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Evaluation of aerodynamic admittance for buffeting analysis
Journal of Wind Engineering and Industrial Aero@namics, 41-44 (1992) 613-624 Elsevier
613
Evaluation of Aerodynamic Admittance for Buffeting Analysis M. K a w a t a n i '~ a n d ti.
Kim ~
Department of C i v i l E n g i n e e r i n g , Osaka U n i v e r s i t y , Yamadaoka 2-1, S u i t a , Osaka 565, Japan
Abstract
In the wind r e s i s t a n t d e s i g n of f l e x i b l e c i v i l e n g i n e e r i n g s t r u c t u r e s such as s u s p e n s i o n b r i d g e s and c a b l e - s t a y e d b r i d g e s , i t i s v e r y i m p o r t a n t to i n v e s t i g a t e the a c t u a l b e h a v i o r of s t r u c t u r e s in n a t u r a l winds. This s t u d y f o c u s e s on t h e b u f l ' e t i n g r e s p o n s e among t h e v a r i o u s a e r o d y n a m i c phenomena, which causes the f a t i g u e and s e r v i c e a b i l i t y problems of f l e x i b l e structures. The a e r o d y n a m i c l ' o r c e s on s t r u c t u r e s in n a t u r a l winds a r e e v a l u a t e d in terms of aerodynamic a d m i t t a n c e and s e l f - e x c i t e d aerodynamic c o e l ' f i c i e n t s . An e f f i c i e n t method i s p r e s e n t e d to o b t a i n the a d m i t t a n c e u s i n g an a c t i v e g u s t g e n e r a t o r . The aerodynamic response of rectangular c y l i n d e r s w i t h a s p e c t r a t i o s o f 2 and 5 i s i n v e s t i g a t e d . The e s t i m a t e d response from power s p e c t r a of t u r b u l e n t flow and the a d m i t t a n c e is COl[Ip a r e d w i t h ttle measured r e s p o n s e in wind t u n n e l t e s t s . Tile e f f e c t s of turbule.nce c l m r a c t e r i s t ics on b u f f e t ing response art., a l s o i n v e s t i g a t e d .
1.
INTRODUCTION
In the d e s i g n of l i n e - l i k e c i v i l e n g i n e e r i n g s t r u c t u r e s such as suspens i o n b r i d g e s and c a b l e - s t a y c , d bridge, s, a g r e a t deal of a t t e n t i o n has been paiti to l.hc aerodynamic b e h a v i o r of s t r u c t u r e s . The aerodynamic b e h a v i o r of f l e x i b l e s t r u c t u r e s may be b r o a d l y c l a s s i f i e d i n t o t h r e e phenomena !11 such as 1) v o r t e x - i n d u c e d o s c i l l a t i o n due to tile v o r t i c e s s e p a r a t e d from l e a d i n g and t r a i l i n g edges of b l u f f body s t r u c t u r e s , 2) b u f l ' e t i n g due to the l'luct u a t i o n of wind v e l o c i t y and 3) f l u t t e r phenomenon caused by the n e g a t i v e damping cl'fects. In tile c o n v e n t i o n a l wind r e s i s t a n t d e s i g n 121, the i n v e s t i g a t i o n s of aerodynamic r e s p o n s e u s u a l l y have been c a r r i e d out in smooth f l o w s , and i t emphasizes the s t a b i l i t y for the f l u t t e r phenomenon and the maximum amplit u d e of 1,he. v o r t e x - i n d u c e d r e s p o n s e . On tile o t h e r hand, t h e b u f f e t i n g phenomenon i s not g e n e r a l l y c o n s i d e r e d , because the a m p l i t u d e of b u f f e t i n g is not so l a r g e as the ~ t r u c t u r e becomes u n s t a b l e . For the r e c e n t f l e x i b l e britiffcs with long span, however, the frequency of the o c c u r r e n c e of I)uf-
0167-6105D2/S05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
614
f e t i n g w i t h c o n s i d e r a b l y l a r g e a m p l i t u d e i s h i g h and i t may c a u s e f a t i g u e or s e r v i c e a b i l i t y p r o b l e m s . T h e r e f o r e , t h e b u f f e t i n g phenomenon must be c o n s i d e r e d in t h e d e s i g n s t a g e . To e v a l u a t e t h e b u f f e t i n g r e s p o n s e , a e r o d y n a m i c f o r c e s on s t r u c t u r e s must be i d e n t i f i e d . The a e r o d y n a m i c f o r c e s a r e u s u a l l y d e f i n e d as t h e s u m m a t i o n of e x t e r n a l buffeting f o r c e and s e l f - e x c i t e d f o r c e [ 3 l . The c o n v e n t i o n a l e v a l u a t i o n [4] f o r t h e b u f f e t i n g r e s p o n s e d e p e n d s upon t h e n u m e r i c a l a n a l y s i s b a s e d on t h e t h r e e - d i m e n s i o n a l t h e o r y of t h e a e r o d y n a m i c f o r c e s . The b u f f e t i n g f o r c e i s e x p r e s s e d i n t e r m s of t h e a e r o d y n a m i c a d m i t t a n c e which i s assumed as a f u n c t i o n a l t y p e r e g a r d l e s s of c r o s s - s e c t i o n a l shapes of bridges. Therefore, the buffeting f o r c e s do n o t e x p r e s s t h e a c t u a l f o r c e s on t h e s t r u c t u r e s with a unique cross-section. To e v a l u a t e t h e a c t u a l b u f f e t i n g r e s p o n s e of s t r u c t u r e s , it is required to investigate t h e a e r o d y n a m i c f o r c e s w o r k i n g on t h e s t r u c t u r e s in n a t u r a l w i n d s . in t h i s s t u d y , an e f f i c i e n t method f o c u s e d on t h e b u f f e t i n g phenomenon is p r e s e n t e d t o o b t a i n t h e a e r o d y n a m i c c o e f f i c i e n t s , such as s e l f - e x c i t e d coefficients and a e r o d y n a m i c a d m i t t a n c e in t u r b u l e n t flow s i m u l a t i n g n a t u ral wind. The t u r b u l e n c e s i m u l a t i o n is c a r r i e d out t h r o u g h an a c t i ' ~ e g u s t g e n e r a t o r which can p r o d u c e t h e t u r b u l e n t flow w i t h a r b i t r a r y tu, oulence p r o p e r t i e s . Two k i n d s of ~ w o - d i m c n s i o n a l r e c t a n g u l a r c y l i n d e r s w i t t i a s p e c t ratios (width/tlepth) of 2 and 5 a r e u s e d in t h e e x p e r i m e n t s , w h e r e two models h a v e d i f f e r e n t cllaracteristics of t h e f l o w s e p a r a t i o n and wake region I l l . Using aerodynamic c o e f f i c i e n t s o b t a i n e d from t h e r e s p o n s e t e s t in t u r b u l e n t flows, the estimation of b u f f e t i n g r e s p o n s e in a r b i t r a r y t,u r i ) u l e n t flows is c a r r i e d o u t , anti t h e c a l c u l a t e d s p e c t r u m of r e s p o n s e i s et)l,i)art,.d w i t h c x p e r imt,~nl,al one.
2. TIII,~ORY FOR I,'.VAI,UATING AERODYNAMIC FORCES 2.1.
I,:quation of motion
Cons l t l e r i n g tht,. v e r t i e a l lilt)l,ion Z( i, ) or a s e c t i o l m l t l a l (;(luation o1' motion may l)e expressed as I ' o l l o w s : ~l(~,(t), 4zh:f+~(t) , (2+f,,)+z(t)}
l,,,(t) , I,~(t),
model, t h e dl I'l'eren-
(1)
wht:rc t+l = mass, h~. = damping r a t i o , 1'~. = n a t u r a l f r e q u e n c y of tile model and I,,+(t) and I,+~(1.) arc,., r e s p e c t i v e l y , the hufl'etI.g~ lift f o r c e and s e i f (+'×c'.itcd l i r t i'oree. In t i l l s s t u d y , t h e a e r o d y n a m i c f o r c e s arc: e × p r e s s e d as rol lows : I,,(I)
(¢,L'B 2){c ( t ) u ( t ) . c+(t)~(t)} ,
I,(t)
(pL=II 2)lll~z~t) L' ' II=zft) B} .
(2) (3)
in which, II - chord l e n g t h oi' the model, p - a i r d e n s i t y , U - mean wind velocity, u ( t ) and w(i,) - f l u c t u a t i n g wind velocity of horizontal and vertical components, (:,,(t) and c,+(t) = c o e f t ' i c i e n t s o f t r a n s f o r m a t i o n ['or
615
horizontal and v e r t i c a l wind c o m p o n e n t s , r e s p e c t i v e l y . Also Ii, and !12 = so-called velocity-dependent and d i s p l a c e m e n t - d e p e n d e n t s e l f - e x c i t e d aerodynamic coefficients, respectively. Substituting E q s . ( 2 ) and (3) i n t o E q . ( 1 ) , t h e f o l l o w i n g e q u a t i o n is d e r i v e d , M[z(t) + {47~h=f=- (pUB/2M)II,iz(t) + {(2zf=) 2 - (pU2/2M)th}z(t)] = (pUB/2){c.(t)u(t) + c.(t)w(t)} .
(4)
E q u a t i o n (4) i s a r e d u c e d e q u a t i o n of motion from E q . ( 1 ) , where t h e damping and s t i f f n e s s coefficients a r e m o d i f i e d by t h e s e l f - e x c i t e d aerodynamic coefficients, and t h e b u f f e t i n g f o r c e i s e x p r e s s e d as an e x t e r n a l f o r c e .
2.2.
Sol f - c x c i t e d c o e f f i c i e n t s Assuming t h a t t h e s e l f - e x c i t e d f o r c e l , s ( t ) i s i n d e p e n d e n t of t h e b u f f e t ing force La(t), aerodynamic coefficients It~ and I1-~ may be o b t a i n e d by t h e m e a s u r e m e n t of a e r o d y n a m i c damping h.. and n a t u r a l f r e q u e n c y f~ of t h e model v i b r a t i n g in a smootl~ flow.
(5) (6) (7)
I[, = -Sz~Mf.{h. + h=(1-r,)}/(pUB) , II= = -2M(27c f.)= ( l - r ~ ) / ( p Us) , r, = f=/f. ,
in which tim I ' r e q u e n c y l'. of s t r u c t u r e in t h e wind i s n e a r l y e q u a l t o f~ in practice, therefore, t h e f r e q u e n c y r a t i o r r = l l e a d s to t h e d i s p l a c e m e n t depc.ndent c o e l ' l ' i c i c n t il.~=O.
2.3.
Aerodynamic admittance The power s p e c t r a l dens i t y f u n c t i o n s Sz ( f ) of v e r t i cal d i s p l a c e m e n t z ( 1. ) and S , , . ( I ' ) e l ' t h e e x t e r n a l I ' o r c e s I , . ( t ) keep the. I ' o l l o w i n g r e l a t i o n s h i p ,
whe.r(; I1(1') I ows :
Ill(f)l'
(S)
In(f) I"S,..(f),
S=(f) =
is
=
tlle f r e q u e n c y
response
I ' u n c t i o n of
1 M2(2gf)4[{1 _ (f/f.)=12 + 4(h=+h,)2(f/f.)2]
Eq.(4)
expressed
as
I'ol-
(9) ,
and a s s u m i n g t t l a t wind v e l o c i t i e s of h o r i z o n t a l c o m p o n e n t and v e r t i c a l component have no c o r r e l a t i o n , tile power s p e c t r u m S , . . ( f ) el' b u f f e t i n g I'orce is g i v e n a s : S,,(f) = (pUB/2)~{IC,,(f)I=S-(f) + IC*(f)l ~S*(f)} ,
(10)
in w h i c h , S . ( I ' ) and S . ( f ) a r e t h e power s p e c t r a of u ( t ) and w ( t ) , r e s p e c t i v e l y , and C,,(f) and C . ( f ) a r e t r a n s f o r m a t i o n f u n c t i o n s from f l u c t u a t i n g
616
wind v e l o c i t i e s of h o r i z o n t a l and v e r t i c a l components t o b u f f e t i n g force, t h a t is c a l l e d a e r o d y n a m i c a d m i t t a n c e . l l e r e , s u p p o s e d is t h e r e s p o n s e t e s t of s t r u c t u r e s in t h e t u r b u l e n t flow whose wind f l u c t u a t i o n is restricted only to horizontal component, i.e., w(t)=O, t h a t is named as u - c o n t r o l l e d t u r b u l e n c e . L e t t i n g t h e power s p e c t r a of v e r t i c a l m o t i o n and f l u c t u a t i n g v e l o c i t y of h o r i z o n t a l component in such c o n d i t i o n as S ~ . ( f ) and S , , ~ ( f ) , r e s p e c t i v e l y , and u s i n g E q s . ( 8 ) t o (10) in which S . ( f ) = O , t h e h o r i z o n t a l a e r o d y n a m i c a d m i t t a n c e C o ( f ) can be o b t a i n e d as f o l l o w s : IC.(f)l = = 4S.,,(f)/{pUB)ZS,,.(f)lii(f)l
(]])
=} .
in t w o - d i m e n s i o n a l t u r b u l e n t flow whose h o r i z o n t a l and v e r t i c a l components are fluctuating, t h e r e s p o n s e of t h e s t r u c t u r e is m e a s u r e d . II. i s n o t e d t h a t t h e l ~ o r i z o n t a l component of t w o - d i m e n s i o n a l t u r b u l e n c e is i d e n l.i(:al t o t h a t of u - c o n t r o l l e d t u r b u l e n t flow m e n t i o n e d a b o v e . The v e r t i c a l a e r o d y n a m i c a d m i t t a n c e C . ( I ' ) is a l s o o b t a i n e d from t h e r e s p o n s e and E q . ( 8 ) as r o l l o w s : IC.(f)l = = 4S,(f)/{pUB)=S.(f)lll(f)l Through tan(;(:
or
the a
l.h(: s l . r u ( : t u r e
mentioned
structure arc
=} - I C . ( f ) l = s . ( f ) / S . ( f )
p roc:ess,
are
the
obtained,
i(h:nl.iricd.
The
aerodynamic
and
the
process
coerl'ic.ients
aerodynamic
o~
t.he
(12)
.
ror(:es
pres(:nl.ed
and
admit-
working
in I.'igu)'(: I.
,.........
Elf= ,~,tooth ( l o w ] . . . . . . . .
,: [-~:,i~t)~~;~i.o?-i;7~, T~-] :
t~,~.(G) ~
:-[~e,==od-3,;;,,~Y~. co~rr~oi,.,,t l,i=] ,, [l'=e¢l. . . . . . . . . . . .l e s )Io. .n.s. .e. . . . f. ,. n. c .
................
I I I C f )~t
1. . . . . . . . . . . ,- . . . . : [
,. . . . .
:[
:
|
X;F'r --:-[
-" ALh~Lo(l~namio a-d' -m" -i ~t t"a' "n-c- e' - C,,(f)_]
..... '"~'":-'"-~"~~"'"' -
,
,,
,
FFT "--'4
I
I
~'"
=
•
: ~Eodyn~m=e edm =t tance Cw( .... , .... . .......... .., ........ ; .,,..
'"
',
i
*
=-[
/~el'od~,nar~ic forces
riguro I. Process to evaluate the aerodynamic forces
]
..~
.... , J :
i P'~er.spe.ctra so(r),s,,(t),s,(r)l --
..... ,
: ~wor s,,oot,., s.,.,(r) s (r~
,, |- i-
)
t.rb.]
!
,
i
" .....
Eln u - c o n t r o l l e d
st,.uct.,..l rospo,,se z.,(jU_J.,
I
I'ln two-dimensional turb.] Structural response z ( t )
',
Eq. (3)
,
:
-
on
lli(:thod is shown
Eq. (2)
,
: :'
617 3. WIND TUNNEL TESTS 3.1.
Turbulence s i m u l a t i o n The wind t u n n e l t e s t s were c a r r i e d out in t h e G ~ t t i n g e n t y p e wind t u n n e l of Osaka U n i v e r s i t y whose c r o s s - s e c t i o n i s 1 . 8 m x 1.8m. An a c t i v e g u s t g e n e r a t o r [5] was d e v e l o p e d and improved t o p r o d u c e t h e t u r b u l e n t flow s i m i l a r to n a t u r a l wind, which has two a r r a y s of p l a t e s and a i r f o i l s [6,7]. The c o n f i g u r a t i o n of t h e g e n e r a t o r i s shown in F i g u r e 2. The a c t i v e a r r a y s of p l a t e s and a i r f o i l s i n d e p e n d e n t l y c o n t r o l t h e h o r i z o n t a l and v e r t i c a l c o m p o n e n t s of wind v e l o c i t y , respectively. As t h e t a r g e t of t u r b u l e n c e s i m u l a t i o n , t h e KArmAn's e x p r e s s i o n s f o r power s p e c t r a of n a t u r a l wind a r e s e l e c t e d such a s : s.(f) = 4I~,UL,,.,{1 + 70.8(fl.,,../U)Z} - ' / ' . S,,,(f) = 41~UL..,,{I + 755.2(fL,,.,,/U) 2} {1 + 2 8 3 . 2 ( f l , , , . , , / U ) ' }
-''/"
(13) (14)
.
where l' = f r e q u e n c y , I . , L=.,, = 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 of h o r i z o n t a l wind v e l o c i t y and I . , L..w = 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 of v e r t i c a l wind v e l o c i t y , r e s p e c t i v e l y . The d e t a i l s of t u r b u l e n c e s i m u l a t i o n method a r e d e s c r i b e d in a n o t h e r paper p r e s e n t e d a t t h i s c o n f e r e n c e I71. Using the gust generator, two t y p e s of t u r b u l e n c e s i m u l a t i o n were c a r r i e d o u t . One is an t w o - d i m e n s i o n a l t u r b u l e n c e s i m u l a t i o n c o n t r o l l i n g wind v e l o c i t y of t h e h o r i z o n t a l and v e r t i c a l components. The o t h e r i s t h e s i m u l a t i o n of an a n o m a l o u s t u r b u l e n c e such t h a t t h e c h a r a c t e r i s t i c s of h o r i z o n t a l component of wind v e l o c i t y a r e i d e n t i c a l to t h o s e of t h e twod i m e n s i o n a l t u r h u l e n c e , however t h e v e r t i c a l component of wind v e l o c i t y is not f l u c t u a t e d , i . e . , a r r a y of a i r f o i l s keeps t h e s t e a d y s t a t e . The t u r b u l e n c e c h a r a c t e r i s t i c s of s i m u l a t e d t u r b u l e n t flows a r e summar i z e d in ' r a h l c ] t o g e t t l e r w i t h t h e t a r g e t o n e s . The c h a r a c t e r ' - u ' in 1,uri)ul(;n(.'e numhers expresses t h e c h a r a c t e r i s t i c s or u - c o n t r o l l e d turbulenc:e. The power spc;ctra ol' t i m g e n e r a t e d t w o - t ] i m e n s i o n a l t u r h u l c n c e T-12
Array of plates '
Array of airfoils I
\ ~--(X/8-1OS-S3D)II U /
\ll
~
'J"~i Mesh (~20)
/W!,t~d tunnel wal CoiI spring ,u(z
~ Dummymodel
:.~"
l
Model
Model
i K--" - I ..,.r',, ,.
-I
"r~
,~D"~ ,oso
Figure 2. Configuration of active gust generator
Insertable working settler!, wall/j :
900
,'I
1~00 Unit :mm
618
and t h e c o r r e s p o n d i n g u - c o n t r o l l e d t u r b u l e n c e T - I 2 - u a r e r e s p e c t i v e l y shown in F i g u r e s '3 and 4, r o r e x a m p l e . The h o r i z o n t a l components of two t u r b u l e n c e s have a good a g r e e m e n t . In t h e u - c o n t r o l l e d turbulences, t h e power s p e c t r u m oi' v e r t i c a l component i s lower t h a n t h a t of t h e t w o - d i m e n s i o n a l t u r b u l e n c e and t h e t u r b u l e n c e i n t e n s i t y is lower t h a n 1.2%, which can be c o n s i d e r e d as t h e smooth in v e r t i c a l component. T h e r e f o r e , t h e t u r b u l e n c e s i m u l a t i o n s of i d e a l f l o w s in t h e p r e s e n t e d t h e o r y were p o s s i b l e t h r o u g h the active gust generator. Table 1 Turbulence characteristics of generated turbulent flows Measured Turbulence
Change
No.
of
T-II T-I2~;
.
T-I3
.
.
.
Iu &
.
T-ll-u
.
T_12_u o" ...T-13-u l'-Sut T-Su2" T-Su3 'l'-Sul-u
Iw
Target
lu+',lw++iLx, u+',Lx.w++ lu ; I, ', (%)',(%); (era) I (era) (%)',< )', 6 ! 3 ', ', 6.21 3.11 10 ,' 5~ ," 37.5 10.0,: 5.2', 14 ', 7 ' ', 14.11 7.41 6 ,' I, 150 ', 6.0', 1.0', l tO ',< I ', ', 10.0', 1.1, 14 ; I ,, i• lbO 'l 5 'l,, 150 ' ,' 350 10 I, ', 10 0" i ,< I ,, 150 ! ! 350 ,' ,'
I.x, u
T-Su2-u'* ,,T-Su3-u 'l'-Swl
f-Sw2"
3 m/s
l
l,x,w
l
','25 l
Lx.u ', Lx.w lu ; I~ ,, Lx.u ', Lx.w (era) ', (era) ( )',( ), (era) : (era)
14.0 i 1.1; 9.7,, 5.5; l
147 145 148 159 145 153 102
10.0'
145
I
9.7, ' 9.5, .i 10.0, 9.5, ; 10.5,' l
, 37.5 10.0, 'r-sw,3 ', ', f87,5 .9,5 ,: ]u, I,x,u : turbulence intensity and scale of ~, l,x,w : turbulence intensity and scale of
" Turbulences ' " l'urbulences
tO , 5 , 150
I i! 'I 37.5 ,' ', ', '
4 m./s
5.2' I
5.3, ' 364 1.0,.! 100. 1.0,, 145 1.~)', 354 4.6' , 139 l
v
"~" 10o~ -ITI_',~.o I]O.glS,01iSUl',~?:51 ltlE'~ i0 {~ 1..... 52, I.J.L._L34, "! ' .....hJ' , ....t}LI .........
4~
.......... .!.-.,'~,-~,il~ lldl~,.., i ..... , ........
,"
r
llor izonta
1
i
COl~IpOllellt.
i.. \
:.
:
141 153 148 99
1 I , i ,, ,l 37.8
145 'I 40.4
,' , ;, ', ,' l 145 , 168 ',
353 96 153 343 152
38.3
27.6 40.4 82.8
: Vem'tical
FI .... ii................ I n,, l l,qi.~7,il ] I..l(_,,/~,)..I.J:~)l[~}l!.~,@_J lO-t I: ...... 1:1'1 ~&_/l#Al~] [#[LJ ....... l! U!J~_qL[[I.gEJ~] ] 4,_~.J
'~" lO-a
F
I
/if
......Ilori Zontal ........... I~lml]
component
:.~:,,, ~itl~
I ~o-'
.......... ,.!~,:..','.'..,! ....... .! ....i.............. :'i./ /
10~
. . . . . .
.,i.~
vo~t,°.l
10-6
10-~
152 I 41.7
10"4 "coaponent ....... Jt i~.~,~!i~,f: ........
10-~' t!" 10~ !-°-'-u~'L-L~' ........... : ............. ' ~ "!~coral,orient - ~ u ~ j ~-a~Ji 10-~
138 ',' 40.1 145 ,' 40.4
I:
u) 10-~ 4~
I...... ~ .\.~..,.:"~,i i ,./" 'i'i'i}~,~'~lil ......!/il.~ ........ ~,o ~ /. i,~ i ' ""~
'-,o.,
6.1, 3.1; I " I 9.7', 5.2', 13.81 7.0.', 5.91 0.91 l l 10.0, 1.0, ! 13.3, 1.1', 38.2 9.7, i 5.3i l 34.6 9.7' I 5.2' I 37.9 10.0,' 5.4, ' . . 9.5', 1.0, i 10.0:1.0 9.6: 1.0,' 25.3 9.4' , 4.6' , 34.6 9.7', 5.21 85,8 9.9', 5.4',
'r-12, T-Su2 and 'i'-Sw2 are same t u r b u l e n t flows. 'r=12-u and T-Su2-u are same turbulent flows.
1.. I (,,/._'~)1. ~)1 ~) I (c,,,) 1(,;~)l
10"2
u
38.7 34.6 36.1
5.2, 145 5.5', 139 horizontal component vertical component
%, 100
i~
it ,' I I l , ; ,l 'I ,' ,i ,' : ', I ',
10~ 10~ r (llz) I'igure 3. Power spectra of t~o-dimensional turbulence
!
' U.J~IL_J_LLbJ..I
10_2-
10_ z
100
........
I
........
101 10~ f (llz) Figure 4. Power spectra of u - c o n t r o l l e d turbulence
619
3.2.
Aerodynamic r e s p o n s e o f r e c t a n g u l a r model Two-dimensional rectangular cylinder models with aspect ratios ( w i d t h / d e p t h ) of 2 and 5 a r e s u p p o r t e d by v e r t i c a l c o i l s p r i n g s as shown in F i g u r e 5. The sway and t o r s i o n a l motions a r e r e s t r i c t e d by p i a n o - w i r e s . The structural characteristics of the r e c t a a g u l a r mode]s a r e shown in Table 2. The s t r u c t u r a l damping of t h e models is made v e r y l i g h t b e c a u s e aerodynamic f o r c e s w o r k i n g on t h e model can be more a c c u r a t e l y i n v e s t i g a t e d from t h e r e s p o n s e of t h e model. The power s p e c t r a of t h e measured r e s p o n s e of t h e models in t h e mean wind v e l o c i t y 3m/s of t u r b u l e n c e T-I2 and T - I 2 - u a r e shown in F i g u r e s 6 and 7, f o r example. To i n v e s t i g a t e the effects of t u r b u l e n c e c h a r a c t e r i s t i c s , s u c h as t u r b u l e n c e i n t e n s i t y and t u r b u l e n c e s c a l e , on t h e aerodynamic r e s p o n s e of models, t h e r e s p o n s e i s measured not only in t h e smooth flow b u t a l s o in t u r b u l e n t f l o w s . The wind v e l o c i t y v e r s u s a m p l i t u d e c u r v e s of t h e r e c t a n g u l a r model w i t h a s p e c t r a t i o of 2 a r e shown in F i g u r e 8 w i t h r e s p e c t to t h e changes of t u r b u l e n c e c h a r a c t e r i s t i c s . In t h e s e f ~ g u r e s , t h e maximum a m p l i t u d e s of v o r t e x - i n d u c e d o s c i l l a t i o n and g a l l o p i n g a m p l i t u d e s in t u r b u l e n t flows become s m a l l e r t h a n t h o s e in t h e smooth flow. From F i g u r e 8 ( a ) , i t i s r e c o g n i z e d t h a t tht~ i n c r e a s e of t u r b u l e n c e i n t e n s i t y d e c r e a s e s t h e v o r t e x - i n d u c e d r e s p o n s e , which i s t h e same t e n d e n c y of t h e r e s u l t in Ref. [61. On t h e o t h e r hand, t h e c h a n g e s of t h e t u r b u l e n c e s c a l e s do not a f f e c t 10-4 re,: t'angu] a r ~.
cylinder
n~}del
10"4 i 10"~ I' in ,.,10 "6 two-dimnsional ...I..!,.............. ~turbulence (T-I2) [I i
|0"~
I
-'o-'r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
,_, 10 -~
.......................... :
cylinder
/
p i nno
'~
--~----I
1o-' ..... i~t;o:di"~'n~ion~i .................
<
lO'=v
,.,.,~,~
\ lO-n coil
spr'inR
:
i
10"4
10"~
"
turbulence
:
(T-I2)
: ,~;~
,:,,:,I ..i 10-s~
...............
.....
........... i.....~......;...........i' in u-controlled
:
10.1~ ........ i , ,,,,,,i ........ i it ......
Figure 5. Supporting system of rectangular cylinder m o d e l
-..
.
" ' l . u-c'ontrollod ..... i ~ ......... 10.1 ~ turbulence (?-I~--~) ....i~ I ..........
wire
........
t,a
. . . . . . . . . .
lO-e
I.
, . . . . . . . . . . . . .
10 "=
10"
10o
fD/U
to.,J" ........ ........ ........ 10"4
10"3
10"2
10"1
10o
fDIU
Figure 6. Power spectra of Figure 7. Power spectra of buffeting response (1:2 model) buffeting response (1:5 model)
Table 2 Structural quantities of rectangular cylinder m~els Aspect r a t i o (B/D)
Weight
Natural frequency
2 (D=6Omm) 5 (D=~O~0m)
2.52 kg.f 2.50 kg.f
5.32 llz 2.95 Hz
Logarithmic decrement
0.002 0.002
620 t he maximum a m p l i t u d e of v o r t e x - i n d u c e d o s c i l l a t i o n as shown in F i g u r e s 8(b) and 8 ( c ) . In t h e r a n g e of reduced v e l o c i t y Ur= 7 to 13, t h e a m p I i t u d e in t u r b u l e n c e i s g r e a t e r t h a n t h a t in smooth f l o w , and t h e e f f e c t s of turbulence characteristics a r e not r e m a r k a b l e . In t h e r a n g e of Ur>13, t h e a m p l i t u d e t e n d s to i n c r e a s e with t h e i n c r e a s e of t u r b u l e n c e i n t e n s i t y I , and I,,, and w i t h t h e d e c r e a s e of t u r b u l e n c e s c a I e of v e r t i c a l component L,,.~. However, in F i g u r e 8(b) t h e change of t u r b u l e n c e s c a l e of h o r i z o n t a l component I. . . . . does not a f f e c t t h e aerodynamic r e s p o n s e of t h e model in t h e whole range of wind v e l o c i t y . The b u f f e t i n g r e s p o n s e of t h e r e c t a n g u l a r c y l i n d e r w i t h a s p e c t r a t i o of 5 is s t r o n g l y a f f e c t e d by t h e change of t u r b u l e n c e i n t e n s i t y as shown in l:igure 9. [n t h e range of U~>15, t h e a m p l i t u d e of t h e model is r e m a r k a b l y i n c r e a s e s w i t h t h e i n c r e a s e of t u r b u l e n c e i n t e n s i t y . T h e r e f o r e , i t can be r e c o g n i z e d t h a t t h e aerodynamic r e s p o n s e of t h e r e c t a n g u l a r c y l i n d e r w i t h a s p e c t r a t i o of 5 i s more s t r o n g l y a f f e c t e d by the f l u c t u a t i n g wind v e l o c i ty than t h a t with a s p e c t r a t i o of 2.
..-.. U,12 ~r~
@ smonth flow 01-11 (h = 5,% I,--3%) AT-I2 (I,:I0%, I,=5%) o t-I.~ (I,;14%, l,,TX)
• smooth flow 0 T-S,d (I.,.,:lOOcm)
0.12
TSu2 (I.~.,: 151]cm) n T-Stn3 (L,.,-350cm)
:
"" OJig ~=~
"" 0.(19 .,~
"s
flog
•
O/i]
frO)
o ,_.
0.00
01~0 5
tO
15
5
U,-'U/fll
Figur'o 8(a). Velocity vs. amplitudo curvo (1:2 model) -, change of intensity I. & l,
~
"
$ smc~)th flow 0 1",%1 (I,,,,qZ,~cm,~ Z~ I"'SwZ(l.,.,~JT.Scm~
O,IZ
" " OIYJ
10
.-.
O,OB
""
0,06
.,.,.
• sm~ot5 flov o r.ll 0,, 5~. X :3x) ,,'~ l',iz (6,10,, I,~,5%}
~ ~/xAtx
OJ))
Ik) 0
092
090
5
tO
15
u,:u/rD
~)
Figure 8(b). Velocity vs. amplitude curve (1:2 model) - change of horizontal scale I,x.u
.
0
15
U,,U/rD
n ~ ~
Figure 8(c). Velocity vs. amplitude curve (l:2 model) - change of vertical scale l,x.w
0
~
A
_~../~¢%oooo
0o
0 o
090 0
tO
20
)O
L.,,,. 40
U,--,U/FI}
Figure 9. Velocity vs, amplitude curve (1:5 model) -change of intensity i.& lw
:1.3. S e l f - e x c i t e d c o e f f i c i e n t s The l o g a r l t h u l l c decrement oi' r e c t a n g u l a r c y l i n d e r s in smooth flows i s measured by means el' t h e f r e e v i b r a t i o n method u s i n g a s i n u s o i d a l o s c i l l a t o r . The a e r o ( l y n a m i c (lamping is g i v e n by t h e s u b t r a c t i o n of s t r u c t u r a l
621 damping from measured damping in smooth flow. Using the E q . ( 5 ) , the s e l f excited aerodynamic coefficient H1 i s o b t a i n e d . T a b l e 3 s u m m a r i z e s t h e o b t a i n e d aerodynamic damping and s e l f - e x c i t e d c o e f f i c i e n t 111 of the models in the wind v e l o c i t y of 3 and 4 m/s.
Table 3 Aerodynamic damping and self-excited coefficient Aspect ratio of model Mean velocit~ (m/s) Aerodynamic damping as logarithmic decrement Self-excited coefficient
2
H~
5
3
4
3
4
0.028
0.180
O. 080
O. 120
-3.32
-16.0
-3.16
-4. "/5
3 . 4 . Aerodynamic a d m i t t a n c e Using the measured r e s p o n s e in t w o - d i m e n s i o n a l and u - c o n t r o l l e d t u r b u l e n c e s , the aerodynamic a d m i t t a n c e of the c y l i n d e r models can be o b t a i n e d through the p r e s e n t e d t h e o r y . The aerodynamic a d m i t t a n c e s a r e o b t a i n e d in v a r i o u s k i n d s o f t u r b u l e n c e s as shown in F i g u r e s 10 and 11. From t h e s e f i g u r e s , i t can be seen t h a t the aerodynamic a d m i t t a n c e of the v e r t i c a l component i s a p p r o x i m a t e l y one o r d e r g r e a t e r than t h a t of h o r i z o n t a l compon e n t . In the case of the r e c t a n g u l a r c y l i n d e r with a s p e c t r a t i o of 5, the F i g u r e 11 shows t h a t the changes of o b t a i n e d aerodynamic a d m i t t a n c e s are very small in change o1' t u r b u l e n c e c h a r a c t e r i s t i c s in the lower range el" r e d u c e d f r e q u e n c y fr=fl)/U < 0 . 0 1 compared w i t h t h o s e of t h e model w i t h a s p e c t r a t i o of 2 as shown in F i g u r e 10. ..~ 10° ~
:
lO" ~
~o~ "~-l~.tt)ii~-.~ ......... i............. -IO ~ E. Ir-lc,.(r)l h,--s% ...... i.. I .....
..
I. Jli ,c,(r)l ,,,--'7%~
• --
_
~
-
lO'i
"
ICu(f)l lu=6%
10"= W ']~lc.(t)l
i
~ ~-IcuCr)l lu--14%
10-4
10"
III11111
I l*lilUl
10-3
lOo
"
!
i
i
..........~ ......... i.............: ........... [
r-lCw(Ol
i
.,bL
I]
I
i-~----i~£I r
......
,
.....I
i lllilil[
i
!
10"a
i iilllll
I 10" ifO/U 10"
(a) Change of lu & lw
~ II]3 F2i0.~ =
~, I0' d I0°
10-I
~(f)l
; . . . . . i ' :t
10-2
lu=lO% .....i ...... 1 "
~°~ ~i.,,i ii- i~iJc,~i£~-3:il ~, ............. [i
I0~
_ llY
"
I°-~ F L,,.,,:3i.s~:,. i,~ox~,'-:r,i ~~ [ I
10-3 I0-~
I0-'
10-3
I0"2
I0"i
(b) Change of Lx.u
Figure 10. Aerodynamic admittance (1:2 model)
fo/u
I0°
I0""
10-3
I0 -2
10"I I0~ fDIU
(c) Change of l,x,w
622
"'°"
' -'° I
-,o.
I
. . . . . . . . . .
10-'10_; ~:"L' ~~'1i'IL--LL-ICu(f)t .~l -Z'~-I';u(' -.~,'Cu(f)I ~'i Il'u'~" uu--~H' IO.~£..I~''I1~ ' I"' 10-~~ I.x,.o-,l'SO~, 10" , ., ,L~.'1.=~.5c=' ! I0-" 10"~ 10-"~ I0-tfDIg 10°
: . . . . . . . . .
.~
lO-'l()_~. I I~'I!!! !'ii !i!'i!i~ i"t ""I 10-"10-~~ ~ ~ 10-~ 10-~ 10-~ 10-~fO/IJ10~
10~
......'......
.',i
.
10-'10_, I "'~ i(~u~'~' !' '~'iiiI'"" / 10-''1It0-~I.x.,,--~SO~.,.~,-m%.I,--.~ ',,,,,,1~/ I0-" ;)-~ 10-~ 10-~fD/U10° (c) Change of l,x,w
(b) Change of Lx.u
(a) Change of lu & Iw
.•
Figure 11. Aerodynamic admittance (1"5 modcl)
4.
F,STIIIIATION
OF B U F F E T I N G
RESPONSE
Using the aerodynamic a d m i t t a n c e o b t a i n e d in tile t u r b u l e n c e T - I 2 , the power s p e c t r a of b u f f e t i n g r e s p o n s e in o t h e r k i n d s of t u r b u l e n c e s a r e c a l c u l a t e d and compared with measured ones in win(l tunnel t e s t s . When the turl)ulence c h a r a c t e r i s t i c s ; U, I . ( I . = I . / 2 ) , Lx.,, and i , x . . are i n d i v i d u a l l y ehang,:d, tile e s t i m a t e d response s p e c t r a are o b t a i n e d as shown in i,'igures 12 and 13 l,ogel, her with the measured ones, r e s p e c t i v e l y . I n t h e s e f i g u r e s , the estimal.(:d resi)ons(: s p e c t r a are a p p r o x i m a t e l y well f i t t e d 1o tile measured Sl)C.,C,'1,ra or th(., reel, a n g u l a r c y l inciers. For the a p l ) r o i ) r i a t e (.,valuation or b u r l ' e t i n g respor.se, il. is rleeded to lll~.,(;st, ignl~.(,, th(,. r e s p o n s e o f s t r u c t , ur(:s ill t h e hroa(l v'ange or l, lirl)lll(,.nt flows Sillllllatinl!~ nlll.lll'al win(is, howcv(;r, the r u l l (}X,tllllilh'll. iOll is a c t u a l l y (11 rri¢,.ul t, i.hroll~h 1,he; wind 1.llnnel l,(,.sts. ' rh e r(:ro re . tim e r r i c : i ( m t illetho(I ror t,h(,, i)r('.cll(;i, oil or l)urrc,,1,ing r(,.sporlse is requir(,.(i, all(! tilt., (:stilna1,1n~ Ill(,,t.h()(i l)rc;sc;n1,(}d here (tan he usel'ul ly al)pl led to such proi)lenls.
I0-4
10"" ,,'7"I0""
,,'7" 10-s
.... ~.~(i,,,.-,t~.'(l
...... i
10-<, 10"~ r.o 10""
......
lO-~
d 10"
...iii~i.i~ ....~.....!.........i.......... I0"* ii
lO-'f I0-11 10-1~ men.~'drcd ............ ! ' ..... 10"~ ............ i.............. i.............. !" II"' lo-' . . . . . . . . . i ..... , , , ~ L 10"4 10-~ 10-~
(a) Response
in
l'""
10-~
10~
10"= I0-I" 10-11 I0-I~ 10"" 10""
fl)/O
of buffeting
......i~VV~i~l.~i.il..
I0 "4
T-12 of 4m/s
Figure 12. Estimation
estimated i i
(b) respc)nse
(1:2 model)
rD/u 10 '~
I0 ":~
Response
I0" I.
ill T-13
i0 n
623 10-4
10-4
...........i............. +...............,•
lO-S ............
"~'~ ¢,0. ++ 10") I
i0_6
v
1°-+ ...... e s t [ m a t o d ........! ............. ...........................'
! .............
1o-' ~ " ~ - - i .............. , " . < . , . : : , ) ....... lO-,r F ...... :
..,'~![I...;P.! ............
,o-,, r,,oa~,,-o~ 10-1:l
!
!
10""
fD/u
I I - -
10-4
10-~
lO-Z
lO't
-o~t°~a
I
111;;
.........
~-i-~!~l~
lO-S( 10-4
10°
Response in T - S u l
(c)
......
lO-S-~
~ "1~
........
..... iii;; .......
lO-il
....... .....+.,,+m .......
•
J ...........
J
!!!~li+ .......+..........'
10-" lO-ll
,o..~.~i.+...............
........................
mcastlred
I0-7 I0"" I0-~
.......~ ................ +i;iil............ -i Jli~| ...........
............
10-3
(d)
10-=
Response
two
lO-i
in T-Swi
F i g u r e 12. E s t i m a t i o n of b u f f e t i n g r e s p o n s e (1:2 model)
10-4
10-s E
A
i
tO "4
i
I0-~
......os~ nlatcd 'ilii..............
I0-6 I0-)
I0-~ v
io'"
lO-e
I0-+ .~ .......... +\ .......... +............ + ..........
10"*
i0-=~ lO-l,
tO-! ~ lO'll
IO-i;
.~+ .............. ~.............. lO'll ............
I
lO'l~
fo/u
10-4 .-"". 10.s 10"6 .,,
,°-'
,
, ,,,,,.i , ,,,,,,~ , ,,,,.,i - Ii--
lO-S
I0"4
(b)
m
+.I
............ +.............. +.............. i.
10"1
Response in T-12 o f 4m/s
(a)
estimated ............i..............;.............
I0-i.~ lO.Z~ ........ i' ........ i' ........ I+ I,L,7:;;; 10"* 10"l 10"= 10"i 10"
d
!....... ineasu red ....... !
10-~
Response
I0-(
i
~!+,+~
Io-o ........... i.....
lO-i
-
in T-I3
I0-S
.... ,,,,,,,,i
10-6
.,.
....... I ...... i ..............
niP,as. rod
I..............
, ...................
i .................. '+"
i ...............
V N
IO-~ lO-e
10-~
-,,.,
.
.....
.
~. . . . . . . . . . . . . .
i .......................
.
i ................
.
i
I0-=1
~°"° ...... e s t i m a t e d ...............
10-I~ ........ e s t i m a t e d .............. i
o+ .....+.................... if .........
10-1J
I0-1=
10-+~
tO-l." lo-,"
rn/u
lO"
i
I
,)castlrcd
lO-i
........ i ........ i ........ i. I . ....... m rl)/U 10.4 10"3 10 "= 10"i 10e
I
i
............ i .............. ~.............. i ............ 10-1." ............ ~.............. ~.............. i ..... ........ i" ........ i' ........ I' ',,.,,i',,' 10"14
(c) Response ill T-SuI
Figure 13. Estimation of buffeting response (1:5 model)
J.
I0"4
10-3
I0-=
I0-=
(d) Response in T-Swl
1o°
fo/u
624 5. CONCLUSIONS The f o l l o w i n g c o n c l u s i o n s can be drawn t h r o u g h o u t t h i s s t u d y . (1) An e f f i c i e n t method to o b t a i n the aerodynamic a d m i t t a n c e in b u f f e t ing a n a l y s i s is presented u s i n g an a c t i v e gust generator wilich produces the t u r b u l e n t flows s i m i l a r to n a t u r a l wind. (2) In t h e w i n d t u n n e l t e s t s , t h e a e r o d y n a m i c r e s p o n s e of t h e r e c t a n g u l a r c y l i n d e r s w i t h a s p e c t r a t i o s o f 2 and 5 i s m e a s u r e d in t h e smooth f l o w and t u r b u l e n t f l o w s . The a e r o d y n a m i c a d m i t t a n c e and s e l f excited aerodynamic coefficients of r e c t a n g u l a r models a r e o b t a i n e d by the p r e s e n t e d method. (3) In t h e c a s e of r e c t a n g u l a r model w i t h a s p e c t r a t i o of 2, t h e a m p l i t u d e of b u f f e t i n g r e s p o n s e t e n d s to i n c r e a s e w i t h t h e i n c r e a s e of turbulence intensity 1,, and I~, and w i t h t h e d e c r e a s e of t u r b u l e n c e s c a l e of v e r t i c n l component I. . . . in the reduced v e l o c i t y U~>13. ilowever, the chane;e of t u r b u l e n c e s c a l e of h o r i z o n t a l component L , . , , does not a f f e c t the aerodynamic r e s p o n s e in the whole range of wind v e l o c i t y . On the o t h e r hand, t h e b u f f e t i n g r e s p o n s e of t h e r e c t a n g u l a r model w i t h a s p e c t r a t i o of 5 is v e r y s t r o n g l y a f f e c t e d by t h e i n c r e a s e of t u r b u le.nce i n t e n s i t y . (4) The o b t a i n e d a d m i t t a n c e s of h o r i z o n t a l and v e r t i c a l components a r e almost t h e same ~ i t h change of t u r b u l e n c e c h a r a c t e r i s t i c s in t h e r a n g e testetJ. (5) The e s t i m a t i o n of b u f f e t i n g response is c a r r i e d out. Ttle estimated r(;sponse is approxinlal, e l y well f i t t e d to the measured one. The presented l)r(:di(',tion is very us(:ful to evaluate the b u f f e t i n g response in the turbtnI(:nl, ['low w i l,h arb i 1,rary charac:l,c,,r i sl, it:s.
A(;KNOWI,I,:I)GMI,:NTS Th(; aul, hors w()tnl(I Ilk(: to thank Proi'. II. I(oi)ayashl ol' ltitsum(,,ikan L;niv(,,rsily r o r Ills l)rt, i)(,,r advice to wind tunrlel test, s, anti I)rol '. Y. I,'ul
7
Simlu,10:. anti S c a n l a n , R . I I . , Wind E f f e c t s on S t r u c t u r e s : An I n t r o d u c t i o n to Wind E n g i n e e r i n g , John WiI(;y & Sons, I n c . , New York, 1978. Ilonshu-Shikoku Bridge A u t h o r i t y , The S p e c l f i c a t l o n s for the Wind R e s i s t ant Design, 1976 (Ill J a p a n e s e ) . S('anlan,lA.II., ,I. Sound and V i b r a t i o n , Vol.60 (1978) 201. I)avenport,A.C;., Proc. ASCE, Vol.88, No.ST3 (1962) 233. Cermak,,l.E., Bienkiewicz,B., P e t e r k a , J . A . avid S c a n l a n , R . I I . , J. Wind I,~tlgine(:rinff and I n d u s t r i a l Aerodynamics, Vol.13 ( 1 9 8 ' } ) 4 6 5 . I(obaya~hi,ll, g a w a t a n i , ~ , and Nakade,O., J. Wind E n g i n e e r i n g and Indust r i a l Aerodynamics, Vol.33 (1990) 101. I(ol)ayashi,ii., i(awatani,l~i, and Kim.tl., Proc. 8th ] n t . Conf. on Wind l,:nginecring (1991).
613
Evaluation of Aerodynamic Admittance for Buffeting Analysis M. K a w a t a n i '~ a n d ti.
Kim ~
Department of C i v i l E n g i n e e r i n g , Osaka U n i v e r s i t y , Yamadaoka 2-1, S u i t a , Osaka 565, Japan
Abstract
In the wind r e s i s t a n t d e s i g n of f l e x i b l e c i v i l e n g i n e e r i n g s t r u c t u r e s such as s u s p e n s i o n b r i d g e s and c a b l e - s t a y e d b r i d g e s , i t i s v e r y i m p o r t a n t to i n v e s t i g a t e the a c t u a l b e h a v i o r of s t r u c t u r e s in n a t u r a l winds. This s t u d y f o c u s e s on t h e b u f l ' e t i n g r e s p o n s e among t h e v a r i o u s a e r o d y n a m i c phenomena, which causes the f a t i g u e and s e r v i c e a b i l i t y problems of f l e x i b l e structures. The a e r o d y n a m i c l ' o r c e s on s t r u c t u r e s in n a t u r a l winds a r e e v a l u a t e d in terms of aerodynamic a d m i t t a n c e and s e l f - e x c i t e d aerodynamic c o e l ' f i c i e n t s . An e f f i c i e n t method i s p r e s e n t e d to o b t a i n the a d m i t t a n c e u s i n g an a c t i v e g u s t g e n e r a t o r . The aerodynamic response of rectangular c y l i n d e r s w i t h a s p e c t r a t i o s o f 2 and 5 i s i n v e s t i g a t e d . The e s t i m a t e d response from power s p e c t r a of t u r b u l e n t flow and the a d m i t t a n c e is COl[Ip a r e d w i t h ttle measured r e s p o n s e in wind t u n n e l t e s t s . Tile e f f e c t s of turbule.nce c l m r a c t e r i s t ics on b u f f e t ing response art., a l s o i n v e s t i g a t e d .
1.
INTRODUCTION
In the d e s i g n of l i n e - l i k e c i v i l e n g i n e e r i n g s t r u c t u r e s such as suspens i o n b r i d g e s and c a b l e - s t a y c , d bridge, s, a g r e a t deal of a t t e n t i o n has been paiti to l.hc aerodynamic b e h a v i o r of s t r u c t u r e s . The aerodynamic b e h a v i o r of f l e x i b l e s t r u c t u r e s may be b r o a d l y c l a s s i f i e d i n t o t h r e e phenomena !11 such as 1) v o r t e x - i n d u c e d o s c i l l a t i o n due to tile v o r t i c e s s e p a r a t e d from l e a d i n g and t r a i l i n g edges of b l u f f body s t r u c t u r e s , 2) b u f l ' e t i n g due to the l'luct u a t i o n of wind v e l o c i t y and 3) f l u t t e r phenomenon caused by the n e g a t i v e damping cl'fects. In tile c o n v e n t i o n a l wind r e s i s t a n t d e s i g n 121, the i n v e s t i g a t i o n s of aerodynamic r e s p o n s e u s u a l l y have been c a r r i e d out in smooth f l o w s , and i t emphasizes the s t a b i l i t y for the f l u t t e r phenomenon and the maximum amplit u d e of 1,he. v o r t e x - i n d u c e d r e s p o n s e . On tile o t h e r hand, t h e b u f f e t i n g phenomenon i s not g e n e r a l l y c o n s i d e r e d , because the a m p l i t u d e of b u f f e t i n g is not so l a r g e as the ~ t r u c t u r e becomes u n s t a b l e . For the r e c e n t f l e x i b l e britiffcs with long span, however, the frequency of the o c c u r r e n c e of I)uf-
0167-6105D2/S05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
614
f e t i n g w i t h c o n s i d e r a b l y l a r g e a m p l i t u d e i s h i g h and i t may c a u s e f a t i g u e or s e r v i c e a b i l i t y p r o b l e m s . T h e r e f o r e , t h e b u f f e t i n g phenomenon must be c o n s i d e r e d in t h e d e s i g n s t a g e . To e v a l u a t e t h e b u f f e t i n g r e s p o n s e , a e r o d y n a m i c f o r c e s on s t r u c t u r e s must be i d e n t i f i e d . The a e r o d y n a m i c f o r c e s a r e u s u a l l y d e f i n e d as t h e s u m m a t i o n of e x t e r n a l buffeting f o r c e and s e l f - e x c i t e d f o r c e [ 3 l . The c o n v e n t i o n a l e v a l u a t i o n [4] f o r t h e b u f f e t i n g r e s p o n s e d e p e n d s upon t h e n u m e r i c a l a n a l y s i s b a s e d on t h e t h r e e - d i m e n s i o n a l t h e o r y of t h e a e r o d y n a m i c f o r c e s . The b u f f e t i n g f o r c e i s e x p r e s s e d i n t e r m s of t h e a e r o d y n a m i c a d m i t t a n c e which i s assumed as a f u n c t i o n a l t y p e r e g a r d l e s s of c r o s s - s e c t i o n a l shapes of bridges. Therefore, the buffeting f o r c e s do n o t e x p r e s s t h e a c t u a l f o r c e s on t h e s t r u c t u r e s with a unique cross-section. To e v a l u a t e t h e a c t u a l b u f f e t i n g r e s p o n s e of s t r u c t u r e s , it is required to investigate t h e a e r o d y n a m i c f o r c e s w o r k i n g on t h e s t r u c t u r e s in n a t u r a l w i n d s . in t h i s s t u d y , an e f f i c i e n t method f o c u s e d on t h e b u f f e t i n g phenomenon is p r e s e n t e d t o o b t a i n t h e a e r o d y n a m i c c o e f f i c i e n t s , such as s e l f - e x c i t e d coefficients and a e r o d y n a m i c a d m i t t a n c e in t u r b u l e n t flow s i m u l a t i n g n a t u ral wind. The t u r b u l e n c e s i m u l a t i o n is c a r r i e d out t h r o u g h an a c t i ' ~ e g u s t g e n e r a t o r which can p r o d u c e t h e t u r b u l e n t flow w i t h a r b i t r a r y tu, oulence p r o p e r t i e s . Two k i n d s of ~ w o - d i m c n s i o n a l r e c t a n g u l a r c y l i n d e r s w i t t i a s p e c t ratios (width/tlepth) of 2 and 5 a r e u s e d in t h e e x p e r i m e n t s , w h e r e two models h a v e d i f f e r e n t cllaracteristics of t h e f l o w s e p a r a t i o n and wake region I l l . Using aerodynamic c o e f f i c i e n t s o b t a i n e d from t h e r e s p o n s e t e s t in t u r b u l e n t flows, the estimation of b u f f e t i n g r e s p o n s e in a r b i t r a r y t,u r i ) u l e n t flows is c a r r i e d o u t , anti t h e c a l c u l a t e d s p e c t r u m of r e s p o n s e i s et)l,i)art,.d w i t h c x p e r imt,~nl,al one.
2. TIII,~ORY FOR I,'.VAI,UATING AERODYNAMIC FORCES 2.1.
I,:quation of motion
Cons l t l e r i n g tht,. v e r t i e a l lilt)l,ion Z( i, ) or a s e c t i o l m l t l a l (;(luation o1' motion may l)e expressed as I ' o l l o w s : ~l(~,(t), 4zh:f+~(t) , (2+f,,)+z(t)}
l,,,(t) , I,~(t),
model, t h e dl I'l'eren-
(1)
wht:rc t+l = mass, h~. = damping r a t i o , 1'~. = n a t u r a l f r e q u e n c y of tile model and I,,+(t) and I,+~(1.) arc,., r e s p e c t i v e l y , the hufl'etI.g~ lift f o r c e and s e i f (+'×c'.itcd l i r t i'oree. In t i l l s s t u d y , t h e a e r o d y n a m i c f o r c e s arc: e × p r e s s e d as rol lows : I,,(I)
(¢,L'B 2){c ( t ) u ( t ) . c+(t)~(t)} ,
I,(t)
(pL=II 2)lll~z~t) L' ' II=zft) B} .
(2) (3)
in which, II - chord l e n g t h oi' the model, p - a i r d e n s i t y , U - mean wind velocity, u ( t ) and w(i,) - f l u c t u a t i n g wind velocity of horizontal and vertical components, (:,,(t) and c,+(t) = c o e f t ' i c i e n t s o f t r a n s f o r m a t i o n ['or
615
horizontal and v e r t i c a l wind c o m p o n e n t s , r e s p e c t i v e l y . Also Ii, and !12 = so-called velocity-dependent and d i s p l a c e m e n t - d e p e n d e n t s e l f - e x c i t e d aerodynamic coefficients, respectively. Substituting E q s . ( 2 ) and (3) i n t o E q . ( 1 ) , t h e f o l l o w i n g e q u a t i o n is d e r i v e d , M[z(t) + {47~h=f=- (pUB/2M)II,iz(t) + {(2zf=) 2 - (pU2/2M)th}z(t)] = (pUB/2){c.(t)u(t) + c.(t)w(t)} .
(4)
E q u a t i o n (4) i s a r e d u c e d e q u a t i o n of motion from E q . ( 1 ) , where t h e damping and s t i f f n e s s coefficients a r e m o d i f i e d by t h e s e l f - e x c i t e d aerodynamic coefficients, and t h e b u f f e t i n g f o r c e i s e x p r e s s e d as an e x t e r n a l f o r c e .
2.2.
Sol f - c x c i t e d c o e f f i c i e n t s Assuming t h a t t h e s e l f - e x c i t e d f o r c e l , s ( t ) i s i n d e p e n d e n t of t h e b u f f e t ing force La(t), aerodynamic coefficients It~ and I1-~ may be o b t a i n e d by t h e m e a s u r e m e n t of a e r o d y n a m i c damping h.. and n a t u r a l f r e q u e n c y f~ of t h e model v i b r a t i n g in a smootl~ flow.
(5) (6) (7)
I[, = -Sz~Mf.{h. + h=(1-r,)}/(pUB) , II= = -2M(27c f.)= ( l - r ~ ) / ( p Us) , r, = f=/f. ,
in which tim I ' r e q u e n c y l'. of s t r u c t u r e in t h e wind i s n e a r l y e q u a l t o f~ in practice, therefore, t h e f r e q u e n c y r a t i o r r = l l e a d s to t h e d i s p l a c e m e n t depc.ndent c o e l ' l ' i c i c n t il.~=O.
2.3.
Aerodynamic admittance The power s p e c t r a l dens i t y f u n c t i o n s Sz ( f ) of v e r t i cal d i s p l a c e m e n t z ( 1. ) and S , , . ( I ' ) e l ' t h e e x t e r n a l I ' o r c e s I , . ( t ) keep the. I ' o l l o w i n g r e l a t i o n s h i p ,
whe.r(; I1(1') I ows :
Ill(f)l'
(S)
In(f) I"S,..(f),
S=(f) =
is
=
tlle f r e q u e n c y
response
I ' u n c t i o n of
1 M2(2gf)4[{1 _ (f/f.)=12 + 4(h=+h,)2(f/f.)2]
Eq.(4)
expressed
as
I'ol-
(9) ,
and a s s u m i n g t t l a t wind v e l o c i t i e s of h o r i z o n t a l c o m p o n e n t and v e r t i c a l component have no c o r r e l a t i o n , tile power s p e c t r u m S , . . ( f ) el' b u f f e t i n g I'orce is g i v e n a s : S,,(f) = (pUB/2)~{IC,,(f)I=S-(f) + IC*(f)l ~S*(f)} ,
(10)
in w h i c h , S . ( I ' ) and S . ( f ) a r e t h e power s p e c t r a of u ( t ) and w ( t ) , r e s p e c t i v e l y , and C,,(f) and C . ( f ) a r e t r a n s f o r m a t i o n f u n c t i o n s from f l u c t u a t i n g
616
wind v e l o c i t i e s of h o r i z o n t a l and v e r t i c a l components t o b u f f e t i n g force, t h a t is c a l l e d a e r o d y n a m i c a d m i t t a n c e . l l e r e , s u p p o s e d is t h e r e s p o n s e t e s t of s t r u c t u r e s in t h e t u r b u l e n t flow whose wind f l u c t u a t i o n is restricted only to horizontal component, i.e., w(t)=O, t h a t is named as u - c o n t r o l l e d t u r b u l e n c e . L e t t i n g t h e power s p e c t r a of v e r t i c a l m o t i o n and f l u c t u a t i n g v e l o c i t y of h o r i z o n t a l component in such c o n d i t i o n as S ~ . ( f ) and S , , ~ ( f ) , r e s p e c t i v e l y , and u s i n g E q s . ( 8 ) t o (10) in which S . ( f ) = O , t h e h o r i z o n t a l a e r o d y n a m i c a d m i t t a n c e C o ( f ) can be o b t a i n e d as f o l l o w s : IC.(f)l = = 4S.,,(f)/{pUB)ZS,,.(f)lii(f)l
(]])
=} .
in t w o - d i m e n s i o n a l t u r b u l e n t flow whose h o r i z o n t a l and v e r t i c a l components are fluctuating, t h e r e s p o n s e of t h e s t r u c t u r e is m e a s u r e d . II. i s n o t e d t h a t t h e l ~ o r i z o n t a l component of t w o - d i m e n s i o n a l t u r b u l e n c e is i d e n l.i(:al t o t h a t of u - c o n t r o l l e d t u r b u l e n t flow m e n t i o n e d a b o v e . The v e r t i c a l a e r o d y n a m i c a d m i t t a n c e C . ( I ' ) is a l s o o b t a i n e d from t h e r e s p o n s e and E q . ( 8 ) as r o l l o w s : IC.(f)l = = 4S,(f)/{pUB)=S.(f)lll(f)l Through tan(;(:
or
the a
l.h(: s l . r u ( : t u r e
mentioned
structure arc
=} - I C . ( f ) l = s . ( f ) / S . ( f )
p roc:ess,
are
the
obtained,
i(h:nl.iricd.
The
aerodynamic
and
the
process
coerl'ic.ients
aerodynamic
o~
t.he
(12)
.
ror(:es
pres(:nl.ed
and
admit-
working
in I.'igu)'(: I.
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,: [-~:,i~t)~~;~i.o?-i;7~, T~-] :
t~,~.(G) ~
:-[~e,==od-3,;;,,~Y~. co~rr~oi,.,,t l,i=] ,, [l'=e¢l. . . . . . . . . . . .l e s )Io. .n.s. .e. . . . f. ,. n. c .
................
I I I C f )~t
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:[
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X;F'r --:-[
-" ALh~Lo(l~namio a-d' -m" -i ~t t"a' "n-c- e' - C,,(f)_]
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I
I
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: ~Eodyn~m=e edm =t tance Cw( .... , .... . .......... .., ........ ; .,,..
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',
i
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/~el'od~,nar~ic forces
riguro I. Process to evaluate the aerodynamic forces
]
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.... , J :
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: ~wor s,,oot,., s.,.,(r) s (r~
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,
i
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:
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617 3. WIND TUNNEL TESTS 3.1.
Turbulence s i m u l a t i o n The wind t u n n e l t e s t s were c a r r i e d out in t h e G ~ t t i n g e n t y p e wind t u n n e l of Osaka U n i v e r s i t y whose c r o s s - s e c t i o n i s 1 . 8 m x 1.8m. An a c t i v e g u s t g e n e r a t o r [5] was d e v e l o p e d and improved t o p r o d u c e t h e t u r b u l e n t flow s i m i l a r to n a t u r a l wind, which has two a r r a y s of p l a t e s and a i r f o i l s [6,7]. The c o n f i g u r a t i o n of t h e g e n e r a t o r i s shown in F i g u r e 2. The a c t i v e a r r a y s of p l a t e s and a i r f o i l s i n d e p e n d e n t l y c o n t r o l t h e h o r i z o n t a l and v e r t i c a l c o m p o n e n t s of wind v e l o c i t y , respectively. As t h e t a r g e t of t u r b u l e n c e s i m u l a t i o n , t h e KArmAn's e x p r e s s i o n s f o r power s p e c t r a of n a t u r a l wind a r e s e l e c t e d such a s : s.(f) = 4I~,UL,,.,{1 + 70.8(fl.,,../U)Z} - ' / ' . S,,,(f) = 41~UL..,,{I + 755.2(fL,,.,,/U) 2} {1 + 2 8 3 . 2 ( f l , , , . , , / U ) ' }
-''/"
(13) (14)
.
where l' = f r e q u e n c y , I . , L=.,, = 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 of h o r i z o n t a l wind v e l o c i t y and I . , L..w = 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 of v e r t i c a l wind v e l o c i t y , r e s p e c t i v e l y . The d e t a i l s of t u r b u l e n c e s i m u l a t i o n method a r e d e s c r i b e d in a n o t h e r paper p r e s e n t e d a t t h i s c o n f e r e n c e I71. Using the gust generator, two t y p e s of t u r b u l e n c e s i m u l a t i o n were c a r r i e d o u t . One is an t w o - d i m e n s i o n a l t u r b u l e n c e s i m u l a t i o n c o n t r o l l i n g wind v e l o c i t y of t h e h o r i z o n t a l and v e r t i c a l components. The o t h e r i s t h e s i m u l a t i o n of an a n o m a l o u s t u r b u l e n c e such t h a t t h e c h a r a c t e r i s t i c s of h o r i z o n t a l component of wind v e l o c i t y a r e i d e n t i c a l to t h o s e of t h e twod i m e n s i o n a l t u r h u l e n c e , however t h e v e r t i c a l component of wind v e l o c i t y is not f l u c t u a t e d , i . e . , a r r a y of a i r f o i l s keeps t h e s t e a d y s t a t e . The t u r b u l e n c e c h a r a c t e r i s t i c s of s i m u l a t e d t u r b u l e n t flows a r e summar i z e d in ' r a h l c ] t o g e t t l e r w i t h t h e t a r g e t o n e s . The c h a r a c t e r ' - u ' in 1,uri)ul(;n(.'e numhers expresses t h e c h a r a c t e r i s t i c s or u - c o n t r o l l e d turbulenc:e. The power spc;ctra ol' t i m g e n e r a t e d t w o - t ] i m e n s i o n a l t u r h u l c n c e T-12
Array of plates '
Array of airfoils I
\ ~--(X/8-1OS-S3D)II U /
\ll
~
'J"~i Mesh (~20)
/W!,t~d tunnel wal CoiI spring ,u(z
~ Dummymodel
:.~"
l
Model
Model
i K--" - I ..,.r',, ,.
-I
"r~
,~D"~ ,oso
Figure 2. Configuration of active gust generator
Insertable working settler!, wall/j :
900
,'I
1~00 Unit :mm
618
and t h e c o r r e s p o n d i n g u - c o n t r o l l e d t u r b u l e n c e T - I 2 - u a r e r e s p e c t i v e l y shown in F i g u r e s '3 and 4, r o r e x a m p l e . The h o r i z o n t a l components of two t u r b u l e n c e s have a good a g r e e m e n t . In t h e u - c o n t r o l l e d turbulences, t h e power s p e c t r u m oi' v e r t i c a l component i s lower t h a n t h a t of t h e t w o - d i m e n s i o n a l t u r b u l e n c e and t h e t u r b u l e n c e i n t e n s i t y is lower t h a n 1.2%, which can be c o n s i d e r e d as t h e smooth in v e r t i c a l component. T h e r e f o r e , t h e t u r b u l e n c e s i m u l a t i o n s of i d e a l f l o w s in t h e p r e s e n t e d t h e o r y were p o s s i b l e t h r o u g h the active gust generator. Table 1 Turbulence characteristics of generated turbulent flows Measured Turbulence
Change
No.
of
T-II T-I2~;
.
T-I3
.
.
.
Iu &
.
T-ll-u
.
T_12_u o" ...T-13-u l'-Sut T-Su2" T-Su3 'l'-Sul-u
Iw
Target
lu+',lw++iLx, u+',Lx.w++ lu ; I, ', (%)',(%); (era) I (era) (%)',< )', 6 ! 3 ', ', 6.21 3.11 10 ,' 5~ ," 37.5 10.0,: 5.2', 14 ', 7 ' ', 14.11 7.41 6 ,' I, 150 ', 6.0', 1.0', l tO ',< I ', ', 10.0', 1.1, 14 ; I ,, i• lbO 'l 5 'l,, 150 ' ,' 350 10 I, ', 10 0" i ,< I ,, 150 ! ! 350 ,' ,'
I.x, u
T-Su2-u'* ,,T-Su3-u 'l'-Swl
f-Sw2"
3 m/s
l
l,x,w
l
','25 l
Lx.u ', Lx.w lu ; I~ ,, Lx.u ', Lx.w (era) ', (era) ( )',( ), (era) : (era)
14.0 i 1.1; 9.7,, 5.5; l
147 145 148 159 145 153 102
10.0'
145
I
9.7, ' 9.5, .i 10.0, 9.5, ; 10.5,' l
, 37.5 10.0, 'r-sw,3 ', ', f87,5 .9,5 ,: ]u, I,x,u : turbulence intensity and scale of ~, l,x,w : turbulence intensity and scale of
" Turbulences ' " l'urbulences
tO , 5 , 150
I i! 'I 37.5 ,' ', ', '
4 m./s
5.2' I
5.3, ' 364 1.0,.! 100. 1.0,, 145 1.~)', 354 4.6' , 139 l
v
"~" 10o~ -ITI_',~.o I]O.glS,01iSUl',~?:51 ltlE'~ i0 {~ 1..... 52, I.J.L._L34, "! ' .....hJ' , ....t}LI .........
4~
.......... .!.-.,'~,-~,il~ lldl~,.., i ..... , ........
,"
r
llor izonta
1
i
COl~IpOllellt.
i.. \
:.
:
141 153 148 99
1 I , i ,, ,l 37.8
145 'I 40.4
,' , ;, ', ,' l 145 , 168 ',
353 96 153 343 152
38.3
27.6 40.4 82.8
: Vem'tical
FI .... ii................ I n,, l l,qi.~7,il ] I..l(_,,/~,)..I.J:~)l[~}l!.~,@_J lO-t I: ...... 1:1'1 ~&_/l#Al~] [#[LJ ....... l! U!J~_qL[[I.gEJ~] ] 4,_~.J
'~" lO-a
F
I
/if
......Ilori Zontal ........... I~lml]
component
:.~:,,, ~itl~
I ~o-'
.......... ,.!~,:..','.'..,! ....... .! ....i.............. :'i./ /
10~
. . . . . .
.,i.~
vo~t,°.l
10-6
10-~
152 I 41.7
10"4 "coaponent ....... Jt i~.~,~!i~,f: ........
10-~' t!" 10~ !-°-'-u~'L-L~' ........... : ............. ' ~ "!~coral,orient - ~ u ~ j ~-a~Ji 10-~
138 ',' 40.1 145 ,' 40.4
I:
u) 10-~ 4~
I...... ~ .\.~..,.:"~,i i ,./" 'i'i'i}~,~'~lil ......!/il.~ ........ ~,o ~ /. i,~ i ' ""~
'-,o.,
6.1, 3.1; I " I 9.7', 5.2', 13.81 7.0.', 5.91 0.91 l l 10.0, 1.0, ! 13.3, 1.1', 38.2 9.7, i 5.3i l 34.6 9.7' I 5.2' I 37.9 10.0,' 5.4, ' . . 9.5', 1.0, i 10.0:1.0 9.6: 1.0,' 25.3 9.4' , 4.6' , 34.6 9.7', 5.21 85,8 9.9', 5.4',
'r-12, T-Su2 and 'i'-Sw2 are same t u r b u l e n t flows. 'r=12-u and T-Su2-u are same turbulent flows.
1.. I (,,/._'~)1. ~)1 ~) I (c,,,) 1(,;~)l
10"2
u
38.7 34.6 36.1
5.2, 145 5.5', 139 horizontal component vertical component
%, 100
i~
it ,' I I l , ; ,l 'I ,' ,i ,' : ', I ',
10~ 10~ r (llz) I'igure 3. Power spectra of t~o-dimensional turbulence
!
' U.J~IL_J_LLbJ..I
10_2-
10_ z
100
........
I
........
101 10~ f (llz) Figure 4. Power spectra of u - c o n t r o l l e d turbulence
619
3.2.
Aerodynamic r e s p o n s e o f r e c t a n g u l a r model Two-dimensional rectangular cylinder models with aspect ratios ( w i d t h / d e p t h ) of 2 and 5 a r e s u p p o r t e d by v e r t i c a l c o i l s p r i n g s as shown in F i g u r e 5. The sway and t o r s i o n a l motions a r e r e s t r i c t e d by p i a n o - w i r e s . The structural characteristics of the r e c t a a g u l a r mode]s a r e shown in Table 2. The s t r u c t u r a l damping of t h e models is made v e r y l i g h t b e c a u s e aerodynamic f o r c e s w o r k i n g on t h e model can be more a c c u r a t e l y i n v e s t i g a t e d from t h e r e s p o n s e of t h e model. The power s p e c t r a of t h e measured r e s p o n s e of t h e models in t h e mean wind v e l o c i t y 3m/s of t u r b u l e n c e T-I2 and T - I 2 - u a r e shown in F i g u r e s 6 and 7, f o r example. To i n v e s t i g a t e the effects of t u r b u l e n c e c h a r a c t e r i s t i c s , s u c h as t u r b u l e n c e i n t e n s i t y and t u r b u l e n c e s c a l e , on t h e aerodynamic r e s p o n s e of models, t h e r e s p o n s e i s measured not only in t h e smooth flow b u t a l s o in t u r b u l e n t f l o w s . The wind v e l o c i t y v e r s u s a m p l i t u d e c u r v e s of t h e r e c t a n g u l a r model w i t h a s p e c t r a t i o of 2 a r e shown in F i g u r e 8 w i t h r e s p e c t to t h e changes of t u r b u l e n c e c h a r a c t e r i s t i c s . In t h e s e f ~ g u r e s , t h e maximum a m p l i t u d e s of v o r t e x - i n d u c e d o s c i l l a t i o n and g a l l o p i n g a m p l i t u d e s in t u r b u l e n t flows become s m a l l e r t h a n t h o s e in t h e smooth flow. From F i g u r e 8 ( a ) , i t i s r e c o g n i z e d t h a t tht~ i n c r e a s e of t u r b u l e n c e i n t e n s i t y d e c r e a s e s t h e v o r t e x - i n d u c e d r e s p o n s e , which i s t h e same t e n d e n c y of t h e r e s u l t in Ref. [61. On t h e o t h e r hand, t h e c h a n g e s of t h e t u r b u l e n c e s c a l e s do not a f f e c t 10-4 re,: t'angu] a r ~.
cylinder
n~}del
10"4 i 10"~ I' in ,.,10 "6 two-dimnsional ...I..!,.............. ~turbulence (T-I2) [I i
|0"~
I
-'o-'r
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
,_, 10 -~
.......................... :
cylinder
/
p i nno
'~
--~----I
1o-' ..... i~t;o:di"~'n~ion~i .................
<
lO'=v
,.,.,~,~
\ lO-n coil
spr'inR
:
i
10"4
10"~
"
turbulence
:
(T-I2)
: ,~;~
,:,,:,I ..i 10-s~
...............
.....
........... i.....~......;...........i' in u-controlled
:
10.1~ ........ i , ,,,,,,i ........ i it ......
Figure 5. Supporting system of rectangular cylinder m o d e l
-..
.
" ' l . u-c'ontrollod ..... i ~ ......... 10.1 ~ turbulence (?-I~--~) ....i~ I ..........
wire
........
t,a
. . . . . . . . . .
lO-e
I.
, . . . . . . . . . . . . .
10 "=
10"
10o
fD/U
to.,J" ........ ........ ........ 10"4
10"3
10"2
10"1
10o
fDIU
Figure 6. Power spectra of Figure 7. Power spectra of buffeting response (1:2 model) buffeting response (1:5 model)
Table 2 Structural quantities of rectangular cylinder m~els Aspect r a t i o (B/D)
Weight
Natural frequency
2 (D=6Omm) 5 (D=~O~0m)
2.52 kg.f 2.50 kg.f
5.32 llz 2.95 Hz
Logarithmic decrement
0.002 0.002
620 t he maximum a m p l i t u d e of v o r t e x - i n d u c e d o s c i l l a t i o n as shown in F i g u r e s 8(b) and 8 ( c ) . In t h e r a n g e of reduced v e l o c i t y Ur= 7 to 13, t h e a m p I i t u d e in t u r b u l e n c e i s g r e a t e r t h a n t h a t in smooth f l o w , and t h e e f f e c t s of turbulence characteristics a r e not r e m a r k a b l e . In t h e r a n g e of Ur>13, t h e a m p l i t u d e t e n d s to i n c r e a s e with t h e i n c r e a s e of t u r b u l e n c e i n t e n s i t y I , and I,,, and w i t h t h e d e c r e a s e of t u r b u l e n c e s c a I e of v e r t i c a l component L,,.~. However, in F i g u r e 8(b) t h e change of t u r b u l e n c e s c a l e of h o r i z o n t a l component I. . . . . does not a f f e c t t h e aerodynamic r e s p o n s e of t h e model in t h e whole range of wind v e l o c i t y . The b u f f e t i n g r e s p o n s e of t h e r e c t a n g u l a r c y l i n d e r w i t h a s p e c t r a t i o of 5 is s t r o n g l y a f f e c t e d by t h e change of t u r b u l e n c e i n t e n s i t y as shown in l:igure 9. [n t h e range of U~>15, t h e a m p l i t u d e of t h e model is r e m a r k a b l y i n c r e a s e s w i t h t h e i n c r e a s e of t u r b u l e n c e i n t e n s i t y . T h e r e f o r e , i t can be r e c o g n i z e d t h a t t h e aerodynamic r e s p o n s e of t h e r e c t a n g u l a r c y l i n d e r w i t h a s p e c t r a t i o of 5 i s more s t r o n g l y a f f e c t e d by the f l u c t u a t i n g wind v e l o c i ty than t h a t with a s p e c t r a t i o of 2.
..-.. U,12 ~r~
@ smonth flow 01-11 (h = 5,% I,--3%) AT-I2 (I,:I0%, I,=5%) o t-I.~ (I,;14%, l,,TX)
• smooth flow 0 T-S,d (I.,.,:lOOcm)
0.12
TSu2 (I.~.,: 151]cm) n T-Stn3 (L,.,-350cm)
:
"" OJig ~=~
"" 0.(19 .,~
"s
flog
•
O/i]
frO)
o ,_.
0.00
01~0 5
tO
15
5
U,-'U/fll
Figur'o 8(a). Velocity vs. amplitudo curvo (1:2 model) -, change of intensity I. & l,
~
"
$ smc~)th flow 0 1",%1 (I,,,,qZ,~cm,~ Z~ I"'SwZ(l.,.,~JT.Scm~
O,IZ
" " OIYJ
10
.-.
O,OB
""
0,06
.,.,.
• sm~ot5 flov o r.ll 0,, 5~. X :3x) ,,'~ l',iz (6,10,, I,~,5%}
~ ~/xAtx
OJ))
Ik) 0
092
090
5
tO
15
u,:u/rD
~)
Figure 8(b). Velocity vs. amplitude curve (1:2 model) - change of horizontal scale I,x.u
.
0
15
U,,U/rD
n ~ ~
Figure 8(c). Velocity vs. amplitude curve (l:2 model) - change of vertical scale l,x.w
0
~
A
_~../~¢%oooo
0o
0 o
090 0
tO
20
)O
L.,,,. 40
U,--,U/FI}
Figure 9. Velocity vs, amplitude curve (1:5 model) -change of intensity i.& lw
:1.3. S e l f - e x c i t e d c o e f f i c i e n t s The l o g a r l t h u l l c decrement oi' r e c t a n g u l a r c y l i n d e r s in smooth flows i s measured by means el' t h e f r e e v i b r a t i o n method u s i n g a s i n u s o i d a l o s c i l l a t o r . The a e r o ( l y n a m i c (lamping is g i v e n by t h e s u b t r a c t i o n of s t r u c t u r a l
621 damping from measured damping in smooth flow. Using the E q . ( 5 ) , the s e l f excited aerodynamic coefficient H1 i s o b t a i n e d . T a b l e 3 s u m m a r i z e s t h e o b t a i n e d aerodynamic damping and s e l f - e x c i t e d c o e f f i c i e n t 111 of the models in the wind v e l o c i t y of 3 and 4 m/s.
Table 3 Aerodynamic damping and self-excited coefficient Aspect ratio of model Mean velocit~ (m/s) Aerodynamic damping as logarithmic decrement Self-excited coefficient
2
H~
5
3
4
3
4
0.028
0.180
O. 080
O. 120
-3.32
-16.0
-3.16
-4. "/5
3 . 4 . Aerodynamic a d m i t t a n c e Using the measured r e s p o n s e in t w o - d i m e n s i o n a l and u - c o n t r o l l e d t u r b u l e n c e s , the aerodynamic a d m i t t a n c e of the c y l i n d e r models can be o b t a i n e d through the p r e s e n t e d t h e o r y . The aerodynamic a d m i t t a n c e s a r e o b t a i n e d in v a r i o u s k i n d s o f t u r b u l e n c e s as shown in F i g u r e s 10 and 11. From t h e s e f i g u r e s , i t can be seen t h a t the aerodynamic a d m i t t a n c e of the v e r t i c a l component i s a p p r o x i m a t e l y one o r d e r g r e a t e r than t h a t of h o r i z o n t a l compon e n t . In the case of the r e c t a n g u l a r c y l i n d e r with a s p e c t r a t i o of 5, the F i g u r e 11 shows t h a t the changes of o b t a i n e d aerodynamic a d m i t t a n c e s are very small in change o1' t u r b u l e n c e c h a r a c t e r i s t i c s in the lower range el" r e d u c e d f r e q u e n c y fr=fl)/U < 0 . 0 1 compared w i t h t h o s e of t h e model w i t h a s p e c t r a t i o of 2 as shown in F i g u r e 10. ..~ 10° ~
:
lO" ~
~o~ "~-l~.tt)ii~-.~ ......... i............. -IO ~ E. Ir-lc,.(r)l h,--s% ...... i.. I .....
..
I. Jli ,c,(r)l ,,,--'7%~
• --
_
~
-
lO'i
"
ICu(f)l lu=6%
10"= W ']~lc.(t)l
i
~ ~-IcuCr)l lu--14%
10-4
10"
III11111
I l*lilUl
10-3
lOo
"
!
i
i
..........~ ......... i.............: ........... [
r-lCw(Ol
i
.,bL
I]
I
i-~----i~£I r
......
,
.....I
i lllilil[
i
!
10"a
i iilllll
I 10" ifO/U 10"
(a) Change of lu & lw
~ II]3 F2i0.~ =
~, I0' d I0°
10-I
~(f)l
; . . . . . i ' :t
10-2
lu=lO% .....i ...... 1 "
~°~ ~i.,,i ii- i~iJc,~i£~-3:il ~, ............. [i
I0~
_ llY
"
I°-~ F L,,.,,:3i.s~:,. i,~ox~,'-:r,i ~~ [ I
10-3 I0-~
I0-'
10-3
I0"2
I0"i
(b) Change of Lx.u
Figure 10. Aerodynamic admittance (1:2 model)
fo/u
I0°
I0""
10-3
I0 -2
10"I I0~ fDIU
(c) Change of l,x,w
622
"'°"
' -'° I
-,o.
I
. . . . . . . . . .
10-'10_; ~:"L' ~~'1i'IL--LL-ICu(f)t .~l -Z'~-I';u(' -.~,'Cu(f)I ~'i Il'u'~" uu--~H' IO.~£..I~''I1~ ' I"' 10-~~ I.x,.o-,l'SO~, 10" , ., ,L~.'1.=~.5c=' ! I0-" 10"~ 10-"~ I0-tfDIg 10°
: . . . . . . . . .
.~
lO-'l()_~. I I~'I!!! !'ii !i!'i!i~ i"t ""I 10-"10-~~ ~ ~ 10-~ 10-~ 10-~ 10-~fO/IJ10~
10~
......'......
.',i
.
10-'10_, I "'~ i(~u~'~' !' '~'iiiI'"" / 10-''1It0-~I.x.,,--~SO~.,.~,-m%.I,--.~ ',,,,,,1~/ I0-" ;)-~ 10-~ 10-~fD/U10° (c) Change of l,x,w
(b) Change of Lx.u
(a) Change of lu & Iw
.•
Figure 11. Aerodynamic admittance (1"5 modcl)
4.
F,STIIIIATION
OF B U F F E T I N G
RESPONSE
Using the aerodynamic a d m i t t a n c e o b t a i n e d in tile t u r b u l e n c e T - I 2 , the power s p e c t r a of b u f f e t i n g r e s p o n s e in o t h e r k i n d s of t u r b u l e n c e s a r e c a l c u l a t e d and compared with measured ones in win(l tunnel t e s t s . When the turl)ulence c h a r a c t e r i s t i c s ; U, I . ( I . = I . / 2 ) , Lx.,, and i , x . . are i n d i v i d u a l l y ehang,:d, tile e s t i m a t e d response s p e c t r a are o b t a i n e d as shown in i,'igures 12 and 13 l,ogel, her with the measured ones, r e s p e c t i v e l y . I n t h e s e f i g u r e s , the estimal.(:d resi)ons(: s p e c t r a are a p p r o x i m a t e l y well f i t t e d 1o tile measured Sl)C.,C,'1,ra or th(., reel, a n g u l a r c y l inciers. For the a p l ) r o i ) r i a t e (.,valuation or b u r l ' e t i n g respor.se, il. is rleeded to lll~.,(;st, ignl~.(,, th(,. r e s p o n s e o f s t r u c t , ur(:s ill t h e hroa(l v'ange or l, lirl)lll(,.nt flows Sillllllatinl!~ nlll.lll'al win(is, howcv(;r, the r u l l (}X,tllllilh'll. iOll is a c t u a l l y (11 rri¢,.ul t, i.hroll~h 1,he; wind 1.llnnel l,(,.sts. ' rh e r(:ro re . tim e r r i c : i ( m t illetho(I ror t,h(,, i)r('.cll(;i, oil or l)urrc,,1,ing r(,.sporlse is requir(,.(i, all(! tilt., (:stilna1,1n~ Ill(,,t.h()(i l)rc;sc;n1,(}d here (tan he usel'ul ly al)pl led to such proi)lenls.
I0-4
10"" ,,'7"I0""
,,'7" 10-s
.... ~.~(i,,,.-,t~.'(l
...... i
10-<, 10"~ r.o 10""
......
lO-~
d 10"
...iii~i.i~ ....~.....!.........i.......... I0"* ii
lO-'f I0-11 10-1~ men.~'drcd ............ ! ' ..... 10"~ ............ i.............. i.............. !" II"' lo-' . . . . . . . . . i ..... , , , ~ L 10"4 10-~ 10-~
(a) Response
in
l'""
10-~
10~
10"= I0-I" 10-11 I0-I~ 10"" 10""
fl)/O
of buffeting
......i~VV~i~l.~i.il..
I0 "4
T-12 of 4m/s
Figure 12. Estimation
estimated i i
(b) respc)nse
(1:2 model)
rD/u 10 '~
I0 ":~
Response
I0" I.
ill T-13
i0 n
623 10-4
10-4
...........i............. +...............,•
lO-S ............
"~'~ ¢,0. ++ 10") I
i0_6
v
1°-+ ...... e s t [ m a t o d ........! ............. ...........................'
! .............
1o-' ~ " ~ - - i .............. , " . < . , . : : , ) ....... lO-,r F ...... :
..,'~![I...;P.! ............
,o-,, r,,oa~,,-o~ 10-1:l
!
!
10""
fD/u
I I - -
10-4
10-~
lO-Z
lO't
-o~t°~a
I
111;;
.........
~-i-~!~l~
lO-S( 10-4
10°
Response in T - S u l
(c)
......
lO-S-~
~ "1~
........
..... iii;; .......
lO-il
....... .....+.,,+m .......
•
J ...........
J
!!!~li+ .......+..........'
10-" lO-ll
,o..~.~i.+...............
........................
mcastlred
I0-7 I0"" I0-~
.......~ ................ +i;iil............ -i Jli~| ...........
............
10-3
(d)
10-=
Response
two
lO-i
in T-Swi
F i g u r e 12. E s t i m a t i o n of b u f f e t i n g r e s p o n s e (1:2 model)
10-4
10-s E
A
i
tO "4
i
I0-~
......os~ nlatcd 'ilii..............
I0-6 I0-)
I0-~ v
io'"
lO-e
I0-+ .~ .......... +\ .......... +............ + ..........
10"*
i0-=~ lO-l,
tO-! ~ lO'll
IO-i;
.~+ .............. ~.............. lO'll ............
I
lO'l~
fo/u
10-4 .-"". 10.s 10"6 .,,
,°-'
,
, ,,,,,.i , ,,,,,,~ , ,,,,.,i - Ii--
lO-S
I0"4
(b)
m
+.I
............ +.............. +.............. i.
10"1
Response in T-12 o f 4m/s
(a)
estimated ............i..............;.............
I0-i.~ lO.Z~ ........ i' ........ i' ........ I+ I,L,7:;;; 10"* 10"l 10"= 10"i 10"
d
!....... ineasu red ....... !
10-~
Response
I0-(
i
~!+,+~
Io-o ........... i.....
lO-i
-
in T-I3
I0-S
.... ,,,,,,,,i
10-6
.,.
....... I ...... i ..............
niP,as. rod
I..............
, ...................
i .................. '+"
i ...............
V N
IO-~ lO-e
10-~
-,,.,
.
.....
.
~. . . . . . . . . . . . . .
i .......................
.
i ................
.
i
I0-=1
~°"° ...... e s t i m a t e d ...............
10-I~ ........ e s t i m a t e d .............. i
o+ .....+.................... if .........
10-1J
I0-1=
10-+~
tO-l." lo-,"
rn/u
lO"
i
I
,)castlrcd
lO-i
........ i ........ i ........ i. I . ....... m rl)/U 10.4 10"3 10 "= 10"i 10e
I
i
............ i .............. ~.............. i ............ 10-1." ............ ~.............. ~.............. i ..... ........ i" ........ i' ........ I' ',,.,,i',,' 10"14
(c) Response ill T-SuI
Figure 13. Estimation of buffeting response (1:5 model)
J.
I0"4
10-3
I0-=
I0-=
(d) Response in T-Swl
1o°
fo/u
624 5. CONCLUSIONS The f o l l o w i n g c o n c l u s i o n s can be drawn t h r o u g h o u t t h i s s t u d y . (1) An e f f i c i e n t method to o b t a i n the aerodynamic a d m i t t a n c e in b u f f e t ing a n a l y s i s is presented u s i n g an a c t i v e gust generator wilich produces the t u r b u l e n t flows s i m i l a r to n a t u r a l wind. (2) In t h e w i n d t u n n e l t e s t s , t h e a e r o d y n a m i c r e s p o n s e of t h e r e c t a n g u l a r c y l i n d e r s w i t h a s p e c t r a t i o s o f 2 and 5 i s m e a s u r e d in t h e smooth f l o w and t u r b u l e n t f l o w s . The a e r o d y n a m i c a d m i t t a n c e and s e l f excited aerodynamic coefficients of r e c t a n g u l a r models a r e o b t a i n e d by the p r e s e n t e d method. (3) In t h e c a s e of r e c t a n g u l a r model w i t h a s p e c t r a t i o of 2, t h e a m p l i t u d e of b u f f e t i n g r e s p o n s e t e n d s to i n c r e a s e w i t h t h e i n c r e a s e of turbulence intensity 1,, and I~, and w i t h t h e d e c r e a s e of t u r b u l e n c e s c a l e of v e r t i c n l component I. . . . in the reduced v e l o c i t y U~>13. ilowever, the chane;e of t u r b u l e n c e s c a l e of h o r i z o n t a l component L , . , , does not a f f e c t the aerodynamic r e s p o n s e in the whole range of wind v e l o c i t y . On the o t h e r hand, t h e b u f f e t i n g r e s p o n s e of t h e r e c t a n g u l a r model w i t h a s p e c t r a t i o of 5 is v e r y s t r o n g l y a f f e c t e d by t h e i n c r e a s e of t u r b u le.nce i n t e n s i t y . (4) The o b t a i n e d a d m i t t a n c e s of h o r i z o n t a l and v e r t i c a l components a r e almost t h e same ~ i t h change of t u r b u l e n c e c h a r a c t e r i s t i c s in t h e r a n g e testetJ. (5) The e s t i m a t i o n of b u f f e t i n g response is c a r r i e d out. Ttle estimated r(;sponse is approxinlal, e l y well f i t t e d to the measured one. The presented l)r(:di(',tion is very us(:ful to evaluate the b u f f e t i n g response in the turbtnI(:nl, ['low w i l,h arb i 1,rary charac:l,c,,r i sl, it:s.
A(;KNOWI,I,:I)GMI,:NTS Th(; aul, hors w()tnl(I Ilk(: to thank Proi'. II. I(oi)ayashl ol' ltitsum(,,ikan L;niv(,,rsily r o r Ills l)rt, i)(,,r advice to wind tunrlel test, s, anti I)rol '. Y. I,'ul
7
Simlu,10:. anti S c a n l a n , R . I I . , Wind E f f e c t s on S t r u c t u r e s : An I n t r o d u c t i o n to Wind E n g i n e e r i n g , John WiI(;y & Sons, I n c . , New York, 1978. Ilonshu-Shikoku Bridge A u t h o r i t y , The S p e c l f i c a t l o n s for the Wind R e s i s t ant Design, 1976 (Ill J a p a n e s e ) . S('anlan,lA.II., ,I. Sound and V i b r a t i o n , Vol.60 (1978) 201. I)avenport,A.C;., Proc. ASCE, Vol.88, No.ST3 (1962) 233. Cermak,,l.E., Bienkiewicz,B., P e t e r k a , J . A . avid S c a n l a n , R . I I . , J. Wind I,~tlgine(:rinff and I n d u s t r i a l Aerodynamics, Vol.13 ( 1 9 8 ' } ) 4 6 5 . I(obaya~hi,ll, g a w a t a n i , ~ , and Nakade,O., J. Wind E n g i n e e r i n g and Indust r i a l Aerodynamics, Vol.33 (1990) 101. I(ol)ayashi,ii., i(awatani,l~i, and Kim.tl., Proc. 8th ] n t . Conf. on Wind l,:nginecring (1991).