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研究生: 林晉緯
Lin, Jin-Wei
論文名稱: 擬三維週期性邊界與Poly-Hexcore網格於鈍體氣動力模擬之驗證與品質評估
Validation and Quality Assessment of Quasi-3D Periodic Boundaries and Poly-Hexcore Mesh in Aerodynamic Simulations of Bluff Bodies
指導教授: 朱世禹
Chu, Shiu-Yu
方中
Fang, Chung
學位類別: 碩士
Master
系所名稱: 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年: 2026
畢業學年度: 114
語文別: 中文
論文頁數: 139
中文關鍵詞: 計算流體力學結構風工程多面體-六面體核心網格擬三維週期性邊界壁面模型大渦模擬
外文關鍵詞: Aero-elasticity, Poly-Hexcore Mesh, Quasi-3D Periodic Boundaries, Wall-Modeled Large Eddy Simulation (WMLES), Vortex shedding
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  • 隨著大跨度橋梁與高層建築的發展,結構物對風荷載的敏感度日益提升。傳統風洞試驗存在成本高昂與縮尺效應等限制,結合計算流體力學(CFD)的數值模擬已成為當今土木結構風工程研究的趨勢。然而,在解析複雜鈍體的三維瞬態氣動力行為時,傳統全六面體網格常面臨前處理耗時與運算資源龐大的瓶頸,而純二維模擬又因缺乏展向渦旋拉伸機制而嚴重高估阻力。為突破運算成本與物理精度的限制,本研究針對高寬比 7 之三維剛性矩形柱模型,導入「多面體-六面體核心網格(Poly-Hexcore)」技術與「擬三維週期性邊界條件」,並系統性地比較雷諾平均(RANS)SST 模型與壁面模型大渦模擬(WMLES)的預測精度與運算效能,並與風洞實驗及前人全六面體網格模擬結果進行對照分析。
    研究結果顯示,嚴格控制近壁面網格正交性為消除低頻雜訊、穩定捕捉卡門渦街特徵的關鍵。Poly-Hexcore 網格不僅能展現出與傳統全六面體網格近乎一致的氣動力預測精度,更大幅降低了運算成本。此外,採用擬三維週期性邊界條件能有效保留三維渦漩在展向上的去相關特徵,並縮減約 60% 的網格總數。在擬三維架構下,WMLES 模型成功突破了傳統模型的過度耗散限制,精準解析出流場中的「雙重不穩定性」。最後透過紊流品質指標進行雙重檢驗,確證本研究所建置之數值模型真實深入了紊流的能量級聯機制,可為未來探討複雜結構雙向流固耦合與動態氣彈行為奠定可靠的數值解析基礎。

    With the rapid development of long-span bridges and high-rise buildings, modern structures have become increasingly sensitive to wind-induced effects. Traditional wind tunnel testing remains a fundamental approach for evaluating structural aerodynamic behavior; however, it is often associated with high experimental costs, long preparation periods, and unavoidable scaling effects. Consequently, numerical simulations based on Computational Fluid Dynamics (CFD) have become an increasingly important tool in structural wind engineering. Nevertheless, accurately analyzing the three-dimensional (3D) transient aerodynamic behavior of complex bluff bodies remains computationally challenging. Traditional full-scale 3D simulations using full-hexahedral meshes often encounter bottlenecks associated with time-consuming preprocessing and substantial computational resource demands. To achieve a balance between computational efficiency and physical accuracy, this study introduces advanced Poly-Hexcore mesh technology and Quasi-3D periodic boundary conditions for a three-dimensional rigid rectangular cylinder model with an aspect ratio of 7. The proposed framework systematically compares the prediction accuracy and computational efficiency of the Reynolds-Averaged Navier-Stokes (RANS) SST k−ω model and Wall-Modeled Large Eddy Simulation (WMLES). The results demonstrate that the combination of Poly-Hexcore meshing and Quasi-3D periodic boundaries can significantly reduce computational requirements while retaining the essential three-dimensional characteristics of the wake. Furthermore, the proposed approach successfully captures the double-instability behavior of the flow field, including the interaction between Kelvin-Helmholtz instability and von Kármán vortex shedding. The findings provide an efficient and physically reliable numerical foundation for future investigations of aeroelastic behavior and fluid-structure interaction (FSI).

    摘要 i Abstract ii 致謝 vii 目錄 viii 表目錄 xiii 圖目錄 xiv 第一章 緒論 1 1.1 研究動機 1 1.2 流體氣動力現象 2 1.2.1 流動類型分類 3 1.2.1.1 全域不穩定流動 3 1.2.1.2 局部不穩定流動 3 1.2.1.3 穩定流動 3 1.2.2 分離 4 1.2.3 再附著 5 1.2.4 尾跡 5 1.2.5 渦散現象 5 1.2.6 鎖定現象 6 1.3 文獻回顧 7 1.4 本文架構 9 第二章 理論介紹 14 2.1 控制方程式 14 2.1.1 雷諾傳輸定理 14 2.1.2 質量守恆方程式 15 2.1.3 牛頓流體應力張量 15 2.1.4 那維爾-史托賀方程式 16 2.2 無因次參數 17 2.2.1 雷諾數 17 2.2.2 史托賀數 18 2.2.3 風力係數 18 2.2.4 庫朗數 19 2.2.5 無因次壁面距離 19 2.3 紊流模型 20 2.3.1 雷諾平均那維爾-史托賀方程式 20 2.3.2 渦黏性假設 21 2.3.3 雙方程式模型 21 2.3.3.1 𝑘−𝜖 模型 22 2.3.3.2 𝑘−𝜔 模型 22 2.3.3.3 SST 𝑘−𝜔 模型 23 2.3.4 大渦模擬理論基礎 24 2.3.5 濾波納維爾-史托克方程式 25 2.3.6 亞格子尺度模型 27 2.3.6.1 Smagorinsky-Lilly 模型 28 2.3.6.2 WALE 模型 29 2.3.6.3 壁面模型大渦模擬 30 2.3.6.4 動能輸運模型 32 2.4 紊流解析度評估指標 33 2.4.1.1 Pope 能量解析指標 34 2.4.1.2 柯爾莫哥洛夫尺度比值 35 2.4.1.3 Celik 渦黏性解析指標 36 2.5 邊界層理論 37 2.6 網格品質指標 39 第三章 三維剛性矩形模型模擬 42 3.1 矩形模型風洞實驗介紹 42 3.1.1 風洞設備介紹 42 3.1.2 剛性模型實驗設置 43 3.1.3 剛性模型實驗結果探討 43 3.1.4 柔性模型實驗設置 43 3.1.5 柔性模型結果討論 44 3.2 網格形狀介紹 45 3.3 計算域配置與邊界條件 46 3.4 模擬設備與求解器設定 47 3.5 近壁面邊界層正交性修正與流場影響 48 3.6 多面體-六面體核心網格效益比較 50 3.7 計算域尺寸之獨立性分析 51 第四章 擬三維剛性矩形模型週期性邊界模擬 73 4.1 二維模擬與三維模擬之差異 73 4.2 擬三維週期性邊界模擬理論 74 4.2.1 渦旋拉伸機制 74 4.2.2 展向相關性理論 76 4.2.3 數值映射原理與連續性條件 77 4.3 展向邊界條件探討 78 4.3.1 對稱邊界之理論定義 78 4.3.2 氣動力特徵分析 79 4.3.3 運算效率比較 81 4.4 擬三維週期性邊界下之大渦模擬性能評估 82 4.4.1 數值模型設定與離散化策略 82 4.4.2 近壁面網格建立與驗證 84 4.4.3 氣動力特性分析 86 4.5 擬三維週期性邊界模擬紊流品質指標驗證 87 第五章 結論與未來展望 110 5.1 結論 110 5.2 未來展望 112 參考文獻 113

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