This document summarizes a study investigating the design performance of modified PARSEC airfoil representation methods using genetic algorithms. The study compares the original PARSEC method to two proposed modifications for representing airfoils. The optimizations aim to maximize airfoil thickness and minimize drag coefficient for transonic and low Reynolds number airfoil design problems. Computational fluid dynamics simulations are performed using structured grids and turbulence models. Results show that the modified PARSEC methods improve the aerodynamic performance around the leading edge compared to the original method.

1. 1
EUROGEN 2011
Mainstream Session 7: Aerospace
Design Performance Investigation of Modified PARSEC
D i P f I ti ti f M difi d
Airfoil Representation Using Genetic Algorithm
•Tomoyoshi Yotsuya
Tokyo Metropolitan University
•Masahiro Kanazaki
Tokyo Metropolitan University
•Kisa Matsushima
Kisa
Toyama University

2. 2
Contents
1. Background
2.
2 Objectives
3. Airfoil Representation Methods
4. Optimization Method
 Multi-objective genetic algorithm (MOGA)
j g g ( )
 Data mining method
5.
5 Computational fluid dynamics
6. Formulations
7. Results
8. Conclusions

3. 3
Background
Development of airfoils
 High fidelity Computational Fluid
Dynamics (CFD) have been applied
to real world design problems with
real-world
high-performance computing.
 Airfoil/wing can be designed using
i f il/ i b d i d i
evolutionally algorithm with CFD Blended wing body aircraft
ffi i l f i f
efficiently for new concept aircraft.
Supersonic aircraft Mars exploration aircraft
Efficient geometry representation is required
for computer aided design.

4. 4
Background
 Effi i airfoil representation
Efficient i f il i
PARSEC(PARametric SECtion) method*
Upper surface and l
U f d lower surface are
f
separately defined.
Parameterization geometrical character
based on knowledge of transonic flow
Easy to understand design information
A few geometrical parameters around
the leading-edge
modification Modified PARSEC method**
Thickness distribution and
camber are designed
designed.
This definition is in theory
of wing section
*Sobieczky, H., “Parametric Airfoils and Wings,” Notes on Numerical Fluid Mechanics, pp. 71-88, Vieweg 1998.
** Matsuzawa, T., et al, Application of PARSEC Geometry Representation to High-Fidelity Aircraft Design by
CFD, K. Matsushima, CD proceedings of 5th WCCM/ ECCOMAS2008, Venice, CAS1.8-4 (MS106), 2008.

5. 5
Objectives
• Investigation of design performance by
Modified PARSEC representation.
representation
– Comparison of airfoil design performance among
original and two proposed modifications
i i l d d difi i
For this investigation, two design p
g , g problem are solved.
1. Conventional transonic airfoil design problem
2. Airfoil design problem for low Reynolds number

6. 6
Airfoil Representation Methods
Original PARSEC (PARSEC11) method
is defined upper and lower surface.
Advantage It can design transonic airfoil with a few design variables.
Ad t d i t i i f il ith f d i i bl
Because the leading-edge radius centre is supposed on the x-axis,
Disadvantage it has difficulty to improve the aerodynamic performance around
h diffi lt t i th d i f d
the leading-edge for an airfoil which has large camber.
→ Only rle decides the leading edge g
y g g geometry.
y
Number of design variables is 11.
upper surface 6 2 n1
zup|low   an  x 2
n 1
lower surface

7. 7
Airfoil Representation Methods
Modified PARSEC method 1
is defined by thickness distribution and camber .
 The leading edge radius centre is always on the camber.
 The thickness distribution is same as symmetrical airfoil by
PARSEC method.
 The camber is defined by a quintic equation.
 Number f design
N b of d i variables is 11.
i bl i 11
Thickness distribution Camber 5
zc   bn  x n
6 2 n1
z t   an  x 2
n 1
n 1
＋

8. 8
Airfoil Representation Methods
Modified PARSEC method 2
is added design p
g parameters for leading edge camber.
g g
 In camber definition, the square root term is added to improve
design performance around the leading edge.
 By adding the root term, the design performance of the
leading-edge is improved.
 N b of d i variables is 12.
Number f design i bl i 12
Camber 5
zc  b0  x   bn  x n
n 1

9. 9
Optimization Method
Adaptive Range Divided Range Multi-Objective
Genetic Algorithm (
g (ARDRMOGA) )
Adaptive Range scheme*
Advantage: global exploration design space
Divided Range scheme**
Advantage: maintain high diversity
The flow chart of ARDRMOGA
*Sasaki, D., et al, “Efficient search for trade-offs by adaptive range multi-objective genetic algorithms,” Journal of Aerospace
Computing, Information and Communication, pp. 44-64, 2005.
**Hiroyasu , T., et al, The new model of parallel genetic algorithm in multi-objective optimization problems (divided range multi-objective
genetic algorithm), IEEE Proceedings of the Congress on Evolutionary Computation 2000, Vol. 1, pp. 333-340, 2000.

10. 10
Optimization Method
Adaptive range (AR)
 Search region is changed according to standard deviation.
 The solution space can be explored without an oversight of
optimum solutions.
 The new decision space is determined based on the
statistics of selected better solutions.
 The new population is generated in the new decision space.

11. 11
Optimization Method
Divided range (DR)
 The population is divided and sorted by design space.
 DR scheme can prevent the crossover between the
scattered parents.
 DR scheme maintain high diversity
diversity.
 Every MDR generation, sorted function is switched.
Every MDR
generation

12. 12
Data Mining Method
Parallel C di
P ll l Coordinate Plot (PCP)
Pl
 One of statistical visualization techniques from high-
dimensional data into two dimensional data.
data
 Design variables and objective functions are set parallel in the
normalized axis.
 PCP shows global trends of design variables and objective
functions.
1.0
0.8
08
0.6
0.4
0.2
02
0.0
v10
v11
v12
v13
v14
dv1
dv2
dv3
dv4
dv5
dv6
dv7
dv8
dv9
L/D
ing
ΔＰ
dv
d
d
d
d
d
d
d
d
d
dv
dv
dv
dv
L
Wwi
Upper bound of ith design variables
and objective functions Normalization
x(dvi ) - min(dvi )
Lower bound of ith design variables P
i
and objective functions max(dvi ) - min(dvi )

13. 13
Formulations
Case1 : Conventional transonic airfoil design
Mach Number : 0.8 (240 m/s)
Reynolds Number : 1 0×107
1.0×10
Altitude : 1.0×104 [km]
Case2 : Airfoil design for low Reynolds number
(to use Mars exploration aircraft project(ISAS/JAXA))
Mach Number : 0.52 (120 m/s)
Reynolds Number: 3 0 104
ld b 3.0×10
Altitude : Ground level
Objective Functions
Maximize Airfoil thickness (t)
Minimize Drag coefficient (Cd)
Subject to lift coefficient (Cl) = target Cl
- Case1 : Cl =0 0, 0.4
0.0, 0 4
- Case2 : Cl =0.6, 0.8

14. 14
CFD Method
Two dimensional Navier-Stokes flow solver
Navier Stokes

 QdV  F  nds  0
t 
Time integration : LU-SGS implicit method
Flux evaluation : Third-order-accuracy
Airfoil grid view
upwind diff
i d differential scheme
ti l h
with MUSCL method
Turbulent model : Baldwin Lomax model
Baldwin-Lomax
Grid : C-H type structured grid
Grid size 23,000 Computational grid
p g

15. 15
Design Variables
Design space for case1
PARSEC method Modified method 1 Modified method2
Cl=0.0 Cl=0.4 Cl=0.0 Cl=0.4 Cl=0.0 Cl=0.4
lower upper lower upper lower upper lower upper lower upper lower upper
rle 0.005 0.040 0.004 0.040 rle 0.005 0.040 0.004 0.040 rle 0.005 0.040 0.004 0.040
αte -8.0 -3.0 -8.0 0.0 xt 0.4 0.5 0.4 0.5 xt 0.4 0.5 0.4 0.5
xup 0.4 0.5 0.3 0.5 zt 0.04 0.10 0.02 0.08 zt 0.04 0.10 0.02 0.08
zup 0.04 0.12 0.04 0.12 zxxt -1.0 -0.4 -1.0 -0.1 zxxt -1.0 -0.4 -1.0 -0.1
zxxup -1.1 -0.4 -1.0 -0.4 βte 4.4 6.4 4.4 6.4 βte 4.4 6.4 4.4 6.4
xlo 0.35 0.50 0.35 0.50 xc 0.30 0.50 0.35 0.50 rc 0.000 0.002 0.000 0.004
zlo -0.08 -0.04 -0.05 0.02 zc 0.00 0.04 0.00 0.07 xc 0.30 0.50 0.35 0.50
zxxlo 0.2 1.0 0.3 1.0 zxxc -0.5 0.0 -0.7 0.0 zc 0.00 0.04 0.00 0.07
βte 4 4 6 6
4.4 6.6 4.0 8.0
40 80 zte -0.01 0 02
0 01 0.02 -0.01 0 02 zxxc -0.5 0 0
0 01 0.02 0 5 0.0 -0.7 0 0
0 7 0.0
zte -0.01 0.02 -0.02 0.02 αte 3.0 8.0 0.0 8.0 zte -0.01 0.02 -0.01 0.02
αte 3.0 8.0 0.0 8.0

16. 16
Design Variables
Design space for case2
PARSEC method Modified method1 Modified method2
Cl=0.6 Cl=0.8 Cl=0.6 Cl=0.8 Cl=0.6 Cl=0.8
lower upper lower upper lower upper lower upper lower upper lower upper
rle 0.004 0.040 0.004 0.040 rle 0.004 0.040 0.004 0.040 rle 0.004 0.040 0.004 0.040
αte -8.0 0.0 -8.0 0.0 xt 0.4 0.5 0.4 0.5 xt 0.4 0.5 0.4 0.5
xup 0.3 0.5 0.3 0.5 zt 0.02 0.08 0.02 0.08 zt 0.02 0.08 0.02 0.08
zup 0.04 0.12 0.04 0.12 zxxt -1.0 -0.1 -1.0 -0.1 zxxt -1.0 -0.1 -1.0 -0.1
zxxup -1.0 -0.4 -1.0 -0.4 βte 4.4 6.4 4.4 6.4 βte 4.4 6.4 4.4 6.4
xlo 0.35 0.5 0.35 0.5 xc 0.35 0.50 0.35 0.50 rc 0.000 0.004 0.000 0.004
zlo -0.05 0.02 -0.05 0.02 zc 0.00 0.07 0.00 0.07 xc 0.35 0.50 0.35 0.50
zxxlo 0.3 1.0 0.3 1.0 zxxc -0.7 0.0 -0.7 0.0 zc 0.00 0.07 0.00 0.07
βte 4 0 8 0
4.0 8.0 4.0 8.0
40 80 zte -0.01 0 02
0 01 0.02 -0.01 0 02 zxxc -0.7 0 0
0 01 0.02 0 7 0.0 -0.7 0 0
0 7 0.0
zte -0.02 0.02 -0.02 0.02 αte 0.0 8.0 0.0 8.0 zte -0.01 0.02 -0.01 0.02
αte 0.0 8.0 0.0 8.0

17. 17
Results
 Case1 : Conventional transonic airfoil design
Case2 : Airfoil design for low Reynolds number

18. 18
Result (case1)
Optimization result
Non-dominated solutions
Design Cl=0 0
=0.0 Design Cl=0 4
0.4
Optimum direction Optimum direction
 There are trade-off between objective functions in each case.
 Modified method could generate good solutions as well as the
original PARSEC method.

19. 19
Result (case1, Cl=0.4)
Thickness of des1
Thi k fd 1
Design Cl=0.4 Thickness distribution
Thickness of des2
0.06 Thickness of des3
0.00
0.0
00 0.5
05 1.0
10
-0.06
0.04
Camber Camber f d 1
C b of des1
Camber of des2
Camber of des3
0.02
Des1 0.00
AoA=-0.6°
Des3
D 3 0.0
00 0.5
05 1.0
10
AoA=-0.3° Des1-3 are selected from non-dominated
Des2 solutions. (t/c are about 0.10 t/c)
AoA=-0.3°
A A 0 3° Des1-3 has maximum camber at trailing edge.
Des3 has largest camber around leading edge.

20. 20
Result (case1, Cl=0.4)
Des1 (PARSEC method) Pressure distribution
-1.00
AoA = -0.6°
-0.50
0.0
00 0.5
05 1.0
10
0.00 upper surface
lower surface
0 50
0.50
-1.00
Des2 (Modified method 1)
AoA = -0.3°
-0.50
0.0
00 0.5
05 1.0
10
0.00 upper surface
lower surface
0 50
0.50
-1.00
Des3 (Modified method 2)
AoA = -0.4°
-0.50
0.0
00 0.5
05 1.0
10
0.00 upper surface
lower surface
0.50
Smooth Cp di ib i in Des3
S h distribution i D 3
-Modified2 has possibility to design
airfoil which achieves lower wave drag.

21. 21
Result (case1, Cl=0.4)
Design information PARSEC method
1.0
PCP visualizes 10 individuals which
achieve low Cd. 0.8
0.6
The trend of αte is same tendency
among three methods. 0.4
The trend of xup and xt is different from 0 20.2
that obtained by modified method 2. 0.0
→Because of rc , xt is smaller to
zup
xup
rle
αte
βte
t
xup
xlo
zte
zlo
xxlo
cd
control leading edge in modification 2.
2
x
zxx
z
zx
Modified method 1 Modified method 2
1.0 1.0
0.8 0.8
0.6 0.6
0.4
04 0.4
04
0.2 0.2
0.0 0.0
rle
zt
zxxt
βte
xc
zc
zxxc
zte
αte
cd
rle
zt
zxxt
βte
rc
xc
zc
zxxc
zte
αte
cd
xt
t
xt
t

22. 22
Results
Case1 : Conventional transonic airfoil design
 Case2 : Airfoil design for low Reynolds number

23. 23
Result (case2)
Optimization result
Non-dominated solutions
Design Cl=0 6
=0.6 Design Cl=0 8
0.8
Optimum direction Optimum direction
 Thinner airfoils can be obtained by modified methods.
 The thinner airfoil cannot be designed by the original
PARSEC method.

24. 24
Result (case2, Cl=0.8)
Design
D i Cl=0.8
08 Thickness distribution Thickness of des4
Thickness of des5
0.05 Thickness of des6
0.00
0.0 0.5 1.0
-0.05
Camber Camber of des4
Camber of des5
0.05 Camber of des6
Des4
D 4
AoA=4.5° 0
0.0 0.5 1.0
Des1-3 are selected from non-dominated
Des5
Des6 AoA=3.5° solutions. (t/c are about 0.07 t/c)
AoA=2.9
AoA=2 9° Each airfoil has large camber.
camber
The surface of Des4 is not smooth.

25. 25
Result (case2, Cl=0.8)
Des4 (PARSEC method) Pressure distribution
-1.50
AoA=4.5°
0.0 0.5 1.0
0.00
0 00
upper surface
1.50 lower surfacd
1 50
-1.50
Des5 (Modified method 1)
AoA=3.5° 0.0 0.5 1.0
0.00
upper surface
1.50 lower surfacd
-1.50
.50
Des6 (Modified method 2) 0.0 0.5 1.0
AoA=2.9° 0.00
upper surface
1.50 lower surfacd
The thickness distributions are smooth in
Des5 and 6.
→Smooth flow on airfoil.

26. 26
Result (case2, Cl=0.8)
Design information PARSEC method
th d
1.0
PCP visualizes 10 individuals which
achieve low Cd. 0.8
The trend of rle is similar. 0.6
In PARSEC method, αte is smaller. 0.4
→ It cannot represent airfoils with
p 0.2
large camber.
0.0
In modified method 2, the influence of rc
t
rle
xup
zup
xxup
xlo
zte
αte
βte
zlo
xxlo
Cd
is significant.
zx
zx
Modified method 1 Modified method 2
1.0 1.0
0.8 0.8
0.6 0.6
0.4
04 0.4
04
0.2 0.2
0.0 0.0
zt
zxxt
βte
zt
zxxt
βte
zxxc
rc
zc
Cd
zxxc
Cd
xt
xt
t
rle
xc
zte
αte
t
rle
xc
zte
αte
zx

27. 27
Conclusions
 Investigation of design performance modified
method PARSEC representation by MOGA
MOGA.
 Solving two kinds of airfoil design problems by MOGA;
1) transonic airfoil, and 2) low Reynolds number airfoil
) , ) y
 Comparisons of design results among original and modifications
– In conventional transonic airfoil design, modified methods
could design good performance airfoil as well as the original
ld d i d f i f il ll th i i l
PARSEC method.
• In modification2, the local shock is weaken.
– In airfoil design for low Reynolds number, modified method
have the potential to design better airfoils than that of the
original method
method.
• Modified method can be represent smooth surface
airfoils with large camber.
• Modified methods design leading edge camber well.

28. 28
Thank you for your attention