A new approach to wind energy

John O. Dabiri

California Institute of Technology jodabiri@caltech.edu

Comparing Wind Power Performance

Turbine efficiency

P

½ρAU3 Cp =

U

A

Comparing Wind Power Performance

Turbine efficiency Wind farm power density

P

½ρAU3 Cp =

U

A

PWF

AWF

PD =

Comparing Wind Power Performance

Turbine efficiency Wind farm power density Cost of electricity

P½ρAU3

Cp =

U

A

PWF

AWFPD =

$¢

kWhLCOE =

The usual starting point: turbine efficiency

Horizontal-axis wind turbine (HAWT)

Vertical-axis wind turbine (VAWT)

VS.

Comparing Wind Power Performance

The usual starting point: turbine efficiency What fraction of wind energy flux through the swept area is converted to electricity?

Horizontal-axis wind turbine (HAWT)

Vertical-axis wind turbine (VAWT)

VS.

Comparing Wind Power Performance

Horizontal-axis wind turbine (HAWT)

Vertical-axis wind turbine (VAWT)

>

Comparing Wind Power Performance

The usual starting point: turbine efficiency What fraction of wind energy flux through the swept area is converted to electricity?

Comparing Wind Power Performance

The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity?

Comparing Wind Power Performance

The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2

U0 , A0

U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2

2)

Comparing Wind Power Performance

The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2

U0 , A0

U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2

2) For steady rotor thrust, U1 = (U0 + U2)/2

Comparing Wind Power Performance

The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2

U0 , A0

U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2

2) For steady rotor thrust, U1 = (U0 + U2)/2 Therefore, P = ¼ρA1 (U0 + U2)(U0

2 – U22)

= ¼ρA1U03[1 – (U2/U0)2 + (U2/U0) – (U2/U0)3]

Comparing Wind Power Performance

The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2

U0 , A0

U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2

2) For steady rotor thrust, U1 = (U0 + U2)/2 Therefore, P = ¼ρA1 (U0 + U2)(U0

2 – U22)

= ¼ρA1U03[1 – (U2/U0)2 + (U2/U0) – (U2/U0)3]

Pmax = 16/27 x (½ρA1U0

3) or 59.3% efficiency (Betz Limit)

Comparing Wind Power Performance

The usual starting point: turbine efficiency What is the maximum fraction of wind energy flux through the swept area that can be converted to electricity? U2 , A2

U0 , A0

U1 , A1 Wind power extracted, P = ½(ρA1U1)(U02 – U2

2) For steady rotor thrust, U1 = (U0 + U2)/2 Therefore, P = ¼ρA1 (U0 + U2)(U0

2 – U22)

= ¼ρA1U03[1 – (U2/U0)2 + (U2/U0) – (U2/U0)3]

Pmax = 16/27 x (½ρA1U0

3) or 59.3% efficiency (Betz Limit) Modern HAWTs approach theoretical

maximum efficiency

Is there room for significant improvement? (besides increasing swept area)

netfirms.com

Comparing Wind Power Performance

Our starting point: wind resource utilization

Comparing Wind Power Performance

Our starting point: wind resource utilization What fraction of wind energy flux into the wind farm volume is converted to electricity?

Comparing Wind Power Performance

Our starting point: wind resource utilization What fraction of wind energy flux into the wind farm volume is converted to electricity?

Frontal kinetic energy flux

Phorz = ½ρAfrontalU3

Comparing Wind Power Performance

Our starting point: wind resource utilization What fraction of wind energy flux into the wind farm volume is converted to electricity?

Frontal kinetic energy flux

Phorz = ½ρAfrontalU3

Planform kinetic energy flux

Pvert ≈ -ρAplanformU <u’w’>

Turbulence velocity fluctuations u’ (streamwise) and w’ (wall-normal) Ensemble average < • >

The planform kinetic energy flux (ρAplanformU <u’w’>)…

The planform kinetic energy flux (ρAplanformU <u’w’>)…

1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010)

The planform kinetic energy flux (ρAplanformU <u’w’>)…

1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010) 2. supersedes the Betz limit as the relevant constraint on wind farm performance

The planform kinetic energy flux (ρAplanformU <u’w’>)…

1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010) 2. supersedes the Betz limit as the relevant constraint on wind farm performance WHY?

• The Betz calculation does not account for wind power in the turbine wake that is extracted by neighboring turbines

leftover

wind power

The planform kinetic energy flux (ρAplanformU <u’w’>)…

1. is the primary power source for most turbines in large-scale wind farms (Cal et. al. 2010) 2. supersedes the Betz limit as the relevant constraint on wind farm performance WHY?

• The Betz calculation does not account for wind power in the turbine wake that is extracted by neighboring turbines

• The Betz calculation does not account for wind power that is not extracted in the region between turbines

Cp = 0.5 Cp = 0.5 Cp = 0.5

Cp = 0 Cp = 0

leftover wind

power

Modelling the planform flux limit

wuUAP planformvert

Modelling the planform flux limit

wuUAP planformvert

0

2

*ln zdz

Uuwu

Assume log wind profile:

friction velocity, u*

von Karman constant, zero plane displacement, roughness length,

4.0

3/2Hd

10/0 Hz

Modelling the planform flux limit

wuUAP planformvert

0

2

*ln zdz

Uuwu

Assume log wind profile:

friction velocity, u*

von Karman constant, zero plane displacement, roughness length,

4.0

U

3/2Hd

10/0 Hz

H

Modelling the planform flux limit

wuUAP planformvert ′′−≈ ρ

( )[ ]

−

==′′−0

2* ln zdz

Uuwu κAssume log wind profile:

friction velocity, u*von Karman constant, zero plane displacement, roughness length,

4.0≈κ

U

H

3/2Hd ≈10/0 Hz ≈

H

Foken 2008

Modelling the planform flux limit

2

310

2

101

32max

ln

4.0

ln

4.0

UU

HHH

UUPD

A

P

planform

vert

The energy flux through the top of the wind farm is:

wuUAP planformvert

0

2

*ln zdz

Uuwu

Assume log wind profile:

friction velocity, u*

von Karman constant, zero plane displacement, roughness length,

4.0

3/2Hd

10/0 Hz

Modelling the planform flux limit

2

310

2

101

32max

ln

4.0

ln

4.0

UU

HHH

UUPD

A

P

planform

vert

The energy flux through the top of the wind farm is:

3

max 11.0 UPD

wuUAP planformvert

0

2

*ln zdz

Uuwu

Assume log wind profile:

friction velocity, u*

von Karman constant, zero plane displacement, roughness length,

4.0

3/2Hd

10/0 Hz

Modelling the planform flux limit

2

310

2

101

32max

ln

4.0

ln

4.0

UU

HHH

UUPD

A

P

planform

vert

The energy flux through the top of the wind farm is:

3

max 11.0 UPD

For ρ = 1.2 kg m-3 and U = 8 m s-1, PDmax = 68 W m-2

wuUAP planformvert

0

2

*ln zdz

Uuwu

Assume log wind profile:

friction velocity, u*

von Karman constant, zero plane displacement, roughness length,

4.0

3/2Hd

10/0 Hz

How do existing wind farms compare to this upper limit?

DJC Mackay 2010

How do existing wind farms compare to this upper limit? 2.5 versus 68 W m-2

DJC Mackay 2010

2.5 versus 68 W m-2

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit

2.5 versus 68 W m-2

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density

2.5 versus 68 W m-2

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density

Power Density Calculation PD = 4 x rated power x capacity factor

π (turbine diameter x turbine spacing) 2

D x S

2.5 versus 68 W m-2

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density

Power Density Calculation PD = 4 x rated power x capacity factor

π (turbine diameter x turbine spacing) 2

D x S Turbine #1 (2.5 MW, 100 m dia.): PD = 2.7 W/m2 Turbine #2 (3.0 MW, 112 m dia.): PD =2.5 W/m2

For six-diameter average turbine spacing and 30% capacity factor…

2.5 versus 68 W m-2

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 1. Turbine spacing requirements directly affect wind farm power density

Power Density Calculation PD = 4 x rated power x capacity factor

π (turbine diameter x turbine spacing) 2

D x S Turbine #1 (2.5 MW, 100 m dia.): PD = 2.7 W/m2 Turbine #2 (3.0 MW, 112 m dia.): PD =2.5 W/m2

For six-diameter average turbine spacing and 30% capacity factor…

If turbine spacing is reduced to four diameters…

Turbine #1 (2.5 MW, 100 m dia.): PD = 6.0 W/m2 Turbine #2 (3.0 MW, 112 m dia.): PD =5.7 W/m2

i.e. power density is more than doubled.

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement

2.5 versus 68 W m-2

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement

d/H

z0/H

Structure spatial density

z 0/H

an

d d

/H

Grimmond and Oke 1999

2.5 versus 68 W m-2

32

101

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement

d/H

z0/H

Structure spatial density

z 0/H

an

d d

/H

Grimmond and Oke 1999

2.5 versus 68 W m-2

existing wind farms

32

101

Whereas modern wind turbines achieve power coefficients that approach the theoretical maximum, existing wind farm performance remains far below the flux limit Why? 2. Turbine spacing requirements indirectly affect the planform kinetic energy flux via the roughness length and zero plane displacement

d/H

z0/H

Structure spatial density

z 0/H

an

d d

/H

Grimmond and Oke 1999

2.5 versus 68 W m-2

existing wind farms

32

101

Increasing turbine spatial density

Increasing z0 and d

Increasing Pvert

Additional challenges for conventional wind energy

∙ Structure size, associated design requirements and materials costs

johnrsweet.com

Paul Anderson

Additional challenges for conventional wind energy

∙ Structure size, associated design requirements and materials costs ∙ Logistics of installation/maintenance

Google Images

Additional challenges for conventional wind energy

∙ Structure size, associated design requirements and materials costs ∙ Logistics of installation/maintenance ∙ Public acceptance - impact on birds/bats - visual signature - acoustic signature - radar signature

A new approach: Optimized arrays of smaller vertical-axis wind turbines

A new approach: Optimized arrays of smaller vertical-axis wind turbines

Power Density Calculation Revisited PD = 4 x rated power x capacity factor

π (turbine diameter x turbine spacing) 2 D x S

A new approach: Optimized arrays of smaller vertical-axis wind turbines

Power Density Calculation Revisited PD = 4 x rated power x capacity factor

π (turbine diameter x turbine spacing) 2 D x S

For six-diameter average turbine spacing and 30% capacity factor…

Windspire Energy VAWT 0.0012 MW, 1.2 m dia.

A new approach: Optimized arrays of smaller vertical-axis wind turbines

Power Density Calculation Revisited PD = 4 x rated power x capacity factor

π (turbine diameter x turbine spacing) 2 D x S

For six-diameter average turbine spacing and 30% capacity factor…

Windspire Energy VAWT 0.0012 MW, 1.2 m dia.

PD = 8.8 W/m2 3X power density at 1/10 HAWT height!

What is the optimal arrangement of VAWTs in a wind farm?

What is the optimal arrangement of VAWTs in a wind farm?

Bio-inspiration: Fish Schooling

‘Optimal’ fish schooling provides our starting point…

Weihs (1975)

Triantafyllou et al. (1995)

≈

primary wind

Potential flow model

1log2

zzizUWVAWT

VAWT complex potential:

uniform flow point vortex (rotation) dipole (blockage)

Potential flow model

1log2

zzizUWVAWT

VAWT complex potential:

General wind farm complex potential:

uniform flow point vortex (rotation) dipole (blockage)

sum over N VAWTs at locations zn

N

n

nnfarm zzzzizUW0

1log

2

Potential flow model

1log2

zzizUWVAWT

VAWT complex potential:

General wind farm complex potential:

uniform flow point vortex (rotation) dipole (blockage)

sum over N VAWTs at locations zn

‘Fish school’ wind farm complex potential:

M

m

N

n

nmnmnmnm

M

m

N

n

nmnmnmnmfish

AzAzAzAz

AzAzAzAzizUW

1 1

12

,

11

,

12

,

11

,

1 1

2

,

1

,

2

,

1

,

loglogloglog2

N

n

nnfarm zzzzizUW0

1log

2

where

bcminaaA

bmcinaaA

bcminaaA

bmcinaaA

nm

nm

nm

nm

2422

422

2422

422

2

,

1

,

2

,

1

,

Potential flow model

2c

b

2a

U

Whittlesey, Liska, Dabiri (Bioinspiration and Biomimetics, 2010)

Potential flow model

Model predicts order-of-magnitude increase in power density

Ra

ted

Po

wer

Den

sity

(W

m-2

)

2c

b

2a

a = 1.2D, b = 0.4D, c = 2D

U

Caltech Field Laboratory for Optimized Wind Energy

Field Study Results Directional dependence of performance at close spacing (1.65 diameters)

• Limited sensitivity to wind direction • Enhanced performance in close proximity

configuration power coefficient

isolated power coefficient Cp

norm =

Field Study Results Four-diameter downwind spacing required to avoid blockage effects

4D downwind spacing

1.65D downwind spacing

U

configuration power coefficient

isolated power coefficient Cp

norm =

Field Study Results 6-VAWT array measured over 250 continuous hours

Field Study Results 6-VAWT array measured over 250 continuous hours

existing wind farms

Planform Kinetic Energy Flux = ρU<u’w’> (W m-2)

Field Study Results 6-VAWT array measured over 250 continuous hours

existing wind farms

Planform Kinetic Energy Flux = ρU<u’w’> (W m-2)

mean power above cut-in wind speed

mean power, continuous

Outlook

How do aerodynamic interactions within the VAWT farm determine the overall performance?

Outlook

How do aerodynamic interactions within the VAWT farm determine the overall performance?

Suppression of vortex shedding by turbine rotation?

Mittal and Kumar, 2003

Outlook

How do aerodynamic interactions within the VAWT farm determine the overall performance?

How can VAWTs be designed to operate optimally in turbulent, near-ground winds?

≈

Outlook

How do aerodynamic interactions within the VAWT farm determine the overall performance?

How can VAWTs be designed to operate optimally in turbulent, near-ground winds?

How can we leverage the smaller VAWT size to improve materials costs, O&M, environmental impact, storage, LCOE?

autoanything.com

Caltech Program in Bio-inspired Wind Energy Field Laboratory (Dabiri) Wind Tunnel Research (Gharib, McKeon) Computational Fluid Dynamics (Colonius) Materials and Manufacturing (Grubbs)

≈ For more info on Field Laboratory:

http://dabiri.caltech.edu/research/wind-energy.html

Acknowledgments

Robert Whittlesey and Sebastian Liska (graduate students, array modeling)Windspire Energy (turbine-data exchange)

Funding:Gordon and Betty Moore FoundationNational Science Foundation

Questions/Comments?

John O. Dabiri California Institute of Technology

jodabiri@caltech.edu