Chemical, Biological and Environmental Engineering Wind 1.

Chemical, Biological and Environmental Engineering

Wind 1

Advanced Materials and Sustainable Energy LabCBEE

How Lift Based Turbines Extract Energy from Fluid

Bernoulli’s Principle - air pressure on top is lower than air pressure on bottom because it has further to travel, creates lift

Airfoil – could be the wing of an airplane or the blade of a wind turbine


Angle of Attack, Lift, and Drag

Increasing angle of attack increases lift, but it also increases drag

When angle of attack is too great, “stall” occurs where turbulence destroys the lift


Wind Turbines“Windmill”- used to grind grain into flour (or pump

water in Holland)

Can have be horizontal axis wind turbines (HAWT) or vertical axis wind turbines (VAWT)

Groups of wind turbines are located in what is called either a “wind farm” or a “wind park”

Important to note: very fast “energy payback” – it takes a few months for a wind turbine to generate (i.e. convert) as much energy as it took to manufacture it!


Lots of ideas, only a few good…


Vertical Axis Wind TurbinesDarrieus rotor - the only vertical axis machine with any

commercial success

Wind hitting the vertical blades (airfoils) generates lift to create rotation

Advantages• No yaw (rotation about vertical axis)

control needed to keep facing into wind

• Heavy machinery located on the ground

Disadvantage• Blades are closer to ground where

windspeeds are lower


Horizontal Axis Wind Turbines“Downwind” HAWT – a turbine with the blades behind

(downwind from) the tower

No yaw control needed- they naturally orient themselves in line with the wind

Shadowing effect – when a blade swings behind the tower, the wind it encounters is briefly reduced and the blade flexes

-Also causes noise


Horizontal Axis Wind Turbines“Upwind” HAWT – blades are in front of (upwind of)

the tower

Most modern wind turbines are this type

Because blades are “upwind” of the tower• Require active yaw control to keep facing into wind• Operate more smoothly and deliver more power


Power in the WindConsider the kinetic energy of a “packet” of air with

mass m moving at velocity v

Divide by time and get power

The mass flow rate is

21KE

2mv

21 passing though APower through area A

2

mv

t

passing though A= = A

mm v

t


Power in the Wind Combining we get

21Power through are A A

2 a v v

31P A

2v

P (Watts) = power in the windρ (kg/m3)= air density (1.225kg/m3 at 15˚C and 1 atm)A (m2)= the cross-sectional area that wind passes throughv (m/s)= windspeed normal to A (1 m/s = 2.237 mph)


Power in the WindPower increases as (wind

speed)3

Doubling the wind speed increases the power by eight

1h x 20mph wind is same energy as 8h x 10 mph wind…-i.e., most power from a turbine is produced at high wind speed for a short time…


Wind Power Classification Scheme


US Wind Resources

http://www.windpoweringamerica.gov/pdfs/wind_maps/us_windmap.pdf


Power in the Wind (cont.)

Power in the wind is also proportional to A

For a conventional HAWT, A = (π/4)D2, so wind power is proportional to the blade diameter squared

Cost is roughly proportional to blade diameter

How do you think cost of wind power scales with turbine diameter?

31P A

2v


Power Curve for Turbine

Cut in speedNot enough energy to justify O&M costs

Cut out speedPark turbine to avoid damage

PlateauGenerator maxed out


Maximum Rotor Efficiency

At the extremes:• Downwind velocity is zero – turbine extracted all of

the energy (for zero time…) • Downwind velocity is the same as the upwind

velocity – turbine extracted no energy…

Albert Betz 1919

Q: What is the ideal extraction of KE from wind so that the turbine extracts the maximum power



Consider wind passing though turbine: as energy extracted, air slows down

2 21

2 dP m v v

ṁ = mass flow rate of air within stream tube

v = upwind undisturbed windspeed

vd = downwind windspeed


Mass Flow RateAt the rotor with area A and, mass flow rate is

If velocity through the rotor vb is the average of upwind velocity v and downwind velocity vd

bm Av

= 2 2

d db

v v v vv m A


Power Extracted by the BladesThen power relationship at the rotor could be

Define new parameter l such that

We can rewrite the power relationship as

2 21

2 2d

b d

v vP A v v

dv

v

2 2 21

2 2b

v vP A v v


Power Extracted by the Blades

Power in the wind

2 2 21

2 2b

v vP A v v

3 2 3 3 3 3

- + - 2 2 2 2

v v v v

3

2 = 1 - 12

v

3

2 = 1 12

v

3 21 11 1

2 2bP Av

Rotor efficiency (CP)


Maximum Rotor EfficiencySo what is the windspeed ratio λ which maximizes the

rotor efficiency, CP ?

2 3

21 11 1 = - + -

2 2 2 2 2PC

20 2 1 3PC

3 1 1 0 1

1

3

Plug into CP to find the maximum rotor efficiency:

2

1 1 1 161 1 = 59.3%

2 3 3 27PC

Maximum efficiency of 59.3% when air is slowed to 1/3 of its upstream speed!“Betz limit”


Number of Rotating BladesWindmills have multiple blades– need to provide high starting torque to overcome weight

of the pumping rod– must be able to operate at low windspeeds to provide

nearly continuous water pumping– a larger area of the rotor faces the wind

Turbines with many blades must operate at lower rotational speeds – as speed increases, turbulence caused by one blade impacts other blades

Most modern wind turbines have two or three blades


Brush wind turbine


Tip-Speed Ratio (TSR)Efficiency is a function of how fast the rotor turns

Define “Tip-Speed Ratio” (TSR) as ratio of speed of tip of blade to windspeed

Rotor tip speed rpm DTip-Speed-Ratio (TSR) =

Wind speed 60v

D = rotor diameter (m) v = upwind undisturbed windspeed (m/s) rpm = rotor speed, (revolutions/min)


Air moved this farAirfoil interacted with this much air, call it Xs

At it takes for wind to reestablish itselfsw w

w

Xv t

v

2Also, for an n bladed turbine, it takes for

next blade to get to same position

st n


Optimal Tip Speed RatioIf ts<<tw then wind turbine is interacting with disturbed air → low

efficiency

If ts>>tw then turbine does not get to all useful air… → low efficiency

Optimal is if ts≈tw

4Then opt n

1It has been shown (empirically) that wind reestablishes itself in

2SX

r

22 s ws w opt

opt w s

X vt t

n v nX

2Since and then tip opt

tip optw w s

v r rv r

v v nX


Optimal Tip Speed RatioThen for a three bladed turbine,

And for a two bladed turbine

41.33 4.19

3opt

42 6.28

2opt


Tip-Speed Ratio (TSR)Rotors with fewer blades reach their maximum

efficiency at higher tip-speed ratios


Impact of Terrain on Windspeed

We saw power depends on cube of windspeed: small change of wind speed can have large impact

System design must consider effect of terrain friction on wind speed– Important in first few hundred meters above ground level– Smooth surfaces (like water) are better– Windspeeds are greater at higher elevations – tall towers

are better– Forests and buildings slow the wind down a lot

Can we quantify impact of terrain and height on wind speed?


Wind Speed Losses as Function of Terrain

v = windspeed at height H

v0 = windspeed at height H0 (H0 is usually 10 m)

α = friction coefficient

Open terrain, α ≈ 1/7 (0.147)

City, α = 0.4;

Calm water, α = 0.1

0 0

v H

v H

Note this is just an approximation, others exist (ex. von Karman’s log velocity profile)


Impact of Terrain on Wind PowerRemember wind power goes as third power of wind

speed.

3

0

v

v

3

300

12 12

AvP

P Av

3

0

H

H


Impact of Terrain on Wind Power

In a town (a≈0.3), windspeed at 100 m is twice that at 10 mAreas with smoother surfaces have less variation with height


Let’s calculate ratio of power at highest point to lowest point on wind turbine with hub at 50m, 30m diameter rotor, α = 0.2

Power in the wind at the top of the blades is 45% higher!

Can cause significant stress (failure)

Rotor Stress

3 0.2

0

65 = 1.45

35

P

P

50 m

35 m

65 m

Picture may not be to scale


As you may expect, turbines interfere with each other…


Wind FarmsIt makes sense to install a large number of wind

turbines in a wind farm or a wind park

Benefits – Able to get the most use out of a good wind site– Reduced development costs– Simplified connections to the transmission system– Centralized access for operations and maintenance

How many turbines should be installed at a site?

What is a sufficient distance between wind turbines so that windspeed has recovered enough before it reaches the next turbine?


Wind Farms

For closely spaced towers, efficiency of array becomes worse as more wind turbines are added


Wind Farms• Previous figure considered square arrays

(but square arrays don’t make much sense)– Rectangular arrays with only a few long rows are better– Recommended spacing is 3-5 rotor diameters between

towers in a row and 5-9 diameters between rows– Offsetting or staggering the rows is common

• Sites commonly have a prevailing wind direction


Average Power in the WindHow much energy can we expect from a wind turbine?

Remember, power goes as cube of wind speed

Therefore we need to know the average of the cube of wind speed…

I.e., we can’t use average windspeed to find the average power in the wind

3 31 1

2 2avg avgavg

P Av A v


Windspeed probability density function (pdf)

If we had a function f(v) that gave windspeed we could calculate average power in wind…

People have examined statistics of windspeed over various locations

A reasonable approximations is the Weibull distribution

• # of hours/year that the wind is between two windspeeds:


Idealized Site Windspeed Data


Weibull p.d.f.

k=2 looks reasonable for wind


Wind Probability Density FunctionsWindspeed probability density function (p.d.f)

Values between 0 and 1

Area under the curve is equal to 1


Weibull p.d.f.Weibull with k=2 has shape similar to windspeed distribution

Often used as first guess when little is known about a particular site

Fairly realistic for a wind turbine site: winds are mostly pretty strong, but there are some periods of low wind and high wind

k-1-

( ) e Weibull p.d.f.

kv

ck vf v

c c

k = shape parameter c = scale parameter

2

-

2

2( ) e Rayleigh p.d.f. (Weibull with k=2)

v

cvf v

c


Rayleigh p.d.f. (Weibull with k=2)

Higher c implies higher average windspeeds


Real Data vs. Rayleigh Statistics

(It is important to gather as much real wind data as possible!)


Average Windspeed using p.d.f.Now that we have a function that approximates wind

speed…

And for average v3

0

( ) avgv v f v dv

3 3

0

( ) avg

v v f v dv


Average windspeed from Rayleigh p.d.f.

For a Rayleigh p.d.f., there is a direct relationship between average wind speed v and scale parameter c (not surprising really)

You can, of course, use this to extract a c for your site

0

( ) avgv v v f v dv

-

20

2e

kv

cvv dvc

0.886

2c c

2=1.128 avgc v v


Rayleigh Statistics – Average Power in Wind

Remember, to find average power in the wind, we needed (v3)avg

If we are still assuming wind speed distribution has a Rayleigh distribution

Then we can put (v3)avg in terms of vavg!

3 3

0

( ) avg

v v f v dv

33 = c

4

2

3 42

0

e 2

v

vvv dv

v

3 33 6=1.91avg avgavg

v v v

2

=1.128 avgc v v


Rayleigh Statistics – Average Power in Wind

Using the expression for (v3)avg in terms of vavg (from Rayleigh distribution assumption), average power in wind is

3 31 1

2 2avg avgavg

P Av A v

36 1

2 avgA v


Not all of the power in the wind is retained - the rotor spills high-speed winds and low-speed winds are too slow to overcome losses (see power curve)

Depends on rotor, gearbox, generator, tower, controls, terrain, and the wind

Overall conversion efficiency (Cp·ηg) is around 30%

Estimates of Wind Turbine Energy

WPBP EP

Power in the Wind

Power Extracted by Turbine

Electric Power

Wind PC

RotorGearbox & Generator

g


Time Variation of Wind

Need to consider when wind blows with respect to the electric load– In the Midwest the wind tends to blow the strongest

when the electric load is the lowest…

Wind patterns vary with geography– Wind can change drastically within hours…– Coastal and mountain regions have steadier winds


Wind Power Variability and Integration

Currently wind is a small fraction of generation– Impact of grid operations is small– As wind power grows it will have larger impact– Impacts expected to range from transient stability (seconds) to

steady-state (power flow)

Because wind turbine output varies as cube of wind speed, small changes in wind speed can have large impact– Current perception is that at the 10%-15% penetration level, wind

may cause system instability– BPA balancing region is ca. 10GW, has signed LGIA for 4GW wind


Wind Power Variability and Integration

The key constraint:

Total power system generation must match the total load plus losses

Sudden generation shortfalls dealt with by maintaining sufficient “spinning reserve” to account for the loss of the largest single generator in region

Spinning reserve: generation that is on-line but not fully used and can be brought into production in very short time period


Renewables Forecasting and the Variability Issue


Wind Power: Deviations of Power Production


Wind Power Deviations For One Year


Number of Occurrences by Magnitude


Capital Cost = $200/kW, $350/kWh Cycle Cost = $0.46/kW·h·cycleOperating Cost = $5/kW·yr Replacement Cost =

0.20 CapitalCost Cycle/2000 ∗ ∗


Minimum cost ES size ($ PU)

Power Energy $/Power

1hr 0.1500 0.8000 0.3366

30min 0.1125 0.4500 0.2031

30 min ANN 0.1125 0.5500 0.2336


Energy Storage


Environmental Aspects of Wind EnergyUS National Academies 2007 report:• Wind systems emit no air pollution and no carbon

dioxide; have essentially no water requirements

• Wind serves to displace energy production from mainly fossil fuel burning: net decrease in emissions

• Other impacts of wind energy are on animals (primarily birds and bats) and humans– Large bird (raptor) mortality is about 0.04 bird/MW/year


Issue: Bird/Bat fatalities


Environmental Aspects of Wind: Birds and Bats

Wind turbines kill birds and bats!

But so do lots of other things

Windows kill between 100 and 900 million per year

Estimated Causes of Bird Fatalities, per 10,000

Source: Erickson, et.al, 2002. Summary of Anthropogenic Causes of Bird Mortality


Environmental Issues: Human Aesthetics

Aesthetics is the primary human concern about wind energy projects (beauty is in the eye of the beholder);

Night lighting (aircraft collision warning) can also be an issue


Environmental Issues: Offshore Wind and Aesthetics

Remember, terrain effect is smallest over water…

Capacity factors are much better off-shore

Offshore wind currently needs to be in shallow water; maximum distance from shore depends on the seabed

Image Source: National Renewable Energy Laboratory


Cape Wind Simulated View, Nantucket Sound, 6.5 miles Distant

Source: www.capewind.org


Environmental: Human Well-BeingSome people living near turbines may be affected by noise and

shadow flicker– Noise comes from gearbox/generator

and aerodynamic interaction of the

blades with the wind– Noise impact is moderate:

50-60 dB up close (40m)

35-45 dB at 300m

• Shadow flicker appears to be issue

in high latitude regions

(lower sun casts long shadows)

10,0

,0

P( ) 20log

Pwhere P is threshold of hearing

rms

rms

rms

I db


Environmental: Human Well-BeingVariables related to annoyance by wind turbine noise– Stress related to turbine noise– Daily hassles– Visual intrusion of wind turbines in the landscape– Age of turbine site – The longer system in operation, the less the annoyance


Anthony L. Rogers, Renewable Energy Research Laboratory, U. Mass. Amherst


Anthony L. Rogers

Renewable Energy Research Laboratory, U. Mass. Amherst

Chemical, Biological and Environmental Engineering Wind 1.

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Transcript of Chemical, Biological and Environmental Engineering Wind 1.