簡諧震盪圓柱流場之閉迴路流體控制

Abstract

本研究旨在應用閉迴路流場控制降低圓柱於均勻流場中進行簡諧震盪產生的升力波動。通過此不可壓縮流的數值模擬的時間平均基流，可將於圓柱附體座標系下的納維-斯托克斯方程式進行線性化。再利用預解分析推導出此流場的線性系統模型，藉此設計出兩個線性反饋控制方案。首先，採用迴路整型法(loop-shaping method)設計出可最大化穩定裕度及抵抗來自週期性邊界條件的干擾的強韌控制器。數值模擬結果顯示, 此控制方案可減少升力波動達5.7%。再者，引入模型參考自適性控制(model reference adaptive control)以處理系統因加入控制器帶來的時變化。本研究採用直接型控制以直接更新時變的自適應控制增益。結果顯示，自適應控制成功降低了30.9%的升力波動。

In this study, closed-loop flow control is implemented in order to attenuate the lift fluctuation of a circular cylinder oscillating harmonically in a uniform stream. Through the numerical simulation of the incompressible flow around the oscillating cylinder, a time-invariant base flow is obtained by averaging the flow over time to linearize the incompressible Navier-Stokes equations in the cylinder-fixed frame. A resolvent-analysis-based model derived from the linearized equations is used to design two linear feedback control schemes. First, the loop-shaping method is adopted to design a robust controller that maximizes the stability margin and rejects the disturbance imposed by the periodic boundary condition. The simulation shows this control scheme can reduce the lift fluctuation by 5.7%. Furthermore, the model reference adaptive control is introduced to deal with time-varying linear plant due to the addition of the controller. A direct approach of this control is adopted to directly update the time-varying adaptive control gains. The results show that the adaptive controller successfully reduce the lift fluctuation by 30.9%.