Airfoil Geometry Parameterization through Shape Optimizer and Computational Fluid Dynamics

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Airfoil Geometry Parameterization through
Shape Optimizer and Computational Fluid
Dynamics

Manas Khurana

The Sir Lawrence Wackett Aerospace Centre


RMIT University

Melbourne
-

Australia


46
th

AIAA Aerospace Sciences Meeting and Exhibit

7
th



10
th

January, 2008

Grand Sierra Resort


Reno, Nevada

Presentation Outline


Introduction


Role of UAVs


Research Motivation & Goals

o
Design of MM
-
UAV

o
Current Design Status



Direct Numerical Optimization


Airfoil Geometry Shape Parameterisation

o
Test Methodology & Results


Flow Solver

o
Selection, Validation & Results Analysis


Optimization

o
Airfoil Analysis



Summary / Conclusion


Questions

www.airliners.net

I
-
view:

www.defense
-
update.com

Introduction


Multi
-
Mission

UAVs



Cost

Effective
;


Designed

for

Single

Missions
;


Critical

Issues

and

Challenges
;


Demand

to

Address

a

Broader

Customer

Base
;


Multi

Mission

UAV

is

a

Promising

Solution
;

and


Provide

Greater

Mission

Effectiveness



Research

Motivation

&

Goals


Project

Goal

-

Design

of

a

Multi
-
Mission

UAV
;

and


Research

Goal



Intelligent

Airfoil

Optimisation

o
Design

Mission

Segment

Based

Airfoil

o
Morphing

Airfoils

Pegasus:

www.NorthropGrumman.com

X
-
45:

www.Boeing.com

RMIT University:

Preliminary RC
-
MM
-
UAV
Design Concept

Aerodynamic Optimisation


Design

Methodology


Direct

Numerical

Optimisation

o
Geometrical

Parameterization

Model
;

and

o
Validation

of

Flow

Solver


Coupling

of

the

two

Methods


Swarm

Intelligence

Optimization



Neural

Networks


DNO

Computationally

Demanding
;


Development

of

an

ANN

within

DNO
;

and


Integrate

Optimisation

Algorithm

within

the

ANN

Architecture

Geometric Representation Technique Features


Key

Requirements


Flexibility

and

Accuracy
;


Cover

Wide

Design

Window

with

Few

Variables
;


Generate

Smooth

&

Realistic

Shapes
;


Provide

Independent

Geometry

Control
;



Application

of

Constraints

for

Shape

Optimization
;

and


Computationally

Efficient



Approaches



Discrete

Approach
;


Shape

Transformations
:

Conformal

Mapping
;


Polynomial

Representations
;

and


Shape

Functions

added

to

Base
-
Line

Profile

Airfoil Shape Transformations


Conformal Mapping Approach


Computationally

In
-
Expensive
;


Joukowski

&

Kármán
-
Trefftz

Transformations
;


Transformation

from

Complex

to


-
Plane
;

and


Five

Shape

Parameters


xc

-

Thickness


yc

-

Camber

towards

leading

edge


xt

-

Thickness

towards

trailing

edge


yt

-

Camber

towards

trailing

edge


n

-

Trailing

edge

angle



Conformal Mapping Restrictions


Limited

Design

Window
;


Divergent

Trailing

Edge

Airfoils

not

possible
;

and


Failure

to

Capture

Optimal

Solution


Airfoil Shape Functions

NACA 0015

Analytic Function


Introduction


Analytical Approach;


Control over Design Variables;


Cover Large Design Window;


Linearly Added to a Baseline Shape;






Participating Coefficient
act as Design
Variables
(

i
); and


Optimization Study to Evaluate Parameters

Population &

Shape Functions

Optimization


Shape Function Convergence Criteria


Convergence Measure Requirements


Flexibility

&

Accuracy
;

and


Library

of

Target

Airfoils



Geometrical Convergence Process


Specify

Base

&

Target

Airfoil
;


Select

Shape

Function
;


Model

Upper

&

Lower

Surfaces
;


Design

Variable

Population

Size

(
2
:
10
)
;


Perturbation

of

Design

Variables
;


Record

Fitness

-

Geometrical

Difference

of

Target

and

Approximated

Section
;




Aggregate

of

Total

Fitness
;

and


Geometrical

Fitness

vs
.

Aerodynamic

Performance

Intelligent Search Agent


Particle Swarm Optimization


Swarm

Approach



Models

Natural

Flocks

and

Movement

of

Swarms
;


Quick,

Efficient

and

Simple

Implementation
;


Ideal

for

Non
-
Convex

Discontinuous

Problems
;



Solution

Governed

by

Position

of

Particle

within

N
-
dimensional

Space
;


Each

Particle

Records

Personal

Fitness



p
best
;


Best

Global

Fitness



g
best
;


Velocity

&

Position

Updates

based

on

Global

Search

Pattern
;

and


Convergence



Particles

Unite

at

Common

Location


J. Kennedy and R. Eberhart, "Particle Swarm Optimization“, presented
at IEEE International Conference on Neural Networks, 1995.



Algorithm

1.
Initialise Particle Swarm

2.
Initialise Particle Velocities

3.
Evaluate Fitness of Each Particle

4.
Update according to:

i.
Velocity Update

ii.
Position Update

5.
Repeat until Convergence Satisfied

Particle Swarm Optimization Set Up


PSO

Structure

/

Inputs

Definition


Velocity

Update
:




Position

Update
:


SPSO

o

0.1
-
10% of
N
DIM


o

c
1

= 2

o

c
2

= 2




0.1
-
10% of N
DIM




‘w’ Facilitates Global Search




‘w’ Facilitates Local Search

Determine ‘pull’ of p
best
& g
best



c
1


Personal Experience


c
2


Swarm Experience

A
-
PSO

o

0.1
-
10% of N
DIM


Maximum Velocity

Inertia Weight (w):

o

c
1

= 2

o

c
2

= 2


Scaling Factors
Cognitive & Social
(c
1

& c
2
)

where


Standard vs. Adaptive PSO


Particle Swarm Optimizer Search Agents

Particle Swarm Optimizer
-

Function Test


Definition
:




Search Domain:




Initialization Range:




Global Minima (Fitness):


Velocity

Fitness

Fitness

Low Velocity = Low Fitness

Particle Swarm Optimizer
-

Function Test


Definition
:




Search Domain:




Initialization Range:




Global Minima (Fitness):


Velocity

Fitness

Fitness

Low Velocity = Low Fitness

Shape Parameterization Results


Summary of Results


Measure of Geometrical Difference


Hicks
-
Henne Most Favorable


Legendre Polynomials
Computationally Not Viable


Aerodynamic Coefficients
Convergence



Geometrical Convergence Plots /
Animations




s


Hicks
-
Henne Geometrical
Convergence




s

Bernstein Geometrical
Convergence


Aerodynamic Convergence Plots /
Animations




s


Hicks
-
Henne Aerodynamic
Convergence




s

Bernstein Aerodynamic
Convergence

Shape Functions Limitations


Polynomial Function Limitation


Local Shape Information;


No Direct Geometry Relationship;


NURBS Require Many Control Points; and


Lead to Undulating Curves


PARSEC Airfoil Representation



6
th

Order Polynomial;






Eleven Variables


Equations Developed as a Function of
Airfoil Geometry; and


Direct Geometry Relationship


H. Sobieczky, “Parametric Airfoil and Wings“, in: Notes on Numerical
Fluid Mechanics, Vol. 68, pp. 71
-
88, 1998

Fitness Magnitude of Shape Functions

PARSEC Airfoils

PARSEC Aerodynamic Convergence

Convergence to Target Lift Curve Slope

Convergence to Target Drag Polar

Convergence to Target Moment

Convergence to Target L/D

PARSEC Design Variables Definition

Effect of Y
UP

on PARSEC Airfoil Aerodynamics


Lift Coefficient

Drag Coefficient


Moment Coefficient

Lift
-
to
-
Drag Ratio

Effect of Y
UP
on PARSEC Airfoil Geometry

Y
UP

Nose Radius

t/c

Camber

Low Y
UP
= Good C
D

Performance

Shape Function Modifications


Airfoil Surface Bumps



Aerodynamic Performance Improvements;


Rough Airfoils Outperform Smooth Sections at Low R
e
;


Control Flow Separation;


Passive & Active Methods for Bypass Transition;


Reduction in Turbulence Intensity; and


Bumps Delay Separation Point



Shape Functions
-

Further Developments


Local Curvature Control;


Roughness in Line with Boundary Layer Height; and


Control over Non
-
Linear Flow Features

Airfoil Surface Bumps to Assist Flow Reattachment



Source:
A.
Santhanakrishnan
and J. Jacob, “
Effect of Regular Surface
Perturbations on Flow Over an Airfoil
”,
-

University of Kentucky,

AIAA
-
2005
-
5145

Ideal Surface


Bumpy Surface


Flow Solver


Computational Fluid Dynamics

Laminar

Turbulent

Flow Solver Validation


Case 1: NASA LS(1)0417 Mod


Validation Data


C
P

Agreement

at

AOA

10

;


Lift

&

Drag

Convergence

over

Linear

AOA
;


Lift



2
%

;

Drag



5
%
;


Solution

Divergence

at

Stall
;

and


Fluid

Separation

Zone

Effectively

Captures

Boundary

Layer

Transition

Flow Solver Validation


Case 2: NACA 0012


Validation Data


C
P

Agreement

at

AOA

11

;


Lift

&

Drag

Convergence

over

Linear

AOA
;


Lift



5
%

;

Drag



7
%
;


Solution

Divergence

at

Stall
;

and


Fluid

Separation

Zone

Effectively

Captures

Boundary

Layer

Transition

Sample Optimization Run


Objective Function





=

2



C
L

= 0.40


Minimize C
D



Optimizer Inputs






Final Solution


Swarm Size

=

20 Particles


r
LE

=

[0.001 , 0.04]




0.0368


Y
TE

=

[
-
0.02 , 0.02]




0.0127


T
eg

=

[
-
2.0


,
-
25

]




-
19.5



T
EW

=

[3.0


, 40.0

]




29.10



X
UP

=

[0.30 , 0.60]




0.4581


Y
UP

=

[0.07 , 0.12]




0.0926


Y
XXU

=

[
-
1.0 , 0.2]





-
0.2791


X
L

=

[0.20 , 0.60]




0.5120


Y
L

=

[
-
0.12 ,
-
0.07]




-
0.1083


Y
XXL

=

[0.2 , 1.20]





0.6949



Results


t/c

= 20%


C
L

= 0.4057


C
D


= 0.0069


Total Iterations = 29

Optimization History Plot

Final Airfoil Shape

Aerodynamic Coefficient Database


Artificial Neural Networks


Artificial Neural Networks


Airfoil Training Database


Geometrical Inputs;


Aerodynamic Coefficient/s Output/s

;


Set
-
up of Transfer Function within the Hidden Layer; and


Output RMS Evaluation

Coefficient of Lift NN Structure

Coefficient of Drag NN Structure

Coefficient of Moment NN Structure


R. Greenman and K. Roth “Minimizing Computational Data Requirements for Multi
-
Element Airfoils
Using Neural Networks“, in: Journal of Aircraft, Vol. 36, No. 5, pp. 777
-
784 September
-
October 1999

Coupling of ANN & Swarm Algorithm

Conclusion


Geometry Parameterisation Method


Six

Shape

Functions

Tested
;


Particle

Swarm

Optimizer

Validated

/

Utilized
;


SOMs

for

Design

Variable

Definition
;

and


PARSEC

Method

for

Shape

Representation



Flow Solver


RANS

Solver

with

Structured

C
-
Grid
;


Transition

Points

Integrated
;


Acceptable

Solution

Agreement
;

and


Transition

Modeling

and

DES

for

High
-
Lift

Flows



Airfoil Optimization


Direct

PSO

Computationally

Demanding
;

and


ANN

to

Reduce

Computational

Data

www.cosmosmagazine.com

www.mathworks.com

Acknowledgements


Viscovery Software GmbH


[http://www.viscovery.net/]

Mr. Bernhard Kuchinka



Kindly provided a trial copy of Viscovery SOMine