本研究使用靜止的圓柱來增強並列雙振動圓柱因渦旋逸出造成的振動響應(在雷諾數為$10^3$及$10^4$兩個案例下）。 為了研究此種被動增強方法，一個結合直接施力沈浸邊界法與大渦法的數值模型用於模擬此問題。 本研究探討在固定阻尼效應下，不同的減速度($U_R^*$)變化下的渦旋逸出振動響應以及所謂的VIVACE(Vortex-Induced Vibration for Aquatic Clean Energy) 效率。 研究分為四個部分來進行：首先是研究在不同的間距下($g^* = d/D = 1.0 - 3.0$)，並列雙圓柱的渦旋逸出振動響應。其次是進行其他參數的研究($m^*$ = 4.0 及 10.0; $\zeta$ = 0.01, 0.025, 0.035 及 0.0625)。第三部分是進行串列(in-line)雙圓柱的被動增強方法的效果。最後則是考慮靜止圓柱與並列雙圓柱成交錯排列時的增強效果。
從第一部分的結果顯示，最佳的間距為1.0到1.2之間(1.0 $\leqslant g^* \leqslant$ 1.2) 其效率會在減速度4到5之間(4.0 $\leqslant U_R^* \leqslant $ 5.0)有很明顯的增加。 超過這個區間，則其效率會小於單一圓柱。第二部分的研究顯示比較高的阻尼比下，在很窄的$U_R^*$ 區間下仍會造成高的VIVACE效率。 而在同樣的振動響應下，比較低的質量比的雙圓柱會造成較低的VIVACE效率。 若在相同的質量-阻尼比下，結果顯示低質量比的例子其造成明顯的效率的減速度區間較大，而再選擇適當的阻尼比可達到最大的VIVACE效率。第三部分的結果則顯示，考慮串排(in-line)時，最佳的間距為$s^*$ $\leqslant$ 0.4，而最佳的直徑比為$d^*$ = 0.4 - 0.6。 這個增強效果最佳的例子在 $U_R^*$ $\geqslant$ 5.0。第四部分考慮交錯排列，結果顯示在$U^*_R$) $\geq 6.0$時，效率會比單一圓柱時有效提升。減少靜止圓柱的直徑，在低分歧區間(lower branch region)也可有效增加效率。

Stationary upstream cylinders were used to enhance the response of vortex-induced vibration (VIV) of side-by-side (SBS) cylinders at moderate Reynolds numbers ($10^3$ and $10^4$). A modified direct-forcing immersed boundary (DFIB) with a large eddy simulation (LES) technique was employed to get the numerical solution. The VIV responses and VIVACE (vortex-induced vibration for aquatic clean energy) efficiency were investigated for various reduced velocities ($U_R^*$ = 2.0 - 12.0) at a constant mass-damping ($m^*\zeta$). This study was divided into four investigations. The first and second investigations studied the VIV responses of SBS cylinders with different gap ratios ($g^* = d/D = 1.0 - 3.0$) and VIV parameters ($m^*$ = 4.0 and 10.0; $\zeta$ = 0.01, 0.025, 0.035 and 0.0625). The third and fourth investigations studied the passive VIV enhancement in the in-line and staggered positions.
From the first investigation, it was found that the optimal gap ratio between the SBS cylinders is in the interval of 1.0 $\leqslant g^* \leqslant$ 1.2. A significant increase in efficiency occurs in the initial excitation region between 4.0 $\leqslant U_R^* \leqslant $ 5.0. Above this range, the efficiency is less than that of a single cylinder. The second investigation showed that the vibrating SBS cylinders with a larger damping ratio results in higher maximum VIVACE efficiency with a narrower $U_R^*$ range for significant efficiency. With almost the same amplitude response, the SBS cylinders with a lower mass ratio will result in lower VIVACE efficiency. Using the same mass-damping parameters, it appears that a low mass ratio could be desirable to increase the $U_R^*$ range of significant VIVACE efficiency and pick the proper damping ratio to reach a high value of maximum VIVACE efficiency. The third investigation with the in-line arrangement showed that the optimal upstream cylinder diameter and spacing are $d^*$ = 0.4 - 0.6 and $s^*$ $\leqslant$ 0.4. Within these ranges, the enhancement of amplitude response and efficiency is observed for $U_R^*$ $\geqslant$ 5.0, while the decrease in amplitude response and efficiency for $U_R^*$ = 4.0 - 4.5 is minimized. Results from the fourth investigation with staggered position showed that the amplitude and efficiency of the staggered cylinders are significantly enhanced at reduced velocity ($U^*_R$) $\geq 6.0$ compared with a single cylinder. Reducing the diameter of the stationary cylinder can effectively improve efficiency, especially in the lower branch region.

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