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題名 | 摩擦因子對引用SMAC方法模擬水躍之影響=Effects of Friction Factor on Application of SMAC Method in Simulating Hydraulic Jump |
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作者 | 施清周; Shih, Ching-chi; |
期刊 | 農業工程學報 |
出版日期 | 19971200 |
卷期 | 43:4 1997.12[民86.12] |
頁次 | 頁36-46+35 |
分類號 | 434.287 |
語文 | chi |
關鍵詞 | 水躍; SMAC方法; 自由面; Hydraulic jump; SMAC method; Free surface; |
中文摘要 | 利用SMAC方法,模擬水躍本體的自由面,控制式為雷諾與連續等方程式,渦度粘 滯係數採用Fischer的經驗公式,並改為深度、斷面平均速度與摩擦因子的函數式,但摩擦 因子為定值。為配合水躍自由面的特徵,前端採用較小的摩擦因子f�窗A而末端改採用較大 的摩擦因子f�砥A其範圍分別為0.0001≦f�窗�0.003,0.03≦f�砥�0.06。模擬自由面與 Rajaratnam 所提的水躍平均 (對時間 ) 剖面比較,其間的差距分為傾向差距與精度差距( 約為標準偏差的二倍。) 標準偏差愈小代表模擬自由面愈趨近於水躍平均剖面的形狀,但不 計傾向差距;同時也顯示模擬自由面愈穩定。故本文探討標準偏差為最小時,相關參數的值 並分析其現象,而上游福祿數的範圍為自 2 到 8,間 距為0.2 |
英文摘要 | The free surface profile of the body of the hydraulic jump is simulated by the SMAC method, based upon the Reynolds equations of motion and the continuity equation. The eddy viscosities are calculated from the Fischer's empirical formula which are changed to a functional relationship of the sectional mean velocity, the depth and the friction factor, and in the course of simulation the friction factor is kept constant. In order to reflect the main characteristics of the hydraulic jump a smaller value of the friction factor f �� is adopted around the toe of the jump, while a much greater value of the friction factor f �� is utilized from the rest of the jump, and the ranges of f �� and f �� are 0.0001 ≦ f �窗� 0.003and 0.03 ≦ f �砥� 0.06 respectively. Simulated free surfaces are compared with the mean free surface profile (taken average with respect to time) as proposed by Rajaratnam of which the deviation consists two parts:the tendency deviation and precision deviation that is approximately two times of the standart deviation. The less the standard deviation, the more agreement of simulated free surfaces with the shape of the mean free surface profile nothing to do with the tendency deviation, and the more stable of simulated free surfaces. Therefore, in the present study, values of the appropiate parameters and their phenomena are analyzed and investigated when the standard deviation is the minimum; and the upstream Froude number ranges from 2 to 8 with an increment of 0.2. |
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