利用沉浸邊界-晶格玻茲曼法探討細長彈性體與周遭流體間力學的交互作用

Abstract

流固耦合是描述流體力學與結構力學之間的多物理場相互作用，不管是大自然或是各種領域中都有廣泛的應用，其中一項重要的應用是以模仿昆蟲與鳥類的拍撲翼飛行模式所設計的微飛行器，比起傳統定翼更加靈活。而近年來有研究指出，適度的翅膀形變，在飛行時能夠提高升力與降低阻力，並能更精確的反映真實的昆蟲飛行，因此將翅膀作為一種彈性結構在相關流固耦合問題中是不可忽視的。然而現階段基於body-conformal網格的數值方法在處理複雜幾何邊界的形變與移動時，會有網格生成而增加計算成本、翅膀交疊使網格過密導致數值耗散等等挑戰，因此本研究旨在開發一套能解決複雜邊界上流固耦合之數值模型，藉由高速圖形處理器平行加速運算進行大規模數值計算，以模擬細長彈性體與周圍流體之交互作用。流體流動使用晶格波茲曼法，與傳統計算流體力學如有限元素法相比更簡單快速且具高度可平行化；彈性體使用沉浸邊界法，通過引入邊界變形力來模擬固體對流體的影響以克服複雜界面網格建置之困難。這兩種方法並用稱為沉浸邊界-晶格波茲曼法，沒有對流體與固體重新劃分網格，克服了網格生成的局限性。 模型驗證的首先模擬了二維通道的層流流動，與解析解和COMSOL模擬軟體比對，能夠捕捉流場正確趨勢。其次驗證二維圓柱體周圍流動，驗證結果得到模型發生卡門渦街的臨界雷諾數與實驗數據接近。彈性體雙向耦合模擬結果分為兩部分，第一部分在圓柱後方連接一條細長彈性體，發現彈性體的振幅與楊氏模數成反比，且當楊氏模數為1.0 [N/mm²]時可以從圓柱後方的渦流中提取到最多的能量。第二部分在均勻流場中放置一條細長彈性體，其上游端固定並改變長度與楊氏模數，發現彈性體存在伸直與拍打雙穩態，可由臨界長度 41 [mm]與臨界楊氏模數0.6 [N/mm²]來控制，最後嘗試兩條細長彈性體，平行放置並研究兩者間距對於其流力作用的影響。

Fluid-structure coupling describes the multi-physical field interaction between fluid mechanics and structural mechanics, and has a wide range of applications in nature and in various fields. One of its important applications is the design of micro air vehicles that mimic the flapping flight patterns of insects and birds, which are more flexible than traditional fixed wings. In recent years, it has been pointed out that moderate wing deformation can improve lift and reduce drag during flight, and can more accurately reflect the real insect flight, so the wing as an elastic structure in the related fluid-structure coupling problem can not be ignored. However, at this stage, the body-conformal lattice-based numerical method has the challenges of increasing the computational cost due to lattice generation and dissipating the value due to overlapping of wings, when dealing with the deformation and movement of complex geometric boundaries. Therefore, this study aims to develop a numerical model that can solve the fluid-solid coupling on complex boundaries, and perform large-scale numerical calculations by parallel accelerated computing with high-speed graphics processors to simulate the interaction between the elastic object and the surrounding fluid. The lattice Boltzmann method is used for fluid flow, which is simpler, faster and more parallelizable than traditional computational fluid mechanics such as the finite element method; the immersion boundary method is used for elastic objects, which introduces boundary deformation forces to simulate the effect of solids on the fluid to overcome the difficulties of complex interface lattice construction. These two methods are used together as the immersed boundary-lattice Boltzmann method, which does not redistribute the lattice between the fluid and the solid, overcoming the limitations of lattice generation. The model validation first simulates the laminar flow in a 2D channel and is able to capture the correct trend of the flow field when compared with the analytical solution and COMSOL simulation software.Next, the flow around the two-dimensional cylinder is verified, and the critical Reynolds number for the occurrence of Karman vortex street in the model is close to the experimental data.The results of the two-way coupling simulation of the elastic object are divided into two parts. In the first part, a slender elastic object is connected behind the cylinder and it is found that the amplitude of the elastic object is inversely proportional to the Young's modulus and the most energy can be extracted from the vortex behind the cylinder when the Young's modulus is 1.0 [N/mm²]. In the second part, a slender elastic object was placed in a uniform flow field with its upstream end fixed and the length and Young's modulus were varied. It was found that the elastic object existed in a bistable state of rest and flapping, which could be controlled by a critical length of 41 [mm] and a critical Young's modulus of 0.6 [N/mm²].Finally, we try to place two slender elastic object in parallel and study the effect of the distance between them on their flow forces.