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研究生：	林建宏 Lin, Jian-hung
論文名稱：	雙球碰撞模式於稠密兩相流中應用極限之探討 Applicability Limit of Binary Collision Model in Dense Particle Flow
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：	2009
畢業學年度：	97
語文別：	中文
論文頁數：	67
中文關鍵詞：	雙球碰撞硬球模式、顆粒碰撞、兩相流、多球碰撞軟球模式
外文關鍵詞：	binary collision hard-sphere model, multiple collision soft-sphere model, two-phase flow
相關次數：	點閱：87 下載：1
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本文中將探討雙球碰撞硬球模式的適用範圍，模擬於一個週期性邊界的環境中，給予空間週期性力場如下：
藉由力場帶動顆粒於空間內的運動，顆粒於空間中受到力場以及靜止流體給予的阻力而於空間內運動，藉此創造出一個顆粒頻繁碰撞的環境來當做碰撞模式適用性比較的標準，本文中定義一個以平均自由徑為特徵長度所得到的平均自由徑空隙率，模擬中發現於顆粒重疊率就有機會降到1％以內。然而模擬中也發現於於硬球模式中不合理的顆粒重疊現象於計算時距小於平均自由時間四個數量及以內都還會隨著計算時距的縮小而有顯著的降低，直到計算時距與平均自由時間的比值後顆粒重疊率降低的幅度就十分平緩了。然而多球碰撞軟球模式的計算時距則需要小於恢復時間兩個數量及以上（）才能準確的模擬出碰撞行為。因此建議使用硬球模式的實機為平均自由淨空係率高於0.7且平均自由時間與顆粒回復時間的比值。如此才能達到節省計算時間以及尚保有模擬的準確性的優點。

The flows laden with particles (or droplets, per se) are in principle split into dilute and dense dispersed-phase regimes. A dense flow is the one in which the motion of particles is dominantly controlled by collisions, in contrast to a dilute flow by the surface forces which are exerted by the carrier phase, and the body force on the particles. Tsuji (2000), further classified the dense flows into two sub-regimes of the collision-dominated (non-dense) flow and contact-dominated (dense) flow. To account for the inter-particle collisions in the simulation, the binary hard-sphere collision model, originally developed by Bird (1994), is commonly employed. However, two prerequisites are embedded in the use of binary collision model. One is that the particle number density must be sufficiently low so that multiple (larger then two) particles collisions are negligible. The other is that the mean free time of two successive inter–particle collisions must be sufficiently larger than the computational time step. In view of these two prerequisites, the binary collision model is clearly inapplicable to the simulation of contact-dominated flow. Instead, the multiple collision model such as the discrete element method (DEM) can play proper job than the simple binary collision model. It is of interest to pursue a quantitative criterion justifying under what dense level of the particle flow the binary collision model becomes inapplicable. A cubic enclosure with length L and periodic boundary conditions in all three directions, in which there are totally 512, 1000, 1728 mono-size hard spheres respectively, is considered in the study. In order to drive particle motion, a three-dimensional sinusoidal gravitational field of {cos⁡〖2πx/L (〖 e〗_i ) ⃑ 〗+cos⁡〖2πy/L (〖 e〗_j ) ⃑ 〗+cos⁡〖2πz/L (〖 e〗_k ) ⃑ 〗} is imposed to the enclosure. On the basis of the prediction accuracy and computational expenditure, a criterion justifying the applicability of the binary collision model in the dense particle flows is then made in the study. It is found that the mean free path void fraction of the particle-laden flow has to be over 0.7 to assure the particle overlapping extent being less than 1% with adopting the binary collision model in the simulation. In addition, the ratio of computational time step to the mean free time has to be less then 〖10〗^(-4) to obtain invariant prediction of the particle overlapping extent.

摘要 ...................................................................................................................... I
ABSTRACT ...................................................................................................... III
目錄 .................................................................................................................... V
圖目錄 .............................................................................................................. VII
表目錄 .............................................................................................................. XII
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 研究目地 ...................................................................................... 4
第二章 數值方法 .......................................................................................... 5
2.1 多球碰撞軟球模式 ...................................................................... 5
2.1.1 接觸力 ....................................................................................... 6
2.1.2 彈性係數 ................................................................................... 9
2.1.3 阻尼係數 ................................................................................. 11
2.14 恢復時間 .................................................................................. 11
2.2 雙體碰撞硬球模式 .................................................................... 12
2.2.1 碰撞檢測 ................................................................................. 13
2.2.2 動量守恆 ................................................................................. 14
2.3 平均自由時間 ............................................................................ 17
2.4 流體阻力 .................................................................................... 18
第三章 模擬問題與結果討論 .................................................................... 19
3.1 模擬問題設定 ............................................................................ 19
3.2 雙體碰撞硬球模式顆粒重疊問題............................................. 21
3.3 資料取樣時間 ............................................................................. 22
3.4 顆粒分佈均勻性 ........................................................................ 24
3.5 模擬結果 ..................................................................................... 24
3.5.1 Case 1, 流體為水、顆粒數512 ................................ 24
3.5.2 CASE 2, 流體為空氣、顆粒數512 .......................... 26
3.5.3 CASE 3, 流體為空氣、顆粒數1000 ....................... 26
3.5.4 CASE 4, 流體為空氣、顆粒數1728 ....................... 27
3.7 多體碰撞軟球模式模擬結果 ............................................ 27
3.8 綜合比較 ............................................................................. 29
第四章 結論與建議 .................................................................................... 33
4-1 結論 ............................................................................................ 33
4-2 建議及未來工作 ........................................................................ 34
參考文獻 ........................................................................................................... 35
                                    

C.T. Crowe, M. Sommerfeld, and Y. Tsuji, Multiphase Flows with Droplets and Particles, CRC Press, 1998
G. A. Bird, Molecular Gas Dynamics and Direct Simulation of Gas Flow, Clarendon Press, Oxford, 1994
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P. A. Cundall, O. D. L. Strack, “A discrete numerical model for granular assemblies”, Geotechnique, 29, 1979, pp.47-65
Y. Tsuji, “Activities in disecrete particle simulation in Japan”, Powder Technology, 113, 2000, pp.278-286
Y.-K. Pan, Numerica Analysis on Particle-Laden Rotating Turbulent Flow, Osaka University, Japan, 2000
許志宏, “含顆粒碰撞機制之氣體-顆粒兩相流場模擬”, 國立成功大學航空太空工程研究所博士論文, 2005

校內：立即公開
校外：2009-08-18公開

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