以沉浸邊界數值法模擬魚類快速啟動之運動

Abstract

快速啟動(fast-start movement)是魚類非常重要且獨特的運動方式，依魚類身體變化的形狀可分為C型啟動和S型啟動。C型啟動是魚類遇到危險時進行脫逃的運動型態，而S型啟動則大多是魚類在捕食獵物時加速的動作。C型啟動是魚將身體彎曲成C的形狀，之後往反方向甩出，藉由與流體的反作用力而改變方向進行逃脫；至於S型啟動原理則是魚類將身體彎曲成S的形狀，進而產生往前的加速度。過去的文獻指出C型啟動的加速度及速度值皆大於S型啟動。本文以一簡單的魚身軀模型來進行C型啟動與S型啟動的模擬，並觀察魚類在進行快速啟動時周圍的流場會如何變化。為簡化分析，流場假設為二維不可壓縮黏性流場。本文使用有限體積數值法(Finite-Volume Method)來計算流場，而魚身軀與流體之間的作用力是應用沉浸邊界法(Immersed Boundary Method)來求解流場運動方程式（Navier-Stokes equations）得出。最後在計算出作用於魚身上的力和力矩後，可以運用牛頓運動定律來預測魚的行進速度及位移和行走距離。本研究探討了數種不同C 型啟動與S型啟動的魚身軀擺動模式，並比較了不同模式下所計算出的各項魚類運動數據及效率。

Fast-start motion is an important and unique swimming mode of fish. According to the curved shape of fish body, fast-start motion can be divided into two types: C-type and S-type. Fish usually use the C-type fast-start to escape from danger, and the S-type fast-start is used in capturing prey. In C-start mode, fish bends its body into C-shape, and then get accelerated towards a new direction by the recoiling beat of its tail. While in S-start mode fish bends its body into an S-shape undulating wave to propel itself in the forward direction. Some scientists found that the maximum acceleration and velocity in C-start mode are usually larger than the S-start mode. In this study, we construct the body movement of a fast-start fish from a simple 2-D model. For simplicity, the flow field generated by fish motion is assumed to be two dimensional. The force acting on the fish body is obtained by solving the Navier-Stokes equations with the Immersed Boundary Method. Once the resultant force and moment acting on the fish body are known, the movement of fish can be advanced by using Newton's second laws. This study considers several kinds of C-type and S-type fast-start modes. Relevant data regarding to fish movement under different fast-start modes are calculated and discussed. Performance efficiencies for different fast-start motions are also compared.