基於預解分析之縱搖圓柱的流場控制

Abstract

本研究基於預解分析提出一個適用於週期性運動剛體的開回路主動式流場控制設計方法，並以雷諾數為 500，司特勞克數為 0.36 的縱遙圓柱作為實例進行驗證。將時間平均的流場作為基底流，應用雷諾分解可將統御方程式線性化，得到一組具有週期性係數的線性系統方程。本研究利用弗洛蓋理論與李亞普諾夫-弗洛蓋轉換，將原本的週期性線性系統轉換成常係數線性系統。至此，預解分析才得以配合擬頻譜，找出在轉換後的常係數線性系統中，最佳的流場控制頻率為司特勞克數 0.1464。以此頻率在原系統中所產生的諧波頻率與次諧波頻率進行流場控制控制，並利用切線方向的物體力模擬制動器的效果，最佳的結果可使升力擾動之相對減量達到 25.7%，達到流場控制提升空氣動力性能的目的。

This study presents an open-loop active flow control design process for a periodic-moving rigid body based on resolvent analysis and validates with a plunging cylinder at a Strouhal number of 0.36 and a Reynolds number of 500. With a time-averaged based flow, the linearized vorticity equation and a linear system with a time-periodic coefficient are obtained. The study applies Floquet's theorem and Lyapunov-Floquet theorem to transform the original linear time-periodic system into a linear time-independent system. The resolvent analysis technique can then be utilized to reveal the optimal actuating frequency, Strouhal number of 0.1464, of the transformed system by depicting its pseudospectrum. According to the harmonic frequencies and the sub-harmonic frequencies in original system, the tangential-direction control is able to reduce relative lift fluctuation up to 25.7\% and enhances the aerodynamic performance.