適用於剛體流固耦合問題的非疊代性沉浸邊界投影法之開發

A non-iterative immersed boundary projection method for rigid-body flow-structure interaction

謝新雨(Hsin-Yu Hsieh)

指導教授 ： 蔡協澄

國立臺灣大學/工學院/機械工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202100201

摘要

本研究開發了計算多個複雜幾何剛體之流固耦合問題的沉浸邊界投影法。在 本方法中，一個流固耦合的剛體之動力和其餘多個剛體之運動與流體的不可壓縮 渦度方程式以隱式耦合。為了使此耦合系統能夠非疊代性地、準確地、有效率地 求解，本方法特別選擇於流固耦合剛體 (稱為「目標」) 之附體座標系下進行計 算。流體方程式與剛體的隱式耦合可使本方法於低固流密度比下仍維持數值穩 定。同時為了施加符合正確物理的剛體動力學，本方法修正了剛體內部虛擬流體 的影響並同時過濾了表面應力因數值方法帶來的振盪。如同過往許多的沉浸邊界 投影法，本方法所得的最終離散方程式能以區塊 LU 分解有效率地求解。本方法 以兩個二維測試問題進行驗證:第一個問題為中性浮力圓柱剛體於平板庫葉流中 的漂移，第二個問題為圓柱剛體的自由落體或自由升體。最後，以本方法模擬流 體驅動垂直軸風力發電機的脈衝性啟動，可得各葉片產生的扭矩和中塔的受力。 此資料於未來的後續研究可用於分析垂直軸風力發電機的葉片空氣動力學、中塔 的疲勞破壞及葉片與中塔之間的交互作用。

關鍵字

沉浸邊界法 ； 流固耦合 ； 剛體固定座標系 ； 剛體運動 ； 精確表面應力

並列摘要

An immersed boundary projection method for ow-structure interaction problems which are involving rigid bodies with complex geometries is presented. Dynamics of a rigid body interacting with fluid flow and kinematics of other rigid bodies undergoing prescribed motions are coupled implicitly with the incompressible vorticity equations. In particular, the method is formulated in a frame of reference fixed on the rigid body under flow-structure interaction (the target) so that the coupled system can be solved non-iteratively, accurately, and efficiently. The implicit coupling of the fluid solver and dynamics and kinematics of rigid bodies ensures the method being stable for low solid-to- fluid mass ratios. The influence of fictitious fluid in- side the rigid body is considered and the spurious oscillations in surface stresses are filtered to impose physically correct rigid body dynamics. Similar to many predecessors of the immersed boundary projection method, the resulting discrete system is solved efficiently using a block-LU decomposition. The method is then validated with two-dimensional test problems of a neutrally buoyant cylinder migrating in a planar Couette flow and a freely falling or rising cylindrical rigid body. Finally, the impulsive start of a ow-driven vertical-axis wind turbine (VAWT) is simulated to obtain the torques generated by the turbine blades and the forces exerted on the tower, which can be used for detail analysis of the aerodynamics of VAWT, the fatigue of the tower, and the interaction between turbine blades and the tower in future investigation.

並列關鍵字

Immersed boundary method ； Flow-structure interaction ； Body-fixed frame ； Rigid-bodies dynamics ； Accurate surface stress

參考文獻

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