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Feasibility of Morphing Aircraft Propeller Blades

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Feasibility of Morphing Aircraft Propeller Blades FEASIBILITY OF MORPHING AIRCRAFT PROPELLER BLADES A Dissertation by Johann Dorfling Master of Science, Wichita State University, 2008 Bachelor of Science, University of Kentucky, 2007 Submitted to the Department of Aerospace Engineering and the faculty of the Graduate School of Wichita State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy July 2014 © Copyright 2014 by Johann Dorfling All Rights Reserved FEASIBILITY OF MORPHING AIRCRAFT PROPELLER BLADES The following faculty members have examined the final copy of this dissertation for form and content, and recommend that it be accepted in partial fulfillment of the requirement for the degree of Doctor of Philosophy with a major in Aerospace Engineering. Kamran Rokhsaz, Committee Chair Walter J. Horn, Committee Member James E. Steck, Committee Member L. Scott Miller, Committee Member Ikramuddin Ahmed, Committee Member Accepted for the College of Engineering Royce Bowden, Dean Accepted for the Graduate School Abu Masud, Interim Dean iii DEDICATION To my dear wife Christin – Thank you for your constant support, encouragement, and love iv Trust in the LORD with all your heart, and lean not on your own understanding; In all your ways acknowledge Him, and He shall direct your paths. Proverbs 3:5,6 v ABSTRACT The aim of this study is to assess the feasibility of variable geometry aircraft propeller blades, the main focus being on the aerodynamic performance. A number of objectives are established to reach this goal, with the development of an aerodynamic model and a blade optimization scheme being among these. The choice of the blade element method coupled with vortex theory and the use of calculus of variations for optimization is the result of an extensive literature review. This review also covers smart materials and their capabilities, and presents a number of structural morphing concepts. The propeller aerodynamic model is presented in detail along with the developed airfoil model and compressibility corrections. Predicted propeller performance parameters are compared with experimental data to validate the model. Both unconstrained and constrained twist optimization are considered and the derivations of the Euler- Lagrange equations are given. Unconstrained twist optimization results show that, regardless of the operating condition (takeoff, climb, or cruise), maximum efficiency occurs at lower thrust and power coefficients than required for those conditions. Constrained optimization supports this observation by showing that a constraint lowers the propeller efficiency. Twist distributions obtained from constrained optimization for the three operating conditions differ significantly but the effect on performance is insignificant. This leads to the conclusion that variable twist is not viable for a typical aircraft mission. Further analysis, however, reveals the possibility of variable twist for a loiter-dash type mission. A study of such a mission profile shows that a morphing propeller would offer a significant performance boost and is indeed feasible. Estimates of actuation power requirements show the required power to be less than the performance gain from a morphing propeller. A structural analysis of a variable camber concept shows the viability of shape memory alloys as an actuator material. vi TABLE OF CONTENTS Chapter Page 1. INTRODUCTION ...............................................................................................................1 1.1 Background..............................................................................................................1 1.2 Research Objective ..................................................................................................3 1.3 Document Layout.....................................................................................................4 2. LITERATURE REVIEW ....................................................................................................6 2.1 Introduction..............................................................................................................6 2.2 Propeller Aerodynamics...........................................................................................6 2.3 Propeller Optimization...........................................................................................15 2.4 Smart Materials and Morphing Structures.............................................................21 2.4.1 Smart Materials.............................................................................................22 2.4.2 Morphing Structures .....................................................................................31 2.5 Chapter Summary ..................................................................................................48 3. PROPELLER PERFORMANCE ANALYSIS..................................................................49 3.1 Introduction............................................................................................................49 3.2 Propeller Aerodynamic Model...............................................................................49 3.2.1 Blade Element Method .................................................................................49 3.2.2 Vortex Theory...............................................................................................55 3.2.3 Airfoil Model Description.............................................................................62 3.3 Model Validation ...................................................................................................77 3.3.1 NACA Technical Report 1309......................................................................77 3.3.2 NACA Technical Report 1375......................................................................87 3.4 Chapter Summary ..................................................................................................91 4. PROPELLER TWIST OPTIMIZATION ..........................................................................93 4.1 Introduction............................................................................................................93 4.2 Calculus of Variations............................................................................................93 4.3 Propeller Twist Optimization.................................................................................97 4.3.1 Unconstrained Optimization .........................................................................97 4.3.2 Constrained Optimization .............................................................................99 4.3.3 Derivatives of the Performance Coefficient Integrands..............................101 4.3.4 Derivative of the Drag Coefficient .............................................................105 4.4 Implementation of Optimization..........................................................................106 4.4.1 Method of Implementation .........................................................................107 4.4.2 Validation of Method..................................................................................110 vii TABLE OF CONTENTS (continued) Chapter Page 4.5 Twist Optimization Results..................................................................................113 4.5.1 Unconstrained Optimization Results ..........................................................115 4.5.2 Constrained Optimization Results ..............................................................117 4.5.3 Analysis of a Loiter-Dash Mission .............................................................122 4.6 Chapter Summary ................................................................................................127 5. STRUCTURAL AND POWER CONSIDERATIONS...................................................128 5.1 Introduction..........................................................................................................128 5.2 Structural Analysis...............................................................................................128 5.2.1 Entire Section Camber Morphing Analysis ................................................129 5.2.2 Tension-Torsion Coupled Blades ...............................................................137 5.3 Thermal Analysis.................................................................................................141 5.3.1 Method of Analysis.....................................................................................142 5.3.2 Results and Discussion ...............................................................................147 5.4 Chapter Summary ................................................................................................152 6. CONCLUSIONS AND FUTURE WORK ......................................................................154 6.1 Conclusions..........................................................................................................154 6.2 Future Work.........................................................................................................157 REFERENCES ............................................................................................................................159 viii LIST OF TABLES Table Page 3.1. Comparison of experimental data and XFOIL predictions....................................................78 4.1. Comparison of problem 3 results with reference [44] .........................................................111 4.2. Definition of the propeller operating conditions..................................................................112
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