Airfoil Design for Mars AircraftUsing Modified PARSEC Geometry Representation

Masahiro KanazakiTokyo Metropolitan University

Tomoyoshi YotsuyaTokyo Metropolitan University

Kisa MatsushimaUniversity of Toyama

Contents Background Objectives Design methods Airfoil representation by modified PARSEC method Evaluation by computational fluid dynamics (CFD) Design optimization by genetic algorithm (GA) Knowledge discovery by scatter plot matrix (SPM)

Formulation ResultsMaximization result of maximum lift to drag ratio (t/c=0.07c, 0.10c) Visualization result by Parallel Coordinate Plot (PCP)

Conclusions

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Background1Image of MELOS

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”Mars airplane” is proposed as a part of the MELOS.

Technical challenges Propulsion Aerodynamic design Structure

・What kind of airfoil/wing geometry achieves higher performance?・Ishii airfoil is one of the promising design.

Difficulty of flight in the Martian atmosphere

1/3 gravity of the earth → Required lift is 1/3. 1% density of the earth → Lift is required to be

hundredfold increased.

3/4 speed of sound → Compressibility should be considered even for relative slow flight.

Background2 4

gravity[m/s2]

density[kg/m3]

Viscosity[10-5Pa・s]

Sonic speed[m/s]

atmospheric constituent

The Earth 9.8 1.17 1.86 345 N2，O2

The Mars 3.2 0.0118 1.36 258 CO2

⇒ Lift of the Mars-airplane have to be about 33rd times lift as much as that of the Earth-airplane.

Knowledge has to be acquired for unknown design problem. Efficient design method is required for Mars-airplane design.

Background3Airfoil representations for unknown design problemB-spline curve, NURBS

Good for use in CAD softwareNot good for use with data mining

PARSEC(PARametric SECtion) method*

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*Sobieczky, H., “Parametric Airfoils and Wings,” Notes on Numerical Fluid Mechanics, pp. 71-88, Vieweg 1998.

Parameterization geometrical character based on knowledge of transonic flowSeparately definition upper surface

and lower surfaceEasy to introduce automated design

method such as genetic algorithmAerodynamic performances can be

explained based on design variables.A few geometrical parameters around the

leading-edge

Background4

Modification of PARSEC representation** Separately defined thickness distribution and camber

This definition is in theory of wing section Successful representation of supersonic airfoil Maintain the beneficial feature of original PARSEC

A few numbers of design variablesAerodynamic performances can be explained by design

variables.

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** K. Matsushima, Application of PARSEC Geometry Representation to High-Fidelity Aircraft Design by CFD, proceedings of 5th WCCM/ ECCOMAS2008, Venice, CAS1.8-4 (MS106), 2008.

Objectives

Design exploration of airfoil for Mars-airplane using modified PARSEC airfoil representationDesign exploration using CFD and GASelection of promising designs and

comparisons of their performances with baseline (Ishii airfoil)Knowledge discovery by means of PCP

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Design methods1 Airfoil representation by modified PARSEC method Designed by thickness distribution and camber . The leading edge radius center is always on the camber.

The thickness distribution is same as symmetrical airfoil by PARSEC. The camber is defined by a quintic equation. By adding the root term for root camber, the design performance of the

leading-edge is improved. Number of design variables is 12.

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2126

1

n

xazn

nt

5

10

n

nnc xbxbz

CamberThickness

Design method2Evaluation by CFDTwo dimensional Reynolds averaged Navier-Stokes flow

solver (RANS)

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

scheme with MUSCL method Turbulent model : Baldwin-Lomax model

Grid : C-H type structured gridGrid size: 11,651 points

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Computational grid

0

ndsFQdVt

10Design method3 Genetic algorithm (GA)

Global optimization Inspired by evolution of life Selection, crossover, mutation

Parallel Coordinate Plot (PCP) For the design problem

visualization One of statistical visualization

techniques from high-dimensional data into two dimensional graph

Normalized design variables and objective functions are set parallel in the normalized axis

Formulation1Design problem (Single objective)

Maximize maximum L/Dsubject to t/c=target t/c (t/c=0.07c, 0.10c)

Computational condition Martian atmosphere Density=0.0118kg/m3

Temperature=241.0KSpeed of sound=258.0m/s

Free streamVelocity=60m/s

Reynolds number：208,235.3Mach number：0.233

Formulation2Design space

0.35 for t/c=0.07c0.50 for t/c=0.10c

Result1Convergence history of GA exploration

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t/c=0.07c t/c=0.10c

t007c-1t007c-2

t010c-1t010c-2

Best design in this generation

Worst design in this generation

Population size: 20 15 generations for t/c=0.07c，11 generations for t/c=0.10c (in progress) In each case, solutions are almost converged. (Maximum l/d 45, and 38,

respectively.) Four promising solutions are picked up.

Result2α vs. l/d

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t0.07c-1 and -2 achieve better performance than baseline. t0.10c-1/-2 achieve almost same maximum l/d, and better

performance at not design point.

Result3α vs. Cl

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t0.07c-1, -2, t0.10c-1, and -2 achieve similar Cl-AoA. l/d is improved because of higher Cl.

Result4α vs. Cd

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In t=0.07c design, drag was increased 5% compared with baseline. In t=0.10c design, drag was increased 10% compared with baseline. Drag minimization also have to be considered for next step.

Result5Geometry and flowfield (t/c=0.07c)

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Baseline (AoA=4.0deg.)

t007c-1(AoA=2.9deg.)

Cp distributions when the airfoil achieves maximum l/d obtained from t007c case

Thickness distribution is similar to baseline. LE radiuses of t007c-1/-2 are smaller than

that of baseline. Cambers of t007c-1/-2 are larger than that

of baseline. Pressure recoveries on the upper surfaces

of t007c-1/-2 are relaxed.

t007c-2(AoA=3.0deg.)

Result6Geometry and flowfield (t/c=0.07c)

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Baseline (AoA=4.0deg.)

Cp distributions when the airfoil achieves maximum l/d obtained from t010c case.

LE radiuses of t007c-1/-2 are smaller than that of baseline.

Cambers of t007c-1/-2 are larger than that of baseline.

Pressure recoveries on the upper surfaces of t010c-1/-2 are also relatively relaxed.

t010c-1(AoA=3.2deg.) t010c-2(AoA=3.3deg.)

Result7 Comparison of parameters among solutions and baseline Modified PARSEC represents Ishii like airfoil by parameter

identification.

t007c-1 t007c-2 t010c-1 t010c-2 Ishii like airfoildv1 LE radius (rle) 0.0040 0.0042 0.0042 0.0053 0.0086

dv2 x-coord. of maximumthickness (xt) 0.2891 0.2891 0.3322 0.3333 0.2000

dv3 z-coord. of maximumthickness (zt) 0.0350 0.0350 0.0500 0.0500 0.0350

dv4curvature at maximumthickness (zxxt) -0.5275 -0.5276 -0.5837 -0.5841 -0.4600

dv5 angle of TE (βte) 7.9650 7.9649 8.7658 8.7707 5.0000dv6 camber radius at LE (rc) 0.0024 0.0024 0.0033 0.0023 0.0016

dv7x-coord. of maximum camber(xc) 0.3276 0.3244 0.3124 0.3123 0.5200

dv8 z-coord. of maximum camber(zc) 0.0352 0.0332 0.0375 0.0379 0.0200

dv9 curvature at maximum camber(zxxc) -0.0269 -0.0212 -0.0049 -0.0077 -0.2500

dv10 z-coordinate of TE (zte) -0.0045 -0.0087 -0.0007 -0.0008 0.0000dv11 angle of camber at TE (αte) 9.3007 9.1802 10.2644 11.2638 4.5000

LE radius small・x coordinate (dv7) of maximum camber comes up to LE.・ LE camber (dv6), maximum camber,(dv8) and TE camber (dv11) tend to be large.

Result8Visualization of design problem (t/c=0.07c)

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l/d>43.0

All solutions obtained by GA

Pick up individuals which achieve better L/D than 43.0

Baseline

Result8Visualization of design problem (t/c=0.07c)

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l/d>43.0

Baseline

To obtain better maximum l/d, Smaller LE radius (dv1), and curvature (dv4) Closer maximum camber position xc (dv7) to LE Larger angle of TE (dv5) Larger curvature maximum camber (dv9) Larger camber angle at TE (dv11) Almost same thickness at 25% chord and 75%

cord compared with baseline

Result9Visualization of design problem (t/c=0.10c)

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All solutions obtained by GA

l/d>4370

Pick up individuals which achieve better L/D than 37.0

Baseline

Result9Visualization of design problem (t/c=0.07c)

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l/d>37.0To obtain better maximum l/d, Smaller LE radius (dv1), and curvature (dv4) Closer maximum camber position xc (dv7) to LE Larger angle of TE (dv5) Larger curvature maximum camber (dv9) Larger camber angle at TE (dv11) Almost same thickness at 25% chord and 75%

cord compared with baseline

Result10Comparison between two cases (t/c=0.07c and t/c=0.10c)

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Almost same design variables (except for thickness) showed better objective function compared with two cases.

Green: t/c=0.07Purple: t/c=0.10

t010c-1

t007c-1

Conclusions Design exploration of airfoil for Mars-airplane

Design optimization using CFD and GA Selections of promising designs and investigations of their

performances Improvement of maximum l/d in t/c=7% case Acquirements of airfoils which achieves relaxed pressure recovery on

the upper surfaceHigher Cl, but higher Cd than baseline

Knowledge discovery by means of ANOVA and SPM to obtain better maximum l/d Smaller LE radius, and uppersurface curvatureCloser maximum camber position xc to LE Larger angle of TE Larger curvature maximum camber Larger camber angle at TE

Further study: Consideration of Cd minimization

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Acknowledgement

We thank members of the Mars-airplane working group in ISAS/JAXA for giving their experimental data and their valuable advices.

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Thank you very much for your kind attention.