本論文研究之主要目的在於透過使用COMSOL Multiphysics進行拍翼流場模擬，對20公分之翼展之拍翼機的計算流體力學進行研究，以估算其三維氣動力數據。COMSOL Multiphysics提供一個全面的模擬環境，其應用於各種程序且依據使用者 之條件提供準確之結果，並降低使用者之進入門檻與難度。本研究將上邊界之條件修改為封閉以進行拍翼三維流場計算，以模擬真實狀況之風洞邊界條件。本研究設定三種不同的速度值(1~2m/s)，進行層流以及紊流條件下之模擬，並與本團隊之風洞實驗結果及各種條件下之數據進行比較。
後續研究可基於本研究模擬真實狀況之拍翼流場研究方式，拓展至雙拍翼流場模擬，並進行編隊飛行之拍翼流場模擬。

The main objective of this thesis is to do the study of the computational fluid dynamics of the flapping wings of 20 cm wingspan by estimating three dimensional(3D) aerodynamic values along with the study of the flow field using the software COMSOL Multiphysics. The COMSOL Multiphysics is a comprehensive simulation software environment for wide array of applications designed to provide the most accurate results which gives the user access to choose most of the conditions by lowering the assumptions its user must make. Most basically the modification of the computational fluid dynamics simulation of a single flapping wing is done by altering the condition of the upper boundary from free to enclosed just like the real wind tunnel boundary condition. The study done is broadly done in three different cases for the single wing in which the lower velocity value of 1m/s and 2 m/s is set up in the laminar model setup and the higher velocity of 3 m/s is done in the turbulent model. Most importantly the comparison between the modified and the previous data is done. And later on, the study of single wing is extended to the wing to wing case which is modeled in a way that the two wings are set between the two-supporting plane in the wing tunnel and the study of the flow field along with the aerodynamic value is done. The simulation of the formation flight study will be done near in future after the successful completion of the study of the wing to wing simulation case.

1.	CHAPTER 1 Introduction		1
1.1 Motivation 	1
1.2 Literature review 	8
2.	CHAPTER 2 COMSOL Multiphysics Simulation	11
2.1 CFD 3D flapping wing simulation – COMSOL Multiphysics11
2.2 Model set up introduction and establishment 	12
2.3 Overview on simulation flow field 	15
2.4 COMSOL Multiphysics laminar condition flap setting 	17
2.5 COMSOL Multiphysics turbulent condition flap setting 	30
2.6 Governing equation 	39
2.7 Flow field properties & Computational Fluid Dynamics 	41
2.8 simulation setting of formation flight of two flapping birds 	42
3.	CHAPTER 3 Results and Discussion	48
4.  CHAPTER 4 Conclusion	63
5.   APPENDIX 1
A-1 Physics selection 	72
A-2 Study type selection 	72
A-3 Wing loading setting 	73
A-4 Wing tunnel and 2 wings import 	73
A-5 Inlet boundary condition 	74
A-6 Symmetry wall condition 	74
A-7 Outlet boundary condition 	74
A-8 Prescribed displacement to the left wing 	74
A-9 Prescribed displacement to the right wing 	75
A-10 Open boundary condition to the walls 	75
A-11 Entire meshing of the model 	75



LIST OF FIGURES
Figure 1. Effect of suction force due to leading edge vortex		7
Figure 2. COMSOL Multiphysics software	12
Figure 3. Physics selection window 	15
Figure 4. Wind tunnel and flapping wing		16
Figure 5. Symmetric flow field 	17
Figure 6. Material selection for wind tunnel 	25
Figure 7. Material selection of the wings	25
Figure 8. Inlet boundary selection in the case of laminar velocity of 1 m/s26
Figure 9. The inlet boundary selection of laminar flow of 2 m/s 	26
Figure 10. Symmetry wall selection of the model	26
Figure 11. The outlet boundary selection of the wind tunnel 	27
Figure 12. The fixed constraint selection of the flapping wing 	28
Figure 13. The prescribed displacement assignment of the wing 	28
Figure 14. The property assignment of the wing 	28
Figure 15. The no slip boundary selection of the wind tunnel	28
Figure 16. Meshing element size setting window 	29
Figure 17. Wing meshing element type 	29
Figure 18. Wind tunnel meshing element type 	29
Figure 19. Total computation time step setting window 	30
Figure 20. Material selection of in Turbulent case 	35
Figure 21. Inlet boundary condition (turbulent model)	35
Figure 22. Symmetry boundary condition (turbulent model)	36
Figure 23. Fixed constraint setting on the wings 	36
Figure 24. Displacement setting to the wings (turbulent model)	36
Figure 25. Linear elastic material setting to wings 	37
Figure 26. No slip wall conditions (turbulent model)	37
Figure 27. Mesh size setting (turbulent model)	37
Figure 28. Mesh type selection of wing (turbulent model)	38
Figure 29. Mesh type selection of wind tunnel (turbulent model)	38
Figure 30. Total computation time setting (turbulent model)	39
Figure 31. Cylindrical flow, unsteady flow fields of Karman vortex 	41
Figure 32. Strouhal instability flow pattern of Karman vortex street 	42
Figure 33. Right wing of the flapping wing MAV 	43
Figure 34. Left wing of the flapping wing MAV 	43
Figure 35. Physics interface selection for the formation flight 	44
Figure 36. Wing to wing setup geometry 	45
Figure 37. Fully meshed model 	46
Figure 38. The no slip boundary condition comparison 	49
Figure 39. Wing Grid Settings (Rougher Grid)	49
Figure 40. Wind tunnel and airfoil grid setting (extremely finer)	50
Figure 41. Comparison of lift graph laminar condition of laminar case     1 m/s 	51
Figure 42. Comparison of lift graph trend laminar case of 2 m/s 	53
Figure 43. Comparison of lift graph trend turbulent case of 3 m/s 	53
Figure 44. Downwash and upwash generation in laminar 1m/s 	55
Figure 45. Downwash and upwash in laminar flow of 2 m/s 	57
Figure 46. Flow field of the flapping wing in case of laminar flow 1m/s	58
Figure 47. Streamline generation of laminar case 1 m/s 	59
Figure 48. Downstroke and upstroke in case of laminar flow 2 m/s 	59
Figure 49 Arrow volume flow field of turbulent condition 2 m/s	60
Figure 50. Streamline generation of laminar case 2 m/s 	61
Figure 51. Streamline flow field of turbulent model 3m/s 	62

LIST OF TABLES

Table I. Parameters used in the formation flight 	43
Table II. Dimension of the wind tunnel in formation flight 	45
Table III. Lift data at different wind speed 	54

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