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AAeroelastic
RRenewable
EEnergy
SSystem
David Chesnutt, Adam Cofield, Dylan Henderson, Jocelyn Sielski, Brian Spears, Sharleen Teal, Nick Thiessen
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Project Goals and Objectives
• Increase performance characteristics and knowledge database of Aeroelastic Energy Device (AED), through research, mathematical modeling, and experimentation.
• Mathematically model AED and its power generation
• Design and build functional prototype of AED
• Test AED to obtain voltage readings and thus power
• Generate database of information on AED to examine power generated
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Coils
Magnets on Either Side of
Membrane
Wires to AC/DC
Converter
Vibrating Membrane
Clamped End
WIND
http://www.humdingerwind.com/Images/press/windbelt_early_proto_lowres.jpg
Windbelt ™ Concept
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Project Specifications
• Generate power for small electronic devices– Device must produce 60 mW
(8.05 × 10-5 hp) of power
• Determine relationship between wind speed and belt tension for various belts; optimize tuning of AED for maximum power– Device should produce power in wind speed
range of 1.2 m/s to 4.9 m/s (4 ft/s to 16 ft/s)
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Project Specifications
• Device should be tunable to operate at maximum efficiency under most common wind speed – Manufacture belt to withstand a 4.9 m/s
(16 ft/s) constant wind
• Device should withstand wind gusts– Manufacture belt to withstand a 16.8 m/s
(55 ft/s) gust
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Tentative Project Specifications
• Electromechanical System – Reduce losses of converting mechanical
power to electrical power
• Power Conditioning System - Minimize losses in electrical signal to
transmit most power possible
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Project Calculations Overview
• Aerodynamics– Flutter, vortex shedding, natural frequency
• Electromechanical– Magnetic flux, AC current, voltage
• Power Conditioning– AC to DC converters
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Project Organization
Aerodynamics ElectromechanicalPower
Conditioning
ARES
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Project OrganizationAerodynamics
Determine Natural Frequency of Belt –
Tension, Vortex Shedding, Elasticity
Build Proof of Concept
Prototype (Alpha)
Determine Frequency Produced
by Aeroelastic Flutter at Various
Windspeeds
Determine Belt Displacement
Function
Prototype for Testing of
Mathematical Model (Beta)
Mathematical Model
Mathematical Model
Refinement
Experimentally Verify Equations with High Speed
Camera
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Project OrganizationElectromechanical
Determine Equations for Variation of
Magnetic Field Flux
Determine Equations for
Current Variation
Mathematical Model
Prototype for Testing of
Mathematical Model (Alpha)
Mathematical Model
Refinement and Adjustment for Beta Prototype
Prototype for Testing of
Mathematical Model (Beta)
Mathematical Model
Refinement
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Project OrganizationPower Conditioning
Circuitry for Power
Conditioning
Power Conditioning Prototype
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Project OrganizationFinal Concept
Beta Prototype from
Aerodynamics Testing
Beta Prototype from
Electromechanical Testing
Prototype from Power
Conditioning
Final Prototype (Gamma)
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CalculationsAeroelasticity and Flutter
• Aeroelasticity: The study of structural deformation due to aerodynamic loading
• Flutter: Vibration of structures due to oscillating fluid motion.
www.wikimedia.org
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• When flow separates in oscillating manner around structure near structure’s natural frequency, lock-in effect occurs – Usually ± 10% the natural frequency of
structure• Shedding frequency forced to match natural
frequency in this region, also with multiples or sub-multiples of natural frequency
• Design intent: create lock-in effect.
CalculationsFlutter and Resonance Lock-In
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• String Theory
• Natural frequency depends solely on tension.
• Beam Theory
• Natural frequency depends on both tension and EI term.
CalculationsCharacterizing Natural Frequencies
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E=3.1GPat=50 micronsb=2.5 cm
CalculationsBelt Vibration Model
bt
y
x
•String theory is almost identical to beam theory when A<<1m^2•How close?
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Accuracy of String TheoryE=3.1GPat=50 micronsb=2.5 cm
CalculationsCan the String Model Be Used?
•Allows modeling of vibrations as string•Simple equations save time
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• Match natural frequency to shedding frequency in order for resonance lock-in to occur.
• Strouhal Number is usually determined experimentally.
• Dependent upon Reynolds number.
• For 300<Re<30000, S~.2
Flow Induced Vibrations, Robert Blevins.
CalculationsStrouhal Number
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CalculationsAlpha Prototype Example
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Flow-Induced Vibration, Robert Blevins.Approx. Values
*Small D values mean small amplitude wakes- once angle of attack is established due to torsional motion, wake grows in width (larger effective D value), increasing minimum velocity required for flutter.
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CalculationsWake Oscillator Model
• Single degree of freedom in y-direction
• Allows calculation of structural displacement function.
• Applicable when 300<Re<30000
• Assumptions:a) Inviscid flow can be assumed outside,
near wake.
b) Well formed vortex sheet with well defined shedding frequency.
c) Vorticity generated only in boundary layer, vortices move downstream.
d) Flow is 2-D.
e) Force exerted on cylinder depends only on velocity and acceleration of averaged flow relative to cylinder.
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Flow Induced Vibration, Robert Blevins.
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CalculationsCalculating Displacement Amplitude
Flow Induced Vibration, Robert Blevins.
Determined experimentally
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• Alpha Model Equation
– N is number of coils
– A is area of coils normal to flux
– B is experimental flux density equation
– x, sinusoidal displacement function
– K is shape factor which contains permeability and magnet intensity
– n is set to fit function to experimental data
CalculationsElectromechanical Model - Alpha
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• Alpha Model– Use Faraday's law to establish magnetic flux
density equation– Use voltage and current readings to establish
flux density equation – Model will help establish a "shape factor" to
predict magnetic flux density– Neglect radial motion of magnets and Lorentz
Force
CalculationsElectromechanical Model - Alpha
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• Beta Model– Aeroelastic force input function– Elastic restoring force function– Lorentz Forces of coils acting on magnets – Neglect radial motion of magnets– Use previous model's flux density relation
with respect to magnet displacement
CalculationsElectromechanical Model - Beta
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• Gamma Model– Collaborate with aeroelastic model
CalculationsElectromechanical Model - Gamma
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• Model displacement, velocity, and acceleration curve
– Need maximum amplitude estimate. – Model forcing function belt will apply to
magnet(s)
• Model torsional frequency
– Important for belt life, determines its importance for power generation
• Incorporate electromagnetic forces on belt as information becomes available.
CalculationsNext Steps
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CalculationsNext Steps
• Develop expressions for y(x,t), θ(x,t), and γ(x,t)– Experimentally verify
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Belt Design
• Using composite materials (thin fabric lamina) special behaviors can be achieved
• By laying-up 2 or more laminae in certain directions, couples behaviors are produced in laminate (bend-twist, extend-twist, etc.)
• Potential control of twisting of belt
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Present Hardware
Tightening Screw
L-Bracket
Base
Membrane
Core Metal
Inductor
Fret
Fret
MagnetsMounting Blocks
Bolt Holes
Electromechanical Alpha Model
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Present Hardware
Magnetic Induction Coils Setup
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Present Hardware
Proof of Concept Model
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