模擬浸沒於液體中具有大範圍尺寸之顆粒行為的數值方法開發

Abstract

多相流問題中，不同尺寸的顆粒與液體交互作用是常見的一種情況，本研究以三種顆粒計算方法模擬液體中大範圍尺寸的顆粒，其中使用Y.J. Chou(2015)的尤拉-拉格朗日法(Eulerian-Lagrangian)和Uhlmann(2005)的直接施力沉浸邊界法(direct forcing immersed boundary method)，尤拉-拉格朗日法將顆粒以點顆粒方式描述，因此通常拿來模擬比網格寬度還小的顆粒，直接施力沉浸邊界法以許多點顆粒模擬出顆粒的邊界，屬於解析的顆粒計算方法，因此可適用於比網格寬度還大許多的顆粒，上述兩個方法在顆粒尺寸接近於網格寬度時，有使用的限制或不精確的問題，因此，本研究開發中等點顆粒法，並以相同模擬條件下靜止顆粒的阻力係數大小進行驗證，從驗證結果得到在顆粒解析度在一定條件下，中等點顆粒的精確度較尤拉-拉格朗日法和直接施力沉浸邊界法好。最後，進行液化床(fluidized bed)及鎧裝沉積(sediment armouring)模擬，實現此套方法在大範圍尺寸顆粒上的可行性。

Particles with different sizes in liquid is one of the common issues in multiphase flow problem. In this paper, three methods are used to calculate the motion of particles with large size range in liquid. We apply Euler-Lagrange method and direct forcing immersed boundary method, Euler-Lagrange method use point particle to describe paritcle in calculation, and it usually used for particle smaller than grid size, direct forcing immersed boundary method is a resolved method using several point particle to describe the boundary of particle, which used for particle much larger than grid size, particles whose size are of the same order of the grid size can rise uncertainties in computation when we use both two methods. In this regard, we developed middle point particle method and discuss the validation with drag coefficient in the same simulation circumstances. This model is then used to simulate fluidized bed and sediment armouring, the results comfirm that this method is feasible to simulate particles with large size range.