Thermo-Fluid Ch 7

Lecture 12: Wind Power

Source of Wind Energy

  • The original source of wind energy is the radiation from the Sun.
    • This radiation is absorbed by the land and sea, heating the surrounding air.
  • Different materials absorb radiation variably, leading to temperature gradients.
    • These gradients cause convection and pressure changes, resulting in winds.
  • The intensity of solar radiation is higher at the equator.
    • This causes warm air to rise from the equator and cooler air to flow in from the north and south.
  • Definition of wind direction: Wind direction is defined by the origin of the wind (e.g., a wind coming from the north is called a northerly wind).
  • Winds are variable, both temporally and spatially.
    • Some areas experience frequent high winds, while others experience very little.
  • The rotation of the Earth significantly affects global wind patterns.

Wind Power

  • Approximately 1-2% of solar power (about 1.37extkW/m21.37 ext{ kW/m}^2) is converted into wind energy.
  • The radius of Earth is approximately 6000 km.
  • The cross-sectional area of Earth receiving solar radiation is estimated to be 1014extm210^{14} ext{ m}^2.
  • Therefore, the available wind power is estimated to be ext 1015extWext{~}10^{15} ext{W}.
    • This amount is 100 times the current global power usage.
  • It is possible only to harness a small amount of this available wind power to meet the world's energy requirements.

Global Wind Patterns

  • Forces from Earth's rotation (centrifugal and Coriolis forces) significantly influence wind patterns.
    • These forces act over distances of hundreds of kilometers from the Earth’s surface.
  • The velocity of a point on Earth is highest at the equator and decreases towards the poles due to Earth’s rotation.
  • Winds achieve large speeds at high altitudes but are limited to within 30-degree latitudes due to flow instability and dissipation.
  • In the Northern Hemisphere, sinking air near the 30-degree latitude creates northeast trade winds and westerly wind belts over Europe.
  • There are three distinct "cells" in each hemisphere:
    • Hadley Cell: Near the equator.
    • Ferrel Cell: At mid-latitudes.
    • Polar Cell: Near the poles.
  • Surface friction and large-scale eddy motions, along with seasonal variations, also influence wind patterns.

Longitude and Latitude

  • Latitude Values:
    • North: 90° to 0°
    • South: 0° to -90°
  • Longitude Values:
    • West: -180° to 0°
    • East: 0° to 180°

Wind Energy Potential

  • Globally, 27% of the Earth's land surface is classified as Class 3 (250-300 W/m² at 50m) or greater, which presents a potential energy output of 50 TW.
    • Utilization of 4% of Class 3 land could provide 2 TW.
  • In the US, approximately 6% of the land is suitable for wind energy development, equating to roughly 0.5 TW.
    • The electricity consumption in the US is approximately 0.4 TW.
  • Offshore installations provide additional wind energy resources.
    • Source: Archer & Jacobsen, Evaluation of Global Wind Power, Stanford University, 2005.

World Wind Potential by Area (TWh/year)

  • Asia: 4.6 TWh/year
  • Western Europe: 4.8 TWh/year
  • Central America: 5.4 TWh/year
  • Africa: 10.6 TWh/year
  • Northern America: 14 TWh/year
  • Eastern Europe: 10.6 TWh/year

Growth in Wind Energy

  • Wind energy is the fastest growing energy source globally.
  • Current global installed capacity exceeds 100,000 MW, with a projected growth of more than 20% per year for the next five years.
  • Wind farms today produce electrical power at a cost of approximately 0.03/kWh0.03/kWh, comparable to coal and natural gas-based power plants.
  • Total installed capacity reached 160,000 megawatts by individuals measuring from 1997 to 2010.

Wind Energy & CO2 Mitigation

  • In the United States, about 1.5 pounds of CO2 are emitted for every kWh of generated electricity.
  • A typical forest can absorb approximately 3 tons of CO2 per acre per year.
  • A single 750-kilowatt (kW) wind turbine produces about 2 million kWh of electricity annually, preventing approximately 1500 tons of CO2 emissions each year.
    • This is equivalent to the CO2 absorption capacity of 500 acres of forest.

Wind Energy Cost Trends

  • The provided cost trends reflect historical costs rather than precise annual historical data, updated June 2002.

Summary of Some Simple Facts about Wind Power Overview

  • Approximately 0.5% of incident solar power converts into wind energy, possibly generating globally around 20 TWe.
  • Wind energy is carbon and pollution-free.
  • Growth rate of wind energy has been 17% annually since 2010.
  • Wind farms contributed to the generation of 433 GW of electricity in 2015, meeting 3.7% of global electricity demand.
  • By 2050, wind energy could produce 15-18% of global electricity.
  • Wind turbine efficiency is typically around 40%; the maximum possible efficiency (Betz Limit) is 59%.

Kinetic Energy of Wind per Unit Volume

  • Kinetic energy of wind per unit volume is defined as:
    • E = rac{1}{2}
      ho u^2
  • The power of wind can be represented as:
    • P = rac{1}{2}
      ho A u^3
    • Where:

    • ho is the air density (1.2 kg/m³)
    • AA is the area swept by the turbine blades
    • uu is the wind speed.

Wind Power (Simple Estimate)

  • Power of the Wind formula:
    • P = rac{1}{2}
      ho v^3 A
  • Where:

    • ho = density of air (1.224 kg/m³)
    • vv = velocity of air in m/s
    • rr = diameter of the rotor in m.

Horizontal Axis Wind Turbine Components

  1. Rotor blades
  2. Hub (attached to low-speed shaft)
  3. Gearbox
  4. Electrical generator
  5. Hydraulic system
  6. Low-speed shaft (20-30 rpm)
  7. High-speed shaft (around 1500 rpm)
  8. Yaw mechanism
  9. Electronic controller
  10. Anemometer
  11. Cooling unit

Darrieus VAWT

  • Vertical Axis Wind Turbines (VAWTs):
    • Do not require a yaw mechanism (direction controller).
    • Easier maintenance compared to Horizontal Axis Wind Turbines (HAWTs), but HAWTs are more cost-effective.

Savonius VAWT and Design Calculations

  • Savonius rotor characteristics with top and front views as seen.

Betz's Limit

  • The maximum power coefficient (CP) is 0.59, corresponding to the theoretical limit for wind turbine efficiency.
  • The conditions for achieving this involve optimal tip speed ratios and other aerodynamic efficiencies.
  • Empirical formulas account for losses due to drag and blade shape efficiency.

Example Problems

  1. Example 7.2: Wind turbine with blades operating at 8 m/s and 15 rpm, assessing blade midpoint and tip width based on mathematical and geometrical relations.
  2. Example 7.3: Assessing maximum power coefficient and output of a turbine with known characteristics at specified conditions.
  3. Example 7.4: Power output calculations of a turbine at different wind speeds, addressing output power adjustments at rated capacity.

Wind Speed Distribution

  • Rayleigh distribution is effectively used for estimating wind speed probabilities at sites with an annual mean speed greater than 4.5 m/s.
  • A specific distribution graph is referenced for better understanding.

Wind Variability and Penetration

  • Acknowledge that wind variability necessitates backup generators for times when the wind is insufficient.
  • Up to ~20% penetration level of wind energy is typically manageable within energy systems.
    • Demand-side management via smart grids and interconnectors can aid in mitigating variability impact.

Wind Farms

  • Proper layout and spacing in wind farms minimize interference between turbines.
    • Recommended spacing is typically 7-8 rotor diameters downwind and 4-5 across wind.
  • Offshore wind farms generally enjoy several advantages over onshore plants, such as:
    • Higher wind speeds
    • Higher capacity factors (39% offshore vs. 22% onshore)
    • Less turbulence and fatigue
  • Typical power densities: approximately 2 MW/km² onshore and 3 MW/km² offshore.

Environmental Impact of Wind Farms

  • Carbon emissions during construction: around 10 tonnes/GWh.
  • Compared to natural gas combined cycle plants (CCGT) that generate ~450 tonnes/GWh, wind has a significantly lower impact.
  • Public sentiment may complicate wind farm installation, especially in scenic or environmentally sensitive areas.
  • Rare bird deaths compared to anthropogenic impacts from vehicles and domestic animals are noted, though precautions on migratory paths remain vital.

Economics of Wind Power

  • The financial viability of wind power involves:
    • Construction and operational capital costs
    • Revenue from electricity sales
    • Interest on capital and discounting of future revenue
    • ‘Learning rates’ where costs fall due to increased production globally.
  • Wind energy has become economically competitive with fossil fuels, achieving grid parity.
  • Offshore wind bids reflect evolving economics, with ongoing reductions in costs anticipated.

Key Points

  • Global onshore wind potential is about 20 TWe against a background of 2014 global electricity demand at 2.5 TWe.
  • Wind power is proportional to the cube of wind speed, with maximum power coefficients and operational factors at play in practical scenarios.
  • Modern turbine specifications vary from rated power of 1.5-5 MW and rotor diameters of 70-125 m.
  • Installation configurations on wind farms ensure efficient operation and energy balance, with an observed rate of capacity growth in wind installations.