Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 1 Major problems have included a technological inability to accurately manufacture very small-scale machines, an inability to power such devices, and the challenge of controlling them. Without an expectation of realization, there has been only marginal interest in the study of aerodynamics at tiny physical scales, but advances in technology have recently begun to make ultra-low Reynolds number flight a real possibility. The growing interest in micro-air-vehicle development has finally created a need for improved understanding of the relevant aerodynamics. The flight regime of micro-aircraft poses numerous challenges for aerodynamic analysis and design, but little experimental or computational work exists for aerodynamic surfaces operating at ultra-low Reynolds numbers (Re) below 10,000. Interest in very small aircraft, operating in the Re=100,000 to Re=150,000 range, has rapidly grown and many such vehicles are currently under development, but research and development at much smaller scales is still in its infancy. Technological advances in micro-fabrication techniques and in the miniaturization of electronics are beginning to make mechanical micro-flight vehicles feasible from a systems and manufacturing standpoint. There are numerous potential applications for these vehicles, but first they must be capable of flight. Much of the work presented here has been motivated by the Mesicopter Micro- Rotorcraft Development Program at Stanford University. The goal of this program, and a major focus of this thesis, is the design, development, and testing of micro-rotors and micro-rotorcraft. The broader goal of this work is to contribute substantially to the foundations of this essentially unexplored segment of applied aerodynamics and flight vehicle design. Aerodynamic research at relevant Reynolds numbers has been severely limited. Experimental airfoil data has been published by Schmitz[2] and Althaus [3], among others, at chord Reynolds numbers as low as 20,000 to 30,000, but in terms of the nature of the viscous effects, this is considerably different from the range of interest below Re=10,000. This data also represents the extreme lower range of operation for many 2
Chapter 1 wind-tunnel facilities and inconsistencies are often apparent in the resulting data. More recent work in experimental airfoil testing at ultra-low Reynolds numbers, some of it concurrent and subsequent to the initial publication of portions of this research [4, 5], has been published by Sunada and Kawachi [6] and as a comprehensive survey of relevant experiments and analyses by Azuma et al.[7]. These results support many of the conclusions put forward here regarding the effects of airfoil geometry on performance. Research into hovering flight at small physical scales has been dominated by studies of the hovering or near-hovering flight of insects and birds. The comprehensive work by Ellington [8] is an excellent example and provides significant insight into the mechanisms of micro-scale hovering flight in nature. Emphasis has typically been placed on the biomechanics of flight and the search for, and modelling of, unsteady aerodynamic mechanisms of high lift such as the ‘clap and fling’ mechanism proposed by Weis-Fogh [9, 10] or the unsteady wake mechanisms proposed by Rayner [11]. Common to all of these studies is a focus on inviscid aerodynamics, with, at most, simple accounting and estimates of viscous effects. As mentioned earlier, nature clearly has found a workable solution, but a key issue that currently prevents translating this large body of work to a man-made vehicle is the complexity of the required flapping motions and the difficulty associated with developing the necessary mechanisms at small scales without suffering significant mass and electromechanical efficiency penalties. This is also without any consideration of the relevant aerodynamic efficiencies. This dissertation seeks to explore the simplest possible solution: a non-articulating rotor operating under steady aerodynamic conditions. 1.2 Thesis Chapter Summary A methodical and progressive approach has been taken to the exploration of the aerodynamic design space at ultra-low Reynolds numbers. Beginning with two- 3
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 and 14: Contents Acknowledgments...........
Page 15 and 16: Chapter 5..........................
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: Chapter 1 Introduction 1.1 Looking
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
Page 65 and 66: 3.5 Effect of Leading Edge Shape an
Page 67 and 68: C l 0.60 0.50 0.40 0.30 0.20 0.10 0
Page 69 and 70: Chapter 3 prominent droop near the
Page 71 and 72: Chapter 3 Small improvements in lif
Page 73 and 74: Chapter 4 Hybrid Method for Rotor D
Page 75 and 76: 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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