SURFACE WIND

Part A Module 1 – Wind Energy

SURFACE BOUNDARY LAYER Wind interacts with natural and man-made surface features • Ground wind speed = zero • The geostropic wind is at some

altitude where wind speed is unaffected by surface features

• Region in between is the surface boundary layer

• Turbulent boundary layer After Grasch and Twele (2002)

SURFACE ROUGHNESS

Scale (physical dimension) of surface roughness important • Higher shear force to air flow • More turbulence generation • “surface friction” – resistance

to air flow over it

ROUGHNESS LENGTH, z0 Empirical relationship (Lettau,1969):

𝑧0 = 0.5 ∙ℎ ∙ 𝑆𝐴𝐻

where h = height of a roughness element S = roughness element cross-sectional area facing wind AH = average horizontal area available to each roughness element • Roughness element assumed to be solid

ROUGHNESS LENGTH EXAMPLE Suburban/country village • Lot

– WL = 30m, DL = 30 m – AH = WL x DL = 900 m2

• House – WH = 20 m, h = 7 m – S = h x WH = 140 m2

• 𝑧0 = 0.5 ∙ 7𝑚 ∙140𝑚2

900𝑚2 = 0.54 m

WL

DL

h

WH

𝑧0~ℎ2𝑊𝐻

𝑊𝐿𝐷𝐿

SURFACE ROUGHNESS CLASS

• Surface terrain divided into four roughness classes

• Representative value for each class

• Roughness length is a continuum Values from European Wind Atlas

Type of terrain Roughness class

Roughness length z0

(m) z0 range

Water areas 0 0.0002 Open country, few surface features

1 0.03 0.02-0.05

Farmland with buildings & hedges

2 0.10 0.08-0.18

Farmland with many trees, forests, villages

3 0.4 0.25-0.6

MORE ROUGHNESS LENGTH Porous roughness elements

(z0)porous = (z0)from formula x porosity • Can be seasonal z0 variability

– e.g. bare trees Flow passes over closely spaced elements (e.g. cities) • Wind velocity profile is moved

upwards by a distance known as the displacement length

LOGARITHMIC DEPENDENCE OF V Prandtl developed a logarithmic expression to represent dependence of wind speed on height, V(z), in a turbulent boundary layer:

𝑉 𝑧 =𝑉∗

𝑘 𝑙𝑙𝑧𝑧0

where z = height above the ground z0 = roughness length, i.e. length scale that characterizes the surface roughness V* is the friction velocity (0.1 – 0.3m/s) k = Karman constant of the air flow in the boundary layer (approximately 0.4)

- Constants V* and k difficult to determine accurately -

LOGARITHMIC WIND SPEED FUNCTION Enables calculation of wind speed at different heights based on a measured wind velocity at a reference height

𝑉 𝑧 = 𝑉𝑟 𝑧𝑟ln 𝑧

𝑧0ln 𝑧𝑟𝑧0

where z0 = roughness length, a physical dimension that characterizes the scale of surface roughness zr = reference height Vr(zr) = measured velocity at the reference height

LOGARITHMIC FUNCTION EXAMPLE

• Extrapolate wind data from standard 10m towers to wind turbine hub height

• 4 roughness classes + city • Rough surface substantially

reduces wind speed at lower heights

0

10

20

30

40

50

60

70

80

90

100

0.8 1 1.2 1.4 1.6 1.8 2

Hei

ght (

m)

V/Vr

Class 0

Class 1

Class 2

Class 3

City

POWER EXPONENT WIND SPEED FUNCTION Alternative to the logarithmic wind speed function

𝑉 𝑧 = 𝑉 𝑧𝑟 ∙𝑧𝑧𝑟

𝛼

where z = height above ground zr is the reference height above ground V(z) is the wind speed at height z α = exponent that depends on surface roughness

SURFACE BOUNDARY IMPLICATIONS

Logarithmic profile of wind normalized by the geostropic wind

– 500 m height chosen for illustration • Higher is better

– More out of boundary layer – Less variation from top/bottom of rotor.

• Open area is better

0

50

100

150

200

250

300

350

400

450

500

0 0.2 0.4 0.6 0.8 1

Hei

ght (

m)

V/VGeostrophic

Class 1 Class 2 Class 3

WIND SPEED VARIES ACROSS ROTOR

• Wind speed plotted vs rotor hub height wind speed – Logarithmic profile

• Significant wind speed variation from rotor bottom to top – 15% class 1 – 17% class 2 – 24% class 3

Rotor hub height

Top of rotor

Bottom of rotor

20

40

60

80

100

120

140

0.8 0.9 1 1.1

Hei

ght (

m)

V/Vrotor hub

Class 1 Class 2 Class 3

SURFACE WIND SUMMARY • Surface roughness elements, both natural and man-made:

– Generate turbulence, which dissipates the wind’s energy near the surface

– Reduce wind speed as ground is approached • Surface roughness characterized by roughness length, z0

– Depends on the nature of the terrain (4 roughness classes) • Logarithmic profile allows wind speed at various heights to be

estimated from a measured wind speed at one height • Implications of the surface boundary layer for wind turbines:

– Higher is better – Open area is better

PRACTICE EXERCISES

REFERENCES • Gasch, R. and J. Twele, ‘Wind Power Plants,” Solarpraxis AG, Berlin, 2002. • Lettau, H. (1969). “Note on aerodynamic roughness-parameter estimation on the

basis of roughness-element distribution,” J. Appl. Met. 8, 828-832. • Troen, I and E.L. Petersen (1989). “European Wind Atlas,” Published for the

Commission of the European Communities Directorate-General for Science, Research and Development, Brussels, Belgium by Riso National Laboratory, Roskilde, Denmark.