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
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Airfoil Geometry Parameterization through Shape Optimizer and Computational Fluid
Dynamics
Manas KhuranaThe Sir Lawrence Wackett Aerospace Centre
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
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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 Airfoilo Morphing Airfoils
‘w’ Facilitates Global Search ‘w’ Facilitates Local Search
Determine ‘pull’ of pbest & gbest
c1 – Personal Experience
c2 – Swarm Experience
A-P
SO
o 0.1-10% of NDIMMaximum Velocity
Inertia Weight (w):
o c1 = 2
o c2 = 2
Scaling Factors Cognitive & Social
(c1 & c2)
;42
2w
2
21 cc where
ijij
ij
bestbest
bestij
gp
pxijISA
ijISAij ew
1
11
Standard vs. Adaptive PSO
kxPrandckxPrandckvwkv igiiii 211
11 kvkxkx iii
Particle Swarm Optimizer Search Agents
Particle Swarm Optimizer - Function Test
1
1
221
2 1)(100)(n
iiii xxxxf
nixi ,...,2,1,100100
0)(),1,...,1( ** xfX
-10-5
05
10
-10
-5
0
5
100
5
10
15
x 105
x
Rosenbrock Function
y
z
3015 ix
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):
0)(),1,...,1( ** xfX
n
iii xxnxf
1
)sin(9829.418)(
nixi ,...,2,1,500500
500250 ix
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
10
1
2
3
4
5
6
7
8
Shape Function
Co
st
Magnitude of Cost Function
BernsteinHicks-HenneLegendreNACAWagner
Geometrical Convergence Plots / Animations
sHicks-Henne Geometrical
Convergence
s Bernstein Geometrical Convergence
Aerodynamic Convergence Plots / Animations
sHicks-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 6th 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
10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Shape Functions
Fitn
ess
Mag
nitu
de
BernsteinHicks-HennePARSECLegendreNACAWagner
Fitness Magnitude of Shape Functions2
16
1
n
nnPARSEC XaZ
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
-5 0 5 10 15 200.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
( )
CL
TargetHicks-HennePARSEC
0 0.02 0.04 0.06 0.08 0.1 0.120.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CD
CL
TargetHicks-HennePARSEC
-5 0 5 10 15 20-0.11
-0.1
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
( )
CM
TargetHicks-HennePARSEC
-5 0 5 10 15 200
50
100
150
( )
L/D
TargetHicks-HennePARSEC
PARSEC Design Variables Definition
Effect of YUP on PARSEC Airfoil Aerodynamics Lift Coefficient Drag Coefficient Moment Coefficient Lift-to-Drag Ratio
Effect of YUP on PARSEC Airfoil GeometryYUP Nose Radiust/c Camber
Low YUP = Good CD Performance
Shape Function Modifications Airfoil Surface Bumps
Aerodynamic Performance Improvements; Rough Airfoils Outperform Smooth Sections at Low Re; 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
6,000Maximum Iteration Count
1.0 x 10-6Residual Solution Convergence
0.32Flow Mach Number
Turbulence Intensity = 0.5%; Viscosity Ratio = 5
Turbulence Intensity = 2%; Viscosity Ratio = 20
Boundary Conditions:InletPressure Outlet
Air as an Ideal GasFlow Medium
6.0 x 106Reynolds Number
- & SA Turbulence ModelingViscous Model
Second Order UpwindDiscretization Scheme
1.055Wall Cell Intervals
96,000Total Mesh Size (approx.)
Segregated Implicit Formulation of RANS
Energy Equations also Solved
Solver
1Wall y+ Range (approx.)
80Circumferential Lines
100Radial Lines
2D Structured C-TypeMesh
6,000Maximum Iteration Count
1.0 x 10-6Residual Solution Convergence
0.32Flow Mach Number
Turbulence Intensity = 0.5%; Viscosity Ratio = 5
Turbulence Intensity = 2%; Viscosity Ratio = 20
Boundary Conditions:InletPressure Outlet
Air as an Ideal GasFlow Medium
6.0 x 106Reynolds Number
- & SA Turbulence ModelingViscous Model
Second Order UpwindDiscretization Scheme
1.055Wall Cell Intervals
96,000Total Mesh Size (approx.)
Segregated Implicit Formulation of RANS
Energy Equations also Solved
Solver
1Wall y+ Range (approx.)
80Circumferential Lines
100Radial Lines
2D Structured C-TypeMesh
Flow Solver Validation – Case 1: NASA LS(1)0417 Mod