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研究生: 麥慶汶
Mai, Ching-Wen
論文名稱: DES型流場模擬中發生於非平滑邊緣鈍體上Gibbs現象的處理方式
Treatment of the Gibbs phenomenon occurred on non-smooth edges of bluff body in DES-type flow simulation
指導教授: 張克勤
Chang, Keh-Chin
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2025
畢業學年度: 113
語文別: 中文
論文頁數: 80
中文關鍵詞: IDDES超車過程Gibbs現象CFD
外文關鍵詞: IDDES, Overtaking process, Gibbs phenomenon, CFD
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  • 本研究旨在針對IDDES於車輛超車之空氣動力學分析時所產生的數值問題及應對策略。由於傳統的RANS模型在處理兩車併行或尾流交互作用等複雜情境時,其預測結果與實驗數據存在顯著差異,本研究採用SST-IDDES此一混合式RANS-LES模型,以期更精確地捕捉大尺度紊流結構。然而,在使用高解析度網格對具有非平滑邊緣的鈍體進行模擬時,會因幾何尖角處物理量的不可微分性而引發Gibbs現象,導致數值結果產生非物理性的震盪。為此,本研究提出針對幾何奇異點與線附近進行局部網格加密的應對方式。結果顯示,此方法能有效抑制抖動,並將阻力係數(C_D)的預測誤差從約14%大幅降低至3%以內。儘管如此,所有模型對側向力係數(C_Y)的預測仍存在相對可觀的誤差 (>10%),其原因為模型對紊流黏滯係數採用等向性假設所致。總結而言,DES紊流模型雖然能更真實地呈現流場,但是其高解析度的需求使其在非平滑幾何上易觸發Gibbs現象,而局部網格加密為一有效的抑制手段。

    This study investigates the numerical issues when applying Detached Eddy Simulation (DES) to the aerodynamic analysis of vehicle overtaking maneuvers. Traditional Reynolds-averaged Navier-Stokes (RANS) models show significant discrepancies between predicted results and experimental data, especially in complex scenarios like two vehicles driving side-by-side or interacting in wakes. To address this, this research employs IDDES, a hybrid RANS-LES (Large Eddy Simulation) model, aiming at more accurate capture of large-scale turbulent structures.
    However, simulating bluff bodies with non-smooth edges using the spectral method, like LES, can trigger the Gibbs phenomenon. This occurs due to the non-differentiability of velocity at sharp edges, leading to non-physical, severe oscillations in the numerical results. To overcome this, the study proposes a strategy of local mesh refinement near geometric singularities and lines.The results demonstrate that this method effectively suppresses oscillations, significantly reducing the prediction error for the drag coefficient (C_D) from approximately 14% to within 3%. Despite this improvement, a substantial discrepancy in predicting the side force coefficient (C_Y) is still observed. It may be attributed to the model's assumption of isotropic turbulent viscosity.
    In conclusion, while DES-type model offers a more realistic representation of flow field, its requirement for high resolution makes them susceptible to the Gibbs phenomenon on non-smooth geometries. Local mesh refinement is an effective suppression technique.

    第一章:緒論 1 1-1 緒論 1 1-2 文獻回顧 3 1-3 研究動機與目的 5 第二章 數學模型與數值方法 10 2-1 統御方程式 10 2-1-1 近壁區RANS模式 10 2-1-2 分離區LES模式 13 2-2 計算域 15 2-3 網格佈置與網格獨立 17 2-4 數值設定 19 第三章 Gibbs現象 26 3-1 初步模擬結果 26 3-2 Gibbs現象 28 3-3 應對方式 30 第四章 結果與討論 37 第五章 結論與未來建議 45 參考文獻 47

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