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
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