Wind Turbine Investigation
The following experiment enables you to:
 Measure the energy in the wind.
 Assess a commercially available wind turbine in an environmental wind tunnel.
 Determine the power curve of a wind turbine and obtain cutin speeds
 Calculate the coefficient of performance of a turbine
 Calculate the Solidity and Tipspeed ratio.
 See how the energy is converted stored and utilised.
 Examine the Beaufort wind scale.
Introduction:
The power available to a wind turbine is the kinetic energy passing per unit time in a column of air with the same cross sectional area A as the wind turbine rotor, travelling with a wind speed U_{0}. Thus the available power is proportional to the cube of the wind speed. See the figure below.
Equipment
The equipment is provided by Marlec and the following information is from their web page but has been modified slightly for this labsheet.
The Rutland 913 is designed for marine use on board coastal and ocean going yachts usually over 10m in length. This unit will generate enough power to serve both domestic and engine batteries on board.
The Rutland 913 is a popular sight in marinas, thousands are in use worldwide, boat owners like it`s clean, aerodynamic lines and its quiet and continuous operation. Without doubt this latest marine model accumulates more energy than any other comparable windcharger available, you`ll always see a Rutland spinning in the lightest of breezes!
 Low wind speed start up of less than 3m/s
 Generates 90w @ 37m/s, 24w @ 20 m/s
 Delivers up to 250w
 Modern, durable materials for reliability on the high seas
 SR200 Regulator  Shunt type voltage regulator prevents battery overcharge
Theory:
During this experiment you will make use of the following equations to calculate key parameters
Key formulae
Energy in the wind E = (watts)
Swept area of rotor A=πR^{2}
Electrical power output P=VxI (watts)
Coefficient of performance
Tip speed ratio
Solidity = blade area/swept area
R is the rotor radius (m)
ρ is air density say 1.23 kg/m^{3}
U_{o} is the wind speed (m/s)
V is voltage (volts)
I is current (amps)
ω (rads/sec) is the angular velocity of the rotor found from
where N is the rotor speed in revs/min
Procedure:
Step 1 Ensure that everything is setup for you and switch on the tunnel.
Step 2 Adjust the wind speed and let it stabilize
Step 3 Measure the wind speed, voltage and current
Step 4 If available measure the rotor speed with the stroboscope.
Repeat steps 2 – 4 for other wind speeds up to a maximum of 10m/s if achievable.
Gather your data by completing tables 1 and 2
Wind speed
U_{o} (m/s)

Beaufort
number

Effect on land

Output voltage
V (volts)

Output current
I (amps)

Rotor speed
N (revs/min)

















































Table 1 measured data
Calculate the following
Rotor radius use a ruler to measure from center to tip of turbine

R =

Swept area A=πR^{2}

A =

Blade area = blade area + hub area
do your best!

=

Solidity = blade area / swept area.

=

Table 2 measured data
Now analyse your data by completing table 3.
Energy in the wind

Electrical power

Coefficient of performance

Tip speed ratio

E = (watts)

P = V x I
(watts)

P/E
(or column 2 /column 1)






































Table 3 Analyse your data
Present your data:
Now present your results in graphical format to give you a better understanding of the data you have gathered and analysed.
Use excel and the xy scatter chart for this.
Graph 1
Plot the values U_{o} (xaxis) against P (y1axis) and E (y2axis).
Graph 2
Plot the values of U_{o} (xaxis) against C_{p} (yaxis).
What conclusions do you draw?
How efficiently are you converting the kinetic energy in the wind into electrical energy that is stored chemically in the batteries?
Write up the laboratory formally and submit to turnitin. Please ensure presentation is clear and quote fully any references.
The Beaufort Wind Speed Scale

Beaufort Number

Wind Speed at 10m height

Description

Wind Turbine effects

Effect on land

Effect at Sea


m/s






0

0.0 0.4


Calm

None

Smoke rises vertically

Mirror smooth

1

0.4 1.8


Light

None

Smoke drifts; vanes unaffected

small ripples

2

1.8 3.6


Light

None

Leaves move slightly

Definite waves

3

3.6 5.8


Light

Small turbines start  e.g. for pumping

Leaves in motion; Flags extend

Occasional breaking crest

4

5.8 8.5


Moderate

Start up for electrical generation

Small branches move

Larger waves; White crests common

5

8.5 11.0


Fresh

Useful power Generation at 1/3 capacity

Small trees sway

Extensive white crests

6

11.0 14.0


Strong

Rated power range

Large branches move

Larger waves; foaming crests

7

14.0 17.0


Strong

Full capacity

Trees in motion

Foam breaks from crests

8

17.0 21.0


Gale

Shut down initiated

Walking difficult

Blown foam

9

21.0 25.0


Gale

All machines shut down

Slight structural damage

Extensive blown foam

10

25.0 29.0


Strong gale

Design criteria against damage

Trees uprooted; much structural damage

Large waves with long breaking crests

11

29.0 34.0


Strong gale


Widespread damage


12

>34.0


Hurricane

Serious damage

Disaster conditions

Ships hidden in wave troughs

Supplementary Theory
The power available to a wind turbine is the kinetic energy passing per unit time in a column of air with the same cross sectional area A as the wind turbine rotor, travelling with a wind speed u_{0}. Thus the available power is proportional to the cube of the wind speed.
We can see that the power achieved is highly dependent on the wind speed. Doubling the wind speed increases the power eightfold but doubling the turbine area only doubles the power. Thus optimising the siting of wind turbines in the highest wind speed areas has significant benefit and is critical for the best economic performance. Information on power production independently of the turbine characteristics is normally expressed as a flux, i.e. power per unit area or power density in W/m^{2}. Thus assuming a standard atmosphere with density at 1.225kg/s :
Wind speed m/s Power W/m squared
5.0 76.6
10.0 612.5
15.0 2067.2
20.0 4900.0
25.0 9570.3
The density of the air will also have an effect on the total power available. The air is generally less dense in warmer climates and also decreases with height. The air density can range from around 0.9 kg/m^{3} to 1.4kg/m^{3}. This effect is very small in comparison to the variation of wind speed.
In practice all of the kinetic energy in the wind cannot be converted to shaft power since the air must be able to flow away from the rotor area. The Betz criterion, derived using the principles of conservation of momentum and conservation of energy gives a maximum possible turbine efficiency, or power coefficient, of 59%. In practise power coefficients of 20  30 % are common. The section on Aerodynamics discusses these matters in detail.
Most wind turbines are designed to generate maximum power at a fixed wind speed. This is known as Rated Power and the wind speed at which it is achieved the Rated Wind Speed. The rated wind speed chosen to fit the local site wind regime, and is often about 1.5 times the site mean wind speed.
The power produced by the wind turbine increases from zero, below the cut in wind speed, (usually around 5m/s but again varies with site) to the maximum at the rated wind speed. Above the rated wind speed the wind turbine continues to produce the same rated power but at lower efficiency until shut down is initiated if the wind speed becomes dangerously high, i.e. above 25 to 30m/s (gale force). This is the cut out wind speed. The exact specifications for designing the energy capture of a turbine depend on the distribution of wind speed over the year at the site.
Performance calculations
Power coefficient C_{p} is the ratio of the power extracted by the rotor to the power available in the wind.
It can be shown that the maximum possible value of the power coefficient is 0.593 which is referred to as the Betz limit.
where
P_{e} is the extracted power by the rotor (W)
V_{¥} is the free stream wind velocity (m/s)
A is area normal to wind (m^{2})
ρ is density of the air (kg/m^{3})
The tip speed ratio (l) is the ratio of the speed of the blade tip to the free stream wind speed.
where
w is the angular velocity of the rotor (rads/sec), and
R is the tip radius (m)
This relation holds for the horizontal axis machine which is the focus of these notes.
The solidity (g) is the ratio of the blade area to the swept frontal area (face area) of the machine
Blade area = number of blades * mean chord length * radius = N.c.R
Mean chord length is the average width of the blade facing the wind.
Swept frontal area is pR^{2}
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