Developments in

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Developments in Evolutionary Algorithms and
Multi Disciplinary Optimisation
A University of Sydney Perspective
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The Team

• Dr. K Srinivas - Leader
• Prof. J. Périaux Advisor
• Prof. S W Armfield
• Dr. E. J. Whitney
• Mr. L. F. Gonzalez
• Mr. S. Nagarathinam
• Mr. D. S. Lee
• Dr. M Sefrioui

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Overview
General aspects of the program K. Srinivas
Discussion of specific examples Mr. Luis Felipe
Gonzalez
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Motivation
Search Space Large
Multimodal Non-Convex
Discontinuous
Traditional Methods- Trade off between
Conflicting Requirements
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Evolutionary Algorithms
Explore large search spaces.
Robust towards noise and local minima
Easy to parallelise
Map multiple populations of points, allowing
solution diversity.
A number of multi-objective solutions
in a
Pareto set or
performing a robust Nash game.
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Multi-Objective Optimisation
Maximise/ Minimise
Subjected to constraints
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Pareto Front
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Drawback of EAs
A typical aerodynamic optimisation relies on
CFD and FEA on structures
CFD Computation is time consuming
Our research addresses this issue in some detail
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Our Contribution
Parallel Computing
Asynchronous Evaluation
Hierarchical Population Topology
Hierarchical Asynchronous Parallel Evolutionary
Algorithms (HAPEA)
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Parallel Computing and Asynchronous Evaluation
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Asynchronous Evaluation
Suspend the idea of generation
Solution can be generated in and out of order
Processors Can be of different speeds
Added at random
Any number of them possible
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Pareto Tournament Selection
Create a tournament
Where B is the selection buffer.
If the new individual x is not dominated any
other in the tournament (Q), then it is
immediately accepted and inserted into the main
population according to the replacement rules.
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Hierarchical Population Topology

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Problems in Aerodynamic Optimisation (1)

• Multidisciplinary design problems involve search
  space that are multi-modal, non-convex or
  discontinuous.
• Traditional methods use deterministic approach
  and rely heavily on the use of iterative
  trade-off studies between conflicting
  requirements.

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Problems in Aerodynamic Optimisation (2)

• Traditional optimisation methods will fail to
  find the real answer in most real engineering
  applications, (Noise, complex functions).
• The internal workings of validated in-house/
  commercial solvers are essentially inaccessible
  from a modification point of view (they are
  black-boxes).

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NASA and US Air force and EAs

• 1 N. Madavan, Turbomachinary airfoil Design
  Optimization using Differential Evolution,
• 2 Thomas A. Zang and Lawrence L. Green,
  Multidisciplinary Design Optimisation Techniques
  Implications and opportunities for Fluid Dynamics
  Research.
• 3 Illinois Genetic Algorithms Laboratory,
  U.S. Air Force Office of Scientific Research,
  F49620-97-1-0050..

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Optimisation of Analytical Test Functions

• Ackley
• MOEAs Examples
• Asynchronous Test Case Sphere Function

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Test Functions Ackley
Increasing number of variables
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Asynchronous Test Case Sphere Function

• Solved on a single population
• Asynchronous
• Assign a small fictitious delay to each
  function evaluation. This will vary uniformly
  between two values fastest and lowest. Evaluate
  asynchronously.
• Synchronous
• Assign the same delay to all individuals in
  advance. Wait until the slowest evaluation is
  completed, as it will occur in practice on a
  cluster of computers.
• Four unknowns4), Stopping Condition 0.0001,
  25 runs. Configurations up to tslowest /tfastest
  5

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MOEA Examples

• Here our EA solves a two objective problem with
  two design variables. There are two possible
  Pareto optimal fronts one obvious and concave,
  the other deceptive and convex

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MOEA Examples

• Again, we solve a two objective problem with two
  design variables however now the optimal Pareto
  front contains four discontinuous regions

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Results So Far
Evaluations CPU Time
Traditional 2311 224 152m 20m
New Technique 504 490 (-78) 48m 24m (-68)

• The new technique is approximately three times
  faster than other similar EA methods.

• A testbench for single and multiobjective
  problems has been developed and tested

• We have successfully coupled the optimisation
  code to different compressible and incompressible
  CFD codes and also to some aircraft design codes
• CFD
  Aircraft Design
• HDASS MSES XFOIL
  Flight Optimisation Software
  (FLOPS)
• FLO22 Nsc2ke
  ADS (In house)

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Applications So Far (1)

• Constrained aerofoil design for transonic
  transport aircraft ? 3 Drag reduction

• UAV aerofoil design
• -Drag minimisation for high-speed transit and
  loiter conditions.
• -Drag minimisation for high-speed transit and
  takeoff conditions.

• Exhaust nozzle design for minimum losses.

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Applications So Far (2)

• Three element aerofoil reconstruction
• from surface pressure data.

• UCAV MDO
• Whole aircraft multidisciplinary design.
• Gross weight minimisation and cruise
  efficiency Maximisation. Coupling with NASA code
  FLOPS
• 2 improvement in Takeoff GW and Cruise
  Efficiency

• AF/A-18 Flutter model validation.

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Applications So Far (3)

• Transonic wing design Two Objectives
• UAV Wing Design

• Wind Tunnel Test on
• Evolved Aerofoils
• Evolved Wings (in progress)
• Evolved Aircrafts (in progress)

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Capabilities

• We are now confident of our ability to optimise
  real industrial/Aeronautical cases, which could
  be three-dimensional, having multi-objective
  criteria or related to multidisciplinary Design
  Optimisation (MDO).

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Technical Resources Parallel Computing

• Computer resources
• Access to a Dell Linux Cluster (Scalable
  Parallel) Theoretical Peak Performance 1860
  Gflops (or 1.82 Tflops)
• Sustain Performance Achieved 1095 Gflops (or
  1.07 Tflops) - using LINPACK measurement

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Technical Resources Analysis Tools

• Aerodynamics/CFD
• FLUENT
• FLO22 (NASA Langley)
• HDASS (In house Navier-Stokes Solver)
• (2D Gridless solver)
• VLMpc ( Vortex lattice method)
• Structural Analysis
• Finite Element Analysis Strand 7 Nastran

• CAD
• Solid Works, Autocad
• Aircraft Design
• FLight Optimisation System (FLOPS) NASA Langley
• AAA (DART corporation)
• ADS (In House)

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Four Representative Examples

• Three Element Aerofoil Euler Reconstruction.
• Aerofoil Optimisation
• Multidisciplinary UAV Design Optimisation
• Multidisciplinary Wing Design Optimisation

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Three Element Aerofoil Euler Reconstruction.

• Problem Definition
• Rebuild from scratch the pressure distributions
  that approximately fit the target pressure
  distributions of a three element aerofoil set.
• Flow Conditions
• -Mach 0.2,
• - Angle of Attack 17 deg
• - Euler Flow, unstructured mesh

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Multi-element aerofoil reconstruction problem
Design variables
The design variables are the position
And rotation of the slat and flap
Upper and lower bounds of position and rotation
are and
respectively
Fitness Function
The fitness function is the RMS error of the
surface pressure coefficients on all the three
elements
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Implementation
Single Population EA (EA SP)
Population size 40
Grid n x 2500
Hierarchical Asynchronous Parallel EA (HAPEA)
Viscous Grid n x 2500
Viscous Grid n x 2000
Viscous Grid n x 1500
Population size 40
Population size 40
Population size 40
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Pressure Distribution
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Candidate and Target Geometries
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Example of Convergence History.
A better solution in lower computing time
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Aerofoil Optimisation

• Problem Definition
• Find the Pareto set of aerofoils for minimum
  total drag at two design points,
• Compare to Nadarajah and RAE 2822.

Property Flt. Cond. 1 Flt Cond.2
Mach 0.75 0.75
Reynolds 9 x 106 9 x 106
Lift 0.65 0.715
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Design Variables Bounding Envelope of the
Aerofoil Search Space
16 Design variables for the aerofoil
Two Bezier curves representation
Six control points on the mean line.

• Constraints
• Thickness gt 12 x/c
• Pitching moment gt -0.065

• Ten control points on the thickness distribution.

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Implementation
Hierarchical Asynchronous Parallel EA (HAPEA)
Model 1 Grid 215 x 36
Model 2 Grid99 x 16
Model 3 Grid 71 x 12
To solve this and other problems standard
industrial flow solvers are being used. In This
case MSES (EulerBL ) M. Drela
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Pareto Front Transonic Aerofoil Design Problem
Flight Condition 1
Compromise
Flight Condition 1
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Aerofoil Optimisation Results

• For a typical 400,000 lb airliner, flying 1,400
  hrs/year
• 3 drag reduction corresponds to 580,000 lbs
  (330,000 L) less fuel burned.

Aerofoil cd cl 0.65 cd cl 0.715
Traditional Aerofoil RAE2822 0.0147 0.0185
Conventional Optimiser Nadarajah 1 0.0098 (-33.3) 0.0130 (-29.7)
New Technique 0.0094 (-36.1) 0.0108 (-41.6)

• 1 Nadarajah, S. Jameson, A, " Studies of the
  Continuous and Discrete Adjoint Approaches to
  Viscous Automatic Aerodynamic Shape
  Optimisation," AIAA 15th Computational Fluid
  Dynamics Conference, AIAA-2001-2530, Anaheim, CA,
  June 2001.

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UAV Conceptual DesignOptimisation Problem

• Minimise two objectives
• Gross weight ? min(WG)
• Endurance ? min (1/E)
• Subject to
• Takeoff lenght lt 1000 ft,
• Alt Cruise gt 40000
• ROC gt 1000 fpm,
• Endurance gt 24 hrs
• With respect to
• external geometry of the aircraft

• Mach 0.3
• Endurance gt 24 hrs
• Cruise Altitude 40000 ft

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Design Variables
In total we have 29 design variables
13 Configuration Design variables
Design Variable Lower Bound Upper Bound
Wing Area (sq ft) 280 330
Aspect Ratio S 18 25.2
Wing Sweep (deg) 0.0 8.0
Wing Taper Ratio 0.28 0.8
Camber
Wing
Twist
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Design Variables

Horizontal Tail Area (sq ft) 65.0 85.0
HT Aspect Ratio 3.0 15.0
HT Taper Ratio 0.2 0.55
HT Sweep (deg) 12.0 15.0
Vertical Tail Area (sq ft) 11.0 29.0
VT Aspect Ratio 1.0 3.2
VT Taper Ratio 0.28 0.62
VT Sweep (deg) 12.0 34.0
Fuselage Diameter 2.6 5.0
Camber
Tail
Twist
Fuselage
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Design Variables Bounding Envelope of the
Aerofoil Search Space
16 Design variables for the aerofoil
Two Bezier curves representation
Six control points on the mean line.

• Constraints
• Thickness gt 12 x/c
• Pitching moment gt -0.065

• Ten control points on the thickness distribution.

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Mission profile
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Design Tools
pMOEA (HAPEA)
Optimisation
FLOPS (Modified to accept user computed
aerodynamic data)
Aircraft design and analysis
A compromise on fidelity models Vortex induced
drag VLMpc Viscous drag friction Aerofoil
Design Xfoil
Aerodynamics
Structural weight analysis
FLOPS
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Implementation
Grid 141x 74x 36 on aerofoil, 20 x 6 on Vortex model
Grid 109x 57x 27 on aerofoil, 17 x 6 on Vortex model
Grid 99x 52x 25 on aerofoil, 15 x 6 on Vortex model
Population size 20
Population size 20
Population size 20
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Convergence history for objective one
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Pareto optimal region
Objective 1 optimal
Compromise
Objective 2 optimal
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Sample of Pareto Optimal configurations
Pareto Member 16
Pareto Member 0
Pareto Member 14
Pareto Member 19
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MOO of transonic wing design for an Unmanned
Aerial Vehicle (UAV)
Minimisation of wave drag and wing weight
Mach Number 0.69
Cruising Altitude 10000 ft
Cl 0.19
Wing Area 2.94 m2
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Procedure
Aerodynamics
Potential Flow Solver (FLO22)
?
approximated as the sum of the span-wise cap
weight to resist the bending moment
Structural Analysis Wing Weight
?

• Lift distribution is replaced by concentrated
  loads
• The local stress has to be less than the ultimate
  shear stress. In this case for Aluminum Alloy

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Design Variables
16 Design variables on three span wise aerofoils

9 Design variables on three span wise aerofoil
section
57 design variables
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Constraints Objective Functions
Minimum thickness
Position of Maximum thickness
Fitness functions
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Implementation
Approach one Traditional EA with single
population model Computational Grid 96 x 12
x 16 Approach two HAPEA
Six machines were used in all calculations
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Pareto fronts after 2000 function evaluations
The algorithm was run five times for 2000
function evaluations and took about six hours to
compute
HAPEA approach
Single population approach
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Convergence history for objective one
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Results
Aerofoil sections for Pareto Member 0 12, 20
Top view of wings on Pareto set
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Aerofoil sections for Pareto member ten (PM10)
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Wing span pressure coefficient distribution
Aspect Ratio 3.5 MACH 0.69 YAW
0.0 ALPHA 0.920 L.E Sweep
10.2 deg L.E Sweep 2 -1.9 deg CD
0.0013
Pareto Member 10
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Top and side view Pareto Wing 10
Top View
Side View
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Work in Progress

• Master of Engineering
• Rotor Blade design and Optimisation using
  evolutionary Techniques
• Adaptive Transonic Wing/Aerofoil Design and MDO
  using Evolutionary Techniques
• Grid-less Algorithms for Design and optimisation
  in Aeronautics
• Undergraduate Projects
• Transonic wing design using DACE (Design of
  Experiments-approximation Theories)
• An empirical study on DSMC for within
  evolutionary Optimisation

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The Challenge

• The use of higher fidelity models is till
  prohibitive, research on surrogate
  modeling/approximation techniques is required.
• MDO is a challenging topic, the last few year
  have seen several approaches for Design and
  optimization using Evolutionary techniques but
  research indicate that it is problem dependent
  and it is still an open problem.
• Access to Dell Linux Cluster is limited for
  benchmarking purposes. Use of higher fidelity
  models is still prohibitive.

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Long term vision

• A robust framework for Aeronautical MDO

Optimiser Set (EAS, gradient hybrid)
Higher Fidelity Models
Conceptual design
Approximation Techniques (RSM.?),
Preliminary design
Database of Case Studies)
CAD Integration
Detailed Design
Parallelization Strategies
Multidisciplinary Analysis
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Limitations

• Higher fidelity analysis codes
• Funding
• Limited access to Dell Linux Cluster for
  benchmarking purposes. Use of higher fidelity
  models is still prohibitive.

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Outcomes (1)

• The new technique with multiple models Lower
  the computational expense dilemma in an
  engineering environment (three times faster)
• Direct and inverse design optimisation problems
  have been solved for one or many objectives.
• Some Multi-disciplinary Design Optimisation (MDO)
  problems have been solved.
• The algorithms find traditional classical results
  for standard problems, as well as interesting
  compromise solutions.
• In doing all this work, no special hardware has
  been required Desktop PCs networked together
  have been up to the task.

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Outcomes (2)

• No problem specific knowledge is required ? The
  method appears to be broadly applicable to
  different analysis codes.
• Work to be done on approximate techniques and use
  of higher fidelity models

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Acknowledgements

• The authors would like to acknowledge Professor
  Steve Armfield and Dr Patrick Morgan at The
  University of Sydney for providing the facilities
  on using the cluster of computers.
• The authors would like to thank Arnie McCullers
  at NASA LARC for providing the FLOPS code.
• The authors would like to thank Professor M.
  Drela, B. Mohammadi and NASA for providing the
  MSES, Nsc2ke and FLO22 codes respectively.
• Also to Professor K. Deb for discussions on
  developments and applications of MOEA during his
  visit to The University of Sydney in 2003.
• The authors would like also acknowledge
  contribution of MER students S. Nagarathinam and
  D.S. Lee, with some of the slides and figures for
  this presentation.

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Questions
70
ADDITIONAL SLIDES
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Funding Sought
DIRECT COSTS    
Personnel    
Postgraduate Student (PhD) / Research Associate 20,000.00 20,000.00
Total Personnel (a) 20,000.00 21,000.00
Equipment    
Computer Resources 4,000.00 0.00
Total Equipment (b) 4,000.00 0.00
Travel    
Two trips to AIAA and US conferences sites. 2,500.00 2,500.00
Total Travel (c) 2,500.00 2,500.00
TOTAL DIRECT COSTS (e) 26,500.00 23,500.00
INDIRECT COSTS    
PIs and any researcher Level A or above x multiplier The University of Sydney  2,000.00  5,000.00
TOTAL INDIRECT COSTS (f) 2,000.00 2,000.00
TOTAL COSTS (h) 28,500.00 25,500.00
72
Justification of Funding Requested

• Personnel A postgraduate student stipend.
  Experimental work at the University labs.
  The intellectual content makes it suitable as a
  two-year project for a PhD student and the
  successful candidate will be required to be
  proficient in a wide range of CFD and
  optimisation techniques.
• Equipment Provision of a PC, that will be put in
  place at the university labs, the requirements of
  this PC are for high performance parallel
  computing resources.
• These characteristics are essential in order
  to compute high fidelity models on the CFD and
  structural analysis.
• Travel Travel expenses, including airfare,
  accommodation and meals to attend to AIAA
  conferences in the US. The U.S. Air force is
  asked to contribute half the cost of producing
  journal papers and registration to conferences.
• Indirect Costs Indirect Costs have been
  calculated for The University of Sydney and using
  the standard multiplier for laboratory research
  (1.25).

73
USYD and AFRL
Computational Fluid Dynamics
Aerodynamics
Aero thermodynamics
Airframe-Propulsion Integration
Airframe-Weapons Integration
Stability and Control
Flight Vehicle Performance
Flow Diagnostics
Aero Configuration Integration

• Possible areas of collaboration within AFRL
  divisions
• AFRL/VAA Aeronautical Science Division
• VAAA The Aerodynamic Configuration Branch
• VAAC The Computational Sciences Branch
• VAAI Aerospace Vehicles Integration and
  Demonstration Branch
• VAS Structures Division
• AFRL/VASD Design and analysis methods
  branch

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Evolutionary Design Optimisation
Evaluation of Candidates
Problem Definition
Compute the flow around the aerofoil sections
and obtain a Cdo estimate for the wing
HAPEA Optimser Setup
Create drag polar on the candidate geometry
Satisfying trim conditions.
Create and evaluate initial population
Analyze each configuration using FLOPS)

• Do While Convergence
• not reached

Compute Objective Functions
Generate and evaluate new candidates
Evolve/ modify design variables on optimiser
until stopping criteria is met.
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Aircraft Design and Analysis

• The FLOPS (FLight OPtimisation System) solver
  developed by L. A. (Arnie) McCullers, NASA
  Langley Research Center was used for evaluating
  the aircraft configurations.
• FLOPS is a workstation based code with
  capabilities for conceptual and preliminary
  design of advanced concepts.
• FLOPS is multidisciplinary in nature and contains
  several analysis modules including weights,
  aerodynamics, engine cycle analysis, propulsion,
  mission performance, takeoff and landing, noise
  footprint, cost analysis, and program control.
• FLOPS has capabilities for optimisation but in
  this case was used only for analysis.
• Drag is computed using Empirical Drag Estimation
  Technique (EDET) - Different hierarchical models
  are being adapted for drag build up using higher
  fidelity models.

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Aerodynamic Analysis
Control Points
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Design Variables Bounding Envelope of the
Aerofoil Search Space
16 Design variables for the aerofoil

• Two Bezier curves representation
• Six control points on the mean line.
• Ten control points on the thickness distribution.
• Constraints
• Thickness gt 12 x/c
• Pitching moment gt -0.065

78
Aerofoil Optimisation (2)
Aerofoil Characteristics cl 0.715
Delayed drag divergence at low Cl
Delayed drag divergence at high Cl
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Aerofoil Optimisation (2)
Aerofoil Characteristics M 0.75
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Design Variables
Description Lower Bound Upper Bound
Wing Aspect Ratio 3.50 7.00
Break to root taper 0.65 0.80
Break to tip taper 0.20 0.45
Wing Chord inboard Sweep, deg 10.00 20.00
Wing Chord outboard Sweep, deg -20.00 0.00
Twist at root, deg 0.00 3.00
Twist at Break, deg -1.00 0.00
Twist at Tip, deg -1.00 0.00
Break location 0.20 0.35