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Optimization of a Flapping Wing

Optimization of a Flapping Wing. Irina Patrikeeva HARP REU Program Mentor: Dr. Kobayashi August 3, 2011. Problem. Objectives Optimize design of a flapping wing and flight kinematics Best design = maximum lift, minimum drag, and minimum power Motivation

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Optimization of a Flapping Wing

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  1. Optimization of a Flapping Wing Irina Patrikeeva HARP REU Program Mentor: Dr. Kobayashi August 3, 2011

  2. Problem Objectives Optimize design of a flapping wing and flight kinematics Best design = maximum lift, minimum drag, and minimum power Motivation Artificial flapping wings for air vehicles Exploration of feasible wing topologies Better understanding of flight kinematics

  3. Structural Model Wing made of thin membrane and beams Topology obtained by cellular division Uniform beam thickness beams membrane

  4. Kinematics Wing is divided into a series of span stations Up-down flapping motion through angle β Plunging motion in z-direction Small elastic deformations z

  5. Wing Topology Generation Propagating cellular division process Each edge assigned a letter Each letter assigned a production rule, e.g. A → B[+A]x[-A]B B → A

  6. Genetic Algorithms Wing configuration encoded as a genome Fitness function Next generation formed from most fit individuals Crossover Random mutations Population evolves towards an optimal solution

  7. Methods DAKOTA: Design Analysis Kit for Optimization Terascale Applications Extensible problem-solving environment Multi-objective genetic algorithm Interface between user supplied code and iterative system analysis method

  8. Program Flow Black-box interface [From DAKOTA User's Manual 5.1]

  9. Problem Formulation Optimize three functions: drag, lift and power coefficients Input design variables: 1445 topology variables: wing mesh 153 kinematics variables: flight motions Given lower and upper bounds No constraints

  10. Flight Representation Fixed frequency ω = 40 rad/s External flow velocity U∞ = 10 m/s Angle of attack α = 4° 3 motions = 3 Fourier series Plunging motion Flapping motion Pitching motion

  11. Using HOSC Concurrent execution of function evaluation DAKOTA automatically exploits parallelism Evaluation of 1 individual < 10 sec

  12. Results Pareto set of optimal solutions for drag CD, power CP, and lift coefficients CL Pareto set is a set of solutions such that it's impossible to improve one coefficient without making either of the other two worse off

  13. Drag-Power-Lift Pareto front Evaluations: 1000 Initial population: 50 Generations: 5 Final set of Pareto optimal solutions (red) Non-optimal solutions from all evaluations (black)

  14. Pareto Optimal Front Initial population: 50 individuals Set of Pareto optimal values: 159 designs

  15. Extremes of Pareto Front Lowest drag coefficient Lowest power coefficient Highest lift coefficient

  16. Optimal drag coefficient design Lowest drag coefficient CD = 0.1672 CP = 0.3493 CL = 0.3418 Cellular representation Wing topology

  17. Optimal power coefficient design Lowest power coefficient CD = 0.1780 CP = 0.3436 CL = 0.3157 Cellular representation Wing topology

  18. Optimal lift coefficient design Highest lift coefficient CD = 0.1945 CP = 0.4738 CL = 0.5491 Cellular representation Wing topology

  19. Problems Optimization is time-consuming Pre-processing and post-processing Convergence of GA's

  20. Conclusions Multiobjective optimization drag-power, lift trade-offs Pareto front optimal solutions

  21. Acknowledgments Thank you Dr. Kobayashi, Dr. Brown, and students of HARP REU Program, and everyone else who helped make this summer great! This material is based upon work supported by the National Science Foundation under Grant No. 0852082. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

  22. Questions?

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