Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 8 further investigation, but do not significantly diminish the utility of the rapid analysis and design method. Experimental testing has also served to both validate the method and expose another potential problem that strongly influences micro-rotor performance. Certain designs, having small hub diameters or high local solidities, exhibited thrust and power levels significantly below predicted values. The two-dimensional aerodynamic studies have demonstrated the strong need to minimize airfoil thickness at ultra-low Reynolds numbers, but the derivation of an aero-structural model for torsional deflections reveals that one consequence of reduced airfoil thickness is a disproportionate increase in torsional deflections due to rotational effects. Failure to account for this in a design can result in reduced incidence and aerodynamic unloading of the rotor. Finally, this progression of work has led to the design and fabrication of prototype micro-rotorcraft. The largest design brings together current existing technologies into a flight-vehicle that could provide a valuable test-bed for further research. Full realization of the smallest of these designs appears to be beyond the state of the art, but it sets the bar for the future. Any complex device requires a convergence of necessary technologies for it to come into existence. Motors, batteries, microelectronics, and many other necessary components are progressing at accelerated rates, driven by the wants and needs of society. The aerodynamics are still in their infancy and progressing slowly. Even if the end product is not viable now, the research must still continue in order to be ready at the point that it all comes together - to do anything else is simply short-sighted. 8.3 Consideration of Future Work This work was not envisioned as all-encompassing, and in that regard it has been an overwhelming success. There are many possible avenues for continued effort. Much can be done to improve and expand upon the methods and analysis completed here, but there 172
Chapter 8 are also opportunities to use this work as a starting point for research in new directions and as a source of supporting technology for work in related fields. In the area of airfoil performance and design there is a fundamental need for more data, whether experimental or computational, to increase the confidence in the results provided not only by INS2d, but by any number of other codes, currently available or in development, that are capable of these calculations. Since its initial publication in 2001, this data has already been used by others outside of the Stanford community as a point of comparison, and these comparisons are welcomed and encouraged, but this work is still very limited and without exception computational. Adding new and relevant experimental data to the almost non-existent current offerings would provide an invaluable counter-point to computational results. High-quality airfoil testing at these Reynolds numbers is a technical challenge due to the possible requirement for a fluid medium other than air. This complicates the acquisition of forces, moments, and pressure distributions, but this should not be a deterrent. Technology has improved significantly since Thom and Swart tested their hand-shaped airfoil in 1940 and it would be exciting to see what modern experimental methods could bring to this problem. Within the scope of airfoil optimization, there is room for improvement over the simple geometry model imposed in Chapter 3. The promising results shown here involve only four design variables. This low number is dictated by the optimization method employed, but application of a more sophisticated optimizer would permit much more freedom in defining the airfoil. One challenge is how to accomplish this efficiently given that the operating points of interest are so close to the steady-state operating limits. The rapid rotor analysis method has been demonstrated and proven as a tool for preliminary design, but the issues of three-dimensional boundary layer effects and wake effects on the prescribed inflow velocities warrant further work. One area of investigation is the effects of vortex dissipation on the wake structure. The OVERFLOW-D results depict fairly rapid dissipation of the wake structure, but it has 173
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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
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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
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 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: the significant performance gains a
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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