Summary of. Atmospheric Wind' .Wind Energy

~ . . .

NASA p TI?

x

'NASA Technical Paper 1389 . . - .

. . .C . .

I .

, Summary o f . Atmospheric

, '

Wind' ,

Design Criteria ,..For .Wind Energy , '

, . . Conversion., System- ,Development' ' - . - - -

"

NASA Technical Paper 1389

TECH LIBRARY KAFB. NM

Summary of Atmospheric Wind Design Criteria For Wind Energy Conversion System Development

Walter Frost The Utziversity of Tennessee Space Institute Tzdlahoma, Tennessee

and

Robert E. Turner George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama

National Aeronautics and Space Administration

Scientific and Technical Information Office

OL34b75

1979

ACKNOWLEDGMENTS

A portion of this work was funded by the George C. Marshall Space Flight Center, Atmospheric Sciences Division under NASA contract NAS8-32118.

The authors have worked very closely with the personnel from NASA Lewis Research Center, Cleveland, Ohio, and have received from them many inputs and much sound advice. In particular, Bob Wolf, Harold Neustadter, and Dave Spera have contributed immensely to the final document. Review of the work with Bill Cliff, Chuck Elderkin, La r ry Wendell, Chris Doran, and others from Battelle Pacific Northwest Laboratories has added significantly to the handbook.

The initiation of the project by George Fichtl, NASA Marshall Space Flight Center , is appreciated.

The authors also wish to thankDonTeague, George Tennyson, and Carl Aspliden from the Wind Characteristics Program, Wind Energy Conversion Branch, Division of Solar Energy, Department of Energy, for their inputs. In particular, Don Teague's guidance has set the tenor of the engineering philosophy contained throughout the report.

TABLE OF CONTENTS

Chapter Page

1.0 INTRODUCTION ............................. 1

2.0 WINDSPEED ............................... 2

2.1 Extreme Wind Speed ....................... 2

2.1.1 Extreme Wind Speed at a Height of 10 m ... 2 2.1.2 Adjustment of Extreme Wind Speed for

Height .......................... 2 2.1.3 Adjustment for Time of Structural Response

to Gust .......................... 2

2.2 MeanWindSpeed ......................... 3

2.2.1 Annual Mean Wind Speed .............. 3 2.2.2 Adjustment of Annual Mean Wind Speed

with Height ....................... 3 2.2.3 Wind Speed Duration Curve ............ 3

3.0 MEAN WIND SPEED VERTICAL GRADIENT ........... 11

4.0 TURBULENCE .............................. 13

4.1 Spectral Model .......................... 13

4.1.1 Spectra ......................... 13 4.1.2 Turbulence Intensity ................. 14

4.2 Discrete Gust Model ....................... 14

4.2.1 Extreme Discrete Gust ............... 14

4.2.1.1 Shape of Longitudinal Extreme Discrete Gust .............. 14

4.2.1.2 Gust Period ............... 15 4.2.1.3 Extreme. Longitudinal Discrete

Gust Amplitude. W ........... 16 1

4.2.2 Cyclic. Discrete Gust Model ........... 16

4.2.2.1 Cyclic. Discrete Gust Shape .... 16 4.2.2.2 Cyclic. Discrete Gust

Amplitude ................. 17 4.2.2.3 Number of Cycles ........... 18

iii

TABLE OF CONTENTS (Concluded)

Chapter Page

5.0 WINDDIRECTION ............................ 33

5 . 1 Wind Direction Probability .................. 33 5.2 Wind Direction Fluctuations .................. 33

iv

L I S T OF ILLUSTRATIONS

Figure

2-1.

2-2.

2-3.

2-4.

2-5.

2-6.

3-1.

4-1.

4-2.

4-3.

4-4.

4-5.

4-6.

Title Page

Extreme wind speed based on risk of exceedance . . . . . . . . 5

Factor for adjusting extreme wind speed with height . . . . . 6

Adjustment factor for response time of structure . . . . . . . 7

Percent area of contiguous USA with annu9 mean wind speed equal to or greater than k Factor for adjusting annual mean wind speed with height. . . 9

h=lO m (wh=30 f t ) . . .... 8

Number of hours per year, T , wind speed is expected to be greater than W (wind speed duration curve) . . . . . . . . 10

Dimensionless vertical gradient in horizontal mean wind speed ..................................... 12

P

Dimensionless turbulence kinetic energy spectra. . . . . . . . 19

Turbulence intensity u -

W 'wh=10 m (dimensionless) . . . . . 20 CY

Period of gust 50-percent coherent over the horizontal distance, Aa = A x . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Period of gust 50-percent coherent over the lateral o r vertical distance, A a = Ay = A z . . . . . . . . . . . . . . . . . . 22

Factor for computing the discrete gust amplitude, W . = k k W , where k is given in Figure 4-9

and = 5 m s - * ......................... 23 1 5 6 h=10 m 6

h=10 m

Factor for computing the discrete gust amplitude, W . = k k F , where k is given in Figure 4-9

and wh=10 m

1 5 6 h=10 m 6 - = 1 0 m s - ~ .... .... .. .............. 24

V

LIST OF ILLUSTRATIONS (Continued)

Page Figure

4-7.

Title

Factor for computing the discrete gust amplitude, W . = k k E where k is given in Figure 4-9

and wh=10 m

1 5 6 h=10 m y 6 - = 1 5 m s - ........................ 25

Factor for computing the discrete gust amplitude, W . = k k E where k is given in Figure 4-9

1 5 6 h=10 m y 6 and 2 25111s- I . . . . . . . . . . . . . . . . . . . . . . . . h=10 m

Factor for adjusting towh . .. .. ...... .. . .. h=10 m

4-8.

26

27 4-9.

4-10. Probability density function of the discrete gust amplitude, W . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ACY 28

Factor for estimating effective rms value, cr for cyclic gusts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eff’ 4-11.

4-12.

29

Factor for calculating the number of times per year the wind speed exceeds the value W . . . . . . . . . . . . . . . . . ACY

30

Zero crossing factor . . . . . . . . . . . . . . . . . . . . . . . 31

32

4-13.

4-14.

5-1.

Scaling factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cumulative probability distribution of angular displacement of mean wind, h = 10 m . . . . . . . . . . . . . . . . . . . . . . . . . 34

5-2. Cumulative probability distribution of angular displacement of mean wind, h = 30 m . . . . . . . . . . . . . . . . . . . . . . . . . 35

Cumulative probability distribution of angular displacement of mean wind, h = 50 m . . . . . . . . . . . . . . . . . . . . . . . . . 5-3.

36

Cumulative probability distribution of angular displacement of mean wind, h = 100 m . . . . . . . . . . . . . . . . . . . . . . 5-4.

37

vi

L I S T OF ILLUSTRATIONS (Concluded)

Figure Title Page

5-5. Cumulative probability distribution of angular displacement of mean wind, h = 150 m ........................ 38

5-6. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle e measured from the direction of the mean wind vector, z =O.OOlm. . . ............................. 39

0

5-7. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle e measured from the direction of the mean wind vector = 0.01 m . . 40 , zo

5-8. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle e measured from the direction of the mean wind vector, z = 0.1 m . . . 0

41

5-9. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle e measured from the direction of the mean wind vector, z = 1.0 m ... 0 42

vii

NOMENCLATURE

a

a Ci

m

A n

t

T

- wh

Effective gust rise time

Coherence function decay constant

Number of crossings per unit time of the dimensionless wind fluctuation fb

ACi

Number of crossings per unit time of the angle e

Height above natural grade

i = 1, 2, 3, . . . , adjustment factor in metric units

i = 1, 2, 3, . . . , adjustment factor in the engineering system of units

Number of standard deviations

Cyclic frequency

Time

Number of hours

Mean horizontal wind speed (averaging period from 10 min to 1 h) at height h

Peak wind speed

Instantaneous horizontal wind speed in excess of the mean; i.e., wG(t) = W ( t ) - Wh

-

Instantaneous wind speed

Wind speed averaged over the period T centered around the peak wind speed

viii

NOMENCLATURE (Continued)

wh

W P

wh c

'h

wAo,

wACY

W CY

X

MEAN

- WIND SPEED

Horizontal wind speed of arbitrary averaging period at height h

Prescribed value of horizontal wind speed

Extreme horizontal wind speed at height h

Effective discrete horizontal gust amplitude; W. = W(T) -

1 - wh

Annual mean horizontal wind speed at height h

Discrete gust amplitude in the direction CY relative to mean wind speed

Dimensionless gust amplitude klOQ WACY &h

Fluctuating component of wind speed, Le. W x = w ( t ) -

w = W y ( t ) , w = wz (t) X - wh, Y Z

Spatial coordinate in the longitudinal direction oriented along the horizontal mean wind vector

Y Spatial coordinate lateral to x

ix

NOMENCLATURE (Concluded)

z

z 0

Greek Symbols

a!

Aa!

t

77

%CY

e

U

U eff

V

7

Spatial coordinate vertical to x

Surface roughness length

Designates the quantity has directional dependence, i. e. , x, Y, or z

Spatial distance over which a gust is assumed coherent

Dimensionless time, t = t/-r

Reduced frequency, 77 = hfih

Reduced frequency characteristic scaling value

Direction of the horizontal wind vector ( e = 0 corresponds to the direction of the horizontal mean wind vector)

Turbulence intensity or r m s value of turbulent fluctuations

Turbulence intensity over a frequency gusts of length scale significant to the investigation, i.e. ,

A n max

CT eff = J uw (QdG

CY B min CY

range associated with problem under

Ratio of W to the effect turbulence intensity ~7 ACY eff

Gust period

Spectral density of turbulence kinetic energy associated with the w fluctuating wind component

CY

X

TECHNICAL PAPER-1389

SUMMARY OF ATMOSPHERIC WIND DESIGN CRITERIA FOR W I N D ENERGY CONVERSION SYSTEM DEVELOPMENT

Chapter 1.0 Introduction

A highly condensed version of Chapters 2 through 5 on wind characteristics from the "Engineering Handbook on the Atmospheric Environmental Guide- lines for U s e in Wind Turbine Generator Development, ? ? NASA TP-1359, is presented in this report. Basic design values of the most significant wind criteria are presented in graphical format. The design values are given without discussion of the physical processes involved o r of the analytical methods used to develop the design curves. For these details the reader should consult the previously mentioned engineering handbook.

Chapter ?. 0 Wind Speed

2.1 Extreme Wind Speed

2.1.1 Extreme Wind Speed at a Height of 10 m

The extreme wind speed at a height of 10 m, ,w

h=lOm (Wk30 ft) 3 is given by Figure 2-1 in terms of r i sk of exceedance. The engineer must select the degree of risk he is willing to accept that the extreme wind speed designed for will be exceeded at least once during the expected life of a Wind Turbine Generator (WTG) . The degree of r i sk conventionally used ranges from aero- space values of 10 percent for an expected life of 25 years to building code values of 63 percent for an expected life of 50 years.

2.1.2 Adjustment of Extreme Wind Speed for Height

The value of wind speed selected from Figure 2-1 is adjusted for height, h, by the adjustment factor, k (k' ), given in Figure 2-2, i. e.,

1 1

i@ = k c h 1 h=10 m 1 h=30 f t ) ( k ' %'

where

% = extreme wind speed at height h h

kl = adjustment factor for height h.

2.1.3 Adjustment for Time of Structural Response to Gust

The extreme wind speed, adjusted for height as described in Section 2.1.2, is further adjusted for the response time of the structure by multiplying by the factor k (k' ) given in Figure 2-3. The adjustment factor is a function

of the extreme wind at height h as determined from Sections 2.1.1 and 2.1.2. 2 2

Three categories based on structure size are specified in this regard:

2

Category a - Structures o r structural components of 20 m (65 ft) or less in extent in any dimension.

Category b - Structures o r structural components larger than 20 m (65 ft) but for which neither the greatest lateral nor vertical dimension exceeds 50 m ( 165 f t ) .

Category c - All structures larger than those in Category b; for Category c, k = 1.0 (k’ = 1.0). 2 2

2.2 Mean Wind Speed

2.2.1 Annual Mean Wind Speed

The approximate areal distribution over the contiguous United States of annual mean wind speed equal to o r greater than $ in Figure 2-4. The designer should select the design value of annual mean wind speed from this curve based on the percentage of the area of the country to which he anticipates sale of the WTG.

h=10 m (‘h=30 f t ) is given

2.2.2 Adjustment of Annual Mean Wind Speed with Height

The adjustment of annual mean wind speed with height is achieved by multiplying the wind speed determined in Section 2.2.1 with the adjustment factor k ( k ’ ) given in Figure 2-5, i.e., 3 3

Gh = k 6 A

3 h=10 m (“iwh=30 ft )

where

Wh = annual mean wind speed at height h A

k = adjustment factor for height h. 3

2.2.3 Wind Speed Duration Curve

The number of hours, T, for which the wind speed, W is expected to be h’

equal to or exceed a prescribed value, W is estimated by PY

3

T = 8766 e-[-n(W /2Wh) . A 2 P (2.3)

Any unit2 can be employed for the wind speed provided they are consistent for W and Wh, respectively. A plot of the wind speed duration curve is given in

Figure 2-6. P

4

RISK OF EXCEEDANCE (%I

Figure 2-1. Extreme wind speed based on risk of exceedance.

90

80

40

HEIGHT, h ( r n )

2 5 10 50 100

HEIGHT, h (ftt)

500 800

Figure 2-2. Factor for adjusting extreme wind speed with height.

6

10 20 100 200 1.36

1.32

1.28

1.24

1.2a

1.16

1 .li

1 .OE 10

T

T 1

I I

CATEGORY a

CATEGORY b

TI n i I I

Figure 2-3.

20 50

(rnph)

100 200

Adjustment factor for response time of structure.

7

5.1

5.l

5.r

5.;

5s

7 In 4.E

I E E

4.f II

< s= 4.4

4.2

4.0

3.8

3.6

3.4

3.2 0 10 20 30 40 50 60 70 80 90 100

AREA (%I

- 13.0

- 12.5

- 12.0

- 11.5

- 11.0

- 10.5

- 10.0

- 9.5 <

- 9.0

- 8.5

- 8.0

Figure 2-4. Percent area of contiguouf USA withAannual mean wind speed equal to or greater than W h=10 m (wh=30 f t > *

8

v) v)

w

Figure 2-5. Factor for adjusting annual mean wind speed with height.

TIME, T (h)

Figure 2-6. Number of hours per year, T, wind speed is expected to be greater than W (wind speed duration curve).

P

Chapter 3.0 Mean Wind Speed Ver t i ca l Grad ien t

The variation of horizontal, mean wind speed with height, A= /Ah, is

presented in Figure 3-1. The wind shear is expressed in dimensionless form (hfih) A E /Ah and is given as a function of height made dimensionless with

surface roughness length, z . Typical values of surface roughness length are given in Table 3-1.

h

h

0

TABLE 3-1. TYPICAL VALUES OF SURFACE ROUGHNESS LENGTH

Sea or large bodies of water

Open country with no obstructions

Open country with scattered windbreaks

Country with many windbreaks, small towns, outskirts of large cities

Surfaces with large and frequent obstructions (e. g. , city centers)

Surface Roughness Length, z 0

10-~ - 10-4

3 x 10-2 - 3 x 10-1 10-2 - 10-1

3 x 10-4 - 3 x 1 0 - 2 - 10-2

3 X 10-5 - 3 x 10-4

10-1 - 1 3 x 10-1 - 3

1 - 4 3 N 13

11

101

htz,

102

htz 0

Figure 3-1. Dimensionless vertical gradient in horizontal mean wind speed.

Chapter 4.0 Turbulence

4.1 Spectral Model

4 . 1 . 1 Spectra

The turbulence kinetic energy spectral densities for the atmospheric boundary layer (to elevations of 150 m) recommended for WTG design are:

Longitudinal

12.3 % hlPn( 1O/z + 1) In(h/z + I)] -' 6 (n\ = A h=lO m 0 0

w '"I X 1 + 192 [hhn( lO/z + 1)m In(h/z -t- 1) ] 5/3

0 h=10 m 0

Lateral

4.0% h [ l n ( 10/zo + 1) Pn(h/z + 1) ] -' A

q w ( 4 = h=10 m 0

Y 1 + 70 [ h h n ( 1O/z + 1) / i $ Pn(h/zo + l ) ] 5/3 0 h=10 m

Vertical

0 . 5 % hlPn(lO/zo + 1) Bn(h/z + 1 ) I - l A Pw ( 4 =

h=lO m 0 (4 .1)

Z 1 + 8[hhn(10/z + 1) /vh=lo Pn(h/z + 1) ] 5/3 0 0

where

@W (2) = spectral density distribution of turbulence kinetic energy

CY

CY = designates either x, y, or z component of the fluctuation w

n = frequency in cycles per second, Hz A

13

- wh=10 m = horizontal mean wind speed at h = 10 m

h = height above natural grade

z = surface roughness length (typical values of surface roughness 0 length, zo, are given in Table 3-1).

The terms h, z and are expressed in meters and meters per second,

respectively. The units for $ are then meters square per second. The sub-

scripts w , w , and w refer to the longitudinal, lateral, and vertical wind speed,

Wh. The coordinate system (x, y, z) is chosen with the x-axis oriented along

the mean wind direction which is assumed to lie in a plane parallel to the Earth’s surf ace.

0’ h=10 m

W CY

- X Y Z

A plot of the turbulence kinetic energy spectra in dimensionless coordinates is given in Figure 4-1. In dimensionless coordinates, the spectra for all three wind speed fluctuations lie on the same curve.

4 . 1 . 2 Turbulence Intensity ( rms Value)

The recommended value of turbulence intensity, (T , is given by W

CY

(T = k4 W W

CY CY h=lO m

where k is given in Figure 4-2 as a function of surface roughness, z and

height, h.

4 0’ CY

4 . 2 Discrete Gust Model

4 . 2 . 1 Extreme Discrete Gust

4 . 2 . 1 . 1 Shape of Longitudinal Extreme Discrete Gus t

The extreme, longitudinal discrete gust shape recommended for design is given by

14

where

t; = t /T ; a = 0 . 1 2 + 0 . 0 5 I n h

and

wG(t;) = instantaneous horizontal wind speed fluctuation about the mean, i .e., wG(t;) = ~ ( t ; ) -Eh

W. = the effective average horizontal, discrete gust amplitude, i.e. , 1 w. = W ( T ) - wh -

1

W ( T ) = the average over the period T of the wind speed centered around the peak wind speed

t = time

T = period of gust

h = height

a = effective gust rise time.

4.2.1.2 Gust Period

The recommended period of the gust in seconds, T, is given in Figures 4-3 and 4-4. The period T is expressed as a function of the spatial distance, A a , over which the gust is 50-percent coherent (i. e., the spatial distance over which the gust is estimated to be effectively uniform or the distance it would engulf). Figure 4-3 gives the period of a gust effectively coherent over a horizontal distance, A a = Ax, and Figure 4-4 gives the period of a gust effectively coherent over either the lateral or the vertical distance, A a = A y = A z, whichever is of interest.

15

4.2.1.3 Extreme, Longitudinal Discrete Gust Amplitude, W. 1

Values of W. are computed from W = k w where k is given in Figures 1 i 5 h 5

4-5 through 4-8 as a function of height, h, period, T , and mean wind speed at the 10-m level, W The value W . represents the three standard deviation

value ( 9 9 percentile). That is, there is only an approximate 1-percent chance that W. will be greater than the value given in Figures 4-5 through 4-8. The

value of b? is computed from h given on the respective figure by the

relationship

h=10 m e 1

1

h=10 m

- - W h = k W

6 h=10 m (4- 3)

where k which is a function of z and h, is determined from Figure 4-9. Thus 6’ 0

W. = k k W 1 5 6 h=10 m

4.2.2 Cyclic, Discrete Gust Model

4.2.2.1 Cyclic, Discrete G u s t Shape

The conventional shape used for a cyclic, discrete gust is:

wGCi ( q ) = w ( 1 - c o s 2 n 5 ) ; 0 1 t; 5 1

AG! (4.4)

where

16

and

T = period of gust

wACY = gust amplitude relative to the mean wind speed in the direction CY

= instantaneous wind speed relative to the mean wind speed in the

G x Gz andW ( 5 ) = W Y ( S ) .

GY

In applying Equation 4.4 the value of T is determined from either Figure 4-3 or 4-4.

4.2.2.2 Cyclic, Discrete Gust Amplitude

The recommended discrete gust amplitude is

WACY - - vk k k (& CY 6 7 h=10 m > *

This value of W represents the gust amplitude average over a year based on

a Rayleigh distribution of wind speed, and v is the ratio W

v is selected by the designer and effectively corresponds to the number of standard deviations represented by the imposed gust amplitude W . The distribution of W is given by the probability density function

A 0

ACY 'Oeff' The value of

ACY ACY

2e-( u2/2) O* ) = 0.441 u W A ~ p ( w A a

A plot of Equation 4.6 is given in Figure 4-10.

Values of k4, , k , and k are given in Figures 4-2, 4-9, and 4-11,

respectively. The expression on the abscissa of Figure 4-11 is a dimensionless quantity. The value of a is 4.5 if CY = x and 7.5 if CY = z or y; A CY is the

distance over which the gust is 50-percent correlated, and vo, is given in

6 7

CY

17

the insert. To complete the definition, a set of discrete gusts of period T is selected according to the following criteria: Let T~ ( W ) be the most probable

period of gust with amplitude W . In Figures 4-5 through 4-8 relationships Aa a r e proposed which relate gust period and gust amplitude. Then

A 0

A T n S ~ / T s n A

0' min 0 max

where n̂ and fi are obtained from known o r assumed response character-

ist ics of the specific wind turbine. The effects of these discrete gusts on a given wind turbine are then predicted by means of a deterministic aero-structural dynamic model. In this way a statistical description of the wind turbine loads is obtained from the statistical description of the wind.

max min

4 . 2 . 2 . 3 Number of Cycles

The number of cycles in wind speed which exceed the gust amplitude,

Aa ( A a , h) , in a given year's exposure to winds having a Rayleigh distribution

is determined from Figures 4-12 and 4-13 by W (the annual mean wind speed at

height h) and Aa (the longitudinal, lateral, o r vertical spatial extent of the gust, i. e. , a gust of size large enough that it is expected to engulf a distance A a ) . Values of k are given in Figure 4-14.

A

h

100

18

1 .o

0.5

0.1

0.05

0.01 0.1 0.5 1 5 10 50 100

A - " 770,

Figure 4-1. Dimensionless turbulence kinetic energy spectra.

zo (m 1

Figure 4-2. Turbulence intensity cr /E w h=10 m (dimensionless).

CY

1000

500

100

50

10

5

1 1 5 10 50 100 300

SPATIAL DISTANCE, Aa (m)

Figure 4-3. Period of gust 50-percent coherent over the horizontal distance, ha, = Ax.

21

1 5 10 50 100 300

SPATIAL DISTANCE, Acu (m)

Figure 4-4. Period of gust 50-percent coherent over the lateral or vertical distance, Acu = A y = Az.

22

3.0

2.5

- v) v) w J z 2 .o 0

z n

v ) 2 w

- Y

Ln

1.5

1 .o

0.5

5 10 50 100

HEIGHT, h (m)

Figure 4-5. Factor for computing the discrete gust amplitude, W . = k k W where k is given in Figure 4-9

1 5 6 h=10 my 6

300

23

1.6

1.4

1.2

1 .o

0.8

0.6

0.4

!

. .! ..-. 1...J...J..:J - . - . . . ; . _ . . - . . . . I 2 1 .... I .... l....! .... !.._; . . . ,...._ * * A + - . I

10 50 100

HEIGHT, h (m)

300


1 5 6 h=10 m y 6 and w = 10 m s-l. h=10 m

24

Figure 4-7. Factor for computing the discrete gust amplitude, W . = k k F , where k is given in Figure 4-9

1 5 6 h=10 m 6 - and wh=10 m = 15 m s-*.

25

0.7

0.6

0.5

0.4

0.3

0.2

0.1 .5 10 50 100

HEIGHT, h (m)


1 5 6 h=10 m y 6 and =- 25 m s-I. h=lO m -

300

26

1 5 10 50 100 300

HEIGHT, h (m)

Figure 4-9. Factor for adjusting! -

h=10 m to Wh.

Figure 4-10. Probability density function of the discrete gust amplitude, W . AQI

A A

WAa = klOaWAcrMlh

Figure 4-12. Factor for calculating the number of times per year the wind speed exceeds the value W . A

ACY

30

10-2

I o7

106

10-1

qox = 0.0144, a, = 4.5 ?ley = 0.0265, a = 7.5 q,, = 0.0962, a, = 7.5

Y

"

lo4 1 o5

1 I 09

108

107

106

a&a(rl,,)/h

F lgure 4-13. Zero crossing factor.

31

w tw

r

SURFACE ROUGHNESS LENGTH, zo (m)

Figure 4-14. Scaling factor.

Chapter 5.0 Wind Direction

5.1 Wind Direction Probability

The cumulative probability of the horizontal wind vector lying within an angle between 0 and e is given in Figures 5-1 through 5-5 as a function of height, h, and surface roughness length, z ( z values are given in Table 3-1). The

angle, e = 0, is the direction in which the mean horizontal wind speed is blowing. The cumulative probability curves are symmetric such that the probability of e lying within the arc 28 is twice the probability of the angle lying between 0 and e.

0 0

5.2 Wind Direction Fluctuations

The number of times per unit time the wind direction fluctuations exceed the angle, e , is given in Figures 5-6 through 5-9 as a function of height, h, L surface roughness length, z and the mean wind speed at a height of 10 m, W . That is, 0’

h=10 m

where is in meters per second and N( e ) is in seconds. Doubling the

value of N ( 0 ) provides the number of times per unit time that the horizontal wind vector fluctuates outside a given arc of 28 (i. e., the number of times per unit time the angle exceeds A€)). These results are relative to a 1-h averaging period.

h=10 m

33

1 2 5 10 20 30 40 50 60 70

PROBABILITY (%I

Figure 5-1. Cumulative probability distribution of angular displacement of mean wind, h = 10 m.

34

100

50

10

5

1 .o 1 2 5 10 20 30 40 50 60 70

PROBABILITY (%I


35

1 2 5 10 20 30 40 50 60 70

PROBABI LlTY 4%)


36

100

50

5

1 .o 1 2 5 10 20 30 40 50 60 70

PROBABILITY (%)


37

1 2 5 10 20 30 40 50 60 70

PROBABI LlTY (%I


38

10 15

0 (deg)

20 25 30

Figure 5-6. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle e measured from the direction

of the mean wind vector, z = 0.001 m. 0

39

Figure 5-7. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle 8 measured from the direction


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~ i g w e 5-8. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle e measured from the direction

of the mean wind vector, z = 0 .1 m. 0

41

Figure 5-9. Factor for computing the number of times per unit time the wind vector fluctuation exceeds the angle 8 measured from the direction


42

1. REPORT NO. 2. GOVERNMENT ACCESSION NO. 3. RECIPIENT'S CATALOG NO.

NASA TP-1389 4 T I T L E AND SUBTITLE 15. REPORT DATE

Summary of Atmospheric Wind Design Criteria for Wind Energy Conversion System Development

January 1979 6. PERFORMING ORGANIZATION CODE

7 . AUTHOR(S) 8. PERFORMING ORGANIZATION REPORT R Walter Frost* and Robert E. Turner

~

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. WORK UNIT NO.

George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama 35812

"280 1 1. CONTRACT OR GRANT NO.

13. TYPE OF REPORT & PERIOD COVEREC ~.

12. SPONSORING AGENCY NAME AND ADDRESS

National Aeronautics and Space Administration Washington, D.C. 20546

Technical Paper

15. SUPPLEMENTARY NOTES

Prepared by Space Sciences Laboratory, Science and Engineering

* The University of Tennessee Space Institute, Tullahoma, Tennessee 37388 16. ABSTRACT

This report presents basic design values of significant wind criteria, in graphical format, for use in the design and development of wind turbine generators for energy research. It is a condensed version of portions of the "Engineering Handbook on the Atmospheric Environmental Guidelines for Use in Wind Turbine Generator Development,"

17. KEY WORDS

19. SECURITY CLASSIF. (of t h h rwartt) 20. SECURITY CLASS

Unclassified $4.50 54 Unclassified 0

MSFC - Form 3 2 9 2 (Rev December 1 9 7 2 ) For sale by National Technical Infornration Service, Springfield, Virginia 22 1 5 1

18. DISTRIBUTION STATEMENT

Category: 15 and 47

IF. (of thlm page) 121. NO. OF PAGES 122. PRICE

NASA-Langley. 1978

I l l 1 I

National Aeronautics, and THIRD-CLASS BULK RATE Space Administration

Washington, D.C. 20546

Postage and Fees Paid National Aeronautics and

NASA451 Space Administration

, - ,

, . ~

Official

Penalty

Business for Private Us 16 1 1IJ,E, 121878 S-00903I)S

DEPT OF THE AIR FORCE AF WEAPONS LABORATORY

RIRTLAND AFB NB 871 17 . a ~ m : TECHNICAL LIBRARY (SUL)

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Summary of. Atmospheric Wind' .Wind Energy

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