任意形狀二維物體外流場長時間模擬之面積擴散渦漩法

Abstract

本論文旨在研發可進行任意幾何形狀之物體外流場長時間模擬之面積擴散渦漩法(Core-spreading vortex method)，其中對流誤差靠分裂融合機制來控制，無滑移邊界由物體邊界上渦片(vortex sheet)強制滿足，計算效率利用快速渦漩法來提高，管外流物體之幾何彈性則以邊界元素法達成。本論文並特別針對長時間模擬的準確性進行設計改良:首先，針對分裂過程中產生之過弱渦泡，利用融合網格搭配由近而遠的搜尋方式，將其移除後把強度分配給附近的非過弱渦泡，以減少渦泡數量，同時維持準確性;接著，選擇最合適的邊界渦片擴散近似解，並將其離散方法最佳化;並且，在過於靠近邊界渦泡之處理中，重新定義過於靠近邊界之區域，因此可讓模擬不再受限於圓柱或方柱等簡單幾何形狀;最後，由於渦泡分布區域隨模擬時間不斷增加，藉由加入流出邊界條件(Outflow boundary condition)的設計，模擬範圍及模擬渦泡數目得到控制，因而可有效率地進行長時間模擬。本論文以低雷諾數下之瞬間啟動、機翼、圓、與橢圓柱物體所引致之流場進行長時間模擬，驗證所提面積擴散渦漩法的可靠性、準確性、及計算效率。

In this thesis, a core-spreading vortex method suitable for a long-time simulation of 2D flows over an arbitrary body is successfully developed. In this vortex method, we employ the splitting and merging skills to control the convection error, an imposition of a vortex sheet on the body to enforce the no-slip boundary condition, the fast vortex method to speed up the computation, and finally the boundary element method to provide the geometry flexibility. This thesis particularly aims at improving the long-time accuracy of the vortex method. Firstly, for the over-weak blobs generated due to blob splitting, we remove them and distribute their strength to nearby non-over-weak blobs through a near-to-far algorithm using the merging grids. Secondly, we determine the appropriate approximation solution and optimized discretization of the vortex sheet diffusion. Thirdly, for treatment of the near-wall blobs, we redefine the near-wall region, which enables the simulation of flows over bodies of arbitrary shape. Finally, an outflow boundary condition is designed and imposed to control the total blob number. The flow induced by the impulsively started airfoil, circular, and elliptic cylinders are simulated and the accuracy and efficiency of the proposed vortex method are confirmed by the agreement between the present simulation results and those in the literatures.