UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Fluctuating lift on cylinders of rectangular cross section in smooth and turbulent flows Namiranian, Farshid 1985

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1985_A7 N35.pdf [ 2.88MB ]
Metadata
JSON: 831-1.0080809.json
JSON-LD: 831-1.0080809-ld.json
RDF/XML (Pretty): 831-1.0080809-rdf.xml
RDF/JSON: 831-1.0080809-rdf.json
Turtle: 831-1.0080809-turtle.txt
N-Triples: 831-1.0080809-rdf-ntriples.txt
Original Record: 831-1.0080809-source.json
Full Text
831-1.0080809-fulltext.txt
Citation
831-1.0080809.ris

Full Text

FLUCTUATING LIFT ON CYLINDERS OF RECTANGULAR CROSS SECTION IN SMOOTH AND TURBULENT FLOWS by FARSHID NAMIRANIAN B.S., UNIVERSITY OF WASHINGTON, U.S.A., 1982 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We accept t h i s t h e s i s as conforming to the r e q u i r e d standard UNIVERSITY OF BRITISH COLUMBIA APRIL, 1985 © FARSHID NAMIRANIAN, 1985 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the UNIVERSITY OF BRITISH COLUMBIA, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that permission f o r ex t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . DEPARTMENT OF MECHANICAL ENGINEERING . UNIVERSITY OF BRITISH COLUMBIA 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: APRIL, 1985 ABSTRACT T h i s t h e s i s p r e s e n t s an e x p e r i m e n t a l i n v e s t i g a t i o n o f t h e f l u c t u a t i n g l i f t ( o r s i d e f o r c e ) c o e f f i c i e n t on f i x e d two d i m e 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 f o r v a r i o u s f r e e s t r e a m t u r b u l e n c e i n t e n s i t i e s a n d s c a l e s . The m e a s u r e m e n t s a r e made u s i n g t u r b u l e n c e p r o d u c i n g d e v i c e s s u c h a s g r i d s and c i r c u l a r r o d s p l a c e d u p s t r e a m o f t h e s t a g n a t i o n l i n e o f t h e m o d e l . M e a s u r e m e n t s a r e r e p o r t e d f o r t h r e e f i x e d r e c t a n g u l a r p r i s m s w i t h B/H of .5, .67 and 1 where H i s t h e f r o n t a l d i m e n s i o n and B i s t h e s t r e a m w i s e w i d t h o f t h e body. The method o f measurement made i t p o s s i b l e t o v a r y t h e body span so t h a t t h e c o r r e l a t i o n o f t h e f l u c t u a t i n g s i d e f o r c e o v e r t h e body span c o u l d be i n v e s t i g a t e d . I t was shown t h a t f o r low t u r b u l e n c e i n t e n s i t y , t h e s p a n w i s e c o r r e l a t i o n o f t h e f l u c t u a t i n g s i d e f o r c e o v e r t h e s q u a r e c y l i n d e r s d e c r e a s e s by a l a r g e amount w i t h i n c r e a s i n g s p a n . F o r h i g h e r t u r b u l e n c e i n t e n s i t y t h i s d e c r e a s e was r e d u c e d , and f o r U ' / U - 1 0 % t h e r e was e s s e n t i a l l y no d e c r e a s e o f f l u c t u a t i n g l i f t c o e f f i c i e n t w i t h i n c r e a s e o f s p a n . i i Table of Contents ABSTRACT i i LIST OF TABLES v LIST OF FIGURES v i NOMENCLATURE ix ACKNOWLEDGEMENTS . x i 1. INTRODUCTION 1 2. Experimental Arrangements 6 2 . 1 Wind Tunnel 6 2.2 Turbulence Producing Devices 6 2.2.1 G r i d s 6 2.2.2 Rods 9 2.3 Models and Mountings 10 2.4 Force Measurements 11 2.5 Pressure Measurements 14 3. R e s u l t s and D i s c u s s i o n For Square S e c t i o n s 15 3.1 Form of R e s u l t s 15 3.2 E f f e c t of Aspect R a t i o 16 3.3 E f f e c t of Turbulence I n t e n s i t y 1 8 3.4 E f f e c t of Length Scale 19 3.5 End E f f e c t s 20 4. R e s u l t s For Other S e c t i o n Shapes 24 4.1 Rectangular S e c t i o n With B/H=.67 24 4.2 Rectangular S e c t i o n Shapes With B/H=.5 25 4.3 Comparison For A l l S e c t i o n Shapes 26 5. C l o s i n g Comments 27 5.1 C o n c l u s i o n s 27 5.2 Comments On The Experimental Method Used 28 i i i BIBLIOGRAPHY 30 APPENDIX A 74 APPENDIX B 77 APPENDIX C 80 i v L I S T OF TABLES 1. U n s t e a d y l i f t c o e f f i c i e n t s r e p o r t e d i n t h e l i t e r a t u r e .34 2. V a l u e s o f X/H, C f AND A/H f o r r e c t a n g u l a r s e c t i o n s . .35 v LIST OF FIGURES 1. Tunnel o u t l i n e 36 2. Decay of l o n g i t u d i n a l i n t e n s i t y of turbulence 37 3. Growth of l o n g i t u d i n a l s c a l e of turbulence with downstream d i s t a n c e 38 4. Sketch of a l i v e s e c t i o n 39 5. Sketch of the load c e l l beam 40 6. Sketch of a t y p i c a l model i n s i d e the wind tunnel . . .41 7. End p l a t e s 42 8. Base p r e s s u r e c o e f f i c e i n t s f o r square c y l i n d e r s in smooth and t u r b u l e n t flows .43 9. R.M.S. l i f t c o e f f i c i e n t s at d i f f e r e n t wind speeds . . .44 10. A t y p i c a l spectrum of the f n and f v 45 11. as a f u n c t i o n of aspect r a t i o f o r square c y l i n d e r s at u'/U-O (with and without end p l a t e s ) 46 12. C£ as a f u n c t i o n of aspect r a t i o f o r square c y l i n d e r s at u'/U=4% (with and without end p l a t e s ) 47 13. C£ as a f u n c t i o n of aspect r a t i o f o r square c y l i n d e r s at u'/U=6% (with and without end p l a t e s ) 48 14. C£ as a f u n c t i o n of aspect r a t i o f o r square c y l i n d e r s at U ' / U = 1 0 % (with and without end p l a t e s ) 49 15. C£ f o r square c y l i n d e r s at u'/U-O along with the a n a l y t i c a l models 50 16. C£ as a f u n c t i o n of i n t e n s i t y f o r a square s e c t i o n with L/H= 1 51 17. C£ as a .function of i n t e n s i t y f o r a square s e c t i o n with L/H=2 52 v i 18. C£ a s a f u n c t i o n o f i n t e n s i t y f o r a s q u a r e s e c t i o n w i t h L/H=4 53 19. C£ a s a f u n c t i o n o f i n t e n s i t y f o r a s q u a r e s e c t i o n w i t h L/H = 8 54 20. C£ a s a f u n c t i o n o f i n t e n s i t y f o r a s q u a r e s e c t i o n w i t h L/H=16 55 21. V a r i a t i o n o f C£ a n d Cp^ w i t h t u r b u l e n c e i n t e n s i t y . . .56 22. C£ a s a f u n c t i o n o f u'/lT f o r a s q u a r e s e c t i o n w i t h L/H=2 ( r o d t u r b u l e n c e ) 57 23. C£ a s a f u n c t i o n o f u'/U f o r a s q u a r e s e c t i o n w i t h L/H=4 ( r o d t u r b u l e n c e ) 58 24. C£ a s a f u n c t i o n o f u'/U f o r a s q u a r e s e c t i o n w i t h L/H=8 ( r o d t u r b u l e n c e ) 59 25. C£ a s a f u n c t i o n o f u'/LT f o r a s q u a r e s e c t i o n w i t h L/H=16 ( r o d t u r b u l e n c e ) 60 26. C o m p a r i s o n b e t w e e n C£ o b t a i n e d u s i n g r o d and g r i d t u r b u l e n c e . . . 61 27. E f f e c t o f i n t e g r a l l e n g t h s c a l e on C£ 62 28. E f f e c t o f gap s i z e ( b e t w e e n t h e dummy end p i e c e s and t h e ' l i v e ' s e c t i o n ) on t h e mean b a s e p r e s s u r e c o e f f i c i e n t . . .63 29. C £ o a s a f u n c t i o n o f u'/U 64 30. C£ a s a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.67 a t u'/U^O 65 31. C£ as a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.67 a t u'/U=4% 66 32. C£ a s a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.67 a t u'/U=6% .67 v i i 33. C£ a s a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.67 a t U ' / U = 1 0 % 68 34. B a s e p r e s s u r r e c o e f f i c i e n t i n smooth a nd t u r b u l e n t f l o w f o r s e c t i o n w i t h B/H=.67 69 35. C£ a s a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.50 a t u'/U^O 70 36. C£ a s a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.50 a t u'/U=4% 71 37. C£ a s a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.50 a t u'/U=6% 72 38. C£ a s a f u n c t i o n o f a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.50 a t U'/U=10% 73 v i i i NOMENCLATURE b :bar width of a g r i d B :streamwise dimension of r e c t a n g u l a r s e c t i o n s C :damping C D :drag c o e f f i c i e n t CL rr.m.s. l i f t c o e f f i c i e n t C £ Q : l o c a l value of C £ , measured over a very sho r t span without end e f f e c t s d :rod diameter dB : d e c i b e l f n : n a t u r a l frequency (Hertz) f v rvortex shedding frequency (Hertz) F rmagnitude of the for c e a p p l i e d to the ' l i v e ' s e c t i o n F 0 : l o c a l f o r c e on a l i v e s e c t i o n F, : l o c a l f o r c e on a l i v e s e c t i o n F 2 : l o c a l f o r c e on a l i v e s e c t i o n F B r t o t a l f o r c e on the l i v e s e c t i o n H : f r o n t a l dimension of r e c t a n g u l a r s e c t i o n s H ( C J ) :mechanical admittance Hz :Hertz, c y c l e s / s e c . k : s t i f f n e s s L :span of the l i v e s e c t i o n L ' : e f f e c t i v e l ength ( L - 2 A ) L X : l o n g i t u d i n a l length s c a l e of turbulence m : ma s s M :mesh width of a g r i d ix Re : R e y n o l d s number = U H/u t :time T : i n t e g r a l t i m e s c a l e u' : l o n g i t u d i n a l component of f l u c t u a t i n g s p e e d U :wind s p e e d (mean) u'/U r t u r b u l e n c e i n t e n s i t y x : d e f l e c t i o n of t h e beam ( a m p l i t u d e of m o t i o n ) i / x 2 :r.m.s d e f l e c t i o n Y r s p a n w i s e d i s t a n c e f r o m t h e mid span of a r e c t a n g u l a r c y l i n d e r o>v : v o r t e x s h e d d i n g f r e q u e n c y ( r a d i a n s / s e c ) c j n r n a t u r a l f r e q u e n c y ( r a d i a n s / s e c ) p : a i r d e n s i t y v r k i n e m a t i c v i s c o s i t y |3 :damping as a f r a c t i o n o f c r i t i c a l ( i . e . /3=C/Cc) A : l e n g t h , a f f e c t e d by end c o n d i t i o n T :time d e l a y X : i n t e g r a l l e n g t h s c a l e o f t h e f o r c e c o r r e l a t i o n x ACKNOWLEDGEMENTS The author c o n s i d e r s himself f o r t u n a t e to have had Dr. I.S.Gartshore as h i s s u p e r v i s o r throughout t h i s study. Thanks to the department of Mechanical E n g i n e e r i n g f o r the use of t h e i r f a c i l i t i e s , and to the t e c h n i c a l s t a f f f o r i t s e f f o r t i n c o n s t r u c t i n g the wind tunnel models and mount ings. F i n a l l y , the author would l i k e to express h i s s i n c e r e thanks to those who c o n t r i b u t e d i n t h i s study in any way. xi 1. INTRODUCTION Forces induced by vortex shedding on c i r c u l a r c y l i n d e r s have been measured by numerous r e s e a r c h e r s . However, the phenomenon of f l u c t u a t i n g s i d e f o r c e s ( f l u c t u a t i n g l i f t ) on r e c t a n g u l a r c y l i n d e r s in smooth and t u r b u l e n t flows has r e c e i v e d l e s s a t t e n t i o n . The f l u c t u a t i n g s i d e f o r c e i s due to a l t e r n a t e shedding of v o r t i c e s from the s i d e s of the c y l i n d e r s ; the v a r i a t i o n of l o c a l pressure d i s t r i b u t i o n due to shedding of the v o r t i c e s causes a time v a r y i n g f o r c e on the c y l i n d e r , at a frequency centered around the vortex shedding frequency. The subject i s of importance because of the e f f e c t s of wind induced v i b r a t i o n s which cause m a t e r i a l f a t i g u e and resonant v i b r a t i o n s of s t r u c t u r e s (resonant v i b r a t i o n s occur when the frequency at which the eddies are shedding away from a c y l i n d e r , i . e . , vortex shedding frequency, matches the n a t u r a l frequency of the c y l i n d e r ) . Resonant v i b r a t i o n s of slender towers, chimney stacks and t r a n s m i s s i o n l i n e s are p o s s i b l e examples. T h i s work d e a l s only with the f l u c t u a t i n g l i f t due to vortex shedding. P a r t i c u l a r l y when turbulence i s present i n the fr e e stream, b u f f e t i n g f o r c e s a r i s e which are spread over a wide range of f r e q u e n c i e s . These are s i g n i f i c a n t f o r bodies of r e c t a n g u l a r s e c t i o n on which flow s e p a r a t i o n f o l l o w e d by permanent reattachment occures, t y p i c a l l y bodies whose streamwise l e n g t h i s l a r g e r than t h e i r f r o n t a l dimension. Such b u f f e t i n g f o r c e s are not expected to be 1 2 s i g n i f i c a n t i n t h e p r e s e n t s t u d i e s s i n c e o n l y r e l a t i v e l y s h o r t s e c t i o n s a r e u s e d . The d i s t i n c t i o n must be made h e r e b e t w e e n l o c a l l i f t a n d l i f t a v e r a g e d o v e r a f i n i t e s p a n . The l i f t p e r u n i t l e n g t h a v e r a g e d o v e r a f i n i t e s p a n i n c l u d e s t h e i m p e r f e c t s p a n w i s e c o r r e l a t i o n o f t h e f o r c e , a n d i s a l w a y s l e s s t h a n t h e l i f t p e r u n i t l e n g t h m e a s u r e d l o c a l l y i f end e f f e c t s do n o t e n t e r . L o c a l f o r c e s a r e f o u n d e i t h e r by d i r e c t l y m e a s u r i n g t h e f o r c e on v e r y s h o r t s p a n s o r by m e a s u r i n g a s e r i e s o f p r e s s u r e s ( e i t h e r s i m u l t a n e o u s l y o r w i t h s u i t a b l e p h a s e c o r r e l a t i o n ) t o deduce t h e l o c a l f o r c e . The use o f p r e s s u r e m e a s u r e m e n t s i s most common s i n c e v e r y s h o r t s p a n l e n g t h s s e n s e o n l y v e r y low f o r c e s w h i c h a r e d i f f i c u l t t o m e a s u r e d i r e c t l y . F o r c e s on l o n g e r s p a n ' l i v e ' s e c t i o n s c a n be m e a s u r e d d i r e c t l y o r d e d u c e d f r o m l o c a l f o r c e s a n d t h e s p a n w i s e c o r r e l a t i o n o f f o r c e . The f o r m e r h a s t h e d i f f i c u l t y t h a t t h e ' l i v e ' s e c t i o n must be p h y s i c a l l y s e p a r a t e d f r o m a d j a c e n t 'dummy' e n d s e c t i o n s . E v e n v e r y n a r r o w g a p s ( a s i n V i c k e r y ' s 1 c a s e ) may g i v e r i s e t o u n w a n t e d f l u c t u a t i n g p r e s s u r e s o r s p a n w i s e p r e s s u r e g r a d i e n t s a n d h e n c e u n w a n t e d f o r c e s on t h e ' l i v e ' s e c t i o n . T hus end e f f e c t s e n t e r i n a v a r i a b l e way, p r o p o r t i o n a l l y l a r g e r e f f e c t s b e i n g p r e s e n t f o r s h o r t e r s p a n s . The d i r e c t measurement of s p a n w i s e f o r c e c o r r e l a t i o n i s d i f f i c u l t b e c a u s e o f t h e need f o r many p r e s s u r e t a p s o r c o m p l i c a t e d f o r c e s e n s o r a r r a n g e m e n t s , a n d i s u s u a l l y r e p l a c e d by a s p a n w i s e c o r r e l a t i o n o f p r e s s u r e s m e a s u r e d a t 3 mid chord and assumed to be e q u i v a l e n t to the c o r r e l a t i o n of f o r c e s . T h i s equivalence i s somewhat d o u b t f u l although i t i s best when measured as a c o r r e l a t i o n of pressure d i f f e r e n c e on e i t h e r s i d e of the model as was done by V i c k e r y 1 . A review of prominent papers in t h i s f i e l d shows that the measurement of l o c a l f l u c t u a t i n g f o r c e s i s f a i r l y common. Of these, Pocha 2, Lee^, W i l k i n s o n ^ , G a r tshore^ and Bearman & Obasaju^, measured f o r c e s on square 2D c y l i n d e r s a l l u s i ng i n t e g r a t i o n of p r e s s u r e s . Fewer w r i t e r s have used f i n i t e span ' l i v e ' s e c t i o n s to measure spanwise averaged f o r c e s . V i c k e r y 1 measured the f l u c t u a t i n g s i d e f o r c e s on a 6in(l5.24cm) by 6in(l5.24cm) square c y l i n d e r of 3in(7.62cm) l e n g t h . The model was mounted on a hollow beam with four e l a s t i c supports and, using a u n i - d i r e c t i o n a l s t r a i n gauge dynamometer mounted w i t h i n the beam, the f l u c t u a t i n g s i d e f o r c e s c o u l d be measured. The gap between the ' l i v e ' s e c t i o n and the dummy ends was set at .01 in(.25mm). In a s i m i l a r study, now c o n s i d e r i n g a c i r c u l a r c y l i n d e r , So & Savkar 7 measured the spanwise c o r r e l a t i o n of the f l u c t u a t i n g s i d e f o r c e s and drag on c i r c u l a r c y l i n d e r s , in smooth and t u r b u l e n t flows f o r d i f f e r e n t Reynolds numbers, us i n g two t h r e e - a x i s measuring lo a d c e l l s at each end of t h e i r t e s t c y l i n d e r . In these t e s t s , the ' l i v e ' span c o u l d vary from 1.5in (38.1mm)to 8in(203.2mm), and a rubber s e a l was used at the ends of the ' l i v e ' s e c t i o n . In t h i s type of experiment, the n a t u r a l frequency of the model i s u s u a l l y made as high as p o s s i b l e by using a 4 l i g h t ' l i v e ' s e c t i o n , s t i f f l y mounted. At most wind speeds, the vortex shedding frequency f v , where f v = SU/H (with S t r o u h a l number S and f r o n t a l dimension H), i s then w e l l below the model n a t u r a l frequency f n . As wind speed i s i n c r e a s e d however, f v approaches f n and l a r g e resonant v i b r a t i o n s occur. These l a r g e motions are u n d e s i r a b l e , f o r reasons which w i l l appear l a t e r , and wind speeds are u s u a l l y r e s t r i c t e d to values f o r which f v / f n ^ 1/4. In V i c k e r y ' s case, fo r example, the n a t u r a l frequency of the model was about 180HZ and V i c k e r y took meaurements f o r vortex shedding f r e q u e n c i e s below 50 c y c l e s / s e c . T y p i c a l r e s u l t s from a l l these papers are summarized i n Table 1. In t h i s t h e s i s , measurements on ' l i v e ' lengths of v a r i o u s spans are used to deduce the f o r c e s to which the s e c t i o n i s s u b j e c t e d . T h i s i s c o n s i d e r e d most r e a l i s t i c because a c t u a l s t r u c t u r e s having s i m i l a r end e f f e c t s are subject to f o r c e s e q u i v a l e n t to those a c t u a l l y measured here, so that the present data i s most l i k e l y to be u s e f u l in d e s i g n . The work to be d e s c r i b e d here i n v e s t i g a t e s the spanwise averaged f l u c t u a t i n g s i d e f o r c e s on sharp edged r e c t a n g u l a r prisms of v a r i o u s spans and shapes, in smooth and t u r b u l e n t flows. The experimental method used i s s i m i l a r to that used by V i c k e r y 1 and So & Savkar^. It has been suggested that the f l u c t u a t i n g side f o r c e v a r i e s with f r e e stream turbulence in a s i m i l a r way to that of the base pressure (see e.g. Gartshore^) . The 5 e x p e r i m e n t a l s t u d y r e p o r t e d h e r e e x p l o r e s t h e p o s s i b i l i t y . I t a l s o shows the e f f e c t of f r e e s t r e a m t u r b u l e n c e and a s p e c t r a t i o ( s p a n / f r o n t a l d i m e n s i o n ) on t h e v o r t e x i n d u c e d f l u c t u a t i n g s i d e f o r c e e x e r t e d on r e c t a n g u l a r s e c t i o n s . 2. EXPERIMENTAL ARRANGEMENTS 2.1 WIND TUNNEL The experiments were conducted i n the U.B.C. low speed, low t u r b u l e n c e , c l o s e d r e t u r n type wind tunnel in which the v e l o c i t y can be v a r i e d between 0 and 46m/s with a turbulence l e v e l of l e s s than . 1%. Three screens smooth the flow at the entrance of the s e t t l i n g chamber and a 7:1 c o n t r a c t i o n a c c e l e r a t e s i t , improving i t s u n i f o r m i t y as i t reaches the t e s t s e c t i o n . The t e s t s e c t i o n i s 2.74m long with a c r o s s s e c t i o n of 91.4 by 68.6cm. Four 45 degrees f i l l e t s , d e c r e a s i n g from 15cm at the upstream to 12cm at the downstream end, o f f s e t the e f f e c t of boundary l a y e r growth i n the t e s t s e c t i o n . The tunnel i s powered by a 15HP d i r e c t c u r r e n t motor, d r i v i n g a commercial a x i a l flow fan with a T h y r i s t e r system of speed c o n t r o l . The pressure drop a c r o s s the c o n t r a c t i o n i s measured on a Betz micro-manometer with a p r e c i s i o n of .02 mm of water. The a i r speed i n the t e s t s e c t i o n i s c a l i b r a t e d a g a i n s t the pressure drop. F i g 1 shows the o u t l i n e of the t u n n e l . 2.2 TURBULENCE PRODUCING DEVICES 2.2.1 GRIDS In the experiment four square mesh g r i d s were used f o r producing d i f f e r e n t l e v e l s of t u r b u l e n c e 6 7 i n t e n s i t y and d i f f e r e n t t u r b u l e n c e s c a l e s . Three of the g r i d s were of r e c t a n g u l a r bars with mesh widths of 9in(228.6mm), 4.5in(114.3mm) & 2in(50.8mm) and bar widths of 2.25in(57.15mm), 1.1 in(27.94mm) & 0.5in{12.7mm) r e s p e c t i v e l y . The f o u r t h g r i d (the sm a l l e s t mesh width g r i d ) had round bars with a mesh width of 0.256 in(6.5mm) and bar diameter of 0.0381(.97mm). G r i d s were mounted at the upstream end of the t e s t s e c t i o n , i n every case. The q u a l i t y of the r e s u l t a n t flow at some d i s t a n c e downstream of the g r i d , has been shown to be n e a r l y i s o t r o p i c homogeneous turbulence superimposed on a uniform mean flow (see f o r example Bains and Peterson 8 ) . Th e r e f o r e , g r i d turbulence appears to be the simplest form of turbu l e n c e f o r two dimensional t e s t s , having a f l a t v e l o c i t y p r o f i l e and a uniform turbulence i n t e n s i t y d i s t r ibut i o n . Bains and Peterson^ found that i f the flow i s to be n e a r l y uniform, the model can be no c l o s e r than 5 to 10 mesh widths from the g r i d . Thus the model p o s i t i o n was chosen to be 72in(183cm) (8 times the l a r g e s t mesh width) away from the g r i d s to have a reasonably uniform flow at the model face f o r a l l cases. The c h a r a c t e r i s t i c s of the turbu l e n c e acheieved by the g r i d s were measured by a s i n g l e hot wire with 8 l i n e a r i z e d response, t r a v e r s e d l o n g i t u d i n a l l y i n the mid span of the t u n n e l . The wire was of tungsten with a diameter of 5 microns. The hot wire system used was a Disa type 55D01 with s u i t a b l e l i n e a r i z e r . A low pass f i l t e r of the type Disa 55D25 was set to remove any frequency higher than 10KHZ. Using s u i t a b l e v o l t m e t e r s the r e l a t i v e t urbulence i n t e n s i t y u'/U was deduced. A t y p i c a l c a l i b r a t i o n curve of the hot wire i s shown i n Appendix A. For each g r i d i n p o s i t i o n i n s i d e the t u n n e l , the hot wire was used to c a l i b r a t e the Betz manometer readings a g a i n s t the tunnel speed, so that the Betz manometer c o u l d be used l a t e r as a measure of mean wind speed. The a u t o c o r r e l a t i o n of the l i n e a r i z e d v e l o c i t y was measured u s i n g a P.A.R. 101 c o r r e l a t o r . The i n t e g r a l time s c a l e was found by i n t e g r a t i n g the auto c o r r e l a t i o n f u n c t i o n over v a r i o u s time d e l a y s . Appendix A shows a t y p i c a l auto c o r r e l a t i o n curve and d e s c r i b e s the method of o b t a i n i n g the i n t e g r a l time s c a l e . Using T a y l o r ' s Hypothesis, the i n t e g r a l l e n g t h s c a l e L x = U«r was deduced. F i g u r e 2 shows the decay of the l o n g i t u d i n a l component of i n t e n s i t y f o r the four g r i d s . Data f o r a u n i p l a n a r g r i d obtained by V i c k e r y ^ agree very w e l l , while the r e s u l t s obtained by Campbell and E t k i n 1 ^ , and S u r r y 1 1 depart from the present data s l i g h t l y . 9 Data f o r a s i m i l a r g r i d from Baines and Peterson^ are somewhat lower. A l s o , the curve u'/U=1.12(x/b)~ 5/ 7 which i s a best f i t to Bains' and Peterson's data f o r d i f f e r e n t g r i d s i s lower than the present v a l u e s . Data from McLaren et a l . 1 2 and L a n e v i l l e 1 3 agree very w e l l . F i g . 3 shows the growth of the l o n g i t u d i n a l s c a l e of turbulence with downstream d i s t a n c e . The r e s u l t agrees f a i r l y w e l l with those of V i c k e r y ^ and L a n e v i l l e 1 3 . The two l i n e s show the s c a t t e r l i m i t f o r c o r r e s p o n d i n g data by Van der Hegge Zignen 2.2.2 RODS As an a l t e r n a t e to the use of g r i d s , a 0.5in(12.7mm) diameter rod was t r a v e r s e d along the t u n n e l , upstream of the square prism c e n t r e l i n e , to produce d i f f e r e n t l e v e l s of upstream t u r b u l e n c e . The rod was p l a c e d between 20d and 70d from the f r o n t face of the model where d i s the rod diameter. T h i s produced i n t e n s i t i e s between 12% and 4% on the rod wake centre l i n e at the model l o c a t i o n . Turbulent i n t e n s i t i e s were found from the measurements of G a r t s h o r e 1 ^ , and i n t e g r a l l o n g i t u d i n a l l e n g t h s c a l e s , again on the rod c e n t r e l i n e , from the measurements of Townsend 1^. 10 2.3 MODELS AND MOUNTINGS For each of the three r e c t a n g u l a r s e c t i o n s of B/H=1, .67 and .5, f i v e models were made with lengths L of; 1.5in(38.1mm), 3in(72.6mm), 6in(152.4mm), 12in(304.8mm) and 24in(609.6mm). Each model had a f r o n t a l dimension H of 1.5in(38.1mm), so that blockage r a t i o s were always 4.2% based on f r o n t a l area (see f i g . 4 f o r model d e t a i l s ) . There was no blockage c o r r e c t i o n a p p l i e d to the data si n c e there i s no secure c o r r e c t i o n technique f o r f l u c t u a t i n g q u a n t i t i e s a v a i l a b l e . In t h i s kind of t e s t , the trend i s more important than any absolute value i n any case. A 29in(736.6mm) aluminum beam with 1/4in(6.35mm) by 1/2in(12.7mm) c r o s s s e c t i o n , having two s t r a i n gauges at each end, was used as a u n i - d i r e c t i o n a l l o a d c e l l . T h i s c o u l d sense the c r o s s stream loads on the ' l i v e ' measuring s e c t i o n attached to i t (see f i g . 5). Two 2in(5'0.8mm) by 2in(50.8mm) holes were made in the roof and f l o o r of the tunnel on a v e r t i c a l l i n e p e r p e n d i c u l a r to the a x i s of symmetry of the tunnel at the d e s i r e d p o s i t i o n . A heavy s t e e l frame, surrounding the tunnel t e s t s e c t i o n was used to h o l d the beam i n p o s i t i o n . The frame stood on four a d j u s t a b l e legs without touching the t u n n e l , so that v i b r a t i o n s of the tunnel would not a f f e c t the frame. The lo a d c e l l beam passed through the holes i n the tunnel w a l l s and was fastened to the frame at each end, by means of s p e c i a l l y made clamps. F i g . 6 gi v e s more d e t a i l s of the mounting. Dummy end p i e c e s were screwed to the tunnel w a l l s 11 and end p l a t e s were mounted on them. The d i s t a n c e from the end p l a t e s to the f l o o r and roof of the tunnel was 1.5in(38.1 mm), so that they were o u t s i d e the tunnel w a l l boundary l a y e r s . S t a n s b y 1 7 showed that end e f f e c t s a l t e r e d the true base pressure over the whole l e n g t h of a 2D c i r c u l a r c y l i n d e r without end p l a t e s . He showed that end p l a t e s improved the base pr e s s u r e to i t s " t r u e " v a l u e . O b a s a j u 1 ^ concluded that f o r sharp edged 2D square c y l i n d e r s , end p l a t e s were again of importance. In t h i s work, one set of end p l a t e s was used f o r a l l models as shown in f i g . 7. For each experiment the ' l i v e ' model's span was screwed to the ce n t r e of the load c e l l beam and the proper dummy end pi e c e s were fastened to the tunnel roof and f l o o r . The gap between the ' l i v e ' s e c t i o n and adjacent dummy end s e c t i o n s was always made l e s s than .02in(.5mm). 2.4 FORCE MEASUREMENTS The average f l u c t u a t i n g s i d e f o r c e s caused by vortex shedding from a two dimensional b l u f f body at zero i n c i d e n c e can be measured over a f i n i t e span by the methods used by V i c k e r y 1 and So & S a v k a r 7 . The average f l u c t u a t i n g s i d e f o r c e i s a l t e r e d by having d i f f e r e n t end c o n d i t i o n s f o r the ' l i v e ' s e c t i o n . In the work to be d e s c r i b e d here two end c o n d i t i o n s were c o n s i d e r e d : a simple gap l e s s then .02in(.5mm) between the ' l i v e ' s e c t i o n and dummy end p i e c e s ; 12 and the same gap but with a set of end p l a t e i d e n t i c a l to those i n f i g . 7 , attached to the ends of the ' l i v e ' s e c t i o n . Each time a model was mounted on the l o a d c e l l beam, a c a l i b r a t i o n of the l o a d c e l l was done as l o a d versus s t r a i n gauge v o l t a g e output. The c a l i b r a t i o n of load versus d e f l e c t i o n was a l s o measured p e r i o d i c a l l y . The n a t u r a l frequency and the damping of each model was d i f f e r e n t because of d i f f e r e n t s i z e s and weights of the models. Using a spectrascope the n a t u r a l frequency of the models was measured p r i o r to the t e s t . T h e i r damping was always l e s s than 1% as a f r a c t i o n of c r i t i c a l , as measured on an o s c i l l o s c o p e . Each model was t e s t e d at wind speeds of 2m/s and h i g h e r . The f l u c t u a t i n g s i g n a l from the s t r a i n gauge bridge a m p l i f i e r was fed i n t o a f i x e d 1 to 100 s i g n a l - a m p l i f i e r and then through a low pass f i l t e r to cut o f f f r e q u e n c i e s near f n , the model n a t u r a l frequency. Using a true r.m.s. voltmeter, the r.m.s. of the f l u c t u a t i n g s i g n a l was read, and from the c a l i b r a t i o n , the r.m.s. d e f l e c t i o n of the beam was found. Using a spectrascope the average vortex shedding frequency at each wind speed was found. For one degree of freedom, the equation of motion of the load c e l l beam i s : mx+cx + kx = F ( t ) = F 1 S i n ( 6 j 1 t ) + F 2 S i n ( c j 2 t ) + Assuming the vortex shedding occurs i n a narrow range 1 3 c e n t e r e d about f v , t h i s can be so l v e d f o r a range of f r e q u e n c i e s to g i v e : j/xVB k ° L = H ( f v ) 1/2 PU 2L where »/x2 i s the r.m.s. of d e f l e c t i o n , B the streamwise dimension of the prism, L l e n g t h of the ' l i v e ' s e c t i o n , k the s t i f f n e s s of the l o a d c e l l beam and H ( f v ) mechanical admittance evaluated at the vortex shedding frequency (see appendix B for more d e t a i l s of the d e r i v a t i o n ) . Using t h i s e quation and the data obtained from the experiment, C£ at each wind speed was found. T h i s method assumes that the f o r c e o s c i l l a t e s near a s i n g l e frequency; the range of vortex f r e q u e n c i e s was not measured i n t h i s experiment, but was l i m i t e d to values l e s s than 20Hz below f n . To make the assumption that the c y l i n d e r s are ' r i g i d ' , the motion of the l i v e s e c t i o n must be very small compared to the s e c t i o n s i z e . The r.m.s. amplitude of the ' l i v e ' s e c t i o n was measured, and was found to be l e s s than . 1% of H in a l l c a s e s . Although i t i s known that c y l i n d e r s are s e n s i t i v e to small motions, t h i s small motion i s assumed here to be n e g l i g i b l e , and the c y l i n d e r s are d e s c r i b e d as r i g i d . 1 4 2.5 PRESSURE MEASUREMENTS Mean base pressure measurements were made on a f i x e d 1.5in(38.1mm) by 1.5in(38.1 mm) square c y l i n d e r spanning the tunnel v e r t i c a l l y . The base pressure was measured to see the e f f e c t of d i f f e r e n t end c o n d i t i o n s and a l s o to compare with the r e s u l t s of L e e 1 ^ and Ob a s a j u 1 ^ . The square prism was prepared with twenty pressure taps on the rear face at the mid chord, spread over most of the t o t a l span. The base pressure was measured i n smooth and t u r b u l e n t flows, with and without end p l a t e s mounted on the model. End p l a t e s were 1.5in(38.1 mm) away from the w a l l s of the tunnel as be f o r e . The base pressures measured in t h i s t e s t are shown i n f i g u r e 8 and are q u i t e comparable to Obasaju's r e s u l t s . 3. RESULTS AND DISCUSSION FOR SQUARE SECTIONS 3.1 FORM OF RESULTS In sharp edged b l u f f bodies l i k e r e c t a n g u l a r prisms the p o i n t of s e p a r a t i o n of the flow .is f i x e d and C Q , drag c o e f f i c i e n t , does not vary for high enough Re. A l l f o r c e c o e f f i c i e n t s should t h e r e f o r e be independent of Reynolds number or of wind speed, provided t r a n s i t i o n to t u r b u l e n c e occurs r a p i d l y in the s e p a r a t i o n shear l a y e r s . T h i s appears to be the case for Re> 10 4 (see e.g. G a r t s h o r e 1 ^ ) . The range of Re in t h i s experiment was 0.5 * 10 4 to 2.2 * 10 4 based on f r o n t a l dimension. If the flow p a t t e r n i s independent of Re, as i s expected, and i f no end e f f e c t s or d i f f i c u l t i e s of measurement occur, the deduced values of C £ should be the same at a l l speeds. Measured r e s u l t s of f l u c t u a t i n g l i f t c o e f f i c i e n t versus wind speed, fo r one case, are p l o t t e d i n f i g . 9. Another e f f e c t which was observed i n some cases, was resonant motion of the load c e l l beam at a speed where f v i s a lower harmonic of f n (see e.g. f i g . 10). Measurements at t h i s wind speed were avoided s i n c e t h i s e f f e c t caused an u n d e s i r a b l e motion of the beam and an i n c r e a s e d r.m.s. f o r c e r e a d i n g . I t was not always p o s s s i b l e to remove t h i s e f f e c t by using a low pass f i l t e r . At high speeds, when the vortex shedding frequency was c l o s e to the n a t u r a l frequency, the amplitude of the n a t u r a l frequency v i b r a t i o n s i n c r e a s e d . Again the r.m.s. v o l t a g e readings were i n c o r r e c t , being higher than the value a p p r o p r i a t e f o r vortex shedding f o r c e s 15 1 6 o n l y . T h i s problem was solved at low speeds by using a low pass f i l t e r to cut out the e f f e c t of n a t u r a l frequency v i b r a t i o n s , but f o r high speeds the low pass f i l t e r a l s o cut out some of the d e s i r a b l e s i g n a l s from the vortex shedding. The data was c o r r e c t e d f o r the e f f e c t of f i l t e r and a m p l i f i e r used. A c a l i b r a t i o n curve f o r the f i l t e r i s shown in appendix A. Choosing an average of the most d e s i r a b l e data p o i n t s , the C£ f o r each model was found (see f i g . 9). When the rod was used as a turbulence producing d e v i c e , C£ was measured at j u s t one speed (4m/s) f o r each ' l i v e ' s e c t i o n at every rod p o s i t i o n . C£ values obtained f o r square s e c t i o n s with end p l a t e s (see f i g s . 11 to 14) are lower than the values obtained with no end p l a t e s . T h i s i s probably because of end e f f e c t s , s i n c e end e f f e c t s (at l e a s t f o r Cp^ and, by analogy f o r C£) seem to be more e x t e n s i v e near end p l a t e s than near gaps, (see e.g. f i g . 28) . 3.2 EFFECT OF ASPECT RATIO As a l r e a d y mentioned, the average f o r c e over a span of the ' l i v e ' s e c t i o n i s expected to become smaller as the span gets longer, because the c o r r e l a t i o n of the f o r c e averaged over the body reduces with span. F i g . 11 shows the measured r e s u l t s f o r the square s e c t i o n in low t u r b u l e n c e . The expected decrease i n C£ occurs only f o r l a r g e r spans, here f o r L/H > 2. For the lowest span l e n g t h , L/H = 1, the e f f e c t 1 7 of gaps between the ' l i v e ' s e c t i o n and the end p i e c e s causes a s i g n i f i c a n t r e d u c t i o n in the measured C£, an e f f e c t much more important i n the short s e c t i o n s than in those of l a r g e r span. As the f r e e stream t u r b u l e n c e i n c r e a s e s , the decrease in C£ with i n c r e a s i n g span becomes l e s s pronounced. F i g s . 11 to 14 i l l u s t r a t e s t h i s i d e a . Apparently, turbulence makes the f l u c t u a t i n g s i d e f o r c e s act more evenly over the span. Put another way, turbulence improves the spanwise c o r r e l a t i o n of the f l u c t u a t i n g s i d e f o r c e s on the square s e c t i o n . One of the reasons f o r t h i s i s t h a t , in t u r b u l e n c e , the shear l a y e r s e p a r a t i n g from the f r o n t c o r n e r s of a square s e c t i o n , i n t e r a c t s s i g n i f i c a n t l y with the a f t e r body and causes the f o r c e s to act evenly over the span; even when the span i s l a r g e t h i s i n t e r a c t i o n a p p a r e n t l y remains q u i t e uniform, s i n c e the averaged c o e f f i c i e n t of the f l u c t u a t i n g s i d e f o r c e decreases only very slowly with i n c r e a s i n g of span. An a n a l y t i c a l framework f o r the e f f e c t of aspect r a t i o on the f l u c t u a t i n g l i f t c o e f f i c i e n t s , can be developed from the rather simple assumption, that the r e l e v a n t c o r r e l a t i o n c o e f f i c i e n t has a simple e x p o n e n t i a l form. With t h i s assumption, the r.m.s. l i f t f o r c e per u n i t l e n g t h averaged over a span L and non-dimensionalized to produce a l i f t c o e f f i c i e n t becomes: C£=C£ ov/2X/L[L/X -1+exp(-L/X) ] 1 / 2 18 where X i s the i n t e g r a l l e n g t h s c a l e of the f o r c e c o r r e l a t i o n averaged over the span, L i s length of the ' l i v e ' s e c t i o n , C £ Q i s the f l u c t u a t i n g l i f t c o e f f i c i e n t measured l o c a l l y and C£ i s the f l u c t u a t i n g l i f t c o e f f i c i e n t averaged over the span. See appendix C f o r d e t a i l s of the d e r i v a t i o n . F i g . 15 shows t y p i c a l measured values of C£ and the p l o t of the above equation f o r s e l e c t e d values of X/H, C £ 0 chosen to f i t the data at l a r g e L/H. The end e f f e c t s which i n c l u d e the d e f i n i t i o n of A are d i s c u s s e d in s e c t i o n 3.5. Present r e s u l t s are l i k e those p r e v i o u s l y reported f o r low t u r b u l e n c e , f o r C £ 0 and X/H (see Tables 1 & 2). For i n c r e a s i n g i n t e n s i t y , however we f i n d that X/H i n c r e a s e s , i n c o n t r a s t to p r e v i o u s r e p o r t s (e.g. r e f . 1). A p o s s i b l e reason f o r the d i f f e r e n c e between the trends in r e f . 1 and those r e p o r t e d here i s t h a t , the values r e p o r t e d in r e f . 1 are measured using pressure taps while the values r e p o r t e d here are ob t a i n e d using the average of the f o r c e over the ' l i v e ' s e c t i o n . 3.3 EFFECT OF TURBULENCE INTENSITY When the turbulence i n t e n s i t y i n c r e a s e s , i t moves the o s c i l a t i n g shear l a y e r s c l o s e r to the s i d e s of the body from which they separate, shortens the unsteady bubble between the s e p a r a t i o n and reattachment and so p r o g r e s s i v e l y reduces the f l u c t u a t i n g s i d e f o r c e on the body. F i g s . 16 to 20 show the c o e f f i c i e n t of f l u c t u a t i n g l i f t f o r d i f f e r e n t l e v e l s of 19 turbulence i n t e n s i t y . I t i s observed that turbulence always reduces the averaged r.m.s. l i f t c o e f f i c i e n t s on square c y l i n d e r s ( i f no end e f f e c t s are p r e s e n t ) , by d i s t u r b i n g the r e g u l a r i t y and spanwise c o r r e l a t i o n of shedding. The f l u c t u a t i n g l i f t f o r the square s e c t i o n shape v a r i e s with fr e e stream turbulence i n a s i m i l a r way to that of the base p r e s s u r e . F i g . '21, comparing measurements of the base pressure and the f l u c t u a t i n g l i f t c o e f f i c i e n t for d i f f e r e n t l e v e l s of turbulence f o r one length of the square s e c t i o n , confirms t h i s idea. The s i m i l a r i t y appears f o r a l l lengths of the square s e c t i o n . F i g s . 22 to 25 show the e f f e c t of turbulence i n t e n s i t y produced behind a rod f o r d i f f e r e n t aspect r a t i o s . The same pa t t e r n i s evident as f o r the case of g r i d t u r b u l e n c e , but the values are not the same. T h i s i s maybe because of the d i f f e r e n t s t r u c t u r e of turbulence generated behind a rod compared to that from a g r i d , or d i f f e r e n c e s i n end e f f e c t s . F i g . 26 shows a comparison between C£ measured using a g r i d and C£ measured u s i n g a rod as turbulence generating d e v i c e s . 3.4 EFFECT OF LENGTH SCALE S i g n i f i c a n t e f f e c t s of turbulence s c a l e on the drag of b l u f f bodies have been rep o r t e d by L e e 2 ^ and Miyata & Miyazaki 2 1 . However, most authors report no e f f e c t of turbulence s c a l e on mean f o r c e s over the range .2<LX/H<18. (e.g. see P e t y 2 2 and L a n e v i l l e & W i l l i a m s 2 ^ ) . Gartshore^ 20 r e p o r t s no e f f e c t or l i t t l e e f f e c t of t u r b u l e n c e . s c a l e on f l u c t u a t i n g f o r c e s , provided L x < H. A comparison between measured f l u c t u a t i n g l i f t c o e f f i c i e n t s for two d i f f e r e n t i n t e g r a l t u r b u l e n c e s c a l e s was made. For two model p o s i t i o n s downstream of the t e s t s e c t i o n , two g r i d s one with mesh s i z e of M=.256in(6.5mm) and the other with mesh s i z e of M=4.5in(114.3mm), were used to produce the same l e v e l of turbulence i n t e n s i t y (4%) and two d i f f e r e n t l e n g t h s c a l e s of .179in(4.55mm) (L X/H=.119) and 1.6in(40.64mm) (L x/H=1.067) r e s p e c t i v e l y at the f r o n t face of the model. No uniform trend in the averaged f l u c t u a t i n g l i f t c o e f f i c i e n t was observed for the two d i f f e r e n t i n t e g r a l l e n g t h s c a l e s generated. F i g . 27 shows the e f f e c t of i n t e g r a l l e n g t h s c a l e on Cf,. 3.5 END EFFECTS End e f f e c t s are p a r t i c u l a r l y important in two dimensional experiments on b l u f f bodies, s i n c e s e p a r a t i o n regions are e a s i l y a l t e r e d by s l i g h t changes in pressure or c r o s s flow f a r from the c e n t r e span. To remove the e f f e c t of the t u n n e l boundary l a y e r , two end p l a t e s were used. O b a s a j u 1 ^ showed the e f f e c t of d i f f e r e n t end p l a t e s on the mean base pressure of a square s e c t i o n . A set of end p l a t e s (see f i g . 7) s p e c i f i e d by Obasaju f o r square s e c t i o n s , was used without e x p l o r i n g t h e i r e f f e c t i v e n e s s ; again a b s o l u t e values are u n l i k e l y to be as important as trends in the present c o n t e x t . Boundary 21 l a y e r s on the end w a l l s c o n f i n i n g the c y l i n d e r under t e s t may be modified as the f r e e stream t u r b u l e n c e i s changed. Some of these problems are d i s c u s s e d by L e e 1 ^ and many experimental s t u d i e s r e p o r t concern over the observed s e n s i t i v i t y to end e f f e c t s . The other end e f f e c t s present in t h i s experiment were the gaps between the ' l i v e ' s e c t i o n of the model and the adjacent dummy end p i e c e s . The gap was always kept l e s s than •02in(.5mm) f o r the main experiments. F i g . 28 shows the e f f e c t of gap s i z e on the mean base pressure c o e f f i c i e n t . As can be seen from the f i g u r e , when the gap s i z e gets b i g g e r , the absolute value of the pressure c o e f f i c i e n t decreases. If there i s a s i m i l a r i t y between the base pressure c o e f f i c i e n t and the c o e f f i c i e n t of f l u c t u a t i n g l i f t , C£ w i l l a l s o decrease as the gap s i z e i n c r e a s e s . T h i s end e f f e c t w i l l be more n o t i c e a b l e i n the short span models, so that C£ f o r the sm a l l e s t model (1.5in(38.1 mm) length) i s lower than f o r the 3in(76.2mm) model, d e s p i t e the opposing trend coming from t h e i r d i f f e r e n t aspect r a t i o s . To i n v e s t i g a t e the e f f e c t of gaps, end p l a t e s s i m i l a r to those used near the tunnel w a l l s on the dummy end p i e c e s were t r i e d at both ends of the ' l i v e ' s e c t i o n l e a v i n g the same gap (<.02in(.5mm)) with the adjacent dummy p i e c e s . In t h i s case a l s o the end p l a t e s on the ' l i v e ' s e c t i o n produced another e f f e c t which again i s shown as change of base p r e s s u r e c o e f f i c i e n t near to the end p l a t e s i n f i g . 8. 22 It was n o t i c e d that end e f f e c t s are l e s s present in high turbulence flows than in low turbulence flow; t h i s shows that turbulence reduces the e f f e c t s of the ends. Comparing f i g . 11 (C£ f o r low turbulence) to f i g . 14 (C£ f o r high turbulence) confirms t h i s matter. A l s o turbulence reduces e f f e c t of gaps on base pressure (see f i g . 28). An a n a l y t i c a l framework f o r the end e f f e c t can be developed to modify that developed f o r the e f f e c t of aspect r a t i o . For t h i s purpose, i t i s assumed that the end c o n d i t i o n s (gaps, end p l a t e s , e t c . ) r e s u l t i n an e f f e c t i v e span (L-2A) s l i g h t l y l e s s than the a c t u a l l i v e span L. T h e r e f o r e , the r.m.s. l i f t f o r c e per u n i t l e n g t h averaged over a span L and non-dimensionalized to produce a l i f t c o e f f i c i e n t becomes: C£=C£ o/2X/L[L' /X -1+exp(-L'/X) ] 1/2 where L'=L-2A Apendix C has a d e r i v a t i o n of t h i s equation. Measured r e s u l t s can be f i t t e d by an equation of the above form to i n f e r e f f e c t i v e values of X, A and C £ o for each t e s t . T y p i c a l measured values of C£ are shown i n f i g . 15, where the above equation i s a l s o p l o t t e d f o r s e l e c t e d values of X /H, C £ o and A/H. In t h i s way, values of the three parameters f o r a l l t e s t s are found. These are summarized in Table 2. Values of C £ Q are shown in f i g . 29. These values are e x t r a p o l a t i o n s of C£ curves (averaged over the span) as 23 a f u n c t i o n o f L/H t o a v a l u e f o r L/H^O ( c o r r e c t e d f o r end e f f e c t s ) . T h e s e v a l u e s a r e n o t c e r t a i n i n some c a s e s , b e c a u s e o f t h e s c a t t e r o f C £ ( a v e r a g e d o v e r t h e spa n ) f o r some ' l i v e ' s e c t i o n s . F o r c o m p a r i s o n , l o c a l v a l u e s o f C £ (C£ ) m e a s u r e d by o t h e r s a r e a l s o p l o t t e d i n f i g . 29. G a r t s h o r e ^ u s e d a r o d a s t h e t u r b u l e n c e p r o d u c i n g d e v i c e f o r t h e t u r b u l e n c e v a l u e s p r e s e n t e d i n f i g . 29, w h i l e L e e ' s ^ t u r b u l e n c e v a l u e s a n d t h e p r e s e n t d a t a a r e m e a s u r e d u s i n g g r i d s a s t h e t u r b u l e n c e p r o d u c i n g d e v i c e s . As n o t e d e a r l i e r , when t h e t u r b u l e n c e i n t e n s i t y i n c r e a s e s , X/H i n c r e a s e s a n d t h e r a t i o A/H, r e p r e s e n t i n g end e f f e c t s , d e c r e a s e s s h o w i n g t h a t end e f f e c t s become l e s s s i g n i f i c a n t a s t h e i n t e n s i t y i n c r e a s e s . I n f i g . 29, t h e p r e s e n t v a l u e s o f C £ o f o r s q u a r e s e c t i o n s (B/H=1) a r e q u i t e a g r e a b l e w i t h t h e l i t e r a t u r e . H o wever, t h e v a l u e s o f C £ q f o r o t h e r s e c t i o n s (B/H=.67 and B/H=.50) a r e d i f f e r e n t t h a n t h e v a l u e s r e p o r t e d by G a r t s h o r e ^ a l t h o u g h t h e t r e n d s a r e s i m i l a r . The d i f f e r e n c e i s p e r h a p s b e c a u s e o f t h e d i f f e r e n t m ethods o f m e a s u r e m e n t s , d i f f e r e n t t u r b u l e n c e p r o d u c i n g d e v i c e s , d i f f e r e n t b l o c k a g e r a t i o s a n d d i f f e r e n t end e f f e c t s . 4 . RESULTS FOR OTHER SECTION SHAPES 4.1 RECTANGULAR SECTION WITH B/H=.67 For t h i s r e c t a n g u l a r shape, C£ for each l i v e span was found at v a r i o u s wind speeds and turbulence i n t e n s i t i e s as was done i n the square s e c t i o n case. The v a l u e s of C£ found f o r t h i s s e c t i o n shape d i d not show such c l e a r trends as f o r the B/H=1 s e c t i o n , and values over a reasonable speed range were not as con s t a n t . In some cases, the values were s c a t t e r e d between ±.4 of the quoted v a l u e s . Despite t h i s u n c e r t a i n t y i n the values, some c o n c l u s i o n s can be drawn. As i s shown in f i g . 30 to 33, C£ decreases very slowly with aspect r a t i o . Although the trend i s not as c l e a r as f o r square s e c t i o n s , i t i s evident that C£ changes s l i g h t l y with turbulence i n t e n s i t y f o r a l l spans. The e f f e c t of i n t e g r a l l e n g t h s c a l e was t e s t e d on the longest span of ' t h i s r e c t a n g u l a r shape, and as i t i s shown i n f i g . 27, there seems to be no e f f e c t of turbulence l e n g t h s c a l e on the f l u c t u a t i n g l i f t c o e f f i c i e n t over the range t e s t e d . Looking at the r e s u l t s obtained f o r the base pressure ( f i g . 34), the e f f e c t of the gap i s again more present i n the low turbulence stream than i n higher t u r b u l e n t flow. I t a l s o shows that the end e f f e c t (because of gaps) may be s l i g h t l y changed with Re, s i n c e the base pressure c o e f f i c i e n t t rend near the gap has changed s l i g h t l y f o r the two d i f f e r e n t Re used. T h i s i s perhaps one of the reasons why the values of C£, in some cases, are d i f f e r e n t f o r d i f f e r e n t speeds. 24 25 4.2 RECTANGULAR SECTION SHAPES WITH B/H=.5 F o r t h i s r e c t a n g u l a r s h a p e a l s o , C£ f o r e a c h s p a n was f o u n d a t d i f f e r e n t s p e e d s as was done f o r t h e o t h e r r e c t a n g u l a r s e c t i o n s . C£ f o r e a c h ' l i v e ' s e c t i o n a t d i f f e r e n t l e v e l s o f f r e e s t r e a m t u r b u l e n c e i n t e n s i t y was d e d u c e d a s b e f o r e . F i g s . 35 t o 38 and f i g . 29 show t h a t t h e r e i s a l m o s t no s i g n i f i c a n t c h a n g e o f C£ w i t h t u r b u l e n c e i n t e n s i t y f o r any of t h e s p a n s t e s t e d . The r e a s o n f o r t h i s i s t h a t , a s t h e t u r b u l e n c e i n t e n s i t y i n c r e a s e s , t h e r e a r c o r n e r o f t h e body w h i c h was i n t e r f e r i n g w i t h t h e s e p a r a t i n g s h e a r l a y e r o f t h e s q u a r e s e c t i o n i n t e r f e r e s i n t h e s e c o n d r e c t a n g u l a r s e c t i o n (B/H=.67) a nd h a s v e r y l i t t l e e f f e c t on t h e a f t e r b o d y o f t h e r e c t a n g u l a r s e c t i o n w i t h B/H=.5 i n t h e r a n g e o f t u r b u l e n c e l e v e l s u s e d . T h e r e f o r e , t h e t u r b u l e n c e l e v e l makes v e r y l i t t l e c h a n g e t o t h e v a l u e o f C£. Howe v e r , f i g s . 35 t o 38 show t h a t C£ d e c r e a s e s a s t h e a s p e c t r a t i o g e t s l a r g e r . A l t h o u g h t h i s t r e n d i s n o t as c l e a r a s i t was i n t h e c a s e o f s q u a r e s e c t i o n s , i t d e m o n s t r a t e s a g a i n t h a t C£ i s l e s s c o r r e l a t e d f o r l o n g e r b o d i e s t h a n f o r s h o r t e r b o d i e s , a s e x p e c t e d . The e f f e c t o f i n t e g r a l l e n g t h s c a l e was t e s t e d on t h e l o n g e s t s p a n o f t h i s r e c t a n g u l a r s h a p e , a n d a s i s shown i n f i g . 27, t h e r e seems t o be no e s s e n t i a l c h a n g e i n C£ w i t h c h a n g e i n l e n g t h s c a l e , o v e r t h e r a n g e t e s t e d . 26 4.3 COMPARISON FOR ALL SECTION SHAPES C o m p a r i n g t h e o v e r a l l v a r i a t i o n o f C£ w i t h t u r b u l e n c e i n t e n s i t y i n t h e r e c t a n g u l a r s e c t i o n s ( i g n o r i n g t h e end e f f e c t s ) , i t c a n be c o n c l u d e d t h a t as t h e t u r b u l e n c e i n t e n s i t y i n c r e a s e s , C£ d e c r e a s e s i n s q u a r e s e c t i o n s . F o r s e c t i o n s w i t h B/H=.67 t h i s d e c r e a s e o f C£ w i t h t u r b u l e n c e i n t e n s i t y i s l o w e r t h a n t h a t f o r t h e s q u a r e s e c t i o n s . F o r s e c t i o n s w i t h B/H=.5, C£ f i r s t r i s e s w i t h i n c r e a s e o f t u r b u l e n c e i n t e n s i t y a n d t h e n d r o p s a s t h e t u r b u l e n c e i n t e n s i t y i s f u r t h e r i n c r e a s e d . L o o k i n g a t t h e v a r i a t i o n o f C£ w i t h a s p e c t r a t i o , t h e r e i s one t r e n d e v i d e n t i n a l l t h e t h r e e r e c t a n g u l a r s e c t i o n s and t h a t i s : C£ a l w a y s d e c r e a s e s w i t h an i n c r e a s e o f a s p e c t r a t i o , L/H ( e x c l u d i n g end e f f e c t s ) , no m a t t e r what t h e l e v e l o f t h e t u r b u l e n c e i n t e n s i t y i s . I n any l e v e l o f t u r b u l e n c e i n t e n s i t y , t h e u n s t e a d y l i f t p e r u n i t l e n g t h d e p e n d s upon s e c t i o n s h a p e . 5 . CLOSING COMMENTS 5 .1 CONCLUSIONS The o b j e c t i v e s of t h i s t e s t were: 1- To i n v e s t i g a t e t h e e f f e c t of t u r b u l e n c e on t h e f l u c t u a t i n g l i f t f o r c e s i n d u c e d by v o r t e x s h e d d i n g on two d i m e 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 . 2- To i n v e s t i g a t e t h e e f f e c t of span or a s p e c t r a t i o (L/H) on t h e a v e r a g e d f l u c t u a t i n g l i f t f o r c e s imposed on t h e body. The s e c t i o n s h a p e s used a r e o f i m p o r t a n c e b e c a u s e t h e y a r e p a r t i c u l a r l y s e n s i t i v e t o f r e e s t r e a m t u r b u l e n c e e f f e c t s . L i t e r a t u r e has shown ( s e e e.g. G a r t s h o r e ^ ) t h a t r e c t a n g u l a r s e c t i o n s w i t h B/H>1 have a more permanent r e a t t a c h m e n t of t h e s e p a r a t i n g s h e a r l a y e r s t o t h e s i d e s o f th e body, i n t u r b u l e n t f l o w , and t h e m a g n i t u d e of C£ i s r e l a t i v e l y s m a l l . F o r s q u a r e s e c t i o n s , an i n c r e a s e i n 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 d C £, t h e d e c r e a s e b e i n g g r e a t e r f o r t h e s m a l l span models t h a n f o r t h e l a r g e o n e s . F o r s e c t i o n s w i t h B/H=.67 t h i s d e c r e a s e was s l o w e r and f o r s e c t i o n s w i t h B/H=.5, C£ i n c r e a s e d f i r s t and t h e n d e c r e a s e d v e r y s l i g h t l y . C£ m e asured f o r s q u a r e s e c t i o n s u s i n g a r o d as t h e t u r b u l e n c e p r o d u c i n g d e v i c e , i n a l l c a s e s , showed a l o w e r v a l u e t h a n t h e C£ measured u s i n g a g r i d a s t h e t u r b u l e n c e 27 28 p r o d u c i n g d e v i c e f o r t h e same i n t e n s i t y . T h i s i s p r o b a b l y b e c a u s e o f t h e d i f f e r e n t s t r u c t u r e s of t u r b u l e n c e b e h i n d a g r i d a n d a r o d . See f i g . 27 f o r c o m p a r i s o n o f g r i d d a t a and r o d d a t a . The e f f e c t o f t u r b u l e n c e s c a l e was c h e c k e d on t h e r e c t a n g u l a r s e c t i o n s a n d t h e r e was no c l e a r t r e n d o b s e r v e d f o r t h e r a n g e o f t h e s c a l e s u s e d . C£, d e c r e a s e d w i t h i n c r e a s i n g span o f t h e ' l i v e ' s e c t i o n i n a l l t h e r e c t a n g u l a r s h a p e s e x c e p t f o r t h e s m a l l s p a n t h a t was e x t e n s i v e l y a f f e c t e d by end c o n d i t i o n s . End c o n d i t i o n s were more o b v i o u s i n t h e s m a l l s p a n s t h a n i n l a r g e o n e s . End e f f e c t s were l e s s s i g n i f i c a n t i n h i g h t u r b u l e n c e i n t e n s i t y t h a n i n l o w t u r b u l e n c e l e v e l s , an e f f e c t o b s e r v e d on C£, and mean b a s e p r e s s u r e s . 5.2 COMMENTS ON THE EXPERIMENTAL METHOD USED The a d v a n t a g e o f u s i n g a s i n g l e beam a s a f o r c e t r a n s d u c e r i s t h a t t h e beam i s s i m p l e t o make a nd t o u s e , and i s v e r y i n e x p e n s i v e , a v o i d i n g o t h e r f o r c e o r p r e s s u r e t r a n s d u c e r s . I t a l s o m e a s u r e s f o r c e d i r e c t l y o v e r a r a n g e o f f o r c i n g f r e q u e n c i e s . End c o n d i t i o n s p l a y an i m p o r t a n t r o l e i n t h e d a t a , a n d gap s must be l e f t a t t h e ends o f t h e l i v e s e c t i o n , n e c e s s a r i l y i n t r o d u c i n g c o m p l i c a t e d ( a l t h o u g h r e a l i s t i c ) e n d e f f e c t s . I n a d d i t i o n , b e c a u s e o f t h e i n c r e a s i n g mass o f t h e l a r g e r s e c t i o n s , t h e r a n g e o f s p e e d s o r f o r c i n g f r e q u e n c i e s t h a t c a n be u s e d i s p r o g r e s s i v e l y d e c r e a s e d . V i b r a t i o n a m p l i t u d e , a l t h o u g h a l w a y s s m a l l i n t h e s e t e s t s , c o u l d 29 i n t r o d u c e f u r t h e r v a r i a b l e s i n some c a s e s . F o r s t r i c t l y 2D t e s t s , two r e l a t e d e f f e c t s must be i n v e s t i g a t e d : t h e end p l a t e s u s e d must be shown t o be e f f e c t i v e so t h a t 2D f l o w i s p r o d u c e d and t h e end g a p s n e c e s s a r i l y p r e s e n t i n t h e p r e s e n t t e s t s must be e l i m i n a t e d . F o r t h e f i r s t e f f e c t , end p l a t e s o f v a r i o u s s i z e s n e e d t o be s t u d i e d w i t h s e c t i o n s o f e a c h g e o m e t r y , p e r h a p s i n c o n j u n c t i o n w i t h v a r i o u s t u r b u l e n c e l e v e l s and v a r i o u s b l o c k a g e r a t i o s . End gaps m i g h t be s e a l e d w i t h a s u i t a b l e g a s k e t o r s e a l i n g r i n g a n d c o u l d be a v o i d e d a l t o g e t h e r i f many p r e s s u r e t a p s were u s e d , p e r h a p s c o n n e c t e d t o s u i t a b l e mani f o l d s . F i n a l l y , a w i d e r a n g e o f B/H c o u l d be c o n s i d e r e d , a nd g r e a t e r a c c u r a c y , t o be more c e r t a i n o f t r e n d s , w o u l d c e r t a i n l y be d e s i r e a b l e . BIBLIOGRAPHY V i c k e r y , B . J . " F l u c t u a t i n g l i f t and d r a g on a l o n g c y l i n d e r of  s q u a r e c r o s s s e c t i o n i n a smooth and i n a t u r b u l e n t  s t r e a m . " , J.F.M. 25, 1966, pp 481 t o 494. P o c h a , J . J . Ph.D. t h e s i s , Department of A e r o n a u t i c a l E n g i n e e r i n g , Queen Mary C o l l e g e , 1 9 7 1 . L e e , B.E. "The e f f e c t of t u r b u l e n c e on t h e s u r f a c e p r e s s u r e  f i e l d of a s q u a r e p r i s m . " , J.F.M. 69, 1975, pp 263 t o 282. ' W i l k i n s o n , R.N. " F l u c t u a t i n g p r e s s u r e s on an o s c i l a t i n g s q u a r e  p r i s m . " , A e r o . Q u a r t e r l y , V o l . 32, P a r t s I and I I , 1981, pp 97 t o 125. G a r t s h o r e , I.S. "Some e f f e c t s of u p s t r e a m t u r b u l e n c e on t h e u n s t e a d y  l i f t f o r c e s imposed on p r i s m a t i c two d i m e n s i o n a l  b o d i e s . " , J . F . E n g . 106, Dec. 1984, pp 418 t o 424. Bearman, P.W. and O b a s a j u , E.D. "An e x p e r i m e n t a l s t u d y of p r e s s u r e f l u c t u a t i o n s on f i x e d and o s c i l a t i n g s q u a r e s e c t i o n c y l i n d e r s . " , J . F . M . 119, 1982, pp 297 t o 321. 30 31 7. So, R.M.C. and Savkar, S.D. " B u f f e t i n g f o r c e s on r i g i d c i r c u l a r c y l i n d e r s i n  c r o s s flows.", J..F.M. 105, 1981, pp 397 to 425. 8. Baines, W.D. and P e terson, E.G. "An i n v e s t i g a t i o n of the flow through screens.", T r a n s a c t i o n s of ASME, J u l y 1951, pp 467 to 480. 9. V i c k e r y , B.J. "On the flow behind a coarse g r i d and i t s use as a  model of atmospheric turbulence in s t u d i e s r e l a t e d  to wind loads on b u i l d i n g s . " , N a t i o n a l P h i s i c a l Lab. Aero. Rep. 1143, March 1965. 10. Campbell,A.C. and E t k i n , B. "The response of a c y l i n d e r i c a l s t r u c t u r e to a  t u r b u l e n t flow f i e l d at s u b c r i t i c a l Reynolds  number.", UTIAS T e c h n i c a l Note 115, J u l y 1967. 11. Surry,•D. "The e f f e t of high i n t e n s i t y turbulence on the  aerodynamics of a r i g i d c i r c u l a r c y l i n d e r at  s u b c r i t i c a l Reynolds number.", UTIAS Report 142, October 1969. 12. McLaren, F.G. and S h e r r a t t , A.F.C. and Morton, A.S. " E f f e c t of f r e e stream tur b u l e n c e on the drag  c o e f f i c i e n t s of b l u f f sharp-edged c y l i n d e r s . " , Nature 223, No. 5208, August 1969, pp 828 to 829. 13. L a n e v i l l e , A. " E f f e c t s of t u r b u l e n c e on wind induced v i b r a t i o n s of  b l u f f c y l i n d e r s . " , Ph.D. t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, 1973. 32 14. Van der Hegge-Zijnen, B.G. "Measurements of the i n t e n s i t y , i n t e g r a l s c a l e and  m i c r o s c a l e of turbulence downstream of three g r i d s  in a stream of a i r . " , A p p l i e d S c i e n t i f i c Research, S e c t i o n A, V o l . 7, 1958, p.149. 1 5 . Gar.tshore , I . S. "The e f f e c t of f r e e stream turbulence on the drag of  twodimensional prisms.", U n i v e r s i t y of Western O n t e r i o , F a c u l t y of Engrg. S c i . Report BLWT, Oct 1973, pp 4 to 73. 16. Townsend, A.A. "The s t r u c t u r e of t u r b u l e n t shear flow.", Cambridge U n i v e r s i t y Press, London, 1956. 17. Stansby, P.K. "The e f f e t of end p l a t e s on the Base pressure  c o e f f i c i e n t of a c i r c u l a r c y l i n d e r . " , Aer. J . , January 1974, pp 36 to 37. 1 8 . Obasaju,E.D. "On the e f f e c t of end p l a t e s on the mean fo r c e s on  square s e c t i o n c y l i n d e r s .", J . Ind. Aero. 5, 1979, pp 179 to 186. 19. Lee, B.E. "The s u s c e p t i b i l i t y of t e s t s on two dimensional  b l u f f bodies to i n c i d e n t flow v a r i a t i o n . " , J . Ind. Aero. 2, 1977, pp 133 to 148. 33 20. L e e , B.E. "Some e f f e c t s o f t u r b u l e n c e s c a l e on t h e mean f o r c e s  on a b l u f f b o d y . " , J . I n d . A e r o . 1, 1975/76, pp 361 t o 370. 21. M i y a t a , T. and M i y a z a k i , M. " T u r b u l e n c e e f f e c t s on a e r o d y n a m i c r e s p o n s e of  r e c t a n g u l a r b l u f f c y l i n d e r s . " , P r o c . 5 t h I n t . C o n f . on Wind E n g i n e e r i n g , 1979, pp 631 t o 642. 22. P e t t y , D.G. "The e f f e c t o f t u r b u l e n c e i n t e n s i t y a n d s c a l e on t h e  f l o w p a s t s q u a r e p r i s m s . " , J . I n d . A e r o . 4, 1979, pp 247 t o 251. 23. L a n e v i l l e , A. a n d W i l l i a m s , C D . "The e f f e c t o f i n t e n s i t y and l a r g e s c a l e t u r b u l e n c e  on t h e mean p r e s s u r e a n d d r a g c o e f f i c i e n t s o f two  d i m e 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 . " , P r o c 5 t h I n t . C o n f . on Wind E n g i n e e r i n g , 1979, pp 397 t o 406. Author Method Model;B/H r .m.s . 11ft coef . u'/U L x/H or L x/2R L ive sec t ion span L/H or L/2R Blockage Vickery Averaged & extrap-olated to loca l 1 1.32 .68 low 10% 1.33 1/2 7.14% Lee Local 1 1.22 1.00 .95 .95 .58 low 4.4% 6.5% 8% 12.55 .97 1.14 .73 .94 3.6% Wilkinson Local 1 1.35 low — Gartshore Local 2 1 1 1 .67 .50 .41 1.10 .92 .70 1.74 1.76 low low 6% 10% low low .2<L/rK2 .2<L*/H<2 8.3% Bearman & Obasaju Local 1 1.20 low 5.5% Pocha Local 1 1.41 low So & Savkar Averaged c i r c u l a r 4*10 4<R<4*10 5 .25 Ato 1.42 . 3.8*10^<k<4*10:> .20 to e1.35 3.5*104<Re<3.8*105 .1 to .75 c 3.5*104<Re<3.8*105 .08 to .75 3.2*104<Re<5*105 .1 to 1.05 10% 10% 10% 10% low .16 to 1.3 1 2 3 5.3 3 15.9% T a b l e 1 . U n s t e a d y l i f t c o e f f i c i e n t s r e p o r t e d i n t h e l i t e r a t u r e B/H=l B/H=.67 B/H=.50 L o A/H C L L o A/H A/H A /H u 7 U Present Results 1.4 1.3 1.2 .8 4.8 8.0 9.6 14.4 .08 .040 .032 <.008 2.4 2.2 2.1 1.6 6.4 4.8 6.4 6.4 .08 .024 .008 1.6 2.0 1.6 1.5 4.8 3.2 6.4 3.2 .08 >.032 <.13 .008 .002 .04 .06 .10 Vickery (1967) 1.32 .68 5.6 3.3 — 0 .10 T a b l e 2. V a l u e s o f X / H , C £ Q A N D A / H f o r r e c t a n g u l a r s e c t i o n s Figure 1: Tunnel o u t l i n e 37 O.50 -I 0.40 _ U 0.10 0.09 0.08 0.07 0.04 — 0.03 • 0.025-0.02 DECAY OF THE LONGITUDINAL INTENSITY OF TURBULENCE V Caapbelland Etkln • Surry 6 Vickery • Balnea and Peterson < • Lanevllle (M=9in.) OLaneville lM=i».51n.) OPresent Data lM=91n.) •Present Data (M=<».5in.) • Present uata IM=2 in.) • Present Data lM=.256in. •8/9. -5/7. A ) u'/U - 2.58 ( x / b ) B) u'/U - 1.12 ( x / b ) U = 5mA •Best f i t to Laneville's data points Best f i t to Baines' and Peterson's 1 1 1 1 1 1 M i l l 10 15 20 25 30 40 50 60 70 60 90 100 2L b 200 F i g u r e 2: D e c a y o f l o n g i t u d i n a l i n t e n s i t y o f t u r b u l e n c e GROWTH OF THE LONGITUDINAL MACRO-SCALE OF TURBULENCE Scatter limit for Van der Heqoe Zllnen data a. Laneville (M=91n.) • Lanevllle (M=i».51n.) • Vickery • Caapbell and Etkln O Surry O Present Data (M=91n.) Present Data (M=l».51n.) Present Data (M=2 In.) O Present Data (M=.2561n.) i I I I I—I— 10 IS 400 600 800 1000 Figure 3: Growth of l o n g i t u d i n a l s c a l e of t u r b u l e n c e w i t h downstream d i s t a n c e Figure 4 : Sketch of a l i v e s e c t i o n 40 -BCD. heavy s t e e l f r a ae e a a a o 3 clasps " ^ L M strain gauges' M Aluminum b r a c k e t s f o r mounting tne ' l i v e ' s e c t i o n on l b s l oad c e l l beam { 1» »l Load c e l l beam mounted i n tne t u n n e l Figure 5: Sketch of the loa d c e l l beam wind tunnel roof brackets to support the damiy pieces end plate h o l l o * duaay end section Screws fastening the ' l i v e ' section to the be as • l i r e ' measuring seetlon fastsnei to the load c e l l bean 021n (.5aa) h o l l o * du^ay end section end plate Figure 6: Sketch of a t y p i c a l model i n s i d e the wind tunnel 42 T 1 .Jin •1.5in-» — 4 . 5 i n 9 i n F i g u r e 7 : E n d p l a t e s 43 Spanwise distribution of Cp along the centreline of base. c .9? "o 0) o O o> v. 3 w w a> in a m -1.6 -\ -1.5 -1.4--1.3--1.2 -1.1--1--0.91 -0.8 -0.7 H -0.6 SQUARE SECTION n » AJJX X X X X X X * 1! X a B a a a B B RA B RA B B n 113 -END M.ATES 0N-S .3 A x x * x x A 8 „ x A • • O D a n x A D° x D H B ^ B B B B B ^ a a B B • NO END PIATES-— I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 - 7 - 6 - 5 - 4 - 3 -2 - 1 0 1 2 3 4 5 6 7 8 Y/H Legend A u'/U~0 x u'/U=4% • u'/U=63 B u'/U=10% B Obosoiu 1979 u'/lH) Figure 8:Base pressure c o e f f i c i n t s for square c y l i n d e r s i n smooth and turbulent flows. CL' at different wind speedsl for a square cylinder of 3in. span 1.4 T 1.2-I-X • A-X "A " X A -X- X -A. X "A 0.8 0 .6 -0.4 0.2 U (m/s) -I 8 Legend A u'/U~0 X u'/U=4% BEST FIT BEST FIT Figure 9: r . m . s . l i f t c o e f f i c i e n t s a t d i f f e r e n t w i n d s p e e d s 80 T A square saction with L/H=16 exposed to a flow of u'/U=0 m o u a. 70 -• 60 -50 •• 40 • 30 -• 20 •• 10 E in II (Amplitude of f n v i b r a t i o n s r i s e s when f n ( i s a harmonic of f v (here at U=3 m/s). -+- -I 30 40 -t 1 50 60 70 80 frequency (HZ) Figure 10: A t y p i c a l spectrum of the f n and f y 46 F i g u r e 11: C £ a s a f u n c t i o n o f a s p e c t r a t i o f o r s q u a r e c y l i n d e r s u ' / L M ) ( w i t h a n d w i t h o u t e n d p l a t e s ) 47 Figure 12: C£ as a function of aspect r a t i o for square cylinders at u'/U=4% (with and without end plates) 48 Figure 13: c£ as a f u n c t i o n of a s p e c t r a t i o f o r square c y l i n d e r s a t u'/U=6% ( w i t h and w i t h o u t end p l a t e s ) Figure 14: C£ as a f u n c t i o n of a s p e c t r a t i o f o r square c y l i n d e r s a t U ' / U=10% ( w i t h and w i t h o u t end p l a t e s ) Figure 15: C£ f o r square c y l i n d e r s at u'/U^O along with the a n a l y t i c a l models 51 Figure 16: C£ as a f u n c t i o n of i n t e n s i t y f o r a square s e c t i o n w i t h L/H=1 52 Figure 17: c£ as a f u n c t i o n of i n t e n s i t y f o r a square s e c t i o n w i t h L/H=2 53 Effect of turbulence intensify on the variation of CL' for a square section with L/H=4 1.4 - i 1.2 41 U 0.8 0.6 0.4-0.2-0.00 0.02 0.04 0.06 U'/U — i — 0.08 Legend d NO ENDPLATES x ENDPLATES ON 0.10 Figure 18:C£ as a f u n c t i o n of i n t e n s i t y f o r a square s e c t i o n w i t h L/H=4 54 Effect of turbulence intensity on the variation of CL' for a square section with L/H=8 1.4 1.2 0.8 0.6 A 0.4 0.2 0.00 0.02 0.04 0.06 U'/U 0.08 Legend A NO ENDPLATES x ENDPLATES ON 0.10 Figure 19:c£ as a f u n c t i o n of i n t e n s i t y f o r a square s e c t i o n w i t h L/H=8 55 Figure 20: C£ as a f u n c t i o n of i n t e n s i t y f o r a square s e c t i o n with L/H=16 56 Base pressure measured in the mid span of a square cylinder c a> jo a> o o a> t_ 3 V) V) a> w a CD -1.6 -1.5-A -1.4--1.3-i -1.2--1.1--1--0.9 -0.8--0.7--0.6 C L" MEASURED ON A SOUARE "LIVE" SECTION OF L/H-Z A X X a — I 1 1 1 1 1 1 1 1 1 1— 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 1.4 1.3 1.2 1.1 CL' r I-0.9 08 r-0.7 0-6 u'/U Legend A with «nd p4ot«« X without «nd plates ° C i ' for no end plates on the '11»e' section and L/H=2 Figure 21: V a r i a t i o n of C£ and C p with t u r b u l e n c e i n t e n s i t y . 57 Figure 22: Cf, as a f u n c t i o n of u'/TJ f o r a square s e c t i o n with L/H=2 (rod turbulence) Figure 23:C£ as a fu n c t i o n of u'/U f o r a square s e c t i o n with L/H=4 (rod turbulence) 59 Figure 24: Cf, as a f u n c t i o n of u'/U f o r a square s e c t i o n w i t h L/H=8 ( r o d t u r b u l e n c e ) 60 Effect of turbulence intensity on the variation of CL' for square sections using rod as the turbutent generating device 0.00 0.02 Legend A L/H=16 NO CMPPIATCS X l/H=16 EHOPIMCS OM 0.12 Figure 25:C£ as a fu n c t i o n of u'/U for a square s e c t i o n with L/H=16 (rod turbulence) 61 CL' for a 3in. span square cylinder without end plates 1.6-1 1.4 C 1.2 J ' a> o O 1-~ 0.8-1 CO c 0.6 "o 2 0.4 0.2-x x —i 1 1 1 1 1 1 1 1 1 1 1 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 U'/U Legend A G r i d t u r b u l « n c « x Rod tu rbu lence F i g u r e 2 6 : C o m p a r i s o n b e t w e e n C £ o b t a i n e d u s i n g r o d a n d g r i d t u r b u l e n c e 62 Effect of turbulence scale on CU on sections with L/H=16 c OJ OJ o o cn "5 o ' 3 . 2-j 1.8-1.6-1.4-1.2-1 0.8-0.6-0 .4 -0.2-Legend A B/H=1 x B/H=.67 • B/H=.5Q —i 1 1 1 1 1 1 1 1 1 1 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Lx/H Figure 27: E f f e c t of i n t e g r a l length s c a l e on Cf 63 Spanwise distribution of Cp along the centreline of base. c a> \o » + -% o u 0> 1_ 3 V) in Vt O m 1.2-3 -1.6 -1.5--1.4--1.3--1. -1.1--1--0.91, -0.8--0.7--0.6 SQUARE SECTION • QB Cft HI CW "fc ffc X P X n • i — a "a H a n !i A A A A A X ^ X X • X * • 9 X O • Y/H H A a a — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i 8 -7 -6 -5 -4 -3 -2 - 1 0 1 2 3 4 5 6 7 8 Legend n iC/UM) no gap x U-/IM) 02ln gap U tf/U~C OWn gap • u*/U=K)% no gap a M-A>=W* -02tN gap Figure 28: E f f e c t of gap s i z e (between the dummy end pieces and the ' l i v e ' s ection) on the mean base pressure c o e f f i c i e n t . 64 Local fluctuating lift coefficient as a function of u'/U 3.2-, Figure 29: C£ 0 as a fu n c t i o n of u'/U 65 Effect of active span on the variation of CU for rectangular sections with B/H=.67 2.4-, 1.6 H 1.2 H 0.8-^ 0.4 Legend |A U'/U~0 -1 1 1 1— 6 8 10 12 -I— 14 -1 16 L/H Figure 30:C£ as a fu n c t i o n of aspect r a t i o f o r c y l i n d e r s with B/H=.67 at u'/U-O Figure 31: C£ as a f u n c t i o n of a s p e c t r a t i o f o r c y l i n d e r s w i t h B/H=.67 a t u'/U=4% 6 7 Figure 32: C£ as a f u n c t i o n of aspect r a t i o f o r c y l i n d e r s with B/H=.67 at u'/U=6% 68 Effect of active span on the variation of CL' for rectangular sections with B/rt=.67 2.4-1 2-1.6-1.2-0.8 0.4 8 L/H 10 12 14 Legend A u'/U=10% -1 16 Figure 3 3 : C£ as a f u n c t i o n of aspect r a t i o f o r c y l i n d e r s with B / H = . 6 7 at U ' / U = 1 0 % 69 Spanwise distribution of Cp base on a section with B/H=.67 -2.4-, , -2.2-1 o o V. 3 in in a> o m -1.8 A -1.6 H -1.4 H -1.2 A A A A • X X X X X X X • • • • • • • a • X 8 I 8 £6 a t • tm rjrna • D • p. bO 1 1 1 1 1 1 1 1 8 -6 -4 -2 0 2 4 6 8 Y/H Legend A U=IOm/i ft l//0>0 X U=Sm/t * u*/U~0 • U=»m/» * ir/UrWX F i g u r e 3 4 : B a s e p r e s s u r r e c o e f f i c i e n t i n s m o o t h a n d t u r b u l e n t f l o w f o r s e c t i o n w i t h B / H = . 6 7 70 Figure 35: c £ as a f u n c t i o n of a spect r a t i o fo r c y l i n d e r s w i t h B/H=.50 at u ' / lM ) Figure 36: c£ as a functi o n of aspect r a t i o f or c y l i n d e r s with B/H-.50 at u'/U=4% 72 Effect of active span on the variation of CL' for rectangular sections with B/H=.50 2.4-, 1.6 1.2 0.8-^ 0.4 H 8 10 L/H 12 — i — 14 l 16 Figure 37: C£ as a function of aspect r a t i o f o r c y l i n d e r s with B/H=.50 at u'/t>6% 7 3 Effect of active span on the variation of CL' for rectangular sections with B/H=.50 2.4-2-1.6 1.2 H 0.8-\ 0.4 4 —r-10 12 L/H —r-14 I 16 Figure 38: C£ as a function of aspect with B / H = . 5 0 at u'/U-10% r a t i o f o r c y l i n d e r s 7 4 APPENDIX A a) Hot Wire C a l i b r a t i o n : The c a l i b r a t i o n f o r the hot wire was found to be DC(volts)=K«U(m/s) where K=.49 for an a i r temperature of 82 degrees F, which was h e l d approximately constant d u r i n g the hot wire t e s t . The f o l l o w i n g f i g u r e shows the c a l i b r a t i o n curve f o r the hot wire. 20T ^15+ 10-0 1 » 6 v (Volts) t i i 75 b)Lenqth S c a l e : A t y p i c a l auto c o r r e l a t i o n curve i s shown below. I n t e g r a l time s c a l e T=f°° R u ( r ) d r was found, measuring the o area under the curve. Using T a y l o r ' s h y p o t h e s i s , i n t e g r a l l e n g t h s c a l e L x was deduced: L X=U«T 0 10 20 30 40 50 m S e C time 7 6 c ) F i l t e r c a l i b r a t i o n : The f i l t e r c a l i b r a t i o n curve was o b t a i n e d using a s i g n a l generator. The amplitude ( i . e . v o l t a g e ) of the generated s i n u s o i d a l s i g n a l was measured by a true-r.m.s. voltmeter. Then, t h i s s i g n a l having a c e r t a i n frequency, was fed i n t o the a m p l i f i e r , then i n t o the f i l t e r with a c e r t a i n low pass s e t t i n g and f i n a l l y i n t o the same true-r.m.s. v o l t m e t e r . The f o l l o w i n g c a l i b r a t i o n curves are obtained by v a r y i n g the s i g n a l frequency f o r c e r t a i n f i l t e r low pass s e t t i n g s . APPENDIX B Methods of measuring r.m.s. f l u c t u a t i n g l i f t c o e f f i c i e n t by  us i n g a simple beam as a load c e l l Consider a beam clamped at both ends exposed to a co n c e n t r a t e d load at i t s cent r e span v a r y i n g s i n u o s o i d a l l y with time. The equation f o r one degree of freedom motion can be w r i t t e n as : mx+cx + k x = F ( t ) = F 1 S i n ( u j l t ) + F 2 S i n ( o j 2 t ) + ... For one s i n u s o i d a l l o a d , the equation of motion i s : mx+cx=F(t)=F 1Sin(cj 1t) x+(c/m)x+(k/m)x= (F 1/m)Sinoj 11 D e f i n i n g /3=c/( 4mk) 1 / 2 as the f r a c t i o n of c r i t i c a l damping and ojn= (k/m) 1/2 as the n a t u r a l frequency, then the equation can be w r i t t e n as: x + 2/36J nx+cjpX= (F , /rrOSinw, t The s o l u t i o n to the above equation i s : x ( t ) = (F 1/k)H(cj, ) C o s ( w 1 t - 0 1 ) where H(co) i s the mechanical admittance and i s : H(co) = {[ 1 - (co/wn ) 2 ] 2 + ( 2/3w/wn ) 2 } ' 1 / 2 and <{> i s the phase angle and i s : tf>=tan-1 {20(u/u n)/[ 1 - ( o / o J n ) 2 ] } 77 7 8 The s q u a r e of t h e s o l u t i o n f u n c t i o n i s : x 2 ( t ) = [ (F , /k)H(to, ) C o s ( w 1 t - 0 1 ) ] 2 Time a v e r a g i n g : J2= (F^/k 2)H 2(w) where F 2 = F 2 S i n 2 (cot) =F 2 / 2 F o r a v a r i e t y o f l o a d i n g f r e q u e n c i e s , t h i s r e s u l t may be e x p r e s s e d i n t h e form of s p e c t r a , d e f i n e d a s : x T=/ 0 0S x x ( c j ) d a ; and F 2 = J"°°SFF (w)dcj 0 0 I n b o t h c a s e s t h e s p e c t r a r e p r e s e n t s t h e c o n t r i b u t i o n t o x 2 o r F 2 from f r e q u e n c i e s n e a r co. Hence S x x ( w ) = ( 1/k 2 ) H 2 ( c o ) S F F ( w ) and P ' = / 0 0 ( 1 / k 2 ) H 2 ( c j ) S F F ( c j ) d ( c j ) 0 I f S F F ( c o ) i s narrow and i s i n a range n o t c l o s e t o con t h e n H(co) o v e r t h i s r ange may be c o n s i d e r e d a p p r o x i m a t e l y c o n s t a n t and e q u a l t o H(co v) where S F F ( w v ) i s t h e peak of t h e f o r c e s p e c t r u m ( i . e . t h e f r e q u e n c y u>v i s t h e v o r t e x s h e d d i n g f r e q u e n c y ) . W i t h t h i s a s s u m p t i o n : v/x2 = ( l / k ) H ( w v ) ,/F 2 7 9 W r i t i n g \/F2 in terms of an r.m.s. l i f t c o e f f i c i e n t C^, where »/F=f=l/2pU2LBCr' then: • x 2/B H(aj v) l/2pU 2L T h i s equation was used to c a l c u l a t e C£ from measured values of i/x 2, f v , U, L and B with k known from c a l i b r a t i o n . APPENDIX C E f f e c t of aspect r a t i o on the f l u c t u a t i n g l i f t c o e f f i c i e n t s , a ) - Model with no end e f f e c t s : £7 By d e f i n i t i o n : H „L ,L: 21. A F 2=; F,dx,/ F 2 d x 2 = ; / F , F 2 d x 2 d X l ° 0 0 0 0 where F| i s the mean square f o r c e on the e n t i r e body where as F, and F 2 are l o c a l f o r c e s per u n i t l e n g t h . D e f i n i n g the f o r c e c o r r e l a t i o n c o e f f i c i e n t as: R F F = FT where Fg= Ff= F2. then .L „L F|=Fo / / R F F d ( x 1 - x 2 ) d x , d x : o o C o n s i d e r i n g a simple form f o r R F F as R F F = exp(-A|x,-x 2|) and s u b s t i t u t i n g i n equation f o r F§ and i n t e g r a t i n g , while knowing t h a t S^FF d(x,-x 2)=X and )/F$ =C£ l/2pU 2LB and F|"= C £ O 1?2pU 2B we get: C£=C£ o/2X/L[L/X -1+exp(-L/X)] 1/ 2 In t h i s e x p r e s s i o n , C L ~+ C L 0 i f L A « 1 and C£ C £ o ( 2 X / L ) 1 / 2 i f L/X » 1 80 81 b ) - Model with end e f f e c t s : Assume A i s the le n g t h r e p r e s e n t i n g the l o s s of l i f t due to each end. Then: F|= F f / L A ; L A R F F ( x , - x 2 ) d x , d x 2 A A Making the same assumptions as i n p a r t (a) and c a r r y i n g out the i n t e g r a t i o n s we f i n d : C L = C L O I / 2 X / L [ L 'A -1+exp(-L'/X) ] 1 / 2 where L'=L - 2 A 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0080809/manifest

Comment

Related Items