Aerodynamics and Design for Ultra-Low Reynolds Number Flight

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Chapter 2 16 Cl 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -2 0 2 4 6 α (deg.) 8 10 12 FIGURE 2.4 MSES and INS2d predicted lift curves for the NACA 4402 and NACA 4404. Flow is fully laminar and Re=1000. C l 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 INS2D, NACA 4402 INS2D, NACA 4404 MSES, NACA 4402 MSES, NACA 4404 INS2D, NACA 4404 INS2D, NACA 4402 MSES, NACA 4404 MSES, NACA 4402 0.0 0.08 0.10 0.12 0.14 0.16 0.18 Cd FIGURE 2.5 MSES and INS2d predicted drag polars for the NACA 4402 and NACA 4404. Flow is fully laminar and Re=1000.
2.4 Flow Field Assumptions The INS2d analyses make use of three assumptions about the flow field: the flow is Chapter 2 incompressible, fully laminar, and steady. Incompressibility is well justified for this application since the highest Mach number encountered by the rotors to be described in Chapter 6 was Mach 0.3. For a broad range of applications, the Mach number will be considerably below this value and the flow is essentially incompressible. The fully laminar flow assumption is more uncertain. Schlichting [17] indicates that transition on a flat plate at zero incidence occurs at Reynolds numbers greater than 350,000, this is in the abscence of any adverse pressure gradient however. The introduction of an adverse pressure gradient as seen in the pressure recovery of an airfoil introduces two possibilities, laminar separation or turbulent transition. The degree of separation that might result in transition and the transition length are the unclear issues, but the alternatives to a fully laminar assumption are even less satisfactory. The flow field could be assumed fully turbulent, which is surely not the case, or transition could be artificially and rigidly imposed at a specified location. Of these three, the fully laminar assumption is the least restrictive and most physically accurate in the range of Reynolds number and angle of attack of interest here. The steady-state assumption represents tremendous computational savings over time- accurate analyses and has been verified with time-accurate computations. Airfoil polars have been generated by increasing the angle of attack until the steady-state solution fails to converge. Analyses were completed at Reynolds numbers of 1000, 2000, 6000, and 12,000. For analyses at Re=6000 and above, failure to converge is taken as an indication of unsteady phenomena in the flow field. For the Re=1000 and Re=2000 cases, the polars have been computed assuming a steady-state flow field, but then a time-accurate analysis has been completed at or above the indicated maximum lift-to-drag ratio angle of attack. This assures the absence of significant unsteady effects in the presented data, 17
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 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: Chapter 2 to diverge if significant
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
Page 77 and 78: 4.2.3 Elimination of Trigonometric
Page 79 and 80: Chapter 4 applications of interest
Page 81 and 82: 4.2.7 The Distinction Between the A
Page 83 and 84: Chapter 4 Two input parameters dete
Page 85 and 86: Chapter 4 simplification, particula
Page 87 and 88: 4.3.3 Conservation of Angular Momen
Page 89 and 90: 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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