以界面捕捉法模擬三維斜水躍問題

Simulation of 3D oblique hydraulic jump by surface capturing method

鄧良俊(Liang-jyun Deng)

指導教授 ： 譚義績

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.00934

摘要

陡坡段的河川或渠道中常形成超臨界流況，水流速度較快且流況複雜，是水力學中主要的研究課題之一。當超臨界流流經束縮渠道，會產生斜水躍，導致洪水位高漲。利用三維數值模式進行斜水躍的模擬時，常會發現水與空氣交界處的密度過渡帶，在水位變化劇烈處逐漸擴大，無法保持合理的厚度，進而使水面位置的判斷發生誤差。本研究以三維二相流模式為基礎，結合體積分率權重法以及等位函數修正法，並搭配調適性網格算則，將密度過渡帶調整至適當的厚度，以利於模擬的順利進行。模式首先以水平單牆斜水躍案例與解析解進行驗證，接著使用於坡床斜水躍案例測試，最後應用於基隆河員山子分洪隧道入口工之流場模擬；模擬結果顯示，本研究發展的模式可適用於複雜的三維斜水躍之模擬，而體積分率權重法以及等位函數修正法可消除密度過渡帶擴散的現象，使模擬水位更趨精確。

關鍵字

三維斜水躍 ； 二相流 ； 體積分率權重法 ； 等位函數修正法 ； 調適性網格算則

並列摘要

It is usually found that the supercritical flow condition in river or open channel occurs at the steep-sloped reach. An oblique hydraulic jump will be generated under the supercritical flow condition through a channel contraction. During the simulation of oblique hydraulic jump using a two phase flow model, the interface band between water and air frequently expands at where the water depth changing severely, and causes the problem of water surface determination. This study is based on a 3D two phase flow model by introducing “Volume Fraction Weighted Method”, “Modified Level Set Method” and “Adapting Grid” to prevent the expanding of interface band. After the model calibration and verification, the model is applied to the simulation of the Keelung River Yuan-shan-tzi diversion work. The results show that the expanding of interface band affects the propagation of water surface significantly during numerical simulation. The proposed model can simulate the oblique hydraulic jump quite accurate, and it has the potential for further applications.

並列關鍵字

3D oblique hydraulic jump ； Two-phase flow ； Volume fraction weighted method ； Modified level set method ； Adaptive grid

參考文獻

[39] 蘇騰鋐，2003，「二維水深平均束縮渠道流場之解析」，國立台灣大學農業工程研究所博士論文

[3] Sturm, T. W., 1985. “Simplified Design of Contractions in Supercritical Flow”, Journal of Hydraulic Engineering, ASCE, 111(5), 871-892

[4] Molls, T., and Chaudhry, M. H., “Depth-Averaged Open-Channel Flow”, Journal of Hydraulic Engineering, Vol.121, No.6, 1995

[5] Causon D. M., Mingham C. G., and Ingram D. M.,“Advances in Calculation Methods for Supercritical Flow in Spillway Channels”, Journal of Hydraulic Engineering , Oct. 1999, pp. 1039-1050

[6] Osher, S. and Sethian, J. A., 1988, “Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. ” Journal of Computational Physics, Vol.: 79, 12-49.