Ava Shahrokhi,Alireza Jahangirian, Nematolah Fouladi
Aerospace Engineering Department Amirkabir University of Technology (Polytechnique)
Tehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil
Method
Contents
• Introduction
• Optimization Methods
• Airfoil Parameterization Methods
• New Combinatory Airfoil Shape Definition
• Results
• Conclusion
Amirkabir UniversityTehran-IRAN
• Why airfoil optimization is important?
Shorter Landing and Takeoff DistancesDecreasing Fuel ConsumptionDecreasing the Power Needed for Actuator Movement
• Optimization Process
1. Definition of Objective Function and Constrains2. Definition of Geometry Using Design Parameters3. Estimation of Objective Function For Basic Geometry4. Seeking Optimum Point Using Optimization Algorithm
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Introduction
1. Gradient Based (Deterministic) Methods
2. Evolutionary (Stochastic) Methods
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Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Optimization Methods
What problems are associated with Gradient Based methods?
1. Objective Function should be differentiable and convex, only in this case the answer might be global.
2. They start from a single point so the optimum they seek is the best in the neighborhood of the current point therefore these methods are basically local.
3. Number of design variables should be limited otherwise it will highly affect the convergence rate or it may leads to a local minimum.
4. Sensitivity information can not be easily extracted form CFD codes.
5. For grids with closer spacing, obtained derivatives can be highly sensitive to the changes in design variables.
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Gradient Based Methods
1. Gradient Based (Deterministic) Methods
2. Evolutionary (Stochastic) Methods
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Optimization Methods
Advantages of Using GA1. They search from a population of point resulting in a global
optimum.
2. They only use objective function NOT its derivatives.
3. Instead of introducing complicated constrains, a limited design space can be used.
4. They can be easily used in discontinuous design spaces where gradient methods are useless.
5. Increase in the number of design variables will not lead to undesirable results.
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Evolutionary Based Methods
Successfully Implementing a GA
1. Choosing suitable initial population.
2. Correct computation of the fitness function.
3. Tuning and selection of the probabilities associated with crossover and mutation.
4. Good representation of the individuals.
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Evolutionary Based Methods
Characteristics of a Suitable Airfoil Parameterization for GA
• Creating an acceptable airfoil shape • Including the parameters that affect the solution
more.• Having enough flexibility required for the most
optimum shape.• Including minimum number of parameters.
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Parameterization Methods
Airfoil Parameterization Methods
1-Bezier Spline 2-PARSEC
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Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Parameterization Methods
New Approach (PARSEC+Sobeiczky)
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Parameterization Methods
Parameter Selection for SobieczkyMethod
-4.00E-02
-2.00E-02
0.00E+00
2.00E-02
4.00E-02
6.00E-02
0.4 0.6 0.8 1 1.2
a=70,n=6,m=1.3a=70,n=6,m=1.5a=70,n=6,m=1.1original
-6.00E-02
-4.00E-02
-2.00E-02
0.00E+00
2.00E-02
4.00E-02
6.00E-02
0.4 0.6 0.8 1 1.2
original70,n=470,n=370,n=570,n=6
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, New Approach
Airfoil Optimization Using GA
1. Airfoil Shape Definition Using Combined Method2. Objective Function Evaluation Using CFD3. Applying GA as Optimizer:
3.1. Selection Among Population3.2. Cross Over and mutate the population to create the new population. 3.3. Objective Function Evaluation for New Generation
4. Checking the Stop Criteria
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Flow Simulation: Conservative 2-D Compressible Navier-Stokes Equations
VIVI GGGFFF −=−= ,
0=∂∂
+∂∂
+∂∂
yG
xF
tQ
++
=
++
=
++
=
+
+=
=
yyyxy
yy
xyV
xxyxx
xy
xxV
II
qu
G
qu
F
vPEPv
uvv
G
uPEuv
Puu
F
Evu
Q
νττ
τ
τ
νττ
ττ
ρρρρ
ρρρρ
ρρρρ
0
,
0
)(
,
)(
,2
2
tttt SyG
xF
tQ
=∂∂
+∂∂
+∂∂
=
=
=
=
=
ky
kyV
kx
kxV
It
Itt
GF
vvk
Guuk
Fk
Q
β
β
ββ
ερρ
ερρ
ρερ
,
,,
−
−=
kC
kPC
PS
k
k
t2
21ρεε
ρε
εε
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
CFD Solver
Double Time Implicit MethodFinite Volume, Cell CenterCentral Difference ApproximationK-έ Method for Turbulence ModelingUnstructured GridSpring Analogy for Grid MovementInitial Airfoil Flow Characteristics is used as Primary Values for Flow Solver
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Grid Movement
1-Primary Mesh 2-Moved Mesh
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Results
M=0.73,α=2.0, Turbulent Boundary Layer, Objective Function=Cl/Cd
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Results
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Results
61.13 0.01093 0.694Design (Combined)
59.090.011210.663Design (PARSEC)
47.900.01340 0.642 RAE-2822
Cl/CdCdClAirfoil
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Results
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
M=0.73,α=2.0, Turbulent Boundary Layer, Objective Function=Cd
Amirkabir UniversityTehran-IRAN
Results
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Amirkabir UniversityTehran-IRAN
1-Initial Airfoil 2-Desiged Airfoil Using Combined Method
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Optimization Using GA
Results
Amirkabir UniversityTehran-IRAN
0.0107
0.0127
0.0160
Cd
0.53
0.30
0.33
Cl
Design (Combined)
Design (PARSEC)
NACA 0012
Airfoil
Conclusion1. in the Current Research:
New airfoil shape parameterization method was used to create a more efficient airfoil shape by considering the parameters which affect the airfoil shape more than other ones.This methods allows for deceasing the maximum thickness of the airfoil to damp the shock while maintaining its Lift by compensate the decrease in the lift at the rear part of the airfoil.
2.Tricks used to speed up the optimization process:-Double Time Implicit Flow Solver-Spring Analogy for Grid Movement- Initial Airfoil Flow Characteristics is used as Primary Guess for Flow Solver
Amirkabir UniversityTehran-IRAN
Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Conclusion
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