Engineering Optimization in Aircraft Design Masahiro Kanazaki Tokyo Metropolitan University Faculty of System Design Division of Aerospace Engineering [email protected]Follow me!: @Kanazaki_M Lecture “Aerodynamic design of Aircraft” in University of Tokyo 20 th January, 2014
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Engineering Optimization in Aircraft Design
Masahiro KanazakiTokyo Metropolitan University
Faculty of System DesignDivision of Aerospace Engineering
Lecture “Aerodynamic design of Aircraft” in University of Tokyo 20th January, 2014
Resume ~ Masahiro KanazakiMarch, 2001 Finish my master course at Graduated school of Mechanical and Aerospace Engineering, Tohoku university March, 2004 Finish my Ph.D. at Faculty at Graduated school of Information Science, Tohoku university
Dr. information science
April, 2004-March, 2008 Invited researcher at Japan Aerospace Exploration AgencyApril, 2008- , Associate Professor at Division of Aerospace Engineering, Faculty of Engineering, Tokyo Metropolitan University
22Optimization Methods based on Heuristic Approach
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.
Optimization Methods based on Heuristic Approach 23
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 multivariate analysis for quantitative information
24Optimization Methods based on Heuristic Approach
Self-organizing map for qualititative information Proposed by Prof. Kohonen Unsupervised learning Nonlinear projection algorithm from high to two dimensional map
Two-dimensional map (Colored by an component, N component plane, for N dimensional input.)
Map can be visualized by circle grid, square grid, Hexagonal grid, …
1.PreparationPrototype vector is randomized.
2.Search similar vector W that looks like XiEach prototype vector is compared with one input vector Xi.
3.Learning1W is moved toward Xi.W = W +α(Xi- W)
4.Learning2W’s neighbors are moved toward Xi.
How SOM is working.
26How to apply to the aircraft designSeveral constraints should be considered.In aircraft design, following constraints are required. Lift=WeightTrim balance
CADHow to represent the geometry.NURBS, B-splinePARSEC airfoil representation
Ex-i: Exhaust manifold design for car engines
27
28
Air cleaner
Intake manifold
Intake port
Intake valve
Air
燃焼室
Muffler
排気マニホールド
Exhaust port
Exhaust valve
Catalysis
Smoothness of exhaust gas
Higher temperatureExhaust manifoldRemove Nox/Cox
Higher charging efficiency
Engine cycle and exhaust manifold
charging efficiency(%)=100×Volume of intake flow/Volume of cylinder
Ex-i: Exhaust manifold design for car engines
Ex-i: Exhaust manifold design for car engines
Exhaust manifoldLead exhaust air from several camber
to one catalysisMerging geometry effect to the powerChemical reaction in the catalysis is
promoted at high temperature.
29
Ex-i: Exhaust manifold design for car engines 30
Evaluations Engine cycle: Empirical one dimensional code Exhaust manifold : Unstructured based three-dimensional Euler code
Ex-i: Exhaust manifold design for car engines 31
Geometry generation for manifold
1. Definition of each pipe
2. Detection the merging line
3. Merge pipes
Ex-i: Exhaust manifold design for car engines 32
排気マニホールドの最適設計 Objective functionMinimize Charging efficiencyMaximize Temperature of
exhaust gas Design variablesMerging point and radius
distribution of pipes
merging3 merging1, 2
Definition of off-spring for merging point and radius
p1 p2
p2 p2
D
B (Maximum temperature)
Ex-i: Exhaust manifold design for car engines 33
1490 1500 1510 1520
85
87.5
90
Cha
rgin
g ef
ficie
ncy
(%)
Temperature (K)
Initial
A
B
CDA (Maximum charging efficiency)
C
Ex-ii) Airfoil design for Mars airplane
~ airfoil representation/ parameterization
34
Ex-ii) Airfoil design for Mars airplane Image of MELOS
35
Ikeshita/JAXA Exploration by winged vehicle
Propulsion Aerodynamics Structural dyanamics
・Atmosphere density: 1% that of the earth・Requirement of airfoil which has higher aerodynamic performance
Ex-ii: Airfoil design for Mars airplane Airfoil representation for unknown design problemB-spline curve, NURBS
High degree of freedomParameterization which dose not considered aerodynamics
PARSEC(PARametric SECtion) method*
36
*Sobieczky, H., “Parametric Airfoils and Wings,” Notes on Numerical Fluid Mechanics, pp. 71-88, Vieweg 1998.
Parameterization based on the knowledge of transonic flow
Define upper surface and lower surface, respectively
Suitable for automated optimization and data mining
Camber is not define directly.→ It is not good for the airfoil design
which has large camber.
Ex-ii: Airfoil design for Mars airplane Modification of PARSEC representation**Thickness distribution and camber are defined,
respectively. Theory of wing section
Maintain beneficial features of original PARSEC Same number of design variables. Easy to understand by visualization because the parameterization is in
theory of wing section
37
** 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.
Ex-ii: Airfoil design for Mars airplane Parameterization of modified PARSEC method
The center of LE radius should be on the camber line, because thickness distribution and camber are defined, respectively.
Thickness distribution is same as symmetrical airfoil by original PARSEC.
Camber is defined by polynomial function. Square root term is for design of LE radius.
38
+
2126
1
n
xazn
nt
5
10
n
nnc xbxbz
CamberThickness
Ex-ii: Airfoil design for Mars airplane Formulation Objective functions
Maximize maximum l/dMinimize Cd0(zero-lift drag)
subject to t/c=target t/c (t/c=0.07c)
EvaluationStructured mesh based flow solver
Baldwin-Lomax turbulent modelFlow condition (same as Martian atmosphere)
dv2 x-coord. of maximum thickness 0.2000 0.6000dv3 z-coord. of maximum thickness 0.0350 0.0350dv4 curvature at maximum thickness -0.9000 -0.4000dv5 angle of TE 5.0000 10.0000dv6 camber radius at LE 0.0000 0.0060dv7 x-coord. of maximum camber 0.3000 0.4000dv8 z-coord. of maximum camber 0.0000 0.0800dv9 curvature at maximum camber -0.2500 0.0100dv10 z-coordinate of TE -0.0400 0.0100dv11 angle of camber at TE 4.0000 14.0000
Ex-ii: Airfoil design for Mars airplane Design result (objective space) Multi-Objective Genetic Algorithm: (MOGA)
41
Des_moga#2
Des_moga#1
Des_moga#3
Trade-off can be found out.
Baseline
Ex-ii: Airfoil design for Mars airplane α vs. l/d, α vs. Cd, α vs. Cl
42
Better solutions could be acquired.
Ex-ii: Airfoil design for Mars airplane Optimum designs and their pressure distributions
43
Des_moga#1 Des_moga#2
Des_moga#3
Ex-ii: Airfoil design for Mars airplane 44
Visualization of design space by PCP
Ex-ii: Airfoil design for Mars airplane 45
l/d>45.0
Visualization of design space by PCP (sorted by max l/d)
Ex-ii: Airfoil design for Mars airplane 46
Cd0<0.0010
Visualization of design space by PCP(sorted by Cd0)
Ex-ii: Airfoil design for Mars airplane 47
Larger LE thickness (th25)→same trend compared with baseline Larger maxl/d should be smaller (dv4(zxx)) (Larger curvature)→TE thickness (th75)
becomes smaller, Smaller Cd0should be larger (dv5),dv4(zxx)→ thickness of TE (th75) becomes
Blue box: Chosen by similarity of color map, Green box: Chosen by ANOVA result
Larger sweep back
⇒ Low boom, high L/D (low drag)
Sweep back@Outboard Camber@Kink75%c
Small camber at LE and large camber at TE
⇒ Low boom, high L/D (high lift)
Ex-iii: Wing design for supersonic transport
Computational efficiency・CAPAS evaluation in 60min./case (including
decision of angle of HT)75 initial samples + 30 additional samples
= total of 105 samples105CFD run×60min.=105hours (about 4-5days)
58
If we use direct GA search with 30population and 100 generation, total of 3000CFD run is needed.If we use only high-fidelity solver (ex. 10hours/case), it takes total of about 40-50days.
ex-iv) Design exploration of optimum installation for nacelle chine
59
Ex-vi: Design exploration for nacelle chine installation 60
Nacelle chine:For improve the stall due to the interaction of the vortex from the nacelle/ pylon and the wing at landing.
Nacelle installation problem: It is difficult to evaluate
complex flow interaction by CFD.
⇒ Introduction of experiment based optimization
61Ex-vi: Design exploration for nacelle chine installation