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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
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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
Table
L I S T OF T A B L E S
Page
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
1
2
3
4
5
6 a
6b
7
8
9
10
Page
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
HCL
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
3
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
M' "
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
I
X
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
15
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.
ANGLE
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.
(I) W
J
H
IL 0
1 f
I
1 I
a
8
6)
8
C9 6)
CP 8
C\1 a
03 (D
f
N
CP
- -
per 1
I D
W~
ON
-
IH9
11
3H
I
(I) W
-I H
LL 0
rY a > !- H
0
0
-I W
> z Q
W
;t 8
8
8
6)
6)
(P
6)
(V
c3 03
(D
v
(V
a
- -
po
r 1
I O
W,J
ON
- LH913H
I
. 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
1 I
0 0
CONF. # l 0 b, PSI - 0 a 0
- 0 - 0
- 0 -
0
- THETA-MAX = -65 DEG 0 -
u 0 1 1 I 0
8 I I
CONF. 12 0 0 PSI - 0
- o A 0 -.I
cl
- 0
0
- b
THETA-MAX = -75 DEG - 0 -
I # I m
PSI - 0
PITCH ANGLE HCL/C=. 98
PITCH ANGLE HCL/C=. 96
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
LL LL
2.00 0 0
Z 0 1C
0 1 . 0 0 - 2 H x 0 I- H a.
.OO
BOX = COLL 13 STAR = W L L #4
. I 1
0 * - ..
0
* 4
*a m
* % * a a
1 * 1 I
3.00 M > IT
L L LL
2.00 0 0
Z 0 Z
cs, 1 . 0 0 - z H I 0 t- n a.
. O @
.OO .50 1 .OO 1.50 2 .00
@ 1 r
*o
- d
-
I I I
.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
2.00
1 .50- LL LL W 0 0
t H 1.00- -1
.50 .OO .50 1 .OO 1.50 2.00
HCL/C
I I I
0
* +O -
-
a I I
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
2.00
1.50
1.00
.50
. O O
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 1 I
- -
t
I * [ - - 0 * * * S tl
- 0 t tl 0 -
0 0 * * Ir
* I 1
1
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
1.00
LL LL W 0
.OO 0
t- G H - 1 . O O
-2 .00 -
1 r I
Po
*# - * t - * D
* Q 0 B *
- 0 + - * 0 *
* 0: - * 0 8 -
L I I
-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
0 b 0
00 * [I u
STAR = COLL +4
- . S O
PITCH ANGLE
- H
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
..
.50
.25
.88
- . 2 5
-.50 -180.00 -90.00 .OO 90.00 180.00
PITCH ANGLE
I . I
- -
0
- * T3
0 I t
* - -
1 1 1
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
-1 6
.50 05 W t- 6
-1 . 0 8
YAW ANGLE
I 1
0 1 0 * * * 0
11 -
- -
1 I
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
I
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
I
- 1' l!!
I -
- -
. O O . 1 I
-30.00 .0a 30.08 60.00
BOX = COLL #I STAR = COLL #2
YAW ANGLE
.08
.50
.OO
.50
.OO
BOX = COLL #3 STAR = COLL #4
F i g u r e 13b. Variation of single collector loads with yaw angle for HCL/C=KI, (configurations 1-4).
2.00
t- 1.50- G W 0 0
W 0 1.00- 141 0 G
-1 4 w .50 W t- Q: -1
.OO
-30.00 .OO 30.00 60.00 YAW ANGLE
.
- - * Ir *
0 0 - 0 3
1
-
- -
I 1
1
- -
-30.00 .00 30.00 60.00
I
, 1 1
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
BOX = COLL #3 STAR = COLL #4
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
I .
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
-
- -
- I
1 1
- -
- -
-
- 1 I
I
-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
I
I
YAW ANGLE
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) .
1 .OO
t. tL w .50 a 0
t- z W s .OO 0 I:
a - .50
3 4 >-
- 1 .OO
I 1 1
- -
- -
0 - *
I 1
-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
[I
2.80
1.75
LL LL W 0 o 1 .50 - t- LL H -1
1.25
1 . 0 0 J
YAW ANGLE
-30.08 .OO 30.00 60.00
I . 0
0
0 * * - - * 0
* -
.)
- -
I 1
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 ) .
.OO
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
- -
0 - -
I I
-38.00 .OO 3 0 . 0 0 6 0 . 0 0 YA'd ANGLE
r
. O O
LI -.50 t. W 0 0
I- L L H - 1 . O O -1
I
13
- -
1 * Ir 0 - -
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
I
.50
.25
.OO
- . 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
I . 1
- -
- - 1
- -
I 1
56
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) .
.50 -
.25
.OO
-.25
- . 5 0 +
Figure 13j. Variation of single collector loads w i t h yaw angle for HCL/C=KI, (configurations 1-4) .
I I
0
- -
* -
- -
I 1
BOX = COLL 13 STAR = COLL #4
-30.00 .OO 30.00 60.00
YAW ANGLE
.58 -
.25
. O O
- .25
-.50
v
u * -
11
- -
- -
I I
-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
2.00
P z 1 .75 - W n U n G
1 . 5 0 - W 0 U
t- L 1-i 1 . 2 5 - -1
1.00.
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
0 0
i I
1 I 1 - --
I
.OO -
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
1 I
-
-
1 I 1
.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.
1
.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 1 1
- -
- -
- -
1 I 1
I . 5 0 *
1 .OO
.50
.OO
I I I
- -
- -
1 I I
.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
1 .OO
- THETA = 0 DEG
-
0 0 0 " 0 0
0 - * 0 0 0 0 0 0 * * ****
Ir * * -
I 1 1
. 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
I 1 1
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 -
C
- d
0
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
.OO
Figure 16b. Effect of row spacing on collector loads (configuration 9) .
I 1 t 1
- 1 - -
- -
1
1 .50 2.08 1 2.50 3.00
3.50
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
17
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
A A
.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.
A 0 0
-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
.S
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
0
t- Z W H 0
1 . 5 0 - L L tL W 0 0
I I I 3
0
PSI = 0 0 b
- * 0 d
0 II 0 * [
0 0 .)
- - 0 * so
0
- - 0
0 * *
1 I 1
F i g u r e 18a. Effect of torque tube on co l l ec to r 1 loads .
1 1
P S I = 0 - 0 p o t
0 0
3
w 1 . 0 0 - 0 rY o CL
-1 9 .50 OL W t- a --I
.OO
- 0 * *
8 o * 0 * 6 * - 0 -
0 0 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.
.50
a. > 21 .25 t- Z W z 0 z .OO tl) Z Y I: 0 - .25
- - 1 I .
PSI - 0 - t! O
d' * * 0 - * * *
0
0 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
I
PITCH ANGLE
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
373C3
7.
30
00
>3
30
30
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30
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3 0
3C
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?P
IP
7 >
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33
5 2:313
PIP
IP
C
3C
J21C
-117C
a
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w
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hr
-er
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ud
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-)
--
I -
I
I I
I
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I-
-
00
00
00
00
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mr
J~
ln
00
00
00
00
30
00
00
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8 D
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90
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
101 7
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 without
V I without
V I I withoat
VII without
IX without
IX without
I X without ( $ = 3 0 ° )
o n n r m - s
1 1
u 7. LLI -
9 3
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
Pr
z*
cw
Nt
2
--
Om
Nm
s
(D
Il
l1
1
I-
T
W
*
u
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-c
vr
c\
pc
u
- x
01
- 0
r.1 - U.
s
I.. W
0
U
wm
a
2
' C
-
ow
u. -
X
C
n
l. r)
J
0
I
2
0
0
U
rn
~o
wm
mm
wm
~r
n
- -
\
CCC6OImFm6CIF
*
c
J
aw
a u
a-
I x
3
- o
ms
-
SW
Y
. W
U
J
Y?
- I C
I-U
C
II
-I
C-
U>
C-
yl
~U
~~
30
0
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 )
max
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
H Y G
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
1.'
0 C'. l J il J 0 0 $1
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 ,
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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
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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
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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
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, 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
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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
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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
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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
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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
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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 )