Background(1/3) 3Ideas 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.
Background(2/3) 4Schematic 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
Background(3/3) 5Design of wing/airfoil Practical use of computational fluid dynamics (CFD) Detail design for new concept aircraft Blended wing body aircraft Mars exploration aircraft Supersonic aircraftRequirement of efficient wing/airfoilrepresentation methods for efficient globaldesign exploration Ability to employ with automated optimizer *NASA’s Vehicle Sketch Pad
Objectives 6Multi-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
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-edgemodification 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 byCFD, K. Matsushima, CD proceedings of 5th WCCM/ ECCOMAS2008, Venice, CAS1.8-4 (MS106), 2008.
Design Methods(2/7) 8Planform 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
Design Methods(4/7) 9Optimization (Overview of EGO) Sampling and Evaluation Evaluations Surrogate model construction Kriging model Evaluation of Multi-objective optimization additional samples and Selection of additional samplesMaximizing EIsSelection 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.
Design Methods (5/7) 10 Knowledge Discovery1 IntegrateAnalysis of VarianceOne of multi-valiate analysis for quantitative informationThe 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 ˆwhere, εis the variance due to design variable xi. Proportion (Main effect)
Design Methods (6/7) 11Knowledge Discovery2Parallel 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.
Design Methods (7/7) 12EvaluationCAD-based Automatic Panel Analysis System (CAPAS) developed in JAXAPotential solver (Evaluated drag is pressure drag.) 2 2 2 ( M 2 1) 2 2 2 0 x y z Computational panel Result
Formulation(1/2) 13Flight 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)
Result(1/6) 15Sampling 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.
Result(2/6) 16Design 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
Result(3/6) 17Design 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.
Result(4/6) 18Comparisons 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
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
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
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.