不可壓縮黏性流體中兩固體圓柱之碰撞模擬

Abstract

流固耦合常見於自然界與工程應用中，是個複雜的難題，也是數值模擬的一大課題。固體在流體中運動，並不侷限於只有單顆固體，而當同時有多顆固體在流體中相對運動時，固體間便有可能發生碰撞。本研究旨在開發更合乎物理意義的碰撞模型，並將其應用於流固耦合的模擬。 回顧前人的碰撞力模型，並列舉出各類方法的優缺點作為參考。處理固體變形作用力方面，以彈性力學推導任意形狀的二維柱體正向碰撞力之的彈性項，並參考彈性水力碰撞理論(elastohydrodynamic collision)，設計適切的碰撞力模型。延續本實驗室所開發的「整合沉浸邊界法與寬頻元素法之流固耦合數值模擬工具」，擴增處理多顆固體的功能，並納入碰撞力模型。 本研究模擬常見的兩圓柱自由落下之「牽引—接觸—滾落」現象，並有良好的準確度。確定方法的準確度後，以等加速度的概念設計模擬工具，分析自由落下的兩圓柱各階段的流場變化。並比較單一圓柱與兩圓柱自由落下的速度差異。儘管本研究有良好的模擬結果，若能再多考慮切線方向的碰撞力，則能使模擬更加貼近真實。

Problem of fluid-structure interaction is common for nature and industrial applications, and it is a difficult problem. It is also an important challenge for numerical simulation. It does not limit on one solid body for cases that solid move relatively in fluid. It would be possible to collide for multi-bodies moving in fluid. This research aims at developing a collision model with physical meaning, and applying it in simulation of fluid-structure interaction. We review several existing collision models and summarize advantages and disadvantages of each ones. For the force come from deformation, we derive the elastic term of normal collision force for two-dimensional cylinders of arbitrary shape. We refer to elastohydrodynamic collision to design a proper collision model. With the collision model, the numerical tool, “a spectral element-immersed boundary method for fluid-structure interaction problems”, developed from our lab, is extended to be able to solve multi-body problems. For the well-known drafting, kissing and tumbling phenomena between two freely falling circular cylinders, we observed equally well in this study. After confirming the accuracy, we adopt the concept of constant acceleration motion in the simulator and explore the flow details of two freely falling circular cylinders. We also compare the velocity difference between one freely falling circular cylinder and two freely falling circular cylinders. In spite of excellent results, a complete model by also taking the tangential component of collision force into consideration will make the proposed collision model more realistic.