wind energy: the myths and the math swc 2014, stevens point- june 18, 2014 dr. david j. laino...
TRANSCRIPT
Wind Energy: The Myths and the Math
SWC 2014, Stevens Point- June 18, 2014
Dr. David J. LainoPrincipal Engineer
Endurance Wind [email protected]
©2014 David Laino (used by permission)
Myths
• “Low wind speed design”• “No cut-out wind speed”• “Revolutionary Advancement”• “Beats Betz”• “Funnels the wind”• “More blades is better”• “No blades is best”
©2014 David Laino
Outline
• Wind energy• What is it?• How do we extract it?• Low and high wind myths• Short tower myth
• Wind Turbine Design• Betz Limit• Efficiency myths
• Turbine Types• Revolutionary technology myths• Rotor solidity myths
• Areas for Innovation
EQUATIONS
AHEAD
©2014 David Laino
“Science Schmience. It spins!”
Wind is an ethereal entity, that can neither be smelled nor seen. In this way it is not unlike the ch’i, prana, or the Jedi Force. It is a mystery that we know is there but cannot fully define. Hence, we do not truly understand wind, so harnessing its mysterious power is fertile ground for discovery and experiment. No experience required.
“All you need in this life is ignorance and confidence; then success is sure. ”
― Mark Twain
©2014 David Laino
Math: Energy in the wind
• Wind is movement of an air mass• Moving mass has kinetic energy• Newtonian Physics: Ek = ½ mv2
• Mass of air = density (r) x Volume• Volume = Area (A) x Velocity (v) x Time (t)
• Kinetic Energy of the Wind:• Ewind = ½ r v3 A t
A
t
v
©2014 David Laino
The Power in the Wind
Power = Energy / time ∴
0 5 10 15 20 25 30 35 40 45 500
10000
20000
30000
40000
50000
60000
70000
80000
90000
Wind Speed, m/s
Pow
er D
ensi
ty, W
/m2
26% increase in wind speed = 2x Power2x wind speed = 8x Power
Pwind = ½ r v3 AEwind = ½ r v3 AtPwind v3
©2014 David Laino
Myth: The Power in Low Wind
0 2 4 6 8 100
100
200
300
400
500
Wind Speed, m/s
Pow
er D
ensi
ty, W
/m2
MATH: (tiny wind speed)3 = tiny numberReal world: Typical cut-in: 4 m/s = 39 W/m2
Claim: Low wind cut-in: 2 m/s = 4.9 W/m2
Reality: Not enough power to overcome real-world inefficiencies
©2014 David Laino
Myth: The High Wind Speed Turbine
Claim: No need to shut down, it operates in hurricane winds!Check: Time at any given wind speed is defined by a distribution
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 440%
2%
4%
6%
8%
10%
12%
14%
16%
8 m/s Rayleigh Wind Speed Distribution
Wind Speed Bin, m/s
Perc
ent o
f Tim
e Sp
ent a
t Win
d Sp
eed
Typical cut-out = 25 m/s
©2014 David Laino
Math: The High Wind Speed Turbine
Energy = Power x time
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 450%
2%
4%
6%
8%
10%
12%
14%
16%
8 m/s Rayleigh Distribution
Wind Speed Bin, m/s
Perc
ent o
f Tim
e Sp
ent a
t Win
d Sp
eed
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 450
10000
20000
30000
40000
50000
60000
Power Density
Wind Speed Bin, m/s
Pow
er D
ensit
y, W
/m2
X
Lots of Power!
Hmmm…
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 450%2%4%6%8%
10%12%14%
8 m/s Energy Density Distribution
Wind Speed Bin, m/s
%of
Ene
rgy
in W
ind
Spee
d Bi
n
Wind energy exposure gain = 0.0001%
Reality: No Time =No Energy
©2014 David Laino
Lesson: What a wind turbine does
Convert the kinetic energy of the moving air into electrical energy
Input: Wind
Output: Electricity
Less Wind
Wind turbine slows the wind as it passes through, reducing the kinetic energy, converting it to mechanical energy.
©2014 David Laino
MYTH: No need for tall towers
• FACT: Obstructions block the wind
• FACT: Friction with the ground slows the wind
• FACT: More height = more wind.
• REALITY: All wind turbines require tall towers to be effective.
• No, you are not special
Wind Shear
©2014 David Laino
MYTH: Betz Limit Applies ONLY to Propeller Turbines
NOUm…
©2014 David Laino
MATH: Betz Limit Proof
Pwind = ½ r v3 A
Pout = ½ {½ r A (vin + vout)/2} (vin 2 - vout 2)
Cp = Pout/Pavail = ½ [1-(vout/vin)2] [1 + vout/vin]
Cp-max = 0.593 @ vout/vin = 0.33
Note:• Purely mathematical • No assumption on turbine type• Applies to ANY wind energy machine
mass flow rate through A drop in speed squared
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vout/Vin
Cp
Avin vout
Pout
©2014 David Laino
©2014 David Laino
MYTH: “Breakthrough: 3x – 50x Energy Output!!!”
• CP = Pcaptured / Pwind
• Power Coefficient• Turbine efficiency
• NO turbine can exceed the Betz Limit
• Modern designs perform admirably
No room for “breakthroughs”
IEC Tested SWT Peak CP
7.42 m2 VAWT 0.22
31.9 m2 HAWT 0.30
290 m2 HAWT 0.42
23.8 m2 HAWT 0.38
23.7 m2 HAWT 0.36
MYTH: Ducted Turbines are Special
A
• FACT: “Swept Area” includes the duct• Venturi effect is real• Velocity increases in a nozzle• Works well for constrained flow
©2014 David Laino
Reality: Wind is Lazy
• The math looks promising• Pwind v3
• But …• Wind turbine’s job is to slow the wind, and• Wind is NOT constrained inside a hose
• Wind takes the path of least resistance
©2014 David Laino
Myth: More Blades = More Energy
• Myth: Propeller turbines let most of the wind pass between the blades
• Reality: Space between spinning blades is small.
• Fewer blades is better• High-speed propeller strikes
the proper balance betweenslowing the wind (its job) andletting it pass (so it doesn’t stop)
wind speedBlade rotational speed
Blade 1 track
Blade 3 track
Blade 2 track
Blade track
©2014 David Laino
If High Solidity is Better, May I suggest…
©2014 David Laino
©2014 David Laino
MYTH: Revolutionary Technology
•New Boat Propeller• Slow, quiet operation• Fish-friendly• Pushes more water• Revolutionary design
•New Wind Turbine• Slow, quiet operation• Bird-friendly• Catches more wind• Revolutionary design
9th century Persian Panemone
©2014 David Laino
Four factors affect wind energy capture potential:
1. Air density2. Wind speed
3. Overall turbine efficiency4. Swept area
E = t ½ r V3 CP A dt
Factors in Wind Turbine Effectiveness
©2014 David Laino
Where else will advances come from?
•Economics: cost of energy• Ease of installation
t = $•Materials
>m = >$• Reliability = $
• Architecture•Mo’ parts = mo’ $
©2014 David Laino