以力元理論探討魚類BCF泳動之尾鰭推進機制

Abstract

本論文將以力元理論探討低雷諾數流場中，有限平板模擬魚類尾鰭在不同史卓荷數(Strouhal Number, St)下進行上下(Heave)擺動之BCF泳動模式的受力機制。透過力元理論分析撓性平板之推力機制，發現推力產生來自於平板加速變形運動所產生的C_Da、流場中渦流而產生的C_Dv以及存在於物體表面的C_Df。其中與流場渦流(Vorticity)有關的C_Dv 與C_Df所提供之推力貢獻，將隨著史卓荷數St和變形量a_0增加時所導致流場中渦流強度增強，而明顯提升。 透過力元理論分析可以清楚了解環繞於平板周圍的渦流結構對於其所造成之受力變化，同時進行定量描述。仔細觀察剛性與撓性平板拍動時，三維流場中流場與C_Dv之分布，發現前緣渦皆對平板產生阻力貢獻；而除了剛性板外，平板周圍的渦流結構皆對於整體撓性平板產生極大之推力貢獻。造成剛性板做上下擺動仰角不變之運動幾乎沒有推力產生之主要因素為輔助勢流，由於輔助勢流包含幾何外型之影響，因此若將剛性板進行些微的撓曲變形，即會造成推力的遽增。 本文最後進行推進效率分析，在撓曲變形平板下以St=0.4的推進效率最佳，不過其所產生之推力值並非最大，因此不管是追求高游動速率還是高續航力，都必須在游動策略上有所取捨。

In this study, we investigate three-dimensional thrust mechanisms of finite rigid and deformable flapping plates simulated as a caudal fin of the BCF (body and/or caudal fin) swimming fish at low Reynold numbers Re=500 from the perspective of force element theory. Three values in Strouhal Number (St=0.2, 0.4 and 0.6) ranged in the nature regime and four stiffness (a_0=0, 0.1, 0.15, and 0.2) of the plate are considered. It is shown that the thrust generation of the flapping plate is mainly dominated by the acceleration of the body C_Da as well as vorticity in the flow field and on the body surface C_Dv and C_Df; moreover, C_Dv and C_Df will dramatically increase accompanied by the increasing in St and a_0 due to the generation of stronger vortices, including two sides of the tip vortices and the trailing-edge vortices. Further, we could precisely quantify the force contribution of each vortex strucuture in the flow field. Carefully examining, it is shown that the leading-edge vortex generated in a stroke of flapping motion provodes resistance contribution. However, the vortices around two sides and the trailing edge of plate enhanced by the deformation have contribution to the thrust except the cases of rigid plate. The main reason that results in nearly zero thrust contribution for the heaving rigid plates is due to geometric effects of the auxiliary potential. Therefore, given by a slight deflection, the flapping plate could sufficiently gain thrust forces to move forward. In a final, the propulsive efficiency η of flapping plates is computed for different St, and show that η attains to the optimum at St=0.4, whilst the thrust force is the greatest at St=0.6. Therefore, no matter how fish pursue high swimming velocities or high cruising endurance, it must be trade-off under a swimming strategy.