[[alternative]]Verification of a numerical model for storm-drainage system

碩士[[abstract]]本研究應用一維性非恆態流水理模式以普里斯曼隱性差分技巧(Preissmann''s Scheme)及聖凡南假設(Saint Venant Hypotheses)推導連續方程式及動量方程式，並以數值雙掃法求解。上、下游邊界條件為設計入流歷線及潮汐水位歷線，並假設一基底流量。假設恆態流情況下，各管渠內之初始水深由上、下游邊界條件及基底流量使用標準步推法(Standard-Step Method)求得。 本模式主要模擬馬蹄型管之明渠流水理現象並以實驗結果驗證實驗之各項參數及其正確性、可靠性。[[abstract]]This research apply Preissmann''s scheme and Double-Sweep Method to establish a model to solve Continuity Equation and Momentum Equation according to Saint Venant Hypotheses. The upstream boundary condition assumed to be designed discharge hydrograph, and the downstream boundary condition assumed to be water stage hydrograph of tidal. The base discharge at each channel is assumed with a small discharge. Assumed the flow is steady, the initial depth of this model involves downstream boundary condition effect and is derived from downstream end using Standard-Step Method. This model mainly to simulate the horseshoe -shaped tube of open channel flow and base on the experiment result to prove the validity and accuracy of each parameter can be tested.[[tableofcontents]]目錄 第一章 前言................................................................................................................1 第二章 文獻回顧........................................................................................................3 第三章 實驗配置與測量方法....................................................................................5 3-1模型參數比..............................................................................................5 3-2渠道配置..................................................................................................6 3-3 模型糙度.................................................................................................6 3-4 儀器設備介紹.........................................................................................7 3-5 量測方法.................................................................................................7 第四章 基礎理論........................................................................................................8 4-1 控制方程式.............................................................................................8 4-2 初始條件與邊界條件.............................................................................9 4-2-1 初始條件.....................................................................................9 4-2-2 上游邊界條件.............................................................................9 4-2-2-1設計流量...................................................................................9 4-2-3 下游邊界條件...........................................................................10 4-3 內部條件...............................................................................................11 4-3-1質量守恆.....................................................................................11 4-3-2能量守恆.....................................................................................11 第五章 數值方法......................................................................................................12 5-1 普里斯曼四點隱性差分法...................................................................12 5-2 差分控制方程式...................................................................................13 5-3 數值雙掃法...........................................................................................14 第六章 結果與討論..................................................................................................15 6-1 數值參數...............................................................................................15 6-2 能量損失係數.......................................................................................16 6-3 驗證比較...............................................................................................17 第七章 結論..............................................................................................................18 參考文獻......................................................................................................................19 附錄一 明渠流之差分控制方程式..........................................................................41 附錄二 係數 、 之回歸式...................................................................................50 附錄三 係數 、 、 之迴歸式...........................................................................51 圖目錄 圖1 實驗渠道示意圖&渠道斷面圖....................................................................20 圖2 自計水位計...................................................................................................21 圖3 資料擷取系統...............................................................................................22 圖4 馬達控制器...................................................................................................23 圖5 差分方法格點之空間權重及時間權重示意圖...........................................24 圖6 UNSTEADY數值模式流程圖.....................................................................25 圖7 =0.6、 =0.7之各人孔尖峰水深比與 值...............................................27 圖8 =0.8、 =0.9之各人孔尖峰水深比與 值...............................................28 圖9 Sample 1 & Sample 2 各人孔之尖峰水深比與C值...................................29 圖10 Sample 3 & Sample 4 各人孔之尖峰水深比與C值.................................30 圖11 Sample 5 & Sample 6 各人孔之尖峰水深比與C值.................................31 圖12 Sample 7 & Sample 8 各人孔之尖峰水深比與C值.................................32 圖13 Sample 1之數值&實驗水位歷線.................................................................33 圖14 Sample 2之數值&實驗水位歷線.................................................................34 圖15 Sample 3之數值&實驗水位歷線.................................................................35 圖16 Sample 4之數值&實驗水位歷線.................................................................36 圖17 Sample 5之數值&實驗水位歷線.................................................................37 圖18 Sample 6之數值&實驗水位歷線.................................................................38 圖19 Sample 7之數值&實驗水位歷線.................................................................39 圖20 Sample 8之數值&實驗水位歷線.................................................................40[[note]]學號: 603480244, 學年度: 10