近年惡劣天氣狀況越來越常發生，而此狀況對於飛機起降時會有顯著的安全影響，因此在本研究中吾人將分析傾盆大雨對於飛機的空氣動力學以及飛行性能的影響。本文選擇美國太空總署NASA的Trap-Wing高升力模型來進行相關的空氣動力學研究，Trap-Wing 是NASA所建立之高升力裝置研究的標準驗證型，經由風洞測試以及CFD模擬驗證。吾人以ANSYS Fluent v16.0 CFD軟體來模擬Trap-Wing於不同攻角時的性能參數改變。此外使用了結合Eulerian-Lagrangian 法則的Discrete Phase Model (DPM)來模擬傾盆大雨現象。而在成功地對Trap-Wing進行驗證後，也會加入傾盆大雨之模擬，並將表面摩擦係數納入考量，以模擬出真實飛機在飛行時的性能表現。對比Trap-Wing在下雨以及無雨之情況下之升阻力性能。在升力係數上各攻角均會明顯下降，而阻力係數在五度至二十度攻角時下雨之阻力係數會上升；但是在二十至三十五度時阻力係數卻是下降的。此外，由於大雨的作用有助於延緩氣流從機翼表面分離，本研究結果將對於未來航機操作及工程分析上有若干參考價值。

In recent years, the severe weather condition has significant impact on the take-off and landing phases of the flight. In this research, we focused on analyzing aerodynamic influences under the heavy rain condition and its physical phenomena will be also discussed. To understand the more realistic configuration during the take-off and landing phases, the recent NASA Trap-Wing model was chosen as the aerodynamic test case for our investigation. Trap-Wing model is now becoming the benchmark of high-lift prediction, and this model including fuselage, main wing, slat and flap, the “1st AIAA CFD High Lift Prediction Workshop (HiLiftPW-1)” provides the data by wind tunnel test and CFD simulation. We implement ANSYS Fluent v16.0 software to simulate the low speed 0.2 Mach number situations, and investigate the performance and flow field would change physically at different angles of attack. In addition, the combined Eulerian-Lagrangian approach of Discrete Phase Model (DPM) was used to simulate the two-phase flow during the heavy rain situation. After successfully validating the Trap-Wing model, then the simulation of heavy rain will be added to the same configuration. Our simulation also took wing and fuselage surface roughness effect into account to simulate more closely the performance of passenger aircraft during its flight in the real high lift devices deployment situation. The effects of liquid water content, angle of attack and 3-D wing span on the distribution of the surface water film are also discussed.
Current work reveal that the lift coefficient would reduce in the heavy rain situation at any AoA and the drag coefficient would increase when the AoA is between 5 to 20 deg, just as we expected; but it will decrease further at the higher AoAs between 20 to 35 deg under the same heavy rain situation. However the Trap-Wing configuration’s lift-to-drag ratio observed a several percent reduction at all angle of attacks. Also based on our research, the heavy rain will postpone the stall angle of attack, and the stall phenomenon is becoming less drastic. This work broadly studies the thickness of water film on a 3-D wing with high lift devices in heavy rain conditions and could be of some reference value for future operation or engineering applications.

Contents
Abstract	III
Contents	V
List of Figures	VII
List of Tables	XIII
Nomenclature	XIV
Chapter 1 Introduction	1
Chapter 2 Research Background	6
2-1 NASA High Lift Trap-Wing	6
2-2 Flow Physics of High Lift Devices	8
2-3 Physics and Influences of Wings in Rain	9
Chapter 3 Numerical Modeling	14
3-1 Physical Model	14
3-2 Governing Equations	15
3-3 Turbulence Model	16
3-4 Heavy Rain Model	18
3-5 Wall Function with Surface Roughness	20
3-6 Mesh Generation	22
3-7 Numerical Solver	26
3-8 Grids Converge	28
Chapter 4 Validation	29
4-1 Validation for Pressure Coefficient Chart	29
4-2 Validation for Lift and Drag	39
Chapter 5 Numerical Results	43
5-1 Surface Roughness	43
5-2 Heavy Rain	46
Chapter 6 Conclusions	73
References	75


 
List of Figures
Figure 1 Different types of the high lift flap [2].	3
Figure 2 Typical high-lift airfoil and its effect on lift coefficient [3].	4
Figure 3 NASA Trap-Wing configuration 1 with slats at 30 deg. and flaps at 25 deg. compared with stowed [4].	6
Figure 4 NASA Trap-Wing installed vertically inside the NASA wind tunnel [4].	8
Figure 5 Theoretical flow models for the various viscous regions [6].	9
Figure 6 Raindrops interaction with the high lift devices [8].	10
Figure 7 Physics of splashing, momentum, heat, and mass transfer on the surface [9].	11
Figure 8 Geometry details of the NASA Trap-Wing model [4].	14
Figure 9 The computational domain of Trap-Wing, 40 ft. wide, 80 ft. height, and 100 ft. length.	15
Figure 10 The top view of the computational domain.	15
Figure 11 The far mesh of the entire computational domain.	24
Figure 12 The mesh of the entire Trap-Wing.	24
Figure 13 The cross section of mesh with the slat main wing and slat.	25
Figure 14 The inflation on the leading edge of the slat and the main wing.	25
Figure 15 The inflation on the flap and the gap between main-wing and flap.	26
Figure 16 Validation of pressure coefficient comparison: AoA=13 deg, 17% wing span [20].	30
Figure 17 Validation of pressure coefficient comparison: AoA=13 deg, 17% wing span.	31
Figure 18 Validation of pressure coefficient comparison: AoA=13 deg, 28% wing span.	31
Figure 19 Validation of pressure coefficient comparison: AoA=13 deg, 41% wing span.	32
Figure 20 Validation of pressure coefficient comparison:AoA=13 deg, 50% wing span.	32
Figure 21 Validation of pressure coefficient comparison: AoA=13 deg, 65% wing span [20].	33
Figure 22 Validation of pressure coefficient comparison: AoA=13 deg, 65% wing span.	33
Figure 23 Validation of pressure coefficient comparison: AoA=13 deg, 70% wing span.	34
Figure 24 Validation of pressure coefficient comparison: AoA=13 deg, 85% wing span.	34
Figure 25 Validation of pressure coefficient comparison: AoA=13 deg, 95% span [20].	35
Figure 26 Validation of pressure coefficient comparison: AoA=13 deg, 95% wing span.	35
Figure 27 Validation of pressure coefficient comparison: AoA=13 deg, 98% span [20].	36
Figure 28 Validation of pressure coefficient comparison: AoA=13 deg, 98% wing span.	36
Figure 29 The pressure contour of NASA Trap-Wing by OVERFLOW CFD simulation: AoA=13 deg, M=0.2, Re=4.3million [20].	37
Figure 30 The pressure contour of NASA Trap-Wing by FLUENT: AoA=13 deg, M=0.2, Re=4.3million.	37
Figure 31 The Mach contour of NASA Trap-Wing by OVERFLOW CFD simulation: AoA=13 deg, M=0.2, Re=4.3million, 50% wing span [20].	38
Figure 32 The Mach contour of NASA Trap-Wing by FLUENT: AoA=13 deg, M=0.2, Re=4.3million, 50% wing span.	38
Figure 33 The lift coefficient vs. AoA of NASA Trap-Wing [20].	41
Figure 34 The lift coefficient vs. AoA of NASA Trap-Wing.	41
Figure 35 The drag coefficient vs. AoA of NASA Trap-Wing [20].	42
Figure 36 The drag coefficient vs. AoA of NASA Trap-Wing.	42
Figure 37 The lift coefficient vs. AoA of NASA Trap-Wing under heavy rain.	48
Figure 38 The drag coefficient vs. AoA of NASA Trap-Wing under heavy rain.	48
Figure 39 Lift coefficient compared with LWC=0 g/m3 and LWC= 29 g/m3 of Trap-Wing.	52
Figure 40 Drag coefficient compared with LWC=0 g/m3 and LWC= 29 g/m3 of Trap-Wing.	52
Figure 41 Lift to drag ratio compared with LWC=0 g/m3 and LWC= 29 g/m3 of Trap-Wing.	53
Figure 42 The drag coefficient vs. AoA of NACA 64-210 high lift configuration experimental data. [8]	53
Figure 43Velocity contours of the Trap-Wing, AoA=13 deg, 28% of wing span, no rain.	55
Figure 44 Velocity contours of the Trap-Wing, AoA=13 deg, 28% of wing span, LWC=29 g/m3.	55
Figure 45 Velocity contours of the Trap-Wing, AoA=13 deg, 95% of wing span, no rain.	56
Figure 46 Velocity contours of the Trap-Wing, AoA=13 deg, 95% of wing span, LWC=29 g/m3.	56
Figure 47 Velocity contours of the Trap-Wing, AoA=33 deg, 28% of wing span, no rain.	57
Figure 48 Velocity contours of the Trap-Wing, AoA=33 deg, 28% of wing span, LWC=29 g/m3.	57
Figure 49 Velocity contours of the Trap-Wing, AoA=33 deg, 95% of wing span, no rain.	58
Figure 50 Velocity contours of the Trap-Wing, AoA=33 deg, 95% of wing span, LWC=29 g/m3.	58
Figure 51 Velocity contours of the Trap-Wing, AoA=37 deg, 28% of wing span, no rain.	59
Figure 52 Velocity contours of the Trap-Wing, AoA=37 deg, 28% of wing span, LWC=29 g/m3.	59
Figure 53 Velocity contours of the Trap-Wing, AoA=37 deg, 95% of wing span, no rain.	60
Figure 54 Velocity contours of the Trap-Wing, AoA=37 deg, 95% of wing span, LWC=29 g/m3.	60
Figure 55 Pressure coefficient contour of Trap-Wing upper surface, AoA=13 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	62
Figure 56 Pressure coefficient contour of Trap-Wing lower surface, AoA=13 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	62
Figure 57 Pressure coefficient contour of Trap-Wing upper surface, AoA=33 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	63
Figure 58 Pressure coefficient contour of Trap-Wing lower surface, AoA=33 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	63
Figure 59 Pressure coefficient contour of Trap-Wing upper surface, AoA=37 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	64
Figure 60 Pressure coefficient contour of Trap-Wing lower surface, AoA=37 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	64
Figure 61 Vorticity contour of Trap-Wing upper surface, AoA=13 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	66
Figure 62 Vorticity contour of Trap-Wing lower surface, AoA=13 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	66
Figure 63 Vorticity contour of Trap-Wing upper surface, AoA=33 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	67
Figure 64 Vorticity contour of Trap-Wing lower surface, AoA=33 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	67
Figure 65 Vorticity contour of Trap-Wing upper surface, AoA=37 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	68
Figure 66 Vorticity contour of Trap-Wing lower surface, AoA=37 deg, (L) LWC=0 g/m3; (R) LWC=29 g/m3.	68
Figure 67 Vortex core region by Q criterion on Trap-Wing model at AoA=13 deg, LWC=0 g/m3.	70
Figure 68 Vortex core region by Q criterion on Trap-Wing model at AoA=13 deg, LWC=29 g/m3.	70
Figure 69 Vortex core region by Q criterion on Trap-Wing model at AoA=33 deg, LWC=0 g/m3.	71
Figure 70 Vortex core region by Q criterion on Trap-Wing model at AoA=33 deg, LWC=29 g/m3.	71
Figure 71 Vortex core region by Q criterion on Trap-Wing model at AoA= 37 deg, LWC=0 g/m3.	72
Figure 72 Vortex core region by Q criterion on Trap-Wing model at AoA=37 deg, LWC=29 g/m3.	72
 
List of Tables
Table 1 Particle properties in different LWC.	20
Table 2 Mesh properties of the Trap-Wing.	23
Table 3 the mesh details of gird converge, AoA=13 deg.	28
Table 4 Lift and drag coefficients at different AoA.	40
Table 5 Value of slat's KS and CS for 4 flight attitudes.	44
Table 6 Value of main wing's KS and CS for 4 flight attitudes.	45
Table 7 Value of flap's KS and CS for 4 flight attitudes.	45
Table 8 Numerical results for NASA Trap-Wing lift coefficients degradation percentage.	49
Table 9 Numerical results for NASA Trap-Wing drag coefficients degradation percentage.	50
Table 10 Numerical results for NASA Trap-Wing lift to drag ratio degradation percentage.	51

References
[1]	Page, F.H., “The Handley Page Wing,” The Aeronautical Journal, June 192l, p. 263.
[2]	Yasuyuki, Y., Irina, V., Akimasa, T., Edwardo, F.F., and Gen, E., “Circulation-controlled high-lift wing for small unmanned aerial vehicle,” ROBOMECH Journal, 2015, p. 3.
[3]	van Dam, C.P., “The Aerodynamic Design of Multi-Element High-Lift Systems for Transport Airplanes,” Progress in Aerospace Sciences 38, 2002, pp. 101–144.
[4]	NASA, “The 1st AIAA CFD High Lift Prediction Workshop (HiLiftPW-1) https://hiliftpw.larc.nasa.gov/index-workshop1.html.”
[5]	Young, A.D., “The Aerodynamic Characteristics of Flaps,” ARC R&M 2622, 1953.
[6]	Bertin, J.J., and Cummings, M.R., “Incompressible Flows Around Airfoils of Infinite Span,” Aerodynamics for Engineers, 5th ed., Pearson Prentice-Hall, New Jersey, 2002, p. 309. 
[7]	Haines, P.A., and Luers, J.K., “Aerodynamic Penalties of Heavy Rain on a Landing Aircraft,” NASA CR-156885, 1982.
[8]	Bezos, G.M., Dunham, R.E., Gentry, G.L., and Melson, W.E., “Wind Tunnel Aerodynamic Characteristics of a Transport-Type Airfoil in a Simulated Heavy Rain Environment,” NASA Technical Paper 3184, August 1992.
[9]	“FLUENT User’s Guide”, FLUENT Inc.
[10]	Rhode, R.V., “Some Effects of Rainfall on Flight of Airplanes and on Instrument Indications,” NACA TN 903, April 1941.
[11]	Dunham, R.E., Jr., “Potential Influences of Heavy Rain on General Aviation Airplane Performance,” AIAA-86-2606, Sept. Oct. 1986.
[12]	Wan, T., and Pan, S.P., “Aerodynamic Efficiency Study under the Influence of Heavy Rain via Two-Phase Flow Approach,” Proceedings of the 27th International Congress of Aeronautical Sciences (ICAS), Nice, France, September 19-24, 2010.
[13]	Valentine, J.R., and Rand, A.D., “A Lagrangian-Eulerian Scheme for Flow Around an Airfoil in Rain,” Int. J. Multiphase Flow, Vol. 32, No. 1, 1995, pp. 639-648.
[14]	Anderson, J.D., “Three-Dimensional Incompressible Flow,” Fundamentals of Aerodynamics, 5th ed., McGraw Hill, New York, 2011, pp. 494-496.
[15]	Ulbrich, C.W., “Natural Variations in the Analytical Form of the Raindrop Size Distribution,” Journal of Applied Meteorology, Vol. 22, 1983, pp. 1764-1775.
[16]	Willis, T.P., and Tattelman, P. “Drop-Size Distributions Associated with Intense Rainfall,” Journal of Applied Meteorology, Vol. 28, January 1989, pp. 3-14.
[17]	Markowitz, A.M., “Raindrop Size Distribution Expression,” Journal of Applied Meteorology, Vol. 15, 1976, pp. 1029-1031.
[18]	Wallace, J.M., and Hobbs, P.V., Atmospheric Science: An Introductory Survey, 2nd ed., U.K. Elsevier, London, 2006.
[19]	Cebeci, T., and Bradshaw, P., Momentum Transfer in Boundary Layers, Hemisphere Publishing Corporation, New York, 1977.
[20]	Sclafani, A.J., Slotnick, J.P., Vassberg, J.C., Pulliam, T.H., and Lee, H. C., “OVERFLOW Analysis of the NASA Trap Wing Model from the First High Lift Prediction Workshop,” 49th AIAA Aerospace Sciences Meeting, 2011.
[21]	Judith, A.H., Mark, C., and Slotnick, J.P., “Overview of the First AIAA CFD High Lift Prediction Workshop,” 49th AIAA Aerospace Sciences Meeting, 2011.
[22]	Wan, T., and C.J. Chou, “Reinvestigation of High Lift Airfoil under the Influence of Heavy Rain Effects,” 50th AIAA Aerospace Science Meeting, Nashville, Tennessee, USA, January 9-12, 2012.