DESIGN PERFORMANCE INVESTIGATION OF MODIFIED PARSEC AIRFOIL REPRESENTATION USING GENETIC ALGORITHM

EUROGEN 2011Mainstream Session 7: Aerospace

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D i P f I ti ti f M difi d PARSECD i P f I ti ti f M difi d PARSECDesign Performance Investigation of Modified PARSEC Airfoil Representation Using Genetic Algorithm

Design Performance Investigation of Modified PARSEC Airfoil Representation Using Genetic Algorithm

•Tomoyoshi YotsuyaTokyo Metropolitan University

•Masahiro KanazakiTokyo Metropolitan University

•Kisa MatsushimaKisa MatsushimaToyama University

ContentsContents2

1. Background2 Objectives2. Objectives3. Airfoil Representation Methods4. Optimization Method Multi-objective genetic algorithm (MOGA)j g g ( ) Data mining method

5 Computational fluid dynamics5. Computational fluid dynamics6. Formulations7. Results8. Conclusions8. Conclusions

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BackgroundBackgroundDevelopment of airfoils High fidelity Computational Fluid High fidelity Computational Fluid

Dynamics (CFD) have been applied to real world design problems with

i f il/ i b d i d i

to real-world design problems with high-performance computing.

Airfoil/wing can be designed using evolutionally algorithm with CFD ffi i l f i f

Blended wing body aircraft

efficiently for new concept aircraft.

Efficient geometry representation is requiredSupersonic aircraft Mars exploration aircraft

for computer aided design.

Effi i i f il i

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BackgroundBackgroundEfficient airfoil representation

U f d l fPARSEC(PARametric SECtion) method*

Upper surface and lower surface are separately defined.Parameterization geometrical character based on knowledge of transonic flowEasy to understand design informationA few geometrical parameters around the leading-edge

modification Modified PARSEC method**

Thickness distribution and camber are designedcamber are 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 byCFD, K. Matsushima, CD proceedings of 5th WCCM/ ECCOMAS2008, Venice, CAS1.8-4 (MS106), 2008.

ObjectivesObjectives5

• Investigation of design performance by Modified PARSEC representationModified PARSEC representation.– Comparison of airfoil design performance among

i i l d d difi ioriginal and two proposed modifications

For this investigation, two design problem are solved.g , g p1. Conventional transonic airfoil design problem2. Airfoil design problem for low Reynolds number

Airfoil Representation MethodsAirfoil Representation Methods6

Original PARSEC (PARSEC11) method

It d i t i i f il ith f d i i blAd tis defined upper and lower surface.

Because the leading-edge radius centre is supposed on the x-axis, it h diffi lt t i th d i f d

It can design transonic airfoil with a few design variables.

Disadvantage

Advantage

it has difficulty to improve the aerodynamic performance around the leading-edge for an airfoil which has large camber.

Disadvantage

→ Only rle decides the leading edge geometry.

upper surface2

126

n

Number of design variables is 11.

y le g g g y

2

1|

xazn

nlowup

lower surface


Modified PARSEC method 1is defined by thickness distribution and camberis 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. N b f d i i bl i 11

Thickness distribution Camber

5nxbz126 n

Number of design variables is 11.

1n

nc xbz

＋

212

1

n

xazn

nt

＋


Modified PARSEC method 2is added design parameters for leading edge camber.

In camber definition, the square root term is added to improve design performance around the leading edge.

g p g g

By adding the root term, the design performance of the leading-edge is improved.

N b f d i i bl i 12 Number of design variables is 12.

5Camber

5

10

n

nnc xbxbz

Optimization MethodOptimization Method9

Adaptive Range Divided Range Multi-Objective Genetic Algorithm (ARDRMOGA)g ( )Adaptive Range scheme*

Advantage: global exploration design spaceDivided 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.


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 The new decision space is determined based on the

statistics of selected better solutions. The new population is generated in the new decision space.The new population is generated in the new decision space.


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 DR scheme maintain high diversity. Every MDR generation, sorted function is switched.

Every MDRgenerationgeneration

Data Mining MethodData Mining Method12

P ll l C di Pl (PCP)Parallel Coordinate Plot (PCP) One of statistical visualization techniques from high-

dimensional data into two dimensional datadimensional data into two dimensional data. Design variables and objective functions are set parallel in the

normalized axis. PCP shows global trends of design variables and objective

functions. 0 81.0

0 20.4 0.6 0.8

0.0 0.2

dv1

dv2

dv3

dv4

dv5

dv6

dv7

dv8

dv9

v10

v11

v12

v13

v14

L/D

ΔＰ ing

Upper bound of ith design variables and objective functions

Lower bound of ith design variables)min(-)( ii dvdvxP

Normalization

d d d d d d d d d dv dv dv dv dv L Δ

Wwi

Lower bound of ith design variables and objective functions )min(-)max( ii

i dvdvP

FormulationsFormulations13

Mach Number : 0.8 (240 m/s)Reynolds Number : 1 0×107

Case1 : Conventional transonic airfoil design

Reynolds Number : 1.0×107

Altitude : 1.0×104 [km]Case2 : Airfoil design for low Reynolds numberCase2 : Airfoil design for low Reynolds number

(to use Mars exploration aircraft project(ISAS/JAXA))Mach Number : 0.52 (120 m/s)

ld b 3 0 104Reynolds Number: 3.0×104

Altitude : Ground level

Objective FunctionsMaximize Airfoil thickness (t)Minimize Drag coefficient (Cd)

Subject to lift coefficient (Cl) = target Cl- Case1 : Cl =0 0, 0 4Case1 : Cl 0.0, 0.4- Case2 : Cl =0.6, 0.8

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CFD MethodCFD Method

Two dimensional Navier-Stokes flow solverTwo dimensional Navier Stokes flow solver0

ndsFQdVt

Time integration : LU-SGS implicit methodFlux evaluation : Third-order-accuracy

i d diff ti l h Airfoil grid viewupwind differential schemewith MUSCL method

Turbulent model : Baldwin-Lomax model

Airfoil grid view

Turbulent model : Baldwin Lomax model

Computational grid

Grid : C-H type structured gridGrid size 23,000 p g

Design VariablesDesign Variables15

Design space for case1

PARSEC methodCl=0.0 Cl=0.4

Modified method 1Cl=0.0 Cl=0.4

Modified method2Cl=0.0 Cl=0.4

lower upper lower upperrle 0.005 0.040 0.004 0.040αte -8.0 -3.0 -8.0 0.0

lower upper lower upperrle 0.005 0.040 0.004 0.040xt 0.4 0.5 0.4 0.5


xup 0.4 0.5 0.3 0.5zup 0.04 0.12 0.04 0.12zxxup -1.1 -0.4 -1.0 -0.4

zt 0.04 0.10 0.02 0.08zxxt -1.0 -0.4 -1.0 -0.1βte 4.4 6.4 4.4 6.4

zt 0.04 0.10 0.02 0.08zxxt -1.0 -0.4 -1.0 -0.1βte 4.4 6.4 4.4 6.4

xlo 0.35 0.50 0.35 0.50zlo -0.08 -0.04 -0.05 0.02zxxlo 0.2 1.0 0.3 1.0β 4 4 6 6 4 0 8 0

xc 0.30 0.50 0.35 0.50zc 0.00 0.04 0.00 0.07zxxc -0.5 0.0 -0.7 0.0

0 01 0 02 0 01 0 02

rc 0.000 0.002 0.000 0.004xc 0.30 0.50 0.35 0.50zc 0.00 0.04 0.00 0.07

0 5 0 0 0 7 0 0βte 4.4 6.6 4.0 8.0zte -0.01 0.02 -0.02 0.02

zte -0.01 0.02 -0.01 0.02αte 3.0 8.0 0.0 8.0

zxxc -0.5 0.0 -0.7 0.0zte -0.01 0.02 -0.01 0.02αte 3.0 8.0 0.0 8.0

Design VariablesDesign Variables16

Design space for case2

PARSEC methodCl=0.6 Cl=0.8



lower upper lower upperrle 0.004 0.040 0.004 0.040αte -8.0 0.0 -8.0 0.0



xup 0.3 0.5 0.3 0.5zup 0.04 0.12 0.04 0.12zxxup -1.0 -0.4 -1.0 -0.4

zt 0.02 0.08 0.02 0.08zxxt -1.0 -0.1 -1.0 -0.1βte 4.4 6.4 4.4 6.4

zt 0.02 0.08 0.02 0.08zxxt -1.0 -0.1 -1.0 -0.1βte 4.4 6.4 4.4 6.4

xlo 0.35 0.5 0.35 0.5zlo -0.05 0.02 -0.05 0.02zxxlo 0.3 1.0 0.3 1.0β 4 0 8 0 4 0 8 0

xc 0.35 0.50 0.35 0.50zc 0.00 0.07 0.00 0.07zxxc -0.7 0.0 -0.7 0.0

0 01 0 02 0 01 0 02

rc 0.000 0.004 0.000 0.004xc 0.35 0.50 0.35 0.50zc 0.00 0.07 0.00 0.07

0 7 0 0 0 7 0 0βte 4.0 8.0 4.0 8.0zte -0.02 0.02 -0.02 0.02

zte -0.01 0.02 -0.01 0.02αte 0.0 8.0 0.0 8.0

zxxc -0.7 0.0 -0.7 0.0zte -0.01 0.02 -0.01 0.02αte 0.0 8.0 0.0 8.0

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ResultsCase1 : Conventional transonic airfoil design

Case2 : Airfoil design for low Reynolds numberCase2 : Airfoil design for low Reynolds number

Result (case1)Result (case1)18

Optimization resultNon-dominated solutions

Design C =0 0 Design Cl=0 4Design Cl=0.0 Design Cl 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.

Result (case1, Cl=0.4)Result (case1, Cl=0.4)19

Thi k f d 1Design Cl=0.4 Thickness distribution

0.06

Thickness of des1Thickness of des2Thickness of des3

0.00 0 0 0 5 1 0

0.04 C b f d 1Camber

-0.06

0.0 0.5 1.0

0.02

0.04 Camber of des1Camber of des2Camber of des3

Camber

0.000 0 0 5 1 0

Des1D 3

AoA=-0.6°0.0 0.5 1.0

Des1-3 are selected from non-dominated solutions. (t/c are about 0.10 t/c)Des2

Des3

A A 0 3°

AoA=-0.3°

Des1-3 has maximum camber at trailing edge.Des3 has largest camber around leading edge.

AoA=-0.3°


Pressure distributionDes1 (PARSEC method) -1.00

-0.50 0 0 0 5 1 0

Pressure distributionAoA = -0.6°

0.00

0 50

0.0 0.5 1.0

upper surfacelower surface

Des2 (Modified method 1)0.50

-1.00

-0.50 0 0 0 5 1 0

AoA = -0.3°

0.00

0 50

0.0 0.5 1.0


Des3 (Modified method 2)

0.50

AoA = -0.4°-1.00

-0.50 0 0 0 5 1 0

S h C di ib i i D 3

0.00

0.50

0.0 0.5 1.0


Smooth Cp distribution in Des3 -Modified2 has possibility to design airfoil which achieves lower wave drag.


0.8 1.0

PARSEC methodDesign informationPCP visualizes 10 individuals which achieve low Cd.

0 20.4 0.6 The trend of αte is same tendency

among three methods.The trend of x and x is different from

achieve low Cd.

0.0 0.2

rle

αte

xup

zup

xup

xlozlo

xxlo βtezte tcd

The trend of xup and xt is different from that obtained by modified method 2.

→Because of rc , xt is smaller to control leading edge in modification 2 x z

zxx zx

1.0 1.0 Modified method 1 Modified method 2

control leading edge in modification 2.

0 40.6 0.8

0 40.6 0.8

0.0 0.2 0.4

0.0 0.2 0.4

rle xt zt

zxxt βte xc zc

zxxc zte

αte tcd rle xt zt

zxxt βte rc xc zc

zxxc zte

αte tcd

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ResultsCase1 : Conventional transonic airfoil design

Case2 : Airfoil design for low Reynolds numberCase2 : Airfoil design for low Reynolds number

Result (case2)Result (case2)23

Optimization resultNon-dominated solutions

Design C =0 6 Design Cl=0 8Design Cl=0.6 Design Cl 0.8

Optimum direction Optimum direction

Thinner airfoils can be obtained by modified methods. The thinner airfoil cannot be designed by the originalThe thinner airfoil cannot be designed by the original

PARSEC method.

Thickness of des4Result (case2, Cl=0.8)Result (case2, Cl=0.8)

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D i C 0 80.05

Thickness of des4Thickness of des5Thickness of des6

Design Cl=0.8 Thickness distribution

0.00 0.0 0.5 1.0

Camber of des4

-0.05

Camber

0.05

Camber of des4Camber of des5Camber of des6

D 4

Camber

00.0 0.5 1.0

Des4AoA=4.5°

Des5Des6Des1-3 are selected from non-dominated

solutions. (t/c are about 0.07 t/c)Each airfoil has large camber

AoA=3.5°AoA=2 9° Each airfoil has large camber.

The surface of Des4 is not smooth.AoA=2.9


Pressure distributionDes4 (PARSEC method) -1.50

0 000.0 0.5 1.0

Pressure distributionAoA=4.5°

0.00

1.50 upper surfacelower surfacd

1 50Des5 (Modified method 1)

-1.50

0.00 0.0 0.5 1.0 AoA=3.5°

1.50 upper surfacelower surfacd

-1.50

Des6 (Modified method 2)

.50

0.00 0.0 0.5 1.0

AoA=2.9°

The thickness distributions are smooth in 1.50

upper surfacelower surfacd

Des5 and 6.→Smooth flow on airfoil.


PARSEC th d

0.8 1.0

PARSEC methodDesign informationPCP visualizes 10 individuals which achieve low Cd.

0.20.4 0.6

d

The trend of rle is similar.In PARSEC method, αte is smaller.

→ It cannot represent airfoils with

In modified method 2, the influence of rcis significant.

0.0 0.2

rle

αte

xup

zup

xxup xlozlo

xxlo βtezte tCd

plarge camber.

zx zx

1.0 1.0 Modified method 1 Modified method 2

0 40.6 0.8

0 40.6 0.8

0.0 0.2 0.4

0.0 0.2 0.4

0.0

rle xt zt

zxxt βte xc zx

zxxc zte

αte tCd

0.0rle xt zt

zxxt βte rc xc zc

zxxc zte

αte tCd

ConclusionsConclusions27

Investigation of design performance modified method PARSEC representation by MOGAmethod PARSEC representation by 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 ld d i d f i f il ll th i i lcould design good performance airfoil as well as the original

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 methodoriginal method.

• Modified method can be represent smooth surface airfoils with large camber.

• Modified methods design leading edge camber well.

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Thank you for your attentionThank you for your attention

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DESIGN PERFORMANCE INVESTIGATION OF MODIFIED PARSEC AIRFOIL REPRESENTATION USING GENETIC ALGORITHM