Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 6 in boundary layer thickness. The reduction in boundary layer thickness increases the effectiveness of the airfoil geometry, particularly aft where the cumulative effects on boundary layer development are greatest. For the optimal airfoil designs of Chapter 3, this means that the kink in the camberline at 80% chord will have much more effect than intended. Detailed comparisons of blade sectional aerodynamics are presented for a single chord- wise station at r/R = 0.48 and 50,760 RPM. This case was selected to minimize tip effects. Reynolds number variations are minor since the rotational velocity term dominates any induced velocities. Cross-flow is minimal up to separation, which occurs aft of 90% chord. The blade-element method predicts that at this station C = 0.45 corresponding to α=2.5 degrees. Pressure and skin friction distributions for this section calculated with INS2d and those taken from the OVERFLOW-D analysis are presented in Figures 6.49 and 6.50. The total pressure thrust agrees within 5%, but the pressure distributions are dramatically different. The OVERFLOW-D section is operating at a lower local angle of attack, but achieves the same pressure thrust with a large increase in the aft loading. The section torque due to skin friction is 30% higher in the three- dimensional case. 148 Cp -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 FIGURE 6.49 Chordline pressure distribution at r/R=0.48, 50k RPM. x/c OVERFLOW-D INS-2D, α = 2.5 INS-2D, α = 1.25
C f 0.125 0.100 0.075 0.050 0.025 0.000 -0.025 Chapter 6 FIGURE 6.50 Distribution of the chord-wise component of skin friction at r/R=0.48, 50k RPM. Also included in these plots is an INS2d calculation at α=1.25 degrees. At this angle of attack the stagnation points in the two-dimensional and three-dimensional cases agree. The pressure and skin friction distributions also agree over the first 50% of the airfoil. This is the effective angle of attack in the OVERFLOW-D result. This close agreement over the front half of the airfoil also serves as a mild validation of the INS2d calculations. The three-dimensional case, however, has 20% greater pressure thrust and 33% higher viscous torque. These discrepancies in sectional details are representative of the entire span, but in spite of this, the predicted global thrust and power agreed on average within 5% with maximum errors under 10%. These large variations in section performance necessitate some way of modeling the rotational effects in order for a blade-element method to be viable beyond preliminary design. Even then, the method may not be useful if, as in this case, the section properties in 3-D mandate a redesign of the airfoil. This particular airfoil is very sensitive to off- design conditions, so it is possible that a different section may exhibit less variation, particularly in the pressure distribution. OVERFLOW-D INS-2D, α = 2.5 INS-2D, α = 1.25 0.2 0.4 0.6 0.8 1.0 x/c 149
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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
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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
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 and 146: Q( r) This problem is solved as a l
Page 147 and 148: Structural Analyses Chapter 6 The m
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: Cl 0.64 0.62 0.60 0.58 0.0 0.2 0.4
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
Page 197 and 198: Chapter 8 are also opportunities to
Page 199 and 200: Chapter 8 formation flight, and man
Page 201 and 202: References [1] Spedding, G.R., Liss
Page 203 and 204: [28] Lamb, Sir Horace, Hydrodynamic
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