Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 3 .....................................................................................................21 Analysis and Design of Airfoils for Use at Ultra-Low Reynolds Numbers xiv 3.1 Introduction......................................................................................................... 21 3.2 General Reynolds Number Effects ..................................................................... 22 3.3 Maximum Section Thickness Effects ................................................................. 30 3.3.1 Effect of Thickness on Drag...................................................................... 30 3.3.2 Effect of Thickness on Lift........................................................................ 32 3.4 Effect of Camber................................................................................................. 35 3.5 Effect of Leading Edge Shape and Constant Thickness Profiles ....................... 41 3.6 Design of Optimal Camberlines for Ultra-Low Reynolds Numbers.................. 43 Chapter 4 .....................................................................................................49 Hybrid Method for Rotor Design and Analysis 4.1 Introduction......................................................................................................... 49 4.2 Derivation of the Rotor Thrust and Torque Equations for Hover and Vertical Climb................................................................................... 50 4.2.1 Fundamental Actuator Ring Equations...................................................... 51 4.2.2 Blade Element Equations........................................................................... 52 4.2.3 Elimination of Trigonometric Terms......................................................... 53 4.2.4 Prandtl Tip Loss Correction....................................................................... 54 4.2.5 Swirl Velocity Considerations................................................................... 54 4.2.6 Uncoupled Equations for the Rotor Induced Velocities............................ 55 4.2.7 The Distinction Between the Analysis and Design Problems ................... 57 4.3 Viscous Swirl Modeling ..................................................................................... 58 4.3.1 Average Wake Deficit Viscous Swirl Model ............................................ 58 4.3.2 Gaussian Wake Viscous Swirl Model ....................................................... 61 4.3.3 Conservation of Angular Momentum Viscous Swirl Model..................... 63 4.4 Development of Stream-Function-Based Vortex Ring Wake Model................. 64 4.5 Higher-Order Modeling of 2-D Viscous Effects ................................................ 70 4.6 Rotor Design and Analysis via Gradient-Based Optimization........................... 71
Chapter 5.....................................................................................................75 Overview of Experimental and Computational Validation Methods 5.1 Introduction......................................................................................................... 75 5.2 Rotor Manufacturing ......................................................................................... 76 5.2.1 Shape Deposition Manufacturing .............................................................. 76 5.2.2 Dual Surface Machining............................................................................ 78 5.2.3 Composite Press Molding.......................................................................... 78 5.3 Experimental Methods........................................................................................ 79 5.4 Discussion of Experimental Error ...................................................................... 86 5.4.1 Motor Power Supply.................................................................................. 87 5.4.2 Determination of Rotor RPM .................................................................... 87 5.4.3 Electronic Force Measurement.................................................................. 88 5.4.4 Test Fixture Errors..................................................................................... 88 5.4.5 Aerodynamic Blockage ............................................................................. 89 5.5 Three-Dimensional Analysis using OVERFLOW-D ......................................... 90 Chapter 6.....................................................................................................95 Design Examples and Comparisons with Experiment 6.1 Introduction......................................................................................................... 95 6.2 Motor Selection and Characterization ................................................................ 96 6.2.1 Myonic 5mm Smoovy Motor .................................................................... 96 6.2.2 Astroflight Firefly Motor........................................................................... 98 6.3 Rotor Design Specifications ............................................................................... 99 6.3.1 Five-Blade 2.2cm Diameter Rotor............................................................. 99 6.3.2 Four-Blade 2.5cm Diameter Rotor .......................................................... 101 6.3.3 Two-Blade Ten Inch Diameter Rotor...................................................... 104 6.4 Comparison of Total Thrust and Power............................................................ 105 6.4.1 Two-Blade Ten Inch Diameter Rotor...................................................... 105 6.4.2 Four-Blade 2.5cm Diameter Rotor .......................................................... 107 6.4.3 Five-Blade 2.2cm Diameter Rotor........................................................... 113 6.5 Effects of Structural Deformation .................................................................... 114 xv
Page 1 and 2: AERODYNAMICS AND DESIGN FOR ULTRA-L
Page 3: I certify that I have read this dis
Page 7 and 8: Abstract Growing interest in micro-
Page 9 and 10: Nomenclature A Rotor disk area B Nu
Page 11 and 12: τ Shear stress ω, Ω Rotor angul
Page 13: Contents Acknowledgments...........
Page 17 and 18: List of Tables 3.1 Effect of Airfoi
Page 19 and 20: List of Figures 2.1 Comparison of I
Page 21 and 22: 5.6 Small test fixture in the large
Page 23 and 24: 6.38 Predicted spanwise thrust dist
Page 25 and 26: Chapter 1 Introduction 1.1 Looking
Page 27 and 28: Chapter 1 wind-tunnel facilities an
Page 29 and 30: 1.3 Summary of Contributions Chapte
Page 31 and 32: Chapter 2 Two-Dimensional Computati
Page 33 and 34: Chapter 2 The artificial compressib
Page 35 and 36: Chapter 2 The control volume method
Page 37 and 38: 2.2.4 Comparison with Experiment Th
Page 39 and 40: Chapter 2 to diverge if significant
Page 41 and 42: 2.4 Flow Field Assumptions The INS2
Page 43 and 44: Chapter 2 The results of these time
Page 45 and 46: Chapter 3 Analysis and Design of Ai
Page 47 and 48: Chapter 3 adverse gradient in the p
Page 49 and 50: The canonical pressure coefficient
Page 51 and 52: Chapter 3 reaches α=5.0 and a lift
Page 53 and 54: ��
Page 55 and 56: Cl 0.50 0.40 0.30 0.20 0.10 0.00 -0
Page 57 and 58: Re=6000 result due to Reynolds numb
Page 59 and 60: FIGURE 3.10 NACA 0002 and NACA 0008
Page 61 and 62: C l C l 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Page 63 and 64: Chapter 3 The maximum L/D for all n
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3.5 Effect of Leading Edge Shape an
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C l 0.60 0.50 0.40 0.30 0.20 0.10 0
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Chapter 3 prominent droop near the
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Chapter 3 Small improvements in lif
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Chapter 4 Hybrid Method for Rotor D
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Q/r D L Chapter 4 FIGURE 4.1 Typica
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4.2.3 Elimination of Trigonometric
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Chapter 4 applications of interest
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4.2.7 The Distinction Between the A
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Chapter 4 Two input parameters dete
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Chapter 4 simplification, particula
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4.3.3 Conservation of Angular Momen
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Chapter 4 moves downstream is less
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Chapter 4 of the pitch angle at the
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FIGURE 4.6 Converged wake streamlin
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Chapter 4 idealized models. The met
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��
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Chapter 5 Overview of Experimental
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1. Substrate Preparation 2. Polymer
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Chapter 5 surface finish and aids i
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FIGURE 5.5 Small test fixture in th
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Chapter 5 The direct influence of t
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FIGURE 5.9 Large test fixture in th
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5.4.1 Motor Power Supply All tests
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Chapter 5 or roughly (+/-) 25% of t
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Chapter 5 newly forming blade tip v
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FIGURE 5.14 Near-body grid geometry
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Chapter 6 Design Examples and Compa
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Chapter 6 capable of speeds up to 1
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FIGURE 6.2 The Astro Flight Firefly
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t/c 0.5 0.4 0.3 0.2 0.1 0.0 FIGURE
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c/R 0.0 0.2 0.4 0.6 0.8 1.0 r/R Cha
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FIGURE 6.10 Carbon-fiber two-blade
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Power Req. (W) 3.5 3.0 2.5 2.0 1.5
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Chapter 6 TABLE 6.1 Comparison of p
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Electro-mechanical Efficiency 0.20
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these variations and possible solut
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upper and lower surface corners of
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Chapter 6 The Sample-1 rotor exhibi
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The static deformations described i
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Q( r) This problem is solved as a l
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Structural Analyses Chapter 6 The m
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Aero-Structural Twist (deg.) 0.00 -
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Thrust (g) 5 4 3 2 1 0 10000 20000
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Thrust (g) 4.5 4.0 3.5 3.0 2.5 2.0
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Torque per unit span (g cm) 0.75 0.
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Thrust per unit span (g) 3.5 3.0 2.
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V total / ωr 1.0 0.9 0.8 Classical
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Torque per unit span (g cm) 0.75 0.
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Chapter 6 Recall that this rotor wa
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Incidence (deg.) 30 25 20 15 10 5 0
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Thrust (g) 9 8 7 6 5 4 3 2 38000 40
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x/R 0.4 0.2 0.0 -0.2 Chapter 6 FIGU
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Cl 0.64 0.62 0.60 0.58 0.0 0.2 0.4
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C f 0.125 0.100 0.075 0.050 0.025 0
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Chapter 7 Micro-Rotorcraft Prototyp
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This vehicle does not currently inc
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FIGURE 7.2 The 65g prototype electr
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7.4 The 150g Prototype Chapter 7 Th
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At hover, with a mass of 153g, the
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Using the 150g prototype as an exam
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Chapter 7 Basic rotor theory has be
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most of the blade. These values are
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Chapter 7 For large scale helicopte
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Chapter 8 Conclusions and Recommend
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the significant performance gains a
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Chapter 8 are also opportunities to
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Chapter 8 formation flight, and man
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References [1] Spedding, G.R., Liss
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[28] Lamb, Sir Horace, Hydrodynamic
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Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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