臺灣博碩士論文加值系統

魚類在水中快速啟動(fast-start movement)是獨特且重要的泳動機制。快速啟動一般分為Ｃ型啟動和Ｓ型啟動。在過去的記錄中Ｃ型啟動常見於魚類脫逃時，而魚類在捕食獵物時則常見使用Ｓ型啟動。從過去的實驗量測中Ｃ型啟動無論是最大的加速度還是最大的速度都大於Ｓ型啟動。過去的研究大多著重於魚類在快速啟動時加速度及速度的量測與計算，但對於魚類快速啟動之流體力學作用機制以及Ｃ型啟動和Ｓ型啟動時魚類周圍的流場變化差異的討論則不多見。本文以一簡化後的魚類模型分別模擬魚類在Ｃ型啟動和Ｓ型啟動時的軀體動作。為簡化分析，流場假設為二維勢流場(potential flow)，並配合非穩態之庫達(Kutta)條件來處理魚尾渦流剝離(vortex sheeding)的現象。本文採用板格法(panel method)來計算此二維勢流場，而作用於魚軀體上的力和力矩則是藉由非穩態柏努力方程式(unsteady Bernoulli equation)來求得。在取得作用於魚身上的力和力矩後，魚在流體中的行進速度與軌跡則可藉由牛頓運動定律得出。本研究分別探討了S型啟動和C型啟動的加速機制，並加以闡述兩種不同的啟動形式所產生的流場變化差異。本研究亦探討了數種不同S型啟動及C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。基本上，在S型啟動模式中魚類運用其尾部擺動時在其後方所形成的初始渦流來增強附近流體的動量變化，並配合適當的身軀形變姿態來協助其向前作加速運動。而在C型啟動模式中魚類則是運用其軀體快速向一側彎曲時流體所提供之反向作用力，並配合作用於軀體上之力矩所造成之旋轉效應來協助其轉向並加速往新的方向行進。由於在C型啟動模式中魚類是順應流場機制來做行進運動，因此相較於S型啟動模式中魚類需克服流體所產生之側向力與力矩以維持其行進方向，C型啟動模式提供較快的行進速率及運動效率。此可解釋魚類在竄逃時多半採用C型啟動模式之原因。

Fast-start swimming is a very special and important type of locomotion of fish. Basically, fast-star motion can be classified into two types: C-type and S-type. It is generally thought that the C-type fast-start is adopted by fish for escape while the S-type fast-start is used in prey capture. Previous experimental data have shown that the maximum acceleration and maximum velocity of fish performing C-start are all significantly greater than that for S-type motion. However, few researches have focused on the discussions of critical flow-mechanisms responsible for fish fast-start motions and clarification of why and how fish can achieve higher acceleration with C-start mode than with S-start mode. The present research investigates numerically the fluid flows generated by empirically modeled fast-start movements of fish. For simplicity, a potential flow is assumed, and the unsteady Kutta condition is applied to handle the vortex-shedding phenomenon at fish tail. The panel method is adopted to solve the flow field numerically, and the force and moment acting on fish body are calculated by using the unsteady Bernoulli equation. Once the force and moment acting on fish are obtained at each instant, motion of fish can then be tracked by applying Newton’s second law. Discussions on force and moment exerting on fish, the moving speed and distance traveled by fish under different types of S-start and C-start movements are provided. Also given are the fluid-dynamics interpretation of the fast-start motion and the explanation of mechanisms that lead to different performances of S-start and C-start modes. Basically in S-start mode, fish receives significant thrust from the momentum of accelerating fluid enhanced by the starting vortex near its tail. While in C-start mode, fish speeds up via a turning motion induced by the fluid force and moment acting on it. Since in C-start mode, fish utilizes the lateral force and moment to assist its turning and speeding rather than resists them, fish moving with C-start mode has faster moving speed and better efficiency of performance than with S-start mode. This can explain why fish normally adopt C-type fast-start mode in its attempt to escape from danger.

國立臺灣大學碩士學位論文口試委員會審定書 i
致謝 ii
摘要 iii
Abstract iv
Table of Contents vi
List of Figures ix
List of Tables xiii
Chapter 1 Introduction 1
Chapter 2 Governing Equation and Numerical Method 9
2.1 Governing Equation of Potential Flow 9
2.2 Boundary Conditions 9
2.3 Unsteady Kutta Conditions 10
2.4 Numerical Method 12
2.4.1 Source/Sink and Vortex Panel Method 12
2.4.2 Discretized Equations 15
2.4.3 Calculation of Thrust Force 19
2.4.4 Some Considerations on Free Vortices 21
2.5 Nondimensionalization of Equations 22
Chapter 3 Models for Fast-start Movements of Fish and Motion Produced by Fluid Force.. 24
3.1 Morphological change of Fish Body Configuration in Fast-start Movement 24
3.1.1 Midline of Fish Body in C-start Movement 24
3.1.2 Midline of Fish Body in S-Start Movement 28
3.1.3 Width Function of Fish Body 30
3.2 Fish Motion Produced by Fluid Force 31
Chapter 4 Simulations of S-start Motions 37
4.1 Test for Convergence of Numerical Solution 39
4.2 Results and Discussion 41
4.2.1 Case S-1 41
4.2.2 Case S-2 45
4.2.3 Case S-3 49
4.2.4 Case S-4 53
4.3 Comparison of Swimming Performance among Different S-start Models 57
Chapter 5 Simulations of C-start Motions 63
5.1 Results and Discussion 66
5.2 Comparison between C-start and S-start Motions 84
Chapter 6 Conclusion and Future Studies 87
6.1 Conclusion 87
6.2 Future Studies 88
Bibliography 90
Appendix A Derivations of the Constants in the Coefficient Matrix of Flow Equation 96

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