流固耦合垂盪圓柱之自適應回饋控制

Abstract

本研究提出一種閉迴路反饋流動控制策略，旨在減緩渦旋引致振動並穩定受流固耦合影響下的剛性圓柱擺動動態。該圓柱可因尾流中渦旋脫落而自由地進行橫向（橫流方向）振盪。數值模擬採用沈浸邊界投影法，結合不可壓縮流的流固耦合數值模型。以靜止圓柱周圍的時間平均流場作為基態，該流場波動微弱，並在圓柱固定座標系中對不可壓縮納維–斯托克斯方程進行線性化。基於該線性系統進行預解分析，構建用於模型參考自適應控制系統的參考模型。研究比較了法向與切向制動兩種作用方式，結果顯示切向制動顯著優於法向制動，分別在升力波動、橫向速度波動與阻力波動方面達到約 85%、84% 與 93% 的減幅。模型參考自適應控制系統框架在適當的自適應學習率範圍內表現出穩定的控制效果，顯示其在有效抑制流固耦合系統中的渦旋引致振動方面的潛力。

This study proposes a closed-loop feedback control strategy to mitigate vortex–induced vibrations and stabilize the plunging dynamics of a rigid circular cylinder undergoing flow–structure interaction (FSI) in a uniform stream. The cylinder is free to oscillate transversely (crossflow) due to vortex shedding in its wake. Numerical simulations are conducted using the immersed boundary projection method, integrating a coupled fluid–structure interaction formulation for incompressible flow. A time–averaged flow field around a stationary cylinder, characterized by minimal fluctuations, serves as the base state to linearize the incompressible Navier–Stokes equations in a cylinder–fixed frame. Resolvent analysis of this linearized system is then employed to derive a reference model for the model reference adaptive control (MRAC) scheme. Both normal and tangential actuation configurations are examined. The results show that tangential actuation significantly outperforms normal actuation, achieving reductions of up to 85% in lift fluctuations, 84% in transverse velocity fluctuations, and 93% in drag fluctuations, all with minimal input power. The MRAC framework demonstrates robust and stable control effectiveness across a suitable range of adaptive learning rates, highlighting its potential for effectively suppressing flow-induced vibrations in fluid–structure interaction systems.