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Hydrodynamics of gas spouting at high temperature Wu, Stanley W. M. 1986

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HYDRODYNAMICS OF GAS SPOUTING AT HIGH TEMPERATURE by S T A N L E Y W. M . WU A T H E S I S SUBMITTED IN P A R T I A L F U L F I L M E N T OF T H E REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D S C I E N C E i n T H E F A C U L T Y OF GRADUATE S T U D I E S D e p a r t m e n t o f C h e m i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d T H E U N I V E R S I T Y OF B R I T I S H COLUMBIA A u g u s t 1986 © S T A N L E Y W. M . WU, 1986 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 at the The U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that 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 of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Chemical E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: August 1986 ABSTRACT The spouted bed technique was developed f o r h a n d l i n g s o l i d s which were too coarse to f l u i d i z e w e l l . In i t s e a r l y stages, i t was p r i m a r i l y used f o r d r y i n g wheat. I t was l a t e r found that spouting has p o t e n t i a l a p p l i c a t i o n i n high temperature o p e r a t i o n s such as c o a l combustion and g a s i f i c a t i o n . However, l i t e r a t u r e review w i l l show that there are very few r e p o r t s on the hydrodynamics of spouted beds at h i g h temperature and/or p r e s s u r e . Most e x i s t i n g c o r r e l a t i o n s or e x p r e s s i o n s are based upon experiments done at room c o n d i t i o n s ; they have not been t e s t e d with data from higher temperatures. The goal of t h i s study was to o b t a i n experimental data at h i g h temperatures, to examine the v a l i d i t y of e x i s t i n g equations and to modify the l a t t e r where a p p r o p r i a t e . Spouting of sand p a r t i c l e s (Ottawa sand) with preheated a i r , ranging from 20 to 420 °C, was conducted i n a 156 mm s t a i n l e s s s t e e l half-column, equipped with a g l a s s p a n e l . The t r a n s p a r e n t s u r f a c e allowed one to measure spout diameter, f o u n t a i n height, annulus h e i g h t and other important parameters which otherwise are d i f f i c u l t to o b t a i n in a f u l l s t a i n l e s s s t e e l column. In a d d i t i o n to a i r , helium and methane, at room c o n d i t i o n s , were a l s o used as spouting gases. With these two gases, i t became p o s s i b l e to i n v e s t i g a t e the e f f e c t of changing gas d e n s i t y at constant i i gas v i s c o s i t y and the e f f e c t of changing gas v i s c o s i t y at constant gas d e n s i t y . The main experimental measurements were of minimum spouting v e l o c i t i e s , spout diameters, maximum spoutable h e i g h t s and bed pre s s u r e drops. For s e l e c t e d runs, a d d i t i o n a l measurements, such as of flow regime maps, p a r t i c l e c i r c u l a t i o n r a t e s , r a d i a l and l o n g i t u d i n a l pressure p r o f i l e s , f o u n t a i n h e i g h t s and annular f l u i d v e l o c i t i e s , were a l s o o btained. In g e n e r a l , i t was found that the range of s t a b l e spouting decreased with d e c r e a s i n g gas d e n s i t y and i n c r e a s i n g gas v i s c o s i t y , hence with i n c r e a s i n g a i r temperature. Some of the e x i s t i n g equations were found to be inadequate. The Mathur and G i s h l e r (1955) equation was u n s a t i s f a c t o r y when t e s t e d a g a i n s t the experimental values of U m s . The ex p r e s s i o n of E p s t e i n and Levine (1978) gave good p r e d i c t i o n of the o v e r a l l bed pressure drop f o r room c o n d i t i o n s but overestimated the e f f e c t of temperature. The McNab (1972) equation f o r e s t i m a t i n g spout diameter worked reasonably w e l l f o r a i r spouting at room temperature but i t unde r p r e d i c t e d at higher temperatures. These equations were e m p i r i c a l l y m o d i f i e d to f i t the new data obtained. Table of Contents ABSTRACT i i LIST OF TABLES v i i LIST OF FIGURES x ACKNOWLEDGMENTS xv. 1 . INTRODUCTION 1 2. LITERATURE REVIEW 5 2.1 S p o u t a b i l i t y of P a r t i c l e s 6 2.2 Minimum Spouting V e l o c i t y 6 2.3 Maximum Spoutable Bed Height 9 2.4 Average Spout Diameter 14 2.5 F l u i d and P a r t i c l e V e l o c i t y i n the Annulus 17 2.6 L o n g i t u d i n a l Pressure P r o f i l e and O v e r a l l Bed Pressure Drop .....18 2.7 R a d i a l Pressure P r o f i l e 22 2.8 Fountain Height 22 2.9 Regime Map 22 3. APPARATUS, BED MATERIALS AND EXPERIMENTAL METHODS ...26 3.1 Choice and D e s c r i p t i o n of Equipment .....26 3.2 Method of Heating 32 3.3 Gas Flow and Instrumentation .....32 3.4 Bed M a t e r i a l 37 3.5 Flowrate Measurements 41 3.6 Program of Study .....41 3.7 Methods of Measurement .....44 3.7.1 Maximum Spoutable Height .....46 3.7.2 O v e r a l l Bed Pressure Drop 47 3.7.3 Minimum Spouting V e l o c i t y 48 3.7.4 Spout Diameter and Spout Shape 49 3.7.5 F l u i d and P a r t i c l e V e l o c i t i e s i n the Annulus 49 3.7.6 R a d i a l and L o n g i t u d i n a l Pressure P r o f i l e s .53 3.7.7 Regime Map 55 3.7.8 Fountain Height 56 3.8 E r r o r C a l c u l a t i o n 56 4. STABILITY OF SPOUTING 57 4.1 S t a b i l i t y 57 4.1.1 E f f e c t of Temperature on S p o u t a b i l i t y 57 4.1.2 E f f e c t of Temperature on Spouting C h a r a c t e r i s t i c s 59 4.2 Regime Maps 61 4.3 Maximum Spoutable Bed Height 67 4.3.1 E f f e c t of O r i f i c e Diameter 67 4.3.2 E f f e c t of P a r t i c l e Diameter 67 4.3.3 E f f e c t of Temperature 71 4.3.4 E f f e c t of f l u i d d e n s i t y and v i s c o s i t y 74 4.3.5 C o r r e l a t i o n of Experimental Data 76 4.4 Mechanisms of Spout Termination at Maximum Spoutable Bed Height 76 5. MINIMUM SPOUTING VELOCITY AND OVERALL BED PRESSURE DROP 86 5.1 Minimum Spouting V e l o c i t y 86 5.1.1 E f f e c t of P a r t i c l e and O r i f i c e Diameters ..86 5.1.2 E f f e c t of Temperature 93 5.1.3 Data C o r r e l a t i o n 93 5.2 O v e r a l l Bed Pressure Drop 98 5.2.1 E f f e c t of O r i f i c e and P a r t i c l e Diameters .104 v 5.2.2 E f f e c t of Temperature 104 5.2.3 Data C o r r e l a t i o n 104 6. SPOUT SHAPE, SPOUT DIAMETER AND FOUNTAIN HEIGHT 116 6.1 Spout Shape and Diameter 116 6.2 Fountain Height 132 7. PRESSURE PROFILES AND FLUID AND PARTICLE VELOCITIES IN THE ANNULUS 1 40 7.1 R a d i a l Pressure P r o f i l e s 140 7.2 L o n g i t u d i n a l Pressure P r o f i l e s 146 7.3 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 152 7.4 L o n g i t u d i n a l P a r t i c l e V e l o c i t y 156 8. CONCLUSIONS AND RECOMMENDATIONS 164 8.1 Co n c l u s i o n s 164 8.2 Recommendations 166 NOTATION 168 REFERENCES 172 APPENDIX A - MAXIMUM SPOUTABLE BED HEIGHT 176 APPENDIX B - PARTICLE SIZE DISTRIBUTIONS 181 APPENDIX C - CALIBRATION CURVES 182 APPENDIX D - EXPERIMENTAL CONDITIONS 193 APPENDIX E - VARIATIONS OF SPOUT DIAMETERS WITH BED LEVEL 200 v i L I S T OF TABLES Table 3.1 T y p i c a l temperature p r o f i l e s . Sand Pp = 2600 kg/m3 and d p = 1.25 mm 35 Table 3.2 P a r t i c l e diameter 38 Table 3.3 P h y s i c a l p r o p e r t i e s of sand p a r t i c l e s used ....40 Table 3.4 Operating c o n d i t i o n s 42 Table 3.5 Dependent v a r i a b l e s measured ....43 Table 3.6 Ranges of v a r i a b l e s s t u d i e d ( p p = 2600 kg/m3, D c = 156 mm) 45 Table 4.1 S p o u t a b i l i t y of sand p a r t i c l e s at d i f f e r e n t c o n d i t i o n s 58 Table 4.2 E f f e c t s of M and pf on H m. D c = 156 mm, D^ = 19.05 mm and dp = 1.25 mm 75 Table 4.3 Maximum spoutable bed hei g h t , experimental versus p r e d i c t i o n s . Sand, Pp = 2600 kg/m3, D c = 156 mm 77 Table 4.4 Comparison between U c and U s H Sand, dp = 1.25 mm, D c = 156 mm 80 Table 5.1a Minimum spouting v e l o c i t y , experimental versus p r e d i c t i o n ( T s = 20 ° C ) . Sand, D c = 156 mm and p p = 2600 kg/m3 87 Table 5.1b Minimum spouting v e l o c i t y , experimental versus p r e d i c t i o n ( T s = 170 °C). Sand, D c = 156 mm and p p = 2600 kg/m3 88 Table 5.1c Minimum spouting v e l o c i t y , experimental versus p r e d i c t i o n ( T s = 300 °C). Sand, D c = 156 mm and p p = 2600 kg/m3 89 v i i Table 5.Id Minimum spouting v e l o c i t y , experimental versus p r e d i c t i o n ( T s = 420 ° C ) . Sand, D c = 156 mm and p p = 2600 kg/m3 90 Table 5.2 Slopes of U m s versus (H /pjO p l o t at d i f f e r e n t c o n d i t i o n s . Sand, Pp = 2600 kg/m3 and D c = 156 mm 97 Table 5.3 Comparison between v a r i o u s v e r s i o n s of Equation 5.1 99 Table 5.4a O v e r a l l pressure drop, experimental data and p r e d i c t i o n by Equation 2.28 ( T s = 20 ° C ) . Sand, D c = 156 mm and p p = 2600 kg/m3 100 Table 5.4b O v e r a l l pressure drop, experimental data and p r e d i c t i o n by Equation 2.28 ( T s = 170 °C). Sand, D c = 156 mm and p p = 2600 kg/m3 101 Table 5.4c O v e r a l l pressure drop, experimental data and p r e d i c t i o n by Equation 2.28 ( T s = 300 °C). Sand, D c = 156 mm and p p = 2600 kg/m3 102 Table 5.4d O v e r a l l pressure drop, experimental data and p r e d i c t i o n by Equation 2.28 ( T s = 420 °C). Sand, D c = 156 mm and p p = 2600 kg/m3 103 Table 5.5 Comparison between experimental and p r e d i c t e d values of U a and -dP/dz at z = H = H m. = 19.05 mm and dp = 1.25 mm 111 Table 6.1a Average spout diameters and corresponding experimental c o n d i t i o n s (Tg = 20 °C) 119 Table 6.1b Average spout diameters and corresponding experimental c o n d i t i o n s ( T s = 170 °C) 121 v i i i T a b l e 6.1c A v e r a g e s p o u t d i a m e t e r s and c o r r e s p o n d i n g e x p e r i m e n t a l c o n d i t i o n s ( T s = 300 °C) 122 T a b l e 6.1d A v e r a g e s p o u t d i a m e t e r s and c o r r e s p o n d i n g e x p e r i m e n t a l c o n d i t i o n s ( T s = 420 °C ) 123 T a b l e 6.2 C o m p a r i s o n between e x p e r i m e n t a l and c a l c u l a t e d v a l u e s o f D s 129 T a b l e 6.3 E x p e r i m e n t a l v a l u e s o f f o u n t a i n h e i g h t 133 T a b l e 6.4 U s H a t s e l e c t e d c o n d i t i o n s 139 T a b l e 7.1 E x p e r i m e n t a l v a l u e s of a n n u l a r p r e s s u r e , dp = 1.2 5 mm, D± = 19.05 mm 141 T a b l e 7.2 E x p e r i m e n t a l v a l u e s o f a n n u l a r f l u i d v e l o c i t y , d p = 1.25 mm, = 19.05 mm 154 T a b l e 7.3 E x p e r i m e n t a l v a l u e s o f p a r t i c l e v e l o c i t y , dp = 1.25 mm, = 19.05 mm 157 T a b l e B.1 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 181 T a b l e C.1 C a l i b r a t i o n d a t a of (~AP S) v e r s u s (-AP a) 191 T a b l e C.2 F i t t i n g p a r a m e t e r s of E q u a t i o n C.15 dp = 1.25 mm, Pp = 2600 kg/m^ and a i r a t a t m o s p h e r i c p r e s s u r e 191 i x L I S T OF F IGURES F i g u r e 1.1 Schematic diagram of a spouted bed 2 F i g u r e 2.1 T y p i c a l p r essure drop versus 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 7 F i g u r e 2.2 Comparison between experimental data and p r e d i c t i o n s by Equation 2.8 (McNab and Bridgwater, 1977) 12 F i g u r e 2.3 Regime map f o r sand, dp = 0.516 mm, Dj_ = 12.7 mm (Chandnani, 1984) 24 F i g u r e 2.4 Regime map f o r sand, dp = 0.516 mm, Di = 19.05 mm (Chandnani, 1984) 25 F i g u r e 3.1 D e t a i l s of the h a l f spouted bed 27 F i g u r e 3.2 D e t a i l s of the o r i f i c e p l a t e s 29 F i g u r e 3.3 Isometric view of the h a l f spouted bed 31 F i g u r e 3.4 Schematic of the o v e r a l l equipment la y o u t ...33 F i g u r e 3.5 D e t a i l s of the f l a n g e d cover 50 F i g u r e 3.6 D e t a i l s of the s t a t i c p ressure probes 51 F i g u r e 3.7 R a d i a l p o s i t i o n f o r p a r t i c l e v e l o c i t y measurements 54 F i g u r e 4.1 P i c t u r e s of d i f f e r e n t regimes 62 F i g u r e 4.2 Regime map f o r a i r - s a n d system at 20 °C 63 F i g u r e 4.3 Regime map f o r a i r - s a n d system at 170 °C ....64 Fi g u r e 4.4 Regime map f o r a i r - s a n d system at 300 °C ....65 F i g u r e 4.5 Regime map f o r a i r - s a n d system at 420 °C ....66 F i g u r e 4.6 E f f e c t of o r i f i c e diameter on maximum spoutable bed height f o r d i f f e r e n t temperatures 68 x F i g u r e 4.7 Fig u r e 4.8 Fig u r e 4.9 Fig u r e 4.10 Fig u r e 4.11 Fig u r e 4.12a Fig u r e 4.12b Fig u r e 4.12c Fig u r e 5.1 Fig u r e 5.2 Fig u r e 5.3 Fig u r e 5.4 Fi g u r e 5.5 Fig u r e 5.6 Fig u r e 5.7 E f f e c t of p a r t i c l e diameter on maximum spoutable bed height f o r d i f f e r e n t temperatures .....70 E f f e c t of temperature on maximum spoutable bed height f o r d i f f e r e n t p a r t i c l e diameters .72 E f f e c t of temperature on maximum spoutable bed height (Comparison between experimental data and p r e d i c t i o n s ) 73 Comparison between experimental data and Equation 2.8 78 E f f e c t of temperature on U m f and u a H m * S a n ^ , dp = 1.25 mm, D c = 156 mm 81 E f f e c t of temperature on U c and U s H . Sand, dp = 1.25 mm, D c = 156 mm, = 12.70 mm ....83 E f f e c t of temperature on U c and u s H m ' Sand, dp = 1.25 mm, D c = 156 mm, = 19.05 mm ....84 E f f e c t of temperature on U c and ^SHn• Sand, dp = 1.25 mm, D c = 156 mm, = 26.64 mm ....85 E f f e c t of p a r t i c l e diameter on U m s 91 E f f e c t of o r i f i c e diameter on U m s 92 E f f e c t of bed temperature on U m s 94 E f f e c t of H/pf on U m s . Sand, dp = 1.25 mm, = 19.05 mm, D c = 156 mm and p p = 2600 kg/m3 95 E f f e c t of o r i f i c e diameter on ~AP S 105 E f f e c t of p a r t i c l e diameter on -AP S 106 E f f e c t of bed temperature on ~AP S 107 x i E f f e c t o f 0 a n d H / H m on ( - A P s ) / ( - A P f ) a s p r e d i c t e d by E q u a t i o n 2 . 2 8 109 C o m p a r i s o n b e t w e e n e x p e r i m e n t a l ( - A P S ) a n d p r e d i c t i o n by E q u a t i o n 2 .28 110 O v e r a l l b e d p r e s s u r e d r o p v e r s u s b e d h e i g h t . T h e two l i n e s r e p r e s e n t E q u a t i o n 5 . 2 113 C o m p a r i s o n b e t w e e n e x p e r i m e n t a l r e s u l t s a n d p r e d i c t i o n by E q u a t i o n s 5 . 3 a n d 5 . 4 115 O b s e r v e d s p o u t s h a p e s 117 E f f e c t o f b e d h e i g h t a n d b e d t e m p e r a t u r e on s p o u t s h a p e . S a n d , d p = 1 .25 mm, D i = 1 2 . 7 0 mm a n d U / U m s * 1 .10 118 E f f e c t o f b e d h e i g h t a n d b e d t e m p e r a t u r e on D s . S a n d , d p = 1 .25 mm, = 1 2 . 7 0 mm a n d U / U m s * 1 .10 124 E f f e c t o f b e d t e m p e r a t u r e on D s . S a n d , dp = 1 .25 mm, = 1 9 . 0 5 mm, U / U m s * 1 .10 . . 1 2 6 C o m p a r i s o n b e t w e e n e x p e r i m e n t a l a v e r a g e s p o u t d i a m e t e r a n d p r e d i c t i o n by E q u a t i o n 2 . 1 6 130 C o m p a r i s o n b e t w e e n e x p e r i m e n t a l a v e r a g e s p o u t d i a m e t e r a n d p r e d i c t i o n by E q u a t i o n 6 . 5 131 E f f e c t o f b e d h e i g h t a n d U / U m s on f o u n t a i n h e i g h t . S a n d , dp = 1 . 2 5 mm, = 1 9 . 0 5 mm . . 1 3 4 E f f e c t o f s p o u t i n g v e l o c i t y a n d p a r t i c l e d i a m e t e r on s p o u t p a r t i c l e v e l o c i t y . F i g u r e 6.8 F i g u r e 6.9 F i g u r e 7.1a F i g u r e 7.1b F i g u r e 7.1c F i g u r e 7.1d F i g u r e 7.2a F i g u r e 7.2b F i g u r e 7.2c F i g u r e 7.2d F i g u r e 7.3 F i g u r e 7.4 G l a s s beads, D c = 152 mm, H/Dc = 3.0, D i/D c = 0.125 (Lim, 1975) 135 E f f e c t of bed height on spout p a r t i c l e v e l o c i t y . D c = 152 mm, D^/Dc = 0.125 and U/U m s =1.1 (Lim, 1 975) 136 E f f e c t of bed temperature on f o u n t a i n h e i g h t . Sand, d p = 1.25 mm, = 19.05 mm ..137 R a d i a l p ressure p r o f i l e s i n the c y l i n d r i c a l s e c t i o n ( T s = 20 °C) 142 R a d i a l p ressure p r o f i l e s i n the c y l i n d r i c a l s e c t i o n ( T s = 170 °C) 143 R a d i a l p r e s s u r e p r o f i l e s i n the c y l i n d r i c a l s e c t i o n ( T s = 300 °C) 144 R a d i a l p r e s s u r e p r o f i l e s i n the c y l i n d r i c a l s e c t i o n ( T s = 420 °C) 145 L o n g i t u d i n a l p r e s s u r e p r o f i l e s , experimental versus p r e d i c t e d ( T s = 20 °C) 147 L o n g i t u d i n a l p r e s s u r e p r o f i l e s , experimental versus p r e d i c t e d ( T s = 170 °C) 148 L o n g i t u d i n a l p r e s s u r e p r o f i l e s , experimental versus p r e d i c t e d ( T s = 300 °C) 149 L o n g i t u d i n a l p ressure p r o f i l e s , experimental versus p r e d i c t e d ( T s = 420 °C) 150 E f f e c t of bed temperature on the 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 , dp = 1.25 mm, D i = 19.05 mm 153 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 x i i i d i s t r i b u t i o n 155 F i g u r e 7.5 P a r t i c l e v e l o c i t y i n the annulus (Run # 7-5-b) 158 F i g u r e 7.6a E f f e c t of bed temperature and bed height on the r a d i a l p r o f i l e s of Vp (z = 40 cm) ...159 F i g u r e 7.6b E f f e c t of bed temperature and bed height on the r a d i a l p r o f i l e s of Vp (z = 30 cm) ...160 F i g u r e 7.6c E f f e c t of bed temperature and bed height on the r a d i a l p r o f i l e s of Vp (z = 20 cm) ...161 F i g u r e 7.7 E f f e c t of bed l e v e l on the r a d i a l - a v e r a g e d p a r t i c l e v e l o c i t y 163 F i g u r e C.1 Schematic set-up f o r rotameter c a l i b r a t i o n .183 F i g u r e C.2 C a l i b r a t i o n curve ( l a r g e rotameter) 186 F i g u r e C.3 C a l i b r a t i o n curve (small rotameter) 187 F i g u r e C.4 S i m p l i f i e d flow diagram of the apparatus ...188 F i g u r e C.5 (-APS) versus ( ~ A P a ) 192 x i v ACKNOWLEDGMENTS I would l i k e to express my a p p r e c i a t i o n to Dr. N. Ep s t e i n and Dr. J . Lim. Under t h e i r s u p e r v i s i o n , t h i s r e s e a r c h work was conducted. In a d d i t i o n , I am g r a t e f u l to the N a t u r a l Sciences and En g i n e e r i n g Research C o u n c i l f o r i t s f i n a n c i a l support. F i n a l l y , I would l i k e to thank the s t a f f s of the Chemical E n g i n e e r i n g Department workshop and s t o r e s f o r t h e i r c o n t i n u i n g a s s i s t a n c e throughout t h i s work. xv 1. INTRODUCTION Many i n d u s t r i a l processes r e q u i r e good c o n t a c t i n g between f l u i d and s o l i d s to a c h i e v e optimum performance. F l u i d i z a t i o n has been c o n s i d e r e d as one of the b e t t e r techniques f o r t h i s purpose. However, i t s a p p l i c a t i o n has been l i m i t e d t o r e l a t i v e l y f i n e p a r t i c u l a t e s o l i d s i n the case of g a s - s o l i d systems. For c o a r s e r m a t e r i a l s , t y p i c a l l y those with p a r t i c l e diameter g r e a t e r than 1 mm, gas f l u i d i z a t i o n o f t e n g i v e s r i s e to the formation of l a r g e bubbles and a tendency towards s l u g g i n g which i s u n d e s i r a b l e . I t was t h i s l i m i t a t i o n which l e d to the d i s c o v e r y and development of the spouted bed technique (Mathur and G i s h l e r , 1955). The flow mechanisms of spouting are q u i t e d i f f e r e n t from those of f l u i d i z a t i o n . However, the spouted bed technique appears to p r o v i d e the same r e s u l t f o r coarse p a r t i c l e s as f l u i d i z a t i o n does f o r f i n e m a t e r i a l s . F i g u r e 1.1 shows s c h e m a t i c a l l y a t y p i c a l spouted bed i n a c y l i n d r i c a l column with a c o n i c a l base. The bed can be c h a r a c t e r i z e d by two d i s t i n c t zones, the spout and the annulus. Under normal c o n d i t i o n s of spouting, a f l u i d , u s u a l l y a gas, e n t e r s v e r t i c a l l y through an o r i f i c e opening at the bottom of the column. The r e s u l t i n g j e t causes a stream of p a r t i c l e s to move upwards r a p i d l y through a c e n t r a l c o r e . T h i s d i l u t e d core i s c a l l e d the spout. The p a r t i c l e s i n the spout, a f t e r r e a c h i n g to a height above the 1 2 FOUNTAIN BED SURFACE SPOUT ANNULUS SPOUT - ANNULUS INTERFACE CONICAL BASE FLUID INLET F i g u r e 1.1 Schematic diagram of a spouted bed 3 bed s u r f a c e , f a l l back as a f o u n t a i n onto the surrounding packed bed, or the annulus, where they are t r a n s p o r t e d downwards by g r a v i t y and, to some extent, r a d i a l l y inwards as a l o o s e l y packed bed. These p a r t i c l e s are r e - e n t r a i n e d i n t o the spout through the spout w a l l over the e n t i r e bed h e i g h t . The f l u i d from the spout seeps through these annular s o l i d s as i t t r a v e l s upwards. T h i s systematic movement of the f l u i d and s o l i d s leads to e f f e c t i v e c o n t a c t between them. Spouted beds e x h i b i t some advantages (Bridgwater, 1982; Lim et a l . , 1984) over c o n v e n t i o n a l f l u i d i z e d beds. They have been used f o r v a r i o u s p h y s i c a l and chemical processes. Recently, high temperature spouting has a t t r a c t e d some a t t e n t i o n because of i t s p o t e n t i a l i n the energy f i e l d . S u c c e s s f u l o p e r a t i o n s i n c l u d e c a r b o n i z a t i o n of caking c o a l (Barton et a l . , 1968, 1969; R a t c l i f f e and Rigby, 1969), g a s i f i c a t i o n , p y r o l y s i s and combustion of caking c o a l (Foong, et a l . , 1980, 1981; J a r a l l a h and Watkinson, 1985; Lim et a l . , 1984) and combustion of low h e a t i n g value f u e l s and wastes (Arbib et a l . , 1981; A r b i b and Levy, 1982; Khoshnoodi and Weinberg, 1978). While the spouted bed technique has shown some f u t u r e i n these a p p l i c a t i o n s , there are s t i l l some questions to be answered. One area which i s s t i l l p o o r l y understood i s the hydrodynamic behaviour of spouted beds at high temperature. 4 A review of the p u b l i s h e d l i t e r a t u r e w i l l i n d i c a t e that most hydrodynamic i n f o r m a t i o n on gas spouting i s f o r ambient c o n d i t i o n s . The e f f e c t of temperature (as w e l l as pressure) .has not been w e l l e s t a b l i s h e d . One other area of u n c e r t a i n t y i s the heat t r a n s f e r . Although the e f f e c t of p r e s s u r e and heat t r a n s f e r are a l s o important, the main concern of t h i s work w i l l be the e f f e c t of temperature. The primary o b j e c t i v e s are to c o l l e c t hydrodynamic data at high temperature and to t e s t them ag a i n s t e x i s t i n g equations and c o r r e l a t i o n s . I t i s important to p o i n t out here that many c o r r e l a t i o n s have been obtained under ambient c o n d i t i o n s and l i m i t e d ranges of the r e l e v a n t v a r i a b l e s . Perhaps, by i n c l u d i n g the r e s u l t s from t h i s work, more a p p l i c a b l e equations can be developed from e x i s t i n g ones. The dependent hydrodynamic parameters of i n t e r e s t are: regime maps, minimum spouting v e l o c i t y , maximum spoutable bed h e i g h t , spout shape and diameter, o v e r a l l bed pressure drop, f o u n t a i n h e i g h t , f l u i d and p a r t i c l e v e l o c i t i e s i n the annulus, l o n g i t u d i n a l and r a d i a l p r e ssure p r o f i l e s . 2. LITERATURE REVIEW Gas spouting at ambient c o n d i t i o n s has been w e l l s t u d i e d i n most a s p e c t s . Many equations are a v a i l a b l e f o r p r e d i c t i n g hydrodynamic parameters at room c o n d i t i o n s . Mathur and E p s t e i n (1974) and l a t e r E p s t e i n and Grace (1984) have o u t l i n e d some of these equations. Information on high temperature spouting i s somewhat sca r c e ; there are only a few p u b l i s h e d a r t i c l e s . The emphasis of these a r t i c l e s has been mainly on performance c h a r a c t e r i s t i c s , r e a c t i o n k i n e t i c s (Ray and Sarkar, 1976; Ingle and Sarkar, 1976) and flow regimes (Khoe et a l . , 1983). The hydrodynamics have not been s t u d i e d . Equations o r i g i n a l l y developed f o r room c o n d i t i o n s are o f t e n used f o r high temperatures, with the assumption that these equations w i l l g ive reasonable p r e d i c t i o n s i f one uses values of gas p h y s i c a l p r o p e r t i e s a p p r o p r i a t e to the a c t u a l o p e r a t i n g c o n d i t i o n s . Since no equations have yet been proposed s p e c i f i c a l l y f o r gas spouting at high temperature, the present review i s c o n f i n e d to e x i s t i n g equations developed at room c o n d i t i o n s , p a r t i c u l a r l y the ones which c o n t a i n gas p r o p e r t i e s as v a r i a b l e s . 5 6 2.1 SPOUTABILITY OF PARTICLES A p p l i c a t i o n s of spouting have been l i m i t e d to coarse p a r t i c l e s (dp > 1 mm). However, spouting of f i n e r p a r t i c l e s has a l s o been r e p o r t e d . Chandnani (1984) gave a review of these p u b l i s h e d a r t i c l e s . He a l s o conducted experiments 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 urn and in d e n s i t y from 900 to 8900 kg/m3. His f i n d i n g s l e a d to the c o n c l u s i o n that f i n e p a r t i c l e s (dp < 1 mm) can be spouted s t e a d i l y i f the f l u i d i n l e t diameter ( o r i f i c e diameter) does not exceed 25.4 times the p a r t i c l e diameter. Observations by Mathur and G i s h l e r (1955) and Ghosh (1965) a l s o support h i s c l a i m . Moreover., he has found that p a r t i c l e d e n s i t y has a n e g l i g i b l e e f f e c t on s p o u t a b i l i t y . These r e s u l t s are a l l based on experiments with a i r at room temperature and atmospheric p r e s s u r e . 2.2 MINIMUM SPOUTING VELOCITY Fi g u r e 2.1 shows a t y p i c a l pressure drop versus s u p e r f i c i a l v e l o c i t y curve f o r spouting of coarse p a r t i c l e s . The minimum ( s u p e r f i c i a l ) spouting v e l o c i t y U m s i s represented by po i n t B. Th i s i s obtained by f i r s t i n c r e a s i n g the f l u i d f l o w r a t e u n t i l p o i n t C i s reached. At t h i s i n s t a n t , the e n t i r e bed becomes mobile and steady spouting s e t s i n . However, t h i s p o i n t i s b e d - h i s t o r y dependent and i s 7 S U P E R F I C I A L V E L O C I T Y F i g u r e 2 . 1 T y p i c a l p r e s s u r e d r o p v e r s u s v e l o c i t y c u r v e f o r a s p o u t e d bed o f c o a r s e p a r t i c l e s 8 n o t e x a c t l y r e p r o d u c i b l e . From p o i n t C, f l o w r a t e i s d e c r e a s e d s l o w l y t i l l p o i n t B, a t w h i c h f u r t h e r d e c r e a s e o f f l o w r a t e w i l l c a u s e t h e s p o u t t o c o l l a p s e and t h e bed p r e s s u r e t o i n c r e a s e s u d d e n l y , as i l l u s t r a t e d i n t h i s f i g u r e . F o r c o a r s e p a r t i c l e s p o u t i n g , i t has been f o u n d t h a t a t t h i s l a t t e r p o i n t ( i . e . , p o i n t B ) , t h e v e l o c i t y i s r e p r o d u c i b l e and hence t a k e n a s t h e minimum s p o u t i n g v e l o c i t y . A number of c o r r e l a t i o n s have been p r o p o s e d f o r p r e d i c t i n g t h i s q u a n t i t y , U m s (Mathur and E p s t e i n , 1974). The most w i d e l y u s e d one seems t o be t h e e m p i r i c a l e q u a t i o n o f Mathur and G i s h l e r ( 1 9 5 5 ) , w h i c h was d e r i v e d from d a t a f o r b o t h g a s - and l i q u i d - s p o u t e d beds w i t h d i a m e t e r s up t o 0.6 m. 1/3 U, ms LDC. 2 g H ( p p - p f ) 2.1 Pf The form o f t h e above e q u a t i o n was d e v e l o p e d u s i n g d i m e n s i o n a l a n a l y s i s ; t h e v a l u e of t h e c o e f f i c i e n t = 1 empi r i c a l l y . A somewhat s i m i l a r e x p r e s s i o n w i t h a d i f f e r e n t v a l u e of t h e c o e f f i c i e n t was d e r i v e d by Ghosh ( 1 9 6 5 ) . The d e r i v a t i o n was b a s e d on a momentum exch a n g e between t h e e n t e r i n g f l u i d and t h e e n t r a i n e d p a r t i c l e s . "dr U. ms 2r? \ | 3 K L D . 2 g H ( p p - p f ) 2.2 Pf 9 Grb a v c i c et a l . (1976), based on t h e i r flow model, d e r i v e d the f o l l o w i n g c o r r e l a t i o n f o r U m s : Umf 1 - a, H Hm. 2.3 where a s i s d e f i n e d as the r a t i o of the area of the spout to that of the bed. Since a s i s much smaller than 1 i n most cases, Equation 2.3 can be f u r t h e r s i m p l i f i e d to ums " umf 1 -H 1 -H, mJ 2.4 2.3 MAXIMUM SPOUTABLE BED HEIGHT The maximum spoutable bed h e i g h t , H m, i s the maximum height at which steady or s t a b l e spouting can be obt a i n e d . Mathur and E p s t e i n (1974) suggested three d i s t i n c t p o s s i b l e mechanisms f o r spout t e r m i n a t i o n when the bed height exceeds H m. They a r e : 1. F l u i d i z a t i o n of Annular S o l i d s 2. Choking of the Spout 3. Growth of I n s t a b i l i t y at the Spout-Annulus I n t e r f a c e Most c o r r e l a t i o n s for p r e d i c t i n g H m are based on the f i r s t mechanism or simply on empiricism. The maximum value of the minimum spouting v e l o c i t y i s denoted U m, i . e . , the minimum spouting v e l o c i t y at the maximum spoutable h e i g h t . Grbavcic et a l . r e p o r t e d that U m 10 was very s i m i l a r to U m f . Although these q u a n t i t i e s are approximately equal, there i s some disagreement regarding the exact r e l a t i o n s h i p between U m and U m f . In g e n e r a l , 'm Umf = b = 1.0 to 1.5 2.5 Using the Mathur and G i s h l e r equation, U m can be determined from: [ dp] " D i " 1/3 - DC- - DC- \ 2 g H m ( p p - P f ) 2.1a Pf U m j , on the other hand, can be estimated from the Ergun (1952) equation, using the e m p i r i c a l approximations of Wen and Yu (1966): ,1 - e mf * 2 < m £ 3 = 1 1 2.6a = 1 4 2.6b S u b s t i t u t i n g Equations 2.6a and 2.6b i n t o Equation A.5 (Appendix A.1) y i e l d s the f o l l o w i n g : d p u m f P f Re mf = 33.7[/l+35.9Xl0" 6Ar - 1] 2.7 Combining Equations 2.5, 2.1a and 2.7, e l i m i n a t i n g U m and U m f , the net r e s u l t i s Hm _ 2i 1 2/3 568b 2' Ar [ j/l+35.9XlO" 6Ar - 1 ] 2 A.7 11 McNab and B r i d g w a t e r (1977) f u r t h e r assumed t h a t b was c o n s t a n t . E q u a t i o n A.7 gave the best f i t t o e x i s t i n g e x p e r i m e n t a l data by t a k i n g b = 1.11, t h a t i s , E q u a t i o n A.7 became 21 rn I 2/3 Hm _ D, *pJ D 700 Ar [/l+35.9XlO" 6Ar - 1 ] 2 2.8 T h i s model, t o g e t h e r w i t h the e x p e r i m e n t a l d a t a a v a i l a b l e , were p l o t t e d as shown i n F i g u r e 2.2. One key f e a t u r e of E q u a t i o n 2.8 i s t h a t i t p r e d i c t s a c r i t i c a l v a l u e of d n d e c r e a s e s w i t h dp. T h i s c r i t i c a l v a l u e i s g i v e n by (see Appendix A.3) ( V c r i t = 6 0 ' 6 . g ( p p - P f >Pf. 1/3 0.00500 = 0.218 + ; A > 0.02 A. 1 4 L i t t m a n e t a l . (1979) dev e l o p e d the f o l l o w i n g c o r r e l a t i o n f o r s p h e r i c a l p a r t i c l e s : 2.9 where A i s d e f i n e d by A = P f U m fu t (pp-pf)g°i 2.10 U m£ i s c a l c u l a t e d from E q u a t i o n A.5 and U t i s e s t i m a t e d from the f o l l o w i n g : Ar = l 8 R e t + 2 . 7 R e t 1 * 6 8 7 ; Re t < 1000 2.11a 1 2 0.01 0.02 0.03 0.04 (1136/Ar)[/I + 35.9X10" 6Ar - I ] 2 F i g u r e 2.2 Comparison between ex p e r i m e n t a l data and p r e d i c t i o n s by Equation 2.8 (McNab and Bridgwater, 1977). The s o l i d l i n e i n d i c a t e s the best f i t . The other two l i n e s show the 95% c o n f i d e n c e l i m i t s . 13 R e t = 1 . 7 4 5 A r 0 - 5 ; R e t > 1000 2.11b and RetM P f d . U t = 2.11c The p a r a m e t e r , A i s a measure of t h e r a t i o o f t h e i n e r t i a l f o r c e o f t h e j e t e n t e r i n g t h e bed t o t h e s p o u t i n g p r e s s u r e d r o p . F o r n o n - s p h e r i c a l p a r t i c l e s , Morgan and L i t t m a n (1982) s u g g e s t e d t h e f o l l o w i n g e x p r e s s i o n s : H m D i 5.13X10" 3 2.54X10" 5 = 0.218 + + ° c 2 Ac6 A 0 2 f o r A^ > 0.014 2.12a = 175(A^ - 0.01) f o r 0.010 < A^ < 0.014 2.12b E q u a t i o n s 2.12a and 2.12b a p p l y f o r p a r t i c l e s l a r g e r t h a n ( d p ) c r i t as g i v e n by E q u a t i o n A.14. A^, l i k e A, i s d e f i n e d by E q u a t i o n 2.10. However, when c a l c u l a t i n g U t and U m £ , t h e shape f a c t o r 0 has t o be t a k e n i n t o c o n s i d e r a t i o n . U m f can a g a i n be e s t i m a t e d from E q u a t i o n A.5 by u s i n g t h e a p p r o p r i a t e v a l u e s o f </> and e m f . U t f o r a s p h e r i c a l p a r t i c l e i s f i r s t c a l c u l a t e d u s i n g E q u a t i o n s 2.11a, 2.11b and 2.11c. The e f f e c t o f c/> on U t i s g i v e n by 14 U t < * < D , , = 5<j>6 - 1.51<t>z + 4 . 090 - 0.516 2.13 U t ( 0=1) Thus U t f o r a n o n - s p h e r i c a l p a r t i c l e i s o b t a i n e d . Morgan and L i t t m a n r e p o r t e d t h a t t h e i r e x p r e s s i o n s f o r H m r e p r e s e n t e d e x i s t i n g d a t a r e a s o n a b l y w e l l , w i t h an a v e r a g e d e v i a t i o n of 24.2%. Morgan and L i t t m a n a l s o p o i n t e d o u t t h a t ( d p ) c r i t m i g h t depend on <j> and e m £ but s t i l l t h e y u s e d t h e v a l u e g i v e n by E q u a t i o n A.14, which was s l i g h t l y i n c o n s i s t e n t w i t h t h e i r e x p r e s s i o n s . To be more p r e c i s e , t h e i r c r i t i c a l v a l u e s h o u l d be d e f i n e d by e x p l i c i t l y i n c l u d i n g t h e e f f e c t of <t> and e m j ( i . e . , E q u a t i o n A.16 i n A p p e n d i x A . 4 ) , r a t h e r t h a n by i m p l i c i t l y u s i n g t h e Wen and Yu a p p r o x i m a t i o n s , E q u a t i o n s 2.6a and 2.6b ( w h i c h a r e i n c o r p o r a t e d i n E q u a t i o n A . 1 4 ) . 2.4 AVERAGE SPOUT DIAMETER T h e r e a r e many e q u a t i o n s a v a i l a b l e f o r e s t i m a t i n g t h e l o n g i t u d i n a l a v e r a g e v a l u e of s p o u t d i a m e t e r , D s (Mathur and E p s t e i n , 1974; L i t t m a n , 1982). B r i d g w a t e r and Mathur (1972) p r o p o s e d a s i m p l i f i e d t h e o r e t i c a l model w h i c h was d e r i v e d from a f o r c e b a l a n c e a n a l y s i s . T h e i r d e r i v e d e q u a t i o n was 3 2 f p f Q s 2 7 = 1 2 ' 1 4 7 T 2 i M D c - D s ) D s 4 B a s e d on a number of a p p r o x i m a t i o n s , E q u a t i o n 2.14 was 15 reduced to a more manageable form: D s = 0.384 G0.5 D c0.75-"b 0.25 2.15 where a l l v a r i a b l e s were expressed i n SI u n i t s of m, kg and s. T h i s equation i s p r i m a r i l y r e s t r i c t e d to a i r spouting. McNab and Bridgwater (1974) l a t e r p o i n t e d out that the model of Bridgwater and Mathur was o v e r s i m p l i f i e d . McNab (1972) a p p l i e d s t a t i s t i c a l a n a l y s i s to e x i s t i n g data and came up with the f o l l o w i n g e x p r e s s i o n : D s = 2.0 • G0.49 D 0.68-0.41 2.16 where a l l v a r i a b l e s were again expressed i n SI u n i t s . The c o e f f i c i e n t , "2.0" should be r e p l a c e d by "0.037" i f B r i t i s h u n i t s are used i n s t e a d . Comparison of the above equation with that of Bridgwater and Mathur shows that the same v a r i a b l e s have been i n c l u d e d and that the dependence on each v a r i a b l e i s of the same order of magnitude; the main d i f f e r e n c e i s i n the value of the f i t t i n g c o e f f i c i e n t . In view of the s i m p l i f i c a t i o n s i n t r o d u c e d by Mathur and Bridgwater, the discr e p a n c y between the two equations can be co n s i d e r e d a c c e p t a b l e . 16 Littman et a l . (1977) developed the f o l l o w i n g e x p r e s s i o n from a theory of flow in the annulus which used the v e c t o r form of the Ergun equation as i t s f i e l d equation: Hm Ds* ( D c 2 - D s * 2 ) = 0.345 D s * -0.384 2.17 Combining the above equation with Equation 2.9, Littman et a l . (1979) came up with an a n a l y t i c a l e x p r e s s i o n i n the form of D * 2. 1 0exp(-0 . 01 8/A) + 1 .0' 3.10 V V 2-0.862 + 0.219 - 0.0053 _Di- Pi. 2.18 The q u a n t i t y , D s* i s the spout diameter at the maximum spoutable bed height, under the minimum spouting c o n d i t i o n . It i s used as the r e f e r e n c e value f o r other bed c o n d i t i o n s . Littman (1982) a l s o r e p o r t e d that under the minimum spouting condi t i on V ^ m s _ > D s* = 0.35 H H m . + 0.65 2.19 and assuming the square root v e l o c i t y r e l a t i o n of Equations 2.15 and 2.16, Equation 2.19 can be r e w r i t t e n as D s * u H" 0.35 + 0.65 \|ums -Hm. -2.20 T h i s procedure f o r e s t i m a t i n g average spout diameter i s 17 r e s t r i c t e d t o A > 0.02 and t o s p h e r i c a l p a r t i c l e s . L i t t m a n (1982) r e p o r t e d good agreement between e x p e r i m e n t a l and c a l c u l a t e d v a l u e s . He a l s o n o t e d t h a t f o r s p o u t i n g of f i n e p a r t i c l e s (0.275 t o 0.995 mm) i n w ater i . e . , low A v a l u e s , E q u a t i o n 2.18 h e l d but E q u a t i o n s 2.19 and 2.20 d i d n o t . Under t h e minimum s p o u t i n g c o n d i t i o n , E q u a t i o n 2.19 was t h e n t o be r e p l a c e d by Ds<ums> ° s * = 0.72 H + 0.28 2.21 2.5 FLUID AND PARTICLE VELOCITY IN THE ANNULUS Mamuro and H a t t o r i (1968) d e r i v e d an e x p r e s s i o n f o r e s t i m a t i n g t h e l o n g i t u d i n a l a n n u l a r f l u i d v e l o c i t y . I t was b a s e d on a f o r c e b a l a n c e on a d i f f e r e n t i a l h e i g h t dz of t h e a n n u l u s , w i t h t h e f o l l o w i n g a s s u m p t i o n s and b o u n d a r y c o n d i t i o n s : 1. D a r c y ' s law a p p l i e s 2. z = 0, U a = 0 3. z = H m, U a = U a H m = U m f They came up w i t h U. U, mf 1 -H m. 2.22 E q u a t i o n 2.22 t e n d s t o o v e r p r e d i c t U a b e c a u s e U m j > U a H . I f m U m f i s r e p l a c e d by t h e measured v a l u e of u a H m ' the e q u a t i o n i s f o u n d t o work b e t t e r . 18 An a l t e r n a t e equation f o r p r e d i c t i n g l o n g i t u d i n a l flow d i s t r i b u t i o n i s that of L e f r o y and Davidson (1969) U. = s i n U aH m TTZ L 2 ^ m J 2.23 Un l i k e the t h e o r e t i c a l approach by Mamuro and H a t t o r i , t h i s equation was based on e m p i r i c a l f i n d i n g s . E p s t e i n et a l . (1978) recommended that Equation 2.23 should be modified to U. = s i n U aH m 7TZ 2H mJ 1/n 2.24 where n i s a flow regime index which v a r i e s from u n i t y (Darcy's law) to a maximum value of 2 ( i n v i s c i d f l o w ) . S o l i d c i r c u l a t i o n r a t e s f o r coarse p a r t i c l e s were measured by Lim (1975). He re p o r t e d that the p a r t i c l e v e l o c i t y i n the annulus was not constant at any f i x e d bed l e v e l ; i t was highest near the spout-annulus i n t e r f a c e and decreased to a minimum at the bed w a l l . The s o l i d c i r c u l a t i o n r a t e was found to i n c r e a s e l i n e a r l y with bed l e v e l , except in the c o n i c a l s e c t i o n of the column. 2.6 LONGITUDINAL PRESSURE PROFILE AND OVERALL BED PRESSURE DROP The pressure g r a d i e n t i n the annulus of a spouted bed may be obtained from the Ergun (1952) equation, 19 ~h = K ^ U a + K * U a 2 2 . 2 5 C o m b i n i n g t h i s e x p r e s s i o n w i t h t h a t o f Mamuro a n d H a t t o r i , i t was shown ( E p s t e i n a n d L e v i n e , 1978) t h a t p - p H 1 = [ 2 ( 0 - 2 ) 0 . 5 ( h 2 - x 2 ) - A P f h ( 2 0 - l ) - ( h 3 - x 3 ) + 0 . 2 5 ( h 4 - x 4 ) } + 3 { 3 ( h 3 - x 3 ) - 4 . 5 ( h 4 - x 4 ) + 3 ( h 5 - x 5 ) - ( h 6 - x 6 ) + 0 . 1 4 3 ( h 7 - x 7 ) } ] 2 . 2 6 w h e r e h = H / H m 2 . 2 7 a x = z / H m 2 . 2 7 b 3K, 0 = 2 + 2 . 2 7 c 2 K 2 U m f a n d K , a n d K 2 a r e g i v e n i n A p p e n d i x A ( E q u a t i o n s A 2 . a a n d A . 2 b ) . T h e t o t a l b e d p r e s s u r e d r o p i s t h u s d e t e r m i n e d by p u t t i n g x = 0, i . e . , - A P S 2 - ( 4/0) - A P f 2 - ( 1/0 ) 3 ( 1 , 5 h - h 2 + 0 . 2 5 h 3 ) ( 3 h 2 - 4 . 5 h 3 + 3 h 4 20-1 - h 5 + 0 . 1 4 3 h 6 ) 2 . 2 8 20 At t h e maximum s p o u t a b l e h e i g h t , h = 1, t h i s e x p r e s s i o n c an be f u r t h e r r e d u c e d t o -AP C max 1 . 5 ( 0 - 2 ) + 1 . 9 2 9 20-1 2 . 2 9 a = 0.75 when 0 = » ( D a r c y ' s Regime) 2.29b = 0.64 when 0 = 2 ( I n v i s c i d Regime) 2.29c or more g e n e r a l l y 0.75 > -AP, -AP > 0.64 2.30 max A s i m p l e r e m p i r i c a l e q u a t i o n was p r o p o s e d by L e f r o y and D a v i d s o n (1969) P-P H -AP, = c o s TTZ 2H 2.31 or dP dz 2H - s i n 7TZ 2H 2.32 A s s u m i n g i n c i p i e n t f l u i d i z a t i o n a t z = H = H m, E q u a t i o n 2.32 can be r e d u c e d t o H 2.33 m 2H m or 21 AP. AP, max = - = 0.637 it 2.34 Th i s constant r a t i o i s i n good agreement with the i n v i s c i d value of the p r e v i o u s model but d i f f e r s from the Darcy Law v a l u e . McNab and Bridgwater (1977) suggested a somewhat d i f f e r e n t c o r r e l a t i o n f o r e s t i m a t i n g the o v e r a l l spouted bed pressure drop: 7 " A p s " "Aps" H" _APf_ A pf. max -Hnu 2.35 where 7 = 0 . 1 D, I J -0.6 2.36 The main f e a t u r e of t h i s e x p r e s s i o n i s the i n c l u s i o n of and D c e x p l i c i t l y as v a r i a b l e s , which the previous two models do not have except i m p l i c i t l y through H m. The value of ( A P s / A P f ) m a x may be determined from the e m p i r i c a l equation of P a l l a i and Nemeth (1969) AP, AP< = 0.8 - 0.01 max 2.37 or i t can be taken as one of the two l i m i t i n g cases i n the f i r s t model (Equation 2.30). 22 2 . 7 RADIAL PRESSURE PROFILE The f l u i d p ressure i n the annulus g e n e r a l l y does not vary r a d i a l l y at any given bed l e v e l s , except i n the c o n i c a l s e c t i o n where the pressure decreases towards the column w a l l (Mathur and E p s t e i n , 1 9 7 4 ; Littman et a l . , 1 9 8 5 ) . The v e c t o r Ergun equation has been a p p l i e d to p r e d i c t the f l u i d flow i n the annulus by Rovero et a l . ( 1 9 8 3 ) and Littman et a l . ( 1 9 8 5 ) . The r a d i a l p r essure p r o f i l e s generated from these two models are c o n s i s t e n t with the r e p o r t e d o b s e r v a t i o n s . 2 . 8 FOUNTAIN HEIGHT Grace and Mathur ( 1 9 7 8 ) proposed the f o l l o w i n g e x p r e s s i o n f o r e s t i m a t i n g the height of the f o u n t a i n , Hp: 2 1 u _ . 1 . 4 6 Hp - e a V s H ' 2 g ( P p - P f ) . 2 . 3 8 2 . 9 REGIME MAP A regime map or phase diagram g i v e s a g r a p h i c a l d e s c r i p t i o n of how a p o t e n t i a l spouted bed system behaves under the i n f l u e n c e of i n c r e a s i n g f l u i d f l o w r a t e and bed h e i g h t . T y p i c a l l y , a complete regime map c o n s i s t s of the f o l l o w i n g r e g i o n s : 1 . S t a t i c (or Fixed) Bed 2 . Coherent (or S t a b l e ) Spouting 3 . P r o g r e s s i v e l y Incoherent Spouting 23 4. B u b b l i n g 5. S l u g g i n g However, i t i s p o s s i b l e t o have a regime map c o n t a i n i n g l e s s than f i v e r e g i o n s . F i g u r e s 2.3 and 2.4 a r e examples of the the two (Chandnani 1984). 2 4 0.0 1.0 2.0 3.0 4.0 A i r f l o w r a t e (standard 1/s) F i g u r e 2.3 Regime map f o r sand, dp = 0 . 5 1 6 mm, Di = 12.7 mm (Chandnani 1984) P.I.S. = P r o g r e s s i v e l y Incoherent Spouting 25 F i g u r e 2.4 Regime map f o r sand, d p = 0.516 mm, D| = 19.05 mm (Chandnani, 1984) 3. APPARATUS, BED MATERIALS AND EXPERIMENTAL METHODS 3.1 CHOICE AND DESCRIPTION OF EQUIPMENT A 156-mm i n s i d e diameter h a l f column was b u i l t . The c o n i c a l s e c t i o n at the bottom had an i n c l u d e d angle of 60°. The main reason f o r using a half-column i s that i t a l l o w s v i s u a l o b s e r v a t i o n , which i s p a r t i c u l a r l y important f o r measuring spout diameter and p a r t i c l e c i r c u l a t i o n r a t e . The v a l i d i t y of using h a l f columns i n spouted bed s t u d i e s has been questioned and was i n v e s t i g a t e d by Whiting and G e l d a r t (1979) and G e l d a r t et a l . (1981). They r e p o r t e d t h a t hydrodynamic data (such as U m s , H m and Vp(R c)) obtained i n a h a l f column were s i m i l a r to those i n a f u l l column. Rovero et a l . (1985), however, have shown that the f r i c t i o n a l e f f e c t caused by the f l a t w a l l cannot be overlooked when measuring the p a r t i c l e v e l o c i t i e s . In the case of spout shapes, Lim (1975) has i n d i c a t e d that the f l a t w a l l i n a h a l f column has a n e g l i g i b l e e f f e c t . Due to the high temperature of the present experiments, the bed was c o n s t r u c t e d of 316 s t a i n l e s s s t e e l . The v e r t i c a l l e ngths of the c o n i c a l and c y l i n d r i c a l s e c t i o n s were 89 and 1067 mm, r e s p e c t i v e l y (Figure 3.1). The h a l f column was f u r n i s h e d with a t o t a l of s i x measuring p o r t s . The f i r s t one was i n the c o n i c a l s e c t i o n and was 38 mm above the o r i f i c e . T h i s p o r t was p r i m a r i l y used f o r measuring p r e s s u r e . The 26 27 F i g u r e 3.1 D e t a i l s of the h a l f spouted bed ( A l l d i m e n s i o n s i n mm) 28 o t h e r s were a l l i n the c y l i n d r i c a l s e c t i o n with v e r t i c a l s e p a r a t i o n s of 152 mm. The p o s i t i o n of the lowest one i n t h i s s e c t i o n was 165 mm above the o r i f i c e . These p o r t s were a l l used f o r s e c u r i n g thermocouples. In a d d i t i o n to these f i v e measuring p o r t s , the c y l i n d r i c a l s e c t i o n was equipped with a s o l i d s d i s charge l i n e which was 216 mm above the o r i f i c e . The bed, as d e s c r i b e d , was not long enough for h a n d l i n g bed h e i g h t s c l o s e to 1 m. However, i n some c o l d runs, H m was found to exceed 1 m, making t h i s column u n s u i t a b l e i n these cases. For t h i s reason, another c y l i n d r i c a l s e c t i o n of 610 mm i n l e n g t h was c o n s t r u c t e d and added to the e x i s t i n g s e c t i o n , r e s u l t i n g i n a t o t a l column height of 1.77 m. The f l u i d i n l e t s e c t i o n was a 26.64 mm ID h a l f pipe with a s t r a i g h t v e r t i c a l l ength of 355 mm, as shown in F i g u r e 3.1. Three o r i f i c e p l a t e s of d i f f e r e n t s i z e s were a l s o made. T h e i r openings were 12.7, 19.05 and 26.64 mm, r e s p e c t i v e l y . An o r i f i c e c o l l a r on each p l a t e extended 3 mm i n t o the bed. For the 12.7 and 19.05 mm p l a t e s , the bottom face was machined so that the flow would converge smoothly. With t h i s type of f l u i d i n l e t , the spouting a c t i o n was more s t a b l e than f o r a simple o r i f i c e . A small i n d e n t a t i o n at the bottom of a l l three o r i f i c e s p l a t e s allowed the i n s e r t i o n of wire screens which prevented p a r t i c l e s from f a l l i n g i n t o the i n l e t pipe d u r i n g s h u t - o f f . The key f e a t u r e s of the o r i f i c e p l a t e s are shown in F i g u r e 3.2. SIZE Dimansions(mm) A B C D E F G S 76.2 41.0 12.70 3.2 3.2 9.5 1.6 M 76.2 41.0 19.05 3.2 3.2 9.5 1.6 L 76.2 41.0 26 64 3.2 3.2 9.5 1.6 F i g u r e 3.2 D e t a i l s of the o r i f i c e p l a t e s 30 The f r o n t panel of the bed was made of 6 mm 'Georgian p o l i s h e d w i r e - g l a s s ' . T h i s type of g l a s s c o u l d not i n i t s e l f w ithstand the high temperatures r e q u i r e d i n t h i s study. However, the wire i n s i d e the g l a s s tended to hold the cracked p i e c e s t o g e t h e r . Any leaks were patched up us i n g m u f f l e r cement ( s u p p l i e d by H o l t L l o y d L i m i t e d of Canada). Although the cement reduced some of the v i s i b i l i t y of the g l a s s , f r o n t a l o b s e r v a t i o n was s t i l l q u i t e adequate. Quartz g l a s s e s were not used because they were expensive. Tempered g l a s s e s were t r i e d , but they f a i l e d at high temperature (about 400 °C) and s h a t t e r e d i n t o many p i e c e s . The top of the column was l o c a t e d d i r e c t l y under an exhaust hood, which reduced the p o s s i b i l i t y of a hig h p r e s s u r e b u i l d u p i n the bed. To reduce mechanical s t r e s s due to the d i f f e r e n t thermal expansion of g l a s s and s t e e l , the g l a s s panel was assembled using a screw and p l a t e d e v i c e as i n d i c a t e d i n Fi g u r e 3.3. The gasket m a t e r i a l between the g l a s s and the s t e e l sheet flange was a compressible high temperature i n s u l a t i n g m a t e r i a l (970-J paper s u p p l i e d by P l i b r i c o L i m i t e d of Canada). T h i s m a t e r i a l worked w e l l ; however, i t had to be r e p l a c e d a f t e r each d i s m a n t l i n g . 3 1 F i g u r e 3.3 I s o m e t r i c view of the h a l f spouted bed 32 3.2 METHOD OF HEATING Heating was provided by c y l i n d r i c a l e l e c t r i c heaters which were mounted on the o u t s i d e of 2-inch Schedule-40 316 S t a i n l e s s S t e e l pipes (heating s e c t i o n s ) . To enhance heat t r a n s f e r , the h e a t i n g s e c t i o n s were packed with ceramic r i n g s . Three h e a t i n g s e c t i o n s were used. Each heating u n i t had a power r a t i n g of 4.0 kW maximum and was c o n t r o l l e d i n d i v i d u a l l y by monitoring the temperature i n the gap between the o u t s i d e w a l l of the pipe and the i n s i d e w a l l of the heater. G l a s s f i b r e i n s u l a t i o n was used to blanket the p i p i n g and the back of the spouted bed to reduce heat l o s s to the surroundings. The f r o n t f l a t s u r f a c e of the spouting column was used fo r o b s e r v a t i o n s and measurements, and i t was t h e r e f o r e covered only d u r i n g the h e a t i n g up p e r i o d . T h i s h e a t i n g set-up was capable of m a i n t a i n i n g o p e r a t i n g bed temperatures up to 420 °C. I t was a r b i t r a r i l y chosen to run at four temperature l e v e l s : 20, 170, 300 and 420 °C. 3.3 GAS FLOW AND INSTRUMENTATION A schematic diagram of the apparatus i s shown in F i g u r e 3.4. Spouting a i r from the main a i r l i n e flowed through e i t h e r one of the rotameters (the smaller one was p r i m a r i l y used fo r low f l o w r a t e ) . From the rotameter, a i r went i n t o the h e a t i n g u n i t where i t was r a i s e d to the d e s i r e d temperature. T h i s preheated a i r then entered the spouted bed |^ <] V A L V E [ X ] TUBE CLAMP THERMOCOUPLE V -CXr-FLOWMETERS -04-- t X h TEMPERATURE CONTROLLERS D I G I T A L D l S P L A Y © © © 1 i i ! ! I H« I S E L E C T I N G SWITCH TTTT I i 11 r -Xf-MAIN A I R L I N E X L H E L I U M / M E T H A N E -X I—1 O i l MANOMETERS Kg N E L E C T R I C if ,;L_. L _ . F O U N T A I N SPOUTED BED F i g u r e 3 .4 S c h e m a t i c of t h e o v e r a l l e q u i p m e n t l a y o u t GO 34 through the o r i f i c e . The spent a i r d i s c h a r g e d i n t o the exhaust hood where i t was d i l u t e d with c o l d e r a i r from the adjacent surroundings. The mixed a i r , which was much c o o l e r than the o r i g i n a l d i s c h a r g e , was f i n a l l y vented to the atmosphere. Temperatures were measured and monitored with Chromel-Alumel ( i . e . , Type K) thermocouples at nine l o c a t i o n s . Three of these thermocouples were p o s i t i o n e d as d e s c r i b e d i n S e c t i o n 3.2 and the temperatures were i n d i c a t e d on the temperature c o n t r o l l e r s . The remaining thermocouples were a l l connected to a d i g i t a l d i s p l a y through a s e l e c t i n g s w i t c h . One of them was l o c a t e d j u s t a f t e r the h e a t i n g u n i t . The others were mounted at the back of the c y l i n d r i c a l s e c t i o n of the h a l f column, with the t i p s extended about 10 mm from the curved inner w a l l s u r f a c e . These thermocouples measured the annular temperature along the bed i n r e g u l a r i n t e r v a l of 152 mm. The average of these v a l u e s was taken as the o v e r a l l bed temperature. Table 3.1 shows some t y p i c a l temperature v a r i a t i o n s with bed l e v e l s together with other r e l e v a n t i n f o r m a t i o n . These data were ob t a i n e d while the experimental equipment was being debugged. During these t r i a l runs, an a d d i t i o n a l thermocouple was i n s e r t e d in the c o n i c a l s e c t i o n (see F i g u r e 3.1) i n order to y i e l d more complete temperature p r o f i l e s . (During a c t u a l runs, t h i s thermocouple i n the c o n i c a l s e c t i o n was r e p l a c e d by a pressure p o r t . ) P r e l i m i n a r y measurements had a l s o i n d i c a t e d Table 3.1 Typical temperature p r o f i l e s . Sand, p •= 2600 kg/m . d = 1.25 mm At steady s t a t e Bed Desired Controllers Ai r Temp. T ime Ht. Temp. Sett i n g from Req'd Temperature p r o f i l e s ( " O heater imm) (°C) (°C) CC) (hr) 2 = 38 165 317 469 621 773 680 170 300 • 280 1.00 168 168 170 171 170 152 630 300 500 -470 .2.25 302 298 302 304 302 25B 530 420 700 660 4 .50 423 415 423 425 382 36 that the r a d i a l temperature g r a d i e n t s i n the annulus were i n s i g n i f i c a n t . These o b s e r v a t i o n s were c o n s i s t e n t with those r e p o r t e d by Zhao (1986). The absolute pressure i n s i d e the rotameter was r e q u i r e d when c a l c u l a t i n g the gas f l o w r a t e (Appendix C). T h i s was achieved by measuring the gauge pres s u r e s before and a f t e r the rotameters using a mercury manometer. The average of the two manometer readings was assumed to be the gauge pressure i n s i d e the rotameter, from which the corresponding absolute pressure was determined. Two other pressure p o r t s were p o s i t i o n e d near the o r i f i c e ; one was 38 mm above the o r i f i c e ( i . e . , i n the c o n i c a l s e c t i o n ) whereas the other one was 25 mm below the o r i f i c e . The gauge pres s u r e s at these two l o c a t i o n s were again measured with a manometer. These readings were used to determined the o v e r a l l pressure drop across the bed and thus the absolute pressure i n the bed as d e s c r i b e d i n S e c t i o n s 3.7.2 and 3.7.3. The mercury manometer had an u n c e r t a i n t y of- ± 4 mm of Hg. For smaller readings which r e q u i r e d b e t t e r p r e c i s i o n , an o i l manometer was used i n s t e a d . T h i s o i l had a s p e c i f i c g r a v i t y of 1.75 and the u n c e r t a i n t y of t h i s o i l manometer was e q u i v a l e n t to ± 0.6 mm of Hg. 37 3.4 BED MATERIAL Only one type of p a r t i c l e was used i n t h i s study. I t was Ottawa sand, s u p l i e d by Indusmin L i m i t e d of Montreal. T h i s sand was mainly s i l i c a (>99%) with t r a c e s of F e 2 0 3 , A l 2 0 3 and CaO. The sand, as r e c e i v e d , had a wide s i z e range. Before i t was used, i t was f i r s t screened to narrow down the s i z e d i s t r i b u t i o n s . Three s i z e s ( s m a l l , medium and large) of sand were employed. The mean p a r t i c l e diameter of each s i z e f r a c t i o n was determined from s i e v e a n a l y s i s as 1 dpi = 3.1 where x^ i s the weight f r a c t i o n of p a r t i c l e s w i t h i n an average adjacent screen a p e r t u r e s i z e of d p i . S e v e r a l measurements were taken f o r each s i z e before and a f t e r the given experiments. The average value of dp was then used, i . e . , dp = ( Z d p j ) / M 3.2 Table 3.2 summarizes such measurements. Apparently, there was only a small r e d u c t i o n i n s i z e d u r i n g runs, thus j u s t i f y i n g the use of Equation 3.2. The s i z e d i s t r i b u t i o n of each measurement i s given i n Appendix B. The d e n s i t y of sand p a r t i c l e s was determined by l i q u i d displacement. Sand p a r t i c l e s were f i r s t coated with a water Table 3.2 P a r t i c l e d iameter S i z e Sample # 1 2 3 Be f o r e 1.043 0.905 0.931 S A f t e r * 0.946 0.879 0.910 Be f o r e 1.281 1.300 1.232 A f t e r * 1.210 1.270 1.195 Be f o r e 1.725 1.731 1.667 L A f t e r * 1.672 1.647 1.514 * Averaoe d u r a t i o n : 6 - 8 hours Average O v e r a l l v a l u e average 0.985 0.966 0.960 0.924 1.255 1.267 1.254 1.232 1.682 1.701 1.678 1.628 0.945 mm 1.250 mm 1.665 mm 3 9 s e a l (Thompson's s e a l ) . A known weight of the coated p a r t i c l e s was placed i n s i d e a 100 ml v o l u m e t r i c f l a s k . The f l a s k was then f i l l e d with water to the 100 ml mark. The a d d i t i o n a l weight measured was the weight of the water added, from which the corresponding volume of water was determined. The d i f f e r e n c e between the volume of water and 100 ml was the volume of the sand p a r t i c l e s , from which the d e n s i t y c o u l d be c a l c u l a t e d . S e v e r a l measurements were made and the average p a r t i c l e d e n s i t y was found to be 2.60 gm/cm3 with an u n c e r t a i n t y of l e s s than 1%. The "random l o o s e " bulk d e n s i t y was determined using the procedure of Oman and Watson (1944). A 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 p a r t i c l e s . With the top end covered, the c y l i n d e r was i n v e r t e d and returned q u i c k l y to the o r i g i n a l u p r i g h t p o s i t i o n . The volume was then noted and the bulk d e n s i t y was thus determined. Such t e s t s were repeated s e v e r a l times to produce an average v a l u e . The annulus of a spouted bed was con s i d e r e d to be a l o o s e l y packed bed and hence i t s bulk d e n s i t y p^ was assumed to be that o b t a i n e d as j u s t d e s c r i b e d . The voidage i n the annulus c o u l d then be determined as e a = 1 " Pb/Pp 3.3 Table 3.3 summarizes the p h y s i c a l p r o p e r t i e s of the sand Table 3.3 Physical properties of sand p a r t i c l e s used "P "t, '» 6 e Temp Umf* (mm) (kg/m3) (kg/m3) (deg) (deg) PC) (m/s) (m/s) 0.945 2600 1300 0.50 34.0 63.5 20 170 300 420 0.51 0.48 0.43 0.40 2. 16 2.38 2.49 2.59 1 .250 2600 1300 0.50 34.0 63.5 20 170 300 420 0.70 0.71 0.67 0.63 2.73 3.04 3.21 3.35 1 .655 2600 1300 0.50 34.0 63.5 20 170 300 420 0.92 0.99 0.98 0.97 3.45 3.86 4 .09 4.30 * estimated from Equation 2.7 «? estimated from Equations 2.11 and 2.13 41 p a r t i c l e s used i n t h i s study. 3.5 FLOWRATE MEASUREMENTS Gas f l o w r a t e s were measured by rotameters which were c a l i b r a t e d a g a i n s t a dry gas meter (model AL 425 by Canadian Meter Co. L t d . ) . Pressure taps were l o c a t e d before and a f t e r the rotameters as d e s c r i b e d i n S e c t i o n 3.3. These pressure taps were connected to an assembly of two U-tube manometers, c o n t a i n i n g a blue o i l ( s p e c i f i c g r a v i t y = 1.75) and mercury ( s p e c i f i c g r a v i t y = 13.6), r e s p e c t i v e l y . These two manometers were a l s o used f o r pressure measurements of the bed. The readings from the manometer allowed the conver s i o n of a measured f l o w r a t e to a corresponding value at a standard c o n d i t i o n of 20 °C and 1 atmosphere. The whole procedure and the r e s u l t i n g c a l i b r a t i o n curves are presented in Appendix C.1. 3.6 PROGRAM OF STUDY In t h i s study, there were three main independent v a r i a b l e s , namely p a r t i c l e diameter, o r i f i c e opening and bed temperature. Table 3.4 g i v e s the c o n d i t i o n s of a l l the performed runs, while Table 3.5 l i s t s the dependent v a r i a b l e s a c t u a l l y measured i n each run. T a b l e 3.4 O p e r a t i n g c o n d i t i o n s Run Spout i n g # gas (mm) 1 A i r 0.945 2 A i r 0.945 3 A i r 0.945 4 A i r 0.945 5 A i r 1 .250 6 A i r 1 .250 7 A i r 1 .250 a A i r 1 .250 9 A i r 1 .665 10 A i r 1 .665 11 A i r 1 .665 12 A i r 1 .665 1 3 A i r 0.945 14 A i r 0.945 15 A i r 0.945 16 A i r 0.945 17 A i r 1 .250 18 A i r 1 .250 19 A i r 1 .250 20 A i r 1 .250 21 A i r 1 .665 22 A i r 1 .665 23 A i r 1 .665 24 A i r 1 .665 25 A i r 0.945 26 A i r 0.945 27 A i r 0.945 28 A i r 0.945 29 A i r 1 .250 30 A i r 1 .250 31 A i r 1 .250 32 A i r 1 .250 33 A i r 1 .665 34 A i r 1 .665 35 A i r 1 . 665 36 A i r 1 . 665 37 Methane 1 .250 38 Hel i u m 1 .250 Temp, (mm) (°C) 19 .05 20 19 .05 170 19 .05 300 19 .05 420 19 .05 20 19 .05 1 70 19 .05 300 19 .05 420 19 .05 20 19 .05 170 19 .05 300 19 .05 420 26 .64 20 26 .64 1 70 26 .64 300 26 .64 420 26 .64 20 26 .64 1 70 26 .64 300 26 .64 420 26 .64 20 26 .64 170 26 .64 300 26 .64 4 20 1 2 .70 20 1 2 .70 1 70 1 2 .70 300 12 .70 420 1 2 .70 20 12 .70 1 70 12 .70 300 12 .70 420 1 2 .70 20 1 2 .70 170 1 2 .70 300 12 .70 420 19 .05 20 19 .05 20 T a b l e 3.5 Dependent v a r i a b l e s measured Run °6 Um 8 — -—- • 1 X X X X 2 X X X X 3 X X X X 4 X X X X 5 X X X X 6 X X X X 7 X X X X a X X X X 9 X X X X 10 X X X X 11 X X X X 12 X X X X 13 X X X X 14 X X X X 15 X X X X 16 X X X X 17 X X X X 18 X X X X 19 X X X X 20 X X X X 21 X X X X 22 X X X X 23 X X X X 24 X X X X 25 X X X X 26 X X X X 27 X X X X 28 X X X X 29 X X X X 30 X X X X 31 X X X X 32 X X X X 33 X X X X 34 X X X X 35 X X X X 36 X X X X 37 X X X X 38 X X X X » V P H R e g I me Map 44 For each run, i f s t a b l e a i r spouting e x i s t e d , the maximum spoutable bed h e i g h t , the c o r r e s p o n d i n g minimum spouting v e l o c i t y and the o v e r a l l bed p r e s s u r e drop were measured. For t h i s same bed h e i g h t , the spout diameter was measured at U ^ 1.10 U m s . Data were a l s o c o l l e c t e d at two other bed h e i g h t s (0.50 H m and 0.75 H m a p p r o x i m a t e l y ) . Spouting gases other than a i r were a l s o used (Runs # 37 and # 38), namely helium and methane. Runs # 5, # 6, # 7 and # 8 were repeated to ensure r e p r o d u c i b i l i t y of experimental data. I t w i l l be shown i n l a t e r chapters that U m s , - A P S , H m and D s are g e n e r a l l y q u i t e r e p r o d u c i b l e . Furthermore, f o r the repeated runs, a d d i t i o n a l measurements were made, namely of l o n g i t u d i n a l and r a d i a l p r essure p r o f i l e s i n the annulus, f l u i d and p a r t i c l e v e l o c i t i e s i n the annulus, regime maps and f o u n t a i n h e i g h t s . The a c t u a l experimental c o n d i t i o n s i n a l l the runs are l i s t e d i n Appendix D, while the ranges of v a r i a b l e s are summarized in Table 3.6. 3.7 METHODS OF MEASUREMENT In the beginning of a t y p i c a l hot run, the e l e c t r i c h e a t e r s were switched on with the temperature c o n t r o l l e r s a l l set at 500 °C. The h e a t i n g s e c t i o n s and the ceramic packing i n s i d e them were pre-heated f o r about 20 minutes before a i r was turned on. The c o n t r o l l e r s were then set to the a p p r o p r i a t e l e v e l s (see Table 3.1). Sands; were poured slowly i n t o the column from the open top. Bed h e i g h t s c o u l d Table 3.6 Ranges of v a r i a b l e s s t u d i e d ( p p = 2600 kg/m3, D c = 156 mm) dp (mm) D £ (mm) H (m) p f (kg/m 3) ji (l0- 5kg/m-s) 0 . 9 4 5 — 1.665 12.70 — 26.64 0.168 — 1.380 0.168 — 1.259 1.09 — 3.20 46 be i n c r e a s e d by adding more sands or decreased by opening the v a l v e on the s o l i d s d i s c h a r g e l i n e . The a i r flowrate was ad j u s t e d a c c o r d i n g l y to maintain a steady spouting c o n d i t i o n . When the bed reached the d e s i r e d temperature w i t h i n ± 5 °C, measurements were then taken as d e s c r i b e d i n the next s u b - s e c t i o n s . When a l l measurements were completed, the heaters were turned o f f and the valve was opened again to d i s c h a r g e the hot sand p a r t i c l e s i n t o a s t a i n l e s s s t e e l bucket. The sands were d r a i n e d mostly by g r a v i t y to the h o r i z o n t a l l e v e l of the dis c h a r g e o u t l e t . F u r t h e r drainage was caused by m a i n t a i n i n g a high a i r f l o w r a t e which subsequently y i e l d e d a high spout f o u n t a i n . Some of the p a r t i c l e s from the f o u n t a i n f e l l through the discharge l i n e i n t o the r e c e i v i n g bucket. With t h i s method, the column c o u l d be emptied i n about 45 minutes. A i r flow was kept on f o r an a d d i t i o n a l 90 minutes to c o o l o f f the whole apparatus. 3.7.1 MAXIMUM SPOUTABLE HEIGHT H m was determined by i n c r e a s i n g the bed height u n t i l s t a b l e spouting c o u l d not be obtained f o r any gas f l o w r a t e . The corresponding l o o s e l y - p a c k e d bed height was then taken as H m. 47 3.7.2 OVERALL BED PRESSURE DROP A p r e s s u r e t a p was l o c a t e d about 25 mm below the o r i f i c e . A c c o r d i n g t o Mathur and E p s t e i n (1974), the p r e s s u r e drop due t o the bed s h o u l d be determined as f o l l o w s : -AP S = / p B 2 - P E 2 + P A T M 2 - P A T M 3.4 where Pg i s the measured a b s o l u t e upstream p r e s s u r e f o r the bed and P E i s the c o r r e s p o n d i n g v a l u e a t the same f l o w r a t e f o r an empty column. I t was found e x p e r i m e n t a l l y t h a t _ A P S was r e p r o d u c i b l e when t h e r e were no s c r e e n s under the o r i f i c e . When s c r e e n s were i n p l a c e , "AP S c o u l d not be d u p l i c a t e d . I t was l a t e r d i s c o v e r e d t h a t the ceramic p a c k i n g i n the h e a t i n g s e c t i o n broke up i n t o s m a l l p i e c e s and randomly b l o c k e d the openings on the bottom s i d e of the s c r e e n s . Moreover, the t o p s i d e of the s c r e e n s was p a r t i a l l y p lugged by the sand p a r t i c l e s i n the bed. The combined e f f e c t of the two caused u n c e r t a i n t y i n the measurements. The s c r e e n s had t o be i n p l a c e t o p r e v e n t sand p a r t i c l e s from e n t e r i n g i n t o the i n l e t s e c t i o n d u r i n g gas s h u t - o f f . To s o l v e t h i s problem, an a l t e r n a t e p r e s s u r e t a p was l o c a t e d 38 mm above the o r i f i c e , a t which the measurement was independent of the s c r e e n c o n d i t i o n s . A c a l i b r a t i o n c u r v e was o b t a i n e d by c o r r e l a t i n g - A P S under no-screen c o n d i t i o n s w i t h the measured manometer v a l u e a t 48 the p r e s s u r e tap above the o r i f i c e . T h i s curve, together with a l l the r e l e v a n t data are presented i n Appendix C.3. The o v e r a l l bed pressure drops were then c a l c u l a t e d from -AP S = [0.171 + 0.976(-AP a)] cm Hg 3.5 where -AP a was the measured p r e s s u r e drop above the o r i f i c e . 3.7.3 MINIMUM SPOUTING VELOCITY The minimum spouting v e l o c i t y was measured by obs e r v i n g the bed through the tr a n s p a r e n t f r o n t p a n e l . The gas flowrate was f i r s t i n c r e a s e d to a value above the minimum spouting c o n d i t i o n and then decreased slowly u n t i l spouting ceased. The gas flow r a t e at which the f o u n t a i n j u s t c o l l a p s e d was taken as the minimum spouting f l o w r a t e . T h i s t e s t was repeated at l e a s t twice to ensure r e p r o d u c i b i l i t y . The v o l u m e t r i c gas fl o w r a t e e n t e r i n g the h a l f bed was c a l c u l a t e d u s i n g Equation C.14 i n Appendix C, assuming the absolute bed pressure was taken as P S = PATM + <-AP s ) /2 3.6 The s u p e r f i c i a l gas v e l o c i t y was subsequently determined by d i v i d i n g the v o l u m e t r i c f l o w r a t e by the c r o s s - s e c t i o n a l area of the bed, i . e . , 7 r D c 2 / 8 f o r a h a l f column. 4 9 3.7.4 SPOUT DIAMETER AND SPOUT SHAPE The spout diameter was measured by h o l d i n g a r u l e r h o r i z o n t a l l y a g a i n s t the t r a n s p a r e n t f r o n t face of the column. Measurements were made at s e v e r a l bed l e v e l s to y i e l d a f u l l spout shape. The area-averaged spout diameter was c a l c u l a t e d as f o l l o w s : D c = 1 H. - J ' H a0 1 1/2 (D s(z)}' :dz 3.7 where D g ( z ) was the measured spout diameter at bed l e v e l , z. The numerical i n t e g r a t i o n was done with "QINT4P", a r o u t i n e d e s c r i b e d by N i c o l (1982). 3.7.5 FLUID AND PARTICLE VELOCITIES IN THE ANNULUS Before measuring the f l u i d v e l o c i t y and pressure p r o f i l e s ( S e c t i o n 3.7.6) i n the annulus, the extension column was removed and r e p l a c e d with a flanged cover (Figure 3.5). The f l u i d v e l o c i t y was determined by means of a s t a t i c p r e s sure probe (Figure 3.6a) which c o n s i s t e d of two s t a i n l e s s s t e e l tubes of 3.1 and 6.4 mm O.D., r e s p e c t i v e l y . The smaller tube was p l a c e d i n s i d e the l a r g e r one, forming the main body. The bottom ends of the tubes were p r o p e r l y c l o s e d o f f with s i l v e r s o l d e r . Two s e t s of four holes (of 0.8 mm diameter) were a l s o d r i l l e d . One set was l o c a t e d on 50 F i g u r e 3.5 D e t a i l s of the f l a n g e d c o v e r ( A l l d i m e n s i o n s i n mm) 5 1 F i g u r e 3.6 D e t a i l s of the s t a t i c p r e s s u r e probes ( A l l d i m e n s i o n s i n mm) 52 the small tube at the bottom part of the probe whereas the other set was on the outer s h e l l with v e r t i c a l s e p a r a t i o n of 18 mm between the two s e t s (of h o l e s ) . Using a Swagelok f i t t i n g , the probe was secured through p o r t T2 i n the f l a n g e d cover to r e s t r i c t any l a t e r a l movement. The nut on the connector was only t i g h t e n e d s l i g h t l y and c o u l d be loosened when a d j u s t i n g the v e r t i c a l p o s i t i o n of the probe d u r i n g measurements. S t a t i c pressure g r a d i e n t s were measured at s e v e r a l bed l e v e l s . The small pressure drops were det e c t e d with a micromanometer (Model MM-3, made by Flow Corp. of Cambridge, Mass.) f i l l e d with b u t a n o l . These readings were converted to f l u i d v e l o c i t i e s v i a a c a l i b r a t i o n c u rve. With the assumption that the annulus i n a spouted bed behaves as a l o o s e l y packed bed of s o l i d s , the c a l i b r a t i o n was done i n a l o o s e bed of the same m a t e r i a l . To ensure uniform ( r a d i a l ) d i s t r i b u t i o n of f l u i d flow, the bed was set at a height w e l l above the maximum spoutable bed h e i g h t , H m. Flowrates and pressure drops were recorded and a c a l i b r a t i o n of pressure drop versus 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 thus obtained (see Appendix C.4). The downward v e l o c i t i e s of annular p a r t i c l e s were determined at the f l a t w a l l of the h a l f column by measuring with a stop watch the time taken f o r a t r a c e r p a r t i c l e to move a s m a l l v e r t i c a l d i s t a n c e of 4 cm. At any given bed 53 l e v e l , z, p a r t i c l e downward v e l o c i t i e s were measured at f i v e r a d i a l p o s i t i o n s as i l l u s t r a t e d i n F i g u r e 3 . 7 . At each r a d i a l p o s i t i o n , three measurements were taken on each s i d e of the spout, r e s u l t i n g i n a t o t a l of s i x readings, from which an average value was determined fo r t h i s l o c a t i o n . The v o l u m e t r i c s o l i d s flow i n a f u l l column annulus at t h i s l e v e l was then given by R c G a ( z ) = / [ V p ( r ) ( 1-e a) (2irr)]dr 3 . 8 R s where V p ( r ) was the measured downward p a r t i c l e v e l o c i t y at r a d i a l d i s t a n c e , r . The r a d i a l - a v e r a g e d p a r t i c l e v e l o c i t y was determined from the f o l l o w i n g equation: R c / [ V D ( r ) (27rr) ]dr ; C(27rr)dr R s 3 . 7 . 6 RADIAL AND LONGITUDINAL PRESSURE PROFILES Another pressure probe ( F i g u r e 3 . 6 b ) was c o n s t r u c t e d . The main body c o n s i s t e d of two s t a i n l e s s tubes of 3.1 and 9 . 5 mm OD, r e s p e c t i v e l y . The inner tube was s e a l e d o f f at the bottom end and bent at an angle of 9 0 ° . A short p i e c e of s t a i n l e s s s t e e l tube of 3 .1 mm OD was s i l v e r s o l d e r e d p e r p e n d i c u l a r l y onto a hole d r i l l e d on the outer s h e l l , making a v e r t i c a l s e p a r a t i o n of 3 cm with the bent s e c t i o n . 54 r« = R s + 0.75(R C-R S) r 3 = R s + 0.50(R C-R S) r 2 = R s + 0.25(R C-R S) = R, SPOUT < P O u / / / / / / / / / / / / / ANNULUS F i g u r e 3.7 R a d i a l p o s i t i o n f o r p a r t i c l e v e l o c i t y measurements 55 H o l e s of 0.8 mm were d r i l l e d on t h e s e two p i e c e s . T h i s p r o b e c o u l d be u s e d t o measure t h e d i f f e r e n t i a l p r e s s u r e d r o p s . F o r t h e p r e s s u r e p r o f i l e s t u d i e s , o n l y t h e o u t l e t c o r r e s p o n d i n g t o t h e b o t t o m t i p was c o n n e c t e d t o a manometer. T h i s p r o b e was i n s e r t e d t h r o u g h p o r t T3 of t h e t o p c o v e r ( F i g u r e 3.5) i n t h e same manner as d e s c r i b e d i n S e c t i o n 3.7.5. At any f i x e d bed l e v e l , z, t h e bed p r e s s u r e s were measured a t f i v e d i f f e r e n t r a d i a l p o s i t i o n s i n t h e a n n u l u s by r o t a t i n g t h e p r o b e . The a v e r a g e o f t h e s e f i v e measurements was t a k e n as t h e a v e r a g e l o n g i t u d i n a l v a l u e a t t h e g i v e n l e v e l . 3.7.7 REGIME MAP A r e g i m e map i s a p l o t o f bed h e i g h t v e r s u s f l u i d f l o w r a t e f o r a g i v e n f l u i d - s o l i d s y s t e m . A t y p i c a l regime map i n c l u d e s f i v e r e g i o n s . T h e s e a r e f i x e d bed, s t e a d y s p o u t i n g , 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 , b u b b l i n g and s l u g g i n g . F o r bed h e i g h t s r a n g i n g f r o m z e r o t o about 1.20 H m, a l l t h e t r a n s i t i o n a l p o i n t s were l o c a t e d by v a r y i n g t h e f l u i d f l o w r a t e s . To be c o n s i s t e n t w i t h t h e method of m e a s u r i n g U m s , a l l t h e t r a n s i t i o n a l p o i n t s were f o u n d w i t h d e c r e a s i n g f l o w . A t any g i v e n bed h e i g h t , t h e f l u i d f l o w r a t e was f i r s t i n c r e a s e d g r a d u a l l y d u r i n g w h i c h t h e regime t r a n s f o r m a t i o n was n o t e d by means of v i s u a l o b s e r v a t i o n s . The f l o w r a t e was t h e n d e c r e a s e d s l o w l y and t h e t r a n s i t i o n a l p o i n t s were t h u s d e t e r m i n e d . T h i s p r o c e d u r e o f d e c r e a s i n g 56 flow was found to y i e l d r e p r o d u c i b l e r e s u l t s . 3.7.8 FOUNTAIN HEIGHT The f o u n t a i n height i s the d i s t a n c e from the annulus bed s u r f a c e to the f o u n t a i n top. I t was measured d i r e c t l y a g a i n s t the f r o n t w a l l . 3.8 ERROR CALCULATION When comparing experimental values with p r e d i c t e d v a l u e s , the f o l l o w i n g d e f i n i t i o n s are used: % dev = CAL - EXP EXP X 100% 3.10 RMS % ERROR = /[£(% d e v ) 2 ] / M 3.11 AVE ERR = [ I ( % dev)]/M 3. 12 where EXP = experimental value CAL = p r e d i c t e d value M = number of data p o i n t s 4. STABILITY OF SPOUTING 4.1 STABILITY 4.1.1 EFFECT OF TEMPERATURE ON SPOUTABILITY Table 4.1 shows the s p o u t a b i l i t y of Ottawa sand under d i f f e r e n t combinations of dp, and T s . The r e s u l t s o b t ained at room temperature are i n e x c e l l e n t agreement with the c r i t e r i o n proposed by Chandnani (1984), that i s , s t a b l e spouting w i l l occur only i f D^/dp < 25.4. T h i s c r i t e r i o n does not p r e d i c t any e f f e c t with bed temperature. In f a c t , i t was d e r i v e d from experiments c a r r i e d out at room c o n d i t i o n s with "only" a i r as spouting medium. However, i t can be seen from Table 4.1 that the bed temperature does have some s i g n i f i c a n t e f f e c t on the s p o u t a b i l i t y . For i n s t a n c e , s t a b l e spouting at D^/dp = 20.2 i s o b t a i n a b l e at room temperature but not at 300 °C or h i g h e r . However, Table 4.1 a l s o shows that s t a b l e spouting i s a c h i e v a b l e at D^/dp = 21.3 at a l l four temperature l e v e l s , which i s s l i g h t l y i n c o n s i s t e n t with the o b s e r v a t i o n s i n the p r e v i o u s case. These two v a l u e s of D^/dp are so s i m i l a r that the d i s c r e p a n c y may be due to the u n c e r t a i n t y i n dp. Another p o s s i b l e e x p l a n a t i o n i s that the r a t i o , D^/dp, may not be s u f f i c i e n t to determine s p o u t a b i l i t y , e s p e c i a l l y f o r n o n - s p h e r i c a l p a r t i c l e s . 57 Table 4.1 S p o u t a b i l i t y of sand p a r t i c l e s a t d i f f e r e n t c o n d i t i o n s 3 P D i / ^ p D c/Di (mm) (mm) 1 .665 12.70 7.6 12.3 1.250 1 2.70 10.2 12.3 1.665 19.05 11.4 8.2 0.945 1 2.70 13.4 12.3 1.250 19.05 15.2 8.2 1 .665 26.64 16.0 5. B 0.945 19.05 20.2 8.2 1 .250 26.64 21.3 5.B 0.945 26.64 28. 2 5.8 D c/dp S t a b l e S p o u t i n g P o s s i b l e ? 20 170 300 420 CC 93 YES YES YES YES 124 YES YES YES YES 93 YES YES YES YES 165 YES YES YES YES 124 YES YES YES YES 93 YES YES YES YES 1 65 YES YES NO NO 124 YES YES YES YES 1 65 NO NO NO NO 5 9 Based on the r e s u l t s o b tained at Di/dp = 20.2, the c r i t e r i o n proposed by Chandnani i s not completely s a t i s f a c t o r y at higher temperatures, at l e a s t f o r n o n - s p h e r i c a l p a r t i c l e s . M o d i f i c a t i o n by i n c l u d i n g the e f f e c t of bed temperature i s necessary. S i n c e both gas d e n s i t y and v i s c o s i t y change with temperature, i t may be more a p p r o p r i a t e to use these two v a r i a b l e s i n s t e a d of temperature to develop a c r i t e r i o n of the form f ( D i f dp, <p, p f , M) < X 4.1 where X i s some c r i t i c a l value or parameter. In t h i s study, however, t h e r e were not s u f f i c i e n t data to d e r i v e such a c r i t e r i o n . 4.1.2 EFFECT OF TEMPERATURE ON SPOUTING CHARACTERISTICS The obvious e f f e c t of i n c r e a s i n g temperature i s the decrease i n H m ( S e c t i o n s 4.2 and 4.3). When o p e r a t i n g at bed h e i g h t s w e l l below H m, i n c r e a s i n g the bed temperature has no observable e f f e c t on the bed behaviour. However, as bed h e i g h t s i n c r e a s e d , the spout c h a r a c t e r i s t i c s changed s i g n i f i c a n t l y with i n c r e a s i n g temperature. At room temperature, when H » H m, f l u i d i z a t i o n was observed at the top s u r f a c e of the annulus. T h i s was i n d i c a t e d by the upward p a r t i c l e entrainment at the annulus s u r f a c e and the s l i g h t l y h igher voidage at the upper part of 60 the annulus. In a d d i t i o n , the spout diameter was found to expand at the bed s u r f a c e and the r e s u l t i n g f o u n t a i n height was r e l a t i v e l y low (compared to the f o u n t a i n height of a shallower bed at s i m i l a r U/U m s c o n d i t i o n ) . F u r t h e r i n c r e a s e i n bed h e i g h t s produced more annulus f l u i d i z a t i o n and a l s o caused the spouting j e t to submerge below the bed s u r f a c e , d i s c h a r g i n g p e r i o d i c a l l y as bubbles. S t a b l e spouting subsequently became unachievable. As the bed temperature i n c r e a s e d , the spouting c h a r a c t e r i s t i c s f o r bed heights near H m were q u i t e d i f f e r e n t from those observed at room c o n d i t i o n s . For the high temperature cases ( i . e . , T s = 420 °C), the spout-annulus i n t e r f a c e near the bed s u r f a c e was found to be s l i g h t l y u n s t a b l e . The i n t e r f a c e followed a r i p p l i n g motion. As bed h e i g h t s approached H m, the i n t e n s i t y of t h i s i n s t a b i l i t y i n c r e a s e d which l e d to the tendency towards p u l s i n g and choking i n the spout. J u s t above H m, the amplitude of these r i p p l e s became g r e a t e r than the spout r a d i u s , r e s u l t i n g i n a p i n c h p o i n t and the formation of a bubble. T h i s regime t r a n s f o r m a t i o n was o b v i o u s l y d i f f e r e n t from that at c o l d c o n d i t i o n s . Though the spout and f o u n t a i n shapes were s i m i l a r to those at room temperature, f l u i d i z a t i o n i n the annulus was not observed at a l l . 61 4.2 REGIME MAPS Fi g u r e 4.1 shows the p h y s i c a l appearance of four d i f f e r e n t flow regimes i n a t y p i c a l spouted bed. St a b l e spouting can be c h a r a c t e r i z e d by two main f e a t u r e s , a steady f o u n t a i n with l i t t l e f l u c t u a t i o n and a s t a b l e spout-annulus i n t e r f a c e (Figure 4.1a). When r i p p l i n g movement s t a r t s to appear at the spout-annulus i n t e r f a c e near the bed s u r f a c e , causing the f o u n t a i n shape to get d i s t o r t e d and the f o u n t a i n height to o s c i l l a t e , the bed becomes l e s s s t a b l e and t h i s phenomenon i s d e s c r i b e d as " p r o g r e s s i v e l y incoherent spouting" (Figure 4.1b). Bubbling s e t s in when the spouting j e t cannot penetrate through the bed. Bubbles then form below the bed su r f a c e and d i s c h a r g e p e r i o d i c a l l y ( F igure 4.1c). I f these bubbles grow to the s i z e s i m i l a r to that of the column diameter before they reach the bed s u r f a c e , s l u g g i n g w i l l then occur (Figure 4.1d). In the present study, regime maps f o r a f i x e d p a r t i c l e and a f i x e d o r i f i c e diameter (dp = 1.25 mm, = 19.05 mm) are presented at four d i f f e r e n t a i r temperatures i n F i g u r e s 4.2, 4.3, 4.4 and 4.5, r e s p e c t i v e l y . The e f f e c t of temperature was c l e a r l y demonstrated by the r e d u c t i o n of H m with i n c r e a s i n g temperature. Moreover, at higher temperatures, a l l other regime boundaries g e n e r a l l y s h i f t downwards, r e s u l t i n g i n smaller regime areas f o r "Steady Spouting". Presumably, i f the temperature were in c r e a s e d to 62 (a) (b) (c) (d) F i g u r e 4.1 P i c t u r e s of d i f f e r e n t r e g i m e s . (a) s t e a d y s p o u t i n g (b) 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 (c) b u b b l i n g (d) s l u g g i n g 63 0 0.5 1 1.5 2 Superficial Velocity, U (m/s) F i g u r e 4.2 Regime map f o r a i r - s a n d system at 20 °C P . I . S . = p r o g r e s s i v e l y incoherent s p o u t i n g 64 1.5 A t i l l • 1—( (1) TJ PQ 0.5 0 Run # 6 D c = 156 mm dp = 1.25 mm D; = 19.05 mm T s = 170 deg G FIXED BED SLUGGING BUBBLING STEADY SPOUTING 0 0.5 1 1.5 Superficial Velocity, U (m/s) F i g u r e 4.3 Regime map f o r a i r - s a n d system at 170 °C P.I.S. = 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 65 1.5 Run # 7 Dc — 156 mm dp = 1.25 mm D| = 19.05 mm T s ss 300 deg C fcuO •rH CD W CD CQ 0.5 0 FIXED BED SLUGGING STEADY SPOUTING 0 0.5 1 1.5 Superficial Velocity, U (m/s) F i g u r e 4.4 Regime map f o r a i r - s a n d s y s t e m a t 300 °G P. I . S . = 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 1 Run # 8 D c = 156 mm — dp = 1.25 mm — Dj = 19.05 mm T s = 420 deg C — / / / / SLUGGING 4 I r/r\ / \ BUBBLING /^4/P.I . S \ — FIXED BED / ° STEADY SPOUTING 0 0.5 1 1.5 2 Superficial Velocity, U (m/s) gure 4.5 Regime map f o r a i r - s a n d system at 420 °C P.I.S. = p r o g r e s s i v e l y incoherent s p o u t i n g 67 s t i l l higher l e v e l s ( i . e . , > 420 °C), the re g i o n of "Steady Spouting" would e v e n t u a l l y decrease to n i l and the corresp o n d i n g regime map would be s i m i l a r to that of F i g u r e 2.4 i n Chapter 2. 4.3 MAXIMUM SPOUTABLE BED HEIGHT 4.3.1 EFFECT OF ORIFICE DIAMETER F i g u r e 4.6 i l l u s t r a t e s the e f f e c t of o r i f i c e diameter on H m at four d i f f e r e n t temperature l e v e l s . I n c r e a s i n g D^ produces lower v a l u e s of H m, p r o v i d e d that other o p e r a t i n g parameters are f i x e d . T h i s observed t r e n d of H m i s c o n s i s t e n t with that of Equation 2.8. 4.3.2 EFFECT OF PARTICLE DIAMETER According to Equation 2.8, H m goes through a maximum at .2 -|1/3 A. 1 4 < dp>crit = 6 0 - 6 . g ( p p - P f ) P f . which was obtained by d i f f e r e n t i a t i n g Equation 2.8 with respect to dp, a f t e r s u b s t i t u t i n g Ar from Equation A.4a, and then s e t t i n g dH m/d(dp) to zero. For a i r sp o u t i n g of sand p a r t i c l e s at atmospheric p r e s s u r e , the c r i t i c a l v a l u e s of dp were c a l c u l a t e d to be 1.3, 1.8, 2.3 and 2.6 mm at 20, 170, 300 and 420 °C, r e s p e c t i v e l y . H m i n c r e a s e s with i n c r e a s i n g dp below the c r i t i c a l value and decreases with i n c r e a s i n g dp 68 F i g u r e 4.6 E f f e c t of o r i f i c e d i a m e t e r on maximum s p o u t a b l e bed h e i g h t f o r d i f f e r e n t t e m p e r a t u r e s 69 above i t . The q u a l i t a t i v e e f f e c t of i n c r e a s i n g dp as p r e d i c t e d by Equations 2.8 and A.14 was observed at 170, 300 and 420 °C but not c o n s i s t e n t l y at room temperature (Figure 4.7). Equations 2.8 and A.14 are based on the approximation of Wen and Yu, i e . , Equations 2.6a and 2.6b. The corresponding values of 0 and e m f are 0.6689 and 0.4744 r e s p e c t i v e l y . The more gen e r a l form of Equation A.14, without the Wen-Yu approximation, i s ( < V c r i t = 2 9 - 5 2 1/3 -L « n f 3 * 3 J M 2 g ( p p - p f )pf. 1/3 A. 1 6 The above equation c l e a r l y i n d i c a t e s that ( d p ) c r j t decreases with i n c r e a s i n g 0. The e f f e c t of e m f i s , however, l e s s obvious. I f Equation A.16 i s d i f f e r e n t i a t e d with respect to emf i t c a n D e shown that f o r 0 < e m f < 1 , d ( d p ) c r i t / d e m f < 0, implying t h a t ( d p ) c r i t decreases with i n c r e a s i n g i n c r e a s i n g e m£ over t h i s range. E x p e r i m e n t a l l y e a was found to be 0.5 but 0, on the other hand, was not measured. If e m f i s assumed equal to e a and 0 equal to or g r e a t e r than 0.6689 (which seems reasonable f o r sand), the r e s u l t i n g ( d p ) c r i t would be smaller than the p r e v i o u s l y estimated v a l u e s . T h i s c o u l d p a r t l y e x p l a i n the discrepancy at room temperature r e p o r t e d e a r l i e r . For i n s t a n c e , the combined e f f e c t of 0 and e m f may lower the (°p) c rj. t to a value between 0.945 and 1.25 mm at room temperature and yet g r e a t e r than 1.665 mm f o r temperatures of 170 °C and higher. In the room temperature case, experimental r e s u l t s suggest a 70 F i g u r e 4.7 E f f e c t of p a r t i c l e d i a m e t e r on maximum s p o u t a b l e bed h e i g h t f o r d i f f e r e n t t e m p e r a t u r e s 71 decrease of H m with i n c r e a s i n g dp. T h i s t r e n d c o u l d be i n t e r p r e t e d here as: H m i n c r e a s e d with dp to a maximum at ( d p ) c r ^ t beyond which H m decreased with i n c r e a s i n g dp. The dashed l i n e i n F i g u r e 4.7 i l l u s t r a t e s t h i s i n t e r p r e t a t i o n . In the higher temperature cases, H m simply i n c r e a s e d with dp because dp < ( d p ) c r j . t . T h i s concept of ( d p ) c r i t a l s o helps to e x p l a i n why the e f f e c t of temperature appears to be gre a t e r f o r s m a l l e r p a r t i c l e s as shown i n F i g u r e 4.8. 4.3.3 EFFECT OF TEMPERATURE The e f f e c t of temperature on H m was examined by d i f f e r e n t i a t i n g Equation 2.8 with respect to Ar while other v a r i a b l e s , such as D c, and dp were kept c o n s t a n t . I t was found that dH m/dAr > 0 f o r a l l v a l u e s of Ar. T h i s i m p l i e s that H m i n c r e a s e s with Ar. For gas spouting, with i n c r e a s i n g temperature, gas d e n s i t y decreases while v i s c o s i t y i n c r e a s e s , which r e s u l t s i n a lower value of Ar and t h e r e f o r e a s m a l l e r value of H m. T h i s trend was supported q u a l i t a t i v e l y by the experimental r e s u l t s as shown in F i g u r e s 4.6, 4.7, 4.8 and 4.9. Equation 2.8 p l u s two other c o r r e l a t i o n s are a l s o i n c l u d e d i n the l a t t e r f i g u r e f o r d i r e c t comparison. Equation 2.9 (Littman et a l . , 1979) p r e d i c t s i n c r e a s i n g H m with i n c r e a s i n g temperature, which c o n t r a d i c t s the experimental o b s e r v a t i o n s . I t i s important to p o i n t out here that under normal circumstances, Equations 2.12a and 2.12b (Morgan and Littman, 1982) should be used 72 F i g u r e 4.8 E f f e c t o f t e m p e r a t u r e on maximum s p o u t a b l e bed h e i g h t f o r d i f f e r e n t p a r t i c l e d i a m e t e r s 73 0 100 200 300 400 T S (deg C) F i g u r e 4.9 E f f e c t of t e m p e r a t u r e on maximum s p o u t a b l e bed h e i g h t (Comparison between e x p e r i m e n t a l d a t a and p r e d i c t i o n s ) 74 i n s t e a d of Equation 2.9 because the l a t t e r i s r e s t r i c t e d to s p h e r i c a l p a r t i c l e s o n l y . U n f o r t u n a t e l y , Equations 2.12a and 2.12b c o u l d not be a p p l i e d s i n c e v a l u e s of A^ were o u t s i d e the r e q u i r e d ranges, while A was w i t h i n the range of a p p l i c a b i l i t y of Equation 2.9. The t h i r d c o r r e l a t i o n in F i g u r e 4.9 i s that of Malek and Lu (1965), rendered f u l l y d i m e n s i o n l e s s : Hm V 0.75 0.4 ~Pf 1 .2 " f 336 — D c w _ D i _ The shape f a c t o r , <j>, i n Equation 4.2 was a r b i t r a r i l y taken as 0.6689, to be c o n s i s t e n t with that i m p l i c i t l y i n Equation 2.8. Although Equation 4.2 i s e n t i r e l y e m p i r i c a l , i t manages to p r e d i c t the c o r r e c t t rend of H m with i n c r e a s i n g temperature. 4.3.4 EFFECT OF FLUID DENSITY AND VISCOSITY Table 4.2 shows how H m v a r i e s with p f and y. At 20 °C, helium and a i r have s i m i l a r M but d i f f e r e n t p£. By comparing the two experimental v a l u e s of H m, the e f f e c t of p^ at constant M can be examined. H m i s higher f o r a i r spouting, implying t hat H m i n c r e a s e s with i n c r e a s i n g p^. On the other hand, the e f f e c t of M at constant p^ can be seen from the remaining columns i n Table 4.2. I t i s c l e a r that H m i n c r e a s e d with d e c r e a s i n g u. In other words, spouting w i l l be more f a v o r a b l e i f the spouting gas i s more dense and l e s s v i s c o u s . The e f f e c t s of gas d e n s i t y and v i s c o s i t y on 75 T a b l e 4 . 2 E f f e c t s o f u a n d p f o n H m . D c = 156 mm, D± = 1 9 . 0 5 mm a n d d p = 1 .25 mm S p o u t i n g g a s He A i r A i r A i r CH, T q ( ° C ) 20 20 170 300 20 p f ( k g / m 3 ) 0 . 1 7 0 1 . 2 5 9 0 . 8 1 5 0 . 6 2 4 0 . 7 0 7 ii ( l 0 - 5 k g / m - s ) 1. 94 1 . 8 0 2 . 35 2 . 8 5 1 .09 H m (m) 0 . 5 3 3 1 . 0 6 7 0 . 6 4 8 0 . 5 4 6 1 .380 76 H m are c o n s i s t e n t with the observed t r e n d of H m w i t h temperature as repo r t e d i n S e c t i o n 4.3.3. 4.3.5 CORRELATION OF EXPERIMENTAL DATA Table 4.3 l i s t s a l l the experimental v a l u e s of H m versus the c a l c u l a t e d values by Equation 2.8 (McNab and Bridgwater, 1977). The g r a p h i c a l comparison i s shown i n F i g u r e 4.10 with the s o l i d l i n e ( i e . , b = 1.11) r e p r e s e n t i n g Equation 2.8. Although there i s some s c a t t e r , i t i s not any worse, i n f a c t i s c o n s i d e r a b l y b e t t e r , than that of F i g u r e 2.2. However, the experimental data of t h i s study suggest a "b" value higher than 1.11. A p p l i n g a l e a s t squares f i t t o the present data y i e l d e d b = 1.23. The r e s u l t i n g equation i s shown i n F i g u r e 4.10 as a dashed l i n e . 4.4 MECHANISMS OF SPOUT TERMINATION AT MAXIMUM SPOUTABLE BED  HEIGHT Chandnani and E p s t e i n (1986) suggested a procedure f o r e s t i m a t i n g H m i f the mechanism f o r spout t e r m i n a t i o n were due to choking. The spout was compared to a standpipe i n which a f l u i d c a r r i e d s o l i d s upwards. Choking o c c u r r e d when the f l u i d v e l o c i t y was reduced below a c r i t i c a l v a l u e , U c. T h i s c r i t i c a l v e l o c i t y c o u l d be estimated from (Leung, 1980) 2 g D s ( e c " 4 ' 7 - 1 ) / ( U c - U t ) 2 = 0.00874p f 0• 7 7 4.3 Table 4.3 Maximum spoutable bed height, experimental versus predictions. Sand. p •- 2600 kg/m . D = • 156 mm Run *• Temp C O dp (mm) D . I (mm) (kg/ms) Expt . H m (m) Pred. H e m (m) % dev 1-1 20 0 .945 19 .05 1 .246 1.80E-05 1 . 168 0.866 -25.85 2-1 170 0 .945 19 .05 0 .802 2.35E-05 0 .419 0.485 15.85 5-1 20 1 .250 19 .05 1 .259 1.80E-05 1 .067 0.940 -11.88 6-1 170 1 .250 19 .05 0 .815 2.35E-05 0 .648 0.616 -4.91 7-1 300 1 .250 19 .05 0 .624 2.B5E-05 0 .546 0.420 -23.06 8-1 420 1 .250 19 .05 0 .514 3.20E-05 0 .413 0.313 -24. 10 9-1 20 1 .665 19 .05 1 .244 1.80E-05 1 .010 0.906 -10.25 10-1 170 1 .665 19 .05 0 .824 2.35E-05 0 .800 0.682 -14.81 11-1 300 1 .665 19 .05 0 .629 2.B5E-05 0 .721 0.516 -28.49 12-1 420 1 .665 19 .05 0 .515 3.20E-05 0 .629 0.411 -34.64 17-1 20 1 .250 26 .64 1. .252 1.80E-05 1 .026 0.750 -26.86 18-1 170 1 .250 26 .64 0. .816 2.35E-05 0 .705 0.493 -30.07 19-1 300 1 .250 26 .64 0. .623 2.85E-05 0 .419 0.336 -19.91 20-1 420 1 .250 26 .64 0. .511 3.20E-05 0 .343 0.250 -27.23 21-1 20 1 .665 26 .64 1. .254 1.80E-05 0. .978 0.727 -25.64 22-1 170 1 .665 - 26 .64 0. .822 2.35E-05 0. .638 0.545 -35.02 23-1 300 1 .665 26 .64 0. .631 2.85E-05 0. .679 0.413 -39.19 24-1 420 1 .665 26. .64 0. 517 3.20E-05 0. .540 0.329 -38.98 25-1 20 0 .945 12. .70 1. 276 1.80E-05 1. .372 1 . 148 -16.29 26-1 170 0 .945 12, .70 0. B14 2.35E-05 0. .724 0.643 -11.25 27-1 300 0 .945 12. .70 0. 622 2.85E-05 0. .635 0.396 -37.67 28-1 420 0. .945 12. .70 0. 511 3.20E-05 0. 486 0.278 -42.83 29-1 20 1. .250 12. .70 1. 261 1.80E-05 1. .276 1 .233 -3.39 30-1 170 1. .250 12. .70 0. 818 2.35E-05 0. 7B1 0.809 3 .58 31-1 300 1 .250 12. .70 0. 629 2.85E-05 0. 654 0. 553 -15.39 32-1 420 1, .250 12. .70 0. 515 3.20E-05 0. 533 0.4 11 -22.83 33-1 20 1. .665 12. 70 1. 245 1.80E-05 1. 029 1 . 188 15.46 34-1 170 1. .665 12. 70 0. 820 2.35E-05 0. 832 0.891 7 . 14 35-1 300 1. .665 12. 70 0. €30 2.B5E-05 0. 743 0.676 -9.00 36-1 420 1, .665 12. 70 0. 519 3.20E-05 0. 654 0. 54 1 - 17.26 37-1 20 1. 250 19. 05 0. 707 1 .09E-05 1. 380 1 .079 -21.80 38-1 170 1. 250 19. 05 0. 170 1 .94E-05 0. 533 0.290 -45.57 P by Equation 2.8 78 Q \ * f Q Q 0.00 0.01 0.02 0.03 0.04 ( 1 l 3 6 / A r ) [ / l + 3 5 . 9 X l O " 6 A r - 1 ] 2 F i g u r e . 4 . 1 0 Comparison between e x p e r i m e n t a l d a t a and E q u a t i o n 2.8 79 i n which e c, the voidage at choking, c o u l d be c a l c u l a t e d from the f o l l o w i n g equation (Smith, 1978): 2-| 1- 4.4 D s J where N i s the Richardson-Zaki index. If choking of spout o c c u r r e d at H m, then U s H and D s H would be equal to U c and D s, r e s p e c t i v e l y . Knowing u s H m ' U a H m a n o ^ D s H m ' t * 1 6 minimum spouting s u p e r f i c i a l v e l o c i t y , U m, c o u l d be determined and thus a l s o H m v i a Equation 2.1a. ( ! - e c ) -2 2Pr (N< N-1 ,2 The accuracy of t h i s method depends very s t r o n g l y on the value of D s H m a n ^ whether choking indeed occurs at H m. E x p e r i m e n t a l l y , D s was found to be l a r g e r at z = H m than at lower l e v e l s . On the other hand, choking i f i t e x i s t e d , g e n e r a l l y occurred below the bed s u r f a c e . Thus using the value of D s at z = H m i s somewhat i n a p p r o p r i a t e . T h i s u n c e r t a i n t y of D s H m makes i t d i f f i c u l t to apply the above method d i r e c t l y to estimate H m f o r cases where choking has been observed. However, an attempt was made to compare some experimental values of U q H with the corresponding m c a l c u l a t e d values of U c. D S H m w a s a r b i t r a r i l y taken as the average spout diameter ( d e f i n e d i n Equation 3.7). These r e s u l t s are l i s t e d i n Table 4.4. F l u i d i z a t i o n of annular s o l i d s appears to be the spouting t e r m i n a t i o n mechanism at room temperatures but i t becomes l e s s dominant at higher temperatures as i n d i c a t e d by the i n c r e a s i n g d i f f e r e n c e between U a H ^ and U m f (Figure 4.11). In a d d i t i o n , Figure Table A.a Comparison between U and U ,, . Sand d m ^ Run TEMP D i U ms m N H ( °C) (mm) (m/s) (m) 5-1 20 19 .05 1. 100 0 .0342 2 .5744 e-1 170 19 .05 1.009 0. .0309 2 .8201 7-1 300 19 .05 0.931 0 .0296 2 . 9365 B-1 420 19 .05 0.871 0 .0283 3 .0163 17-1 20 26 .64 1.108 0. .0344 2. .5749 18-1 170 26. .64 1.048 0. .0334 2. .8199 19-1 300 26. .64 0.949 0. 0300 2. .9371 20-1 4 20 26. .64 0.947 0. 0288 3. .0174 29-1 20 12. .70 1 . 153 0. 0331 2. .5737 30-1 170 12. .70 0.959 0. 0295 2. .8195 31-1 300 12. 70 0.847 0. 0292 2. ,9353 32- 1 420 12. 70 0.801 0. 0280 3. 0159 1.25 mm. D_ = 156 mm U IT) uaH m (m/s) (m/s ) (m/s) (m/s ) 0.9353 7.60 9 .00 0 .702 0.70 0.9501 7.74 8 .76 0 .705 0.69 0.9559 7.95 8 .44 0 .666 0.65 0.9599 8.09 9 0 .634 0.57 0.9351 7.64 9 .03 0 .702 0.70 0.S480 8.04 8 .47 0, .705 0.69 0.9556 8.01 8. .69 0. .666 0.65 0.9597 8. 16 10. .61 0. 634 0.57 0.9364 7.47 10. 72 0. 701 0.70 0.9513 7.56 8. . 16 0. 705 0.69 0.9561 7 .89 6. 26 0. 665 0.65 0.9602 8.04 7 . 72 0. 633 0.57 o 81 0.75 0.70 o > fc 0.65 0.60 0.55 0 u m f 156 mm 1.250 mm 100 200 300 T S (deg C) 400 F i g u r e 4.11 E f f e c t of t e m p e r a t u r e on u m f and U a H Sand, d p = i.25 mm, D c = 156 mm 82 4.12a shows that ^sHm a P P r o a c n e s U c at h i g h temperatures and e v e n t u a l l y becomes smal l e r than U c. T h i s means that as temperatures i n c r e a s e s , the choking of the spout begins to overtake annular f l u i d i z a t i o n as the c o n t r o l l i n g f a c t o r . These r e s u l t s are c o n s i s t e n t with experimental o b s e r v a t i o n s ( S e c t i o n 4.1.2). F i g u r e s 4.12b and 4.12c, however, do not show the same c o n c l u s i o n . In these two cases, u s H m w a s f° u n <3 to be g r e a t e r than U c even at high temperatures. The i n c o n s i s t e n c y i s probably due to the f a c t that U s H ^ i s very s e n s i t i v e to the value of D q H . A small change i n D q u can m m cause s i g n i f i c a n t v a r i a t i o n i n U s H . A d d i t i o n a l d i s c r e p a n c y may a l s o be a t t r i b u t e d to the inexactness of Equations 4.3 and 4.4. An a l t e r n a t e way to i n t e r p r e t the r e s u l t s i s to examine the r a t i o s of D^/dp. These values are 10.2, 15.2 and 21.3, r e s p e c t i v e l y , i n F i g u r e s 4.12a, 4.12b and 4.12c. I t appears that the choking of the spout at high temperatures only occurs at a low value of D^/dp as shown in F i g u r e 4.12a. At higher r a t i o s , spout t e r m i n a t i o n (at high temperatures) may be due to the growth of i n s t a b i l i t y at the spout-annulus i n t e r f a c e . T h i s procedure of Chandnani and E p s t e i n (1986) r e q u i r e s a c c u r a t e v a l u e s of DcT_i in order to y i e l d reasonable b nm e s t i m a t e s of H m f o r cases where choking i s the t e r m i n a t i o n mechanism. Unless there i s a way of a c c u r a t e l y determining D s H without conducting an a c t u a l experiment, i t i s not very u s e f u l f o r design purposes. 83 F i g u r e 4.12a E f f e c t o f t e m p e r a t u r e on U c and u"sH m Sand, dp = 1.25 mm, D c = 156 mm, V± = 12.70 mm 84 12 Dc I ! 1 : r — = 156 mm 11 D| = 19.05 mm dP = 1.250 mm (in/ 10 — >•> / o o — ra Veloi y U s H m j — • 8 — u Flui 7 • *" 6 C I I 1 ) 100 200 300 T S (deg C) 400 F i g u r e 4.12b E f f e c t of t e m p e r a t u r e on U c and u s H m Sand, dp = 1.25 mm, D c = 156 mm, = 19.05 mm / 85 12 11 ~ cn o O i — * > TJ • i—t 10 9 B 6 Di = 156 mm 26.64 mm 1.250 mm - Q. m •--a— U, 0 100 200 300 T S (deg C) 400 F i g u r e 4 . 1 2 c E f f e c t o f t e m p e r a t u r e on U c and U s H m S a n d , d D = 1.25 mm, D c = 156 mm, = 2 6 . 6 4 mm 5. MINIMUM SPOUTING VELOC ITY AND OVERALL BED PRESSURE DROP 5.1 MINIMUM SPOUTING VELOCITY Minimum spouting v e l o c i t i e s were measured using the method d e s c r i b e d i n S e c t i o n 3.7.3. U m s appeared to be more d i f f i c u l t to o b t a i n at high temperatures. The main reason was that even a small adjustment of the flowmeter could amount to a s i g n i f i c a n t change i n the v o l u m e t r i c flowrate fo r a higher temperature c o n d i t i o n because of the smaller f l u i d d e n s i t y . Thus, when measuring the a i r f l o w r a t e s at higher temperatures, the s m a l l e r flowmeter (see F i g u r e 3.4) was employed to y i e l d a b e t t e r p r e c i s i o n . Tables 5.1a, 5.1b, 5.1c and 5.1d l i s t a l l the experimental c o n d i t i o n s and the corresponding r e s u l t s f o r U m s . 5.1.1 EFFECT OF PARTICLE AND ORIFICE DIAMETERS The e f f e c t s of dp and D^ on U m s are shown in F i g u r e s 5.1 and 5.2, r e s p e c t i v e l y . At room c o n d i t i o n s , f o r any given bed h e i g h t s , the values of U m s are higher f o r bigger p a r t i c l e s and l a r g e r o r i f i c e openings. The same trends a l s o occur at high temperatures (420 °C). These o b s e r v a t i o n s 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 Equation 2.1. 86 Table 5.1a Minimum spouting ve l o c i t y . experimental versus prediction (T - 2 0 'C) . Sand, D * 15G mm and p - 2600 kg/m Run # d p. (mm) D 1 (mm) H m (m) H (m) (kg/m3) u ^* ms (m/s) ms (m/s) Eq. 2 .1 % dev ms (m/s) Eq. 5.2 % dev 1-1 0. .945 19. 05 1. . 168 1 . 16B 1. .246 0. .830 0. .659 -20 .6 0 .832 0.2 1-2 0 .945 19. 05 1. . 16B 0, .889 1 .233 0, .685 0, .57B -15 .6 0 .739 7.8 1-3 0. .945 19. 05 1 . 168 0, .578 1 .220 O, .643 0 .469 -27 . 1 0 .612 -4.7 5-1 1 .250 19. 05 1, .067 1 , .067 1 .259 1. . 100 0, .829 -24 .6 1 .065 -3.1 5-2 1 .250 19. .05 1, .067 0, .803 1 .238 0. .876 0, .726 -17 . 1 0 .943 7 . 8 5-3 1. .250 19. 05 1, .067 0. .518 1 .222 0. .782 0. .586 -25 .0 0. .779 -0.4 9-1 1 .665 19. 05 1, .010 1. .010 1 .244 1. .314 1 . .081 -17 .7 1, .404 6.9 9-2 1 .665 19. 05 1, .010 0. .730 1 .231 1. , 122 0. .924 -17 .7 1. .220 8.7 9-3 1 .665 19. 05 1, .010 0, .502 1 .218 0. .960 0. .770 -19 .8' 1. .035 7 . 8 17-1 1 .250 26. 64 1 .026 1. .026 1 .252 1. . 108 0. .912 -17 .7 1, . 129 1 .9 17-2 1 .250 26. 64 1 .026 0 .832 1 .241 0. .957 0, .825 -13 .8 1, .031 7 . 8 17-3 1 .250 26. 64 1 .026 0, .521 1 .221 0. .851 0, .65B -22 .7 0, .841 -1.1 21-1 1 .665 26. .64 0 .978 0, .978 1 .254 1. ,497 1. . 185 -20, .9 1. .488 -0.6 21-2 1 .665 26. ,64 0 .978 0, .632 1 .242 1. .300 1. .098 -15 .6 1, .388 6 . 8 21-3 1 .665 26. 64 0 .978 0, .559 1 .223 1. . 138 0. .907 -20 .3 1. . 169 2.7 25-1 0 .945 12. 70 1 .372 1. .372 1 .276 0. ,906 0. .617 -32. .0 0. .811 -10.5 25-2 0 .945 12. 70 1, .372 1. . 118 1 .252 0. 763 0. .562 -26. .3 0. ,745 -2.3 25-3 0 .945 12. ,70 1 .372 0, .727 1 .229 o. ,620 0. .457 -26 .2 0. .618 -0.3 29-1 1 .250 12. ,70 1 .276 1 .276 1 .261 1. , 153 0. .792 -31 .4 1. ,054 -8.6 29-2 1 .250 12. ,70 1 .276 0, .946 1 .242 0. .974 0. .687 -29 .5 0. 927 -4.9 29-3 1 .250 12. ,70 1 .276 0. .635 1 .226 0. B34 0. .566 -32. . 1 0. .779 -6.5 33-1 1 .665 12. ,70 1 .029 1 .029 1 .245 1. 383 0. .953 -31 . 1 1. ,294 -6.4 33-2 1 .665 12. ,70 1 .029 0, .762 1 .230 1. ies 0. ,825 -30. .4 1. 136 -4 . 1 33-3 1 .665 12. 70 1 .029 0, .533 1 .216 1. 026 0. .694 -32 , .3 0. 973 -5. 1 5-4 1 .250 19 . ,05 1 .073 1, .073 1 .259 1. 04 5 0. ,832 -20. .4 1. 068 2.2 5-5 1 .250 19 . ,05 1 .073 1 . 0 1 0 1 .254 0. 998 0 , . BOB -19. .0 1. 041 4 . 3 5 -6 1 .250 19 . ,05 1 .073 0 .813 1 .238 0. 873 0 . ,730 -16. . 4 0 . 948 8.6 5-7 1 .250 19 . ,05 1 .073 0 .597 1 .227 0. 831 0 , . 62B -24. .4 0 . 829 -0.2 5-B 1 .250 19. ,05 1 .073 0 . 444 1 .217 0. 750 0 . . 544 -27. .5 0. 729 -2.9 5-9 1 .250 19 . 05 1 .073 0 .279 1 .209 0. 670 0 , .433 -35. , 4 0 . 594 -11.3 37-1 1 .250 19 . ,05 1 .380 1 . 380 0 .707 1 . 537 1. ,258 - 18 . , 1 1. 394 -9.3 37-2 1 .250 19. 05 1 .380 1 .067 0 .695 1. 4 54 1. 1 16 -23. . 2 1. 250 -14.0 37-3 1 .250 19 . 05 1 .380 0 .705 0 .683 1. 168 0 . 915 -21 . ,7 1. 04 5 -10.6 37-4 1 .250 19 . ,05 1 .380 0 .254 0 .670 0. e 5 5 0 , , 5 5 5 -35. . 1 0 . 6 6 8 -21.9 38- 1 1 .250 19 . 05 0 .533 0 . 533 0 . 170 1. 362 1 . ,596 17 . , 2 1. 342 -1.5 38-2 1 .250 19 . 05 0 .533 0 .403 0 . 169 1. 178 1. .392 18 . 2 1. 187 0.8 38-3 1 .250 19 . 05 0 .533 0 .273 0 . 168 1. 04 3 1. 149 10. , 1 1. OOO -4.2 OD —1 experimental value Table 5.1b Minimum spouting velocity, experimental versus prediction (T $ = 170 C) / 3 Sand, D_ * 15G mm and p * 2600 kg/m Run D i H U * ms ms E Q . 2 . 1 Ums b V Eq. 5.2 tl (mm) (mm) (m) (m) (kg/m3) (m/s) (m/s) % dev (m/s) % dev 2-1 0 .945 19. .05 0.41S 0. 419 0, .802 -o. 576 0. .492 -14 .5 0 .594 3.2 2-2 0 .945 19 .05 0.419 0. 292 0 .799 0. 548 0. .412 -24 .8 0 .507 -7 .5 2-3 0 .945 19 .05 0.419 0. 203 0, .797 0. ,415 0. .344 -17 . 1 0 .432 4 . 1 6-1 1 .250 19. .05 0.64B 0. 648 0, .815 1. O09 0. .803 -20 .4 0 .960 -4.9 6-2 1 .250 19 .05 0.648 0. 451 0, .806 O. 868 0. .674 -22 .4 0 .B19 -5.6 6-3 1 .250 19. .05 0.648 0. 292 0. .801 0. ,731 0. .544 -25. .6 0 .677 -7.4 10-1 1 .665 19 .05 0.800 0. 800 0, .824 1 . 263 1. . 182 -6, .4 1 .415 12.0 10-2 1 .665 19. .05 0.800 0. 597 0. .814 1. 157 1. ,027 -11 , .2 1 .247 7.7 10-3 1 .665 19. .05 0.800 0. 400 0 .805 1 . 034 0. .846 -18 , .2 1 , .047 1 .2 18-1 1 .250 26. .64 0.705 0. 705 0, .816 1. .048 0. .936 -10 .6 1 , .073 2.4 18-^ 2 1 .250 26. .64 0.705 0. .568 0 .809 0. 951 0. .844 -11, .2 0, .977 2.B 18-3 1 .250 26 .64 0.705 0. .356 0, .802 0. 824 0. .671 -18, .5 0, .796 -3.4 22-1 1 .665 26 .64 0.838 0. 838 0, .822 1 . 567 1. .355 -13, .5 1. .557 -0.6 22-2 1 .665 26 .64 0.838 0. 625 0, .813 1. 319 1. . 177 -10, .8 1. .371 4 .O 22-3 1 .665 26 .64 0.838 0. 422 0 .805 1. 177 0. .972 -17. .4 1, , 155 -1 .8 26-1 0 .945 12, .70 0.724 0. ,724 0, .814 0. 600 0. ,561 -6. .5 0. .690 14 .9 26-2 0 .945 12, .70 0.724 0. ,549 0 .807 0. 532 0. 491 -7 . 8 0. ,611 14 .9 26-3 0 .945 12 .70 0.724 0. 356 0 .801 0. 452 0. .396 -12. .3 0. .505 11 .B 30-1 1 .250 12 .70 0.781 0. .781 0 .818 0. 959 0. .769 -19, .8 0. 952 -0.7 30-2 1 .250 • 12 .70 0.781 0. .565 0 .809 . 0. 797 0. .658 -17. .4 0. B27 3.8 30-3 1 .250 12 .70 0.781 0. ,387 0. .801 0. 674 0. ,547 -18. .8 0. ,701 4 . 1 34-1 1 .665 12 .70 0.832 0. .832 0 .820 1. 569 1. ,056 -32. .7 1. ,318 -16.0 34-2 1 .665 12 .70 0.832 0. ,619 0 .810 1. 305 0. ,916 -29. .8 1. , 160 -11.1 34-3 1 .665 12 .70 0.832 0. ,406 0 .802 1. 056 0. .746 -29. .3 0. 965 -B.6 6-4 1 .250 19 .05 0.648 0. .648 0 .813 0. 978 0. 804 - 17 . 8 0. 960 -1.8 6-5 1 .250 19 .05 0.648 0. .464 0 .806 0. 860 0, ,683 -20. .6 0. ,630 -3.6 6-6 1 .250 19 .05 0.648 0. ,267 0 .799 0. 689 0. ,520 -24 , .5 0. 651 -5.6 * experimental value oo Co Table 5.1c Minimum spouting velocity, experimental versus prediction (T 5 = 300 'O SBnd, D * 156 mm and P = 2S00 kg/m Run D 1 Hm H U * ms ums fay Eq. 2 . 1 ms ' Eq. 5.2 (mm) (mm) (m) (m) (kg/m3) (m/s) (m/s) % dev (m/s) %. dev 7-1 1 .250 19.05 0.546 0.546 0 .624 0. .931 0. .843 -9 .5 0 .956 2.6 7-2 1 .250 19.05 0.546 0.413 0 .621 0, .875 0. .734 -16 . 1 0 .645 -3.4 7-3 1 .250 19.05 0.546 0.279 0. .618 0. .773 0. .606 -21 .7 0 .712 -B.0 11-1 1 .665 19.05 0.721 0.721 0 .629 1 . 348 1. .284 -4 .7 1 .452 7.8 11-2 1 .665 19.05 0.721 0.521 0 .624 1 . 159 1 . 096 -5 .4 1 .260 8.7 11-3 1 .665 19.05 0.721 0.359 0. .620 0. .991 0. .912 -7 .9 1 .070 B.O 19-1 1 .250 26.64 0.419 0.419 0. .623 0. .949 0. .826 -12 .9 0 .916 -3.5 19-2 1 .250 26.64 0.419 0.324 0 .620 0. 896 0. 72B -18, .7 0 .818 -8.7 19-3 1 .250 26.64 0.419 0.219 0. .617 0. .782 0. 600 -23 .3 0 .68B -12.0 23-1 1 .665 26.64 0.679 0.679 0. .631 1. 528 1. ,392 -B, .8 1 .523 -0.3 23-2 1 .665 26.64 0.679 0.508 0. .625 1. 307 1. ,209 -7 , .4 1 .342 2.7 23-3 1 .665 26.64 0.679 0.343 0. .620 1. . 166 0. ,998 -14 , .4 1, . 130 -3. 1 27-1 0 .945 12.70 0.635 0.635 0. .622 0. .581 •0. 601 3 .5 0 .699 20.4 27-2 0 .945 12.70 0.635 0.476 0. .620 0. .495 0. ,521 5. .3 0 .616 24 .5 27-3 0 .945 12.70 0.635 0.311 0. .618 0. 451 0. 422 -6 . 4 0, .51 1 13.2 31-1 1 .250 12.70 0.654 0.654 0. .629 0. 847 0. 803 -5. .3 0, .945 11.5 31-2 1 .250 12.70 0.654 0.495 0. .623 0. .736 0. 702 -4 , .7 0 . B37 13.7 31-3 1 .250 12.70 0.654 0.311 0. .618 0. .580 0. 558 -3 , B 0, .683 17 .6 35-1 1 .665 12.70 0.743 0.743 0. .630 1. 403 1. 139 - 18. .8 1, .346 -4 . 1 35-2 1 .665 12.70 0.743 0.543 0. .625 1. 178 0. 977 -17 . 1 1, . 173 -0.5 35-3 1 .665 12.70 ' 0.743 0.365 0. .619 1. 010 0. 805 -20, .3 0, .986 -2.4 7-4 1 .250 19.05 0.546 0.546 0. .626 0. 892 0. 84 1 -5. .6 0. .955 7 . 1 7-5 1 .250 19.05 0.546 0.413 0. .622 0. 852 0. 734 -13. ,8 0, ,845 -0.8 7-6 1 .250 19.05 0.546 0.311 0. .619 0. 787 0. 639 - 18 . B 0, ,746 -5.2 7-7 1 .250 19.05 0.546 0.267 0. .61B 0. 740 0. 592 -20. .0 0. , G97 -5.8 * experimental value Table 5. Id Minimum spouting v e l o c i t y , experimental versus prediction (T_ = 420 "'C). Sand, D •= 155 mm and p * 2600 kg/m Run dP (mm) D 1 (mm) H m (m) H (m) (kg/m3) U * ms (m/s) (m/s) Eq. 2.1 % dev um „ by s ' (m/s) Eq. 5.2 % dev 8-1 1.250 19.05 0.413 0.413 0. .514 0. 871 0 .807 -7 .3 0 .B89 2. 1 8-2 1.250 19.05 0.413 0.267 0. .511 0. B13 0 .651 -19 .9 0 .734 -9.7 8-3 1.250 19.05 0.413 0.206 0. .510 0. 670 0 .573 -14 .4 0 .655 -2. 1 12-1 1.665 19.05 0.629 0.629 0. .515 1 . 311 1. .326 1 . 1 1. .443 10.0 12-2 1.665 19.05 0.629 0.457 0. .512 1 . 235 1. . 134 -B .2 1, .254 1 .5 12-3 1.665 19.05 0.629 0.305 0. .510 1 . 001 0. .928 -7 .3 1. .049 4.8 20-1 1.250 26.64 0.343 0.343 0. .511 0. 947 0, .826 -12 .8 0. . 8B4 -6.6 20-2 1.250 26.64 0.343 0.241 0. .510 0. 843 0 .693 -17 .8 0. .756 -10.3 20-3 1.250 26.64 0.343 0.16B 0. .509 0. 695 0, .579 -16 .7 0. .645 -7.2 24-1 1.665 26.64 0.540 0.540 0. .517 1. 473 1. .371 -7 .0 1. .450 -1.6 24-2 1.665 26.64 0.540 0.406 0. .513 1. 322 1, . 194 -9 .7 • 1. .282 -3. 1 24-3 1.665 26.64 0.540 0.254 0. .511 1. 147 0. .946 -17 .5 1. .042 -9.2 2B-1 0.945 12.70 0.486 0.486 0. .511 0. 573 0, .580 1 .2 0. .655 14 .3 28-2 0.945 12.70 0.486 0.362 0. .510 0. 516 0. .501 -3 .0 0. .575 11.3 28-3 0.945 12.70 0.486 0.229 0. .509 0. 419 0. .399 -4 . B 0. 469 12.0 32-1 1.250 12.70 0.533 0.533 0. .515 0. 801 0. .801 -0 .0 0. .911 13.7 32-2 1.250 12.70 0.533 0.400 0. .513 0. 707 0. .695 -1 .7 0. .802 13.5 32-3 1.250 12.70 0.533 0.232 0. .510 0. 559 0. .531 -5 . 1 0. 631 12.B 36-1 1.665 12.70 0.654 0.654 0. .519 1. 321 1, . 176 -10 .9 1. 339 1 .4 36-2 1.665 12.70 0.654 0.486 0. .515 1. 131 1. .018 -10 .0 1. 176 4.0 36-3 1.665 12.70 0.654 0.311 0. .511 0. 952 0. .818 -14 .0 0. 967 1 .6 8-4 1.250 19.05 0.413 0.413 0, .514 0. 860 0, .807 -6 . 1 0. 889 3.4 8-5 1.250 19.05 0.413 0.270 0. .511 0. 801 0. .655 -18 .2 . 0. 738 -7.9 * ex p e r i m e n t a l v a l u e 91 1.250 D O 0.945 • O 0 0.4 0.8 1.2 1.6 Bed Height (m) F i g u r e 5.1 E f f e c t of p a r t i c l e d i a m e t e r on U m s 1.6 1.2 O.fl 0.4 0 dn -1 156 mm 1.665 mm D i (mm) 20°C 420°C 26.64 • • 19.05 O 12.70 • O 0.4 0.8 1.2 Bed Height (m) F i g u r e 5.2 E f f e c t o f o r i f i c e d i a m e t e r on U ms 93 5.1.2 EFFECT OF TEMPERATURE F i g u r e 5.3 i l l u s t r a t e s the e f f e c t of bed temperatures on U m s f o r a f i x e d p a r t i c l e s i z e and o r i f i c e diameter. Though there i s some o v e r l a p p i n g among the data p o i n t s , t h i s f i g u r e g e n e r a l l y i n d i c a t e s that f o r a given bed h e i g h t , U m s i n c r e a s e s with i n c r e a s i n g temperature as p r e d i c t e d by Equation 2.1. Supporting evidence i s a l s o given i n F i g u r e s 5.1 and 5.2. 5.1.3 DATA CORRELATION Experimental values of U m s were compared with the values c a l c u l a t e d by Equation 2.1. For a i r spouting at room temperature, Equation 2.1 und e r p r e d i c t e d U m s by about 30% fo r the s m a l l e s t o r i f i c e diameter (Table 5.1a). The d e v i a t i o n decreased to around 20% f o r the l a r g e s t D^. T h i s equation appeared to work b e t t e r with i n c r e a s i n g temperature (Tables 5.1b, 5.1c and 5.1d). Equation 2.1 r e p o r t e d l y g i v e s good p r e d i c t i o n s of U m s at room c o n d i t i o n s but not i n the present case. One p o s s i b l e e x p l a n a t i o n may be the inadequate knowledge of how to s p e c i f y dp f o r use i n Equation 2.1 in the case of n o n - s p h e r i c a l p a r t i c l e s . Using Equation 2.1 as a base, assuming Pp >> p+r while dp, D c and D^ are f i x e d , the e f f e c t of H/p^ on U m s can be examined. F i g u r e 5.4 i l l u s t r a t e s a t y p i c a l example. For t h i s 94 1.2 in 13 0.8 cn 0.6 0.4 0 A • X 20 dag C 170 deg C 300 dag C 420 dag C A A • • a, A x + + + D c = 156 mm Dj = 19.05 mm d„ = 1.25 mm 0.2 0.4 0.6 0.8 1 Bed Height (m) 1.2 F i g u r e 5.3 E f f e c t of bed t e m p e r a t u r e on U ms 95 10 CO § . . 1-1 CO a 0.1 o A + X o V 0.1 Air at 20 deg C Air at 170 deg C Air at 300 deg C Air at 420 deg C C H 4 at 20 deg C He at 20 deg C i i i i i i I i H / P f (m 4 /kg) I I I I I I I 10 F i g u r e 5.4 E f f e c t of H/p<: on U m s . Sand, dp = 1.25 mm, = 19.05 mm, D c = 156 mm and p p = 2600 kg/m The s o l i d l i n e i n d i c a t e s t h e b e s t f i t . 96 p l o t , a l e a s t squares f i t produced a slope of 0.33. The slopes f o r other c o n d i t i o n s were a l s o c a l c u l a t e d (Table 5.2). Although the experimental data d i d not always f i t w e l l , there was a c l e a r i n d i c a t i o n t h a t the slope (based on t h i s work) was l e s s than 0.50 ( i . e . , the value i n Equation 2.1). Manurung (1964) has repo r t e d s i m i l a r f i n d i n g s . He noted that Equation 2.1 overestimates the e f f e c t of bed height on U m s . The e f f e c t s of dp and were not i n v e s t i g a t e d i n d i v i d u a l l y because H/pj was not f i x e d . However, i t was p o s s i b l e to f i t the experimental data to the f o l l o w i n g e x p r e s s i o n : Ums = K (2gH) co . Pi . 5.1 where K, a, r, co and £ were found by a p p l y i n g the l e a s t squares method to experimental data. In t h i s case, H and (pp-pf)/pf were t r e a t e d as two separate v a r i a b l e s . The best f i t r e s u l t e d when K, a, T, CO and £ were equal to 8.452, 1.038, 0.2213, 0.4437 and 0.2688 r e s p e c t i v e l y . Based on these r e s u l t s , the e f f e c t s of dp, , H and ( p p - p f ) / p f on U m s have not been adequately d e s c r i b e d by Equation 2.1. Moreover, the values of co and £ are q u i t e d i f f e r e n t from each other, i n d i c a t i n g t h a t H and ( P p - P f ) / P f should not be grouped as one s i n g l e parameter. The c a l c u l a t e d values of U m s from t h i s c u r v e - f i t model are t a b u l a t e d a l o n g s i d e those 97 T a b l e 5.2 S l o p e s of U m s v e r s u s (H/p f) p l o t a t d i f f e r e n t c o n d i t i o n s . Sand, p p = 2600 kg/m 3 and D_ - 156 mm dp D i S l o p e of l n ( U m s ) (mm) (mm) v e r s u s l n ( H / p f ) 0.945 12.70 0.54 0.945 19.05 0.48 1.250 12.70 0.44 1.250 19.05 0.33 ** 1.250 26.64 0.38 1.665 12.70 0.35 1.665 19.05 0.33 1.665 26.64 0.37 ** see F i g u r e 5.4 98 by Equation 2.1 i n T a b l e s 5.1a, 5.1b, 5.1c and 5.1d. More curve f i t t i n g s were done by f o r c i n g some of the c o e f f i c i e n t s i n Equation 5.1 to equal those i n Equation 2.1. The r e s u l t s are summarized i n Table 5.3, with the best f i t i d e n t i f i e d as I . F i r s t of a l l , there i s some t h e o r e t i c a l j u s t i f i c a t i o n to assume (o = 0.5 (Ghosh, 1965). The r e s u l t i n g e x p r e s s i o n ( c u r v e - f i t I I ) i s d i m e n s i o n a l l y c o n s i s t e n t . Based on the value s i n the f i r s t two c u r v e - f i t s , a i s not very d i f f e r e n t from u n i t y and i t i s t h e r e f o r e set to 1.0 i n a d d i t i o n t o making a; = 0.5 i n c u r v e - f i t I I I . F i n a l l y , r e s u l t s from III suggest that i t i s reasonable to take r as 1/3. With CJ = 0.5, a = 1.0 and r = 1/3, a l e a s t squares f i t produces IV. Equation 2.1 i s a l s o i n c l u d e d i n t h i s t a b l e f o r comparison. The second, t h i r d and f o u r t h c u r v e - f i t s are b a r e l y worse than the f i r s t one but Equation 2.1 i s c l e a r l y i n f e r i o r . I f one assumes that Equation 2.1 c o r r e c t l y p r e d i c t s the q u a n t i t a t i v e e f f e c t s of dp, and H on U m s , c u r v e - f i t IV w i l l be recommended over the other t h r e e . 5.2 OVERALL BED PRESSURE DROP Tables 5.4a, 5.4b, 5.4c and 5.4d summarize a l l the experimental c o n d i t i o n s and the cor r e s p o n d i n g values of -AP S. These experimental values of -AP S were obtained u s i n g the method o u t l i n e d i n S e c t i o n 3.7.2. When measuring U m s , i t was n o t i c e d that ~AP S d i d not change s i g n i f i c a n t l y with Table 5.3 Comparison between various versions of Equation 5.1 AVE RMS Curve-F1t K e T u e ERR (%) % ERR I(EXP-CAL) 2 I 8. .452 1 .038 0. .2213 0. .4437 0. .2688 1 .04 8.31 0.610 II 5. .694 1 .008 0. .2854 0. .5000* 0. ,3004 0.78 8.49 0.686 I I I 6 .208 1 .000* 0. .3343 0. .5000* O. 2979 0.65 8 .44 0.749 IV 6 .665 1 .000* 0. .3333* 0. .5000* 0. .2890 0.71 8 .45 0.751 Eq. 2.1 1 . 000 1 .000 0. .3333 0. .5000 0. 5000 -15. 14 18.31 3.823 EXP •= experimantal value CAL = c a l c u l a t e d value Exponent f i x e d at t h i s value Table 5.4B Overall pressure drop. experimental data and p r e d i c t i o n Dy E o u a t i o n 2 . 28 (T = 2 0 ' C ) SBnd. = 156 mm and P p = 2600 kg/m 3 Run H H/H ' m d p D . l H Cm) (mm) (cm) 1-1 1. 16B 1 , .000 0.945 1 .905 1-2 0. 8B9 0, .761 0.945 1 .905 1-3 0. 578 0, .495 0.945 1 .905 5-1 1. 067 1, .000 1 .250 1 .905 5-2 0. 803 0. .753 1 .250 1 .905 5-3 0. 518 0 .485 1.250 1 .905 9-1 1. 010 1. .OOO 1 .665 1 .905 9-2 0. 730 0. .723 1 .665 1 .905 9-3 0. 502 0. .497 1.665 1 .905 17-1 1. 026 1. .000 1.250 2 .664 17-2 o. 832 0. .811 1.250 2 .664 17-3 0. 521 0. .508 1.250 2 .664 2-1-1 0. 978 1. .000 1 .665 2 .664 21-2 0. 832 0. .851 1 .665 2 .664 21-3 0. 559 0, .572 1.665 2 .664 25-1 1. 372 1, .000 0.945 1 .270 25-2 1. 118 0, .815 0.945 1 .270 25-3 0. 727 0. .530 0.945 1 .270 29-1 1. 276 1, .000 1 .250 1 .270 29-2 0. 946 0 .741 1.250 1 .270 29-3 0. 635 0 .498 1 .250 1 .270 33-1 1. 029 1 .000 1 .665 1 .270 33-2 0. 762 0 .741 1 .665 1 .270 33-3 0. 533 0 .518 1 .665 1 .270 5-4 1. 073 1 .000 1 .250 1 .905 5-5 1. 010 0 .941 1 .250 1 .905 5-6 0. 813 0 .758 1 .250 1 .905 5-7 0. 597 0 .556 1 .250 1 .905 5-8 0. 444 0 .414 1 .250 1 .905 5-9 0. 279 0 .260 1 .250 1 .905 37-1 1. 380 1 . OOO 1 .250 1 .905 37-2 1. 067 0 .773 1 .250 1 .905 37-3 0. 705 0 .511 1 .250 1 .905 37-4 0. 254 0 . 184 1 .250 1 .905 38-1 0. 533 1 .000 1 . 250 1 .905 38-2 0. 403 0 .756 1 .250 1 .905 38-3 0. 273 0 .512 1 .250 1 .905 s s (ki\l/m2) (kN/m2) dev 7 .80 10 .64 36 .45 5 .67 7 . 10 25 .21 3 .44 3 .44 -0 . 12 10 .01 9 .51 -4 .99 6 .49 6 . 16 -4 .98 3 .82 2 .86 -25 .29 7 .46 8 .81 18 .20 5 .27 5 .28 0 .08 3 . 11 2 .66 -14 .40 8 .66 9. . 14 3 .21 6 .95 6 .68 . -3. .86 3 .60 2 .99 -17 . 1 1 9, .24 8. .53 -7 .68 7 . 24 6. .67 -7 . 86 3 . 97 3 . 36 -15 . .36 12 .98 12. .49 -3 . 82 B. .90 9 . 26 4 . 05 5 . 03 4 . 56 -9 . 46 10. .43 11 . 37 B . 98 7 . 20 7 . 19 -0. . 11 4 . 52 3. .58 -20. 88 7 . 75 B . 98 15 . 79 5 . 20 5. .60 7 . 64 2, .78 2. .94 5. .71 9 . 97 9 . 56 -4 . 05 9 . 24 B . 76 -5 . 23 6 . 52 6 . 27 -3 . 69 6 . 61 3 _ .69 - 19 . 91 2 . S5 2. 12 -28 . 05 1 . .57 0. B4 -46 . 27 12 . 77 12 . 12 -5 . 13 B . 90 B . 15 - e . 49 5 . 37 3 _ 90 -27 . 35 1 . .29 0. 48 -62 . 51 6 .  14 £ . 99 20. 47 2 . 95 3 . 34 13 . 1 1 1 . 72 1 . 78 3 . 93 o o * experimental value P calculated value Table 5.4b Overall pressure d r o p , experimental data and p r e d i c t i o n by Equation 2.28 (~5 Sand. D c 156 mm Bnd /> «= 2600 kg/m Run H H (m) H/H IT) d P (mm) D1 (cm) (kN/m2) (kN/m2) dev 2-1 0, .41S 1.000 0 .945 1 .905 2 . 12 3 .90 B4 . 16 2-2 0 .232 0.697 0 .945 1 .905 1 , .43 2 .29 60.57 2-3 0, .203 0.484 0 .945 1 .905 0 .89 1 .25 40.78 6-1 0. .648 1 .OOO 1 .250 1 .905 5. .41 5 .91 9.21 6-2 0. .451 0.696 1 .250 1 .905 3, .26 3 .43 4 .98 6-3 0. .292 0.451 1 .250 1 .905 1. .88 1 .62 -13.78 10-1 0 .800 1 .000 1 .665 1 .905 7. .77 • 7 . 14 -8. 13 10-2 0. .597 0.746 1 .665 1 .905 5 .27 ,4 .57 -••.3.33 10-3 0. .400 0.500 1 .665 1 .905 2. .99 2 .27 -24.09 18-1 0, .705 1.000 1 .250 2 .664 5. .67 6 .43 13.47 18-2 0 .568 0.B06 1 .250 2 .664 4 , .06 4 .69 15.72 18-3 0. .356 0.505 1 .250 2 .664 2. . 12 2 . 16 2.14 22-1 0. .838 1.000 1 .665 2 .664 7 . 33 7 .48 2.05 22-2 0 .625 0.746 1 .665 2 .664 5. .06 4 .78 -5.47 22-3 0. .422 0.504 1 .665 2 .664 2. .95 2 .41 - 18.25 26-1 0. .724 1.000 0 .945 1 .270 5. .33 6 .73 26.30 26-2 0. .549 0.758 0 .945 1 .270 3. .59 4 .51 25.75 26-3 0 .356 0.492 0 .945 1 .270 1 . 87 2 .22 1B .95 30-1 0 .781 1.000 1 .250 1 .270 6. . 18 7 . 13 15.30 30-2 0 .565 0.723 1 .250 1 .270 3. .97 4 .39 10.67 30-3 0 .387 0.496 1 .250 1 .270 2. .01 2 .32 14 .97 34-1 0 .832 1 .000 1 .665 1 .270 6 . 82 7 .43 8 .92 34-2 0 .619 0.744 1 .665 1 .270 4 . 35 4. .73 8 .66 34-3 0 .406 0.488 1 .665 1 .270 2. .23 2 .26 1 .46 6-4 0 .648 1 .000 1 .250 1 .905 5. . 12 5 .91 15.58 6-5 0 .464 0.716 1 .250 1 .905 3 . ,25 3 .59 10.47 6-6 0 .267 0.412 1 .250 1 .905 1 . 42 1 .37 -3 .06 * experimental value P c a l c u l a t e d value Table 5.4c Overall pressure drop. experimental date and p r e d i c t i o n by Equation 2.28 (Tj. = 300 'C) Sand, D c « 156 mm and 2600 kg/ 3 . m Run H m V D1 - % H (m) (mm) (cm) (kN/m2) (kN/m2) dev 7-1 0 .546 1. OOO 1 .250 1 .905 3 .59 5 .06 41 .03 7-2 0. .413 0. ,756 1 .250 1 .905 2 .68 3 .37 25. S2 7-3 0. .279 0. .511 1 .250 1 .905 1 .55 1 .78 14.81 11-1 0. .721 1 . ,000 1 .665 1 .905 5 .22 6 .55 25.41 11-2 O, .521 0. .723 1 .665 1 .905 3 .65 4 .02 9.87 1 1-3 0. .359 0. .498 1 .665 1 .905 2 .32 2 . 13 -8.34 19-1 0. .419 1. .000 1 .250 2 .664 3 .20 3 .88 21 . 17 19-2 0. .324 0. .773 1 .250 2 .664 2 . 14 2 .68 24.97 19-3 0. .219 0. .523 1 .250 2 .664 1 .31 1 .42 8.28 23-1 0 .679 1. .000 1 .665 2 .664 5 .84 6 .16 5.56 23-2 0. .508 0. ,748 1 .665 2 .664 3 .93 4 .00 1 .78 23-3 0. .343 0. ,505 1 .665 2 .664 2 .06 2 .06 -0.05 27-1 0. .635 1. ,000 0 .945 1 .270 2 .99 5 .97 99.50 27-2 0. .476 0. 750 0 .945 1 .270 2 . 13 3 .95 85.22 27-3 0. .311 0. ,490 0 .945 1 .270 1. .44 1 .99 37.86 31-1 0 .654 1. .000 1 .250 1 .270 5 .07 6 .06 19.38 31-2 0. .495 0. ,757 1 .250 1 .270 3 .28 4 .04 23. 17 31-3 0. .311 0. ,476 1 .250 1 . 270 1 .45 1 .88 29.22 35-1 0 .743 1. .000 1 .665 1 .270 5 .33 6 .75 26.56 35-2 0. .543 0. ,731 1 .665 1 .270 3 .80 4 .21 10.91 35-3 0. .365 0. .491 1 .665 1 .270 2 .01 2 . 14 6.69 7-4 0, .546 1. 000 1 .250 1 .905 • 4, . 18 5 .06 20.93 7-5 0. .413 0. ,756 1 .250 1 .905 2 .80 3 .37 20.21 7-6 0. .311 0. ,570 1 .250 1 .905 1 .84 2 . 14 15.86 7-7 0 .267 0. ,489 1 .250 1 .905 1 .51 1 .64 8.78 * experimental value P calculated value o Table 5,4d Overall pressure drop. experimental data and p r e d i c t i o n by Equation 2 . 2B (T = 420 'C) Sand. D c = 156 mm and 'p = 260C Run H H/H m dP-H (m) (mm) 8-1 0 .413 1 .OOO 1 .250 8-2 0 .267 0 .646 1 .250 8-3 0 .206 0 .499 1 .250 12-1 0 .629 1 . 000 1 .665 12-2 0 .457 0 .727 1 .665 12-3 0 .305 0 .485 1 .665 20-1 0 .343 1. .000 1 .250 20-2 0 .241 0, .703 1 .250 20-3 0 . 16B 0 .490 .1 .250 24-1 0 .540 1 .000 1 .665 24-2 0 .406 0 .752 1 .665 24-3 0 .254 0 .470 1 .665 28-1 0 .4B6 1. .000 0 .945 28-2 0 .362 0 .745 0 .945 2B-3 0 .229 0 .471 0 .945 32-1 0 .533 1. .000 1 .250 32-2 0 .4O0 0, .750 1 .250 32-3 0 .232 0, .435 1 .250 38-1 0 .654 1. .000 1 .665 36-2 0 .486 0 .743 1 .665 36-3 0 .311 0 .476 1 .665 8-4 0 .413 1. .000 1 .250 B-5 0 .270 0 .654 1 .250 * experimental value P m3 D i (cm) (kN/m2) (kN/m2) •/. dev 1 .905 2.73 3.86 41 .49 1 .905 1 .42 2.02 42.62 1 .905 1 .04 1.32 27.05 1 .905 2.98 5.78 93.66 1 .905 1 .94 3.60 85.78 1 .905 1 .04 1 .82 74.69 2.664 1 .38 3.21 133.00 2.664 1 .25 1.92 53.48 2.664 0.87 1.06 22.37 2.664 4.01 4.96 23.60 2.664 2.35 3.26 38.46 2 .664 1 .44 1.48 2.71 1 .270 1 .67 4.59 174.85 1 .270 1 .23 3.02 144.53 1 .270 0.85 1.45 70.59 1.270 2.99 4.98 66.49 1.270 2.31 3.29 42.51 1 .270 0.99 1.34 36. 18 1.270 4 .90 6.01 22.43 1 .270 3.08 3.88 25.96 1 .270 1 .50 1.83 21 .86 1 .905 2 .82 3.86 36.78 1 .905 1 .53 2.06 34 .65 lc u l a t e d value o 104 f l o w r a t e s i f U/U m s > 1. T h e r e f o r e , -AP S was a r b i t r a r i l y taken as the value measured at U * 1.05 ums* 5.2.1 EFFECT OF ORIFICE AND PARTICLE DIAMETERS The e f f e c t s of D^ and dp on -AP S are i l l u s t r a t e d i n F i g u r e s 5.5 and 5.6, r e s p e c t i v e l y . The r e s u l t s i n d i c a t e that -AP S does not depend s t r o n g l y on e i t h e r D^ or dp. In a d d i t i o n , the data p o i n t s in these two f i g u r e s tend to suggest that - A P S i s a l s o independent of bed temperature. 5.2.2 EFFECT OF TEMPERATURE The r e s u l t s of _ A P S versus H obtained at d i f f e r e n t temperatures and with d i f f e r e n t spouting gases are shown i n F i g u r e 5.7. A l l the data p o i n t s appear to l i e on the same curve. T h i s means that the bed temperature and gas p r o p e r t i e s have only n e g l i g i b l e e f f e c t s and _ A P S mainly depends on H. 5.2.3 DATA CORRELATION The experimental values of ~AP S were compared with the c a l c u l a t e d values by Equation 2.28 (see Tables 5.4a, 5.4b, 5.4c and 5.4d). -APf i n Equation 2.28 was estimated from (Pp-pf)g(1 - e a ) H . At room temperature, p r e d i c t e d values of -AP S were g e n e r a l l y in good agreement with experimental 105 16 12 CO I 8 0 0 D i (mm) 20°C 420 26.64 • • 19.05 D O 12.70 • o o • D • <>cf 1 D c — 156 mm dp =» 1.665 mm 0.4 0.8 1.2 Bed Height (m) 1.6 F i g u r e 5.5 E f f e c t of o r i f i c e d i a m e t e r on ~AP S 106 16 (mm) 1.665 1 20°C • 1 420°C • l • 12 1.250 O •a 0.945 • o c M 8 • • — cn I 4 — • D D c - 156 mm 0 • O o o 1 1 Dj = 12.70 mm 1 0 0.4 0.8 1.2 1 Bed Height (m) F i g u r e 5.6 E f f e c t of p a r t i c l e d i a m e t e r on - A P S 1 07 16 12 CO B 0 0 • Air at 20 deg C O Air at 170 deg C A Air at 300 deg C O Air at 420 deg C V CHJ at 20 dog C X He at 20 deg C 8 4 • • • D c °= 156 mm Dj = 19.05 mm dp = 1.250 mm 0.4 0.8 12 Bed Height (m) 1.6 F i g u r e 5.7 E f f e c t o f bed t e m p e r a t u r e on - A P S 108 v a l u e s . As temperature i n c r e a s e d , however, Equation 2.28 overestimated - A P S , p a r t i c u l a r l y f o r the s m a l l e s t o r i f i c e . T h i s equation a l s o p r e d i c t s t h at -AP s/-APf i n c r e a s e s s l i g h t l y with temperature at f i x e d H/Hm (Figure 5.8) but t h i s does not agree with the experimental data. In f a c t , i t was found that at a f i x e d bed h e i g h t , the measured value of -AP S at 420 °C was s i m i l a r to that at room temperature (see F i g u r e 5.7) but the values of H/Hm f o r these two cases were q u i t e d i f f e r e n t because of the higher H m i n the l a t t e r case. Equation 2.28 was t h e r e f o r e not s u i t a b l e f o r p r e d i c t i n g -AP S at high temperature. F i g u r e 5.9 shows how Equation 2.28 compares with experimental r e s u l t s . Equation 2.28 was d e r i v e d with the f o l l o w i n g assumpt i o n s : 1- u a H m = umf a n d 2. -dP/dz = ( P p - p f ) ( 1 - e a ) g at H m If the annular s o l i d s are not completely f l u i d i z e d at H m, these assumptions would not apply and some m o d i f i c a t i o n s would be r e q u i r e d . Table 5.5 i l l u s t r a t e s how U a H and (-dP/dz) H v a r i e d as temperature changed. The values of U a H were determined by e x t r a p o l a t i o n of experimental data (see Chapter 7). (-dP/dz) H , on the other hand, was determined nm from the c a l i b r a t i o n curve of (-AP) versus U a. The pressure drop at u a H ^ was d i v i d e d by the v e r t i c a l d i s t a n c e between the two measuring p o i n t s of the s t a t i c pressure probe (Figure 3.6a) to y i e l d the p r e s s u r e g r a d i e n t . There i s 109 F i g u r e 5.8 E f f e c t of 0 and H/H m on ( - A P S ) / ( - A P f ) as p r e d i c t e d by E q u a t i o n 2.28 1 10 F i g u r e 5.9 Comparison between experimental (-AP S) and p r e d i c t i o n by Equation 2.28 T a b l e 5 . 5 Compar i s o n b e t w e e n e x p e r i m e n t a l a n d p r e d i c t e d v a l u e s of U a and - d P / d z a t z = H = H m Dj = 19 . 05 mm a n d d p = 1 . 2 5 mm Run Temp H m U a H m @ u m f * - ( d P / d z ) H @ H m - ( d P / d z ) m # r o (m) ( m / s ) ( m / s ) ( k N / m 3 ) ( k N / m 3 ) 5-4 20 1 .073 0 . 7 0 0 . 7 0 11 .741 1 2 . 7 5 3 6-4 170 0 .648 0 . 6 9 0 .71 1 1 . 3 8 0 1 2 . 7 5 3 7-4 300 0 . 5 4 6 0 . 6 5 0 . 6 ? 9 . 7 3 0 1 2 . 7 5 3 8-4 420 0 .413 0 . 5 7 0 . 6 3 8 . 3 9 7 1 2 . 7 5 3 @ e x p e r i m e n t a l v a l u e * c a l c u l a t e d v a l u e by E q u a t i o n 2.7 ** c a l c u l a t e d v a l u e by ( p. D~Pf ) ( 1 - e a ) g 1 12 strong evidence that with i n c r e a s i n g temperature, assumtions 1 and 2 would f a i l . I f U m f were r e p l a c e d by ^aHm' & would change but i t s e f f e c t would be s m a l l , as shown i n F i g u r e 5.8. Using an experimental r a t h e r than a c a l c u l a t e d value of -APf would show some s l i g h t improvement f o r r e s u l t s at high temperature but at the same time might c r e a t e l a r g e r d e v i a t i o n s f o r those at room c o n d i t i o n s . Hence t h i s kind of m o d i f i c a t i o n i s s t i l l u n s a t i s f a c t o r y . Experimental r e s u l t s i n d i c a t e d that the e f f e c t of temperature on spouted bed pressure drop was not s i g n i f i c a n t . The d i s t r i b u t i o n of data p o i n t s as shown in F i g u r e s 5.7 and 5.9 c o u l d be w e l l d e s c r i b e d by the simpler e x p r e s s i o n of Manurung (1964), -AP S = p bgH/[1+(t/H)] 5.2 where 0.81 (tanfl) 1 - 5 n " [ 12 ] ( D e > D c d p 1 0.78 l J 5.3 and 8 i s the angle of i n t e r n a l f r i c t i o n . I f 4> i s taken as 0.6689 (to be c o n s i s t e n t with the Wen and Yu a p p r o x i m a t i o n s ) , the two extreme val u e s of t which bracket a l l the c o n d i t i o n s of the present experiments are 1.1578 and 0.2343 r e s p e c t i v e l y . P u t t i n g these c o n s t a n t s i n t o Equation 5.2 produced the curves shown in F i g u r e 5.10. Almost a l l the 113 f i g u r e 5.10 O v e r a l l bed p r e s s u r e drop v e r s u s bed h e i g h t The two l i n e s r e p r e s e n t E q u a t i o n 5.2 1 14 data p o i n t s were w e l l w i t h i n these two boundaries. Equation 5.2 can be rearranged to y i e l d the f o l l o w i n g e x p r e s s i o n H = --APS- t" 1 + -- Pb9. H Using the s p e c i f i c value of t which a p p l i e s to each run, a l l the experimental data are r e p l o t t e d as [ ( - A P s ) / ( p b g ) ] [ 1 + ( t / H ) ] versus H i n F i g u r e 5.11. Equation 5.4 i s represented by the 45° s t r a i g h t l i n e through the o r i g i n . Apparently, the f i t i s poor. The reason f o r t h i s c o u l d be the a r b i t r a r y d e f i n i t i o n of t given by Equation 5.3, an e m p i r i c a l c o r r e l a t i o n which may be l i m i t e d i n scope. Although the Manurung equations d i d not compare w e l l with the present data on an a b s o l u t e b a s i s , they d i d show some c o n s i s t e n c y with the experimental o b s e r v a t i o n s , that i s , the e f f e c t s of temperature and f l u i d p r o p e r t i e s on _ A P S were c o r r e c t l y i n d i c a t e d as i n s i g n i f i c a n t . 1 1 5 0 0.4 0.8 1-2 1.6 H (m) F i g u r e 5.11 Comparison between e x p e r i m e n t a l r e s u l t s a n d p r e d i c t i o n by E q u a t i o n s 5.3 and 5.4 The p r e d i c t i o n i s i n d i c a t e d by the 45° l i n e . 6. SPOUT SHAPE, SPOUT DIAMETER AND FOUNTAIN HEIGHT 6.1 SPOUT SHAPE AND DIAMETER In t h i s work, two general types of spout shapes were observed ( F i g u r e 6.1). In both cases, the spout diameter expanded i n the c o n i c a l r e gion and then converged s l i g h t l y . Above the c o n i c a l r e g i o n , the spout diameter remained constant f o r type (b) whereas f o r type ( a ) , the spout diameter was p r i m a r i l y constant but d i v e r g e d near the bed s u r f a c e . The bed temperature had a n e g l i g i b l e e f f e c t on the spout shape. The only s i g n i f i c a n t f a c t o r a f f e c t i n g the spout shape appeared to be the d i m e n s i o n l e s s bed h e i g h t , namely H/H m ( F i g u r e 6.2). Type (a) was found at bed h e i g h t s c l o s e to H m. As bed h e i g h t s became lower, the spout shape approached type (b). The average spout diameter was determined using Equation 3.7. Tables 6.1a, 6.1b, 6.1c and 6.1d summarize a l l the experimental c o n d i t i o n s and the corresponding r e s u l t s while the experimental v a l u e s of spout diameter versus bed l e v e l are given i n Appendix D. The v a r i a t i o n of the average spout diameter (D g) with bed height and bed temperature i s shown in F i g u r e 6.3. At a given temperature, D s i n c r e a s e d with i n c r e a s i n g bed h e i g h t . On the other hand, at a f i x e d bed height, the t r e n d of D s 116 1 1 7 (a) (b) F i g u r e 6.1 Observed spout shapes 1.5 1 ~ 0.5 -0 1 2 3 4 Rs (cm) (a) N 1.5 0 1 2 3 4 Rs (cm) (b) 1 -0.5 -0 1 2 3 4 Rs (cm) ( c ) LEGEN.D 20 deg C 170 deg C 300 deg C •-- *20 deg C F i g u r e 6.2 E f f e c t of bed h e i g h t and bed t e m p e r a t u r e on s p o u t shape. Sand, dp = 1.25 mm, = 12.70 mm, U / U m s ~ 1.V0. (a) H = H m, (b) H = 0.75 H m and (c) H 0.50 H m CD T a b l e 6 . 1 a A v e r a g e s p o u t d i a m e t e r s a n d c o r r e s p o n d i n g e x p e r i m e n t a l c o n d i t i o n s ( b e d t e m p e r a t u r e = 2 0 ° C ) R u n H m U /U ms G ( k g / m 2 s ) d P (mm) D 1 (mm) ( k g / m 3 ) ( k g / m s ) ( c m ) D s * ( c m ) d e v D *• s ( cm) % d e v 1 - 1 - a 1 OOO 1 0 7 5 1 112 0 . 9 4 5 19 0 5 1 2 4 6 1 . 8 0 E - 0 5 3 . 1 7 9 3 . 144 -1 10 2 9 7 8 - 6 . 3 4 1 - 2 - a 0 7G1 1 0 9 5 0 9 2 5 0 . 9 4 5 19 0 5 1 2 3 4 1 . 8 0 E - 0 5 2 . 8 7 6 2 . 8 7 3 - 0 11 2 7 5 7 - 4 . 14 1 - 3 - a 0 4 9 5 1 124 0 8 8 2 0 . 9 4 5 19 0 5 1 2 2 0 1 . 8 0 E - 0 5 2 . 8 3 4 2 . 8 0 6 - 0 97 2 7 0 9 - 4 . 4 0 5 - 1 - a 1 0 0 0 1 0 8 5 1 4 9 9 1 . 2 5 0 19 0 5 1 . 2 5 6 1 . 8 0 E - 0 5 3 . 4 1 6 3 . 6 3 9 6 54 3 381 -1 . 0 2 5 - 2 - a 0 7 5 3 1 121 1 2 1 7 1 . 2 5 0 19 . 0 5 1 . 2 3 9 1 . 8 0 E - 0 5 . 3 . 0 6 2 3 . 2 8 6 7 32 3 . 101 1 . 2 8 5 - 3 - a 0 4 8 5 1 1 10 1 0 6 2 1 . 2 5 0 19 .05 1 . 2 2 3 1 . 8 0 E - 0 5 2 . 9 1 7 3 . 0 7 4 5 38 2 . 9 3 4 0 . 5 9 9 - 1 - a 1 0 0 0 1 0 5 3 1 721 1 . 6 6 5 19 . 0 5 1 . 2 4 4 1 . B O E - 0 5 3 . 6 9 4 3 . 8 9 4 5 42 3 . 6 0 0 - 2 . 56 9 - 2 - a 0 7 2 3 1 0 4 4 1 4 3 9 1 . 6 6 5 19 0 5 1 2 2 9 1 . 8 0 E - 0 5 3 . 444 3 . 5 6 7 3 58 3 3 4 2 - 2 . 9 5 9 - 3 - a 0 4 9 7 1 123 1 3 1 2 1 . 6 6 5 19 0 5 1 . 2 1 7 1 . 8 0 E - 0 5 3 . 2 8 4 3 . 4 0 9 3 82 3 2 2 0 -1 . 9 4 1 7 - 1 - a 1 OOO 1 0 2 6 1 4 2 4 1 . 2 5 0 26 64 1 . 2 5 2 1 . 8 0 E - 0 5 3 . 4 4 3 3 . 5 4 9 3 08 3 3 1 0 - 3 . 8 7 1 7 - 2 - a 0 811 1 1 19 1 3 2 8 1 . 2 5 0 26 64 1 . 2 4 0 1 . 8 0 E - 0 5 3 . 2 7 2 3 . 4 3 0 4 82 3 . 2 2 0 -1 . 5 9 1 7 - 3 - a 0 5 0 8 1 122 1 166 " 1 . 2 5 0 26 .64 1 .221 1 . 8 0 E - 0 5 3 . 0 4 2 3 . 2 1 8 5 78 3 . 0 5 7 0 . 4 9 2 1 - 1 - a 1 0 0 0 1 011 1 9 0 0 1 . 6 6 5 26 .64 1 .261 1 . 8 0 E - 0 5 3 . 8 4 8 4 . 0 8 8 5 27 3 . 7 4 9 - 3 . 4 6 2 1 - 2 - a 0 8 5 0 1 109 1 7 9 2 1 . 6 6 5 26 .64 1 . 2 4 2 1 . 8 0 E - 0 5 3 . 7 1 9 3 . 9 7 2 6 8 0 3 . 6 6 5 -1 . 4 6 2 1 - 3 - a 0 5 7 2 1 148 1 5 9 6 1 . 6 6 5 26 64 1 2 2 4 1 . 8 0 E - 0 5 3 .4 18 3 . 7 5 3 9 8 0 3 . 501 2 . 4 2 2 5 - 1 - a 1 0 0 0 1 0 2 9 1 188 0 . 9 4 5 12 7 0 1 . 2 7 5 1 . 8 0 E - 0 5 3 . 0 3 3 3 . 2 4 7 7 0 7 3 . 0 4 4 0 . 3 7 2 5 - 2 - a 0 8 1 5 1 1 10 1 0 6 0 0 . 9 4 5 12 7 0 1 . 2 5 2 1 . 8 0 E - 0 5 2 . 8 5 7 3 .071 7 4 9 2 . 9 1 2 1 . 9 4 2 5 - 3 - a 0 5 3 0 1 124 0 8 5 7 0 . 9 4 5 12 7 0 1 . 2 2 9 1 . 8 0 E - 0 5 2 . 6 2 3 2 . 7 6 7 5 5 0 2 . 6 7 0 1 . 8 0 2 9 - 1 - a 1 0 0 0 1 0 4 7 1 5 2 3 1 . 2 5 0 12 7 0 1 261 1 . 8 0 E - 0 5 3 . 308 3 . 6 6 8 10 88 3 . 4 0 1 2 . 8 0 2 9 - 2 - a 0 741 1 081 1 3 0 8 1 . 2 5 0 12 7 0 1 . 2 4 2 1 . 8 0 E - 0 5 3 . 0 9 4 3 . 4 0 4 10 0 3 3 . 197 3 . 3 4 2 9 - 3 - a o 4 9 8 1 124 1 149 1 . 2 5 0 12 70 1 . 2 2 6 1 . 8 0 E - 0 5 2 . 8 4 3 3 . 195 12 37 3 . 0 3 4 6 . 7 2 3 3 - 1 - a 1 0 0 0 1 0 4 5 1 7 9 9 1 . 6 6 5 12 70 1 2 4 5 1 . 8 0 E - 0 5 3 . 5 7 7 3 . 9 8 0 1 1 26 3 . 6 6 9 2 . 5 6 3 3 - 2 - a 0 74 1 1 108 1 6 1 6 1 . 6 6 5 12 70 1 2 3 0 1 . 8 0 E - 0 5 3 .311 3 . 7 7 6 14 04 3 . 5 1 4 6 . 1 3 3 3 - 3 - a 0 5 1 8 1 1 10 1 • 3 8 5 1 . 6 6 5 12 70 1 216 1 . 8 0 E - 0 5 3 . 1 1 5 3 .501 12 39 3 . 2 9 7 5 . 8 6 5 - 6 - a 0 7 5 8 1 0 7 5 1 163 1 . 2 5 0 19 0 5 1 238 1 . 8 0 E - 0 5 2 . 9 7 4 3 . 2 1 4 8 06 3 . 0 4 2 2 . 2 7 5 - 6 - b 0 7 5 8 1 128 1 2 2 0 1 . 2 5 0 19 0 5 1 . 2 3 8 1 . 8 0 E - 0 5 3 .091 3 . 2 9 0 6 44 3 . 105 0 . 4 6 5 - 6 - c 0 7 5 8 1 190 1 2 8 6 1 . 2 5 0 19 05 1 . 2 3 7 1 . 8 0 E - 0 5 3 . 124 3 . 3 7 6 8 0 7 3 . 178 1 . 72 5 - 9 - a 0 2 6 0 1 0 5 8 0 8 5 7 1 . 2 5 0 19 05 1 . 2 0 9 1 . B O E - 0 5 2 . 8 7 6 2 . 7 6 7 - 3 78 2 . 6 8 3 - 6 . 7 2 5 - 9 - b 0 2 6 0 1 118 0 9 0 5 1 . 2 5 0 19 05 1 2 0 9 1 . 8 0 E - 0 5 2 9 3 0 2 . 8 4 2 - 3 0 0 2 . 7 4 7 - 6 . 26 5 - 9 - c 0 2 6 0 1 179 0 9 5 5 1 . 2 5 0 19 05 1 2 0 9 1 . 8 0 E - 0 5 3 . 0 0 6 2 . 9 1 8 - 2 93 2 .811 - 6 .47 c o n t i n u e d vo Run *• H/Hm U/U ms G (ke/m 2s) d P (mm) D i (mm) (kg/m3) V (kg/ms) (cm) (cm) dev D n s ( cm) /» dev 37-1-a 1 . ,000 1 .064 1 . . 157 1 .250 19 .05 0.707 1 .09E-05 3.646 3.206 -'12 .OB 3 .2B9 -9 .80 37-2-e 0. ,773 1 .075 1 , OB6 1 .250 19 .05 0.695 1 .D9E-05 3.36B 3. 10B -7 .73 3 .215 -4 .54 37-3-a 0. .511 1 .093 0. .872 1 .250 19 .05 0.683 1 .09E-05 3. 142 2.791 -11. . 1B 2 .938 -6 .49 37-4-a 0. 184 1 .075 0. .616 1 .250 19 .05 0.670 1 .09E-05 2.497 2.354 -5 . 73 2 .54 1 1 .77 37-4-b 0. . 184 1 . 1 17 0. .639 1 .250 19 .05 0.670 1 .09E-05 2.547 2.396 -5. .91 2 .5B2 • 1 .36 37-4-c 0. . 184 1 . 170 0. .670 1 .250 19 .05 0.669 1 .09E-05 2.642 2.453 -7 , . 16 2 .636 -0.21 38-1-a 1. .000 1 . 129 0. .261 1 .250 19 .05 0.170 1 .94E-05 2.732 1.545 -43. .43 2 .B15 3.02 38-2-a 0. .756 1 .068 0. .212 1 .250 19 .05 0.169 1 .94E-05 2.585 1.396 -46. .01 2 .576 -0.33 3B-2-b 0. .756 1 . 1 12 0. .221 1 .250 19 .05 0. 169 1 .94E-05 2.629 1 .424 -45, .82 2 .623 -0.22 38-2-c 0. .756 1 . 174 0. .233 1 .250 19 .05 0. 169 1 .94E-05 2.663 1.462 -45. . 11 2 .684 0.79 38-3-a 0. .512 1 .050 0. . 184 1 .250 19 .05 0. 168 1 .94E-05 2.457 1.302 -47 . OO 2 .427 -1 .22 3B-3-b 0. .512 1 .095 0. . 192 1 .250 19 .05 0. 168 1 .94E-OS 2.595 1 .330 -48 . 77 2 .472 -4 .73 38-3-c 0. .512 1 . 178 0. .206 1 .250 19 .05 0. 168 1 .94E-05 2.641 1 .376 -47 . B9 2 .549 -3.49 & experimental value P calculated value by Equation 2.16 (McNab equation)-H c a l c u l a t e d value by Equation 6.5 to o Table 6.1b Average spout diameters and corresponding experimental conditions (bed temperature = 170 °CI Run m U/U ms G d P D 1 H ( kg/ m2s) (mm) (mm) 2-1-a 1 000 1 101 0 508 0 .945 19 05 2-2-a 0 697 1 104 0 483 0 .945 19 05 2-3-a 0 484 1 099 0 363 0 .945 19 05 6-1-a 1 000 1 089 0 896 1 .250 19 05 6-2-a 0 696 1 1 14 0 779 1 .250 19 05 6-3-a 0 451 1 100 0 644 1 .250 19 05 10-1-a 1 000 1 07 1 1 1 14 1 .665 19 05 10-2-a 0 746 1 1 15 1 050 1 .665 19 05 10-3-a o 500 1 092 o 909 1 .665 19 05 18-1-a 1 000 1 098 0 939 1 .250 26 64 18-2-a 0 806 1 134 0 873 1 .250 26 64 18-3-a 0 505 1 117 0 737 1 .250 26 64 22-1-a 1 OOO 1 050 1 352 1 .665 26 64 22-2-a 0 746 1 123 1 204 1 .665 26 64 22-3-a 0 504 1 131 1 071 1 .665 26 64 26-1-a 1 000 1 108 0 541 0 .945 12 70 26-2-a 0 758 1 102 0 473 0 945 12 70 26-3-a 0 492 1 091 0 395 0 945 12 70 30-1-a 1 OOO 1 086 0 851 1 250 12 70 30-2-a 0 723 1 099 0 709 1 250 12 70 30-3-a 0 496 1 104 0 596 1 250 12 70 34-1-a 1 000 1 052 1 353 1 .665 12 70 34-2-a 0 744 1 088 1 152 1 .665 12 70 34-3-a 0 488 1 093 0 926 1 665 12 70 6-5-a 0 716 1 079 0 748 1 .250 19 05 6-5-b 0 716 1 162 0 806 1 250 19 05 6-5-c 0 716 1 208 0 837 1 250 19 05 6-6-a 0 4 12 1 039 0 572 1 250 19 05 6-6-b 0 412 1 122 0 618 1 250 19 05 6-6-c 0 412 1 180 0 650 1 250 19 05 & experimental value is calculated value by Equation 2.16 (McNab equation) H c a l c u l a t e d value by Equation 6.5 pf f D B D p •/„ D # '/. 5 ° 5 (kg/m3) (kg/ros) (cm) (cm) dev (cm) dev 0 802 2 35E-05 2 928 2 142 -26 86 2 482 -15 22 0 799 2 35E-05 2 499 2 089 -16 39 2 431 -2 71 0 797 2 35E-05 2 470 1 816 -26 46 2 150 -12 96 0 815 2 35E-05 3 094 2 828 -8 59 3 160 2 13 0 806 2 35E-05 3 001 2 64 1 -12 00 2 983 -0 59 0 801 2 35E-05 2 836 2 406 -15 17 2 752 -2 96 0 823 2 35E-05 3 496 3 147 -9 99 3 463 -0 94 0 814 2 35E-05 3 289 3 057 -7 06 3 386 2 94 0 805 2 35E-05 3 225 2 848 -11 68 3 191 -1 06 0 816 2 35E-05 3 337 2 894 -13 28 3 224 -3 40 0 809 2 35E-05 3 161 2 792 -11 66 3 131 -0 95 0 802 2 35E-05 3 054 2 570 -15 85 2 917 -4 50 0 822 2 35E-05 3 536 3 460 -2 15 3 767 6 54 0 813 2 35E-05 3 399 3 269 -3 83 3 594 5 74 0 805 2 35E-05 3 300 3 087 -6 47 3 426 3 81 0 814 2 35E-05 2 632 2 209 -16 08 2 540 -3 48 0 807 2 35E-05 2 402 2 068 -13 90 2 403 0 02 0 801 2 35E-05 2 294 1 893 -17 47 2 227 -2 93 0 818 2 35E-05 2 952 2 758 -6 58 3 087 4 57 0 809 2 35E-05 2 748 2 522 -8 23 2 861 4 1 1 0 801 2 35E-05 2 676 2 316 -13 45 2 661 -0 55 0 820 2 35E-05 3 456 3 461 0 15 3 771 9 12 0 811 2 35E-05 3 302 3 199 -3 12 3 528 6 85 0 802 2 35E-05 3 141 2 874 -8 49 3 220 2 51 0 806 2 35E-05 2 978 2 589 - 13 07 2 931 - 1 57 0 806 2 35E-05 3 048 2 685 - 11 90 3 028 -0 67 0 806 2 35E-05 3 175 2 735 - 13 85 3 078 -3 07 0 799 2 35E-05 2 781 2 270 -18 38 2 616 -5 93 0 799 2 35E-05 2 838 2 358 - 16 93 2 705 -4 68 0 799 2 35E-05 2 890 2 417 -16 38 2 765 -4 32 Table 6.1c Average spout diameters and corresponding experimental conditions ( b e d t e m p e r a t u r e = 3 0 0 C ) Run H / H n , ro U/U ms G d P if (kB/m2s) (mm) 7-1-8 1 .000 1. .105 0.643 1 .250 7-2-B 0.756 1. . 113 0.605 1 .250 7-3-a 0.510 1, . 106 0.529 1 .250 11-1-8 1 .000 1. .064 0.902 1 .665 11-2-a 0.723 1. .179 0.855 1 .665 11-3-e 0.498 1. . 126 0.693 1 .665 19-1-a 1.000 1. .093 0.646 1 .250 19-2-a 0.773 1. .090 0.605 1 .250 19-3-8 0.523 1. . 106 0.534 1 .250 23-1-8 1 .000 1. .080 1 .042 1 .665 23-2-8 0.748 1, .113 0.910 1 .665 23-3-a 0.505 1. . 124 0.813 1 .665 27-1-8 1 .000 1.046 0.378 0 .945 27-2-B 0.750 1 .0B3 0.332 0 .945 27-3-8 0.490 1 . 100 0.306 0 .945 31-1-8 1.000 1 . 105 0.589 1 .250 31-2-8 0.757 1 .096 0.503 1 .250 31-3-B 0.476 1 . 103 0.395 1 .250 35-1-8 1.000 1 .071 0.948 1 .665 35-2-a 0.730 1 . 117 0.822 1 .665 35-3-a 0.491 1 . 104 0.690 1 .665 7-5-8 0.75G 1 .055 0.559 1 .250 7-5-b 0.756 1 . 112 0.589 1 .250 7-5-c 0.75G 1 . 160 0.614 1 .250 7-7-B 0.489 1 .049 0. 479 1 .250 7-7-b 0.489 1 . 111 0.508 1 .250 7-7-c 0. 4B9 1 . 162 0.531 1 .250 & experimental value p calculated value by Equation 2.16 (McNab * calculated value by Equation 6.5 (mm ) (kg/m3) (kg/ms) (cm) 19. .05 0. 625 2. .B5E-05 2 .955 19 .05 0. 621 2. .B5E-05 2 .810 19 .05 0. 618 2 . 85E-05 2 .803 19. .05 0. 629 2, .85E-05 3 .43B 19 .05 0. 626 2. .B5E-05 •3 .260 19 .05 0. 620 2. .85E-05 3, .05B 26 .64 0. 623 2. •B5E-05 3, .000 26 .64 0. 620 2. .85E-05 2 .946 26 .64 0. 617 2. B5E-05 2. .829 26 .64 0. 631 2. 8SE-05 3, .500 26. .64 0. 625 2. 85E-05 3. .275 26 .64 0. 620 2. B5E-05 3, .238 12. .70 0. 622 2. 85E-05 2. .468 12 .70 0. 620 2. 85E-05 2, .278 12 .70 0. 618 2. .B5E-05 2, .031 12 .70 0. 629 2. .85E-05 2 .916 12 .70 0. 623 2. 85E-05 2, .686 12 .70 0. 618 2. 85E-05 2, .596 12 .70- 0. 631 2. .B5E-05 3 .395 12 .70 0. 624 2. .85E-05 3, .251 12 .70 0. ,619 2. 85E-05 2 .898 19 .05 0. 622 2. .85E-05 2 .631 19 .05 0. 622 2. .B5E-05 2 .874 19 .05 0. 622 2. .85E-05 2 .977 19 .05 0. 618 2. 85E-05 2 .757 19 .05 0. ,618 2. .85E-05 2 , .805 19 .05 0. 618 2 . 85E-05 2 .B48 equatIon) D s * 0 v s (cm) dev (cm) dev 2.404 - 18 .65 3 .029 2.50 2.333 - 16 .97 2 .955 5.18 2. 185 -22 .06 2 .792 -0 . 3B 2.B37 -17 .47 3 .501 1 .84 2.764 - 15 .21 3 .426 5. OB 2.494 - 18 .45 3 . 136 2.55 2.409 - 19 .69 3 .038 1 .26 2 . 333 -20 . 80 2 .557 0.37 2. 195 -22 .42 2 .805 -0.85 3 .045 - 12 .99 3 .724 6.39 2.B50 - 12 .98 3 .521 7.51 2 . 697 - 16 .72 3 .361 3 .79 1 .853 -24 .92 2 .409 -2.37 1 .739 -23 .67 2 .280 O.OB 1 .671 - 17 .74 2 . 203 B.45 2 . 303 -21 .03 2 .911 -0. 18 2.131 -20 .65 2 .726 1 . 46 1 . B93 -27 .07 2 . 460 -5.23 2.907 - 14 .36 3 .574 5.28 2.711 - 16 .60 3 .37 1 3.68 2.488 - 14 . 13 3 . 132 8.06 2.244 -20 .72 2 .E55 0.B3 2 . 303 - 19 . 88 2 .920 1 .60 2 . 350 -21 .06 2 . 973 -0.13 2 .0B1 - 2* .52 2 . 675 - 2 . 9B 2 . 142 - 2 3 . 65 2 . 744 -2.18 2 . 189 - 2 3 . 15 2 : 797 - 1 . BO Table 6.1d Average spout diameters and corresponding experimental conditions (bed temperature = Run H'Hm U/U ms E d P D i D 6 * 0 V 0 ft s % 0 ( k g / m 2sj (mm) (mm) (kg/m3) (kg/ms) (cm) (cm) dev (cm) dev 8-1-a 1 ooo 1 . 101 0 493 1 .250 19 05 0 514 3 20E-05 2 834 2 110 -25 53 2 905 2 .50 8-2-a 0 646 1 . 105 0 458 1 .250 19 05 0 511 3 20E-05 2 796 2 036 -27 19 2. 818 0.80 8-3-a 0 499 1 . 100 0 375 1 .250 19 05 0 510 3 20E-05 2 616 1 846 -29 45 2 . 586 -1.15 12-1-a 1 000 1 . 103 0 744 1 .665 19 05 0 515 3 20E-05 3 514 2 582 -26 52 3 . 470 -1 .26 12-2-a 0 727 1 . 127 0 713 1 .665 19 05 0 512 3 20E-05 3 233 2 529 -21 79 3 . 412 5.54 12-3-a 0 485 1 . 120 0 571 1 .665 19 05 0 510 3 20E-05 2 957 2 268 -23 30 3 . 103 4 .92 20-1-a 1 000 1 .027 0 497 1 .250 26 64 0 511 3 20E-05 2 876 2 119 -26 33 2 . 920 1 .52 20-2-a 0 703 1 . 106 0 476 1 .250 26 64 0 510 3 20E-05 2 811 2 074 -26 20 2 . 867 2.00 20-3-a 0 490 1.114 0 394 1 .250 26 64 0 509 3 20E-05 2 740 1 891 -30 99 2. 643 -3 .53 24-1-a 1 000 1 . 124 0 857 1 .665 26 64 0 517 3 20E-05 3 449 2 767 -19 77 3 . 685 6.85 24-2-a 0 752 1 . 124 0 762 1 .665 26 64 0 513 3 20E-05 3 386 2 612 -22 85 3 . 510 3.66 24-3-a 0 470 1.112 0 652 1 .665 26 64 0 511 3 20E-05 3 053 2 420 -20 73 3. 284 7.57 28-1-a 1 OOO 1 . 101 o 323 0 .945 12 70 0 510 3 20E-05 2 478 1 715 -30 77 2. 422 -2 .24 28-2-a 0 745 1 .077 0 284 0 .945 12 70 0 509 3 20E-05 2 059 1 611 -21 77 2. 292 11 .33 28-3-a 0 471 1 . 126 0 240 0 .945 12 70 0 508 3 20E-05 1 941 1 483 -23 59 2. 132 9 .86 32-1-a 1 000 1 .095 0 452 1 .250 12 70 0 515 3 20E-05 2 796 2 023 -27 66 2. 796 -0.00 32-2-a 0 750 1 . 103 0 400 1 .250 12 70 0 513 3 20E-05 2 591 1 905 -26 48 2 655 2.46 32-3-a 0 435 1 . 104 0 315 1 . 250 12 70 0 510 3 20E-05 2 562 1 695 -33 86 2. 398 -6 .42 36-1-a 1 000 1 .086 0 746 1 .665 12 70 0 519 3 20E-05 3 312 2 585 -21 94 3 466 4 .66 36-2-a 0 743 1 . 108 0 645 1 .665 12 70 0 515 3 20E-05 3 212 2 407 -25 05 3 262 1 .55 36-3-a 0 476 1 . 108 0 539 1 .665 12 70 0 511 3 20E-05 2 880 2 205 -23 45 3 024 5.01 8-5-a 0 654 1 .041 0 426 1 .250 19 05 0 511 3 20E-05 2 714 1 965 -27 61 2 731 0.63 8-5-b 0 654 1 .094 0 448 1 .250 19 05 0 511 3 20E-05 2 809 2 014 -28 31 2 791 -0.63 8-5-c 0 654 1.191 0 488 1 .250 19 05 0 511 3 20E-05 2 908 2 100 -27 79 2 897 -0. 39 & experimental value is c alculated value by Equation 2.16 (McNab equation) H calculated value by Equation 6.5 • 20 deg C A 170 deg C O 300 deg C + 420 deg C 0 0.4 0.8 1.2 H (m) gure 6.3 E f f e c t of bed h e i g h t and bed t e m p e r a t u r e on Sand, d D = 1.25 mm, D i = 12.70 mm, U/U m s ~ 1 125 with T s was somewhat i n c o n c l u s i v e based on t h i s f i g u r e . The e f f e c t of the bed temperature i s best i l l u s t r a t e d i n F i g u r e 6.4. At a constant bed h e i g h t ( i . e . , H * 27 cm) and a constant value of U/U m s, D S was observed to decrease only s l i g h t l y with i n c r e a s i n g bed temperature. Thus the e f f e c t of the bed temperature was not s i g n i f i c a n t . F i g u r e 6.4 a l s o shows the t r e n d of D S with the bed temperature as p r e d i c t e d by McNab's c o r r e l a t i o n , Equation 2.16. I t c l e a r l y demonstrates that t h i s equation i s not s u i t a b l e f o r e s t i m a t i n g D S at high bed temperature. In g e n e r a l , McNab's c o r r e l a t i o n worked f a i r l y w e l l f o r a i r spouting at room c o n d i t i o n s (see Table 6.1a). As temperature i n c r e a s e d , however,. i t u n d e r p r e d i c t e d the average diameter (Tables 6.1b, 6.1c and 6.1d). I t can be seen from Table 6.1a that the McNab equation was a l s o u n s a t i s f a c t o r y f o r Run # 38 i n which helium gas was the spouting medium. The method of Littman (1982) was not a p p l i c a b l e because i t was r e s t r i c t e d to s p h e r i c a l p a r t i c l e s . Based on the t h e o r e t i c a l model of Bridgwater and Mathur (1972), an a l t e r n a t e equation was developed. S t a r t i n g with t h e i r model, 3 2 f p f Q s 2 -= r = 1 2.14 T T 2 ^ ( D C - D S ) D S 4 the f o l l o w i n g assumptions were made: 126 4.5 3.5 a to Q 2.5 1.5 1 1 • Expert m e n i a l D c = 156 mm D; = 19.05 mm dp => 1.250 mm — H ^ 27 cm Equation 6.5 — v. • y ^ — M c N a b E q u a t i o n ... I i _.l I 0 100 200 300 T S (deg C) 400 F i g u r e 6.4 E f f e c t o f bed t e m p e r a t u r e on D s . Sand, dp = 1.25 mm, Dj = 19.05 mm, U / U m s 1.10 1 27 1. f = k,Resa = k, [ 4 Q s p f / M 7 r D s ] a 2. Q s = k 2Q f c = 0.25k 2?rD c 2G/p f 3. \\i = k 3 p b g 4. (D c-D s) = k 0 D c Equation 2.14 then becomes Q2+<L-Q 3+2a M a ( p b p f g ) D s 4 + a = 1 where k = 32k, ( 4 / 7 r ) a ( k 2 r r / 4 ) 2 + a 7 T 2 ( k 3 k a ) Equation 6.1 can be reduced to " D s 4 P f Pb9~ - V "GDC2" a . G 2 D C 3 . — N 6.1 6.2 6.3 In the above e x p r e s s i o n , k, a and both groups are di m e n s i o n l e s s . A p p l y i n g a l e a s t squares f i t to a l l the experimental data y i e l d e d k = 438.8 and a = -0.4708. Equation 6.1 can a l s o be r e w r i t t e n as D s -•G2 + aD^3 + 2ar\-\ l/(4+a) 6.4 The equation of Bridgwater and Mathur (Equation 2.15) can be recovered with the f o l l o w i n g c o n d i t i o n s : 1 . k, = 0.08 ; a = 0 1 28 4. k, = 1 .0 5. g = 9.81 m/s 2 6. p f = 1.20 kg/m3 S u b s t i t u t i n g k = 438.8 and a = -0.4708 i n t o Equation 6.4 g i v e s - G0.4333 D 0.5832^0.1334-D_ = 5.606 n „ n„ , 6.5 L ( p b p f g ) ° - 2 8 3 4 J As seen i n F i g u r e 6.4, Equation 2.16 o v e r p r e d i c t s the e f f e c t of temperature on the average spout diameter whereas Equation 6.5 p r o v i d e s b e t t e r agreement. Table 6.2 summarizes the average d e v i a t i o n s between the experimental v a l u e s and the c a l c u l a t e d values by these two equations f o r d i f f e r e n t f l u i d c o n d i t i o n s . The d e f i c i e n c y of Equation 2.16 i s c l e a r l y demonstrated . Equation 6.5, on the other hand, shows e x c e l l e n t agreement with the experimental r e s u l t s i n each of the s i x c o n d i t i o n s . F i g u r e s 6.5a and 6.5b i l l u s t r a t e the o v e r a l l a p p l i c a b i l i t y of Equation 6.5 as compared to Equation 2.16. T h i s proposed e x p r e s s i o n ( i . e . , Equation 6.5) appears to work b e t t e r than McNab's. I t i s a l s o d i m e n s i o n a l l y c o n s i s t e n t , which i s another advantage over the McNab e x p r e s s i o n . D c and p b were not v a r i e d i n t h i s study. Hence Equation 6.5 has not been t e s t e d f o r the e f f e c t s of these two parameters. Table 6.2 Comparison between e x p e r i m e n t a l and c a l c u l a t e d v a l u e s of D 5 S p o u t i n g Temp gas (°C) A i r 20 A i r 170 A i r 300 A i r 420 Methane 20 H e l i u m 20 McNab E q u a t i o n AVERAGE RMS ERROR % (%) ERROR 5.6 7.3 -12.2 13.6 -19.5 19.9 -25.B 26.0 -8.3 8.7 -46.3 46.3 E q u a t i o n 6.5 AVERAGE RMS ERROR % (%) ERROR -0.4 3.7 -0.8 5.3 1.B 3.9 2.3 4.7 -3.0 5.2 -0.9 2.6 1 3 0 2 3 4 D s (Calculated) , cm F i g u r e 6.5a Comparison between e x p e r i m e n t a l average spout d i a m e t e r and p r e d i c t i o n by E q u a t i o n 2.16 1 3 1 F i g u r e 6.5b Comparison between e x p e r i m e n t a l average spout d i a m e t e r and p r e d i c t i o n by E q u a t i o n 6.5 132 6.2 FOUNTAIN HEIGHT At steady spouting, a l l observed f o u n t a i n shapes were b a s i c a l l y p a r a b o l i c . Fountain h e i g h t s i n c r e a s e d with U/U m s but decreased with i n c r e a s i n g bed height (Table 6.3 and F i g u r e 6.6). Chandnani (1984) r e p o r t e d s i m i l a r f i n d i n g s f o r f i n e p a r t i c l e s p o u t i n g . The data r e p o r t e d by Grace and Mathur (1978) i n d i c a t e the same trend with i n c r e a s i n g U/U m s but the e f f e c t of the bed height i s not completely c l e a r . However, i n most cases, f o u n t a i n heights were indeed smaller f o r higher bed h e i g h t s . The e f f e c t of U/U m s and bed height on spout p a r t i c l e v e l o c i t y ( F i g u r e s 6.7 and 6.8) has been r e p o r t e d by Lim (1975). F i g u r e 6.7 i l l u s t r a t e s that V s H i n c r e a s e s with U/U m s, which e x p l a i n s the e f f e c t of U/U m s on Hp i n Fi g u r e 6.6, v i a Equation 2.38. F i g u r e 6.8, on the other hand, does not c l e a r l y i n d i c a t e any e f f e c t of bed height on V s H , and hence p r o v i d e s no obvious e x p l a n a t i o n f o r the e f f e c t of H i n Fig u r e 6.6. The f l u i d v e l o c i t y i n the spout at the bed s u r f a c e , U s H , was estimated from measured values of U a^ and D s H (Table 6.4). For smaller bed h e i g h t s , U s H was found to be higher than f o r l a r g e r bed h e i g h t s . With the assumption that h i g h e r U s H produces higher V s H and since Hp i s d i r e c t l y p r o p o r t i o n a l t o V s H 2 as i n d i c a t e d i n Equation 2.38, higher f o u n t a i n h e i g h t s w i l l be expected from higher U s H . These r e s u l t s are c o n s i s t e n t with those shown i n F i g u r e 6.6 T a b l e 6.3 E x p e r i m e n t a l v a l u e s of f o u n t a i n h e i g h t Run Temp H U/Ums Hp # CO (m) (cm) 5-6-a 20 0,813 1.076 13.74 5-6-b 20 0.813 1 . 128 21 .54 5-6-c 20 0.813 1 . 190 26.88 5-9-a 20 0.279 1 .058 17.88 5-9-b 20 0.279 1.118 24.02 5-9-c 20 0.279 1 . 179 28.64 6-5-a 170 0.464 1 .079 12.22 6-5-b 170 0.464 1.162 16.93 6-5-c 170 0.464 1 .208 22.86 6-6-a 170 0.267 1 .039 16.18 6-6-b 170 0.267 1 . 122 21.45 6-6-c 170 0.267 1 . 180 25.29 7-5-a 300 0.413 1 .055 10.24 7-5-b 300 0.413 1.112 15.98 7-5-c 300 0.413 1 . 1 60 20. 58 7-7-a 300 0.267 1 .049 14.34 7-7-b 300 0.267 1.111 19.02 7-7-c 300 0.267 1 . 1 62 23.80 8-5-a 420 0.270 1 .041 10 .00 8-5-b 420 0.270 1 .094 1 3.08 8-5-c 420 0.270 1.191 17.88 134 F i g u r e 6.6 E f f e c t of bed h e i g h t and U/U m s on f o u n t a i n h e i g h t . Sand, d p = 1.25 mm, D-x = 19.05 mm 1 35 0 0.2 0.4 0.6 •» 0.8 LO Z/H F i g u r e 6.7 E f f e c t of s p o u t i n g v e l o c i t y and p a r t i c l e d i a m e t e r on spout p a r t i c l e v e l o c i t y . G l a s s beads, D c = 152 mm, H/D c =3.0, D i / D c = 0.125 (Lim, 1975) 7 c m F i g u r e 6.8 E f f e c t of bed h e i g h t on spout p a r t i c l e v e l o c i t y . D r = 152 mm, D^/Dc = 0.125, U/U m s = 1.1 ( L i m , 1975) 1 3 7 F i g u r e 6,9 E f f e c t of bed t e m p e r a t u r e on f o u n t a i n h e i g h t . Sand, d D = 1.25 mm, = 19.05 mm 138 A l l the observed f o u n t a i n s were g e n e r a l q u i t e s t a b l e r e g a r d l e s s of bed temperatures but they s t a r t e d to f l u c t u a t e up and down as U/U m s i n c r e a s e d . At an approximately f i x e d bed h e i g h t , the f o u n t a i n h e i g h t decreased with i n c r e a s i n g bed temperature ( F i g u r e 6.9 and Table 6.3). T h i s can be e x p l a i n e d i n terms of momentum t r a n s f e r . At a lower temperature, the higher mass flow ra t e of gas at a given v e l o c i t y causes higher spout p a r t i c l e v e l o c i t i e s which produce higher f o u n t a i n h e i g h t s as p r e d i c t e d by Equation 2.38. Table 6 . 4 U s H at selected conditions R u n H U/ Ums H F DSH U U a H * UsH * (m) (cm) (m) (m/s) (m/s) (m/s) 5-6-b 0.813 1.12B 21.54 0.038 0.985 0.687 5.68 5- 9-b 0.279 1.118 24.02 0.029 0.749 0.560 6.00 6- 5 -b 0.464 1.162 16.93 0.03B 0.999 0.675 6.11 6- 6 -b 0.267 1.122 21.45 0.028 . 0.773 0.551 7.41 7- 5 -b 0.413 1.112 15.9B 0.033 0.947 0.639 7.49 7-7-b 0.267 1.111 19.02 0.029 0.822 0.528 8.99 * determined from experimental data * UsH - I U D c 2 - U a H ( D c 2 . - D s H 2 ) l / D s H 2 7. PRESSURE PROFILES AND FLU ID AND PART ICLE V E L O C I T I E S IN THE ANNULUS 7.1 RADIAL PRESSURE PROFILES R a d i a l pressure p r o f i l e s i n the annulus were measured as d e s c r i b e d i n S e c t i o n 3.7.6. The r e s u l t s are l i s t e d i n Table 7.1 and p l o t t e d i n F i g u r e s 7.1a, 7.1b, 7.1c and 7.1d. The r a d i a l pressure p r o f i l e s above the c o n i c a l s e c t i o n f o r a l l four runs were e s s e n t i a l l y f l a t but f o r Run # 5-6-b, there were some s l i g h t decreases near the column w a l l . T h i s can be e x p l a i n e d i n terms of the w a l l e f f e c t , that i s , the volume adjacent to the w a l l has a higher voidage than the r e s t of the annulus, thus p r o v i d e s an e a s i e r passage f o r gas flow and subsequently produces the observed drops towards the column w a l l as shown i n F i g u r e 7.1a. For the other three runs ( i . e . , Runs # 6-5-b, # 7-5-b and # 8-5-b) i n which the bed h e i g h t s were much lower than that of Run # 5-6-b (see Table 7.1), there was no decrease i n pre s s u r e at the w a l l . T h i s means that the w a l l e f f e c t becomes l e s s s i g n i f i c a n t f o r lower bed h e i g h t s . In g e n e r a l , the r e s u l t s i n d i c a t e constant r a d i a l p r essure i n the annulus f o r any given bed l e v e l s above the c o n i c a l r e g i o n . T h i s i s i n good agreement with the p r e v i o u s l y r e p o r t e d r e s u l t s (Mathur and E p s t e i n , 1974). In a d d i t i o n , the bed temperature had no observable e f f e c t on the shape of the pressure p r o f i l e s . 1 40 T a b l e 7.1 E x p e r i m e n t a l v a l u e s o f a n n u l a r p r e s s u r e . d = 1 .25 mm, D = 19 .05 mm P 1 Run Temp H H a U/U ms 2 P x in di f f . rad. pos 1 1 . (kN/m2) Mean It C O ( I D ) (m) (m) r«=3 . B 5 .2 6 . 4 7 .3 7 . 7 cm (kN/m2 5-6-b 20 0.813 0.B40 1.128 0 .70 1 .67 1 .63 1 .63 1 .60 1 .4B 1 .60 0 .50 3 .84 3 .80 3 .76 3 .76 3 .73 3.78 0 .30 5 .69 5 .66 5 .69 5 .74 5 .66 5.69 0 . 10 6 . 18 6 . 18 6 . 18 6 . 18 6 . 10 6. 16 0 .05 6 .49 6 .45 6.47 0 .00 6.52 G-5-b 170 0.464 0.480 1 . 162 0 .40 0 .67 0 .67 0 .67 0 .65 0 .65 0.66 0. .30 1 .71 1 .67 1 . 69 1 .68 1 .GB 1 .67 0. . 15 2 .BO 2 .76 2 .76 2 .77 2 .77 2.77 0, .05 3 , .21 3 .24 3.23 0. .00 3.25 7-5-b 300 0.4 13 0.430 1 . 1 12 0. .35 0. .69 0 .69 0. .69 0. 68 0. .67 0.68 0. ,25 1 . .52 1 .52 1 . .52 1 . 52 1 . .51 1.52 0. 15 2 . 20 2 .20 2 . 20 2 . 17 2. . 17 2. 19 0. .05 2 . 68 2 .66 2.68 0. 00 2.77 8-5-b 420 0.270 0.2B5 1 .094 0. 25 0. 19 0. . 19 0. 19 0. 19 0. 19 0. 19 0. 20 0. 57 0, .57 0. 57 0. 55 0. 56 0.56 0. 15 0. 81 0. B1 0. 80 0. 80 0. 60 0.80 0. 10 1 . 1 1 1 . .09 1. 09 1 . 07 1 . 05 1 .08 0. 05 1 . 37 1 . . 37 1 .37 0.00 1.52 1 42 8 O H 0 I X N— r • — * — Z 1 = 10 cm •4 1—- — 1 — z = 30 cm - : h A— — —&~£ z = 50 cm — — : Q—-; 1 — e — — e — 1 z = 70 1 cm — 0 R s 3 6 R c 9 12 r in cm F i g u r e 7.1a R a d i a l p r e s s u r e p r o f i l e s i n the c y l i n d r i c a l s e c t i o n ( T s » 20 °C) R c = column r a d i u s ; R s = average spout r a d i u s 143 H 1 r—\ z = 15 cm & A A A~£ 2 = 30 cm -e e—e-€ 2 = 40 cm 0 R s 3 i 6 R c r in cm 9 12 gure 7.1b R a d i a l p r e s s u r e p r o f i l e s i n the c y l i n d r i c a l s e c t i o n ( T s = 170 °C) R c = column r a d i u s ; R s = average spout r a d i 1 44 H 1 h z = 15 cm -£ A A-£ z = 25 cm Q Q ^ z = 35 cm 0 i 6 R c r in cm 9 12 gure 7.1c R a d i a l p r e s s u r e p r o f i l e s i n the c y l i n d r i c a l s e c t i o n ( T s = 300 °C) R c = column r a d i u s ; R s = average spout r a d i u s 1 45 B CO 6 s I a. o 0 X 1 X — 1 — X — 1 — x - » i i 1 A 1 A 1 1 1 A A U U (~\ u a t i ° L J v . z = 10 cm 2 = 15 cm z = 20 cm z = 25 cm 6 R C r in cm 9 12 F i g u r e 7.Id R a d i a l pressure p r o f i l e s in the c y l i n d r i c a l s e c t i o n ( T s = 420 °C) R c = column r a d i u s ; R s = average spout r a d i u s 146 7.2 LONGITUDINAL PRESSURE PROFILES D i v i d i n g Equation 2.26 e x p r e s s i o n which d e s c r i b e s p r o f i l e s i n the annulus, i e . , by Equation 2.28 y i e l d s an the l o n g i t u d i n a l pressure P-P H (2/3-4)/(x)+3g(x) = 1 - 7.1 -AP S (20-4)/(h)+3*(h) where fix) = 1.5 X 2 " X 3 + 0.25 X 4 7.2a gix) = 3x 3 " 4 . 5 x 4 + 3 x 5 " X 6 + 0 .143x 7 7.2b The v a r i a t i o n of ( P - P H ) / ( - A P s ) with z depends on two parameters, namely h ( i . e . , H/Hm) and 0. These parameters are, i n t u r n , r e l a t e d to the p a r t i c l e and f l u i d p r o p e r t i e s . Equation 2.31, on the other hand, i s independent of these two parameters. F i g u r e s 7.2a, 7.2b, 7.2c and 7.2d show the d i f f e r e n c e between these two e x p r e s s i o n s under four chosen c o n d i t i o n s (Runs # 5-6-b, # 6-5-b, # 7-5-b and # 8-5-b), together with the experimental r e s u l t s . In each case, Equations 7.1 and 2.31 produce almost i d e n t i c a l p r o f i l e s with very small d e v i a t i o n . Both equations work w e l l at room temperature (Figure 7.2a) but o v e r p r e d i c t at higher temperatures ( F i g u r e s 7.2b, 7.2c and 7.2d). 147 cn O H o I O H o.a 0.6 0.4 0.2 0 A I I 1 1 A Experimental — — — — — - Run # 5-6-b \ 0 C - 156 mm \ 1.25 mm \ D, = 19.05 mm \ T S = 20 dag C \^ H / H m = 0.758 \ ••• Lefroy and Davidson (Eq. 2.31) ^ Epstein and Lev ine /? = 3.67 I I I 1-0 0.2 0.4 0.6 z / H 0.8 F i g u r e 7.2a L o n g i t u d i n a l p r e s s u r e p r o f i l e s , e x p e r i m e n t a l v e r s u s p r e d i c t e d ( T s = 20 °C) 1 4 8 F i g u r e 7.2b L o n g i t u d i n a l p r e s s u r e p r o f i l e s , e x p e r i m e n t a l v e r s u s p r e d i c t e d ( T s = 170 °C) 1 4 9 0 0.2 0.4 0.6 0.8 1 z / H F i g u r e 7.2c L o n g i t u d i n a l p r e s s u r e p r o f i l e s , e x p e r i m e n t a l v e r s u s p r e d i c t e d ( T s = 300 °C) 150 0 0.2 0.4 o.a o.a 1 z/Ii F i g u r e 7.2d L o n g i t u d i n a l p r e s s u r e p r o f i l e s , e x p e r i m e n t a l v e r s u s p r e d i c t e d ( T s = 420 °C) 151 Equation 2.31 does not p r e d i c t any e f f e c t with bed temperature and y i e l d s the same p r o f i l e f o r a l l four experimental c o n d i t i o n s . For Equation 7.1, the e f f e c t of bed temperature i s expressed through j3 (and p a r t i a l l y through H m i m p l i c i t l y ) . The ( i n d i v i d u a l ) e f f e c t of /3 can be seen from F i g u r e s 7.2a and 7.2c, using the Lefroy-Davidson l i n e as r e f e r e n c e . With H/H m f i x e d , higher /3 y i e l d s lower ( P - P H ) / ( - A P s ) f o r any given values of z/H. Since /3 i n c r e a s e s with i n c r e a s i n g bed temperature, t h e r e f o r e Equation 7.1 p r e d i c t s that i f H/H m i s f i x e d , a higher bed temperature w i l l produce lower ( P - P H ) / ( - A P s ) . The experimental r e s u l t s (from Runs # 5-6-b and # 7-5-b) show a s i m i l a r q u a l i t a t i v e t r e n d , that i s , (P-P H ) / ( - A P s ) decreases with i n c r e a s i n g bed temperature. However, Equation 7.1 i s s t i l l somewhat u n s a t i s f a c t o r y because q u a n t i t a t i v e l y i t s p r e d i c t e d v a l u e s do not compare w e l l with experimental v a l u e s at higher temperatures. Improvement of Equation 7.1 can be made by r e p l a c i n g U m f of Equation 2.27c with the measured value of U=u . As i n d i c a t e d i n Table 7.2 of the next s u b - s e c t i o n , at a Hm room temperature, u a H m w a s approximately equal to U m f ; at higher temperatures, i t was s l i g h t l y s m a l l e r and the d i f f e r e n c e i n c r e a s e d with temperature. Hence u s i n g u a H m i n s t e a d of U m f i n Equation 2.27c g e n e r a l l y produces higher values of |3 and hence lower v a l u e s of ( P - P H ) / ( - A P s ) by Equation 7.1. However, ( P - P H ) / ( - A P g ) i s not very s e n s i t i v e to 0, as shown i n F i g u r e s 7.2a and 7.2c. Hence t h i s improvement was too small to account f o r the measured 152 d i f f e r e n c e s observed a t high temperatures. 7.3 LONGITUDINAL FLUID VELOCITY S e c t i o n 3.7.5 d e s c r i b e d how the f l u i d v e l o c i t i e s i n the annulus (U a) were determined. A l l measurements of U a were made at a f i x e d r a d i a l p o s i t i o n and the data are presented i n F i g u r e 7.3. There i s no obvious t r e n d regarding the e f f e c t of bed temperature and i t i s a l s o c l e a r that a l l data p o i n t s do not f a l l on the same curve. In order to i n t e r p r e t the data on U a and compare them with e x i s t i n g equations, i t i s important to determine u a H m ' which was not measured e x p e r i m e n t a l l y . However, Lim (1975) has shown that under any f i x e d c o n d i t i o n s of D c, D^, U/U m s, bed m a t e r i a l and spouting f l u i d , U a at any given z i s independent of bed height. In a d d i t i o n , U a r i s e s r a p i d l y with z and l e v e l s o f f to a constant v a l u e . These two unique f e a t u r e s make i t p o s s i b l e to e x t r a p o l a t e to u a H m f r o m data obtained at bed h e i g h t s below H m. Table 7.2 l i s t s the experimental r e s u l t s of U a versus z together with the values of U a H obtained by e x t r a p o l a t i o n . These f i n a l r e s u l t s are then p l o t t e d in F i g u r e 7.4 where they are compared to Equation 2.22 with u a H m r e p l a c i n g U m f (Mamuro and H a t t o r i , 1968), Equation 2.23 (L e f r o y and Davidson, 1969) and Equation 2.24 with n = 2 (modified L-D). Equation 2.23 c o n s i s t e n t l y underpredicted whereas the m o d i f i e d v e r s i o n , Equation 2.24, showed b e t t e r agreement. Equation 2.22 d i d not work p e r f e c t l y e i t h e r , but 1 53 CO cd o.a 0.6 0.4 0.2 • • o o o • A o o a 8 o A § A A • Air at 20 deg C O Air a t 170 deg C A Air at 300 deg C O Air a t 420 deg C 0 1 0 0.2 0.4 0.6 z in m 0.8 F i g u r e 7,3 E f f e c t of bed t e m p e r a t u r e on the 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 . d p = 1.25 mm, = 19.05 mm an i 01 S3 o to o o o to o 01 o CD CJ to CD in co O CD o w o o co cn to to CO O O O O O O O O O O O O o o o o o o o o o o o o o o o O -» to to o -* to to to to o -» to to & o ^  ^  io ii) i> in ~ i in O in O in in o in O in O oi W O W O O O O i Ui O 0) O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O to to <o in tn (J ff» (O O w to CD CO cn b O U h b J to w t r> u i i n Ul -A CO ID * . CO Ul Cf) IO O CD -0 OI to O -» O) to to -» co oi oi cn cn ^ -» co o cn co -4 M H o o - J i> to in O to to o cn ^ t o ^ m u i c n c n c n ~ I M U J - J - J D I I O f c o o on oi O o on to o o o cn to O o o cn o i 8 o 8 1 5 5 F i g u r e 7.4 L o n g i t u d i n a l a n n u l a r f l u i d v e l o c i t y d i s t r i b u t i 156 i t was not any worse than Equation 2.24. S i m i l a r s c a t t e r has been noted by E p s t e i n et a l . , 1978. 7.4 LONGITUDINAL PARTICLE VELOCITY Rovero et a l . (1986) have p o i n t e d out that the f l a t w a l l i n a h a l f column causes p a r t i c l e s to slow down due to f r i c t i o n . T h i s e f f e c t becomes very dominant at the corner between the f l a t and round w a l l s . The p a r t i c l e v e l o c i t y measured at the f l a t w a l l of a h a l f column i s t h e r e f o r e lower than that at the same r a d i a l p o s i t i o n i n a f u l l column. Hence, the procedure d e s c r i b e d i n S e c t i o n 3.7.5 would not g i v e very a c c u r a t e r e s u l t s . However, f o r purposes of comparison and q u a l i t a t i v e a n a l y s i s , t h i s method i s probably adequate. Table 7.3 l i s t s a l l the measured r e s u l t s and F i g u r e 7.5 shows a set of t y p i c a l r e s u l t s . The p a r t i c l e v e l o c i t y g e n e r a l l y i n c r e a s e d with bed l e v e l but decreased with i n c r e a s i n g r a d i u s . The only exception was near the f l u i d i n l e t ( i . e . , i n the c o n i c a l s e c t i o n ) where the v e l o c i t y next to the spout w a l l was somewhat higher than that at the upper bed l e v e l s . T h i s phenomenon i s the r e s u l t of reducing c r o s s - s e c t i o n a l area i n the cone. The e f f e c t of bed temperature on Vp i s shown i n F i g u r e s 7.6a, 7.6b and 7.6c which compare the p a r t i c l e v e l o c i t i e s at Table 7.3 Experimental values of particle velocity, d •«= 1.25 mm D •= 19 05 mm P i Run . Temp H H a 2 V p(r.) V, p ( r , ) Vrj) V p(r.) V tl (°C) (m) (m) (m) (cm/s) (cm/s) (cm/s) (cm/s) (cm/s) (cm/s) 5-6-B 20 0.813 0.840 1. 128 0.80 4 .969 4 .776 4 .598 4 .329 3.002 4 .315 0.70 4 .040 3 .883 3.578 3.436 2.222 3 .411 0.60 3. 195 2 .789 2.304 1 .959 1. 199 2. 129 0.50 2.532 2 .448 2. 103 1 .94-4 0.742 1 .929 0.40 1.779 1 .720 1.491 1 . 114 0.289 1 .213 0.30 1 .626 1 .339 1.034 0.750 0. 190 O.B72 0.20 1 .064 1 .053 0.669 0.2B7 0.0SB 0.512 0. 10 1 .704 1 . 166 0. 142 0.0 O.O 0.341 0.05 3.717 1 .211 0.0 0.0 0.0 0.815 6-5-b 170 0.464 0.4B0 1.162 0.45 2.597 2 .513 1.871 1 .467 0.657 1 .700 0.40 1 .878 1 .594 1 .429 1. 199 0.360 1 .230 0.30 1.855 1 .331 1.011 0.811 0. 182 0.893 0.20 1 .236 0 .886 0.696 0.370 0. 117 0.521 0. 10 2. 120 2 .044 0.559 0. 100 0.0 0.667 0.05 4.211 O .612 0.0 O.O 0.0 0/551 7-5-b 300 0.413 0.430 1.112 0.40 2. 143 1 .668 1.486 1.325 0.405 1 .323 O.30 1 .617 1 .  182 0.946 0.830 0. 190 0.857 0.20 1.345 0 .765 0.557 0.363 0.D90 0.469 0. 10 2.661 1 . 073 0.213 0.0 0.0 0.351 0.05 4 .878 0. .797 0.0 0.0 0.0 0.656 6-5-b 420 0.270 0.285 1 .094 0.25 3.315 1. . 289 0.841 0.384 0. 109 0:692 0.20 1 .9B0 1. . 188 0.765 0.325 0.069 0.592 0. 15 1 .928 1. .059 0.424 0. 238 0.0 0.457 0. 10 2.525 2 . 176 0. 270 0.0 0.0 0.613 0.05 4.115 0. 838 0.0 0.0 0.0 0.610 Definec by Equation 3.9 Ui -o 1 58 2 4 6 8 r in cm F i g u r e 7.5 P a r t i c l e v e l o c i t y i n the a n n u l u s (Run ft 7-5-b) 1 59 p. > 0 0 z = 4 0 . 0 c m O Run # 5-6-b A Run 1'6-5-b + Run # 7-5-b + 6 6 6 8 r m cm F i g u r e 7.6a E f f e c t r a d i a l of bed t e m p e r a t u r e p r o f i l e s of V p (z .= and b e d h e i g h t on the 4 0 cm) 1 60 5 r 1 2 = 1 30.0 c m " 1 4 o Run j} 5-6-b CO A Run if 6-5-b S" 3 + Run # 7-5-b o >—< -i-H > — A -0 — 1 — • 1 AO + 1 6 ffl 2 4 6 r in cm F i g u r e 7.6b Ef fec t r a d i a l of bed temperature p r o f i l e s of V D (z and bed h e i g h t on the = 30 cm) 161 fl a 0 0 + A z = 20 .0 c m A + O Run # 5-6 - b A Run # 6-5 - b + Run # 7-5 - b X Run # 8-5 -b 8 r m c m F i g u r e 7.6c E f f e c t of bed t e m p e r a t u r e and bed h e i g h t on the r a d i a l p r o f i l e s of V p (z = 20 cm) 162 the same bed l e v e l s but f o r d i f f e r e n t bed h e i g h t s and t e m p e r a t u r e s . Other parameters, such as dp, D^, D c and U/U m s were f i x e d . There were no s i g n i f i c a n t d i f f e r e n c e s i n the p a r t i c l e v e l o c i t i e s under these c o n d i t i o n s , i n d i c a t i n g t h a t f o r any g i v e n bed l e v e l , V p ( r ) was independent of bed h e i g h t and t e m p e r a t u r e . W i t h t h i s a s s u m p t i o n , the r a d i a l - a v e r a g e d p a r t i c l e v e l o c i t y f o r a l l f o u r runs was de t e r m i n e d u s i n g E q u a t i o n 3.9 and the f i n a l r e s u l t s a r e p l o t t e d on a s i n g l e graph ( F i g u r e 7.7). A l t h o u g h t h e r e was some s c a t t e r , most of the p o i n t s seemed t o l i e on one c u r v e . T h i s average p a r t i c l e v e l o c i t y , Vp g e n e r a l l y i n c r e a s e d w i t h bed l e v e l , e x c e p t i n the c o n i c a l s e c t i o n , where i t d e c r e a s e d w i t h i n c r e a s i n g bed l e v e l . 0 1 63 • Air at 20 deg C G Air at 170 deg C A Air at 300 deg C o Air at 420 deg C • • O fl * 9 o 8 ° a 0 20 40 60 00 z in cm gure 7.7 E f f e c t of bed l e v e l on the r a d i a 1 - a v e r a g e d p a r t i c l e v e l o c i t y 8. CONCLUSIONS AND RECOMMENDATIONS 8.1 CONCLUSIONS 1. E x p e r i m e n t a l v a l u e s of U m s were compared t o the Mathur and G i s h l e r e q u a t i o n ( i . e . , E q u a t i o n 2.1), which worked r e a s o n a b l y w e l l a t h i g h temperature c o n d i t i o n s but c o n s i s t e n t l y u n d e r p r e d i c t e d a t room t e m p e r a t u r e , w i t h d e v i a t i o n s up t o 30%. A p p l y i n g s t a t i s t i c a l a n a l y s i s t o a l l the d a t a from t h i s work produced exponents which a r e somewhat d i f f e r e n t from t h o s e of the M a t h u r - G i s h i e r e q u a t i o n , but the magnitude of c o r r e s p o n d i n g exponents were r o u g h l y of the same o r d e r . A l t h o u g h the Mathur and G i s h l e r e q u a t i o n was found t o be u n s a t i s f a c t o r y over the e n t i r e range of t e m p e r a t u r e s , i t d i d manage t o p r e d i c t c o r r e c t l y t h e q u a l i t a t i v e v a r i a t i o n of U m s w i t h each v a r i a b l e . 2. The e q u a t i o n of E p s t e i n and L e v i n e ( i . e . , E q u a t i o n 2.28) gave good p r e d i c t i o n of bed p r e s s u r e drop f o r room c o n d i t i o n s but i t o v e r e s t i m a t e d the e f f e c t of te m p e r a t u r e . I t i s i m p o r t a n t t o note t h a t t h i s e x p r e s s i o n i s based on the assumption of a n n u l a r f l u i d i z a t i o n at H m. E x p e r i m e n t a l r e s u l t s , however, i n d i c a t e d t h a t the spout t e r m i n a t i o n mechanism a t h i g h temperature might be due t o c h o k i n g of the spout or i n s t a b i l i t y of the sp o u t - a n n u l u s i n t e r f a c e , r a t h e r than f l u i d i z a t i o n of t h e " e n t i r e " annulus s u r f a c e . T h i s would e x p l a i n the d i s c r e p a n c y . 164 165 3. The spout diameter data f o r a i r at room c o n d i t i o n s were i n good agreement with those c a l c u l a t e d by the McNab equation ( i . e . , Equation 2.16). The same equation was, however, found to be u n r e l i a b l e f o r a i r spouting at higher temperatures and f o r helium at room temperature; i t f a i l e d to i n c l u d e f l u i d v i s c o s i t y as a v a r i a b l e and a l s o appeared to overestimate the e f f e c t of f l u i d d e n s i t y . A se m i - e m p i r i c a l e x p r e s s i o n has been developed, by i n c l u d i n g both d e n s i t y and v i s c o s i t y as parameters, and i t seems to work much b e t t e r than the McNab equation. 4. Experimental v a l u e s of H m were compared to the McNab and Bridgwater e x p r e s s i o n ( i . e . , Equation 2.8). Although i t c o n s i s t e n t l y g i v e s low estimates of H m, i t c o r r e c t l y p r e d i c t s the observed t r e n d . For a i r spouting, H m decreased with i n c r e a s i n g temperature, i n d i c a t i n g that steady spouting became more d i f f i c u l t . A l l other e s t a b l i s h e d equations f o r H m which f a i l to i n c l u d e the e f f e c t of temperature or p r e d i c t the opposite t r e n d of H m with temperature w i l l not be a p p l i c a b l e f o r design purposes at high temperatures. 5. H m i n c r e a s e d with i n c r e a s i n g pj but decreased with i n c r e a s i n g M (see Table 4.2). T h i s i s c o n s i s t e n t with the observed e f f e c t of temperature on H m. 6. The 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 was reasonably w e l l d e s c r i b e d by the Mamuro and H a t t o r i equation 166 ( i . e . , Equation 2.22) and the m o d i f i e d L e f r o y and Davidson equation ( i . e . , Equation 2.24 with n = 2), p r o v i d e d that U m f was r e p l a c e d by U->H . T h i s i s s i g n i f i c a n t s i n c e U a H becomes m m sm a l l e r than U m f as the temperature i n c r e a s e s . T h i s o b s e r v a t i o n f u r t h e r suggested that at high temperature, annular f l u i d i z a t i o n might not be the spout t e r m i n a t i n g mechanism. 7. The l o n g i t u d i n a l p r e s s u r e p r o f i l e s i n the annulus c o u l d be represented by the L e f r o y and Davidson equation ( i . e . , Equation 2.31). The more complicated e x p r e s s i o n of E p s t e i n and Levine ( i . e . , Equation 7.1) worked w e l l a l s o , but d i d not produce b e t t e r p r e d i c t i o n . 8. The temperature d i d not have any s i g n i f i c a n t e f f e c t on the p a r t i c l e c i r c u l a t i o n r a t e i n the annulus. The r a d i a l - a v e r a g e p a r t i c l e v e l o c i t y was found to i n c r e a s e with bed l e v e l , except at the c o n i c a l s e c t i o n , where the c r o s s - s e c t i o n a l area was s m a l l e r . 8.2 RECOMMENDATIONS 1. One p a r t i c u l a r area of i n t e r e s t i s the e f f e c t of v i s c o s i t y and d e n s i t y on the s p o u t a b i l i t y of p a r t i c l e s . Based on the r e s u l t s f o r H m, these two v a r i a b l e s cannot be ignor e d . Future study i n t h i s area should a l s o i n c l u d e Dj and d D s i n c e they too have been found to be important 167 f a c t o r s . 2. The e f f e c t o f p r e s s u r e on t h e h y d r o d y n a m i c s i s a l s o i m p o r t a n t . In a d d i t i o n , by o p e r a t i n g t h e s p o u t e d bed u n d e r s e l e c t e d c o n d i t i o n s of p r e s s u r e a n d t e m p e r a t u r e , i t becomes f e a s i b l e t o i n v e s t i g a t e t h e i n d i v i d u a l e f f e c t o f v i s c o s i t y u n d e r t h e c o n d i t i o n o f c o n s t a n t d e n s i t y . T h i s i s p o s s i b l e b e c a u s e t h e gas v i s c o s i t y i n c r e a s e s w i t h t e m p e r a t u r e b u t i s n o t v e r y s e n s i t i v e t o c h a n g e i n p r e s s u r e , w h e r e a s t h e d e n s i t y c a n be k e p t r o u g h l y c o n s t a n t by f i x i n g t h e r a t i o o f P / T . 3. D a t a f r o m a f u l l y c y l i n d r i c a l c o l u m n s h o u l d be o b t a i n e d f o r c o m p a r i s o n . NOTATION a s A s/Ac A " f u m f u t / [ ( P p - P f  ) ( 3 B i ] Ar d p 3 ( p p - p f ) p f g / M 2 A c Column c r o s s - s e c t i o n a l area (m 2) A s Spout c r o s s - s e c t i o n a l area (m 2) b Um/Umf dp Average p a r t i c l e diameter (m) dpi Mean diameter of adjacent screen a p e r t u r e s (m) dpj R e c i p r o c a l mean diameter from s i e v e a n a l y s i s (m) D c Column diameter (m) O r i f i c e diameter (m) D s ( z ) Spout diameter at z (m) D s Area-averaged spout diameter (m) Dg* D s at H = H m and U = U m s (m) D s H D s at z = H (m) D s H m D s a t 2 = Hm <m> f F r i c t i o n f a c t o r 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 p fU (kg/m 2s) G a Volumetric f l o w r a t e of s o l i d s (m 3/s) h H/Hm H Loosely packed bed height (m) H a Annulus height (m) Hp Fountain height (m) H m Maximum spoutable bed height (m) 168 169 k Constant i n Equation 6.1 k! , k 2, k 3 and k„ Constants i n Equation 6.2 K, a, T, o) and £ Parameters i n Equation 5.1 K, C o e f f i c i e n t i n Ergun equation (kg/m 3s) K 2 C o e f f i c i e n t i n Ergun equation (kg/m*) M Number of p a r t i c l e s i z e measurements or of data p o i n t s n Flow regime index N Richardson-Zaki index P Pressure (N/mz) PATM Atmospheric pressure (N/m2) P B Absolute pressure measured upstream with the s o l i d s i n the bed (N/m2) P E Absolute pressure measured upstream without the s o l i d s i n the bed (N/m2) P H Absolute pressure at z = H (N/m2) P s Absolute pressure i n the bed (N/m2) P z Absolute pressure i n the bed at z (N/m2) -AP Pressure drop a c r o s s the bed (N/mz) -AP a Pressure drop measured above the o r i f i c e (N/mz) -APf Minimum f l u i d i z a t i o n p r essure drop (N/m2) -AP S Minimum spouting pressure drop (N/m^) Q s Volumetric f l o w r a t e i n the spout (m 3/s) Q t T o t a l v o l u m e t r i c f l o w r a t e of f l u i d (m 3/s) r R a d i a l d i s t a n c e from the spout a x i s (m) 170 R e m f U m f P f V " Re t U tp fd p/M R c Column r a d i u s (m) R s Spout r a d i u s (m) t D e f i n e d i n Equation 5.2 (m) Tg Average bed temperature (°C, °K) U S u p e r f i c i a l f l u i d v e l o c i t y (m/s) U a ( z ) S u p e r f i c i a l annulus f l u i d v e l o c i t y at z (m/s) U a H U a at z = H (m/s) u a H m U a at z = H m (m/s) U c Choking v e l o c i t y (m/s) U m U m c. at H = H m (m/s)  s  v m / ^ / U m £ 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 (m/s) U m s S u p e r f i c i a l minimum spouting v e l o c i t y (m/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 the spout (m/s) U s H U s at z = H (m/s) u s H m U s at z = H m (m/s) U t Terminal v e l o c i t y of a p a r t i c l e (m/s) Vp(r) Annular p a r t i c l e v e l o c i t y at r (downward) (cm/s) Vp Radial-averaged annular p a r t i c l e v e l o c i t y (cm/s) v s H 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) x z/H m x^ 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 dp^ z, 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 (m) a Index in Equation 6.1 p b Bulk s o l i d s d e n s i t y (kg/m 3) 171 F l u i d d e n s i t y (kg/m-5) Pp True p a r t i c l e d e n s i t y (kg/m^) e a Annulus voidage e c Voidage at choking e m f Voidage at minimum f l u i d i z a t i o n 4> Shape f a c t o r of the p a r t i c l e s = s p h e r i c i t y P 2 + ( 3 K 1 / 2 K 2 U m f ) ^ Net downwards f o r c e per u n i t volume exerted by the s o l i d s (kg/m 2s 2) M F l u i d v i s c o s i t y (kg/m-s) K, TJ Parameters i n Equation 2.2 X S p o u t a b i l i t y parameter 6 Angle of i n t e r n a l f r i c t i o n (°) 6 Angle of repose (°) 7 Defined by Equation 2.36 REFERENCES A r b i b , H. 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APPENDIX A - MAXIMUM SPOUTABLE BED HEIGHT A.1 DERIVATION OF H m At the minimum f l u i d i z a t i o n c o n d i t i o n , the Ergun (1955) equation becomes: dP <~&mt ' ( P p - » f ) ( l - e m f > 9 = R i u m f + K 2 umf' A. 1 where 1 5 0 M ( ! - e m f ) 2 K1 = K, = ( ^ p ) 2 e m f 3 1 . 7 5 p f ( 1 - e m f ) * d p e m f A.2a A. 2 b M u l t i p l y i n g Equation A.1 by P f d p 3* emf 1.7 5M 2 ( 1 - e m f ) i t can be shown that R emf + 8 5 - 7 1 1 - e mf -Re mf - 0.571 e m f - ^ A r = 0 A.3 where Ar = Re mf P __P___ M 2 P f u m f d p A. 4a A.4b 176 177 Equation A.3 can be s o l v e d t o y i e l d P f u m f d p Re mf ~ = 42.86 1-e mf r - 3 i emf 1+311X10" 6 <j>6Ar { L(1-*mf> 2J - 1 A.5 An e x p r e s s i o n f o r H m i s o b t a i n e d by combining Equations 2.5, 2.1a and A.5 to e l i m i n a t e U m and U m f : Hm _ 2 i D IJ 2 / 3 918b 2' Ar 1 - e mf l 2 r * 3 i emf 1+311X10" 6 <p6kr [ d - m f ) 2 J A. 6 T h i s e x p r e s s i o n i s reduced by s u b s t i t u t i n g 4> and e m f with 0.6689 and 0.4744, r e s p e c t i v e l y : Hm ~ 2n i J 2/3 568b^ Ar [/1+35.9X10" 6Ar - 1 ] 2 A.7 A.2 EFFECT OF TEMPERATURE ON H m When temperature i n c r e a s e s , f l u i d d e n s i t y decreases while v i s c o s i t y i n c r e a s e s , which r e s u l t s i n a lower value of Ar i f dp i s f i x e d . Hence, the e f f e c t of temperature can be r e l a t e d to the e f f e c t of Ar. Equation A.7 i s r e w r i t t e n as H m = C,[/1/Ar + 35.9X10" 6 - / l / A r ] 2 A. 8 and 178 dH, m d A r = C, [/1 / A r + 35.9X10- 6 - i/1 / A r ] 1 1 A r 3 > Ar 3+35.9X1 0 " 6 A r 4 _ A . 9 > 0 f o r A r > 0 i m p l y i n g t h a t H m i n c r e a s e s w i t h A r a n d t h u s d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e . A . 3 C R I T I C A L P A R T I C L E DIAMETER S u b s t i t u t i n g E q u a t i o n A . 4 a i n t o E q u a t i o n A . 7 , t h e r e s u l t c a n be r e w r i t t e n a s H m 1+ C 3 d 3 - 1 = C 1 C Mdp4 d P 1 L " p . A . 1 0 a n d dH m d d r = 2C: 1 c 3 + — \laP ° P L aP 1 + C 3 d 3 -4 - C 3 + d 1 3 d ' • a p a p A . 1 1 ( d p ) c r i t i s f o u n d by s e t t i n g d ( H m ) / d ( d p ) e q u a l t o z e r o . T h e s o l u t i o n i s t h e n 179 ( V c r i t 3 = 8 / C 3 A. 1 2 I t can be shown from Equations A.4a and A.7 that <Pp~Pf )gpf" C, = 35.9X10- 6 Therefore < d p>crit = 6 0 - 6 . ( p p _ p f ^gpf. A..4 EFFECT OF <f> AND emf ON ( d p ) r r ^ 1 -1/3 A. 1 3 A. 1 4 If Equation A.6 i s used i n s t e a d of Equation A.7 when d e r i v i n g ( d p ) c r j _ t , C 3 of Equation A. 11 w i l l be d e f i n e d by emf 3 V.,r(p p-Pf>gpf" C 3 = 311X10 <t>' A. 1 5 and ( V c r i t = 2 9 - 5 2 " ( 1 - m f ) 2 " 1/3 " . e m f 3 * 3 - _9 (Pp~Pf >Pf. 1 / 3 A. 1 6 which c l e a r l y shows how ( d p ) c r ^ t v a r i e s with <j>. The e f f e c t of e m f can be i l l u s t r a t e d by d i f f e r e n t i a t i n g ( d p ) c r ^ t with respect to e m f . In f a c t , i t i s e a s i e r to d i f f e r e n t i a t e ( d p ) c r i t 3 . F i r s t , Equation A.16 i s r e w r i t t e n as ( d p ) c r i t 3 - c 2 1 + — emf 3 emf 2 emf-A. 1 7 180 and d ( d p ) c r i t : = C, de mf -3 4 3 emf emf -4 -1 + •mf - C f l [ ( e m f - l ) ( e m f - 3 ) ] / 6 m f ' A. 18 < 0 f o r 0 < e m f < 1 which means t h a t ( d p ) c r - i t 3 a n d n e n c e ^ d p ^ c r i t d e c r e a s e s w i t h i n c r e a s i n g e m£ Table B.1 Particle size distributions Size Range (mm) BEFORE EXPERIMENTS Weight friction for sample ***» SMALL 1.41 - 1. 19 1.19 - 1.00 1 .00 - 0.841 0.841 - 0.595 0.595 - 0.354 0.O059 0.5170 0.3863 0.0906 0.O0O1 0.0030 0.3957 0.3686 0.2092 0.0235 0.0044 0.4287 0.3920 0.1605 0.0145 0.0053 0.5735 0.3258 0.0944 0.0010 **" MEDIUM 2 .OO 1 .68 1.41 1 . 19 1 .00 0.841 0.595 1 .68 1.41 1 . 19 1 .00 0.84 1 0.595 0. 354 0.0021 0.2280 0.5246 0.2276 0.0136 0.0040 0.0002 0.0015 0.2684 0.5257 0.1920 0.0090 0.0031 0.0003 0.0024 0.1996 0.4905 0.2538 0.0256 0.0207 0.0075 0.0062 0.1836 0.5438 0.2326 0.0179 0.0125 0.0034 LARGE ***• 3B 00 1 .68 1.41 1 . 19 1 .00 0.641 - 2 .00 - 1 .68 - 1 . 4 1 - 1.19 - 1 .00 - 0.84 1 - 0.595 0.1270 0.1213 O.1038 0.1 1 4 4 0.5126 0.5288 0.5078 0.4877 0.3147 0.0307 0.0087 0.0027 0.0037 0.3064 0.0315 0.0072 0.0026 0.0023 0.3046 0.04 50 0.0147 0.0056 0.0186 0.3005 0.0649 0.0227 0.0056 0.0043 AFTER EXPERIMENTS Weight friction for sample *' O.0054 0.4B30 0.3553 0. 1448 0.0115 0.0035 0.3370 0.4019 0.2139 0.0438 O.0032 0.3888 0.3913 0. 1972 0.0195 0.0037 0.5190 0.3445 0.1256 0.0071 0.0024 0.0030 0.0018 0.0111 0.1556 0.4928 0.2855 0.0336 0.0214 0.0086 0.2142 0.5387 0.2180 0.0153 0.0076 0.0032 0.1308 0.5018 0.2881 0.0436 0.0237 0.0103 1898 5114 2485 0259 01 14 0020 O.1052 0. 4600 0.34 12 0.0674 0.0158 0.0054 0. 1 0 1 4 0 . 4 7 4 8 0.3140 0.0G59 0.0201 0.0085 0.0836 0. 3870 0.3133 0.1049 0.0429 0.0183 0.0050 0.0153 0.0498 0 . 1 0 7 7 0 . 5 3 4 f i 0 . 2 5 6 0 O . C 5 6 5 0 . 0 2 4 3 C . C 3 8 6 0 . 0 1 0 1 APPENDIX C - CAL IBRATION CURVES C.1 FLOWMETER CALIBRATION FOR GASES For a r o t a m e t e r , the g o v e r n i n g e q u a t i o n i s 2 g V F ( p F - p f ) p f l 1 / 2 G = C D A 2 _Ap[ 1 - (A 2/A 1 ) 2 ] C. 1 where Vp = volume of the f l o a t Pp = d e n s i t y of the f l o a t ( u s u a l l y >> p f ) Pf = d e n s i t y of the gas A, = c r o s s - s e c t i o n a l a r e a of the tube A 2 = a r e a of annulus between the f l o a t and tube Ap = maximum c r o s s - s e c t i o n a l a r e a of the f l o a t C D = drag c o e f f i c i e n t G = mass f l o w r a t e of gas The c o e f f i c i e n t C D depends on the shape of the f l o a t and the Reynolds number f o r the f l o w t h r o u g h the a n n u l a r space of area A 2. I f the f l o a t i s kept a t a f i x e d v e r t i c a l p o s i t i o n , C D can be assumed c o n s t a n t . E q u a t i o n C.1 then becomes G = B,/pf" C.2 F i g u r e C.1 i l l u s t r a t e s t he schematic s e t - u p f o r the rot a m e t e r c a l i b r a t i o n . I f the i d e a l gas law i s assumed, and 182 R O T A M E T E R V A L V E PR = - [ P i + P 2 ] / 2 ATMOSPHERE I G A S M E T E R P M V M T M pM = rp3+p«']/2 F i g u r e C . 1 S c h e m a t i c s e t - u p . f o r r o t a m e t e r c a l i b r a t i o n 184 T M = T R = 20 °C, then V R = V M and M C.3 G R = P R V R = ? R V M • M C.4 where p R = f l u i d d e n s i t y i n r o t a m e t e r . Combining E q u a t i o n s C.2 and C.4 y i e l d s B , = V M L P R . C.5 A s t a n d a r d c o n d i t i o n of P = 1 atm and T = 20 °C was chosen, S u b s t i t u t i n g E q u a t i o n C.5 i n t o E q u a t i o n C.2 g i v e s 'STD M ' M VTz] Vp STD C.6 and V STD 'STD = V M ' ' S T D L P R J \ | P S T D M PR C.7 For i d e a l gas PR PSTD PSTD C.8 S u b s t i t u t i n g t h i s r e l a t i o n i n t o E q u a t i o n C.7 g i v e s VSTD " V M M V M R^STD-C . 9 185 where P M = a b s o l u t e pressure of the gas meter P R = a b s o l u t e pressure of the rotameter Pgipjj = 1 atm V M = measured v o l u m e t r i c f l o w r a t e (gas meter) VSTD = corresponding v o l u m e t r i c flowrate f o r 1 atm and 20 °C Using Equation C.9, two c a l i b r a t i o n curves were produced ( F i g u r e s C.2 and C.3). C.2 FLOWRATE IN THE SPOUTED BED F i g u r e C.4 i s a s i m p l i f i e d flow diagram of the experimental apparatus. A p p l y i n g the i d e a l gas law, v s = V R P R T S PS TR. C. 1 0 From the rotameter reading, V S T D was determined from the c a l i b r a t i o n curves ( i . e . , F i g u r e s C.2 and C.3). T h i s value i s not equal to the a c t u a l v o l u m e t r i c f l o w r a t e (V R) through the rotameter. However, i t has been shown that f o r a gas rotameter that = B , //pTT C. 1 1 T h e r e f o r e 0 20 40 60 80 100 Rotameter reading F i g u r e C.2 C a l i b r a t i o n c urve ( l a r g e r o t a m e t e r ) E X H A U S T ROTAMETER PR VALVE SPOUTED BED V , F i g u r e C.4 S i m p l i f i e d flow diagram of the apparatus 189 V R V STD PSTD PR C. 12 and VR _ VSTD PSTD = V STD STD C. 13 S u b s t i t u t i n g Equation C.13 i n t o Equation C.10 g i v e s V S " VSTD STD 1 PR P R T S P S T R J = V STD v / PSTD PR C. 1 4 where Vg = vo l u m e t r i c f l o w r a t e through the spouted bed VSTD = v o l u m e t r i c f l o w r a t e taken from the c a l i b r a t i o n c u r v e ( s ) PSTD = ^ atm P R = absolute pressure of the rotameter Pg = absolute pressure of the spouted bed T R = temperature of the rotameter(°K) Tg = temperature of the spouted bed(°K) The same c a l i b r a t i o n curves ( i . e . , F i g u r e s C.2 and C.3) c o u l d be used f o r d i f f e r e n t gases by making a p p r o p r i a t e c o r r e c t i o n s , i . e . , r e p l a c i n g PSTD^PR ^ n Equation C.12 by MSTD PSTD / - TSTD - / i n which M R and Mg T D are molecular weights. Note that f o r the same gas at the same temperature, the above r a t i o would 190 be reduced t o ( P S T ^ / P R ) . C.3 CALIBRATION CURVE FOR -AP S VERSUS ~AP a Data and the r e s u l t i n g c u r v e a r e shown i n T a b l e C.1 and F i g u r e C.5. C.4 CALIBRATION FOR THE STATIC PRESSURE PROBE The c a l i b r a t i o n d a t a of p r e s s u r e drop v e r s u s U a were f i t t e d t o a second o r d e r p o l y n o m i a l , i . e . , -AP = d,U a + d 2 U a 2 C. 1 5 w i t h U a i n m/s and -AP i n i n c h e s of b u t a n o l . The r e s u l t s a r e summarized i n T a b l e C.2. T a b l e C.1 C a l i b r a t i o n d a t a of (-AP S) v e r s u s (-AP a) (cm of Hg) (cm of Hg) Ta b l e C.2 F i t t i n g parameters of E q u a t i o n C.15 dp = 1.25 mm, p p = 2600 kg/m 3 and a i r a t a t m o s p h e r i c p r e s s u r e . Run Temp d, d 2 . # ( C) 5 20 0.99232 0.71996 6 170 1.05510 0.60319 7 300 1.05856 0.42582 8 420 1.08820 0.39660 192 F i g u r e C.5 ~ A P S v e r s u s ~ A P a APPENDIX D - EXPERIMENTAL CONDITIONS O t t a w a S a n d , p p = 2600 k g / m 3 Run Gas Temp d P D i H H / H m # ( ° C ) (mm) (mm) (m) 1-1 AIR 20 0 . 9 4 5 19 .05 1 .168 1 .000 1 .000 1 - 1 - a AIR 20 0 . 9 4 5 19 .05 1 . 168 1 .000 1 .075 1-2 AIR 20 0 . 9 4 5 19 .05 1 . 1 68 0.761 1 .000 1-2 - a AIR 20 0 . 9 4 5 19 .05 1 . 168 0.761 1 .095 1 -3 AIR 20 0 . 9 4 5 19 .05 1 . 1 68 0 . 4 9 5 1 .000 1 - 3 - a AIR 20 0 . 9 4 5 19 .05 1 . 168 0 . 4 9 5 1.124 2- 1 AIR 170 0 . 9 4 5 19 .05 0 . 4 1 9 1 .000 1 .000 2- 1 - a AIR 170 0 . 9 4 5 1 9 .05 0 . 4 1 9 1 .000 1.101 2-2 AIR 170 0 . 9 4 5 19 .05 0 . 4 1 9 0 . 697 1 .000 2-2 -a AIR 170 0 . 9 4 5 19 .05 0 . 4 1 9 0 . 6 9 7 1.104 2 -3 AIR 170 0 . 9 4 5 19 .05 0 . 4 1 9 0 . 484 1 .000 2 - 3 - a A IR 170 0 . 9 4 5 19 .05 0 . 4 1 9 0 . 4 8 4 1 .099 5-1 AIR 20 1 . 250 1 9 . 0 5 1 .067 1 .000 1 .000 5 - 1 - a AIR 20 1 . 250 19 .05 1 .067 1 .000 1 .085 5-2 AIR 20 1 . 250 1 9 .05 1 .067 0 . 7 5 3 1 .000 5-2 - a AIR 20 1 . 250 1 9 . 0 5 1 .067 0 . 7 5 3 1.121 5-3 AIR 20 1 . 250 1 9 . 0 5 1 .067 0 . 4 8 5 1 .000 5 - 3 - a AIR 20 1 .250 1 9 . 0 5 1 .067 0 . 4 8 5 1.110 6-1 AIR 170 1 .250 1 9 . 0 5 0 . 6 4 8 1 .000 1 .000 6- 1 - a AIR 170 1 . 250 1 9 . 0 5 0 . 6 4 8 1 .000 1 .089 6-2 AIR 170 1 . 250 1 9 . 0 5 0 .648 0 . 6 9 6 1 .000 6-2 - a AIR 170 1.250 19 .05 0 . 6 4 8 0 . 6 9 6 1.114 6 -3 AIR 170 1 .250 1 9 . 0 5 0 . 6 4 8 0.451 1 .000 6 - 3 - a AIR 170 1 .250 19 .05 0 . 6 4 8 0.451 1 . 100 7- 1 AIR 300 1 . 250 1 9 . 0 5 0 . 546 1 .000 1 .000 7-1 - a AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 1 .000 1 . 1 05 7-2 AIR 300 1 . 250 1 9 .05 0 . 5 4 6 0 . 7 5 6 I .000 7-2 -a AIR 300 1 .250 19 .05 0 . 5 4 6 0 .756 1.113 7 -3 AIR 300 1 .250 19 .05 0 . 5 4 6 0 . 5 1 0 1 .000 7 - 3 - a AIR 300 1 . 250 1 9 .05 0 . 5 4 6 0 . 5 1 0 1 . 106 8-1 AIR 420 1 . 250 19 .05 0 .413 1 .000 1 .000 fl - 1 - a AIR 420 1 . 250 1 9 .05 0 .413 1 .000 1.101 8-2 AIR 420 1 .250 19 .05 0 .413 0 . 646 1 . 000 8-2 -a AIR 420 1 . 250 19 .05 0 .413 0.646 1 .105 8 -3 AIR 420 1 .250 19 .05 0 .413 0.499 1 .000 8 - 3 - a AIR 420 1 . 250 19 .05 0 .413 0 . 499 1 . 1 00 CONTINUED 193 194 Run Gas Temp V D i H H/ Hm U/ Ums « ( °C) (mm) (mm) (m) 9-1 AIR 20 1 .665 19.05 1.010 1 .000 1 .000 9-1-a AIR 20 1 .665 19.05 1.010 1 .000 1 .053 9-2 AIR 20 1 .665 19.05 1.010 0.723 1 .000 9-2-a AIR 20 1 .665 19.05 1.010 0.723 1 .044 9-3 AIR 20 1 .665 19.05 1.010 0 . 497 1 .000 9-3-a AIR 20 1 .665 19.05 1.010 0 . 497 1.123 1 0- 1 AIR 1 70 1 .665 19.05 0.800 1 .000 1 .000 10-1-a AIR 170 1 .665 19.05 0.800 1 .000 1 .071 1 0-2 AIR 170 1 .665 19.05 0.800 0.746 1 .000 10-2-a AIR 170 1 .665 19.05 0.800 0.746 1.115 10-3 AIR 170 1 .665 19.05 0.800 0.500 1 .000 10-3-a AIR 170 1 .665 19.05 0.800 0.500 1 .092 11-1 AIR 300 1 .665 19.05 0.721 1 .000 1 .000 11-1-a AIR 300 1 .665 19.05 0.721 1 .000 1 .064 1 1-2 AIR 300 1 .665 19.05 0.721 0.723 1 .000 11-2-a AIR 300 1 .665 19.05 0.721 0. 723 1 . 179 1 1-3 AIR 300 1 .665 19.05 0.721 0.498 1 .000 11-3-a AIR 300 1 .665 19.05 0.721 0.498 1 . 126 1 2- 1 AIR 420 1 .665 19.05 0.629 1 .000 1 .000 12-1-a AIR 420 1 .665 19.05 0.629 1 .000 1.103 1 2-2 AIR 420 1 .665 19.05 0.629 0.727 1 .000 12-2-a AIR 420 1 .665 19.05 0.629 0.727 1 . 1 27 1 2-3 AIR 420 1 .665 1 9.05 0.629 0 . 485 1 . 000 12-3-a AIR 420 1 .665 19.05 0.629 0 . 485 1 . 1 20 1 7- 1 AIR 20 1 .250 26.64 1 .026 1 . 000 1 .000 17-1-a AIR 20 1 .250 26.64 1 .026 1 .000 1 . 026 1 7-2 AIR 20 1 .250 26.64 1 .026 0.811 1 . 000 17-2-a AIR 20 1 .250 26.64 1 .026 0.811 1.119 17-3 AIR 20 1 .250 26. 64 1 .026 0.508 1 .000 17-3-a AIR 20 1 .250 26.64 1 .026 0.508 1.122 18- 1 AIR 170 1 .250 26.64 0.705 1 . 000 1 . 000 18-1-a AIR 170 1 .250 26. 64 0.705 1 .000 1 . 098 1 8-2 AIR 1 70 1 .250 26. 64 0 .705 0 . 806 1 . 000 1 8-2-a AIR 170 1 .250 26. 64 0.705 0 . 806 1.134 1 8-3 AIR 170 1 .250 26. 64 0.705 0 . 505 l . 000 18-3-a AIR 170 1 . 250 26.64 0.705 0 . 505 1.117 CONTINUED 195 Run Gas Temp D i H U/ Ums II ( ° C ) (mm) (mm) (m) 19-1 AIR 300 1 .250 2 6 . 6 4 0 . 4 1 9 1 .000 1 .000 1 9 - 1 - a AIR 300 1 .250 2 6 . 6 4 0 . 4 1 9 1 .000 1 .093 1 9 - 2 AIR 300 1 .250 2 6 . 6 4 0 . 4 1 9 0 .773 1 .000 1 9 - 2 - a AIR 300 1 .250 2 6 . 6 4 0 . 4 1 9 0 .773 1 .090 1 9 - 3 AIR 300 1 .250 2 6 . 6 4 0 . 4 1 9 0. 523 1 .000 1 9 - 3 - a AIR 300 1 .250 2 6 . 6 4 0 . 4 1 9 0. 523 1 . 106 2 0 - 1 AIR 420 1 .250 2 6 . 6 4 0 . 3 4 3 1 .000 1 .000 2 0 - 1 - a AIR 420 1 .250 2 6 . 6 4 0 . 343 1 . 000 1 .027 2 0 - 2 AIR 420 1 .250 2 6 . 6 4 0 . 3 4 3 0 .703 1 .000 2 0 - 2 - a AIR 420 1 .250 2 6 . 6 4 0 . 3 4 3 0 .703 1 . 106 2 0 - 3 AIR 420 1 .250 2 6 . 6 4 0 . 3 4 3 0 .490 1 .000 2 0 - 3 - a AIR 420 1 .250 2 6 . 6 4 0 . 3 4 3 0 . 4 9 0 1.114 21-1 AIR 20 1 .665 2 6 . 6 4 0 . 9 7 8 1.000 1 .000 21 - 1-a AIR 20 1 .665 2 6 . 6 4 0 . 9 7 8 1 .000 1.011 2 1-2 AIR 20 1 .665 2 6 . 6 4 0 . 9 7 8 0 . 8 5 0 1 .000 2 1 - 2 - a AIR 20 1 .665 2 6 . 6 4 0 . 9 7 8 0 .850 1 . 109 2 1 - 3 AIR 20 1 .665 2 6 . 6 4 0 . 9 7 8 0 .572 1 .000 2 1 - 3 - a AIR 20 1 .665 2 6 . 6 4 0 .978 0 .572 1.148 2 2 - 1 AIR 170 1 .665 2 6 . 6 4 0 .838 1 .000 1 .000 2 2 - 1 - a AIR 170 1 .665 26^64 0 .838 1 .000 1 .050 2 2 - 2 AIR 170 1 .665 2 6 . 6 4 0 .8 38 0 .746 1 .000 2 2 - 2 - a AIR 170 1 .665 2 6 . 6 4 0 . 8 3 8 0 .746 1.123 2 2 - 3 AIR 170 1 .665 2 6 . 6 4 0 .838 0. 504 1 .000 2 2 - 3 - a AIR 1 70 1 .665 2 6 . 6 4 0 .838 0. 504 1.13 1 2 3 - 1 AIR 300 1 .665 2 6 . 6 4 0 . 6 7 9 1 .000 1 .000 2 3 - 1 - a AIR 300 1 .665 2 6 . 6 4 0 . 6 7 9 1.000 1 .080 2 3 - 2 AIR 300 1 .665 2 6 . 6 4 0 . 6 7 9 0 .748 1 .000 2 3 - 2 - a AIR 300 1 .665 2 6 . 6 4 0 . 6 7 9 0 .748 1.113 2 3 - 3 AIR 300 1 .665 2 6 . 6 4 0 . 6 7 9 0 . 5 0 5 1 .000 2 3 - 3 - a AIR . 300 1 .665 2 6 . 6 4 0 . 6 7 9 0. 505 1 . 1 24 2 4 - 1 AIR 420 1 .665 2 6 . 64 0 . 5 4 0 1 . 0 0 0 1 .000 2 4 - 1 - a AIR 420 1 .665 2 6 . 6 4 0 . 5 4 0 1 . 0 0 0 1.124 2 4 - 2 AIR 420 1 .665 26 .64 0 . 5 4 0 0 . 7 5 2 1 . 0 0 0 2 4 - 2 - a AIR 420 1 .665 2 6 . 6 4 0 . 5 4 0 0 . 752 1.124 2 4 - 3 A l R 420 1 .665 26 .64 0 . 5 4 0 0 . 4 7 0 1 . 0 0 0 2 4 - 3 - a AIR 420 1 .665 2 6 . 64 0 . 540 0 . 470 1.112 CONTINUED 196 Run G a s Temp V D i H H / " m l J / U m s 1 ( ° c ) (mm) (mm) (m) 25-1 A I R 20 0 . 9 4 5 1 2 . 7 0 1 . 372 1 . 000 1 . 000 2 5 - 1 - a A I R 20 0 . 9 4 5 1 2 . 7 0 1 . 372 1 . 000 1 . 0 2 9 2 5 - 2 A I R 20 0 . 9 4 5 1 2 . 7 0 1 . 372 0 . 8 1 5 1 . 0 0 0 2 5 - 2 - a A I R 20 0 . 9 4 5 1 2 . 7 0 1 . 372 0 . 8 1 5 1 . 1 1 0 2 5 - 3 A I R 20 0 . 9 4 5 1 2 . 7 0 1 . 372 0 . 5 3 0 1 . 0 0 0 2 5 - 3 - a A I R 20 0 . 9 4 5 1 2 . 7 0 1 . 372 0 . 530 1 . 1 2 4 2 6 - 1 A I R 170 0 . 9 4 5 1 2 . 7 0 0 . 7 2 4 1 . 000 1 . 000 2 6 - 1 - a A I R 170 0 . 9 4 5 1 2 . 7 0 0 . 7 2 4 1 . 000 1 . 1 08 2 6 - 2 A I R 170 0 . 9 4 5 1 2 . 7 0 0 . 7 2 4 0 . 7 5 8 1 . 000 2 6 - 2 - a A I R 170 0 . 9 4 5 1 2 . 7 0 0 . 7 2 4 0 . 7 5 8 1 . 102 2 6 - 3 A I R 170 0 . 9 4 5 1 2 . 7 0 0 . 7 2 4 0 . 492 1 . 000 2 6 - 3 - a A I R 170 0 . 9 4 5 1 2 . 7 0 0 . 7 2 4 0 . 4 9 2 1 .091 27-1 A I R 300 0 . 9 4 5 1 2 . 7 0 0 . 635 1 . 0 0 0 1 . 0 0 0 2 7 - 1 - a A I R 300 0 . 9 4 5 1 2 . 7 0 0 . 6 3 5 1 . 0 0 0 1 . 0 4 6 2 7 - 2 A I R 300 0 . 9 4 5 1 2 . 7 0 0 . 635 0 . 7 5 0 1 . 0 0 0 2 7 - 2 - a A I R 300 0 . 9 4 5 1 2 . 7 0 0 . 6 3 5 0 . 7 5 0 1 . 0 8 3 2 7 - 3 A I R 300 0 . 9 4 5 1 2 . 7 0 0 . 6 3 5 0 . 4 9 0 1 . 0 0 0 2 7 - 3 - a A I R 300 0 . 9 4 5 1 2 . 7 0 0 . 635 0 . 490 1 . 1 00 28-1 A I R 420 0 . 9 4 5 1 2 . 7 0 0 . 4 8 6 1 . 000 1 . 0 0 0 2 8 - 1 - a A I R 420 0 . 9 4 5 12^70 0 . 486 1 . 000 1.101 2 8 - 2 A I R 420 0 . 9 4 5 1 2 . 7 0 0 . 4 8 6 0 . 7 4 5 1 . 0 0 0 2 8 - 2 - a A I R 420 0 . 9 4 5 1 2 . 7 0 0 . 486 0 . 7 4 5 1 . 0 7 7 2 8 - 3 A I R 420 0 . 9 4 5 1 2 . 7 0 0 . 486 0 .471 1 . 0 0 0 2 8 - 3 - a A I R 420 0 . 9 4 5 1 2 . 7 0 0 . 486 0 .471 1 .126 2 9 - 1 A I R 20 1 . 2 5 0 1 2 . 7 0 1 . 276 1 . 000 1 . 000 2 9 - 1 - a A I R 20 1 . 250 1 2 . 7 0 1 . 276 1 . 000 1 . 0 4 7 2 9 - 2 A I R 20 1 . 2 5 0 1 2 . 7 0 1 . 276 0 .741 1 . 000 2 9 - 2 - a A I R 20 1 .250 1 2 . 7 0 1 . 2 7 6 0 .741 1 .081 2 9 - 3 A I R 20 1 . 250 1 2 . 7 0 1 . 2 7 6 0 . 4 9 8 1 . 000 2 9 - 3 - a A I R 20 1 . 250 1 2 . 7 0 1 . 2 7 6 0 . 4 9 8 1 . 1 24 30-1 A I R 170 1 . 250 1 2 . 7 0 0 .781 1 . 0 0 0 1 . 000 3 0 - 1 - a A I R 170 1 . 250 1 2 . 7 0 0 .781 1 . 000 1 . 0 8 6 30 -2 A I R 170 1 . 250 1 2 . 7 0 0 .781 0 . 7 2 3 1 . 000 3 0 - 2 - a A I R 170 1 . 250 1 2 . 7 0 0 .781 0 . 7 2 3 1 . 099 3 0 - 3 AIR 170 1 . 250 1 2 . 7 0 0 .781 0 . 4 9 6 1 . 000 3 0 - 3 - a A I R 170 1 . 250 1 2 . 70 0 .781 0 . 4 96 1 . 1 0 4 CONTINUED 197 Run G a s Temp V D i H U / U m s it ( ° C ) (mm) (mm) (m) 31-1 A I R 300 1 . 2 5 0 1 2 . 7 0 0 . 6 5 4 1 . 000 1 . 000 3 1 - 1 - a A I R 300 1 . 2 5 0 1 2 . 7 0 0 . 6 5 4 1 . 000 1 . 105 3 1 - 2 A I R 300 1 . 250 1 2 . 7 0 0 .654 0 . 7 5 7 1 . 000 3 1 - 2 - a A I R 300 1 . 250 1 2 . 7 0 0 .654 0 . 7 5 7 1 . 0 9 6 3 1- 3 A I R 300 1 . 250 1 2 . 7 0 0 . 6 5 4 0 . 4 7 6 1 . 000 3 1 - 3 - a A I R 300 1 . 2 5 0 1 2 . 7 0 0 .654 0 . 4 7 6 1 . 103 3 2 - 1 A I R 420 1 . 250 1 2 . 7 0 0 . 5 3 3 1 . 000 1 . 000 3 2 - 1 - a A I R 420 1 . 2 5 0 1 2 . 7 0 0. 533 1 . 000 1 . 095 3 2 - 2 A I R 420 1 . 250 1 2 . 7 0 0 . 5 3 3 0 . 7 5 0 1 . 000 3 2 - 2 - a A I R 420 1 . 250 1 2 . 7 0 0 . 533 0 . 7 5 0 1 . 103 3 2-3 A I R 420 1 . 250 1 2 . 7 0 0 . 5 3 3 0 . 4 3 5 1 . 000 3 2 - 3 - a A I R 420 1 . 2 5 0 1 2 . 7 0 0 . 5 3 3 0 . 4 3 5 1 . 104 3 3 -1 A I R 20 1 . 6 6 5 1 2 . 7 0 1 . 0 2 9 1 . 0 0 0 1 . 000 3 3 - 1 - a A I R 20 1 . 6 6 5 1 2 . 7 0 1 . 0 2 9 1 . 0 0 0 1 . 0 4 5 3 3 - 2 A I R 20 1 . 6 6 5 1 2 . 7 0 1 . 0 2 9 0 .741 1 . 000 3 3 - 2 - a A I R 20 1 . 6 6 5 1 2 . 7 0 1 . 029 0 .741 1 . 108 3 3 - 3 A I R 20 1 . 6 6 5 1 2 . 7 0 1 . 0 2 9 0 . 5 1 8 1 . 000 3 3 - 3 - a A I R 20 1 . 665 1 2 . 7 0 1 . 0 2 9 0 . 5 1 8 1 . 1 1 0 3 4-1 A I R 1 70 1 . 6 6 5 1 2 . 7 0 0 . 8 3 2 1 . 000 1 . 000 3 4 - 1 - a A I R 1 70 1 . 6 6 5 1 2 . 7 0 0 . 8 3 2 1 . 0 0 0 1 .052 3 4 - 2 A I R 170 1 . 665 1 2 . 7 0 0 . 8 3 2 0 . 7 4 4 1 . 000 3 4 - 2 - a A I R 1 70 1 . 6 6 5 1 2 . 7 0 0 . 8 3 2 0 . 7 4 4 1 .088 3 4 - 3 A I R 1 70 1 . 6 6 5 1 2 . 7 0 0 . 8 3 2 0 . 488 1 . 0 0 0 3 4 - 3 - a A I R 170 1 . 6 6 5 1 2 . 7 0 0 . 8 3 2 0 . 4 8 8 1 . 0 9 3 3 5 - 1 A I R 300 1 . 6 6 5 1 2 . 7 0 0 . 7 4 3 1 . 000 1 . 000 3 5 - 1 - a A I R 300 1 . 6 6 5 1 2 . 7 0 0 . 7 4 3 1 . 000 1.071 35 -2 A I R 300 1 . 6 6 5 1 2 . 7 0 0 . 7 4 3 0 . 7 3 0 1 . 000 3 5 - 2 - a A I R 300 1 . 6 6 5 1 2 . 7 0 0 . 7 4 3 0 . 7 3 0 1 .117 35 -3 A I R 300 1 . 6 6 5 1 2 . 7 0 0 . 7 4 3 0 .491 1 . 000 3 5 - 3 - a A I R 300 1 . 6 6 5 1 2 . 7 0 0 . 7 4 3 0 .491 1 . 104 3 6 - 1 A I R 420 1 . 6 6 5 1 2 . 7 0 0 . 6 5 4 1 . 000 1 . 000 3 6 - 1 - a AIR 420 1 . 6 6 5 1 2 . 7 0 0 . 654 1 . 000 1 . 086 36 -2 A I R 420 1 . 6 6 5 1 2 . 7 0 0 . 654 0 . 743 1 . 000 3 6 - 2 - a AIR 420 1 . 6 6 5 1 2 . 7 0 0 . 6 5 4 0 . 7 4 3 1 . 108 36 -3 A I R 420 1 . 665 1 2 . 7 0 0 . 6 5 4 0 . 476 1 . 000 3 6 - 3 - a A l R 420 1 . 6 6 5 1 2 . 7 0 0 . 6 5 4 0 . 476 1 . 1 08 CONTINUED 198 Run Gas Temp D i H H/ Hm U/ Ums tf CO (mm) (mm) (m) 37-1 METHANE 20 1 .250 19.05 1 . 380 1 .000 1 .000 37-1- a METHANE 20 1 .250 19.05 1 . 380 1 .000 1 .064 37-2 METHANE 20 1 .250 19.05 1 . 380 0.773 1 .000 3 7-2-a METHANE 20 1 .250 19.05 1 .380 0.773 1 .075 37-3 METHANE 20 1 .250 19.05 1 . 380 0.511 1 .000 37-3- a METHANE 20 1 .250 1 9.05 1 . 380 0.511 1 .093 37-4 METHANE 20 1 .250 19.05 1 . 380 0 . 1 84 1 .000 37-4- a METHANE 20 1 .250 1 9.05 1 . 380 0.184 1 .075 37-4- b METHANE 20 1 .250 1 9.05 1 . 380 0. 184 1.117 37-4- c METHANE 20 1 .250 19.05 1 .380 0.184 1 . 170 38- 1 HELIUM 20 1 .250 19.05 0 .53 3 1 .000 1 .000 38-1- a HELIUM 20 1 .250 19.05 0 .533 1 .000 1 . 129 38-2 HELIUM 20 1 .250 19.05 0 .533 0.756 1 .000 38-2- a HELIUM 20 1 .250 19.05 0 . 533 0. 756 1 .068 38-2- b HELIUM 20 1 .250 1 9.05 0 . 533 0.756 1.112 38-2- c HELIUM 20 1 .250 19.05 0 .533 0.756 1.174 38-3 HELIUM 20 1 .250 19.05 0 . 533 0.512 1 .000 38-3- a HELIUM 20 1 .250 19.05 0 .533 0.512 1 .050 38-3- b HELIUM 20 1 .250 19.05 0 . 533 0.512 1 .095 38-3- c HELIUM 20 1 .250 19.05 0 .533 0.512 1 . 178 CONTINUED 199 Run G a s Temp d P D i H ft CO (mm) (mm) (m) 5-4 A I R 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 1 .000 1 . 000 5 -5 A I R 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 0 .941 1 . 000 5 -6 AIR 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 0 . 7 5 8 1 . 000 5 - 6 - a A I R 20 1 . 250 1 9 . 0 5 1 . 0 7 3 0 . 7 5 8 1 . 075 5 - 6 - b A I R 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 0 . 7 5 8 1 . 1 28 5 - 6 - c A I R 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 0 . 7 5 8 1 . 190 5-7 A I R 20 1 . 250 1 9 . 0 5 1 . 0 7 3 0 . 5 5 6 1 . 000 5-8 AIR 20 1 . 250 1 9 . 0 5 1 . 073 0 . 4 1 4 1 . 000 5-9 AIR 20 1 . 250 1 9 . 0 5 1 . 0 7 3 0 . 2 6 0 1 . 000 5 - 9 - a AIR 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 0 . 260 1 . 058 5 - 9 - b AIR 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 0 . 260 1 .118 5 - 9 - c A I R 20 1 . 2 5 0 1 9 . 0 5 1 . 0 7 3 0 . 2 6 0 1 . 179 6-4 AIR 170 1 . 6 6 5 1 9 . 0 5 0 . 6 4 8 1 . 000 1 . 0 0 0 6-5 AIR 170 1 . 250 1 9 . 0 5 0 . 6 4 8 0 . 7 1 6 1 . 0 0 0 6 - 5 - a AIR 170 1 . 250 1 9 . 0 5 0 . 6 4 8 0 . 7 1 6 1 . 0 7 9 6 - 5 - b A I R 1 70 1 . 250 1 9 . 0 5 0 . 6 4 8 0 . 7 1 6 1 .162 6 - 5 - c AIR 1 70 1 . 2 5 0 1 9 . 0 5 0 . 6 4 8 0 . 7 1 6 1 . 2 0 8 6-6 AIR 1 70 1 . 250 1 9 . 0 5 0 . 6 4 8 0 . 4 1 2 1 . 0 0 0 6 - 6 - a AIR 170 1 . 250 1 9 . 0 5 0 . 6 4 8 0 . 4 1 2 1 . 0 3 9 6 - 6 - b AIR 170 1 . 250 1 9 . 0 5 0 . 6 4 8 0 . 4 1 2 1 .122 6 - 6 - c AIR 1 70 1 . 250 1 9 . 0 5 0 . 6 4 8 0 . 4 12 1 . 180 7-4 AIR 300 1 . 2 5 0 1 9 . 0 5 0 . 5 4 6 1 . 000 1 . 0 0 0 7-5 AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 0 . 7 5 6 1 . 0 0 0 7 - 5 - a AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 0 .756 1 . 0 5 5 7 - 5 - b AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 0 . 7 5 6 1 .112 7 - 5 - c AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 0 . 7 56 1 . 1 60 7-6 AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 0 . 5 7 0 1 . 0 0 0 7-7 AIR 300 1 . 250 1 9 . 0 5 0 . 546 0 . 4 8 9 1 . 0 0 0 7 - 7 - a AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 0 . 489 1 . 0 4 9 7 - 7 - b AIR 300 1 . 250 1 9 . 0 5 0 . 5 4 6 0 . 4 8 9 1.111 7 - 7 - c AIR 300 1 . 250 19 .05 0 . 5 4 6 0 . 48 9 1 .162 8-4 AIR 420 1 . 250 1 9 . 0 5 0 . 4 1 3 1 . 000 1 . 000 8 -5 AIR 4 20 1 . 250 1 9 . 0 5 0 . 4 1 3 0 . 654 1 . 000 8 - 5 - a AIR 420 1 . 250 1 9 . 0 5 0 . 4 1 3 0 .654 1 .04 1 8 - 5 - b AIR 420 1 . 250 1 9 . 0 5 0 . 4 1 3 0 . 6 5 4 1 . 094 8 - 5 - c AIR 420 1 . 250 1 9 . 0 5 0 . 4 1 3 0 . 6 5 4 1.191 APPENDIX E - VARIATIONS OF SPOUT DIAMETERS WITH BED L E V E L Run H 1-1-a 2 (cm) Os(cm) Run * 2-1-a z(cm) Os(cm) Run * 5-1-a 2(cm) Ds(cm) Run H 6-1-a z(cm) Os(cm) 0 1 .9 0 1.9 0 1 .9 0 1 . 9 5 3 .2 5 2.6 5 3 . t 5 3.0 to 3 .6 10 3.0 10 3 4 10 3 • •» 15 3 .0 15 2.8 15 3 .2 15 3 . 2 20 3, .0 20 2.9 20 3 .0 20 3 .0 30 2 . 9 30 3. t 30 3 .0 30 3.0 40 2 .9 40 3 40 3 .0 40 3.0 50 2 .9 43 3.9 50 3 . 1 50 3.0 60 2 . 9 60 3 . 3 60 3 . 3 70 3 , . 1 70 3 . , 5 66 4 . 2 80 3 . 1 80 3. 7 90 3 . 2 Run * 2-2-a 90 3 . 9 100 3, .5 100 4 . 1 t 10 3 . 7 108 4 . .5 Run H 6-2-a 121 4 .0 z(cm) Os(cm) 0 1 . .95 2 . 9 10 3 .5 15 3 . 2 20 3. .0 30 2 . 7 40 2 .7 50 2 . 7 60 2 .7 70 2 .a BO 2  99 1 3 .6 Run » 1-3-a z(cm) Ds(cm) 0 1 .9 Run it 1-2-a . S 2 .5 10 2 .8 15 2 .6 z(cm) Ds(cm) 20 2 .4 25 2 .4 30 2 .5 Run » 2-3-a z(cm) Ds(cm) O 2.5 5 7.5 10 12.5 15 17.5 20 22 1 .9 2.4 2.7 Run » 5-2-a z(cm) Ds(cm) 0 1 .9 5 3 .0 10 3 .4 15 3 .0 20 3, . 1 30 3 O 40 3 .0 50 3 .O 60 3 . 1 70 3 . 2 ao 3 . 3 82 3 . 6 Run H 5-3-a z(cm) Ds(cm) O 1 . 90 t . 9 5 2 . 9 5 2 . 7 IO 3 . 3 IO 3 . 2 15 3 . , 1 15 3 . .0 20 2 . a20 2 .a 30 2 . a 30 2 7 40 2 940 2 , . 7 50 3 . 2 50 2 , .9 52 3 . 4 60 3 . 3 z(cm) Ds(cm) O 5 IO 15 20 30 40 49 Run * 6-3-a z(cm) Ds(cm) O 5 10 15 20 25 30 200 201 Run It 7-1-a Run * 8- 1-a Run U 9- 1-a Run H 10-1-a z(cm) Ds(cm) z(cm) Ds(cra) z(cm) Os(cm) z (cm) Os (cm 0 1.9 0 1 .9 0 1 . 9 0 1 .9 5 2.8 5 2.a 5 3 . 3 5 3 .3 10 3.3 10 3.3 to 3 . 9 10 3.8 15 3.0 15 2 . a IS 3 7 15 3.6 20 2.8 20 2.8 20 3 . 3 20 3 . 4 30 2.8 25 2.a 30 3.4 30 3 . 3 40 2.9. 30 2. a 40 3.5 40 3 . 3 50 3 . 3 35 2.8 50 3 . 5 50 3 . 3 55 3 . 7 40 2 . 9 60 3 . 6 60 J . 6 42 3.3 70 3 . 7 70 3.8 ao 3 . a ao 4 .0 90 4.0 83 4 . 3 Run H 7-2-a t 10 4 . 2 Run It 8-2-a t 15 4 . 2 z(cm) Os(cm) Run It 10-2-a 0 1 . 95 2 . a 10 3 . , 2 15 2 . a 20 2 .  a 30 2 .a 40 2 . a 44 3 . 2 Run it 7-3-a z(cra) Qs(cm) 0 5 10 15 20 25 29 . 5 1 .9 2.a z(cra) Oa(cm) 0 5 10 15 20 25 29 1 .9 2.7 3 . 2 2.8 2 . 8 2. a 2.a Run a 9-2-a z(cm) Os(cm) Run It 8-3-a z(cm) Os(cm) O 5 to 15 20 30 40 50 60 72 I .9 3 . 3 3.8 3.2 3.2 3.3 3.4 3.5 3 . 6 4 . 2 0 5 10 15 20 22 Run tt 9-3-a z(cm) Os(cm) 0 1 , , 9 5 3 . 3 10 3 . a 15 3 , .5 20 3 , . 2 30 3 , . 2 40 3, . 2 45 3 . 2 51 3, .a z(cm) Os(cm) O 5 10 15 20 30 40 50 62 1 .9 3.2 3.8 3 . 4 3 . 2 3.2 3 . 2 3 . 3 3.7 Run It 10-3-a z(cm) Os(cm) 0 5 10 15 20 30 4 1 t .9 3.0 3 . 7 3 . 3 3 . 2 3 . 2 3 . 5 202 Run M 11- 1-a Run It 12-1-a Run U 17- 1-a Run it 18- 1-a 2 (cm) Os(cm) z (cm) Os(cm) z(cm) Ds(cm) z (cm) Ds (cm 0 1.9 0 1.9 0 2.7 0 2.7 a 3.3 5 3.0 5 3.4 5 3 . 4 10 3.8 10 3.5 10 3.8 10 3.7 15 3.5 15 3.3 15 3.6 15 3.4 20 3.3 20 3.2 20 3.2 20 2.9 30 3.3 30 3.3 30 3. t 30 3.0 40 3.3 40 3.6 40 3.2 40 3 . 1 50 3.4 50 3.8 50 3 . 2 50 3 . 1 60 3.S 67 4.2 60 3.2 60 3 . 3 76 4 . t 70 3.2 70 4 . 2 80 3.4 75 4.6 90 3.6 Run # 12-2-a 100 3.8 Run * I l-2-a 1 10 4 . 2 11S 4.6 Run It 18-2-a 2 (cm) Os(cm) z(cm) Da(cm) • z(cra) Ds(cm! 0 1.9 Run » 17-2-a 0 1.9 5 3.0 5 3.2 10 3.4 0 2 . 7 10 3. a 15 3.3 z(cm) Os(cm) 5 3.2 15 3.4 20 3.2 10 3.6 20 3.2 30 3.2 15 3.4 30 3.2 40 3.4 . 0 2.7 20 2 . a 40 3.2 47 3.7 . 5 3.4 30 2 . 8 50 3.3 10 3.8 40 2 . 9 55 3.8 15 3.5 50 3.4 20 3. 1 58 4 . 3 Run n 12-3-a 30 3 . t 40 3. 1 Run '» 1 1-3-a 50 3.1 z(cm) Oa(cm) 60 3 . 2 Run It 18-3-a 70 3.3 z(cm) Os(cm) ao 3 . 5 0 1 . 9 87 3.8 z (cm) Dslcm! 5 3.0 0 1.9 to 3.2 5 3. t 15 3.0 0 2 . 7 10 3.5 20 2.9 Run U 17-3-a 5 3.0 15 3 . 1 25 2.9 10 3 . 4 20 3.0 3 I 3 . 2 15 3.0 30 3.0 z(cm) Os(cm) 20 2 . 4 35 3.2. 25 2 . 6 30 3 . 1 0 2 . 7 •10 J . 7 5 3 . 3 10 3 . 4 15 3 . 2 20 2 . a 30 2 . a 40 3.0 50 3.2 53.5 3 . 4 ( 203 Run * 19- 1-a Run * 20-1-a Run H 21-1-a Run * 22- 1-a z(cm) Ds(cm) z(cm) Os(cm) z(cm) Os(cm) z (cm) Ds(cm] 0 2.7 0 2.7 0 2 . 7 0 2 . 7 5 3.0 S 2.9 5 3.7 5 3.4 10 3.4 10 3.3 IO 3 . 9 10 3.8 15 3. 1 15 2.9 15 3 . 7 15 3.6 20 2.8 20 2.7 20 3 . 4 20 3. 4 30 2.9 25 2.7 30 3 . 5 30 3.4 40 3.2 30 2 . 7 40 3 . 6 40 3.4 43 3 . 7 35.5 3.3 SO 3.6. 50 3 . 5 60 3 . 9 60 3 . 5 70 3 . 9 70 3.5 80 4.0 80 3 . 7 Run it 19-2-a Run It 20-2-a 90 4 .0 92 4 .2 100 4 . 1 1 10 4 . 4 z(cm) Ds(cm) z(cm) Os(cm) 1 17 4.7 Run It 22-2-a O 2.7 0 2.7 5 3.0 2.5 2.7 Run It 21-2-a z(cm) Os (cm 10 3 . 2 5 2.8 15 3.0 7.5 3 .O 20 2 . 6 10 3.2 z(cm) Ds(cm) 0 2 . 7 25 2 . 7 12.5 3.0 5 3.4 30 3 . 2 15 2.8 10 3.8 32.5 3.4 17.5 2 . 6 0 2.7 15 3.6 20 2.6 5 3 . 5 20 3 . 3 22.5 2.6 10 3 . 8 30 3.3 25 2!9 15 3.6 40 3.3 Run it 19-3-a 20 3 . 3 50 3.4 SO 3 . 4 60 3.5 40 3 . 1 65 3 . 7 z (cm) Ds(cm) Run U 20-3-a 50 3 . 7 60 3 . a 70 4 .0 0 2.7 z(cra) Os(cm) 80 4 . 3 Run It 22-3-a 2.5 2 8 ; 88 4 .5 5 3.0 7 . 5 3. 1 0 2.7 Z(cm) Ds( cm 10 3.2 2.5 2.7 12.5 2.8 5 2.8 Run 1 2l-3-a 15 2.7 7.5 3.1 0 2 . 7 17.5 2 . 6 10 2.6 Os(cm) 5 3 . 2 20 2 . 5 12.5 2.6 2 (cm) 10 3 . 7 22 2.6 15 2.6 15 3 . 5 18 2.9 20 3 . 2 0 2.7 30 3 . 3 5 3 .4 40 3 . 3 10 3.7 43 . 5 3 . 6 15 3.5 20 3 . 2 30 3 . 3 40 3.4 50 3.6 57 3.8 204 Run » 23- 1-a Run » 24-1-a Run It 25-1-a Run M 26- 1-a z(cm) Os(cm) z(cm) Os(cm) z(cm) Ds(cm) z (cm) Os(cm) 0 2.7 0 2.7 0 t .3 0 1.3 5 3.4 5 3.2 5 3.0 5 2 . 5 10 3.8 10 3.6 10 3.2 10 2 . 7 15 3 .e 15 3.4 20 3 . I 20 2 . 4 20 3.3 20 3.3 30 2.7 30 2.5 30 3.4 30 3.4 40 2 . 7 40 2.6 40 3 . 4 40 3.5 50 2 . 7 50 2.6 50 3 . 4 50 3.6 60 2.8 60 2 .6 60 3 . 6 58 4 . 1 70 2 . a 70 3 . 2 74 4.0 80 2.8 74 . 5 3.6 90 2.9 100 3.0 Run » 24-2-a 1 to 3. 1 Run * 23-2-a (20 3.2 Run It 26-2-a 130 3.3 z(cm) Os(crn) 140 3.5 z(cra) Ds(cm) 150 3.7 z(cm) Os(cm) 155 4. 1 O 2.7 0 2.7 5 3. 1 0 1 . 3 5 3 . 3 to 3.6 5 2.5 10 3.8 . 15 3.4 Run * 25-2-a IO 2 .6 15 3.5 20 3.2 15 2.4 20 3 . 1 25 3.3 20 2.4 30 3.2 30 3.4 z(cm) Ds(cm) 30 2.4 40 3 . 1 35 3.6 40 2.4 50 3.5 40 3.8 50 2 . 4 53 3.9 42 4.0 0 1 . 3 55 . 5 2 . 4 S 2.6 10 3. 1 20 2.9 Run H 23-3-a Run It 24-3-a SO 2 . a Run It 26-3-a 40 2.7 50 2 . 7 z (cm) Ds(cm) z(cm) Oa(cm) 60 2.7 z(cm) Dslcm) 70 2 . 7 80 2 . a 0 2.7 0 2.7 90 2.9 0 1 . 3 5 3.1 5 3.0 100 3. 1 5 2 . 4 10 3 . 5 10 3.4 1 to 3 . 2 10 2 . 4 15 3 . 3 12.5 3.3 116 3 . 8 15 2 . 3 20 3 . 2 15 3.2 20 2 . 3 25 3.2 17.5 2.8 25 2 . 3 30 3 . 2 20 2.9 30 2 . 3 35 3 . 7 23 2.9 Run It 25-3-a 3 5 2 . 3 26 3.4 z(cm) Ds(cm) 0 1 . 35 2. 6 10 2. 9 20 2. 6 30 2. .6 40 2 .6 50 2 .6 60 2 . 6 70 2 . 7 74 3 . 3 205 Run » 27- t-a Run H 28-t-a Run H 29- 1-a Run * 30-1-a 2 (cm) Os(cm) z(cm) Os(cm) z(cm) Os(cm) Z (cm) Os(cm) 0 1.3 0 t .3 0 1 .3 0 1 . 3 5 2.4 5 2.3 5 3.0 5 2.7 10 2.6 10 2.5 to 3.4 10 3.4 15 2.4 15 2.3 20 2.9 15 3 . 1 20 2.3 20 2.2 30 3.0 20 2.6 30 2.4 25 2.3 40 3.0 30 2.7 40 2.5 30 2.3 50 3. 1 40 2.8 50 2.5 35 2.3 60 3 . 1 50 2.8 60 2.7 40 2.3 70 3 . 1 60 2.9 65 3.3 45 3. 1 ao 3.2 70 3 . 3 50.5 3.8 90 3.3 80 3.8 too 3.5 82 4 .O 1 10 3.7 Run * 27-2-a 120 3.9 Run * 28-2-a 134 4 . 1 Run * 30-2-a 2 (cm) Os(cm) z(cm) Oa(cm) Run U 29-2-a z(cm) Ds(cm) 0 t . 3 5 2.4 0 1 .3 IO 2 . 5 5 2.2 z(cm) Ds(cm) 0 1 . 3 15 2.3 10 2.4 5 2 . 6 20 2.2 15 2.0 10 3.2 25 2.2 20 2.0 0 1.3 15 2.9 30 2.2 • 25 2.0 5 2.6 2 0 2.6 35 2 . 3 30 2.0 10 3.2 30 2.6 40 2.3 37 2.0 15 3 . 0 4 0 2.6 49 2 4 20 2.9 50 2 . 9 30 2 . 9 59 3 . 4 40 2 . 9 Run » 2B-3-a 50 2 . 9 Run » 27-3-a 60 3 . 0 2 (cm) Ds(cm) 70 3 . 2 Run H 3 0 - 3-a ao 3 . 4 2 (era) Ds(cm) 90 3 . 6 99 3 .9 z (cm) D s (cm 0 1.3 0 1 . 3 2.5 1 . 6 5 2 . 1 5 2 . 2 0 1 . 3 10 2 . 3 7.5 2 . 4 Run M 2 9 - 3 - a 5 2 . 6 15 2 . 0 IO 2.1 10 3 . 2 2 0 2 . 0 12.5 1 .9 15 2 . a 25 2 . 0 15 t. a z (cm) Ds(cm) 2 0 2 . 5 3 0 2 . 0 20 1 . 9 25 2 . 5 3 1.5 2 . 1 23 . 5 1.9 3 0 2 . 5 o 1 . 3 35 2 . U 5 2 . 6 AO 3 . 1 IO 3 . 2 15 3 . 0 20 2 . a 30 2.8 40 2.8 50 2 . 9 60 3.0 65 3 . 2 206 R u n » 31-1-a Run » 32-1-a Run U 33- 1-a Run M 34- 1-a z(cm) Ds(cm) z(cm) Os(cm) z (cm) Ds(cm) Z (cm) Ds (cm 0 1 .3 0 1 .3 0 1 .3 0 1 .3 5 2.6 5 2.6 5 3.8 5 3.7 10 3.3 10 3.3 10 4 .0 10 4.0 15 3. 1 15 2.8 15 3.7 15 3.7 20 2.7 20 2.7 20 3 . 2 20 3.2 30 2 . 7 30 2.7 30 3.2 30 3 . 2 40 2.7 40 2.8 40 3.3 40 3 . 2 50 2.9 50 3.0 SO 3.3 50 3.2 eo 3.3 55 3.4 60 3.3 60 3.3 69 3 . 7 70 3.5 70 3.5 80 3.7 80 3.8 90 3.9 9 1 4 . 2 Run H 32-2-a 100 4 . 1 Run » 31-2-a 1 10 4.3 z(cm) Os(cm) Run * 34-2-a z(cm) Os(cm) Run M 33-2-a 0 1.3 z(cm) Ds(cm! 0 1.3 5 2.6 5 2.6 10 3.2 z(cm) Ds(cm) 10 3.2 IS 2.7 0 1 .3 15 2.8 20 2.5 5 3.7 20 2.6 23 2.S O 1. 3 IO 4.0 25 2.6 30 2.3 . 5 3.6 15 3.4 30 2.6 35 2.3 10 4.0 20 3 . 1 40 2.7 40.3 2.6 15 3.6 30 2.8 5 1 2.8 20 3.2 40 3.0 30 3.0 50 3.3 40 3.0 60 3 . 7 Run » 32-3-a 50 3. 1 66 4.0 R u n » 31-3-a 60 3.3 70 3.S z(cra) Os(cm) 80 4 .O z( cm) Ds(cm) Run M 34-3-a 0 1 .3 0 t . 3 5 2.6 Run » 33-3-a z(cm) Ds (cm 5 2.6 10 3. 1 10 3 . t 15 2.5 15 2 . 7 20 2 . 4 z(cm) Os(cm) 0 1 . 3 2 0 2 . 5 23 2 . 4 5 3 . 4 25 2 . 5 IO 3 . 9 3 0 2 . 5 O 1 . 3 15. 3 . 4 3 1 2 . 5 5 3 . 4 20 2 . 7 IO 3 . 3 25 2 . 7 15 3 . 3 • O 2 . 7 20 2 . 9 35 3 . 1 30 2 . 9 4 1 3 . 8 40 3 . 0 50 3 . 3 53 3 . 8 Run H z(cm) 35- 1-a Os(cm) Run # 36-1-a z(cro) Ds(cro) 0 1 . 35 3, .6 10 3 .8 15 3 .7 20 3 , .4 30 3 .2 40 3 .2 50 3 .2 60 3 .4 70 3 .6 77 4 .0 0 1 . 35 3. 1 10 3. 7 15 3. 2 20 3, ,2 30 3 , . 2 40 3, , 3 50 3, .4 60 3 .5 68 3 .9 Run * 35-2-a z(cm) Os(cm) 0 1 . .35 3 . 1 10 3. 5 15 3. .2 20 3. .2 30 3 . 2 40 3. .3 50 3, .4 58 3 .7 Run » 36-2-a z(cm) Os(cm) 0 1 . 3s 3. 1 10 3. 5 15 3. ,2 20 3. .2 30 3. .2 40 3, ,2 45 3. .4 50 3 .8 Run » 35-3-a z(cra) Ds(cra) O 1.3 5 3.2 10 3.4 15 2.8 20 2.8 25 2.B 30 2.8 37 2.8 Run » 36-3-a z(cro) Os(cm) O 1.3 5 3.0 10 3.2 15 3.0 20 2.7 25 2.8 3 1 3.0 208 Run H 37- 1-a Run # 37-4-a Run U 38-1-a Run H 30-3-a z(cm) Os(cm) z(cm) Ds(cm) z(cm) Ds(cm) z (cm) 0s(cm) 0 1.9 0 1.9 0 1.9 0 1 .9 to 3.a 5 2.9 5 3 . 2 5 2 . 8 20 3.3 10 2.7 10 2.8 10 2.6 30 3.2 IS 2.4 15 2.6 15 2.3 40 3 . 2 20 2.3 20 2.6 20 2 . 3 50 3 . 2 28.S 2.2 30 2.6 28.5 2 . 3 ao 3.4 40 2.6 too 4 .0 50 2.9 120 4.2 54 .5 3.2 140 4.6 Run » 37-4-b Run M 38-3-b z(cro) Ds(cm) Run » 38-2-a 2(cm) Ds(cm) Run H 37-2-a z(cro) Ds(cm) 0 1 . 9to 3 . 5 20 3 . .2 30 3 , . 1 50 3 .2 60 3 . 1 90 3 .6 1 to 4 . 5 Run H 37-3-a z ( c m ) D s ( c m ) 0 t . 9 10 3 . 5 2 0 2 9 30 2 . 9 4 0 3 . 0 5 0 3 ; . 0 6 0 3 . 3 6 5 3 . 5 7 1 4 . 0 0 s 10 IS 20 28.5 Run » 37-4-c z(cm) Ds(cm) O 5 to 15 20 2B . 5 t .9 3.0 2.8 2.6 2 . 5 2.4 z(cm) Os(cm) 0 '5 10 15 20 30 4 1 Run » 38-2-b z(cm) Os(cm) o 1 . 9 5 2 . 9 10 2 . 7 15 2 . 5 20 2 . . 5 30 2 . 6 4 t 2 . a 0 5 10 15 20 28.5 Run * 38-3-c z(cm) Ds(cm) 0 5 IO 15 20 28 . 5 t .9 2 . 9 2 . 9 2 . 5 2 . 5 2.5 Run U 3 B -Z(CIH) O s ( c m ) O 5 10 15 20 30 4 I 209 Run H 5-6-a z(crn) Ds(cm) 0 1 .9 5 3 .0 10 3 . 3 15 2 .8 20 2 .9 30 2 .9 40 2 .9 50 3 O 60 3 , .0 70 3. . 1 80 3. .3 81.5 3, ,5 Run * 5-6-b z(cm) Ds(cm) 0 1 .9 5 3 , .0 10 3. .5 15 3. . 1 20 3, . 1 30 3 .0 40 3 . o 50 3 . 0 60 3 . t 70 3 .3 BO 3 , 5 8 1.5 3 . a Run * 5-6-c z(cm) Os(crn) 0 1 . 95 3 . ,0 IO 3 . 5 15 3 , . 2 20 3 . 1 30 3 O 40 3 .0 50 3 .0 60 3 . 1 70 3 . 3 80 3 . 7 8 1.5 3 .9 Run * 5-9-a Run » 6-5-a R U n » 6-6-a z(cm) Os(cro) z(cm) Ds(cm) z(cm) Os(cm) 0 1 . 9 0 1 . 9 0 1 . 95 2. .7 5 3 . 0 5 2 .a 10 3 .5 10 3 .5 IO 3 . 2 15 3 . 1 15 3 . 2 15 2 . 8 20 2 .7 20 2 .6 20 2 . 7 25 2 . 7 30 2 .6 25 2 . 7 28.5 2, .9 40 3 . 2 28 . 5 2 . 7 48 3 . 6 Run * 5-9-b z(cra) Os(cm) Run * 6-5-b Z(CIR) Ds(cra) Run it 6-6-b z(cm) Os(cm) 0 1 . .9 0 . 9 • 5 2 . 8 0 1 . . 9 5 2 . a 10 3. .5 5 3 . 0 10 3 . 3 IS 3 . 1 10 3 . 5 15 2 . 9 20 2 .8 15 3 , . 2 20 2 . 7 25 2 .8 20 2 . 7 25 2 . . a 28.5 2 .9 30 2 . 7 28 . 5 2 . a 40 3 . 3 48 3 . B Run it 5-9-c z(cm) Os(cm) O 5 10 15 20 25 28.5 1 .9 2.9 3.6 3. I 2.9 2.9 3.0 Run It 6-5-c z(cm) Os(cm) O 5 10 15 20 30 40 48 1 . 9 3 . I 3.6 3 . 2 Run U 6-6-c z(cfn) Ds(cm) O 5 10 15 20 25 28 . 5 o Run It 7-5-a z(cm) Os(cm) Run » z(cm) 7-7-a Ds(cro) Run » a-S-a z(cm) Os(cm) 0 1 . 95 2. a 10 3 .2 15 2 . 7 20 2 . 7 25 2 . 7 30 2 . 9 35 2 . 9 43 3 .2 Run it 7-5-b zCcm) Qs(cm) 0 1 . 9 5 2 , . a 10 3 . 2 15 2 . a 2 0 2 . a 25 2 . a 3 0 2 . 9 3 5 2 .9 4 3 3 . 3 R u n u 7 - 5 - c z ( c m ) D s ( c m ) 0 1 . 9 5 2 , . a 10 3 . 2 15 3 , , 1 2 0 2 . 9 2 5 2 . 9 3 0 3 . . 0 35 3 . 0 •13 3 . 5 0 1.9 5 2.7 10 3.3 15 2.7 20 2.7 25 2.7 28.5 2.7 0 1.9 5 2.5 10 3.3 15 2.7 20 2.7 25 2.7 28.5 2.7 Run * 7-7-b R ( J n g a - 5 - b z(cm) Os(cm) • z(cro) Ds(cm) O 1.9 0 1.9 5 2.8 5 2.6 10 3.3 10 3.4 15 2.7 15 2.8 20 2.7 20 2.8 25 2.8 25 2.8 28.5 2.9 28.5 2.8 Run H 1-1-a z(cm) Ds(cm) Run # 8-5-c z(cm) Os(cm) O 1 .9 5 2.8 10 3.4 15 2.7 20 2.7 25 2.9 28.5 3.1 O 1.9 5 2.7 10 3.5 15 2.9 20 2.9 25 2.9 28.5 3.0 

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