MULTI-POINT DESIGN OF A SUPERSONIC WING USING MODIFIED PARSEC AIRFOIL REPRESENTATION
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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
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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
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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
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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|
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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
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Result(1/6)Sampling results
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|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
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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)
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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)
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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
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Thank you for your kind attention.
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