本研究將先進行文獻回顧來簡介渦流尾流模擬的概況，接著定義幾種不同的渦流模式，並且在往後的章節介紹相關會應用到的方程式與數值方法。首先會從Lentink等人的研究出發，參照他們的實驗設定進行二維的模擬，並分別設有flapping (heaving與pitching組合，無相位差)、flapping-90 (heaving與pitching組合，有90°相位差)、heaving (垂直上下擺動)與pitching (前後轉動)等4種不同運動模式並搭配多種不同擺動頻率來進行二維平板的尾流模擬。再藉由觀察模擬結果的流場尾流之渦流模式及其阻力值與升力值來做比較，並且討論其中幾種具代表性的流場之渦流模式。從我們的模擬結果可以看出各種不同的運動模式配上不同的無因次化波長所造成的渦流模式皆不相同: 波長越大造成的P跟S越多，波長越小造成的P跟S越少。接著再利用Dynamic mode decomposition (DMD)與來分析流場結構，其結果將呈現DMD模態皆是對稱、反對稱或不對稱的模式，尤其疊加運動(flapping與flapping-90)會比單純運動(heaving 與 pitching)更容易發生不對稱的情況。最後再對流場進行快速傅立葉轉換(Fast Fourier Transform, FFT)來觀察其特徵值與頻率的關聯性。

This study will begin with a literature review to provide an overview of the simulation of vortex wakes. Subsequently, various vortex patterns will be defined, and relevant equations and numerical methods to be used in the following chapters will be introduced. The initial simulations will be based on Lentink et al.'s research and following their experimental settings. Four different motion patterns will be considered for two-dimensional wake simulations of a flat plate: flapping (combination of heaving and pitching without phase difference), flapping-90 (combination of heaving and pitching with a 90° phase difference), heaving (vertical up and down motion), and pitching (forward and backward rotation). These motion patterns will be combined with different oscillation frequencies to simulate the wake. By observing the simulated wake patterns, drag, and lift values, a comparison will be made, and several representative wake patterns will be discussed. Our simulation results demonstrate that the vortex patterns vary for different motion patterns and non-dimensional wavelength: larger wavelength results in more P and S vortices, while smaller wavelengths lead to fewer P and S vortices. Next, the Dynamic Mode Decomposition (DMD) will be utilized to analyze the flow field structures. The DMD analysis will reveal symmetric, anti-symmetric, or asymmetric modes, with a tendency for more occurrences of asymmetric situations when superimposing motions (flapping and flapping-90) compared to single motions (heaving and pitching). Finally, the flow field will undergo Fast Fourier Transform (FFT) analysis to examine the correlation between eigenvalues and frequencies.

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