近代汽車的外形設計與操作性能息息相關，而空氣動力學更是影響汽車性能的重要因子。在本論文中，吾人初步探討汽車空氣動力學和幾種不同降雨量之傾盆大雨，及其對汽車空氣動力學的影響與相關物理現象。在工業設計上對於汽車空氣動力學已有許多標準的驗證模型，例如Ahmed body、SAE reference model和DrivAer model，本研究選擇Ahmed body及DrivAer model兩種模型來進行相關空氣動力學的研究，前者為汽車空氣動力學中較經典且簡單的實驗模型，後者為近年較現代且真實的汽車實驗模型。吾人使用基於有限體積法(FVM)的計算流體力學軟體ANSYS Fluent v16.0來模擬Ahmed body和DrivAer model周圍的流場現象，計算域網格則使用CutCell法來進行生成，此外，傾盆大雨的二相流模式使用結合Eulerian-Lagrangian approach的Discrete Phase Model (DPM)來建構。在成功的對兩種汽車模型進行驗證後，針對傾盆大雨之模擬，吾人考慮三種汽車行進速度與三種大雨量，結果發現在不同車速時，流經車體表面的流體加速性均有變小的趨勢，使得流場內壓力有著顯著的變化，此結果將造成兩種外形汽車的阻力各有不同的改變量，而負升力則有類似的變小趨勢。期待本研究結果能夠成為未來汽車工業的參考，甚或能增進汽車之行駛安全。

Automobile configuration design is closely related to its operational performance, and aerodynamics is one of the most influential factors for modern automobile maneuverability. In this thesis, we not only investigate on the preliminary aerodynamics of automobiles, but also deal with some physical phenomenon of automotive aerodynamic behavior under some severe rain conditions. There are several major benchmark models for the aerodynamic study on automobiles, such as Ahmed body, SAE reference model, and DrivAer model. The Ahmed body and the DrivAer model are chosen for our automotive aerodynamics research. The first model is a classical reference model with a simple shape, and the second model is a more realistic and newer model created by Technical University of Munich. The Finite Volume Method (FVM) code ANSYS Fluent v16.0 was implemented to simulate the flow field of Ahmed body and DrivAer model, and their grids are generated by cutcell assembly meshing method. In addition, we used the Discrete Phase Model (DPM) which is the combined Eulerian-Lagrangian approach to modeling the two-phase flow for the heavy rain condition. In the case of heavy rain, it is found that the acceleration of fluid flow through the body surface becomes smaller, and the pressure distribution of the flow field will also change significantly. According to our result, the drag of these two models has different effects due to their different degree of bluntness, and the negative lift of both configurations will be reduced.

Contents
Abstract	III
Contents	V
List of Figures	VII
List of Tables	XIV
Nomenclature	XVI
Chapter 1 Introduction	1
Chapter 2 Research Background	5
2.1 Aerodynamics of Automobile	5
2.2 Ahmed body	9
2.3 DrivAer model	11
2.4 Heavy Rain	12
Chapter 3 Numerical Modeling	15
3.1 Geometry Model Construction	15
3.2 Governing Equations	17
3.3 Grid Generation	17
3.4 Flow Solver and Turbulence Model	21
3.5 Numerical Setup	23
3.6 Heavy Rain Modeling	26
Chapter 4 Validation	31
4.1 Ahmed body	31
4.2 DrivAer model	36
Chapter 5 Numerical Results	43
5.1 Scale Conversion of Ahmed Body	43
5.2 Heavy Rain Condition of Ahmed Body	44
5.3 Scale Conversion of DrivAer Model	46
5.4 Heavy Rain Condition of DrivAer Model	50
Chapter 6 Conclusions	71
References	73

List of Figures
Figure 1 When designing a car, it is influenced by many requirements. It   should consider the careful balance between them is required by the market [6].	5
Figure 2 Aerodynamic forces and moments on the automobile. [6]	7
Figure 3 Drag coefficient vs. slant angle (a)simple body (b)automobile. [6]	9
Figure 4 The wake and vortices behind the automobile. [6]	9
Figure 5 Geometry of the Ahmed body. [8]	10
Figure 6 Drag coefficients for various slant angles of the Ahmed body. [1]	11
Figure 7 Geometry of DrivAer model with Fastback. [2]	12
Figure 8 DrivAer model with different rear-top. [2]	12
Figure 9 Computational domain of the Ahmed body case.	16
Figure 10 Computational domain of the DrivAer model case.	16
Figure 11 Mesh of Ahmed body in global view.	19
Figure 12 Mesh of Ahmed body in local view	20
Figure 13 Mesh of FSwMwoW in global view.	20
Figure 14 Mesh of FSwMwoW in local view.	21
Figure 15 Inflation layers between the hood and windshield of FSwMwoW.	21
Figure 16 Computational domain with boundary configuration of Ahmed case.	24
Figure 17 Computational domain with boundary configuration of DrivAer case.	24
Figure 18 Injection plane of DrivAer model.	28
Figure 19 Setup of the heavy rain in the Discrete Phase Model.	29
Figure 20 Physics of splashing, momentum, heat, and mass transfer on the surface by ANSYS [13].	30
Figure 21 Lift coefficients vs. time of Ahmed body.	32
Figure 22 Drag coefficient and lift coefficient of the Ahmed case.	32
Figure 23 Velocity profile of the Ahmed case at central symmetry plane (z = 0 mm).	34
Figure 24 Velocity contour of the Ahmed case at central symmetry plane (z = 0 mm).	34
Figure 25 Pressure contour of the Ahmed case at central symmetry plane (z = 0 mm).	35
Figure 26 Vortex core region by lambda-2 criterion on Ahmed body with pressure contour (body surface and symmetry plane)	35
Figure 27 Drag coefficient converge history of FSwMwoW.	36
Figure 28 Lift coefficient converge history of FSwMwoW.	37
Figure 29 Drag coefficient and lift coefficient of the FSwMwoW.	37
Figure 30 Y-plus distributions on DrivAer model surface along the x-direction of FSwMwoW.	38
Figure 31 Pressure coefficient distributions over the top surface at central symmetry plane of FSwMwoW.	39
Figure 32 Pressure coefficient distributions over the bottom surface at central symmetry plane of FSwMwoW.	39
Figure 33 Velocity contour of the FSwMwoW at central symmetry plane.	40
Figure 34 Pressure contour of the FSwMwoW at central symmetry plane.	40
Figure 35 Vortex core region by lambda-2 criterion on DrivAer model with pressure contour (body surface and symmetry plane) (a)Mirror wake (b)A-pillar vortex (c)Rear Vortex.	41
Figure 36 Drag coefficient and lift coefficient compared with no rain and LWC= 29 g/m3 of Ahmed body.	44
Figure 37 Velocity contours on the symmetry plane of the rear top of Ahmed body (a)No rain (b)LWC=29 g/m3.	45
Figure 38 Vorticity contours and velocity vectors of the Ahmed body in the rearview (a)No rain (b)LWC=29 g/m3	45
Figure 39 Pressure coefficient distributions over surface at central symmetry plane of Ahmed body under different LWC.	46
Figure 40 Drag and lift coefficient with different scale conversion and solver (a) 40% scaled, V∞=40 m/s and steady solver (b) 100% scaled, V∞=16 m/s and steady solver (c) 100% scaled, V∞=16 m/s and transient solver.	49
Figure 41 Y-plus distributions on DrivAer surface along the x-direction. (a) 40% scaled, V∞=40 m/s (b) 100% scaled, V∞=16 m/s.	49
Figure 42 Drag coefficient converges history of LWC=29 g/m3.	50
Figure 43 Lift coefficient converges history of LWC=29 g/m3.	51
Figure 44 Drag and lift coefficient compared with different LWC.	52
Figure 45 Wall shear contours of the FSwMwoW on the surface (a)No rain (b)LWC=39 g/m3.	53
Figure 46 Velocity contours of the FSwMwoW at the central symmetry plane (a)No rain (b)LWC=19 g/m3.	54
Figure 47 Velocity contours of the FSwMwoW at the central symmetry plane (a)No rain (b)LWC=29 g/m3.	55
Figure 48 Velocity contours of the FSwMwoW at the central symmetry plane (a)No rain (b)LWC=39 g/m3.	55
Figure 49 Pressure contours of the FSwMwoW at the central symmetry plane (a)No rain (b)LWC=19 g/m3.	55
Figure 50 Pressure contours of the FSwMwoW at the central symmetry plane (a)No rain (b)LWC=29 g/m3.	56
Figure 51 Pressure contours of the FSwMwoW at the central symmetry plane (a)No rain (b)LWC=39 g/m3.	56
Figure 52 Pressure coefficient distributions over the top surface at central symmetry plane of FSwMwoW under different LWC.	57
Figure 53 Pressure coefficient distributions over the bottom surface at central symmetry plane of FSwMwoW under different LWC.	57
Figure 54 Pressure contours of the FSwMwoW at the 50% location from symmetry to side (a)No rain (b)LWC=29 g/m3.	58
Figure 55 Pressure contours of the FSwMwoW at the 80% location from symmetry to side (a)No rain (b)LWC=29 g/m3.	58
Figure 56 Pressure contours of the FSwMwoW at the 90% location from symmetry to side (a)No rain (b)LWC=29 g/m3.	58
Figure 57 Vortex core region by lambda-2 criterion on DrivAer model with pressure contour (body surface and symmetry plane) (a)No rain (b)LWC=29 g/m3.	59
Figure 58 Pressure contours of the FSwMwoW in front view (a)No rain (b)LWC=19 g/m3.	60
Figure 59 Pressure contours of the FSwMwoW in front view (a)No rain (b)LWC=29 g/m3.	60
Figure 60 Pressure contours of the FSwMwoW in front view (a)No rain (b)LWC=39 g/m3.	60
Figure 61 Pressure contours of the FSwMwoW in the rearview (a)No rain (b)LWC=19 g/m3.	61
Figure 62 Pressure contours of the FSwMwoW in the rearview (a)No rain (b)LWC=29 g/m3.	61
Figure 63 Pressure contours of the FSwMwoW in the rearview (a)No rain (b)LWC=39 g/m3.	61
Figure 64 Drag and lift coefficients vs. Reynolds number. The curves are fitted by the fourth-order polynomial.	62
Figure 65 Drag and lift coefficient compared with different free stream velocity under LWC=29 g/m3.	63
Figure 66 Pressure coefficient contours of the FSwMwoW at the central symmetry plane under LWC=29 g/m3 (a)V∞ =16 m/s (b)V∞ =22.22 m/s.	64
Figure 67 Pressure coefficient contours of the FSwMwoW at the central symmetry plane under LWC=29 g/m3 (a)V∞ =16 m/s (b)V∞ =27.78 m/s.	65
Figure 68 Pressure coefficient contours of the FSwMwoW in front view under LWC=29 g/m3 (a)V∞ =16 m/s (b)V∞ =22.22 m/s.	65
Figure 69 Pressure coefficient contours of the FSwMwoW in front view under LWC=29 g/m3 (a)V∞ =16 m/s (b)V∞ =27.78 m/s.	65
Figure 70 Pressure coefficient contours of the FSwMwoW in front view under LWC=29 g/m3 (a)V∞ =16 m/s (b)V∞ =22.22 m/s.	66
Figure 71 Pressure coefficient contours of the FSwMwoW in front view under LWC=29 g/m3 (a)V∞ =16 m/s (b)V∞ =27.78 m/s.	66
Figure 72 Pressure coefficient distribution over the top surface at central symmetry plane of FSwMwoW compared with different free stream velocity under LWC=29 g/m3.	67
Figure 73 Pressure coefficient distribution over the bottom surface at central symmetry plane of FSwMwoW compared with different free stream velocity under LWC=29 g/m3.	67
Figure 74 Comparison of water film height contour (a) Film height contour at 50MPH (22.22m/s) from Karbon et al. [3] (b) Case of 27.78m/s under LWC=29 g/m3.	69
Figure 75 Particles trace of DrivAer model along the x-direction.	69
Figure 76 Particles trace of DrivAer model in local view.	70
 
List of Tables
Table 1 Grid properties of the Ahmed body.	18
Table 2 Grid properties of the DrivAer model.	19
Table 3 Boundary conditions of two cases in ANSYS Fluent.	23
Table 4 Numerical setups of Ahmed body in ANSYS Fluent.	25
Table 5 Numerical setups of DrivAer model in ANSYS Fluent.	25
Table 6 Particle properties in different LWC.	27
Table 7 Skin friction drag and pressure drag coefficient compared with Ahmed body and DrivAer model.	42
Table 8 Drag and lift coefficient compared with the different scale in same Reynolds number of Ahmed body.	43
Table 9 Skin friction drag and pressure drag coefficient compared with different LWC.	45
Table 10 Drag and lift coefficient compared with the different scale in same Reynolds number of DrivAer model.	47
Table 11 Drag and lift coefficient compared with the different solver.	48
Table 12 Skin friction drag and pressure drag coefficient compared with the different scale in same Reynolds number.	49
Table 13 Drag and lift coefficient under different LWC.	51
Table 14 Skin friction drag and pressure drag coefficient compared with different LWC.	53
Table 15 Drag and lift coefficient under different free stream velocity under LWC=29 g/m3.	63
Table 16 Skin friction drag and pressure drag coefficient compared with different free stream velocity under LWC=29 g/m3.	63
Table 17 Drag and lift coefficient under different free stream velocity without water film model under LWC=29 g/m3.	68

References
[1]	Ahmed, S.R., Ramm, G., and Faltin, G., “Some Salient Features of the Time-averaged Ground Vehicle Wake,” SAE Technical Paper, No.840300, 1984.
[2]	Heft, A.I., Indinger, T., and Adams, N.A., “Introduction of a New Realistic Generic Car Model for Aerodynamic Investigations,” SAE Technical Paper, No.2012-01-0168, 2012.
[3]	Karbon, K.J., and Longman, S.E., “Automobile Exterior Water Flow Analysis Using CFD and Wind Tunnel Visualization,” SAE Technical Paper, No.980035, 1998.
[4]	Gaylard, A.P., Kirwan, K., and Lockerby, D.A., “Surface Contamination of Cars: A Review,” Journal of Automobile Engineering, Vol. 231(9), 2017, pp. 1160-1176.
[5]	Hu, X., Liao, L., Lei, Y., Yang, H., Fan, Q., Yang, B., Chang, J., and Wang, J., “A Numerical Simulation of Wheel Spray for Simplified Vehicle Model Based on Discrete Phase Method,” Advances in Mechanical Engineering, Vol. 7(7)1-8, 2015.
[6]	Hucho, W.H., and Souran, G., “Aerodynamics of Road Vehicles,” Annual Review of Fluid Mechanics, Vol. 25, 1993, pp. 485-537.
[7]	Jakirlic, S., Jester-Zurker, R., and Tropea, C., “9th ERCOFTAC/IAHR/COST Workshop on Refined Turbulence Modelling,” EROCFTAC Bulletin, October 2001.
[8]	Meile, W., Brenn, G., Reppenhagen, A., Lechner, B., and Fuchs, A., “Experiments and Numerical Simulations on the Aerodynamics of the Ahmed Body,” CFD Letters, Vol. 3(1), March 2011.
[9]	Khan, R.S., and Umale, S., “CFD Aerodynamic Analysis of Ahmed Body,” Journal of Engineering Trends and Technology, Vol. 18, December 2014.
[10]	“NASA Will Study Heavy Rain Effect on Wing Aerodynamics,” Aviation Week & Space Technology, February 1989.
[11]	Thompson, B. E., and Jang, J., “Aerodynamic Efficiency of Wings in Rain,” Journal of Aircraft, Vol. 33, No. 6, 1996.
[12]	Thompson, B. E., Jang, J., and Dion, J. L., “Wing Performance in Moderate Rain,” Journal of Aircraft, Vol. 32, No. 5, 1995.
[13]	“ANSYS FLUENT Theory Guide,” ANSYS Inc., November 2011.
[14]	“ANSYS Mesh User’s Guide,” ANSYS Inc., November 2010.
[15]	Kloek, L.J.R., “A Validation Study on the Rooftop Flow Behaviour of Road Vehicles,” M.S. thesis, Delft University of Technology, November 2013.
[16]	Wojciak, J., Schnepf, B., Indinger, T., and Adams, N. “Study on the Capability of an Open Source CFD Software for Unsteady Vehicle Aerodynamics,” SAE International Journal of Commercial Vehicles, Vol. 5(1), July 2012.
[17]	Willis, T.P., and Tattelman, P. “Drop-Size Distributions Associated with Intense Rainfall,” Journal of Applied Meteorology, Vol. 28, January 1989.
[18]	Dunham, R.E. Jr., “The Potential Influence of Rain on Airfoil Performance,” Von Karman Institute for Fluid Dynamics, 1987.
[19]	Ulbrich, C.W., “Natural Variations in the Analytical Form of the Raindrop Size Distribution,” Journal of Applied Meteorology, Vol. 22, 1983, pp. 1764-1775.
[20]	Markowitz, A.M., “Raindrop Size Distribution Expression,” Journal of Applied Meteorology, Vol. 15, 1976, pp. 1029-1031.