本研究利用一個具虛擬力的沉浸邊界法來模擬一圓柱體在一均勻流場中所產生的渦漩引致振動現象。由於結構物後方渦漩逸散所產生不穩定的流體作用力會造成結構物的振動, 事實上, 此振動在鎖相放大情形發生時更可能會造成結構物的毀損。在目前建立的數值模式中, 受到低雷諾數流之均勻流場下的圓柱可以僅在與流動垂直方向下及其兩方向(與流動平行方向及垂直方向)下做運動。此外, 其邊界對於兩自由度振盪圓柱的影響也在本研究中呈現。透過流場可視化的分析, 其衰減速度的變化和邊界-結構的間隙比變化在渦漩引致圓柱體振動問題中被討論。此圓柱所受之氣動力係數可在時域與頻域中呈現。在鎖相放大的區段, 不受邊界影響之圓柱其相位圖可呈現細長的八字形以及橢圓形的運動。另外當考慮邊界的效應時, 其圓柱相位圖在鎖相放大區段可觀察到一較為渾圓的橢圓形運動。此外, 渦漩逸散的模態也是本研究所探討之方向, 一般稱為2S 的渦漩逸散現象可在圓柱處於低頻振動時被發現, 但當圓柱振幅變大時, 即可觀察到C(2S)模態。當考慮邊界效應時, 其圓柱展現了單一渦漩逸散的模態。本數值研究經與他人之數值與實驗結果相比有良好之一致性, 故本數值研究可用來做研究渦漩引致振動的有效工具。

A numerical study of the vortex-induced vibration (VIV) of a flexible supported circular cylinder using the direct-forcing immersed boundary (DFIB) method incorporating the virtual force term is investigated. The fluctuating hydrodynamic forces may cause the vibration of the structure due to vortex shedding behind it. In reality, this vibration phenomenon may result in the failure of the structure especially for the so-called lock-in/synchronization phenomenon. The present study shows that a dynamically mounted circular cylinder 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. Furthermore, the effect of a plane boundary is considered on the VIV of two-degree-of-freedom vibrating circular cylinder. The effects of reduced velocity and gap ratio on VIV are discussed. Hydrodynamic coefficients of a freely vibrating cylinder are analyzed in time and spectral domains. The cylinder without the influence of a plane boundary orbits the slightly oval-shaped and eight-shaped motions in the lock-in regime. However, the nearly round oval-shaped motion is observed only in the lock-in region when the plane boundary is
taken into account. Moreover, the 2S and the C(2S) vortex shedding modes can be found at low amplitude vibration and large amplitude vibration, respectively. When the plane boundary is considered, only a single vortex street is found. The comparisons against the published experimental and numerical data well-prove the capability of the present DFIB model. This proposed model can be useful for the investigation of VIV of the structures.

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