Mean Wind Forces on Parabolic Trough Solar...

SAND80-7023 Unlimited Release UC-62 Distribution

RECORD COPI oo mn rAnr CROIn6POB

Mean Wind Forces on Parabolic - Trough Solar Collectors

J. A. Peterka, J. M. Sinou, and J. E. Cerrnak Colorado State University

4 P,tzr);lrtscj for Sar,clla N ;~ t~o i , a I Lat ,ora tor~es under Contrac t No 13.2412

Issued by Sandia Laboratories, operated for the United States

Department of Energy by Sandia Corporation.

NOTICE

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor

the Department of Energy, nor arly of their employees, nor

any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal

liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process cjisclosed, or represents that its use would not infringe privately owned rights.

Printed in the United States of America

Available from National Technics1 lnformalon Ssrvics U. S Dopartrnent of Commerce 6286 Port Royal Road Springfield, VA 221 61 Price: Printed Copy $6.50 ; Miwoflchr $3.00

SAND80-7023 U n l i m i t e d R e l e a s e P r i n t e d May 1 9 8 0

D i s t r i b u t i o n C a t e q o r y U C - 6 2

MEAN W I N D FORCES ON PARABOLIC-TROUC11 SOLAR COLLECTORS

J. A . p e t e r k a J . M . S i n a u J. E. Cermak

F l u i d M e c h a n i c s a n d Wind E n g i n e e r i n g P r o q r a n F l u i d Dynamics a n d D i f f u s i o n L a b o r a t o r y

D e p a r t m e n t o f C i v i l E n g i n e e r i n g C o l o r a d o S t a t e U n i v e r s i t y

F o r t C o l l i n s , CO 8 0 5 2 3

P r e p a r e d f o r S a n d i a N a t i o n a l L a b o r a t o r i e s u n d e r C o n t r a c t No. 1 3 - 2 4 1 2

TABLE OF CONTENTS

Section Page

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii .............................................. List of Figures i v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols v

1 . INTRODUCTION .

2 . EXPERIMENTAL CONFIGURATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 . 1 Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 . 2 Flow Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 . 3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 . INSTRUMENTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . 1 Velocity Profiles 8 3 . 2 Flow Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 . 3 Force and Moment Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 . 4 Force and Moment Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . TEST PSSULTS 13

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . 1 Single Collector Loads 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . 2 Array Field Loads 14

. . . . . . . . . . . . . . . . . . . . . 4 . 3 Smoke Visualization of Fence Effect 18 4 . 4 Calculation of Full-scale Loads . . . . . . . . . . . . . . . . . . . . . . . . . 19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . CONCLUSIONS 22

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

...................................................... FIGURES 2 4

TABLES ....................................................... 75

L I S T OF T A B L E S

Motion picture scene guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Velocity and turbulence intensity profile . . . . . . . . . . . . . . . . . 77

Determination of 8 for configurations 1-4 . . . . . . . . . . . . . . 78 max

Effect of height HCL on single collector loads at 0 = 0. + = 0 for configurations 1-4 . . . . . . . . . . . . . . . . . . . . . . . 79

Effect of height HCL 0. n single collector ioads at emax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + = 0 for configurations 1-4 80

Matrix of single collector loads at HCL/C = KI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (configurations 1 - 4 ) 81

Loads for various gap spacings for configuration 5 . . . . . . . . 85

Data for establishment of row spacing R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (configuration 9) 86

Loads on array fields (configurations 5 - 9 ) . . . . . . . . . . . . . . . . 87

Effect of fences on array field loads . . . . . . . . . . . . . . . . . . . . . 90

Effect of berms on array field loads . . . . . . . . . . . . . . . . . . . . . . 93

Loads with a torque tube on collector 1 . . . . . . . . . . . . . . . . . . . 95

Effect of 0 on pitching moment coefficients (configurations 1 - 4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Effect of height HCL on single collector pitching moment coefficients at 0 = 0 and $ = 0 (configurations 1 - 4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Effect of height HCL on single collector pitching moment coefficients at 0 = emax and $ = 0 (configurations 1 - 4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Matrix of single collector pitching moment . . . . . . . . . . . coefficients at HCL/C = KI (configurations 1 - 4 ) 99

Pitching moment coefficients for various gap spacings (configuration 5 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Pitching moment coefficients for establishment of row spacing R (configuration 9) . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Pitching moment coefficients for array fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (configurations 5 - 9 ) 105

LIST TABLES

Table Page

2 0 Effects of fences and berms on array fields, pitching moment coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l o 8

2 1 Pitching moment coefficients with a torque tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (configuration 1) 109

LIST OF FIGURES

F i g u r e

M e t e o r o l o g i c a l wind t u n n e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

C o l l e c t o r s h a p e s f o r c o n f i g u r a t i o n s 1-4 . . . . . . . . . . . . . . . . . . . 26

C o l l e c t o r mounted on f o r c e b a l a n c e . . . . . . . . . . . . . . . . . . . . . . . . 28

C o l l e c t o r and f o r c e b a l a n c e mount . . . . . . . . . . . . . . . . . . . . . . . . . 29

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C o o r d i n a t e System 30

C o l l e c t o r i n a r r a y s f o r c o n f i g u r a t i o n s 5-9 . . . . . . . . . . . . . . . . 32

Berm ar rangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Array f i e l d i n t h e wind t u n n e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Approach v e l o c i t y and t u r b u l e n c e p r o f i l e . . . . . . . . . . . . . . . . . . 35

D e t e r m i n a t i o n o f Omax ( c o n f i g u r a t i o n s 1-4) . . . . . . . . . . . . . . . . 36

E f f e c t o f h e i g h t on c o e f f i c i e n t s a t 8 = 0 . tJ = 0 ( c o n f i g u r a t i o n s 1 - 4 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

E f f e c t o f h e i g h t on l i f t a t Omax. 6 = 0 ( c o n f i g u r a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 4 ) 41

V a r i a t i o n o f s i n g l e c o l l e c t o r l o a d s w i t h p i t c h a n g l e f o r HCL/C=KI. $ = 0 ( c o n f i g u r a t i o n s 1-4) . . . . . . . . . . . . . . . . . . . . . . 42

V a r i a t i o n o f s i n g l e c o l l e c t o r l o a d s w i t h yaw a n g l e f o r . . . . . . . . . . . . . . . . . . . . . . . . . . . . ACL/C=KI. ( c o n f i g u r a t i o n s 1-4) 48

E f f e c t o f t h e rim a n g l e . 4 on c o l l e c t o r l o a d s . . . . . . . . . . . . . 58

E f f e c t o f gap w i d t h on l o a d s f o r c o n f i g u r a t i o n 5 . . . . . . . . . . 61

E f f e c t o f row s p a c i n g on c o l l e c t o r l o a d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( c o n f i g u r a t i o n 9 ) 63

I n f l u e n c e o f a r r a y f i e l d c o n f i g u r a t i o n and f e n c e s on c o l l e c t o r l o a d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 6

. . . . . . . . . . . . . . . . E f f e c t o f t o r q u e t u b e on c o l l e c t o r 1 l o a d s 70

E f f e c t o f a p p l y i n g c o r r e c t i o n t o c o l l e c t o r 1 . . . . . . . . . . . . . . 72

.................... Smoke v i s u a l i z a t i o n o f upwind b a r r i e r s 73

LIST OF SYMBOLS

c o n s t a n t

s u b s c r i p t , r e f e renced t o t h e base of foundat ion o r a c o n s t a n t

a p e r t u r e width of t h e c o l l e c t o r ( s e e F igure 5 )

p a r a b s l i c f o c a l d i s t a n c e

d i s t a n c e between t h e c e n t e r of g r a v i t y G and t h e p i v o t p o i n t

v o l t a g e

s u b s c r i p t r e f e renced t o t h e f o c a l p o i n t F

t o t a l f o r c e app l i ed t o t h e c o l l e c t o r i n t h e x-z p lane

l a t e r a l f o r c e , p o s i t i v e a long t h e x a x i s ( s e e F igure 5 )

fence h e i g h t

l i f t f o r c e , p o s i t i v e a long t h e z a x i s ( s ee F igu re 5)

fence d i s t a n c e upwind of l ead c o l l e c t o r

l a t e r a l f o r c e c o e f f i c i e n t

l i f t f o r c e c o e f f i c i e n t

gap width ( s e e F igu re 6 )

s u b s c r i p t re ferenced t o t h e c e n t e r of g r a v i t y of t h e t rough G

d i s t a n c e between t h e c o l l e c t o r p i v o t p o i n t and t h e f o r c e ba lance a x i s ( s e e F igu re 4)

d i s t a n c e between t h e c o l l e c t o r p i v o t p o i n t and t h e f l o o r ( s e e F igu re 4 )

s e l e c t e d r a t i o HCL/C t o run c o n f i g u r a t i o n s 1-4

c o l l e c t o r l e n g t h

r o l l i n g moment about x a x i s P r o l l i n g moment c o e f f i c i e n t

p i t c h i n g moment about y a x i s B

p i t c h i n g moment c o e f f i c i e n t about yg a x i s

p i + c h i n g moment about y a x i s F

LIST OF SYMBOLS

pitching moment coefficient about yF axis

pitching moment about yG axis

pitching moment coefficient about yc axis

pitching moment about y axis P

pitching moment coefficient about yp axis

yawing moment about z axis

yawing moment coefficient about z axis

constant

pivat point reference location

tunnel dynamic pressure at collector pivot point height HCL

tunnel dynamic pressure at the top of the boundary layer (45 inches high)

row spacing

projected area of the collector, S=LC

velocity

wind speed at H height 0

coordinate system at pivot point (see Figure 5)

coordinate system at base of foundation (see Figure 5)

pitch angle or elevation angle (see Figure 5)

pitch angle where the maximum'-lift occurs

kinematic viscosity

air density

parabolic rim angle (see Figure 2)

yaw angle or azimuth angle (see Figure 5)

coordinate system for definition of collector shape

1. INTRODUCTION

S t r u c t u r e s such a s p a r a b o l i c t r o u g h s o l a r c o l l e c t o r s a r e be ing

c o n s i d e r e d f o r power p l a n t t h e r m a l s o u r c e s . A s i g n i f i c a n t f a c t a r

i n f l u e n c i n g t h e economic v i a b i l i t y of t h e s e c o l l e c t o r s i s t h e magni tude

o f t h e wind l o a d and t h e r e s u l t i n g s t r u c t u r a l r e q u i r e m e n t s . The s h a p e

o f t h e c o l l e c t o r , i t s h e i g h t above t h e g round , t h e c o l l e c t o r p i t c h

a n g l e , t h e number and a r rangement o f c o l l e c t o r s i n a n a r r a y and t h e

d i r e c t i o n o f t h e wind a r e s e v e r a l p a r a m e t e r s which can modify t h e l o a d s

a p p l i e d t o t h e c o l l e c t o r . S i n c e a n a n a l y t i c a l o r a numer ica l approach

cannot be c o n s i d e r e d f o r s u c h a compl ica ted geometry , a s i m u l a t i o n i n a

wind t u n n e l i n which t h e a t m o s p h e r i c boundary l a y e r i s modeled was

conducted a t t h e r e q u e s t o f Sand ia L a b o r a t o r i e s ( 1 ) .

The purpose o f t h i s s t u d y was t o i n v e s t i g a t e c h a r a c t e r i s t i c s of

mean wind l o a d s produced by a i r f l o w i n and around s e v e r a l c o n f i g u r a t i o n s

of p a r a b o l i c t r o u g h s o l a r c o l l e c t o r s w i t h and w i t h o u t a wind f e n c e .

Four b a s i c p a r a b o l i c s h a p e s were i n v e s t i g a t e d a s s i n g l e u n i t s and one

shape was s t u d i e d a s p a r t o f s e v e r a l a r r a y f i e l d s . One 1:25 s c a l e model

of each p a r a b o l i c shape was c o n s t r u c t e d f o r mounting on a f o r c e b a l a n c e

t o measure two f o r c e s and t h r e e moments. The e f f e c t s o f s e v e r a l

dominant v a r i a b l e s were i n v e s t i g a t e d i n t h i s s t u d y : wind-azimuth ( o r

yaw), t r o u g h e l e v a t i o n ( o r p i t c h ) a n g l e , a r r a y f i e l d c o n f i g u r a t i o i i , and

p r o t e c t i v e wind f e n c e c h a r a c t e r i s t i c s . A l l nicasurements were made i n a

b o u n d a r y - l a y e r f low deve loped by t h e m e t e o r o l o g i c a l wind t u n n e l a t t h e

F l u i d Dynamics and D i f f u s i o n L a b o r a t o r y o f Colorado S t a t e U n i v e r s i t y .

The p r i m a r y c o n s i d e r a t i o n i n model ing wind f o r c e s on s t r u c t u r e s i n

a wind t u n n e l i s t h a t t h e wind c h a r a c t e r i s t i c s i n t h e t u n n e l s i m u l a t e

n a t u r a l b o u n d a r y - l a y e r winds a t t h e a c t u a l s i t e . I n g e n e r a l , t h i s

r e q u i r e s t h a t t h e v e r t i c a l d i s t r i b u t i o n o f mean v e l o c i t y and t u r b u l e n c e

i n t h e wind- tunne l boundary l a y e r match t h o s e a t t h e s i t e and t h a t t h e

Reynolds numbers o f t h e model and t h e p r o t o t y p e b e e q u a l . I n a d d i t i o n ,

t h e s m a l l - s c a l e n o d e l must be g e o m e t r i c a l l y s i m i l a r t o i t s p r o t o t y p e . A

d e t a i l e d d i s c u s s i o n o f t h e s e r e q u i r e m e n t s and t h e i r implementa t ion i n

t h e w i n d - t u n n e l env i ronment can be found i n r e f e r e n c e s 2 , 3 , and 4 .

The c o n s t r u c t i o n o f a 1:25 s c a l e model o f t h e p r o t o t y p e s t r u c t u r e

and i t s immediate s u r r o u n d i n g s ( i n t h i s c a s e , a f l a t , open a r e a ) ,

submerged i n a t u r b u l e n t boundary l a y e r of t h e m e t e o r o l o g i c a l wind

t u n n e l shown i n F i g u r e 1 , s a t i s f i e s a l l t h e above c r i t e r i a e x c e p t t h o s e

of e q u a l Reynolds numbers and s i m i l a r i t y of t u r b u l e n c e i n t e n s i t y and

s c a l e .

UD I n t h e Reynolds number 7, v i s t h e same f o r b o t h t h e t u n n e l and

t h e f u l l - s c a l e s t r u c t u r e . Because of t h i s , t h e wind- tunne l a i r s p e e d ,

U , would have t o be 25 t i m e s t h e f u l l - s c a l e v a l u e i f t h e model and

p r o t o t y p e Reynolds numbers a r e t o be e q u a l . T e s t i n g a t such h i g h wind

s p e e d s i s n o t f e a s i b l e . However, f o r Reynolds numbers l a r g e r t h a n

4 2 x 10 f o r sha rp -edged s t r u c t u r e s where t h e f low s e p a r a t i l ~ n p o i n t i s

f i x e d , t h e r e i s no s i g n i f i c a n t change i n t h e v a l u e s of a e r o d y n a n i c

c o e f f i c i e n t s a s t h e Reynolds number i n c r e a s e s . For f lows o v e r cu rved

s u r f a c e s , t h e v e l o c i t y r e q u i r e d f o r Reynolds number independence r a n g e s

5 from below 10 t o n e a r l y lo6 depend ing on s u r f a c e roughness o f t h e

curved s u r f a c e and t u r b u l e n c e s t r u c t u r e i n t h e a p p r o a c h f l o w . S i n c e

7 t y p i c a l Reynolds number v a l u e s a r e lo6-10 f o r h igh-wind, f u l l - s c a l e

f low and a b o u t 7 x l o4 f o r wind- tumle l f l o w s , a c c e p t a b l e f low s i m i l a r i t y

i s a c h i e v e d w i t h o u t e q u a l i t y o f Reynolds numbers f o r c a s e s where f low

s e p a r a t i o n i s f i x e d a t t h e edge of t h e ~ a r a b o l i c c o l l e c t o r . F o r c a s e s

where f low s e p a r a t i o n c o u l d b e on t h e smooth c u r v a t u r e of t h e back o f

t h e c o l l e c t o r , a s m a l l Reynolds number dependence may he i n c l u d 2 d i n

t h e s i m u l a t i o n . Because o f t h e l a r g e t u r b u l e n c e i n t e n s i t y i n t h e

s g p r o a c h f l o w , Reynolds number dependence i s e x p e c t e d t o be q u i t e s m a l l .

A t a model s c a l e of 1 :25 , t h e l a r g e r s c a l e s c f t u r b u l e n c e I n t h e

a tmo,pher ic boundary l a y e r a r e n o t s i m u l a t e d i n t h e wind- tunne l f l o w .

q a ~ e v e r , b ~ c ~ g s e t h e f low a b o u t t h e p a r a b o l i c t r o u g h a p p r o x i m a t e s t h e

f low ah,ut a f l s t p l a t e a t e l e v a t i o n a n g l e s n e a r t o z e r o d e g r e e s and

b e c s u s e t h e i n t e g r i ; s c a l e o f t h e turbulence i n t h e wind t u n n e l was 2

t.c 3 t imes t h e l a r g e s t d imension of t h e model c o l l e c t o r , t h e i n f l u e n c e

of t h e s c a l e o f t u r b u l e n c e was n o t e x p e c t e d t o be s i g n i f i c a n t ( 5 ) .

Ev idence e x i s t s which d e m o n s t r a t e s some i n f l u e n c e of t u r b u l e n c e i n t e n s i t y

on d r a g o f f l a t p l a t e s (5,6,7). Because t h e t u r b u l e n c e i n t e n s i t y

d i f f e r e n c e between t h e c u r r e n t s i m u l a t i o n and a s i m u l a t i o n w i t h comple te

similarity of t u r b u l e n t s t r u c t u r e i s n o t l a r g e , t h e e f f e c t s due t o

t u r b u l e n c e i n t e n s i t y s h o u l d be s m a l l (a few p e r c e x t a t m o s t ) . For

c a s e s where a n ups t ream c o l l e c t o r d i s t u r b s t h e approach f l o w , t u r b u l e c c e

c h a r a c t e r i s t i c s a r e dominated by t h e wake c h a r a c t e r i s t i c s o f t h e

ups t ream o b j e c t and p o s s i b l e d i f f e r e n c e s due t o t u r b u l e n c e i n t e n s i t y

s h o u l d f u r t h e r d c c r e a s e .

2. EXPERIMENTAL CONFIGURATION

2 . 1 Wind Tunnel

The s t u d y was conduc ted i n t h e m e t e o r o l o g i c a l wind t u n n e l of t h e

F l u i d Dynamics and D i f f u s i o n L a b o r a t o r y a t Co lo rado S t a t e U n i v e r s i t y .

T h i s low-speed, c l o s e d - c i r c u i t wind t u n n e l ( F i g u r e 1 ) i s c h a r a c t e r i z e d

by a long (96 f t ) s l i g h t l y d i v e r g i n g t e s t s e c t i o n , 6 f t - 8 i n . wide ( a t

t h e t u r n t a b l e ) and 6 f t h i g h t o d e v e l o p a n a p p r o p r i a t e a t m o s p h e r i c

boundary l a y e r s i m u l a t i o n . The c e i l i n g i s a d j u s t a b l e t o a v o i d a p r e s s u r e

g r a d i e n t a l o n g t h e t e s t s e c t i o n . T h i s f a c i l i t y i s d r i v e n by a 400 HP

v a r i a b l e p i t c h p r o p e l l e r w i t h v e l o c i t y v a r y i n g c o n t i n u o ~ ~ s l y from 0 . 5 f p s

up t o 100 f p s . The t u r n t a b l e where t h e t e s t s were conduc ted ( 6 % f t

d i a m e t e r ) was l o c a t e d n e a r t h e downstream end o f t h e t e s t s e c t i o n . The

ambien t t e m p e r a t u r e was c o n t r o l l e d a t 24OC.

2 . 2 Flow S i m u l a t i o n

The p u r p o s e . o f t h e s t u d y was t o e v a l u ~ t e l o a d s on c o l l e c t o r s

i n an a t m o s p h e r i c boundary l a y e r deve loped o v e r a n open f l a t a r e a ,

1 c h a r a c t e r i z e d by a - t h power law. S i n c e i t was i r ~ p o s s i b l e t o model t h e 7

comple te boundary l a y e r , t h e s i m u l a t i o n was conduc ted i n a 45 i n . deep

boundary l a y e r , whose mean v e l o c i t y power law exponen t was 0 . 1 5 . T e s t s

were run w i t h a v e l o c i t y a t 45 i n . of a b o u t 80 f p s . The v e l o c i t y arid

t u r b u l e n c e p r o f i l e s a r e shown i n F i g u r e 8 and t a b u l a t e d i n T a b l e 2 .

The shape o f t h e boundary l a y e r was o b t a i n e d by means of s e l e c t e d

roughness on t h e wind- tunne l f l o o r ups t ream o f t h e model. F o r t y f e e t o f

t e s t s e c t i o n l e n g t h were covered w i t h 1 i n . cubes fo l lowed by a 40 ft

l e n g t h o f pegboard w i t h 0 . 2 5 i n . d i a m e t e r pegs p r o j e c t i n g 0 . 5 i n . above

a pegboard b a s e . I n a d d i t i o n t o t h e f l o o r r o u g h n e s s , f o u r t r i a n g u l a r

s p i r e s e x t e n d i n g from t h e f l o o r t o t h e c e i l i n g were i n s t a l l e d a t t h e

t e s t s e c t i o n e n t r a n c e i n o r d e r t o g e t a t h i c k e r bounda ry l a y e r t h a n

would o t h e r w i s e b e o b t a i n e d .

2 . 3 The Model

The p r o t o t y p e o f t h e s o l a r c o l l e c t o r was a 6 f t w ide and 2 2 . 5 f t

l o n g p a r a b o l i c s h a p e d u n i t mounted e n d - t o - e n d i n rows . I n o r d e r t o f i t

t h e d i m e n s i o n s o f t h e t u r n t a b l e , t h e 1 :25 s c a l e was c h o s e n . The mode l s

were b u i l t o f b r a s s .

F o u r d i f f e r e n t s h a p e s o f p a r a b o l i c c o l l e c t o r s were c o n s t r u c t e d

v a r y i n g t h e rim a n g l e @ ( F i g u r e 2 ) . The p a r a b o l i c s h a p e w a s tlcfiricci

by t h e e q u a t i o n :

whe re t h e rim a n g l e @ i s r e l a t e d t o t h e a p e r t u r e C

The s e t o f f o u r c o l l e c t o r s , c a l l e d t h e m e t r i c u n i t s , we re e a c h a b l e

t o be mounted on t h e f o r c e b a l a n c e a s shown i n F i g u r e s 3 and 4 . T h e i r

h e i g h t and e l e v a t i o , ~ a n g l e c o u l d b e v a r i e d m a n u a l l y . The f o r c e b a l a r l c c

was f i x e d t o t h e w i n d - t u n n e l t u r n t a b l e s o t h a t measu red f o r c e s a n d

moments were r e f e r r e d t o a c o o r d i n a t e s y s t e m f i x e d w i t h r e s p e c t t o t h e

t u r n t a b l e . The c o o r d i n a t e s y s t e m u s e d i s shown i n F i g u r e 5 . A f u r t h e r

e x p l a n a t i o n o f t h e c h o s e n c o o r d i n a t e s y s t e m and n o n m e n c l n t u r e would be

b e n e f i c i a l . I t i s common p r a c t i c e t o r e f e r t o t h e t h r e e components o f

f o r c e r e s o l v e d i n t h e wind a x i s s y s t e m a s d r a g , c r o s s - w i n d , a c d l i f t

f o r c e s and t o t h e componen t s r e s o l v e d i n t h e body a x i s s y s t e m a s a x i a l ,

s i d e , and norrnzl f o r c e s . T h i s i s l o g i c a l due t o t h e f a c t t h a t a t z e r o

yaw a n g l e and z e r o p i t c h a n g l e , mos t a e r o d y n a m i c s h a p e s ( a i r p l a n e s ,

r o c k e t s , e t c . ) h a v e t h e i r " a x i s " a l i g n e d w i t h t h e w i n d . However , s i n c e

t h e " a x i s " o f a s o l a r c o l l e c t o r t r o u g h i s no rma l t o t h e wind a t z e r o

a z i m u t h a n g l e , i t was f e l t t h a t r e f e r r i n g t o a n " a x i a l " f o r c e c o u l d be

m i s l e a d i n g . T h e r e f o r e , " l a t e r a l " f o r c e w i l l b e u s e d t o d e s i g n a t e t h a t

component o f f o r c e a c t i n g l a t e r a l t o t h e a x i s o f t h e c o l l e c t o r t r o u g h

and " l o n g i t u d i n a l " f o r c e t h a t component a c t i n g a l o n g ( p d r a l l e l t o ) t h e

a x i s o f t h e t r o u g h ( s e e F i g u r e 5 ) . L i f t f o r c e w i l l s t i l l be t h a t

component p e r p e n d i c u l a r t o t h e g round ( i . e . , t h a t f o r c e t e n d i n g t o

" l i f t " t h e c o l l e c t o r o f f i t s f o u n d a t i o n ) .

E l e v b t i o n a n g l e s o f t h e c o l l e c t o r c o u l d b e s e t t o 1 d e g r e e w h i l e

a z i m u t h p o s i t i o n i n g u s i n g t h e t u r n t a b l e was a c c u r a t e t o a b o u t 0 . 2

d e g r e e s . The f o u r m e t r i c c o l l e c t o r s , e a c h mounted a l o n e i n t h e wind

t u n n e l were c a l l e d c o n f i g u r a t i o n s 1-4 ( F i g u r e 2 ) .

F i v e c o n f i g u r a t i o n s o f c o l l e c t o r a r r a y s were used i n t h e s t u d y .

Each was composed o f d i f f e r e n t c o m b i n a t i o n s o f rows w i t h e a c h row b e i n g

formed by t h r e e a l i g n e d c o l l e c t o r s s i m i l a r t o t h e c o l l e c t o r c o n f i g u r a -

t i o n 1 ($ = 90') ( F i g u r e 6 ) . The l a r g e s t a r r a y , c o n f i g u r a t i o n 9 , c o u l d

be s e t on t h e t u r n t a b l e , s u c h t h a t a r o t a t i o n o f t h e t u r n t a b l e moved the

e n t i r e a r r a y , and t h e r e l a t i v e p o s i t i o n o f t h e m e t r i c c o l l e c t o r r e f e r r e d

t o t h e o t h e r s remained unchanged . A v iew o f t h e a r r a y f i e l d i n t h e wind

t u n n e l i s shown i n F i g u r e 7 .

A s t u d y o f t h e e f f e c t s o f wind b a r r i e r s on c o l l e c t o r l o a d s was

c o n d u c t e d by u s i n g 4 f e n c e s made o f p e r f o r a t e d s h e e t m e t a l , punched w i t h

0 . 3 7 5 i n . d i a m e t e r h o l e s , which p r o v i d e d a 23 p e r c e n t p o r o s i t y . The

h e i g h t s o f t h e s e f e n c e s were 1 , 2 , 3 and 4 i n c h e s . Two 2 i n . f e n c e s

were u s e d , one w i t h a 23 p e r c e n t p o r o s i t y and a m o d i f i e d one w i t h 18

p e r c e n t p o r o s i t y . The f e n c e s were t r i e d a t s e v e r a l d i s t a n c e s i n f r o n t

o f t h e c o l l e c t o r a r r a y s .

T h r e e s o l i d berms of h e i g h t s 1 , 2 , and 3 i n . were u s e d t o d e t e r m i n e

t h e i n f l u e n c e on l o a d s o f e a r t h berms upwind. The 1 i n . berm had a

l i n e a r s l o p e w i t h a b a s e w i d t h o f 2 i n . ( F i g u r e 6 b ) . The 2 i n . berm

was composed o f t h e 1 i n . berm w i t h a t r a p e z o i d a l s h a p e o f 1 i n . h e i g h t

and b a s e w i d t h o f 4 i n . p l a c e d be low i t . The 3 i n . berm was formcd by

~ n s e r t i n g a 1 i n . h i g h s e c t i o n be tween t h e two p o r t i o n s o f t h c 2 i n .

berm ( F i g u r e 6 b ) .

S i n c e t h e p o s s i b i l i t y o f c o n t r o l l i n g t h e p i t c h a n g l e o f t h e f u l l -

s c a l e p r o t o t y p e w i t h a 1 f t d i a m e t e r t o r q u e t u b e w a s u n d e r cons lde r ' 3 t l n r l ,

t h e e f f e c t s p roduced by a 0 . 5 i n . d i a m e t e r " t o r q u e t u b e " a t tach( . ( ! t o ti](.

b a c k o f t h e c o l l e c t o r were me ' i sured .

3 . INSTRUMENTATION

3 . 1 V e l o c i t y P r o f i l e s

To d e t e r m i n e t h e approach boundary- layer c h a r a c t e r i s t i c s , v e l o c i t y

and t u r b u l e n c e i n t e n s i t y p r o f i l e s were measured o v e r t h e t u r n t a b l e w i t h

no c o l l e c t o r i n p l a c e . These t e s t s were performed w i t h U r n = 80 f p s a t

t h e t o p of t h e boundary l a y e r 43 i n . above t h e f l o o r .

Data were o b t a i n e d w i t h a s i n g l e h o r i z o n t a l 0 . 0 0 1 i n . p l a t i n u m h o t -

f i l m p r o b e . A v e r t i c a l t r a v e r s e c o n t r o l l e d d i r e c t l y by an o n - l i n e

computer s u p p o r t e d t h e p r o b e . The o u t p u t from a Thermo-System, I n c .

c o n s t a n t t e m p e r a t u r e anemometer was d i r e c t e d t o a d a t a a c q u i s i t i o n

sys tem c o n s i s t i n g of a Hewle t t Packard 21 MX minicomputer , d i s k , c a r d

r e a d e r , and p r i n t e r and i n c l u d i n g a P r e s t o n S c i e n t i f i c a n a l o g - t o - d i g i t a l

c o n v e r t e r , Digi-Data d i g i t a l t a p e d r i v e and T e k t r o n i x p l o t t e r . Data

we=e a c q u i r e d and p r o c e s s e d under s o f t w a r e c o n t r o l .

C a l i b r a t i o n o f t h e h o t - w i r e anemometer was performed u s i n g a

Thermo-Systems c a l i b r a t o r (Model 1125) . The c a l i b r a t i o n d a t a were f i t

t o a v a r i a b l e exponen t K i n g ' s Law r e l a t i o n s h i p o f t h e form:

E~ = A + Bun

where E i s t h e h o t - w i r e o u t p u t v o l t a g e , U t h e v e l o c i t y and A , B , and n

a r e c o e f f i c i e n t s s e l e c t e d t o f i t t h e d a t a . The above r e l a t i o n s h i p was

used t o d e t e r m i n e t h e mean v e l o c i t y a t measurement p o i n t s u s i n g t h e

measured mean v o l t a g e . The f l u c t u a t i n g v e l o c i t y i n t h e form Urms

( roo t -mean-square v e l o c i t y ) was o b t a i n e d from:

2 E E rms u = rms B n un"

where E r m s i s t h e root-mean-square v o l t a g e o u t p u t from t h e anemometer.

For i n t e r p r e t a t i o n t u r b u l e n c e measurements were d i v i d e d by t h e mean

v e l o c i t y a t t h e h e i g h t o f t h e measurement. T h i s r e s u l t i s t h e

t u r b u l e n c e i n t e n s i t y U / U . rms

3 . 2 Flow V i s u a l i z a t i o n

T t i s t s e f u l t o o b s e r v e f low p a t t e r n s a b o u t t h e c o l l e c t o r s t o

d e t e r m i n e how l o a d s a r e a p p l i e d t o t h e c o l l e c t o r s o r how an ups t ream

f e n c e d e f l e c t s f low o v e r t h e c o l l e c t o r s t o d e c r e a s e l o a d s . T i t an ium

o x i d e smoke was r e l e a s e d from s o u r c e s w i t h i n and upst ream of t h e a r r a y

f i e l d and a mot ion p i c t u r e r e c o r d was o b t a i n e d o f t h e f low p a t t e r n s .

T h i s nlovie shows t h e s e p a r a t i o n around a c o l l e c t o r , t h e t u r b u l e n t and

low v e l o c i t y f low w i t h i n t h e a r r a y f i e l d , and t h e e f f e c t of an upwind

f e n c e . An o u t l i n e of t h e c o n t e n t o f t h e movie i s g i v e n i n T a b l e I .

3 . 3 Force and Moment Medsurement

F o r c e s and moments a p p l i e d t o e a c h m e t r i c u n i t were measured w i t h a

s i x component I N C A s t r a i n gage b a l a n c e . Only f i v e o f t h e s i x components

(two f o r c e s and t h r e e moments) were measured. Each c o l l e c t o r was f i x e d

t o t h e b a l a n c e a s shown i n F i g u r e s 2 and 3 . The b a l a n c e was, i n t u r n ,

a t t a c h e d t o t h e t u r n t a b l e . I n t h i s way, f o r c e s and moments were

measured w i t h r e s p e c t t o a c o o r d i n a t e sys tem r e f e r r e d t o t h e c o l l e c t o r

and n o t t o t h e f low d i r e c t i o n .

The s t r a i n - g a g e b r i d g e s o f t h e f o r c e b a l a n c e were moni tored by

Honeywell Acudata 118 Gage C o n t r o l / A m p l i f i e r U n i t s , which p r o v i d e d

e x c i t a t i o n t o t h e b r i d g e and a m p l i f i e d t h e b r i d g e o u t p u t . The s i g n a l s

were f i l t e r e d by a 100 Hz low p a s s f i l t e r and a n p l i f i e d by a d . c .

a m p l i f i e r b e f o r e b e i n g p r o c e s s e d by t h e o n - l i n e d a t a a c q u i s i t i o n sys tem

d e s c r i b e d p r e v i o u s l y . Zeros and d a t a were recorded f o r 3 minutes w i t h a

100 Hz sample r a t e .

C a l i b r a t i o n o f t h e f o r c e b a l a n c e was performed b e f o r e and a f t e r t h e

s t u d y . F o r c e s and moments were a p p l i e d t o t h e b a l a n c e by dead w e i g h t s

hung from a k n i f e edge r i n g . The b a l a n c e had a l i n e a r r e s p o n s e on each

c h a n n e l . I n t e r a c t i o n s between c h a n n e l s were s m a l l and were accounted

f o r i n t h e c a l i b r a t i o n . A check o f t h e c a l i b r a t i o n was performed by

a p p l y i n g known l o a d s t o a c o l l e c t o r on t h e f o r c e b a l a n c e i n p l a c e i n

t h e wind t u n n e l . By u s i n g t h e c a l i b r a t i o n m a t r i x , t h e l o a d s were

r e c o v e r e d w i t h i n 3 p e r c e n t .

3 . 4 Force and Yoment C o e f f i c i e n t s

F o r c e s and moments measured on t h e c o l l e c t o r s were c o n v e r t e d i n t o

nondimensional c o e f f i c i e n t s t o p e r m i t e a s e o f scal . ing t o f u l l - s c a l e

f o r c e s and moments. The d e f i n i t i o n s f o r f o r c e and moment c o e f f i c i e n t s

f o l l o w . Moments were t r a n s f e r r e d from t h e b a l a n c e c e n t e r o f a c t i o n t o

e i t h e r t h e X p , Y p , Z a x e s a t t h e c o l l e c t o r p i v o t p o i n t o r t o t h e X B , P

Y B , 2 a x e s a t ground l e v e l . The l a t e r a l f o r c e c o e f f i c i e n t i s E

where Fx i s t h e l a t e r a l f o r c e , q i s t h e dynamic p r e s s u r e 0.5~u' i n t h e C

approach f low a t t h e h e i g h t HCL ( h e i g h t o f t h e c o l l e c t o r p i v o t ) above

t h e f l o o r , and S = LC i s a c h a r a c t e r i s t i c a r e a o f t h e c o l l e c t o r . The

i i f t f o r c e c o e f f i c i e n t i s --

where FL i s t h e l i f t f o r c e .

The r o l l i n g moment c o e f f i c i e n t i s t h e moment c o e f f i c i e n t a b o u t t h e

X a x i s P

where M A p i s t h e d i m e n s i o n a l moment a b o u t t h e Xp a x i s .

The yawing moment c o e f f i c i e n t i s t h e moment c o e f f i c i e n t a b o u t t h e Z

a x i s

where M ' i s t h e d i m e n s i o n a l moment a b o u t t h e Z a x i s . z

The p i t c h i n g moment c o e f f i c i e n t was c a l c u l a t e d f o r t h e momenL M ' Y p

a b o u t t h e Y p a x i s t h r o u g h t h e p i v o t p o i n t

o r f o r t h e moment M ' a b o u t t h e YB a x i s a t ground l e v e l Y B

Values o f L, C , S and s t a n d a r d h e i g h t HCL f o r e a c h c o i l e c t o r a r e

o u t l i n e d below:

COLLECTOR W B E R = 1 2 3 4

R i m Angle 9 0 O 40° 65 O 120°

A p e r t u r e C ( i n c h e s ) 2.80 2 . 9 2 2 . 9 4 3 . 0 0

Length L ( i n c h e s ) 10 .8 10 .8 10.8 1 0 . 8

S u r f a c e S ( i n c h e s 2 ) 30.24 3 1 . 5 4 3 1 . 7 5 32.16

S t a n d a r d H e i g h t o f C o l l e c t o r C e n t e r l i n e r e f . t o t h e f l o o r , HCL ( i n c h e s ) 2.10 1 .99 2 . 0 6 2.55

H C L / C = K I

F o c a l l e n g t h dF

C e n t e r of g r a v i t y p o s i t i o n d G 0.26 0 . 0 9 0 .16 0 . 5 2

F o r t e s t s i n which t h e h e i g h t HCL o f t h e c o l l e c t o r above t h e ground

was v a r i e d , qc f o r f o r c e and moment c o e f f i c i e n t c a l c u l a t i o n s was b a s e d

on t h e v e l o c i t y a t t h e a c t u a l HCL used f o r t h e t e s t .

P i t c h i n g moment c o e f f i c i e n t s w i t h r e s p e c t t o t h e c e n t e r o f g r a v i t y

G and t o t h e f o c a l p o i n t F o f t h e c o l l e c t o r t r o u g h were c a l c u l a t e d . The

n o t a t i o n s a r e r e f e r r e d t o F i g u r e 5b. The f o r c e a c t i n g on t h e c o l l e c t o r

w i t h t h e Xp - Z p p l a n e i s

11 ai = c o s CI

I,$ = s i n a

The p i t c h i n g moment a round t h e f o c a l p o i n t F w i l l be

= M I - lltll dF s i n ( a + 0 ) YP

= M' - dF ( s i n a c o s 0 + s i n 0 c o s a ) YP

= M ' - (FL dF cos 0 + Fx dF s i n 0 ) YP

Using t h e same deve lopment , t h e p i t c h i n g moment around G i s :

M ' = M ' - ( I L dG c o s 0 + Fx dG s i n 0) Y G Y p

i n t e rms o f c o e f f i c i e n t s :

4 . TEST RESULTS

4 . 1 S i n g l e C o l l e c t o r Loads

The f o u r d i f f e r e n t s h a p e s o f c o l l e c t o r s , model c o n f i g u r a t i o n s 1-4

w i t h v a r y i n g rim a n g l e , were t e s t e d a l o n e t o d e t e r m i n e t h e e f f e c t o f

c o l l e c t o r shape and t o e s t a b l i s h a b a s e l i n e f o r comparison w i t h a r r a y

f i e l d t e s t s . The f i r s t s t e p was t o d e t e r m i n e a t a h e i g h t HCL/C - 1 and

f o r approach az imuth $I = 0 , t h e p i t c h a n g l e emax f o r which t h e l i f t was

maxirnurn. These d a t a a r e shown i n F i g u r e 9 f o r t h e f o u r c o l l e c t o r s and

a r e t a b u l a t e d i n T a b l e 3 . A t t h i s v a l u e of Bmax and a t 0 = 0, t h e

h e i g h t of t h e c e n t e r l i n e o f e a c h c o l l e c t o r HCL was v a r i e d . These d a t a

a r e t a b u l a t e d i n T a b l e s 4 and 5 . S e l e c t e d p o r t i o n s o f t h e s e d a t a vhere

l o a d s were l a r g e r a r e p r e s e n t e d i n F i g u r e s 10 and 1 1 . The e f f e c t of

c o l l e c t o r h e i g h t above ground i s n o t d r a m a t i c i n c o e f f i c i e n t form w i t h

t h e most r a p i d changes i n c o e f f i c i e n t s o c c u r r i n g f o r s m a l l s p a c i n g from

t h e ground. P i t c h i n g moment a b o u t t h e ground l e v e l was most i n f l u e n c e d

by h e i g h t e f f e c t s a s would b e e x p e c t e d .

I n o r d e r t o d e t e r m i n e t h e e f f e c t s o f p i t c h a n g l e 0 and yaw a n g l e

$ on t h e l o a d s , a s t a n d a r d h e i g h t o f c o l l e c t o r was s e l e c t e d ( H C L / C =

0 . 7 5 , 0 . 6 8 , 0 . 7 0 and 0 .80 f o r c o l l e c t o r c o n f i g u r a t i o n s 1-4) and load

measurements were o b t a i n e d f o r a m a t r i x o f p i t c h and yaw a n g l e s . Yaw

a n g l e $ (approach wind d i r e c t i o n ) ranged from -15' t o +60° w h i l e p i t c h

a n g l e 9 ranged from -135O t o +180°. The r e s u l t s of t h e s e t e s t s a r e

l i s t e d i n Tab le 6 . S e l e c t e d p o r t i o n s o f t h e d a t a a r e p l o t t e d i n F i g u r e s

12 and 1 3 . S e v e r a l comments r e g a r d i n g t h e s e d a t a can be made. The

f o r c e c o e f f i c i e n t s a r e r e l a t i v e l y i n s e n s i t i s , t o c o l l e c t o r s h a p e f o r

+ = 0 ( F i g u r e 1 2 a , b ) . P i t c h i n g moment depends somewhat on c o l l e c t o r

shape ( F i g u r e 1 2 c , d ) , b u t t r e n d s t o i n c r e a s i n g o r d e c r e a s i n g l o a d w i t h

c u r v a t u r e of c o l l e c t o r a r e mixed. Yawing moments f o r v a r y i n g p i t c h a t

t) = 0 ( F i g u r e 12e) were n e a r z c r o a s e x p e c t e d . R o l l i n g moments f o r t h e

same c o n d i t i o n s ( F i g u r e 1 2 f ) s h o u l d be z e r o , b u t showed moment

c o e f f i c i e n t s from z e r o t o 0 . 5 dllpending on p i t c h a n g l e . T e s t l o a d i n g

d u r i n g b a l a n c e c a l i b r a t i o n d i d n o t show t h i s b e h a v i o r i n r o l l i n g

moment--the c a u s e o f t h e s e moments remains u a e x p l a i n e d . I t i s d o u b t f u l

t h a t t h e y a r i s e from s m a l l i m p e r f e c t i o n s i n model s h a p e . L a t e r a l and

l i f t f o r c e s became more dependent on c o l l e c t o r shape a t d i f f e r e n t yaw

a n g l e s ( F i g u r e s 1 3 a , b , e , f ) . An e x p l i c i t d i s p l a y o f t h e e f f e c t o f

rim a n g l e i s shown i n F i g u r e 1 4 .

The c o e f f i c i e n t s o b t a i n e d i n t h e c a s e o f one c o l l e c t o r o n l y coiild

be compared w i t h t h e d r a g c o e f f i c i e n t o f a f l a t p l a t e o r a c y l i n d e r .

I n Tab le 6a ( c o n f i g u r a t i o n 1 )

Fxp = 1 . 4 2 a t 0 = 0'

Fxp = 1 .06 a t 0 = 180'

The d r a g c o e f f i c i e n t f o r a f l a t p l a t e w i t h t h e l e n g t h g r e a t e r t h a n

t h e w i d t h i s

C = 1 . 2 D i f t h e p l a t e i s o f f i n i t e l e n g t h t o wid th r a t i o .

I n o u r c a s e , we have an i n t e r m e d i a t e c a s e where t h e boundary can

have some e f f e c t s .

A t o u r range o f Reynolds number, t h e d r a g on a n i n f i n i t e l e n g t h

c y l i n d e r i s a b o u t 1 . 2 f a r from t h e ground and d e c r e a s e s somewhat f o r

f i n i t e l e n g t h c y l i n d e r s t o a b o u t 0 . 8 f o r l e n g t h t o d i a m e t e r r a t i o s

s i m i l a r t o t h e L/C r a t i o o f t h e c o l l e c t o r used f o r t h i s s t u d y .

4 . 2 Array F i e l d Loads

C o n f i g u r a t i o n 5 was formed by a d d i n g two c o l l e c t o r s i d e n t i c a l i n

shape t o c o l l e c t o r 1 a s shown i n F i g u r e 6 . The gap s p a c i n g G between

t h e c e n t e r m e t r i c c o l l e c t o r and t h e two o u t e r c o l l e c t o r s was v a r i e d i n

c o n f i g u r a t i o n 5 t o f i n d t h e optimum s p a c i n g t o be used f o r l o a d

measurements on c o n f i g u r a t i o n s 5-9. With t h e s t a n d a r d l e g s shown i n

F i g u r e 4 , i t was n o t p o s s i b l e t o o b t a i n a gap s p a c i n g l e s s t h a n

G / C = 0 . 5 4 . A l t e r n a t e l e g s were c o n s t r u c t e d which a l lowed a s m a l l e r

G / C . Cardboard t a p e d t o t h i s m o d i f i e d c o l l e c t o r p e r m i t t e d gaps a s s m a l l

a s G / C = 0 . 0 6 t o be o b t a i n e d . These d a t a a r e shown i n T a b l e 7 . The

d a t a f o r b o t h s e t s o f l e g s a r e shown i n F i g u r e 15 . The d i s c o n t i n u i t y

between t h e two c o l l e c t o r t y p e s was p r o b a b l y due t o t h e i n f l u e n c e of t h e

modi f i ed l e g geometry . Very l i t t l e i n f l u e n c e o f gap s p a c i n g on l o a d s

can be o b s e r v e d . A gap w i d t h o f 0 .54 was s e l e c t e d f o r t h e s t a n d a r d gap

~ i d t h f o r t h e s u b s e q u e n t c o l l e c t i o n o f l o a d d a t a on c o n f i g u r a t i o n s 5 - 9 .

I n o r d e r t o e s t a b l i s h row s p a c i n g R f o r t h e c o l l e c t o r a r r a y f i e l d

s t u d i e s ( s e F i g u r e 6 ) , row s p a c i n g v a l u e s o f R / C = 2 . 0 , 2 . 5 , sad 3 . 0 i n

c o n f i g u r a t i o n 9 were used f o r s e l e c t e d d a t a a c q u i s i t i o n . These d a t a a r e

p r e s e n t e d i n T a b l e 8 . On t h e b a s i s of t h e s e d a t a i n c o n j u n c t i o n w i t h

e v a l u a t i o n by t h e sponsor o f s p a c e r e q u i r e d f o r c o l l e c t o r a c c e s s , a rox

s p a c i n g o f R J C = 2 .25 was s e l e c t e d f o r a l l f u r t h e r d a t a c o l l e c t i o n on

t h e a r r a y f i e l d . F i g u r e 16 shows s e l e c t e d d a t a from T a b l e 8 and d a t a

from f u r t h e r t e s t s on c o n f i g u r a t i o n 9 ( T a b l e 9 ) a t a row s p a c i n g of

R / C = 2 . 2 5 .

To d e t e r m i n e t h e o r i g i n o f t h e peak i n t h e l i f t c o e f f i c i e n t a t

R / C = 2 . 2 5 , €I = Omax shown i n F i g u r e 16b, a smoke v i s u a l i z a t i o n s t u d y

was conduc ted . The f low p a t t e r n s were h i g h l y v a r i a b l e w i t h t i m e ;

however t h e e s s e n t i a l c h a r a c t e r i s t i c s o f t h e f low c o u l d be observed

and a r e shown i n F i g u r e 16c . High v e l o c i t y f low was observed j u s t above

the c o l l e c t o r s f o r a l l t h r e e row s p a c i n g s , R / C = 2 . 0 , 2 . 2 5 , 2 . 5 . I n

a d d i t i o n , a t endency was observed f o r t h e h i g h v e l o c i t y f low t o remain

a t t a c h e d t o t h e curved r e a r s u r f a c e and t o b e p u l l e d downward

i n t e r m i t t e n t l y under t h e t r a i l i n g c o l l e c t o r . T h i s t endency was

observed t o be s t r o n g e r a t R / C = 2.25 t h a n f o r e i t h e r R / C = 2 . 0 o r

R / C = 2 . 5 . F o r R / C = 2 . 0 , l e s s q u a n t i t y o f h i g h v e l o c i t y f low was

observed t o p a s s under t h e edge o f t h e t r a i l i n g collector w h i l e f o r

R / C = 2 . 5 , t h e p e r c e n t a g e of t ime when h i g h v e l o c i t y f low p a s s e d under

t h e edge of t h e t r a i l i n g c o l l e c t o r was reduced a s compared t o t h e c a s e

a t R / C = 2 . 2 5 . T h i s may i n d i c a t e t h a t s h o r t - d u r a t i o n l i f t l o a d s a t

R / C = 2 . 5 cou ld be much h i g h e r t h a n t h e mean and comparable t o s h o r t -

d u r a t i o n l i f t l o a d s a t R / C = 2 . 2 5 . With t o r q u e t u b e s a t t a c h e d t o t h e

c o l l e c t o r s , no h i g h v e l o c i t y f low was p e r m i t t e d u n d e r n e a t h t h e

c o l l e c t o r s - - a d i s t i n c t improvement o v e r t h e c a s e w i t h o u t t o r q u e t u b e s .

A m a t r i x o f c o n d i t i o n s v a r y i n g wind az imuth $ and p i t c h a n g l e 0

were used t o o b t a i n l o a d s on c o n f i g u r a t i o n s 5-9 u s i n g a gap G / C = 0 . 5 4

and row s p a c i n g R / C = 2 . 2 5 . These d a t a a r e t a b u l a t e d i n Tab le 9 . While

o b t a i n i n g d a t a on t h e v a r i o u s c o n f i g u r a t i o n s , f e n c e s and berms of v a r i o u s

h e i g h t s were p l a c e d i n f r o n t o f t h e f i r s t row of t h e a r r a y a t v a r y i n g

d i s t a n c e s . T a b l e 10 shows t h e f e n c e h e i g h t s FH/C and p lacements FS/C,

c o l l e c t o r p i t c h a n g l e , c o l l e c t o r c o n f i g u r a t i o n and f o r c e and moment

d a t a . For some c a s e s , a 0 . 5 i n . t o r q u e t u b e was a t t a c h e d t o t h e back o f

t h e c o l l e c t o r t o d e t e r m i n e i t s i n f l u e n c e on t h e l o a d s . T a b l e 11 shows

c o n d i t i o n s f o r t h e s t u d y o f e f f e c t s o f an upwind berm. Excep t f o r Runs

300 and 3 0 2 , a l l d a t a on t h e i n f l u e n c e of f e n c e s o r berms were o b t a i n e d

v i t h $ = 0 . The i n f l u e n c e o f a r r a y f i e l d c o n f i g u r a t i o n and f e n c e s on

s e l e c t e d l o a d s i s shown i n F i g u r e 1 7 . These d a t a i n d i c a t e t h a t l o a d s

d r o p d r a m a t i c a l l y w i t h e i t h e r a s i n g l e c o l l e c t o r ups t ream o r w i t h a

f e n c e u p s t r e a m . The i n f l u e n c e o f f e n c e h e i g h t i s shown i n F i g u r e 1 7 d .

'The l o a d s w i t h a t o r q u e t u b e a t t a c h e d t o a s i n g l e c o l l e c t o r

( c o n f i g u r a t i o n 1 ) were d e t e r m i n e d f o r a r a n g e o f p i t c h a n g l e s a t i j = 0 .

These d a t a a r e shown i n T a b l e 1 2 . A compar ison of s i n g l e c o l l e c t u r

l o a d s w i t h and w i t h o u t t h e t o v 4 u e t u b e i s shown i n F i g u r e 18 . The

t o r q u e t u b e had some e f f e c t on t h e l o a d s . The t o r q u e t u b e on a s i n g l e

c o l l e c t o r d e c r e a s e d t h e l i f t a t 2 Omax and a t f3 = t 90' bllt i n c r e a s e d

s l i g h t l y t h e l a t e r a l f o r c e and t h e o v e r t u r n i n g moment M YB '

I n c r e a s e s

i n l a t e r a l f o r c e and o v e r t u r n i n g moment o c c u r r e d a t s m a l l e r v a l u e s o f

t h e c o e f f i c i e n t s . F u r t h e r m o r e , i t h a s been s e e n t h a t i n an a r r a y f i e ! d ,

t h e t o r q u e t u b e c r e a t e s a b l o c k a g e on t h e f i r s t row, p r o t e c t i n g t h e

f o l l o w i n g row. Then t h e f low between two c o l l e c t o r rows becomes

s t a g n a n t . The p r e s e n c e of t h e t o r q u e t u b e showed modera te e f f e c t s on

a r r a y f i e l d l o a d s ( T a b l e 1 0 ) .

Moments a b o u t t h e f o c a l p o i n t , F , and c e n t e r o f g r a v i t y , G ,

a r e compared w i t h moments a?-.~ut p o i n t s P and B i n T a b l e s 13 t o 2 1 .

Because v a r i a t i o n of t h e s e moments w i t h - ~ a r i o u s i n d e p e n d e n t v a r i a b l e s

( 0 , f o r example) i n c l u d e s o t h e r v a r i a b l e s a s w e l l ( h e i g h t o f p o i n t F o r

G ) , t h e s e d a t a were n o t p l o t t e d . I n many c a s e s , d i f f e r e n c e s i n moments

between P , F and G a r e s m a l l .

Because o f f low l e a k a g e i n t o t h e f o r c e b a l a n c e compartment d u r i n g

t h e i n i t i a l s t a g e s o f t e s t i n g , s m a l l e r r o r s were i n t r o d u c e d i n t o t h e

d a t a . T h i s problem was d i s c o v e r e d and c o r r e c t e d a f t e r d a t a on t h e f i r s t

f o u r c o n f i g u r a t i o n s were o b t a i n e d . A c o r r e c t i o n t o t h e d a t a was d e v i s e d

by r e r u n n i n g some d a t a on c o n f i g u r a t i o n s 1 and 4 and c a l c u l a t i n g

c o r r e c t i o n f a c t o r s . F i g u r e 19 g i v e s a n example o f t h e c o r r e c t i o n

sliowing t h e o r i g i n a l d a t a u n c o r r e c t e d , t h e o r i g i n a l d a t a w i t h t h e

c o r r e c t i o n f a c t o r a p p l i e d , and t h e r e r u n d a t a w i t h t h e l e a k a g e p r o b l e m

f i x e d . T h i s f a c t o r i s b a s e d o n f o r c e and moments e v a l u a t e d upon t h e

f o r c e b a l a n c e a c t i o n p o i n t w h i c h i s d i f f e r e n t f rom t h e p i v o t P . The

c o r r e c t i o n a p p e a r e d t o work well . A l l d a t a r e p o r t e d h e r e i n a r e

c o r r e c t e d where c o r r e c t i o n s were r e q u i r e d .

4 . 3 Smoke V i s u a l i z a t i o ? o f F e n c e E f f e c t --

The p r e v i o u s s e c t i o n showed t h e d r a m a t i c d e c r e a s e i n l o a d s which

o c c u r s when a n upwind c o l l e c t o r o r wind f e n c e i s i n c l u d e d . F i g u r e 20

shows f l o w v i s u a l i z a t i o n p h o t o g r a p h s wh ich h e l p t o e x p l a i n why t h i s

o c c u r s . F i g u r e 20a shows f l o w s w e e p i n g o n t o t h e l e a d c o l l e c t o r w i t h o u t

b e n e f i t o f a wind f e n c e . The c o l l e c t o r s e e s t h e f u l l e f f e c t o f t h e w i n d .

F i g u r e 20b shows t h e low v e l o c i t y , s e p a r a t e d f l o w r e g i m e b e h i n d t h e l e a d

c o l l e c t o r wh ich p r o v i d e s p r o t e c t i o n t o downst ream rows f rom t h e f u l l

f o r c e o f t h e w i n d . I n F i g u r e 2 0 c , a low f e n c e c f h e i g h t FH/C = 0 . 3 6 i s

shown. T h i s f e n c e d o e s n o t p r o v i d e s i g n i f i c a n t p r o t e c t i o n ; t h e wlnd

f l o w i s d e f l e c t e d upward somewhat , b u t s t i l l i m p i n g e s on t h e l e a d

c o l l e c t o r . F i g u r e 20d shows a p o r o u s f e n c e o f FH/C = 0 . 7 1 . Here t h e

low v e l o c i t y r e g i o n b e h i n d t h e f e n c e i s j u s t h i g h e r t h a n t h e c o l l e c t o r ,

e v e n t h o u g h t h e f e n c e h e i g h t i s s m a l l e r t h a n t h e c o l l e c t o r h e i g h t . A s

shown I n F i g u r e 1 7 d , ttris h e i g h t f e n c e p r o v i d e s a l r o s t maxlmum d e c r e a s e

i n l i f t o r l a t e r a l f o r c e f o r z e r o o r n e g a t i v e p i t c h a n g l e s . F o r p o s i t i v e

p l t r h a n g l e s , a s l i g h t l y h i g h e r f e n c e may b e r e q u i r e d t o p r o v i d e maximum

l o a d d e c r e a s e s , s i n c e t h e t o p o f t h e c o l ' e c t o r would b e a t a h i g h e r

e l e v a t i o n .

4 . 4 C a l c u l a t i o n o f F u l l - S c a l e Loads

The f o r c e and moment c o e f f i c i e n t s p r e s e n t e d i n t h i s r e p o r t can be

used t o d e t e r m i n e c o r r e s p o n d i n g f o r c e s and moments on f u l l - s c a l e

c o l l e c t o r s o f t h e same geometry and f i e l d a r r a y c o n f i g u r a t i o n i n an

open-coun t ry env i ronment . T h i s i s p o s s i b l e because t h e f o r c e and moment

c o e f f i c i e n t s a r e c o n s t a n t s a s l o n g a s t h e Reynolds number i s s u f f i c i e n t l y

h i g h ( s e e Chap te r 1 ) . F u l l - s c a l e f o r c e s and moments can be d e t e r m i n e d by

m u l t i p l y i n g t h e c o e f f i c i e n t s by v a l u e s o f q c , S and C a p p r o p r i a t e t o t h e

f u l l - s c a l e environment a s demons t ra ted below by an example .

C o n s i d e r a s i n g l e exposed c o l l e c t o r 6 f t wide and 2 2 . 5 f t l o n g (C =

6 f t , L = 2 2 . 5 f t ) a t s e a l e v e l exposed t o d q u a s i s t e a d y wind [J o f 3 0

30 mph a t 30 f t e l e v a t i o n i n a n open c o u n t r y environment ( 0 . 1 4 exponen t

power law p r o f i l e f o r mean v e l o c i t y ) . The shape of t h i s c o l l e c t o r i s

assumed t o be s i m i l a r t o c o n f i g u r a t i o n 1 ( 4 = 9 0 ° ) , w i t h a h e i g h t of t h e

c e n t e r l i n e such t h a t : H C L / C = 0 . 7 5 . I t i s d e s i r e d t o c a l c u l a t e t h e

l a t e r a l f o r c e F i n t h e X d i r e c t i o n and t h e p i t c h i n g moment M abou t t h c Y I'

r o t a t i 0 1 1 p o i n t of t h e c o l l e c t o r from t h e f o r c e c o e f f i c i e n t Fxp and moment

c o e f f i c i e n t M f o r z e r o ? i t c h a n g l e ( 0 = 0 ) and z e r o wind a n g l e ($ = 0 ) . Y p

From t h e e q u a t i o n s f o r f o r c e and moment c o e f f i c i e n t s ( s e c t i o n 3 . 4 )

From T a b l e 6 , f o r c o n f i g u r a t i o n 1 , wind az imuth = 0 , p i t c h a n g l e = 0 :

From t h e c o l l e c t o r s i z e :

L = 22.5 f t , C = 6 f t

S = LC = (22.5 f t ) ( 6 f t ) = 135 f t 2

HCL = 0.75 C = 0.75 (6 f t ) = 4.5 f t

To d e t e r m i n e q : C

2 9, = o'5pUHcL

2 (q, = 0.00256 UHCL i f UHCL i s in mph and qc is in pounds p e r s q u a r e

f o o t , s e e r e f . 8 )

Using a mean v e l o c i t y p r o f i l e w i t h a 0.14 power law,

2 Thus qc = 0.00256 (23.0) = 1.35 p s f .

The f o r c e s t h e n become

The moment arm o f the force from the p i v o t point is:

where \\?I\ = /fl

5 . CONCLUSIONS

Wind f o r c e s a c t i n g on p a r a b o l i c t r o u g h s o l a r c o l l e c t o r s were modeled

i n a b o u n d a r y - l a y e r wind t u n n e l i n which a t m o s p h e r i c winds were s i m u l a t e d

Wind l o a d s were measured on f o u r c o l l e c t o r s w i t h d i f f e r e n t rim a n g l e s .

Loads were a l s o o b t a i n e d on s e v e r a l a r r a y f i e l d c o n f i g u r a t i o n s i n c l u d i n g

wind f e n c e s .

The f o l l o w i n g c o n c l u s i o n s can be drawn:

1 . Maximum l i f t on a s i n g l e c o l l e c t o r o c c u r s f o r n e g a t i v e p i t c h a n g l e s

( c o l l e c t o r p o i n t e d downward) and o c c u r s a t d i f f e r e n t p i t c h a n g l e s

f o r d i f f e r e n t rim a n g l e s .

2. Maximum l a t e r a l f o r c e on a s i n g l e c o l l e c t o r o c c u r s f o r wind d i r e c t l y

i n t o a c o l l e c t o r a t z e r o p i t c h a n g l e .

3 . Maxil~ia i n p i t c h i n g moments on a s i n g l e c o l l e c t o r t ended t o o c c u r

a t more t h a n one p i t c h a n g l e .

4 . C o l l e c t o r s downwi3d o f o t h e r c o l l e c t o r s showed l a r g e d e c r e a s e s i n

wind l o a d .

5 . Wind l o a d s on a c o l l e c t o r i n a n a r r a y f i e l d d i r e c t l y exposed t o

winds d e c r e a s e d d r a m a t i c a l l y w i t h i n c l u s i o n o f a n a p p r o p r i a t e l y

d e s i g n e d f e n c e upwind.

6 . Gap s p a c i n g between c o l l e c t o r s i n a row d i d n o t a f f e c t c o l l e c t o r

l o a d s s i g n i f i c a n t l y .

7 . Row s p a c i n g i n a n a r r a y f i e l d had a s l i g h t i n f l u e n c e on c o l l e c t o r

l o a 6 s e s p e c i a l l y a t t h e p i t c h a n g l e which g i v e s maximum l i f t .

REFERENCES

1 . McBride, D . P . , S t a t i c F o r c e T e s t s on P a r a b o l i c Trough S o l a r C o l l e c t o r s , P r e t e s t I n f o r m a t i o n R e p o r t No. -- 395, Sand ia L a b o r a t o r i e s , Albuquerque, New Mexico.

2 . Cermak, J . E . , Aerodynamics o f B u i l d i n g s , Annual Review -- of F l u i d Mechanics , Vol . 8 , 1976.

3 . Cermak, J . E . , L a b o r a t o r y S i m u l a t i o n o f t h e Atmospher ic Boundary L a y e r , AIAA -- J l . , Vol. 9 , September 1971.

4 . Cermak, J . E . , A p p l i c a t i o n s o f F l u i d Mechanics t o Wind E n g i n e e r i n g , A Freeman S c h o l a r L e c t u r e , ASME -- J 1 . - of F l u i d s E n g i n e e r i n g , Vol . 9 7 , No. 1 , March 1975.

5 . Bearman, P . W . , Turbu lence E f f e c t s on B l u f f Body Mean Flow, T h i r d U.S . N a t i o n a l Conference -- on Wind E n g i n e e r i n g R e s e a r c h , p p . 265-272, 1978.

6 . Bearman, P , W . , An I n v e s t i g a t i o n o f t h e Forces on F l a t P l a t e s Normal t o a T u r b u l e n t Flow, J 1 . - - F l u i d Mechanics , Vol . 4 6 , p p . 177-198, 1971.

7 . Nakamura, Y . and Tonionari, Y . , The E f f e c t o f Turbu lence on t h e Drag of R e c t a n g u l a r P r i s m s , T r a n s a c t i o n s J a p a n S o c i e t y o f - A e r o n a u t i c a l and Space S c i e n c e , Vol. 19 , pp . 81-86, 1976. -

8 . American N a t i o n a l S t a n d a r d s I n s t i t u t e , American N a t i o n a l S t a n d a r d B u i l d i n g Code Requirements - f o r Minimum Design Loads - i n B u i l d i n g s and O t h e r S t r u c t u r e s . ANSI S t a n d a r d A58.1, 1 9 7 2 .

FIGURES

\ RIM ANGLE 4 W

P L A N E jA I

Figure 2a. Collector shapes for configurations 1-4

CONFIGURATION I RIM ANGLE = 90'

CONFIGURATION 2 RIM ANGLE = 40'

CONFIGURATION 3' RIM ANGLE 65

CONF!GURATION 4 RIM ANGLE = 120°

Figure 2b. Collector shapes for configurations 1-4.

Collector 4

Collector 1

F i g u r e 3 . Collector mounted on force balance.

L A T E R A L

I YAWING

MOMENT

ROLLING MOMENT P

Figure 5a. Coordinate system.

I G = CENTER OF GRAVITY

/ F = FOCAL POINT 2

Figure 5b. Coordinate system.

F i g u r e 7. Array field in the wind tunnel.

rY a > !- H

- LH913H

. 0 -- 1 2 0 . 0 -90.0 -60.0 -30.0

PITCH ANGLE ~ c ~ / c = 1 . 0 3

PITCH ANGLE HCL/C=. 99

F i g u r e 9a. Determination of 8 (configurations 1-4). max

CONF. # l 0 b, PSI - 0 a 0

- 0 - 0

- THETA-MAX = -65 DEG 0 -

u 0 1 1 I 0

CONF. 12 0 0 PSI - 0

- o A 0 -.I

THETA-MAX = -75 DEG - 0 -

I # I m

PSI - 0

Figure 9b. Determination of Om,, (configurations 1-4).

BOX = COLL 11 STAR = COLL #2 2.00

t- Z W H

BOX = COLL #3 STAR = COLL #4

Figu re 10a. Effect of height on coefficients at 0 = 0, 9 = 0 (.configurations 1-4).

BOX = COLL # l

. O O STAR = COLL 12

BOX = COLL 13 STAR = COLL #4

Figure lob . Effect of height on coefficients at 8 = 0, JI = 0 (configurations 1-4) .

* B O X = COLL f l STAR = W L L CZ

Figure 10c. Effect of height on coefficients at '3 = 0, $ = 0 [configurations 1-4) .

3 .00 m >- Z

2.00 0 0

Z 0 1C

0 1 . 0 0 - 2 H x 0 I- H a.

BOX = COLL 13 STAR = W L L #4

0 * - ..

* % * a a

1 * 1 I

3.00 M > IT

L L LL

2.00 0 0

cs, 1 . 0 0 - z H I 0 t- n a.

.OO .50 1 .OO 1.50 2 .00

.OO .50 1 .OO 1.50 2.00 HCL/C

BOX = COLL # l STAR = COLL #2

rlgure 11. Effec t of h e i g h t on l i f t a t emax, $ = O ( c o n f i g u r a t i o n s 1 - A ; .

BOX = COLL 13 STAR = COLL 1 4

1 .50- LL LL W 0 0

t H 1.00- -1

.50 .OO .50 1 .OO 1.50 2.00

* +O -

PITCH ANGLE

B O X = C O L L # l STAR = W L L #2

B O X = C O L L #3 STAR = C O L L f 4

PITCH ANGLE

Figure 12a. Variation of single collector loads with pitch angle for H C L / C = K I , $ = 0 (configurations 1-4).

-180.00 -90.00 .00 90.00 180.00

I * [ - - 0 * * * S tl

- 0 t tl 0 -

0 0 * * Ir

BOX = COLL # I 2.00

STAR = COLL 12

-90.00 .00 90.80

PITCH ANGLE

Figure 12b. Variation of single collector loads with pitch angle for HCL/C=KI, $ = 0 (configurations 1 - 4 1

B O X = COLL #3 STAR = COLL 1 4 2.00

LL LL W 0

t- G H - 1 . O O

-2 .00 -

*# - * t - * D

* Q 0 B *

- 0 + - * 0 *

* 0: - * 0 8 -

-180.00 -80.00 .OO 90.00 180.00

PITCH ANGLE

BOX = COLL +? 1 . O O

BOX = CULL # l STAR = COLL #2 1 . O O

00 * [I u

STAR = COLL +4

- . S O

PITCH ANGLE

Figure 12c. Variation of single co l l ec to r loads with pitch a n g l e f o r t!CL/C=KI, JI = 0 [configurations 1-4).

- 1 .OO 1 I 1

-188.00 -90.00 .00 90.00 180.00

PITCH ANGLE

BOX = COLL + 1 STAR = COLL #2

- . s d I t I 1

-180.00 -90.00 .OO 90.00 1 80 .

PITCH ANGLE

Figure 12e. Variation of single collector loads with pitch angle for H C L / C = K I , $ = 0 (configurations 1-4).

BOX = COLL #3 STAR = COLL +4

- . 2 5

-.50 -180.00 -90.00 .OO 90.00 180.00

PITCH ANGLE

- * T3

BOX = COLL * 1 STAR = COLL +2 1 .OO

PITCH ANGLE

BOX = COLL #3 STAR = COLL +4 1 .OO

PITCH ANGLE

Figure 12f. Variation of single collector loads with pitch angle for HCL/C=KI, $ = 0 (configurations 1-4).

THETA = 0 DEG, HCL/C = KI

YAW ANGLE

BOX = COLL + l STAR = WLL +2 2.80.

t- Z W H 0 1 . 5 0 - W LL LL W 0 0

W 1.00

0 Oi: 0 L

.50 05 W t- 6

-1 . 0 8

YAW ANGLE

0 1 0 * * * 0

BOX = COLL #3 STAR = COLL +4

Figure 13a. V a r i a t i o n . o f s i n g l e c o l l e c t o r loads wi th yaw a n g l e f o r H C L / C = K I , ( con f igu ra t ions 1-4) .

-30.00 . O O 30.00 60.00

2.00 t- Z W H 0 H 1 .50 - LL L L W 0 0

w 1 .00 - 0 E C> LL

-1 6. .50 01: W I-- Q: _I

- 1' l!!

. O O . 1 I

-30.00 .0a 30.08 60.00

BOX = COLL #I STAR = COLL #2

YAW ANGLE

F i g u r e 13b. Variation of single collector loads with yaw angle for HCL/C=KI, (configurations 1-4).

t- 1.50- G W 0 0

W 0 1.00- 141 0 G

-1 4 w .50 W t- Q: -1

-30.00 .OO 30.00 60.00 YAW ANGLE

- - * Ir *

0 0 - 0 3

-30.00 .00 30.00 60.00

THETA = 0 DEG, HCL/C = K I

YAW ANGLE

BOX = COLL # 1 STAR = W L L *2 1 .00 .

LL t. w .50 0 0

t- z W I:

. O O 0 x C3 z -.50 3r a >

- 1 . O O

YAW ANGLE

Figure 13c. Variation of singie collector loads with yaw angle for H C L / C = K I , (configurations 1-4) .

-30.00 . O O 30.00 60.00

1 . O O

LL L L w .50 0 0

t- Z W r . O O 0 I: C3

5 -.50 13 4 >

- 1 . O O

-30.80 .OO 30.00 60.00

- 1 1 -

THETA = 180 DEG, HCL/C = KI

BOX = C O L L # l STAR = COLL 12 1.00- 1

YAW ANGLE

BOX = C O L L #3 STAR = COLL 1 4

Figure 13d. Variation of single collector loads with yaw angle for HCL/C=KI , (configurations 1-4) .

t. tL w .50 a 0

t- z W s .OO 0 I:

a - .50

3 4 >-

- 1 .OO

-30.00 .OO 30.00 60.00

THETA = THETA-MAX, HCL/C = KI

YAW ANGLE

BOX = COLL # 1 STAR = COLL #2

BOX = COLL #3 STAR = COLL 1 4

LL LL W 0 o 1 .50 - t- LL H -1

1 . 0 0 J

YAW ANGLE

-30.08 .OO 30.00 60.00

0 * * - - * 0

Figure 13e. Variation of single col,lector loads w i t h yau angle for H C L / C = K I , (configurations 1-4).

THETA = - THETA-MAX, H C L K = KI

BOX = COLL # l STAR = COLL #2

Figure 13 f . V a r i a t i o n of s i n g l e c o l l e c t o r loads wi th yaw ang le f o r HCL/C=KI, ( c o n f i p ~ r a t i o n s 1 -4 ) .

t. -.50 t. W 0 0

I- LL H - 1 . O O -1

- 1 .50

BOX = COLL 13 STAR = COLL C4

a r + * I I

-38.00 .OO 3 0 . 0 0 6 0 . 0 0 YA'd ANGLE

LI -.50 t. W 0 0

I- L L H - 1 . O O -1

1 * Ir 0 - -

-1.50. I I >

-313.00 .OO 30.00 68.00 YAW ANGLE

YAW ANGLE

BOX = COLL #3 STAR = COLL 1 4 .50

YAW ANGLE Figure 13g. Variation of single collector loads with yaw

sngle for HCL/C=KI , [configurations 1-4).

THETA = - THETA-MAX, HCL/C = KI

BOX = COLL #3 .50

BOX = COLL * I STAR = COLL #2

STAR = COLL #4

.OO 30.00

YAW ANGLE

- . 25

- . S O a

Figure 13h. Variation of single ccllector loads with yaw angle for HCL/C=KI, (configurations 1 - 4 ) .

-30.00 .OO 30.00 60.00 YAW ANGLE

THETA = THETA-MAX, HCL/C = KI

BOX = COLL # 1 STAR = COLL $2 1 . @ O

. O O -30.00 .OO 30.00

YAW ANGLE

BOX = COLL #3 STAR = COLL #4 1 . @ O

. O O -30.00 .OO 30.00

YAW ANGLE Figure 13i. Variation of single collector loads with yaw

angle for H C L / C = K I , (configurations 1-4) .

- . 5 0 +

Figure 13j. Variation of single collector loads w i t h yaw angle for HCL/C=KI, (configurations 1-4) .

BOX = COLL 13 STAR = COLL #4

-30.00 .OO 30.00 60.00

YAW ANGLE

-30.00 .OO 30.00 60.00 YAW ANGLE

BOX = THETA = 0 DEG STAR = THETA = 180 DEG 2.00

I- Z W H 0 H 1.63 LL LL W 0 0

w 1.25 0 CY. 0 LL

--I a .88 OI W l- 4

COLLECTOR R I M ANGLE,PHI

Figu re 14a. Effect on the rim angle Q on collector loads.

THETA = THETA-MAX

COLLECTOR RIM ANGLE,PHI

P z 1 .75 - W n U n G

1 . 5 0 - W 0 U

t- L 1-i 1 . 2 5 - -1

THETA = - THETA-MAX

F i g u r e 14b. E f f e c t on t h e rim angle @ on collcctor loads .

1 I 1 - --

t- Z W H -.50 U n G G W 0 U

t- - 1 . O O G Y -1

- 1 .501

.00 45.00 90.00 135.00

_1 180.00

COLLECTOR R I M ANGLE,PHI

.OO 45.08 90.00 135.08

1 180.08

COLLECTOR RIH ANGLE,PHI

BOX: THETA = THETA-MAX STAR: THETA = - THETA-MAX

Figure 14c. Effect on the rim angle $ on collector loads.

.50 a. >- 2I

G G W .25 0 U

I- Z W .OO x 0 x C3

- . 2 5 H I. 0 I- H

- . s o *

BOX: THETA = 0 DEG, STAR: THETA = 180 DEG

.0Q 45.00 90.00 135.00 180.00

I . 5 0 *

.00 45.00 90.00 135.00 180.00

COLLECTOR RIM ANGLE,PHI

GAP WIDTH G/C

BOX: STANDARD LEGS, STAR: ALTERNATE LEGS

Figure 15a. Effec t of gap width on loads for configuration 5.

2 . 0 0 t- Z W H

1 . 7 5 - LL LL W 0 0

w 1.50 0 OI 0 'iL

1 .25 - a CY W t- a -I

- THETA = 0 DEG

0 0 0 " 0 0

0 - * 0 0 0 0 0 0 * * ****

Ir * * -

. O O 1 .OO 2 .00 3 . 0 0 4 . 0 9

BOX: STANDARD LEGS, STAR: ALTERNATE LEGS 2 . 5 0

1 . O O .08 1 .OO 2.00 3.00 4.08

GAP WIDTH, G / C

THETA = THETA-MAX

0 - O ~ ~ o o o " O n O o

**** * * * * * * - a

BOX: STANDARD LEGS, STAR: ALTERNATE LEGS

* THETA = THETA-MAX

- - * *

* a 0 * * 0 " 0 0

* * a 0 0 0 - 0

+ 1 1 I a

GAP WIDTH, G/C

F i g u r e 15b. Effect of gap width on loads for configuration 5.

1 I r 1

THETA = 0 DEG -

P S I = 0 DEG -

0 I 1 1

2.00 2.50 3.00 3 . 5 0 ROW SPACING R/C

Figu re 16a. E f f e c t o f row spac ing on c o l l e c t o r lozds ( c o n f i g u r a t i o n 9) .

THETA = -68 DEG

BOX: PSI - 8 DEG, DELTA: PSI - 15 DEG

ROW SPACING R/C

STAR: PSI - 30 DEG

ROU SPACING R/C

1 . 0 0 -

t- Z .75 W H 0 n G G W

.50 0 0

t- L L n .25 -1

Figure 16b. Effect of row spacing on collector loads (configuration 9) .

I 1 t 1

- 1 - -

1 .50 2.08 1 2.50 3.00

R/C = 2.0 0 = Bmax

Q = Qmax

R/C = 2.25 t3= Bmax WITH TORQUE TUBE

Figure 16c. E f f e c t of the row s p a c i n g upon t h e flow pattern.

BOX: THETA = 0 DEG, NO FENCE STAR: THETA = 180 DEG, NO FENCE

DELTA: THETA = 0 DEG, WITH FENCE ' 2 . 0 0

t-i 0 H 1.5a LL

CONFIGURATION #

Figure 1 7 a . Influence of ai-ray field configuration and fences on collector loads.

BOX: THETA = -68 DEG, NO FENCE DELTA: THETA = -60 DEG, WITH FENCE

2 .00 - -- -- 1

0 FH/C = 1.07, FS/C-= 3 . 0

I- z 1 . 5 0 - - W H U t-i b,

1 . 0 0 - - W 0 U

t- LL n .50 - -I

.0B I -.----- I

4.00 6.00 8.00 1 10.00

f- - 1 .50 G t-i -1 - 2 . 0 0

CONFIGURATION #

BOX: THETA = 60 DEG, NO FENCE

CONFIGURATION #

Figure 17b. In f luence of a r r a y f i e l d c o n f i g u r a t i o n and f ences on c o l l e c t o r l oads .

BOX: THETA = -60 DEG, NO FENCE DELTA: THETA = -60 DEG, WITH FENCE

CONFIGURATION ,3

BOX: THETA = 0 DEG, NO FENCE STAR: THETA = 180 DEG, NO FENCE

. - ' - - - - - ----I.-- --

m DELTA: THETA = 8 DEG, WITH FENCE 7 >- = 1.58 0

t- Z w FH/C = 1.07, FS/C = 3 . 0 z 1.00 0 r: * CI) z H

.50 f U t- H .OO A Ir a.

-4.00 6.00 8.00 10.00

CONFIGURATION #

Figure 17c. I l l f luence o f a r r a y f i e l d c o n f i g u r a t i o n and f ences on c o l l e c t o r l oads .

FENCE HEIGHT, FH/C

BOX: LATERAL FORCE THETA = 0 DEG PSI - 0 DEG

STAR: L IFT THETA = -60 DEG PSI 0 DEG 2 . 0 I 1 1

Figure 17d. Influence of array field configuration and fences on collector loads.

1 . 5 - t- z W Y 0 ti 1 . 0 - L G W 0 0

FS/C = 3.0 - CONFIGURATION 6

- - 0 * * Qr

0 0 - 1 I

. 0 .5 1.0 1.5

PITCH ANGLE

BOX: WITHOUT TORQUE TUBE

2.00 STAR: WITH TORQUE TUBE

PITCH ANGLE

t- Z W H 0

1 . 5 0 - L L tL W 0 0

I I I 3

PSI = 0 0 b

- * 0 d

0 II 0 * [

0 0 .)

- - 0 * so

F i g u r e 18a. Effect of torque tube on co l l ec to r 1 loads .

P S I = 0 - 0 p o t

w 1 . 0 0 - 0 rY o CL

-1 9 .50 OL W t- a --I

- 0 * *

8 o * 0 * 6 * - 0 -

- I I 1 _I

BOX: WITHOUT TOROUE TUBE STAR: WITH TOROUE TUBE . I I

I P S I - 0

PITCH ANGLE 1C

Figure 18b. Effect of torque tube on collector 1 loads.

a. > 21 .25 t- Z W z 0 z .OO tl) Z Y I: 0 - .25

- - 1 I .

PSI - 0 - t! O

d' * * 0 - * * *

O P 0 - t- Y L: " 0 a.

- . S 0 n 1

-180.00 -90.00 . O O 90.00 180.e0

PITCH ANGLE

BOX: ORIGINAL DATA, UNCORRECTED DELTA: ORIGINAL DATA, CORRECTED

2.0, STAR: CORRECT DATA, WITH NO LEAK

PITCH ANGLE

Figure 19. Effect of applying correction to collertor 1.

TABLES

Tab le 1. MOTION PICTURE SCENE GUIDE

Table 2 . VELOCITY AND TURBULENCE INTESS IT; PROF I L E

7 8 . 4 1 7 9 . 9 7 S O . 53

- -."t'?

r.l I.'.

rt ,.> -1 (., 5

F O Q T H C C Q U D I ~ P Q Q O Q C J L I C C O L L C C T O P E O ~ C C U U ~ n o n c u ~ C O C F F ~ C I E N T C F I L E - U ~ I I C : ~ D C L ~ I

C O N F I G U R R T I O N 1 i = ; a c L = l o S O :!;cHE; H E ! G H T E F F E C T A T T H E T A ~ A I . C D L L ~ I

F I T C ~ H C L ; ~ F X P F z F n x P n Y P n z P

O R 7 9 F O R T H E S R Y C ! 9 P R l ? Q 9 9 L ! C C O L L E C T P F F : > k ? C E 4 3 3 ? 3 ? E 9 T C ? E F F : C ! E ? i i 3 F ! L E - N A ~ E ' ~ K C H ~

C O N F i G U R A T I O N 2 C = 2 3 2 L = ; Q q 9 I H t H E S 3E!GH: Q' T H E T A ? l R % . C O L ? t 2

I P I T C H H C L : ~ F X P F Z P n x P n v P 3 z P P I T C H H C L / C F Z P F Z P n K P n Y P n z p

D B T A F O R T H E S A Y D I A P A R R B O L I C C O L L E C T O ~ F O R C E ~ N D ~ O ~ E N T C O E F F I C I E N T S F I L E - N A M E : H D C L ~ ~

C O N F I G U R A T I O N 3 c = 2 3 4 L = 1 0 8 0 I N C H E S H E I G H T E F F E C T R T T H E T A ~ ~ X , C O L L B ~

P I T C H H C L / C F X P F Z P M X P H S P H Z P P I T C H H C L / C F X P F Z P R K P U Y P f l Z P

P I T C H HcL;C F X P F 72 n x p n '; P n Z P P I T C H H C L / i F X P F Z P n % F n Y P n z P

T a b l e 7. LOADS FOR V A R I O U S GAP S P A C I N G S FOR C O N F I G U W T I O N 5

O G T G F O R T H E S f i N D I G P A R G B O L I C C O L L E C T @ : F O R C E 9 N D t l O t l E N T C O E F F I C I E t i i 5

C O N F I G U R I T I O N 5 C = 2 8 0 L : i t 8,) : t l C H E 5 G G P S T l l D t . G N E C O L L E C T O R R O U

D A T A F O R T H E S A H D I O P A R A S O ! : C C D L L E C T O P F O D C E I H D t l O V E N T C O E F F ! C I E N T S F I L E - H A H E : 9 D G R P 2

C O N F I G U R R T I O N 5 C = z a a L = 1 0 S O I N C H E S :;OP S T U D Y . O N E C D L L E C T O R R O U . ALTERNATE LEGS

P I T C H G / C F X P F Z P n x p n v p ~ Z P P : T C H G , / C F ; Q F Z P n x p U Y P n z p

1 ~ t ) i e \) .I. I . ~ , I I ) F ov ~ R R A ) I I I L I P , l c o b , t . l ( ; o n t ~ r 5 - 9 ;

DATA F O R THE S O H D l R P A R A B O L I C COLLECTOR F O R C E O N D H O ~ E N T C O E F F I C I E N T S F I L E - N A M E : ~ ~ B P O U

CCNF ! C U R A T I O N 8 C = 2 8 0 L = 1 0 80 I N C H E S F C " R COLLECTOR ROUS. R / C = 2 2 5

U I N D P I T C H F X P F ZP R X P R Y P n z P M I N D P I T C H F X P F Z P n x P R Y P n z p A L ' I B AHCLE A Z I B wNCCE

0 0 0 0 I 0 2 9 0 3 - 2 3 - 1 0 0 1 2 0 0 0 3 1 3 7 2 1 - 1 1 - 0 8 0 - 3 0 00 0 6 2 6 1 4 - 2 3 - 22 0 - 1 3 5 0 0 8 2 8 0 2 - 1 0 0 0 0 30 00 3 7 1 0 2 3 - 23 - 2 0 o 1 3 5 0 0 5 5 5 a 3 o - 35 - 0 8 0 - 4 5 00 2 1 4 1 1 0 - 2 5 - 1 7 0 1 8 0 O f 2 0 2 6 1 7 - 0 9 - 0 4 0 4 5 00 4 8 - 1 3 1 2 - 3 3 - 1 4 1 5 0 0 0 0 0 2 7 2 0 - 0 1 - 0 6 0 - 6 0 00 3 6 8 6 2 6 - 1 2 - 1 2 1 5 - i d 00 3 9 7 1 0 4 - 22 - 0 8 0 6 0 00 4 6 - 3 1 2 5 - 06 - 0 1 1 5 C Q 0 0 4 6 2 6 1 1 - 1 4 - 0 7 0 - 7 5 00 3 2 9 9 1 6 - 1 8 - 1 1 1 5 1 3 0 0 0 1 9 2 3 - 0 8

O3 - 1 4 - 0 9

0 7~ 00 4 7 - 2 1 0 7 - 25 - 0 8 3 0 1) 0 0 1 0 3 2 2 0 - 04 3 -90 00 15 6 8 0 8 - 1 3 - 01 3 0 -60 OG 2 9 6 9 2 6 - 0 0 - 1 3 0 90 00 2 9 1 4 13 - 10 - 06 3 0 C o 00 3 7 - 1 5 0 2 - 1 6 - 2 3 0 -120 0 1 4 3 8 2 4 - 2 6 - 10 30 1 8 0 00 2 0 3 3 2 4 - 1 5 - 06

D L T R F O R THE SRWDIR P A R I B O L l C CCLLECTOR F O R C E R H O ROREHT COL ; r IC IEM;S F I L E - N L B E : n D 9 R O Y

C O U F I C U R L T l O N 9 C s 2 8 0 L = 13 8 6 I N C H E S S I X COLLECTOR R O U S . R / C = 2 2 9

U I H D P I T C H F X P F Z P n x p ~ Y P N Z P UIND P I T C H F X P F z P H X P ~ Y P B Z P A Z I B A H C L E ~ 2 I t l H ~ G L E

0 0 00 2 0 2 6 1 7 - 35 - 1: 0 1 2 1 ~ 0 0 3 3 3 6 1 1 0 9 - 05 0 - 3 0 0 0 1 1 2 2 1 0 0 7 - 0 1 0 - 1 3 5 0 1 I 2 - 0 8 - 1 8 - 15 0 3 0 0 0 I 6 2 8 1 1 - 2 3 - 20 0 1 3 5 0 0 5 1 3 6 0 5 - 4 0 0 - 4 5 00 2 1 3 3 1 2 - 0 2 0 1 8 5 0 0 1 7 2 2 2 0 - 1 5 I :! 0 4 5 OC 3 2 1 2 0 8 - 4 1 1 i k 1 5 IJ 0 0 2 0 2 '3 2 1 - 3 8 - 2 > 0 -10 00 2 7 7 3 0 8 0 8 0 1 15 - 6 f i 0 0 18 5 e 1 9 1 2 - 9 1 0 6 0 03 2 9 - 0 3 1 9 - 2 0 - 1 6 15 6 0 0 0 3 4 - 0 2 9 6 - 2 9 - 29 0 -!? 0 0 2 3 7 2 0 s - "2 - 0 1 1 5 1 8 0 0 0 2 ! 3 1 2 9 - 20 - 14 o , ., 00 3 o - 0 3 2 2 - 1 1 - o a 3 0 (J 0 0 3 3 5 2 4 - 2 3 - 2; 0 - 9 0 0 0 2 4 4 6 - 0 3 - 3 4 - 1 4 3 0 - b 1 7 0 0 2 4 6 4 3 rj 3 5 - 0 $ 0 9 0 0 0 2 2 1 L 2 5 - 0 0 - 0 7 30 6 1 ~ 0 0 3 2 0 6 0 5 - 23 - 1 1 0 - 1 2 0 0 1 0 3 5 19 - 2 5 - 1 0 3 0 1 8 0 3 0 2 7 1 6 - 1 0 - 1 8

D A T R F O R T H S s a n o I n P n R a t i o L i : C O L L E C T O R F O R C E P N D n Q ' ! L d T C C E F F I C I E H T S

C O n F I G V R A T l O N 6 C = 2 8 0 L = l o S O I N C H E S TWO C O L L E C T O R F O U S , P / t = Z 2 5

Y l n D P I T C H F X P F Z P U X P M Y P N Z P A z I n . R W C L E

M ! N D P I T C H F X P FL'F N X P A Z I f l U N G L E

D A T h F O R T H E S A H D I A P A R A B O L I C C O L L E C T O R F O 2 C E A N D t lONE!4T C O E F F l C l E H T S F I L E - H A H E : H D 7 R O U

C O N F l C U R A T I O N 7 c a 2.a0 L = 1 6 . S O l H C H E S T H R E E C O i L E C 7 D E E O a S , R t ' C - 2 2 5

H I N D P I T C H F x P F Z P n x p n y P H Z P A Z I N . C\HCLE

U I N D P I T C H F X P F Z P n x P M Y P R Z P A 2 I H R N G L E

0~0000000000000300000~00c~ooooo

5 2:313

Table 10a. FENCE STUDY

SPACE BETWEEN FENCE THE FENCE AND CONF IGURATION

FH/ C FS/C ANGLE TOAQUE TUBE

2 12 0 V w i t h o u t 7 n

2 -60 V w i t h o u t

3 0 V w i t h o u t

3 - 6 0 \' withou t

3 0 VI w i t h o u t

2 78 3 . 7 1 a l t fence 3 0 V I w i t h o u t

2 79 0 . 7 1 alt fence 3 -60 VI w i t h o u t

2 80 1 . 0 7 3 0 VI w i t h o u t

I 2 84 0 . 3 6 3 0 VI w i t h

2 86 0 .36 3 -60 V I w i t h o u t

2 8 7 0 . 3 6 3 0 VI w i t h o u t

288 0 . 7 1 a l t fence 3 -60 V I w i t h

2 89 0 . 7 1 a l t fence 3 0 V I w i t h

2 9 0 1 . 0 7 3 120 VI w i t h

Table lob. FENCE STUDY (CONTINUED)

F i l e : MDFNCl

SPACE BETWEEN FENCE THE FENCE AND CONFIGURATION

HE I GHT F I R S T COLL. ROW P I T C H KITH OR KITHOUT RUN # FH/C F S / C ANGLE TORQUE TUBE

VI with

VI without

V I without

V I I withoat

VII without

IX without

I X without ( $ = 3 0 ° )

o n n r m - s

u 7. LLI -

Table lla. BERM STUDY

F i l e : MDBEKM

SPACE BETWEEN BERM THE BERM AND

HE I GHT F I R S T COLL. ROW PITCH RUN # FH/C F S / C ANGLE CONFIGURATION

r.1 - U.

CCC6OImFm6CIF

Table 14. EFFECT OF HEIGHT HCL ON SINGLE COLLECTOR PITCHING MOMENT COEFFICIENTS AT 8 = 0, $ = 0 (CONFIGURATIONS 1-4)

C O N F I G L I R A T I O N 1 F I L E ! I n n € : ~ D C D H I

C = 2 8 0 L = 1 0 8 0

H E I G H T E F F E C T I T T V E T R = O , C O L L R l

C P I I F I C I ! F A T I O N 2 F I L E NRRE : R O C O H 2

C = 2 3 2 L = 1 0 . 8 0

H E I G H T E F F E C T I T T H E T I = O , C O L L D Z

P l T C H t l C L / C i l Y P M Y 8 M Y F N Y C R I l C L E

P I T C H H C L i C ll Y P M Y 8 M Y F t t Y G H H C L E

C O t I F I G U R I T I O H 3 F I L E WORE: R D C D U 3

H E I G H T E F F E C T I T T H E T R = O , C O L L # 3

C O t I F l C U R O T I O N 4 F I L E N I H E : H D C D t l 4

C = 3 0 0 L = 1 0 8 0

H E ! C H T E F F E C T A T T H E T I = O . C O L L N 4

P I T C H H C L / C ~ Y P M Y 0 ( I l l C L E

P I T C H H C L i C U Y P ~ Y B M Y F H Y C r i M t L E

T a b l e 15. EFFECT OF HEIGHT HCL ON SINGLE COLLECTION PITCHING MOMENT COEFFICIENTS AT 0 -0 , $ = 0 (CONFIGURATIONS 1 - 4 )

C O H F I G U Q I I I O N 3 F I L E H A H E : t l D C L t l 3

C 3 2 - 4 L = 1 0 . 8 3

H E I G H T E ' F E C T O T I H E T O H I X . C O L L I 3

C O N F I C U R R T I O H 2 F I L E N o M 5 : M D C L n 2

C = 2 9 2 L = 1 0 8 0

H E I G H T E F F E C T I T T H E T R t l A X , C O L L 1 2

P I T C H H C L / C H Y P ~ Y B H Y F n v t n ~ l 2 L E

P I T C H H C L / C M Y P ~ Y B n Y F M Y c A H C L E

T a b l e 16a. MATRIX O F S I N G L E COLLECTOR PITC. I ING MOMENT COEFFICIENTS AT HCL/C = KI (COIIFIGIJRATION 1)

C U I I F I C ~ J R R T I O

C = 2 8 0

O W E S I N G L E C

1 5 ( J 113 1 : -6: f ~ 0 15 65 00 1 5 1811 f)h

3 0 2 00 .?O - 1 , 00 3 0 15 00 3 0 - 2 9 00 3 0 3 0 90 3 0 - 4 5 . 0 0 3 0 4 5 00 3 J - 6 (J ( J (1

3 0 60 fJ0 - 6 5 0 6

3 0 45 00 3 0 - , 5 1, 0 3 0 7 5 90 10 - 7 3 '.'O

9 0 00 :: -135 t.10 3:' 1 3 5 0 0 3 0 IEO 00 1 5 0 00 4 5 - 6 5 00 4 5 6 5 00 4 5 10'100 6 0 0 00 60 - 1 5 0 0 4 (I 1 5 00 bc' - 3 U U o 6 0 30 00 6 0 - 4 5 00 c c 4 5 00 6 0 -60 o0

'J 6 0 00

tI I ;I LE N A U F : M D

L = 10 8 0

O L L E C T O R , R I f l A N G L E

T a b l e 16b . MATRIX O F S I N G L E COLLECTOR PITCHING MOMENT C O E F F I C I E N T S AT HCL/C = K~ (CONFIGURATION 2)

"able 16c. MATRIX 9F SINGLE COLLECTOR PITCHING MOMENT COEFFICIENTS AT HCL/C = KI (CONFIGURATION 3)

C O t I F I t V R A T I O N 3 F I L E N A M E : R D C O L 3

C = 2 9 4 L = 1 0 6 0

OtlE S I N G L E C O L C E t T O R , R l I I f l t I C L E = 6 S

0 0 0 - 1 5 . 0 0

1 5 . 0 0 - 3 0 0 0 3 u 0 0

- 4 5 . 0 0 4 5 . ' . ' C

-b"O h u 6 0

- 7 0 . 0 0 7 0 rjo

- 7 5 0 0 7 5 , 00

- 9 3 0 0 ' 3 1 ~ . 00

- 1 3 5 . 0 0 1 3 S . 0 0 1 e o . 0 0

11 rj 0 - 7 0 0 0

: 0 . 0 0 1 0 3 9 0

0 0 0 - 7 0 0 0

7 0 u o 1 0 0 0 0

Table 1Gd. MATRIX OF SINGLE COLLECTOR PITCHING MOMENT COZFFICIENTS AT HCL/C = K I (CONFIGURATION 4)

C O I I T I C l J R f i T I O I I 4 FILE N O M E : n D C O L 4

C = 3 v O L = 1 0 . 8 0

O N E S l ! I C L E COLLECTOR , R I 14 AWGLE=120

I I i t I D P I T C H f l y P h Y B It Y f f l y C k ; r n A N G L E

Table 17. PITCHING MOMENT COEFFICIENTS FOR VARIOUS GAP SPACINGS (CONFIGURATION 5)

C @ t I F l C l ! R ~ T I O W 5 F I L E H R H E : t f D l P 0 0

r; = 2 817 L = 1 0 8 0

C ~ F S T n n Y . U I I E C O L L E C T O R R O N

0 C'. l J il J 0 0 $1

-6 5 - 6 5 . L 5 . 5 5 - 6 5 - 6 5

C O N F l t L l R R T 1 O N 5 F l L E H R R E : f l D S O P 2

r: = 2 8 0 L . 1 0 . 8 0

C A P S T U D Y t 6 L T E R H 6 T E L E G S

Table 18. PITCHING MOMENT COEFFICIENTS FOR ESTABLISHMENT OF ROW SPACING R (CONFIGURATION 9)

C O t I F l C l ~ P A T I O N f F I L E H R f l E : R D R Z . O

I I I t i D P I T C H ! l Y P m y 8 R Y F ii; I n f i t l r ;LE

R O V S T U D Y , R O U S P R C I N C - 2 5 + t

Y I H O P I T C H R Y P R Y R n Y F n :. c k Z l M P N C L E

C O t I T I C l ~ R ~ T I O N 9 F I L E t l f l f l E ~ M D R 3 . 0

C = 2 0 0 L = 10 80

R D U S T U D Y , R O U S P A C I M C * 3 O * C

U I N D P l T C H H Y P R Y 9 H Y F M Y C k z l n 9 N C L E

Table 19a. PITCHING MOMENT COEFFICIENTS FOR W Y FIELDS (CONFIGURATION 5)

C D l t F I C U R R T I O N 5 F I L E H h H E IMDED I T

C L 2 8 0 L = 1 0 . 8 0

OHE ROY OF THREE C O L L E C T O R S t C / C = . 5 3 6

d I U D P I T C H M Y P M Y 8 M Y F M Y C A Z I M ANGLE

Table 1 9 b . PITCHING MOMENT COEFFICIENTS FOR ARRAY FIELDS (CONFIGURATIONS 6-7)

C O t I F l C f I P Q T I O N 6 F I L E H R M E t H D 6 R O U

c = 2 1 0 L = 1 0 e o T U D C O L L E C T O R R O U S * R / C ' 2 29

C O I I F I t l J R I 2 T I O H 7 F I L E M A R E : R D 7 Q O U

C = 2 80 L = 10 8 0

T H E E E C O L L E L T O R R O U S , R / C = Z 2 5

Table 19c. PITCHING MOMENT COEFFICIENTS FOR ARRAY FIELDS (CONFIGURATIONS 8-9)

C O H F l G U R f l T I O H 8 F I L E N R N E : f l D 8 R O Y

C e 2 8 0 L = 1 0 . 8 0

F O U R C O L L E C T O R R O U S t R / C a 2 . 2 5

C O t l F l G U R R T I O H 9 F I L E Ht2ME I M D S R O U

C = 2 8 0 L = 1 0 . 8 0

$1): C O L L E C T O R R O U S , R / C . 2 2 5

W I N D P I T C H f l Y P M Y @ R Y F U Y G A Z I t l U N C L E

Table 20. E F F E C T S OF FENCES AND BERMS ON ARRAY F I E L D S , PITCHISG MOMENT C O E F F ICI ENTS

F I L E H f i R E : P l D F H C E

C = 2 9 0 L = 1 0 . 8 0

F E t I C E S T U D Y

RI! tI 4 H Y P H Y B H Y F ll Y C

F l L E N i I N E : R D F H C 1

C = 2 . 8 0 L a 1 0 . 8 0

F E N C E S T U D Y

FILE H f i t l E : f l D B E R R

B E f i l 4 S T U D Y

Table 21. PITCHING MOMENT COEFFICIENTS WITH A TORQUE TUBE (CONFIGURATION 1)

C P I I F I C L ! f : A T I O N 1 F I L E N A M E : f l D T O R l

r: = 2 . 8 9 L - 1 0 . 8 9

' P F ' I V E :UPE E F F E C T S , C D L L # l Q L O t l E

V I t I D P I T C H M t 'P H Y E! If YF /!'I G 2 I rlt4GLF:

DISTRIBUTION:

S o l a r T o t a l E n e r g y P r o g r a m Amcr i c a n T e c h n o l o g i c a l U n i v e r s i t y P. 0. Box 1 4 1 6 K i l l e e n , TX 7 6 5 4 1 A t t n : B. L. Hale

A r q o n n e N a t i o n a l L a b o r a t o r y ( 3 ) 3 7 0 0 S o u t h C a s s A v e n u e A r g o n n e , I L 6 0 4 3 9 A t t n : W . W. S c h e r t z

R. W i n s t o n

D r . A . E a l a k r i s h n a n A c r o s ; > a c e S y s t e m s D i v i s i o n : \ c u ~ - c x C o r p o r a t i o n 4 8 5 C l y d e A v e n u e M o u n t a l n V i e w , CA 9 4 0 4 2

lie>-inan Bank Bl ( !c . 5 3 6 , Rm. 3 4 0 J e t P r o p u l s i o n L a b o r a t o r y 1 3 3 N o r t h A l t a d e n a D r i v e P a s a d e n a , CA 9 1 1 0 3

2 c i t t e 1 1 e ? l e m o r l a l I n s t l t u t e P a c l f l c N o r t h w e s t L a b o r a t o r y P . 0. Box 9 9 9 R l c k l a n d , WA 9 9 3 5 2 A t t n : K . D r u m h e l l e r

J o e B o g e t i c h I I \ . p t ' r i o n , I n c . 7 2 1 4 V a l t e c C o u r t B o u l d e r , CO 8 0 3 0 1

L y n n B r o c k k i a r r l s o n R a d i a t o r D i v i s i o n G e n e r a l Yotors C o r p o r a t i o n L o c k ~ 3 r t , NY 1 4 0 9 4

B r o o k h a v e n N a t i o n a l L a b o r a t o r y A s s o c i a t e d U n i v e r s i t i e s , I n c . U p t o n , L I , N Y 1 1 9 7 3

G r c r ] B r u c k e r S u n t e c S y s t e m s 2 1 0 1 ; ; ' adda le D r i v e S t . P a u l , EI:J 5 5 1 1 9

D r . J a c k C h e r n e E n e r g y S y s t e m s G r o u p TRW, I n c . One S p a c e P a r k R e d o n d o B e a c h , CA 9 0 2 7 8

J . P h i l i p Dechob. C o l u m b i a G a s S e r v i c e S 1 7 s t e m 1 6 0 0 D u b l i n Road C o l u m b u s , OIi 4 3 2 1 5

D a n n y D e f f e n k a u c h S o u t h w e s t R e s e a r c h I n s t i t u t e 6 2 2 0 C u l e b r a R o a d S a n A n t o n i o , TX 7 8 2 8 4

H a n s D e h n e A c u r e x Corporation 4 8 5 C l y d e A v e n u e M o u n t a l n V i e w , CA 3 4 0 4 2

N a r k D i l e l l o G e n e r a l E l e c t r i c Company7 (Rn. ? On56 ) P . 0 . Box 8 6 6 1 P h i l a d e l p h i a , PA 1 3 1 0 1

V i n c e D ~ I ) ~ . , . . A B l d q . 11 G e n e r a l E l e c t l - i c Conpan:: P . 0 . Box 8 6 6 6 P h i l a d e l p h i a , PA 1 9 1 0 1

EPRI 3 4 1 2 H i l l v i e w A v e n u e P a l o A l t o , CA 9 4 3 0 3 A t t r . : J . E . B i a g e r

E d i s o n E l e c t r i c I n s t i t u t e 9 0 P a r k A v e n u e New Y o r k , N Y l O O l G A t t n : L . 0 . E l s a e s s e r ,

Di rec tor o f R e s e a r c h

B e r n a r d E l d r i d a e J a c o b s - D e l S o l a r S l . s t e n s , I n c . 2 5 1 S o u t h L a k e A v e n u e P a s a d e n a , CA 9 1 1 0 1

E n e r g y I n s t i t u t e 1 7 0 0 L a s L o m a s A l b u q u e r q u e , NM 8 7 1 3 1 A t t n : J . D r i t t

A l b e r t F o n a T h e BDM C o r p o r a t i o n 2 6 0 0 Yale B o u l e v a r d SE A l b u q u e r q u e , NM 8 7 1 0 6

Mark G e l d e r l o o s H . A . W i l l i a m s a n d A s s o c i a t e s 9 8 0 W . H e n d e r s o n C o l u m b u s , OH 4 3 2 2 0

C e o r n i a I n s t i t u t e o f T e c h n o l o g y F i t l a n t a , GA 3 0 3 3 2 A t - t n : J . D . I q a l t o n

G e o r g i a P o w e r Company 2 7 0 P e a c h t r e e P . 0 . Box 4 5 4 5 , T i t l a n t & , G A 3 0 3 0 2 A t t r , : it!. H e n s l e y

V i c e P r e s i d e n t E c o n o m i c s < : e r v i c e s

C e o r q c G o r a n s o n V i k ~ n q S o l a r S ~ ~ s t e m s , I n c . 3 4 6 7 O c c a n V l c w B l v d . S l e n d a l e , CA 9 1 2 0 9

S h e l l e y G o r d o n C h l l t o n E n u i n e e r i n g 1 5 7 0 L i n d a Way S p a r k s , NV 8 9 5 1 2

D r . G o p a l G u p t a T o s t e r \ < i h e e l e r D e l . r e l o p n e n t C o r ? . 1 2 P e a c h T r e e H i l l Road I , l 7 v 1 n c ; s t o n , N J 0 7 0 3 3

( ; i 1 ki~----cra D e l M a n u f a c t u r i n g Company 9 0 5 M o n t e r e y P a s s Road M o n t e r e y P a r k , CA 9 1 7 5 4

G u s f i u t c h l n s o n S o l a r F : ~ n c t l c s , I n c . 8 1 2 0 C h a n c e l l o r Row D a l i a s , TX 7 5 2 4 7

Yr. L e o n a r d J a f f e S t o p 5 0 7 - 2 2 8 J c t P r o p u l s i o n L a b o r a t o r y 4 8 0 0 Oak G r o v e D r i v e P a s a d e n a , CA 9 1 1 0 3

, J e t P r o p u l s i o n L a b o r a t o r y 4 8 0 0 Oak G r o v e D r i v e I ' ; ~ s a d c n ; l , CA 3 1 1 0 3 A t - t n : V . C . T r u s c e l l o

L a w r c n c c B e r k e l e y L a b o r a t o r y I , n i v c r s ~ t y - o f California

i X c r k e l c \ . , CA 9 4 7 2 0 A t t n : iLi. W a l l i q

1 , a w r c n c e L l v e r r n o r e L a b o r a t o r y I ' n i \ ~ e r s l t y o f C a l l f o r n l a P . 0 . Box 8C8 L l v c r r n o r e , CA 9 4 5 0 0 A t t n : W. C . C l c k l n s o n

I . E a r l L e w i s W e s t e r x D e c r e l o p a e n t L a b o r 2 t o : - i c s

D i v i s i o n F o r d A e r o s p a c e G C o n ~ ~ u n ic?t if-':! :;

C o r p o r a t i o ; ~ 3 4 3 9 F a b i a n \\;a:.. P a l o A l t o , CA 9 4 3 0 3

L o s A l a m o s S c i e n t i f i c i , ~ b o : - ~ t . o r ~ ~ ~ ( ' I

L o s A l a ~ ; l o s , :::: 8 7 5 4 5 A t t n : J . D . B a l c o r n b

D . D. Ban:,:ston D. F . G r i r , n e r

James ?iag i n n i s T e a m , I n c . 1 4 0 I./. Broadb:ai9 = 4 1 T u c s o n , AZ 8 5 7 0 1

NASA-Lewis R e s e a r c h Center C l e v e l a n d , OH 4 4 1 3 5 A t t n : R . r !yland

Ne!? ?lexica S t a t e Z;;it:ersi' i :' S o l a r E n e r q y D c > l r t n e n t . L a s C r u c e s , 3'1 38991

, . Oak Ridc je N a t l o n a l L a b o r a t o r y . i - 1

P . 0 . Box Y Oak R i d c c , TS 3 7 8 3 0 A t t n : J . R . R l ~ \ ~ l n s

C . V. C h e s t e r J . ; o h n s o n S . I . K a p l a n

O f f i c e of Techno1on: - Assess~ec: U. S . C o n q r s s s L J a s h i n g t o n , D. C . 2 0 5 1 6 A t t n : D r . F. K e l l : ;

PRC E n e r q l - A n a l y s i s C c . 7 6 0 0 O l d S p r i n a H o u s e R d . M c L e a n , VA 2 7 1 0 2 A t t n : K . T . C h e r i a n

S o l a r E n e r g y R e s e a r c h I n s t l t u t c (4) 1 5 3 6 C o l e BL7:d. G o l d e n , CO 8 0 4 0 1 A t t n : C . J . B l s h o u

K . Bro!:'n B . i. R u t l e r Y . D . C o t l t n n Z . F l n c c : o l d B . P . G u p t a D. K e a r n f ~ y r . 1 : r e l t h A . R a b l J . T h o r n t o n L . M r l q H . L u a f f e n h u r q c r L i b r a r y ( 2 )

[ Ioward S t e e l e S t o p 5 0 7 - 2 3 9 J e t P r o p u l s i o n L a b o r a t o r y 4 8 0 0 Oak G r o v e D r i l . r e P a s a d e n a , CA 9 1 1 0 3

U . S . D e p a r t m e n t o f E n e r q l r ( 6 ) A l b u q u e r q u e O p e r a t i o n s O f f i c e P . 0. Box 5 4 0 0 A l b u q u e r q u e , NM 8 7 1 8 5 A t t n : D . L . K r e n z

D . G r a v e s G . N . P a p p a s C . B. Q u i n n J . R . R o d e r J . W e l s i g e r

L . S . D e p a r t m e n t o f E n e r g y D l v l s ~ o n o f E n e r g y S t o r a a e

S y r ; t e m s k i a s h l n g t o n , D . C . 2 0 5 4 5 A t t n : J . C a h l m e r

t i . S . D e p a r t m e n t o f E n e r g y (6) D l v l s l o n of S o l a r T h c r m a l

Cncr( ; l7 S y s t e m s l i l a s h l n q t o n , D . C . 2 0 5 4 5 :it t ! ~ : R . fi. A n n a n

G . W . B r a u n >I. U. G u t s t e i n J . E. K a n n e l s

. 17 1 1 e r ,J . D o l l a r d

C. S . D e p a r t m e n t o f E n e r g y Los A n q c l c s O p c r a t l o n s O f f ~ c e 350 S . ' C l q c u r o a S t r e e t , Suite 2 8 5 L o s t \ n g e l e s , CA 9 0 0 7 1 A t t n : F r e d G l a s k i

U . S . D e ? a r t m e n t o f E n e r g y S a n r r a n c i s c o O p e r a t i o n s O f f i c e 1 3 3 3 E o r a d w a y , W e 1 i s F a r q o B l d g . O a k l a n d , C4 9 4 6 1 2 A t t n : R . W . Hughc!?

I l n l v p r s i t y o f Dcl a w a r e r n s t 1 t u t e of F :ners l9 C o n v e r s i o n N e w a r k , Dl: 1 3 7 1 1 A t t n : K . W . BDer

I j n l v e r s i t y o f New M e x i c o ( 2 ) D e p a r t m e n t o f M e c h a n i c a l Eng . Alt ~ q u c r q u e , NM 8 7 1 1 3 A t t n : W. A . C r o s s

M . F:. W i l d e n

R o b e r t W . b l e a v e r J e t P r o p u l s i o n L a b o r a t o r y 4 8 0 0 Oak G r o v e D r i v e P a s a d e n a , C A 3 1 1 0 3

L e e E . W i l s o n E n e r g e t i c s C o r p o r a t i o n 8 3 3 E . A r a p a h o Road S u i t e 2 0 2 R i c h a r d s o n , TX 7 5 0 8 1

S t a n Y o u n g b l o o d A c u r e x C o r p o r a t i o n 4 8 5 C l y d e A v e n u e N o u n t a i n V i e w , CA 9 4 0 4 2

C. W i n t e r C. N. G a b r i e l S . B . M a r t i n R . S . P inkharn G . M . Heck A . N a r a t h J . H . S c o t t G . E . B r a n d v o l d B . W. P l a r s h a l l R. P . S t r o m b e r s R . H . B r a a s c h n . G . S c h u e l e r H . N . P o s t V . L . Dugan J . V . O t t s J . F . B a n a s R . L . C h a m p l o n S . T h u n b o r g W . P. S c h i m r n e l J . A . L e o n a r d D . E . R a n d a l l ( 2 5 ) K . K a l l y J . K . G a l t F. L . Vook 0 . E . J o n e s H . C. H a r d e e R . C. R e u t e r , J r . D. E. S h u s t e r A . A . L i e b e r M . M. Newsom R . C. Maydew H. I?. V a u g h n C. K . P e t e r s o n S . McAlees, J r . D . D . McBr l d e ( 1 0 ) R . E . T a t e Pi . R . B a r t o n J . K . C o l e G . J . S i n ~ m o n s R . S . C l a a s s e n M . J . D a v i s H . J . S a x t o n F . P. G e r s t l e E . A . A a s W . G . W i l s o n T . L . W e r n e r ( 4 ) W . L. G a r n e r ( 3 ) F o r DOE/TIC ( U n l i m i t e d R e l e a s e )

Mean Wind Forces on Parabolic Trough Solar...

Documents

Transcript of Mean Wind Forces on Parabolic Trough Solar...

Jorunal article. Parabolic solar trough

Simulation and Performance Evaluation of Parabolic Trough ...

closed parabolic trough

Parabolic Trough Workshop - InfoHouseinfohouse.p2ric.org/ref/18/17996.pdfeffective Parabolic Trough Collector qObjective Design and prototyping of an advanced cost effective Parabolic

Parabolic Trough Solar Plants

SOLAR PARABOLIC TROUGH - US Department of Energy · PDF fileSOLAR PARABOLIC TROUGH ... Parabolic trough technology is currently the most proven solar thermal electric ... solar electric

A closed parabolic trough solar collector · A closed parabolic trough solar collector Gang Xiao 30th October 2007 Parabolic trough[1] is the most mature technology for large scale

SAM Parabolic Trough Updates

Durability Testing of Parabolic Trough Receivers ...

Optical Qualification of Parabolic Trough Receivers with · PDF fileOptical Qualification of Parabolic Trough ... Motivation of DLR to do qualification of parabolic trough receivers

Parabolic Trough

Techno-economical evaluation of parabolic trough ...

Parabolic-Trough Solar Water Heating

New Trends in Designing Parabolic trough Solar ... · 2. Description of parabolic-trough solar concentrators The parabolic-trough solar concentrators are one of the basic elements

Advanced Low-Cost Receiver for Parabolic Trough … AM...Advanced Low-Cost Receiver for Parabolic Trough Solar Power ... Parabolic Trough Solar Field –Cost Drivers ... Collector

PARABOLIC TROUGH SOLAR CONCENTRATOR

CSP Parabolic trough

Chapter 5 Parabolic Trough Technology

IEA CSP Workshop · IEA CSP Workshop: Frank Lenzen, 03.03.2014 ... Parabolic trough collector Linear Fresnel collector ... Investigated parabolic trough, ...

Parabolic Trough Design