二維位勢流場中平板以形變與剛體模式擺動所產生之推力比較

Abstract

魚類在水中快速啟動是非常獨特的泳動機制。過去有相當多的研究是針對魚類在穩態泳動時周遭所引生的流場來進行觀察與量測，並以簡單的流體力學理論來解釋魚前行力的來源及推估其值。然而對於魚類快速啟動時如何有效利用流體流動形態於瞬間產生極大推力之論述則並不多見。本文以一無厚度的波浪狀形變平板來模擬魚快速啟動時尾部的擺動動作。為簡化分析，流場假設為二維勢流場(potential flow)，並配合非穩態之Kutta條件來處理平板末端渦流剝離(vortex shedding)的現象。本文採用板格法(panel method)來計算此二維勢流場，而作用於平板上的推力則是藉由求解非穩態Bernoulli方程式來得出。為了比較平板形變擺動模式與剛體擺動所產生之推力，本文提出了三種比較基準，計算的結果顯示無論在何種基準之下平板以形變模式擺動一周期的最大推力、平均推力以及平板前行的位移量皆大於剛體模式之擺動。本研究亦探討了數種不同的平板形變擺動模式，藉以說明魚類如何巧妙應用魚尾擺動時在其後方所形成的初始渦流，並配合適當的形變姿態來協助其向前作加速運動。

Fast-start swimming of fish is a very special type of locomotion. Many existing studies involved using the DPIV flow-visualizing technique to measure the flow field around a steadily swimming fish and exploiting the basic fluid dynamic theories to interpret the source of the propulsion force. However, few researches had focused on the area of how fish utilize the dynamic of the flow field to produce large thrust in the fast-start motion. In this study, we model the body movement of a fast-start fish by a 2-D zero-thickness flat plate with prescribed undulating motions. For simplicity, a potential flow is assumed, along with the unsteady Kutta condition to simulate the vortex-shedding phenomenon at the end of the flat plate. The panel method is adopted to solve the flow field numerically, and the force acting on the flat plate is calculated by using the unsteady Bernoulli equation. In order to compare the thrust generated by an undulating plate with that by a rigid flat plate, three different standards of comparison are proposed. Calculated results show that under all standards, the propelling force and forwarding distance produced by a flat plate with undulating motion are larger than that produced by a rigid-body motion. The present research also compares and discusses several different types of flat-plate undulating motions, with a view to explain how a fish benefits from the impetus of the starting vortex generated by its swinging tail and properly adjusts its configuration to help accelerate itself through the fluid.