulics, but wall function concept in the computational fluid dynamics. Therefore, this study is based on the concept of three-dimensional computational fluid dynamics to simulate open channel flows. The commercial STAR-CD code is adopted to simulate the horizontal channel flows and hydraulic jump flows. Parameters of the wall function and volume of fluid method (VOF) in the code are examined to find their influences on the variance of free surface. According to the simulation results of horizontal channel flows, this code can be applied to cases with Manning’s value between 0.0111 and 0.0135. For the cases of hydraulic jump flow, the best jump profile is obtained with volume of fluid value 0.7 for Froude number 6.65, but volume of fluid value 0.5 for Froude number 2.9. In the same time, this code has the capability of simulating discontinuous free surface flows.