The effects of planform on low
aspect ratio flexible wings Zuo Linxuan, Wang Jinjun Graduate Student, Beijing University of Aeronautics and Astronautics, China
[email protected]
Outline
Introduction Experimental Set-Up Aerodynamics for Rigid Models Impact of Model Flexibility Discussions Conclusions
1 Introduction
The research about MAV (Micro-Air-Vehicles) has become a hotspot field since 1992.
The difficulty subjects are focused on engine power/low reynolds number aerodynamics/control and communication/micro-sensor.
Comparison of MAV with common airplane, MAV has low speed and small size, the viscosity of air will become large, it likes insect swims in honey.
It needs to study low reynolds number aerodynamics for supporting better design of MAV.
Some investigations have shown the planform of MAV has effects on aerodynamics on low reynolds number[1].
The study of Torres and Muller[1] has shown the factors of effect on aerodynamics from high to low are aspect ratio/planform/reynolds number.
■ Objects of our study 1.Effect of planform (sweep angle) on aerodynamics on low Reynolds number. 2.To know about general characteristics of MAV with low aspect ratio on low Reynolds number.
2 Experimental Set-Up
Λ
A
A-A
Λ/ o
0
5
10
15
20
25
30
X /mm
200
191
182
173
163
151
142
Λ/ o
35
40
45
50
55
60
64
X /mm
130
116
100
81
57
27
0
200 450 Χ t A
Sketch of models (unit：mm)
Experiments are conducted in D1 low speed open circuit wind tunnel at BUAA, which has an elliptical cross section with a minor axis of 760 mm and a major axis of 1020 mm. The experimental section length of the wind-tunnel is 1450 mm.
The free stream velocity is 20 m/s in the experiments, which results in chord Reynolds number around 2.73×105 .
3 Aerodynamics of rigid models 1.2
1.0
40 45 50 Polhamus
1.0
0.6
0.4
0.2
CL
0 5 10 15 20 26 30 35 Polhamus
0.0 0
10
20
30
40
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
50
0
°
1.2
0 5 10 15 20 25 30 35 Prandtl
0.6
20
30
40
0
50
° 1.0
0.8
0.6
0.2
0.2
0.2
0.0
0.0
0.0
10
20
°
30
40
50
°
30
40
50
0.6
0.4
0
20
0.8
0.4
0.4
10
56 60 64 Prandtl
1.2
CD
CD
0.8
1.0
CD
1.0
10
40 45 50 Prandtl
1.2
56 60 64 Polhamus
1.0
CL
0.8
CL
1.2
1.2
0
10
20
30
°
40
50
0
10
20
°
30
40
50
Polhamus’ equation[2]:
CL
K P Sin Cos 2
KV Cos Sin 2
K P : depends on λ, Λ and the leading edge shape of the wing, it’s related with potential flow lift.
KV : approximately equals to π, it’s related with vortex flow lift.
Prandtl’s equation[3]:
CD
CD0
C D 0 : zero-lift drag coefficient.
K : induced drag factor.
KC L
2
For these three groups of models, KP is equal to 1.5, 1.7 and 1.9, respectively. Kv is all around 3.1.
CD0 is almost the same for these three groups of models, the value is equal to 0.03. With further increase in sweep angle, K is equal to 0.4、0.39 and 0.36 for these three groups of models, respectively.
■ The Hysteresis Phenomenon The hysteresis phenomenon exists in lift and drag coefficient curves when the sweep angle of the wing is in the range of 5°～50°, the maximum hysteresis range is 4 degrees of attack angle. 1.2
1.0
0.8
0.6
CL
Increasing Decreasing
0.4
0.2
0.0
-0.2 0
10
20
30
°
40
50
4 Impact of Model Felexibility 1.2
1.2
0 10 25 40 50 65 Prandtl
1.0 1.0
0.8 0.8
0 10 25 40 50 64 Polhamus
0.4
0.2
0.6
CD
CL
0.6
0.4
0.2
0.0 0.0
-0.2 0
10
20
30
°
40
50
0
10
20
30
°
40
KP for these models are all around 1.6, CD0 are about 0.02 and K are approximately 0.43.
50
■ The Hysteresis Phenomenon
■ Comparison of Aerodynamics Between Rigid and Flexible Models
5 Discussions
1.2
1.2
1.0
1.0
0.8
0.8
0 5 10 15 20 26 30 35 Polhamus
0.6
0.4
0.2
CL
CL
■ Stall Charateristics 56 60 64 Polhamus
0.6
0.4
0.2
0.0
0.0 0
10
20
30
°
40
0
50
a=
°
10
20
°
30
40
50
■ Flexibility
a= °
a= °
a=
°
a=
°
a=
°
■ Hysteresis
1.2
1.0
0.8
0.6
CL
Increasing Decreasing
0.4
a=
0.2
0.0
-0.2 0
10
20
30
°
40
50
°
6 Conclusions
The lift curve shows good linearity before stall and the empirical equations make a satisfying prediction before stall. For rigid models, the KP of each group increases gradually for these 3 groups, however, the K decreases. For flexible models, sweep angle almost has no effect on KP and K. Flexibility has great effects on astall and CLmax. When ﹤40°, astall and CLmax for the flexible wings are smaller than that of rigid ones, however, as sweep angle increases the stall and the CLmax of flexible wings are nearly the same with that of rigid ones. Lift and drag coefficient curves exist hysteresis in the following range of sweep angle: = 10°～35° for the flexible models, and = 5°～ 50° for the rigid models. It’s may contributed to the flow structure changed abruptly.
Thanks
