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Gas spouting of fine particles Chandnani, Pratap P. 1984

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GAS SPOUTING OF FINE PARTICLES By PRATAP P. CHANDNANI B.Tech. Indian I n s t i t u t e of Technology, Bombay, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Chemical Engineering) We accept t h i s t h e s i s as conforming to the required standard J u l y 1984 ® Pratap P. Chandnani, 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of CKHl CArL The U n i v e r s i t y of B r i t i s h Columbia 1956 Main M a l l Vancouver, Canada V6T 1Y3 Date WQ. I , If** DE-6 (3/81) - i i -ABSTRACT Spouting i s a w e l l e s t a b l i s h e d g a s - s o l i d s c o n t a c t i n g technique f o r coarse p a r t i c l e s ( d p ^> 1 mm) which are not r e a d i l y f l u i d i z e d . Spouting of f i n e p a r t i c l e s (dp < 1 ram), however, i s a sp a r s e l y touched sub j e c t : the few reports i n the l i t e r a t u r e are not i n complete harmony with each other, and they lead to a somewhat confused p i c t u r e about the s p o u t a b i l i t y of f i n e p a r t i c l e s . Experiments were conducted i n a 152-mm diameter transparent c o n i c a l - c y l i n d r i c a l half-column with p a r t i c l e s ranging i n s i z e from 90 to 1000 ym and i n d e n s i t y from 900 to 8900 kg/m3. The d i f f e r e n t flow regimes which r e s u l t on varying bed height and gas v e l o c i t y f o r a given p a r t i c l e species were c a r e f u l l y observed, video-taped and mapped. The c r i t e r i a of both G e l d a r t (1973) and Molerus (1982) f o r spoutable p a r t i c l e s ( c l a s s i f i e d as Group D by Geldart) were shown to be u n s a t i s -f a c t o r y . F o l l o w i n g Ghosh (1965), however, i t was found that formation of a s t a b l e spout was ensured only i f a c r i t i c a l r a t i o (25.4 i n our experiments) of i n l e t o r i f i c e s i z e to p a r t i c l e diameter was not exceeded. Measurements were a l s o made of bed pressure drops, s o l i d s c i r c u l a t i o n patterns and r a t e s , dead zones, l o n g i t u d i n a l annular gas v e l o c i t y p r o f i l e s , spout contours and fo u n t a i n h e i g h t s . I t was found that the mechanism by which spouting i s terminated i n a coarse p a r t i c l e bed, namely, f l u i d i z a t i o n of the annulus, could not account f o r i t s termination i n the present beds. The hypothesis that termination was caused instead by choking of the spout was r e i n f o r c e d by the f a c t that the theory of choking i n standpipes could be applied to s a t i s f a c t o r i l y p r e d i c t the end of s t a b l e spouting. - i i i -TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGMENTS x i CHAPTER 1 - INTRODUCTION 1 CHAPTER 2 - LITERATURE REVIEW 5 2.1 S p o u t a b i l i t y of Fine P a r t i c l e s and the Conditions A f f e c t i n g I t 5 2.1.1 E f f e c t of i n l e t s i z e 5 2.1.2 E f f e c t of p a r t i c l e s i z e and density 11 2.2 B a s i c Spouting Parameters 13 2.2.1 Minimum spouting v e l o c i t y 13 2.2.2 Maximum spoutable bed depth 14 2.2.3 Spout diameter 16 2.2.4 Fountain height 17 2.3 Regime Maps 17 2.4 L o n g i t u d i n a l Annulus F l u i d v e l o c i t y and O v e r a l l Bed Pressure Drop 19 2.5 Annular P a r t i c l e V e l o c i t y P r o f i l e and S o l i d C i r c u l a t i o n Rate 23 2.6 I n d i r e c t Approaches Relevant to Spouting of Fine P a r t i c l e s . . . 24 CHAPTER 3 - APPARATUS AND BED MATERIALS 27 3.1 Choice and D e s c r i p t i o n of Experimental Apparatus 27 - i v -Page 3.2 Bed M a t e r i a l s 33 CHAPTER 4 - REGIME MAPS AND CRITERIA FOR FINE PARTICLE SPOUTING 41 4.1 Experimental Procedure 41 4.2 Res u l t s and Their A n a l y s i s 44 4.2.1 Influence of i n l e t diameter 44 4.2.2 E f f e c t of p a r t i c l e s i z e 53 4.2.3 E f f e c t of p a r t i c l e d e n s i t y 58 4.2.4 Minimum and maximum spouting v e l o c i t i e s 58 4.2.5 E f f e c t of bed height, maximum spoutable bed depth, and s t a b l e j e t length 60 4.2.6 P r e d i c t i o n of regime transformation.... 64 CHAPTER 5 - OVERALL BED PRESSURE DROP AND LONGITUDINAL FLUID VELOCITY IN THE ANNULUS 70 5.1 Measurement Technique 70 5.1.1 O v e r a l l bed pressure drop 70 5.1.2 L o n g i t u d i n a l f l u i d v e l o c i t y i n the annulus 71 5.2 Res u l t s and Di s c u s s i o n 72 5.2.1 O v e r a l l bed pressure drop 72 5.2.2 Annular l o n g i t u d i n a l gas v e l o c i t y 79 - v-Page CHAPTER 6 - ANNULAR PARTICLE VELOCITY AND CIRCULATION RATE 84 6.1 Measurement Technique 84 6.2 Results and Their I n t e r p r e t a t i o n 87 6.2.1 E f f e c t of bed depth and U/U m s 90 6.2.2 E f f e c t of p a r t i c l e s i z e 92 6.2.3 E f f e c t of cone angle 92 CHAPTER 7 - SPOUT SHAPE, SPOUT DIAMETER AND FOUNTAIN HEIGHT ... 95 7.1 Measurement Technique 95 7.2 R e s u l t s and Di s c u s s i o n 95 7.2.1 Spout shape and diameter 95 7.2.2 Fountain height 98 CHAPTER 8 - CONCLUSIONS AND RECOMMENDATIONS 104 8.1 Conclusions 104 8.2 Recommendations For Further Work 106 NOTATION 107 REFERENCES 110 APPENDICES A - Rotameter C a l i b r a t i o n Curves 113 B - S o l i d Free Pressure Drop Curves 117 C - S t a t i c Pressure Probe C a l i b r a t i o n In a Loose Packed Bed 121 D - Experimental Data 123 D.l Pressure drop vs. flow rate 126 D.2 Annular gas v e l o c i t y 135 D.3 S o l i d c i r c u l a t i o n rate 136 D.4 Spout diameter and region of c i r c u l a t i o n .• • • • ^ 0 - v i -LIST OF TABLES Pages Table 3.1 P r o p e r t i e s of bed m a t e r i a l s 36 Table 3.2 P a r t i c l e s i z e d i s t r i b u t i o n s 38 Table 4.1 Operating conditions i n t h i s work vs. those of Heschel and Klose (1981) 42 Table 4.2 Experimental values of minimum spouting v e l o c i t y vs. eq. (2.3) 61 Table 4.3 Experimental vs. predicted maximum spoutable bed depths 63 Table 4.4 Experimental and pre d i c t e d j e t p e n e t r a t i o n depths f o r H > ^ , Q = Q m F 65 Table 4.5 P r e d i c t i o n of maximum s t a b l e spouting v e l o c i t y (= U c) by choking c r i t e r i o n vs. experimental value [= U g(H)] 67 Table 4.6 Maximum spoutable bed depth, experimental vs. p r e d i c t i o n through the theory of choking 69 Table 5.1 Ra t i o AP /AP _ « Cn - experimental and ,ms, raF u t h e o r e t i c a l 78 Table 7.1 L o n g i t u d i n a l l y averaged spout diameter (experimental vs. predicted) 101 - v i i -LIST OF FIGURES Page Figure 1.1 Schematic diagram of a spouted bed 2 Figure 2.1a Regime map. Sand, dp = 0.42 -0.83 mm, D c = 15.2 cm, d^ ^ = 1.25 cm (Mathur and G i s h l e r , 1955) 7 Figure 2.1b Regime map. Sand, d p = 0.42 -0.83 mm, D c = 15.2 cm, d j [ = 1.58 cm (Mathur and G i s h l e r , 1955) 7 Figure 2.2 Phase diagram. Semicoke, dp = 1-5 mm, D c = 23.5cm, d± = 3.05 cm, (Mathur and G i s h l e r , 1955) 8 Figure 2.3 Pressure drop vs. v e l o c i t y data of Heschel and Klose (1981). PVC, d = 90 ym, P p = 1.27 g/cm3, p b = 0.565 g/cm3, a i r at 80% r e l a t i v e humidity 9 Figure 2.4 T y p i c a l pressure drop vs. v e l o c i t y curve f o r a spouted bed of coarse p a r t i c l e s 10 Figure 2.5 Geldart (1973) and Molerus (1982) c r i t e r i a on a l o g - l o g p l o t . P a r t i c l e s below the l i n e are termed 'non - spoutable' and above i t as ' spoutable' . 12 Figure 2.6 ( A P m s / AP mp) vs. (H/D c) f o r d i f f e r e n t values of 8 (Morgan and Littman, 1980) 22 Figure 3.1 D e t a i l s of the two h a l f c y l i n d r i c a l columns 28 Figure 3.2 Photograph of the o r i f i c e p l a t e s 29 Figure 3.3 D i f f e r e n t i n l e t types (without any c o n t r a c t i o n of the i n l e t ) f o r column 2 30 Figure 3.4 Schematic of the o v e r a l l equipment layout 32 Figure 3.5 Photograph of the equipment 34 Figure 3.6 Schematic diagram of the s t a t i c pressure probe 35 - v i i i -Page Figure 4.1 T y p i c a l pressure drop vs. flow r a t e c h a r a c t e r i s t i c s obtained upon repeating the c o n d i t i o n s of Heschel and Klose (1981) 45 Figure 4.2a C r i t i c a l i n l e t diameter range f o r steady spouting vs. p a r t i c l e diameter 47 Figure 4.2b C r i t i c a l i n l e t diameter (mid - p o i n t s of the ranges shown i n f i g . .4.2a) vs. p a r t i c l e diameter 48 Figure 4.3 Regimes on spouting p a r t i c l e s with d < 350 um 50 P Figure 4.4a Regime map. Sand, dp = 401 um, d^ = 4.5 mm 51 Figure 4.4b Regime map. Sand, dp = 401 Mm, d^ = 6 mm 51 Figure 4.5 Photographs of the d i f f e r e n t regimes shown i n f i g . 4.4 52 Figure 4.6 T r a n s i t i o n betwen regimes along X 1 X 5 i n f i g . 4.4b with i n c r e a s i n g flow 54 Figure 4.7 E f f e c t of i n l e t s i z e on v a r i o u s regimes. Sand, d„ = 516 pm (a) d± = 6 mm (b) d± = 12.7 mm (c) d± = 19.05 mm (above the c r i t i c a l l i m i t f o r steady spouting) 55 & 56 Figure 4.8 Regime map - e f f e c t of i n l e t diameter. G l a s s , dp = 710 ym (a) = 6.0 mm (b) d ± = 12.7 mm 57 Figure 4.9 G e l d a r t (1973) and Molerus (1982) c r i t e r i a f o r s p o u t a b i l i t y on a l o g - l o g scale 59 Figure 5.1a Pressure drop vs. flow rate c h a r a c t e r i s t i c s for d i f f e r e n t bed h e i g h t s . PVC, d = 186 um, d. = 4.5 mm 74 P i Figure 5.1b Pressure drop vs. flow rate f o r d i f f e r e n t bet h e i g h t s . Sand, d p = 516 um, d. = 6 mm. 74 - i x -Page Figure 5.1c E f f e c t of p a r t i c l e s i z e on pressure drop. Sand, H= 41 cm, d^ = 6 mm 7 5 Figure 5.2a Stagnant zone and region of c i r c u l a t i o n with i n c r e a s i n g flow r a t e . PVC, dp = 186 ym, d^ = 4.5 mm, H = 19.5 cm, A i r at 80% r e l a t i v e humidity 76 Figure 5.2b Stagnant zone and region of c i r c u l a t i o n w i t h i n c r e a s i n g dp. Sand, H = 41cm, d^ = 6 mm 77 Figure 5.3 L o n g i t u d i n a l annular gas v e l o c i t y - expt. vs. theor. Sand, U/Ums = 1 • 18 , d. = 6 mm, d =516 ym 80 l p Figure 5.4 L o n g i t u d i n a l annular gas v e l o c i t y d i s t r i b u t i o n . Sand, dp = 401 ym, d^ = 6mm, U/U m e = 1.18 81 ms Figure 5.5 Ef e c t of p a r t i c l e s i z e , i n l e t diameter and bed height on l o n g i t u d u a l annular gas v e l o c i t y . Sand, U/U =1.18 82 ' ms Figure 6.1 Nodal points for p a r t i c l e v e l o c i t y determination 85 Figure 6.2 a & b Rad i a l and a x i a l p a r t i c l e v e l o c i t y gradients i n the annulus. Sand, dp = 516 ym, H = 50 cm, dL = 6 mm, U/U = 1.08 88 & 89 Figure 6.2c R a d i a l l y averaged annular p a r t i c l e v e l o c i t y f o r data i n f i g s . 6.2a and 6.2b 89 Figure 6.3 E f f e c t of bed height and i n l e t f l u i d v e l o c i t y on s o l i d s flow rate i n the annulus. Sand, d]_ = 6 mm (a) dp = 401 ym (b) d = 516 ym 91 P Figure 6.4 E f f e c t of p a r t i c l e s i z e on G a. Sand, d i = 6 mm, (a) U/U m s = 1.08 (b) U/U m g = 1.18 93 Figure 6.5 E f f e c t of cone angle on G a. Sand, d = 516 ym, d._ = 6 mm, U/U m g = 1.08 94 Page Figure 7.1 D i f f e r e n t spout shapes observed 96 Figure 7.2 E f f e c t of bed height on spout diameter. Sand, d = 516 um, d. = 6 mm, U/U = 1.08 97 p ' i ms Figu r e 7.3a E f f e c t of U/Uras on spout diameter. Sand, d p = 516 um, d^ = 6 mm 97 Figu r e 7.3b E f f e c t of U/U m s on spout diameter. ~P Figure 7.4 V a r i a t i o n of spout diameter w i t h p a r t i c l e s i z e , d± = 6 mm, U/U m s = 1.08 100 Polypropylene, d = 299 um, d± = 2.8 mm 99 Figure 7.5 E f f e c t of cone angle on spout shape. Sand, dp = 516 um, d-L = 6 mm, U/U = 1.08 100 ms Figure 7.6 E f f e c t of bed height on H_ 102 F Figure 7.7 E f f e c t of p a r t i c l e s i z e on 102 - x i -ACKNOWLEDGEMENTS I g r e a t l y appreciate the guidance and encouragement of Dr. N. Ep s t e i n at every stage of t h i s p r o j e c t . I am als o than k f u l to Dr. J.R. Grace and Dr. C.J. Lim f o r t h e i r very h e l p f u l suggestions an d i s c u s s i o n s . A l l my f r i e n d s also deserve s p e c i a l c r e d i t f o r making my stay here a pleasant one. Graduate f e l l o w s h i p from the U n i v e r s i t y of B r i t i s h Columbia f o the l a s t one year i s g r a t e f u l l y acknowledged. - 1 -CHAPTER 1 INTRODUCTION The s i g n i f i c a n c e of s o l i d - f l u i d c o n t a c t i n g devices i n v o l v i n g the motion of the f l u i d as w e l l as the s o l i d s has grown considerably i n recent years. F l u i d i z a t i o n i s the most widely accepted technique of t h i s type today. In the f i f t i e s , the spouted bed technique was developed f o r processing coarse p a r t i c l e s (dp _> 1 mm) f o r which gas f l u i d i z a t i o n becomes i n c r e a s i n g l y non-uniform as the p a r t i c l e s i z e i s increased ( s l u g g i n g or poor q u a l i t y aggregative f l u i d i z a t i o n then occurs - Mathur and E p s t e i n , 1974). A spouted bed involve s a j e t of f l u i d i s s u i n g out of a c e n t r a l opening i n t o the bottom of an i n i t i a l l y f i x e d bed of p a r t i c l e s . As shown i n F i g . 1.1, i f the i n j e c t i o n rate of the f l u i d i s high enough, the r e s u l t i n g c e n t r a l 'spout' causes a stream of p a r t i c l e s to r a p i d l y r i s e above the bed i n t o a 'fountain' which showers the p a r t i c l e s back onto the surrounding 'annulus', where the p a r t i c l e s slowly move downward and s l i g h t l y inward as a moving packed bed. F l u i d from the spout p r o g r e s s i v e l y leaks i n t o the annulus, while p a r t i c l e s from the annulus s h o r t - c i r c u i t back i n t o the spout. The o v e r a l l system thereby becomes a composite of a c e n t r a l l y located dilute-phase cocurrent-upward transport region surrounded by a dense-phase moving packed bed with countercurrent p e r c o l a t i o n of the f l u i d . A more organized motion of the s o l i d s than i n a f l u i d i z e d bed i s thus e s t a b l i s h e d , with e f f e c t i v e f l u i d - s o l i d - 2 -FOUNTAIN BED SURFACE SPOUT ANNULUS SPOUT-ANNULUS INTERFACE CONICAL BASE FLUID INLET F i g . 1.1. Schematic diagram of a spouted bed - 3 -c o n t a c t i n g and unique hydrodynamics. Other d i f f e r e n c e s from a f l u i d i z e d bed i n c l u d e the use i n a spouted bed of coarse p a r t i c l e s (e.g. i n the mm r a t h e r than the 100 um range), bed diameters which to date have only r a r e l y exceeded 1 metre, a simple o r i f i c e gas i n l e t r ather than an elaborate gas d i s t r i b u t i o n g r i d , and a r e s u l t i n g bed pressure drop which i s considerably l e s s than that required to support the buoyed weight of the s o l i d s as i n f l u i d i z a t i o n . Through the years, various m o d i f i c a t i o n s and analogs of the spouted bed concept have evolved. These include the s p o u t - f l u i d bed, r e c i r c u l a t i n g beds ( w i t h a d r a f t tube), j e t ( s ) i n a f l u i d i z e d bed, e t c . Some of these have been summarized by F i l l a et a l (1983). Although the spouted bed f o r coarse p a r t i c l e s ( d p >^  1 mm) has been studied quite i n t e n s i v e l y , not much inf o r m a t i o n e x i s t s on the use of a spouted bed f o r f i n e p a r t i c l e s ( d p < 1 mm). The fragmentry i n f o r m a t i o n a v a i l a b l e on f i n e p a r t i c l e spouting d i f f e r s considerably from one worker to another, i s sometimes even c o n t r a d i c t o r y and f a i l s to give any d e f i n i t e conclusions. The present work i n v o l v e s a d e t a i l e d study of the f i n e p a r t i c l e spouted bed. The present research focuses p r i m a r i l y on t e s t i n g the r e s u l t s of previous workers, on i d e n t i f y i n g and c h a r a c t e r i z i n g the various flow regimes involved and on developing c r i t e r i a f o r * s t a b l e spouting of f i n e p a r t i c l e s . The hydrodynamic studies i n c l u d e : regime maps, p a r t i c l e *'Stable spouting' implies a steady spout w a l l , steady f o u n t a i n w i t h a w e l l defined shape etc. as shown i n f i g . 1.1. c i r c u l a t i o n rate i n the annulus, l o n g i t u d i n a l annular f l u i d v e l o c i t y d i s t r i b u t i o n , f o u n t a i n shape and h e i g h t , spout shape and diameter, and o v e r a l l pressure drop. Comparison of the data obtained w i t h e x i s t i n g c o r r e l a t i o n s f o r coarse p a r t i c l e s , and use of the i n f o r m a t i o n from other r e l a t e d areas to e x p l a i n some of the observed phenomena, c o n s t i t u t e d secondary o b j e c t i v e s of t h i s work. - 5 -CHAPTER 2 LITERATURE REVIEW "Although spouting of coarse p a r t i c l e s (dp 2. 1 111111) ^ s a w e l l e s t a b l i s h e d phenomenon, spouting of f i n e p a r t i c l e s i s a very sparsely touched su b j e c t . The few reports that do e x i s t on spouting of f i n e p a r t i c l e s are not i n complete harmony w i t h each other. The basic problem s t i l l r e v olves around whether f i n e p a r t i c l e s are spoutable or not, and i f so, under what c o n d i t i o n s , and how do the r e s u l t i n g beds d i f f e r from a r e g u l a r spouted bed of coarse p a r t i c l e s . The present review examines the l i t e r a t u r e a v a i l a b l e on spouting of f i n e p a r t i c l e s , both through d i r e c t and i n d i r e c t s t u d i e s . Some of the basic hydrodynamic features of a spouted bed r e l e v a n t to the present study are a l s o reviewed. 2.1 Spoutability of Fine Particles and the Conditions Affecting It 2.1.1 Effect of i n l e t size U n t i l 1981 i t was ge n e r a l l y thought that f i n e p a r t i c l e s ( s i z e as small as 80 to 100 mesh) can be made to spout only i f the o r i f i c e s i z e was less than 30 times the p a r t i c l e diameter (Ghosh, 1965). The r e s u l t i n g j e t becomes so small that i t e n t r a i n s very few p a r t i c l e s and so the region of s o l i d c i r c u l a t i o n i s l i m i t e d to a region very close to the spout. Ghosh based h i s c r i t e r i o n on the data c o l l e c t e d i n a 15.2 cm diameter s p l i t column with 165 um glass beads. The r e s u l t s of Rooney - 6 -and Harrison (1974) were found to obey Ghosh's c r i t e r i o n f o r a c r i t i c a l i n l e t to p a r t i c l e s i z e r a t i o which must not be exceeded i n order to achieve steady spouting. They report that i n c r e a s i n g the i n l e t diameter beyond t h i s c r i t i c a l s i z e gave r i s e to bubbling or slugging. The regime maps of Mathur and G i s h l e r (1955) f o r sand p a r t i c l e s of 420 to 830 ym, displayed i n f i g s . 2.1a and 2.1b, f o l l o w Ghosh's c r i t e r i a . F i g . 2.2 shows that a much l a r g e r region of steady spouting i s t y p i c a l of a coarse p a r t i c l e spouted bed. In 1981, however, two East German s c i e n t i s t s , Heschel and K l o s e , reported spouting of PVC powder having a mean diameter of 90 ym i n a 30 cm diameter c y l i n d r i c a l column with an i n l e t s i z e of 25.4 mm, i . e . dj/dp = 282, f a r above the d-j/dp = 30 suggested by the previous workers. Their r e s u l t s showing pressure drop vs. flow rate were most unusual i n that they e x i b i t e d two peaks as shown i n f i g . 2.3. This i s quit e d i f f e r e n t from the c h a r a c t e r i s t i c s of a regu l a r coarse p a r t i c l e spouted bed, shown i n f i g . 2.4 f o r comparison. The f i r s t peak i n f i g . 2.3 corresponds to a gas j e t breaking through the bed i n an unsteady manner, forming a c r a t e r shaped area around i t . The c i r c u l a t i o n of s o l i d s was reported to be apparent only near the j e t and the 'annulus' was at r e s t . The foot of the second peak i s a t t r i b u t e d to the onset of steady spouting of the bed, a f t e r which the pressure drop remains constant with flow. In a conventional spouted bed, however, steady spouting sets i n when the pressure f i r s t drops ( f o o t of the peak i n F i g . 2.4) and there i s no second peak. - 7 -175 150 1 2 5 z t-o. UJ o o UJ CD 1 0 0 75 5 0 1 i i O 0 c \ S L U G G I N G fv ^ " S T A T I C f B E D / J / o / / - / \ B U B B L I N G A / P ^  / / o / / 0- / / 1 0 / / *- / /J z k Q w A I UJ 1 I * / / o / • / ° / 0 / l P R O G R E S S I V E L Y I N C O H E R E N T S P O U T I N G , 1 , 1 , 0.15 0 . 2 0 0 . 2 5 0 . 3 0 0 . 3 5 0 . 4 0 0 .45 S U P E R F I C I A L . AIR V E L O C I T Y , m/stc F i g u r e 2.1a. Regime map. Sand, (3^=0.42-0.83 irm, Dc=15.2 cm, d ^ l . 2 5 cm (Mathur and G i s h l e r , 1955). BUSBLif- 'G S L U G G I N G 02 0 J 0 •> 05 SUPERF IC IAL AIP V E L O C I T Y. m/sec Figure 2.1b. Regime ITHD. Sand, d =0.42-0.83 mm, D =15.2 cm, ^ P c d ^ l . 5 8 cm (Mathur and G i s h l e r , 1955). - 8 -04 0.6 0.8 1.0 1.2 SUPERF IC IAL AIR VELOCITY, m/jec F i g u r e 2.2. Phase diagram. Semicoke, d^=l-5 ram, d.=3.05 cm (Mathur and E p s t e i n , 1974). - 9 -0-0 0.9 1.8 2.7 3.6 4.5 SUPERFICIAL GAS VELOCITY, cm/s. 5.4 6.3 Figure 2.3. Pressure drop vs. v e l o c i t y data o f Heschel and K l o s e (1981) 3 3 PVC, d p=0.09 mm, p^=1270 kg/m , p b=565 kg/m . F l u i d used: A i r a t 80% r e l a t i v e humidity. - 10 -S U P E R F I C I A L V E L O C I T Y Figure 2.4. T y p i c a l pressure drop vs. v e l o c i t y curve f o r a spouted bed o f coarse p a r t i c l e s . - 11 -2.1.2 Effect of particle size and density Another c l a s s i f i c a t i o n attempting to d i s t i n g u i s h between spoutable and non-spoutable p a r t i c l e s was derived by Geldart (1973) and modified by Molerus (1982). Geldart (1973) concluded that p a r t i c l e s f o r which: tend to form s t a b l e spouts and c l a s s i f i e d them as "Group D' p a r t i c l e s . Molerus (1982) c l a s s i f i e d spoutable p a r t i c l e s (Group D) as those f o r which the dynamic pressure exerted by the f l u i d exceeds a d i s t i n c t value depending on the p a r t i c l e s i z e and d e n s i t y d i f f e r e n c e between the p a r t i c l e and the f l u i d . He proposed the l i m i t i n g c o n d i t i o n f o r s p o u t a b i l i t y as: The c r i t e r i a of Geldart (1973) and Molerus (1982) both become l i n e a r on a l o g - l o g p l o t ( F i g . 2.5) and p r e d i c t : 1. That p a r t i c l e s f a l l i n g below the given l i n e i n F i g . 2.5 are non-spoutable and those f a l l i n g above the l i n e are spoutable. 2. That i n c r e a s i n g the p a r t i c l e s i z e and density d i f f e r e n c e between the p a r t i c l e and the f l u i d enhance t h e i r s p o u t a b i l i t y . 3. No e f f e c t of i n l e t diameter on s p o u t a b i l i t y . (p - p ) d^ > 10 P f P — 2 6 g(ym) (cm ) (2.1) (2.2) -, 12 -d (mm) P F i g u r e 2.5. G e l d a r t (1973) and Molerus (1982) c r i t e r i a on a l o g - l o g p l o t . P a r t i c l e s below the l i n e are termed as 'non-spoutable' and above i t as 'spoutable'. - 13 -2.2 Basic Spouting Parameters 2.2.1 Minimum spouting velocity This i s the minimum s u p e r f i c i a l v e l o c i t y required to maintain a c e r t a i n bed i n a s t a b l e spouting c o n d i t i o n . I t i s represented by p o i n t B i n F i g . 2.4, i . e . the v e l o c i t y at which the pressure drop across the bed s t a r t s to r i s e again upon decreasing the f l u i d flow*. Although a number of equations are a v a i l a b l e i n the l i t e r a t u r e f o r p r e d i c t i n g the minimum spouting v e l o c i t y , U m s , (Mathur and E p s t e i n , 1974), the most commonly used one i s s t i l l the Mathur-Gishler e m p i r i c a l equation (1955) which i s based on data from both gas and l i q u i d spouted beds: r d -, rd -.1/3 r 2 g ( p n - p ) H-] l / 2 Ghosh (1965) a l s o derived an equation f o r the minimum spouting v e l o c i t y , based on a momentum balance between the p a r t i c l e s and the f l u i d at the f l u i d i n l e t . His equation, which i s q u i t e s i m i l a r i n form to the Mathur-Gishler equation, provides some t h e o r e t i c a l basis f o r i t : 1/2 •2g( P_ - p f) Hi U = l ^ - r - |-£ I I I L — — (2.4) [2kn'-|l/2 P p l f ms [ 3 J _ D J L p f *In the case of very f i n e p a r t i c l e s (dp < 350 urn) steady spouting i s observed at a v e l o c i t y greater than that shown i n f i g . 2.4, The gas simply bubbles through between points B and C (somewhat a r b i t a r i l y chosen here) and steady spouting sets i n only at point C. Geldart (1981) recommends C as the p o i n t for determining U r a s for these p a r t i c l e s , since point C i s f a i r l y r e producible i n a f u l l column a l s o . - 14 -A more recent c o r r e l a t i o n f o r U m s comes from Grbavcic et a l (1976) based on t h e i r flow model: U / U _ - ka , , m S f * = [ l'-Cl -H/y 3 ] (2.5) a For a m a j o r i t y of systems, - m 2 • and a a « 1 - !-=• I . k =1 whence ^ f L = 1 - 1 - H / ^ ) 3 ( 2 - 5 a ) mF 2.2.2 Maximum spoutable bed depth The maximum spoutable bed depth, H M, i s the maximum bed height a t which a s t a b l e spout can be maintained. Mathur and E p s t e i n (1974) have reported three d i f f e r e n t mechanisms f o r spout termination when the bed height exceeds % . They are: 1. F l u i d i z a t i o n of the annular s o l i d s . 2. Choking of the spout. 3. Growth of an i n s t a b i l i t y at the spout-annulus i n t e r f a c e . - 15 -The f i r s t mechanism i s known to occur i n a re g u l a r spouted bed of coarse p a r t i c l e s and the second mechanism has been reported to p r e v a i l i n the case of f i n e p a r t i c l e s (Littman et a l , 1977). Various c o r r e l a t i o n s f o r H M have been l i s t e d by Mathur and E p s t e i n (1974) and Kim (1982). For p a r t i c l e s w i t h average diameter l e s s than 1 mm, HJ»J increases with i n c r e a s i n g p a r t i c l e s i z e , and decreases when p a r t i c l e s i z e exceeds about 1.2 mm. A maximum thus occurs i n a H M vs. dp curve, somewhere near d p = 1 mm. Only the c o r r e l a t i o n s showing an i n c r e a s i n g trend of H M w i t h d p are thus r e l e v a n t to t h i s study, where d p < 1mm. One of the c o r r e l a t i o n s developed by Littman et a l (1977), by simultaneous s o l u t i o n of pressure and v e l o c i t y d i s t r i b u t i o n i n the annulus of a spouted bed using c o n t i n u i t y and the vector form of Ergun's equation, i s : M s 2 2 (D - D Z) c s 0.34.5 -0.384 (2.6) Another expression comes from Morgan and Littman (1979): / D c = (0.218 + 0.005/A + 2.5 x 10 Ik ) * (2.7a) A > 0.014 - 16 -D / D = 175 (A - 0.01) - j - C ; (2.7b) i 0.01 < A < 0.014 where A i s defined by equation (2.14). I t has been reported by Geldart et a l (1981) that % i n a h a l f column i s u s u a l l y about 15% l e s s than that i n a f u l l column, probably due to gas-wall and p a r t i c l e - w a l l f r i c t i o n . 2.2.3 Spout diameter Spout diameters are u s u a l l y measured i n a h a l f - c y l i n d r i c a l column. Lim and Mathur (1974) used X-ray photography to determine spout shape and s i z e i n a f u l l column and found that the f l a t surface i n a h a l f column had n e g l i g i b l e e f f e c t on the spout geometry. An e m p i r i c a l c o r r e l a t i o n f o r the l o n g i t u d i n a l l y averaged spout diameter at the minimum spouting c o n d i t i o n i s due to McNab (1972): ms 1.48 G 0- 4 9 D ° - 6 8 ms c 0.41 (2.9a) For a gas v e l o c i t y above minimum spouting we have, according to McNab (1972): D U J s L msJ ms 1/2 (2.9b) - 17 -2.2.4 Fountain height Grace and Mathur (1978) proposed an expression f o r es t i m a t i n g f o u n t a i n height, Hp, based on a momentum i n t e g r a l over the fo u n t a i n : The fo u n t a i n shape has been reported to be approximately p a r a b o l i c i n most cases. 2.3 Regime Maps The f i r s t regime maps r e l e v a n t to f i n e p a r t i c l e spouting appeared i n the work, of Mathur and G i s h l e r (1955) and are shown i n f i g s . 2.1a and 2.1b. More r e c e n t l y Littman and Morgan (1984) suggested a c h a r a c t e r i z a t i o n of spouting regimes by a parameter C Q, where: 1.46 V 2g ( P p - P f) (2.10) C = / 1 [1 - e s (Z')] ms dZ' , V = Z/H (2.11) AP ms + (2.12a) AP mF ( 1 " emF> ( p p " P f ^ H - 18 -AP AP ms (2.12b) mF This a n a l y s i s i s based on momentum equations f o r gas and s o l i d s . When equation (2.11) i s subjected to the boundary c o n d i t i o n s : e s (0) = 1 and e (1) ms s ms mF (2.13) i t i s observed that only f o r values of C 0 between 0.215 and 0.785 does e g(Z') decrease monotonically ( e g ( Z T ) should decrease monotonically to be c o n s i s t e n t with the p h y s i c a l observations, since p a r t i c l e s enter the spout throughout the bed h e i g h t ) . However f o r C Q > 0.785, e g(Z') was found to s t a b i l i z e only when e s(0) < 1, which would req u i r e p a r t i c l e s to be present at the spout i n l e t . The l a t t e r has been experimentally observed when 855 um glass beads are spouted w i t h a i r (Littman et a l , 1977). A l s o , i n the case of spouting of f i n e p a r t i c l e s with water, C 0 has been found to average around 0.85 and e g (0) < 1 (Kim, 1982). Kim (1982) a l s o suggested that spouting of f i n e p a r t i c l e s w i t h water c o n s t i t u t e d a new spouting regime because h i s experimental data on H M, Dg and AP r a g were not s a t i s f a c t o r i l y p r e d i c t e d by the c o r r e l a t i o n s f or coarse p a r t i c l e s . He a l s o found that while spout termination i n the case of f i n e p a r t i c l e spouting with a i r occurred due to choking of the spout, the termination mechanism i n the case of a water spouted f i n e p a r t i c l e bed was annular f l u i d i z a t i o n . - 19 -Annular f l u i d i z a t i o n a l s o p r e v a i l s as the spout termination mechanism i n a conventional spouted bed of coarse p a r t i c l e s . C 0 < 0.215 i s i n t e r p r e t e d as the case where very shallow beds are used and the spout i s simply a hole blowing through with very few p a r t i c l e s entrained i n s i d e i t . Morgan and Littman (1982) a l s o use a parameter A, re p r e s e n t i n g the r a t i o of j e t i n e r t i a to bed pressure drop f o r c e s , to c h a r a c t e r i z e regimes. Their dimensionless p l o t of mA vs. A f o r p r e d i c t i n g the maximum spoutable height e x i b i t s a break i n the p l o t f o r a value of A around 0.02. This break i s a t t r i b u t e d to the t r a n s i t i o n to a new spouting regime. A i s defined as: A = Umf UT Pf> g d. (2.14) and can be modified f o r n o n - s p h e r i c i t y . 2.4 Longitudinal Annulus Fluid Velocity and Overall Bed Pressure Drop The equation which has proven to be the most s u c c e s s f u l f o r p r e d i c t i n g the l o n g i t u d i n a l annular f l u i d v e l o c i t y f o r coarse p a r t i c l e s i s a c o n t r i b u t i o n of Mamuro and H a t t o r i (1968/1970) f o r a bed at i t s maximum spoutable bed height: U a 3 TZ - 1 - ( l - z / h m > mF (2.15) - 20 -Darcy's law was assumed to be v a l i d i n the annulus and l e d t o : AP ms AP ( P p - P f) (1 - eA> g ^ = 0.75 (2.16) The boundary c o n d i t i o n s used were: ( i ) Z = 0, U = 0 ( i i ) Z = H M, U a = U a ( H M ) = U, mF mF = ( P p _ P f ) ( 1 _ ^ g (2.17) I t was found experimentally that U a (H M) i s about 10 to 15% l e s s than U mp ( E p s t e i n et a l , 1978) and hence eq. (2.15) should be modified t o : U 1 - (1 -Z/ )• (2.18) Lefroy and Davidson (1969) formulated the f o l l o w i n g equation f o r l o n g i t u d i n a l pressure d i s t r i b u t i o n , based on t h e i r e m p i r i c a l f i n d i n g s : (2.19) - 21 -I t was shown by Ep s t e i n et a l (1978) that applying the v e l o c i t y r e l a t i o n s h i p : " § = K'U/ (2.20) where n, the flow regime index t y p i c a l l y v a r i e s from 1 (Darcy's law) a t the bottom of the annulus to as much as 2 ( i n v i s c i d flow) at Z = H^. By combining eqns. (2.19) and (2.20) at any Z and at Z = H^, U a S i n fnz I 1 / n (2.21) K J U a ( V Recently, Morgan and Littman (1980) derived a general spout-annular i n t e r f a c i a l boundary c o n d i t i o n f o r the pressure d i s t r i b u t i o n at the spout w a l l : AP ms Z =H P a ( Z ) - P a ( H ) . Z f ( A P m s 7 * V z - Z 1 H L (AP m s/ A P m F ) z = H J < 2' 2 2> For any f l u i d - p a r t i c l e system, i n a bed of height H < H^, they a l s o predicted AP m s/AP m F vs. H/Dc through a parameter 9 ( f i g . 2.6) where 8 was c o r r e l a t e d by: d. = 7.18 (A - •—• ) + 1.07; (2.23) A < 0.07 - 22 -i 1 ~i r H/Oc F i g u r e 2.6. P a t i o o f minimum spouting pressure drop t o minimum f l u i d i z a t i o n pressure drop vs. r a t i o o f bed height t o column diameter f o r d i f f e r e n t v a lues of 6 (Morgan and Littman, 1980). - 23 -and A i s given by eqn. (2.14). Their f i n d i n g s f o r s e v e r a l values of 9 showed that eq. (2.21) s a t i s f i e d the quarter cosine p r o f i l e of Lefroy and Davidson (1969) very c l o s e l y . I t a l s o s a t i s f i e d the Grbavcic c o n d i t i o n (1976): -dP a dZ which states that the pressure gradient or the v e l o c i t y (eqn. (2.20)) at any bed l e v e l i s independent of the bed height above i t , for any p a r t i c u l a r column, f l u i d and s o l i d s . Thus eqn. (2.15) a p p l i e s f o r H <^  Hj^. Eqn. (2.21) and the Grbavcic c o n d i t i o n were e a r l i e r shown to be imcorapatible w i t h each other by E p s t e i n et a l (1978). 2.5 Annular Particle Velocity Profile and Solid Circulation Rate For p a r t i c l e s that f a l l i n the r e g u l a r spouted bed of coarse p a r t i c l e s regime (dp >^  1 mm), r a d i a l and a x i a l v e l o c i t y p r o f i l e s were measured by Lim (1975). He found that the annulus p a r t i c l e v e l o c i t y decreased from the spout w a l l to the column w a l l at any bed l e v e l , i . e . a r a d i a l gradient e x i s t s . The p a r t i c l e v e l o c i t y at any f i x e d r a d i a l p o s i t i o n decreased from the bed surface to the c o n i c a l - c y l i n d r i c a l j u n c t i o n , a f t e r which i t increased again to the gas i n l e t . The o v e r a l l s o l i d c i r c u l a t i o n rate increased from the bottom to the top, having a constant r a t e of increase beyond the c o n e - c y l i n d r i c a l j u n c t i o n . = constant * f(H) Z = constant (2.24) cons tant - 24 -No i n f o r m a t i o n , however, i s a v a i l a b l e on the annular p a r t i c l e v e l o c i t y i n the case of f i n e r s o l i d s (dp < 1 mm). 2.6 Indirect Approaches Relevant to Spouting of Fine Particles The g r i d region of a f l u i d i z e d bed i s believed to have a close resemblance to a spouted bed, since gas i s s u i n g above the o r i f i c e s i s i n the form of small 'spouts' and the u n d e r - f l u i d i z e d p a r t i c l e s r e s t on the p i t c h areas between the spouting o r i f i c e s . The bed above these submerged 'spouts' i s f l u i d i z e d . Fakhimi et a l (1983) used t h i s way of l o o k i n g at the g r i d region to determine the height of the entrance e f f e c t : F i l l a et a l (1983) have r e c e n t l y compared f u l l y developed spouts and gas j e t s i s s u i n g i n t o a f l u i d i z e d bed. They conclude, that although the a v a i l a b l e spout and j e t models are both based on gas and s o l i d s mass and momentum balances, they d i f f e r i n a u x i l i a r y equations. These a u x i l i a r y equations, which have been tested against experimental data, r e l a t e to pressure g r a d i e n t s , gas entrainment/disentrainment, s o l i d s c o n c e n t r a t i o n and p a r t i c l e v e l o c i t y p r o f i l e s . However, a correspondence may be e s t a b l i s h e d between the maximum height at which a bubble forms from the t i p of a j e t and the maximum spoutable bed depth. S i t (1981) was yet another i n v e s t i g a t o r who a p p l i e d spouted bed - 25 -theory to study mass t r a n s f e r from the spout to the dense phase where a stream of gas enters a f l u i d i s e d bed through a c e n t r a l l y placed n o z z l e . In h i s case a s t a b l e spout was observed only up to about 15 cm from the entrance, above which i t discharged as bubbles. A number of c o r r e l a t i o n s e x i s t i n the l i t e r a t u r e f o r e s t i m a t i n g the j e t p e n e t r a t i o n depth, and these have been reviewed by Blake et a l (1983) and S i t (1981). Most of these s t u d i e s , however, i n v o l v e a gas j e t i s s u i n g i n t o a f l u i d i z e d bed, and the e f f e c t of f l u i d i z a t i o n (or a u x i l i a r y flow i n t o the annulus) on the j e t p e n e t r a t i o n depth (or length of the submerged s t a b l e spout) i s q u i t e s i g n i f i c a n t . The c o r r e l a t i o n of Basov et a l (1969) had no a u x i l i a r y flow and i s therefore r e l e v a n t to the present work. His c o r r e l a t i o n i s : h = d Q 0.35 (2.26) 0.007 + 0.566d or P where, h = j e t p e n e t r a t i o n depth i n cm. dp = p a r t i c l e s i z e i n um. Qor = o r i f i c e f l o w rate i n cm Blake et a l (1983) suggest that the f o l l o w i n g c o r r e l a t i o n s represent the upper and the lower l i m i t s , r e s p e c t i v e l y , of j e t p e n e t r a t i o n i n a f l u i d i z e d bed: (2.27a) - 26 -i - "-2 i p 0.707 2 0.451 (2.27b) where V = gas v e l o c i t y through the o r i f i c e . A l l the a v a i l a b l e data have thus been shown to have d e v i a t i o n s up to ± 45%. H a t t o r i and Takeda (1978) used a side o u t l e t spouted bed with an inner d r a f t tube f o r con t a c t i n g p a r t i c l e s as small as 270 um. In t h i s system the c i r c u l a t i o n of s o l i d s depends on the entrainment of p a r t i c l e s at the bottom of the d r a f t tube. These i n v e s t i g a t o r s proposed a model f o r p r e d i c t i n g the gas conversion i n such a system. The conversion i n the case of non-porous c a t a l y s t p a r t i c l e s increased w i t h decrease i n p a r t i c l e s i z e due to the higher surface-to-volume r a t i o of the smaller p a r t i c l e s . - 27 -CHAPTER 3 APPARATUS AND BED MATERIALS 3.1 Choice and Description of Experimental Apparatus Two 15.2 cm diameter h a l f columns, having an included cone angle of 36.4 and 60 degrees r e s p e c t i v e l y , were used ( F i g . 3.1). A h a l f column i s believed to represent the behaviour i n a f u l l column qu i t e adequately f o r many purposes and f o r a wide v a r i e t y of m a t e r i a l s spouted (Geldart et a l , 1981). The major advantage i n using a h a l f column i s that i t allows d i r e c t observation of spout shape and diameter, and r a d i a l p a r t i c l e v e l o c i t y g r a d i e n t s , as w e l l as v i s u a l i z a t i o n of the flow regimes involved along wi t h t h e i r t r a n s i t i o n p o i n t s . The two columns were made of p l e x i g l a s s , w i t h the f l a t surface made of g l a s s . S e m i c i r c u l a r o r i f i c e s of diameters 2.8, 4.5, 6.0, 7.5, 9.0, 12.7, 16.0, 19.05, 23.2 and 28 mm were u t i l i z e d . The i n l e t of each of these o r i f i c e s protruded 2 mm i n t o the bed as shown i n F i g . 3.2. An o r i f i c e of t h i s type gives very good s t a b i l i t y to the spout (Mathur and Eps t e i n , 1974). For the 36.4 degree cone angle column, s p e c i a l o r i f i c e p l a t e s , with the o r i f i c e tapered at the same cone angle, were f a b r i c a t e d . The use of such plates a t the bottom provided a smooth i n l e t connection to the half c i r c u l a r i n l e t tube, avoiding any c o n t r a c t i o n of the i n l e t f l u i d ( F i g . 3.3). Three d i f f e r e n t i n l e t s i z e s of t h i s type of o r i f i c e were used - 25.4 (when no o r i f i c e p l a t e was used), 12.7 and 10.1 mm. A CONICAL SECTION 19.3 cm AUXILIARY FLOW LINES RESSURE TAP HONEYCOMBED FLOW STRAIGHTENERS Fi g u r e 3.1. D e t a i l s of the two h a l f c y l i n d r i c a l columns. - 29 -F i g u r e 3.2. Photograph of the o r i f i c e p l a t e . Tube attachment i s f o r alignment purposes. ALL DIMENSIONS IN MMS. HALF CIRCULAR TUBE FULL CIRCULAR TUBE HONEY COMBED FLOW STRAIGHTNERS -HALF CIRCULAR TUBE -FULL CIRCULAR TUBE o Figure 3.3. D i f f e r e n t i n l e t types (without c o n t r a c t i o n o f the i n l e t f l u i d ) f o r column 2. - 31 -cone angle of 36.4 degrees and such an i n l e t design was made to maintain the same column geometry as used by Heschel and Klose (1981). A v e r t i c a l pipe of 3.18 cm I.D. and length 30 cm, w i t h appropriate grooves for holding the o r i f i c e p l a t e (see F i g . 3.2) and an u n d e r l y i n g wire mesh (250 mesh f o r dp = 98 um and 65 mesh f o r a l l other p a r t i c l e s ) , was used to connect the incoming a i r l i n e to the base of the column ( i t could be used for each of the two columns). 'Honeycombed' flow s t r a i g h t e n e r s were f i x e d i n s i d e the pipe. A pressure tap was located 5 cm below the bed i n l e t i n the i n l e t p i p e . The pressure tap was connected through a T - j o i n t to two U -tube manometers c o n t a i n i n g a l i q u i d of s p e c i f i c g r a v i t y 0.827 and mercury (sp. gr. 13.6), r e s p e c t i v e l y . The manometer f o r the l i g h t e r l i q u i d was used f o r low pressure drop measurements and was f i t t e d w i t h an i n l e t v a l v e which was kept closed when the pressure drop was high, i n order to avoid any s p i l l a g e of the l i q u i d . The 60 degree cone angle column was used f o r most parts of t h i s work. Whenever i t was not used, the cone angle i s s p e c i f i e d . The 60 degree cone angle column had an a u x i l i a r y f l u i d i z i n g l i n e to the annulus and could therefore be operated a l s o as e i t h e r a s p o u t - f l u i d or a f l u i d i z e d bed. In order to remove any s t a t i c c l i n g while using small s i z e d polymers, the incoming a i r was h u m i d i f i e d . Two 10.16 cm diameter columns with a combination of Raschig r i n g s and B e r l saddles as packing m a t e r i a l s were used i n p a r a l l e l f o r t h i s purpose ( F i g . 3.4). Fine wire mesh was placed at d i f f e r e n t l e v e l s i n between the packings to obtain a good d i s p e r s i o n of a i r bubbles i n water. Both the h u m i d i f i e r s - 33 -were capable of contacting a i r and water c o u n t e r c u r r e n t l y to ensure high humidity while using polymers. A dry a i r stream was als o connected to the h u m i d i f i c a t i o n s e c t i o n o u t l e t to c o n t r o l the humidity. Humidity was measured using dry-bulb and wet-bulb thermometers. A i r flow rates were measured by e i t h e r of the two rotameters, which were c a l i b r a t e d using a dry gas meter*. The smaller rotameter was used f o r small flow rates only. The upstream a i r pressure was measured by a pressure gauge. F i g . 3.4 summarizes the o v e r a l l equipment layout and F i g . 3.5 i s a p i c t u r e of the same. Annulus gas v e l o c i t y p r o f i l e s were measured by using a s t a t i c pressure probe, the same probe as used by Lim (1975) - F i g . 3.6. Two con c e n t r i c s t a i n l e s s s t e e l tubes of unequal lengths having an O.D. of 1.6 mm and 4.8 ram r e s p e c t i v e l y , c o n s t i t u t e d the main body of the probe. The two ends were f i t t e d with 22 gauge hypodermic needles, bent at r i g h t angles 1.2 cm from t h e i r t i p s , the v e r t i c a l s e p e r a t i o n between the t i p s being 2 cm. S t a t i c pressure drops were measured using a raicroraanometer** having a l e a s t count of 0.00254 cm b u t y l a l c o h o l (sp. gr. 0.821). 3.2 Bed Materials A wide v a r i e t y of p a r t i c l e s ranging i n s i z e from 90 urn to 1000 um and i n s p e c i f i c g r a v i t y from 0.9 to 8.9 were employed. Table 3.1 *Model A.L425, made by Canadian Meter Co. L t d . **Model MM-3, made by Flow Corp., Cambridge, Mass. F i g u r e 3.5. Photograph o f the equipment. - 35 -f la t su r facey of c o l u m n 4.8 m m O.D. d i a g r a m not to s c a l e to i n c l i n ed manomete r — probe holder 120 cm 2 cm - H [ 4 — ^ ^ - 2 2 Gauge 1.2 cm hypodermic needle F i g u r e 3.6. Schematic diagram of the s t a t i c pressure probe. Table 3.1: Prop e r t i e s of bed m a t e r i a l s M a t e r i a l d P (pm) (g/cmd) (g/cm 3) (degrees) (degrees) UmF (cm/s) PVC PVC Polypropylene S i l i c a Sand S i l i c a Sand S i l i c a Sand S i l i c a Sand S i l i c a Sand Bronze Copper N i c k e l N i c k e l N i c k e l Glass Glass 98 185.6 299.5 196 280 401 516.4 1000 176.4 458.5 238.3 545 635 710 845 1.270 1.270 0.900 2.660 2.665 2.657 2.648 2.661 7.906 8.811 8.906 8.912 8.900 4.506 2.417 0.526 0.564 0.518 1.467 1.557 1.552 1.533 1.557 4.649 5.190 5.255 5.258 5.245 2.665 1.423 0.586 0.556 0.425 0.449 0.416 0.408 0.427 0.415 0.412 0.411 0.410 0.410 0.411 0.408 0.409 76.7 66.5 61.3 66.0 61.4 58.8 57.5 66.3 52.0 57.8 52.7 52.0 52.0 47.4 50.6 30.6 32.1 29.3 33.2 32.8 32.2 34.8 36.9 26.3 29.2 28.1 27.4 26.6 24.1 25.0 0.49 1.67' 4.25 4.55 9.29 16.70 22.38 56.19 46.61 - 37 -summarizes the p h y s i c a l p r o p e r t i e s of the p a r t i c l e s used. The diameter used here i s the mean-diameter obtained a f t e r sieve a n a l y s i s as f o l l o w s : (3.1) where i s the weight f r a c t i o n of p a r t i c l e s having an aperture mean diameter, ap^* Table 3.2 gives the s i z e d i s t r i b u t i o n f o r PVC, polypropylene, bronze, copper and the three s i l i c a sands used. The glass and n i c k e l p a r t i c l e s were f a i r l y s p h e r i c a l i n shape, and uniform i n s i z e . The d e n s i t i e s of each of the p a r t i c l e s were determined by measuring the volume of l i q u i d d i s p l a c e d when a known weight of s o l i d s i s poured i n t o a graduated c y l i n d e r . The d e n s i t i e s of PVC (***GEON 30 and GEON 212) and polypropylene// were supplied by the manufacturers. The bulk d e n s i t y measurements were c a r r i e d out i n accordance w i t h the procedure of Oman and Watson (1944). A 500 c.c. graduated c y l i n d e r was p a r t i a l l y f i l l e d with a known weight of s o l i d s , closed at i t s open end and i n v e r t e d , then returned back q u i c k l y to i t s o r i g i n a l p o s i t i o n . The te s t was repeated s e v e r a l times to ensure good r e p r o d u c i b i l i t y . The ***Trade name used by B.F. Goodrich Co. L t d . //Supplied by Hercules Canada L t d . Table 3.2: P a r t i c l e s i z e d i s t r i b u t i o n s (a) PVC (GEON 212) d P i (um) 180 150 125 90 75 63 31 d = 98 um P x. 1 0.027 0.066 0.42 0.425 0.028 0.019 0.016 (b) PVC (GEON 30) d P i (um) 215 165 135 105 d = 185.6 um P x. 1 0.488 0.469 0.0352 0.0078 (c) Polypropylene d P i (um) 458 384 .. 301 255 188 d = 299.5 um P x. l 0.043 0.01712 0.6733 0.0424 0.0701 (d) Bronze d p (um) 252 195 165 128 d = 176.4 um P x. l 0.182 0.330 0.477 0.012 Table 3.2: coat'd.... (e) S i l i c a Sand d P i dim) 215 165 135 105 d =196 pm P X i 0.501 0.468 0.020 0.011 [f) S i l i c a Sand d p i (pm) 640 548 458 386 323 223 d = 401 um P X i 0.105 0.171 0.306 0.186 0.128 .105 S i l i c a Sand d p i (um) 655 548 458 386 220 d = 516.4 \im P x. 1 0.281 0.403 0.205 0.054 0.058 - 40 -weight of the s o l i d s d i v i d e d by the volume the above procedure, gave the random loose This enabled the c a l c u l a t i o n of e^, voidage (the annulus of a spouted bed i s a (3.4) Tests f o r angle of repose and angle of i n t e r n a l f r i c t i o n were c a r r i e d out i n accordance with the methods o u t l i n e d by Zenz and Othmer (1960). For measuring the angle of i n t e r n a l f r i c t i o n ( a ) , a c y l i n d e r of I.D. 6.4 cm, having a 1 cm hole at the bottom and open at the top, was u t i l i z e d . S o l i d s were poured to a height of about 35 cm and allowed to d r a i n . The height of the bed at which a depression f i r s t occurred i n the center of the bed surface was noted, and the r a t i o of t h i s height to the c y l i n d e r I.D. recorded as the tangent of the angle of i n t e r n a l f r i c t i o n ( a ) . The angle of repose ($) was measured as the angle made by the heap of the drained s o l i d s with the h o r i z o n t a l . The t e s t s were done se v e r a l times to ensure reproducible r e s u l t s . The minimum f l u i d i z a t i o n v e l o c i t y , Um~p, was determined experimentally i n the h a l f column by a c t i v a t i n g the a u x i l i a r y flow l i n e s and maintaining bed heights above 80 cm to ensure uniform d i s t r i b u t i o n of flow. occupied by the s o l i d s a f t e r -packed bulk d e n s i t y , the spouted bed annulus loose-packed bed) as: - 41 -CHAPTER 4 REGIME MAPS AND CRITERIA FOR FINE PARTICLE SPOUTING As discussed i n chapters one and two, there e x i s t s s i g n i f i c a n t controversy regarding the s p o u t a b i l i t y of f i n e p a r t i c l e s . The f i r s t p a rt of t h i s work therefore involved t e s t i n g the g e n e r a l i z a t i o n s of the previous workers (Mathur and Gishler-1955; Ghosh-1965; Geldart-1973; Rooney and Harrison-1974; Heschel and Klose-1981; Molerus-1982). The r e s u l t s were used to obtain regime maps l i k e the ones shown i n F i g s . 2.1a and. 2.1b, which summarize the d i f f e r e n t ' s t a t e s ' of a system under various operating c o n d i t i o n s . The va r i o u s flow regimes along w i t h the t r a n s i t i o n points were c a r e f u l l y examined and videotaped, and the in f l u e n c e of d i f f e r e n t parameters on these regimes s t u d i e d . 4.1 Experimental Procedure To s t a r t w i t h , the work of Heschel and Klose (1981), which e x h i b i t e d most unusual r e s u l t s , was repeated i n a h a l f column of h a l f the s i z e used i n t h e i r work. The bed m a t e r i a l and the i n l e t f l u i d used were very close to t h e i r s . The tapered o r i f i c e s shown i n F i g . 3.3 were used to maintain e x a c t l y the same i n l e t c o n d i t i o n s (no c o n t r a c t i o n at the i n l e t ) . Table 4.1 summarizes the operating c o n d i t i o n s i n t h i s work and i n that of Heschel and Klose (1981). Subsequent runs were a l s o made i n the 60 degree cone angle column wi t h i n l e t s i z e s from 2.8 to 28 mm and a wide v a i e t y of p a r t i c l e s ranging i n s i z e from 170 um to 1000 um and i n dens i t y from 0.9 to 8.9 g/cm3 (Table 3.1). Table 4.1: Operating conditions i n t h i s work vs. those of Heschel and Klose (1981) Heschel & Klose (1981) This work 1. Column d i a . = 30 cm ( f u l l column) 1. Column diameter = 15.2 cm ( h a l f column) I n l e t diameter = 25.4 mm (no c o n t r a c t i o n of the f l u i d at the i n l e t ) I n l e t diameter = 25.4, 12.7 & 10.1 mm (no c o n t r a c t i o n of the f l u i d at the i n l e t ) 2. S o l i d used: PVC (d = 90 urn) P 2. S o l i d used: PVC (d = 98.8 um) P 3. F l u i d : A i r (R.H. = 80%) 3. F l u i d : A i r (R.H. = 80%) 4. H = 40, 55 and 75 cm. 4. H = 15 to 80 cm. (Note: R.H. = R e l a t i v e humidity) - 43 -For o b t a i n i n g the regime maps (e.g. F i g . 4.4), s o l i d s were poured i n t o the column, s t a r t i n g with a low bed height, and t h e i r loose packed bed height* measured. The a i r flow r a t e was increased g r a d u a l l y and the t r a n s i t i o n points ( t r a n s i t i o n between d i f f e r e n t regimes) noted. The fl o w r a t e was then decreased to the minimum spouting f l o w r a t e and then increased again, the t r a n s i t i o n points being noted once more. This procedure was subsequently repeated f o r l a r g e r bed h e i g h t s . A l l regime maps were constructed while decreasing the flow, and were then quite r e p r o d u c i b l e when the flow was increased once again. This procedure was e s s e n t i a l i n order to obtain a l l the regimes, as during s t a r t - u p the bed often went s t r a i g h t from the f i x e d packed c o n d i t i o n to the bubbling regime (to point X i n F i g . 4.4a, f o r example, escaping the steady spouting and the p r o g r e s s i v e l y incoherent spouting regimes). A l s o , t h i s procedure becomes c o n s i s t e n t with the d e f i n i t i o n of U m s based on decreasing flow (Chapter 2, Sec. 2.2.1). The regime t r a n s i t i o n s were marked by d i s t i n c t v i s u a l observations, as discussed i n the next s e c t i o n . The regime maps were constructed f o r d i f f e r e n t i n l e t s i z e s . Some p r e l i m i n a r y work was a l s o c a r r i e d out i n a f u l l column w i t h a cone angle of 30° and diameter 15.2 cm to reproduce the q u a l i t a t i v e observations of Heschel and Klose (1981). The f u l l column was a l s o employed f o r q u a l i t a t i v e l y confirming the existence of d i f f e r e n t regimes and f o r c o l l e c t i n g data i n some l a t e r work. *The loose packed bed height r e f e r s here to the bed height obtained by c o l l a p s e of the bed from the spouting c o n d i t i o n . - 44 -The e f f e c t of p a r t i c l e d ensity and s i z e on s p o u t a b i l i t y was studied f o r each of the s o l i d s l i s t e d i n Table 3.1. For every s o l i d , the i n l e t s i z e was p r o g r e s s i v e l y increased ( s e v e r a l bed heights were used f o r each i n l e t s i z e ) u n t i l no steady spouting was achievable. A few runs were a l s o repeated i n the f u l l column. 4.2 Results and Their Analysis 4.2.1 Influence of inlet diameter The observations i n the 36° half-column w i t h i n l e t s i z e s of 25.4, 12.7 and 10.1 mm and with no f l u i d c o n t r a c t i o n at the i n l e t , using 98 ym PVC, were q u i t e d i f f e r e n t from those of Heschel and Klose (1981). The pressure drop vs. flow curve shown i n Figure 4.1 was obtained with the 12.7 mm o r i f i c e . The j e t broke through and discharged as bubbles r i s i n g up c e n t r a l l y , forming a crater-shaped area around i t , at the foot of the peak (point A). This coincided with the observations of Heschel and Klose (1981) at the foot of t h e i r f i r s t peak ( F i g . 2.3). Upon i n c r e a s i n g the f l o w , bubbles grew i n number and s i z e and the pressure drop f l u c t u a t e d . The s o l i d s were c a r r i e d up i n the wake of the bubbles (which were mostly at the center of the column) and moved down i n the 'annulus' (which could be c a l l e d the 'emulsion phase' as i n a f l u i d i z e d bed). At the curved rear w a l l of the column, the s o l i d s appeared to be moving downwards i n a p u l s a t i n g manner. Further increase i n flow did not cause any s i g n i f i c a n t r i s e i n pressure drop, but simply l e d to s l u g g i n g , where the bubbles became equal to the diameter of the column. Thus the second peak reported by Heschel and Klose (1981) di d not appear o •5? 0.0 0.2 0.4 0.6 0.8 1.0 Q ( s t d . l / s ) F i g u r e 4.1. T y p i c a l pressure drop vs. flow r a t e c h a r a c t e r i s t i c s obtained upon r e p e a t i n g the c o n d i t i o n s o f Heschel and Klose (1981). PVC, d =0.098 mm, d.=12.7 mm, H=37. P 1 F l u i d used: A i r a t 80% r e l a t i v e humidity. - 46 -at a l l , and steady spouting was never observed. Further increase of flow led to pneumatic transport of the s o l i d s from the column. The same observations were also made when the f u l l column was u t i l i z e d . Spouting was only seen to occur when the i n l e t s i z e was reduced to l e s s than 25 times the p a r t i c l e diameter. Beyond t h i s l i m i t of i n l e t diameter, bubbling or slugging occurred. The occurrence of t h i s c r i t i c a l value of i n l e t diameter beyond which steady spouting did not occur was confirmed f o r a wide v a r i e t y of s o l i d s (Table 3.1) and the r e s u l t s are shown i n F i g . 4.2a. The l i m i t i n g i n l e t diameter f o r spouting i s shown as a range, since the o r i f i c e s i z e s used increased stepwise i n s i z e . The lower l i m i t of each v e r t i c a l l i n e represents the highest i n l e t s i z e employed at which steady spouting was achievable and the upper l i m i t represents the lowest i n l e t s i z e used at which no spouting occurred. The mid-point of each of the i n l e t s i z e ranges i n F i g . 4.2a was then taken as a r e p r e s e n t a t i v e value of the c r i t i c a l i n l e t diameter f or steady spouting. These were p l o t t e d i n F i g . 4.2b and l i n e CC^ obtained by l i n e a r r e gression of these points (almost no f o r c i n g through the o r i g i n was r e q u i r e d ) . Hence f o r steady spouting to occur, d. < 25.4 d (4.1) l - p Lines AA[ and BB^ were obtained by l i n e a r r e g r e s s i o n of the upper and the lower l i m i t s , r e s p e c t i v e l y , i n F i g . 4.2a, without any f o r c i n g through the o r i g i n . These represent the d e v i a t i o n s from Eq. (4.1) (AA^ - 47 Polypropylene 0.90 ^£ (g/cm3) V PVC O S i l i c a sand • Glass • Glass Bronze X Copper A N i c k e l 1.27 2.66 2.42 4.56 7.90 8.80 8.90 d (mm) P Figure 4.2a. C r i t i c a l i n l e t diameter range f o r steady spouting - 48 -1 I I l 1 1 1 1 1 1 C l _ SOLID 3 P p (g/cm ) Y — • Polypropylene 0.90 / — V PVC li.27 y — O S i l i c a sand 2.66 / — • Glass 4.56 y — % Glass 2.42 / — A Bronze 7.90 / — X' Copper 8.80 / — A N i c k e l 8.90 A / # O A / BUBBLING — — — STEADY SPOUTING — — A/OB — — • — — c 1 1 1 1 1 1 1 1 1 1 0 0.2 0 .4 0.6 0.8 1.0 d (mm) P Figure 4.2b. C r i t i c a l i n l e t diameter (mid-points o f the ranges shown i n Fig.4.2a) f o r steady spouting. - 49 -has a slope of 28.2 and BB^ a slope of 23.2). The r e s u l t s obtained i n t h i s work support the observations of Ghosh (1965) and of Rooney and Harrison (1974). The c r i t e r i o n of Ghosh, which postulates a c r i t i c a l i n l e t diameter 30 times the p a r t i c l e diameter, i s f a i r l y c lose to the upper l i m i t of d e v i a t i o n (slope of l i n e AAj = 28.2). The r e s u l t s of t h i s work do not agree with those of Heschel and Klose (1981), who probably mistook non-homogenous f l u i d i z a t i o n f o r spouting. Spouting of 186 ym PVC, 300 ym polypropylene and 196 ym s i l i c a sand showed three regimes: f i x e d bed, bubbling and steady spouting upon i n c r e a s i n g and decreasing the flow, provided Eq. (4.1) was obeyed. Upon i n c r e a s i n g the flow, the j e t f i r s t broke through as bubbles ( p o i n t B i n F i g . 2.4) and formed a steady spout when the f l o w r a t e was f u r t h e r increased ( p o i n t C i n F i g . 2.4). The r e g i o n of s o l i d c i r c u l a t i o n increased with i n c r e a s i n g flow. The c i r c u l a t i o n of s o l i d s was very poor and a very large stagnant zone e x i s t e d at a l l times ( F i g . 4.3b). The region of s o l i d c i r c u l a t i o n was much enhanced when p a r t i c l e s above 400 ym i n s i z e were u t i l i z e d . These p a r t i c l e s a l s o allowed a much higher bed depth to be spouted with a very small or no stagnant zone, thus representing a more p r a c t i c a l system. For such p a r t i c l e s , provided the maximum i n l e t diameter f o r steady spouting i s not exceeded, regime maps s i m i l a r to F i g . 4.4a were obtained. The various regimes are p i c t o r i a l l y represented i n F i g . 4.5. Steady spouting i s c h a r a c t e r i z e d by the presence of a steady f o u n t a i n , having a d e f i n i t e shape (approximately p a r a b o l i c ) and a steady spout-annulus i n t e r f a c e with no disturbances or waves ( F i g . 4.5a). P r o g r e s s i v e l y incoherent spouting I 8 (a) (b) Figure 4.3. Regimes w i t h spouting p a r t i c l e s w i t h d^< 0.35 ran. (a) Bubbling occurs between p o i n t s B and C i n Fig.2.4, (b) steady spouting s e t s i n beyond p o i n t C (Fig.2.4) -the t r a c e r p a r t i c l e s show the r e g i o n o f c i r c u l a t i o n . (a) (W ( C ) Figure 4 5. P i c t u r e s o f d i f f e r e n t r e g i e s shown i n F i g . 4.4. (a) steady spouting (b) p r o g r e s s x v e l y i n c o h e r e n t spouting (c) b u b b l i n g (d) s l u g g i n g . Sand, dp=0.516 mn, d.=6.0 nm. (d) - 53 -(P.I.S.) sets i n when the fountain shape gets d i s t o r t e d and waves s t a r t to appear along the spout-annulus i n t e r f a c e near the bed s u r f a c e . The t r a n s i t i o n from P.I.S. to bubbling occurs when the j e t sinks below the bed surface and discharges as bubbles. This t r a n s i t i o n can be v i s u a l i z e d as the amplitude of the waves (or disturbances) i n P.I.S. becoming equal to the spout r a d i u s , l e a d i n g to a pinch point and thereby the formation of a bubble. When the r i s i n g bubbles become equal to the s i z e of the column, as they approach the bed s u r f a c e , slugging sets i n . An i n t e r e s t i n g phenomenon occurs when the bed height i s between B and C i n F i g . 4.4b. For example, on i n c r e a s i n g the flow along the l i n e XjXg, steady spouting occurs between X 2 and X 3. Beyond X 3, P.I.S. sets i n and upon f u r t h e r increase of flow to Xu., steady spouting once again occurs. Spouting beyond X^, however, leads to a very high f o u n t a i n and the bed surface i s c o n i c a l as compared to i t s i n v e r t e d cone shape between X 2 and X 3. F i g . 4.6 f u r t h e r e l u c i d a t e s t h i s p o i n t . This behaviour i s also r e t r a c e a b l e upon decreasing the flow. Figure 4.7 demonstrates the e f f e c t of i n l e t s i z e on the d i f f e r e n t regimes. As the i n l e t s i z e i n c r e a s e s , the region of steady spouting decreases ( a l s o shown i n F i g s . 4.4 and 4.8) and upon exceeding the l i m i t i n Eq. (4.1), i t vanishes a l t o g e t h e r . 4.2.2 Effect of particle size The e f f e c t of i n c r e a s i n g p a r t i c l e s i z e i s p a r t i a l l y r e f l e c t e d i n F i g . 4.2. Increasing the p a r t i c l e s i z e allows a bigger i n l e t s i z e to be used f o r steady spouting. A l s o , use of bigger p a r t i c l e s magnifies the (a) (b) (c) F i g u r e 4.6. T r a n s i t i o n between regimes along i n F i g . 4.4b w i t h i n c r e a s i n g f l o w r a t e . (a) steady spouting (b) p r o g r e s s i v e l y incoherent spouting (c) steady spouting - 56 -- 58 -region of steady spouting as depicted by F i g s . 4.4b, 4.7b and 4.8b. For p a r t i c l e s with mean diameter greater than 1 mm, the region of steady spouting i s much l a r g e r and P.I.S. i s almost non-existent. (Refer to F i g . 2.2). 4.2.3 Effect of particle density The c r i t e r i a of s p o u t a b i l i t y given by G e l d a r t (1973) and Molerus (1982) (Equations 2.1 and 2.2 r e s p e c t i v e l y ) suggest that 1non-spoutable' p a r t i c l e s can become 'spoutable' i f t h e i r d e n s i t y i s increased s u f f i c i e n t l y (Chapter 2, Section 2.1.2). For example i n F i g . 4.9 a p a r t i c l e at p o i n t K i s i n the non-spouting zone. However, i f i t s d e n s i t y i s r a i s e d , keeping i t s s i z e the same, i t can be made to spout ( p o i n t L i n F i g . 4.9). However, data c o l l e c t e d over a wide v a r i e t y of p a r t i c l e s ( s i z e 170 to 1000 um and d e n s i t y 0.9 to 8.9 g/cm ) show n e g l i g i b l e e f f e c t of d e n s i t y on s p o u t a b i l i t y . This can e a s i l y be i n f e r r e d from F i g . 4.2. A l s o , i n F i g . 4.9, a number of s t a b l e spouting points f a l l i n the s o - c a l l e d 'non-spoutable' regions of Geldart (1973) and Molerus (1982). Some of these r e s u l t s were a l s o confirmed i n the f u l l column. 4.2.4 Minimum and maximum spouting velocities The minimum spouting v e l o c i t y , U m s , was p r e d i c t e d by the Mathur-Gishler equation, Eq. (2.3), w i t h an average d e v i a t i o n of ± 10%. For p a r t i c l e s greater than 400 um i n s i z e , U m g was taken as the s u p e r f i c i a l i n l e t v e l o c i t y at which the pressure drop across the bed - 59 -Fi g u r e 4.9. G e l d a r t ' s (1973) and Molerus' (1982) c r i t e r i a f o r s p o u t a b i l i t y on a l o g - l o g s c a l e . Data p o i n t s shown represent p a r t i c l e s f o r steady spouting was achievable i n t h i s work. - 60 -rose again upon decreasing the flow. For p a r t i c l e s smaller than 400 um i n s i z e , U m s was taken as the minimum v e l o c i t y at which steady spouting occurred (Chapter 2, Section 2.2.1, poi n t C i n F i g . 2.4). Table 4.2 summarizes the r e s u l t s . I t i s seen that f o r p a r t i c l e s l e s s than 400 um i n s i z e , when point B i n F i g . 2.4 i s used, the d e v i a t i o n s between experimental values and those p r e d i c t e d by Eq. (2.3) are over 40%, but when poi n t C i s chosen (steady spouting occurs only beyond C), the d e v i a t i o n s are much smaller. The p r e d i c t i o n of U m s f o r p a r t i c l e s greater than 400 um by Eq. (2.3) are much improved. For these p a r t i c l e s (dp > 400 um), as i s c o n v e n t i o n a l l y done, B was the p o i n t chosen to represent the experimental value of U m s . As seen from the regime maps i n F i g s . 4.4, 4.7 and 4.8, above a c e r t a i n minimum bed height there e x i s t s a maximum spouting v e l o c i t y beyond which s t a b l e spouting ceases to occur. This'maximum spouting v e l o c i t y approaches the minimum spouting v e l o c i t y , narrowing the r e g i o n of steady spouting, as the i n l e t s i z e i s increased to i t s c r i t i c a l value ( F i g . 4.7, f o r example). The maximum spouting v e l o c i t y i s a l s o an i n d i c a t o r of regime transformation and can be predicted as discussed i n Section 4.2.6. 4.2.5 Effect of bed height, maximum spoutable bed depth, and  stable jet length I t i s i n t e r e s t i n g to note that the regime maps i n F i g . 4.4, 4.7 and 4.8 are quite reproducible by keeping the flow rate set at a constant value and changing the bed height. In F i g . 4.7a, f o r example, Table 4.2: Experimental values of minimum spouting v e l o c i t y vs. Equation 2.3 S o l i d d P d i H Ums* < m / s ) Ums ( m / s ) ms (m/s) % dev. // (um) (mm) (cm) Expt. Expt. Eq. (2.3) PVC 185.6 2.8 12.6 0.010 0.013 0.015 +13 .96 PVC 185.6 2.8 17.3 0.013 0.021 0.018 -14 .29 PVC 185.6 4.5 19.5 0.015 0.025 0.022 -12 .00 Polypropylene 299.5 2.8 19.8 0.026 0.027 0.028 +3 .70 Polypropylene 299.5 4.5 20.0 0.027 0.028 0.030 +9 .24 Polypropylene 299.5 6.0 23.0 0.031 0.033 0.037 +12 .12 Sand 196 2.8 15.0 0.018 0.022 0.025 + 13 .64 Sand 196 4.5 14.5 0.018 0.024 0.028 +16 .67 Sand 196 4.5 19.5 0.022 0.029 0.033 +13 .79 Bronze 176.4 2.8 15.0 0.029 0.035 0.041 +17 .14 Sand 401 4.5 30.0 - 0.093 0.095 +2 .31 Sand 401 4.5 41.0 - 0.118 0.108 -8 .48 Sand 401 4.5 49.6 - 0.125 0.119 -4 .79 Sand 401 6.0 15.0 - 0.0714 0.072 +0 .84 Sand 401 6.0 30.0 - 0.107 0.102 -4 .76 Sand 401 6.0 41.0 - 0.122 0.119 -2 .54 Sand 401 9.0 30.0 - 0.111 0.117 +5 .12 Sand 401 9.0 41.0 - 0.121 0.136 +12 .4 Sand 516.4 6.0 30.0 - 0.157 0.133 -15 .22 Sand 516.4 6.0 41.0 - 0.172 0.158 -7 .97 Sand 516.4 6.0 50.0 - 0.184 0.173 -6 .19 Sand 516.4 12.7 30.0 - 0.158 0.164 +3 .87 Sand 516.4 12.7 41.0 - 0.178 0.196 +10 .11 Glass 710 6.0 40.5 - 0.328 0.281 -14 .33 Glass 710 6.0 50.8 - 0.353 0.313 -11 .33 Glass 710 12.7 41.0 - 0.372 0.361 -2 .96 Glass 710 12.7 52.0 - 0.398 0.407 +2 .26 Sand 1000 6.0 41.0 - 0.318 0.298 -6 .28 Sand 1000 • 12.7 41.0 — 0.374 0.382 +2 .14 *Taken as point B i n F i g . 2.4. //Calculated as ^ d i e t e d - Expt. x ^ Expt. - 62 -keeping the flow r a t e f i x e d and i n c r e a s i n g the bed height along the v e r t i c a l l i n e MQ e x h i b i t s points N, 0 and P as the t r a n s i t i o n p o i n t s . These points are q u i t e close to the t r a n s i t i o n s obtained by the e a r l i e r method. As described i n Section 2.2.2, spout termination at the maximum spoutable bed height, H M, i n the case of f i n e p a r t i c l e s occurs due to choking of the spout. The data f o r % are shown i n ta b l e 4.3. I t can be seen that the maximum spoutable bed depth decreases w i t h i n c r e a s i n g i n l e t diameter and decreasing p a r t i c l e s i z e . The trend i s the same as that observed by Rooney and H a r r i s o n (1974). The equations reviewed i n S e c t i o n 2.2.2 are tested against experimental data and presented i n Table 4.3. Both equations o v e r p r e d i c t H^ by more than 100% and hence cannot be recommended for f i n e p a r t i c l e s . These equations, developed s e m i - e m p i r i c a l l y based on coarse p a r t i c l e data, do not represent the f i n e p a r t i c l e behaviour adequately. Nor does the footnoted equation. Although G e l d a r t et a l (1981) found that H M i n a h a l f column i s g e n e r a l l y about 10 to 15% lower than i n a f u l l column, t h i s f i n d i n g s t i l l does not account for the high discrepancy between the experimental and the predicted r e s u l t s of the present study. However, when H^ i s c a l c u l a t e d by the new method described i n the next s e c t i o n (Table 4.6), the d e v i a t i o n of the p r e d i c t e d values from the experimental ones i s l e s s than 30%, which i s reasonable as discussed l a t e r . In the bubbling regime, as shown i n F i g . 4.5, a s t a b l e j e t of Table 4.3: Experimental vs. predicted maximum spoutable bed depths* S o l i d dp (ym) d . l (mm) H M (cm) (Expt.) H M (cm) (Eq. 2.6) H M (cm) (Eq. 2.7) H M (cm) PVC 186 2.8 28.3 + + + 4.5 26.4 + + + Polypropylene 299 2.8 26.2 + + + 4.5 22.0 + + + 6.0 20.5 + + + S i l i c a sand 196 2.8 26.2 + + + 4.5 20.5 + + + S i l i c a Sand 401 4.5 49.6 128.9 @ 77.4 6.0 46.8 121.2 @ 63.9 7.5 45.6 116.4 @ 55.1 9.0 43.6 101.1 @ 48.8 S i l i c a Sand 516 6.0 58.5 108.1 @ 95.5 7.5 55.4 103.6 @ 82.3 9.0 52.5 91.4 @ 72.8 12.7 48.5 80.6 @ 57.9 Glass 710 6.0 55.5 85.9 198.5 196.5 7.5 55.0 81.2 158.5 169.3 9.0 52.1 76.1 132.1 150.0 12.7 50.8 72.4 93.6 119.2 + cannot be determined f o r these, since H barely exceeds H c and since the region of c i r c u l a t i o n changes s i g n i f i c a n t l y with flowrate and along the bed height. No r e p r e s e n t a t i v e value of D c can thus be used. @ A i s below the minimum value required i n Eq. 2.7 (A = 0.01). * H M i s a l s o predicted by a new method i n the next s e c t i o n . // Predicted by H = 700(D 2/d )(D / d j 2 / 3 [(1 + 35.9 x 10" 6 A r ) 1 / 2 - 1 ] 2 / A r , see E p s t e i n and Grace (1984). M c p c i - 64 -length h i s seen d i s c h a r g i n g as bubbles. The s t a b l e j e t length f l u c t u a t e s by about ± 3 era due to formation and discharge of bubbles at i t s t i p . I t i s f u r t h e r observed from F i g s . 4.4, 4.7 and 4.8 that as the i n l e t f l u i d f l o w r a t e becomes equal to the minimum f l u i d i z a t i o n flowrate f o r a deep enough bed (H _> H M ) , a j e t d i s c h a r g i n g as bubbles i s observed. The s t a b l e j e t length i s experimentally found to be independent of bed height f o r H > HM. In Eq. (2.25), s u b s t i t u t i n g U mF f o r U thus gives the s t a b l e j e t l e n g t h : (4.2) Table 4.4 compares the experimental r e s u l t s w i t h the p r e d i c t i o n s from Eqns. 4.2, 2.25 and 2.26. I t i s observed that Eq. (4.2) i s c l o s e r to the experimental data than the other two. 4.2.6 Prediction of Regime Transformation The phenomenon of t r a n s i t i o n from s t a b l e spouting to bubble formation at the spout top appears to be analagous to choking i n standpipes. In a standpipe where a f l u i d i s c a r r y i n g s o l i d s , choking (or s l u g formation) occurs as the gas v e l o c i t y i s reduced below a c r i t i c a l value, c a l l e d the choking v e l o c i t y (Leung, 1980). The phenomeon e s s e n t i a l l y occurs due to i n c r e a s i n g s o l i d s concentration (or decreasing voidage) upon reducing the gas flow. The recommended Table 4.4: Experimental H > V * = 1 and • predicted j e t p e n e t r a t i o n depths f o r S o l i d d P ( um) d i (mm) h (cm) Expt. h (cm) (Eq. 4.2) h (cm) (Eq. 2.26) L i m i t s of h (cm) (Eq. 2.27) S i l i c a Sand 516 6.0 35.2 ± 3 37.2 25.3 19.7 - 52.6 S i l i c a Sand 516 12.7 27.1 ± 3 30.9 25.3 7.7 - 20.5 S i l i c a Sand 401 6.0 24.0 ± 3 29.8 22.9 15.8 - 42.2 S i l i c a Sand 401 9.0 21.6 ± 3 27.8 22.9 8.8 - 23.5 Glass 710 6.0 41.4 ±3 35.3 32.9 27.9 - 74.5 Glass 710 12.7 36.7 ± 3 32.3 32.7 9.4 - 25.1 - 66 -equation for p r e d i c t i n g the choking v e l o c i t y , U c, i s : 2gD(eT 4' 7 - l ) / ( U c - U T ) 2 = 0.074 p 0 / 7 7 (4.3) i n which e c, the voidage at choking, may be p r e d i c t e d by the semi-empirical equation of Smith (1978): - 9 2 p n „ l 9 U T 2 ( 1 - e c } - V^Tf [ n £ c ] i D ( 4 ' 4 ) where UTJ i s the free s e t t i n g v e l o c i t y of a s i n g l e p a r t i c l e , D i s the standpipe diameter and n the Richardson-Zaki index. These equations with Ds, the spout diameter, r e p l a c i n g D, were ap p l i e d to c a l c u l a t e U C , which would then correspond to U G (= volumetric flow r a t e through the spout/spout c r o s s - s e c t i o n a l area) at the bed surface at the point of choking ( t r a n s i t i o n from steady spouting to bubbling). F u r t h e r , by using the e x p e r i m e n t a l l y obtained flow d i s t r i b u t i o n between the spout and the annulus (Chapter 5 ) , the experimental U g(H) at choking can be determined. The d e v i a t i o n s between the two values are shown i n Table 4.5. The p r e d i c t i o n i s reasonably good, p a r t i c u l a r l y for higher bed depths, probably because Eqn. (4.4) i s based on data c o l l e c t e d from air-sand systems. Although the v a l i d i t y of Eqn. (4.3) i s often questioned (Leung, 1980) for pipe diameters greater than 50 to 100 mm, i t was s u i t a b l e f o r t h i s work Table 4.5: P r e d i c t i o n of maximum stable spouting v e l o c i t y (= U c) by choking c r i t e r i o n vs. experimental value [= U S(H)] S o l i d H (cm) d. l (mm) U* (m/s) c (Theor.) U g ( H ) @ (m/s) (Expt.) A dev. Sand (516 um) 50 6.0 6.16 6.71 -8.20 Sand (516 Mm) 41 6.0 6.04 7.12 -15.17 Sand (516 um) 30 6.0 5.98 7.59 -21.21 Sand (516 ym) 41 12.7 6.02 5.58 +7.89 Sand (401 ym) 41 6.0 5.24 5.87 -10.73 Sand (401 um) 30 6.0 5.21 6.95 -25.03 Glass (710 um) 50 6.0 9.68 8.64 +12.03 Glass (710 um) 41 6.0 9.61 11.44 -16.00 @ Calculated as: [Q c " U a(H) (A c - A s ) ] / A s where the values of U a(H) used were determined as shown i n Chapter 5. * Calculated from eqns. (4.3) and (4.4). - 68 -where spout-diamter, Ds, was at most 30 mm. As the spout termination occurs due to choking of the spout at maximum spoutable bed depth (H^), the v e l o c i t y at the spout top can be equated to U c, i . e . : W = U c ( 4 * 5 ) and knowing the flow d i s t r i b u t i o n i n the annulus (Chapter 5 ) , the t o t a l i n l e t flow can be determined. This flow, when equated to A Q U ^ i n the Mathur-Gishier equation, can be used to c a l c u l a t e Yty[. Table 4.6 shows that t h i s method p r e d i c t s w i t h i n about 30% of the ex p e r i m e n t a l l y observed v a l u e s . However, si n c e the predicted value i s always greater than the experimental value i n the h a l f column, the d i f f e r e n c e can be accounted f o r i n part by the observation of Geldart et a l ( 1 9 8 1 ) that H^ i n a h a l f column i s about 1 5 % l e s s than i n a f u l l column. The use f o r f i n e p a r t i c l e s of the Mathur-Gishier equation, which i s an e m p i r i c a l c o r r e l a t i o n s f o r coarse p a r t i c l e s , may account f o r the remaining 1 5 % d e v i a t i o n . Table 4.6: Maximum spoutable bed depth (H^), experimental vs. p r e d i c t i o n through theory of choking S o l i d d i ( m m ) HM HM * % dev.* (Expt.) (Theor.) S i l i c a Sand 6.0 46.8 58.6 + 25.2 (401 um) S i l i c a Sand 12.7 48.5 62.6 + 29.1 (516 um) S i l i c a Sand 6.0 58.5 71.2 + 21.7 (516 um) Glass 12.7 50.8 66.4 + 30.1 (710 um) * Calc u l a t e d as Theor. - Expt. x Expt. # Calculated by s u b s t i t u t i n g (U • A + U 0(H M) • A )/A for U i n the Mathur-Gishler equation (Eq. 2.3). - 70 -CHAPTER 5 OVERALL BED PRESSURE DROP AND LONGITUDINAL FLUID VELOCITY IN THE ANNULUS 5.1 Measurement Technique The o v e r a l l bed pressure drop was measured by using e i t h e r of the two U-tube manometers connected i n p a r a l l e l ( F i g . 3.4). The manometers contained a l i q u i d of s p e c i f i c g r a v i t y 0.827 and mercury (sp. gr. 13.6), r e s p e c t i v e l y . The manometer co n t a i n i n g the l i g h t e r f l u i d was used f o r measuring lower pressure drops and could be shut off by means of a valve ( F i g . 3.4) when the pressure drop was beyond i t s range, i n which case the Hg manometer was used. The pressure tap was located 5 cm below the bed i n l e t . As noted by Mathur and Epste i n (1974), the pressure drop measured by such a technique i n c l u d e s the pressure drop both across the o r i f i c e p l a t e and across the bed. For obtaining the pressure drop due to the bed alone, the pressure drop recorded at the same flow rate with the column empty (no s o l i d s ) must be subtracted from the measured value at the upstream pressure tap l o c a t i o n as fo l l o w s : 5.1.1 Overall bed pressure drop AP = [(P ) " ( P 2 - P 2 ) + P 2 ] E a tra a tm 1/2 - P (5.1) atm a tm - 71 -where Pg i s the measured absolute upstream pressure with the bed i n the column, i s the measured absolute upstream empty column pressure at the same flow rate and P a t m i - s t n e atmospheric pressure. As an approximation, one can a l s o use: AP - P B - P E (5.2) 5.1.2 Longitudinal fl u i d velocity in the annulus The annular gas v e l o c i t y was determined by use of a s t a t i c pressure probe ( F i g . 3.6), which measured the v e r t i c a l s t a t i c pressure gr a d i e n t along the annulus. The probe was supported mid-way between the spout and the column w a l l s , with the hypodermic needles f a c i n g the curved surface. The probe was capable of being lowered to any l o n g i t u d i n a l p o s i t i o n i n the bed. Measurements were taken at 5 cm i n t e r v a l s , s t a r t i n g from 2 cm below the bed surface. The pressure gradient was measured by use of a micromanoraeter*. The above mentioned technique i s based upon the assumption that the annulus i s a l o o s e l y packed bed of s o l i d s . A c a l i b r a t i o n of pressure drop vs. s u p e r f i c i a l f l u i d v e l o c i t y was therefore done i n a loose packed bed of the same m a t e r i a l . The bed height was w e l l above the maximum spoutable bed depth ( H M ) . Half-column no. 1 ( F i g . 3.1) was used, w i t h the a u x i l i a r y flow ( f l u i d i z a t i o n ) l i n e a c t i v e , so that the gas was uniformly d i s t r i b u t e d . Uniform f l u i d d i s t r i b u t i o n was *Model MM-3 made by Flow Corp., Cambridge, Mass. - 72 -f u r t h e r ensured by checking that no s i g n i f i c a n t r a d i a l gradients e x i s t e d . I t was a l s o found that when the bed was close to minimum f l u i d i z a t i o n , f o r each of the s o l i d m a t e r i a l s ^measured " ( % " ^ ( 1 " £mF> ( 0 ' 0 2 ) ^ ( 5' 3> (where 0.02 m represents the v e r t i c a l d i s t ance between hypodermic needles), which f u r t h e r confirmed the r e l i a b i l i t y of the technique. Appendix C summarizes the c a l i b r a t i o n f o r each of the bed m a t e r i a l s i n v e s t i g a t e d . 5.2 Results and Discussion 5.2.1 Overall pressure drop For the case of spouting 98 um PVC, maintaining conditions very s i m i l a r to those of Heschel and Klose (1931) (Table 4.1), pressure drop vs. f l o w r a t e curves were s i m i l a r to that shown i n F i g . 4.1. The two pressure drop peaks as reported by Heschel and Klose (1981) ( F i g . 2.3) were never obtained even when 186 um PVC and the f u l l column were used. The peak shown i n F i g . 4.1 i s a t t r i b u t e d to the j e t breaking through the bed i n the form of bubbles, with the manometer f l u c t u a t i n g about 1 to 1.5 cm of l i q u i d of s p e c i f i c g r a v i t y 0.827. The f l u c t u a t i o n s became greater with i n c r e a s i n g flow, which e v e n t u a l l y led to slugging. P r e l i m i n a r y data c o l l e c t e d i n a f u l l column e x h i b i t e d the same trend. Such a trend i s t y p i c a l of a f l u i d i z e d bed. When the r a t i o of i n l e t to p a r t i c l e diameter was l e s s than 25.4 - 73 -(Eq. 4.1), steady spouting was achieveable and the pressure drop vs. f l o w r a t e c h a r a c t e r i s t i c s shown i n F i g s . 5.1a and 5.1b are t y p i c a l . The pressure drop upon spouting increases s l i g h t l y with i n c r e a s i n g flow, and more so with f i n e r s o l i d s . This can be a t t r i b u t e d to the i n c r e a s i n g r e g i o n of c i r c u l a t i o n (more pronounced i n f i n e r s o l i d s — F i g s . 5.2a and b) w i t h i n c r e a s i n g flow. The pressure drop increases with i n c r e a s i n g bed height ( F i g s . 5.1a and 5.1b) and decreasing p a r t i c l e s i z e ( F i g . 5.1c). The stagnant zone decreases with i n c r e a s i n g spouting v e l o c i t y ( F i g . 5.2a) and i n c r e a s i n g p a r t i c l e s i z e ( F i g . 5.2b), which i s a l s o r e f l e c t e d i n the pressure drop curve f l a t t e n i n g out as i n F i g . 5.1c. The measured A P m s / ^ p m F [minimum spouting pressure drop/minimum f l u i d i z a t i o n pressure drop, the denominator being given by (pp - pf) g ( l - e^) H] , a l s o used as an approximation of the regime c h a r a c t e r i z a t i o n parameter, C 0, by Morgan and Littman (1984) (Eq. 2.12), i s tabulated i n Table 5.1. The t h e o r e t i c a l values of AP m s/AP mp are c a l c u l a t e d from F i g . 2.6 f o r comparison, and i t i s seen that agreement with the experimental data i s good. I t i s a l s o i n most cases seen that the measured r a t i o AP m s/AP mp i s u s u a l l y above 0.7 when the bed height approaches the maximum spoutable bed depth. This i s not i n complete agreement with the regime c h a r a c t e r i z a t i o n of Morgan and Littman (1984), who s t a t e that for spouting of f i n e p a r t i c l e s w i t h a gas, C Q i s above 0.785 (Chapter 2, S e c t i o n 2.3). I t should, however, be noted that the values of C 0 obtained are a l l between 0.215 and 0.785, a c r i t e r i o n imposed f o r steady spouting of coarse p a r t i c l e s (as opposed to f i n e ) by the above workers. - 74 -i r 2.0 4.0 6.0 Q ( s t d . l / s ) 8.0 F i g u r e 5.1a. Pressure drop vs. f l o w r a t e f o r d i f f e r e n t bed heights. PVC, d =0.186 mm, d.=4.5 mm. p l ,H=50 cm H=4'l cm •H=30 cm _L 0.0 1.0 . 2.0 Q ( s t d . l / s ) 3.0 Fi g u r e 5.1b. Pressure drop vs. flow r a t e f o r v a r i o u s bed hei g h t s . Sand, d =0.516 mm, d.=6.0 mm. P • i - 75 -o oo o ID to 3 <3 O <3" O CM •d =0.401 mm P d =1.0 mm_ P J _ _L J L 0.0 1.0 4.0 2.0 3.0 Q ( s t d . l / s ) F i g u r e 5.1c. E f f e c t of p a r t i c l e s i z e on pressure drop. Sand, H=41 cm, d^=6.0 mm. S o l i d l i n e s represent i n c r e a s i n g flow and dashed l i n e s represent decreasing flow. - 76 -F l u i d used: /Air a t 80% r e l a t i v e humidity. - 77 -d (nm) A 0.401 2 3 4 5 6 7 r (cm) F i g u r e 5.2b. Stagnant zone and region o f c i r c u l a t i o n w i t h i n c r e a s i n g p a r t i c l e s i z e . Sand, d.j=6.0 mm, H=41 cm. Table 5.1: Ratio AP / AP „ " C o -rns mF experimental and t h e o r e t i c a l S o l i d A d i H (cm) AP /AP „ ms mF AP /AP „ ms mF (Eq. 2.14) (mm) (Expt.) (Theor.) S i l i c a Sand 401 um 3.79 x 1 0 - 3 6.0 30.0 0.574 0.467 S i l i c a Sand 401 um 3.79 x 10" 3 6.0 41.0 0.716 0.568 S i l i c a Sand 401 ym 3.79 x 10~ 3 6.0 46.8 L 0.748 0.593 S i l i c a Sand 516 Wm 6.4 x 10" 3 6.0 41.0 0.396 0.532 S i l i c a Sand 516 ym 6.4 x 1 0 - 3 6.0 50.0 T 0.590 0.621 S i l i c a Sand 516 um 6.4 x 10~ 3 6.0 58.5 0.703 0.684 S i l i c a Sand 516 um 3.02 x 10~ 3 12.7 41.0 T 0.516 0.586 S i l i c a Sand 516 Mm 3.02 x 10" 3 12.7 55.5 T 0.719 0.724 Glass 710 ym 0.021 6.0 30.0 0.412 0.402 Glass 710 ym 0.021 6.0 41.0 T 0.558 0.518 Glass 710 ym 0.021 6.0 55.5 T 0.667 0.657 Glass 710 ym 0.01 12.7 30.0 0.429 0.512 Glass 710 ym 0.01 12.7 41.0 0.516 0.636 Glass 710 ym 0.01 12.7 50.8 0.689 0.691 T denotes that H = H M - 79 -5.2.2 Annular longitudinal gas velocity The f l u i d v e l o c i t y i n the annulus increases along the bed height as observed i n F i g s . 5.3, 5.4 and 5.5. No s i g n i f i c a n t r a d i a l gradients of the f l u i d v e l o c i t y i n the annulus were observed i n the c y l i n d r i c a l p o r t i o n of the column. This i s co n s i s t e n t w i t h the data of S i t (1981), who used a s i m i l a r half-column. His system was a submerged spout with the annulus aerated through a d i s t r i b u t o r p l a t e . His data showed that r a d i a l gradients of annular f l u i d v e l o c i t y e x i s t e d only to about 5 cm from the d i s t r i b u t o r p l a t e , a f t e r which they were n e g l i g i b l e . The e f f e c t of bed height was found to be n e g l i g i b l e ( F i g . 5.5). t h i s i s c o n s i s t e n t w i t h the c o n d i t i o n of Grbavcvic et a l (1976): U a * f(H) (5.4) Z = constant H^ = constant i . e . the f l u i d v e l o c i t y i n the annulus at any bed l e v e l i s independent of the bed height above i t f o r any p a r t i c u l a r bed. The e f f e c t of p a r t i c l e diameter and i n l e t s i z e on the annular gas v e l o c i t y i s shown i n F i g . 5.5. The gas v e l o c i t y i n the annulus increases w i t h increases i n both p a r t i c l e diameter and i n l e t diameter. I t i s i n t e r e s t i n g to note that i n a l l the cases examined, the annular gas v e l o c i t y at Z = % i s w e l l below U mp, the minimum f l u i d i z a t i o n v e l o c i t y . I t i s found that Ua(H{4) i s about 0.6 to 0.7 times U mp (e.g. Figures 5.3 and 5.4). This value of U a(H M) i s CN CM O CM 00 CN 00 i r u _ _ -O mF ft*,' _L 10 20 30 40 Z (cm) ' 50 60 Figure 5.3. L o n g i t u d i n a l annular gas v e l o c i t y - experimental vs. t h e o r e t i c a l . Sand, d^=0.516 mm, U/U =1.18, d.=6.0 mm. L-D: Lefroy-Davidson (1969), M-M: Mamuro-Hattori (1968/1970). / mS l CO o - 81 -F i g u r e 5.4. L o n g i t u d i n a l annular gas v e l o c i t y d i s t r i b u t i o n . Sand, d =0.40 mm, U / U ^ ^ l . 18, d^=6.0 nm. L-D: Lefroy-Davidson (1969), M-H: Mamuro-Hattori (1968/1970). - 82 -CN 10 \ CO f0 _E l — 0.516 6.0 41.0 A. 516 6.0 50.0 • .516 12.7 50.0 • -401 6.0 46.8 Q.401 6.0 35.0 r.401 9.0 43.6 • 8 T AO t *n • *3 I • A 6 ft-6 T T J I L 0 10 20 30 40 50 Z (cm) F i g u r e 5.5. E f f e c t o f p a r t i c l e diameter, i n l e t s i z e and bed h e i g h t on l o n g i t u d i n a l annular gas v e l o c i t y . Sand, U/U =1.18. - 82a -s i g n i f i c a n t l y l e s s than the Ua(H{^) i n the case of a standard spouted bed of coarse p a r t i c l e , where i t i s about 0.9 to 1.0 times Urap. This f u r t h e r supports the v i s u a l observation of the spout termination mechanism at the maximum spoutable bed depth, H^ - The spout termiantion mechanism i n the case of f i n e p a r t i c l e s occurs due to choking of the spout, as compared to f l u i d i z a t i o n of the annular s o l i d s i n a coarse p a r t i c l e spouted bed. Also, i n a spouted bed of coarse p a r t i c l e s : where v"p(HM) i s the r a d i a l l y averaged p a r t i c l e v e l o c i t y i n the annulus at Z = H^. The term U*a(H{4) i n Equation (5.5) represents a superimposition of the downward moving s o l i d motion on the gas movement i n the v e r t i c a l d i r e c t i o n . In the case of f i n e s o l i d s , the s o l i d s i n the annulus move more slowly as the p a r t i c l e s i z e i s reduced (Chapter 6 ) , and so superimposing the s o l i d motion on the gas s t i l l does not account f o r the large d i f f e r e n c e between Ua(H{^) and U mp. The Lefroy-Davidson (1969) equation, when used i n i t s o r i g i n a l form: U * u mF (5.5) U = U mF Sin ( 2H, ) (5.6) a M h i g h l y o v e r p r e d i c t s the v e l o c i t y i n the annulus ( F i g s . 5.3 and 5.4). - 83 -However, In Eq. (5.6) when U r ap i s replaced by U a ( H M ) , which i s determined e x p e r i m e n t a l l y , the p r e d i c t i o n i s very good when compared with the experimental data. The Mamuro-Hattori (1968/1970) equation, which has been quite s u c c e s s f u l for coarse p a r t i c l e s , a l s o overpredicts the gas v e l o c i t y i n the annulus even when U 3 ( H M ) i s s u b s t i t u t e d f o r U m]p. The experimental points and the p r e d i c t i o n s through various equations can be seen i n F i g s . 5.3 and 5.4 f o r the case of 401 and 516 um sand p a r t i c l e s . The good f i t for the experimental data obtained by the modified Lefroy-Davidson equation should not be very s u r p r i s i n g , since t h i s equation, although e m p i r i c a l , f o l l o w s c l o s e l y the r e s u l t s obtained by a s e m i - t h e o r e t i c a l a n a l y s i s of Morgan and Littman (1980) for a wide v a r i e t y of systems ( r e f e r to Section 2.4). I t should be noted that the flow regime index, n, i s set to u n i t y (Darcy's law) i n using Eqn. (2.20) since the p a r t i c l e Reynolds number i n the annulus i s w e l l below 10 f o r the case of f i n e p a r t i c l e s . Measurements i n the c o n i c a l region were not made due to u n c e r t a i n t y of the gas flow p a t t e r n near the i n l e t ( r e c i r c u l a t i o n ) and of the voidage d i s t r i b u t i o n i n t h i s region ( E l j a s , 1975). CHAPTER 6 ANNULAR PARTICLE VELOCITY AND CIRCULATION RATE The p a r t i c l e v e l o c i t y i n the annulus i n the r a d i a l and a x i a l d i r e c t i o n s f o r coarse p a r t i c l e s has been measured by Lim (1975) using a h a l f column. From these d a t a , he also obtained the volumetric flow r a t e of s o l i d s i n the annulus, which i s a measure of s o l i d c i r c u l a t i o n r a t e . No i n f o r m a t i o n , however, e x i s t s on the s o l i d c i r c u l a t i o n r a t e for f i n e p a r t i c l e spouting. 6.1 Measurement Technique The p a r t i c l e v e l o c i t i e s were measured i n the l o n g i t u d i n a l as w e l l as the r a d i a l d i r e c t i o n s at the f l a t surface of the h a l f column. The f l a t surface of the column was di v i d e d i n t o nodal points along the r a d i a l and the a x i a l d i r e c t i o n s as shown i n f i g u r e 6.1. At each a x i a l p o s i t i o n (a f i x e d Z) , the r a d i a l distances of nodal points were 1.5, 3.0, 4.5 and 7.5 cm, r e s p e c t i v e l y , from the ce n t r e . Measurements were made with the aid of colo r e d t r a c e r p a r t i c l e s (same as the bed m a t e r i a l but colored by a water i n s o l u b l e dye*). At each node the t r a c e r p a r t i c l e was v i s u a l l y followed and timed over a distance of 2.4 cm, f o r example along X1X2 i n f i g u r e 6.1. The spout-annulus i n t e r f a c e ( r = r^) also served as a nodal p o i n t . Measurements were also made at the centre of the curved surface (point C i n Figure 6.1) f a r t h e s t away from the *Waterproof Ink ( J i f f y Marker) by Shachihata, Japan. - 85 -TOP VIEW r (cm) 2.4 on vr=1.5 3,0 4.5 7.5 SPOUT WALL (NOT TO SCALE) Z=50 cm 45 40 38 35 F i g u r e 6.1. Nodal p o i n t s f o r p a r t i c l e v e l o c i t y 30 27 25 22 20 18 15 11.7 7.9 4.1 0.0 determination. S^S^ represent the i n t e r -f ace between the stagnant zone and the r e g i o n o f s o l i d c i r c u l a t i o n . j u n c t i o n of the f l a t f r o n t surface and the curved p o r t i o n of the column. P a r t i c l e v e l o c i t y at f i v e d i f f e r e n t r a d i a l ( r ^ . . . . ^ ) p o s i t i o n s f o r each bed l e v e l s was thus determined. A stagnant zone e x i s t e d at the bottom i n most cases as discussed i n Chapter 5 (also r e f e r to F i g . 5.2). This zone i s bounded by S^S2 and the column w a l l i n Figure 6.1. The region of c i r c u l a t i o n (d/2 i n F i g . 6.1) was also noted along various bed l e v e l s , Z. The volumetric s o l i d s flow i n the annulus at any bed l e v e l Z i s : , rk+l = d / 2 G a = G (Z) = / v ( r ) ( l - E . ) (2Ttr)dr (6.1) a a p A i where v p ( r ) represents the downward p a r t i c l e v e l o c i t y ( which v a r i e s i n the r a d i a l d i r e c t i o n ) f o r any f i x e d bed l e v e l , Z. v p ( r ) can be f i t t e d as a s t r a i g h t l i n e between points r^and r 2 , r 2 and r 3 , r 3 and r ^ , and r 4 and r s , r e s p e c t i v e l y , for any bed l e v e l Z. This w i l l lead to four d i f f e r e n t regions to be used f o r i n t e g r a t i o n i n equation (6.1) (marked as 1, 2, 3, and 4 i n F i g . 6.1 - top view). For each of these r e g i o n s , v ( r ) = Atr + B i (6.2) where constants A^ and can be evaluated for each region a p p r o p r i a t e l y . Equation (6.1) thus becomes: - 87 -G = 2u(l-e.) I J 1 (A.r + B.)rdr a A . L, 1 l l i = l r ± (6.2a) k A. . 1=1 (6.2b) where: A. = % ) r . , , - r. l + l I (6.3) and 3. = v p ( r . ) - A.r. f o r any f i x e d bed l e v e l , Z. For bed l e v e l s where no stagnant zone e x i s t s , k=4 and = r5 (d = D c ) . For the bottom p o r t i o n , however, where a stagnant zone does e x i s t , r^+i = d/2 (d < D c ) , so that the c r o s s - s e c t i o n a l area of the moving annulus i s a p p r o p r i a t e l y accounted f o r by equation (6.1). This method thus accounts f o r the dead zone at the bottom and the v a r i a t i o n of spout diameter along the Z d i r e c t i o n ( r j = D g/2, at any Z ) . 6.2 Results and their Interpretation The p a r t i c l e v e l o c i t y i n the annulus increases w i t h i n c r e a s i n g bed l e v e l , Z, f o r the region above the stagnant zone (H c* < Z < H); f o r Z < H c', however, the v e l o c i t y decreases w i t h i n c r e a s i n g Z f o r the region nearer to the spout w a l l (see F i g . 6.2). This happens due to c o n t r a c t i n g c r o s s - s e c t i o n a l area f o r Z = H c to Z = 0. - 88 -- 89 -en CO o "3* O O O O ChO J I ! L (b) 0.8 0.4 0.6 Z'=Z/H Fi g u r e 6.2b. V e r t i c a l p a r t i c l e v e l o c i t i e s i n the annulus. (same system as as i n Fig.6.2a). Arrows i n d i c a t e end of stagnant zone. -3* U3 O 1 |> CN 0.0 0.2 0.4 0T6~ Z'=Z/H "078" F i g u r e 6.2c. R a d i a l l y averaged annular p a r t i c l e v e l o c i t y f o r data i n Figs.6.2a and 6.2b. Arrows i n d i c a t e the end of the stagnant zone. - 90 -The r a d i a l l y averaged p a r t i c l e v e l o c i t y c a l c u l a t e d as: (1 - e )A A a (6.4) where G a as obtained by equation 6.2b i s used to generate F i g 6.2c. These observations are q u a l i t a t i v e l y c o n s i s t e n t with the data of Lim (1975) f o r coarse p a r t i c l e s . The r a d i a l gradients of p a r t i c l e v e l o c i t y i n the annulus are, however, much steeper f o r f i n e p a r t i c l e s than those reported f o r coarse p a r t i c l e s by Lim (1975). I t was a l s o observed that the p a r t i c l e v e l o c i t y at the j u n c t i o n of the f l a t f r o n t w a l l and the curved surface ( p o i n t J i n F i g . 6-1 top view) was s i g n i f i c a n t l y lower than the v e l o c i t y measured at point C ( F i g . 6.1-top view), f a r away from the j u n c t i o n J (e.g. J' and C i n F i g . 6.2a). This shows that there i s a r e t a r d i n g e f f e c t on the movement of the p a r t i c l e s due to the merger of the two surfaces at the j u n c t i o n J . The e f f e c t of various operating parameters, which include bed h e i g h t , i n l e t a i r v e l o c i t y , p a r t i c l e s i z e and cone angle on the s o l i d c i r c u l a t i o n r a t e was a l s o i n v e s t i g a t e d . 6.2.1 Effect of bed depth and U/U _ ms The p a r t i c l e v e l o c i t y at any point i n the annulus (and therefore the v o l u m e t r i c s o l i d s flow rate) increases w i t h i n c r e a s i n g bed depth ( F i g . 6.3). The r e s u l t s of Lim (1975) with coarse p a r t i c l e s show that - 91 -Z'=Z/H F i g u r e 6.3. E f f e c t o f H and U/U. on G . Sand, d.=6.0 mm. (a) d =0.40 mm, ms a i p (b) d =0.516 mm. Arrows i n d i c a t e end o f stagnant zone. - 92 -f o r H c < Z < H, where H c i s the height of the cone, G a increases l i n e a r l y with Z. For the case of f i n e p a r t i c l e s , however, as shown i n Figure 6.3, G a vs. Z becomes approximately l i n e a r only above the bed l e v e l where the stagnant zone ceases to e x i s t . This stagnant zone at the bottom of the bed corresponds to the n a t u r a l cone formed by the region of s o l i d c i r c u l a t i o n . The e f f e c t of U/U m s i s a l s o r e f l e c t e d i n F i g . 6.3. Increasing U/U m s f o r a given system increases G a due to i n c r e a s i n g entrainment of p a r t i c l e s i n the spout. 6.2.2 Effect of particle size I n c r e a s i n g the p a r t i c l e s i z e f o r otherwise i d e n t i c a l beds gives r i s e to a higher p a r t i c l e v e l o c i t y at any f i x e d point i n the bed. This r e s u l t s i n a higher s o l i d s f l o w r a t e as shown i n Figure 6.4. As i n Fig u r e 6.3, G a vs. Z/H above the stagnant zone i s approximately l i n e a r . 6.2.3 Effect of cone angle The e f f e c t of cone angle i s shown i n Figure 6.5. Reducing the included cone angle from 60 degrees to 36.4 degrees increases the annular s o l i d s flowrate by about 35 to 45 percent. I t was a l s o observed that the stagnant zone i n the 60 degree cone angle column- disappeared when the 36.4 degree cone angle column was used. - 93 -o VC o o CN o 0 1 1 1 1 1 1 1 ' 1 —A" d (mm) p (g/cm ) _E A " " - • 0.401 2.66 A- " ^ O 0.516 2.66 A - " ' - v 0.710 4.56 ^ „ V" A 0.845 2-45./ — / / — / / A / — / / / ,* / / *•** car-— ja - -- A ' // _ _ B " —-i—i i I 1 1 1 i i .0 0.2 0.4 0.6 0 , 8 Z'=Z/H (a) o VD in o o CN d p (mm) p p (g/cm ) ° 07401 2.66 O 0.516 2.66 (b) 0.0 Fi g u r e Z'=Z/H 4. E f f e c t of p a r t i c l e s i z e on G d.=6.0 mm. (a) U/U =1.08, /s i n d i c a zone. H=30 cm, H=41 cm. (b) U/UniS=1.18. V e r t i c a l arrows d i c a t e end o f the stagnant - 94 -H (cm) 0.0 0.2 0.4 0.6 0.8 Z'=Z/H Figu r e 6.5. E f f e c t o f cone angle on G^. Sand, d =0.516 inn, d_^ =6.0 mm, U/U =1.08. V e r t i c a l arrows i n d i c a t e the end of the mS stagnant zone. - 95 -CHAPTER 7 SPOUT SHAPE, SPOUT DIAMETER AND FOUNTAIN HEIGHT 7.1 Measurement Technique The spout diameter was measured along the bed l e v e l by takin g photographs at the f l a t f r o n t surface. These p i c t u r e s were i n the form of s l i d e s and were enlarged by p r o j e c t i n g on a screen. The ma g n i f i c a t i o n was recorded and the true spout diameter thus determined. The f o u n t a i n height was d i r e c t l y measured as the d i s t a n c e from the bed surface to the foun t a i n top. 7.2 Results and Discussion 7.2.1 Spout shape and diameter The spout displayed four d i f f e r e n t shapes as shown i n Figure 7.1. The f i r s t two types (a and b) occurred i n the 60 degree cone angle column, where there was a r a p i d expansion i n the cone region and the l a s t two types (c and d) were observed when the cone angle was 36.4 degrees. The s l i g h t c o n t r a c t i o n of the spout near the bed surface as shown i n F i g s . 7.1a and c appeared i n most cases. However, a somewhat expanding spout shape near the bed surface was observed f o r very high flow r a t e s and bed heights below X 1 X 5 i n F i g . 4.4b (a l s o r e f e r to F i g s . 4.6a and c ) . The spout diameter increased with i n c r e a s i n g bed height as shown i n Figures 7.2 and 7.3a. The spout diameter above the end of the \l ON (a) (b) - (c) (d) /  0 i ° Figure 7.1. D i f f e r e n t spout shapes observed, (a) a =60, low flow r a t e , (b)a=60, h i g h f l o w r a t e , (c) a'=36.4* low flow r a t e , (d)a'=36.4, hig h flow r a t e . - 97 -J L 10 20 30 Z (cm) J !_ 40 F i g u r e 7.2. E f f e c t o f bed he i g h t on spout diameter. Sand, d =0.516 mm, U / U ^ l . 0 8 , d.=6.0 mm. P o i r -»— a * i H (cm) • 30 A 50 " - U / U m S = 1 - 0 8 ^ = 1 . 1 8 J L J 1 1 L 10 20 30 Z (cm) 40 F i g u r e 7.3a. E f f e c t o f U/U^ on spout diameter. Sand, d =0.516 mm, d.=6.0 rrm. ^ i - 98 -stagnant zone was nearly uniform f o r deep beds. Increasing the i n l e t f l u i d v e l o c i t y increased the spout diameter as i l l u s t r a t e d by Figure 7.3. For deep enough beds, the spout diameter above the stagnant zone was nearly uniform ( F i g . 7.3a) and the spout expansion followed Equation (2.9b) very c l o s e l y . I n creasing the p a r t i c l e diameter increased the spout diameter f or a f i x e d value of U/U m s as shown i n Figure 7.4. The e f f e c t of cone angle on D s i s di s p l a y e d by Figure 7.5. Decreasing the cone angle a f f e c t s the spout s i z e and shape only i n the c o n i c a l r e g i o n * and has n e g l i g i b l e e f f e c t i n the remaining p o r t i o n of the bed, where D s i s ne a r l y uniform along Z ( F i g . 7.5). McNab's c o r r e l a t i o n (Eq. 2.9) undepredicted the l o n g i t u d i n a l l y averaged spout diameter by as much as 35% i n some cases, as shown i n Table 7.1. 7.2.2 Fountain height Fountain height increased with increase i n U/U m s as shown i n Figures 7.6 and 7.7. This occurs because, f o r a given bed, the higher the i n l e t gas v e l o c i t y , the higher i s the p a r t i c l e v e l o c i t y i n the spout (Lim, 1975), which i n turn leads to a higher f o u n t a i n (Eq. 2.10). Increasing the bed height lowers the fou n t a i n height ( F i g s . 7.6 and 7.7), w h i l e a p a r t i c l e s i z e increase leads to an increase i n foun t a i n height as shown by the r e s u l t s i n Figure 7.6. *The c o n i c a l region i n the case of the 60° cone angle extends to the end of the stagnant zone. When the cone angle i s 36.4°, no stagnant zone was observed. - 99 -- 100 -solid V 1 ™ 0 pp_ ( g / c m ] .401 2.66 O .516 2.66 u g l a s s .710 4.56 • g l a s s .845 2.45 A Figure 7.4. V a r i a t i o n o f spout diameter w i t h p a r t i c l e s i z e . d.=6.0 mm, u / u ^ i ' o e . 10 20 30 Z (an) T •3- •" 6 -8-8 ' - s f e -0-D-0- a =60 o o o a'=36.4° -L 10 20 30 Z (cm) 40 50 F i g u r e 7.5. E f f e c t o f cone angle on spout shape. Sand, d =0.516 mm, U/U =1.08, d.=6.0 mm. mS I Table 7.1: L o n g i t u d i n a l l y averaged spout diameter (experimental vs. predicted) S o l i d d P d. l H (cm) U D g (mm) D (mm s ( ym) (mm) U ms (Expt.) (Eq. 2." PVC 186 4.5 19.5 3.98 17.6 13.8 PVC 186 4.5 19.5 4.12 18.2 15.2 Sand 196 4.5 15.0 2.12 11.3 6.4 Sand 196 4.5 15.0 3.77 14.7 8.4 Polypropylene 299 2.8 19.8 1.03 11.8 7.9 Polypropylene 299 2.8 19.8 1.30 14.2 8.9 Propylene 299 2.8 19.8 2.42 16.1 12.0 Sand 401 4.5 30.0 1.08 13.6 11.1 Sand 401 4.5 30.0 1.18 14.6 11.8 Sand 401 4.5 41.0 1.18 15.3 11.5 Sand 401 6.0 30.0 1.08 13 .9 10.5 Sand 401 6.0 30.0 1.18 14.7 12.2 Sand 401 6.0 41.0 1.08 14 .9 10.5 Sand 401 6.0 41.0 1.18 15.5 12.2 Sand 401 9.0 41.0 1.08 15.1 10.9 Sand - 516 6.0 41.0 1.08 16.5 12.6 Sand 516 6.0 41.0 1.18 17.3 13.7 Sand 516 12.7 41.0 1.08 16.9 12.7 Glass 710 6.0 30.0 1.08 19.8 12.5 Glass 845 6.0 30.0 1.08 20.9 17.9 - 103 -The fountain shape was approximately p a r a b o l i c i n a l l cases. , The foun t a i n shown i n F i g . A.6a does not extend over the e n t i r e c r o s s - s e c t i o n a l area of the column and i s therefore c a l l e d an 'underdeveloped' f o u n t a i n . The bed surface i n t h i s case appears as an i n v e r t e d ( i . e . opposite the c o n i c a l base) cone. As the flow r a t e i s increased f u r t h e r (with H <_ X 1 X 5 as i n F i g . 4.4b), the bed surface becomes c o n i c a l i n the same sense as the column base and the fou n t a i n spreads over the e n t i r e annulus, as seen i n Figure 4.6c. In t h i s case the f o u n t i a n i s termed ' f u l l y developed.' In the case of p a r t i c l e s ' where d p > 400 ym, e i t h e r of the fountain types ( F i g . 4.6a or 4.6c) may p r e v a i l , depending on the f l o w r a t e . - 104 -CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 8.1 Conclusions 1. Fine p a r t i c l e s ( d p < 1 ram) can be made to spout s t e a d i l y provided that the f l u i d i n l e t diameter does not exceed 25 times the p a r t i c l e diameter. This supports the observations of Mathur and G i s h l e r (1955), Ghosh (1965), Rooney and Harrison (1974) but does not agree with the observations of Heschel and Klose (1981). 2. P a r t i c l e d e n s i t y has no s i g n i f i c a n t e f f e c t on s p o u t a b i l t y , thus c o n t r a d i c t i n g the c r i t e r i a of Geldart (1973) and Molerus (1982) f o r s p o u t a b i l i t y . 3. The various regimes observed when p a r t i c l e s w i t h d p < 350 ym are spouted (provided d-^  _< 25.4 d p) are: Fixed bed, bubbling and steady spouting. When the p a r t i c l e s w i t h d p ^> 400 ym are employed, the associated regimes are: Fixed bed, steady spouting, p r o g r e s s i v e l y incoherent spouting, bubbing and slugging. The region of steady spouting increases with i n c r e a s i n g p a r t i c l e s i z e and decreasing i n l e t s i z e . The Mathur-Gishler equation (Eq. 2.3) was found to p r e d i c t U m s reasonably w e l l . However, a l l the conventional equations f o r H^ f a i l e d to represent the experimental values adequately. I t was a l s o e x p e r i m e n t a l l y found i n the bubbling regime that the s t a b l e j e t l e n g t h was independent of the bed height f o r H >_ H M. The theory developed by Fakhimi et a l (1983) was found to p r e d i c t t h i s s t a b l e j e t length q u i t e w e l l at U = U r a F-- 105 -4. A change i n the spout termination mechanism i n the case of f i n e p a r t i c l e spouting (choking vs. annular f l u i d i z a t i o n as i n coarse p a r t i c l e s ) was confirmed. Furthermore, the theory of choking i n standpipes was s u c c e s s f u l l y a p plied to p r e d i c t the regime transformation from steady spouting w i t h i n ± 14%. This approach a l s o predicted w i t h i n ± 30%, which i s f a r b e t t e r than the p r e d i c t i o n s of by the conventional equations. 5. The r a t i o C Q « A P m s / A P m F used as a regime c h a r a c t e r i z a t i o n f a c t o r by Morgan and Littman (1984) was below 0.7 i n most cases. These workers s t a t e that C 0 should be greater than 0.785 f o r the case of f i n e p a r t i c l e spouting. However, the t h e o r e t i c a l and experimental values of C Q were i n good agreement. 6. The l o n g i t u d i n a l gas v e l o c i t y i n the annulus was w e l l represented by the Lefroy-Davidson (1969) equation, provided the experimental value of U a(H M) was used instead of U m F. The Mamuro-Hattori (1968/1970) equation, which has been very s u c c e s s f u l w i t h coarse p a r t i c l e s (dp >^  1mm), always overpredicted U a(Z) f o r f i n e p a r t i c l e s . I t was found that Ua(H{4) « (0.66 to 0.7) U m F f o r f i n e p a r t i c l e s as opposed to U a(H^) « (0.9 - 1.0) U m F i n the case of coarse p a r t i c l e s , which f u r t h e r supports the postulated change i n spout termination mechanism i n the case of f i n e p a r t i c l e s (where no annular f l u i d i z a t i o n , as f o r coarse p a r t i c l e s , o ccurs). 7. The r a d i a l gradients of p a r t i c l e v e l o c i t y were found to be much steeper than f o r coarse p a r t i c l e s . The s o l i d c i r c u l a t i o n r a t e - 106 -increased w i t h i n c r e a s i n g p a r t i c l e s i z e , U/Uras, bed height and decreasing cone angle. Decreasing the cone angle from 60° to 36.4° el i m i n a t e d the stagnant zone near the i n l e t . 8. The spout diameter increased with i n c r e a s i n g flow r a t e , bed height and p a r t i c l e s i z e . A l t e r i n g the cone angle a f f e c t e d the spout shape only i n the c o n i c a l r e g i o n . The fou n t a i n height a l s o increased w i t h i n c r e a s i n g U/Ums a n d p a r t i c l e s i z e and decreasing bed height. 8.2 Recommendations for Further Work 1. Q u a n t i t a t i v e data on the various regime transformations i n an e x a c t l y s i m i l a r f u l l y c y l i n d r i c a l column should be c o l l e c t e d f o r comparison. 2. The theory of s t a b i l i t y may be a p p l i e d to study the occurrence of waves (or disturbances) at the spout-wall as the bed goes from the s t e a d i l y spouting regime to p r o g r e s s i v e l y incoherent spouting to the formation of a bubble at the spout top. This approach may a l s o be used to p r e d i c t regime transformation. - 107 -NOTATION Aa/ A c a n d 2 / d 2 1 c A Defined by Eq. (2.14) Ar dP ( p p " Pf> P f g / y 2 ^a Annulus c r o s s - s e c t i o n a l area (m 2) A c Column c r o s s - s e c t i o n a l area (m2) A s Spout c r o s s - s e c t i o n a l area (m2) Co Defined by eq. (2.11) d Diameter of s o l i d c i r c u l a t i o n r e g ion (cm) d i I n l e t diameter (mm) d P P a r t i c l e diameter ( ym) d P i Aperture mean diameter (ym) D Standpipe diameter (mm) Dc Column diameter (cm) Ds Spout diameter (mm) g A c c e l e r a t i o n due to g r a v i t y (m/s 2) G ms P u ms (g/cm 2s) Volumetric flow rate of s o l i d s (cm 3/s) h J e t p e n e t r a t i o n depth (cm) H Loose-packed bed height (cm) »c Height of the cone (cm) H c Height of the stagnant zone (cm) H F Fountain height (cm) H M Maximum spoutable bed depth (cm) k Constant - 108 -K' Constant m H w d./D2 M 1 c n Flow regime index P Pressure (kN/m2) P a(Z) F l u i d pressure at spout-annulus i n t e r f a c e (kN/m2) P a t m Atmospheric pressure (kN/ra 2) P3 Absolute pressure measured upstream with the s o l i d s (kN/m2) Pg Absolute pressure measured upstream without the s o l i d s (kN/m2) AP Pressure drop accross the bed (kN/m ) A?nis Minimum spouting pressure drop (kN/m ) AP mp Minimum f l u i d i z a t i o n pressure drop (kN/m ) Q I n l e t f l u i d flow r a t e ( s t d . l / s ) I n l e t f l u i d flow r a t e at choking ( s t d . l / s ) Q Minimum f l u i d i z a t i o n f l o w rate ( s t d . l / s ) mr U S u p e r f i c i a l i n l e t f l u i d v e l o c i t y (cm/s) U a(Z) S u p e r f i c a l annulus f l u i d v e l o c i t y a t any bed l e v e l , Z (cm/s) U a(H) U a at Z = H (cm/s) U a(H M) U a at Z = H M (cm/s) U c S u p e r f i c i a l choking v e l o c i t y i n standpipe (cm/s) U mp S u p e r f i c i a l minimum f l u i d i z a t i o n v e l o c i t y (cm/s) U m s S u p e r f i c i a l minimm spouting v e l o c i t y (cra/s) U s(0) F l u i d i n l e t v e l o c i t y (cm/s) U S(Z) S u p e r f i c i a l f l u i d v e l o c i t y i n spout (cm/s) U S(H) U s at Z = H (cm/s) - 109 -Ux Terminal v e l o c i t y of a s i n g l e p a r t i c l e (cm/s) Annular p a r t i c l e v e l o c i t y (cm/s) V P V P R a d i a l l y averaged annular p a r t i c l e v e l o c i t y (cm/s) Vgfl P a r t i c l e v e l o c i t y i n the spout at Z = H (cm/s) Weight f r a c t i o n of p a r t i c l e s having an aperture mean diameter of d P i Z V e r t i c a l d i s t a n c e from the f l u i d i n l e t (cm/s) p Bulk, d e n s i t y (g/cm ) b p F l u i d d e n s i t y (g/cm ) f p P a r t i c l e d e n s i t y (g/cm ) P Annulus voidage e c Voidage at choking Voidage at minimum f l u i d i z a t i o n e g(Z') Spout voidage a t Z' = Z/H e (0) e at Z' = 0 s s e (1) e at Z' = 1 s s 9 Defined by eq. 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G e l d a r t , D., Hemsworth, A., Sundavara, R. and Whiting, K.J., "A Comparison of Spouting and J e t t i n g i n Round And Half-Round F l u i d i z e d Beds", Can. J . Chem. Eng., 59_, 638 (1981). 11. Ghosh, B., "A Study on the Spouted Bed, P a r t I - A T h e o r e c t i c a l A n a l y s i s " , Indian Chem. Eng., _7 ( 1 ) , 16 (1965). 12. Grabavcic, Z.B., Vukovic, D.V., Zdanski, F.K. and Litman, H., " F l u i d Flow P a t t e r n , Mimimum Spouting V e l o c i t y and Pressure Drop i n Spouted Beds", Can. J . Chem. Eng., _54_, 33 (1976). 13. Grace, J.R. and Mathur, K.B., "Height And Structure of the Fountain Region Above of the Spouted Beds", Can. J . Chem. Eng., 5_6_, 533 (1978). - I l l -14. H a t t o r i , H. and Takeda, K., "Side-Outlet Spouted Bed With Inner D r a f t Tube For Small-sized S o l i d P a r t i c l e s " , J . Chem. Eng. Japan, J J_(2), 125 (1978). 15. Heschel W. and Klose , E., "The Flow Behaviour Of Very Fine P a r t i c l e s In The Spouted Bed", Chem. Techn., 33_, 122 (1981). 16. Kim, S.J., Ph.d. Thesis, Rensselaer P o l y t e c h n i c I n s t i t u t e , Troy, N.Y. (1982). 17. Leung, L.S., "The Ups And Downs of Gas-Solids Flow: A Review", i n ' F l u i d i z a t i o n ' , Ed. by Grace, J.R. and Mastsen, J.M., Plenum Press, N.Y., 25 (1980). 18. L e f r o y , G.A. and Davidson, J.F., "The Mechanics Of Spouted Beds, Trans. I n s t n . Chem. Engrs., 47_, T120 (1969). 19. Lira, C.J., "Gas Residence time D i s t r i b u t i o n and Related Flow P a t t e r n s i n Spouted Beds", Ph.D. Thesis, Univ. B r i t i s h Columbia, Vancouver (1975). 20. Lim, C.J. and Mathur, K.B., 'Residence Time d i s t r i b u t i o n of Gas i n Spouted Beds", Can. J . Chem. Eng., 52, 150 (1974). 21. Littman, H., Morgan, M.H., I I I , Vukovic, D.V., Zdanski, F.K. and Grbavcic, Z.B., "A Theory f o r P r e d i c t i n g The Maximum'Spoutable Height In A Spouted Bed", Can. J . Chem. eng., _55_, 427 (1977). 22. Mamuro, T. and H a t t o r i , H., "Flow P a t t e r n Of F l u i d In spouted Beds", J . Chem. Eng. Jap., j _ , 1 (1968)/Correction, J . Chem. Eng. Jap., 3, 119 (1970). 23. Mathur, K.B. and G i s h l e r , P.E., "A Technique For Contacting Gases With S o l i d P a r t i c l e s " , AIChE J . , 1_, 157 (1955). 24. Mathur, K.B. and E p s t e i n , N., 'Spouted Beds', academic Prese N.Y. (1974). 25. McNab, G.S.,"Prediction of Spout Diameter', B r i t . Chem Eng. Proc. Tech., 17_, 532 (1972). 26. Molerus, 0., ' I n t e r p r e t a t i o n Of Geldart's Type A, B, C and D Powders By Taking Into Account I n t e r p a r t i c l e Cohesion Forces", Powder Technol., 33_, 81 (1982). 27. Morgan, M.H. I l l and Littman, H., "General R e l a t i o n s h i p s For The Minimum Spouting Pressure Drop R a t i o , AP m s/AP mp, and The Spout-Annular I n t e r f a c i a l Condition In A Spouted Bed", i n ' F l u i d i z a t i o n ' , Ed. by Grace, J.R. and Masten, J.M., Plenum P r e s s , N.Y., 287 (1980). - 112 -28. Morgan, M.H. , I I I and Littman, H. , I & EC Fundamentals, _21_, 23 (1982). 29. Morgan, M.H., I I I and Littman, H., "Spout Voidage D i s t r i b u t i o n , S t a b i l i t y and P a r t i c l e C i r c u l a t i o n Rates In Spouted Bed Of Coarse P a r t i c l e s " , to be published i n Chem. Eng. S c i . 30. Rooney, N.M. and H a r r i s o n , D., "Spouted Beds Of Fine P a r t i c l e s " , Powder Technol. , 9_, 227 (1974). 31. S i t , Song - P., "Grid Region And Coalescence Zone Gas Exchange In F l u i d i z e d Beds", Ph.D. Thesis, M c G i l l U n i v e r s i t y (1981). 32. Smith, T.N., " L i m i t i n g Volume F r a c t i o n s i n V e r t i c a l Penumatic Transport', Chem. Eng. S c i . , 33_, 745 (1978). 33. Zenz, F.A. and Othmer, D.F. , " F l u i d i z a t i o n and F l u i d - P a r t i c l e  Systems", Reinhold P u b l i s h i n g Corp., N.Y. (1960). - 113 -APPENDIX A ROTAMETER CALIBRATION CURVES - 115 -- 116 -A i r flowrate converted to standard c o n d i t i o n s (20°C and 1 atm upstream pressure) from a c t u a l operating c o n d i t i o n s : Q (20°C, 1 atm) = Q* (1.7) ? * +° where Q = a i r flow rate at 20°C and 1 atm Q* = a i r flow rate under operating T and P T = i n l e t upstream temperature (°C) P = i n l e t upstream guage pressure (kPa). - 117 -APPENDIX B SOLIDS FREE PRESSURE DROP CURVES - 121 -APPENDIX C STATIC PRESSURE PROBE CALIBRATION IN A LOOSE PACKED BED Table C . l : Pressure d r o p - v e l o c i t y r e l a t i o n s h i p s f o r l o o s e l y packed bed M a t e r i a l A 2 A 3 Ai+ A 5 Variance S i l i c a Sand (dp = 401 um) -0.002213 0.429850 -0.000968 0.000000 0.000000 0.028674 S i l i c a Sand (dp = 516 um) 10.609846 -1.269200 +0.118332 -0.003496 0.000038 0.015006 Glass (dp = 710 ym) 0.071533 1.611811 -0.018936 0.000228 -0.000001 0.000267 U = A i + A 2 (Ah) + A 3 ( Ah) 2 + A 4 ( Ah) 3 + A 5 ( A h ) 5 where U = f l u i d v e l o c i t y i n cms/s and Ah = displacement of the microraanometeric f l u i d i n mms. - 123 -APPENDIX D EXPERIMENTAL DATA Table D.l: Run Nos. used f o r subsequent data p r e s e n t a t i o n No. P a r t i c l e d p (um) H (cm) d. (mm) l U/U ms a 1 (deg. 1 sand 401 30.0 4.5 1.08 60 2 sand 401 30.0 4.5 1.18 60 3 sand 401 41.0 4.5 1.18 60 4 sand 401 30.0 6.0 1.08 60 5 sand 401 30.0 6.0 1.18 60 5a sand 401 35.0 6.0 1. 18 60 6 sand 401 41.0 6.0 1.08 60 7 sand 401 41.0 6.0 1.18 60 7a sand 401 46.8 6.0 1.18 60 8 sand 401 30.0 9.0 1.08 60 9 sand 401 43.6 9.0 1.08 60 10 sand 516 30.0 6.0 1.08 60 11 sand 516 30.0 6.0 1.18 60 12 sand 516 41.0 6.0 1.08 60 13 sand 516 41.0 6.0 1.18 60 14 sand 516 50.0 6.0 1.08 60 15 sand 516 48.5 12.7 1.08 60 16 sand 516 41.0 6.0 1.08 36.4 17 sand 516 50.0 6.0 1.18 36.4 18 glass 710 30.0 6.0 1.08 60 18a glass 710 55.5 6.0 1.08 60 19 glass 845 30.0 6.0 1.08 60 20 PVC 185.6 15.0 2.8 1.95 60 Table D.1: Continued... jn No. P a r t i c l e d p (um) H (cm) d^ (mm) U/U ms a* (de^ 21 PVC 185.6 15.0 2.8 2.48 60 22 PVC 185.6 15.0 2.8 3.69 60 23 PVC 185.6 14.5 4.5 3.70 60 24 PVC 185.6 14.5 4.5 5.50 60 24a PVC 185.6 19.8 4.5 2.00 60 24b PVC 185.6 19.8 4.5 3.00 60 24c PVC 185.6 19.8 4.5 3.59 60 25 Polypropylene 299 19.8 2.8 1.03 60 26 Polypropylene 299 19.8 2.8 1.30 60 27 Polypropylene 299 19.8 2.8 2.42 60 28 Polypropylene 299 20.0 4.5 3.63 60 29 Polypropylene 299 20.0 4.5 5.00 60 30 Polypropylene 299 20.0 4.5 6.37 60 31 Polypropylene 299 23.0 6.0 3.42 60 32 Polypropylene 299 23.0 6.0 5.01 60 33 Sand 196 15.0 2.8 1.68 60 34 Sand 196 15.0 2.8 3.18 60 35 Sand 196 15.0 4.5 2.12 60 36 Sand 196 15.0 4.5 3.77 60 37 Sand 196 19.5 4.5 1.61 60 38 Sand 196 19.5 4.5 3.66 60 39 Bronze 176.4 15.0 2.8 1.24 60 40 Bronze 176.4 15.0 2.8 2.03 60 - 126 -D.1 Pressure drop vs. flow r a t e S i l i c a sand: dp = 401 urn, d-£ = 6 mm, H = 30 cm • Q AP( t) AP( +) 0.107 1.14 0.86 0.156 1.63 0.98 0.214 2.25 1.09 0.292 2.64 1.26 0.381 2.81 1.31 0.467 3.01 1.52 0.553 3.46 1.94 0.740 3.96 2.23 0.860 4.11 2.49 0.955 4.61 2.90 0.971 5.26 2.60 1.198 5.60 3.61 1.327 3.70 3.70 1.457 4.67 4.54 1.627 5.70 5.70 Note: AP(+) AP(+) - Pressure drop with i n c r e a s i n g flow - Pressure drop with decreasing flow - 127 -S i l i c a sand: d p = 401 ym, d^ = 6 mm, H = 41 cm • Q AP( +) AP( +) 0.083 1.35 -0.136 1.75 -0.215 2.42 0.89 0.295 3.13 1.11 0.386 3.75 1.92 0.564 4.96 2.49 0.663 5.51 3.22 0.881 7.09 3.88 1.110 7.86 5.51 1.128 8.60 4.48 1.257 9.07 4.94 1.405 8.95 5.31 1.544 5.90 5.90 1.734 6.22 6.22 1.820 6.84 6.84 1.951 6.96 6.95 2.144 6.98 6.98 - 128 -S i l i c a sand: d p = 516 um, d^ = 6 mm, H =• 30 cm • Q AP(+) AP( +) 0.083 0.67 0.46 0.136 1.28 0.68 0.215 1.63 0.82 0.385 2.00 0.98 0.561 2.31 1.04 0.757 2.78 1.13 1.000 3.60 1.18 1.242 4.01 1.26 1.384 4.22 1.45 1.430 4.29 2.61 1.442 3.67 2.22 1.529 3.61 2.84 1.550 3.02 3.00 1.729 3.11 3.10 1.915 3.18 3.18 2.248 3.20 3.20 2.464 3.32 3.32 2.750 3.41 3.41 - 129 -S i l i c a sand: d D = 516 ym, d^ = 6 mm, H = 41 cm • Q AP(+) AP( 4-) 0.083 0.67 -0.135 1.24 -0.214 1.45 -0.382 2.01 1.42 0.559 2.40 1.61 0.757 3.01 2.15 0.998 3.65 2.58 1.238 4.55 2.89 1.486 4.88 3.98 1.553 - 3.17 1.724 5.36 3.22 1.965 4.67 -2.046 3.76 3.74 2.500 3.88 3.85 3.010 4.06 4.06 3.388 4.09 4.09 - 130 -S i l i c a sand: d p = 516 ym, d^ = 6 mm, H = 5 0 cm • Q AP(t) AP(+) 0.093 0.68 -0.136 1.15 0.89 0.215 1.65 1.28 0.385 2.31 1.71 0.561 3.02 2.20 0.760 4.12 2.98 1.000 5.63 3.39 1.242 6.48 4.08 1.539 8.08 4.31 1.647 8.36 4.52 1.683 8.41 3.71 1.760 - 3.74 1.873 - • 4.08 1.927 8.96 4.39 2.061 4.42 4.40 2.125 4.48 4.45 2.286 4.58 4.55 2.400 4.60 4.60 2.561 4.62 4.62 2.980 4.65 4.65 - 131 -S i l i c a sand: d p = 1000 ym, d^ = 6 mm, H = 41 cm • Q AP( +) AP( +) 1.57 1.16 -1.75 1.35 1.29 1.88 1.68 1.71 2.15 1.82 ' 1.81 2.36 2.16 2.16 2.55 2.62 2.48 2.86 2.88 1.51 3.05 3.15 1.51 3.31 3.58 1.51 3.52 4.00 1.51 3.72 4.67 1.52 4.00 1.52 1.52 4.25 1.54 1.54 4.50 1.59 1.59 - 132 -Glass: d p = 710 ym, dji = 6 mm, H = 41 cm Q AP(t) AP(+) 1.62 2.95 -1.85 3.86 3.76 2.12 4.42 4.25 2.40 5.28 4.80 2.87 6.62 5.72 3.08 7.50 6.39 3.31 8.36 4.92 3.52 8.45 4.98 3.78 5.05 5.01 4.00 5.11 5.10 4.26 5.15 5.15 4.96 5.36 5.36 5.66 5.37 5.37 - 133 -PVC: d p = 196 um, d± = 6 mm AP Q H = 14.5 cms H = 19.5 cms H = 26.0 cms 0.025 0.35 0.042 0.61 0.80 1.05 0.072 _ 1.15 1.51 0.091 0.94 0.110 0.50 1.32 1.88 0.126 0.51 0.72 1.01 0.161 0.52 0.200 - 0.82 1.28 0.225 0.55 0.300 0.64 1.00 1.73 0.408 0.71 1.31 2.25 0.495 0.78 1.71 2.76 0.568 0.88 0.600 - 1.95 3.03 0.625 1.00 0.680 1.16 0.700 - 2.22 3.36 - 134 -S i l i c a Sand: d p = 196 ym, d^ = 4.5 ram, H = 19.5 cm • Q AP(+) AP( +) 0.097 2.55 1.56 0.132 3.62 1.83 0.158 3.87 2.18 0.215 - 2.18 0.230 3.85 1.50 0.295 1.53 1.52 0.383 1.61 1.60 0.472 1.69 1.67 0.658 2.05 2.05 0.895 2.83 2.83 1.000 3.30 3.30 - 135 -D.2: Annulus Gas V e l o c i t y Z U Z U Z U a a a 17.5 4.85 17.5 5.04 17.5 5.42 21.5 5.90 21.5 6.02 21.5 6.48 26.5 6.81 26.5 6.85 26.5 7.33 31.0 7.61 31.0 7.48 31.0 8.16 33.5 7.96 33.5 8.00 33.5 8.56 36.0 8.32 36.0 8.79 41.0 8.98 41.0 9.18 46.3 9.20 43.0 9.19 Run No. 12 Run No. 14 Run No. 15 Z U Z IT Z LI a a a 16.5 6.85 15.5 6.42 15.7 7.56 21.0 8.14 21.0 7.78 21.0 8.83 26.5 9.21 26.5 9.27 26.5 9.71 31.0 10.14 31.0 10.09 31.0 10.64 36.0 11.62 36.0 11.63 36.0 11.84 41.0 12.12 41.0 12.17 41.0 12.93 46.0 13.10 46.0 13.41 49.0 13.93 48.0 13.56 Run No. 18a 16.5 11.45 21.0 15.60 26.5 19.12 31.0 21.47 36.0 23.86 41.0 25.12 46.0 26.88 55.0 28.21 - 136 -D.3: S o l i d s C i r c u l a t i o n Rate Run No. 4 Run No. 5 Z/H G ZH G a a 0.986 21.2 0.986 24.4 0.900 20.1 0.900 21.9 0.833 18.2 0.833 20.2 0.733 14.6 0.733 15.5 0.600 10.8 0.600 13.0 0.500 6.7 0.500 7.5 0.390 5.8 0.390 7.2 0.263 5.2 0.263 5.6 0.137 2.2 0.137 2.7 Run No. 6 Z/H G o a 0.976 27.4 0.854 22.6 0.732 21.5 0.659 20.5 0.610 19.9 0.537 17.9 0.439 9.2 0.366 6.3 0.285 5.6 0.193 5.5 0.100 3.6 Run No. 7 ZH G a 0.976 34.2 0.854 28.7 0.732 25.8 0.659 25.2 0.610 24.0 0.537 21.2 0.439 10.1 0.366 7.6 0.285 6.5 0.193 6.4 0.100 4.2 - 137 -Run No. 10 Z/H G a 0.976 28.3 0.900 27.8 0.833 25.2 0.733 21.5 0.667 18.0 0.600 13.8 0.500 11.2 0.390 7.6 0.263 5.9 0.137 4.0 Run No. 12 Z/H G a 0.976 36.4 0.927 32.9 0.854 31.1 0.732 28.8 0.659 28.2 0.610 27.4 0.537 25.9 0.488 20.9 0.439 15.8 0.366 11.3 0.285 8.1 0.192 7.0 0.100 3.6 Run No. 11 ZH G a 0.976 34.8 0.900 32.6 0.833 28.5 0.733 25.7 0.667 21.6 0.600 16.7 0.500 13.1 0.390 8.1 0.263 6.7 0.137 4.2 • Run No. 13 ZH G a 0.976 41.7 0.927 39.0 0.854 35.2 0.732 34.3 0.659' 32.5 0.610 31.7 0.537 30.1 0.488 22.2 0.439 17.4 0.366 11.8 0.285 8.9 0.192 7.4 0.100 5.3 - 138 -Run No. 14 Run No. 16 Z/H G a ZH G a 0.980 51.3 0.976 44.5 0.900 42.6 0.854 41.2 0.800 41.3 0.732 39.5 0.760 39.8 0.610 37.0 0.700 36.3 0.546 35.6 0.600 35.3 0.442 32.7 0.540 34.2 0.378 30.0 0.500 32.4 0.249 16.0 0.440 31.1 0.115 9.7 0.400 24.3 0.360 16.8 0.300 12.2 0.234 9.0 0.158 7.3 0.082 4.8 Run No. 17 Z/H G 0.986 64.0 0.900 59.9 0.800 52.6 0.700 46.8 0.600 43.3 0.500 39.9 0.448 40.2 0.362 38.2 0.310 32.4 0.204 21.8 0.094 10.4 Run No. 18 ZH G a 0.986 64.4 0.900 63.1 0.833 61.4 0.733 58.4 0.667 57.5 0.600 53.9 0.500 50.9 0.370 46.8 0.243 33.5 0.191 24.8 0.098 14.1 - 139 -Run No. 19 Z/H G a 0.980 66.6 0.880 66.0 0.813 62.7 0.713 61.0 0.647 60.1 0.580 56.4 0.480 60.4 0.390 47.5 0.263 42.4 0.191 31.4 0.098 18.6 - 140 -D.4: Spout Diameter and Region of C i r c u l a t i o n Run No. 1 Run No. 2 z D d Z D d s s 30.0 13.0 15.2 30.0 13.5 15.2 27.0 13.0 15.2 27.0 13.5 15.2 25.0 13.0 15.2 25.0 13.5 15.2 22.0 13.0 15.2 22.0 13.5 15.2 20.0 13.0 15.2 20.0 14.1 15.2 18.0 13.5 13.3 18.0 14.1 13.3 15.0 13.5 10.2 15.0 14.5 10.3 11.7 14.0 7.6 11.7 15.6 7.8 7.9 15.1 6.1 7.9 17.0 6.3 4.1 17.1 4.0 4.1 17.0 4.1 1.6 9.4 2.9 1.6 9.5 3.0 Run No. 3 Run No. 4 Z D d Z D d s s 40.0 14.6 15.2 30.0 "12.5 15.2 37.0 14.8 15.2 27.0 12.5 15.2 35.0 14.8 15.2 25.0 13.0 15.2 30.0 15.1 15.2 22.0 13.0 15.2 25.0 15.1 15.2 18.0 14.0 13.3 22.0 15.1 15.2 15.0 14.0 10.4 20.0 15.1 14.8 11.7 14.5 7.8 15.0 15.1 9.1 7.9 16.1 6.3 11.7 15.1 7.3 4.1 14.5 4.1 7.9 16.9 5.8 1.6 10.5 3.0 4.1 18.5 4.1 1.6 9.1 3.0 - 141 -Run No. 5 Run No. 6 z D d Z D d s s 30.0 14.0 15.2 40.0 13.0 15.2 27.0 14.0 15.2 35.0 13.5 15.2 25.0 14.0 15.2 30.0 14.1 15.2 22.0 14.0 15.2 27.0 14.1 15.2 18.0 14.5 13.3 25.0 14.1 15.2 15.0 14.5 10.5 22.0 14.1 15.2 11.7 16.1 8.1 18.0 14.1 13.3 7.9 16.5 6.3 15.0 14.5 9.2 4.1 14.5 4.3 11.7 14.5 7.4 1.6 10.6 3.0 7.9 14.5 5.8 4.1 13.1 4.1 1.6 10.1 3.0 Run No. 7 Z D d s 40.0 15.0 15.2 35.0 15.0 15.2 30.0 15.0 15.2 27.0 15.0 15.2 25.0 15.0 15.2 22.0 15.5 15.2 18.0 15.5 13.3 15.0 15.5 9.4 11.7 16.5 7.5 7.9 17.5 6.4 4.1 14.0 4.6 1.6 10.6 3.0 Run No. 8 Z D s d 30.0 13.0 15.2 27.0 13.0 15.2 25.0 13.0 15.2 22.0 13.0 15.2 20.0 13.0 15.2 18.0 13.5 13.3 15.0 14.5 10.5 11.7 15.5 7.9 7.9 16.5 6.6 4.1 19.5 4.2 1.6 11.0 3.0 - 142 -Run No. 9 Run No. 10 z D d Z D d s s 40.0 14.5 15.2 30.0 14.0 15.2 35.0 14.5 15.2 27.0 14.5 15.2 30.0 14.5 15.2 25.0 15.0 15.2 25.0 14.5 15.2 22.0 15.0 15.2 20.0 15.0 14.6 20.0 15.5 15.2 15.0 15.6 9.3 18.0 15.5 15.2 11.7 17.0 7.5 15.0 16.0 13.2 7.9 18.1 5.8 11.7 17.5 9.6 4.1 18.1 4.1 7.9 19.0 7.3 1.6 11.5 3.1 4.1 17.1 4.4 1.6 11.0 3.1 Run No. 11 Z D d s 30.0 15.0 15.2 27.0 15.0 15.2 25.0 15.5 15.2 22.0 15.5 15.2 20.0 16.0 15.2 18.0 16.5 15.2 15.0 17.1 13.4 11.7 18.1 9.6 7.9 19.5 7.5 4.1 17.2 4.9 1.6 11.1 3.2 Run No. 12 Z D d 40.0 15.0 15.2 38.0 15.0 15.2 35.0 15.0 15.2 30.0 15.0 15.2 27.0 15.0 15.2 25.0 15.5 15.2 22.0 15.5 15.2 20.0 16.1 15.2 18.0 16.2 15.2 15.0 17.1 13.3 11.7 19.2 9.7 7.9 20.4 7.4 4.1 17.5 4.4 1.6 13.1 3.1 - 143 -Run No. 13 Run No. 14 z D d Z D d s s 40.0 15.5 15.2 49.0 16.5 15.2 38.0 15.5 15.2 45.0 16.5 15.2 35.0 15.5 15.2 40.0 16.5 15.2 30.0 15.5 15.2 38.0 16.5 15.2 27.0 15.5 15.2 35.0 16.5 15.2 25.0 15.5 15.2 30.0 16.5 15.2 22.0 16.0 15.2 27.0 16.5 15.2 20.0 16.0 15.2 25.0 16.5 15.2 18.0 16.5 15.2 22.0 16.5 15.2 15.0 17.1 13.5 20.0 16.5 15.2 11.7 19.3 9.9 18.0 17.1 15.2 7.9 20.6 7.7 15.0 17.5 13.3 4.1 17.5 4.9 11.7 18.5 9.7 1.6 13.5 3.3 7.9 20.0 7.6 4.1 17.5 4.8 1.6 12.1 3.1 Run No. 15 Run No. 16 Z D s d Z D s d* 40.0 16.5 15.2 40.0 15.1 -35.0 16.5 15.2 35.0 15.1 -30.0 16.0 15.2 30.0 15.1 -25.0 15.8 15.2 25.0 15.1 -20.0 16.8 15.2 22.4 15.1 -15.0 18.0 13.3 18.1 15.1 -11.7 19.1 9.8 15.5 15.0 -7.9 20.4 7.6 10.2 15.0 -4.1 20.4 4.5 4.7 13.5 -1.6 9.5 3.2 2.4 9.5 -1.2 6.0 — - 144 -Run No. 17 Run No. 18 z D s d* Z D s d 50.0 16.1 - 29.4 18.1 — 45.0 16.5 - 26.4 18.5 , -40.0 16.5 - 24.4 19.1 -35.0 16.5 - 21.4 19.1 -30.0 16.5 - 19.4 19.5 -25.0 16.5 - 17.7 20.0 -22.4 16.2 - 14.4 20.4 -18.1 16.0 - 11.1 23.3 -15.5 15.8 - 7.3 25.5 -10.2 15.2 - 3.5 16.0 -4.7 14.0 -2.4 8.9 -1.2 6.0 — Run No. 19 Run No. 20 Z D s d* Z D s d 29.4 19.0 - 15.0 - 8.1 26.4 19.0 - 13.1 8.1 5.9 24.4 19.0 - 11.7 10.2 4.5 21.4 19.0 - 7.9 11.5 3.7 19.4 19.5 - 7.0 12.0 3.3 17.4 19.5 - 4.2 10.0 2.5 14.4 22.0 - 2.9 8.5 2.0 11.7 25.2 - 1.6 7.1 1.35 7.9 24.5 -4.1 23.5 — *No stagnant zone exis ted and d = D c . - 145 -Run No. 21 Run No. 22 z D s d Z D s d 15.0 - 6.8 15.0 — 8.0 13.1 8.1 5.2 13.1 10.0 5.8 11.7 10.1 4.8 11.7 12.6 4.4 7.9 13.2 4.2 7.9 14.3 3.6 7.0 12.5 3.7 7.0 14.4 3.2 4.2 10.5 3.1 4.2 11.6 2.5 2.9 9.6 2.6 2.9 10.0 2.0 1.6 7.0 1.8 1.6 8.0 1.3 Run No. 23 Run No. 24 Z D s d Z D s d 13.1 14.5 6.8 13.3 19.9 7.9 11.7 17.2 5.2 11.7 20.8 6.4 9.6 18.4 4.8 9.6 21.8 5.8 7.9 17.9 4.2 7.9 19.8 5.4 5.6 15.8 3.7 5.6 17.2 4.5 4.1 13.7 3.1 4.1 14.5 3.8 3.1 12.0 2.6 3.1 11.8 3.3 1.6 10.1 1.8 1.6 10.2 2.2 *No stagnant zone e x i s t e d and d = D„. - 146 -Run No. 24a Run No. 24b z D d Z D d s s 19.8 - 15.2 19.4 - 15.2 17.0 16.7 11.3 17.0 - 12.5 15.0- 18.8 9.3 15.0 - 10.7 11.7 20.5 6.6 11.7 - 6.9 9.6 20.8 5.2 9.6 - 8.2 7.9 18.8 3.9 7.9 - 5.7 5.6 16.2 2.9 5.6 - 4.8 4.1 13.7 2.3 4.1 - 4.0 3.1 12.9 1.9 3.1 - 3.1 1.6 9.6 1.5 1.6 — 2.4 Run No. 24c Z d 19.0 - 15.2 17.0 - 13.0 15.0 - 11.2 11.7 - 8.2 9.6 - 6.9 7.9 - 5.9 5.6 - 4.8 4.1 - 4.3 3.1 - 3.7 1.6 - 2.9 - 147 -Run No. 25 Run No. 26 z D s d Z D s d 19.0 - 10.2 19.0 - 15.0 18.0 11.4 8.8 18.0 11.6 10.2 15.0 11.5 8.0 15.0 11.6 9.2 11.7 10.6 6.7 11.7 12.1 8.0 9.6 11.9 5.9 9.6 13.7 7.3 8.5 12.8 5.1 8.5 14.7 6.6 5.6 13.7 4.4 5.6 14.7 5.4 4.1 13.7 3.7 4.1 12.6 4.4 3.1 11.9 3.0 3.1 10.0 3.8 1.6 9.3 2.4 1.6 6.9 3.0 Run No. 27 Run No. 28 Z D s d Z D s d 19.0 - 15.2 20.0 25.3 15.2 18.0 13.0 11.3 18.0 26.4 11.3 15.0 14.0 10.4 15.0 23.9 10.2 11.7 14.5 8.9 11.7 20.7 8.6 9.6 18.2 8.1 9.6 20.7 7.9 8.5 19.8 7.2 8.5 20.0 7.0 5.6 18.2 5.9 5.6 17.1 5.6 4.1 13.5 5.0 4.1 14.3 4.9 3.1 10.9 4.2 3.4 12.5 4.3 1.6 7.3 3.3 1.6 9.3 3.2 - 148 -Run No. 29 Run No. 30 z D s d Z D s . d • 20.0 20.9 15.2 20.0 22.2 15.2 18.0 23.8 11.4 18.0 25.5 11.9 15.0 24.5 10.4 15.0 28.4 10.8 11.7 25.1 8.8 11.7 26.8 9.2 9.6 22.5 8.0 9.6 23.9 8.3 8.5 20.9 7.2 8.5 21.4 7.4 5.6 17.7 5.8 5.6 17.7 5.9 4.1 14.5 5.4 4.1 15.2 5.6 3.4 11.6 4.4 3.4 12.8 4.6 1.6 9.0 3.3 1.6 9.9 3.3 Run No. 31 Run No. 32 Z D s d Z D s d 22.0 26.5 15.2 22.0 26.7 15.2 20.0 28.8 12.7 20.0 29.0 13.3 18.0 28.8 11.6 18.0 30.5 12.2 15.0 26.8 10.5 15.0 30.5 11.5 11.7 25.9 9.0 11.7 28.0 10.6 9.6 22.9 8.0 9.6 25.0 9.3 8.5 20.9 7.3 8.5 23.0 8.6 5.6 17.4 6.1 5.6 19.0 7.4 4.1 14.8 5.3 5.6 19.0 5.7 3.4 13.4 4.5 3.4 13.5 4.7 1.6 9.9 3.5 1.6 10.0 3.5 - 149 -R u n N o . 33 Run N o . 34 z D d Z D d s s 15.0 - - 15.0 - 10.8 11.7 9.5 6.2 11.7 6.7 7.7 9.6 10.3 5.8 9.6 13.3 6.7 8.5 10.8 5.1 8.5 15.8 6.0 5.6 14.0 4.2 5.6 18.4 4.9 4.1 13.0 3.8 4.1 14.8 4.7 . 3.4 10.6 3.2 3.4 13.3 3.8 1.6 6.1 2.6 1.6 6.7 2.8 R u n N o . 35 Z D d 15.0 — 10.6 11.7 11.4 6.2 9.6 11.4 4.9 8.5 12.3 4.3 5.6 12.7 3.6 4.1 11.8 3.1 3.4 10.9 2.7 1.6 3.2 2.3 R u n N o . 36 Z D d s 15.0 — 12.3 11.7 15.0 7.7 9.6 15.0 6.7 8.5 15.9 6.2 5.6 14.6 5.0 4.1 13.7 4.1 3.4 10.9 3.5 1.6 8.2 2.8 - 150 -Run No. 37 Run No. 38 z D s d Z D s d 19.5 - 13.8 19.5 15.3 15.2 18.0 11.4 • 8.5 18.0 15.3 11.8 15.0 11.4 5.8 15.0 17.4 9.7 11.7 12.5 4.6 11.7 19.6 8.6 9.6 12.5 4.2 9.6 20.7 7.7 8.5 13.6 3.8 8.5 20.2 7.1 5.6 13.6 3.2 5.6 17.4 5.5 4.1 11.9 2.8 4.1 14.7 4.7 3.4 9.8 2.3 3.4 11.4 3.7 1.6 8.7 2.2 1.6 9.3 3.4 Run No. 39 Run No. 40 Z D s d Z D s d 15.0 6.7 8.4 15.0 4.9 11.8 11.7 6.9 6.6 11.7 6.0 8.6 9.6 6.9 5.7 9.6 7.4 7.2 8.5 6.9 5.1 8.5 8.1 6.4 5.6 7.4 4.8 5.6 7.7 5.6 4.1 6.7 4.2 4.1 7.4 4.8 3.4 6.2 3.2 3.4 6.0 4.1 1.6 4.2 3.0 1.6 4.9 3.5 - 151 -D.5: Fountain Height S o l i d d p d. U/U m s H H p Sand 196 2.8 1.14 15.0 36.5 Sand 196 2.8 1.43 15.0 45.5 Sand 196 2.8 1.86 15.0 58.5 Sand 196 4.5 1.84 14.5 41.0 Sand 196 4.5 2.41 14.5 54.5 Sand 196 4.5 3.00 14.5 69.0 Sand 196 4.5 3.56 14.5 75.5 Sand 196 4.5 4.13. 14.5 77.5 Sand 196 4.5 4.81 14.5 79.5 Sand 196 4.5 5.66 14.5 84.5 Sand 196 4.5 1.58 19.5 74.5 Sand 196 4.5 1.88 19.5 90.5 Bronze 176.4 2.8 1.24 15.0 24.2 Bronze 176.4 2.8 1.53 15.0 38.0 Bronze 176.4 2.8 1.76 15.0 42.1 Bronze 176.4 2.8 2.03 15.0 52.0 Sand 401 4.5 1.08 30.0 10.7 Sand 401 4.5 1.18 30.0 18.0 Sand 401 4.5 1.08 41.0 9.0 Sand 401 4.5 1.18 41.0 17.2 Sand 401 4.5 1.08 49.6 8.8 Sand 401 4.5 1.18 49.6 14.2 Sand 401 4.5 1.20 49.6 16.6 Sand 401 6.0 1.08 15.0 10.0 Sand 401 6.0 1.18 15.0 19.0 Sand 401 6.0 1.32 15.0 26.0 Sand 401 6.0 1.50 15.0 32.1 Sand 401 6.0 1.67 15.0 42.2 Sand 401 6.0 1.87 15.0 46.0 Sand 401 6.0 1.01 30.0 9.4 Sand 401 6.0 1.08 30.0 12.8 Sand 401 6.0 1.11 30.0 15.1 Sand 401 6.0 1.18 30.0 19.5 Sand 401 6.0 1.01 41.0 7.1 Sand 401 6.0 1.08 41.0 10.8 Sand 401 6.0 1.13 41.0 14.2 Sand 401 6.0 1.23 41.0 19.5 Sand 401 6.0 1.27 41.0 21.0 Sand 401 9.0 1.02 30.0 10.4 Sand 401 9.0 1.09 30.0 12.5 \ - 152 -S o l i d d d, U/U H H„ p i ms F Sand 401 9.0 Sand 401 9.0 Sand 401 9.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 6.0 Sand 516 12.7 Sand 516 12.7 Sand 516 12.7 Glass 710 6.0 Glass 710 6.0 Glass 710 6.0 Glass 845 6.0 Glass 845 6.0 Glass 845 6.0 Glass 845 6.0 Glass 845 6.0 Glass 845 6.0 1.02 41.0 10.1 1.07 41.0 13.0 1.10 41.0 15.8 1.01 30.0 10.2 1.02 30.0 11.2 1.06 30.0 14.1 1.11 30.0 16.2 1.14 30.0 18.2 1.16 30.0 20.7 1.015 41.0 8.2 1.05 41.0 9.5 1.06 41.0 10.9 1.11 41.0 13.0 1.16 41.0 15.8 1.21 41.0 18.5 1.24 41.0 20.0 1.015 50.0 5.8 1.05 50.0 8.5 1.10 50.0 10.8 1.12 50.0 13.2 1.14 50.0 14.5 1.16 50.0 16.5 1.19 50.0 18.5 1.01 41.0 9.5 1.04 41.0 13.5 1.08 41.0 18.2 1.01 30.0 14.0 1.05 30.0 20.0 1.24 30.0 29.5 1.02 30.0 11.8 1.05 30.0 14.3 1.07 30.0 15.4 1.11 30.0 19.0 1.17 30.0 22.3 1.23 30.0 26.8 

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