T h is dissertation has been 65 13,214 m icrofilm ed exactly as received CORINO, Edward Robert, 1936- A VISUAL INVESTIGATION OF THE WALL REGION IN TURBULENT FLOW. The Ohio State U niversity, Ph.D., 1965 Engineering, chem ical University Microfilms, Inc., Ann Arbor, Michigan
A VISUAL INVESTIGATION OP THE WALL REGION IN TURBULENT PLOW DISSERTATION P re se n te d i n P a r t i a l F u lf illm e n t o f th e R equirem ents f o r th e D egree D octor o f P h ilo so p h y in th e G raduate S ch o o l o f The Ohio S ta te U n iv e rs ity By Edward R obert C orino, B.S c. Ch. E., M.Sc. * * * * * * The Ohio S ta te U n iv e rs ity 1965 Approved by De_ Aflvlsefr E n g in e e rin g
ACKNOWLEDGMENTS I wish t o e x p re ss my s in c e re thanks to my a d v is e r, D r. R. S. Brodkey, f o r h is d i r e c t i o n and a d v ic e d u rin g a l l s ta g e s o f t h is s tu d y. His deep p e rs o n a l i n t e r e s t and e n th u sia sm p ro v id ed much needed encouragem ent d u rin g d i f f i c u lt tim e s. I would a ls o l i k e to e x p re ss my g r a t i tu d e f o r the g e n e r a l environm ent he e s ta b lis h e d f o r s tu d y and r e s e a r c h, and f o r p ro v id in g s u b s t a n t i a l f i n a n c i a l a s s is ta n c e from a N a tio n a l S cience F oun d atio n g r a n t (G-14807) which su p p o rte d th is stu d y. I want to th an k D r. J. H. K o ffo lt, Chairman o f the D epartm ent of Chem ical E n g in e e rin g f o r h is c o n tin u e d i n t e r e s t d u rin g my s ta y in th e d e p artm e n t and f o r p ro v id in g f i n a n c i a l a s s is ta n c e in th e form of a s s i s t a n t s h i p and fe llo w s h ip. The Dow Chem ical Company m ost g r a c io u s ly and prom ptly p ro v id e d the tr ic h lo r o e th y le n e used in t h i s work whenever th e r e q u e s t was made o f them. There i s no way to a d e q u a te ly acknowledge th e c o n t r i b u tio n s and e f f o r t s o f my w ife, M arlene, who was p a ti e n t and u n d e rsta n d in g and an e n d le ss s p rin g of encouragem ent and optim ism. M oreover, h e r e n th u s ia s t i c co n cu rren ce i n the g ra d u a te e d u c a tio n program u n d e rta k e n is d e e p ly a p p re c ia te d. ii
F in a lly, I w ish to acknow ledge my p a re n ts f o r p r o v id in g th e environm ent w hich p o in te d me i n t h i s d i r e c ti o n, and p a r t i c u l a r l y my f a t h e r who d id not l i v e to re a d t h i s. l i i
CONTENTS Page ACKNOWIEDGMENTS... I i ILLUSTRATIONS... v i T A B IE S...v i i i NOMENCLATURE... INTRODUCTION... i x I EQUIPMENT AND EXPERIMENTAL PROCEDURES... 10 1. G en eral D e s c rip tio n... 10 2. Plow S y s t e m... 16 a. P ip in g and M e t e r i n g... 16 b. F lu id and P a r t i c l e s... 26 3. P h o to -O p tic a l System... 45 a. C a m e r a... 46 b. F i l m... 48 c. L i g h t i n g... 49 d. O p tic a l A rrangem ents... 51 e. Mechanism f o r Camera M o v e m e n t... 58 4. Camera V ie w p o in ts... 66 a. W all V i e w... 66 b. Top V i e w... 71 c. T rip W i r e... 75 d. O ther V i e w s... 75 5. Hot Film A n em o m eter... 75 6. Dye I n j e c t i o n... 80 7. D isc u ss io n o f M e t h o d... 82 8. Methods of Film A n a ly sis... 84 EXPERIMENTAL... 91 1. Hot F ilm M e a s u re m e n ts... 91 2. G en eral D e s c rip tio n o f W all R egion-w all View.. 99 3. E je c tio n P ro cess as F u n c tio n o f Reynolds N u m b e r... 102 4. D e ta ile d D e s c r ip tio n o f E je c tio n P ro c ess.... I l l 5. F u rth e r D e ta ils of E je c tio n S t e p... 148 6. 7. Top View A n a l y s i s...152 T u rb u le n t C h a ra c te r and D ista n c e from W all... 160 iv
C ONTENTS c o nt inued Page 8. E f f e c t of T r i p s...162 9. Dye S t u d y...166 10. Summary and Composite D e s c r i p t i o n... 167 DEDUCTIONS AND H Y PO TH ESIS...176 DISCUSSION AND COMPARISON WITH OTHER D A T A... 183 1. V is u a liz a tio n S tu d ie s... 183 2. I n d i r e c t S tu d ie s... 198 3. D ir e c t M easurem ents... 215 4. R e la te d E xperim ents... 227 RECAPITULATION... 229 CONCLUSIONS... 233 RECOMMENDATIONS... 235 APPENDIXES...237 BIBLIOGRAPHY...252 AUTOBIOGRAPHY... 256 v
I ILLUSTRATIONS F ig u re Page 1. Schem atic o f Flow System... 2. P h o to -O p tic a l System...... 15 3. Flow Equipm ent...... 17 4. G en eral View o f T est S e c tio n...... 18 5. D e ta ile d View o f T e s t S e c tio n...... 19 6. H y d ra u lic D rive f o r C a rria g e... 7- R otam eter C a li b r a t i o n...... 25 8. O r if ic e M eter C a lib r a tio n...... 27 9. V is c o s ity M easurem ent...... 34 10. Lamp and S u p p o r t......... 52 11. R e fra c tio n E f f e c t...... 54 12. C a rria g e V e lo c ity M easurem ent... 13. W all View... 14. Top View... 15. P o s itio n in g S c a le...... 74 1 6. Hot Film C a lib r a tio n...... 81 17. Mean V e lo c ity P r o f i l e...... 94 18. u 1 D i s t r i b u t i o n... X 19. E vent F requency...... 97 20. D istu rb e d P e rce n tag e... 21. E je c tio n Angle D i s t r i b u t i o n... v l
ILLUSTRATIONS- - c o n tin u e d F ig u re Page 22. F requency D i s t r i b u ti o n of E je c tio n Angles.... 133 2 3. P h o tographic Sequence of E je c tio n... 137 24. P h o to g rap h ic Sequence of E je c tio n... 138 2 5. Shear L a y e r s...141 26. P hotographic Sequence of "Two Layer V e lo c ity ".. 146 27. O r ie n ta tio n o f P lanes of V i e w...158 28. W all R egion S t r u c t u r e...182 29 R e la tiv e T u rb u le n t I n t e n s i t i e s... 216 30. R e la tiv e T u rb u le n t I n t e n s i t i e s... 217 31. T u rb u le n t E nergy B alance In W all R e g i o n...222 32. T urbulence E nergy P ro d u c tio n R a t e... 223 33* P ro c e sse s in T u rb u le n t E nergy B alance... 225 34. A n a ly sis G r i d...244 35 A pparent E je c tio n T r a je c to r y... 247 3 6. A ctu al E je c tio n T r a je c to r y... 248 37. Depth o f F ie ld a t W a l l...250 vii
TABLES T able Page 1. P r o p e r tie s o f T r ic h lo ro e th y le n e... 28 2. D e c e le ra tio n V e lo c ity... 113 3. A ccele a ti o n V e l o c i t y... 119 4. W allw ard P l o w... 122 5. E je c tio n V e lo c ity and Angle... 126 6. Two L ayer V e l o c i t y...144 7* D u ra tio n of E v e n t s... 150 8. D i s t r i b u t i o n of I n t e r a c t io n Z o n e...152 9. L a te r a l D e v ia tio n s... 159 viii
NOMENCLATURE A S lope o f E vs U curve D E Ej[(n) m o le c u la r d i f f u s i v l t y v o l t s (o u tp u t o f h o t film probe) L ag ran g ian en erg y d i s t r i b u t i o n fu n c tio n I RMS m eter re a d in g (m illiam p ) K in s ta n ta n e o u s lo c a l mass t r a n s f e r c o e f f i c i e n t K NRe NRex Ngc N_ Pr Noe. P (Pr ) y R U a v g. l o c a l mean mass t r a n s f e r c o e f f i c i e n t R eynolds number based on av erag e v e lo c ity - p ip e flow R eynolds number based on X d i s t a n c e - f l a t p la te flow Schm idt number P r a n d tl number e i t h e r NSc o r Npr p re s s u re p ro d u c tio n o f tu r b u le n t en erg y p ip e r a d iu s a v erag e flow v e lo c it y ^ l o c a l mean av erag e v e lo c ity, i th component in s ta n ta n e o u s v e lo c ity, i th component, U-j_ = + u i W.. d i r e c t v isc o u s d i s s i p a t i o n a 3 6 M./2 (pp+pf )d2 b c a c t u a l e j e c t i o n v e lo c it y n e g a tiv e of c a r r ia g e v e lo c it y ix
p a r t i c l e d ia m e te r a p p a re n t le n g th o f p a r t i c l e t r a v e l f u n c tio n f a c t o r c o e f f i c i e n t a p p a re n t e je c t i o n v e lo c ity s u b s c r ip t in d ex f o r component f l u c t u a t i n g mass t r a n s f e r c o e f f i c i e n t tfa d ia l p o s itio n tim e ^ i u* ( ' t S C / p )1/2 in s ta n ta n e o u s tu r b u le n t v e lo c it y f l u c t u a t i o n r o o t mean sq u a re v a lu e o f u^ L ag ran g ian p a r t i c l e v e lo c it y, i th component L ag ran g ian v e lo c it y o f f l u i d, i th component a x i a l c o o rd in a te i n p o la r c o o rd in a te system c o o rd in a te norm al to f l a t p la te i n r e c ta n g u la r c o o rd in a te (R -r)u * a p p a re n t e j e c t i o n a n g le c a l i b r a t i o n v a lu e f o r RMS m eter L ag ran g ian i n t e g r a l s c a le o f tu rb u le n c e eddy d i f f u s i v i t y a n g u la r c o o rd in a te in p o la r c o o rd in a te s tim e in s u rfa c e ren e w a l t h e o r ie s p a ra m eter f o r s t r e a k sp a c in g
c o r r e l a t i o n c o e f f i c i e n t f o r s t r e t c h sp a cin g x m o le c u la r v i s c o s i t y c o e f f i c i e n t k in e m a tic v i s c o s i t y Pp p a r t i c l e d e n s ity p^ or p f l u i d d e n s ity (X red u ced volume r s h e a r s t r e s s f o r w a ll) xi
INTRODUCTION The Im portance o f th e re g io n n e a r a s o l i d boundary on f l u i d m o tio n s has been acknow ledged sin c e P ra n d tl (44) p ro posed th e boundary la y e r h y p o th e s is. In I t s m ost g e n e r a l c o n te x t, th e boundary la y e r i s t h a t f l u i d n e a r a boundary where the v isc o u s e f f e c t s become im p o rta n t and s tr o n g ly In flu e n c e th e f l u i d m o tio n s. At la rg e d is ta n c e s from th e boundary, th e i n e r t i a l e f f e c t s c o m p le te ly dom inate th e flo w, th e v isc o u s e f f e c t s a re n e g li g i b le. 'Hie boundary la y e r conc e p t i s v a lid f o r b o th la m in a r and tu r b u le n t flow, a lth o u g h i n th e l a t t e r case th e p resen c e of tu rb u le n c e c r e a te s a d d i t i o n a l c o m p le x itie s. The lam in ar boundary la y e r has y ie ld e d to m ath e m a tic a l a t t a c k and p r e s e n ts no g r e a t problem. The tu r b u le n t boundary la y e r, much as tu r b u le n t s h e a r flow in g e n e r a l, has n o t been s u c c e s s f u lly t r e a te d by rig o ro u s m athem a tic a l a p p ro a c h e s. The d i f f i c u l t y, o f c o u rs e, a r i s e s from th e p re se n c e In the e q u a tio n s o f m otion o f n o n - lin e a r term s which g iv e r i s e to an i n f i n i t e s e t o f e q u a tio n s. F or s p e c i a l c a s e s, o r where a knowledge o f th e v e l o c i t y f i e l d p e rm its s i m p l i f i c a t i o n o f th e e q u a tio n s, some s o lu tio n s a re p o s s ib le. To t r e a t m ost c a s e s, how ever, th e g e n e ra l approach has been t o abandon th e r ig o ro u s m athem atics and em ploy e m p iric a l and ph en om enological te c h n iq u e s. W hile many o f th e s e r e s u l t s 1
s u c c e s s f u lly p r e d ic t mean flow c h a r a c t e r i s t i c s o r e f f e c t s, th e y can n o t r e v e a l any new in fo rm a tio n ab o u t tu r b u le n t c h a r a c t e r i s t i c s o r tim e -d e p e n d en t o c c u rre n c e s. In t h i s c a te g o ry a re th e w ell-know n " P ra n d tl m ixing le n g th " (45) and "Von Karman s i m i l a r i t y " (6 9 ) h y p o th e s e s. T hese, j u s t a s th e o th e rs which fo llo w e d, a tte m p te d to e s t a b l i s h a r e l a t i o n betw een th e R eynolds s t r e s s e s and th e mean m otions o f th e v e lo c it y f i e l d so t h a t th e e f f e c t s of th e t u r b u le n t f l u c t u a t io n s co u ld be t r e a t e d in much th e same m anner as manner as m o le c u la r t r a n s p o r t m echanism s. The n e c e s s i t y o f a c c o u n tin g f o r th e d isa p p e a ra n c e o f th e tu rb u le n c e f l u c t u a t i o n s a t th e s o l i d w a ll le d to th e a r b i t r a r y d i v i s i o n o f th e boundary la y e r i n to th r e e re g io n s, th e tu r b u le n t c o re, th e t r a n s i t i o n or b u f f e r re g io n, and th e s u b la y e r r e g io n. Hie l a t t e r was fo rm e rly c a lle d th e la m in a r s u b la y e r because th e f l u i d m otions w ith in i t were h e ld to be c o m p le te ly la m in a r. L a te r t h i s was shown to be u n tru e, and th e term s u b la y e r o r v isc o u s s u b la y e r was s u b s t i t u t e d. In th e d is c u s s io n to fo llo w, th e combined s u b la y e r and t r a n s i t i o n r e g io n w i l l be c a lle d th e w a ll r e g io n. More r e c e n t l y o th e r a u th o rs have proposed v e lo c it y d i s t r i b u t i o n r e l a t i o n s w hich do n o t r e q u ir e t h i s a r b i t r a r y d i v i s i o n. One o f th e m ost s u c c e s s f u l i s P ai* s (42) e q u a tio n f o r th e mean v e l o c i t y p r o f i l e. Some a u th o rs, Munk (3 8 ), Townsend (6 4 ), E in s te i n and L i (8 ), and S te rn b e rg (59) > have proposed o th e r e m p ir ic a l o r s e m i- t h e o r e t ic a l m odels o r r e l a t i o n s to e x p la in th e tu r b u le n t
c h a r a c t e r i s t i c s of boundary la y e r flo w s. None have been o v e rly s u c c e s s f u l. A lthough i t s n a tu re i s n o t f u l l y known, th e w a ll re g io n i s s u f f i c i e n t l y w e ll c h a r a c te r iz e d to in d ic a te i t s extrem e im portance i n th e c o n tr o l o f t r a n s p o r t phenomena and th e g e n e ra tio n and m ain ten an ce o f tu r b u le n c e. C o n sid erin g th e f i r s t e f f e c t, th e r e l a t i v e l y sm a ll amount of m ixing w ith in th e s u b la y e r compared to t h a t o f th e co re c au se s th e t r a n s p o r t in t h i s re g io n to proceed p r im a r ily by m o le c u la r mechanism s, and c o n se q u e n tly, i t o c cu rs more slo w ly h ere th a n e ls e w h e re. A la r g e number o f a r t i c l e s have appeared which a tte m p t to p r e d ic t th e r a te s of t r a n s p o r t by a s s ig n in g v a rio u s c h a r a c t e r i s t i c s to t h i s re g io n, and d e v e lo p in g m odels o r r e l a t i o n s from th e s e a ssu m p tio n s. Many o f th e f a m i li a r a n a lo g ie s betw een momentum and h e a t and mass t r a n s f e r use su ch an a p p ro a ch. In a number of c a s e s, n o ta b ly, Von Karman (1 0 ), Sum m erfield (6 0 ), T ay lo r (6 1 ), and D e is s le r and E lan (7)* th e s e ap p ro ach es have been u n s u c c e s s fu l i f th e NSc or Npr ^ 1. These approaches a l l had th e common f a i l i n g o f not p e rm ittin g any m ixing to o c c u r in th e s u b la y e r. Simi l a r tre a tm e n ts by L in, Putnam, and M oulton (34) and D e is s le r (6 ), w hich d id assume some m ixing i n th e s u b la y e r, were more s u c c e s s f u l even a t h ig h Ngc and Npr v a lu e s. A nother group approached the problem by assum ing m odels a f t e r th e f a s h io n o f th e H igbie (19)> D anckw erts (5) s u rfa c e ren ew al th e o ry, and d e riv in g r e l a t i o n s f o r t r a n s f e r r a t e s from th e s e m odels.
Among th e more s u c c e s s f u l a re H a r r io tt (1 8 ), H a n ra tty (1 6 ), and Toor and M archello (3 6, 6 3 ). A ll th e s e tre a tm e n ts have one th in g in common. They a l l b e g in by assum ing a p a r t i c u l a r c h a r a c te r f o r th e w a ll r e g io n. Prom th e s e assu m p tio n s, e q u a tio n s f o r mass t r a n s f e r r a t e s o r c o e f f i c i e n t s a re d ev elo p ed. These e q u a tio n s u s u a lly c o n ta in one o r more p aram eters which m ust be e v a lu a te d from e x p e rim e n ta l d a ta. Upon e v a lu a tin g th e p aram eters in t h i s fa s h io n, n e a r ly a l l th e m odels can be made to p r e d ic t, over a lim ite d range o f NSc v a lu e s, th e p ro p er dependency of th e t r a n s f e r c o e f f i c i e n t on Nsc as g iv e n by e x p e rim e n ta l d a ta. O u tsid e t h i s Ngc range th e p re d ic te d dependency i s u s u a lly i n c o r r e c t. A lthough th e re i s q u ite a v a r i e t y in th e c h a ra c t e r of th e assumed m odels, th e f a c t t h a t many can be made to ag ree w ith th e same e x p e rim e n ta l d a ta d e m o n stra te s th e i n s e n s i t i v i t y o f th e r e s u l t s to th e a ssu m p tio n s. This i n s e n s i t i v i t y p re c lu d e s any p o s s i b i l i t y o f d e c id in g which o f th e s u c c e s s f u l m odels m ost a c c u ra te ly d e p ic ts th e tr u e n a tu re o f the w a ll re g io n o r th e tr a n s p o r t mechanism on th e b a s is of t h e i r su c ce ss in p r e d ic tin g t r a n s f e r r a t e s or " c o n c e n tra tio n " p r o f i l e s. M oreover, because th e e x p e rim e n ta l r e s u l t s r e f l e c t averaged or i n t e g r a l v a lu e s, th e y cannot d e fin e the i n s t a n tan eo u s o r f l u c t u a t i n g c h a r a c te r o f th e re g io n. Q uite th e c o n tr a r y i s t r u e. Ihe n a tu re o f th e w a ll re g io n m ust be known b e fo re th e p ro p er model can be s e le c te d.
The im p o rtan ce o f the w a ll r e g io n in th e g e n e ra tio n and m aintenance o f tu rb u le n c e has been e x p e rim e n ta lly demons t r a t e d. Since th e k i n e t i c e n e rg y o f tu rb u le n c e i s c o n tin u o u s ly d i s s i p a te d to h e a t th ro u g h v isc o u s e f f e c t s, a co n tin u o u s su p p ly o f new tu rb u le n c e m ust be c re a te d w ith in th e flow i f th e q u a s i- s te a d y s t a t e c h a r a c te r o f tu r b u le n t boundary la y e r flow i s to be m a in ta in e d. The so u rce o f th e e n e rg y i s th e mean flow, b u t as y e t the mechanism o f t r a n s f e r i s unknown. The i n v e s ti g a t i o n s by L au fer (31) f o r p ip e flow, and K leb an o ff (26) and Townsend (6 5 ) f o r flow over a f l a t p l a t e, c l e a r l y d e m o n stra te d t h a t th e g e n e r a tio n o f tu rb u le n c e i s a maximum w ith in th e w a ll re g io n, and t h a t th e d i s s i p a t i o n a ls o i s a maximum t h e r e. In a d d itio n, L au fer (31) and Townsend (66) each d e term in ed th e d i s t r i b u t i o n w ith r e s p e c t to the w a ll of th e c o n v e rsio n o f mean flow e n erg y to tu rb u le n c e. In b o th c a se s th e maximum o c c u rre d i n th e w a ll r e g io n. These m easurem ents were made w ith h o t w ire anem om eters and have re v e a le d a g r e a t d e a l ab o u t th e p r o p e r tie s o f tu r b u le n t flo w. They showed t h a t v e l o c i t y f l u c t u a t i o n s e x i s t w ith in th e s u b la y e r. They have n o t, how ever, succeeded i n d e s c r ib in g why tu r b u le n c e g e n e r a tio n i s a maximum in th e w a ll re g io n o r how i t o c c u rs. One d i f f i c u l t y o f h o t w ire m easurem ents I s i n i n t e r p r e tin g th e s i g n a l in term s o f a p h y s ic a l p ic tu r e o f th e f l u i d m o tio n s. There a re more d i r e c t o b s e rv a tio n s o f th e n a tu re o f th e w a ll re g io n. Page and Townsend (10) observed d i s t i n c t
d e p a rtu re s from lam in ar flow w ith in th e s u b la y e r, b u t r e v e a le d l i t t l e e l s e. More r e c e n t l y R u n s ta d le r (50) used dye i n j e c t i o n and v is u a l-p h o to g ra p h ic te c h n iq u e s to make a d e t a i l e d i n v e s t i g a t i o n of th e boundary la y e r o ver a f l a t p l a t e. H is stu d y re v e a le d t h a t th e w a ll re g io n p o sse sse d a d i s t i n c t s t r u c t u r e and a d e f i n i t e, n o n -re g u la r tim e -d e p e n d en t m o tio n. The above d is c u s s io n was p re s e n te d to d e m o n stra te th e im portance o f th e w a ll re g io n and to em phasize th e need f o r g r e a t e r knowledge o f i t s c h a r a c t e r. The la c k o f knowledge co n cern in g t h i s r e g io n i s due i n p a r t to th e d i f f i c u l t i e s of o b ta in in g a c c u ra te m easurem ents and o b s e rv a tio n s w ith in i t. T his i s a r e s u l t of th e e x tre m e ly sm a ll dim ensions in v o lv e d. F or exam ple, in a 2 -in c h pip e f o r l iq u i d s, i. e., t r i c h l o r o - e th y le n e, a t NRe = 5 0,0 0 0 th e e n t i r e s u b la y e r r e g io n y+ = 5, i s c o n ta in e d i n 0.004 in c h e s. Any probe o r i n j e c t i o n d e v ic e in tro d u c e d in to th e r e g io n w i l l have d im en sio n o f th e o rd e r o f m agnitude o f th e re g io n. In a d d itio n, f o r l i q u i d s, th e n e c e s s i t y o f p ro v id in g p h y s ic a l s tr e n g th to th e probes cau ses them to be l a r g e r th a n th o se used i n g a s e s. What i s r e q u ire d i s a method o f i n v e s ti g a t i o n w hich can r e v e a l th e c h a r a c te r o f th e w a ll r e g io n and y e t does n o t r e q u ir e th e I n tr o d u c tio n o f any m easuring d e v ic e i n to th e flo w. A q u a l i t a t i v e p h y s i c a l p ic tu r e o f th e s t r u c t u r e o f th e flow coupled w ith q u a n t i t a t i v e m easurem ents would be v e ry v a lu a b le.
T his p re s e n t stu d y was u n d ertak en to dev elo p a te c h nique which would p e rm it an in v e s ti g a t i o n o f the w a ll re g io n b u t which would n o t r e q u ir e the in tr o d u c tio n of any dev ice in to i t. This te c h n iq u e i s th e n used in an in te n s iv e stu d y o f th e f l u i d m o tio n s. The o b je c tiv e of th e stu d y i s to c h a r a c te r iz e th e n a tu re of th e w a ll re g io n in tu r b u le n t p ip e flow and to d eterm in e from t h i s p h y s ic a l p ic tu r e th e manner in which th e w a ll re g io n causes th e e f f e c t s a t t r i b u t e d to i t. In a d d itio n, t h i s knowledge should p erm it th e s e l e c t i o n of th e tr a n s p o r t model, i f any, which i s in b e s t a g re e ment w ith the a c tu a l n a tu re o f the r e g io n. I f no model a g re e s, s u g g e stio n s f o r a new one can be proposed. S p e c if ic a lly, th e i n v e s tig a tio n e n t a i l s a v i s u a l- p h o to g rap h ic stu d y of th e w a ll re g io n in f u l l y tu r b u le n t p ip e flo w. The te c h n iq u e developed employs c o ll o i d a l s iz e d p a r t i c l e s suspended in th e f l u i d as t r a c e r s, and r e q u ir e s no i n j e c t i o n or th e in tr o d u c tio n o f any m easuring d e v ic e in to th e flo w. High speed ( 65O-IOOO fram es/seco n d ) m otion p ic tu r e s o f th e m ag n ified w a ll re g io n a re ta k e n as th e cam era i s tra n s p o rte d dow nstream w ith th e flo w. T his i s th e f i r s t tim e t h a t such p ic tu r e s of th e w a ll re g io n in tu r b u le n t pipe flow have been o b ta in e d. In a c i r c u l a r p ip e, t h i s re g io n would n o t n o rm ally be v i s i b l e because o f th e l i g h t r e f r a c t i o n a t th e p ip e w a ll. This problem was e lim in a te d by u sin g in th e flow system a liq u id t h a t had th e same r e f r a c t i v e in d ex as th e g la s s p ip e, and su rro u n d in g th e pipe w ith a view ing
c e l l o f th e same f l u i d. The m otion p ic tu r e s a re a n aly ze d to o b ta in a d e ta il e d p h y s ic a l d e s c r ip tio n, su p p o rte d by q u a n tit a t i v e m easurem ents, o f th e n a tu re o f th e f l u i d m otions in th e w a ll r e g io n. U iese r e s u l t s a re combined w ith th e g e n e r a l knowledge o f t u r b u le n t flow to produce an h y p o th e s is which d e s c rib e s th e f l u i d b e h a v io r in t h i s re g io n, and e x p la in s i t s s ig n if ic a n c e in th e g e n e r a tio n and m aintenance o f tu r b u le n c e. In a d d itio n, th e e f f e c t of th e c h a r a c te r of th e w a ll re g io n on tra n sp o rt-p h e n o m e n a i s e x p lo re d, and s u g g e s tio n s f o r a new m odel to p r e d ic t t r a n s f e r r a t e s a re p re s e n te d. The m ain body o f t h i s work i s d iv id e d in to two p a r t s. i n P a r t 1 th e e x p e rim e n ta l te c h n iq u e t h a t has been developed and th e equipm ent used a re p re s e n te d and d is c u s s e d. A lthough th e u n d e rly in g p r i n c i p le s o f th e te c h n iq u e, and in f a c t th e b a s ic te c h n iq u e, have been known f o r many y e a rs, a c o n s id e r a b le amount o f developm ent was n e c e s s a ry to p ro v id e th e c a p a b i l i t i e s re q u ire d f o r t h i s i n v e s ti g a t i o n. In P a r t 2 th e e x p e rim e n ta l r e s u l t s a re p re s e n te d and th e h y p o th e s is p ro p o sed, m iese a re d is c u s s e d and compared w ith p e r t i n e n t d a ta a v a i la b l e in th e l i t e r a t u r e. In a d d itio n to t h i s w r i t t e n t e x t, th e re i s a m otion p ic tu r e f ilm a v a ila b le which shows th e im p o rta n t f e a tu r e s
o f th e w a ll r e g io n w hich a re d is c u s s e d i n t h i s work.*1 In f a c t, s in c e many o f th e c h a r a c t e r i s t i c s o f th e w a ll re g io n show a d e f i n i t e tim e dependency and in v o lv e r e l a t i v e m otions o f v a rio u s k in d s, th e y a re more r e a d i l y ob serv ed i n th e s e m otion p ic t u r e s th an i n s t i l l p h o to g ra p h s. kniis i s a s i l e n t, b la c k and w h ite, 16 mm. m otion p i c t u r e. A lo a n copy i s a v a ila b le on r e q u e s t to M otion P ic tu r e D iv is io n, The Ohio S ta te U n iv e r s ity, 1 8 8 5 N e il Avenue, Columbus, Ohio 43210. R equest 11A V isu a l I n v e s tig a t i o n o f th e W all R egion in T u rb u le n t F lo w," Chem ical E n g in e e rin g. Tliere i s a h a n d lin g ch arg e o f a p p ro x im a te ly $3. 0 0.
EQUIPMENT AND EXPERIMENTAL PROCEDURES G en eral d e s c r i p t io n In t h i s s e c tio n a g e n e ra l d e s c r i p t io n o f th e equipm ent and e x p e rim e n ta l p ro c e d u re s w i l l he p r e s e n te d. The d e t a i l s o f th e d i f f e r e n t p ie c e s o f equipm ent and p ro ce d u res w i l l be d is c u s s e d l a t e r. The equipm ent may be d iv id e d i n to two p a r t s ; th e flow system and th e p h o to - o p tic a l sy stem. The flo w sy stem cons i s t e d o f a 150 g a llo n ta n k (A )1 from w hich th e t e s t f l u i d was pumped by a c e n t r i f u g a l pump (B) th ro u g h th e v a rio u s c o n tr o l v a lv e s (C) to th e t e s t s e c t i o n. The t e s t s e c tio n was a 10 f o o t le n g th of 2" I.D. Pyrex g la s s p ip e (D) which was e n c lo se d in a view ing c e l l (E ). T h is s e c tio n was p re ceded by a s t r a i g h t le n g th made up o f 20 f e e t (2-10 f o o t s e c tio n s ) o f 2" I.D. g la s s p ip e (P ), and 4 f e e t o f 2" sc h ed u le 40 s t e e l p ip e. 151686 p ip e s e c tio n s w ere su p p o rte d by s t e e l b ra c e s which were b o lte d to th e c o n c re te f l o o r. The end o f th e t e s t s e c tio n was co nnected to 6 f e e t of s t e e l p ip e w hich was jo in e d t o th e r e t u r n p ip e. T his s e c t i o n o f p ip e conta in e d th e o r i f i c e m eter (G) u sed to m e te r th e h ig h r a t e s o f flo w. A ro ta m e te r (H) was used to m e te r th e low r a t e s o f ^L etters r e f e r to marked p a r ts i n F ig u re 1. 10
11 flo w. The p ip in g system, in c lu d in g th e t e s t s e c tio n, th u s com prised a c lo s e d lo o p. In th e s e c tio n o f p ip e dow nstream o f th e t e s t s e c tio n a f i l t e r ( I ) was lo c a te d w hich co u ld remove a l l s o l i d s l a r g e r th a n 5 m ic ro n s. One o f th e therm o co u p le s ( j ) used to c o n tin o u s ly re c o rd th e f l u i d te m p e ra tu re was a ls o lo c a te d in t h i s s e c t i o n. To e lim in a te p o s s ib le end e f f e c t s, o n ly th e c e n t r a l p a r t o f th e 10 f o o t t e s t s e c tio n was u se d. T ric h lo ro e th y le n e was s e le c te d as th e t e s t f l u i d p r i m a rily because i t s r e f r a c t i v e in d ex c lo s e ly approxim ated th e r e f r a c t i v e in d ex o f th e g l a s s. The view ing c e l l was a ls o f i l l e d w ith tr ic h lo r o e th y le n e f o r th e same re a s o n. W ith th e g la s s p ip e c o m p le te ly co vered w ith l iq u id o f th e same r e f r a c t i v e in d ex as th e g l a s s, th e problem s o f r e f r a c t i o n were e lim in a te d, and the w a ll re g io n could be exam ined. In o rd e r to mark th e f l u i d elem en ts so t h a t th e m otions would be v i s i b l e, v e ry f in e p a r t i c l e s o f "Seemag"-1- magnesium oxide were suspended in th e l iq u i d. d ia m e te r o f 0.6 m ic ro n s. These p a r t i c l e s had an av erag e The p a r t i c l e c o n c e n tr a tio n was dense enough so t h a t a la r g e number o f p a r t i c l e s ap p eared w ith in th e f i e l d o f view s im u lta n e o u s ly, b u t s u f f i c i e n t l y d i l u t e so t h a t p a r t i c l e - p a r t i c l e i n t e r a c t i o n a lm o st n e v er o c c u rre d. Hie t e s t f l u i d ap p eared p e r f e c t l y c l e a r and c o lo r le s s i n norm al l i g h t, and o n ly u n d er d a rk f i e l d illu m in a tio n were th e p a r t i c l e s v i s i b l e. Then th e y ap p eared as b r ig h t ^Comm ercial p ro d u c t o f PMC C o rp o ra tio n.
+ rn <tt : : & M------ l Lur Figure I. Schematic of Flow System to
13 p o in ts o f l i g h t a g a in s t a d a rk background. T his i s a r e s u l t o f th e w ell-know n T y n d all e f f e c t. I t sh o u ld be em phasized t h a t th e s e p a r t i c l e s were suspended in th e f l u i d a t a l l tim es and no i n j e c t i o n was re q u ire d d u rin g a ru n. CHie p h o to - o p tic a l system c o n s is te d o f a l l th e l i g h t i n g, p h o to g ra p h ic, and o p t i c a l equipm ent needed to re c o rd th e p a r t i c l e m otions on f ilm. S ince th e p a r t i c l e m otions were v e ry r a p id, a h ig h speed m o tio n p ic tu r e cam era (A)-*- was used a t film in g sp eed s of 650 to 1000 fram es p e r seco n d. These co rre sp o n d to s h u t t e r speeds o f 0.0 0 0 5 to 0.0 0 0 3 3 se co n d s. The le n s system o f th e cam era was a d ap ted to produce images o f th e a re a of i n t e r e s t o f 4.3X and 2X m a g n ific a tio n. These m ag n ified im ages g r e a t l y enhanced th e a b i l i t y o f th e system to d e fin e th e f l u i d m otions w ith in th e v e ry narrow w a ll r e g io n. B ecause of th e h ig h film in g sp e ed s, th e m a g n ific a t i o n, and th e d a rk f i e l d illu m in a tio n, a v e ry in te n s e l i g h t so u rc e was r e q u ir e d. An u l t r a - h i g h p re s s u re D.C. m ercury a rc lamp (B) was used, and th e beam was fo cu sed by means o f a s p h e r ic a l m irro r th ro u g h s l i t s i n to th e f i e l d o f view. The e lim in a tio n o f th e r e f r a c t i o n problem caused by th e curved p ip e w a ll was m entioned under th e d is c u s s io n o f th e t e s t f l u i d. The use o f a m ercury a rc lamp and n o t a m onochrom atic l i g h t so u rc e p re v e n te d th e com plete e lim in a tio n o f any e f f e c t o f r e f r a c t i o n, b u t th e sm a ll e f f e c t w hich rem ained was used ^ Letter r e f e r s to marked p a r t s o f F ig u re 2.
14 to good ad v an tag e as a means o f lo c a tin g th e in s id e pip e w a ll i n th e p h o to g ra p h s. F or re a s o n s w hich w i l l be d is c u s s e d more f u l l y l a t e r, i t was found to be a d i s t i n c t ad v an tag e to have th e c a p a b ili t y o f moving th e e n t i r e p h o to - o p tic a l system dow nstream w ith th e flow d u rin g p h o to g rap h y. T his n a t u r a l l y re q u ire d t h a t th e f i e l d o f view be k e p t i n fo cu s d u rin g th e movement, and a ls o t h a t no m ech an ical v ib r a tio n s which m ight a f f e c t th e p h o to - o p tic a l system be p r e s e n t. To accom plish t h i s an 8 - f o o t la th e bed (C) was a lig n e d w ith th e pipe and b o lte d to th e c o n c re te f l o o r. The l a th e c a r r ia g e (D) w hich i s d e sig n e d to s l i d e alo n g the ground s t e e l ways was f i t t e d w ith a heavy s t e e l fram e (E) which su p p o rte d th e cam era (A) and l i g h t so u rce (B ). T his c a r r ia g e was d r iv e n down the la th e bed a t c lo s e ly c o n tr o lle d c o n s ta n t speeds by an h y d ra u lic p i s t o n. In t h i s manner th e e n t i r e re c o rd in g system co u ld be moved w ith th e flow, and a t any p r e - s e le c te d sp e ed, This m eant t h a t any l o c a l mean a x i a l v e l o c i t y i n th e w a ll re g io n co u ld be m atched by th e c a r r ia g e v e lo c it y, and, th e r e f o r e, t h a t a p a r t i c u l a r segm ent of f l u i d co u ld be k e p t in view as th e f l u i d m o tio n s d e v e lo p e d. The e x p e rim e n ta l ru n s were conducted i n th e fo llo w in g f a s h io n. The flow c o n d itio n s o r R eynolds number d e s ir e d was e s ta b lis h e d by a d ju s tin g th e c o n tr o l v a lv e s in th e flow sy stem. The a r e a o f view and a x i a l p o s i t io n w ith in th e t e s t s e c t i o n were s e l e c te d, and th e p h o to - o p tic a l system a lig n e d
nx light path Figure 2 Photo Optical System H
and focused a c c o rd in g ly. The film in g speed d e s ir e d was s e t on the p ro p er c o n tr o l s. The c a r r ia g e speed was s e le c te d, and the c o n tr o ls f o r th e h y d ra u lic d riv e mechanism a d ju s te d. I f th e c a r r ia g e was to rem ain s t a ti o n a r y d u rin g th e ru n, th e photography was begun a t t h i s p o in t. I f, however, th e c a r r ia g e were to move, i t was f i r s t moved upstream beyond th e p o in t where photography was to be i n i t i a t e d, and th en s t a r t e d dow nstream. When i t reach ed the i n i t i a t i o n p o in t, th e cam era was tu rn e d on. In t h i s fa s h io n, any p o s s ib le a c c e le r a tio n e f f e c t s a s s o c ia te d w ith th e c a r r ia g e m otion were e lim in a te d b e fo re p h o tography was begun. The film s r e s u l ti n g from th e s e ru n s were an aly zed in d e t a i l to provide th e d e s ir e d in fo rm a tio n co n cern in g th e n a tu re of the f l u i d m otions in th e w a ll re g io n. This a n a l y t i c a l procedure i s d e sc rib e d in a n o th e r s e c tio n. P hotographs of th e equipm ent ap pear in F ig u re s 3* 4, 5, and 6. Flow system P ip in g and m e te rin g. With th e e x c e p tio n o f th e t e s t s e c tio n and th e e n tr y s e c tio n p reced in g i t, a l l p ip in g was 2 in ch, sch ed u le 40, g a lv a n iz e d s t e e l. The j o i n t s were a l l th re a d e d e x c e p t f o r th e co n n ec tio n s to th e pump and th e g la s s p ip e t e s t s e c tio n. These were fla n g e d. The h o ld in g ta n k was carbon s t e e l and had a 150 g a llo n c a p a c ity. I t was e n t i r e l y c lo se d e x c e p t f o r th e i n l e t and o u t l e t p o rts and a
Figure3. Flow Equipment
18 Figure 4. General View of Test Section
19 Figure 5. Detailed View of Test Section
F i g u r e 6. Hydraulic Drive for Carriage ro o
vent l i n e. Before the equipment was assem bled, the in t e r io r s were thorough ly scrubbed w ith tr ic h lo r o e th y le n e to remove d ir t and g r e a se. A fter assem bly the e n tir e system was flu sh ed w ith pure tr ic h lo r o e th y le n e which was then d rain ed. The c e n tr ifu g a l pump was a l l iro n w ith an e ig h t-in c h diam eter, six -v a n ed im p e lle r. I t was rated a t 50 gpm. a t 70 f e e t o f head fo r water a t 1750 rpm. A la rg e r motor was in s t a lle d to provide s im ila r c a p a b ilit ie s fo r pumping the denser tr ic h lo r o e th y le n e. As F igures 1 and 3 show, the o u tle t lin e was f i t t e d w ith a by-pass lin e and c o n tr o l v a lv e, and two flow l i n e s. One of the l a t t e r was o f tw o-inch diam eter pip e, and was used fo r flow r a te s in ex cess of 2.5 gpm. The other flow lin e was o f 1/2 inch pipe and contained a rotam eter. This l i n e was used f o r low flow r a t e s where more a c c u ra te c o n tr o l and flow r a t e re a d in g s th a n were p o s s ib le w ith the l a r g e r d ia m e te r l i n e and th e o r i f i c e m eter were o b ta in e d. By e i t h e r r o u te, the f l u i d proceeded to th e f o u r - f o o t s t e e l s e c tio n which j u s t p reced ed the f i r s t o f th r e e te n - f o o t s e c tio n s o f Pyrex g la s s p ip e. T his p ip e had an i n t e r n a l d ia m e te r of tw c in c h e s. T eflo n g a sk e te d f la n g e s. The s e c tio n s were co n n ected by The g a s k e ts and j o i n t s were v e ry c a r e f u l l y a lig n e d and f i t t e d to reduce t h e i r p o s s ib le a c tio n as d is tu rb a n c e g e n e r a to r s. The t e s t s e c tio n a c t u a l l y used was s i t u a t e d i n th e c e n t r a l p o r tio n o f th e l a s t le n g th of g la s s p ip e, a t l e a s t fo u r f e e t dow nstream of th e n e a r e s t j o i n t. T his was a p re c a u tio n a ry m easure to make c e r t a i n t h a t
th e m otions o b served w ith in th e t e s t s e c tio n were n o t i n f l u 22 enced by end e f f e c t s. The m ost d e s ir a b le c o n d itio n, of c o u rs e, would have been to u se a co n tin u o u s t h i r t y - f o o t le n g th o f p l a s t i c p ip e and e lim in a te th e j o i n t s e n t i r e l y. U n fo rtu n a te ly, th e re q u ire m e n ts t h a t th e p ip e be t r a n s p a r e n t, and t h a t th e f l u i d flo w in g w ith in i t be c le a r and c o lo r l e s s, N ew tonian, o f low v i s c o s i t y, and, m ost Im p o rta n t, have an in d ex of r e f r a c t i o n e q u a l to t h a t o f th e p ip e, e lim in a te d a l l p o t e n t i a l f l u i d s e x c e p t h y d ro ca rb o n s. Of th e s e, the ones o f p ro p e r in d e x o f r e f r a c t i o n a ls o a tta c k e d th e p l a s t i c. Thus, g la s s p ip e was th e o n ly a l t e r n a t i v e, and te n - f o o t le n g th s th e o n ly p r a c t i c a l le n g th s a v a i l a b l e. T his q u e s tio n o f th e e f f e c t o f th e j o i n t s on th e flo w was exam ined th e o r e t i c a l l y and e x p e rim e n ta lly, and th e r e s u l t s a re d is c u s s e d i n a l a t e r s e c t i o n. I t can be s a f e l y concluded t h a t in th e p r e s e n t stu d y th e j o i n t s had no e f f e c t on th e m otions o b serv ed w ith in th e f l u i d in th e t e s t s e c tio n. The tw e n ty - f o u r - f o o t le n g th o f g la s s p ip e w hich p re ceded th e t e s t s e c tio n was d e sig n ed to a s su re t h a t f u l l y d ev elo p ed tu r b u le n t flow e x is te d w ith in th e t e s t s e c tio n. S c h lic h tin g (53) c a lc u la te d th e e n tr y le n g th needed f o r p ip e o r ch an n el flow to e s t a b l i s h a f u l l y dev elo p ed p r o f i l e in la m in a r flo w. He o b ta in e d v a lu e s o f th e o rd e r o f 80-200 d ia m e te rs. T u rb u le n t p r o f i l e s r e q u ir e much s h o r te r e n tr y
23 le n g th s. Latzko (30) p re s e n te d th e r e l a t i o n = 0.693 (NRe)1/ ' 1 f o r th e e n tr y le n g th re q u ire d to e s t a b l i s h a tu r b u le n t p ro f i l e in a p ip e. I f th e upper Reynolds number o f t h i s s tu d y i s s u b s titu te d i n to t h i s r e l a t i o n, an e n tr y le n g th o f 10.4 d ia m e te rs is p r e d ic te d. However, Hinze (20) says t h a t t h is r e l a t i o n g iv e s v a lu e s which a re alw ays le s s th a n th o se m easured e x p e rim e n ta lly. K irs te n (2 5 ) m easured e n tr y le n g th s e x p e rim e n ta lly and found t h a t 50 to 100 d ia m e te rs, depending on NRe, u s u a lly were s u f f i c i e n t to e s t a b l i s h th e flo w. N ikuradse (41) found t h a t f o r d is tu rb e d e n t r i e s 25 to 40 d iam ete rs were s u f f i c i e n t. Hinze in rev iew in g th ese v a lu e s s t a t e s t h a t 40 d ia m e te rs can be used as a minimum v a lu e. In th e p re s e n t c a se, th e e n tr y was d is tu r b e d, and the e n tr y le n g th o f n e a r ly 145 d ia m e te rs s a t i s f i e s even th e m ost extrem e re q u ire m e n t. Thus i t may be s a f e l y assumed t h a t f u l l y developed tu r b u le n t flow e x is te d w ith in th e t e s t s e c t i o n. This assum ption was l a t e r checked by h o t film anemometer m easurem ents and found to be v a lid. The end o f th e t e s t s e c tio n was connected to a s i x - f o o t s e c tio n o f s t e e l pipe which was i n tu r n Jo in ed to th e r e t u r n l i n e. W ithin t h i s s e c tio n a S e la s F lo tro n ic f i l t e r w ith S e rie s F ty p e M ic r o -F ilte r elem ent was p o s itio n e d. This elem ent removed a l l p a r t i c l e s o f d ia m e te r g r e a t e r th a n 5 m ic ro n s. The f l u i d was c o n tin u o u sly passed th rough t h i s
24 f i l t e r, The f i l t e r p o r o s ity i s, o f c o u rs e, much g r e a t e r th a n th e av erag e p a r t i c l e d ia m e te rs of th e s o l i d s used, b u t i t was d e sig n e d to p r im a r ily remove any e x tra n e o u s d i r t o r agglom era tio n s from th e sy ste m. An elem ent o f 0.5 m icron p o r o s ity would have r e q u ir e d im p r a c tic a lly h ig h p re s s u re dro p s f o r h ig h flow r a t e s, and so was n o t u se d. P e rio d ic ex am in a tio n o f th e f i l t e r e lem en t showed t h a t a g g lo m e ra tio n o f th e magnesium oxide was n o t o c c u rrin g, and i t seemed re a s o n a b le to assume t h a t th e m a jo r ity o f p a r t i c l e s were s t i l l o f th e o rd e r o f 0.6 m ic ro n s. At th e v e ry end of t h i s s e c tio n a packing g la n d was lo c a te d which a ffo rd e d th e means o f moving a p o s itio n in g s c a le a x i a l l y w ith in th e t e s t s e c t i o n. A therm ocouple w e ll was a ls o lo c a te d h e re, and d u rin g ru n s th e te m p e ra tu re o f th e f l u i d was c o n tin u o u s ly re c o rd e d. Wie g la s s p ip e s and le a d - in p ip e s were su p p o rte d by s t e e l c r a d le s which were b o lte d to th e c o n c re te f l o o r. The r e t u r n lin e was b o lte d to th e v e r t i c a l s u p p o rts o f th e s e c r a d l e s. I t was n e c e s s a ry to know th e av erag e flow v e lo c it y s in c e th e R eynolds number was a b a s ic p a ra m e te r i n th e s tu d y. T h is was m easured by e i t h e r th e r o ta m e te r, f o r flow r a t e s o f 2.5 gpm. o r l e s s, o r th e o r i f i c e m e te r, f o r l a r g e r flow r a t e s. The ro ta m e te r was c a l i b r a t e d by w eighing th e e f f l u x c o lle c te d a t a p a r t i c u l a r s c a l e s e t t i n g f o r a tim ed i n t e r v a l. The c a l i b r a t i o n cu rv e a p p e a rs in F ig u re 7.
25 100 9 0 80 70 60 50 E 40 * 30 20 0 0.5 1.0 L5. 2.0 2.5 3.0 G. P. M. Figure 7. Rotameter Calibration
F or h ig h e r flow r a t e s, and c o n se q u e n tly f o r m ost ru n s, th e o r i f i c e m eter was u se d. T his c o n s is te d o f a s ta n d a rd fla n g e tap p ed o r i f i c e fla n g e and a s t a i n l e s s s t e e l, sh a rp edged o r i f i c e p l a t e. A m ercury m anometer was used to m easure the p re s s u re d i f f e r e n t i a l a c ro s s th e o r i f i c e p l a t e. T his o r i f i c e p la te was preced ed by 36 f e e t o f s t r a i g h t p ip e which c o n ta in e d a s in g le u n io n 20 f e e t u p stre am o f th e o r i f i c e. T his a s s u re d th e p ro p e r flow c o n f ig u r a tio n th ro u g h th e o r i f i c e. The m e te r was c a l ib r a t e d by th e tim ed w eighing te c h n iq u e d e s c rib e d above, and th e c a l i b r a t i o n curve a p p e a rs in F ig u re 8. F or th e low er flow r a t e s where th e two c a l i b r a t i o n c u rv e s o v e rla p, th e in d e p e n d e n tly m easured c a l i b r a t i o n s a g re e v e ry w e ll. Over a p e rio d o f a number o f e x p e rim e n ta l ru n s th e re was an u n a v o id a b le te m p e ra tu re r i s e i n th e f l u i d due to the pumping e n e rg y in p u t. T his n e c e s s i t a t e d an ap p roxim ate s e t t i n g f o r R eynolds number by use o f th e m e te rs, and a c a l c u l a t i o n o f th e a c t u a l R eynolds i n w hich th e te m p e ra tu re r i s e was ta k e n i n to a c c o u n t. The d if f e r e n c e was alw ays q u ite sm a ll. F or any p a r t i c u l a r ru n, th e p e rio d o f tim e in v o lv e d was so s h o r t t h a t no te m p e ra tu re r i s e o f any s ig n if ic a n c e was p o s s ib le d u rin g th e ru n i t s e l f. F l u i d. S ince g la s s p ip e had to be used in th e system, f o r th e re a so n s d e s c rib e d e a r l i e r, th e problem th e n became one o f s e l e c ti n g the l i q u i d which would m atch th e r e f r a c t i v e in d e x o f th e g la s s and have th e o th e r d e s i r a b l e p r o p e r tie s as
27 90 80 70 o» *o 60 50 30 20.co 0 2 4 6 8 10 12 Gallons per Minute Figure 8. Orifice Meter Calibration
28 w e ll. T ric h lo ro e th y le n e was the m ost s a t i s f a c t o r y f l u i d. I t s p e r tin e n t p r o p e r tie s a re l i s t e d in Table 1. Most im port a n t i s th e f a c t t h a t i t s r e f r a c t i v e in d ex i s 1.474 a t 25 C. The Pyrex g la s s p ip e has a r e f r a c t i v e in d ex o f 1.4727 f o r sodium D l i g h t and 1.477 f o r pure b lu e l i g h t. Since the l i g h t source used was not m onochrom atic, no a tte m p t was made to ach iev e agreem ent in th e t h ir d d ecim al p la c e of th e r e f r a c t i v e in d ic e s o f the pipe and f l u i d. TABLE 1 P r o p e r t i e s : NEU-TRIR TRICHLOROETHYLENE* A c le a r, c o lo r l e s s, nonflam mable l iq u id, f r e e of suspended m a tte r B o ilin g p o in t a t 760 mm. H g...87.1 C. S p e c ific g r a v i t y a t 2 5 / 2 5 C...1.459 S p e c ific g r a v i t y a t 6 0 / 6 0 F...1-473 R e f ra c tiv e in d ex a t 2 5 C...1.474 V is c o s ity a t 20 C., c e n tis to k e s... 0.384 V is c o s ity a t 60 C., c e n tis to k e s... 0.287 *NEU-TRIR o f th e Dow Chem ical Co., M idland, M ichigan. The e x p e rim e n ta l tec h n iq u e r e q u ire d t h a t th e f l u i d elem ents be marked f o r v i s u a l i z a t i o n by sm a ll p a r t i c l e s inhomogeneous w ith th e tr ic h lo r o e th y le n e. I d e a lly, th e p a r t i c l e s should be sm a ll I n s iz e and o f th e same d e n s ity as th e f l u i d. The p o s s i b i l i t y o f a m ix tu re o f liq u id s which would be Inhomogeneous w ith th e m ain f l u i d and y e t have th e same d e n s ity was c o n sid e re d, b u t th e d i f f i c u l t y o f d is p e r s in g
29 such p a r t i c l e s in s u f f i c i e n t l y f in e form, and m a in ta in in g t h i s d is p e r s io n a t h ig h c o n c e n tra tio n w ith o u t c o a le se n c e upon re p e a te d c i r c u l a t i o n was too g r e a t to w a rra n t e x te n s iv e s tu d y. S o lid p a r t i c l e s o f v e ry sm a ll s iz e were a v a i l a b le, b u t th e y a l l had d e n s i t i e s g r e a t e r th a n th e f l u i d. F o r tu n a te ly a compromise co u ld be re a c h e d. I f th e p a r t i c l e s o f s o lid m a te r i a l were s u f f i c i e n t l y sm a ll, th e f a c t t h a t t h e i r d e n s ity was g r e a t e r th an t h a t o f th e f l u i d would be compens a te d by th e sm a ll s iz e, and th e y would s t i l l f a i t h f u l l y fo llo w th e f l u i d m o tio n s. "Seemag" g rad e magnesium oxide was s e le c te d as th e s o l i d. I t s p a r t i c l e s iz e was e x c e lle n t, and i t s shape and d e n s ity were a c c e p ta b le. I t a ls o d id n o t r e a c t w ith th e tr ic h lo r o e t h y le n e, and, b ein g in o rg a n ic and h ig h ly d is p e rs e d, showed no ten d en cy to a g g lo m e ra te. 1516 p a r t i c l e shape was r a t h e r im p o rta n t s in c e a p a r t i c l e n e a r ly e q u a l i n th e th re e dim ensions was c o n sid e re d b e t t e r th a n p l a t e s o r f l a k e s. One re a s o n I s t h a t such a p a r t i c l e a p p e a rs much th e same under the l ig h t i n g c o n d itio n s used r e g a r d le s s o f th e o r i e n t a t i o n, but a p la te o r f la k e se e n edgew ise would be v e ry d i f f e r e n t from one se e n b ro a d s id e. The g e n e r a l c r y s t a l s t r u c t u r e o f magnesium oxide and s ta te m e n ts from th e m a n u fa c tu re r in d ic a te d t h a t i t would be th r e e d im e n sio n a l in th e m anner d e s c rib e d above. TJiis was su p p o rte d by exam inat i o n w ith an e le c t r o n m ic ro sc o p e. Tfte m ost im p o rta n t f e a t u r e, how ever, was th e p a r t i c l e s i z e. Seemag as a n a ly z e d by th e m a n u fa c tu re r w ith a F is h e r Sub-S ieve S iz e r was d e s c rib e d as
having an a v erag e d ia m e te r o f 0. 5-0.6 m ic ro n s, w ith a p p ro x i 30 m a te ly 0.6 $ r e t a in e d on a 325 mesh s c r e e n. 'Hie ap p roxim ate p a r t i c l e d e n s ity was 3*59 as compared to tr ic h lo r o e th y le n e which has a d e n s ity o f a p p ro x im a te ly 1.4 6. The p a r t i c l e s were d is p e r s e d i n pure t r ic h lo r o e th y le n e, and th e m ix tu re f i l t e r e d th ro u g h a 50 m icron and f i n a l l y a 5 m icron f i l t e r. S ince th e i n i t i a l d is p e r s in g p ro ced u re d id n o t produce a g r e a t enough c o n c e n tr a tio n o f p a r t i c l e s i n th e f l u i d, th e e n t i r e p ro c e ss was re p e a te d u n t i l th e d e s ir e d conc e n t r a t i o n was re a c h e d. At one p o in t pure tr ic h lo r o e th y le n e was d i s t i l l e d o f f and a c o n c e n tra te d re s id u e r e t a in e d. T his was l a t e r found t o be u n n e c e ssa ry. The m ost d e s ir a b le conc e n t r a t i o n was d e te rm in e d by t r i a l and e r r o r. V arious conc e n tr a tio n s were p re p a re d and photographed under c o n d itio n s s im ila r to th o se used i n an a c t u a l ru n. These p h o to g rap h s were exam ined f o r p a r t i c l e c o n te n t and d e g re e o f p a r t i c l e - p a r t i c l e i n t e r a c t i o n. The o b je c tiv e in t h i s s i t u a t i o n was to a r r i v e a t a c o n c e n tr a tio n where a s u f f i c i e n t l y la rg e number o f p a r t i c l e s a p p eared i n each fram e o f th e f ilm and y e t were d is p e rs e d enough so t h a t c o n ta c t betw een p a r t i c l e s was n o t a problem. The f i r s t i s n e c e s s a ry i f one hopes to d e fin e th e f in e s c a le d tu r b u le n t m o tio n s, s in c e i f a d i l u t e c o n c e n tra tio n i s p r e s e n t, th e s e p a r a tio n d is ta n c e betw een p a r t i c l e s w i l l p o s s ib ly be g r e a t e r th a n th e s c a le o f th e t u r b u le n t m otion, and th e r e f o r e no m easurem ent o f i t would be p o s s ib le. This em phasizes a n o th e r re a s o n why e x tre m e ly sm a ll p a r t i c l e
31 d ia m e te rs a re n e c e s s a ry in a stu d y o f t h i s ty p e, f o r o n ly i f th e p a r t i c l e s a re v e ry sm a ll compared t o th e s c a le o f th e tu rb u le n c e can one hope to a c h ie v e a la rg e enough c o n c e n tra t i o n to d e li n e a t e t h i s m otion and y e t n o t have p a r t i c l e - p a r t i c l e i n t e r a c t i o n. The c o n c e n tr a tio n f i n a l l y a c c e p te d f u l f i l l e d b o th o b j e c ti v e s. The r e s u l t i n g f l u i d used in a l l ru n s e x h ib ite d a p a r t i c l e c o u n t i n any g iv e n fram e o f th e o rd e r o f 50 to 100 o r more, and p a r t l c l e - p a r t i c l e c o l l i s i o n s were o b serv ed o n ly v e ry r a r e l y. A fram e u s u a lly had dim ens io n s o f O.O69 x 0.0 9 5 in ch e s and m ight be th o u g h t of in v o lv in g a volume o f f l u i d o f th e o rd e r of 1.8 x 1 0 -it cu b ic in c h e s. A rough c a l c u l a t i o n o f c o n c e n tr a tio n g iv e s a v a lu e o f 55*6 p a r t i c l e s / c u b i c in c h, b u t th e volume o ccu p ied by a l l p a r t i c l e s, assum ing a cu b ic shape 0.6 m icrons on an edge, i s l e s s th a n 1 x 10"^fo o f th e t o t a l volum e. H iese p a r t i c l e s were u n ifo rm ly d i s t r i b u t e d th ro u g h o u t th e f l u i d. The f l u i d ap p eared c l e a r and c o lo r l e s s in norm al l i g h t i n g, and even a f t e r s ta n d in g u n d is tu rb e d f o r months i n a s e a le d la r g e d ia m e te r v e s s e l th e p a r t i c l e s d id n o t s e t t l e o u t o f su sp e n s io n. Under p ro p e r l i g h t i n g c o n d itio n s Brownian m o tio n was v i s i b l e. T his m otion was, how ever, of such r e l a t i v e l y sm a ll m agnitude compared to th e f l u c t u a t i n g m o tio n s o f th e f l u i d t h a t i t was n e v er a p p a re n t when th e f l u i d was flo w in g. Even m o tio n p i c t u r e s ta k e n a t h ig h speed o f la m in a r flow s f a i l e d to r e v e a l any e v id e n ce o f Brownian m o tio n, and i t was
32 concluded t h a t th e s e m otions would n o t be a f a c t o r when th e a n a ly s is f o r t u r b u le n t m otions was u n d e rta k e n. A lthough th e p a r t i c l e s d id n o t s e t t l e o u t o f th e s u s p e n sio n upon s ta n d in g, th e y a re s t i l l s u b je c t to th e fo rc e of g r a v i t y. T his would cau se a downward movement as th e f l u i d flow ed th ro u g h th e t e s t s e c t i o n. An e s tim a te o f th e e x te n t of t h i s movement may be made by c o n s id e rin g th e te rm in a l v e lo c it y of a s p h e r ic a l s o l i d p a r t i c l e suspended in a non- tu r b u le n t f l u i d. S ince t h i s tre a tm e n t Ig n o re s th e e f f e c t s o f tu rb u le n c e and Brownian m otion i t r e p r e s e n ts an extrem e c a s e. "Hie p a r t i c l e d ia m e te r s e le c te d f o r c a l c u l a t i o n i s 5 m icrons w hich a g a in i s th e w o rst p o s s ib le c a s e. The te r m in a l v e lo c it y i s Ut = TBIT ( P f P p ) 6 = 1, 7 9 x 1 0 " 3 f t - / s e c. The im p o rta n t tim e f o r c o n s id e r a tio n i s th e p e rio d d u rin g w hich th e p a r t i c l e i s view ed. A re a s o n a b le v a lu e f o r t h i s tim e i s 3 x 10 3 seconds so th e p a r t i c l e can d ro p 6.4 x 10 5 in c h e s w h ile in view. Comparing t h i s to th e v i s cous s u b la y e r th ic k n e s s a t NRe = 50,000 o f a p p ro x im a te ly 4 x 1 0 3 in c h e s shows t h a t th e w o rst p o s s ib le case g iv e s a movement of a p p ro x im a te ly 1. 6% o f th e s u b la y e r th ic k n e s s. For a s m a lle r p a r t i c l e d ia m e te r and low er NRe th e e f f e c t i s much l e s s. The a d d it i o n o f s o l i d s t o a l i q u i d co u ld c o n c e iv a b le a f f e c t th e v i s c o s i t y, e s p e c i a l l y i t s N ew tonian c h a r a c t e r.
33 W hile magnesium oxide does n o t show t h i s c h a r a c t e r i s t i c, and th e r e f o r e was v e ry u n lik e ly a t th e e x is ti n g d i l u t e concent r a t i o n s to a f f e c t th e f l u i d, th e r e a re c o l l o i d a l m a te r ia ls w hich i n v e ry sm a ll q u a n t i t i e s d r a s t i c a l l y change l iq u i d v i s c o s i t i e s. T h ere fo re a check o f th e f l u i d v i s c o s i t y both b e fo re and a f t e r p a r t i c l e a d d itio n was made. A long c a p i l l a r y tu b e v is c o s im e te r was used, and th e v a r i a t i o n in s h e a r r a t e n e c e s s a ry f o r d e te rm in a tio n o f d e p a r tu r e s from N ew tonian v i s c o s i t y was o b ta in e d by v a ry in g th e h e ig h t o f th e c o n s ta n t head ta n k above th e c a p i l l a r y i n l e t. The m easurem ents f o r pure and p a r t i c l e c o n ta in in g t r ic h lo r o e th y le n e gave c o n g ru e n t s t r a i g h t lin e s when * was p l o tt e d a g a in s t d r APr/2L, which showed t h a t th e two f l u i d s had i d e n t i c a l, ^ T T c o n s ta n t (w ith r e s p e c t to sh e a r r a t e ) v i s c o s i t i e s. The slo p e o f t h i s p l o t in d ic a t e s th e v i s c o s i t y, and i t was found to be 3.6 1 x 10"^ a t 27.5 C. B ils compares w ith th e f t - s e c p u b lis h e d v a lu e s o f 3*64 x 10"^ l b m /f t- s e c. The cu rv e s a p p e a r i n F ig u re 9* The q u e s tio n as to how w e ll th e suspended p a r t i c l e s fo llo w th e tu r b u le n t m otions w a rra n ts some d is c u s s io n. The p a r t i c u l a r s i t u a t i o n a t hand i s a s p e c i a l c a se o f th e broad f i e l d concerned w ith p a r t i c l e - f l u i d m o tio n s i n t u r b u le n t flo w. Of t h i s f i e l d, a r e c e n t a r t i c l e by Soo ( 5 7 ) s t a t e s, A part from th e s tu d ie s o f a s in g le s o l i d p a r t i c l e i n th e t u r b u le n t f i e l d o f a f l u i d, s tu d ie s of dynam ics o f a g a s - s o l i d su sp e n sio n as a w hole have 1Soo (5 7 ), P. 33.
34 ro lo X o o> V) T5 X 13 *o suspension o pure trichloro^ ethylene 27.5 O 2 4 6 8 ' 10 PR/2L (lbf/ft2 x 10"2) Figure 9. Viscosity Measurement
35 e i t h e r e x clu d ed tu rb u le n c e or have been c o m p le te ly e m p ir ic a l.... A s o l u t io n i s n o t even a v a ila b le f o r th e s t a t i s t i c a l fo rm u la tio n o f sim ple t u r b u l e n t p ip e flo w, where th e tu rb u le n c e i s nonhomogen eo u s. Even when one assum es an i s o t r o p ic tu r b u le n t f i e l d, th e s o l u t io n o f th e problem o f m otion of a s in g le p a r t i c l e i s a t b e s t academ ic. In o th e r w ords, th e problem h as n o t been so lv e d e x c e p t f o r a v e ry few sim ple c a s e s. Most t h e o r e t i c a l tre a tm e n ts which e x i s t r e q u ir e a la rg e number o f s im p lify in g assum ptions to even p e rm it the r e l a t i o n s to be w r i t te n. F o r tu n a te ly, th e p r e s e n t c a se does f i t some o f th e s e a ssu m p tio n s, and, m oreover, th e v e ry sm a ll p a r t i c l e s iz e p e rm its a d d it i o n a l s i m p l i f i c a t i o n. N e v e rth e le s s, a rig o ro u s t h e o r e t i c a l o r e x p e rim e n ta l p ro o f t h a t th e p a r t i c l e s fo llo w th e tu r b u le n t m otions can n o t be g iv e n. E x p e rim e n ta l s tu d ie s o f t h i s problem have u t i l i z e d p a r t i c l e s o f much g r e a t e r dim ensions th a n th o se used i n th e p r e s e n t s tu d y. The s m a lle s t p a r t i c l e s used in r e p o r te d e x p e rim e n ts were o f th e o rd e r o f 50 tim es the d ia m e te r o f th e p r e s e n t p a r t i c l e s, and i n m ost s tu d ie s th e s iz e was much g r e a t e r th a n t h i s. For exam ple, Soo (57) used g la s s sp h e re s o f 100-200 m icrons d ia m e te r. Kada and H a n ra tty (24) used g l a s s and copper sp h e re s of 0.0 0 3 9 and.0 0 7 9 in c h e s d ia m e te r r e s p e c t iv e ly. S ince both e x p e rim e n ta l and t h e o r e t i c a l s tu d ie s show th e im portance o f th e p a r t i c l e s iz e on th e f l u i d - p a r t i c l e i n t e r a c t i o n s, e x tr a p o la t io n o f e x p e rim e n ta l r e s u l t s f o r la rg e sp h e re s to th e p r e s e n t c ase m ust be done w ith r e s e r v a t i o n s.
36 F or exam ple, l a r g e r p a r t i c l e s w ith d e n s i t i e s g r e a t e r th a n th e f l u i d w i l l s e t t l e due to g r a v ity, and a s t r a t i f i c a t i o n o r p a r t i c l e c o n c e n tra tio n g r a d ie n t w i l l o c cu r i n th e p ip e. In the p r e s e n t stu d y, no such e f f e c t o c cu rs because th e p a r t i c le s, w h ile d e n se r th a n th e f l u i d, do n o t s e t t l e. P a r t i c l e s o f dim ensions o f th e same o rd e r o f m agnitude as th e s c a le o f tu rb u le n c e would e x te n d o v er a la r g e enough d is ta n c e so t h a t th e y co u ld be in flu e n c e d by th e d i f f e r e n t v e lo c it y f l u c t u a tio n s w hich co u ld e x i s t over t h i s d i s t a n c e. Very sm a ll p a r t i c l e s which a re much s m a lle r th a n th e s c a le o f tu rb u le n c e would be in flu e n c e d by o n ly th e v e lo c it y f l u c t u a t i o n s o ver th e d is ta n c e e q u a l to t h e i r d im en sio n s, and th u s would m ost l i k e l y be a f f e c te d by a s in g le f l u c t u a t i o n a t any one tim e. I n the w a ll re g io n, th e f l u i d has z ero v e lo c it y a t th e w a ll, and th e re i s a s te e p v e lo c it y g r a d ie n t o v er a sm a ll d is t a n c e. F or p a r t i c l e s o f f i n i t e s i z e, s l i p m ust o ccu r a t th e w a ll because th e p a r t i c l e e x te n d s o u t from th e w a ll a d is ta n c e e q u a l to i t s own d ia m e te r and e x p e rie n c e s th e a c c e le r a tin g fo r c e s o f th e f l u i d o v er t h a t d i s t a n c e. O bviously, th e s m a lle r th e p a r t i c l e d ia m e te r, th e more n e a r ly i t w i l l r e p r e s e n t th e f l u i d m o tio n s in th e w a ll re g io n. P a r t i c l e s o f 0.6 o r even 5*0 m icrons d ia m e te r can o b v io u sly approach to d is ta n c e s v e ry n e a r th e w a ll and s t i l l fo llo w th e f l u i d m o tio n s. In a d d itio n, th e s te e p v e lo c it y g r a d ie n t o p e ra tin g o v er th e d ia m e te r o f l a r g e r p a r t i c l e s can cause p a r t i c l e s p in and se co n d a ry m o tio n s, b u t t h i s e f f e c t i s much le s s
37 pronounced f o r e x tre m e ly sm all p a r t i c l e s. F in a lly, the f l u i d elem ents a re deform able and i n tu r b u le n t flow e x p e rience s tr e tc h in g and o th e r d e fo rm a tio n s. S o lid p a r t i c l e s do n o t deform under the fo rc e s which deform the f l u i d, so la rg e p a r t i c l e s of o rd e r of th e dim ensions o f th e f l u i d elem ent w i l l not rem ain w ith th e elem ent d u rin g such m o tio n s. P a r t i c l e s which a re v e ry much sm a lle r th an th e elem ents w i l l. T his la c k of s l i p betw een p a r t i c l e and f l u i d elem ent does n o t c re a te d is tu rb a n c e s i n th e f l u id which can occur when s l i p i s p re s e n t. For a l l th ese re a so n s, the above c a u tio n re g a rd in g the e x te n s io n o f e x p e rim e n ta l r e s u l t s to th e p re s - s e n t case was g iv e n. N e v e rth e le ss, th e tre n d s shown by th e e x p e rim e n ta l d a ta can be u t i l i z e d. Of s p e c ia l v alu e a re th o se concerned w ith p a r t i c l e s iz e and c o n c e n tra tio n e f f e c t s. In a l l th e ex p erim e n ts, th e p a r t i c l e s more n e a rly follow ed th e f l u i d m otions and c re a te d few er s id e e f f e c t s as th e p a r t i c le s iz e and c o n c e n tra tio n were d e c re a se d, and as t h e i r d e n s ity approached t h a t of th e f l u i d. Kada and H a n ra tty (24) u sin g th e p a r t i c l e s d e sc rib e d e a r l i e r found t h a t f o r volume c o n c e n tra tio n s o f le s s th a n 1. 5 $ in w a te r, th e p resen ce of th e p a r t i c l e s had l i t t l e o r no m easurable e f f e c t on th e d i f f u s i o n of mass in tu r b u le n t flow. Hinze (2 0 )^ in in tro d u c in g t h i s s u b je c t s t a te d, In the o th e r extrem e c a se, namely, when the c o n c e n tra tio n o f p a r t i c l e s i s v e ry low, we may ^ i n z e (2 0 ), pp. 352-3 5 3 -
33 n e g le c t the in te r f e r e n c e of th e p a r t i c l e s and r e g a rd each p a r t i c l e as being a lo n e in th e tu r b u le n t flow f i e l d. I f th e p a r t i c l e s a re b ig compared w ith th e s c a le o f tu rb u le n c e, the m ain e f f e c t of th e tu rb u le n c e on th e p a r t i c l e w i l l be to in c r e a s e i t s flow r e s i s t a n c e, and the p a r t i c l e s w i l l, a t m ost, more o r l e s s fo llo w th e slow l a r g e - s c a l e t u r b u le n t m otions o f th e f l u i d. I f, on th e o th e r hand, th e p a r t i c l e s a re very sm a ll compared w ith th e s m a lle s t s c a le of th e tu rb u le n c e, th e y w i l l ten d to fo llo w a l l tu rb u le n c e components o f th e f l u i d. The p resen t case s a t i s f i e s both r e s t r i c t i o n s. The p a r t ic le s e x i s t in very low co n c en tr a tio n s, and th ey are very sm all compared to the sm a lle st s c a le o f tu rb u len ce. For example, M ickelsen (37) measured a E u lerian m icro sca le of 4500 m icrons fo r tu rb u len t flow o f a ir in an e ig h t inch p ip e. From L ee s (32) d ata, measurements in water a t Np^e = 41,000 y ie ld a m icr o sc a le, ^ g, o f 0.234 cm. N eith er o f th ese were measured in the w a ll reg io n, but even though the s c a le of turbu len ce i s known to decrease as the w a ll i s approached, I t does n o t d e c re a s e to th e p o in t where i t has a s c a le of 0.6 o r even 5*0 m ic ro n s. The low er l i m i t to th e s c a le of tu rb u le n c e i s s e t by en erg y c o n s id e r a tio n s s in c e th e r a t e o f v isc o u s d i s s i p a t i o n o f tu r b u le n t en erg y in c r e a s e s g r e a t l y as th e s c a le o f tu rb u le n c e d e c r e a s e s. A g r e a t amount of e x tre m e ly sm a ll s c a le tu rb u le n c e would d i s s i p a t e th e t u r bulence en erg y a t such a h ig h r a t e t h a t tu rb u le n c e co u ld n o t be m a in ta in e d by th e c o n v e rsio n o f mean flow en erg y w hich Is i t s s o u rc e. Thus, tu rb u le n c e o f an e x tre m e ly sm a ll s c a le c an n o t be p re s e n t in any s i g n i f i c a n t am ount. S ince th e
39 p a r t i c l e s used i n th e p r e s e n t stu d y a re much s m a lle r th a n th e low er l i m i t o f th e s c a le o f tu rb u le n c e, th e y n o t o n ly can fo llo w th e f l u i d m o tio n s, b u t a ls o p ro v id e a ssu ra n c e t h a t th e y a re n o t m asking f i n e - s c a l e m otions because o f t h e i r s i z e. As a p re lu d e to a more r e a l i s t i c and c o r r e c t t r e a t m ent, a sim ple c a l c u l a t i o n may be made to d e te rm in e i f i t i s re a s o n a b le to e x p e c t th e p a r t i c l e to fo llo w th e f l u c t u a t i o n s. As a m odel, assume t h a t a p a r t i c l e i s surrounded by a f l u i d e lem en t i n i t i a l l y a t r e s t w hich su d d e n ly undergoes an a c c e l e r a ti o n a j. B ecause of th e im p u lsiv e s t a r t o f th e m o tio n, t h i s i s an extrem e c a s e. The p a r t i c l e w ith in t h i s e lem en t w i l l be a c c e le r a te d a c c o rd in g to th e fo rc e s e x e rte d upon i t, and c o n c e iv a b ly co u ld have an a c c e l e r a ti o n a p q u ite d i f f e r e n t from t h a t of th e f l u i d. Bor s im p li c it y th e o n ly fo rc e assum ed to a c t i s t h a t d e s c rib e d by Stoke*s law, Fp = 3pd (u f-u p ). As th e a n a ly s is in Appendix I shows, o th e r f o r c e s a re a c tin g, some in a nega'tive d i r e c t i o n to th e above f o r c e, b u t th e y w i l l be sm a ll f o r sm a ll v e lo c it y d i f f e re n c e s and a re n e g le c te d f o r t h i s sim ple c a s e. Prom t h i s m odel and the assu m p tio n t h a t th e f l u i d elem en t a c c e le r a te s from zero v e l o c i t y to Uf i n tim e t, th e r e l a t i o n i s o b ta in e d. C le a rly, i f (d2pp/l8n,t)< g: 1, th e n u^ = up. For an extrem e c a se ta k e u^ = 0.5 f t. / s e c., d = 5 m icrons
1*0 in s te a d o f 0.6 m ic ro n s, and t e q u a l to th e tim e o f a s in g le m o tio n p ic tu r e fram e, i. e., 1.2 5 x 10 3 s e c., th e r e l a t i o n becomes Uf = Up (. 0 0 7 6 + 1 ). F or t h i s sim ple a n a ly s is o f a v e ry extrem e case th e d i f f e r ence in f l u i d and p a r t i c l e v e lo c it y i s n e g li g i b le. In a f a r more r e a l i s t i c tre a tm e n t of t h i s q u e s tio n, H lnze (20) p re s e n ts a m o d ific a tio n of T ch en 's (62) t h e o r e t i c a l tre a tm e n t o f the m otion o f a sm a ll p a r t i c l e suspended in a t u r b u le n t f l u i d. T his tre a tm e n t in v o lv e s a r a t h e r r e s t r i c t i v e l i s t o f c o n d itio n s and a ssu m p tio n s, and th e developm ent i s r a t h e r in v o lv e d a lth o u g h i t i s b a s i c a l l y a f o rc e b a la n ce on th e p a r t i c l e. These a re p re s e n te d in Appendix I alo n g w ith an o u tlin e o f th e d ev elopm ent. The r e l a t i o n which i s p e r t i n e n t t o the q u e s tio n a t hand i s a ffl + b2 g U1P = a ra 1 U lf where u^p = L ag ran g ian tu r b u le n t v e lo c it y o f p a r t i c l e Uj_f = L ag ran g ian t u r b u le n t v e lo c it y o f f l u i d = L agrangian I n t e g r a l tim e s c a le f o r f l u i d ( t h is term i s u s u a lly c o n sid e re d a m easure o f th e lo n g e s t tim e d u rin g w hich, on th e average, a p a r t i c l e p e r s i s t s i n m otion in a g iv e n d i r e c t i o n ).
41 a = ----------- = 9*24 x 104 ( f o r th e p r e s e n t c ase ) (2pp + pf )a2 where 3pf b _ ------------------- 2PP + Pf = 0.502 ( f o r th e p r e s e n t case) [L = f l u i d v i s c o s i t y p = p a r t i c l e d e n s ity Jr pf = f l u i d d e n s i ty d = p a r t i c l e d ia m e te r The e f f e c t o f the e x tre m e ly sm a ll p a r t i c l e d ia m e te r i s a p p a r e n t. For a l l i n t e n t s and p u rp o se s, = u.j^.2, i. e., th e p a r t i c l e m otions e q u a l th e f l u i d m o tio n s. However, i t must be r e c a l l e d t h a t a number o f assu m p tio n s a re in c lu d e d i n th e d ev elo p ed r e l a t i o n, so th e tre a tm e n t i s n o t r ig o r o u s. The d eg ree to w hich th e p r e s e n t case ap p roaches th e assumed s i t u a ti o n i s d is c u s s e d in th e A ppendix. There have been o th e r t h e o r e t i c a l develo pm ents, n o ta b ly one by F r ie d la n d e r (1 2 ). In t h i s one to o th e e f f e c t o f th e sm a ll p a r t i c l e s iz e i s overw helm ing so t h a t th e p a r t i c l e m otions fo llo w th e f l u i d m otions in s p i t e o f th e d e n s i ty d i f f e r e n c e s. These t h e o r e t i c a l r e l a t i o n s have n o t in c lu d e d th e e f f e c t of th e p resen c e o f a s o l i d boundary on th e p a r t i c l e f l u i d m o tio n s. Soo and T ien (58) t r e a t e d t h i s problem t h e o r e t i c a l l y f o r a s im p lif ie d flo w sy stem. They c o n sid e re d
th e e f f e c t of an i n f i n i t e w a ll on a s i n g l e, s p h e r ic a l p a r t i c l e 42 suspended i n a s e m i - i n f i n i t e tu r b u le n t f l u i d. The p a r t i c l e d ia m e te r was assumed to be s m a lle r th a n th e m ic ro s c a le o f th e tu r b u le n c e. L ocal is o tr o p y and f u l l y dev elo p ed flow were a ls o assum ed to e x i s t. The p e r t i n e n t r e l a t i o n produced was u. yr r 2<r,, K ii i/k2 erf $ 1/2 2 where UP = i n t e n s i t y o f p a r t i c l e v e l o c i t y f l u c t u a t i o n u ^2 1/2 = i n t e n s i t y o f f l u i d v e lo c it y f l u c t u a t i o n G = a reduced volume yq = d is ta n c e p a r t i c l e i s from w a ll (uf2) = L ag ran g ian tim e m ic ro s c a le o f tu rb u le n c e b - at 2a2 (pp + p /2 ) a = p a r t i c l e ra d iu s They p r e s e n t a p l o t o f ^ L - v e rs u s K w ith as a Vo* u f p a ra m e te r of d is ta n c e from th e w a ll. 11118 p l o t shows t h a t
2 f o r v a lu e s o f K < 0.2, th e v alu e o f uf - up I s z e ro, 43 u f i. e., a t K = 0.3 th e r a t i o i s l e s s th a n 0.0 3. For th e p r e s e n t stu d y, K may be e v a lu a te d as fo llo w s u sin g L e e 's m easurem ents a t N^e = 41,000 in w a te r f o r uf 2 and te rm s. For t h i s c a l c u l a t i o n "a" i s ta k e n as 2.5 m icro n s. _ 1 /2 Uf2 = 2.3 3 cm /sec g = 0.234 cm.; /^T - 2.4 6 se c. b = = 13.9x103 2 ( 6.25x 10-8 ) ( 3.6 - K = /----- = I. 36XIO- 4 (2.46)(13 9x103) K i s c l e a r l y l e s s th a n 0.2, which a g a in em phasizes th e s tro n g e f f e c t o f p a r t i c l e d ia m e te r. L a te r i n th e same a r t i c l e th e a u th o rs show th e e f f e c t o f th e w a ll on p a r t i c l e s o f 100 m icrons d ia m e te r. Due to th e s te e p v e lo c it y g r a d ie n t and the r e s u l t i n g p a r t i c l e r o t a t i o n, a magnus e f f e c t becomes im p o rta n t. Why t h i s i s p ro b a b ly n o t so f o r th e sm a ll p a r t i c l e s o f th e p r e s e n t stu d y has a lre a d y been d is c u s s e d. In a d d itio n, i t can be s a id t h a t such an e f f e c t o r th e r e s u l t s from i t were n o t o bserved in th e m otion p i c t u r e. A ll o f th e p re c e d in g argum ents w ere made to show t h a t th e f i n e p a r t i c l e s used i n t h i s stu d y a d e q u a te ly fo llo w th e
44 f l u i d m o tio n so t h a t t h e i r m otions in tu r b u le n t flow may be assumed to be th e same as the tu r b u le n t f l u i d m o tio n s. W hile th e argum ents were n o t rig o r o u s, th e ev id en ce s tr o n g ly s u p p o rts t h i s c o n te n tio n. M oreover, no i n v a l i d a t i o n o f th e assu m p tio n was found e i t h e r i n th e t h e o r e t i c a l o r th e e x p e r i m e n ta l ev id en ce c o n s id e re d. The consensus of m ost a u th o rs on t h i s s u b je c t a g re e s w ith H in z e 's s ta te m e n t t h a t i f th e p a r t i c l e s a re sm a ll enough th e y w i l l a d e q u a te ly fo llo w th e t u r b u le n t f l u i d m o tio n s. The q u e s tio n as to w hether th e tr ic h lo r o e th y le n e w ets th e s o l i d and th e p o s s ib le e f f e c t s of th e p a r t i c l e b e h av io r i f i t does n o t i s now c o n s id e re d. A lthough no m easurem ent o f th e c o n ta c t an g le o f th e air-m agnesium o x i d e - t r ic h l o r o e th y le n e system was a v a ila b le, ex am in a tio n of th e v a lu e s f o r s i m il a r system s and f o r f l u i d s o f s im ila r s u rfa c e te n s io n in d ic a te t h a t th e s o l i d i s w et by th e l i q u i d. A ctual e x p e r i-. ence w ith th e m a te r ia ls in d ic a te d t h a t t h i s assu m p tio n was j u s t i f i e d. In a d d itio n, th e su sp e n sio n was p re p a re d f a r i n advance of th e tim e o f u s e, and i t e x p e rie n c e d c o n tin u a l a g i t a t i o n over t h i s p e rio d of tim e. Both f a c t o r s would ten d t o overcome any r e s i s t a n c e to w e ttin g. U ie re fo re, th e r e i s no re a s o n to b e lie v e t h a t th e s o l i d s u rfa c e was n o t w et by th e f l u i d. D e sp ite t h i s c o n c lu sio n, i t m ight be of v a lu e to c o n s id e r th e e f f e c t s on th e p a r t i c l e m otions w hich m ight o c cu r i f i t were n o t w e t. F i r s t, v e ry la r g e a i r bubbles
su rro u n d in g th e p a r t i c l e c an n o t e x i s t because a g i t a t i o n w ith in th e flow would q u ic k ly sh e a r them o f f. t h in f ilm of a i r can su rro u n d th e p a r t i c l e. Thus, o n ly a This a i r - s o l i d p a r t i c l e would n o t be much l a r g e r th a n th e s o l i d p a r t i c l e, and would have a d e n s ity more n e a r ly e q u a l to t h a t o f th e f l u i d. The a i r film would n e c e s s a r il y be t i g h t l y bound to the s o l i d s u r f a c e, and s l i p betw een th e f ilm and th e p a r t i c l e would be n i l. Hie f o r c e s due to th e f l u c t u a t i o n s of th e am bient f l u i d would a c t on th e a i r - s o l i d p a r t i c l e in th e same f a s h io n as f o r the s o l i d p a r t i c l e, and i t has a lr e a d y been d e m o n stra te d t h a t th e r e l a t i v e v e lo c it y betw een the s o l i d p a r t i c l e and th e f l u i d elem en t i s v e ry s m a ll. Thus one cannot e x p e c t th e r e s u l t i n g sh e a r to remove the a i r f ilm in a s te a d y s t a t e c a s e. I t i s q u ite re a s o n a b le, th e r e f o r e, to e x p e c t t h a t th e p resen c e o f an a i r film on th e p a r t i c l e w i l l n o t a f f e c t i t s m otion to any a p p re c ia b le e x t e n t. Of c o u rs e, such a f ilm would have g r e a t e f f e c t s f o r he&t and mass t r a n s f e r to th e s o l i d, b u t t h i s i s o f no c o n ce rn in th e p r e s e n t s i t u a t i o n. P h o to - o p tic a l system T his s e c t i o n d e s c r ib e s a l l th e equipm ent and p ro ced u res used to o b ta in th e p h o to g rap h s o f th e flo w. I t a ls o d is c u s s e s th e d i f f e r e n t cam era v iew p o in ts and th e ad v an tag es o f e a c h.
Camera. As was d is c u s s e d in th e in tr o d u c tio n, th e v e ry n a tu re of tu r b u le n t flow, i. e., random, ra p id m otions, r e q u ir e s t h a t some means o th e r th a n v is u a l ex am in atio n be p ro v id ed f o r any d e ta il e d o b s e rv a tio n o f i t s c h a r a c t e r i s t i c s. Not o n ly i s a perm anent re c o rd o f th e s e m otions re q u ire d f o r com parison when flow c o n d itio n s a re changed, b u t some means m ust be pro v id ed to d is p la y th e ra p id m otions a t a reduced sp e ed. The h ig h speed m otion p ic tu r e camera i s id e a l f o r th e se p u rp o se s. I t p ro v id es th e means of slow ing th e m otions to an i n t e l l i g i b l e l e v e l and, e q u a lly im p o rta n t, p ro v id es a perm anent re c o rd f o r com parison. For th e s tu d y of tu r b u le n t flow, i t has a g r e a t advantage over h ig h speed s t i l l photograp h y because i t p ro v id es an o rd ere d p ro g re s s io n o f tim e and a c o n tin u ity o f m otion. One can w atch tim e dependent sequences d e v e lo p. In s t i l l photography one i s fo rc e d in to a p o s itio n o f random sam p lin g. The ta s k of ta k in g a la rg e enough q u a n tity of s in g le photo grap hs to d e p ic t a tim e dependent sequence of e v e n ts, and th en i n te r p r e t i n g t h i s sam pling w ith o u t having knowledge beforehand o f the e v e n ts o r o rd e r o f o ccu rren ce i s an alm ost in su rm o u n tab le one. The cam era used in t h i s stu d y was a 16 mm F a sta x WF3 h ig h -sp e ed m otion p ic tu r e cam era w ith a film c a p a c ity o f 100 f e e t (4000 fra m e s). I t has a r a te d fram ing speed o f from 150 to 8000 f r a m e s /s e c., b u t was o p e ra te d in t h i s stu d y a t betw een 650 and 1000 fra m e s /s e c. depending on c o n d itio n s. T his l im i t a t i o n was s e t f o r two re a s o n s. F i r s t th e amount of l i g h t
47 a v a ila b le to expose th e f ilm was lim ite d even though an e x tre m e ly pow erful so u rce was u sed, i h i s i s because much of th e l i g h t in p u t p a sse s d i r e c t l y th ro u g h th e f l u i d and i s n o t tr a n s m itte d to the cam era by th e p a r t i c l e s ( r e c a l l t h a t th e d i r e c t i o n o f view i s a t r i g h t a n g le s to th e d i r e c t i o n o f l i g h t i n p u t ). I t was p o s s ib le to o b ta in ex p o su res as h ig h as 2000 fra m e s/se c o n d, b u t o n ly a t th e c o s t o f a c o n s id e ra b le r e d u c tio n in q u a l i t y o f th e im ages and c o n te n t. The second re a s o n f o r th e l i m i t a t i o n i s t h a t a t h ig h e r speeds th e r e a l tim e re c o rd e d on th e 100 f e e t of f ilm becomes d r a s t i c a l l y red u ced so t h a t th e re i s a g r e a t e r chance o f a d e v e lo p in g o r s e q u e n tia l ty p e o c cu rren c e bein g m isse d. For exam ple, a t 1000 f ra m e s /s e c. th e e n t i r e 100 f e e t o f f ilm w i l l be exposed i n a p p ro x im a te ly 4 se co n d s, and a t 2000 fra m e s /s e c. the tim e i s 2 se c o n d s. For th e s e re a s o n s, i t was d e cid ed t h a t th e b e s t c o u rse of a c tio n would be to use th e speeds o f 650 to 1000 fra m e s/se c o n d. At th e s e sp e ed s, th e s h u t t e r speeds a re 5.1 x 10 ^ and 3.3 x 10 ^ seconds r e s p e c t iv e ly. The h ig h -sp e e d m otion p ic tu r e s re c o rd a m otion w hich o c cu rs v e ry r a p i d l y i n r e a l tim e and p e rm it th e o b se rv e r to view t h a t m o tio n in a g r e a t l y ex ten d ed tim e i n t e r v a l. F or exam ple, a t % e = 50000the l o c a l mean a x i a l v e lo c it y a t y+ = 25 i s 0.8 2 f t. / s e c. Under th e c o n d itio n s o f th e s e e x p e rim e n ts th e m a g n ifie d f i e l d o f view co v ers a r e a l a x i a l le n g th o f 0.095 in c h e s. A p a r t i c l e o f f l u i d would tr a v e r s e t h i s f i e l d i n 0.0 0 9 7 seconds which i s to o f a s t f o r th e
u n aid ed eye to fo llo w much l e s s d is c e r n any f l u c t u a t i n g m o tio n. At 800 f r a m e s /s e c. t h i s p a r t i c l e would a p p ea r i n a p p ro x im a te ly 7 fram es o f f ilm and t r a v e l 0.095 in c h e s. I f now th e f ilm i s p ro je c te d f o r view ing a t 7 fra m e s/se c o n d, t h i s same m otion has been ex te n d ed over a p e rio d o f one second, an ad v an tag e o f 100/ 1. T his ad v an tag e n o t o n ly p e rm its more d e t a i l e d o b s e rv a tio n s, b u t p e rm its more a c c u ra te m easurem ents as w e ll. An a d d it i o n a l im provem ent i s o b ta in e d b y moving the cam era w ith th e a x i a l flo w as w i l l be e x p la in e d l a t e r. Since t h i s g r e a t l y enhances th e c a p a b i l i t i e s o f th e system, f u r t h e r d is c u s s io n w i l l be d e fe rre d u n t i l th e n. The cam era has a tim in g l i g h t w hich a u to m a tic a lly Im p rin ts i n th e f ilm m argin tim in g m arks a t th e r a t e of 120 m a rk s/se c o n d. These marks p e rm it th e c a l c u l a t i o n o f fram ing r a t e, b u t more im p o rta n t th e y p e rm it an a c c u ra te c a l c u l a t i o n o f th e r e a l tim e w hich h as e la p s e d f o r a p a r t i c u l a r o c c u r re n c e, r e g a r d le s s o f th e r e l a t i v e tim e th e v iew er i s u s in g. T h is was used e x te n s iv e ly to m easure v e l o c i t i e s and th e d u ra t i o n of e v e n ts, and the p ro ced u re w i l l be d is c u s s e d in th e a p p ro p r ia te s e c tio n. F ilm. The co m b in atio n o f h ig h speed p h o to g rap h y and lim ite d a v a ila b le l i g h t f o r ex p o su re p la c e d se v e re r e q u i r e m ents on th e type of f ilm to be u se d. I t was found t h a t Kodak #2475 R ecording f i lm (fo rm e rly Royal-X P an), w hich i s th e f a s t e s t film a v a i la b l e, perform ed a d e q u a te ly under th e c o n d itio n s o f t h i s stu d y, and was used e x c lu s iv e ly f o r
p a r t i c l e f ilm s. T his film, a f t e r developm ent, produced a b la c k and w h ite n e g a tiv e p r i n t w h erein the p a r t i c l e s appeared as d a rk sp o ts on a l i g h t background. This n e g a tiv e p r i n t was used i n a l l su b seq u en t a n a ly s e s. The e n la rg e d photographs shown in F ig u re s 23, 24, and 26 were made from th e s e negativ e s and ap pear as p o s itiv e p r i n t s. I t sh ould be noted re g a rd in g th e s e p r i n t s t h a t c o n sid e ra b le image q u a l i t y was l o s t d u rin g enlargem ent and p r in tin g, and th e p o s itiv e s a re used here s o le ly f o r i l l u s t r a t i v e p u rp o se s. A ll a n a ly se s were made on the n e g a tiv e m otion p ic tu r e s because t h e i r q u a l i t y and c o n te n t, even when e n la rg e d 100 tim es in p r o je c tio n, were s u p e r io r to th e p o s itiv e p r i n t s. L ig h tin g. D ark f i e l d illu m in a tio n such as was used i n t h i s stu d y r e q u ir e s t h a t th e d i r e c t i o n o f l i g h t Imput be a t a p p ro x im ate ly r i g h t a n g le s to the d i r e c t i o n of view. Thus th e l i g h t e v e n tu a lly re a c h in g the cam era m ust f i r s t be r e f l e c t e d o r r e f r a c t e d by th e sm a ll p a r t i c l e s suspended i n th e f l u i d. As th e c o n c e n tra tio n o f th e se p a r t i c l e s was r e l a t i v e l y d i l u t e, o n ly a v e ry sm all f r a c t i o n of th e t o t a l l i g h t in p u t e v e n tu a lly reach ed the cam era. Most p assed d i r e c t l y th rough th e e s s e n t i a l l y c l e a r f l u i d. The b rig h tn e s s o f th e p a r t i c l e s i s dependent upon th e b rig h tn e s s o f the l i g h t so u rc e, and n o t th e t o t a l illu m in a tio n. A lso, a law o f p h y sic s s t a t e s t h a t g iv e n a l i g h t source o f a c e r t a i n i n t r i n s i c b rig h tn e s s th e b rig h tn e s s o f any image form ed from th e so u rce by w hatever means cannot exceed th e i n t r i n s i c
b r ig h tn e s s of th e s o u rc e. The l i g h t en erg y p e r u n i t a re a may be in c r e a s e d by fo c u s in g, b u t n o t th e i n t r i n s i c b r i g h t n e ss (S e a rs, 54) A pplied to th e p a r t i c u l a r case a t hand, t h i s means t h a t th e b r ig h tn e s s o f th e p a r t i c l e s can n o t be in c re a s e d by lamps of h ig h e r w a tta g e o r by fo c u s in g i n t o th e f i e l d th e beams o f la rg e l i g h t so u rc e s u n le s s th e i n t r i n s i c b r ig h tn e s s of th e so u rce i s in c r e a s e d. One may, o f c o u rse, illu m in a te a l a r g e r a re a and th e r e f o r e see more p a r t i c l e s, b u t the i n t e n s i t y of th e b r i g h t e s t p a r t i c l e i s fix e d by th e s o u rc e. The f i e l d of view i n th e p r e s e n t c ase was q u ite sm a ll so a so u rce of la r g e dim en sio n s was n o t needed. Hie lamp s e le c te d was an Osram HB0-109 su p e r p re s s u re m ercury a rc lamp. I t h as a v e ry sm a ll a rc (0.3 x 0.3 mm) s u i t a b l e f o r th e p r e s e n t p u rp o se s, and th e h ig h e s t i n t r i n s i c b r i g h t n ess o f any com parable l i g h t so u rc e, 140,000 c a n d le s /s q. cm. T his lamp was o p e ra te d by a D.C. power su p p ly a t 100 w a tts. The power su p p ly was equipped w ith a "low r i p p l e " a tta c h m e n t to a s su re more u n ifo rm o p e r a tio n o f th e a rc r e g a r d le s s o f f l u c t u a t i o n s in th e l i n e v o lta g e to th e power su p p ly. Hie lamp body was q u a r tz. Hie lamp was e n c lo se d i n a m e ta l h o u sin g w ith an a p e ra tu re c e n te re d a t th e a r c. The l i g h t was fo cu sed by a f r o n t s u r f a c e, s p h e r i c a l m ir r o r lo c a te d behind th e a rc a t a fix e d p o s i t io n t o g iv e an optimum image o f th e a r c. Focusing o f the image in th e f i e l d o f view was accom plished by movement of th e e n t i r e h o u sin g alo n g m e ta l g u id e s. A djustm ent in
th r e e d ir e c tio n s was p o s s ib le. A d ju sta b le s l i t s were f a s ten e d to th e h ousing to provide a narrow lin e o f illu m in a tio n in th e f i e l d o f view, and in c re a s e the c o n tr a s t betw een the illu m in a te d and d a rk f i e l d. The beam was, however, w ider th a n th e d ep th o f f i e l d o f the o p t ic a l system, so th e l a t t e r d eterm in ed the d e p th o f view and n o t th e l i g h t beam. A photograph o f th e lamp, h ousing and su p p o rts ap p ears in F ig u re 10. The lamp a ls o ap p ears in th e photographs of th e mechanism used to move th e p h o to - o p tic a l system w ith th e flow as i s d e s c rib e d. Those a re F ig u re s 4 and 5. O p tic a l a rra n g e m e n ts. The o v e r - a l l o p t i c a l system i s d e p ic te d in F ig u re 2, and in th e photographs o f F ig u re s 4 and 5 In a d d itio n to th e lamp a lre a d y d e s c rib e d, th e re a re two o th e r im p o rta n t p a r t s. F i r s t th e re i s the view ing c e l l m entioned e a r l i e r. This i s a c e l l open a t th e to p which c o m p le te ly e n c lo se s th e g la s s t e s t s e c tio n. I t i s shown in F ig u re s 4 and 5. The base and one v e r t i c a l sid e a re the su p p o rt c ra d le f o r th e p ip e. In th e r e a r v e r t i c a l su p p o rt a number o f a d ju stm e n t screw s a re lo c a te d. TSiese a re used in th e alig n m en t o f th e t e s t s e c tio n w ith th e lin e o f t r a v e l of th e cam era, and w i l l be d is c u s s e d when t h i s m a tte r is d e s c rib e d i n a l a t e r s e c tio n. The ends o f the c e l l a re s e a le d to th e p ip e. The f r o n t, o r fa c e o f th e c e l l tow ard th e l i g h t so u rc e, i s 1/4" p la te g la s s and ru n s th e e n t i r e le n g th of the p ip e, as does th e c e l l. This w a te r tig h t c e l l can be f i l l e d
Figure 10. Lamp and Support 52
w ith pure tr ic h lo r o e th y le n e so t h a t th e e n t i r e t e s t s e c tio n 53 i s submerged i n th e f l u i d. S ince t h i s f l u i d has e s s e n t i a l l y th e same in d e x o f r e f r a c t i o n as th e g la s s p ip e, and s in c e th e f l u i d is in s id e th e p ip e as w e ll, th e r e f r a c t i o n of l i g h t due to th e curved p ip e w a lls i s m inim ized, and th e w a ll a re a can be view ed from above as in d ic a te d i n F ig u re 11. T his r e s u l t i s v e ry im p o rta n t as i t a llo w s th e s tu d ie s to be made i n c i r c u l a r p ip e s. W ithout t h i s view c e l l and th e t r lc h o lo r e t h y le n e w ith in th e p ip e, th e w a ll a re a, and p a r t i c u l a r l y th e s u b la y e r, would n o t be v i s i b l e f o r s tu d y. The c e l l s e rv e s a second purpose as w e ll. The in te n s e l i g h t beam fo c u se d on th e exposed p ip e w a ll would r a p i d l y h e a t th e g la s s in th e a re a o f fo c u s, and co u ld cau se convect i o n c u r r e n ts w hich a t low flo w r a t e s m ight in tro d u c e e x tr a n eous m otions in to th e p i c t u r e s. The p la te g la s s and c e l l f l u i d e f f e c t i v e l y a b so rb t h i s h e a t so t h a t th e problem i s e lim in a te d. In a d d itio n, th e movement o f th e l i g h t so u rce w ith th e flow d u rin g th e ru n s p re v e n ts th e l o c a l re g io n s o f th e c e l l o r p ip e w a ll from becoming h e a te d, a lth o u g h t h i s i s n o t l i k e l y under m ost c irc u m sta n c e s o f o p e ra tio n anyway. T h is q u e s tio n o f l o c a l h e a tin g was exam ined e x p e rim e n ta lly by p h o to g rap h in g la m in a r flow s w ith th e l i g h t s t a t i o n a r y a t a p a r t i c u l a r a x i a l p o s i t i o n. Not o n ly a re th e s e c o n d itio n s m ost conducive to p ro d u cin g h e a t e f f e c t s, b u t th e lam in ar flo w would m ost r e a d i l y show th e s e e f f e c t s i f th e y e x i s t e d. No such e f f e c t s were o b se rv e d.
54 ojr tight poth water x*distance > from wall for total internal reflection trichloroethy lene view cell x«0.0009 Figure I I. Refraction E ffect
The le n s e s o f th e cam era com prise th e second p a r t of 55 th e o p t i c a l system. Tliese le n s e s were ad ap ted to produce m a g n ific a tio n s o f 4.3X and 2X. Some m a g n ific a tio n o f th e f i e l d of view was n e c e s s a ry f o r d e t a i l e d i n v e s t i g a t i o n o f th e f l u i d m otions because th e s u b la y e r and w a ll r e g io n a re o f such sm a ll d im en sio n s. F or exam ple, a t Nr6 = 2 0,000 th e th ic k n e s s o f th e re g io n o u t to y+ = 15 i s o f th e o rd e r o f 0.025 in c h e s in a 2 -in c h d ia m e te r p ip e. The amount o f l i g h t from the p a r t i c l e s which re a c h e s a u n i t a re a of f ilm f o r exposure i s in v e r s e ly p r o p o r tio n a l to th e e x te n s io n tu b e le n g th betw een th e len s and th e f ilm p la n e which produces th e m ag n ifie d im age. S ince th e amount o f a v a ila b le l i g h t from the p a r t i c l e s was lim ite d, any in c r e a s e in m a g n ific a tio n re q u ire d a p ro p o rtio n a te d e c re a se in fram ing speed f o r p h o to g rap h s of com parable q u a l i t y. Thus one must pay f o r in c re a s e d in fo rm a tio n from m a g n if ic a tio n by red u ced in fo rm a t i o n from slo w er fram ing speeds o r p o o re r q u a l i t y im ages. The above m a g n ific a tio n s r e p r e s e n t a com prom ise. I t was d e cid ed t h a t h ig h e r m a g n ific a tio n s would be s a c r i f i c e d f o r h ig h e r fram in g speeds b ecause th e l a t t e r were f e l t to be more n e c e s s a ry. The low er m a g n ific a tio n s w ere a ls o chosen f o r a second r e a s o n. view d e c r e a s e s. As th e m a g n ific a tio n in c r e a s e s, th e f i e l d of At h ig h e r m a g n ific a tio n s th e f i e l d of view would become v e ry sm a ll, and c e r t a i n a s p e c ts o f th e f l u i d.m otion w hich were l a r g e r i n s c a le th a n th e f i e l d would n o t be d e fin e d. The 4.3X m a g n ific a tio n was found to be m ost
56 s a t i s f a c t o r y as i t p ro v id ed s u f f i c i e n t e n la rg e m e n t o f th e w a ll r e g io n t o p e rm it d e t a i l e d i n v e s t i g a t i o n s, b u t s t i l l p ro v id ed a la rg e f i e l d of view. The f i e l d o f view a v a ila b le a t 4.3X was 0.0 9 5 in ch e s m easured p a r a l l e l to th e p ip e w a ll, and 0.0 6 9 in c h e s m easured alo n g a r a d iu s p e rp e n d ic u la r1 to th e d i r e c t i o n o f view. For 2X th e r e s p e c tiv e dim en sio n s were 0.205 in c h e s and 0.147 in c h e s. The dim ensions were m easured by p h o to g rap h in g a ru le d s c a le w ith th e a p p ro p ria te le n s e s, and m easuring th e image o b ta in e d. Each m a g n ific a tio n a ls o had a d e p th of f i e l d a s s o c i a te d w ith i t. The d e p th o f f i e l d i s d e fin e d as th e th ic k n e s s o f a p lan e p e rp e n d ic u la r to th e d i r e c t i o n o f view in which a l l o b je c ts a re i n fo c u s. For v e ry h ig h m a g n ific a tio n s t h i s d ep th i s s h a rp ly d e fin e d, b u t f o r low m a g n if ic a tio n s, such as th o se used in t h i s stu d y, th e re i s a d eg ree o f s u b je c tiv e judgm ent as to what i s r e a l l y i n fo cu s and what i s n o t. The d e p th o f f i e l d was d eterm in ed by p h o to g rap h in g w ith th e a p p ro p ria te le n s e s f o r each m a g n ific a tio n a h a i r l i n e mounted on th e in c lin e d fa c e of a 45 r i g h t a n g le p rism. The r e s u l t ing p h o to g rap h s showed a l i n e w hich was s h a r p ly i n fo cu s over a g iv en d is ta n c e, l e s s w e ll fo cu sed o v er a n o th e r d is ta n c e, and so on u n t i l i t was com plely o u t of f o c u s. By m easuring th e le n g th o f th e l in e to th e d e g re e o f fo c u s d e s ir e d, and knowing th e m a g n ific a tio n, th e d e p th of f i e l d can be
57 c a lc u la te d from th e fo llo w in g r e l a t i o n d e p th o f f i e l d = li ( s in 45 ) M where L i s the le n g th m easured on the p h o to g rap h, and M i s th e m a g n if ic a tio n. T his was done f o r each m a g n ific a tio n a t th e f s to p s used i n th e e x p e rim e n ta l ru n s. The g ra d u a l d e t e r i o r a t i o n of th e l i n e fo cu s i n th e p h o tographs in tro d u c e d some a r b i t r a r i n e s s in to th e s e l e c t i o n o f a w orking d e p th f o r th e a c t u a l e x p e rim e n ta l f ilm s, b u t a f t e r c a r e f u l ex am in a tio n o f image q u a l i t y o f th e p a r t i c l e film s and th e d e p th of fo c u s p h o to g rap h s, the d e p th o f 0.027 in ch e s was s e le c te d f o r 4.3X and 0.0 4 1 in c h e s f o r 2X. The d eg ree o f c h o ic e was n o t g r e a t. For exam ple, th e 4.3X m a g n if ic a tio n m ust have a w orking d e p th betw een 0.022 and 0.027 in c h e s. The f i e l d o f view i s th u s seen to be a volume o f f l u i d w hich f o r 4.3X i s.095 x.069 x.027 In ch es i n a x ia l, r a d i a l and l in e o f s i g h t r e s p e c t iv e ly. This i s d e p ic te d i n th e draw ings in F ig u re 13. S ince th e f i e l d of view i s a d im en sio n a t a p a r t i c u l a r m a g n ific a tio n, th e djlmensionless o r y+ d is ta n c e o f the w a ll re g io n encom passed by a s in g le fram e w i l l v a ry w ith th e R eynolds number. Thus a t NRe = 20,000 th e f u l l fram e w id th w i l l in c lu d e a y+ of a p p ro x im a te ly 45 w h ile a t NRe = 50,000 t h i s same w id th w i l l in c lu d e a y+ o f a p p ro x im a te ly 9 0.
Mechanism to p ro v id e cam era m o tio n. D uring the p r e lim in a ry I n v e s tig a tio n s le a d in g to th e e x p e rim e n ta l t e c h n iq u e s e v e n tu a lly used, i t was found to be v e ry d e s i r a b l e to move th e cam era w ith th e mean a x i a l flo w. There were two im p o rta n t re a so n s f o r t h i s. The d i f f i c u l t i e s w ith l ig h t i n g, m a g n ific a tio n, and fram ing speed have a lr e a d y been d is c u s s e d. I f th e cam era i s h e ld s t a t i o n a r y a t a p a r t i c u l a r a x ia l p o s i t i o n, th e fram ing speed m ust be in c re a s e d to slow down s u f f i c i e n t l y th e mean a x i a l v e l o c i t i e s so t h a t th e f l u i d w i l l rem ain in view f o r long enough p e rio d o f tim e to p erm it a n a ly s is o f i t s m o tio n s. T his in c re a s e i n fram ing speeds r e s u l t s i n a d e c re a se i n image q u a l i t y i f th e m a g n ific a tio n i s h e ld c o n s ta n t, o r n e c e s s i t a t e s a d e c re a s e i n m a g n ific a tio n to m a in ta in image q u a l i t y. In e i t h e r c a se a d e c re a se in in fo rm a tio n r e s u l t s. A lso, th e problem o f r e a l tim e exam ined i n a s in g le 100 fo o t r o l l o f film i s p r e s e n t. T his to o has been d is c u s s e d p re v io u s ly. I f th e tim e i s red u ced to to o sm a ll a v a lu e, th e number of r e e l s exposed must in c re a s e g r e a t l y i f a re a so n a b le sam pling o f th e random e v e n ts o f tu r b u le n t m o tio n i s to be o b ta in e d. Hie second re a so n f o r th e movement was th e d is c o v e ry t h a t w ith th e cam era fo llo w in g th e s e le c te d f l u i d e le m e n ts, th e developm ent of c e r t a i n m otions co u ld be r e a d i l y o b serv ed, and th e v a rio u s m easu rem ents co u ld be more e a s i l y made. T his w i l l be d is c u s s e d a t le n g th l a t e r i n t h i s s e c tio n.
59 S ince th e m ajor problem was In slow ing down th e a x i a l flow, th e p ro c e ss o f moving th e cam era and l i g h t so u rce dow nstream w ith th e flow would g r e a t l y red u ce th e r e l a t i v e m otion betw een th e cam era and th e a x i a l flo w. R e tu rn in g to th e exam ple used e a r l i e r, c o n s id e r th e c ase where the cam era i s moved dow nstream a t 0.5 6 f t. / s e c. The l o c a l mean v e lo c it y a t y+ = 25 i s s t i l l 0.8 2 f t. / s e c., b u t now th e r e l a t i v e v e l o c i t y i s o n ly 0.2 6 f t. / s e c. Perform ing th e same c a l c u l a t i o n as b e fo re, i t i s found t h a t th e p a r t i c l e o f f l u i d a p p ea rs i n a p p ro x im a te ly 24 fram es I n s te a d of 7 as b e fo re. In o rd e r to acco m p lish th e same r e s u l t w ith o u t cam era movement, th e fram ing speed would have had to be n e a r ly 2500 fra m e s /s e c. as compared to 800 f ra m e s /s e c. A d d itio n a lly, th e r e i s th e added f e a tu r e of fo llo w in g a p a r t i c u l a r elem ent f o r a g iv e n tim e and d i s t a n c e. The d e p a r tu re s from a x i a l flo w caused by th e tu r b u le n t m otions a re a ls o more r e a d i l y a p p a re n t becau se th e y e x h i b i t l a r g e r a p p a re n t a n g le s of d e v ia tio n from th e a x is. H ius, as l a t e r c a l c u l a t i o n s w i l l show, a n g le s o f th e o rd e r of 10 and 20 can a p p ear as 90 d e v ia tio n s from th e a x is when th e p ro p e r a x i a l m otion o f th e cam era i s used. T his p e rm its th e s e a n g le s to be more a c c u r a te ly m easured, and a ls o makes m inor d e v ia tio n s more v i s i b l e. S ince t h i s r e l a t i v e m otion o n ly o p e ra te s i n th e a x i a l d i r e c ti o n, i t does n o t reduce the a p p a re n t r a d i a l o r a n g u la r f l u c t u a t i o n s. T hese, how ever, a re sm a ll compared to th e lo c a l mean a x i a l v e l o c i t i e s. L a u f e r 's (31) m easurem ents i n a i r show t h a t a t
60 y+ = 25 a t 50,000 NRe the u^, f l u c t u a t i o n i s o n ly 5$ o f th e l o c a l mean a x i a l v e lo c ity, and th e u^ i n t e n s i t y i s a p p ro x i m a te ly 12$. These v e l o c i t i e s a re r e a d i l y slowed down f o r a n a ly s is a t 800 to 1000 fram e s/se co n d, and though th e y r e p r e s e n t average v a lu e s, even th e l a r g e r f l u c t u a t i o n s c o n ta in e d i n t h i s average w i l l be v i s i b l e i n th e m otion p i c t u r e s. In a l l th e se exam ples th e h ig h e s t Reynolds number s tu d ie d in th e ex p erim en ts has been used sin c e i t p ro v id es th e m ost se v e re c o n d itio n s. Since th e te c h n iq u e can a d e q u a te ly handle th e s e c o n d itio n s, i t can e a s i l y handle th e le s s se v ere cond i t i o n s imposed by low er Reynolds number. In a d d itio n, a t p o s itio n s v e ry n e ar the w a ll th e a b s o lu te m agnitude of th e f lu c tu a tin g v e l o c i t i e s d e c re a se s so a g a in th e above exam ples a re extrem e c a s e s. W hile th e cam era i s moving downstream, i t i s e s s e n t i a l t h a t the fo cu s be m a in ta in e d and t h a t no d is tu r b in g v i b r a tio n s o c cu r. To a s su re b oth o f th e s e c o n d itio n s, an 8 -f o o t la th e bed was a lig n e d p a r a l l e l to th e t e s t s e c tio n, and b o lte d to the f l o o r. The la th e c a r r ia g e, d esig n ed to s l i d e down th e ground s t e e l ways o f the bed, was f i t t e d w ith th e n e c e ssa ry su p p o rts to c a r r y th e cam era and lig h tin g system. The c a r r ia g e and su p p o rts were v e ry heavy and n o t s u s c e p tib le to v i b r a t io n s. The su p p o rts f o r th e cam era and l i g h t source were a d ju s ta b le to p erm it p ro p er fo c u s in g, and th e camera su p p o rt had an ad ju stm en t screw f o r f in e fo c u s in g. They a p p ear in th e photographs o f F ig u re s 4 and 5 where th e p o s i-
o f the la th e bed i s shown. The f i n a l a lig n m en t of th e t e s t s e c tio n to the l in e o f t r a v e l of th e cam era was made by th e a d ju stm e n t screw s i n th e r e a r fa c e o f th e t e s t s e c tio n c r a d le. A m icroscope w ith a g r id e y e p ie c e was m ounted in p la c e o f the cam era, and th e c a r r ia g e was slo w ly moved down th e bed w h ile th e p ip e w a ll was s ig h te d th ro u g h th e m ic ro sco p e. A djustm ents were made u n t i l th e w a ll over th e e n t i r e le n g th o f th e t e s t s e c tio n d e v ia te d no more th a n.03 in c h e s from p a r a l l e l. Over s h o r t s e c tio n s used f o r m ost o f th e s tu d ie s th e a lig n m en t was much b e t t e r. No f u r t h e r im provement of th e a lig n m en t was p o s s ib le because o f th e f l e x i b i l i t y of th e g la s s p ip e and th e n e c e s s ity of n o t having any s o l i d s u p p o rt on th e to p o r f r o n t fa c e o f th e p ip e. F o r tu n a te ly, t h i s a lig n m en t was n o t a problem. The p o s itio n o f the w a ll was c l e a r l y v i s i b l e i n th e f i e l d o f view, and p r i o r to each ru n i t was a lig n e d so t h a t i t would a p p ea r in a l l fra m e s. T h is n e c e s s i t a t e d s a c r i f i c i n g p a r t o f a fram e by having th e w a ll p o s i t io n w ith in th e fram e a t some a x i a l p o s itio n s so t h a t a t o th e r a x i a l p o s itio n s th e w a ll would j u s t be a lig n e d w ith th e edge of th e fram e. Over th e s h o r t s e c tio n s used f o r m ost s tu d ie s th e a lig n m e n t was q u ite good and th e w a ll co u ld be m a in ta in e d a t th e v e ry edge o f th e fram e. I t was o n ly o v er long segm ents o f th e t e s t s e c t i o n where th e f u l l e f f e c t o f th e m isalig n m en t was v i s i b l e. Ih e se long s e c tio n s were used f o r h ig h R eynolds numbers and a t th e s e R eynolds number th e y+ r e g io n e n c lo se d
62 by a f u l l fram e i s much g r e a t e r th a n t h a t f o r low Reynolds num bers, so th e r e s u l t was t h a t th e lo s s o f p a r t o f th e fram e d id n o t r e a l l y cau se any l o s s of th e y+ re g io n s tu d ie d when compared to th e low er R eynolds num bers. V e r tic a l alig n m en t was e s ta b lis h e d by m ounting a f e e l e r gauge on th e c a r r ia g e and keep in g i t i n c o n ta c t w ith th e p ip e s u rfa c e w h ile a d ju stm e n ts were made. The d riv e mechanism f o r the c a r r ia g e c o n s is te d o f an h y d ra u lic p is to n w ith s p e c i a l l y com pensated v a lv in g and pumping a p p a ra tu s to a s s u re ste a d y, v i b r a t io n f r e e movement. The p i s to n was co n n ected d i r e c t l y to the c a r r i a g e. The r a t e of t r a v e l o f th e p is to n c o n tr o lle d th e c a r r ia g e movement, and was c o n tin u o u s ly a d ju s ta b le from m o tio n le s s to 1 f t./ s e c o n d. Once th e c o n tr o l was s e t, o f c o u rse, the v e lo c it y was cons t a n t. A p h o to g rap h o f th e p is to n and su p p o rt equipm ent a p p e a rs as F ig u re 6. The speed a d ju stm e n t on the p is to n was n e c e ssa ry becau se th e cam era o r c a r r ia g e m otion was to be m atched t o a p a r t i c u l a r l o c a l mean a x i a l v e lo c it y which v a rie d b oth w ith y+ p o s i t io n and R eynolds num ber. F or th e w a ll views ( to be d e s c rib e d l a t e r ) i t was found t h a t th e b e s t p h otographs were o b ta in e d i f th e c a r r ia g e v e lo c it y was m atched to th e l o c a l mean a x i a l v e l o c i t y a t y+ = 11. For o th e r view s, o th e r p o s i t io n s o f m atching were s e l e c te d. When th e c a r r ia g e v e lo c it y m atched a p a r t i c u l a r flow v e lo c ity, th e r e s u l t i n g p h o to g rap h s showed zero r e l a t i v e v e lo c it y f o r t h a t p o s itio n, and g ra d u -
63 a l l y in c r e a s in g r e l a t i v e v e l o c i t i e s as the d is ta n c e from t h i s p o s i t io n was in c re a s e d b oth w allw ard and outw ard tow ard th e c e n t e r l i n e. N a tu ra lly, th e a p p a re n t d i r e c t i o n o f flow on one sid e o f t h i s p la n e was th e o p p o site o f th e flow on th e o th e r. S ince t h i s r e l a t i v e m otion was m easured i n th e l a t e r a n a ly s e s, i t was e s s e n t i a l t h a t th e c a r r ia g e speed be known q u i te a c c u r a te ly f o r each ru n so t h a t a b s o lu te v e l o c i t i e s co u ld be d e te rm in e d. To re c o rd the c a r r ia g e v e lo c ity, a nichrom e rib b o n w ith a c o n s ta n t and a c c u r a te ly known r e s i s ta n c e p e r f o o t was cem ented to an i n s u l a t i n g s t r i p on a nonb e a rin g f la t- g r o u n d s u rfa c e of the la th e bed which p a r a l le l e d th e tra c k s down w hich th e c a r r ia g e moved. A s l i d i n g c o n ta c t was e s ta b lis h e d betw een t h i s rib b o n and an arm s e c u re ly f a s te n e d to th e c a r r i a g e. A m ercury c e l l was connected th ro u g h a v a r ia b le r e s i s t a n c e c i r c u i t to th e ends o f th e nichrom e rib b o n so t h a t a c o n s ta n t v o lta g e d ro p p e r u n i t le n g th was m a in ta in e d. A lso p erm an en tly co n n ected to one end o f th e rib b o n was a le a d w ire w hich was one in p u t t o a Baush and Lomb VOM-5 r e c o r d e r. The o th e r in p u t was from th e s l i d in g c o n ta c t. As th e c a r r ia g e moved, th e v o lta g e d ro p m easured betw een th e s e two le a d s was re c o rd e d on th e r e c o r d e r s t r i p c h a r t which was d r iv e n a t a known c o n s ta n t sp e ed. Tlie c a r r i a g e v e lo c it y was d e te rm in e d from th e slo p e o f th e lin e tr a c e d on th e s t r i p c h a r t and th e c a l ib r a t e d v o lta g e drop
64 p e r f o o t o f th e w ire. For c o n s ta n t c a r r ia g e speed, th e l i n e was s t r a i g h t, and t h i s p ro v id ed an a d d it i o n a l check on th e c o n sta n c y o f c a r r ia g e m otion d u rin g a ru n. The v a r ia b le r e s i s t a n c e s th ro u g h w hich th e b a t t e r was connected to th e r e s i s t a n c e rib b o n were used to p ro v id e a s e l e c t i o n o f v o lta g e d ro p s w ith in th e w ire a p p ro p r ia te f o r the v a rio u s c a r r ia g e speeds to be m easured. a p p ea rs in F ig u re 12. A sch em atic draw ing o f t h i s device A fte r each days e x p e rim e n ts, the v o lta g e d ro p p e r u n it le n g th o f th e r e s i s t a n c e w ire was c a l ib r a t e d u sin g a p r e c is io n p o te n tio m e te r. To check th e r e c o rd in g d ev ice and th e c o n sta n c y o f th e c a r r ia g e movement, a s t e e l ta p e was mounted on th e pipe s u r f a c e, and h ig h speed m otion p ic tu r e s ta k e n of i t w hile th e c a r r ia g e was moved dow nstream. Hie c a r r ia g e v e l o c i t y was re c o rd e d and c a l c u l a t e d. Two d i f f e r e n t b u t r e p r e s e n ta tiv e v e l o c i t i e s were checked in t h i s f a s h io n. The tim in g m arks on th e f ilm and th e s c a le image in th e fram es p e rm itte d an a c c u ra te c a l c u l a t i o n o f th e a b s o lu te c a r r ia g e v e lo c it y f o r each in c h o r f r a c t i o n o f an in c h o f c a r r ia g e movement. In a c t u a l i t y, 3 in ch segm ents were exam ined. I t was found t h a t th e r e was no v a r i a t i o n in c a r r ia g e v e l o c i t y from segm ent to segm ent, i. e., I t was c o n s ta n t. The v e lo c it y d eterm in ed i n t h i s f a s h io n a g re ed w ith th e v a lu e s g iv e n by the r e c o r d e r. The p h o to g ra p h ic a lly d e te rm in e d v e l o c i t i e s were 0.6 8 0 and 0.2 0 8 f t. / s e c., and th e r e c o r d e r v a lu e s were 0.679 and 0.209 f t. / s e c. r e s p e c t i v e l y. Hie film s a ls o showed t h a t
Sliding Contact on Carriage Resistance Ribbon L - v ' Switch Battery Resistance Selector Recorder Figure 12. Carriage Velocity Measurement
66 th e re was no v i b r a t io n o f th e system which a f f e c te d th e p h o to g rap h s. Camera v iew p o in ts A lthough th e cam era l i n e of s ig h t o f n e c e s s ity m ust be a t r i g h t a n g le s to th e l i g h t beam, th e re i s some cho ice as to the p o s itio n o f fo c u s. In t h i s s e c tio n th e d i f f e r e n t p o s itio n s used w i l l be d e s c rib e d. W all view. The fo llo w in g d is c u s s io n w i l l be much c le a r e r i f F ig u re 13 i s used in c o n ju n c tio n w ith i t. As p a r t (a) of t h i s f ig u r e show s, th e l i g h t beam e n te rs th e f i e l d a t r i g h t a n g le s to the l in e o f s ig h t of the cam era. The cam era i s fo cu sed on a h o r iz o n ta l plane AB ( p a r t c) a t th e v e r t i c a l c e n t e r l i n e of th e pipe w ith th e i n t e r i o r pipe w a ll a lig n e d w ith th e edge o f the fram e. P a rt (b) o f t h i s f ig u r e i s in c lu d e d to show th e o r i e n t a t i o n o f th e v a rio u s p la n e s i n p o la r c o o rd in a te s. In f u tu r e re fe re n c e s to t h i s view, th e s e p la n e s w i l l be used to d e s c rib e th e lo c a tio n of v a rio u s e v e n ts. I f th e cam era were focused o n ly a t th e g eo m etric p lan e AB, th e p lan e would c o in c id e w ith the r x p la n e o f th e p o la r c o o rd in a te s. However, a s p a r t (c) shows, th e camera a c t u a l l y "se es" a c e r t a i n d is ta n c e on e i t h e r sid e o f t h i s p lan e alo n g th e lin e o f s ig h t due to the d e p th of f i e l d o f th e le n s system. S ince th e le n s e s p re s e n t f l a t s u rfa c e s p a r a l l e l to AB f o r th e cam era to view, th e se p lan e s s e p a ra te d from AB by th e o n e -h a lf th e dep th o f f i e l d w i l l
67 View in Film Frame rg plane plane ch069*ld Direction of View Plane A B.069 ' Figure 13. Wall View
n o t c o in c id e w ith th e r x p la n e s a t t h a t p o s i t io n. However, because of th e e x tre m e ly sm a ll dim ensions o f th e f i e l d o f view, the a c t u a l d if f e r e n c e i s i n s i g n i f i c a n t and no d i f f e r e n t i a t i o n w i l l be made i n f u tu r e d is c u s s io n s. P a r t (d) i l l u s t r a t e s t h i s p o i n t. AEDC i s th e o p t i c a l f i e l d and ABDC i s th e p o la r c o o rd in a te f i e l d. T his c o u ld, o f c o u rs e, be av o id ed th ro u g h th e u se o f r e c ta n g u la r c o o rd in a te s, b u t th e y would cau se c o n fu s io n when o th e r view s a re c o n s id e re d. Because of th e d e p th o f f i e l d, the cam era a c t u a l l y 's e e s 1* a volume o f f l u i d and n o t a p la n e, a lth o u g h th e th ic k n e s s o f t h i s p la n e i s q u ite t h i n. S ince th e o p t i c a l system can n o t show th r e e d im e n sio n a l e f f e c t s in th e m otion p i c t u r e s, th e p a r t i c l e s w ith in t h i s volume a l l a p p ea r to be on a s in g le r x p la n e, and i n t h i s view th e re i s no a c c u ra te means of d e te rm in in g a t w hich r x p la n e w ith in th e volume th e y axe lo c a te d. In m ost f u tu r e d e s c r i p t io n s, th e p o s itio n s o f p a r t i c l e s i n t h i s view w i l l be d e s c rib e d w ith o u t re g a rd to th e p o s s ib le s e p a r a tio n in the d i r e c t i o n. For m ost c a se s t h i s s e p a r a tio n i s so sm a ll t h a t i t has no g r e a t e f f e c t on th e o b s e rv a tio n s so ig n o rin g i t does n o t c r e a te any problem s For th o se s i t u a t i o n s where i t may be o f im p o rtan ce, s p e c i f i c m ention i s made o f i t. A lso, p a r t i c l e m otions w i l l be d e s c rib e d i n term s o f movements, a lo n g th e p o la r c o o rd in a te s i. e., x, r, and 9. To be a b s o lu te ly r ig o r o u s, one can n o t sa y t h i s b ecau se of th e in congruence o f th e o p t i c a l and
69 c o o rd in a te p la n e s, and th e i n a b i l i t y to d e te rm in e m otions in th e 9 d i r e c t i o n. The d if f e r e n c e s o ccu r o n ly fo r th e r and 9 c o o rd in a te s, and a re v e ry s l i g h t b ecause o f the s m a ll dim ens io n s. Whenever n e c e ssa ry, and i n th e f i n a l a n a ly s is where th e o b s e rv a tio n s from d i f f e r e n t view s are com piled, an a tte m p t i s made to p ro v id e a th re e d im e n sio n a l p i c t u r e. H iis th re e d im e n sio n a l m otion w i l l have i t s m ost im p o rta n t e f f e c t on v e lo c it y m easurem ents. The q u e s tio n o f e r r o r s in tro d u c e d i n th e se cases I s d is c u s s e d i n a l a t e r s e c t i o n and in A ppendix I I. D uring th e e x p e rim e n ta l ru n s, th e l i g h t beam was fo cu sed th rough the s l i t s i n to th e d e s ire d f i e l d o f view by a d ju s tm e n t o f i t s p o s itio n on the m e ta l s u p p o rt g u id e s. For th e w a ll view, i t was fo c u se d a t th e v e r t i c a l c e n te r lin e a t th e in s id e s u rfa c e of th e pip e w a ll. The camerawas th en a lig n e d w ith th e pipe w a ll so t h a t th e i n t e r i o r w a ll was j u s t w ith in th e fram e. The w a ll co u ld be se e n as a th in b r i g h t l i n e due to th e im p e rfe c t m atch o f In d ex of r e f r a c t i o n betw een th e p ip e and th e f l u i d. The o u ts id e s u rfa c e of th e p ip e c o u ld a ls o be se e n i f th e p o s itio n of th e cam era were moved tow ards i t, th u s i t was assum ed t h a t t h i s l i n e was th e in s id e w a l l. Hie assu m p tio n was checked by i n s e r t i n g a r u le d s c a le i n t o the pip e such t h a t i t s i n i t i a l g r a d u a tio n was i n c o n ta c t w ith th e in s id e w a ll, and th e n exam ining i t v i s u a l l y and p h o to g r a p h ic a lly. The r e s u l t s showed c o n c lu s iv e ly t h a t th e b r i g h t l in e was th e in s id e w a ll, and t h a t i t d id not
70 e x te n d any s i g n i f i c a n t d is ta n c e in to th e w a ll r e g io n. This i s due to th e t h in la y e r o f focus and illu m in a tio n, and the v e ry sm all c u rv a tu re o f th e pipe w a ll o v er t h i s th ic k n e s s. The r e f r a c t i o n of th e l i g h t beam from w ith in th e pipe a t th e pipe w a ll was c a lc u la te d f o r th e su b la y e r r e g io n. At a d is ta n c e o f 0.0 0 2 from th e w a ll (e q u iv a le n t to y+ - 2 a t NRe = 50,000 and le s s f o r o th e r NRe v a lu e s ) th e I n c id e n t beam had an a n g le o f 86 2 3 ', and the r e f r a c t e d beam an an g le of 87 1 9 ' This shows t h a t v ery l i t t l e d i s t o r t i o n o c c u rs. A s im ila r c a l c u l a t i o n was made to d eterm in e th e d i s ta n c e from th e w a ll a t which th e l i g h t beam would have to o r ig in a te in o rd e r to be t o t a l l y r e f l e c t e d i n t e r n a l l y a t the p ip e w a ll. T his d is ta n c e was 0.0009 in c h e s. This i s o nly an a p p ro x im atio n because m onochrom atic l i g h t was n o t used, b u t i t i s a good e s tim a te. This d is ta n c e can be c o n sid e re d th e d is ta n c e which th e w a ll r e f r a c t i o n e f f e c t in tr u d e s in to th e s u b la y e r. A c tu a lly, due to th e f a c t t h a t a t a n g le s n e a r th e an g le of t o t a l r e f l e c t i o n a la rg e amount of l i g h t i s r e f l e c t e d, a lth o u g h some i s tr a n s m itte d, one can e x p e c t t h a t a d a rk re g io n s l i g h t l y l a r g e r th a n 0.0009 in ch e s w i l l e x i s t i n th e s u b la y e r. Some l i g h t i s tr a n s m itte d over t h i s re g io n, how ever, so th e m otions w ith in th e re g io n sh ould s t i l l be v i s i b l e. Once th e cam era was a lig n e d, i t was locked i n p lac e on th e su p p o rt member so no f u r t h e r l a t e r a l movement was p o s s ib le. I t was th e n fo cu sed by a s l i d in g and screw
71 a d ju s tm e n t i n th e v e r t i c a l p la n e, and th e n lo ck ed in p la c e h e re as w e ll. Top v iew. F ig u re 14 d e t a i l s the d i f f e r e n t a s p e c ts o f t h i s view. As p a r t (a) shows, th e l i g h t e n te r s a t r i g h t a n g le s to th e cam era l in e o f s i g h t, b u t i n t h i s case th e l i g h t i s d i r e c te d to th e i n t e r i o r w a ll re g io n a t th e to p, h o r i z o n t a l c e n t e r l i n e p o s i t io n o f th e p ip e. The pipe o r ie n t a t i o n i s th e same as i n F ig u re 13 so a com parison can be m ade. S ince th e re i s a x i a l symmetry in p ip e flo w, t h i s view i s e s s e n t i a l l y r o t a t e d 90 from th e w a ll view. The l i n e of s i g h t i s now alo n g th e r c o o rd in a te, and th e p la n e s p e rp e n d i c u l a r to th e d i r e c t i o n o f view a re X p la n e s. The comments made b e fo re c o n ce rn in g th e congruence o f th e o p t ic a l p la n e s and th e g e o m e tric p la n e s a p p ly in t h i s case as w e ll, a s do th e comments ab o u t th e th re e d im e n sio n a l movement of th e p a r t i c l e s. These m otions a re c o n sid e re d to o c cu r in th e X p la n e s, and th e r e f o r e would be m otions p a r a l l e l to th e lin e o f s ig h t i n th e w a ll view, j u s t a s th e m o tio n s o f th e w a ll view i n th e r x p lan e a re p a r a l l e l to th e lin e o f s ig h t in t h i s view. A lthough th e s e v ie w p o in ts were used s e p a r a te ly, c a r e f u l a n a ly s is o f each s e r i e s o f film s p e rm itte d a th re e d im e n sio n a l p ic tu r e o f th e f l u i d m otions to be c o n s tru c te d. S ince th e w a ll o f th e p ip e d id n o t a p p e a r in t h i s view, th e cam era a lig n m e n t p ro ced u re became more e l a b o r a t e. A p o s itio n in g s c a le, w hich i s shown i n F ig u re 15, was i n s e r te d i n t o th e p ip e from th e dow nstream end by a long s t e e l ro d.
View in Film Frame $ o 8. 4r 1 1 Qx plane rg Diane wivm 2s Direction of View 027" <-.069 J ------ >- c. C. Figure 14. Top View
The b ra ss c o l l a r su p p o rtin g th e s c a le was d esig n ed to push th e edge o f the s c a le a g a in s t th e in s id e p ip e w a ll su rfa c e a t the v e r t i c a l c e n t e r l i n e ( t h a t i s a t p lan e AB of F ig u re 13). T his placem ent i s shown in F ig u re 15. In t h i s p o s itio n, th e s c a le c o in c id e d w ith th e AB p la n e. The cam era must be p o s i tio n e d n o t o n ly w ith r e s p e c t to r x plane of F ig u re 1*1 but w ith r e s p e c t to th e 0X p lan e as w e ll. For t h i s view, th e c e n te r of th e fram e was a lig n e d w ith th e rx p lan e which c o in c id e d w ith th e CD p lan e of F ig u re 1*1, p a r t ( c ). U iis was the p ip e c e n te r lin e as m easured h o r i z o n t a l l y from the w a ll. To make t h i s alig n m en t, th e v ie w fin d e r of th e camera was s ig h te d in on th e a p p ro p ria te s c a le re a d in g which c o r responded to the pipe r a d iu s, and th e l a t e r a l movement mechanism locked i n p la c e. The o th e r a d ju stm en t concerned th e fo c u sin g o f th e cam era on th e QX p lan e a t th e in s id e p ip e w a ll. This was accom plished by r o t a t in g th e b ra s s c o l l a r so t h a t i t s s u rfa c e was fa c in g the earner. The camera was th en fo cu sed on th e su rfa c e such t h a t th e upper l i m i t of th e dep th o f f i e l d c o in c id e d w ith th e s u r f a c e. Since the c o l l a r was in c o n ta c t w ith th e pip e w a ll, t h i s a d ju stm en t m eant t h a t th e e n t i r e d e p th of f i e l d was a v a ila b le f o r viewin g from th e in s id e pipe w a ll r a d i a l l y inw ard. A fte r t h i s a d ju stm e n t, the s c a le was r e t r a c t e d downstream out o f th e t e s t s e c tio n in to th e s e c tio n of s t e e l pipe which fo llo w ed th e t e s t s e c tio n. I t th e r e f o re co u ld n o t a f f e c t th e flow.
pipe scale ^'ffore ik P sitionin l n 9 S e a l e
75 T rip w ir e. w ire was r e q u ir e d. In a few c a se s th e p re se n c e of a t r i p TSie t r i p u sed in th e s e c a se s was a c i r c l e o f s p r in g s t e e l w hich when I n s e r te d i n t o th e p ip e had an o u ts id e d ia m e te r j u s t e q u a l to th e in s id e p ip e d ia m e te r. The w ire had a c i r c u l a r c r o s s e c tio n and a d ia m e te r o f 0.0032 in c h e s. I t was p o s itio n e d a x i-s y m m e tric a lly, and was h e ld p la c e by i t s own te n s io n. Both to p and w a ll view s were used i n th e s e r i e s o f ru n s w ith t h i s t r i p w ire. O ther v ie w s. The lim ite d dim ensions o f th e f i e l d o f view p e rm itte d o b s e rv a tio n s to o n ly sm a ll y+ p o s itio n s when th e cam era was fo c u se d a t th e w a ll. In o rd e r to exam ine the f l u i d m otions a t g r e a t e r y+ v a lu e s, i t was n e c e s s a ry to fo cu s th e camera a t g r e a t e r d is ta n c e s from th e w a ll as m easured along th e AB p la n e o f F ig u re 13. The r e s u l t i n g view s were e s s e n t i a l l y th e same as th e w a ll view, b u t d i s p la c e d v a ry in g d is ta n c e s from th e w a ll. In o rd e r to p o s i t io n th e cam era, th e s c a l e d e v ic e d e s c rib e d i n th e to p view s e c t i o n was used. In t h i s c a se, o f c o u rs e, th e fo c u s was a t th e p la n e AB. Hot f i lm Anemometer A l i n t r o n i c Model 40W L in e a r C o n sta n t T em perature H ot- Film Anemometer w ith a th erm o co u p le -ty p e r o o t mean sq u are m eter was used f o r m easuring l o c a l mean v e l o c i t i e s and tu r b u l e n t f l u c t u a t i o n i n t e n s i t i e s. 'Hiis u n i t w i l l n o t be d e s c rib e d in d e t a i l h e re as a r a t h e r com plete d is c u s s io n h as
been p re s e n te d e lsew h ere by Hubbard (2 2 ). B a s ic a lly th e u n i t m easures th e v e lo c it y o f th e f l u i d by i n d ic a tin g th e v o lta g e re q u ire m e n t needed to m a in ta in th e c o n s ta n t tem p eratu r e of th e h o t f ilm o f th e p ro b e. The i n t e r n a l c i r c u i t r y p ro v id e s a l i n e a r r e l a t i o n betw een th e e f f e c t s o f th e f l u i d v e l o c i t y on th e probe and th e o u tp u t s i g n a l. Two probe c o n fig u r a tio n s were u sed. One was a r i g h t a n g le wedge probe where th e se n sin g elem ent o r h o t f ilm was p o s itio n e d on a t h i n g la s s wedge s e t a t r i g h t a n g le s to th e probe a x is. By i n s e r t i n g t h i s probe th ro u g h th e w a ll o f th e p ip e, th e U A and u v e l o c i t i e s co u ld be m easured. The o th e r c o n fig u ra t i o n had a f l a t s u rfa c e a t th e end o f the probe where th e s e n sin g elem ent was p o s itio n e d. T his probe was i n s e r te d th ro u g h th e p ip e w a ll w ith th e se n sin g s u rfa c e f lu s h w ith th e w a ll. I t i s p a r t i c u l a r l y s e n s i t iv e to u^ f l u c t u a t i o n s. Both probes were pu rch ased from L in tr o n ic, and as such were s ta n d a rd u n i t s. The s e n sin g elem en t o f p la tin u m was 1 mm. i n le n g th, 0.2 mm. w ide, and had a th ic k n e s s o f 1.5 x 1 0 "5 mm. A sp ectru m a n a ly z e r was a ls o used to a n a ly z e th e o u tp u t s ig n a ls from th e h o t f ilm probe f o r th e p resen c e o f p e rio d ic d is tu r b a n c e s. The m odel used was by Panoram ic, and had a so n ic a n a ly z e r which co u ld m easure th e in p u t s i g n a l in th e fre q u e n c y ran g e o f 20 to 2 2,500 c p s, and a su b so n ic u n it w hich a n a ly z e s th e in p u t s i g n a l in th e ran g e o f 0.5 to 2,2 5 0 c p s. Both had a d ju s tm e n ts f o r s e t t i n g th e c e n te r
77 fre q u e n c y, and f o r a d ju s tin g th e fre q u e n c y span exam ined. A more e x te n s iv e d is c u s s io n o f t h i s u n it a p p ea rs i n Lee (3 2 ). The p ro b es were I n s e r te d i n t o th e pipe th ro u g h a h o le d r i l l e d i n to th e p ip e w a l l. S ince th e p resen c e o f t h i s h o le co u ld c o n c e iv a b ly have caused some d is tu rb a n c e s d u rin g th e p h o to g rap h ic s t u d i e s, i t was n o t d r i l l e d u n t i l th e s e were com pleted. As t h i s ho le was d r i l l e d in th e p ip e w h ile i t was i n s t a l l e d i n th e system, i t was n o t e x a c tly c e n te re d. T his n e c e s s i t a t e d an a c c u ra te d e te rm in a tio n of th e probe p o s i t io n when I t was i n s t a l l e d, so t h a t th e v e l o c i t y and rms m easurem ents w ith r e s p e c t to r a d i a l p o s i t io n co u ld be made. The probe was mounted In a h o ld in g d ev ice and co u ld be moved h o r i z o n t a l l y. The s c a le on th e d ev ice was g ra d u a te d in h u n d re th s of an in ch and had a v e r n ie r which co u ld be re a d to th e n e a r e s t th o u sa n th of an in c h. The v e r t i c a l p o s i t io n o f th e probe was d e te rm in e d by o p t i c a l means u sin g a m ic ro sc o p e. S ince t h i s was a p p a re n tly th e f i r s t tim e a h o t f ilm probe had been used i n a h y d ro carb o n system, th e p ro p e r o v e r h e a t r a t i o f o r th e h o t f ilm had t o be d e te rm in e d. A pproxim ate c a l c u l a t i o n s f o r th e h e a t t r a n s f e r from a c y lin d e r i n tu r b u le n t flo w in g a i r, w a te r, and t r i c h l o r o e t h y l i n e were made, and knowing th e p ro p e r o v e rh e a t r a t i o f o r a i r and w a te r, an ap p ro x im ate s e t t i n g f o r t r ic h lo r o e th y le n e was o b ta in e d. T h e r e a f te r i t was a m a tte r o f t r i a l and e r r o r to o b ta in th e s e t t i n g which would g iv e a s t r a i g h t l i n e c a l i b r a -
t i o n curve o f o u tp u t v o lta g e v e rsu s v e lo c it y. B ecause no e x te n s iv e m easurem ents w ith th e h o t f ilm probe were p lanned, and s a t i s f a c t o r y r e s u l t s co u ld be o b ta in e d f o r th e m easurem ents d e s ir e d w ith o u t an a b s o lu te ly s t r a i g h t l in e c a l i b r a t i o n c u rv e, no e x te n s iv e stu d y of th e m ost d e s i r a b l e o v e r h e a t r a t i o was made. I n d ic a tio n s from th e s tu d y re v e a le d t h a t a s t r a i g h t lin e curve co u ld be o b ta in e d a t h ig h e r o v e r h e a t r a t i o s th a n th o se e v e n tu a lly u se d. Ih e s e h ig h e r r a t i o s were n o t employed because th e system was n o t equipped w ith a h e a t ex ch an g er to c o n tr o l th e f l u i d te m p e ra tu re, and the e q u ilib riu m f l u i d te m p e ra tu re a f t e r h o u rs of o p e ra tio n was to o g r e a t to p e rm it s ta b le o p e ra tio n a t th e h ig h o v e rh e a t r a t i o s. The o v e rh e a t r a t i o used was 1.1 6. The h o t f ilm probe i s c a l ib r a t e d by c au sin g some known o r m easured v e l o c i t y to flo w p a s t i t and re c o rd in g th e v o lta g e o u tp u t from th e m easuring c i r c u i t as t h i s v e l o c i t y i s s y s te m a tic a lly changed. U su a lly a m easuring d e v ic e such a s a p i t o t tu b e i s used to d ete rm in e th e flow p a s t th e p ro b e. In th e p r e s e n t stu d y, how ever, p h y s ic a l c irc u m sta n c e s re q u ire d t h a t an a l t e r n a t e method be found s in c e such a m easuring d e v ic e c o u ld n o t be p la c e d in th e t e s t s e c tio n w ith o u t m ajor changes in i t s d e s ig n. F or c a l i b r a t i o n, th e probe was p o s i tio n e d w ith in th e t e s t s e c tio n v e ry n e a r to th e p ip e c e n te r. The v e l o c i t y o f flow p a s t i t was changed by changing th e av erag e a x i a l flo w r a t e as m easured by th e o r i f i c e m e te r and r o ta m e te r. The l o c a l mean a x i a l v e lo c it y p a s t th e probe was
c a lc u la te d from th e a v erag e v alu e by f i r s t assum ing t h a t a tu r b u le n t p r o f i l e e x is te d i n th e s e c t i o n. Then by u sin g B ro d k ey 's (1) e x te n s io n o f P a i 's (42) e q u a tio n s, th e o v e r - a l l av erag e v e lo c it y co u ld be r e l a t e d to the maximum v e l o c i t y. From th e s e v a lu e s, and P a i 's r e l a t i o n f o r th e tu r b u le n t v e lo c it y p r o f i l e, th e l o c a l mean a x i a l v e lo c it y a t th e probe p o s i t io n f o r each av erag e v e lo c it y co u ld be c a lc u la te d. These e q u a tio n s have been shown to be q u ite a c c u ra te, Brodkey (1 ), so th e o n ly d i f f i c u l t y i s w ith th e assu m p tio n o f a t u r b u le n t p r o f i l e. I f i t does n o t e x i s t, th e n th e c a l i b r a t io n curve i s i n e r r o r. S in ce th e c a l i b r a t i o n m easurem ents a re made w ith th e probe a t a fix e d p o s itio n, and th e v e lo c it y p r o f i l e m easurem ents a re made a t a fix e d R eynolds number by moving th e p ro b e, an e r r o r in th e c a l i b r a t i o n m easurem ents w i l l be r e f l e c t e d i n th e v e l o c i t y p r o f i l e m easurem ents, and a norm al t u r b u le n t p r o f i l e would n o t be o b ta in e d. U iis th e n p ro v id e s an i n d i r e c t check on th e assu m p tio n f o r th e c a l i b r a t i o n m ethod. I f th e m easured p r o f i l e a g re e s w e ll w ith th e t h e o r e t i c a l p r o f i l e f o r t u r b u le n t flo w, th e n one can conclu d e t h a t th e c a l i b r a t i o n was s a t i s f a c t o r y sin c e t h i s a g re e ment co u ld n o t have been a tt a i n e d u n le s s th e n e c e s s a ry a ssu m p tio n made d u rin g th e c a l i b r a t i o n s t e p was t r u e. I f a poor m easured p r o f i l e Is o b ta in e d, th e r e s u l t s a re In c o n c lu s iv e, b u t would in d ic a te t h a t a tu r b u le n t p r o f i l e does n o t e x i s t i n th e t e s t s e c t i o n. The pro ced u re I s n o t a l l t h a t one would d e s i r e, b u t f o r th e lim ite d p u rp o ses o f th e h o t
80 w ire m easurem ents in t h i s stu d y, i. e., to d e te rm in e i f th e flo w in th e t e s t s e c t i o n i s f u l l y t u r b u le n t, i t i s a d e q u a te. The c a l i b r a t i o n curve a p p e a rs in F ig u re 16. A rem ark ab le r e s u l t o f th e u se of th e h o t f ilm probe i n tr ic h lo r o e th y le n e was th e e x c e ll e n t s t a b i l i t y o f o p e ra t i o n. The l i t e r a t u r e c o n ta in s many r e f e r e n c e s to th e d i f f i c u l t i e s e n co u n tere d and in a c c u ra c ie s in tro d u c e d by th e d r i f t o f th e probe o u tp u t when i t i s used in w a te r. In th e p r e s e n t stu d y, once the f l u i d had re a c h e d c o n s ta n t te m p e ra tu re, the probe o p e ra tio n was c o m p le te ly s t a b le f o r p e rio d s o f h o u rs, and n e v er showed a s y s te m a tic d r i f t. Dye i n j e c t i o n F or a b r i e f sequence o f ru n s dye was i n je c t e d i n to th e w a ll a r e a through th e h o le in th e p ip e w a ll where the h o t film probe had b een i n s e r t e d. A g la s s tube o f a p p ro x i m a te ly 2 m illim e te r s I.D. and O.D. a p p ro x im a te ly t h a t o f th e h o le was in s e r te d i n to th e p ip e w a ll, b u t d id n o t e x te n d to th e in s id e w a ll s u r f a c e. Dye was i n je c t e d th ro u g h t h i s tu b e, i n to th e h o le i n th e p ip e w a ll and th e n i n t o th e w a ll r e g io n. A sm a ll c e n t r i f u g a l pump and n eed le v alv e were u sed to cont r o l th e dye flow r a t e. W ith th e l i g h t so u rc e and film s e n s i t i v i t y, Sudan I I I re d dye was found to be m ost s a t i s f a c t o r y.
81 x 13 E 20 (volts) 30 40 Figure 16. Hot Film Calibration
82 D is c u s s io n o f method The e x p e rim e n ta l method used i n t h i s s tu d y has some d i s t i n c t advantages o ver o th e r type v i s u a l i z a t i o n m ethods which i n j e c t o r d is p la c e a dye or use b l r e f r i n g e n t f l u i d. Even i f th e l a t t e r co u ld show s u f f i c i e n t d e t a i l to r e v e a l th e f in e s tr u c tu r e of f l u i d m otions ( t h i s a b i l i t y has y e t to be d e m o n stra te d ), th e f a c t t h a t th e f l u id s a re h ig h ly non-n ew tonian in c h a r a c te r in tro d u c e s a number o f u n c e r ta in t i e s and unknowns in to an a lre a d y complex problem. F or one th in g, th e mean v e lo c it y p r o f i l e cannot be a c c u ra te ly p re d ic te d f o r such f l u i d s. Dye o r p a r t i c l e i n j e c t i o n te c h n iq u es r e q u ir e a mechanism to i n j e c t th e m a te r ia l in to th e flow, and in th e w a ll re g io n s th e a f f e c t of such a mechanism can be a so u rce of co n ce rn. The p r e s e n t m ethod, of c o u rse, r e q u ir e s no i n j e c t i o n s in c e th e p a r t i c l e s m arking th e flow a re u n ifo rm ly d i s t r i b u t e d throughout th e f l u i d. T iis d i s t r i b u tio n p ro v id e s a n o th e r d i s t i n c t advantage o v e r dye i n j e c t io n m ethods. In th e s e l a t t e r the t r a c e r f l u i d i s i n je c te d a t a p o in t o r lin e, and th e f l u i d m otions cause the t r a c e r to sp re ad and assume v a rio u s c o n fig u r a tio n s. From th e s e conf i g u r a t io n s, in fo rm a tio n concerning th e f l u i d m otion i s deduced. The d i f f u s i o n and sp re ad o f th e dye i s an u n s te a d y s t a t e p ro c e s s. W hile i t m ight s a t i s f a c t o r i l y d e lin e a te th e f l u i d m otions in a s te a d y - s ta te flo w, f o r tu r b u le n t flow i t i s l e s s s a t i s f a c t o r y. T his i s e s p e c i a l l y tr u e in th e w a ll re g io n where th e f l u i d m otions e x h ib it l o c a l l y a d i s t i n c t
u n ste a d y s t a t e n a tu re beyond t h a t o f th e q u a s i- s te a d y s t a t e t u r b u le n t flo w. I n t h i s re g io n, th e com b in atio n o f a d e v e lo p in g dye f i e l d w ith a d e v e lo p in g v e lo c it y f i e l d compounds th e d i f f i c u l t y o f i n t e r p r e t a t i o n. A nother f a c t o r i s th e uneven d i s t r i b u t i o n o f dye a f t e r developm ent has proceeded f o r a tim e. 01113 le a v e s h ig h dye c o n c e n tra tio n s in a re a s of low v e lo c it y and d e p le te s th e dye i n th e a re a o f h ig h v e lo c it y. Thus th e m otions of th e f l u i d in th e h ig h v e lo c it y re g io n s a re n o t m arked. W ith th e u n ifo rm ly d i s t r i b u t e d p a r t i c l e s o f th e p r e s e n t stu d y b oth o f th e s e d isa d v a n ta g e s a re rem oved. In a d d itio n th e p a r t i c l e s p e rm it a more d e t a i l e d stu d y o f th e f i n e s tr u c tu r e because th q r mark v e ry sm a ll elem en ts o f f l u i d and n o t la rg e re g io n s as dye d o e s. F in a lly, because th e p a r t i c l e s a re n o t se g re g a te d o r d i s s i p a te d w ith tim e, th e y p e rm it th e stu d y o f a d e v e lo p in g m otion o ver a lo n g e r p e rio d o f tim e th a n do i n j e c t i o n m ethods. F or u n ste a d y s t a t e flo w, t r a c e r s I n je c te d a t a p o in t produce s tr e a k lin e s w hich d e fin e n e it h e r s tre a m lin e s n or th e p a th s of in d iv id u a l f l u i d e le m e n ts. The p a r t i c l e s, bein g d i s t r i b u t e d and m arking l o c a l f l u i d e le m e n ts, d e fin e th e s e p a th s and th u s a re p a th l i n e s. OSiis i s a fu n d am en tal d i f f e r e n ce, and a lth o u g h f o r sim ple u n ste a d y flow s s t r e a k l i n e s, s tr e a m lin e s, and p a th lin e s may be c a lc u la te d from one a n o th e r and a knowledge of th e v e lo c it y f i e l d, f o r u n ste a d y tu r b u le n t m otion t h i s i s im p o s sib le.
84 Methods o f f ilm a n a ly s is A ll a n a ly s e s o f th e f l u i d m otions were made from th e m otion p ic tu r e film s because image q u a l i t y was l o s t d u rin g p r i n t i n g. The m otion p ic tu r e s to be an aly zed were s e le c te d s o l e l y on the b a s is o f image q u a l i t y w ith o u t re g a rd to co n t e n t. T his p re lim in a ry sc re e n in g was n e c e s s a ry because i t was f e l t t h a t i f film s o f w id e ly d i f f e r e n t q u a l i t y were u sed, th e re would be a s tro n g p o s s i b i l i t y o f a t t r i b u t i n g c e r t a i n o b s e rv a tio n s to flo w b e h a v io r when in a c t u a l i t y th e y were due o n ly to th e f a i l u r e o r a b i l i t y to see som ething because o f a poor o r good im age. Only film s o f good, com para b le q u a l i t y were used i n th e d e ta il e d a n a ly s e s. For a n a ly s is, th e film s were p r o je c te d by a m otion a n a ly s is p r o je c to r o n to a sc re e n r u le d in to a r e c ta n g u la r g r i d. speed and d i r e c t i o n o f p r o je c tio n co u ld be c o n tr o lle d. 03ie The p r o je c te d image m ag n ifie d the film image by 93X so t h a t th e film s ta k e n a t 4.3X showed th e w a ll r e g io n m ag n ifie d 400X on th e s c r e e n. The in c re a s e in m a g n ific a tio n by th e p r o j e c t o r made th e o b s e rv a tio n s and m easurem ents e a s i e r by r e v e a lin g a l l t h a t was on th e film on an expanded s c a l e. I t co u ld n o t, o f c o u rse, do more th a n t h i s, so i n a r e a l se n se th e im p o rta n t m a g n ific a tio n was th e one a t w hich th e film s were ta k e n. T his one s e t s th e l im i ts on c o n te n t. The r u l in g s on th e s c re e n were drawn to th e s c a le o f th e m ag n ified image so t h a t each l i n e o f th e g r id c o rre sp o n d e d to a g iv e n dim ension o f th e w a ll r e g io n. To be c e r t a i n t h a t th e p ro p e r
m a g n ific a tio n and alig n m en t were used f o r a l l a n a ly s e s, th e g r id was marked w ith re fe r e n c e l i n e s w hich co rre sp o n d e d to 85 m arks on a c a l i b r a t i o n f i lm. T h is film c o n ta in e d an image o f a g r id where th e sp a c in g betw een l in e s was a c c u r a te ly m easured w ith a m icroscope equipped w ith a m icrom eter e y e p ie c e. By a lig n in g th e s c r e e n c a l i b r a t i o n m arks w ith th e c o rre sp o n d in g m arks on th e p r o je c te d image of th e c a l i b r a t i o n f ilm, p ro p e r m a g n ific a tio n o f th e p ro je c te d image was a t t a i n e d. Hie p r o j e c to r was a d a p te d to count e l e c t r i c a l l y th e number o f fram es of film p r o je c te d. T his was done by i n s t a l l i n g a m in ia tu r e m ic ro sw itc h under the f ilm advance s p ro c k e t w heel and c o n n e c tin g i t th ro u g h a sw itc h to an e l e c t r i c im pulse c o u n te r. As th e sp ro c k e t w heel tu rn e d, i t opened and c lo s e d th e m ic ro sw itc h one tim e f o r each fram e. The sw itc h in th e c o u n te r c i r c u i t was n o rm ally open, so th e c o u n te r d id n o t b e g in c o u n tin g u n t i l i t was c lo s e d, and sto p p ed when i t was r e l e a s e d. H iis a b i l i t y to count fram es was n e c e s s a ry f o r th e d e te rm in a tio n o f r e a l tim e as opposed to p r o je c tio n tim e which was much slo w e r. The c o u n te r was p e r i o d i c a l l y c a l i b r a t e d by u sin g a s tro b o ta c to m easure the sp ro c k e t w heel r e v o lu tio n s. As was m entioned i n th e cam era d e s c r i p t io n, tim in g m arks, which ap p ea re d as d i s t i n c t d a rk s tr e a k s, were a u to m a tic a lly im p rin te d on th e f ilm m argin a t 120 m a rk s/se c o n d. By m easuring th e number o f fram es o f f ilm covered by th e tim -
86 in g m ark one could c a lc u la te the film in g speed in fra m e s / seco n d. To f a c i l i t a t e t h i s c a lc u la tio n, th e le n g th of th e mark was m easured, and knowing t h a t a frame m easured 7*6 mm from c e n t e r l i n e to c e n te r lin e of a d ja c e n t sp ro c k e t h o le s, th e fram ing speed was c a lc u la te d as fo llo w s fram es/seco n d = 00833 Then by co u n tin g the number o f fram es d u rin g w hich a p a r t i c u l a r e v e n t o c c u rre d, one could c a lc u la te th e r e a l tim e o f o c c u rre n c e. T his proved to be an e x c e lle n t means o f tim in g ev en ts of v e ry s h o rt d u r a tio n because the h ig h -sp e ed photography caused even th ese e v e n ts to a p p ear over a la rg e number of fram es, v ery seldom le s s th a n 20 and u s u a lly m ore, and th e low -speed p r o je c tio n p e rm itte d the e v e n t to be seen and th e fram es a c c u r a te ly co u n ted. A ll of th e tim ed e v e n ts d e s c rib e d in l a t e r s e c tio n s were m easured by t h i s m ethod. Among th e most im p o rta n t m easurem ents made a re th o se o f p a r t i c l e v e l o c i t i e s and t r a j e c t o r i e s. In each o f th e camera view s, b u t in p a r t i c u l a r th e w a ll view, th e m otions o f p a r t i c l e s o r f l u id elem ents a c ro s s th e p r o je c tio n g r id was q u ite r e a d i l y d eterm in ed. In many c a se s th e p a r t i c l e s e x h ib ite d a s t r a i g h t o r only s l i g h t l y curved t r a j e c t o r y, so t h a t by re c o rd in g the g r id c o o rd in a te s a t th e beginning and end o f a p a r t i c u l a r movement, and co u n tin g th e fram es e la p se d, the v e lo c ity o f the p a r t i c l e as w e ll as th e t r a j e c t o r y co u ld be c a lc u la te d. This p ro cedure n e g le c ts th e th re e d im e n sio n al movement of th e p a r t i c l e, i. e., movement alo n g th e l in e of
87 s i g h t, and so u n d e re s tim a te s th e v e lo c it y i n m ost c a s e s. S ince some e s tim a te o f th e e x te n t o f t h i s th re e d im e n sio n a l movement i s a v a ila b le from th e two view s, th e p o t e n t i a l e r r o r can be e s tim a te d. T his i s done in Appendix I I where th e method o f c a l c u l a t i o n i s a ls o p re s e n te d. The o b s e rv a tio n and m easurem ent o f t r a j e c t o r y and u r o r Uq f l u c t u a t i o n s i s g r e a t l y enhanced by th e f a c t t h a t th e c a r r ia g e moves w ith th e flo w. T his movement re d u c e s the r e l a t i v e m otion betw een th e cam era and th e lo c a l mean a x i a l v e lo c ity, and th e a p p a re n t a x i a l v e l o c i t y i s o f te n of th e same m agnitude as th e up o r uq v e lo c it y. On th e film s th e s e m otions a p p ear as d e v ia tio n s from a x i a l flo w. S ince th e cam era moves w ith th e flow, th e s e d e v ia tin g p a r t i c l e s rem ain in view f o r a lo n g e r p e rio d o f tim e, and th e r e f o re t r a v e l a g r e a t e r o b se rv a b le d i s t a n c e. A lso, sin c e th e t r a j e c t o r y o r a n g le o f d e v ia tio n i s c a lc u la te d from th e r e l a t i o n tanoc = B/Aj where CC = a p p a re n t d e v ia tio n a n g le, B = u r o r u@, and A = Ux, any a p p a re n t d e c re a s e i n Ux in c re a s e s th e a n g le OC and makes th e d e v ia tio n s more v i s i b l e and more a c c u r a te ly m easured. The m otion o f the cam era i s m atched to th e l o c a l mean a x i a l v e l o c i t i e s a t s e le c te d y+ p o s i t i o n s. At th e s e p o s itio n s th e p a r t i c l e m otions have a p p ro x im a te ly z e ro r e l a t i v e v e l o c i t i e s, and a r e v e r s a l o f a p p a re n t d i r e c t i o n o f Ux v e lo c it y o c cu rs as one moves from th e w a ll tow ard t h i s y+ p o s itio n and th e n beyond i t. D uring any ru n, th e c a r r ia g e v e lo c it y
88 i s c o n s ta n t, so i f th e p o s i t io n o f zero r e l a t i v e v e lo c it y changes, i t m ust mean t h a t th e Ux v e lo c it y has changed. T his p e rm its some o b s e rv a tio n o f la rg e f l u c tu a tio n s in th e x com ponent, b u t g e n e r a lly th e s e f l u c t u a t i o n s a re n o t as r e a d i l y observed o r m easured as u r o r u q. O ther p a r t i c u l a r m ethods o f a n a ly s is a re d is c u s s e d d u rin g th e p r e s e n ta tio n of e x p e rim e n ta l r e s u l t s sin c e th e y a re more m ean in g fu l i n t h a t c o n te x t. In a d d itio n to th e v a rio u s m easurem ents, th e d i f f e r e n t film s were c a r e f u l l y and s y s te m a tic a lly a n aly zed f o r q u a l i t a t i v e in fo rm a tio n c o n c e rn in g th e f l u i d m o tio n s. The p o s i t i o n o f o c cu rren c e and dim ensions o f v a rio u s o c c u rre n c e s co u ld be r e a d i l y n o ted because o f the s c a le d g r id on which th e y were p r o je c te d. From th e o b s e rv a tio n s o f th e movement o f p a r t i c l e s s e p a ra te d by v a rio u s d is ta n c e s, some e s tim a te a s to th e s iz e o f th e d is tu rb a n c e s co u ld be o b ta in e d. I f a group o f p a r t i c l e s c o v e rin g a g iv e n re g io n o f th e g r id moved to g e th e r as a d e v ia tin g elem en t, i t could s a f e l y be assumed t h a t th e y w ere a l l p a r t o f a s in g le d is tu r b e d eddy. S ince th e s c a le o f th e s e d is tu r b a n c e s in th e w a ll re g io n was le s s th a n th e f i e l d o f view, t h i s method was q u ite e f f e c t i v e. O fte n more th a n one group o f p a r t i c l e s co u ld be o b serv ed w ith in th e f i e l d, each group moving d i f f e r e n t l y from th e cfcher, b u t a t th e same tim e. In o rd e r to d e te rm in e the p o s itio n o f o c cu rren c e o f any e v e n t from th e p r o je c te d im age, i t was n e c e s s a ry to
a l i g n th e w a ll o f th e p ip e as i t ap peared in th e image w ith 89 th e l in e c o rre sp o n d in g to th e w a ll on th e g r i d. Once t h i s was done a l l p o s itio n s r e l a t i v e to th e w a ll were f i x e d. Due to th e im p e rfe c t m atching o f th e in d ex o f R e f ra c tio n, a t h i n d a rk l i n e a p p e a rs i n th e m otion p ic tu r e s a t th e w a ll p o s i t i o n. T his was d e s c rib e d e a r l i e r and th e v e r i f i c a t i o n t h a t i t was th e i n t e r i o r w a ll was d is c u s s e d. E a r l i e r, some c a l c u la tio n s p e r ta in in g to th e e x te n t of th e e f f e c t o f th e r e f r a c t i o n o f th e l i g h t were p re s e n te d and d is c u s s e d. At t h a t tim e th e e s tim a te d a re a a f f e c te d had a w id th o f a p p ro x im a te ly 0.0 0 0 9 in c h e s, a lth o u g h th e p o s s i b i l i t y o f a somewhat le s s a f f e c te d a re a o f g r e a t e r w id th was a ls o d is c u s s e d. A check was made o f th e se e s tim a te s by i n s e r t i n g th e s c a le in to th e t e s t s e c tio n and ta k in g s t i l l p h o to g rap h s of i t. These p h o to g rap h s showed t h a t th e darkened a r e a e x is te d, b u t th e p resen c e o f th e m e ta l s c a le and su p p o rts in c re a s e d th e w id th and p a r t i c u l a r l y th e d e n s i ty o f th e d a rk l i n e. The s t i l l p h o tographs showed a v e ry d e n se, s h a rp ly d e fin e d l in e w h ile th e m otion p ic t u r e s w ith o u t th e s c a le showed a somewhat d if f u s e d a rk a r e a w ith in w hich p a r t i c l e s were s t i l l v i s i b l e. The l in e became d a rk e r as th e w a ll was a p p ro ach ed. T his i s in agreem ent w ith th e t h e o r e t i c a l c a l c u l a t i o n s. O ther s t i l l p h o to g rap h s were ta k e n under l ig h t i n g c o n d itio n s where th e r e f l e c t i o n s from th e m e ta l s c a le were a lm o st e lim in a te d, and th e s e showed no encroachm ent o f th e d a rk r e g io n i n to th e s u b la y e r. The s t i l l p h o to g rap h s m entioned e a r l i e r,
th e r e f o r e, r e p r e s e n t an extrem e case and a re u s e f u l i n s e t 90 t in g th e extrem e l i m i t s of th e e f f e c t of th e r e f r a c t i o n. I t m ust he em phasized t h a t in th e m otion p ic tu r e s o f th e w a ll a re a the r e f r a c t i o n e f f e c t d o es not approach th e s e l im i ts in s iz e o r d e n s ity. C a re fu l e x am in a tio n o f th e m otion p ic tu r e s showed t h a t p a r t i c l e m otions were v i s i b l e w ith in th e darkened r e g io n. T his r e g io n was alw ays very sm a ll compared to th e fram e w id th, and was v e ry d a rk o n ly w ith in an e x tre m e ly narrow l i n e a t th e w a ll- s id e of th e r e g io n. D uring the a n a ly s is, t h i s d a rk lin e was a lig n e d w ith the l i n e on th e g r i d c o r r e sponding to th e w a l l. The l a c k of a b s o lu te p r e c is io n in lo c a tin g th e w a ll cau ses some u n c e r ta in ty i n th e lo c a tio n, w ith r e s p e c t to th e w a ll, o f p a r t i c u l a r e v e n ts, b u t t h i s u n c e r ta in ty was d e f i n i t e l y l e s s th a n 0.002 in ch es which g iv e s a maximum u n c e r t a i n t y le s s th a n 2 u n its a t 5 0,000 Nrs, and c o n s id e ra b ly le s s th a n th a t a t low er R eynolds num bers. The e f f e c t o f r e f r a c t i o n was n o t p r e s e n t i n th e to p view, and i t a ffo rd e d an e x c e lle n t o p p o r tu n ity to examine th e s u b la y e r r e g io n. The o b s e rv a tio n s from t h i s view g e n e r a lly confirm ed those made in th e w a ll view.
EXPERIMENTAL Hot f ilm m easurem ents C h ro n o lo g ic a lly, th e m easurem ents w ith th e h o t film probe were made a f t e r th e p h o to g ra p h ic stu d y was co m p leted. T his was n e c e s s a ry s in c e th e use o f th e probe r e q u ir e d t h a t a h o le be d r i l l e d in to th e p ip e w a ll a t th e t e s t s e c tio n, and i t was e s s e n t i a l to a v o id th e p o s s ib le in tr o d u c tio n o f d i s tu rb a n c e s due to the p re se n c e o f th e h o le d u rin g th e p h o to g ra p h ic stu d y. In the d e s c r i p t i o n o f th e equipm ent i t was n o ted t h a t an e n tr y le n g th was d e sig n e d to p e rm it the e s ta b lis h m e n t o f f u l l y d ev elo p ed tu r b u le n t o r la m in a r flow w ith in th e t e s t s e c t i o n. S ince th e e n tr y le n g th a c t u a l l y used exceeded the c a lc u la te d v a lu e, th e assu m p tio n t h a t th e flo w was f u l l y d ev elo p ed seemed v a li d. N e v e rth e le ss when th e u n ste a d y n a tu re o f th e w a ll r e g io n was d isc o v e re d, i t was deemed o f v a lu e to m easure th e p r o f i l e to c o n firm th e assu m p tio n. No extrem e d e g re e s o f a c c u ra c y were a tte m p te d because e x te n s iv e m o d if ic a tio n o f th e equipm ent would have been r e q u ir e d to a t t a i n them. These re fin e m e n ts a re p r im a r ily o f im p o rtan ce when e x te n s iv e m easurem ents of tu r b u le n t c h a ra c t e r i s t i c s a re t o be made, and th e i n t e n t in t h i s c a se was to m easure a mean v e lo c it y p r o f i l e. 91
The s u c c e s s f u l a p p lic a tio n o f the h o t f ilm equipm ent i n a l i q u i d h y d ro carb o n system, and i t s e x c e ll e n t s t a b i l i t y 92 has been d is c u s s e d i n th e equipm ent s e c t i o n. The im portance o f such s ta b le o p e r a tio n f o r tu rb u le n c e m easurem ents may be e s tim a te d by re a d in g any o f th e a r t i c l e s where such m easurem ents i n l iq u i d system s have been a tte m p te d. A lthough th e c a l i b r a t i o n curve o b ta in e d f o r th e o v e r h e a t r a t i o o f 1.1 6 was n o t a s t r a i g h t l i n e, i t was s t a t i s - f a c t o r y f o r th e d e s ir e d m easurem ents. T ie c a l i b r a t i o n curve a p p e a rs in F ig u re 16. For a c c u ra te v e lo c it y f l u c t u a t i o n o r R eynolds s t r e s s m easurem ents, a s t r a i g h t l i n e c a l i b r a t i o n curve i s e s s e n t i a l. No e x te n s iv e e x a m in a tio n o f th e c o n d i tio n s re q u ire d to a t t a i n a s t r a i g h t lin e c a l i b r a t i o n curve was a tte m p te d in t h i s system, b u t i n one t r i a l u sin g an o v e rh e a t r a t i o o f 1.24 a much s t r a i g h t e r l i n e was o b ta in e d. U n fo r tu n a te ly as th e f l u i d te m p e ra tu re in c re a s e d the probe began to show v e ry e r r a t i c o p e ra tio n. T h is was n o t th e u s u a l d r i f t i n a p a r t i c u l a r d i r e c t i o n common to u n s ta b le o p e ra tio n i n l i q u i d sy stem s, b u t a sudden jump o f th e o u tp u t to a p a r t i c u l a r v a lu e a t w hich i t rem ained f o r a tim e, and th e n a jump i n th e o p p o site d i r e c t i o n to a new v a lu e. Tapp ing th e probe u s u a l ly re tu rn e d th e o u tp u t to th e o r i g i n a l h ig h v a lu e. W hile a c tin g in t h i s fa s h io n, the probe was exam ined under a m icroscope and t i n y b u b b les co u ld be se en sh ed d in g from i t s s u r f a c e. The f l u i d te m p e ra tu re a t t h i s
tim e was 41 C and s in c e i t has a t o i l i n g p o in t o f 87 C i t was concluded t h a t th e e r r a t i c b e h a v io r was due to i n c i p i e n t b o ilin g a t th e p ro b e. The low er o v e rh e a t r a t i o n ev er showed t h i s b e h a v io r. S ince th e system proved to be so s t a b le, f u tu r e e x p erim e n ts a re planned u sin g i t to m easure v a rio u s p r o p e r tie s of t u r b u le n t flo w, i. e., s p e c tr a, Reynolds s t r e s s e s... fc l i q u i d sy ste m s. F or th e s e s t u d i e s, a h e a t exchanger to c o n tr o l th e f l u i d te m p e ra tu re i s p lan n e d. The v e lo c it y p r o f i l e a c ro s s th e pipe was m easured f o r NRe = 21, 000. T his p r o f i l e i s p re s e n te d in F ig u re 17. A lso p re s e n te d in t h i s f ig u r e i s th e p r o f i l e p re d ic te d by P a ^ s (42) e q u a tio n a s g iv e n by Brodkey ( 1 ). S-M a >2 = _ 1-S M w ith S = 13.5 and M = 20. The m easured p r o f i l e i s u n m ista k a b ly t h a t o f f u l l y t u r b u le n t flow and a g re e s re a s o n a b ly w e ll w ith th e p r e d ic te d p r o f i l e. The d i f f e r e n c e s, e s p e c i a l l y in th e w a ll a re a, m ost l i k e l y a r i s e from th e f a i l u r e to c o r r e c t f o r th e p re se n c e of th e w a ll and p o s s ib le p o s itio n in g e r r o r s. The fiim le n g th o f th e probe i s 0.039 in c h e s, and t h i s i s e q u a l to n e a r ly o n e -h a lf th e s u b la y e r th ic k n e s s under th e flow c o n d itio n s, so t h i s to o c o n tr ib u te s to th e d i f f e r e n c e.
94 1.0.8 max.6.4 calculated profile (Pai,42) o present data < _ to outer wall present data Q_to inner wall 0 0 2.4 Figure 17. r/r 6 8 1.0 Mean Velocity Profile
95 P o s itio n in g e r r o r s can e a s i l y a r i s e b ecause, as was e x p la in e d in th e equipm ent s e c tio n, a com bination of o p t i c a l and d i r e c t m easurem ents were re q u ire d to d eterm in e th e lo c a tio n of th e p ro b e. The d a ta p o in ts f o r p o s itio n s on e i t h e r s id e o f th e proposed p ip e c e n te r lin e show a u n ifo rm ity i n t h a t each s e t f a l l s alm o st e x c lu s iv e ly on o p p o site s id e s of th e p re d ic te d c u rv e. I f one supposes t h a t th e o r i g in a l m easurem ent of probe placem ent was s l i g h t l y i n e r r o r, a c o r r e c tio n f o r t h i s e r r o r would s h i f t each s e t o f p o in ts tow ards one a n o th e r and in to congruence w ith the p re d ic te d c u rv e. Even w ith o u t any a tte m p t a t c o rr e c tio n, the m easured p r o f i l e s a t i s f i e s th e o r i g i n a l i n t e n t. I t e s ta b lis h e s th e f a c t t h a t th e flow i s f u l l y tu rb u le n t i n the t e s t s e c tio n. S im u lta n eo u sly w ith the p r o f i l e m easurem ents d a ta were ta k e n f o r d e te rm in in g the ro o t mean sq u are (rm s) v alu e o f th e ux f l u c t u a t i o n. In t h i s c a lc u la tio n, however, th e la c k o f a s t r a i g h t lin e c a l i b r a t i o n curve o f the o u tp u t v o lta g e E v e rsu s v e lo c it y p re se n te d a problem. The r e l a t i o n f o r d e te rm in in g u^. from th e re a d in g I o f th e rms m eter i s ux A ^ i 1 where A i s th e s lo p e of the c a l i b r a t i o n curve and ^ i s a c a l i b r a t i o n c o n s ta n t f o r the rms m e te r. W ith a curved l i n e, o f c o u rse, th e slo p e i s c o n tin u a lly ch an g in g. However, i f one i s w illin g to a c c e p t c e r t a i n in a c c u ra c ie s th e d i s t r i b u t i o n
o f w ith p o s itio n can s t i l l be o b ta in e d. The rms m e te rin g c i r c u i t m easures f l u c t u a t i o n s ab o u t th e mean v a lu e E which 96 i s known in t h i s case f o r a l l c o rre sp o n d in g I v a lu e s. From t h i s know ledge, the p o s i t io n on th e c a l i b r a t i o n curve i s fix e d and th e slo p e A a t t h a t p o in t may be d e term in ed g r a p h i c a l l y. T his pro ced u re can be re p e a te d f o r a l l I v a lu e s. Of c o u rs e, th e g r a p h ic a l d e te rm in a tio n o f a s lo p e i s s u b je c t to la rg e p o s s ib le e r r o r s, but f o r t u n a t e l y i n t h i s c a se the slo p e i s changing o n ly g r a d u a lly i n th e a re a o f i n t e r e s t. I f one does n o t p la c e to o g r e a t an em phasis on th e a b s o lu te m agnitu d e s o b ta in e d, th e c a l c u l a t i o n i s c e r t a i n l y w orth d o in g. The r e s u l t i n g cu rv e a p p e a rs in F ig u re 18 alo n g w ith the s i m il a r m easurem ents by L au fer (3 1 ), Lee (3 2 ), and Cohen (3)» Each o f th e se l a t t e r was f o r p ip e flow a t 41,000 Nr 8. No d a ta a re a v a ila b le f o r NRe = 2 0,0 0 0, b u t L au fer a ls o m easured the d i s t r i b u t i o n a t 410,000 NRe and the r e s u l t s i n d ic a t e o n ly a sm all e f f e c t on th e cu rv e s due to Reynolds num ber. L a u f e r 's d a ta a re f o r a i r w h ile L e e 's and C ohen's a re f o r w a te r, and L e e 's i s a s in g le ru n. F or th e m easurem ents i n w a te r, se v e re problem s w ith probe s t a b i l i t y were e x p e r i enced and n e i t h e r Lee n o r Cohen p la c e d a g r e a t d e a l o f c o n f i dence i n th e m easurem ents as a r e s u l t o f t h i s. The agreem ent betw een th e m easured cu rv e and L a u f e r 's d a ta i s r e a s o n a b le. The c u rv e s c e r t a i n l y show th e same g e n e r a l shape and in c r e a s e i n valu e a s th e w a ll i s a p p ro ach ed. The a b s o lu te v a lu e s d e p a rt from L a u f e r's as th e w a ll i s app ro ach ed, b u t th e o rd e r
97 2.0 1.6 / J y" x( > r / s u / u 1.2 p - 0.8 0.4 c5 presen t data N =21500 < Re 1 Loufe r (31) > Cohen (3) ( > Lee (3 2) 0 0 2.4.6.8 1.0 r /R Figure 18. u '% Distribution
98 o f m agnitude i s th e same. B ecause o f th e r e l a t i v e s iz e o f th e probe and su b la y e r th ic k n e s s, no a tte m p t co u ld be made to m easure th e f l u c t u a t i o n s v e ry n e a r th e w a ll as L au fe r d id i n a i r. The com parison o f th e m easurem ents by L au fe r i n a i r w ith th e p re s e n t m easurem ents in a l i q u i d i s a c c e p ta b le p ro v id ed th e R eynolds number s i m i l a r i t y i s t r u e. There i s no re a so n f o r n o t b e lie v in g t h a t i t i s so, and w ith s ta b le probe o p e ra tio n i n l iq u id s th e v a l i d i t y can be r ig o r o u s ly t e s t e d. W ith th e same wedge probe as was used above, in p o s i t i o n a t a p p ro x im a te ly th e pipe c e n t e r l i n e, th e o u tp u t s ig n a l was exam ined on a spectrum a n a ly z e r f o r ev id en ce o f p e r io d ic i t y. I n t i a l l y a wide fre q u e n c y span was exam ined, and when i t showed no r e g u l a r i t y, narrow fre q u e n c y spans were exam ined. In p a r t i c u l a r th e low er bands of th e o rd e r o f th e fre q u e n c y o f o c cu rren c e o f w a ll re g io n e j e c t i o n were exam ined. A lso, m u ltip le s o f th e p u ls a tio n s which m ight o r i g in a te w ith in th e c e n t r i f u g a l pump were scan n ed. In a l l c a se s no r e g u la r p e r i o d i c i t y was o b se rv e d. The o u tp u t ap p eared to be comp l e t e l y random. A second probe, d e s c rib e d e a r l i e r as a s u rfa c e probe, was p o s itio n e d w ith th e f ilm f lu s h w ith th e in n e r w a ll o f th e p ip e. T his probe i s p a r t i c u l a r l y s e n s i t i v e to f l u c t u a t i o n s norm al to th e w a ll, and i t was used to d e te c t any r e g u la r p e r i o d i c i t y o r i g in a ti n g from m ec h an ica l so u rc e s which m ight in tr u d e upon th e w a ll a r e a. None were d e te c te d. The probe
99 was a ls o used i n an a tte m p t to o b serve th e e f f e c t s o f th e e j e c t i o n p ro c e ss b u t t h i s was u n s u c c e s s fu l. T his i s not s u r p r is in g s in c e th e e j e c t i o n p ro c e ss i s random i n n a tu re and any a tte m p t to d is c e r n such e v e n ts a g a in s t a b a s i c a l l y random background i s n o t l i k e l y to be s u c c e s s f u l. In a d d i t io n, l a t e r a n a ly s is o f th e m o tio n p ic tu r e s showed t h a t th e e j e c t i o n p ro c e ss a t NRe = 20,000 d id n o t p e n e tr a te to the w a ll v e ry o f te n so even th e e x p e c te d h ig h i n t e n s i t y p u lse could n o t be o b serv ed v e ry o f te n. In a d d itio n to v is u a l o b se rv a tio n s o f th e cathode r a y tu b e sc re e n o f the spectrum a n a ly z e r, tim e exposure p h o to g rap h s were ta k e n o f the sc re e n w ith a s ix te e n second sweep p e rio d and a f u l l s c a le w id th of 0-20 c p s. T his i s a p p ro x im a te ly th e fre q u e n c y o f e j e c t i o n s. N othing which c o u ld be r e l a t e d to th e e j e c t i o n e v e n ts was o b se rv ed. In summary, th e h o t film e x am in a tio n produced th re e v a lu a b le r e s u l t s. I t e s t a b l is h e d th e p resen c e o f a f u l l y d ev elo p ed tu r b u le n t flow in th e t e s t s e c tio n, i t produced an u^ d i s t r i b u t i o n w hich a g re e d w ith o th e r p u b lis h e d d a ta, and i t d e m o n stra te d t h a t the f l u i d d id n o t p o sse ss any r e g u la r p e r i o d i c i t y such as m ig h t a r i s e from m ech an ical v i b r a t i o n s. o f w a ll In the n e x t s e c tio n a d e ta il e d d e s c r i p t io n o f th e f l u i d m otions in th e w a ll r e g io n w i l l be p re s e n te d. These d e s c r ip tio n s a re th e r e s u l t o f e x te n s iv e ex am in a tio n s of
numerous m otion p ic t u r e s ta k e n of d i f f e r e n t flow c o n d itio n s and from d i f f e r e n t view s. S ince th e d e s c r i p t io n o f th e m otions i s q u ite com plex, each s te p o f th e p ro c e ss i s d e s c rib e d i n d e t a i l s e p a r a te ly and in th e o rd e r i n w hich i t o c c u rre d. A d d itio n a lly, the o b s e rv a tio n s from each d i f f e r e n t cam era view a re d e s c rib e d s e p a r a te ly, a lth o u g h th e y a re, o f c o u r s e,d e s c r ip tio n s of th e same e v e n ts seen from a d i f f e r e n t p o s i t io n. T his e n a b le s the r e a d e r to be o r ie n te d to the p a r t i c u l a r a d v an tag e s and d isa d v a n ta g e s of th e d i f f e r e n t view s, and th e re b y p e rm its a more m ean in g fu l and c r i t i c a l i n t e r p r e t a t i o n o f th e d e s c r i p t io n s. W hile t h i s form at r e s u l t s in a c l e a r e r, more d e ta il e d d e s c r i p t i o n o f th e i n d i v id u a l o c c u rre n c e s, i t n e c e s s a r il y p re s e n ts a somewhat d i s j o in t e d p ic tu r e o f th e e n t i r e p ro c e s s. T his s e c tio n t h e r e fo re i s d e sig n ed t o give to th e re a d e r a v e ry b r i e f, unencum bered, o v e r - a l l view in to which th e more d e ta il e d d e s c r ip tio n s may be p laced i n t h e i r p ro p e r p e r s p e c tiv e. A ll t h a t w i l l be d e s c rib e d h e re and e lsew h e re i s much c l e a r e r when seen i n the m otion p i c t u r e s, and th e r e f o r e a m otion p ic tu r e made up o f s e l e c ti o n s from th e o r i g i n a l film s i s a v a ila b le f o r lo a n. The s in g le m ost im p o rta n t f e a tu r e of th e w a ll r e g io n ( 0 ^ y + S 35) in f u l l y developed tu r b u le n t flo w i s th e f a c t t h a t i t i s p e r i o d i c a l l y d is tu r b e d by th e e j e c t i o n o f d i s c r e te f l u i d e le m e n ts from th e w a ll a r e a outw ard tow ard th e c e n te r of th e p ip e. These e je c t i o n s a re v e ry l o c a l e v e n ts,
101 and occur random ly In both space and tim e. The e j e c t i o n of th e s e low Ux v e lo c it y elem en ts in to re g io n s o f much g r e a te r UY v e lo c it y cau ses tu rb u le n c e to be g e n e ra te d, and t h i s in tu r n d is tu r b s th e e n t i r e w a ll re g io n, even to th e w a ll i t s e l f. The e x is te n c e of th e s e e v e n ts means t h a t th e f u l l y developed tu r b u le n t flow i n th e w a ll re g io n i s n o t in a q u a s i s t e a d y - s t a te c o n d itio n but in f a c t e x h ib its a l o c a l l y u n ste ad y n a tu re which ta k e n as an av erag e produces th e s t e a d y - s t a te n a tu re of tu r b u le n t flo w. The a c t u a l e je c t i o n o f f l u i d i s o n ly a p a r t o f a sequence o f e v e n ts which to one degree o r a n o th e r ap pear w ith the e j e c t i o n in a d e f i n i t e o rd e r. Of cou rse th e re a re v a r ia tio n s of th e sequence and a l l o f th e s te p s do n o t appear a l l o f th e tim e n o r in th e e x a c t fa s h io n d e s c rib e d, b u t on th e average i t proceeds as f o llo w s. F i r s t th e f l u i d i n a r e l a t i v e l y sm a ll re g io n n e a r the w a ll e x p e rie n c e s a d e c e le r a tio n o f th e l o c a l mean a x i a l v e lo c i t y. T his g e n e r a lly occurs i n th e y+ span o f 0 ^ y* ~ 35 and as such co u ld be i n te r p r e t e d as a th ic k e n in g o f th e su b l a y e r. T his i s fo llo w ed by the e n tr y in to th e re g io n from upstream o f a la rg e mass o f f l u i d which p o sse sse s th e s te a d y - s t a t e lo c a l mean a x ia l v e lo c ity. This f l u i d ten d s to a c c e le r a te the r e ta r d e d f l u i d in the re g io n, b u t because i t does not e x te n d a l l th e way to th e w a ll i t o n ly succeeds in c r e a tin g a re g io n o f h ig h sh e a r a t th e boundary betw een i t and the r e ta r d e d f l u i d, lliis i s q u ic k ly fo llo w ed by th e
102 e je c t i n g o f a low Ux v e l o c i t y f l u i d elem ent outw ard from th e w a ll in to th e h ig h v e l o c i t y re g io n. The r e s u l t i n g i n t e r a c t i o n o f th e s e f l u i d stre am s cau se s a g r e a t amount o f c h a o tic m o tio n which sp re a d s b oth outward and w allw ard. T his i s th e n fo llo w ed by a mass o f f l u i d e n te r in g from u p stream w ith a g r e a t e r Ux v e lo c it y th a n th e i n t e r a c t i n g f l u i d. T his mass sweeps th e f i e l d o f th e f l u i d and r e - e s t a b l i s h e s th e l o c a l mean a x i a l v e lo c ity p r o f i l e. The b a s ic c h a r a c te r o f th e p ro c e ss i s n o t a f u n c tio n o f R eynolds number, b u t th e fre q u e n c y o f o c c u r r e n c e and i n t e n s i t y i s. The c h a r a c te r o f th e d is tu r b e d m otions changes as th e d is ta n c e from th e w a ll i s in c r e a s e d. By a y+ = 70 p o s itio n, th e c h a r a c t e r i s t i c s o f th e w a ll re g io n a re e s s e n t i a l l y l o s t and th e c h a r a c te r o f th e o u te r r e g io n has a s s e r te d i t s e l f. The w a ll r e g io n m otions a re of sm a ll s c a le, l o c a l i n n a tu r e, and e x h ib i t a b ru p t, in te n s e movements. The o u te r r e g io n has a l a r g e r s c a le w ith le s s a b ru p t movements and le s s i n t e n s i t y o f f l u c t u a t i n g m o tio n s. No e je c t i o n s o r ig in a te anywhere b u t w ith in th e w a ll re g io n. T h e e j e c t i o n p ro c e ss as a f u n c tio n o f R eynolds number The m otion p ic t u r e s o f th e w a ll a re a f o r R eynolds numbers o f 2300 to 5 0,0 0 0 were exam ined f o r ev id en ce o f th e e j e c t i o n p ro c e ss and to d e te rm in e th e e f f e c t o f Reynolds number on th e c h a r a c te r and fre q u e n c y o f i t s o c c u rre n c e. In
103 a l l th e p h o to g rap h s th e w a ll view was used a t a m a g n ific a t i o n o f 2X o r 4.3X. For NRe = 2300 th e v e lo c ity p r o f i l e e x h ib ite d in th e m otion p ic tu r e s showed o n ly a v e ry g ra d u a l change in l o c a l mean a x i a l v e lo c it y from th e w a ll o u t to th e edge o f th e f i e l d of view, a d is ta n c e of y+ = 22. S ince th e tu r b u le n t p r o f i l e would e x h ib i t a much s te e p e r g r a d ie n t th a n t h i s, th e flow was assumed to be la m in a r. A lso, th e re i s a com plete absence of any d e p a r tu re s from th e smooth flow p a r a l l e l to the w a ll. At NRe = 5360 th e tu r b u le n t v e lo c it y p r o f i l e i s q u ite e v id e n t. L ocal v e l o c i t i e s were checked by th e tim in g method d e s c rib e d i n an e a r l i e r s e c tio n, and were found to ag ree w e ll w ith v e l o c i t i e s p re d ic te d by P a i 's r e l a t i o n s f o r the v e lo c it y p r o f i l e. T his flow d is p la y s th e f i r s t ev id en ce of th e u n ste a d y n a tu re o f th e w a ll re g io n. I t a p p e a rs as an o c c a s io n a l d e c e le r a t i o n - a c c e le r a t i o n sequence o f th e lo c a l mean a x i a l v e lo c it y. No s i g n i f i c a n t d e p a rtu r e s from th e a x i a l flow were o b serv ed, but g e n e r a lly the flow ap p eared more a g it a t e d th an p re v io u s ly. Upon in c r e a s in g th e Reynolds number to 11,280 th e d e c e le r a t i o n - a c c e le r a t i o n sequence o f th e l o c a l mean a x i a l v e lo c it y was o b served to occur w ith in c re a s e d freq u e n c y, ab o u t once p e r second on th e a v erag e, and was more c l e a r l y d e fin e d th a n in e a r l i e r c a s e s. The d e c e le r a tio n p ro c e ss i s th e g ra d u a l rep la ce m e n t, w ith in a l o c a l a re a near* th e w a ll, o f
104 f l u i d, which p o ss e s se s th e l o c a l mean a x i a l v e lo c it y o f f u l l y tu r b u le n t flow, by f l u i d of a red u ced a x i a l v e lo c ity. T his l a t t e r e n te r s w ith th e mean flow from u p stream, and u s u a lly does n o t a f f e c t th e f l u i d below y+ = 3* This r e ta r d e d s t a t e p e r s i s t s f o r a b r i e f p e rio d and th e n i s p a r t i a l l y removed by the re a p p e a ra n c e from u p stream o f f l u i d having th e norm al l o c a l mean a x i a l v e l o c i t y. The m a jo r ity o f th e p a r t i c l e s a re moving a x i a l l y, b u t some few have s i g n i f i c a n t d e p a r tu r e s from the a x ia l in both d i r e c t i o n s. These c o n s t i t u t e th e f i r s t n o ta b le d e p a rtu r e s from p u re ly a x i a l flo w. At t h i s R eynolds number th e f i r s t e v id e n ce of an e f f e c t c a l le d "two la y e r v e lo c ity " o c c u rre d. T his i s th e o b se rv a t i o n o f two m asses o f f l u i d a t i d e n t i c a l r a d i a l p o s itio n s h av in g d i s t i n c t l y d i f f e r e n t a x i a l v e l o c i t i e s. W ith th e o p t i c a l system used, th e s e m asses co u ld be s e p a ra te d by a maximum d is ta n c e o f 0.0 2 7 in c h e s alo n g th e l in e o f s i g h t. T his phenomenon w i l l be d is c u s s e d i n g r e a t e r d e t a i l i n a l a t e r s e c tio n. When th e film s ta k e n a t NRe = 21,000 were s tu d ie d, the f u l l n a tu re o f th e w a ll r e g io n was r e v e a le d. The e n t i r e sequence of e v e n ts su rro u n d in g the e j e c t i o n p ro c e ss were re p e a te d a number o f tim es in e x c e lle n t d e t a i l. Here f o r th e f i r s t tim e was u n m ista k ab le e v id e n ce o f th e e j e c t i o n of f l u i d from th e w a ll re g io n outw ard, and th e su b seq u en t i n t e r a c t io n w ith th e mean flo w. The m a jo r ity o f e je c t e d elem en ts
o r ig in a te d i n th e re g io n 5 S y+ S 15* t u t some o r ig in a te d as 105 n e a r th e w a ll as y+ = 2.5 - The e v e n ts o c c u rre d a t random i n t e r v a l s, and betw een e v e n ts th e f l u i d i n th e r e g io n was s t i l l i n an a g i t a t e d s t a t e due p r im a r ily to th e e f f e c t s o f th e p re c e d in g e v e n t. D uring th e e a r l y s ta g e s of th e e v e n t p ro c e ss and th e e j e c t i o n i t s e l f, th e "two la y e r v e lo c ity " e f f e c t was o b se rv e d. Upon in c r e a s in g th e Reynolds number in s te p s to 5 0, 0 0 0, the a n a ly s is showed t h a t the changes which o c cu rred were n o t in th e b a s ic c h a r a c te r of th e e j e c t i o n p ro c e s s, b u t i n th e i n t e n s i t y and fre q u e n c y o f o c c u rre n c e o f th e s e e v e n ts. W ith each in c r e a s e in R eynolds number th e re was an in c r e a s e i n th e number and i n t e n s i t y o f e j e c t i o n e v e n ts, so t h a t by NRe = 52,000 th e e v e n ts o c c u rre d so o fte n and a t such c lo s e i n t e r v a l s t h a t even in th e p e rio d s betw een e v e n ts th e f l u i d was h ig h ly a g i t a t e d, and i t was e x tre m e ly d i f f i c u l t to d e term in e where one e v e n t ended and th e n e x t began. A lso, th e r e was an in c r e a s e i n th e i n t e n s i t y of th e c re a te d tu r b u le n c e, and th e r e f o r e th e e f f e c t was more c l e a r l y f e l t in th e re g io n s v e ry n e ar th e w a ll. I n i t i a l l y, i n o rd e r to a s s ig n a q u a n t i t a t i v e v a lu e to th e r e l a t i o n s h i p betw een fre q u e n c y o f o ccu rren ce and R eynolds number, an a tte m p t was made to count the in d iv id u a l e v e n ts which o c c u rre d d u rin g a g iv e n tim e p e rio d. H iis m ethod was s a t i s f a c t o r y f o r R eynolds numbers o f 20,000 o r low er, b u t above NRe = 3 0,0 0 0 th e d i f f i c u l t y o f s e p a r a tin g in d iv id u a l
106 e v e n ts from each o th e r and the In te rv e n in g f l u c t u a t i o n s became so g r e a t t h a t co n fid e n ce in th e co u n ts was g r e a t l y re d u c e d. I t was p o s s ib le to o b ta in w id e ly d i f f e r e n t co u n ts f o r the same m o tio n p ic tu r e s depending upon th e c r i t e r i a employed f o r s e p a r a tin g e v e n ts. S ince th e d i f f i c u l t y in c re a s e d w ith in c r e a s in g R eynolds number, th e re was no way to com pensate f o r the p o s s ib le e r r o r. In a l l c a se s i t was p o s s ib le to d u p lic a te a count w ith in re a s o n a b le l im i ts i f th e same f ilm sequence was viewed a number o f tim es in s u c c e s s io n. I f one r e tu rn e d to th e f ilm a f t e r an i n t e r v a l o f a week, th e o r i g i n a l co u n t could n o t im m ed iately be d u p lic a te d, b u t a f t e r a number of view ings one co u ld d u p lic a te i t w ith in th e same l im i ts as th e f i r s t t r i a l s. F or exam ple, one case a t NRe = 40,000 th e f i r s t count gave 18 e v e n ts and th e second 2 1. In o rd e r to p re v e n t an e r r o r due to a change i n c r i t e r i a over a p e rio d o f tim e, a l l th e film s used i n th e e v e n t c o u n t a n a ly s is w ere viewed i n sequence d u rin g a s in g le tim e p e rio d w ith two c o u n ts made i n s u c c e s s io n f o r each f ilm. T his f i n a l c o u n tin g was done, how ever, o n ly a f t e r th e film s had been c a r e f u l l y exam ined a l a r g e r number o f tim es to e s t a b l i s h a p ro p e r c r i t e r i a. The r e s u l t s a p p ea r in F ig u re 19. Each p o in t on th e g rap h r e p r e s e n ts th e r e s u l t s o f a s in g le f i lm. The in c r e a s e in th e number o f o c c u rre n c e s w ith R eynolds number i s u n m ista k ab le and c o n s i s t e n t. The r a t i o o f th e number o c c u rrin g a t Nr6 = 5 0,0 0 0 to th o se a t Nr6 = 20,000 i s
107 / C < sz 3 o o c a> > Ui CD O O - o o 0 10 20 NRe (thousands) 50 Figure 19. Event Frequency
108 a p p ro x im a te ly 5 /1. A ll co u n ts a re f o r a p p ro x im a te ly a s i x second i n t e r v a l o f r e a l tim e. Because o f th e d i f f i c u l t i e s e n c o u n te re d i n th e p re c e d in g m ethod o f a n a l y s i s, an a l t e r n a t e method o f o b ta in in g e s s e n t i a l l y th e same in fo rm a tio n was d e v is e d. An e l e c t r i c c o u n te r was used to count the number o f m otion p ic tu r e fram es i n w hich th e f l u i d in th e w a ll re g io n was s i g n i f i c a n tly d is tu r b e d. From t h i s count and th e knowledge o f th e a c t u a l number of fram es p e r second a t which th e f ilm was exposed, one co u ld d e te rm in e th e p e rc e n ta g e o f th e t o t a l photographed i n t e r v a l d u rin g which th e w a ll re g io n was s i g n i f i c a n t l y d is tu r b e d. In t h i s m ethod i t i s n o t n e c e s s a ry to s e p a ra te i n d iv id u a l e v e n ts i f th e y o v e rla p o r i f th e i n t e r vening d is tu r b a n c e s a re v e ry i n te n s e. I f th e y exceed a minimum i n t e n s i t y th e y a re in c lu d e d. I t i s n e c e s s a ry, how ever, to e s t a b l i s h a minimum f o r w hat c o n s t i t u t e s a s i g n i f i c a n t d is tu r b a n c e o f th e w a ll re g io n. There were n e a r ly alw ays some d e p a rtu re s from p u re ly a x i a l flow v i s i b l e in th e w a ll r e g io n. To in c lu d e each sm a ll f l u c t u a t i o n would d e f e a t the purpose o f th e a n a ly s is s in c e th e i n t e n t i s to r e l a t e th e m easurem ent to th e e j e c t i o n e v e n t and n o t i t s a f t e r e f f e c t s. E x te n siv e e x a m in a tio n o f th e film s p e rm itte d a low er l i m i t to be e s t a b l is h e d q u ite r e a d i l y s in c e th e i n t e n s i t i e s o f th e m o tio n d i r e c t l y co n n ected to th e e j e c t i o n e v e n t a re q u ite pronounced. To Improve on th e c o n s is te n c y of th e m easurem ents, th e film s were exam ined i n s u c c e s s io n o v er a
109 s in g le c o n tin u o u s p e rio d w ith two tim in g s g iv e n to each f ilm. The d u p lic a tio n o f r e s u l t s by the method was much g r e a t e r th a n th e p re c e d in g. For exam ple, i n one c a se a t NRe = 40,000 th e two tim in g s gave v a lu e s o f 55«2$ and 5 1. 7$. Good a g re e m ent betw een m easurem ents made a f t e r an i n t e r v a l o f weeks co u ld be o b ta in e d. F ig u re 20 shows th e r e s u l t s o f t h i s a n a l y s i s. Each p o in t i s th e av erag e o f two m easurem ents f o r a p a r t i c u l a r f ilm. The film s used were th e same ones exam ined i n the number c o u n t. As b e fo re, th e In c re a s e w ith R eynolds number i s u n m ista k ab le and c o n s i s t e n t. The w a ll r e g io n i s s i g n i f i c a n t l y d is tu r b e d a p p ro x im a te ly 16$ of th e tim e a t N^e = 2 0,000 and n e a r ly 68$ o f th e tim e a t NRe = 5 0,0 0 0. T his i s a r a t i o o f 4.3 / 1. Both th e r a t i o and th e g e n e ra l shape of th e c u rv e s show t h a t th e two methods a re in ag reem en t. The u n u s u a lly low v a lu e s a t NRe = 43,000 can p ro b a b ly be a t t r i b u t e d to the i n f e r i o r q u a l i t y of th e p h o to g rap h ic image on th e film used f o r th o se a n a ly s e s. T his p o o re r q u a l i t y co u ld e a s i l y have o bscured some o f th e s i g n i f i c a n t m o tio n. In summary, the a n a ly s is shows t h a t th e n a tu re o f th e e v e n ts i n th e w a ll r e g io n i s In d ep en d en t o f R eynolds number, b u t shows a s tro n g dependency on i t w ith re g a rd t o fre q u e n c y o f o c cu rren c e and i n t e n s i t y.
no 70 o Percent of Total Time Disturbed 60 50 40 30 20 o 8 <9 o o o o o o o o o 10 0 1 0 20 30 40 50 Npe (thousands) Figure 20. Disturbed Percentage
Ill D e ta ile d d e s c r i p t io n o f e v e n ts w a ll view In the d e s c r i p t io n s o f t h i s s e c tio n, th e cam era p o s i t i o n was t h a t d e s c rib e d as th e w a ll view In th e e x p e rim e n ta l p ro c e d u re s s e c tio n. I t would be o f v a lu e to th e r e a d e r to r e f e r to t h i s d e s c r i p t io n to p r o p e r ly o r i e n t h im s e lf b e fo re p ro c e e d in g. In the p re c e d in g s e c tio n s v a rio u s a s p e c ts o f f l u i d m otion in th e w a ll r e g io n were b r i e f l y d is c u s s e d, and a condensed d e s c r i p t io n o f the e j e c t i o n p ro c e ss was p re s e n te d. In t h i s s e c tio n th e d e t a i l s o f t h i s p ro c e ss w i l l be exam ined, and each s te p o f th e e v e n t w i l l be d is c u s s e d i n th e o rd e r of i t s o c c u rre n c e. I t m ust be r e c a l l e d t h a t the e j e c t i o n p ro c e ss i s b a s i c a l l y random in i t s n a tu r e, and th e r e f o r e th e fo llo w in g e v e n ts do n o t alw ays o c cu r e x a c tly as d e s c rib e d. At h ig h e r Reynolds numbers th e fre q u e n c y of o c cu rren c e and th e h ig h s t a t e o f a g i t a t i o n o f te n a c t to obscure o r e lim in a te c e r t a i n o f th e s t e p s. The e j e c t i o n of f l u i d elem en ts i s, how ever, th e p rim a ry f e a tu r e o f th e w a ll re g io n, and i t i s alw ays re c o g n iz a b le. What fo llo w s th e n i s a com posite p ic tu r e d e riv e d from a d e ta il e d e v e n t a n a ly s is o f numerous m otion p ic t u r e s ta k e n o f d i f f e r e n t flow c o n d itio n s. The n o te s of th e d e t a i l e d a n a ly s is o f each m otion p ic tu r e a re to o volum inous to p r e s e n t h e re, b u t th e y a re p re s e rv e d and c o u ld be exam ined to r e v e a l th e in d iv id u a l v a ria n c e s as w e ll as th e g e n e ra l c o n s is te n c y o f th e p ro c e s s.
112 D e c e le r a tio n. The f i r s t s te p o f th e p ro c e ss u s u a lly In v o lv ed a d e c e le r a t i o n o f th e l o c a l mean a x i a l v e l o c i t y o f th e f l u i d. The a re a o f f l u i d a f f e c te d was g r e a t e r th a n 0.0 9 5 in ch e s in le n g th ( t h i s i s maximum le n g th of f i e l d ), b u t the d is ta n c e from th e w a ll a f f e c te d was o f th e o rd e r o f th e fram e w id th o f O.O69 in c h e s. E vidence from o th e r so u rc e s i n d ic a t e s t h a t th e d im ension a f f e c t e d along th e l i n e o f s ig h t was of th e o rd e r of 0.0 2 7 in c h e s. Thus i n th e r and 9 dim ensions th e e v e n t was q u ite sm a ll and l o c a l in n a tu r e. The d e c e le r a t i o n e f f e c t was r e a l l y th e g ra d u a l re p la c e m e n t o f f l u i d p o s s e s s in g th e norm al l o c a l mean v e lo c it y w ith f l u i d from u p stre a m t h a t had a l o c a l mean a x i a l v e lo c it y o f s m a lle r m ag n itu d e. The a c t u a l e x te n t o f th e d e c e le r a t i o n v a rie d g r e a t l y from a b a re ly p e r c e p tib le d if f e r e n c e to c a se s where th e e n t i r e f i e l d above a p a r t i c u l a r y+ v alu e was moving i n e s s e n t i a l l y p lug flo w ( i. e., l i t t l e o r no v e lo c it y g r a d i e n t above y+ = 10 to edge of fram e) a t a reduced v e l o c i t y. The d isa p p e a ra n c e o f a v e lo c it y g r a d ie n t from th e r e g io n i s a s t r i k i n g e f f e c t s in c e i n norm al tu r b u le n t flow th e r e g io n p o ss e s se s a v e ry s te e p g r a d i e n t. The v e l o c i t i e s o f i n d i v i d u a l p a r t i c l e s w hich were r e p r e s e n ta tiv e o f th e p a r t i c u l a r re g io n o f flow were m easured f o r th e d e c e le r a tio n p e rio d and th e p e rio d p re c e d in g i t. These v e l o c i t i e s, m easured d u rin g a number o f d i f f e r e n t o c c u rre n c e s, a re p re s e n te d i n T able 2 alo n g w ith th e l o c a l mean a x i a l v e l o c i t i e s c a lc u la te d u sin g
113 TABLE 2 DECIERATION VELOCITY Run D e c e l C alcu D e c e l C alcu No. B efore e r a t i o n l a t e d D uring e r a t i o n l a t e d y+... T fc - -...TTv'" 164 4.11.095 5 ^.11.122 5.8.11.135 8.7.11.1 9 2 10.11.213 165 6.4.113. 146 8.7.113.1 9 2 6. 4-3 0 *.113.146-. 3 8 168 4.6.182.11 11.5.82.235 6.4.182.146 8.7.182.1 9 2 225 1 0.6.332.338 16.4.332.29 9.0.332.318 12.3*.332.379 1 2.3.332 379 224 7-4.332.278 18.5.432.46 7.4.117.2 7 8 9.0.262.318 30.45.55 12.3*.332 379 221 2 0.5 *.575.62 2 7.5.658.697 18*.6 0 5.5 8 6 223 9.5.46.42 16-21.46. 5 6 -.6 2 8 155 1 4.5.353.27 16.1 6 7.285 7.193.16 8.125.18 11.5.365.235 8.7.09.1 9 2 20.331.32 2.9.09.07 D enotes absence o f u su a l v e l o c i t y g r a d i e n t.
114 TABLE 2 continued B efore A D e c e le r a tio n % D uring D e c e le r a tio n A % 1 0 0 (Calc>.005 +58 -.0 1 2-9.8 -.0 2 5-1 8.5 -.0 8 2-43 -.0 3 3-2 2.6 -.1 0 3-4 8.4.0 7 2 +65 -.0 5 9-31.0 3 6 +24.7 -.0 3 3-2 2.6 -.0 0 6-1.8 -.2 6 7-70.024 + 7.5 -.0 5 3-2 2.5.084 +30 -.0 1 0-5.039 4 9.2 +.04 +13-8.08 +3 -.0 4 7-12.033 +20.6 -.0 3-6.5.130 +5 5.3 -.1 0 1-3 6.3.011 +3.4 -.0 5 6-1 7.6.02 +2 8.5 -.1 1-1 9.6 -.0 4 7-1 2.4 -.0 4-6.5 -.0 3-4 +.02 +3.4 -.1 0-1 7.9 -.1 7-27 -.1 1 8-4 1.4 -.0 5 5-2 9.4 -.1 0 2-53 A = Ux m easured - Ux c a l c u l a t e d.
P a i 's e q u a tio n. These l a t t e r a re, of c o u rs e, mean v e l o c i t i e s w h ile the m easured v e l o c i t i e s sire in s ta n ta n e o u s and in c lu d e th e tu r b u le n t a x i a l com ponent. One m ig h t be r e l u c t a n t, th e r e f o r e, to compare any o f the m easured v e l o c i t i e s w ith each o th e r o r th e c a lc u la te d to o b ta in e v id e n ce of d e c e le r a tio n, because one does n o t know j u s t w hat th e e f f e c t of th e tu r b u le n t component i s f o r any s in g le p a r t i c l e. The s i t u a tio n, how ever, i s n o t t h a t h o p e le ss because i t m ust be r e c a l l e d t h a t w h ile th e se m easurem ents a re f o r in d iv id u a l p a r t i c l e s, th e y a re r e p r e s e n ta t iv e of a n e n t i r e mass of p a r t i c l e s a l l o f which e x h i b i t th e same g e n e r a l v e lo c it y. T h e re fo re, w h ile no s in g le a b s o lu te v e lo c it y sh o u ld be c o n sid e re d too s tr o n g ly, th e p r o p e r tie s of the group as a whole can be s i g n i f i c a n t when compared to th e c a lc u la te d v a lu e s o r to th e o th e r m easured v a lu e s ta k e n as a w hole. A lso, o f c o u rse, th e p re se n c e of th e p l u g - li k e flow cannot be e x p la in e d as a r e s u l t o f a tu r b u le n t f l u c t u a t i o n o r an e r r o r in m easurem ent, but d e f i n i t e l y shows t h a t th e norm al tu r b u le n t p r o f i l e i s d i s t o r t e d by red u ced v e l o c i t i e s. Hie m otion p ic t u r e s make t h i s a b u n d a n tly c l e a r s in c e th e y p ro v id e th e c o n ti n u i ty o f m o tio n which p e rm its com parisons o f th e a d ja c e n t p e rio d s o f flow. R e fe rrin g to Table 2, i f th e m easured v e l o c i t i e s o f th e f l u i d which p rec ed e d the d e c e le r a t i o n a re compared w ith th e c a lc u la te d lo c a l mean v e l o c i t i e s i t i s found t h a t 71$ o f th e m easured v e l o c i t i e s were g r e a t e r to some d eg ree th a n th e c a l c u l a t e d. C o n v e rse ly, n e a r ly 91$
o f th e m easured v e l o c i t i e s of th e d e c e le r a tio n p e rio d were slo w e r th an th e c a lc u la te d lo c a l v e l o c i t i e s. S ince th e same m easuring pro ced u re was used i n b o th c a s e s, th e same e r r o r s i n th e m easurem ent a re l i k e l y to o c c u r. Yet f o r one p e rio d th e la rg e m a jo r ity o f v e l o c i t i e s a re g r e a t e r th a n the c a lc u la te d and f o r th e n e x t p e rio d the overw helm ing m a jo r ity o f th e m easured v e l o c i t i e s are s m a lle r th a n th e c a l c u l a t e d. A change o f such m agnitude cannot be a t t r i b u t e d to e x p e r i m e n ta l e r r o r. The d e p a rtu re s i n each group from th e c a lc u la te d a re n o t s u r p r is in g sin c e th e y a re in s ta n ta n e o u s v e l o c i t i e s and would be e x p e c te d to d i f f e r from th e a v e ra g e. The e r r o r s i n th e m easurem ent o f the v e l o c i t i e s u s u a lly a c t to produce v a lu e s which a re to o low (see Appendix 2 ). The m easurable p a r t o f th e e r r o r i s o n ly o f th e o rd e r of 3$ o r le s s o f th e t o t a l v e lo c it y, and w hile t h i s i s a f a c t o r i n c o n s id e rin g th e a b s o lu te v a lu e s o f the v e lo c it y i t c an n o t be used to e x p la in th e c o n s i s t e n t manner i n w hich th e v e lo c it y m easurem ents of th e o b serv ed d e c e le r a te d f l u i d f a l l below th o se of th e f l u i d v e l o c i t i e s su cceed in g i t. The t o t a l i t y o f e v id e n c e s u p p o rts the o b s e rv a tio n t h a t the d e c e le r a t i o n p e rio d i s a d e c re a s e i n th e mean a x i a l v e lo c it y w ith in a r a t h e r sm a ll a re a o f th e p ip e w a ll. The l o c a l mean a x i a l v e l o c i t i e s, f o r th e y+ p o s itio n s a t which th e r e ta r d e d flow v e l o c i t i e s were m easured, were c a lc u la te d f o r a lam in ar p r o f i l e d i s t r i b u t i o n. I t was found t h a t th e m agnitude o f th e r e ta r d e d flo w v e lo c it y was much g r e a t e r th a n t h a t w hich would
117 have e x is te d f o r a lam in ar p r o f i l e. The p a r t i c u l a r e f f e c t i s u s u a lly o f r a t h e r s h o r t d u ra tio n r e l a t i v e to th e e j e c t i o n s te p. A c c e le r a tio n. T his s te p in th e sequence of e v e n ts c lo s e ly fo llo w ed th e d e c e le r a tio n s te p. I t d em o n strated th e g r e a t e s t v a r i a t i o n in c h a r a c te r, b u t sin c e th e s e v a r ia n ts o c cu rred a t th is p a r t i c u l a r sta g e of th e developm ent, th e y a re c o n sid e re d under t h i s s e c tio n. These v a r i a ti o n s d id n o t c o r r e la te w ith any flow p a ra m eters, b u t seemed to occur q u ite random ly even to th e e x te n t t h a t two s u c c e ss iv e e v e n ts o c c u rrin g in the same e x p e rim e n ta l ru n could d i f f e r m arkedly a t t h i s s te p. This n a t u r a l l y causes some d i f f i c u l t y in d e s c rib in g i t s n a tu re, b u t sin c e i t g e n e r a lly appeared in two forms th e se w i l l be d e s c rib e d. Most f r e q u e n tly a la rg e mass o f f l u i d e n te re d the r e ta r d e d f i e l d from an upstream p o s itio n w ith an a x ia l v e lo c it y g r e a t e r th an t h a t of th e f l u i d w ith in the f i e l d. The d i r e c ti o n o f flow was g e n e r a lly p a r a l l e l to the w a ll o r a t a sm all angle d ir e c te d inw ards tow ards i t. U su a lly i t e n te re d th e f i e l d above a y+ = 15 p o s itio n and th e n p ro ceeded a c ro s s th e f i e l d. T his s te p was alw ays fo llo w ed v e ry q u ic k ly by th e e j e c t i o n s te p. Sometimes th e e j e c t i o n would o ccu r j u s t as th e f l u i d e n te re d th e f i e l d, w h ile a t o th e r tim es i t o c c u rre d a f t e r th e a c c e le r a tio n p ro c e ss was begun, b u t alw ays b e fo re the e n t i r e f i e l d was c o m p lete ly a c c e le r a te d.
118 When the f l u i d had a s l i g h t w allw ard t r a j e c t o r y i t d is p la c e d th e f i e l d f l u i d w allw ard as w e ll as a x i a l l y. Ihe i n s t a n tan eo u s v e l o c i t i e s o f r e p r e s e n ta tiv e p a r t i c l e s of th e e n t e r in g stre am were m easured f o r v a rio u s ru n s, and the r e s u l t s ap p ear i n Table 3» The g e n e ra l agreem ent of th e s e v e lo c i t i e s w ith th o se c a lc u la te d f o r the l o c a l mean v e lo c it y in d ic a te t h a t t h i s stre am of f l u i d may w e ll be th e norm al s t e a d y - s t a te tu r b u le n t v e lo c it y r e - e s t a b l i s h i n g i t s e l f. The a re a in v o lv ed in th e se movements was a t l e a s t th e s iz e of th e f i e l d of view (. 0 9 5 " x *065") and in d ic a tio n s were t h a t i t was c o n s id e ra b ly l a r g e r, e s p e c i a l l y i n th e a x ia l d i r e c t i o n. The e n tr y of t h i s stream in to th e r e ta rd e d f i e l d o fte n r e s u l te d in an im m ediate i n t e r a c t i o n between i t and the p a r t i c l e s in the f i e l d. I t tended to sweep a l l b e fo re i t and a c c e le r a te i t downstream o u t of th e f i e l d. On o th e r o c ca sio n s i t e n te re d th e f i e l d but seemed to be on a s l i g h t l y d i f f e r e n t r x p lan e th a n th e f i e l d p a r t i c l e s because i t d id n o t im m ediately a f f e c t them. In th e se cases a "two la y e r v e lo c ity " was e v id e n t where the h ig h e r a x ia l v e lo c ity stream would move p a s t low er v e lo c it y f i e l d p a r t i c l e s which were a p p a re n tly a t th e same r p o s itio n. G ra d u ally as i t proceeded a c ro ss the f i e l d i t would b eg in to a f f e c t the f i e l d p a r t i c l e s and a c c e le r a te them. As i t began to i n t e r a c t, the "two la y e r v e lo c ity " e f f e c t began to d is a p p e a r. When t h i s stre am has a s l i g h t w allw ard t r a j e c t o r y, th e
119 TABLE 3 ACCELERATION VELOCITY M easured V e lo c ity y+ p o s itio n s Angle to C a lc u la te d Ux tr a v e le d W all V e lo c ity, Ux.464 1 2-1 6 0.3 7 4 -.4 3 1.459 2 4.6-1 4.5 3.5 1 7 -..491 2 8.7 0.546.458 11.5 0.3 6 6.494 1 6-2 0 0.4 3 8 -.4 8 1.540 25-32 3.5 2 -.5 7.570 2 0-3 0 4 1 /2.48 -.5 6.572 2 4.6 0.5 1 8.491 16.4 0.438.584 34 0 57.203 5.7-1 2.3 0.2 2 6 -.3 7 9.50 3.3-1 6 6 1/ 2. 5 6 9 -.4 3 8.449 2 0. 5-1 2.3 5.4 8 1 -.3 7 9.714 3 1.8 0.72.714 42 0.765.611 15.9 0. 6 8 -.7 2 9.714 32-26 0.729-.6 8.5 8 2 15.9 0.552.331 1 1.6-9.5 0.4 7 -.4 2 1.303 5.3-3.2 0.2 7 3 -.1 4 2.748 53 0.8.517 2 9-1 2 60.5 4 7 -.3 7 4.4 9 8 2 4.6-9 5.5.5 1 7 -.3 1 8.404 1 4.5-5 -7 3.4 1 0 -.2 2 6 535 33-21 40.5 7 5 -.4 8 5 515 1 8.5-9 3.461 -.3 1 8.282 20-14 6 4 0.3 2 -.2 6 5.223 8.7-5 40. 1 9 -.1 2 0.238 1 1.5-8.7 7.2 3 5 -.1 9.37 32-23 6.3 8 6 -.3 4.361 21-16 30491.3 2 5 -.2 8 5.496 2 9-2 0 4.5.3 7 3 -.3 8 0.33 1 1.5-6.4 5.5.2 3 5 -.1 4 5.26 14-5 60.2 6 5 -.1 2 0
120 p a r t i c l e s w hich p e n e tra te d e e p ly in to th e su b la y e r a re r e ta r d e d and o f te n lo se t h e i r i d e n t i t y and flow o u t o f th e f i e l d w ith in th e s u b la y e r. O thers re-em erg e w ith th e e je c te d f l u i d. The e n te r in g stre am u s u a lly d id an e f f e c t i v e jo b o f a c c e le r a tin g and d is p la c in g the f l u i d above a p a r t i c u l a r y+ p o s i t io n. Below t h i s p o s i t i o n i t o n ly v e ry g r a d u a lly began to a f f e c t the r e ta r d e d f l u i d. T h e re fo re a t th e tim e o f e j e c t i o n th e re was o f te n a v ery s h a rp in te r f a c e betw een th e a c c e le r a te d and the r e ta r d e d f l u i d. This c r e a te s a v e ry h ig h s h e a r and h ig h v o r t i c i t y la y e r. The o th e r m a n if e s ta tio n which was observed a t t h i s s ta g e o c c u rre d much le s s o f t e n than th e p re c e d in g. T5ie f l u i d e n te re d th e f i e l d from u p stream w ith a la rg e w allw ard v e lo c i t y and a t a sm a ll an g le t o th e w a ll. As in th e p re v io u s c a s e, th e mass o f f l u i d in v o lv e d was l a r g e r th a n th e f i e l d o f view. The p a r t i c l e s p e n e tra te d in to th e w a ll re g io n and many e n te r e d th e s u b la y e r. Most of th e s e l a t t e r l o s t t h e i r i d e n t i t y and w ere c a p tu re d by the s u b la y e r f l u i d and passed o u t o f th e f i e l d w ith i t. O ften as t h i s mass o f f l u i d was p ro c e e d in g w allw ard th e re was a sim u lta n e o u s e j e c t i o n of w a ll r e g io n f l u i d outw ard. These e le m e n ts were on a s m a lle r s c a le th a n th e w allw ard flo w. The two opposing flow s coe x is te d b u t d id n o t i n t e r a c t alth o u g h th e y w ere c l e a r l y p a ssin g one a n o th e r. U iis im p lied t h a t th e y were on s e p a r a te r x p la n e s s e p a ra te d by some d is ta n c e alo n g th e l i n e o f
121 s i g h t. The a x i a l and r a d i a l com ponents o f th e w allw ard flow were alw ays g r e a t e r th an th e c o rre sp o n d in g v e l o c i t i e s f o r th e outw ard e j e c t i o n. The a n g le of ap p ro ach to th e w a ll was a p p ro x im a te ly 5-15 > w h ile the a n g le o f e j e c t i o n on th e same c o o rd in a te system s was a p p ro x im a te ly 170. From th e a n a ly s is o f th e film s and th e v e lo c it y m easurem ents i t was concluded t h a t th e s e were two s e p a r a te flow s and n o t two p a r t s o f a l a r g e r c i r c u l a t i o n. There were c a se s where th e w allw ard flow i n te r a c t e d w ith th e outw ard e j e c t i o n and te m p o r a rily r e ta r d e d i t. G radually* th e w allw ard flow d im in ish e d and the outw ard e j e c t i o n s dom inated the f i e l d. The above d e s c r i p t io n i s a ls o a n o th e r exam ple o f "two la y e r v e l o c i t y." T able 4 c o n ta in s some m easurem ents o f the r a d i a l and a x i a l v e l o c i t i e s o f th e w allw ard flo w and th e a n g le o f app ro ach to th e w a ll. For some flow s th e r a d i a l v e lo c it y was n e a r ly 20$ o f th e l o c a l mean a x i a l v e l o c i t y. The sm a ll a n g le o f approach to th e w all* and th e r a t h e r c lo s e agreem ent betw een th e m easured a x i a l v e lo c it y and the l o c a l mean a x i a l v e lo c it y c a lc u la te d f o r th e y+ span o v er which th e o th e r v e lo c it y was m easured in d ic a te s t h a t w herever the w allw ard flow o r ig in a te d i t has by th e tim e o f o b s e rv a tio n a c q u ire d th e l o c a l mean a x i a l v e lo c it y. E je c tio n e v e n t. The e j e c t i o n o f f l u i d elem en ts from w ith in th e w a ll re g io n outw ard tow ard th e pip e c e n t e r l i n e i s both th e m ost s t r i k i n g and m ost Im p o rta n t p a r t o f th e e j e c t i o n p ro c e ss which c h a r a c te r iz e s th e f l u i d m otion in th e w a ll r e g io n. An e j e c t i o n
122 TABLE 4 WALLWARD FLOW V eloci t y Angle to W all A x ial V elo. R a d ia l V elo. y+ Span A pprox. C alc. A x ia l V elo..2 6 8 1 5 1 3.259.075 2 6-1 1.5 357-.235.2 6 8 15 1 0 *.259.073 2 3-8.7.3 4 0 -.1 9 2.345 8 13».341.0 5 0 29-19.3 7 3 -.3 1 0.6 7 6 5 24 *.673.064 2 1. 2-1 1.6.6 2 8 -.4 7.6 6 9 7 o 1 5,.664.084 3 1.8-1 5.9.7 2 8 -.5 5 2.6 3 1 5 3 7 '.6 2 8.0 6 2 3 7.1-1 8.746-.5 8 6 559 7 8 '.555.0 6 9 2 6.4-1 3.8. 6 8 5 -.4 6 5.756 9 3 '.746.1 2 1 42-16.7 6 5 -.5 5 5.665 11? 8 *.6 5 2.1 2 8 64-21.8 1 7 -.6 2 7.6 1 5 11 19*.6 0 3.121 64-37.8 1 7 -.7 9 5.597 14 5 *.579.146 58-26. 8 0 -.6 8 Is d e s c rib e d as th e s w if t and sudden movement outw ard from th e re g io n of th e pipe w a ll o f sm a ll elem ent o f f l u i d which was fo rm e rly flo w in g a x i a l l y w ith in th e w a ll re g io n. The fre q u e n c y o f e j e c t i o n i s a f u n c tio n o f R eynolds number, in c r e a s in g as i t i n c r e a s e s. I t s b a s ic c h a r a c te r, how ever, i s in d ep e n d en t of such mean flow p a ra m e te rs. The p ro c e ss is random w ith r e s p e c t to tim e and p o s i t io n alo n g th e p ip e w a ll, and shows no r e g u l a r i t y in tim e o f d u r a tio n o r in th e i n t e r v a ls betw een o c c u rre n c e s w ith in any g iv e n s e t of c o n d itio n s. S ince th e y a re fu n d a m e n ta lly random e v e n ts, th e y d e m o n stra te d a c e r t a i n d eg ree o f v a r i a ti o n, b u t th e b a s ic c h a r a c te r o f th e e j e c t i o n e v e n t i s unchanging and alw ays re c o g n iz a b le. The e j e c t i o n o f f l u i d from th e w a ll r e g io n o c c u rre d a f t e r th e d e c e le r a t i o n s te p and w h ile the a c c e l e r a ti o n s te p
was In p r o g r e s s. S ince th e two o f te n o c c u rre d in c o n ju n c t io n, th e m otion p ic t u r e s were c a r e f u l l y exam ined f o r e v i dence t h a t th e a c c e le r a tin g stre a m was a d i r e c t c a u s i t iv e f a c t o r o f th e e j e c t i o n s te p, b u t no such re la tio n w a s d i s c o v e re d. At tim es th e re was some i n t e r a c t i o n betw een the f l u i d composing th e e n te r in g stre am and the f l u i d from w hich th e e j e c t i o n a ro s e, but m ost o f te n th e i n t e r a c t i o n o c c u rre d o n ly a f t e r the e j e c t i o n had begun. The mass o f f l u i d from w hich th e e j e c t i o n s a ro se was p a r t o f th e r e ta r d e d re g io n n e a r th e w a ll. I t p o sse sse d a l l o f th e p r o p e r tie s o f t h i s re g io n, in c lu d in g a r e l a t i v e l y u n d is tu rb e d o r o n ly m ild ly d is tu r b e d a x i a l v e l o c i t y. The p a r t i c l e s which ap p eared in th e e je c t e d elem en t were c l e a r l y in view w ith in th e f i e l d, moving a x i a l l y, p a r a l l e l to th e w a ll, b e fo re th e y were e je c te d o u tw a rd s. I t was concluded th e r e f o r e t h a t th e a c c e l e r a ti n g stre a m and th e e j e c t i o n were two s e p a r a te p a r ts o f an o v e r - a l l p ro c e s s, b u t a p p a r e n tly n e i t h e r caused th e o th e r. f i e l d. The e je c t i o n s o r ig in a te d w ith in th e f l u i d i n th e There was no m ethod of d e te rm in in g how t h e i r c r e a t i o n was c o n n ected, i f a t a l l, to th e l a r g e r c i r c u l a t i o n s and d is tu r b a n c e s o f th e m ain stre a m. Once th e s te p s p re c e d in g an e j e c t i o n had o c c u rre d, th e e j e c t i o n I t s e l f proceeded v e ry r a p i d l y from th e e a r l y s ta g e s to th e f u l l y dev elo p ed s ta g e. At t h i s sta g e th e re was a c o n tin u in g e j e c t i o n o f f l u i d outw ard f o r v a ry in g p e rio d s o f tim e, and th e n th e e j e c t i o n s te p g r a d u a lly c e a se d.
Sortie in d ic a tio n of th e d u r a tio n o f t h i s s te p i s g iv e n in a 124 l a t e r s e c tio n. The elem ent o f f l u i d c o n s t it u t in g an e je c t i o n was v e ry l o c a l in c h a r a c te r. On numerous o c c a sio n s th e e j e c t io n f i r s t appeared a t a p a r t i c u l a r p o s itio n w ith in th e f i e l d, and w h ile i t was i n p ro g re ss o th e r e je c tio n s o c c u rre d a t a d ja c e n t dow nstream p o s i t io n s. At tim es th e s e e je c tio n s appeared to be moving in a connected fa s h io n, i. e., were c o r r e l a t e d, b u t a t o th e r tim es th e re appeared two o r more sim u l tan eo u s e je c t i o n s w ith in th e same f i e l d which were q u ite u n co n n ected. R e c a llin g t h a t th e f i e l d of view was a p p ro x i m a te ly 0.0 9 5 in c h e s long, one can o b ta in some id e a o f th e s iz e and l o c a l n a tu re of the e le m e n ts. Movement in a conn e c te d fa s h io n i s d e s c rib e d as the movement of two or more p a r t i c l e s in such a way t h a t, a lth o u g h th e y a re s e p a ra te d by a d is ta n c e, th e y c l e a r l y d e s c rib e s im ila r p a th s, w ith re g a rd to speed and t r a j e c t o r y, d u rin g th e same i n t e r v a l of tim e. The maximum d is ta n c e over which t h i s occurs i s c a lle d the d is ta n c e o f connected movement. T his was used as a guide to i d e n t i f y th e d i f f e r e n t l o c a l e je c tio n s when more th an one was o c c u rrin g a t a p a r t i c u l a r tim e. In a l l c a se s o b serv ed, the d is ta n c e o f connected movement was le s s th a n th e le n g th of th e f i e l d o f view, 0.0 9 5 in c h e s, and most o fte n o f th e o rd e r o f 0.0 6-0.0 3 in c h e s. T his dim ension was m easured a x i a l l y alo n g th e pip e w a ll and may be c o n sid e re d th e base o f the e je c te d e le m e n t.
125 Most o f th e e le m e n ts o r ig in a te d w ith in th e s e c tio n o f th e w a ll r e g io n bounded by 5 S y+ 5 1 5. T able 5 shows th e r e g io n o f o r i g i n of th e m a jo r ity o f th e e je c t i o n s as w e ll as th e p o s i t io n n e a r e s t th e w a ll from w hich an e j e c t i o n was o b serv ed to o c c u r. In i t one can see t h a t ev en below = 5* and in f a c t a t y+ = 2.5, a few e je c t i o n s o r i g in a te d. Below th e s e p o s i t io n s, s i g n i f i c a n t d e p a rtu re s from th e p u re ly a x i a l flow were ob serv ed, b u t th e y n ev er escap ed th e re g io n a s an e je c te d e le m e n t. I t w i l l be shown l a t e r t h a t much o f th e a c t i v i t y i n th e s u b la y e r re g io n r e s u l te d from th e e j e c t i o n p ro c e s s. I t w i l l be r e c a l l e d t h a t th e d e c e le r a t i o n - a c c e le r a t i o n sequence p re c e d in g a n e j e c t i o n d i s t o r t e d the v e l o c i t y p r o f i l e i n th e w a ll r e g io n and o f t e n c re a te d a h ig h sh e a r l a y e r. 1516 d eg ree to w hich t h i s o c c u rre d and the p o s i t io n of th e h igh s h e a r i n t e r f a c e v a rie d g r e a t l y sin c e e ac h s t e p was in d e p e n d e n t o f th e o th e r, and each showed wide v a r i a t i o n. A l a t e r s e c t i o n w i l l show t h i s q u a n t i t a t i v e l y. Hiere a r e, th e r e f o r e, a number o f s e p a r a te f a c t o r s which a f f e c t th e e j e c t i o n e l e m ent. On the a v e ra g e, i t w i l l have an a x i a l v e l o c i t y compone n t r e p r e s e n ta t iv e o f the y+ re g io n from which i t came. However, th e l o c a l mean a x i a l v e lo c ity a t a p a r t i c u l a r y+ p o s i t io n i s n o t t h a t g iv e n by th e norm al tu r b u le n t v e l o c i t y p r o f i l e f o r l o c a l mean v e lo c it y, but i s in flu e n c e d by th e d eg ree o f d i s t o r t i o n o f t h i s p r o f i le by th e d e c e le r a t i o n - a c c e l e r a ti o n se q u e n c e. S in c e i n many c a se s th e a x i a l v e lo c it y
TABLE 5 EJECTION VELOCITY AND ANGIE y+ Span P o s itio n o f O rig in R a tio o f Run E je c t. A ctual R a d ia l y+ Span8, o f Most R a d ia l V elo. D eepest No. Re Angle V elo. V elo. Me a s. P a r t ic le s u* O rig in 165 2 0,6 5 0 11.159.0 3 2 6-2 0 5 1.135 7.134.0 1 6 7-17.567 7 n.134.0 1 6 5-14.567 3 17.124.0 3 6 8-2 9 1.277 18.1 2 8.04 17-32 1.418 9.141.022 7-14.780.8 1 6 1.5.175.005 7.5-9.177 5.175.016 6-10.567 6.5.223.025 11.5-17.887 14.231.057 1 1. 5-2 9 7.5-1 5 2.021 5 15.5.2 5 2.0 6 8 17-35 2.411 8.248.036 1 1. 5-2 0 1.277 15.233.0 6 2 0-3 5 2.128 12.5.220.047 15-32 1.667 10.236.04 7*5-17 1.418 166 20,650 6.209.023 9-23 CM H 1 cr 167 2 1,1 6 6 12.176.037 1 4-29 6.4-1 6 1.312 4 15.223.058 17.3-35 6.4-8.7 2.057 13.139.031 11.5-20 1.099 6.222.024 7.5-1 1.5.851 9.5.175.029 1 6-27 1.028 168 21,080 7.21.026 13-32 4-7.5 CM CM r 3 126
TABLE 5 continued y+ Span of O rig in R a tio P o s itio n o f Run E je c t. A ctu al R a d ia l y+ Span3- o f Most R a d ia l V elo. D eepest No. Re Angle V elo. V eol. Me a s. P a r t ic le s u* O rig in 225 31,240 7.231.0 2 7 3.3-1 2 4-9.675 2.5 4.229.016 3-3 -5.7.40 6.242.026 5.7-1 2.65 6.5.294.033 7-4-20.825 4.408.026 4-16.65 15.362.092 1 2-29 2.3 14.3 8 0.093 12-33 2.33 224 30,640 5 3.15.026 9-21 7.4-1 2.3.650 4 5.341.029 11-25.725 5.5.248.024 11-18.6 0 0 5.336.028 9-25.700 5.352.030 6.5-2 1 750 4.302.022 6-1 6.55 3-5.380.024 14-29.600 12.3 6 6.078 2 0-5 0 10.7-25 1.95 6 9-5.338.055 20-45 1.375 3.5 3.54..022 7-25.550 10.362.063 12-45 1.575 8.5.3 0 8.046 16-37 1.15 6.5.2 9 8.033 11*21 5.7-1 4.825 12.2 7 6.059 12-33 5.7-1 2 1.475 3 7-5.431.057 16-29 9.5-2 1 1.425 15.212.054 9-25 1.35 18.244.075 12.3-33 1.875 20.5.306.108 16-41 2.7 0 221 40,670 18.135.041 4-16 5.3-1 1.6.796 4 127
TABLE 5» continued y+ Span P o s itio n o f O rig in R a tio o f Run E je c t. A ctual R a d ia l y+ Spana o f Most R a d ia l V elo. D eepest No. Re Angle V elo. V elo. M eas. P a r t ic le s u* O rig in 9.515.079 16-42 1.534 13.441.097 9.5-4 7 1.883 7.498.063 9.5-3 2 1.223 5 594.051 1 1. 6-3 2 1..990 11.465.1 1 8 5.3-5 3 5.3-1 6 1.7 2 8 14.5.473.1 1 8 5.3-5 3 2.291 10.6 2 0.1 0 8 9.5-4 2 2.097 13.461.103 7-37 1.999 13.536.1 2 0 9.5-4 8 2.330 9.5.6 8 6.112 1 1.6-42 2.174 223 41,090 11.469.089 16-37 1 1.6-1 8.5 1.7 2 8 3 10.486.087 18-42 I.689 9.510.077 14-42 1.495 8.5.392.0 5 6 1 1.6-3 1. 8 1.1 2 6 12.471 099 11.6-37 1.9 2 2 11.6 8 3.1 3 2 21-47 2.563 5.5 6 1.049 16-32 9.5-1 6.951 7 7-5.52.0 6 8 11.6-37 1.3 2 0 6.5.52.0 6 8 11.6-37 1.107 9.43.0 6 6 9.5-2 6 1.2 8 1 7.0.441.0 5 2 14-26 1.009 8.436.059 9.5-2 1 1.146 8.415.057 7.4-2 6 1.1 0 7 7.383.048 7.4-2 6.952 12.0 1 9 4-1 1.5 0.074 2 0,2 3 0 21.032 1.134 at his i s o n ly re g io n s e le c te d f o r m easurem ent and does n o t mean p a r t i c l e s o r ig in a te d h e re. 128
i n th e r e g io n o f o r i g in o f th e e j e c t i o n s i s s t i l l r e ta r d e d a t th e tim e o f e j e c t i o n, th e a x i a l v e lo c it y o f th e e je c t e d f l u i d w i l l be r e t a r d e d. The random ness and p o s s ib le v a r i a t io n s w ith in each o f th e s e s te p s em phasize the s tro n g dependency o f th e e je c t i o n e v e n t on l o c a l c o n d itio n s. This elem en t was e je c te d outw ard tow ard th e u n re ta rd e d r e g io n o f much g r e a t e r a x i a l v e l o c i t y. As th e e lem en ts e n te r e d t h i s re g io n, th e y i n te r a c t e d w ith the f l u i d th e r e, and th e r e s u l t in g m o tio n s were v e ry v i o le n t and c h a o t i c. Not o n ly was th e r e i n t e r a c t i o n betw een th e e je c te d f l u i d and the mean stre a m, b u t when more th a n one e j e c t i o n elem en t ap p eared w ith in th e same r e g io n o r tim e span, th e i n t e r a c t i o n o c c u rre d among a l l th r e e o r more f l u i d m a sse s. The m otions m ight be c h a r a c te r iz e d as v e ry d is o rg a n iz e d w ith th e p a r t i c l e s having s h o r t, a b ru p t movements and sudden changes of d i r e c t i o n and sp e ed. The g e n e r a l movement of th e e n t i r e re g io n was, of c o u rs e, dow nstream, b u t th e c h a o tic m otions sp re a d o u t in a l l d i r e c t i o n s, and th e more v io le n t ones rea ch e d ev en to th e s u b la y e r and w a ll. In t h i s manner th e in n e r p a r ts o f th e s u b la y e r r e g io n were d is tu r b e d by th e e j e c t i o n. The end r e s u l t, in a d d it i o n to th e c r e a tio n o f t h i s t u r b u le n t m o tio n, was t h a t th e e je c t e d elem en t was d is r u p te d and a c c e le r a te d a x i a l l y a t th e expense o f th e mean stre am, and was co n v ected dow nstream. dow nstream. Hie c h a o tic m otion c o n tin u e d as i t proceeded S ince th e e le m e n ts o r i g i n a l l y p o sse sse d an
130 outw ard d ir e c te d r a d i a l v e l o c i t y component, th e f l u i d contin u e d to sp re a d outw ard. The e je c te d elem ent o r i g i n a l l y p o sse sse d an a n g le to th e w a ll of th e o rd e r o f 5-2 0 o, d i r e c te d dow nstream, but as i t e n te r e d th e re g io n o f h ig h e r a x ia l v e l o c i t y i t was a c c e l e r a te d dow nstream a t a much red u ced a n g le. The t y p i c a l t r a j e c t o r y o f an e je c te d e le m e n t was a s l i g h t l y curved p ath d i r e c te d dow nstream a t a r e l a t i v e l y sm a ll angle to th e w a ll. No t i g h t r o t a t i o n o f th e f l u i d elem en ts was o bserved e x c e p t on a v e ry few o c c a s io n s. The d is ta n c e w hich an elem ent moved outw ard b e fo re b ein g a c c e le r a te d and d is r u p te d depended upon th e p o s itio n o f th e h ig h sh e a r i n t e r f a c e, i. e., th e n a tu re of th e p r o f i l e i n th e w a ll r e g io n. In some c ases th e I n te r f a c e o c c u rre d v e ry n e a r th e p o s i t io n o f o r i g in, and th e elem en ts were alm o st im m ed iately a f f e c t e d. In some few c a s e s, how ever, no i n t e r f a c e a p p eared w ith in th e f i e l d ( t h i s o f te n o c c u rre d d u rin g the w allw ard flo w o r when th e d e c e le r a t i o n to o k th e p lu g - lik e flo w fo rm ), a d is ta n c e which ran g ed from a y+ = 40 to 7 5. In th e s e In s ta n c e s th e e je c te d elem en t l e f t th e f i e l d e s s e n t i a l l y u n a ffe c te d and w ith a s u b s t a n t i a l r a d i a l v e lo c it y com ponent. There was no way o f a s c e r ta in in g i f i n th e s e c a se s a s h e a r r e g io n form ed beyond y+ = 7 5 * Hie v e l o c i t i e s and t r a j e c t o r i e s o f th e e je c t e d p a r t i c le s were m easured and th e r e s u l t s a p p ea r in T able 5- The method o f m easurem ent I s d is c u s s e d in t h e s e c tio n on e x p e r i m e n ta l p ro ce d u res and Appendix I I. TCiese m easurem ents a re,
o f c o u rse, o n ly approxim ate, but th e y a re s u f f i c i e n t l y a c c u ra te to c o n tr ib u te v a lu a b le in fo rm a tio n about the e j e c t i o n p ro c e ss. The a n g le o f e j e c t i o n showed a c o n s id e ra b le v a r i a t i o n from ev en t to e v e n t, b u t t h i s i s n o t s u r p r is in g in view o f the e a r l i e r c o n s id e r a tio n s. The l a r g e s t angle o b serv ed was 21, and the d i s t r i b u t i o n ranged from 1.5 to 2 1. The minimum a n g le m easured has no r e a l s ig n if ic a n c e. The p a r t i c l e s chosen f o r th e s e m easurem ents were r e p r e s e n ta t iv e of the p a r t i c u l a r e je c t i o n, and a number o f p a r t i c l e s w ith in each elem ent were s e le c te d. W ith in any g iv e n elem ent th e re o c cu rred a d i s t r i b u t i o n of a n g le s, b u t t h i s was much sm a lle r th an th e d i s t r i b u t i o n among the d i f f e r e n t e j e c t i o n s. The a n g le of e j e c t i o n was p lo tte d a g a in s t R eynolds number, and the d i s t r i b u t i o n ap p ears in F ig u re 21. I t can be se e n t h a t th e d i s t r i b u t i o n s are a l l s im ila r f o r the Reynolds numbers c o n sid e re d, and, th e r e f o r e, t h a t th e re i s no dependency o f the e j e c t i o n angle on R eynolds num ber. F ig u re 22 i s a fre q u e n c y d i s t r i b u t i o n curve f o r the e j e c t i o n an g le and in c lu d e s v a lu e s f o r a l l Reynolds num bers. The m ost fre q u e n t angle o f e je c t i o n i s 8.5. The independence o f th e e j e c t i o n a n g le w ith re g a rd to Reynolds number h as some i n t e r e s t i n g co n sequences. I f one r e f e r s to T ables 2 and 3, i t i s se en t h a t w h ile a d e c e le r a t i o n and a c c e le r a tio n do o c cu r, th e r e s u l t i n g v e l o c i t i e s a re s t i l l a f u n c tio n of R eynolds number and r e f l e c t th e norm al d i s t r i b u t i o n o f lo c a l mean a x i a l v e lo c it y. The a x i a l v e lo c it y
132 24 Ejection Angle (degrees) 20 16 12 8 o o S> o o o 03" o o o o o o nr 6 O < a <3 CO o o nr o o o o CO o o 0 c5> CD 10 20 30 40 50 Npe (thousands) Figure 21. Ejection Angle Distribution
133 20-12 0 2 6 14 18 10 22 E jection Angle (degrees) Figure 22. Frequency Distribution of Ejection Angles
component of th e e je c t e d e le m e n t, sin c e i t o r i g in a te s i n t h i s re g io n, m ust a ls o have t h i s dependency on R eynolds number, i. e., i t i s l a r g e r f o r l a r g e r Nfte However, i f th e e j e c t i o n a n g le i s in d ep e n d en t o f Reynolds number, th e n th e r a d i a l v e lo c it y component m ust in c re a s e w ith in c r e a s in g R eynolds number, f o r t h i s i s th e o n ly way th e a n g le can rem ain u n a ff e c te d. T h is, o f c o u rs e, i s c l e a r l y e v id e n t in Table 5. I t i s c l e a r t h a t w h atev er th e mechanism i s t h a t cau ses th e e j e c t i o n, i t m ust in some manner be r e l a t e d to th e mean flow p a ra m e te rs as r e f l e c t e d by th e R eynolds number. U n fo rtu n a te ly, th e v e ry random ness o f th e e j e c t i o n p ro c e s s, w hich g iv e s such a wide d i s t r i b u t i o n o f a n g le s w ith in any s e t of flow c o n d itio n s, and i t s v e ry s tro n g dependency on l o c a l c o n d itio n s p re c lu d e s th e p o s s i b i l i t y o f c o r r e l a t i n g th e p r e s e n t m easurem ents w ith mean flow p a ra m e te rs. The m easured r a d i a l v e lo c it y component ranged from a v e ry sm a ll p e rc e n ta g e o f th e a x i a l v e lo c it y component t o a h ig h o f 30$ o r m ore. The m ost common v a lu e was 10$ - 20$ of th e a x i a l com ponent. I t m ust be rem embered, o f c o u rs e, t h a t th e s e a re in s ta n ta n e o u s m easurem ents and n o t av erag e m easurem ents o f f l u c t u a t i n g i n t e n s i t i e s such a s a h o t w ire would g iv e. F ig u re s 23 and 24 show two e je c t i o n s i n a sequence o f s t i l l p h o to g ra p h s. I t w i l l be n o ted t h a t In each case th e sequence b eg in s w ith th e p a r t i c l e a t a p p ro x im a te ly y+ = 23 and t h a t th e m otion p ro ceed s o u t to a y+ = 60. T his sh o u ld
135 n o t be i n t e r p r e t e d as ev id en ce t h a t the e j e c t i o n began a t y+ = 2 3. This segm ent o f the e j e c t i o n t r a j e c t o r y was s e le c te d because i n th e s t i l l p h o to g rap h s i t most c l e a r l y showed the r a d i a l movement due to th e la r g e d isp la c e m e n t. I d e a l ly, th e segm ent o c c u rrin g w ith in y+ = 30 sh ould have been s e le c te d, b u t t h i s d id n o t rep ro d u c e w e ll from the m o tio n p i c t u r e, and the sequence would have been m e a n in g le ss. This i s a r e s u l t of two f a c t o r s. F i r s t i t i s v e ry d i f f i c u l t to show by a s e r i e s of s t i l l p h o to g rap h s th e r e l a t i v e v e l o c i t i e s and cont i n u i t y o f m otion t h a t a m otion p ic tu r e image p ro v id e s. Secondly, th e image q u a l i t y o f th e p r i n t made from th e m otion p ic tu r e s was much p o o re r th a n th e o r i g i n a l and much d e t a i l and even p a r t i c l e s were l o s t due to th is d e c re a s e in q u a l i t y. To show th e e j e c t i o n in y+ ls 30 re g io n would have r e q u ir e d a c o n s id e ra b le e n la rg e m e n t of th e m otion p i c t u r e f ilm ( r e c a l l t h a t f o r a n a ly s is th e p r o je c te d image was n e a r ly 100 tim es t h a t o f th e film im ag e). At such m a g n ific a tio n s the p r i n t i s u s e le s s as n e a r ly a l l d e t a i l s a re l o s t. The F ig u re s 23 and 24 th e r e f o r e r e p r e s e n t a compromise betw een a d e s ir e to show an e j e c t i o n e v e n t and p r a c t i c a l i t y. In F ig u re 23 th e e j e c t i o n i s a p p a re n t because i t in v o lv e s th e l a t e r s ta g e s of th e e v e n t when th e outw ard movement a f t e r I n t e r a c t i o n p r e v a i l s. Hie a x i a l v e lo c it y o f th e p a r t i c l e i s n e a r ly t h a t of th e lo c a l mean v e l o c i t y in d ic a tin g t h a t a c c e l e r a t i o n h as o c c u rre d. The p a r t i c l e s o f i n t e r e s t are marked w ith a rro w s. The w a ll view i s used, and a l l m otions in th e p h o to g rap h s
136 a re r e l a t i v e to th e c a r r ia g e v e lo c it y which i s in d ic a te d. A d jacen t to th e p h o tographs i s a s e r i e s of s k e tc h e s drawn to s c a le w hich show th e a p p a re n t t r a j e c t o r y. The a c tu a l t r a j e c t o r y i s a ls o p l o tt e d to s c a l e. The p a r t i c l e m otions a re i n th e r x p la n e, and the e j e c t i o n an g le t o th e w a ll i s a p p ro x im a te ly 1 0.5 d i r e c te d dow nstream. F ig u re 24 shows a s l i g h t l y d i f f e r e n t c a s e. As b e fo re, th e o u te r segm ent of th e e j e c t i o n was s e le c te d p r im a r ily because i t i s m ost v i s i b l e in th e s t i l l p h o to g ra p h s. However, u n lik e F ig u re 23 th e p a r t i c l e s in t h i s case s t i l l have a d e c e le r a te d a x i a l v e lo c it y as ev id en ced by th e f a c t t h a t th e y a re moving a t a p p ro x im a te ly th e c a r r ia g e speed which i s below th e l o c a l mean a x i a l v e l o c i t y a t a l l y+ p o s itio n s tr a v e r s e d by the p a r t i c l e s. T his i s c l e a r from th e sk e tc h o f th e a p p a r e n t p r o f i l e where the c a r r ia g e m otion i s ta k e n in to a c c o u n t. S ince th e p a r t i c l e s a re n o t a c c e le r a te d by th e a x i a l v e lo c it y as th e y t r a v e l outw ard, one m ust conclude t h a t l o c a l l y th e mean a x i a l v e lo c it y i s d e c e le r a te d, and t h a t th e norm al v e lo c it y p r o f i l e does n o t e x i s t th e r e. 01118 im p lie s t h a t th e h ig h s h e a r in te r f a c e e x i s t s f u r t h e r o u t, o r as th e m otion p ic t u r e s show, a sh a rp i n t e r f a c e w i l l a p p ear w ith in th e r e g io n when h ig h e r v e l o c i t y f l u i d e n te r s from u p stre am. As b e fo re, th e a p p a re n t t r a j e c t o r y i s p l o tt e d, b u t now i t i s v e ry d i f f e r e n t th an th e a c t u a l t r a j e c t o r y because the p a r t i c l e m otions so c lo s e l y app ro x im ate the c a r r ia g e v e l o c i t y. The a c t u a l t r a j e c t o r y i s a l s o p l o t t e d.
Actual Trajectory Apparent Trajaatory f 0.0219 «#.' Ky t* 0.0176 t> 0.0128 Seal# (X05~ t-0.0085 50 y+ 30 to 0 ~7*~ Otraction Moan Flow Carrtoga velocity t-0.0057 0.460 ft./sac. t" 0.0014 ace. Moan Velocity Pro Hit 1^,^41,000 y,+ t«0.1.4.7 1.0 Velocity (ft./eoe.) 23. Fluid Ejection-Wall View
Actual Trajectory y _ T..0486 Apparent Trajectory t«.0 3 9 0 t-.0292 h Scale 0. T Direction of Flow Carriage Velocity t».oi95 Apparent Velocity Profile t-,0097 sec. 0.24 ft./iec. i- w 3 - Normal Velocity y* 40- Profile t-0 NR#* 19000 Ejection- Wall View tt./eec.
139 These sequences g iv e o n ly a f a i n t I n d ic ti o n o f what can be d is c e rn e d on th e m otion p ic tu r e s b u t th e y do I n d ic a te th e e j e c t i o n e v e n t and even th e r e t a r d a t i o n o f th e l o c a l w a ll r e g io n d u rin g th e e j e c t i o n p ro c e s s. For a f u l l u n d e r s ta n d in g, th e m otion p ic tu r e s m ust be c a r e f u l l y s c r u t in i z e d under h ig h ly m ag n ifie d p r o je c tio n. Sweep. Hie e j e c t i o n p a r t o f th e p ro c e ss i s u s u a lly te rm in a te d by a stre am of f l u i d which e n te r s th e f i e l d from u p stream and which p o sse sse d a g r e a t e r a x i a l v e lo c it y th a n much o f th e f l u i d w ith in th e f i e l d. This stre am u s u a lly had no r a d i a l component and d id n o t c o n ta in any h ig h i n t e n s i t y, sm a ll s c a le tu r b u le n c e. At tim es th e stre a m im m ed iately i n te r a c t e d w ith the f l u i d i n th e f i e l d and a c c e le r a te d i t dow nstream. In e f f e c t i t sw ept i t c le a r of th e rem ain in g r e ta r d e d f l u i d and r e - e s t a b l i s h e d an ap p ro x im atio n to a norm al tu r b u le n t v e lo c it y p r o f i l e in th e a r e a. On some o c c a sio n s th e e n te r in g stre a m d id n o t i n t e r a c t w ith th e p a r t i c l e s, b u t ap p eared to p ass them much i n th e fa s h io n of th e "two la y e r v e l o c i t y." A fte r a tim e, how ever, th e e n t e r in g stre am seemed to e n cro ac h upon th e f i e l d f l u i d and e v e n tu a lly i n te r a c t e d w ith i t. In b o th c a se s the i n t e r a c t i o n u s u a lly produced some c h a o tic m otion. W hile t h i s a c tio n t e r m in ated th e c y c le o f e v e n ts, i t d id n o t mean t h a t a l l d i s tu rb a n c e s i n th e w a ll re g io n d is a p p e a re d. H iere rem ain m inor d is tu r b a n c e s.
140 Two la y e r v e l o c i t y. The e f f e c t c a lle d "two la y e r v e lo c ity " appeared in th e m otion p ic tu r e s as two la rg e m asses o f p a r t i c l e s, each p o s s e s s in g a d i s t i n c t i v e v e lo c ity, w hich occupied th e same r a d i a l o r y+ span b u t d id n o t i n t e r a c t w ith one a n o th e r. I t sh ould be em phasized t h a t th e comp a ris o n was made betw een e n t i r e la y e r s and n o t in d iv id u a l p a r t i c l e s. A few exam ples of t h i s appearance have been d e s c rib e d In c o n ju n c tio n w ith o th e r a s p e c ts o f th e e j e c t i o n phenomenon. S ince th e p a th s o f th e s e la y e r s o f te n c ro sse d o r were o th e rw ise opposed, the im p lic a tio n from th e v is u a l a n a ly s is o f th e film s was t h a t th e y o ccupied two d i f f e r e n t rx p la n e s and were s e p a ra te d by some d is ta n c e alo n g th e l in e o f s i g h t. The d e p th o f f i e l d o f th e o p t i c a l system was such t h a t I t a ffo rd e d a d is ta n c e of a p p ro x im a te ly 0.027 in c h e s alo n g th e l i n e o f s ig h t t o be in fo c u s. T his prelim in a ry c o n c lu s io n was su p p o rte d by q u a n t i t a t i v e m easurem ents. Some d i s t i n c t i o n sh ould be made betw een th e s h e a r la y e r, and th e "two la y e r v e l o c i t y." Both, o f c o u rse, a re s h e a r la y e r s o f a s o r t, b u t th e y occur In d i f f e r e n t p la n e s. The s h e a r la y e r o c cu rs as a r e s u l t of a la r g e Ux v e lo c it y d if f e r e n c e over a sm a ll r d is t a n c e, and a p p e a rs a s a r a t h e r sh a rp i n te r f a c e betw een two 9x p la n e s. Bie "two la y e r v e lo c ity " o c cu rs as a r e s u l t o f d i f f e r e n t Ux v e l o c i t i e s i n two r x p la n e s. U iis w i l l p e rh a p s be made c l e a r e r by r e f e r r i n g to th e s k e tc h below.
141 shear layer ( 0x plane two layer rx plane F ig. 2 5. Shear L a y e rs. T his phenomenon was u s u a lly o b serv ed i n a s s o c i a t io n w ith th e e v e n ts of th e e j e c t i o n p ro c e s s, b u t d id n o t ap p ear each tim e an e j e c t i o n o c c u rre d. I t s ap p earan ce u s u a lly was n o ted when th e norm al o o urse o f th e e j e c t i o n p ro c e ss r e q u ire d two stre am s o f d i f f e r e n t c h a r a c te r to i n t e r a c t, i. e., d u rin g th e a c c e l e r a t i o n s te p, d u rin g th e e j e c t i o n, o r d u rin g th e sweep a f t e r th e e j e c t i o n. In a l l o f th e s e, I f th e stream s were on d i f f e r e n t p la n e s p e rp e n d ic u la r to th e l in e o f s i g h t, a "two la y e r " e f f e c t would be p o s s ib le. On th e few o c c a sio n s when i t was n o t a s s o c ia te d w ith an e j e c t i o n, th e d e c e le r a t i o n o f th e l o c a l mean stre a m had o c c u rre d so th e same f a c t o r s a p p l i e d. A lthough o th e r e v id e n c e I n d ic a te s I t can n o t be so, i t seems o f v a lu e to b r i e f l y c o n s id e r th e e f f e c t o f th e w a ll c u rv a tu re on t h i s o b s e r v a tio n. For th e w a ll view, the l i n e o f s i g h t i s a t th e p ip e w a ll th ro u g h h o r i z o n t a l p la n e s p a r a l l e l to th e h o r i z o n t a l d ia m e te r of th e p ip e. See F ig u re 13. The o p t i c a l sy stem has a d e p th o f f i e l d o f 0.0 2 7 in c h e s alo n g t h i s l i n e. I f one p la c e s th e u p p er e x tr e m ity o f t h i s
142 f i e l d a t th e pipe w a ll where th e h o r iz o n ta l p ip e d ia m e te r i n t e r s e c t s i t, one would have th e low er e x tre m ity a t a p lan e removed 0.0 2 7 in ch e s from i t a lo n g th e l in e o f s i g h t. S ince th e pip e w a ll i s cu rv ed, a p o in t on t h i s low er p la n e d i r e c t l y below one on th e upper p lan e w i l l be s l i g h t l y n e a r e r the w a l l. The v e lo c it y g r a d ie n t i s q u ite s te e p n e a r th e w a ll, so th e q u e s tio n i s w hether t h i s d isp la c e m e n t i s s u f f i c i e n t to cause a la rg e enough v e lo c it y d if f e r e n c e betw een th e p o in ts i n th e two p la n e s to e x p la in th e "two la y e r " e f f e c t. This c a l c u l a t i o n a p p e a rs in Appendix I I I, and c l e a r l y shows t h a t th e e f f e c t of th e c u rv a tu re i s to o sm a ll by s e v e r a l o rd e rs o f m agnitude to be a f a c t o r. A lso, i t was no ted t h a t the e f f e c t was n o t se en a t a l l tim e s b u t o n ly a t c e r t a i n tim e s. Tie p resen c e of two la y e r s moving in d i s t i n c t l y d i f f e r e n t d i r e c tio n s a ls o could n o t be e x p la in e d by th e c u rv a tu r e. The a x i a l v e l o c i t i e s o f s e le c te d p a r t i c l e s r e p r e s e n ta t i v e of each la y e r were m easured, and r e l a t i v e v e l o c i t i e s c a l c u l a t e d. The a b i l i t y to make th e s e m easurem ents, and th e a c c u ra c y o f the m easurem ents was enhanced by th e f a c t t h a t th e cam era was moved a t a p a r t i c u l a r a x i a l v e lo c it y i n th e flo w d i r e c t i o n. Thus in m ost c ase s th e slo w er moving p a r t i c l e s had p r a c t i c a l l y a z ero o r even a n e g a tiv e a x ia l v e lo c it y r e l a t i v e to th e cam era w h ile the f a s t e r ones moved a x i a l l y p a s t i t. T his e lim in a te d th e n e c e s s ity o f d is c rim in a tin g betw een two s im ila r a p p e a rin g v e l o c i t i e s, and p e r m itte d th e m easurem ent o f ev en sm a ll r e l a t i v e m o tio n s. T his
same g e n e r a l p ro ced u re a ls o enhanced the m easurem ent of e j e c t i o n a n g le s m entioned e a r l i e r. By keeping a r a d i a l l y moving p a r t i c l e i n view f o r a lo n g e r tim e w ith th e moving cam era, an a n g le o f 10, f o r exam ple, can a p p ea r as an a n g le o f 60-7 0 in th e m otion p i c t u r e s. The r e s u l t s of th e s e m easurem ents a p p ea r i n T able 6. I t sh o u ld be s t a t e d t h a t th e r e s u l t s in g e n e r a l r e f l e c t th e ten d e n cy to s e l e c t f o r m easurem ent th o se exam ples f o r which th e r e l a t i v e m o tio n betw een la y e r s was m ost e v id e n t and th e r e f o r e o f la rg e m agnitude. The upper l i m i t of th e r e l a t i v e v e l o c i t i e s, th e r e f o r e, has more s ig n if ic a n c e th a n th e lo w er. The r a t i o o f f a s t e r to slo w er v e l o c i t i e s has a maximum o f 2.9 / 1. The m ost common r a t i o, how ever, i s 1.5 /1. The t a b l e a ls o in c lu d e s a com parison o f th e a b s o lu te a x i a l v e lo c it y o f th e h ig h e r speed la y e r w ith the c a lc u la te d l o c a l mean a x i a l v e lo c it y f o r th e same y+ p o s i t io n. In g en e r a l th e agreem ent betw een th e two I s q u ite good, and one can conclude t h a t the h ig h e r speed la y e r i s m ost l i k e l y som ething ap p ro ach in g norm al tu r b u la n t flow w h ile th e slo w er speed la y e r I s r e ta r d e d flo w. One sequence o f m easurem ents In T able 6 i s f o r th e p r e v io u s ly m entioned c ase where a w a llward and outw ard flow c o e x is te d. They a ls o su p p o rt th e g e n e r a l view o f th e e f f e c t. There a r e o th e r o bserved p r o p e r tie s o f t h i s "two la y e r v e lo c ity " e f f e c t which shed a d d it i o n a l l i g h t on i t s o r i g i n. I n d is c u s s in g i t s ap pearance in a s s o c i a t io n w ith o th e r s te p a
144 TABLE 6 TWO LAYER VELOCITY R e la tiv e v e lo. a b s o l. ( f t / s e c ) A c tu a l v e l o. R a tio o f h ig h e r y+ range C a lc. p r o - h ig h e r v e lo. a b s o l. where f i l e v e lo low er ( f t. / s e c ) o c cu r f t. / s e c..2 1 6 2.9+.3 2 6.2 0.319.189 2.7.299 23.340.1 1 2 2.0.2 2 2 5.1 2 2.119 2.0.229 1 1. 5-2 0.2 2 3 -.3 1 9.129 1.7.316 18.31.1 3 6 1.7.323 16.304.1 3 6 1.7.318 ----- ------.1 2 0 1.7.302 ------ -.117 1.6.299 ------ ------.0 7 8 1.4.2 6 0 ------ ------.105 1.6.287 2 0.2.32.123 1.7.305 1 7.3.312. 066 1.4.247 1 4.9.289. 066 1.4.247 14.4.289.1 6 1 1.5.481 25-45. 5 2 1 -.6 0.132 1.5.464 2 2. 5-1 6. 5.5 0 2 -.4 4 2.254 1.8.5 8 0 29-37.5 5 -.5 7 8.225 1.7.557 16.4.438.2 0 2 1.6.534 15.4.423.147 1.5.471 33-20. 5 6 9 -.4 7 6.139 1.4.465 7.4-1 2.2 7 8 -.3 7 4.174 1.5.489 12-9.3 7 4 -.3 1 8.163 1.5.495 5.4 8 1 -.4 4 2.1 6 1 1.5.493 33-29.5 6 9 -.5 5.1 3 8 1.4.470 2 0.5.481.179 1.5.503 41-33.5 9 -.5 '.2 2 1 1.7.553 2 0.5-1 6.4.4 8 1 -.4 3 8.225 1.7.550 3 3-2 0.5. 5 6 9 -.4 8 1.2 1 0 1.6.542 2 4.6-1 6.4. 518-.4 3 8.169 1.5.501 2 0.5-2 8.7.4 8 1 -.5 5.104 1.3.436 2 0.5.481.155 1.5.487 29.55.127 1.4.457 1 4.5.411.171 1.3.687 3 1.8-9.5,. 728-.4 2 1.1 8 0 1.4.70 3 7 *1-2 1.2. 7 4 6 -.6 2 8.085 1.2.605 2 6.4-1 5.9. 6 85-.5 5 2 ro 0 Ui 1 M
TABLE 6. continued 145 A c tu a l R a d ia l v e l o c i t y A ngle to w a ll v e l o c i t y.2 6 8 15 1 0 r -.0 7 5.2 6 8 15 13' -.0 7 3.345 8013' -.0 5 0.124 3.70 +.036.1 2 8 18 +.040.1 4 1 9 +.0 2 2 o f th e e j e c t i o n e v e n t, i t was observed th a t o fte n th e e f f e c t w ould d isa p p e a r as th e d egree o f in t e r a c t io n o f th e two l a y - e r s in c r e a s e d. T h is im p lie s th a t th e two la y e r s were s e p a r - a te d b u t g ra d u a lly approached one a n o th e r or became s u f f i c i e n t l y e n e rg e tic to i n t e r a c t. F ig u re 26 shows th e "two la y e r v e lo c ity " i n a s e r i e s o f s t i l l p h o to g rap h s. A ll t h a t was sa id p re v io u s ly re g a rd in g image q u a li t y o f th e p r i n t s a p p lie s h e re as w e ll. As a r e s u l t, th e b r ig h t p a r t i c l e s mark the f l u id in v o lv e d in th e e v e n t, b u t th e le s s b r ig h t p a r t i c l e s, which i n th e m otion p ic tu r e s show th e e x te n t o f the m asses in v o lv e d, a re m is sin g. As b e fo re, a l l m otions in th e photographs a re r e l a t i v e to th e c a r r ia g e v e lo c ity which i s in d ic a te d. The w a ll view was used as shown by th e s k e tc h. A djacent to each photograph i s a sk e tc h drawn to s c a le d e p ic tin g th e r a d i a l and r e l a t i v e a x i a l p o s i t io n o f th e two m asses. Hie norm al l o c a l mean v e lo c it y p r o f i l e and the a p p a re n t v e lo c ity p r o f i l e c l e a r l y show t h a t th e r e l a t i v e m otion o f the f l u id m asses cannot be
146 t * 0108 Schematic of Two Layer Elements 50 t*.0068 t*.0 0 5 4 I----------------1 0 05" Scale Apparent Velocity Profile t.0041 Mean Velocity Carriage Velocity t» 0 sec. Mean Vilocity Profile + r - Nr# - 3 0,0 0 0 0.332 Figure 2 6. Two Layer Velocity.1.2.3.4.5 Velocity ft/sec.