1) The study aimed to perform multi-point aerodynamic design of a supersonic wing using an efficient global optimization methodology. 2) The methodology used a modified PARSEC airfoil representation and kriging model-based genetic algorithm for efficient global optimization. 3) The design explored maximizing lift-to-drag ratio at high and low Mach cruise speeds, finding many potential designs and discovering that camber of the kink and root airfoils most affected performance at high Mach while thickness curvature at kink and root did so at low Mach.

1. 10th WORLD CONGRESS ON COMPUTATIONAL MECHANICS
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)

2. Contents 2
 Background
 Objectives
 Design Methods
 Geometry representation
 Efficient global optimization (EGO)
 Analysis of design space
 Formulations
 Objective functions
 Design space
 Results
 Conclusions

3. Background(1/3) 3
Ideas of next generation supersonic transport
 Aerodynamic design/ Conceptual design
JAXA’s low-boom/ Aerion’s SBJ
low drag concept
• Low drag design
• Aerodynamically designed • Cruise over sea at M = 1.60
for reductions of drag and • Cruise over land at M = 1.15
sonic boom intensity ⇒No sonic boom is heard on
the ground because of the
• Cruise Mach number: 1.6
“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.

4. Background(2/3) 4
Schematic illustration of flight profile
M = 1.15 M = 1.60
Shock wave
“Mach cutoff effect”
Landing No boom Sonic boom Take-off
Ground Sea
 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

5. Background(3/3) 5
Design of wing/airfoil
 Practical use of computational fluid
dynamics (CFD)
Detail design for new concept
aircraft
Blended wing body aircraft
Mars exploration
aircraft
Supersonic aircraft
Requirement of efficient wing/airfoil
representation methods for efficient global
design exploration
 Ability to employ with automated optimizer
*NASA’s Vehicle Sketch Pad

6. Objectives 6
Multi-point aerodynamic design of a supersonic
wing by means of the efficient global wing design
methodology
Employment and investigation of modified
PARametric SECtion (PARSEC) airfoil
representation
Efficient global optimization
Kriging model
Genetic Algorithm
Lift to drag ratio (L/D) maximization at high and
low Mach number supersonic cruse
Design knowledge discovery

7. Design Methods(1/7) 7
 Efficient airfoil representation
PARametric SECtion (PASEC) method*
Upper surface and lower surface are
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.
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.

8. Design Methods(2/7) 8
Planform
 Planform is fixed to NEXST1 design
 Carlson’s warp design
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

9. Design Methods(4/7) 9
Optimization (Overview of EGO) Sampling and Evaluation
Evaluations
Surrogate model construction
Kriging model
Evaluation of Multi-objective optimization
additional samples
and Selection of additional samples
Maximizing EIs
Selection by k-means clustering Genetic Algorithms
Termination?
No
Yes
Knowledge discovery
Knowledge based design
EI(Expected Improvement)：The balance between optimality and uncertainty
 y  f max 
ˆ  y  f max 
ˆ
E I x   ( y  f max )
ˆ   s    ,  ：standard distribution,
 s   s  normal density
Jones, D. R., “Efficient Global Optimization of Expensive Black- s ：standard error
Box Functions,” J. Glob. Opt., Vol. 13, pp.455-492 1998.

10. Design Methods (5/7) 10
Knowledge Discovery1
Integrate
Analysis of Variance
One of multi-valiate analysis for quantitative information
The main effect of design variable xi:
i ( xi )     y( x1 ,....., xn )dx1 ,..., dxi 1 , dxi 1 ,.., dxn  
ˆ
variance
where:
     y( x1 ,....., xn )dx1 ,....., dxn
ˆ
μ1
Total proportion to the total variance:
 i  xi  dxi
2
pi  2
    y ( x1 ,...., xn )    dx1 ...dxn
ˆ
where, εis the variance due to design variable xi.
Proportion (Main effect)

11. Design Methods (6/7) 11
Knowledge Discovery2
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.

12. Design Methods (7/7) 12
Evaluation
CAD-based Automatic Panel Analysis System (CAPAS) developed in JAXA
Potential solver (Evaluated drag is pressure drag.)
 2  2  2
( M 2  1) 2
 2
 2
0
x y z
Computational panel Result

13. Formulation(1/2) 13
Flight profile at supersonic cruise
Mach 2.0 (19,000m)
Mach 1.15 (12,000m)
Objective functions
Maximize L/D at Mach2.00
subject to CL=0.107
Maximize L/ D at Mach 1.15
subject to CL=0.108
Minimize |ΔCM|
•Trim drag of designs will similar to NEXST1.
ΔCM：Difference moment coefficent between designed
wing and baseline (CM,NEXST-1= -0.028)

14. Formulation(2/2) 14
Design space

15. Result(1/6) 15
Sampling results
DesB
|CM|
DesA
Baseline
L/D |CM|
M=2.00 13.4 0.0025
DesA
M=1.15 13.9 0.0056
M=2.00 13.0 0.0033
DesB
M=1.15 15.5 0.0017
M=2.00 11.3 0.0000
Baseline
M=1.15 11.9 0.0000
 Many solutions could be founded out around optimum directions.
 |CM| of optimum solutions was low. ⇒ almost same trim drag as baseline.

16. Result(2/6) 16
Design space (L/D@M=2.00)
Blue line: Baseline
 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

17. Result(3/6) 17
Design space (L/D@M=1.15)
Blue line: Baseline
 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.

18. Result(4/6) 18
Comparisons of designed airfoil
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

19. Result(5/6) 19
 Flowfield comparison among DesA, DesB, and NEXST1 (M=2.00)
upper lower upper lower upper lower
DesA DesB Baseline
 The gradiant of Cp on the upper surfae of DesA-B is gentler than that of
baseline. → reduction of wave drag

20. Result(6/6) 20
 Flowfield comparison among DesA, DesB, and NEXST1 (M=1.15)
upper lower upper lower upper lower
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

21. Conclutions 21
 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 obtained
 Camber 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
Thank you for your kind attention.