我們使用浸入式邊界方法對流過八字形運動的蜻蜓翅膀——單翼和串聯翼——的流體進行數值模擬，分析了氣動升力和阻力係數。通過網格獨立性測試以及時間步長獨立性測試，爲後續模擬獲得適當的網格間隔和CFL數。進一步進行不同翼縱橫比的流動模擬，以研究蜻蜓翅膀縱橫比對流場的影響。此外，進行昆蟲飛行的相位偏移和串聯翼中心距離對性能的影響分析。在升力爲正的前提下，根據升力與阻力係數之比的最大絕對值，得到阻力係數最小和升力係數最大的每個翅膀和串聯翼在不同中心距離下的最佳相位偏移，表明此相位偏移最適合蜻蜓飛行。因此蜻蜓可以採用不同的相位偏移來控制飛行。此外，特徵正交分解分析的結果表現出頻率的奇偶性。

Numerical simulations are performed using immersed boundary methods for flow over dragonfly wings, single and in tandem arrangements, performing figure-eight motion. Mechanics of aerodynamic lift and drag coefficients are analyzed. Grid independence test, as well as time-step independence test, is conducted to get the appropriate grid interval, and CFL for the subsequent simulations. Simulations of flow with various aspect ratios of the wing are further conducted to investigate the effects of aspect ratio on the flow field. Furthermore, Performance analyses on phase shift and tandem-wing center distance for insect flight are performed. The best phase shift (% of period) for each wing and combined wings with different tandem-wing center distance based on the largest absolute value of ratio of lift to drag coefficient with positive lift makes the minimum CD and maximum CL achieved, indicating that such phase shift is best for dragonfly lift generation. And different phase shift can be adopted by dragonfly to control its flight. Also, results of proper orthogonal decomposition analysis show some parity of frequency.

Abstract ii
List of Figures vii
List of Tables x
1 Introduction 1
1.1 Introduction 1
1.2 Unsteady Mechanism in Insect Flight 2
1.2.1 Delayed Stall 3
1.2.2 Rotational Circulation 3
1.2.3 Wake Capture 3
1.3 Literature Survey 4
1.3.1 Insect Flight 4
1.3.2 Tandem-wing Phase Shift and Center Distance 7
1.3.3 Proper Orthogonal Decomposition (POD) 8
1.4 Motivations and Objectives 10
2 Methodology 17
2.1 Immersed Boundary Method (IBM) 17
2.1.1 Mathematical Formulation 17
2.1.2 Numerical Scheme 18
2.1.3 Forcing Strategies 19
2.2 Determinations of Lift and Drag Forces 20
2.3 Proper Orthogonal Decomposition (POD) 21
2.4 Complete Solution Procedure 22
3 Results and Discussion 25
3.1 Wing Kinematics 25
3.2 Grid Independence Study 26
3.3 Time-step Independence Study 26
3.4 Effect of Aspect Ratio 26
3.4.1 Reynolds Number Based on Translational Velocity 27
3.4.2 Reynolds Number Based on Maximal Velocity 27
3.5 Effect of Phase Shift and Tandem-wing Center Distance 28
3.6 Proper Orthogonal Decomposition (POD) 30
4 Concluding Remarks 62
4.1 Conclusion 62
4.2 Recommendation for Future Work 63

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