Transcript Physics 201 - University of Virginia

PHYS 1110
Lecture 17
Professor Stephen Thornton
November 1, 2012
October 30 was canceled because someone
thought we would have bad weather.
Reading Quiz
Why is there a breeze from ocean to shore on a
hot summer day at the beach?
A) Because the specific heat of sand is greater
than that of water.
B) Because the specific heat of sand is
less than that of water.
C) Because there is usually a high pressure
area over the ocean water.
D) Because there is usually a low pressure
area over the ocean water.
E) None of the above are true.
Reading Quiz
Why is there a breeze from ocean to shore on a
hot summer day at the beach?
A) Because the specific heat of sand is greater
than that of water.
B) Because the specific heat of sand is
less than that of water.
C) Because there is usually a high pressure
area over the ocean water.
D) Because there is usually a low pressure
area over the ocean water.
E) None of the above are true.
Quiz today, November 1 (was October
30) on
Ch. 5 Thermodynamics
Ch. 6 Fossil Fuels
Ch. 7 Hydropower only
You may bring in one regular sheet of
paper with anything written on it that
you wish. Quiz will start at 10:20 am.
Figure 8-1 World capacity of
wind power, 1996-2010.
The United States wind industry is robust.
The US generating capacity increased more
than 15% in 2010 and another 31% in 2011
to more than 50,000 MW. This represented
about 25% of the new electric generation
capacity in the U.S. in 2010, and commercial
wind energy turbines are located in 38 states.
Utility scale
0.9 - 4 MW and larger
Industrial scale
50-700 kW
Residential scale 400 W to 50 kW
Figure 8-2 (a) A depiction of a
square sail boat that might have been
used on the Nile River centuries ago.
(b) A felucca sailboat near Luxor
favored by southerly winds on the
Nile River. The river current moves
them north.
Figure 8-3 Schematic of a panemone,
an early Persian device used for
pumping water. The axis is vertical.
It is known that the
Persians developed a
vertical axis system
called the panemone
around 700 AD for
pumping water.
A Dutch windmill operating in 1994 with many improved
features including a mechanism to turn the rotor into the
wind. The living quarters are seen on the first floor. This
windmill was used to pump water up one meter from one
irrigation pond to another in the Netherlands.
Old windmill used in
the 20th century across
the Great Plains of
Midwestern United
States to pump water
for irrigation and
drinking. Some were
even used to generate
electricity.
Scientists in the United Kingdom, the United States, and
Denmark all produced wind powered machines that produced
electricity by the 1890s. Larger wind turbines intended for
connection to the electrical grid were developed in the former
Soviet Union in 1931, and a 1.24 MW unit was built in
Vermont in 1941 to produce electricity during WW II.
Although Denmark and Germany continued to develop wind
turbine technology after WW II, general interest went up and
down depending on oil prices. With the oil embargoes of the
1970s, the price of oil went up dramatically, and wind power
research jumped into high gear. A tremendous amount of
progress has been made since the mid-1970s. The Danes
have been particularly active in windmill technology as is
evidenced by the heavy production of electricity by wind
power today.
Air is a fluid, and pressure is a measure of the force
transmitted in a fluid. Pressure is the force per unit area
acting in a direction perpendicular to the surface of an
object’s area.
F
pº
A
1 Pa = 1 N/m
2
1 atm = 1.013 ´ 105 Pa = 14.7 lbs/in 2
Wind blows because of differences in air pressure. The Earth
heats various locales of the Earth differently creating the high
pressure areas (H) and low pressure areas (L) that we see on
weather maps. Air pressure on Earth is due to the gravitational
force of all the air above us. The air pressure naturally decreases
with elevation.
Hurricane Sandy - Sunday,
October 28, 2012. Low pressure
High and Low pressure areas.
M = rV
A = area
L = length
V = AL = Avt
2
KE particle = mv / 2
KEsystem =
1
2
2
Mv =
1
2
2
r Vv =
1
2
2
r Avtv =
1
r Av t
2
Power is energy/time
KE 1
3
P=
= r Av
t
2
3
The density of air r
and air pressure p
decrease with
elevation
(altitude).
r (height h) = 1.225 (1- 1.06´ 10
- 4
h) kg/m
air pressure p = 101325(1- 2.26´ 10
- 5
5.26
h)
3
Pa
Let’s apply our equation
for power P to wind
turbines. The area A is
the area swept by the
turbine blades. The
power goes up with the
square of the blade
length.
1
P = r Av 3
2
A schematic indicating the improvement in wind power with the
diameter of the turbine blades (tip to tip). An approximate doubling of
the diameter from 44 m to 80 m increases the possible wind power
from 600 kW to 2500 kW for a typical wind turbine.
In practice a wind turbine cannot completely convert all the wind
power given by Equation (8-8) into electricity. Some of the wind
must pass through the wind turbine as shown the figure. A
theoretical calculation done by the German physicist Albert Betz
in 1919 established that no wind turbine can extract more than
16/27 = 0.593 (Betz limit) of the wind power to mechanical
energy. If all the wind were able to be converted to mechanical
energy by the wind turbine, then no more wind would be able to
enter the blade area. Some air must pass through.
Even though the Betz limit is a theoretical limit
based on certain assumptions, we will refer to
this limit as an efficiency, because it is not
really possible to reach the Betz limit. A very
efficient wind turbine will have a value of
~0.4 or lower, and typical values are as low as
0.1 – 0.3. We rewrite the Power equation using
this efficiency e.
1
3
P = r e Av
2
During the day warm air over land rises, and
cooler air from the ocean rushes in to
displace it resulting in a sea breeze.
During the night warm air over the ocean
rises, and cooler air from land rushes in to
displace it resulting in a land breeze.
The valleys are
heated by the sun
during the day
causing hot air (lower
pressure) to rise
towards the mountain.
The reverse happens
after the sun goes
down.
One wants to take advantage of the prevailing
winds when siting a wind turbine, because the
highest winds occur when the prevailing winds
are in the same direction as the valley winds.
This addition of mountain-valley and prevailing
winds can be quite effective in wind turbine
output during the summer. The prevailing winds
also help in the winter months when the
mountain-valley breezes are weaker. The
prevailing winds will still provide some wind to
produce electricity.
There are many other different types of special winds.
These include Chinook (east off the Rocky Mountains), Santa
Ana (down the canyons of southern California towards the
Pacific Ocean), Sirocco (wind from hot Sahara desert towards
Mediterranean in North Africa and Southern Europe), mistral
(cold, dry wind in France coming from the north and
northwest especially through the Rhone valley), bora (a gusty
wind along the Adriatic east coast and elsewhere prevalent in
the winter due to high-pressure over the interior mountains),
and etesian (a strong, dry summer wind from the north over
the Aegean Sea between Greece and Turkey due to high
pressure in the Balkans and low pressure over Turkey). Note
that many of these special winds are from the Mediterranean
Sea where experienced sailors have documented these winds
for centuries.
Quiz
Why is there a breeze from shore to ocean at
night on a hot summer day at the beach?
A) Because the specific heat of sand is larger
than that of water.
B) Because the specific heat of sand is
smaller than that of water.
C) Because there is usually a high pressure
area over the ocean water.
D) Because there is usually a low pressure
area over the ocean water.
E) None of the above are true.
Quiz
Why is there a breeze from shore to ocean at
night on a hot summer day at the beach?
A) Because the specific heat of sand is larger
than that of water.
B) Because the specific heat of sand is
smaller than that of water.
C) Because there is usually a high pressure
area over the ocean water.
D) Because there is usually a low pressure
area over the ocean water.
E) None of the above are true.
The average solar radiation is greatest near
the equator where air is warmed at the surface and rises. This
results in low air pressure centered on the equator in a region
known as the Intertropical Convergence Zone (ITCZ).
This begins a process that produces regional and global wind
patterns, known as the prevailing winds. There is a wide
tropical zone, two temperate and two polar zones.
Note the
latitudes of
the Polar
Zone,
Temperate
Zone , and
Tropics.
The tropics receive more sun
throughout the year than the
temperate zone, which in turn
receives more sun than the
polar zones. This unequal
heating of the Earth is
responsible for the large
global wind movements. As
air above the equator is
heated, it rises to create
regions of low pressure. Air
from regions of high pressure
is pulled into the equatorial
region to replace the low
pressure air that moved up to
higher altitudes.
A depiction of the
general trade winds
and the three cells.
This diagram is
very simplified but
helps explain the
prevailing winds
around the globe.
Think about what happens in the United States during the
winter months. The warmer air in the temperate zone
rises creating a low pressure, but the Arctic region has
colder, denser air at high pressure, because the sun hardly
touches the North Pole in the winter. This pressure
difference pulls the jetstream more and more to the south
bringing cold Arctic wind over much of the central and
eastern United States. We often see the weather maps
with those bitter cold fronts moving south. When spring
comes and the sun finally shines on the North Pole again,
the polar air is warmed, and the pressure difference is less
pronounced.
The trade winds are a consistent source of good wind
quality and are a potentially large source of reliable
electricity from wind turbines. There is a band of low
pressure air near the equator and the high pressure bands
between the tropical and temperate zones and the low
pressure bands between the temperate and polar bands.
These high and low pressure regions dominate the wind
patterns. The trade winds obviously obtained their name
from the sailing ships that carried goods between Europe
and the new Americas. The ITCZ band near the equator is
more commonly known as the doldrums, because sailing
ships could be stuck for weeks before ocean currents finally
moved them in into the trade winds. It was crucial for
sailing ships to be able to sail into the wind. Sailors did not
look forward to crossing the equator.
A schematic diagram of how lake-effect snow falls
near large bodies of water like south and east of the
Great Lakes.
Schematic of Coriolis effect. Wind from the
North Pole blows south towards the Equator, but
while the air is moving, the Earth is rotating so
the air ends up being further east. The apparent
effect is that the wind turned to the right.
This is a modification of the winds shown previously
with the Coriolis Effect added. The common names of
the global wind patterns are the trade winds, easterlies,
and westerlies. Warm air rises and cold air descends at
the poles.
Doldrums The doldrums are a thin band around the
Equator called the ITCZ band earlier where the wind is
calm. The trade winds from the two hemispheres meet
where they are heated and rise. The area is generally at
low pressure.
Trade Winds The trade winds are winds that generally
flow from a high pressure area near 300 latitude (see the
Hadley Cell). Air tends to flow from a high-pressure
region at 300 to a low-pressure region at the Equator.
The Coriolis Effect causes the winds to curve somewhat
towards the west. The Trade Winds are also called the
Prevailing Easterlies, because the winds appear to
originate from the east. Winds tend to be named from
the direction is which they originate.
Prevailing Westerlies Air masses above the 300 latitude
(also called the horse latitudes) tend to flow north toward
low pressure at 600 latitude called the Subpolar Low. The
Coriolis Effect turns the air flow towards the east, resulting
in an air flow from the southwest to the northeast. This is
the region of much of the United States, and many of our
weather fronts do travel from the southwest to the
northeast. The Prevailing Westerlies are also just called the
westerlies.
Polar Easterlies The atmospheric air masses over the
North Pole cools, then sinks towards the Earth’s surface
because it is a denser air mass and forms a high-pressure
region that sends the air down towards the 600 latitude.
The Coriolis Effect turns the air towards the west to form
the Polar Easterlies or simply the Easterlies.
Global wind speeds at 80 m height.
Offshore speeds are not shown. Generally the yellow and
red sites are best. Blue and green are not so good, and this
includes most of the tropics.
The National Renewable Energy Laboratory has the
responsibility to produce wind speed maps to help
develop wind resource potential for wind farms and
individual wind turbines in the US. An area with an
annual average wind speed around 6.5 m/s and greater at
80-m height is generally considered to have suitable
wind resource for wind development.
This map eliminates the land-based regions unlikely
to be developed with wind farms for various reasons
(land use, economic, or environmental).
50 m height.
Includes
offshore
sites.
Average Depth
Superior – 149 m
Michigan – 85 m
Huron – 59 m
Erie – 19 m
Ontario – 86 m
Quiz
What are the prevailing winds here in
Charlottesville?
A)
B)
C)
D)
E)
Doldrums
Trade
Westerlies
Polar
Temperate
Quiz
What are the prevailing winds here in
Charlottesville?
A)
B)
C)
D)
E)
Doldrums
Trade
Westerlies
Polar
Temperate
Placement of Wind Turbines
The wind profile power law is a relationship
between height h and wind speed:
1
7
v æ
hö
ç
÷
= çç ÷
÷
÷
v0 è h0 ø
open smooth land
1
9
ö
v æ
h
÷
= ççç ÷
÷
v0 è h0 ÷
ø
open water
See Examples 8-2 and 8-3.
Anemometers are used to
measure wind speed.
Table 8-1 Wind Speed vs. Angle
Angle
90°
85°
80°
75°
70°
65°
m/s
0.0
2.6
3.6
4.5
5.3
5.9
km/h
0.0
9.3
13.1
16.2
18.9
21.4
Description_____________________________
Calm; smoke rises vertically
Light breeze; smoke drifts; leaves rustle
Gentle breeze; leaves and twigs in motion
Moderate breeze; raises dust and loose paper
Fresh breeze; small trees sway
Fresh to strong breeze; crested waves form on
inland waters
60°
6.6
23.9
Strong breeze; large branches in motion
55°
7.3
26.4
Strong breeze; difficulty with umbrellas
50°
8.0
28.9
Near gale; whole trees in motion
45°
8.7
31.4
Near gale; impedes progress
40°
9.5
34.2
Gale; breaks twigs off trees
35°
10.4
37.4
Gale;
30°
11.5
41.3
Strong gale; slight structural damage
25°
12.8
45.9
Strong gale; tiles lift off roof
20°
14.4
52.0
Storm; seldom experienced inland
Anything beyond this is a violent storm or a hurricane accompanied by
widespread damage.
A wind turbine needs to be located away from turbulent
wind flow, because even light turbulence will degrade the
performance of a wind turbine; it cannot react quickly to rapid
changes in wind direction. Heavy turbulence could decrease
equipment life or result in equipment damage. Turbulence can be
detected by using a kite with ribbons as shown in the figure or by
tying a long ribbon to a pole or mast to see if it unfurls and streams
smoothly in high winds from various directions.
Both the tower on the smooth hillside and on top
of the hill are to be avoided because of turbulence
on top of the hill and wind blockage on the side of
the hill.
(top) Nearby trees are to be avoided. Either place the
wind turbine at least 100 m away or place it at least twice above the
tree level. (bottom) Similarly, a high tower will be needed near an
ocean cliff to avoid turbulence.
Turbulence is to be
avoided at all cost.
Obstacles like a building can affect air flow over
a wide area and are to be avoided unless tall
towers are utilized.
Table 8-2 Classification of Wind
Speeds for Wind Turbine Siting at 50 m
Class
I
II
III
IV
V
VI
VII
Rating
Poor
Marginal
Fair
Good
Excellent
Outstanding
Superb
Wind Speed (m/s)
0 – 5.6
5.6 – 6.4
6.4 – 7.0
7.0 – 7.5
7.5 – 8.0
8.0 – 8.8
8.8 – 11.0
Quiz
Where is a good place to place a wind
turbine?
A) On top of a hill.
B) An open space surrounded by trees.
C) On a tall tower on a cliff above the
ocean.
D) Behind a tree, but barely taller than
the tree.
E) On a smooth hillside.
Quiz
Where is a good place to place a wind
turbine?
A) On top of a hill.
B) An open space surrounded by trees.
C) On a tall tower on a cliff above the
ocean.
D) Behind a tree, but barely taller than
the tree.
E) On a smooth hillside.
If we know the average wind speed at a particular site, then we can use
data and calculations to determine the amount of time that wind blows
at a particular wind speed. Measurements have been made at many
locations, and the curve shown below at the Lee Ranch in Colorado
during 2002 is typical. The red histogram is the measured data, and
solid red line is the Rayleigh model distribution for the same average
wind speed.
Wind Power Production
We showed data for the number of hours wind blew at a given speed
at Lee Ranch during 2002. However, we would like a better idea of
the actual power produced when the wind blows against a wind
turbine. The power equation was derived for a single wind speed,
but we know that the wind speed varies tremendously throughout
the year. We would like to determine a better result for the
mechanical power, and thus the electrical power expected
throughout the year. The wind may not be blowing in one part of
the country at a given time, but it will be blowing at another
location. We are primarily interested in the total electrical
production, and we are neglecting for the time being the problems
of connecting electricity to the electrical grid and the distribution of
electrical power around the grid.
1
P = r e Av3
2
The mean wind speed throughout the year
will be different at different locations. We show below the
Rayleigh distribution for several mean wind speeds.
Remember that the average wind speed is the arithmetic
average of the speeds. The most probable speed is the peak
of the distribution shown below.
The Rayleigh
distribution is
given for a
variety of mean
wind speeds.
.
We take the power equation and use the mean
speed v , wind turbine diameter D and
efficiency.
3
2 3
P = r eD v
4
This is the power expected annually for a wind turbine
having blade diameters D (tip to tip), efficiency e , and
mean annual wind speed . Even this equation is too
optimistic, because there are cut-in minimum wind
speeds of about 4 m/s (~10 mph) to initiate the
electrical generation, and there are cut-off maximum
wind speeds of 20-35 m/s (45-80 mph) to prevent
damage to the wind turbine in high winds.