5.1 結論
1. 本研究採用垂直水平分離演算(VHS)的概念,發展擬似三維水理模式。水 平方向採用正交曲線座標系統,垂直方向採用σ 座標系統。
2. 本研究之水平二維模式採用隱式雙階分割操作趨近法,當移流項和擴散項 的效應很小時,在模擬時可以忽略第一步驟(即僅需求解壓力與底床剪應力 項),增進數值模式應用上的彈性及穩定性。
3. 模式考量了科氏力及風剪力的影響,以風剪垂直環流場及艾克曼螺旋的案 例檢驗,風剪垂直環流場案例的模擬結果與解析解之均方根誤差為
0.0011;而艾克曼螺旋案例的流速剖面在縱方向及側方向之均方根誤差分 別0.0109 與 0.0126,證明加入此二作用力項對模擬結果影響之正確性。
4. 本研究著重在彎道的應用,以緩彎、急彎及連續彎案例進行模式測試工作。
(1) 在緩彎案例,以兩種不同的流量進行模擬,不論是水深平均流速、彎道 中的二次流或水位超高的現象,均可得到不錯的結果。水深平均流速和 水深之模擬結果與實驗值之均方根誤差皆很小,而擬似三維模式在水深 方向的流速剖面亦與實驗值相近,可看出模式在緩彎模擬的可靠性。
(2) 在急彎案例,二次流效應明顯,反應在彎道的側向流速及水位超高現 象,其內、外岸的分佈均與實驗值接近。側向流速在內岸之垂直梯度較 大、外岸較小,與實驗相符,而由實驗結果可看出在外岸接近水面處出 現與二次流反向的小渦流,本模式為靜水壓假設且紊流模式採用零方程 式,因此無法模擬出此現象。研究並與二維模擬結果比較,可看出擬似 三維模式較二維模式適用於急彎的案例,特別是在接近彎道內岸處之流 速有明顯的差異。
(3) 在連續彎案例,因為彎道反曲使得流速在兩個彎道的分佈有明顯的不 同,本模式能正確模擬斷面的流速分佈,而水平二維模式則是有較大的
誤差。由側向流速分佈圖可看出,從第一個彎道經過中間直線道至第二 個彎道,整個二次流的轉換過程,模擬結果與實驗值一致。由以上結論 證明本模式適用於蜿蜒渠道的模擬。
5.2 建議
1. 本研究尚無考量密度變化對流場的影響,而視密度為常數,未來的研究可 將此加入考量,模擬分析密度梯度對水理的影響。
2. 本模式僅發展水理部分,將來可放入污染傳輸與沉滓運移的機制,結合密 度變化應用於異重流的分析。
3. 紊流模式的處理上,仍採用最簡單的零方程式(zero-equation)模式求解,所 以在紊流模式的發展上,未來可進一步擴展為二方程式(two-equation)之紊流 模式(如 k-ε 或 k-ω 紊流模式),並對這些模式進行適用性分析。
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