PHYS 1110
Lecture 18
Professor Stephen Thornton
November 6, 2012
Reading Quiz
What are the prevailing winds here in
Charlottesville?
A)
B)
C)
D)
E)
Doldrums
Trade
Westerlies
Polar
Temperate
Reading Quiz
What are the prevailing winds here in
Charlottesville?
A)
B)
C)
D)
E)
Doldrums
Trade
Westerlies
Polar
Temperate
Good job on Homework 3.
Homework 4 due Tuesday, November
13, 2012.
Quiz 1 average
74 ± 21
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
Placement of Wind Turbines
The wind profile power law is a relationship
between height h and wind speed:
1
7
ö
v æ
h
÷
= ççç ÷
÷
÷
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.
The power, according to Equation (8-11),
depends on the cube of the speed. The power
will peak at a factor
3
v
= 1.91
3
v
We expect the energy (or power) spectra to peak for
speed almost a factor of 2 higher than the mean wind
speed or 1.6 times the most probable speed. We can
now understand the energy spectra shown in Figure 826. It peaks at higher speeds than the wind speed
distribution itself because of the v 3 factor.
.
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 , 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.
e
Pressure can be impressive!
F
p=
A
Tanker car collapse
Workers steam cleaned
tanker car, then closed all
the valves and left for the
night.
Conceptual Quiz
You are walking out
on a frozen lake and
you begin to hear
the ice cracking
beneath you. What
is your best strategy
for getting off the ice
safely?
A) stand absolutely still and don’t move a muscle
B) jump up and down to lessen your contact time
with the ice
C) try to leap in one bound to the bank of the lake
D) shuffle your feet (without lifting them) to move
towards shore
E) lie down flat on the ice and crawl toward shore
Conceptual Quiz
You are walking out
on a frozen lake and
you begin to hear
the ice cracking
beneath you. What
is your best strategy
for getting off the ice
safely?
A) stand absolutely still and don’t move a muscle
B) jump up and down to lessen your contact time
with the ice
C) try to leap in one bound to the bank of the lake
D) shuffle your feet (without lifting them) to move
towards shore
E) lie down flat on the ice and crawl toward shore
As long as you are on the ice, your weight is pushing down. What
is important is not the net force on the ice, but the force exerted on
a given small area of ice (i.e., the pressure!). By lying down flat,
you distribute your weight over the widest possible area, thus
reducing the force per unit area.
Fluid dynamics tells use the relationship between the
speed of fluids and pressure. It is an inverse relationship:
high speed, low pressure – low speed, high pressure. This
is part of the Bernoulli principle (or equation).
Let’s do some demos.
• Blow across a piece of paper.
• Blow between two pieces of paper.
Do some more demos:
Blow air around objects.
Atomizer – see later
Toilet paper gun.
Curveball – see later
Wings are designed to cause air to
flow faster over top of the wing. Causes
pressure differential resulting in lift.
High speed, low pressure
Low speed, high pressure
True for birds and airplane wings, but not the whole story!
Force on a Roof Due to Wind Speed
Very high speed, low pressure
Very low speed, normal pressure
Roof might blow off
during hurricane!
Air Circulation in a Prairie Dog Burrow
Lower P
An Atomizer – Fast air (low pressure)
causes fluid to rise in tube.
Do demo
Pitot tube
used to measure
the speed of
airplanes.
Why does a baseball or softball curve?
Increased air speed.
Lower pressure.
v
F
Spinning ball drags air
ball
Lower air speed.
Higher pressure
Throw
curveballs.
Let’s divide into groups and study
Lift and Drag
VAWT
HAWT
Describe good aerofoil
Apparent wind
3 kW VAWT machine made in China. It is suitable
for a residence, but needs a battery back up.
The Darrieus wind turbine is
one of the most efficient of the
VAWT, because it is lift based.
However, it also produces large
torque ripple and stress on the
tower, which leads to increased
maintenance and downtime. It
normally requires an external
start-up device, because of
difficulties in making it selfstarting. It has a huge
advantage in urban settings,
because of wind changes
around buildings and trees. It
needs no yawing mechanism.
The Savonius VAWT is one of the simplest wind turbines,
because they are drag-type devices. They consist of two or
three scoops having their outside curved to reduce drag when
moving against the wind. Schematic of a Savonius VAST
with three air scoops. Note the curved feature on the back
reduces drag when moving against the wind.
VAWT devices are becoming
more sophisticated. This device
is rated at 4 kW and can be
mounted on the ground or on top
of a building, including a house.
It is very quiet even during high
winds. A new VAWT Darrieustype wind turbine, which its
Chinese manufacturer says has
increased durability and power
production, but with lower
vibration and drag. This device
can be installed with a tie in to
the electrical grid and battery
back up is an option.
Advantages and disadvantages of
VAWT.
A HAWT with three blades has turned into the wind. The
wind blows across the wing, shaped as an aerofoil, to
give lift to the wing and cause it to rotate clockwise.
As the angle of attack is increased, the lift continues to increase
until at large angles, the blade stalls, turbulence increases, and the
lift decreases. There is an optimum angle that generates the
maximum lift. It is very easy to demonstrate lift and the angle of
attack. Roll your window down while sitting in the passenger seat
of an automobile and hold your arm and hand straight out level to
the road with your thumb held tight to your fingers and facing the
wind. Now slowly rotate your hand to increase the angle of attack.
Probably before you reach 300 you will reach the point that the lift
force dramatically increases, and you will not be able to hold your
arm in place.
The lift increases as the angle of attack increases until the
point is reached that the lift decreases, and the drag sharply
increases. Considerable research has gone into the shape of
aerofoils, and these shapes are now well known. We want the
lift to be much larger than the drag, and this happens
somewhat before the stall approaches as shown at 300.
Characteristics of a good aerofoil are as follows:
1)
2)
3)
4)
5)
High lift to drag ratios.
Smooth gradual curves.
Round leading edge and sharp trailing edge.
Smooth surfaces.
Good construction and materials to support large
forces and stresses.
6) Low thickness to chordline length ratios.
Divide into groups and study
Control mechanisms
Wind farms
Offshore wind farms
Environmental concerns
Safety
Economics
Wind energy pros and cons
The scenario for having 20% Wind Energy in
the United States by 2030.
Cumulative installed capacity of wind power
capacity projected by 2030. The gradual increase
of offshore capacity is indicated.