流能轉換為再生能源其中一個重要的議題。為了設計新的流能轉換器，需要一個有效率的流體模擬模式來估算轉換性能。因此本研究使用C++語言建置了一個以有限體積法及直接施力沈浸邊界法為基礎的流動動量方程式求解數值模式來模擬層流與紊流流動。針對三維結構物(如球或圓柱體）的流引致震動的物理現象特別建立數值模式。程式中並有以OpenMP為基礎的平行計算功能。在對流項的離散方面採用QUICK方法來進行。而在紊流特性的計算方面是使用大渦法來進行。而模式中的壓力波松方程式則使用雙共軛梯度穩定法來求解。

所建立的數值模式用於模擬數個相關的流場例子。首先考慮一個在均勻流受到渦漩逸出而震動的圓球(雷諾數=300)並與已發表文章比較驗證。進一步探討圓球前如果放置另一小圓球的震動影響。並研究小球的大小與位置的影響。結果發現，如果小球如果夠近大球，則會影響“鎖相放大”提早開始，同時發生“鎖相放大”期間也會增大，另外在"鎖相放大“階段會增大大球的振幅。

第二個例子則是探討在雷諾數 = 3,900的紊流中圓柱的渦漩引致震動。這個研究中探討了兩個不同的計算區間大小以及三組不同的邊界條件造成的影響。結果發現較大的計算區間會增進計算結果的精度，特別是在較遠的尾流區。另外，在兩側的邊界使用週期性條件和對稱條件對於數值結果也有明顯的影響。

在第三個例子中，對於數值參數影響渦引致震動的計算結果進行研究。雖然網格獨立性研究會在鎖相放大的區間外進行並獲得適合的網格大小，但是更細的網格會影響在鎖相放大區間渦引致震動。例如在層流階段(Re = 90-115)，形成穩定的震動的流場的演化會受到影響。而在紊流中(Re = 1,000)，初始條件由靜止、逐漸加速、逐漸減速三個不同的情況的影響也被研究。遲滯現象被發現在鎖相放大區間當使用加速、減速的不同初始條件的時候。最後，研究所產出的數值模式亦可用於模擬多根圓柱在均勻流中同時產生渦引致震動現象。

Flow energy conversion is an important topic in renewable energy. To design a novel flow energy converter, an efficient flow solver is necessary to estimate the conversion performance. Therefore, a 3-D Navier-Stokes solver has been developed in C++ using finite volume method (FVM) and direct-forcing immersed boundary method (DFIB) for laminar and turbulent flows. It has been tailored to study vortex-induced vibration (VIV) of 3-D structures such as spheres and cylinders. Parallel computation has been implemented using OpenMP. QUICK (quadratic upstream interpolation for convective kinematics) scheme has been adopted for the velocity differencing scheme and the Smagorinsky model for the turbulent flow scales to conduct large eddy simulation (LES). Bi-conjugate gradient stabilized method (Bi-CGSTAB) was used to solve the pressure Poisson equation.

Several cases studies were conducted using this solver. In the first study, laminar flow with Re=300 over a sphere undergoing VIV was analyzed and validated using published literature. Later, the effect of introducing a small stationary sphere upstream of the vibrating sphere was investigated with variation of the size of the small sphere and the distance between the spheres. It was found that the upstream sphere, if placed close enough to the oscillating sphere, led to an increased amplitude of vibration of the sphere during the "lock-in" or synchronization region. It also affected the onset of the synchronization and elongated its duration.

For the second study, a circular cylinder was considered in turbulent flow at Re=3,900 and the effect of two computational domain sizes and three different sets of boundary conditions was investigated. The larger computational domain was able to increase the accuracy of the results, especially in the far wake region. Moreover, switching the lateral boundaries between periodic and symmetry conditions enabled the numerical simulation to approach two different experimental results, which gave an interesting insight into the reasons for the contradiction in those results.

In the third study, the effects of some numerical parameters on laminar and turbulent flows over a cylinder were investigated. Despite a regular grid independent study outside the lock-in region, it was found that further refinement of the grid affected VIV in the lock-in region in both laminar and turbulent flows. For laminar flows (Re=90-115), the evolution of VIV flow to a stable vibrating pattern was also affected. In turbulent flows (Re=1,000), the effect of initial conditions on the VIV of the cylinder was also investigated with the rest, increasing reduced velocity and decreasing reduced velocity initial conditions. A hysteresis effect was observed in the lock-in region because the decreasing initial condition led to lower amplitudes of vibration. Finally, the solver has been used to conduct some preliminary studies with multiple cylinders undergoing VIV.

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