近年來拍翼微飛行器變得越來越受重視，也使得更多人投入微飛行器的研究，但大多數微型拍翼飛行器研究都是分析在晴天下飛行的蟲類及小型鳥類。過去幾年間，台灣曾發生許多因惡劣天氣所引發的災害，如像是極大量的暴雨或是使人困在山區的濃霧等情況，在這些特殊情況下，使用微型拍翼飛行器來進行偵測或是協助搜救能顯著的增加救難效率。雖然微型拍翼飛行器能靈活的運動，但也因為其輕巧、靈活的特性，在飛行過程中非常容易受到周遭大氣環境變化的影響。因此，微型拍翼飛行器在特殊大氣環境下飛行性能變化是本研究團隊長期研究的一項重要課題。
  在本研究中我們依據名為Morpho peleides的蝴蝶建立其幾何外形，使用GAMBIT和ANSYS前處理軟體產生網格，並結合軟體FLUENT中UDF(User Define Function)及動態網格機制來模擬蝴蝶在不同攻角的拍翼飛行，大雨計算則是運用FLUENT內建DPM模組(Discrete Phase Model)來模擬蝴蝶在惡劣天氣下飛行空氣動力性能變化。
  本研究中吾人嘗試使用四種不同網格數的網格來進行驗證，結果不管是在升力係數還是阻力係數全都得出相近且幾乎一樣的數值。根據幾個蝴蝶固定在不同攻角下晴天飛行的結果，我們得知當蝴蝶在飛行時隨著攻角的上升，整個拍動週期的平均升力也會跟著增加，且升力係數曲線的趨勢會與真實擺動身體飛行的蝴蝶更加近似。最後我們比較在晴天及大雨下的飛行狀況，蝴蝶在大雨的情況下飛行，升力係數會較晴空時顯著的下降，並且升力減少的百分比會隨著攻角的上升而減少。在降雨量為25 g/m3時，升力減少的百分比會從618.6%減少至60.389%。當降雨量為39 g/m3時，則會從1057%降至101.537%。因此，吾人認為拍翼飛行受到大雨的影響程度可以透過提高拍翼的攻角而得到緩解。

In recent years, flapping wing technology is becoming more popular, and Micro Air Vehicle (MAV) has received great attention from researchers. For most people their desired MAV performance is limited in the flapping mode of small birds and insects under clear weather situation. But in past years Taiwan has experienced many disasters caused by detrimental and severe weather, such as extremely heavy rain and very thick fog. In such cases if MAV could put into use to help the rescue mission, it could significantly improve the efficiency of rescue. However, the insect-like MAV is very small and light, and it's very sensitive to sudden change of atmospheric surroundings. Therefore, maintain the flapping wing MAV flight quality in extreme weather will be an important issue.
  In this study, we constructed a geometric model of the butterfly based on a true Morpho peleides and created a grid system by GAMBIT and ANSYS preprocessing software, then use the CFD software FLUENT combine with the User Define Function (UDF) to analyze the relationship between the flow field and other aerodynamic phenomenon. For our simulation, we programing a grid convergence process first to verify the simulation of our 3-D butterfly flapping motion, and the flapping-wing aerodynamic parameters such as lift coefficient and drag coefficient are almost same with four grid systems in clam atmospheric condition.
  According to several cases, we can find some result. When the butterfly increases the pitch angle of flapping motion in forward flight, the lift coefficient will increase too. Then the trend of the lift coefficient curve will more approximate with the lift coefficient of the true butterfly in forward flight. In our abnormal atmospheric cases, we used the Discrete Particles Model (DPM) in FLUENT to simulate the 3-D butterfly flapping motion in heavy rain condition. In our result, the average values of lift coefficient under the heavy rain condition are lower than the case in normal atmospheric condition. When the liquid water content (LWC) is 25 g/m3, the reduction rate of lift coefficient would be reduced to 60.389% from 618.6% with the rising angle of attack. In the situation of the liquid water content is 39 g/m3, the reduction rate of lift coefficient will decrease from 1057% to 101.537% with the gradual increase in the angle of attack. Therefore, the effect of the heavy rain can be relieved by changing the angle of attack in forward flight, and the higher angle of attack can relieve more impact of heavy rain.

Content
Abstract:	III
List of Tables	VII
List of Figures	VIII
Nomenclatures	XI
Chapter 1	1
Introduction	1
Chapter 2	4
Research Background	4
2-1 Literature Review of Flapping	4
2-2 Heavy Rain	9
2-3 Fog	10
Chapter 3	13
Numerical Modeling	13
3-1 Geometry Model Construction and Grid Generation	13
3-2 Preprocessing	17
3-3 Governing Equations	20
3-4 Dynamic Mesh	20
3-5 Flow Solver	22
3-6 Discrete Phase Model	26
3-7 Case of Heavy Rain	30
Chapter 4	33
Results and Discussion	33
4-1 The Verification of 2-D Simulation	33
4-2 The Verification of 3-D Simulation	35
4-3 Numerical Simulation under the Different Angles of Attack	36
4-4 Numerical Simulation of the Heavy Rain and Fog	38
Chapter 5	68
Conclusion	68
References	71
Appendix A	74
Appendix B	76

List of Tables
Table 3.1 The parameters of the geometric half butterfly mode.	14
Table 3.2 The number of the unstructured grids	14
Table 3.3 The parameter of the flapping motion	18
Table 4.1 Classification of the cases	41
Table 4.2 Mean lift in different numerical simulation	41
Table 4.3 Classification of the different grids	41
Table 4.4 Average lift and drag coefficient in different case	41
Table 4.5 The lift coefficient in three different time	42
Table 4.6 The drag coefficient in three different time	42
Table 4.7 The parameters of the heavy rain.	42
Table 4.8 Numerical results for flapping wing of lift coefficients degradation percentage for heavy rate case (LWC= 25 g/m3)	43
Table 4.9 Numerical results for flapping wing of lift coefficients degradation percentage for heavy rate case (LWC= 39 g/m3)	43
Table 4.10 Numerical results for flapping wing of lift coefficients for heavy rate case in different time (LWC= 25 g/m3)	44
Table 4.11 Numerical results for flapping wing of lift coefficients for heavy rate case in different time (LWC= 25 g/m3)	44
Table 4.12 The lift coefficient of case 2 in heavy rain condition	45
Table 4.13 The lift coefficient of case 3 in heavy rain condition	45
Table 4.14 The lift coefficient of case 4 in heavy rain condition	45
Table 4.15 The lift coefficient of case 5 in heavy rain condition	46
Table 4.16 The parameters of fog	46
Table A.1 Average lift and drag coefficient in different case	74

List of Figures
Fig. 1.1 Reynolds number range for flight vehicles.	3
Fig. 2.1 Clap and fling Mechanism	5
Fig 2.2 Flapper flow visualization with smoke released from the leading edge wing at different time.	6
Fig. 2.3 Compare the 2-D linear translation with 3-D flapping translation 	7
Fig. 2.4 Saturation vapor pressure	12
Fig. 3.1 (a) A real butterfly model and (b) a geometric butterfly model.	15
Fig. 3.2 The Calculated domain.	16
Fig. 3.3 Grids around the flapping-wing	16
Fig 3.4 The 3-D flapping motion.	18
Fig. 3.5 The solutions loop for FLUENT solve process	19
Fig. 3.6 1D control volume	25
Fig. 3.7 Heat, mass, and momentum transfer between discrete and continuous phase	29
Fig. 4.1 Grids and calculated domain	47
Fig. 4.2 The 2-D flapping motion	47
Fig. 4.3 Lift vs. period comparing with references	48
Fig. 4.4 Drag vs. period comparing with references	48
Fig. 4.5 Pressure contour at different instants	49
Fig. 4.6 The lift and drag coefficient in different grid types.	50
Fig. 4.7 The lift and drag coefficient in different grid types.	50
Fig. 4.8 The forward flight butterflies lift and drag coefficient.	51
Fig. 4.9 The lift and drag coefficient profile in one period	51
Fig. 4.10 The lift coefficient profile in six periods	52
Fig. 4.11 The drag coefficient profile in six periods	52
Fig. 4.12 The pressure contour of case 2	53
Fig. 4.13 The pressure contour of case 3	54
Fig. 4.14 The pressure contour of case 4	55
Fig. 4.15 The pressure contour of case 5	56
Fig. 4.16 The lift and drag coefficient profile in one period (LWC=25 g/m3)	57
Fig. 4.17 The lift and drag coefficient profile in one period (LWC=39 g/m3)	57
Fig. 4.18 The lift coefficient profile in one period (LWC = 25&39 g/m3)	58
Fig. 4.19 The pressure contour of case 2 in the heavy rain conditions (LWC=25 g/m3)	59
Fig. 4.20 The pressure contour of case 3 in the heavy rain conditions (LWC=25 g/m3)	60
Fig. 4.21 The pressure contour of case 4 in the heavy rain conditions (LWC=25 g/m3)	61
Fig. 4.22 The pressure contour of case 5 in the heavy rain conditions (LWC=25 g/m3)	62
Fig. 4.23 The pressure contour of case 2 in the heavy rain conditions (LWC=39 g/m3)	63
Fig. 4.24 The pressure contour of case 3 in the heavy rain conditions (LWC=39 g/m3)	64
Fig. 4.25 The pressure contour of case 4 in the heavy rain conditions (LWC=39 g/m3)	65
Fig. 4.26 The pressure contour of case 5 in the heavy rain conditions (LWC=39 g/m3)	66
Fig. 4.27 The lift coefficient profile in ten periods	66

References

[1]	Tai, Y. C. and Ho, C. M., “MEMS Wing Technology for a Battery-powered Ornithopter,” The 13th IEEE International Conference on Micro Electro Mechanical Systems, pp. 799-804, 2000.
[2]	Mueller, J. T. and DeLaurier, J. D., “An Overview of Micro Air Vehicle Aerodynamics,” Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, Vol. 195, pp. 1-9, 2001.
[3]	Weis-Fogh, T., “Quick Estimates of Flight Fitness in Hovering Animals,” Including Novel Mechanisms for Lift Production, The Journal of Experimental Biology, Vol. 59, pp. 169-230, 1973.
[4]	Sane, S. P., “The Aerodynamics of Insect Flight,” The Journal of Experimental Biology, Vol. 206, pp. 4191-4208, 2003.
[5]	Ellington, C.P. et al., “Leading-edge Vortices in Insect Flight,” Nature, Vol. 384, pp. 626-630, 1996.
[6]	Maxworthy, T., “Experiments on the Weis-Fogh Mechanism of Lift Generation by Insects in Hovering Flight. Part 1. Dynamics of the ‘Fling’,” J. Fluid Mech., Vol. 93, pp. 47-63, 1979.
[7]	Betts, C.R. and Wotton, R.J. “Wing Shape and Behavior in Butterflies: a Preliminary Analysis,” The Journal of Experimental Biology, Vol. 138, pp. 271-288, 1988.
[8]	Brodsky, A.K. “Vortex Formation in the Tethered Flight of the Peacock Butterfly Inachis Io L. (Lepidoptera, Nymphalidae) and Some Aspects of Insect Flight Evolution,” The Journal of Experimental Biology, Vol. 161, pp. 77-95, 1991.
[9]	Wang, Z. J., “Two Dimensional Mechanism for Insect Hovering,” Physical Review Letters, Vol. 85, No.10, pp. 2216-2219, 2000.
[10]	Sun, M. and Du, G., “Lift and Power Requirements of Hovering Flight in Drosophila Virilis,” The Journal of Experimental Biology, Vol. 205, pp. 2413-2427, 2002.
[11]	Trizila, P., Kang, C., Visbal, M. and Shyy, W., “A Surrogate Model Approach in 2D versus 3D Flapping Wing Aerodynamic Analysis,” AIAA Journal, pp. 2008-5914.
[12]	Trizila, P., “Aerodynamics of Low Reynolds Number Rigid Flapping Wing under Hover and Freestream Conditions,” Ph.D. Dissertation, Michigan University, 2011.
[13]	Liu, H. and Kawachi, K., “A Numerical Study of Insect Flight,” J. of Comp. Physics, Vol. 146, No.1 pp. 124-156, 1998.
[14]	Huang, H. and Sun, M, “Forward Flight of a Model Butterfly: Simulation by Equations of Motion Coupled with the Navier–Stokes Equations,” Acta Mechanica Sinica, Vol. 28, pp. 1590-1601, 2012.
[15]	Shyy, W., Berg, M. and Ljungqvist, D., “Flapping and Flexible Wings for Biological and Micro Air Vehicles,” Progress in Aerospace Sciences, Vol. 35, No. 5, pp. 455-506, 1999.
[16]	Wang, W. Z, “A Study of 3-D Flapping Wing Performance under Severe Weathers,” MS thesis, Tamkang University, 2012.
[17]	Huang, C. K., “Numerical Simulation of Gust Wind and Heavy Rain on Aerodynamic Driven Devices,” Ph.D. Dissertation, Tamkang University, 2011.
[18]	Rhode, R. V., “Some Effects of Rainfall on Flight of Airplanes and on Instrument Indications,” NACA TN 903, 1941.
[19]	Donald, C., Meteorology Today: An Introduction to Weather, Climate, and the Environment. Cengage Learning, 2009.
[20]	Dudley, R. “Biomechanics of Flight in Neotropical Butterflies:  Morphometrics Kinematics,” The Journal of Experimental Biology, Vol. 150, pp. 37-53, 1990.
[21]	FLUENT 6.2’s User Guide.
[22]	Dunham, R. E. Jr., “The Potential Influence of Rain on Airfoil Performance,” Von Karman Institute for Fluid Dynamics, 1987.
[23]	Markowitz, A. M., “Raindrop Size Distribution Expression,” Journal of Applied Meteorology, Vol. 15, 1976, pp. 1029-1031.
[24]	Willis, P. T., “Functional Fits to Some Observed Drop Size Distributions and Parameterization of Rain,” Journal of Atmospheric Science, Vol. 41, No. 9s, 1984, pp. 1648-1661.
[25]	Ulbrich, C. W., “Natural Variations in the Analytical Form of the Raindrop Size Distribution,” Journal of Applied Meteorology, Vol. 22, 1983, pp. 1764-1775.
[26]	Shyy, W. et al. “Recent Progress in Flapping Wing Aerodynamics and Aeroelasticity,” Progress in Aerospace Sciences, Vol. 46, pp. 284-327, 2010.
[27]	Eldridge, Ralph G., “The Relationship between Visibility and Liquid Water Content in Fog,” Journal of the Atmospheric Sciences, Vol. 28, pp.1183–1186, 1971.