MULTI-POINT DESIGN OF A SUPERSONIC WING USING MODIFIED PARSEC AIRFOIL REPRESENTATION

Tomoyoshi Yotsuya (Tokyo Metropolitan University)○Masahiro Kanazaki (Tokyo Metropolitan University)

Yoshikazu Makino(Japan Aerospace Exploration Agency)Kisa Matsushima (University of Toyama)

10th WORLD CONGRESS ON COMPUTATIONAL MECHANICS

Contents Background Objectives Design MethodsGeometry representationEfficient global optimization (EGO)Analysis of design space

FormulationsObjective functionsDesign space

Results Conclusions

2

Background(1/3)Ideas of next generation supersonic transportAerodynamic design/ Conceptual design

3

Aerion’s SBJJAXA’s low-boom/ low drag concept

• Low drag design• Cruise over sea at M = 1.60• Cruise over land at M = 1.15

• Aerodynamically designed for reductions of drag and sonic boom intensity

• Cruise Mach number: 1.6⇒No sonic boom is heard on the ground because of the “Mach cutoff effect.”

・Horinouchi, S., Conceptual Design of a Low Boom SSBJ, AIAA-2005-1018 (2005).・Kanazaki, M., "Efficient Multi-Disciplinary Design Exploration of Silent Super Sonic Transport," International Workshops on Advances in Computational Mechanics, 2010.

Background(2/3)Schematic illustration of flight profile

In this concept, cruises over land at a low Mach number and cruises over sea at a high Mach.

Requirement of high aerodynamic performance be achieved at a high as well as a low Mach number cruise.

⇒Efficient multi-point design

4

Take-offLanding

Ground

Shock wave

Sea

Sonic boomNo boom

M = 1.15 M = 1.60

“Mach cutoff effect”

5Background(3/3)

Practical use of computational fluid dynamics (CFD)

Detail design for new concept aircraft

Supersonic aircraft

Mars exploration aircraft

Blended wing body aircraft

Requirement of efficient wing/airfoil representation methods for efficient global design exploration Ability to employ with automated optimizer

*NASA’s Vehicle Sketch Pad

Design of wing/airfoil

6ObjectivesMulti-point aerodynamic design of a supersonic

wing by means of the efficient global wing designmethodologyEmployment and investigation of modified

PARametric SECtion (PARSEC) airfoil representationEfficient global optimizationKriging modelGenetic Algorithm

Lift to drag ratio (L/D) maximization at high and low Mach number supersonic cruseDesign knowledge discovery

Design Methods(1/7) 7Efficient airfoil representation

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

Thickness distribution and camber are designed.This definition is in theory of wing section

PARametric SECtion (PASEC) method*

*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.

Modified PARSEC method**

Design Methods(2/7)PlanformPlanform is fixed to NEXST1 design

Carlson’s warp design

8

Wing area 10.12 m2 Span length 4.718 Aspect ratio 2.20

Taper ratio (inboard) 0.52 Taper ratio (outboard) 0.20

Sweep back angle (inboard) 66.0 deg. Sweep back angle (outboard) 61.2 deg.

MAC length 2.754 m

9Design Methods(4/7)

EI(Expected Improvement)：The balance between optimality and uncertainty

sfy

ssfy

fyIE maxmaxmax

ˆˆ)ˆ( x , ：standard distribution,

normal density

：standard errors

Selection by k-means clustering

Maximizing EIs

Surrogate model construction

Multi-objective optimization

and Selection of additional samples

Sampling and Evaluation

Evaluation of additional samples

Termination?

Yes

Knowledge discovery

Knowledge based design

No

Kriging model

Genetic Algorithms

Evaluations

Jones, D. R., “Efficient Global Optimization of Expensive Black-Box Functions,” J. Glob. Opt., Vol. 13, pp.455-492 1998.

Optimization (Overview of EGO)

Design Methods (5/7) 10

niinii dxdxdxdxxxyx ,..,,,...,),.....,(ˆ)( 1111

nn dxdxxxy ,.....,),.....,(ˆ 11

nn

iii

dxdxxxy

dxxip

...),....,(ˆ 12

1

2

The main effect of design variable xi:

where:

Total proportion to the total variance:

where, εis the variance due to design variable xi.

variance

Inte

grat

e

μ 1

Proportion (Main effect)

Analysis of VarianceOne of multi-valiate analysis for quantitative information

Knowledge Discovery1

Design Methods (6/7) 11

Parallel Coordinate Plot (PCP) 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. Global trends of design variables can be visualized using

PCP.

Knowledge Discovery2

Design Methods (7/7) 12

Potential solver (Evaluated drag is pressure drag.)

0)1( 2

2

2

2

2

22

zyxM

Computational panel Result

Evaluation CAD-based Automatic Panel Analysis System (CAPAS) developed in JAXA

Formulation(1/2)Flight profile at supersonic cruise

Objective functionsMaximize L/D at Mach2.00

subject to CL=0.107Maximize L/ D at Mach 1.15

subject to CL=0.108 Minimize |ΔCM|

13

Mach 2.0 (19,000m)Mach 1.15 (12,000m)

ΔCM：Difference moment coefficent between designed wing and baseline (CM,NEXST-1= -0.028)

•Trim drag of designs will similar to NEXST1.

Formulation(2/2)Design space

14

Result(1/6)Sampling results

15

|CM| DesA

DesB

Many solutions could be founded out around optimum directions. |CM| of optimum solutions was low. ⇒ almost same trim drag as baseline.

L/D |CM|

M=2.00 13.4 0.0025M=1.15 13.9 0.0056M=2.00 13.0 0.0033M=1.15 15.5 0.0017M=2.00 11.3 0.0000M=1.15 11.9 0.0000

DesA

DesB

Baseline

Baseline

Result(2/6) 16

Design space (L/D@M=2.00)

Camber of kink and root airfoil (dv17, dv18, and dv22) have predominant effect to L/D at high Mach number cruise. Camber of baseline design has same value as the design

exploration result. Curvature of thickness at kink (dv8) is also important

parameter. Baseline design also has similar variables. Single-point result

Blue line: Baseline

Result(3/6) 17

Design space (L/D@M=1.15)

Zxxt, which decides Curvature of thickness, at kink and root airfoil (dv7, dv8) have predominant effect to L/D at low Mach number cruise. dv8 (kink) of baseline design has same value as the design exploration

result. dv7 (root) of optimum design for lower Mach number cruise is less than that

of baseline design. → Inboard wing has flat upper surface.

Blue line: Baseline

Result(4/6)Comparisons of designed airfoil

18

DesA DesB Baseline DesA-B has negative camber at the root airfoil while baseline has positive

camber. → lower pressure drag at high Mach number cruise. Airfoil of DesB at kink has positive camber around trailing edge. → rear

loading type airfoil

Result(5/6) Flowfield comparison among DesA, DesB, and NEXST1 (M=2.00)

19

DesA DesB Baseline

The gradiant of Cp on the upper surfae of DesA-B is gentler than that ofbaseline. → reduction of wave drag

upper lower upper lower upper lower

Result(6/6) Flowfield comparison among DesA, DesB, and NEXST1 (M=1.15)

20

DesA DesB Baseline

DesB is ‘rear loading’ type pressure distribution. → reduction of wave drag DesA and DesB have higher Cp around LE than that of Baseline

upper lower upper lower upper lower

Conclutions Multi-point aerodynamic design of a supersonic wing Efficient global wing design methodology

modified PARSEC airfoil representation Efficient global optimization

Kriging model based genetic algorithm Design exploration and knowledge discovery

Lift to drag ratio (L/D) maximization at high and low Mach number Many sample designs could be obtainedCamber of kink and root airfoil have predominant effect to L/D at high

Mach number cruise.• Curvature of thickness at kink is also important parameter at high Mach number cruise.

Curvature of thickness at kink and root airfoil have predominant effect to L/D at low Mach number cruise.

Future work: application of present methodology to design of wing-fuselage-stabilizer configuration, Multi-point design including transonic condition

21

Thank you for your kind attention.