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
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Airfoil Geometry Parameterization through Shape Optimizer and Computational Fluid
Dynamics
Manas KhuranaThe Sir Lawrence Wackett Aerospace Centre
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
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
n
iii
AirfoilInitiali xfxyxy
1)()(),(
i
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
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.1
-0.05
0
0.05
0.1
0.15
Comparison of Airfoil Shape Configuration for Geometrical Shape Parameterisation
x/c
y/c
Base: NACA 0015Target 1: NASA LRN(1)-1007Target 2: NASA LS(1)-0417ModTarget 3: NASA NLF(1)-1015
‘w’ Facilitates Global Search ‘w’ Facilitates Local Search
Determine ‘pull’ of pbest & gbest c1 – Personal Experience c2 – Swarm Experience
A-PSO
o 0.1-10% of NDIMMaximum Velocity
Inertia Weight (w):
o c1 = 2o c2 = 2
Scaling Factors Cognitive & Social
(c1 & c2)
;42
2w2
21 cc where
ijij
ij
bestbest
bestij
gp
pxijISA
ijISAij ew
111
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
05
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
Cos
t
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 Functions216
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 = 5Turbulence 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 RANSEnergy 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 = 5Turbulence 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 RANSEnergy 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
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