1

AAeroelastic

RRenewable

EEnergy

SSystem

David Chesnutt, Adam Cofield, Dylan Henderson, Jocelyn Sielski, Brian Spears, Sharleen Teal, Nick Thiessen

22

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

33

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

44

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)

55

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

66

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

77

Project Calculations Overview

• Aerodynamics– Flutter, vortex shedding, natural frequency

• Electromechanical– Magnetic flux, AC current, voltage

• Power Conditioning– AC to DC converters

8

Project Organization

Aerodynamics ElectromechanicalPower

Conditioning

ARES

9

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

10

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

11

Project OrganizationPower Conditioning

Circuitry for Power

Conditioning

Power Conditioning Prototype

12

Project OrganizationFinal Concept

Beta Prototype from

Aerodynamics Testing

Beta Prototype from

Electromechanical Testing

Prototype from Power

Conditioning

Final Prototype (Gamma)

13

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

14

• 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

15

• String Theory

• Natural frequency depends solely on tension.

• Beam Theory

• Natural frequency depends on both tension and EI term.

CalculationsCharacterizing Natural Frequencies

16

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?

17

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

18

• 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

19

CalculationsAlpha Prototype Example

19

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.

20

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.

20

Flow Induced Vibration, Robert Blevins.

21

CalculationsCalculating Displacement Amplitude

Flow Induced Vibration, Robert Blevins.

Determined experimentally

22

• 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

23

• 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

24

• 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

25

• Gamma Model– Collaborate with aeroelastic model

CalculationsElectromechanical Model - Gamma

26

• 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

27

CalculationsNext Steps

• Develop expressions for y(x,t), θ(x,t), and γ(x,t)– Experimentally verify

28

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

2929

Present Hardware

Tightening Screw

L-Bracket

Base

Membrane

Core Metal

Inductor

Fret

Fret

MagnetsMounting Blocks

Bolt Holes

Electromechanical Alpha Model

3030

Present Hardware

Magnetic Induction Coils Setup

31

Present Hardware

Proof of Concept Model

3232