本論文旨在由空氣動力參數分析出四旋翼無人機，在劇烈或不穩定的天氣條件下所表現出的物理現象。本篇研究的參數皆由計算流體力學軟體ANSYS Fluent v16.0所模擬而成。在開始正式的研究之前必須驗證所使用軟體之準確性，吾人選擇了APC 10x4.7 的葉片來做為驗證的案例，文章內將會和可靠的實驗數據進行比對。在四旋翼全機的部分，我們將專注於推力係數，亦會進行網格點收斂的測試。基於飛安的議題，本篇論文會深入探討當四旋翼無人機垂直掉落時的終端速度和可能致死率；最後，本論文會探討四旋翼無人機在各種惡劣的天氣條件下的性能表現，像是在強陣風或是強降雨的條件之下。吾人期待本篇論文可以幫助整個無人機產業，創造出更為安全的系統亦或是操作模式。

In this thesis, we are expecting to discover not only the aerodynamic parameters of the quad-copter, but also the physical phenomenon during the quad-copter flying in severe or abnormal weather conditions. The final goal is to analyze the physical phenomenon through the aerodynamic parameters and their vehicle performance behaviors. These parameters would be simulated by ANSYS Fluent v16.0 which is one of the Computational Fluid Dynamics (CFD) software, it is a popular, powerful, and convenient CFD tool to use. Before starting the research, we have to validate the simulation tool to make sure it is accurate enough to use, so a single propeller “APC 10x4.7” is chosen as our benchmark case to validate, and its power coefficient is computed and compared with satisfactory results.
After the validation we could start on the full-size quad-copter calculation, engaging the thrust coefficient simulation and a grid convergence test is implemented. Based on the references we had found and due to the recent aviation safety concerns, quad-copter going into a free-fall condition would take a major part in this research, resulting different free-fall terminal velocities and degrees of lethality. Last but not least, we will simulate the worst realistic situation in severe weather condition, such as flying in the heavy rain and different sinusoidal gust wind conditions, for both the hover and forward flight situations. It is found that the heavy rain effect is not as severe as the downdraft or the horizontal gust wind situations. There will be lots of UAVs in the future, but nowadays only a few papers involve an in-depth study of quad-copter falls into detrimental situations. It is hoped this research can help the UAV industries and academia to understand more about how severe weather can impact UAV’s performance and what should designers and operators do when quad-copter encounter each severe situations.

Contents
Abstract:	III
Contents	V
List of Figures	VII
List of Tables	XIV
List of Symbols	XV
Chapter 1 Introduction	1
Chapter 2 Research Background	4
2.1 Aerodynamics of Quad-copter	4
2.2 Literature Review	8
2.3 APC 10x4.7 Propeller	11
2.4 Full-Size Quad-copter	12
2.5 Gust Wind	15
2.6 Heavy Rain	15
2.7 Free-fall	16
Chapter 3 Numerical Modeling	18
3.1 Geometry Model Construction	19
3.2 Grid Generation	22
3.3 Governing Equations	26
3.4 Multiple Reference Frame	27
3.5 Flow Solver and Turbulence Modeling	29
3.6 Numerical Setup	30
3.7 Gust Wind Profile	31
3.8 Discrete Phase Model (DPM)	32
Chapter 4 Results and Discussion	36
4.1 Validation	36
4.2 Full-size Quad-copter Thrust Coefficient	43
4.3 Gird Convergence	47
4.4 Free-fall Conditions	50
4.5 Heavy Rain Conditions	54
4.6 Gust Wind during Hover	56
4.7 Gust Wind during Forward Flight	78
Chapter 5 Conclusions	93
References	96

 
List of Figures
Figure 1 DJI Phantom quad-copter. [1]	3
Figure 2 Decompositions of total blade-relative velocity W at radial location r. [5]	5
Figure 3 Blade geometry and velocity triangle at a random radius blade position. [5]	5
Figure 4 Velocity components in forward flight. [7]	8
Figure 5 Standard APC Slow Flyer 10 x 4.7 propeller blade.	11
Figure 6 Data of APC 10x4.7 propeller in chart. [15]	12
Figure 7 Top-view of quad-copter’s 3-D geometry construction.	13
Figure 8 Side-view of quad-copter’s 3-D geometry construction.	13
Figure 9 Full-size configuration of quad-copter.	14
Figure 10 Computational domain and disk of the propeller.	20
Figure 11 Rotor disk area of the propeller.	20
Figure 12 Computational domain and full-size quad-copter.	21
Figure 13 Rotor disk area and full-size quad-copter.	21
Figure 14 Mesh of single propeller and computational domain in global view.	23
Figure 15 Mesh of rotor disk area and propeller in global view.	24
Figure 16 Inflation on propeller cross-section in local view.	24
Figure 17 Mesh of computational domain and full-size quad-copter in global view.	25
Figure 18 Mesh of full-size quad-copter and rotor disk area in global view.	25
Figure 19 Inflation on quad-copter’s cross-section in local view.	26
Figure 20 Stationary and moving reference frames. [19]	27
Figure 21 Geometry with one rotating impeller. [19]	28
Figure 22 Geometry with two rotating impellers. [19]	29
Figure 23 Gust wind profile.	31
Figure 24 Reflect boundary condition under DPM. [19]	34
Figure 25 Trap boundary condition under DPM. [19]	34
Figure 26 Escape boundary condition under DPM. [19]	34
Figure 27 Rotor disk area using MRF scheme.	36
Figure 28 Propeller velocity contour at 4319 RPM.	40
Figure 29 Propeller velocity contour at 6528 RPM.	40
Figure 30 Pressure contour during 6528 RPM (Upper surface).	41
Figure 31 Pressure contour during 6528 RPM (Lower surface).	41
Figure 32 Velocity contour in side-view during 4319 RPM.	42
Figure 33 Velocity contour in side-view during 6528 RPM.	42
Figure 34 Propeller rotating direction. [25]	43
Figure 35 Full vehicle hover thrust coefficient. [26]	45
Figure 36 Velocity contour of full-size quad-copter at 4319 RPM.	46
Figure 37 Velocity contour of full-size quad-copter at 6528 RPM.	46
Figure 38 Grid convergence results for 4319 RPM case.	48
Figure 39 Grid convergence results for 6528 RPM case.	48
Figure 40 Quad-copter’s velocity vector at 4319 RPM.	49
Figure 41 Quad-copter’s velocity vector at 6528 RPM.	50
Figure 42 Free-fall collision (90˚). [3]	51
Figure 43 Drag force distribution during 0 RPM.	53
Figure 44 Drag force distribution during 4319 RPM.	53
Figure 45 Drag force distribution during 6528 RPM.	54
Figure 46 Droplet traces on quad-rotor created by DPM method under heavy rain of LWC=19 g/m3	55
Figure 47 Quadcopter thrust coefficient vs. different wind direction at 4319 RPM.	57
Figure 48 Thrust coefficient profile with gust wind direction from 0˚ at 4319 RPM during hover.	58
Figure 49 Thrust coefficient profile with gust wind direction from 45˚ tilted downward at 4319 RPM during hover.	58
Figure 50 Thrust coefficient profile with gust wind direction from 90˚ at 4319 RPM during hover.	59
Figure 51 Thrust coefficient profile with gust wind direction from -45˚ tilted upward at 4319 RPM during hover.	60
Figure 52 Thrust coefficient profile with gust wind direction from -90˚ updraft at 4319 RPM during hover.	60
Figure 53 Velocity vector of gust wind direction from 0˚ at 4319 RPM during hover.	61
Figure 54 Velocity vector of gust wind direction from 45 ˚ tilted downward at 4319 RPM˚ during hover.	61
Figure 55 Velocity vector of gust wind direction from 90˚ downdraft at 4319 RPM during hover.	62
Figure 56 Velocity vector of gust wind direction from -45˚ tilted upward at 4319 RPM during hover.	62
Figure 57 Velocity vector of gust wind direction from -90˚ updraft at 4319 RPM during hover.	63
Figure 58 Velocity contour of gust wind direction from 90˚ downdraft at 4319 RPM during hover.	63
Figure 59 Velocity contour of gust wind direction from -90˚ updraft at 4319 RPM during hover.	64
Figure 60 Q-criterion of gust wind direction from 90 ˚ downdraft at 4319 RPM during hover.	64
Figure 61 Q-criterion of gust wind direction from -90 ˚ updraft at 4319 RPM during hover.	65
Figure 62 Vorticity contour of gust wind direction from 0˚ at 4319 RPM during hover.	66
Figure 63 Vorticity contour of gust wind direction from 45 ˚ tilted downward at 4319 RPM during hover.	66
Figure 64 Vorticity contour of gust wind direction from 90˚ downdraft at 4319 RPM during hover.	67
Figure 65 Vorticity contour of gust wind direction from -45 ˚ tilted upward at 4319 RPM during hover.	67
Figure 66 Vorticity contour of gust wind direction from -90˚ updraft at 4319 RPM during hover.	68
Figure 67 Quadcopter thrust coefficient vs. different wind direction at 6528 RPM.	69
Figure 68 Compare 4319 RPM and 6528 RPM cases’ thrust coefficient.	71
Figure 69 Thrust coefficient profile with gust wind direction from 0˚ at 6528 RPM during hover.	71
Figure 70 Thrust coefficient profile with gust wind direction from 45˚ tilted downward at 6528 RPM during hover.	72
Figure 71 Thrust coefficient profile with gust wind direction from 90˚ downdraft at 6528 RPM during hover.	72
Figure 72 Thrust coefficient profile with gust wind direction from -45˚ tilted upward at 6528 RPM during hover.	73
Figure 73 Thrust coefficient profile with gust wind direction from -90˚ updraft at 6528 RPM during hover.	73
Figure 74 Velocity vector of gust wind direction from 0˚ at 6528 RPM during hover.	74
Figure 75 Velocity vector of gust wind direction from 45˚ tilted downward at 6528 RPM during hover.	74
Figure 76 Velocity vector of gust wind direction from 90˚ downdraft at 6528 RPM during hover.	75
Figure 77 Velocity vector of gust wind direction from -45˚ tilted upward at 6528 RPM during hover.	75
Figure 78 Velocity vector of gust wind direction from -90˚ updraft at 6528 RPM during hover.	76
Figure 79 Velocity contour of gust wind direction from -90˚ updraft at 6528 RPM during hover.	76
Figure 80 Velocity contour of gust wind direction from -90˚ updraft at 6528 RPM during hover.	77
Figure 81 Q-criterion of gust wind direction from 90˚ downdraft at	77
Figure 82 Q-criterion of gust wind direction from -90˚ updraft at	78
Figure 83 Velocity contour with 10.7 m/s forward speed.	79
Figure 84 Quadcopter thrust coefficient vs. different wind direction during forward flight.	81
Figure 85 Thrust coefficient profile without gust wind direction during forward flight.	83
Figure 86 Thrust coefficient profile with gust wind direction from 0˚ during forward flight.	83
Figure 87 Thrust coefficient profile with gust wind direction from 45˚ tilted downward during forward flight.	84
Figure 88 Thrust coefficient profile with gust wind direction from 90˚ downdraft during forward flight.	84
Figure 89 Thrust coefficient profile with gust wind direction from -45˚ tilted upward during forward flight.	86
Figure 90 Thrust coefficient profile with gust wind direction from -90˚ updraft during forward flight.	86
Figure 91 Comparing three different conditions’ thrust coefficient.	86
Figure 92 Q-criterion and velocity vector of gust wind direction from 0˚ during forward flight.	87
Figure 93 Q-criterion and velocity vector of gust wind direction from 45˚ tilted downward during forward flight.	87
Figure 94 Q-criterion and velocity vector of gust wind direction from -45˚ tilted upward during forward flight.	88
Figure 95 Q-criterion of gust wind direction from 90˚ updraft during forward flight.	88
Figure 96 Q-criterion of gust wind direction from -90˚ updraft during forward flight.	89
Figure 97 Vorticity contour without gust wind during forward flight	89
Figure 98 Vorticity contour without gust wind during forward flight (Aerial view) 90
Figure 99 Vorticity contour of gust wind direction from 0˚ during forward flight (Side view).	90
Figure 100 Vorticity contour of gust wind direction from 0˚ during forward flight (Aerial view).	91
Figure 101 Vorticity contour of gust wind direction from 45˚ tilted downward during forward flight.	91
Figure 102 Vorticity contour of gust wind direction from -45˚ tilted upward during forward flight.	92
 
List of Tables
Table 1 CT and CP of APC 10x4.7 propeller in different RPM. [15]	18
Table 2 Setup details for the mesh of single propeller.	23
Table 3 Boundary conditions of singe propeller and full-size quad-copter.	30
Table 4 Single rotor simulation results for 2377 RPM case.	37
Table 5 Single rotor simulation results for 4319 RPM case.	37
Table 6 Single rotor simulation results for 6528 RPM case.	38
Table 7 Single rotor simulation results for 2377 RPM case with different numbers of cells and turbulence models.	39
Table 8 Full-size quad-copter thrust coefficient in different RPM and number of cells.	44
Table 9 Grid convergence results for 4319 RPM case.	47
Table 10 Grid convergence results for 6528 RPM case.	47
Table 11 Terminal velocity in different RPM.	52
Table 12 Table of quad-copter in free-fall condition flying at 500 ft.	52
Table 13 LWC=19 g/m3 set-up.	54
Table 14 Comparison between flying in heavy rain and no rain condition.	56
Table 15 Results and data in hover during 4319 RPM.	56
Table 16 Results and data in hover during 6528 RPM.	68
Table 17 Thrust provided by four rotor blades.	80
Table 18 Drag force with no angle of attack.	80
Table 19 Results and data in forward flight.	81

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