本研究利用結合了虛擬力的沉浸邊界法來模擬一個球體受均勻流場產生的渦旋所引起的振動現象。由結構物後方渦旋逸散所產生的不穩定的流體作用力會造成結構物的振動，尤其是在鎖相放大區域可能會造成結構物的損壞。在當前研究中，低雷諾數下均勻流場中的球體可以在僅垂直方向及同時具有與流動平行和垂直兩個方向上運動。此外，流場入流速度將作為本文對於渦旋引致振動效應的主要研究因素，數值模擬的球體所受之氣動力係數可以在時域以及頻域當中呈現。在鎖相放大的遲滯驟升部分可以求得球體所受升阻力係數之極大值，此時渦旋振蕩頻率與球體自然頻率近乎相等，振動處於軟性鎖相放大模式。髮夾模式和螺旋模式會在不同入流速度引起的振動區域被分別發現。此次數值模擬證實了沉浸邊界法對研究渦旋引致球體振動具有可行性。

A numerical study of the vortex-induced vibration (VIV) of an elastically mounted sphere using the direct-forcing immersed boundary (DFIB) method incorporating the virtual force term is undertaken. The fluctuating hydrodynamic forces may cause damage when a solid structure interacts with fluid flow. Especially in the so-called lock-in situation, the vibration phenomenon results in the failure of the structure. The present study shows that a dynamically mounted sphere is allowed to vibrate transversely only or both in the in-line and the transverse directions in a uniform flow at a moderate Reynolds number of 300. The effect of reduced velocity on VIV is discussed in this study. Aerodynamic coefficients of a freely vibrating sphere are analyzed in time and spectral domains. The maximums of the lift coefficient and the drag coefficient show hysteresis jump at the low end of the lock-in region. The ratio between the vortex shedding frequency and the natural frequency of the structure reveals the so-called soft lock-in. Moreover, two shedding mode hairpin and spiral mode are found in different vibration response regimes. This study proves the capability of the proposed DFIB model can be useful for the investigation of VIV of the structure.

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