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| 研究生： |
戴源宏 Tai, Yuan-Hung |
|---|---|
| 論文名稱： |
GPU版壓力基底的晶格波茲曼法模擬流體-顆粒交互作用之問題 GPU Version Pressure-Based Lattice Boltzmann Method for Fluid-Particle Interaction Problems |
| 指導教授： |
林三益
Lin, San-Yih |
| 學位類別： |
博士 Doctor |
| 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： | 英文 |
| 論文頁數： | 139 |
| 中文關鍵詞： | 晶格波茲曼法 、沉浸邊界法 、不可壓縮流 、流體化 、有效應力 、砂湧 、繪圖處理器 、平行運算 、彈性碰撞 、體積比函數 |
| 外文關鍵詞： | Lattice Boltzmann, Immersed Boundary, Direct forcing, Particulate Flow, Fluid-Particle, Sedimentation, Fluidized bed, Fluidization, GPU, Parallel Computing, CUDA, Elastic Collision |
| 相關次數： | 點閱：120 下載：2 |
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本文的目的是使用以壓力為基底的晶格波茲曼法(Pressure-based Lattice Boltzmann Method, LBM)，代替那維爾史托克方程式(Navier-Stokes Equation)，去求解不可壓縮黏性流場。探討多顆球體在黏性流體中的三維運動模擬。以彈性碰撞模型處理顆粒之間接觸行為，以沉浸邊界法(Immersed Boundary Method,IBM)處理複雜邊界的問題，再求解固體和液體之間交互作用的行為。在沉浸邊界法中，使用體積比函數(volume fraction function)去描述固體邊界。以單顆/兩顆/多顆球體去模擬顆粒在黏性流體中發生的現象，包含牽引、輕微接觸、翻滾(drafting、kissing、tumbling)的行為，以及多顆沉積時的瑞利-泰勒不穩定現象(Rayleigh-Taylor instability)。接下來以多顆球體以不同尺寸、密度及數目，模擬顆粒流體化及所需要的壓力差或入口速度大小，探討其中因壓差導致顆粒間有效應力消失而產生流體化的現象，採用有效應力的觀念，決定湧砂現象所需的壓力差。計算結果與理論值比較不論尺寸、密度、顆粒數目都有一致性的結果，顆粒層數較多時，二維的效應減小，和理論值越接近，密度較大的結果也較佳。程式本身再結合具有大量運算效能的GPU繪圖處理器(Graphics Processing Units)的平行運算，以不同的技巧來加速迴圈的運算速度。以大量的執行緒並利用GPU晶片內大量的核心，加上多維降為一維矩陣的排列方式，以獲得較高的計算效率去處理較大的網格及顆粒數目。相較傳統單一核心的CPU，至少有十倍至幾十倍的計算速度，可節省大量的計算時間，與平行電腦相比所需要的資源較少。
Two major topics of fluid-particle interaction problems are investigated here. First one is about sedimentation problems and second one is about fluidization problems. In settling problems, single particle, two particles, and 1260 particles are demonstrated to investigate phenomena. In fluidization area, one particle is validated. Then 400(20x20) particles are applied with hydraulic gradient with different sizes and densities. After this, 500(5x5x20) particles are also represented with different density. The major goal is to determine how large the pressure gradient to fluidized the particles when comparing with theoretical value.
A direct-forcing IB-LBM is introduced to solve the problems. The IB method enforces the fluid velocity equal to the particle velocity. An elastic spring model is applied to compute the interaction forces due to particle-particle or particle-wall collision. Many pressure-based schemes are excellent in low-speed incompressible flow and the problems in thesis are in this area. Thus, pressure-based LBM is implemented with higher order in accuracy. On the other hand, the density-based schemes are good to handle the high-speed and compressible flows. Due to the massive computation is required; a GPU-version program is used to accelerate the computing speed.
First, sedimentation of one particle is performed with experiments. Then two particle with drafting-kissing tumbling phenomenon is observed and the Rayleigh-Taylor instability can be seen in 1260 particles. The fluidization velocity of a single particle is performed well with experimental data and fluidization speed is also explained with several equations. Then, fluidization of many particles (20x20) in a narrow enclosure is simulated. The normalized effective stress is defined to check if the fluidization occurs with an applied average hydraulic pressure. The higher pressure is required to fluidize the particles with the wall effects. When 500(5x5x20) even 2000(10x10x20) particles are applied, the difference between average hydraulic gradient and theoretical one is much closer. If the particles sample number is enough, the result is very good. It speeds up from 10 to 70 times than a traditional LBM does with GPU parallelization and it will save much time to solve a big problem.
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