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

46th AIAA Aerospace Sciences Meeting and
Exhibit 7th 10th January, 2008 Grand Sierra
Resort Reno, Nevada
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Presentation Outline

• Introduction
• Role of UAVs
• Research Motivation Goals
• Design of MM-UAV
• Current Design Status
• Direct Numerical Optimization
• Airfoil Geometry Shape Parameterisation
• Test Methodology Results
• Flow Solver
• Selection, Validation Results Analysis
• Optimization
• 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
• Design Mission Segment Based Airfoil
• Morphing Airfoils

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Aerodynamic Optimisation

• Design Methodology
• Direct Numerical Optimisation
• Geometrical Parameterization Model and
• 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

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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

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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

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Airfoil Shape Functions

• 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

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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 (210)
• Perturbation of Design Variables
• Record Fitness - Geometrical Difference of Target
  and Approximated Section
• Aggregate of Total Fitness and
• Geometrical Fitness vs. Aerodynamic Performance

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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 pbest
• Best Global Fitness gbest
• 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.
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Particle Swarm Optimization Set Up

• PSO Structure / Inputs Definition
• Velocity Update
• Position Update

Standard vs. Adaptive PSO
SPSO

• c1 2
• c2 2

• Determine pull of pbest gbest
• c1 Personal Experience
• c2 Swarm Experience

A-PSO

• c1 2
• c2 2

Scaling Factors Cognitive Social (c1 c2)

• ? w Facilitates Global Search
• ? w Facilitates Local Search

Inertia Weight (w)
where

• 0.1-10 of NDIM

• 0.1-10 of NDIM

• 0.1-10 of NDIM

Maximum Velocity
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Particle Swarm Optimizer - Function Test

• Definition
• Search Domain
• Initialization Range
• Global Minima (Fitness)

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Particle Swarm Optimizer - Function Test

• Definition
• Search Domain
• Initialization Range
• Global Minima (Fitness)

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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
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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
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PARSEC Aerodynamic Convergence
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PARSEC Design Variables Definition
Effect of YUP on PARSEC Airfoil Geometry
Effect of YUP on PARSEC Airfoil Aerodynamics
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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
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Flow Solver Computational Fluid Dynamics
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Flow Solver Validation Case 1 NASA LS(1)0417
Mod

• Validation Data
• CP 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

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Flow Solver Validation Case 2 NACA 0012

• Validation Data
• CP 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

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Sample Optimization Run

• Objective Function
• ? 2?
• CL 0.40
• Minimize CD
• Optimizer Inputs ? Final Solution
• Swarm Size 20 Particles
• rLE 0.001 , 0.04 ? 0.0368
• YTE -0.02 , 0.02 ? 0.0127
• Teg -2.0? , -25? ? -19.5?
• TEW 3.0? , 40.0? ? 29.10?
• XUP 0.30 , 0.60 ? 0.4581
• YUP 0.07 , 0.12 ? 0.0926
• YXXU -1.0 , 0.2 ? -0.2791
• XL 0.20 , 0.60 ? 0.5120
• YL -0.12 , -0.07 ? -0.1083
• YXXL 0.2 , 1.20 ? 0.6949
• Results

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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

?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
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Coupling of ANN Swarm Algorithm
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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

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Acknowledgements

• Viscovery Software GmbH
• http//www.viscovery.net/
• Mr. Bernhard Kuchinka
• Kindly provided a trial copy of Viscovery SOMine