Optimum Propeller Design for Electric Uavs

Optimum Propeller Design for Electric UAVs

David Lee Wall

A thesis submitted to the Graduate Faculty of Auburn University in partial fulﬁllment of the requirements for the Degree of Master of Science

Auburn, Alabama August 4, 2012

Keywords: Propeller, Design, Optimization

Approved by

Gilbert Crouse, Associate Professor of Aerospace Engineering Roy Hartﬁeld, Professor of Aerospace Engineering Brian Thurow, Associate Professor of Aerospace Engineering George Flowers, Dean of the Graduate School, Professor of Mechanical Engineering Abstract

A propeller behaves as a rotating wing producing lift in the direction of the axis of rotation. Many previous propeller optimization methods have been developed, but usually focus on piston or turboprop applications. This study discusses the more fundamental propeller theories and uses a hybrid blade element momentum theory to model the propellers. A brushless motor model is developed and coupled with the propeller theory in an optimizer. Two single point optimizations are made, one for a climb condition and the other for a cruise condition. A third optimization is presented with optimization at climb and cruise conditions. The optimizations are conducted with a hybrid pattern/search particle swarm optimizer. The airfoils for the propellers are optimized with the same optimizer and a simplex method. Multiple objective functions are evaluated for each of the conditions. One having non-dimensional values and another with dimensional values. Dimensional values prove to provide better results for all of the conditions. The optimized cruise propellers display smaller chords, higher pitches, and larger diameters while the optimized climb propellers have larger chords, lower pitches and smaller diameters. The multipoint optimization yields higher pitches with chords and diameters between the single point optimizations. All optimized propellers show improvement over comparable baseline propellers.

ii Acknowledgments

I would like to thank my parents, Larry and Patsy Wall, for their loving support over the years. I would like to thank Dr. Gilbert Crouse for his guidance with this thesis and studies. I would also like to thank Dr. Brian Thurow and Dr. Roy Hartﬁeld for their help throughout my stay at Auburn University.

iii Table of Contents

Abstract ...... ii Acknowledgments ...... iii List of Figures ...... vii List of Tables ...... xii List of Abbreviations ...... xiv 1 Introduction ...... 1 2 Airfoils ...... 3 2.1 Airfoil Basics ...... 3 2.2 Parameterization of Airfoils ...... 4 2.2.1 Bezier Curves ...... 4 2.2.2 Bernstein Polynomials Representation of the Unit Shape Function . .6 2.3 XFOIL ...... 8 3 Propellers ...... 10 3.1 Basics of Propellers ...... 10 3.1.1 Geometry ...... 10 3.1.2 Other Parameters ...... 11 3.1.3 Types ...... 12 3.2 Propeller Theories ...... 12 3.2.1 Momentum Theory ...... 13 3.2.2 Simple Blade Element Theory ...... 16 3.2.3 Hybrid Momentum Blade Element Theory ...... 22 4 Electric Motors ...... 29 4.1 Brushed DC Electric Motors ...... 29

iv 4.2 Brushless DC Electric Motors ...... 33 5 Optimization Methods ...... 35 5.1 Particle Swarm ...... 35 5.2 Pattern Search ...... 36 5.3 Hybrid Pattern Search/Particle Swarm Method ...... 36 5.4 Simplex Method ...... 37 6 Implementation ...... 38 6.1 Airfoil Optimization ...... 38 6.2 Propeller Optimization ...... 41 7 Results ...... 46 7.1 Airfoil Optimization ...... 47 7.2 Validation of Propeller Code ...... 48 7.2.1 Validation Results for Baseline Cruise Propeller ...... 49 7.2.2 Validation Results for Baseline Climb Propeller ...... 51 7.2.3 Validation Results for Baseline Climb Cruise Propeller ...... 54 7.3 Propeller Optimized for Cruise ...... 56 7.4 Propeller Optimized for Climb ...... 67 7.5 Propeller Optimized for Climb-Cruise ...... 76 7.6 Cruise, Climb, and Climb-Cruise Comparisons ...... 85 8 Conclusio