navier- stokes optimization using genetic algorithm and...

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


Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Introduction

1. Gradient Based (Deterministic) Methods

2. Evolutionary (Stochastic) Methods


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.


Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Gradient Based Methods

1. Gradient Based (Deterministic) Methods

2. Evolutionary (Stochastic) Methods


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.


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.


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.


Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Airfoil Parameterization Methods

Airfoil Parameterization Methods

1-Bezier Spline 2-PARSEC



New Approach (PARSEC+Sobeiczky)



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


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


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



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



Grid Movement

1-Primary Mesh 2-Moved Mesh



Results

M=0.73,α=2.0, Turbulent Boundary Layer, Objective Function=Cl/Cd



Results


Results

61.13 0.01093 0.694Design (Combined)

59.090.011210.663Design (PARSEC)

47.900.01340 0.642 RAE-2822

Cl/CdCdClAirfoil



Results


M=0.73,α=2.0, Turbulent Boundary Layer, Objective Function=Cd


Results



1-Initial Airfoil 2-Desiged Airfoil Using Combined Method


Results


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


Navier- Stokes Optimization Using Genetic Algorithm and a Flexible Parametric Airfoil Method, Conclusion

navier- stokes optimization using genetic algorithm and...

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