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研究生: 宋孟橋
Song, Meng-Chiao
論文名稱: 影響顆粒碰撞模擬因素探討
Investigation of Effective Factors on Particles Collision 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: 2012
畢業學年度: 100
語文別: 中文
論文頁數: 95
中文關鍵詞: 雙體碰撞硬球模式歷史作用力附加質量作用力顆粒重疊
外文關鍵詞: binary hard-sphere model, added mass force, history force, particle overlapping extent
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  • 本研究的目標有兩點,一種是探討BBO equation在此模擬環境中的適用性,另一種則是探討要如何降低顆粒運動數值計算過程中不合理的顆粒重疊行為,為了降低此現象的發生,而其時間步階應該如何選用。
    由模擬之結果中皆顯示出,當顆粒間發生碰撞頻率越高時,其顆粒所受到之歷史作用力以及附加質量作用力皆會與之提升,但是這兩項作用力的貢獻仍然可以將其忽略不計。因此,在傳統只考慮顆粒所受之體力與阻力的顆粒碰撞之一般簡化運動方程式當中,依然可以適用在顆粒與顆粒間碰撞的模擬中。
    在顆粒間的碰撞模擬當中,本研究採用雙體碰撞硬球模式的方法去進行模擬。而在採用雙體碰撞之硬球模式當中的先決條件就是時間步階的選取要夠小,這樣才能區分出碰撞發生的前後,並且時間步階要遠小於顆粒的平均自由時間。而在本研究當中找出了一個較具量化的結果:當時間步階小於平均自由時間一個數量級的時候,亦即∆t⁄τ_c =O(〖10〗^(-1)),此時可以確保顆粒重疊的程度小於1%之內。

    There are two objectives in this thesis. One is to investigate the necessity of the use of the BBO equation in the simulation of the inter-particle collision process. The other is to avoid the particle overlapping occurred in the calculation procedure of the particles’ motion and collisions.
    It is found that the influences of the history force and the added mass force are indeed increased when the inter-particle collisions become more frequently in the motion of particles, but their contributions to the equations of motion can be still neglected. Thus, the conventional simplified equations of motion which consider the drag and body forces only are still applicable in the simulation of particles’ motion with considerate inter-particle collisions.
    To account for the inter-particle collisions in the simulation of particles’ motion, the uncoupling technique of binary hard-sphere model is employed. One prerequisite for adopting the binary hard-sphere model is that the computational time step (∆t), which is used in the time integration of the equations of motion, must be sufficiently shorter than the mean free time (τ_c) for the binary particle collision. A more quantitative criterion of ∆t⁄τ_c =O(〖10〗^(-1)) is concluded in this study. This criterion permits the particle overlapping extent to fall within 1%.

    摘要 I Abstract II 誌謝 III 目錄 IV 表目錄 VI 圖目錄 VIII 符號說明 XIII 第一章 緒論 1 1.1前言 1 1.2文獻回顧 2 1.3研究目標 3 第二章 數值模擬方法 4 2.1硬球模式 4 2.1.1碰撞檢驗 4 2.1.2動量守恆 5 2.2軟球模式 9 2.2.1接觸力 10 2.2.2彈性係數 13 2.2.3阻尼係數 15 2.2.4恢復時間 15 2.3平均自由時間 16 2.4流體阻力 16 2.5 Basset-Boussinesq-Oseen equation 17 2.5.1球體阻力 17 2.5.2 壓力梯度及剪力 18 2.5.3 附加質量力(added mass force) 18 2.5.4 歷史作用力(history force) 19 2.6 黏滯力矩(viscous torque) 21 2.7 數值方法 22 2.8 一般簡化方程式 23 第三章 模擬問題設定與結果討論 24 3.1模擬問題設定 24 3.1.1模擬環境 24 3.1.2週期性力場 25 3.1.3模擬參數 25 3.1.4 顆粒阻力方程式 26 3.2 程式運作流程 26 3.3硬球模式之顆粒重疊問題 27 3.4取樣資料及統計時間 28 3.5顆粒速度分布 30 3.6 均勻性分布 30 3.7模擬結果 32 3.7.1顆粒數量512顆 32 3.7.2顆粒數量1000顆 32 3.7.3顆粒數量1728顆 33 3.8比較與討論 33 第四章 總結與未來建議 38 4.1總結 38 4.2未來工作建議 39 參考文獻 40

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