Understanding Wind Energy: Origins, Blade Theory, and Power Extraction - Prof. Matt Ryan A, Study notes of Agricultural engineering

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AGR 225 Day 3

• 1. Partner Presentations – topic by Friday
• 2. Review
• 3. Where does wind come from?
• 4. Basic Blade theory

Wind and Turbine Blades

Laymen’s Perspective Or As much aero engineering as the average person cares to know

Review: Estimating Costs

• A household appliance is used 10 hours per week. It is plugged into a household outlet (assume 120V) and draws 1A when it is running. The utility charges $.10/kWh. How much money is spent over one year?

Review: Estimating Costs

• A household appliance is used 10 hours per week. It is plugged into a household outlet (assume 120V) and draws 1A when it is running. The utility charges $.10/kWh. How much money is spent over one year?

120V * 1A = 120W

120W * 10 hrs/wk = 1200 Wh/week 1200 Wh/week * 52 weeks/yr = 62,400 Wh/yr 62,400 Wh/yr * 1 kWh/1,000 Wh = 62.4 kWh/yr

62.4 kWh/yr * $.10/kWh = $6.24/yr

Electricity conversion Wheel O’ Fun

Where does wind come from?

• On a macro/global scale, the magnitude and direction of wind is a result of:

1. Uneven heating of earth’s surfaces -> jet streams and cells (Hadley, Ferrell, polar) between equator-> 30, 30-60, 60-90 degrees

2. Coriolis Effect -> in the Northern Hemisphere, things veer right http://tinyurl.com/yvurcs

Where does wind come from?

ISU Farm 2009 met tower energy rose

ISU Farm 2009 met tower energy rose

Where does wind come from?

• On a micro/regional scale

1. Uneven specific heat capacity of various surfaces, especially water v. land -Water has a higher specific heat capacity than land. Warm air over land rises during the day. Warm air over water rises at night.

Effect of Height

• Height affects wind speed!
• “Boundary Layer” - > drag/friction near Earth’s surface (same as in a hydraulic pipe)

Height affects wind speed!

ISU Farm (Lexington, IL) 2008 wind shear profile Power Law Fit: Ux = Uy * (Zx/Zr)^a

Height affects wind speed!

• Power Law Fit: Ux = Ur * (Zx/Zr)^a
• a = Wind Shear Exponent
• Generic a = 1/7 = 0.143, but site-specific!
• Measured a for ISU Farm in 2008 = 0.
• Higher a -> greater wind shear (forest, large obstructions, etc.)

Wind “Mixing”

• Mixing occurs to different degrees depending on the amount of incident solar radiation
• Daytime with high solar irradiation -> “well- mixed” conditions because of updrafts
• Night-time with no solar radiation -> “stratified” conditions

Wind “Mixing”

ISU Farm 2008 Diurnal Average Wind Speed Profile

Wind Seasonal Variation

• Created by interactions between cells (Hadley, Ferrel, polar)
• Jet stream is stronger in winter months

Wind Seasonal Variation

ISU Farm 2008 Seasonal wind velocity profile

Power Available in the Wind

• So power is proportional to the density of air, the square of blade length, and the cube of wind velocity

3 2

P   AV

Blade Basics

• Betz limit = the maximum fraction of the power in the wind that can theoretically be extracted
• Betz limit = 59.3%

Power Converted to Electricity

• is the Coefficient of Performance

3 2

P  Cp  AV

Cp

Blade Basics

• Bernoulli’s Principle = a re-statement of Conservation of Energy (First Law of Thermodynamics)
• Kinetic energy + Stored energy (height, compression, chemical) = constant

Blade Basics

• Another important concept in blade theory: Newton’s 3rd^ Law: For every action there is an equal and opposite reaction -> Angle of attack is important
• Blade Force diagram – be able to show the forces acting on a blade

Blade Basics

• Vortex generators: act to create turbulent flow

  • air flow “sticks” to blade surfaces -> postpones the onset of stall

Blade Basics

• Velocity at blade tip is higher -> to maintain efficient angle of attack, blade profile must “twist”
• What is maximum tip speed?

Blade Basics

• What is maximum tip speed?
• About 150-200 mph (depends on model). For GE 1.5 sle w/ 37m blades, max tip speed = about 165 mph