Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 6 The importance of the operational deflections for micro-rotors becomes apparent if Eqn.6.1 is considered with the restrictions of constant chord and thickness along a blade: This may be further manipulated to show a predominant dependence of θ on ωR (the tip speed) and the inverse of the thickness ratio squared. The tip speeds of the micro-rotors presented here are roughly one third to one fourth those of full scale helicopter rotors, but t/c is reduced by a factor of three to four and dominates. This effect is also seen on large scale rotors, but for the development of small rotors it should be considered an essential component of design. Large rotors typically have some form of collective control that can be used to partially compensate for the loss of incidence, but the only control available to the micro-rotors is RPM. The effects of the aerodynamic forces are not negligible and are strongly coupled to the structural deformations. The pitching moment coefficient is typically insensitive to angle of attack and provides a relatively small nose down moment that works in unison with the structural moment due to rotation. However, the local lift coefficient is obviously very sensitive to the incidence angle and, for a positive lift coefficient, opposes the inertial effects of rotation. The correct deflected rotor solution would be at structural equilibrium and operating at lift coefficients representative of the equilibrium geometry. This requires some form of iteration. Ideally this would be integrated into the design process, but at this time that has not been implemented. For the purpose of the analyses presented here, several iterations have been carried out manually at each rotor speed, but the solutions are not fully converged, meaning that the assumed lift coefficients used for the structural analyses do not precisely match the predicted value from the final performance analyses. 122 dθ 3 2 ( r) -----ρ 1 – dR 12 matω --- 1 G( t ⁄ c) 2 = -------------- cos( ζ+ θ) sin( ζ+ θ) dR tip ∫ r (6.6)
Structural Analyses Chapter 6 The method described above has been applied to five cases consisting of the aluminum four-blade rotor, the epoxy large-hub and small-hub four-blade rotors, and the two previously described versions of the five-blade 2.2cm rotor. The initial geometries are taken as the designed geometries, no static deformations are included. The aluminum rotor is constructed of 7075-T6 aluminum. The material properties used are E=72 GPa, G=27Gpa, and ρ=2796 kg/m 3 . The epoxy rotors are constructed from Adtec EE 501/530 epoxy. The shear properties of this resin have been approximated from the results of tensile testing reported by Kietzman [42]. The UTS and elongation to failure have been used do obtain an approximate Young’s modulus of 4.2GPa. Typically this should be based upon yield characteristics, but this data was not available. Since typical values of Poisson’s ratio are between 0.2 and 0.3 for many materials, a value of 0.2 has been assumed, yielding an approximate shear modulus of G=1.75GPa. The use of UTS and the lower Poisson’s ratio results in a conservative stiffness value. The aluminum four-blade rotor was found to have the smallest static deformations of the samples tested and is expected to be significantly stiffer. For these reasons it is included essentially as a baseline analysis, since the effects of rotation should be minimal in this case. The predicted torsional deflections for the aluminum and epoxy large-hub four- blade rotors at five different operating speeds is presented in Figure 6.25. The aluminum rotor performs as expected with minimal deflection, typically under 0.25 degrees, but the epoxy rotor fares worse both in magnitude and the amount of variation over the speed range. 123
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AERODYNAMICS AND DESIGN FOR ULTRA-L
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I certify that I have read this dis
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Abstract Growing interest in micro-
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Nomenclature A Rotor disk area B Nu
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τ Shear stress ω, Ω Rotor angul
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Contents Acknowledgments...........
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Chapter 5..........................
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List of Tables 3.1 Effect of Airfoi
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List of Figures 2.1 Comparison of I
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5.6 Small test fixture in the large
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6.38 Predicted spanwise thrust dist
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Chapter 1 Introduction 1.1 Looking
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Chapter 1 wind-tunnel facilities an
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1.3 Summary of Contributions Chapte
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Chapter 2 Two-Dimensional Computati
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Chapter 2 The artificial compressib
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Chapter 2 The control volume method
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2.2.4 Comparison with Experiment Th
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Chapter 2 to diverge if significant
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2.4 Flow Field Assumptions The INS2
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Chapter 2 The results of these time
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Chapter 3 Analysis and Design of Ai
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Chapter 3 adverse gradient in the p
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The canonical pressure coefficient
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Chapter 3 reaches α=5.0 and a lift
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��
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Cl 0.50 0.40 0.30 0.20 0.10 0.00 -0
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Re=6000 result due to Reynolds numb
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FIGURE 3.10 NACA 0002 and NACA 0008
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C l C l 0.8 0.7 0.6 0.5 0.4 0.3 0.2
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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
Page 95 and 96: Chapter 4 idealized models. The met
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Page 99 and 100: Chapter 5 Overview of Experimental
Page 101 and 102: 1. Substrate Preparation 2. Polymer
Page 103 and 104: Chapter 5 surface finish and aids i
Page 105 and 106: FIGURE 5.5 Small test fixture in th
Page 107 and 108: Chapter 5 The direct influence of t
Page 109 and 110: FIGURE 5.9 Large test fixture in th
Page 111 and 112: 5.4.1 Motor Power Supply All tests
Page 113 and 114: Chapter 5 or roughly (+/-) 25% of t
Page 115 and 116: Chapter 5 newly forming blade tip v
Page 117 and 118: FIGURE 5.14 Near-body grid geometry
Page 119 and 120: Chapter 6 Design Examples and Compa
Page 121 and 122: Chapter 6 capable of speeds up to 1
Page 123 and 124: FIGURE 6.2 The Astro Flight Firefly
Page 125 and 126: t/c 0.5 0.4 0.3 0.2 0.1 0.0 FIGURE
Page 127 and 128: c/R 0.0 0.2 0.4 0.6 0.8 1.0 r/R Cha
Page 129 and 130: FIGURE 6.10 Carbon-fiber two-blade
Page 131 and 132: Power Req. (W) 3.5 3.0 2.5 2.0 1.5
Page 133 and 134: Chapter 6 TABLE 6.1 Comparison of p
Page 135 and 136: Electro-mechanical Efficiency 0.20
Page 137 and 138: these variations and possible solut
Page 139 and 140: upper and lower surface corners of
Page 141 and 142: Chapter 6 The Sample-1 rotor exhibi
Page 143 and 144: The static deformations described i
Page 145: Q( r) This problem is solved as a l
Page 149 and 150: Aero-Structural Twist (deg.) 0.00 -
Page 151 and 152: Thrust (g) 5 4 3 2 1 0 10000 20000
Page 153 and 154: Thrust (g) 4.5 4.0 3.5 3.0 2.5 2.0
Page 155 and 156: Torque per unit span (g cm) 0.75 0.
Page 157 and 158: Thrust per unit span (g) 3.5 3.0 2.
Page 159 and 160: V total / ωr 1.0 0.9 0.8 Classical
Page 161 and 162: Torque per unit span (g cm) 0.75 0.
Page 163 and 164: Chapter 6 Recall that this rotor wa
Page 165 and 166: Incidence (deg.) 30 25 20 15 10 5 0
Page 167 and 168: Thrust (g) 9 8 7 6 5 4 3 2 38000 40
Page 169 and 170: x/R 0.4 0.2 0.0 -0.2 Chapter 6 FIGU
Page 171 and 172: Cl 0.64 0.62 0.60 0.58 0.0 0.2 0.4
Page 173 and 174: C f 0.125 0.100 0.075 0.050 0.025 0
Page 175 and 176: Chapter 7 Micro-Rotorcraft Prototyp
Page 177 and 178: This vehicle does not currently inc
Page 179 and 180: FIGURE 7.2 The 65g prototype electr
Page 181 and 182: 7.4 The 150g Prototype Chapter 7 Th
Page 183 and 184: At hover, with a mass of 153g, the
Page 185 and 186: Using the 150g prototype as an exam
Page 187 and 188: Chapter 7 Basic rotor theory has be
Page 189 and 190: most of the blade. These values are
Page 191 and 192: Chapter 7 For large scale helicopte
Page 193 and 194: Chapter 8 Conclusions and Recommend
Page 195 and 196: 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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