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Heat transfer in circulating fluidized beds Wu, Richard Lap 1989

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HEAT TRANSFER IN CIRCULATING FLUID IZED BEDS By RICHARD LAP WU B . E n g . , M c G i l l U n i v e r s i t y , 1982 M . E n g . , M c G i l l U n i v e r s i t y , 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department of Chemica l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA August 1989 © R i c h a r d Lap Wu, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada Department DE-6 (2/88) - i i -A B S T R A C T Heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds was s t u d i e d i n both a 7.3 m h i g h , 152 x 152 mm s q u a r e , p i l o t - s c a l e combustor and a 9.3 m h i g h , 152 mm ID t r a n s p a r e n t c o l d model u n i t . R e s u l t s were o b t a i n e d for p a r t i c l e s of mean s i z e 171-299 fim at s u p e r f i -c i a l gas v e l o c i t i e s from 4 to 9.5 m/s and f o r s o l i d s c i r c u l a t i o n 2 r a t e s up to 70 kg/m . s . For the combustor , r e s u l t s o b t a i n e d by u s i n g membrane w a l l s and a v e r t i c a l tube as heat t r a n s f e r s u r f a c e s show a s t r o n g i n f l u e n c e of the c r o s s - s e c t i o n a l a r e a -averaged suspens ion d e n s i t y on t i m e - a v e r a g e d , l e n g t h - a v e r a g e d s u s p e n s i o n - t o - s u r f a c e heat t r a n s f e r c o e f f i c i e n t . The i n f l u e n c e of s u p e r f i c i a l gas v e l o c i t y i s found to be s m a l l . R a d i a t i o n becomes s i g n i f i c a n t at suspens ion temperatures h i g h e r than 400 C and at low suspens ion d e n s i t i e s . Heat t r a n s f e r c o e f f i c i e n t s were a l s o found to v a r y wi th the l a t e r a l p o s i t i o n of the t u b e . The v e r t i c a l l e n g t h of heat t r a n s f e r s u r f a c e i s shown to be an important parameter , a l l o w i n g seemingly d i s c r e p a n t p u b l i s h e d r e s u l t s to be r e c o n c i l e d . For the c o l d model u n i t , sudden and d r a m a t i c peaks i n i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t s were measured u s i n g an i n s t a n t a n e o u s heat t r a n s f e r p r o b e . S imultaneous heat t r a n s f e r and c a p a c i t a n c e measurements suggest t h a t these peaks are caused by the a r r i v a l s of p a r t i c l e s t r a n d s at the heat t r a n s f e r s u r f a c e . Two-probe heat t r a n s f e r measurements suggest the e x i s t e n c e of a c h a r a c t e r i s t i c r e s i d e n c e l e n g t h f o r the s t r a n d s at the w a l l i n t h i s co lumn. - i i i -A proposed heat transfer model, based on an o v e r a l l core-annulus flow s tructure in the r i s e r , and per iod ic formation, movement along the w a l l , and d i s i n t e g r a t i o n of strands in the annulus, gives reasonable agreement with a wide range of published data . It accounts success fu l ly for the effects of heat transfer surface length and p a r t i c l e s i ze s . However, the e f fect of the heat transfer surface conf igurat ion on the flow pattern of p a r t i c l e s must also be taken into account to give improved agreement with experimental data . - i v -T A B L E O F C O N T E N T S Page ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENT x i i i CHAPTER 1 INTRODUCTION 1 CHAPTER 2 HEAT TRANSFER IN CIRCULATING FLUIDIZED BED COMBUSTOR 8 2.1 INTRODUCTION 8 2.2 LOW TEMPERATURE STUDY 9 2 .2 .1 E x p e r i m e n t a l Equipment 9 2 .2 .2 R e s u l t s and D i s c u s s i o n 17 2.3 HIGH TEMPERATURE STUDY 30 2 .3 .1 E x p e r i m e n t a l Equipment 30 2 .3 .2 R e s u l t s and D i s c u s s i o n 34 CHAPTER 3 INSTANTANEOUS LOCAL HEAT TRANSFER AT ROOM TEMPERATURE 59 3.1 INTRODUCTION 59 3.2 EXPERIMENTAL APPARATUS AND PROCEDURE 60 3 . 2 . 1 C i r c u l a t i n g F l u i d i z e d Bed F a c i l i t i e s 60 3 .2 .2 Instantaneous Heat T r a n s f e r Measurement I n s t r u m e n t a t i o n 63 3 . 2 . 3 C a p a c i t a n c e Probe 73 3 .2 .4 High Speed Cinematography 78 3.3 RESULTS AND DISCUSSION 78 3 . 3 . 1 S i n g l e Probe Experiment ' 78 3 .3 .2 Double Probe Experiment 86 3 .3 .3 S imultaneous Heat T r a n s f e r Probe and C a p a c i t a n c e Probe Experiment wi th High Speed Cinematography 96 - V -P a 9 e CHAPTER 4 MODELLING OF HEAT TRANSFER IN CIRCULATING FLUIDIZED BEDS 10 2 4.1 INTRODUCTION 102 4.2 MODEL FORMULATION AND CIRCULATING FLUIDIZED BED HYDRODYNAMICS 104 4 . 2 . 1 Hydrodynamics 104 4 . 2 . 2 Model F o r m u l a t i o n 109 4.3 COMPARISON OF MODEL WITH EXPERIMENTAL RESULTS 122 CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 141 5.1 CONCLUSIONS 141 5.2 RECOMMENDATIONS FOR FUTURE WORK 143 NOMENCLATURE 145 REFERENCES 149 APPENDIX 1 Sample C a l c u l a t i o n s and E r r o r E s t i m a t i o n of S u s p e n s i o n - t o - S u r f a c e Heat T r a n s f e r C o e f f i c i e n t from Membrane W a l l 156 APPENDIX 2 T a b u l a t i o n of E x p e r i m e n t a l Heat T r a n s f e r C o e f f i c i e n t Data 159 APPENDIX 3 FORTRAN Computer Program for C o n t r o l l i n g the Temperature of the Ins tantaneous Heat T r a n s f e r Probe . 168 APPENDIX 4 E s t i m a t i o n of E r r o r Caused by the P r o t e c t i v e P l a s t i c F i l m . 171 APPENDIX 5 BASIC Computer Program for Model C a l c u l a t i o n s 172 - v i -L I S T O F T A B L E S T a b l e 2.1 P a r t i c l e s i z e a n a l y s e s and f l u i d i z a t i o n p r o p e r t i e s f o r the two Ottawa sands used i n S e c t i o n 2 . 2 . Page 13 Table 2.2 P a r t i c l e thermal time c o n s t a n t s i n a i r and the c o r r e s p o n d i n g l e n g t h s t r a v e l l e d at a p a r t i c l e v e l o c i t y of 1.26 m/s . P a r t i c l e p r o p e r t i e s : Pp=2650 k g / m 3 ; c p p = 8 0 0 J / k g . K . T a b l e 2.3 F l u i d i z a t i o n p r o p e r t i e s of sand and s o r b e n t used i n S e c t i o n 2 . 3 . 28 35 Table 2.4 P a r t i c l e s i z e a n a l y s e s f o r v a r i o u s runs i n S e c t i o n 2 . 3 . 36 Table 2.5 Comparison of e x p e r i m e n t a l data wi th heat t r a n s f e r c o e f f i c i e n t s for the v e r t i c a l tube at three suspens ion t e m p e r a t u r e s . 41 T a b l e 2.6 Re levant e x p e r i m e n t a l d e t a i l s of some p u b l i s h e d s t u d i e s on heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds . 56 Tab le 3.1 P a r t i c l e s i z e a n a l y s e s and f l u i d i z a t i o n p r o p e r t i e s f o r the Ottawa sand used i n Chapter 3. 64 T a b l e 3.2 Comparison of measured heat t r a n s f e r c o e f f i c i e n t s and p r e d i c t e d c o e f f i c i e n t s from c o r r e l a t i o n s for the cases of n a t u r a l c o n v e c t i o n and f o r c e d c o n v e c t i o n . 74 Tab le 3.3 T a b l e 4.1 Frames of f i l m taken for s t r a n d s to f a l l 0.152 m and the c o r r e s p o n d i n g c a l c u l a t e d f a l l i n g v e l o c i t i e s ( in i n c r e a s i n g order) at four suspens ion d e n s i t i e s . Time f r a c t i o n s of w a l l coverage for s t r a n d s of d i f f e r e n t vo idages at four suspens ion d e n s i t i e s . 100 110 - v i i -L I S T OF FIGURES F i g u r e 1.1 F i g u r e 2.1 F i g u r e 2.2 F i g u r e 2.3 F i g u r e 2.4 F i g u r e 2.5 F i g u r e 2.6 F i g u r e 2.7 F i g u r e 2.8 A t y p i c a l c i r c u l a t i n g f l u i d i z e d bed combustor ( K u l l e n d o r f and A n d e r s s o n , 1986). Schematic of the c i r c u l a t i n g f l u i d i z e d bed f a c i l i t y used i n S e c t i o n 2 . 2 . P r i n c i p a l r e a c t o r v e s s e l showing p o s i t i o n s of heat t r a n s f e r s u r f a c e s and of thermocoup le s . P r e s s u r e taps are at the same h e i g h t s as the thermocouple s , on the o p p o s i t e w a l l . A l l d imens ions are i n mm. (a) P lan view and (b) S e c t i o n view of membrane w a l l s used i n S e c t i o n 2 . 2 . A l l d imens ions are i n mm. Average heat t r a n s f e r c o e f f i c i e n t for membrane w a l l s u r f a c e s ( thermocouple 1-8 i n F i g u r e 2.3b) f o r 188 [im sand as a f u n c t i o n of suspens ion d e n s i t y . Open and f i l l e d symbols r e f e r to the upper and lower exchange s u r f a c e s r e s p e c t i v e l y . Q 2 / Q 1 i - s t n e r a t i o of secondary to p r i m a r y a i r f l o w r a t e s . Average heat t r a n s f e r c o e f f i c i e n t for membrane w a l l s u r f a c e s ( thermocouple 1-8 i n F i g u r e 2.3b) f o r 356 i^m sand as a f u n c t i o n of suspens ion d e n s i t y . Open and f i l l e d symbols r e f e r to the upper and lower exchange s u r f a c e s r e s p e c t i v e l y . Q ^ / Q - j ^ i n a l l c a s e s . I n f l u e n c e of s u p e r f i c i a l gas v e l o c i t y on average heat t r a n s f e r c o e f f i c i e n t at three d i f f e r e n t suspens ion d e n s i t i e s f o r the 188 fim sand . I n f l u e n c e of suspens ion temperature on average heat t r a n s f e r c o e f f i c i e n t at three d i f f e r e n t suspens ion d e n s i t i e s f o r the 188 /*m s a n d . T y p i c a l l o n g i t u d i n a l p r o f i l e s of heat t r a n s f e r c o e f f i c i e n t and suspens ion d e n s i t y f o r (a) upper s u r f a c e , and (b) lower s u r f a c e . C o e f f i -c i e n t s are o b t a i n e d between thermocouples 1-3, 3-6 , 6-8 i n F i g u r e 2.3b f o r the 188 sand . Page 3 10 12 15 18 19 20 22 23 - v i i i -Page F i g u r e 2.9 Comparison between e x p e r i m e n t a l heat t r a n s f e r c o e f f i c i e n t s o b t a i n e d wi th the 1.53 m l o n g heat t r a n s f e r s u r f a c e s i n the p r e s e n t s tudy and e a r l i e r measurements of o ther workers f o r much s h o r t e r heat t r a n s f e r probes ( M i c k l e y and T r i l l i n g , 880 mm; Kiang e t a l . , 57 mm; F r a l e y et a l . , 150 mm; Kobro and B r e r e t o n , 100 mm). 26 F i g u r e 2.10 Heat t r a n s f e r c o e f f i c i e n t f o r s e c t i o n of upper heat exchange s u r f a c e from thermocouple 1-3 (see F i g u r e 2.3b) v e r s u s suspens ion d e n s i t y f o r both the 188 and 356 fim sands . 29 F i g u r e 2.11 S i m p l i f i e d schemat ic of the c i r c u l a t i n g f l u i d i z e d bed combust ion f a c i l i t y used i n S e c t i o n 2 . 3 . 31 F i g u r e 2.12 (a) P l a n view and (b) S e c t i o n view of the membrane w a l l heat t r a n s f e r s u r f a c e used i n S e c t i o n 2 . 3 . A l l d imens ions are i n mm. 33 F i g u r e 2.13 Average heat t r a n s f e r c o e f f i c i e n t for the v e r t i c a l tube v e r s u s suspens ion d e n s i t y at four suspens ion t e m p e r a t u r e s . For 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 , see Table 2 . 4 . Bottom l i n e : Run 3; U=6.5 m/s . Other l i n e s : Run 1; U=6.6-8 .6 m/s . 37 F i g u r e 2.14 Average heat t r a n s f e r c o e f f i c i e n t for the membrane w a l l v e r s u s suspens ion d e n s i t y at three suspens ion t e m p e r a t u r e s . Bottom l i n e : Run 5 i n Tab le 2 .4 ; U=7.4 m/s . Other l i n e s : Run 4 i n Tab le 2 .4 ; U=8.7-9 .5 m/s . 39 F i g u r e 2.15 C r o s s - p l o t of average heat t r a n s f e r c o e f f i -c i e n t versus suspens ion temperature f o r the v e r t i c a l tube ( s o l i d l i n e s ) and the membrane w a l l (broken l i n e s ) at four suspens ion d e n s i t y l e v e l s . " 43 F i g u r e 2.16 Average heat t r a n s f e r c o e f f i c i e n t versus suspens ion d e n s i t y f o r four d i f f e r e n t l a t e r a l tube p o s i t i o n s at two suspens ion t e m p e r a t u r e s . Top four c u r v e s : Run 2 i n Table 2 .4 ; U=9.3 m/s; T S U S p = 8 5 4 ± 3 C . Bottom four c u r v e s : Run 3 i n Table 2 . 4 ; U=6.5 m/s; T s u s p = 3 4 3 ± 1 3 C . 45 -ix-Page F i g u r e 2.17 F i g u r e 2.18 F i g u r e 2.19 F i g u r e 2.20 F i g u r e 2.21 F i g u r e 2.22 F i g u r e 3.1 F i g u r e 3.2 F i g u r e 3.3 F i g u r e 3.4 C r o s s - p l o t of average heat t r a n s f e r c o e f f i -c i e n t v e r s u s l a t e r a l tube p o s i t i o n f o r two suspens ion d e n s i t i e s and two suspens ion t e m p e r a t u r e s . S o l i d l i n e s : Psusp = 15 k g / m 3 ; Broken l i n e s : P S u s p = 6 0 k g / m 3 . Curves 1 ,2: T s u s p = 3 4 3 c / ' Curves 3 , 4 : T s u s p = 854 C . L o c a l heat t r a n s f e r c o e f f i c i e n t o b t a i n e d (a) near the w a l l , and (b) around the column a x i s as a f u n c t i o n of l o c a l suspens ion d e n s i t y by Soga e t a l . (1987) (as r e p o r t e d i n Y o s h i d a and Mineo , 1989) . L o c a l heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l versus Z f o r two suspens ion t e m p e r a t u r e s . p S U S p=54 k g / m 3 ; Run 5 i n Tab le 2 . 4 . Heat t r a n s f e r c o e f f i c i e n t averaged over Z versus Z for two suspens ion t e m p e r a t u r e s . P S U S p=54 k g / m 3 ; Run 5 i n Tab le 2 . 4 . Comparison of p u b l i s h e d heat t r a n s f e r r e s u l t s . For e x p e r i m e n t a l d e t a i l s , see T a b l e 2 . 6 . C r o s s - p l o t of average heat t r a n s f e r c o e f f i -c i e n t versus v e r t i c a l t r a n s f e r s u r f a c e l e n g t h for three ranges of mean p a r t i c l e s i z e s . Psusp= 5 0 k g / m 3 . Schematic of the c o l d model c i r c u l a t i n g f l u i d i z e d bed . A l l d imens ions are i n m. P o s i t i o n s of heat t r a n s f e r p r o b e : 1 - Top (Y=8.61 m); 2 - M i d d l e (Y=4.04 m); 3 - Bottom (Y=0.84 m) . Schematic of the c i r c u i t f or c o n t r o l l i n g the temperature of the heat t r a n s f e r p r o b e . V a r i a t i o n s of e l e c t r i c a l r e s i s t a n c e of heat t r a n s f e r probe as a f u n c t i o n of probe t e m p e r a t u r e . F r o n t and s e c t i o n views of the probe assembly c o n s i s t i n g of p l a s t i c f i l m , p l a t i n u m c o a t e d g l a s s , and guard h e a t e r . A l l d imens ions are i n mm. 47 50 52 53 55 57 61 66 68 70 F i g u r e 3.5 90% response t imes ( i n ms) of (a) exposed , and (b) covered probe assembly to a s t ep change i n heat t r a n s f e r c o e f f i c i e n t . 72 Page F i g u r e 3.6 F i g u r e 3.7 F i g u r e 3.8 F i g u r e 3.9 F i g u r e 3.10 F i g u r e 3.11 F i g u r e 3.12 F i g u r e 3.13 F i g u r e 3.14 F i g u r e 3.15 F i g u r e 3.16 F i g u r e 3.17 S i m p l i f i e d schemat ic of the c a p a c i t a n c e p r o b e . A l l d imens ions are i n mm. B l o c k diagram of the c a p a c i t a n c e probe system showing p r i n c i p a l system components ( B r e r e t o n , 1987). C r o s s - s e c t i o n a l a r e a - a v e r a g e d suspens ion d e n -s i t y at three d i f f e r e n t a x i a l column p o s i t i o n s as a f u n c t i o n of s o l i d s c i r c u l a t i o n r a t e . T y p i c a l t r a c e s of i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t measured at three d i f f e r e n t a x i a l column p o s i t i o n s . G s=52 k g / m ^ . s . A x i a l v a r i a t i o n s of (a) t ime-averaged heat t r a n s f e r c o e f f i c i e n t , and (b) a r e a - a v e r a g e d suspens ion d e n s i t y a long the r i s e r . T ime-averaged heat t r a n s f e r c o e f f i c i e n t as a f u n c t i o n of suspens ion d e n s i t y at three d i f f e r e n t a x i a l column p o s i t i o n s . V a r i a t i o n s of a b s o l u t e and n o r m a l i z e d s t a n d a r d d e v i a t i o n s of the i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t measured at (a) Top , (b) M i d d l e , and (c) Bottom a x i a l p o s i t i o n s of the r i s e r as a f u n c t i o n of suspens ion d e n s i t y . T y p i c a l t r a c e s of two s imul taneous i n s t a n t a -neous heat t r a n s f e r c o e f f i c i e n t s . a=0.152 m; P S U S p=44.2 k g / m 3 ; G s =60.3 k g / m 2 . s . C o e f f i c i e n t of c r o s s - c o r r e l a t i o n versus time lag at three d i f f e r e n t suspens ion d e n s i t i e s and f i v e s e p a r a t i o n d i s t a n c e s . Psusp (^9 / m ^) : (a) 44 .2 ; (b) 28 .7 ; (c) 1 4 . 8 . Probe s e p a r a -t i o n d i s t a n c e (m): (1) 0 .152; (2) 0 .305; (3) 0 .457; (4) 0 .610; (5) 0 .762 . Maximum c r o s s - c o r r e l a t i o n c o e f f i c i e n t versus s e p a r a t i o n d i s t a n c e at three d i f f e r e n t suspens ion d e n s i t i e s . Three d e f i n i t i o n s of the " c h a r a c t e r i s t i c " r e s i d e n c e l e n g t h for the s t r a n d s : a. l nt 0 . 5 ' ° t a n ' 75 77 80 81 83 85 87 89 V a r i a t i o n s of a g ^ , a t a n , a n ^ a i n t a s a f u n c t i o n of suspens ion d e n s i t y . 90 92 93 95 - x i -Pacje F i g u r e 3.18 F i g u r e 4.1 F i g u r e 4.2 F i g u r e 4.3 F i g u r e 4.4 F i g u r e 4.5 F i g u r e 4.6 F i g u r e 4.7 F i g u r e 4.8 F i g u r e 4.9 T y p i c a l t r a c e s of s imul taneous i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t and c a p a c i t a n c e s i g n a l at three d i f f e r e n t a r e a - a v e r a g e d suspens ion d e n s i t i e s ( k g / m 3 ) : (a) 46 .7 ; (b) 32 .0; (c) 1 5 . 3 . C u m u l a t i v e t ime f r a c t i o n of w a l l coverage by s t r a n d s wi th vo idage e versus 1 -e at four d i f f e r e n t suspens ion d e n s i t i e s . D i s c r e t i z a t i o n scheme for the c u m u l a t i v e t ime f r a c t i o n of w a l l coverage p l o t s i n F i g u r e 4 . 1 . Time f r a c t i o n of w a l l coverage v e r s u s suspen-s i o n d e n s i t y f o r s i x d i f f e r e n t s t r a n d vo idages , I l l u s t r a t i o n of the proposed heat t r a n s f e r model for c i r c u l a t i n g f l u i d i z e d beds . 95% heat p e n e t r a t i o n d i s t a n c e versus v e r t i c a l d i s t a n c e t r a v e l l e d by a t y p i c a l s t r a n d of 250 fim sand at 1.26 m/s f o r four d i f f e r e n t s t r a n d v o i d a g e s . Comparison of model p r e d i c t i o n wi th the e x p e r i m e n t a l da ta from F i g u r e 3.11 for three d i f f e r e n t n . Comparison of model p r e d i c t i o n wi th the e x p e r i m e n t a l da ta of Basu and Nag (1987) two p a r t i c l e s i z e s . f or F i g u r e 4.10 I n f l u e n c e of s t r a n d ' s r e s i d e n c e l e n g t h , L , on the p r e d i c t e d v a r i a t i o n s i n L - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l s u r f a c e . m=0.05 k g / m 2 . s ; 5=1 mm. C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l data wi th same e x p e r i m e n t a l c o n d i t i o n s as i n F i g u r e 4 . 9 . 98 107 108 111 112 119 125 126 Comparison of model p r e d i c t i o n wi th the e x p e r i m e n t a l da ta of Kobro and B r e r e t o n (1986) for two p a r t i c l e s i z e s at T =25 C . 127 c susp P r e d i c t e d v a r i a t i o n s i n l o c a l heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l s u r f a c e f o r four d i f f e r e n t L . m=0.05 k g / m 2 . s ; 5=1 mm. C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l d a t a from F i g u r e 2.19 wi th U=7.5 m/s , d =241 fim, p =54 kg/m3, T =407 C . P S U S p 129 3 susp 131 - x i i -P a 9 e F i g u r e 4.11 I n f l u e n c e of s t r a n d ' s f a l l i n g v e l o c i t y , U F i g u r e 4.12 F i g u r e 4.13 on the p r e d i c t e d v a r i a t i o n s i n L - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l s u r f a c e . S o l i d l i n e s : p e r i o d i c renewals of s t r a n d c o n t a c t (Eq. 4 . 1 ) ; m=0.05 kg /m^. s ; 5=1 mm. Broken l i n e s : no renewal of s t r a n d c o n t a c t . C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l da ta wi th same e x p e r i m e n t a l c o n d i t i o n s as i n F i g u r e 4 . 9 . 132 Comparison of p r e d i c t e d v a r i a t i o n s i n L -averaged heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l s u r f a c e ( s o l i d l i n e s ) w i th e x p e r i m e n t a l da ta f o r two d i f f e r e n t m and 5. Broken l i n e : no renewal of s t r a n d c o n t a c t . C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l da ta wi th same e x p e r i m e n t a l c o n d i t i o n s as i n F i g u r e 4 . 9 . 133 Comparison of model p r e d i c t i o n wi th e x p e r i -mental d a t a for the membrane w a l l from F i g u r e 2.14 wi th T S U S p = 4 1 0 C . S o l i d l i n e s : p e r i o d i c renewals of s t r a n d c o n t a c t (Eq . 4 . 1 ) ; m=0.05 k g / m ^ . s . Broken l i n e : no renewal of s t r a n d c o n t a c t . 136 F i g u r e 4.14 Comparison of model p r e d i c t i o n wi th the e x p e r i m e n t a l d a t a of F e u g i e r e t a l . (1987) for three p a r t i c l e s i z e s . Curves a: p e r i o d i c renewals of s t r a n d c o n t a c t (Eq. 4 . 1 ) ; m=0.05 kg /m^. s ; 5=1 mm. Curves b : no renewal of s t r a n d c o n t a c t . 137 - x i i i -A C K N O W L E D G E M E M T The success of t h i s t h e s i s owes deep ly to the e f f o r t s of many i n d i v i d u a l s . F i r s t , I want to thank my s u p e r v i s o r s , D r . John R. Grace and D r . C . J im L i m , for t h e i r con t in u ou s g u i d a n c e , e n l i g h t e n m e n t , s u p p o r t , and encouragement over the course of t h i s work. A l s o , I want to thank D r . C l i v e M . H . B r e r e t o n for h i s many u s e f u l d i s c u s s i o n s and h i s a s s i s t a n c e wi th the c o l d model CFB u n i t . I am a l s o i n d e b t e d to D r . Robert L e g r o s , D r . Hongzhong L i , J i a n s h e n g Zhao, Ningde Wang, Weimiao Y u , Hugh A c k r o y d , R i c h a r d S e n i o r , and D r . Jamal Chaouki f or t h e i r p a r t i c i p a t i o n and o f t e n l a t e n i g h t e f f o r t s i n o b t a i n i n g many of the e x p e r i m e n t a l d a t a . The f i n a n c i a l suppor t of E n e r g y , Mines and Resources Canada , M a c M i l l a n B l o e d e l L i m i t e d , the Pulp and Paper Research I n s t i t u t e of Canada , and the N a t u r a l S c i e n c e s and E n g i n e e r i n g Research C o u n c i l of Canada i s a l s o g r a t e f u l l y acknowledged. F i n a l l y , I want to thank my wife f o r her p e r s e v e r a n c e and u n d e r s t a n d i n g over the p a s t few y e a r s . Her c o n t i n u o u s encourage -ment and c o n f i d e n c e i n me are more than v i t a l to the success o f t h i s t h e s i s . - 1 -C H A P T E R 1 I N T R O D U C T I O N C i r c u l a t i n g f l u i d i z e d beds have become p o p u l a r i n a p p l i c a t i o n s i n v o l v i n g g a s - s o l i d s r e a c t i o n s l i k e c a l c i n a t i o n and c o m b u s t i o n . Dur ing the p a s t decade , c o n s i d e r a b l e i n t e r e s t i n c i r c u l a t i n g f l u i d i z e d bed combust ion has been genera ted due to i t s s i g n i f i c a n t advantages over c o n v e n t i o n a l b u b b l i n g f l u i d i z e d bed combustors . B o i l e r s u s i n g c i r c u l a t i n g bed t echno logy are now c a p t u r i n g a major p o r t i o n of the market f or i n d u s t r i a l and u t i l i t y s c a l e b o i l e r s . Though the surge of i n d u s t r i a l and academic i n t e r e s t i n c i r c u l a t i n g f l u i d i z e d beds s t a r t e d o n l y r e c e n t l y , i n v e s t i g a t i o n s of what i s known today as " fas t f l u i d i z a t i o n " began as e a r l y as 1940. Lewis and G i l l i l a n d (1950) were among the f i r s t to r e p o r t the f a s t f l u i d i z a t i o n phenomenon. They r e p o r t e d a suspens ion 3 d e n s i t y of about 160 kg/m at a s u p e r f i c i a l gas v e l o c i t y of about 2.5 m/s . Broad commercia l a p p l i c a t i o n s of c i r c u l a t i n g f l u i d i z e d beds were i n i t i a t e d o n l y i n the l a s t f i f t e e n y e a r s or so by L u r g i Chemie und H u t t e n t e c h n i k GmBh of F r a n k f u r t , West Germany. Two such s u c c e s s f u l commercia l a p p l i c a t i o n s r e p o r t e d by Reh (1986) are c a l c i n a t i o n of aluminum h y d r o x i d e to a lumina and a d s o r p t i o n of hydrogen f l u o r i d e from e f f l u e n t gases from H a l l c e l l s p r o d u c i n g aluminum. S ince t h e n , c i r c u l a t i n g f l u i d i z e d beds have found i n c r e a s i n g l y important a p p l i c a t i o n s i n the combust ion of c o a l as w e l l as a wide v a r i e t y of other s o l i d f u e l s such as p e a t , wood c h i p s , and pe tro l eum c o k e . -2-In a c i r c u l a t i n g f l u i d i z e d b e d , the g a s - s o l i d s m i x t u r e does not form a bed , as i n the c o n v e n t i o n a l b u b b l i n g f l u i d i z e d bed . R a t h e r , i t operates i n the f a s t f l u i d i z a t i o n regime i n which h i g h v e l o c i t y gas i s brought i n t o i n t i m a t e c o n t a c t w i th f i n e s o l i d p a r t i c l e s to form an e n t r a i n e d s u s p e n s i o n , wi th the p a r t i c l e s be ing c o n t i n u o u s l y c a p t u r e d and r e c y c l e d . F i g u r e 1.1 shows a t y p i c a l c i r c u l a t i n g f l u i d i z e d bed combustor . The s u p e r f i c i a l gas v e l o c i t y i s of the order of 5-10 m/s and the o v e r a l l vo idage t y p i c a l l y ranges from 0 .9 -0 .98 (as compared to 1-3 m/s and 0 . 6 -0.75 r e s p e c t i v e l y for c o n v e n t i o n a l b u b b l i n g f l u i d i z e d b e d s ) . The mean p a r t i c l e s i z e for c i r c u l a t i n g bed combustors i s , moreover , somewhat f i n e r than f o r b u b b l i n g bed combustors ( t y p i c a l l y 50-500 i^m compared to t y p i c a l l y 1-3 mm) . The combinat ion of h i g h e r s u p e r f i c i a l gas v e l o c i t y wi th f i n e r p a r t i c l e s employed i n c i r c u l a t i n g beds c r e a t e s a s i g n i f i c a n t l y h i g h e r r a t e of e n t r a i n -ment. T h i s mandates the c o n t i n u o u s r e c a p t u r e and r e c y c l e of the e n t r a i n e d s o l i d s to the base of the r e a c t o r . The hydrodynamics of c i r c u l a t i n g f l u i d i z e d beds depend, t h e r e f o r e , not on ly on gas v e l o c i t y and s o l i d p r o p e r t i e s but a l s o on the r a t e of s o l i d s r e c i r c u l a t i o n . When viewed through a t r a n s p a r e n t w a l l , the s t a t e of f a s t f l u i d i z a t i o n seems to c o n s i s t of waves or f a l l i n g s t r a n d s of s o l i d p a r t i c l e s . These dense s t r u c t u r e s undergo r a p i d c o a l e s c e n c e and d e c o m p o s i t i o n , g i v i n g r i s e to e x c e l l e n t g a s / s o l i d s c o n t a c t i n g . C i r c u l a t i n g f l u i d i z e d beds o f f e r many advantages i n h a n d l i n g combust ion of v a r i o u s s o l i d f u e l s . These i n c l u d e : -3 -GAS PRIMARY AIR 40-80% F i g u r e 1.1 A t y p i c a l c i r c u l a t i n g f l u i d i z e d bed combustor ( K u l l e n d o r f and A n d e r s s o n , 1986). -4-( i) Lower e m i s s i o n s of N0 x due to s taged p r i m a r y and secondary a i r i n t r o d u c t i o n as w e l l as r e l a t i v e l y low and u n i f o r m combust ion temperatures ( u s u a l l y 750-950 C ) . ( i i ) Reduced e m i s s i o n s of SO due to the use of f i n e x p a r t i c l e s of a sorbent l i k e l imes tone or d o l o m i t e to e f f e c t i n - s i t u s u l p h u r c a p t u r e , ( i i i ) Due to the v i g o r o u s s o l i d s m i x i n g , f l e x i b i l i t y i n h a n d l i n g a wide v a r i e t y of f u e l s i n c l u d i n g l i g h t and s t i c k y s o l i d s , h i g h m o i s t u r e c o n t e n t f u e l s , h i g h ash and h i g h s u l p h u r c o a l s , ( iv) E x c e l l e n t turndown and l o a d f o l l o w i n g c a p a b i l i t y as w e l l as s i m p l e r c o n t r o l due to the a b i l i t y to v a r y the s u s p e n s i o n - t o - c o o l i n g - s u r f a c e heat t r a n s f e r c o e f f i -c i e n t s through c o n t r o l of s o l i d s c i r c u l a t i o n r a t e , (v) Fewer f u e l feed p o i n t s due to improved l a t e r a l s o l i d s m i x i n g . (vi) Lower f u e l c o s t s due to improved f u e l combust ion e f f i c i e n c y , c l a i m e d to be t y p i c a l l y 98-99%. A r g u a b l y , many of the above l i s t e d advantages can a l s o be a c h i e v e d by c o n v e n t i o n a l b u b b l i n g f l u i d i z e d bed combustors i f c y c l o n e ash i s r e c y c l e d and a i r i n t r o d u c t i o n i s s t a g e d . However, c i r c u l a t i n g f l u i d i z e d beds do o f f e r the d i s t i n c t advantages of e x c e l l e n t and s imple turndown as w e l l as the f l e x i b i l i t y to handle a v a r i e t y of f u e l s . For most of the a p p l i c a t i o n s i n v o l v i n g c i r c u l a t i n g f l u i d i z e d beds , e f f e c t i v e heat e x t r a c t i o n from the r e a c t o r i s an important -5-c o n s i d e r a t i o n i n the equipment d e s i g n . For a c i r c u l a t i n g f l u i d i z e d bed steam b o i l e r , f or i n s t a n c e , steam i s produced by v a p o r i z i n g water , u t i l i z i n g the heat generated from the combust ion r e a c t i o n . D i f f e r e n t p o s s i b i l i t i e s e x i s t as to where to e x t r a c t heat from the r e a c t o r . Due to the h i g h v e l o c i t i e s i n c i r c u l a t i n g f l u i d i z e d beds , i n t e r n a l h o r i z o n t a l heat t r a n s f e r s u r f a c e s are avo ided because of severe tube e r o s i o n and s o l i d s a t t r i t i o n . In g e n e r a l , heat i s e x t r a c t e d v i a exposed v e r t i c a l membrane w a t e r w a l l s u r f a c e s which form the s u r r o u n d i n g w a l l of the r e a c t o r v e s s e l , bounding the combust ion r e g i o n above p o r t s which i n t r o d u c e secondary a i r . For very l a r g e u n i t s , such as the 110 WW C o l o r a d o Ute u n i t at N u c l a , C o l o r a d o , a d d i t i o n a l i n - b e d e s u r f a c e s may p r o j e c t as wing w a l l s at r i g h t ang les to the c o n t a i n i n g w a t e r w a l l s . A d d i t i o n a l heat i s e x t r a c t e d e x t e r n a l l y i n some i n s t a l l a t i o n s by d i v e r t i n g some s o l i d s from the r e t u r n l e g i n t o an e x t e r n a l heat exchanger . Heat may a l s o be e x t r a c t e d from the c y c l o n e ( s ) and from the f l u e gas v i a a c o n v e c t i o n p a s s . For most u n i t s , at l eas t ' 50% of the o v e r a l l heat removal i s from the r e a c t o r i t s e l f ( e x t e r i o r or i n t e r n a l w a t e r w a l l s ) . Knowing how the heat t r a n s f e r c o e f f i c i e n t between the g a s -s o l i d s suspens ion and the c o o l i n g s u r f a c e s v a r i e s wi th o p e r a t i n g c o n d i t i o n s i s c r i t i c a l to the s u c c e s s f u l o p e r a t i o n of c i r c u l a t i n g f l u i d i z e d bed b o i l e r s s i n c e turndown i s commonly a c h i e v e d by v a r y i n g the suspens ion d e n s i t y i n the u n i t (Kobro and B r e r e t o n , 1986) . D e s p i t e the importance of be ing ab le to p r e d i c t heat t r a n s f e r c o e f f i c i e n t s i n c i r c u l a t i n g f l u i d i z e d beds , e x p e r i m e n t a l data are few i n number. Moreover , most r e s e a r c h on heat t r a n s f e r - 6 -i n c i r c u l a t i n g f l u i d i z e d beds has remained l a r g e l y e m p i r i c a l . M o d e l l i n g at tempts are f u r t h e r h i n d e r e d by the f a c t tha t p u b l i s h e d data are ex treme ly s c a t t e r e d when compared a g a i n s t one a n o t h e r . A l though there are e m p i r i c a l c o r r e l a t i o n s a v a i l a b l e , t h e i r u s e f u l n e s s i s s e v e r e l y l i m i t e d when a p p l i e d to o ther equipment or c o n d i t i o n s . Another approach commonly f o l l o w e d i n s t u d i e s of heat t r a n s f e r and hydrodynamics i s to use d i m e n s i o n a l a n a l y s i s to i d e n t i f y key d i m e n s i o n l e s s groups and reduce the number of v a r i a b l e s . I f one were to compi le a l i s t of q u a n t i t i e s a f f e c t i n g s u s p e n s i o n - t o - s u r f a c e heat t r a n s f e r to v e r t i c a l membrane w a t e r w a l l s i n c i r c u l a t i n g f l u i d i z e d bed systems, one might w r i t e : h = f ( p , d , p a r t i c l e s i z e d i s t r i b u t i o n , k , c , g , gas p p p PP d e n s i t y , gas s p e c i f i c heat c a p a c i t y , gas v i s c o s i t y , k^, U , G , T , T c , e , e P, column d i a m e t e r , column s susp ' s u r f susp ' s u r f h e i g h t , b , s t a r t i n g h e i g h t of heat t r a n s f e r s u r f a c e , roughness of heat t r a n s f e r s u r f a c e , d iameter of heat t r a n s f e r tube , f i n (or web) width of membrane w a t e r w a l l , e x i t h e i g h t , e x i t w i d t h , d i s t a n c e from top of column to top of e x i t , d i s t r i b u t o r h o l e s p a c i n g , d i s t r i b u t o r h o l e d i a m e t e r , h e i g h t of s o l i d s r e - e n t r y ) (1.1) T h i s l i s t c o n t a i n s no fewer than 31 q u a n t i t i e s . With 4 d imens ions ( i . e . , mass, l e n g t h , t i m e , and t e m p e r a t u r e ) , t h i s would suggest 27 d i m e n s i o n l e s s g r o u p s . Even t h i s l i s t may be i n c o m p l e t e , for example , i f there i s secondary a i r i n t r o d u c t i o n . Whi le i t might be p o s s i b l e to e l i m i n a t e some of these v a r i a b l e s ( e . g . , k and gas s p e c i f i c heat c a p a c i t y t u r n out to be P -7-un important i n low v e l o c i t y f l u i d i z e d bed heat t r a n s f e r ) , a f o r m i d a b l e l i s t would s t i l l r e s u l t . Hence, e x t e n s i v e use of d i m e n s i o n a l a n a l y s i s appears to be f u t i l e at t h i s p o i n t . C l e a r l y , there are needs for a l a r g e r body of e x p e r i m e n t a l da ta e x t e n d i n g the range and d e t a i l i n g the e f f e c t of r e l e v a n t o p e r a t i n g v a r i a b l e s . In a d d i t i o n , t h e r e are needs f o r a b e t t e r fundamental u n d e r s t a n d i n g of the heat t r a n s f e r mechanism i n v o l v e d and for an adequate model to p r e d i c t v a r i a t i o n s of heat t r a n s f e r c o e f f i c i e n t i n c i r c u l a t i n g f l u i d i z e d beds . Conforming to the above o b j e c t i v e s , t h i s t h e s i s i s o r g a n i z e d i n t o the f o l l o w i n g s e p a r a t e , s e l f - c o n t a i n e d but complementary c h a p t e r s , each wi th i t s own d i s t i n c t emphas i s . Chapter 2 d e t a i l s the s tudy of heat t r a n s f e r i n a p i l o t - s c a l e c i r c u l a t i n g f l u i d i z e d bed combustor . Chapter 3, on the o ther hand, d e s c r i b e s a more fundamental s tudy of heat t r a n s f e r mechanism i n a c o l d model c i r c u l a t i n g f l u i d i z e d bed . Chapter 4 p r e s e n t s a model f o r heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds , drawing on the r e s u l t s d i s c u s s e d i n i t s two p r e c e d i n g c h a p t e r s . T h i s t h e s i s i s then t e r m i n a t e d i n Chapter 5, wi th a summary of c o n c l u s i o n s and some a p p r o p r i a t e recommendations for f u t u r e work. -8-C H A P T E R 2 H E A T T R A N S F E R I N C I R C U L A T I N G F L U I D I Z E D B E D C O M B U S T O R 2.1 I N T R O D U C T I O N At the ou t se t of t h i s s t u d y , there was a severe l a c k of e x p e r i m e n t a l da ta on heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds . Most p u b l i s h e d data a v a i l a b l e then were a l s o d e f i c i e n t i n the sense tha t they were o b t a i n e d for very s m a l l heat t r a n s f e r s u r f a c e s suspended w i t h i n the i n t e r i o r o f s m a l l - s c a l e columns opera ted at room t e m p e r a t u r e , as reviewed by Grace (1986). In a d d i t i o n , e f f e c t s of many o p e r a t i n g v a r i a b l e s such as s u p e r f i c i a l gas v e l o c i t y and s o l i d s c i r c u l a t i o n r a t e on heat t r a n s f e r remained u n c l e a r . Moreover , these e x p e r i m e n t a l da ta show extreme s c a t t e r when compared a g a i n s t one a n o t h e r . T h i s s t u d y , m o t i v a t e d by the above c o n c e r n s , focused on c o n d u c t i n g s y s t e m a t i c s tudy of the e f f e c t of v a r i o u s o p e r a t i n g v a r i a b l e s and o b t a i n i n g heat t r a n s f e r da ta which sh ou ld be u s e f u l for the d e s i g n of l a r g e - s c a l e c i r c u l a t i n g f l u i d i z e d bed combust ion b o i l e r s . In order to c l o s e l y conform to i n d u s t r i a l p r a c t i c e , exper iments were performed i n a p i l o t - s c a l e c i r c u l a t i n g f l u i d i z e d bed u n i t . The s p e c i f i c c o n f i g u r a t i o n s of heat t r a n s f e r s u r f a c e s employed i n t h i s s t u d y , namely a w a t e r - c o o l e d membrane w a l l and a long v e r t i c a l t u b e , as w e l l as the e x p e r i m e n t a l c o n d i t i o n s chosen , a l s o c o r r e s p o n d c l o s e l y to those i n i n d u s t r y . The p r e s e n t chapter i s d i v i d e d i n t o two r e l a t e d p a r t s : S e c t i o n 2.2 t r e a t s the low temperature (150-350 C) s t u d y , whi l e -9-S e c t i o n 2.3 p r e s e n t s the h i g h temperature (350-880 C) s t u d y . Over the span of t h i s work, there were a number o f m o d i f i c a t i o n s added to the equipment . These m o d i f i c a t i o n s were needed e i t h e r for improv ing the o p e r a t i o n of the u n i t or for implementing ins truments from other r e s e a r c h which shared the same c i r c u l a t i n g bed f a c i l i t y (Grace and L i m , 1987; Grace et a l . , 1989a) . As a r e s u l t , there are minor v a r i a t i o n s i n the equipment used for d i f f e r e n t p a r t s of t h i s s t u d y . These v a r i a t i o n s are n o t e d , where r e l e v a n t , i n the f o l l o w i n g s e c t i o n s . 2.2 LOW TEMPERATURE STUDY 2 . 2 . 1 E x p e r i m e n t a l Equipment The equipment used f o r the low temperature s tudy i s the p i l o t - s c a l e c i r c u l a t i n g f l u i d i z e d bed combust ion f a c i l i t y i n i t s o r i g i n a l c o n f i g u r a t i o n at the U n i v e r s i t y of B r i t i s h C o l u m b i a . T h i s i s d e s c r i b e d i n d e t a i l e l sewhere (Grace et a l . , 1987; Grace and L i m , 1987). The heat t r a n s f e r work performed by the author was i n t e g r a t e d wi th o ther fundamental s t u d i e s and f u e l t e s t i n g s t u d i e s . A schemat ic of the major e x p e r i m e n t a l components i s shown i n F i g u r e 2 . 1 . The r e f r a c t o r y - l i n e d r e a c t o r column i s 7.32 m h i g h and 152 x 152 mm i n c r o s s - s e c t i o n . Preheated p r i m a r y a i r was i n t r o d u c e d through a d i s t r i b u t o r p l a t e wi th three t u y e r e s and s i x h o l e s per tuyere at the bottom of the co lumn. Secondary a i r was fed through two p a i r s of d i r e c t l y opposed a i r p o r t s of 32 mm diameter l o c a t e d 0.9 m above the d i s t r i b u t o r p l a t e , on two f a c i n g w a l l s . S o l i d s e n t r a i n e d i n the column were c o n t i n u o u s l y W a t e r • -Fuel • Sorbent * 1 Sorbenl Hopper Rotary Feeder N i t r o g e n P r o p a n e ^ -V Fue l Hopper or Na tu r a l G a s A i r • Secondary A i r -M- I Secondary Cyc lone P r i m a r y C y c l o n e Reactor W a l e r Ou t Heat Transfer Surface -M—QD—> - M H 3 » Screw feede r Burner P r i m a r y A i r Over f low Receive! L-Valve B e d -Dra in Receiver • a v A i h Receiver W a l o r In I > - O f f - G a s ' W a l e r O u t W a l e r In O f f - G a s C o o l e r A o r a f f a n A i r F i g u r e -2.1 Schematic of the c i r c u l a t i n g f l u i d i z e d bed f a c i l i t y used in S e c t i o n 2 .2 . -11-c a p t u r e d by a 0.31 m ID r e f r a c t o r y - l i n e d p r i m a r y c y c l o n e and r e t u r n e d to the column 0.4 m above the d i s t r i b u t o r from a 0.1 m ID s t a n d p i p e through an L - v a l v e (Knowlton and H i r s a n , 1978). The s o l i d s r e c i r c u l a t i o n r a t e was c o n t r o l l e d by v a r y i n g the amount of a e r a t i o n a i r to the L - v a l v e . Most f i n e p a r t i c l e s not c a p t u r e d by the p r i m a r y c y c l o n e were c a p t u r e d wi th a 0 . 2 m ID secondary c y c l o n e and c o u l d be r e t u r n e d to the bottom of the r e a c t o r . E x p e r i m e n t a l d a t a were o b t a i n e d by o p e r a t i n g the u n i t as a hot c i r c u l a t i n g f l u i d i z e d bed wi th no combust ion i n s i d e the r e a c t o r . A p r e h e a t e r burner tha t c o u l d be fed wi th e i t h e r n a t u r a l gas or propane was used to heat the u n i t . The e n t i r e r e a c t o r column was in s t rumented wi th thermocouples and p r e s s u r e taps at 0.61 m i n t e r v a l s a long o p p o s i t e w a l l s to moni tor the b u l k temperatures and suspens ion d e n s i t y p r o f i l e s . The l o c a t i o n s of the thermocouples and p r e s s u r e taps are shown i n F i g u r e 2 .2 . Thermocouples were i n s e r t e d about 76 mm i n t o the co lumn. P a r t i c l e s used for t h i s p a r t of the p r o j e c t were two Ottawa sands of 188 and 356 fim s u r f a c e - v o l u m e mean d iameter wi th a p a r t i c l e 3 d e n s i t y of 2640 kg/m . The mean p a r t i c l e s i z e s are c a l c u l a t e d from the i n v e r s e of 2 ( x . / d .) where x. i s the weight f r a c t i o n of l pi' I 3 p a r t i c l e s which have an average s i z e of d ^ de termined by s i e v e a n a l y s i s . The measured minimum f l u i d i z a t i o n v e l o c i t i e s f o r a i r at room temperature and p r e s s u r e are 51 and 95 mm/s for the two sands r e s p e c t i v e l y . Tab le 2.1 summarizes the key p r o p e r t i e s of these two sands . Heat t r a n s f e r da ta were o b t a i n e d from two n e a r l y i d e n t i c a l heat t r a n s f e r s u r f a c e s , each 1.53 m long and 148 mm wide, l o c a t e d -12-TO C Y C L O N E F i g u r e 2 . 2 P r i n c i p a l r e a c t o r v e s s e l s h o w i n g p o s i t i o n s o f h e a t t r a n s f e r s u r f a c e s and o f t h e r m o c o u p l e s . P r e s s u r e t a p s a r e a t t h e same h e i g h t s as t h e t h e r m o c o u p l e s , on t h e o p p o s i t e w a l l . . A l l d i m e n s i o n s a r e i n mm. -13-TABLE 2.1 P a r t i c l e S i z e A n a l y s e s and F l u i d i z a t i o n P r o p e r t i e s f o r the Two Ottawa Sands Used i n S e c t i o n 2 . 2 . S i z e Range Sand 1 Sand 2 (/*m) (Wt. %) (Wt. %) 850-710 0.1 0.0 710-600 0.5 2.4 600-495 1.8 14.2 495-420 2.4 27.2 420-351 2.2 20.7 351-297 6.0 19.7 297-250 10.1 5.8 250-208 21.8 4.0 208-180 20.4 3.0 180-150 13.3 1.3 150-125 11.4 1.0 125-106 5.4 0.3 106-90 3.3 0.2 90-61 0.9 0.1 61-53 0.3 0.1 53-45 0.1 0.0 45-0 0.0 0.0 Mean P a r t i c l e S i z e (^ tm) 188 3 P a r t i c l e D e n s i t y (kg/m ) 2637 C a l c u l a t e d T e r m i n a l S e t t l i n g V e l o c i t y f or Mean S i z e at Room 1.2 Temperature and P r e s s u r e (m/s) Minimum F l u i d i z a t i o n V e l o c i t y at Room Temperature and 51 Pres sure (mm/s) Voidage at Minimum F l u i d i z a t i o n 0.46 356 2642 2.8 95 0.42 -14-on one w a l l of the column b e g i n n i n g 1.22 and 4.27 m, r e s p e c t i v e -l y , above the d i s t r i b u t o r p l a t e , as shown i n F i g u r e 2 . 2 . Each s u r f a c e c o n s i s t s of four i d e n t i c a l , ha l f - embedded , s chedule 80, v e r t i c a l , s t a i n l e s s s t e e l , w a t e r - c o o l e d tubes connected l o n g i t u -d i n a l l y by f l a t f i n s 7.0 mm t h i c k to form a membrane w a l l . F i g u r e 2.3 shows a p l a n view and a s e c t i o n view of the s u r f a c e s . The f i n s are f l u s h wi th the r e f r a c t o r y s u r f a c e above and below. One of the c e n t r a l tubes i n each s u r f a c e i s in s t rumented wi th e i g h t thermocouples l o c a t e d a p p r o x i m a t e l y 150 mm a p a r t . Temperatures and f l o w r a t e s of water i n t u r b u l e n t f low i n s i d e the tubes are r e c o r d e d . T h i s enables one to c a l c u l a t e the average heat t r a n s f e r c o e f f i c i e n t (between thermocouples 1 and 8) or the heat t r a n s f e r c o e f f i c i e n t f o r the s u r f a c e between any two thermocoup le s . The procedure for c a l c u l a t i n g the heat t r a n s f e r c o e f f i c i e n t and the e r r o r s i n v o l v e d are i l l u s t r a t e d i n Appendix 1. A l though the predominant heat t r a n s f e r r e s i s t a n c e f o r the p r e s e n t c o n d i t i o n s i s on the c i r c u l a t i n g bed s i d e of the membrane s u r f a c e s , the r e s i s t a n c e of the c o o l i n g water s i d e , e s t i m a t e d from the c o r r e l a t i o n of S l e i c h e r and Rouse (1975), and by the tube i t s e l f have been s u b t r a c t e d . T h i s c o r r e c t i o n i s t y p i c a l l y about 15%. The c o r r e c t i o n procedure i s i l l u s t r a t e d by sample c a l c u l a t i o n s i n Appendix 1. The r e p o r t e d heat t r a n s f e r c o e f f i c i e n t s are t h e r e f o r e s u s p e n s i o n - t o - e x p o s e d s u r f a c e v a l u e s . Heat t r a n s f e r c o e f f i c i e n t s can be based on: (1) The exposed tube s u r f a c e areas a lone (2) The t o t a l p r o j e c t e d s u r f a c e a r e a , or (3) The t o t a l of the exposed tube s u r f a c e areas and F i g u r e 2.3 (a) P lan view and (b) S e c t i o n view of membrane w a l l s used i n S e c t i o n 2 .2 . A l l d imens ions are i n mm. -16-the areas of the f i n s between the t u b e s . A l l membrane w a l l c o e f f i c i e n t s r e p o r t e d i n t h i s t h e s i s r e f e r to the l a s t of t h e s e , i . e . , the t o t a l exposed heat t r a n s f e r a r e a . To o b t a i n c o e f f i c i e n t s based on areas (1) or (2 ) , the da ta r e p o r t e d here should be m u l t i p l i e d by 1.46 or 1 .33, r e s p e c t i v e l y . Area (3) was used here because i t i s the most l o g i c a l and c o n v e n t i o n a l ( i n c h e m i c a l e n g i n e e r i n g ) c h o i c e . A l though the f i n i s not as e f f e c t i v e as an e q u i v a l e n t exposed tube area (Bowen et a l . , 1989) due to the i n c r e a s e d d i s t a n c e f o r heat c o n d u c t i o n , the temperature d i s t r i b u t i o n s a long the f i n and the tube are s t i l l q u i t e u n i f o r m , as e v i d e n t from i t s low B i o t number (Bi t y p i c a l l y 0 . 1 ) . Suspens ion d e n s i t i e s r e p o r t e d here are c r o s s - s e c t i o n a l area mean va lues e s t i m a t e d from measured p r e s s u r e p r o f i l e s . In t h i s t e c h n i q u e , the p r e s s u r e drop i s e n t i r e l y a s c r i b e d to the h y d r o s t a t i c p r e s s u r e or the weight of the s o l i d s and f l u i d per u n i t a r e a . The combined e f f e c t s of g a s - w a l l and s o l i d s - w a l l f r i c t i o n , and s o l i d s a c c e l e r a t i o n are assumed to be n e g l i g i b l e . T h i s g i v e s the c r o s s - s e c t i o n a l a r e a - a v e r a g e d suspens ion d e n s i t y as P = - • ± ^ (2 1) ^susp g ' dY T h i s t e c h n i q u e i s commonly used to i n f e r suspens ion d e n s i t i e s , wi th r e a s o n a b l e a c c u r a c y (Van Swaaij et a l . , 1970; Capes and Nakamura, 1973). E q u a t i o n 2.1 has a l s o been shown to be a c c u r a t e to w i t h i n 10% by Turner (1978) f o r a 152 mm ID co lumn. R e c e n t l y , Hartge et a l . (1986) showed tha t the p r e s s u r e drop measurement t echn ique y i e l d e d r e s u l t s i n c l o s e agreement wi th those o b t a i n e d - 1 7 -by 7 - r a y t e c h n i q u e coup led wi th a c a p a c i t a n c e p r o b e . 2 .2 .2 R e s u l t s and D i s c u s s i o n T i m e - a v e r a g e d , l e n g t h - a v e r a g e d s u s p e n s i o n - t o - s u r f a c e heat t r a n s f e r c o e f f i c i e n t s (from thermocouple 1 to 8 i n F i g u r e 2.3b) are p l o t t e d a g a i n s t a r e a - a v e r a g e d suspens ion d e n s i t y i n F i g u r e s 2.4 and 2.5 f o r sand p a r t i c l e s of mean d iameter 188 and 356 fim, r e s p e c t i v e l y . The open and f i l l e d symbols r e s p e c t i v e l y r e p r e s e n t c o e f f i c i e n t s measured f o r the t o t a l upper and lower heat t r a n s f e r s u r f a c e s . The heat t r a n s f e r c o e f f i c i e n t da ta p l o t t e d i n these two f i g u r e s and i n the remain ing f i g u r e s i n t h i s t h e s i s are t a b u l a t e d i n Appendix 2. Appendix 2 a l s o g i v e s the 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 . In both c a s e s , the heat t r a n s f e r c o e f f i c i e n t i n c r e a s e s wi th suspens ion d e n s i t y . The two curves i n F i g u r e s 2.4 and 2.5 f o r the two sands are a lmost i d e n t i c a l , a l though the heat t r a n s f e r c o e f f i c i e n t s f o r the l a r g e r sand appear to be somewhat lower at low suspens ion d e n s i t i e s (<25 3 kg/m ) . There appear to be no s y s t e m a t i c d i f f e r e n c e s between the upper and lower exchange s u r f a c e s and no s y s t e m a t i c i n f l u e n c e of the s e c o n d a r y - t o - p r i m a r y a i r r a t i o . The v a r i a t i o n of l e n g t h - a v e r a g e d s u s p e n s i o n - t o - s u r f a c e heat t r a n s f e r c o e f f i c i e n t as a f u n c t i o n of s u p e r f i c i a l gas v e l o c i t y f o r the 188 ^m sand i s shown i n F i g u r e 2 . 6 . The l i n e s drawn are l e a s t - s q u a r e s r e g r e s s i o n l i n e s f o r each va lue of suspens ion d e n s i t y . I t i s observed tha t s u p e r f i c i a l gas v e l o c i t y does not s i g n i f i c a n t l y a f f e c t the heat t r a n s f e r c o e f f i c i e n t once the -18-F i g u r e 2.4 Average heat t r a n s f e r c o e f f i c i e n t for membrane w a l l s u r f a c e s ( thermocouple 1-8 i n F i g u r e 2.3b) for 188 fim sand as a f u n c t i o n of s u s p e n s i o n d e n s i t y . Open and f i l l e d symbols r e f e r to the upper and lower exchange s u r f a c e s r e s p e c t i v e l y . Q 2 / Q 1 i s the r a t i o of secondary to p r i m a r y a i r f l o w r a t e s . -19-F i g u r e 2.5 Average heat t r a n s f e r c o e f f i c i e n t for membrane w a l l s u r f a c e s ( thermocouple 1-8 i n F i g u r e 2.3b) for 356 fim sand as a f u n c t i o n of suspens ion d e n s i t y . Open and f i l l e d symbols r e f e r to the upper and lower exchange s u r f a c e s r e s p e c t i v e l y . Q 0 / Q , = 0 i n a l l c a s e s . F i g u r e 2.6 Inf luence of s u p e r f i c i a l gas v e l o c i t y on average heat t r a n s f e r c o e f f i c i e n t at three d i f f e r e n t suspension d e n s i t i e s for the 188 jum sand . -21-suspens ion d e n s i t y i s e s t a b l i s h e d . T h i s shou ld not be s u r p r i s i n g s i n c e the c o n t r i b u t i o n of the gas c o n v e c t i v e component to the heat t r a n s f e r c o e f f i c i e n t i s expected to be s m a l l compared to the p a r t i c l e c o n v e c t i v e component (Grace , 1986) . One e x p e r i m e n t a l p o i n t f o r no p a r t i c l e s i n the r e a c t o r i s shown i n F i g u r e 2.6 for c o m p a r i s o n . The measured heat t r a n s f e r c o e f f i c i e n t f o r t h i s 2 c a s e , 18 W/m . K , i s i n good agreement wi th p u b l i s h e d c o r r e l a -t i o n s , f o r example , tha t of S l e i c h e r and Rouse (1975). The i n f l u e n c e of suspens ion temperature on the average heat t r a n s f e r c o e f f i c i e n t i s shown i n F i g u r e 2.7 f o r the 188 fim sand at three suspens ion d e n s i t i e s , wi th the l i n e s aga in c o r r e s p o n d i n g to l e a s t - s q u a r e s l i n e a r f i t t i n g . As for s u p e r f i c i a l gas v e l o c i t y , the e f f e c t of suspens ion temperature on the heat t r a n s f e r c o e f f i c i e n t i s min imal i n the temperature range s t u d i e d (150-400 C ) . The independent e f f e c t s of s u p e r f i c i a l gas v e l o c i t y and suspens ion temperature were a l s o observed to be very s m a l l f o r the 356 fim sand . The above weak i n f l u e n c e of s u p e r f i c i a l gas v e l o c i t y and suspens ion temperature on heat t r a n s f e r c o e f f i c i e n t was conf i rmed r e c e n t l y by S e k t h i r a e t a l . (1988) for 300 fim sand . The ranges of s u p e r f i c i a l gas v e l o c i t y and suspens ion temperature they i n v e s t i g a t e d are 5-11 m/s and 100-350 C , r e s p e c t i v e l y . A n a l y s i s of heat t r a n s f e r c o e f f i c i e n t s f o r p a r t - l e n g t h s a long the upper heat t r a n s f e r s u r f a c e shows tha t the c o e f f i c i e n t decreases r a p i d l y wi th d e c r e a s i n g h e i g h t , wi th the maximum heat t r a n s f e r c o e f f i c i e n t o c c u r r i n g at the top of the s u r f a c e i n a l l c a s e s . F i g u r e 2.8a shows some t y p i c a l p r o f i l e s of the heat t r a n s f e r c o e f f i c i e n t as a f u n c t i o n of the p o s i t i o n a l on g the 1 40 150 200 250 300 350 400 450 T °C I F i g u r e 2.7 In f luence of suspens ion temperature on average heat t r a n s f e r c o e f f i c i e n t at three d i f f e r e n t suspens ion d e n s i t i e s for the 188 fim sand . -23-500 300 CO a D a." 100 — F i g u r e 2.8 0.2 1.0 1.5 0.2 1.0 1.5 Z, m Z, m (a) UPPER SURFACE (b) LOWER SURFACE T y p i c a l l o n g i t u d i n a l p r o f i l e s of heat t r a n s f e r c o e f f i c i e n t and suspens ion d e n s i t y f o r (a) upper s u r f a c e , and (b) lower s u r f a c e . C o e f f i c i e n t s are o b t a i n e d between thermocouples 1-3, 3 -6 , 6-8 i n F i g u r e 2.3b for the 188 fim s a n d . Other c o n d i t i o n s Curve AP (kPa) 12.93 11.76 9.60 3.82 U(m/s) 6.5 5.6 4.4 4.4 •susp C~) 240 G s ( k g / m 2 s ) Q 2 / Q i 69 0.4 190 28 1.0 200 not de termined 0.0 333 not de termined 0.0 -24-upper s u r f a c e measured downward from i t s t o p . The c o r r e s p o n d i n g d e n s i t y p r o f i l e s are a l s o shown i n F i g u r e 2 . 8 a . The t r e n d i s q u i t e d i f f e r e n t for the lower heat t r a n s f e r s u r f a c e , as shown i n F i g u r e 2 . 8 b . The v a r i a t i o n i n c o e f f i c i e n t over the upper s u r f a c e suggests the e x i s t e n c e of a l a y e r of downflowing s o l i d s a long the upper p a r t of the combustor w a l l s (and thus over the upper heat t r a n s f e r s u r f a c e ) , w i th f r e s h s o l i d s c o n s t a n t l y coming i n t o c o n t a c t w i t h the top p a r t o f the heat t r a n s f e r s u r f a c e and then t r a v e l l i n g down a long the membrane w a t e r w a l l s u r f a c e . E x i s t e n c e of a p r e d o m i n a n t l y downflowing l a y e r of s o l i d s at the w a l l of a f a s t f l u i d i z e d bed has been r e p o r t e d by B i e r l et a l . (1980), W e i n s t e i n e t a l . (1984), and B r e r e t o n and Stromberg (1986). The c l o s e n e s s of the s lope v a l u e s of the heat t r a n s f e r c o e f f i c i e n t p r o f i l e l i n e s to 0.5 i n F i g u r e 2 .8a suggests that p a r t i c l e renewal i n t h i s l a y e r of s o l i d s at the w a l l may be m i n i m a l . The p a r t i c l e mot ion i n the lower p a r t of the column i s l i k e l y to be l e s s r e g u l a r than that on the upper s u r f a c e , wi th p a r t i c l e s moving sometimes upward and sometimes downward over the lower s u r f a c e . P a r t i c l e mot ions tha t are p r e d o m i n a n t l y downward at the top but both upward and downward lower i n the v e s s e l are c o n s i s t e n t wi th v i s u a l o b s e r v a t i o n s i n a s e p a r a t e c o l d model c i r c u l a t i n g f l u i d i z e d bed u n i t of 152 mm diameter used i n exper iments d e s c r i b e d i n Chapter 3. The up-and-down mot ion of p a r t i c l e s p a s s i n g over the lower heat t r a n s f e r s u r f a c e p r o b a b l y e x p l a i n s the minima i n the heat t r a n s f e r c o e f f i c i e n t p r o f i l e s observed at the middle of the lower s u r f a c e . The i n c r e a s e i n the -25-suspens ion d e n s i t y over the lower p a r t of the s u r f a c e , F i g u r e 2 .8b , p r o b a b l y a l s o c o n t r i b u t e s to the sharp i n c r e a s e i n the heat t r a n s f e r c o e f f i c i e n t measured at the bottom of the lower s u r f a c e . Some d i s c u s s i o n of the i n f l u e n c e of the l e n g t h of heat t r a n s f e r s u r f a c e i s r e l e v a n t h e r e . The v e r t i c a l l e n g t h of heat t r a n s f e r s u r f a c e s shou ld be an important c o n s i d e r a t i o n i n p r e s e n t i n g heat t r a n s f e r r e s u l t s f o r c i r c u l a t i n g f l u i d i z e d bed u n i t s . T h i s can be i l l u s t r a t e d by comparing the p r e s e n t r e s u l t s , averaged over the l e n g t h of the exchanger s u r f a c e s from thermo-c o u p l e 1 to 8 i n F i g u r e 2 .3b , w i th p r e v i o u s l y r e p o r t e d da ta i n the l i t e r a t u r e ( M i c k l e y and T r i l l i n g , 1949; Kiang e t a l . , 1976; F r a l e y et a l . , 1983; Kobro and B r e r e t o n , 1986). From F i g u r e 2 . 9 , i t i s apparent tha t the p r e s e n t r e s u l t s are s i g n i f i c a n t l y lower than the p r e v i o u s da ta f o r p a r t i c l e s of comparable s i z e . A l s o , very l i t t l e i n f l u e n c e of p a r t i c l e s i z e i s d i s c e r n i b l e i n the p r e s e n t r e s u l t s . I t shou ld be n o t e d , however, that a l l p r e v i o u s da ta (except for those of M i c k l e y and T r i l l i n g , 1949) are l o c a l heat t r a n s f e r , c o e f f i c i e n t s measured u s i n g s m a l l heat t r a n s f e r probes ( e . g . , w a t e r - c o o l e d heat f l u x p r o b e , e l e c t r i c h e a t i n g element) wi th s i z e s of the order of c e n t i m e t e r s . I t seems l i k e l y tha t p a r t i c l e sheets of o r d e r 10-20 mm t h i c k t r a v e l l i n g pas t these s m a l l probes are f a r from a c h i e v i n g thermal e q u i l i b r i u m with the heat t r a n s f e r s u r f a c e , whereas p a r t i c l e s p a s s i n g a long an extended s u r f a c e , as i n the p r e s e n t c a s e , come c l o s e to r e a c h i n g the s u r f a c e temperature when they l eave the s u r f a c e and hence have a much lower d r i v i n g f o r c e f o r heat t r a n s f e r . T h e r e -f o r e , heat t r a n s f e r measurements u s i n g s h o r t heat t r a n s f e r probes 800 T T CM* 100 20 l I I I Mickley & Trilling Kiang et al. Kobro & Brereton Fraley et a|. This Work d p » jum 10 susp' 100 kg/m; i I 800 F i g u r e 2.9 Comparison between e x p e r i m e n t a l heat t r a n s f e r c o e f f i c i e n t s obta ined with the 1.53 m long heat t r a n s f e r s u r f a c e s in the presen t s tudy and e a r l i e r measurements of other workers f o r much s h o r t e r heat t r a n s f e r probes (Mickley and T r i l l i n g , 880 mm; Kiang et a l . , 57 mm; F r a l e y et a l . , 150 mm; Kobro and B r e r e t o n , 100 mm). -27-r e s u l t i n s i g n i f i c a n t l y h i g h e r heat t r a n s f e r c o e f f i c i e n t s than the much longer membrane w a l l s i n the p r e s e n t work. In a d d i t i o n , the i n f l u e n c e of p a r t i c l e s i z e becomes much l e s s s i g n i f i c a n t for longer s u r f a c e s s i n c e the r e s i d e n c e time of p a r t i c l e s at the s u r f a c e i s much longer than the p a r t i c l e thermal t ime c o n s t a n t f o r both s m a l l and l a r g e r p a r t i c l e s . T h i s can be seen more c l e a r l y from Tab le 2.2 which shows the thermal time c o n s t a n t s f o r p a r t i c l e s of d i f f e r e n t s i z e s at d i f f e r e n t ambient t e m p e r a t u r e s , as c a l c u l a t e d from the p a r t i c l e thermal time c o n s t a n t e x p r e s s i o n d e r i v e d by Gl icksman (1988), p c d 2 = PP P ( 2 . 2 ) p 36k g A l s o shown i n Tab le 2.2 are the c o r r e s p o n d i n g l e n g t h s t r a v e l l e d by the p a r t i c l e s d u r i n g r at a f a l l i n g v e l o c i t y of 1.26 m/s (obta ined l a t e r i n Chapter 3 ) . A secondary cause of the lower c o e f f i c i e n t s i n the p r e s e n t work compared with p r e v i o u s s t u d i e s i s t h a t the f i n s i n our membrane w a l l s are not as e f f e c t i v e as an e q u i v a l e n t area of exposed tube s u r f a c e (Bowen et a l . , 1989). F i g u r e 2.10 p l o t s the heat t r a n s f e r c o e f f i c i e n t measured between thermocouples 1 and 3 at the upper s u r f a c e versus suspens ion d e n s i t y f o r both the 188 and the 356 am sands . The l o c a l heat t r a n s f e r c o e f f i c i e n t s between thermocouples 1 and 3 show more s c a t t e r but are g e n e r a l l y h i g h e r than the average c o e f f i c i e n t s . Moreover , the p a r t i c l e s i z e e f f e c t i s more e v i d e n t , wi th the s m a l l e r p a r t i c l e s showing h i g h e r c o e f f i c i e n t s -28-TABLE 2.2 P a r t i c l e Thermal Time C o n s t a n t s i n A i r and the C o r r e s p o n d i n g Lengths T r a v e l l e d at a P a r t i c l e V e l o c i t y of 1.26 m / s . P a r t i c l e P r o p e r t i e s : p p=2650 k g / m 3 ; c p p =800 J / k g . K . Susp . P a r t i c l e Thermal Length Temp. Diameter Time Cons tant T r a v e l l e d (C) (/Am) (s) (xn) 100 0.023 0.029 25 200 0.092 0.116 300 0.208 0.262 400 0. 369 0.465 100 0.019 0.024 100 200 0.077 0.097 300 0.173 0.218 400 0.307 0.387 100 0.012 0.015 400 200 0.049 0. 062 300 0.109 0.137 400 0.194 0.244 -29-F i g u r e 2.10 Heat t r a n s f e r c o e f f i c i e n t for s e c t i o n of upper heat exchange s u r f a c e from thermocouple 1-3 (see F i g u r e 2.3b) versus suspens ion d e n s i t y for both the 188 and 356 fim sands . -30-than the l a r g e r p a r t i c l e s at the same suspens ion d e n s i t y . Thus , F i g u r e 2.10 i s i n a c c o r d wi th the p r e c e d i n g d i s c u s s i o n on the l e n g t h of heat t r a n s f e r s u r f a c e . F i g u r e s 2.9 and 2.10 imply t h a t c i r c u l a t i n g f l u i d i z e d bed combustor d e s i g n e r s sh ou ld e x e r c i s e c a u t i o n when u s i n g a v a i l a b l e heat t r a n s f e r d a t a from the l i t e r a t u r e . As heat t r a n s f e r s u r f a c e s i n b o i l e r s tend to be long and i n the form of membrane w a l l s , underdes ign i s p o s s i b l e i f l o c a l heat t r a n s f e r c o e f f i c i e n t s o b t a i n e d wi th m i n i a t u r e heat f l u x s u r f a c e s are u s e d . 2.3 HIGH TEMPERATURE STUDY 2 . 3 . 1 E x p e r i m e n t a l Equipment The c i r c u l a t i n g f l u i d i z e d bed combust ion f a c i l i t y d e s c r i b e d i n S e c t i o n 2 .2 .1 was a l s o used i n t h i s p a r t of the s t u d y . However, i n a l l the e x p e r i m e n t s , the lower heat t r a n s f e r s u r f a c e was removed and o n l y the upper s u r f a c e was used , as shown i n F i g u r e 2 . 1 1 . Data were o b t a i n e d from two d i f f e r e n t heat t r a n s f e r s u r f a c e s : a v e r t i c a l tube and a membrane w a l l . S e v e r a l m o d i f i -c a t i o n s , d e s c r i b e d b r i e f l y below and i n d e t a i l e l sewhere (Legros et a l . , 1989; Grace et a l . , 1989a), were made to the u n i t a f t e r the heat t r a n s f e r da ta from the tube were o b t a i n e d . A schemat ic of the major components of the m o d i f i e d u n i t i s shown i n F i g u r e 2 .11 . The r e f r a c t o r y - l i n e d r e a c t o r column i s aga in 7.32 m h i g h and 152 x 152 mm i n c r o s s - s e c t i o n . For the s t u d i e s wi th the membrane w a l l t r a n s f e r s u r f a c e , the bottom s e c t i o n of the r e a c t o r column was a r e f r a c t o r y - l i n e d s t a i n l e s s s t e e l s e c t i o n wi th i t s -31-Priimary Cyclone Heat Transfer Surface Water Fuel Hoppers Air Vent Secondary Cyclone Riser L-Valve F i g u r e 2.11 S i m p l i f i e d schemat ic of the c i r c u l a t i n g f l u i d i z e d bed combust ion f a c i l i t y used i n S e c t i o n 2 . 3 . -32-i n s i d e t a p e r e d from a 51 x 152 mm c r o s s - s e c t i o n to 152 x 152 mm c r o s s - s e c t i o n over i t s 1.22 m h e i g h t to p r o v i d e an a c c e l e r a t i o n zone , r e d u c i n g s i n t e r i n g and a g g l o m e r a t i o n . P r i m a r y a i r was i n t r o d u c e d through a h o r i z o n t a l h a l f - p i p e c u t a long i t s a x i s to form a d i s t r i b u t o r wi th twenty 9.5 mm diameter o r i f i c e s d r i l l e d on i t s c u r v e d s u r f a c e . Secondary a i r was p r e h e a t e d wi th o f f - g a s i n a heat exchanger b e f o r e be ing i n t r o d u c e d i n t o the co lumn. In a d d i t i o n , an e d u c t o r was used to r e t u r n f i n e s c a p t u r e d i n the secondary c y c l o n e to the bottom of the r e a c t o r . The f i r s t s e t of heat t r a n s f e r da ta was o b t a i n e d from a 1.22 m l o n g , 12.7 mm OD w a t e r - c o o l e d s t a i n l e s s s t e e l tube b e g i n n i n g 4.57 m above the d i s t r i b u t o r . T h i s tube was n o r m a l l y p o s i t i o n e d t o u c h i n g the r e f r a c t o r y s u r f a c e midway between two faces of the co lumn. I t c o u l d a l s o be moved to the a x i s of the column or i n t e r m e d i a t e l a t e r a l p o s i t i o n s . Both the i n l e t and o u t l e t t emperatures as w e l l as the f l o w r a t e s of the c o o l i n g water were r e c o r d e d , a l l o w i n g the t o t a l heat f l u x to be c a l c u l a t e d . In the second se t of e x p e r i m e n t s , a 1.59 m long by 148 mm wide w a t e r - c o o l e d membrane w a l l was used as the heat t r a n s f e r s u r f a c e , b e g i n n i n g 4.27 m above the d i s t r i b u t o r on one w a l l of the co lumn. S i m i l a r to those used i n S e c t i o n 2 . 2 . 1 , t h i s s u r f a c e c o n s i s t e d of four i d e n t i c a l , ha l f -embedded tubes connected by f i n s (see F i g u r e 2 . 1 2 ) . One of the c e n t r a l tubes was i n s t r u -mented with ten thermocouples a p p r o x i m a t e l y 150 mm a p a r t . Both the temperatures and f l o w r a t e s of the water i n s i d e the tube were r e c o r d e d . As b e f o r e , heat t r a n s f e r c o e f f i c i e n t s r e p o r t e d here are s u s p e n s i o n - t o - e x p o s e d s u r f a c e va lues based on the t o t a l _ J Fin 21.3 OD Tube •////////// (a) 130 150 150 150 145 145 150 150 150 145 125 — Water Out 21.3 OD Tube Thermocouple Coupling -Manifold — Water In (b) e 2.12 (a) P lan view and (b) S e c t i o n view of the membrane w a l l heat t r a n s f e r s u r f a c e used i n S e c t i o n 2 . 3 . A l l dimensions are in mm. -34-exposed areas of the tubes and the f i n s . The combust ion f u e l used i n the tube heat t r a n s f e r e x p e r i -ments was Minto c o a l from New B r u n s w i c k , premixed wi th E lmtree l i m e s t o n e a l s o from New B r u n s w i c k . H i g h v a l e c o a l was used as the f u e l i n the membrane w a l l e x p e r i m e n t s . In a l l e x p e r i m e n t s , O l i v i n e sands were used as the i n e r t bed m a t e r i a l s . The measured minimum f l u i d i z a t i o n v e l o c i t i e s f o r a i r at room temperature and p r e s s u r e are 71 and 43 mm/s f o r the sand and the l i m e s t o n e r e s p e c t i v e l y . Some r e l e v a n t p h y s i c a l p r o p e r t i e s of the sand and l imes tone are summarized i n T a b l e 2 . 3 . A t y p i c a l c o m p o s i t i o n of the bed m a t e r i a l s i s about 20% sand , 55% l i m e s t o n e , wi th the remainder ash and c h a r . D e t a i l e d p a r t i c l e s i z e a n a l y s e s f o r the v a r i o u s runs are g i v e n i n Tab le 2 . 4 . The mean p a r t i c l e s i z e s l i s t e d are a l l de termined as b e f o r e , i . e . , as l / l (x ^ / d ^ ) . 2 .3 .2 R e s u l t s and D i s c u s s i o n The v a r i a t i o n s of t i m e - a v e r a g e d , l e n g t h - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t wi th suspens ion d e n s i t y are p l o t t e d i n F i g u r e 2.13 for the v e r t i c a l tube at four d i f f e r e n t suspens ion temperatures wi th the tube t o u c h i n g the near w a l l of the co lumn. As i n p r e v i o u s work, suspens ion d e n s i t i e s are c r o s s - s e c t i o n a l average v a l u e s e s t i m a t e d from the p r e s s u r e p r o f i l e s i n the r i s e r . In a l l c a s e s , the average heat t r a n s f e r c o e f f i c i e n t i n c r e a s e s l i n e a r l y wi th suspens ion d e n s i t y . The l i n e s shown are l e a s t -squares b e s t - f i t l i n e s . Whi le there are s m a l l d i f f e r e n c e s i n the s u p e r f i c i a l gas v e l o c i t y f o r the four d i f f e r e n t symbols , and the -35-TABLE 2.3 F l u i d i z a t i o n P r o p e r t i e s of Sand and Sorbent Used i n S e c t i o n 2.3. O l i v i n e 70 Sand Elmtree Limestone Mean P a r t i c l e S i z e (/xm) 241 3 P a r t i c l e Density (kg/m ) 3066 Minimum F l u i d i z a t i o n V e l o c i t y at Room Temperature and 71 Pressure (mm/s) Voidage at Minimum F l u i d i z a t i o n 0.46 210 2400 43 0.44 -36-TABLE 2.4 P a r t i c l e S i z e Analyses f o r V a r i o u s Runs i n S e c t i o n 2.3. Si z e Range Run 1 Run 2 Run 3 Run 4 Run 5 r>m) (Wt. %) (Wt. %) (Wt. %) (Wt. %) (Wt. %) 1410+ 1.5 0.4 0.2 0.0 0.0 1410-1000 0.8 0.8 0.5 0.0 0.0 1000-707 2.7 4.3 3.3 0.2 0.0 707-500 13.2 10.8 16.0 0.3 0.0 500-354 30.3 20.8 34.7 2.6 5.8 354-250 21.4 24.5 23.3 38.0 48.6 250-177 14.4 18.5 13.7 45.6 36.1 177-125 6.8 10.5 5.0 10.1 6.6 125-88 3.4 5.0 1.7 1.9 1.7 88-53 2.6 2.1 0.7 0.8 1.2 53-44 0.9 0.5 0.2 0.1 0.0 44-0 2.0 1.8 0.7 0.4 0.0 Mean P a r t i c l e S i z e (fim) 241 227 299 222 241 -37-F i g u r e 2.13 Average heat t r a n s f e r c o e f f i c i e n t f o r the v e r t i c a l tube versus suspens ion d e n s i t y at four suspens ion t e m p e r a t u r e s . For 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 , see Tab le 2 . 4 . Bottom l i n e : Run 3; U=6.5 m/s . Other l i n e s : Run 1; U=6.6-8.6 m/s . -38-average p a r t i c l e s i z e f o r the lowest suspens ion temperature i s s l i g h t l y l a r g e r , the e f f e c t of these v a r i a b l e s on the average heat t r a n s f e r c o e f f i c i e n t are s m a l l f o r a long heat t r a n s f e r s u r f a c e as d i s c u s s e d i n S e c t i o n 2 . 2 . 2 . S i n c e r a d i a t i o n i s s m a l l f o r the lowest suspens ion temperature of 343 C and the f a c t o r s which i n f l u -ence the p a r t i c l e c o n v e c t i v e and gas c o n v e c t i v e components of heat t r a n s f e r are not g r e a t l y i n f l u e n c e d by t e m p e r a t u r e , the d i f f e r e n c e between t h i s l i n e and the o ther l i n e s g i v e s a good e s t i m a t e of the r a d i a t i o n c o n t r i b u t i o n to the average heat t r a n s f e r c o e f f i c i e n t . The s i m i l a r i t y i n the s l o p e s f o r the four l i n e s suggests t h a t r a d i a t i o n i s r e l a t i v e l y independent of suspens ion d e n s i t y , even when the suspens ion d e n s i t y approaches zero (where the tube "sees" the o ther three hot w a l l s ) . However, the f r a c t i o n of the t o t a l t r a n s f e r which i s due to r a d i a t i o n v a r i e s s t r o n g l y wi th the suspen-s i o n d e n s i t y , r a d i a t i o n be ing the predominant heat t r a n s f e r mecha-nism for d i l u t e (low load) systems at t y p i c a l combust ion tempera-t u r e s (850-900 C ) . T h i s compares wi th b u b b l i n g f l u i d i z e d bed com-b u s t i o n systems where r a d i a t i o n t y p i c a l l y accounts f o r o n l y about 20% of the t o t a l t r a n s f e r , even at low loads (Ozkaynak et a l . , 1983) . The c o r r e s p o n d i n g v a r i a t i o n s of average heat t r a n s f e r c o e f f i c i e n t wi th suspens ion d e n s i t y for the membrane w a l l are shown i n F i g u r e 2.14 f o r three suspens ion t e m p e r a t u r e s . A g a i n , the average c o e f f i c i e n t i n c r e a s e s l i n e a r l y wi th suspens ion d e n s i t y , a l though the r a t e of i n c r e a s e i s i n g e n e r a l not as s teep as for the t u b e . As i n the p r e v i o u s c a s e , the s l o p e s of the b e s t - f i t l i n e s i n F i g u r e 2.14 are very s i m i l a r to each o t h e r . In c i r c u l a t i n g f l u i d i z e d bed combust ion s t u d i e s , as i n 200 CN # E 150 100 o 870±14 • 681 ±18 o 410 ±15 0 Figure 2.14 20 40 i susp 60 80 kg/rrf Average heat transfer coefficient for the membrane wall versus suspension density at three suspension temperatures. Bottom line: Run 5 in Table 2.4; U=7.5 m/s. Other lines: Run 4 in Table 2.4; U=8.8-9.5 m/s. -40-b u b b l i n g f l u i d i z e d beds , i t i s common to assume t h a t the heat t r a n s f e r c o e f f i c i e n t can be e s t i m a t e d from h = h + h + h , (2.3) gc pc rad v ' where h and h are the gas c o n v e c t i v e and p a r t i c l e c o n v e c t i v e gc pc components, r e s p e c t i v e l y , wh i l e h r a ^ i s the r a d i a t i v e component. T a b l e 2.5 shows the comparison of the c a l c u l a t e d heat t r a n s f e r c o e f f i c i e n t s based on E q . 2.3 wi th the e x p e r i m e n t a l v a l u e s for the v e r t i c a l tube from F i g u r e 2 .13 . The comparison i s made at 3 two suspens ion d e n s i t i e s of 15 and 60 kg/m . h ^ c i s e s t i m a t e d from the c o r r e l a t i o n of S l e i c h e r and Rouse (1975) f o r an empty co lumn. I t i s r e c o g n i z e d tha t the gas f low p a t t e r n i n the presence of s o l i d s i s d i f f e r e n t from that i n an empty co lumn. However, s i n c e t h i s component i s g e n e r a l l y s m a l l , the e s t i m a t e from an empty column i s s u f f i c i e n t as a f i r s t a p p r o x i m a t i o n . The r a d i a t i v e component, h r a ( j / i s e s t i m a t e d by t r e a t i n g the g a s -s o l i d s suspens ion as a gray body such tha t 4 4 ff(T - T *) h . = SH2E 5 H £ l _ ! (2.4) (1/e + 1/e , - 1) (T - T .) v ' susp s u r f ' susp s u r f where T and T , are the temperatures of the suspens ion and susp s u r f c c the tube s u r f a c e , r e s p e c t i v e l y . Both the e m i s s i v i t y v a l u e s , e and e c , are se t equa l to 0.91 to f i t the r e s u l t s f or the susp s u r f h i g h e s t suspens ion temperature of 880 C by e x t r a p o l a t i n g the b e s t - f i t l i n e to p =0. The d i f f e r e n c e between the b e s t - f i t ' s u s p -41-TABLE 2.5 Comparison of E x p e r i m e n t a l Data wi th Heat T r a n s f e r C o e f f i c i e n t s for the V e r t i c a l Tube at Three Suspens ion Temperatures* Susp. Den. A v g . Susp. Temp. Tube S u r f Temp Gas Conv . Comp. P a r t . Conv. Comp. Rad. Comp. T o t a l E s t . h E x p t . Data h (kg/m 3 ) (C) (W/m 2 .K) 15 701 83 13 19 68 100 106 15 587 56 13 19 48 80 89 15 343 45 14 19 22 55 62 60 701 83 13 76 68 157 166 60 587 56 13 76 48 137 144 60 343 45 14 76 22 112 110 * Based on E q . 2.3 wi th E m i s s i v i t i e s and P a r t i c l e C o n v e c t i v e Component E s t i m a t e d from the R e s u l t s at 880 C , and the Gas C o n v e c t i v e Component O b t a i n e d from the C o r r e l a t i o n of S l e i c h e r and Rouse (1975). -42-l i n e of the e x p e r i m e n t a l d a t a at 880 C and the sum of h ^ c and h i s taken to be h , which i s then assumed to a p p l y a l s o at rad pc c c the lower t e m p e r a t u r e s . Chen e t a l . (1988) r e c e n t l y suggested that r a d i a t i v e and c o n v e c t i v e heat t r a n s f e r occur s i m u l t a n e o u s l y throughout the g a s -s o l i d s suspens ion and i n t e r a c t i n a n o n l i n e a r manner. They have a l s o proposed a model to account f o r t h i s s imul taneous heat t r a n s f e r . However, the r e s u l t i n g system of n o n l i n e a r , f o u r t h -order d i f f e r e n t i a l e q u a t i o n s has to be s o l v e d n u m e r i c a l l y . D e s p i t e i t s o v e r - s i m p l i f i c a t i o n , E q . 2.3 p r o v i d e s a u s e f u l p r a c t i c a l b a s i s f o r e s t i m a t i n g heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds , as can be seen from the e x c e l l e n t agreement between the c a l c u l a t e d and the e x p e r i m e n t a l heat t r a n s f e r c o e f f i c i e n t s i n Tab le 2 . 5 . F i g u r e s 2.13 and 2.14 are c r o s s - p l o t t e d i n F i g u r e 2.15 to show the v a r i a t i o n s of the average heat t r a n s f e r c o e f f i c i e n t wi th suspens ion temperature at four d i f f e r e n t suspens ion d e n s i t y l e v e l s f o r both the v e r t i c a l tube at the w a l l and the membrane w a l l . I t can be seen from F i g u r e 2.15 tha t r a d i a t i o n s t a r t s to become a s i g n i f i c a n t f a c t o r beyond a suspens ion temperature of about 400 C f o r both heat t r a n s f e r s u r f a c e s . The r e l a t i v e magnitude of r a d i a t i o n i n c r e a s e , however, i s q u i t e d i f f e r e n t f o r the two d i f f e r e n t g e o m e t r i e s . The v e r t i c a l tube has a much l a r g e r r a d i a t i v e i n c r e a s e than the membrane w a l l at the same suspens ion t e m p e r a t u r e . T h i s i s p r o b a b l y due to the b e t t e r view f a c t o r enjoyed by the tube as compared to the membrane w a l l , where the hal f -embedded tubes "see" t h e i r r e l a t i v e l y c o o l -43-200 400 600 800 1000 susp F i g u r e 2.15 C r o s s - p l o t of average heat t r a n s f e r c o e f f i c i e n t versus s u s p e n s i o n temperature f o r the v e r t i c a l tube ( s o l i d l i n e s ) and the membrane w a l l (broken l i n e s ) at four suspens ion d e n s i t y l e v e l s . -44-p a r t n e r s to a s i g n i f i c a n t e x t e n t . The e m i s s i v i t y of the two s u r f a c e s c o u l d a l s o be somewhat d i f f e r e n t . F i g u r e 2.15 a l s o i n d i c a t e s tha t the two s e t s of c u r v e s are c l o s e r t o g e t h e r at suspens ion temperatures below 400 C . T h i s i s expec ted s i n c e the e f f e c t of r a d i a t i o n d i m i n i s h e s as the suspens ion temperature d e c r e a s e s . R e s i d u a l d i f f e r e n c e s are then no doubt due to the d i f f e r e n t geometr ies of the s i n g l e tube and the membrane s u r f a c e . Andersson et a l . (1987) r e c e n t l y r e p o r t e d a l i n e a r i n c r e a s e i n l o c a l heat t r a n s f e r c o e f f i c i e n t w i th suspens ion temperature (from 740 to 900 C) , f or 240 fim sand at the w a l l of a 2.5 MW, 8.5 m h i g h , 0.7 x 0.7 m c i r c u l a t i n g f l u i d i z e d bed combustor , at 3 suspens ion d e n s i t y l e v e l s of 20, 100, and 200 kg/m . T h e i r d a t a show a l i n e a r r e l a t i o n s h i p between the l o c a l heat t r a n s f e r c o e f f i c i e n t and the a r e a - a v e r a g e d suspens ion d e n s i t y , s i m i l a r to F i g u r e s 2.13 and 2 .14 . R e s u l t s o b t a i n e d by Basu and Konuche (1988) u s i n g a 25.4 mm diameter r a d i a t i o n probe a l s o show a s t r o n g i n c r e a s e i n r a d i a t i o n when the bed temperature was 3 i n c r e a s e d from 650 to 900 C at a suspens ion d e n s i t y of 20 kg/m . Bed temperatures at v a r i o u s l a t e r a l p o s i t i o n s were a l s o measured by moving thermocouples r a d i a l l y a c r o s s the co lumn, midway between two w a l l s . There were no s i g n i f i c a n t l a t e r a l v a r i a t i o n s found i n the bed t e m p e r a t u r e . On the o ther hand , a s i g n i f i c a n t dependence of the average heat t r a n s f e r c o e f f i c i e n t on the v e r t i c a l t u b e ' s l a t e r a l p o s i t i o n was observed and i s shown i n F i g u r e 2.16 which p l o t s the v a r i a t i o n s of heat t r a n s f e r c o e f f i c i e n t w i th suspens ion d e n s i t y for four d i f f e r e n t l a t e r a l p o s i t i o n s and two suspens ion t e m p e r a t u r e s . A l though the s u p e r f i -- 4 5 -I I I I I I I I i 0 20 40 60 80 Psusp . k 9 / m 3 Figure 2.16 Average heat transfer coefficient versus suspension density for four different lateral tube positions at two suspension temperatures. Top four curves: Run 2 in Table 2.4; U=9.3 m/s; Ts u s p=854±3 C. Bottom four curves: Run 3 in Table 2.4; U=6.5 m/s; Ts u s p=343±13 C. -46-c i a l gas v e l o c i t i e s and p a r t i c l e s i z e s a g a i n d i f f e r e d s l i g h t l y , the e f f e c t s of these v a r i a t i o n s on the heat t r a n s f e r c o e f f i c i e n t are s m a l l as shown above . The d i f f e r e n c e between the two se t s of c u r v e s i s t h e r e f o r e p r e d o m i n a n t l y due to the temperature e f f e c t . For the lower temperature of 343 C , the p o s i t i o n near the w a l l always e x h i b i t s the h i g h e s t heat t r a n s f e r c o e f f i c i e n t compared to the o ther three p o s i t i o n s i n the range of suspens ion d e n s i t y 3 i n v e s t i g a t e d (0-60 kg/m ) . The t r e n d , however, i s q u i t e d i f f e r -ent f o r the h i g h e r temperature of 854 C where the c e n t e r of the column a lmost always e x h i b i t s the h i g h e s t c o e f f i c i e n t . For low 3 suspens ion d e n s i t y (<20 kg/m ) , the heat t r a n s f e r c o e f f i c i e n t d e c r e a s e s from the c e n t e r of the column to a minimum near the 3 w a l l . For h i g h e r suspens ion d e n s i t y (>30 kg/m ) , the heat t r a n s f e r c o e f f i c i e n t decreases as the tube moves from the c e n t e r towards the w a l l of the column b e f o r e i n c r e a s i n g a g a i n when the tube i s immedia te ly a d j a c e n t to the w a l l . The i n f l u e n c e of the l a t e r a l p o s i t i o n i s b e t t e r i l l u s t r a t e d i n F i g u r e 2.17 which i s a c r o s s - p l o t of F i g u r e 2 .16 , the heat t r a n s f e r c o e f f i c i e n t p l o t t e d v e r s u s the l a t e r a l p o s i t i o n of the v e r t i c a l tube at two suspens ion d e n s i t y l e v e l s . For the lower temperature of 343 C where the e f f e c t of r a d i a t i o n i s s m a l l , p a r t i c l e s are r e l a t i v e l y e v e n l y d i s p e r s e d at low suspens ion d e n s i t i e s . T h i s i s r e f l e c t e d i n the s i m i l a r heat t r a n s f e r c o e f f i c i e n t s a c r o s s the c r o s s - s e c t i o n of the column f o r the suspens ion d e n s i t y of 15 kg/m"^. As the suspens ion d e n s i t y i n c r e a s e s , the w a l l r e g i o n d i s p l a y s the h i g h e s t p a r t i c l e c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t due to the development of a -47-CN ' y/y, F i g u r e 2.17 C r o s s - p l o t of average heat t r a n s f e r c o e f f i c i e n t versus l a t e r a l tube p o s i t i o n for two suspens ion d e n s i t i e s and two s u s p e n s i o n t e m p e r a t u r e s . S o l i d l i n e s : P s u s p = 1 5 k g / m 3 ; Broken l i n e s : P s u s p = 6 0 k g / m 3 Curves 1,2: T s u s p = 3 4 3 C ; Curves 3 ,4 : T s u s p = 8 5 4 C . -48-denser w a l l l a y e r i n which p a r t i c l e s tend to congregate and move downward a long the w a l l . On the o ther hand, f o r the h i g h e r temperature of 854 C where r a d i a t i o n has a s i g n i f i c a n t e f f e c t , the r e l a t i v e l a t e r a l p o s i t i o n of the v e r t i c a l tube p l a y s a more important r o l e due to the s h i e l d i n g e f f e c t . As the tube i s moved from the c e n t e r of the column where i t can "see" a l l four hot w a l l s to a p o s i t i o n next to a p a r t i a l l y c o o l e d w a l l , the r a d i a t i v e heat t r a n s f e r d e c r e a s e s . T h i s e x p l a i n s the decrease i n the heat t r a n s f e r c o e f f i c i e n t at low suspens ion d e n s i t y as the tube i s moved from the c e n t e r of the column to the w a l l . With an i n c r e a s e i n suspens ion d e n s i t y and the development of a denser w a l l r e g i o n , the heat t r a n s f e r c o e f f i c i e n t near the w a l l a l s o i n c r e a s e s . I t i s i n t e r e s t i n g to note t h a t the more c o m p l i c a t e d curve 4 i n F i g u r e 2.17 can be o b t a i n e d by super impos ing the d i f f e r e n c e between c u r v e s 1 and 2 wi th curve 3. T h i s aga in i n d i c a t e s tha t i t i s r e a s o n a b l e to t r e a t the v a r i o u s terms i n E q . 2.3 s e p a r a t e l y and a d d i t i v e l y . I t i s worthwhi le to note t h a t the r a d i a l p r o f i l e s of l eng thwise averaged heat t r a n s f e r c o e f f i c i e n t , shown i n F i g u r e 2 .17 , c o u l d be d i f f e r e n t from those of l o c a l heat t r a n s f e r c o e f f i c i e n t . Soga e t a l . (1987) measured r a d i a l v a r i a t i o n s of l o c a l heat t r a n s f e r c o e f f i c i e n t i n a 205. mm ID column wi th 46 (im FCC p a r t i c l e s at room t e m p e r a t u r e . The probe used i s a s p h e r e -shaped hea ter of 20 mm d i a m e t e r . In a l l c a s e s , l o c a l heat t r a n s f e r c o e f f i c i e n t decreases from the column a x i s to a minimum near y / y Q = 0 . 6 - 0 . 8 , b e f o r e i n c r e a s i n g a g a i n near the w a l l s u r f a c e , s i m i l a r to p r o f i l e 4 i n F i g u r e 2 .17 . B i et a l . (1989) r e p o r t e d -49-s i m i l a r r a d i a l p r o f i l e s o f l o c a l heat t r a n s f e r c o e f f i c i e n t i n a 186 mm ID column wi th 280 jim s i l i c a g e l , a g a i n at room tempera-t u r e . The r a d i a l min ima, however, were observed m o s t l y i n the upper p a r t of the column at h i g h s u p e r f i c i a l gas v e l o c i t i e s . C o n t r a r y to the above two s t u d i e s , no r a d i a l minima i n l o c a l heat t r a n s f e r c o e f f i c i e n t were observed by T a t e b a y a s h i et a l . (1988) in a 492 mm ID column wi th 70 fim FCC p a r t i c l e s , u s i n g a probe s u p p l i e d by Soga et a l . (1987). Ins tead of undergo ing a minimum, the l o c a l c o e f f i c i e n t i n c r e a s e d from the column a x i s to near the w a l l s u r f a c e , s i m i l a r to p r o f i l e 2 i n F i g u r e 2 .17 . Moreover , as shown i n F i g u r e 2 . 1 8 a , the l o c a l heat t r a n s f e r c o e f f i c i e n t o b t a i n e d by Soga et a l . (1987) near the w a l l s u r f a c e i s a s t r o n g f u n c t i o n of the a r e a - a v e r a g e d suspens ion d e n s i t y but i s o n l y weakly i n f l u e n c e d by the s o l i d s c i r c u l a t i o n r a t e (or s u p e r f i c i a l gas v e l o c i t y ) . T h i s i s s i m i l a r to what i s o b t a i n e d here f o r the l e n g t h - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t from a membrane w a l l , as shown i n F i g u r e s 2.4 to 2 . 6 . On the o ther hand, the l o c a l heat t r a n s f e r c o e f f i c i e n t at the column a x i s i s s t r o n g l y i n f l u e n c e d by the s o l i d s c i r c u l a t i o n r a t e but i s o n l y a weak f u n c t i o n of the a r e a - a v e r a g e d suspens ion d e n s i t y , as shown i n F i g u r e 2 .18b . T h i s d i f f e r e n c e i s s i g n i f i c a n t s i n c e i t seems to suggest the e x i s t e n c e of two s e p a r a t e heat t r a n s f e r mechanisms i n a c i r c u l a t i n g f l u i d i z e d b e d , wi th the w a l l r e g i o n b e i n g dominated by a r e l a t i v e l y dense downflowing l a y e r of p a r t i c l e s wh i l e the r e g i o n near the a x i s i s dominated by a d i l u t e upf lowing c o r e . A l s o , the s t r o n g dependence on s o l i d s c i r c u l a t i o n f l u x shown by the l o c a l heat t r a n s f e r c o e f f i c i e n t at the a x i s suggests - S O -E '— o . 10> T 10 10 conditions y / y» C - 3 U G S 0.7 0.8 0.9 1.2 8.5 • o 2 1.S 8.5 <> X 2.0 8.5 • o 2 1.2 17.7 a o X 1.5 17.7 CJ o X 2.0 17.7 (J <> z 2.0 34.0 u z 10» 10' C kg /m ' ] 10' 17.7 - s - • -34.0 „ E 5 G . = 8.5 kg/m>s 0 a ™ (b) 10' 10 ' • • 10 conditions y/yo [ - ] U 0.0 0.4 -1.2 8.5 O a -1 1.5 8.5 O _ 2.0 8.5 O " u _ 1.2 17.7 © •2 t.5 17.7 © H 2.0 17.7 o a -2.0 34.0 0 Q 10' 10" C kg /m ' ] F i g u r e 2.18 L o c a l heat t r a n s f e r c o e f f i c i e n t o b t a i n e d (a) near the w a l l , and (b) around the column a x i s as a f u n c t i o n of l o c a l suspens ion d e n s i t y by Soga et a l . (1987) (as r e p o r t e d i n Yosh ida and Mineo , 1989). -51-that i t may be reasonab le to t r e a t the heat t r a n s f e r i n the core of the column as tha t i n d i l u t e pneumatic c o n v e y i n g . In a d d i t i o n to the average heat t r a n s f e r c o e f f i c i e n t s , l o c a l heat t r a n s f e r c o e f f i c i e n t s a long the membrane w a l l were a l s o o b t a i n e d for two suspens ion t e m p e r a t u r e s . The p r o f i l e s are p l o t t e d i n F i g u r e 2.19 where Z i s the p o s i t i o n a long the membrane w a l l measured downward from i t s t o p . S i m i l a r to the t r e n d r e p o r t e d i n S e c t i o n 2 . 2 . 2 , the l o c a l heat t r a n s f e r c o e f f i c i e n t decreases w i th i n c r e a s i n g Z , s u g g e s t i n g a p r e d o m i n a n t l y downflowing w a l l l a y e r next to the membrane w a l l s u r f a c e , wi th f r e s h hot s o l i d s coming i n t o c o n t a c t w i th the top p a r t of the s u r f a c e . As the two c u r v e s are o b t a i n e d f o r the same suspens ion d e n s i t y , t h e i r d i f f e r e n c e s are p r e d o m i n a n t l y due to the e f f e c t of t empera ture . The l a r g e r d i f f e r e n c e s near the top of the s u r f a c e compared to the bottom are p r o b a b l y due to some c o o l i n g of the w a l l l a y e r p a r t i c l e s as they t r a v e r s e the membrane w a l l s u r f a c e , thus r e d u c i n g the r a d i a t i o n t r a n s f e r to the s u r f a c e . There i s a growing consensus ( e . g . Hartge et a l . , 1986; Bader e t a l . , 1988; Rhodes e t a l . , 1988) tha t s o l i d p a r t i c l e s i n c i r c u l a t i n g f l u i d i z e d beds tend to move upward i n a d i l u t e c e n t r a l c o r e , whi l e many then move downward i n a denser w a l l l a y e r . The tendency for s o l i d p a r t i c l e s to s t a y .in the downflowing w a l l l a y e r makes the v e r t i c a l l e n g t h of heat t r a n s f e r s u r f a c e at the w a l l one of the c r i t i c a l parameters i n any heat t r a n s f e r s t u d y . T h i s i s i l l u s t r a t e d i n F i g u r e 2.20 where h^, d e f i n e d as the heat t r a n s f e r c o e f f i c i e n t averaged over v e r t i c a l l e n g t h Z s t a r t i n g from the top of the membrane w a l l , i s p l o t t e d F i g u r e 2.19 L o c a l heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l versus Z for two suspens ion t e m p e r a t u r e s . P s u s p = 5 4 k g / m 3 ; Run 5 i n Table 2 . 4 . F i g u r e 2.20 Heat t r a n s f e r c o e f f i c i e n t averaged over Z v e r s u s Z for two suspens ion t e m p e r a t u r e s . Psusp = 5 4 k g / m 3 ; Run 5 i n Table 2 .4 . -54-a g a i n s t Z f o r both suspens ion t e m p e r a t u r e s . In both c a s e s , h z drops r a p i d l y w i th Z , much as f o r l a m i n a r f low over a f l a t p l a t e . As the l a y e r of p a r t i c l e s sweeps down a long the heat t r a n s f e r s u r f a c e , i t g r a d u a l l y approaches thermal e q u i l i b r i u m wi th the s u r f a c e s i n c e there i s l i t t l e renewal i n t h i s l a y e r . T h i s reduces the d r i v i n g f o r c e f o r heat t r a n s f e r , thus p r o d u c i n g a much lower t r a n s f e r c o e f f i c i e n t . I t i s c l e a r from F i g u r e 2.20 t h a t , depending on the v e r t i c a l l e n g t h of the heat t r a n s f e r s u r f a c e , heat t r a n s f e r c o e f f i c i e n t s can d i f f e r by up to 200%. T h i s h e l p s to e x p l a i n e a r l i e r , seemingly d i s c r e p a n t , p u b l i s h e d r e s u l t s as shown below. In g e n e r a l , h i g h e r heat t r a n s f e r c o e f f i c i e n t s are o b t a i n e d by u s i n g very s h o r t heat t r a n s f e r s u r f a c e s . As the l e n g t h of heat t r a n s f e r s u r f a c e i n c r e a s e s ( e . g . , over 1 m), there i s l e s s i n f l u e n c e of l e n g t h on the heat t r a n s f e r c o e f f i c i e n t . F i g u r e 2.21 shows some p r e v i o u s l y p u b l i s h e d heat t r a n s f e r r e s u l t s f o r c i r c u l a t i n g f l u i d i z e d beds toge ther wi th the p r e s e n t ones . The r e s u l t s may be grouped i n t o three r e l a t i v e l y narrow ranges of mean p a r t i c l e s i z e : 87-95 fim, 170-188 fim, and 227-250 /xm. In each c a s e , sand p a r t i c l e s were employed, and a l l r e p o r t e d r e s u l t s f a l l w i t h i n the suspens ion d e n s i t y range of 3 0-100 kg/m . Some r e l e v a n t e x p e r i m e n t a l d e t a i l s of these p u b l i s h e d s t u d i e s are summarized i n T a b l e 2 . 6 . Reported heat t r a n s f e r c o e f f i c i e n t s i n F i g u r e 2.21 are c r o s s - p l o t t e d i n F i g u r e 2.22 a g a i n s t b , the v e r t i c a l l e n g t h of heat t r a n s f e r s u r f a c e , at 3 a t y p i c a l c i r c u l a t i n g bed suspens ion d e n s i t y of 50 kg/m . In s p i t e of the d i f f e r e n t e x p e r i m e n t a l equipment and o p e r a t i n g F i g u r e 2.21 Comparison of p u b l i s h e d heat t r a n s f e r r e s u l t s . For e x p e r i m e n t a l d e t a i l s , see T a b l e 2 . 6 . -56-TABLE 2.6 Re levant E x p e r i m e n t a l D e t a i l s of Some P u b l i s h e d S t u d i e s on Heat T r a n s f e r i n C i r c u l a t i n g F l u i d i z e d Beds . Curve Authors Mean P a r t . S i z e A v g . Susp. Temp. V e r t i c a l Length of Heat T r a n s f . Sur face (/*m) (C) (mm) l a l b Basu & Nag (1987) II II II 87 227 35 38 25 25 2 F e u g i e r et a l . (1987) § 95 400 950 3a 3b Kobro & B r e r e t o n (1986) II II it 170 250 25 25 100 100 4 Wu et a l . (1987) + 188 277 1530 5 Wu et a l . ( 1989) f 171 35 22 6a 6b T h i s Work - Tube* " " - Membrane W a l l * 241 241 880 410 1220 1590 * S ince o n l y the p a r t i c l e c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t has been r e p o r t e d , the gas c o n v e c t i v e c o e f f i c i e n t e s t i m a t e d from S l e i c h e r and Rouse (1975) has been added. The heat t r a n s f e r s u r f a c e l e n g t h , which i s not g i v e n i n the p a p e r , i s o b t a i n e d from Gl i cksman (1988). ''"These da ta are i d e n t i c a l to those r e p o r t e d i n F i g u r e 2.4 i b t h i s t h e s i s except that the average c o e f f i c i e n t s were c a l c u l a t e d for i n l e t and o u t l e t water temperatures i n s t e a d of from thermocouple 1-8. E f f e c t of the h i g h e r suspens ion temperature was e s t i m a t e d from E q . 2 .4 . 1 These d a t a are i d e n t i c a l to those r e p o r t e d i n F i g u r e 3.11 in t h i s t h e s i s . * E f f e c t of the h i g h e r suspens ion temperature was e s t i m a t e d from E q . 2 .4 . F i g u r e 2.22 C r o s s - p l o t of average heat t r a n s f e r c o e f f i c i e n t versus v e r t i c a l t r a n s f e r s u r f a c e l e n g t h f o r three ranges of mean p a r t i c l e s i z e s . Psusp = 50 k g / m 3 . -58-c o n d i t i o n s i n these s t u d i e s , F i g u r e 2.22 c l e a r l y demonstrates the s t r o n g i n f l u e n c e of heat t r a n s f e r s u r f a c e l e n g t h , i n much the same manner as i n F i g u r e 2 .20 . In a d d i t i o n , i t can be seen from F i g u r e 2.22 t h a t the i n f l u e n c e of mean p a r t i c l e s i z e d i m i n i s h e s wi th l onger heat t r a n s f e r s u r f a c e . For longer s u r f a c e s , the p a r t i c l e r e s i d e n c e t imes on the s u r f a c e become much l a r g e r than the thermal time c o n s t a n t s f o r both l a r g e and s m a l l p a r t i c l e s . T h i s , however, i s not t r u e f o r s h o r t e r s u r f a c e s where the s i z e of p a r t i c l e s becomes a s i g n i f i c a n t f a c t o r , w i th the s m a l l e s t p a r t i c l e s e x h i b i t i n g the h i g h e s t p a r t i c l e c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t and hence the h i g h e s t average c o e f f i c i e n t s at low temperatures (Grace , 1986). The r e s u l t s and c o n c l u s i o n s p r e s e n t e d i n t h i s c h a p t e r , c o u p l e d w i t h r e s u l t s i n the l i t e r a t u r e (summarized by G r a c e , 1986 and G l i c k s m a n , 1988) and the e x p e r i -mental l o c a l i n s t a n t a n e o u s heat t r a n s f e r measurements to be p r e s e n t e d i n the next c h a p t e r , p r o v i d e a b a s i s for m o d e l l i n g the heat t r a n s f e r p r o c e s s i n r i s e r s o p e r a t i n g i n the f a s t f l u i d i z e d bed reg ime . T h i s i s the s u b j e c t of Chapter 4. -59-CHAPTER 3 INSTANTANEOUS LOCAL HEAT TRANSFER AT ROOM TEMPERATURE 3.1 INTRODUCTION D e s p i t e the growing p o p u l a r i t y of c i r c u l a t i n g f l u i d i z e d beds i n v a r i o u s g a s - s o l i d s r e a c t i o n a p p l i c a t i o n s , many fundamental p r o p e r t i e s remain p o o r l y u n d e r s t o o d . U n d e r s t a n d i n g of heat t r a n s f e r , f o r example , i s m o s t l y e m p i r i c a l , a l t h o u g h most c i r c u l a t i n g bed a p p l i c a t i o n s r e q u i r e an a c c u r a t e knowledge of heat t r a n s f e r between the g a s - s o l i d s suspens ion and t r a n s f e r s u r f a c e s on the w a l l or e x t e n d i n g i n t o the r i s e r . In order to g a i n some i n s i g h t i n t o t h i s heat t r a n s f e r p r o c e s s , a s m a l l i n s t a n t a n e o u s heat t r a n s f e r probe was deve loped and used to o b t a i n i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t s at the w a l l of a c o l d model c i r c u l a t i n g bed for a s u p e r f i c i a l gas 2 v e l o c i t y of 7 m/s and s o l i d s c i r c u l a t i o n r a t e s up to 70 kg/m .s at three d i f f e r e n t a x i a l p o s i t i o n s a long the co lumn. For some c o n d i t i o n s , s imul taneous measurements u s i n g two i n s t a n t a n e o u s heat t r a n s f e r probes were o b t a i n e d . In a d d i t i o n , some s imul taneous heat t r a n s f e r and hydrodynamic data were o b t a i n e d u s i n g a heat t r a n s f e r probe and a c a p a c i t a n c e probe which measures i n s t a n t a n e o u s l o c a l s o l i d s c o n c e n t r a t i o n . H igh - sp eed c inematography was a l s o used f o r some of these e x p e r i m e n t a l c o n d i t i o n s . -60-3.2 EXPERIMENTAL APPARATUS AND PROCEDURE 3 . 2 . 1 C i r c u l a t i n g F l u i d i z e d Bed F a c i l i t i e s The c o l d model c i r c u l a t i n g f l u i d i z e d bed equipment used i n the exper iments c o n s i s t s of a r i s e r where s o l i d p a r t i c l e s are e n t r a i n e d i n the f a s t f l u i d i z a t i o n reg ime , two c y c l o n e s , a column f o r the s torage of r e c i r c u l a t i n g p a r t i c l e s , and an L - v a l v e ( F i g u r e 3 . 1 ) . The p l e x i g l a s r i s e r column i s 9.3 m t a l l and 152 mm i n i n s i d e d i a m e t e r . I t has been d e s c r i b e d p r e v i o u s l y by B u r k e l l (1986) and B r e r e t o n (1987). E n t r a i n e d p a r t i c l e s l e a v i n g the r i s e r are c a p t u r e d i n a p r i m a r y c y c l o n e l o c a t e d at the top of the s t o r a g e co lumn. The p r i m a r y c y c l o n e d i f f e r s from c o n v e n t i o n a l c y c l o n e s i n t h a t i t s bottom opens d i r e c t l y to the s torage column r a t h e r than through a cone . T h i s i n c r e a s e s the throughput of s o l i d s at h i g h s o l i d s c i r c u l a t i o n r a t e s . The s t o r a g e column i s 5.94 m t a l l and 343 mm i n i n s i d e d i a m e t e r . P a r t i c l e s are r e c i r c u l a t e d to the bottom of the r i s e r v i a an L - v a l v e c o n s i s t i n g of v e r t i c a l and h o r i z o n t a l 152 mm ID p l e x i g l a s co lumns , 3.1 m and 0.91 m l o n g , r e s p e c t i v e l y , j o i n e d to form an L shape. The r a t e of s o l i d s r e c i r c u l a t i o n i s de termined by t r a c k i n g i n d i v i d u a l p a r t i c l e s i n the downflow l e g of the L - v a l v e and assuming p l u g f low a c r o s s the s e c t i o n . T h i s t echn ique has been shown by B u r k e l l (1986) to p r o v i d e r e a s o n a b l y a c c u r a t e measurement for t h i s column p r o v i d i n g the measurements are made s e v e r a l d iameters above the ver tex of the L - v a l v e . The s o l i d s c i r c u l a t i o n r a t e i s c o n t r o l l e d by a d j u s t i n g the a e r a t i o n j u s t above the ver tex of the L - v a l v e . To f a c i l i t a t e the -61-Riser 9.30 Secondary Cyclone Primary Cyclone 5.94 Storage Column t Air 3.10 valve F i g u r e 3.1 Schemat ic of the c o l d model c i r c u l a t i n g f l u i d i z e d bed . A l l d imens ions are i n m. P o s i t i o n s of heat t r a n s f e r p r o b e : 1 - Top (Y=8.61 m); 2 - M i d d l e (Y=4.04 m); 3 - Bottom (Y=0.84 m). -62-r e c i r c u l a t i o n of s o l i d s , p a r t i c l e s i n the s t o r a g e column above the L - v a l v e are kept i n a s t a t e of minimum f l u i d i z a t i o n . F i n e r p a r t i c l e s not caught by the p r i m a r y c y c l o n e are c a p t u r e d by a secondary c y c l o n e and r e t u r n e d to the s torage co lumn. Both the r i s e r and the s torage column as w e l l as the L - v a l v e are c o n s t r u c t e d of 6.4 mm t h i c k t r a n s p a r e n t p o l y a c r y l i c m a t e r i a l f o r easy v i s u a l hydrodynamic o b s e r v a t i o n . In order to add f l e x i b i l i t y , the b u l k of the r i s e r i s composed of four 1.37 m s e c t i o n s , f i v e 0.46 m s e c t i o n s , and one 0.91 m s e c t i o n which are t o t a l l y i n t e r c h a n g e a b l e . The heat t r a n s f e r probe i s mounted i n one of the 0.46 m s e c t i o n s and can be i n s t a l l e d at d i f f e r e n t h e i g h t s . Compressed a i r from a blower i s i n t r o d u c e d to the bottom of the r i s e r through a p e r f o r a t e d p l a t e d i s t r i b u t o r wi th 6.3 mm openings d r i l l e d on a 12.7 mm square p i t c h . A l t h o u g h the column i s equipped f o r the a d d i t i o n of secondary a i r (see B r e r e t o n , 1987) , a l l measurements r e p o r t e d here are for a l l the r i s e r a i r (except f o r the s m a l l amount of a e r a t i o n a i r used to c o n t r o l the L - v a l v e ) i n t r o d u c e d as p r i m a r y a i r through the d i s t r i b u t o r p l a t e . An o r i f i c e f lowmeter i s used to measure the a i r f low to the r i s e r . P r e s s u r e p r o f i l e s a lon g the r i s e r are m o n i t o r e d with a p r e s s u r e t r a n s d u c e r u t i l i z i n g v a r i o u s p r e s s u r e taps l o c a t e d at r e g u l a r i n t e r v a l s of 0.46 m a lon g the co lumn. T h i s a l l o w s s o l i d s suspens ion d e n s i t y p r o f i l e s to be d e t e r m i n e d . P a r t i c l e s used i n the exper iments were Ottawa sand of s u r f a c e - v o l u m e mean d iameter 171 fim de termined by s i e v e a n a l y s i s d e s c r i b e d p r e v i o u s l y . The s i z e d i s t r i b u t i o n and other key p r o p e r t i e s of the p a r t i c l e s are -63-g i v e n i n Tab le 3 . 1 . 3 . 2 . 2 Instantaneous Heat T r a n s f e r Measurement I n s t r u m e n t a t i o n The main components of the i n s t r u m e n t a t i o n used i n t h i s s tudy are the i n s t a n t a n e o u s heat t r a n s f e r probe and the c i r c u i t des igned to c o n t r o l and m a i n t a i n the probe at c o n s t a n t tempera-t u r e . Ins tantaneous heat t r a n s f e r c o e f f i c i e n t s were o b t a i n e d by measur ing the power r e q u i r e d to h o l d the probe temperature c o n s t a n t . The i n s t a n t a n e o u s heat t r a n s f e r probe c o n s i s t s of a t h i n p l a t i n u m f i l m d e p o s i t e d on an a p p r o x i m a t e l y 10 x 10 mm p i e c e of g l a s s . In order to make a c c u r a t e l o c a l i n s t a n t a n e o u s heat t r a n s f e r measurements, i t i s neces sary f o r both the probe area and i t s mass to be s m a l l . I t i s a l s o d e s i r a b l e t h a t the i n s t a n t a n e o u s heat f l u x from the probe and i t s temperature be de termined wi th r e l a t i v e ease and h i g h a c c u r a c y . A t h i n p l a t i n u m f i l m coated on a g l a s s support meets these requ irements and s p e c i f i c a t i o n s . S i m i l a r i n s t a n t a n e o u s heat t r a n s f e r probes have been used by p r e v i o u s workers such as Tuot and C l i f t (1973) and C a t i p o v i c (1979). These e a r l i e r probes s u f f e r e d the d i s a d v a n t a g e tha t e i t h e r the probe temperature was not m a i n t a i n e d c o n s t a n t or t h a t a complex ana log c i r c u i t was needed. The p r e s e n t probe d e s i g n employs s imple d i g i t a l c o n t r o l to m a i n t a i n the probe temperature c o n s t a n t . To d e p o s i t the p l a t i n u m f i l m on g l a s s , a s m a l l amount of p l a t i n u m s o l u t i o n (Enge lhard I n d u s t r i e s L i q u i d B r i g h t P l a t i n u m -64 -TABLE 3.1 P a r t i c l e S i z e A n a l y s e s and F l u i d i z a t i o n P r o p e r t i e s f o r the Ottawa Sand Used i n Chapter 3. S i z e Range (fim) Mean P a r t i c l e S i z e (^ im) P a r t i c l e D e n s i t y (kg/m 3 ) C a l c u l a t e d T e r m i n a l S e t t l i n g V e l o c i t y f or mean s i z e at Room Temperature and P r e s s u r e (m/s) Minimum F l u i d i z a t i o n V e l o c i t y at Room Temperature and P r e s s u r e (mm/s) Weight % 707-500 0.1 500-354 2.3 354-250 14.6 250-177 43.6 177-125 27.5 125-88 6.9 88-53 3.0 53-44 1.2 44-0 0.8 171 2650 0.99 31 Voidage at Minimum F l u i d i z a t i o n 0.43 -65-No. 05X) was f i r s t a p p l i e d to the s u r f a c e of a p i e c e of 1 nun t h i c k g l a s s wi th a f i n e b r u s h . I t was then l e f t to dry f o r a few hours and then heated to about 200 C i n an oven . T h i s drove o f f the v o l a t i l e o r g a n i c m a t e r i a l s i n the p l a t i n u m s o l u t i o n l e a v i n g a t h i n f i l m of p l a t i n u m on the g l a s s s u r f a c e . The oven temperature was then r a i s e d to about 650 C , j u s t below the m e l t i n g p o i n t of g l a s s . T h i s bonded the p l a t i n u m f i l m onto the g l a s s s u r f a c e and produced a r o b u s t f i l m . A f t e r i t was c o o l e d to room t e m p e r a t u r e , the p l a t i n u m c o a t e d g l a s s was cu t to the d e s i r e d s i z e . Lead wires were then s o l d e r e d onto two o p p o s i t e edges of the p l a t i n u m f i l m . The r e s i s t a n c e of the p l a t i n u m f i l m t y p i c a l l y ranges from 5 to 6 ohms. The heat t r a n s f e r probe forms p a r t of the c i r c u i t des igned to m a i n t a i n the probe temperature c o n s t a n t ( F i g u r e 3 . 2 ) . I t i s connected at one end to a programmable d i r e c t c u r r e n t power s u p p l y (Lambda LDS-X-02) and at the o ther to a r e f e r e n c e r e s i s t o r of known r e s i s t a n c e . C u r r e n t from the power s u p p l y passes through the probe and the r e f e r e n c e r e s i s t o r b e f o r e i t i s grounded . T h i s causes the p l a t i n u m f i l m to heat up l i k e any r e s i s t a n c e h e a t i n g e l ement . V o l t a g e s b e f o r e and a f t e r the p r o b e , V^ and ^2 r e s p e c t i v e l y , are measured and d a t a l o g g e d u s i n g an A / D -D/A i n t e r f a c e c a r d (Tecmar Labmaster TM-40) connected to an IBM XT P e r s o n a l Computer. S ince the r e f e r e n c e r e s i s t a n c e , R^, i s known, the c u r r e n t p a s s i n g through the c i r c u i t , I , can be c a l c u l a t e d from I = V 2 / R f (3.1) Power Supply H.T. Probe A/D-D/A Interface Resistor A/WVV Ground i ON IBM XT Computer F i g u r e 3.2 Schematic of the c i r c u i t f or c o n t r o l l i n g the temperature of the heat t r a n s f e r p r o b e . -67-Th e r e s i s t a n c e of the p r o b e , R p b » - i s g i v e n by R p b = ( W / 1 <3-2> which , u s i n g E q . 3 . 1 , becomes R p b " R f ( V l - V 2 ) / V 2 ( 3 ' 3 ) The temperature of the p r o b e , T p b r can be o b t a i n e d from the r e s i s t a n c e of the probe s i n c e the probe r e s i s t a n c e v a r i e s n e a r l y l i n e a r l y w i t h t e m p e r a t u r e . F i g u r e 3.3 shows a t y p i c a l p l o t of the v a r i a t i o n of probe r e s i s t a n c e wi th probe t e m p e r a t u r e . These r e s u l t s were o b t a i n e d by measuring the r e s i s t a n c e of the probe immersed i n a water bath at d i f f e r e n t t e m p e r a t u r e s . T , i s c o n t r o l l e d by v a r y i n g the v o l t a g e drop a c r o s s the probe c i r c u i t through the programmable power s u p p l y . The computer c o n t i n u a l l y m o n i t o r s the v o l t a g e drop a c r o s s the probe and computes the probe t e m p e r a t u r e . I f the probe temperature i s lower than the se t p o i n t , the probe r e s i s t a n c e w i l l a l s o be lower . The computer , employ ing s imple feedback c o n t r o l a c t i o n , then i n c r e a s e s the programming v o l t a g e to the power supp ly which i n t u r n r a i s e s the v o l t a g e a c r o s s the probe c i r c u i t . T h i s i n c r e a s e s the power to heat up the f i l m and b r i n g s i t s temperature back to the se t p o i n t . A l i s t i n g of the computer program code for c o n t r o l l i n g the probe temperature and for d a t a l o g g i n g i s g i v e n i n Appendix 3. The d a t a l o g g i n g speed , t y p i c a l l y se t at 80 p o i n t s per second , can be v a r i e d by the u s e r . -68-F i g u r e 3.3 V a r i a t i o n s of e l e c t r i c a l r e s i s t a n c e of heat t r a n s f e r probe as a f u n c t i o n of probe t e m p e r a t u r e . The p l a t i n u m f i l m f u n c t i o n s s i m u l t a n e o u s l y as both a hea ter element and as a temperature s e n s o r . At any i n s t a n t , the power d i s s i p a t e d by the f i l m i s g i v e n by q = K V 1 - V 2 ) (3.4) w h i c h , u s i n g E q . 3 . 1 , can be r e w r i t t e n as q = V 2 ( v i - V 2 ) / R f ( 3 * 5 ) The i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t can then be o b t a i n e d from h . = q / A ( T , - T ) (3.6) I ^' v pb susp v ' where A i s the f i l m area and T g u s p i s the suspens ion t e m p e r a t u r e . The probe i s mounted at one end of a guard hea ter c o n s i s t i n g of a 57 mm long aluminum rod 22 mm i n d iameter ( F i g u r e 3 . 4 ) . The h e a t i n g element i s a c a r t r i d g e h e a t e r (Chromalox CIR-1020) i n s e r t e d i n t o the middle of the rod from i t s o ther e n d . The temperature of t h i s guard heater as measured by a t h e r m i s t o r i s m a i n t a i n e d at a temperature s l i g h t l y lower than that of the p r o b e . T h i s m i n i m i z e s heat l o s s from the back of the p r o b e . A l s o , i t s t a b i l i z e s and l i m i t s the temperature v a r i a t i o n s of the g l a s s s u p p o r t . D u r i n g our e x p e r i m e n t s , the average probe temperature and the guard hea ter temperature were m a i n t a i n e d at about 83 C and 80 C r e s p e c t i v e l y . T h i s d i f f e r e n c e was needed to m a i n t a i n the s t a b i l i t y of the c o n t r o l l e r . Al lowance was made for C o l u m n W a l l FRONT VIEW P l a s t i c F i l m \ P r o b e N \ i si T h e r m i s t o r C a r t r i d g e H e a t e r SECTION VIEW ure 3.4 Front and s e c t i o n views of the probe assembly c o n s i s t i n g of p l a s t i c f i l m , p l a t i n u m coated g l a s s , and guard h e a t e r . A l l d imens ions are i n mm. -71-t h i s temperature d i f f e r e n c e i n d e t e r m i n i n g the heat t r a n s f e r c o e f f i c i e n t . The heat t r a n s f e r probe assembly , shown i n F i g u r e 3 . 4 , can respond r a p i d l y to a change i n heat t r a n s f e r c o e f f i c i e n t because i t s temperature i s m a i n t a i n e d v e r y n e a r l y c o n s t a n t . The maximum d e v i a t i o n from the se t p o i n t t emperature i s o n l y about 1 C . T h i s m i n i m i z e s the e f f e c t of thermal i n e r t i a . The 90% response time of the probe assembly to a s t ep change i n heat t r a n s f e r c o e f f i -c i e n t i s measured to be about 20 ms. I t i s l engthened to about 45 ms i n the a c t u a l exper iments because a t h i n p l a s t i c f i l m ( p o l y v i n y l i d e n e c h l o r i d e ) 10 fim t h i c k i s used to cover the p l a t i n u m f i l m to p r o t e c t i t from wear due to the p a r t i c l e s . These response t imes were de termined by an a i r j e t i n t e r m i t t e n t l y i n t e r r u p t e d by a r o t a t i n g p e r f o r a t e d d i s k . F i g u r e 3.5 shows the two r e s p e c t i v e t imes taken for the exposed and c o v e r e d probe assembly to respond to a s t ep change i n heat t r a n s f e r c o e f f i -c i e n t . The e r r o r caused by the added thermal r e s i s t a n c e of the p r o t e c t i v e f i l m i s e s t i m a t e d to be l e s s than 2%, as shown i n Appendix 4. The heat t r a n s f e r probe i s mounted f l u s h wi th the i n n e r w a l l of the column, and a t h e r m i s t o r i s i n s e r t e d 50 mm i n t o the column from the o p p o s i t e s i d e to r e c o r d the suspens ion t e m p e r a t u r e , T S U S p / needed i n E q . 3 . 6 . To v e r i f y i t s a c c u r a c y , the i n s t a n t a n e o u s heat t r a n s f e r probe was used to o b t a i n t i me- averaged heat t r a n s f e r c o e f f i c i e n t s for n a t u r a l c o n v e c t i o n and f o r c e d c o n v e c t i o n i n a i r . In the f i r s t c a s e , the probe was o r i e n t a t e d v e r t i c a l l y i n an e n c l o s e d environment and the heat t r a n s f e r c o e f f i c i e n t i n n a t u r a l F i g u r e 3.5 90% response times ( in ms) of (a) exposed , and (b) covered probe assembly to a s t ep change i n heat t r a n s f e r c o e f f i c i e n t . -73-c o n v e c t i o n was measured. In the second c a s e , heat t r a n s f e r c o e f f i c i e n t s were measured f o r f o r c e d c o n v e c t i o n i n l a m i n a r f low over a f l a t p l a t e at d i f f e r e n t a i r v e l o c i t i e s . The probe was mounted f l a t and f l u s h wi th the s u r f a c e at one edge of a f l a t p l a t e . The e n t i r e assembly was then i n s e r t e d i n t o a wind t u n n e l capab le of d e l i v e r i n g v a r i o u s a i r f l o w r a t e s . The a i r v e l o c i t i e s i n s i d e the t u n n e l were measured wi th a hot wire anemometer (Kurz Model 441) . As shown i n T a b l e 3 . 2 , heat t r a n s f e r c o e f f i c i e n t s o b t a i n e d e x p e r i m e n t a l l y are i n s a t i s f a c t o r y agreement w i th those o b t a i n e d from c o r r e l a t i o n s p u b l i s h e d i n the l i t e r a t u r e . 3 . 2 . 3 C a p a c i t a n c e Probe M i n i a t u r i z e d c a p a c i t a n c e probes have found c o n s i d e r a b l e use i n f l u i d i z a t i o n r e s e a r c h for d e t e r m i n i n g l o c a l hydrodynamic f e a t u r e s (Grace and Baeyans , 1986). Both B r e r e t o n (1987) and Herb et a l . (1989) have used c a p a c i t a n c e probes to s tudy the a x i a l and r a d i a l s o l i d s c o n c e n t r a t i o n v a r i a t i o n s i n c i r c u l a t i n g f l u i d i z e d beds . In t h i s s t u d y , a c a p a c i t a n c e probe was used i n some of the exper iments to measure l o c a l i n s t a n t a n e o u s s o l i d s c o n c e n t r a t i o n i n the v i c i n i t y of the heat t r a n s f e r p r o b e . T h i s c a p a c i t a n c e probe was adapted d i r e c t l y from one used i n p r e v i o u s work i n t h i s department ( B r e r e t o n , 1987) but wi th an extended l e n g t h . S ince many d e t a i l s of the p r o b e ' s c o n s t r u c t i o n and c a l i b r a t i o n p r o c e d u r e were r e p o r t e d by B r e r e t o n , o n l y a b r i e f summary of the probe i s g i v e n h e r e . The c a p a c i t a n c e probe d e s i g n i s shown i n F i g u r e 3 . 6 . The -74-TABLE 3.2 Comparison of Measured Heat T r a n s f e r C o e f f i c i e n t s and P r e d i c t e d C o e f f i c i e n t s from C o r r e l a t i o n s f o r the Cases of N a t u r a l C o n v e c t i o n and F o r c e d C o n v e c t i o n . Gas V e l o c i t y Measured h P r e d i c t e d h* (m/s) (W/m 2 . K) N a t u r a l C o n v e c t i o n 0.0 7.5 12.2 3.3 73.5 70.7 F o r c e d C o n v e c t i o n 4.1 4.7 86.6 92.1 78.4 84.5 5.3 99.8 89.8 * C o r r e l a t i o n s are taken from K r e i t h and B l a c k (1980). To BNC (( Coaxial \ Coupling Live Probe Probe Sheath Wire Tip F i g u r e 3.6 S i m p l i f i e d schematic of the c a p a c i t a n c e p r o b e . A l l d imensions are i n mm. -76-probe sheath i s c o n s t r u c t e d from 6.4 mm OD 4.6 mm ID s t a i n l e s s s t e e l t u b i n g . At one end of the s h e a t h , a 3.2 mm OD 2.2 mm ID s t a i n l e s s s t e e l t u b i n g i s p r e s s - f i t t e d i n t o a 6.4 mm OD bush ing e x t e n d i n g the sheath by 20 mm to form the probe t i p . The l i v e probe component, made of a 0.6 mm d i a m e t e r , r i g i d , s i n g l e s t r a n d , s t a i n l e s s s t e e l w i r e , p r o t r u d e s 5 mm from the sheath at the probe t i p . T h i s wire i s h e l d r i g i d and i n s u l a t e d from the sheath by a s i n g l e , c o n t i n u o u s , magnesium o x i d e , thermocouple i n s u l a t o r which i s i n t u r n h e l d r i g i d i n the sheath u s i n g ceramic cement. The w ire i s connected to a BNC c o a x i a l c o u p l i n g at the o ther end of the s h e a t h . The c a p a c i t a n c e probe forms p a r t of a t r a n s i s t o r i z e d tuned o s c i l l a t i n g c i r c u i t whose o s c i l l a t i n g frequency v a r i e s as a f u n c t i o n of the probe c a p a c i t a n c e (see F i g u r e 3 . 7 ) . The v a r i a -t i o n i n c a p a c i t a n c e i s f i r s t c o n v e r t e d to a frequency modulated s i g n a l f or e a s i e r t r a n s m i s s i o n . The f requency modulated s i g n a l i s then demodulated i n a r e a c t a n c e c o n v e r t e r to g i v e a v o l t a g e output p r o p o r t i o n a l to the s h i f t from the base f r e q u e n c y . A c o m m e r c i a l l y a v a i l a b l e r e a c t a n c e c o n v e r s i o n system, the D i s a 51E01 r e a c t a n c e c o n v e r t e r , combined with a type 51E02 o s c i l l a t o r and 51E02 t u n i n g p l u g , i s used i n the c a p a c i t a n c e probe c i r c u i t . The c a p a c i t a n c e probe i s capab le of measuring s i g n a l s u p . t o a f requency of 100 KHz.• The output from the c a p a c i t a n c e probe i s a n e a r l y l i n e a r f u n c t i o n of the voidage i n the measurement zone for vo idages rang ing from 0.5 to 1.0 and i s not s e n s i t i v e to the d i s t r i b u t i o n of s o l i d s i n the measurement zone. Be fore the r u n s , the c a p a c i t a n c e probe was clamped t i g h t l y Probe 3 F M Signal Voltage Signal Variable Fixed Capacitance C i I Resonant Oscillating Circuit Demodulator F i g u r e 3.7 Block diagram of the c a p a c i t a n c e probe system showing p r i n c i p a l system components ( B r e r e t o n , 1987). -78-to a support s t r u c t u r e and was i n s e r t e d i n t o the column from a p o r t d i a m e t r i c a l l y o p p o s i t e the heat t r a n s f e r probe such tha t the probe t i p came w i t h i n 1 mm of the heat t r a n s f e r probe s u r f a c e . D u r i n g the r u n s , s i g n a l s from both the c a p a c i t a n c e probe and the heat t r a n s f e r probe were logged s i m u l t a n e o u s l y u s i n g the Tecmar i n t e r f a c e c a r d as d e s c r i b e d i n S e c t i o n 3 . 2 . 2 . 3 . 2 . 4 High Speed Cinematography For some e x p e r i m e n t a l c o n d i t i o n s , the hydrodynamics at the column w a l l were recorded wi th the a i d of h i g h speed movies taken p r i m a r i l y for a n a l y z i n g the movement of the waves of p a r t i c l e s or s t r a n d s at the column w a l l . I t was hoped t h a t some r e l i a b l e e s t i m a t e s of the s t r a n d s ' f a l l i n g v e l o c i t y c o u l d be o b t a i n e d by a n a l y z i n g the p i c t u r e s i n a f rame-by- frame f a s h i o n . A h i g h speed camera (Hycam Model 400) and 16 mm b l a c k - a n d - w h i t e movie f i l m (Kodak 7277 4X r e v e r s a l f i l m ) were used toge ther wi th a p p r o p r i a t e l i g h t i n g . To a v o i d excess r e f l e c t i o n from the p o l y a c r y l i c column w a l l , f r o n t l i g h t i n g was p l a c e d above and below the area of i n t e r e s t on i t s l e f t and r i g h t . For one c a s e , back l i g h t i n g was used e x c l u s i v e l y . F r o n t l i g h t i n g was found to g i v e b e t t e r r e s u l t s . The speed used f o r a l l f i l m s was 400 frames per second . 3.3 RESULTS AND DISCUSSION 3 . 3 . 1 S i n g l e Probe Experiment In the f i r s t p a r t of t h i s s t u d y , a heat t r a n s f e r probe was -79-used to o b t a i n heat t r a n s f e r c o e f f i c i e n t s at three d i f f e r e n t h e i g h t s a long the column at v a r i o u s s o l i d s c i r c u l a t i o n r a t e s up 2 to about 70 kg/m .s and at a f i x e d s u p e r f i c i a l gas v e l o c i t y of 7 m/s . These d i f f e r e n t v e r t i c a l p o s i t i o n s are d e s i g n a t e d Top , M i d d l e , and Bottom, c o r r e s p o n d i n g to 8.61 m, 4.04 m, and 0.84 m above the d i s t r i b u t o r , r e s p e c t i v e l y . The v a r i a t i o n of c r o s s -s e c t i o n a l a r e a - a v e r a g e d s o l i d s suspens ion d e n s i t y w i th s o l i d s c i r c u l a t i o n r a t e at the t h r e e p o s i t i o n s i s shown i n F i g u r e 3 . 8 . At most s o l i d s c i r c u l a t i o n r a t e s , there are s i g n i f i c a n t l y d i f f e r e n t suspens ion d e n s i t i e s at d i f f e r e n t h e i g h t s a long the co lumn. The midd le of the column always e x h i b i t s the lowest suspens ion d e n s i t y , whereas the bottom and the top h a v e . h i g h e r suspens ion d e n s i t i e s , wi th the top somewhat h i g h e r than the 2 bottom at c i r c u l a t i o n r a t e s below 55 kg/m . s . Note tha t t h i s b e h a v i o r o c c u r s for an abrupt or r e s t r i c t e d e x i t geometry; the i n c r e a s e i n suspens ion d e n s i t y i n the upper p a r t of the column would not occur f o r a smooth or u n r e s t r i c t e d e x i t ( B r e r e t o n , 1987; J i n e t a l . , 1988) . T y p i c a l v a r i a t i o n s of l o c a l i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t wi th time at three d i f f e r e n t l e v e l s are shown i n F i g u r e 3 . 9 . At the same s u p e r f i c i a l gas v e l o c i t y and for s i m i l a r s o l i d s c i r c u l a t i o n r a t e s , the i n s t a n t a n e o u s t r a c e s show sudden and dramat i c peaks i n heat t r a n s f e r c o e f f i c i e n t at a l l h e i g h t s . These peaks are caused by s t r a n d s or sheets of p a r t i c l e s sweeping pas t the probe s u r f a c e a long the column w a l l , as conf i rmed by v i s u a l o b s e r v a t i o n of the hydrodynamic p a t t e r n s i n the w a l l r e g i o n of the co lumn. T h i s i s f u r t h e r conf i rmed from the -80-160 CO -*120 C L CO D c£ 80 c Q c o *co 1.40 CO D CO — o - — Top v — Middle — Bottom 80 S o l i d C i r c u l a t i o n R a t e , G s , k g / m 2 . s ure 3 . 8 C r o s s - s e c t i o n a l a r e a - a v e r a g e d suspens ion d e n s i t y at three d i f f e r e n t a x i a l column p o s i t i o n s as a f u n c t i o n of s o l i d s c i r c u l a t i o n r a t e . F i g u r e 3.9 T y p i c a l t r a c e s of i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t measured at three d i f f e r e n t a x i a l column p o s i t i o n s . G s=52 k g / m 2 . s . -82-s imul taneous heat t r a n s f e r probe and c a p a c i t a n c e probe t r a c e s , d i s c u s s e d i n S e c t i o n 3 . 3 . 3 below. The c h a r a c t e r ( i . e . , magnitude and frequency) of these peaks , however, i s q u i t e d i s t i n c t i v e for t r a c e s measured at the three h e i g h t s , i n d i c a t i n g d i f f e r e n t l o c a l g a s - s o l i d s hydrodynamics at these p o s i t i o n s . Before r e s u l t s were a n a l y z e d , i t was neces sary to e s t a b l i s h t h a t the heat t r a n s f e r s i g n a l s from the i n s t a n t a n e o u s probe are both s t a t i o n a r y and e r g o d i c . T h i s was e s t a b l i s h e d a c c o r d i n g to the c r i t e r i a of Bendat and P i e r s o l (1986) which r e q u i r e tha t d i f f e r e n t s e c t i o n s of the same time h i s t o r y have s i m i l a r means and v a r i a n c e s w i t h i n the l i m i t of sampl ing v a r i a n c e . T h e r e f o r e , the d a t a can be a n a l y z e d u s i n g v a l u e s from a s i n g l e c o n t i n u o u s s i g n a l . F i g u r e 3.10a p l o t s the a x i a l v a r i a t i o n s of l o c a l t i m e -averaged heat t r a n s f e r c o e f f i c i e n t at three s i m i l a r s o l i d s c i r c u -l a t i o n r a t e s and for the same s u p e r f i c i a l gas v e l o c i t y of 7 m/s . As b e f o r e , c o e f f i c i e n t data p l o t t e d here and i n F i g u r e 3.11 are t a b u l a t e d i n Appendix 2. For a l l s o l i d s c i r c u l a t i o n r a t e s , t r a n s f e r c o e f f i c i e n t s decrease from the bottom to the midd le of the column and i n c r e a s e a g a i n near the t o p . These v a r i a t i o n s are very s i m i l a r to the t r e n d of a r e a - a v e r a g e d suspens ion d e n s i t y as shown i n F i g u r e 3 .10b , c o n f i r m i n g the s t r o n g i n f l u e n c e of s u s p e n s i o n d e n s i t y on l o c a l heat t r a n s f e r c o e f f i c i e n t . S i m i l a r i n v e r t e d a x i a l v a r i a t i o n i n l o c a l heat t r a n s f e r c o e f f i c i e n t at the w a l l has been r e p o r t e d by F u r c h i et a l . (1988) for 196 g l a s s spheres i n a 6 m h i g h , 72 mm ID co lumn. However, t o t a l l y o p p o s i t e , and somewhat s u r p r i s i n g , a x i a l v a r i a t i o n s i n l o c a l heat t r a n s f e r c o e f f i c i e n t at the w a l l were r e c e n t l y r e p o r t e d by lOr ,— Q O / G s ,kg/m 2 .s_ • 52 o 36 ao • O a \ \ \ \ \ " \ ^ ^ \ \ \ o • _ _ l I 59 0 0 100 200 300 400 500 Average H.T. Coefficient, h,W/m2.K (a) 101 1 r >-*--6 '55 H 0 -I r \ \ \ \ G s,kg/m^.s o 59 • 52 o 36 0 _L 0 40 80 120 160 Suspension Density, PSUSp, kg/m3 (b) F i g u r e 3.10 A x i a l v a r i a t i o n s of (a) t ime-averaged heat t r a n s f e r c o e f f i c i e n t , and (b) a r e a - a v e r a g e d suspens ion d e n s i t y a long the r i s e r . -84-Yosh ida and Mineo (1989) who quoted the r e s u l t s o f Soga et a l . (1987). Another a s s o c i a t e d g r o u p , T a t e b a y a s h i et a l . (1988), o b t a i n e d s i m i l a r a x i a l v a r i a t i o n s . Both groups used an i d e n t i c a l heat t r a n s f e r probe d e s i g n : a 20 mm diameter s p h e r i c a l h e a t e r . U n l i k e p r e v i o u s workers , these two groups o b t a i n e d maximum l o c a l heat t r a n s f e r c o e f f i c i e n t s near the midd le of t h e i r co lumns, wi th lower l o c a l c o e f f i c i e n t s near the bottom and the t o p . U n f o r t u -n a t e l y , no a x i a l p r o f i l e s of suspens ion d e n s i t y were r e p o r t e d by T a t e b a y a s h i et a l . (1988) or Y o s h i d a and Mineo (1989). Thus , i t i s not p o s s i b l e to determine whether t h e i r d i f f e r e n t a x i a l heat t r a n s f e r c o e f f i c i e n t p r o f i l e s are caused by d i f f e r e n t a x i a l s u s p e n s i o n d e n s i t y p r o f i l e s . The s i g n i f i c a n t e f f e c t o f suspens ion d e n s i t y on the l o c a l heat t r a n s f e r c o e f f i c i e n t i s a g a i n shown i n F i g u r e 3.11 where the l o c a l t ime-averaged c o e f f i c i e n t i s p l o t t e d a g a i n s t the a r e a -averaged suspens ion d e n s i t y for the three a x i a l p o s i t i o n s . Except 3 for suspens ion d e n s i t i e s lower than 40 kg/m , there e x i s t s an almost i d e n t i c a l r e l a t i o n s h i p between l o c a l heat t r a n s f e r c o e f f i -c i e n t and suspens ion d e n s i t y f o r a l l three l e v e l s . At d e n s i t i e s 3 lower than 40 kg/m , l o c a l heat t r a n s f e r c o e f f i c i e n t s measured at the midd le p o s i t i o n are lower than those at the top and bottom p o s i t i o n s , a l though they a l l converge to the same va lue at zero s o l i d s c i r c u l a t i o n ( i . e . , f or gas c o n v e c t i o n a l o n e ) . The d i f f e r -ence at low suspens ion d e n s i t i e s i s p r o b a b l y r e l a t e d to d i f f e r e n t r a d i a l d i s t r i b u t i o n s of s o l i d s at the three l e v e l s . The l o c a l heat t r a n s f e r c o e f f i c i e n t s i n F i g u r e 3.11 are h i g h e r than l o c a l c o e f f i c i e n t s r e p o r t e d by Kobro and B r e r e t o n (1986), Basu and Nag -85-0 4 0 8 0 1 2 0 Suspension Density, P s u s p , kg/m3 1 6 0 F i g u r e 3.11 Time-averaged heat t r a n s f e r c o e f f i c i e n t as a f u n c t i o n of suspens ion d e n s i t y at three d i f f e r e n t a x i a l column p o s i t i o n s . -86-(1987), and F u r c h i e t a l . (1988). T h i s i s due to the much s h o r t e r l e n g t h of our heat t r a n s f e r s u r f a c e compared to p r e v i o u s probes and i s c o n s i s t e n t w i th our f i n d i n g s d i s c u s s e d i n Chapter 2, and wi th other f i n d i n g s d i s c u s s e d by Gl i cksman (1988) . I t i s c l e a r from F i g u r e 3.11 tha t the l o c a l t i m e - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t does not v a r y much wi th a x i a l p o s i t i o n once the same l o c a l c r o s s - s e c t i o n a l a r e a - a v e r a g e d suspens ion d e n s i t y i s e s t a b l i s h e d , except at low suspens ion d e n s i t y . However, the r e s p e c t i v e i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t t r a c e s e x h i b i t d i f f e r e n t c h a r a c t e r i s t i c s . F i g u r e 3.12 shows v a r i a t i o n s of the a b s o l u t e and n o r m a l i z e d s t a n d a r d d e v i a t i o n s of the i n s t a n t a n e o u s c o e f f i c i e n t s as a f u n c t i o n of suspens ion d e n s i t y . I t i s apparent from these p l o t s tha t there are d i f f e r e n c e s i n the i n s t a n t a n e o u s s i g n a l s for the three a x i a l p o s i t i o n s , even though t h e i r t i m e - a v e r a g e d v a l u e s f a l l a lmost on the same c u r v e . T h i s i s s i g n i f i c a n t because i t shows c l e a r l y tha t the s t r o n g c o r r e l a t i o n between suspens ion d e n s i t y and t i m e -averaged heat t r a n s f e r c o e f f i c i e n t shown i n F i g u r e 3.11 i s somewhat f o r t u i t o u s , wi th p r o b a b l e c o u n t e r - b a l a n c i n g of d i f f e r e n t c o n t r o l l i n g f a c t o r s , r a t h e r than the a r e a - a v e r a g e d suspens ion d e n s i t y i t s e l f be ing the s o l e c o n t r o l l i n g f a c t o r . 3 .3 .2 Double Probe Exper iments In the second p a r t of t h i s s t u d y , i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t s were o b t a i n e d s i m u l t a n e o u s l y from two heat t r a n s f e r probes at the w a l l near the middle of the h e i g h t of the -87-40 80 120 160 susp (c) F i g u r e 3.12 V a r i a t i o n s of a b s o l u t e and n o r m a l i z e d s t a n d a r d d e v i a t i o n s of the i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t measured at (a) Top , (b) M i d d l e , and (c) Bottom a x i a l p o s i t i o n s of the r i s e r as a f u n c t i o n of suspens ion d e n s i t y . -88-column at a f i x e d s u p e r f i c i a l gas v e l o c i t y of 7 m/s . The upper probe was f i x e d at 4.34 m above the d i s t r i b u t o r and was a l i g n e d v e r t i c a l l y wi th the lower p r o b e . The d i s t a n c e , a , s e p a r a t i n g the two p r o b e s , was v a r i e d from 0.152 to 0.762 m at r e g u l a r i n t e r v a l s of 0.152 m. For each d i s t a n c e a , s imul taneous da ta were o b t a i n e d f o r three d i f f e r e n t a r e a - a v e r a g e d suspens ion d e n s i t i e s r a n g i n g 3 from about 15 to 44 kg/m . F i g u r e 3.13 shows some t y p i c a l s imul taneous t r a c e s of the two i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t s . In order to determine the degree of c o r r e l a t i o n of the two t r a c e s , the s imul taneous heat t r a n s f e r c o e f f i c i e n t s were t r e a t e d s t a t i s t i c a l l y u s i n g the c r o s s - c o r r e l a t i o n p r o c e d u r e . A s t a t i s t i c s so f tware package , STATGRAPHICS, r u n n i n g on an IBM XT p e r s o n a l computer , was used to per form the c r o s s - c o r r e l a t i o n . The c a l c u l a t e d c o e f f i c i e n t of c r o s s - c o r r e l a t i o n , r , i s p l o t t e d a g a i n s t t ime lag i n F i g u r e 3.14 for f i v e d i f f e r e n t s e p a r a t i o n d i s t a n c e s and three suspens ion d e n s i t i e s . I t can be seen from F i g u r e 3.14 t h a t the degree of c r o s s - c o r r e l a t i o n decreases r a p i d l y wi th i n c r e a s i n g s e p a r a t i o n d i s t a n c e and wi th d e c r e a s i n g suspens ion d e n s i t y . I t shou ld be noted that s i n c e most of the p r o f i l e s show a low degree of c r o s s - c o r r e l a t i o n , c a u t i o n sh ou ld be used when t r y i n g to i n t e r p r e t these p l o t s . However, f o r p r o f i l e s tha t show some s i g n i f i c a n t degree of c r o s s - c o r r e l a t i o n ( i . e . , p r o f i l e s l a , l b , and 2a i n F i g u r e 3 . 1 4 ) , t h e i r r e l a t i v e l y f l a t shapes i n d i c a t e t h a t there i s a r a t h e r wide spectrum of v e l o c i t i e s for the waves of p a r t i c l e s or s t r a n d s at the w a l l of the co lumn. N e v e r t h e l e s s , the f a c t t h a t the maxima of these p r o f i l e s are l o c a t e d on the l e f t s i d e of the time lag s c a l e F i g u r e 3.13 T y p i c a l t r a c e s of two s imul taneous i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t s . a=0.152 m; Psusp=44.2 k g / m 3 ; G s =60.3 kg /m^.s . -90-(a) (b) (0 (1) (3) (2) c o 4 o •0.4 0.4 -0.4 0 0.4 l . O l — i 1 ' r --0.4 0 0.4 — l . Q —1—1— • — • — r - n l . O i — • — ' (4) © o4 i </> O -0.4 0 0.4 "-0.4 0 0.4 ' -0.4 0 0.4 *~ l.Ol—« r — , , r—, l .Ol—. • . • r—i l . O r - r n 1 r 0.4 0 0.4 -0.4 0 0.4 Time Lag (s) •0.4 0 0.4 Figure 3.14 Coefficient of cross-correlation versus time lag at three different suspension densities and five separation distances. Psusp (kg/m3): (a) 44.2; (b) 28.7; (c) 14.8. Probe separation distance (m): (1) 0.152; (2) 0.305; (3) 0.457; (4) 0.610; (5) 0.762. -91 -(i.e., negative time lag) indicates a predominantly downward velocity. This is consistent with the visual observation at the column wall where waves of particles or strands can be seen sweeping predominantly downward along the wall, with occasional upward motion interspersed. From profiles la and l b , a downward strand velocity of 1.62 m/s can be estimated i f the time lag corresponding to the maximum in each of the profiles is used. The maximum coefficient of cross-correlation, r , for each ' max' of the profiles shown in Figure 3.14 is plotted against the separation distance, a, for three suspension densities in Figure 3 . 1 5 . Since our main interest is in the downward direction, only the negative time lag scale is considered when plotting the maximum correlation coefficient. It can be seen from Figure 3.15 that ^m a x decreases rapidly with increasing separation distance. Also, the rate of decrease is more pronounced with decreasing suspension density. Figure 3.15 suggests that the length a strand wi l l descend at the wall depends on the area-averaged suspension density. The higher the suspension density, the further the strand will descend at the wall before i t disinte-grates. Moreover, i t can be seen that r does not decrease to max zero, but rather tends to a small base value, r , in a l l cases. o' It is possible for one to estimate from Figure. 3.15 a "characteristic" residence length for the strands. Figure 3.16 shows three different procedures for estimating such length: (1) a^ - the length on the x-axis corresponding to r =0.5. max -92-F i g u r e 3.15 Maximum c r o s s - c o r r e l a t i o n c o e f f i c i e n t v e r s u s s e p a r a -t i o n d i s t a n c e at three d i f f e r e n t s u s p e n s i o n d e n s i t i e s . -93-F i g u r e 3.16 Three d e f i n i t i o n s of the " c h a r a c t e r i s t i c " r e s i d e n c e l e n g t h for the s t r a n d s : ag.s, atan* a i n t « -94-(2) a t a n - t n e p o i n t where the t a n g e n t , drawn to the curve at a=0, i n t e r s e c t s the x - a x i s . (3) a i n t ~ the l e n g t h o b t a i n e d by i n t e g r a t i n g the area bounded by the c u r v e and r =r , or max o a i n t = 1 - r A ' d r m a x ( 3 ' 7 ) o r J • o The three c h a r a c t e r i s t i c r e s i d e n c e l e n g t h s f o r the s t r a n d s as d e f i n e d above are o b t a i n e d for three suspens ion d e n s i t i e s and p l o t t e d i n F i g u r e 3.17 as a f u n c t i o n of suspens ion d e n s i t y . I t can be seen from F i g u r e 3.17 tha t a . _ and a. . are very s i m i l a r fc).D m t to each other wh i l e a t a n i s a p p r o x i m a t e l y twice the magnitude of the o ther two. The l i n e f i t t e d to a. . i n F i g u r e 3.17 can be l n t ^ expressed as a. . = 0.0178 p 0-596 i n t "susp v ' S ince the waves of p a r t i c l e s or s t r a n d s f a l l m o s t l y a long the w a l l , i t i s c o n c e i v a b l e tha t any roughness at the w a l l would s i g n i f i c a n t l y a f f e c t the c h a r a c t e r i s t i c r e s i d e n c e l e n g t h of the s t r a n d s . C o n s e q u e n t l y , as the r e s u l t s p r e s e n t e d i n F i g u r e 3.14 were o b t a i n e d in our r e l a t i v e l y smooth column, the c h a r a c t e r i s t i c r e s i d e n c e l e n g t h of the s t r a n d s p l o t t e d i n F i g u r e 3.17 may not a p p l y to other columns wi th d i f f e r e n t i n t e r n a l s u r f a c e c o n f i g u r a -t i o n s . For i n s t a n c e , an i n t e r n a l s u r f a c e in the form of v e r t i c a l membrane w a l l i s l i k e l y to p r o l o n g the r e s i d e n c e l e n g t h of the F i g u r e 3.17 V a r i a t i o n s suspens ion of a 0 . 5 , d e n s i t y . a t a n » a n ( 3 a i n t a s a f u n c t i o n of -96-s t r a n d s , wh i l e one i n the form of h o r i z o n t a l tubes w i l l l i k e l y impede the downward f low of the s t r a n d s and s h o r t e n t h e i r c h a r a c t e r i s t i c r e s i d e n c e l e n g t h . To support the above argument, a s p e c i a l 0.46 m long t r a n s p a r e n t column s e c t i o n was made wi th h a l f of i t s i n t e r n a l s u r f a c e i n the form of a v e r t i c a l membrane w a l l s i m i l a r to F i g u r e 2 .12 . V i s u a l o b s e r v a t i o n of hydrodynamics at the w a l l conf i rmed tha t p a r t i c l e s moving a lon g the membrane w a l l behave d i f f e r e n t l y from those moving a long an u n o b s t r u c t e d (smooth) w a l l . As the membrane w a l l i s formed by j o i n i n g v a r i o u s v e r t i c a l tubes by narrow f i n s , the space between the tubes o f f e r s some p r o t e c t i o n f o r the s t r a n d p a r t i c l e s a g a i n s t the v a r i o u s f a c t o r s ( e . g . , t u r b u l e n c e ) which promote d i s p e r s i o n and m i x i n g of the s t r a n d s . As a r e s u l t , p a r t i c l e s f a l l i n g a lon g the f i n s or webs between the tubes tend to move downward i n the p r o t e c t e d r e g i o n , thus p r o l o n g i n g the c h a r a c t e r i s t i c r e s i d e n c e l e n g t h of the s t r a n d s f o r a membrane w a l l . The above p o i n t has g r e a t b e a r i n g on the heat t r a n s f e r model p r e s e n t e d i n the next c h a p t e r . 3 . 3 . 3 S imultaneous Heat T r a n s f e r Probe and C a p a c i t a n c e Probe Exper iments wi th High Speed Cinematography In the t h i r d p a r t of t h i s s t u d y , s imul taneous measurements were made with an i n s t a n t a n e o u s heat t r a n s f e r probe and a c a p a c i t a n c e p r o b e , both l o c a t e d 3.74 m above the d i s t r i b u t o r . The c a p a c i t a n c e probe was i n s e r t e d i n t o the column from a p o r t d i a m e t r i c a l l y o p p o s i t e the heat t r a n s f e r probe such tha t the t i p of the probe wire came w i t h i n 1 mm of the heat t r a n s f e r probe -97-s u r f a c e . Data were o b t a i n e d for a r e a - a v e r a g e d suspens ion 3 d e n s i t i e s from 15 to 47 kg/m at a s u p e r f i c i a l gas v e l o c i t y of 7 m/s . F i g u r e 3.18 shows some t y p i c a l s imul taneous t r a c e s of both heat t r a n s f e r and c a p a c i t a n c e probe s i g n a l s at three d i f f e r e n t a r e a - a v e r a g e d suspens ion d e n s i t i e s . The q u a l i t a t i v e appearance of the c a p a c i t a n c e s i g n a l s o b t a i n e d are s i m i l a r to those o b t a i n e d by B r e r e t o n (1987) and Herb et a l . (1989). A more comprehensive a n a l y s i s of the c a p a c i t a n c e s i g n a l s i s p r e s e n t e d i n S e c t i o n 4 . 2 . 1 i n the next c h a p t e r . Comparisons of the c a p a c i -tance s i g n a l s wi th the heat t r a n s f e r s i g n a l s show t h a t , in g e n e r a l , the c a p a c i t a n c e probe s i g n a l s are more r e f i n e d and show more d e t a i l s . The peaks i n the c a p a c i t a n c e s i g n a l are a l s o more dramat i c and sudden. In c o n t r a s t , the heat t r a n s f e r s i g n a l s are l e s s r e f i n e d and show l e s s d e t a i l s . I t s peaks are a l s o l e s s d r a m a t i c . These t r e n d s can be e x p l a i n e d by the d i f f e r e n t response t imes and measur ing volumes of the two p r o b e s . S ince i t s response time i s much f a s t e r than t h a t of the heat t r a n s f e r p r o b e , the c a p a c i t a n c e probe r e v e a l e d more d e t a i l s of the time v a r i a t i o n s i n l o c a l s o l i d s c o n c e n t r a t i o n . A l s o , s i n c e the c a p a c i t a n c e probe has a s m a l l e r measur ing volume than i t s c o u n t e r p a r t , i t s s i g n a l s showed more d r a m a t i c peaks due to a reduced p r o b a b i l i t y of a v e r a g i n g of s o l i d s c o n c e n t r a t i o n i n i t s measur ing volume. Moreover , the o c c a s i o n a l l a c k of agreement between the two s i g n a l s i s a l s o due to the f a c t that the measuring volumes of the two probes d i d not c o i n c i d e e x a c t l y s i n c e the measuring volume of the c a p a c i t a n c e probe does not extend more than 1 mm beyond the l i v e wire at i t s probe t i p -98-CN * £ 350 250 150-350 250-150-250 150 50 -- H.T. Probe Cap. Probe — -1.0 -0.5 8 10 - H.T. Probe (b) Cap. Probe — CO •1.0 -05 8 10 - H.T. Probe (c) Cap. Probe — -1.0 - 0 5 8 10 Time , s F i g u r e 3.18 T y p i c a l t r a c e s of s imul taneous i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t and c a p a c i t a n c e s i g n a l at three d i f f e r e n t a r e a - a v e r a g e d suspens ion d e n s i t i e s (kg/m 3 ) (a) 46 .7 ; (b) 32 .0; (c) 1 5 . 3 . -99-( B r e r e t o n , 1987). T h e r e f o r e , i t i s c o n c e i v a b l e t h a t some p a r t i c l e s t r a n d s d e t e c t e d by the c a p a c i t a n c e probe d i d not make c o n t a c t w i th the heat t r a n s f e r probe and cause a change i n the heat t r a n s f e r c o e f f i c i e n t , or v i c e v e r s a . N e v e r t h e l e s s , i t i s apparent from F i g u r e 3.18 t h a t , i n g e n e r a l , the sudden and d r a m a t i c peaks observed i n the i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t t r a c e s c o r r e s p o n d c l o s e l y wi th s i m i l a r peaks i n the c a p a c i t a n c e t r a c e s . T h i s suggests t h a t the abrupt i n c r e a s e s i n heat t r a n s f e r c o e f f i c i e n t are caused by the a r r i v a l s of p a r t i c l e p a c k e t s at the s u r f a c e of the heat t r a n s f e r p r o b e . I t a l s o c o n f i r m s for the f i r s t t ime the impor tant r o l e of these p a r t i c l e s t r a n d s i n c i r c u l a t i n g f l u i d i z e d bed heat t r a n s f e r and a f f i r m s the predominance of the p a r t i c l e c o n v e c t i v e component as suggested i n Chapter 2. D u r i n g the above r u n s , hydrodynamics at the middle l e v e l of the column i n the v i c i n i t y of the two probes were a l s o r e c o r d e d u s i n g h i g h - s p e e d c inematography . These f i l m s were then a n a l y z e d frame-by- frame to o b t a i n an e s t i m a t e on the f a l l i n g v e l o c i t y of the s t r a n d s i n the w a l l l a y e r . The number of frames taken f o r a s t r a n d to f a l l 0.152 m at the w a l l are t a b u l a t e d i n T a b l e 3.3 for four a r e a - a v e r a g e d suspens ion d e n s i t i e s . The c o r r e s p o n d i n g c a l c u l a t e d f a l l i n g v e l o c i t y of the s t r a n d i s a l s o g i v e n i n parenthese s i n T a b l e 3 . 3 . I t i s apparent from Tab le 3.3 tha t there e x i s t s a r a t h e r wide d i s t r i b u t i o n of f a l l i n g v e l o c i t i e s f o r the s t r a n d s at a l l suspens ion d e n s i t i e s . T h i s i s s i m i l a r to what has been suggested i n F i g u r e 3 .14 . I t seems a l s o from Tab le 3.3 t h a t there i s no s y s t e m a t i c i n f l u e n c e of suspens ion d e n s i t y on -100-TABLE 3.3 Frames of F i l m Taken f o r S trands to F a l l 0.152 m and the C o r r e s p o n d i n g C a l c u l a t e d F a l l i n g V e l o c i t i e s ( in I n c r e a s i n g Order) at Four Suspens ion D e n s i t i e s . Susp . D e n s i t y 15.3 28.1 32.0 46.7 (kg/m 3 ) Frames ( V e l o c i t y , m/s) 22 (2.77) 23 (2.65) 29 (2.10) 41 (1.49) 46 (1.33) 48 (1.27) 50 (1.22) 51 (1.20) 52 (1.17) 53 (1.15) 56 (1.09) 66 (0.92) 30 (2.03) 30 (2.03) 34 (1.79) 36 (1.69) 43 (1.42) 51 (1.20) 58 (1.05) 59 (1.03) 68 (0.90) 70 (0.87) 72 (0.85) 96 (0.64) 28 (2.18) 32 (1.91) 33 (1.85) 36 (1.69) 41 (1.49) 41 (1.49) 45 (1.35) 45 (1.35) 49 (1.24) 50 (1.22) 54 (1.13) 63 (0.97) 33 (1.85) 37 (1.65) 38 (1.60) 41 (1.49) 46 (1.33) 49 (1.24) 50 (1.22) 55 (1.11) 56 (1.09) 65 (0.94) 72 (0.85) 80 (0.76) Average 44.8 (1.36) 53.9 (1.13) 43.1 (1.41) 51.8 (1.18) S t d . Dev. 13.6 (0.62) 20.4 (0.49) 10.1 (0.36) 14.6 (0.34) -101-the f a l l i n g v e l o c i t i e s . By a v e r a g i n g a l l the v e l o c i t i e s i n Tab le 3 . 3 , one can o b t a i n 1.26 m/s as the average f a l l i n g v e l o c i t y f o r the s t r a n d s at the w a l l . T h i s compares r e a s o n a b l y w e l l wi th 1.62 m/s o b t a i n e d i n S e c t i o n 3 . 3 . 2 by us ing the time l a g c o r r e s p o n d i n g to the maximum c r o s s - c o r r e l a t i o n c o e f f i c i e n t of p r o f i l e s l a and l b i n F i g u r e 3 .14 . I t i s i n t e r e s t i n g to note t h a t Gl i cksman (1988) measured f a l l i n g v e l o c i t i e s i n the range of 1-1.8 m/s w i th a v i d e o camera by i n j e c t i n g 80 jU,m sand p a r t i c l e s i n t o an upward gas stream i n a 100 mm diameter t r a n s p a r e n t co lumn. T h i s range of f a l l i n g v e l o c i t i e s , which was not s t r i c t l y measured i n a c i r c u l a t i n g f l u i d i z e d b e d , appears to be on the h i g h s i d e of v e l o c i t i e s r e p o r t e d . Hartge et a l . (1988) r e p o r t e d f a l l i n g v e l o c i t i e s i n the range of 1-1.2 m/s u s i n g an o p t i c a l probe i n a 400 mm diameter c i r c u l a t i n g f l u i d i z e d bed with 85 fim FCC p a r t i c l e s . Recent work on tube e r o s i o n i n c i r c u l a t i n g f l u i d i z e d beds suggests s t r a n d f a l l i n g v e l o c i t i e s of the order of 1 m/s ( G e l d a r t , 1989) . Moreover , r e c e n t n u m e r i c a l work on the hydrodynamics i n c i r c u l a t i n g f l u i d i z e d beds by Tsuo (1989) suggests tha t s t r a n d f a l l i n g v e l o c i t i e s are i n the range of 1-1.25 m/s . The r e s u l t s and c o n c l u s i o n s p r e s e n t e d i n t h i s chapter not on ly h e l p to e l u c i d a t e the heat t r a n s f e r mechanisms, but a l s o p r o v i d e us w i th much i n f o r m a t i o n on the hydrodynamics in a c i r c u l a t i n g f l u i d i z e d bed . As shown i n the next c h a p t e r , t h i s hydrodynamic i n f o r m a t i o n has been h e l p f u l i n f o r m u l a t i n g the heat t r a n s f e r model p r e s e n t e d in t h i s t h e s i s . 5 -102-CHAPTER 4 MODELLING OF HEAT TRANSFER IN CIRCULATING  FLUIDIZED BEDS 4.1 INTRODUCTION As i n t e r e s t i n heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds c o n t i n u e s to grow, more heat t r a n s f e r s t u d i e s and e x p e r i m e n t a l r e s u l t s are b e i n g r e p o r t e d . However, many of these r e s u l t s show g r e a t v a r i a t i o n and s c a t t e r when compared, even when t h e i r e x p e r i m e n t a l c o n d i t i o n s appear to be s i m i l a r . T h i s hampers d e s i g n e f f o r t s for c i r c u l a t i n g f l u i d i z e d bed r e a c t o r s and makes e x t e n s i v e and c o s t l y e m p i r i c a l t e s t i n g n e c e s s a r y . In order to e x p l a i n the u n d e r l y i n g heat t r a n s f e r mechanisms and to a i d the d e s i g n of equipment , i t i s neces sary to formula te a f e a s i b l e heat t r a n s f e r model for c i r c u l a t i n g f l u i d i z e d beds . Given tha t the s y s t e m a t i c s tudy of c i r c u l a t i n g f l u i d i z e d beds i s o n l y very r e c e n t , i t i s not s u r p r i s i n g t h a t l i t t l e has been done on the m o d e l l i n g f r o n t . Most work has been based on the p e n e t r a t i o n or packet theory approach o r i g i n a l l y proposed by M i c k l e y and F a i r b a n k s (1955) for b u b b l i n g f l u i d i z e d beds . Subbarao and Basu (1986) proposed a model u s i n g the packet theory i n which c l u s t e r s of s o l i d s and v o i d s reach the heat t r a n s f e r s u r f a c e a l t e r n a t i v e l y . They v i s u a l i z e d the v o i d s i n a c i r c u l a t -ing f l u i d i z e d bed as gas bubbles which have e i t h e r grown to t h e i r maximum s t a b l e s i z e or to the column s i z e . Heat t r a n s f e r to v o i d s / b u b b l e s was n e g l e c t e d , whi l e heat t r a n s f e r to c l u s t e r s was -103-m o d e l l e d by t r a n s i e n t heat c o n d u c t i o n . Comparison was made on ly wi th the da ta of F r a l e y et a l . (1983), the o n l y s tudy at t h a t time which p r o v i d e d s o l i d s mass f l u x da ta needed as i n p u t to the model . However, agreement was, at b e s t , m a r g i n a l . T h i s model was l a t e r r e f i n e d by Basu and Nag (1987) to take i n t o account the heat t r a n s f e r to v o i d s / b u b b l e s and a l s o the emerging ev idence tha t s o l i d s tend to aggregate near the w a l l of the column to form a c o r e - a n n u l u s s t r u c t u r e . The r e s u l t i n g model i s a two-parameter f i t t i n g model w i th the parameters be ing the r a t i o of s o l i d s c o n c e n t r a t i o n near the w a l l to the c r o s s - s e c t i o n a l average and the v o l u m e t r i c c o n c e n t r a t i o n of s o l i d s i n the v o i d s . Agreement wi th e x p e r i m e n t a l da ta i s on ly f a i r . S e k t h i r a e t a l . (1988) r e c e n t l y proposed another model based on heat t r a n s f e r to s i n g l e p a r t i c l e s based on a model o r i g i n a l l y proposed by Z i e g l e r e t a l . (1964). S o l i d p a r t i c l e s are assumed to move down the heat t r a n s f e r s u r f a c e a t t h e i r t e r m i n a l v e l o c i t y and r e c e i v e thermal energy by c o n v e c t i o n from the f l u i d s u r r o u n d -ing the p a r t i c l e s . T h i s model showed r e a s o n a b l e agreement when compared wi th t h e i r own e x p e r i m e n t a l d a t a . However, no comparisons wi th other da ta were r e p o r t e d . In t h i s s t u d y , we p r e s e n t a heat t r a n s f e r model u t i l i z i n g r e c e n t developments i n the u n d e r s t a n d i n g of hydrodynamics and heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds . The model i s based on unsteady heat c o n d u c t i o n to waves of s t r a n d s of p a r t i c l e s f a l l i n g a long the heat t r a n s f e r s u r f a c e . These f a l l i n g s t r a n d s of p a r t i c l e s are assumed to d i s p e r s e and reform p e r i o d i c a l l y i n the annulus l a y e r of an o v e r a l l c o r e - a n n u l u s s t r u c t u r e . -104-4.2 MODEL FORMULATION AND CIRCULATING FLUIDIZED BED HYDRODYNAMICS 4 .2 .1 Hydrodynamics The c l o s e r e l a t i o n s h i p between heat t r a n s f e r and hydrodynam-i c s i n c i r c u l a t i n g f l u i d i z e d beds cannot be overemphas ized . In order to model heat t r a n s f e r i n a p h y s i c a l l y r e a l i s t i c manner, i t i s important to ach i eve a r e a s o n a b l e u n d e r s t a n d i n g of the l o c a l and o v e r a l l hydrodynamics i n c i r c u l a t i n g f l u i d i z e d beds . There i s an emerging consensus among r e s e a r c h e r s t h a t a major f e a t u r e of the o v e r a l l f low s t r u c t u r e i n c i r c u l a t i n g f l u i d i z e d beds i s t h a t of the c o r e - a n n u l u s t y p e . In s imple terms, there e x i s t s a r e l a t i v e l y d i l u t e upf low core i n which s o l i d p a r t i c l e s are e n t r a i n e d upward by a h i g h v e l o c i t y gas s t ream, and a much denser annulus l a y e r near the column w a l l i n which s o l i d p a r t i c l e s congregate and f a l l as dense s t r u c t u r e s s i m i l a r to waves of s t r a n d s or s t r e a m e r s . Such o b s e r v a t i o n s have been r e p o r t e d by W e i n s t e i n et a l . (1986) u s i n g an x - r a y imaging t e c h n i q u e , B r e r e t o n (1987) and Herb et a l . (1989) u s i n g c a p a c i t a n c e p r o b e s , H o r i o et a l . (1988) and Hartge et a l . (1988) u s i n g o p t i c a l p r o b e s , and Bader e t a l . (1988) and Rhodes et a l . (1989) u s i n g mass f l u x p r o b e s , among o t h e r s . As heat t r a n s f e r s u r f a c e s are commonly l o c a t e d at the column w a l l f o r most c i r c u l a t i n g f l u i d i z e d bed a p p l i c a t i o n s , the i n f l u e n c e of the downflowing w a l l l a y e r on heat t r a n s f e r i s paramount. The f a l l i n g v e l o c i t y of s t r a n d s i n the w a l l l a y e r , the l e n g t h of t h e i r s tay at the w a l l , and the time f r a c t i o n s of -105-w a l l coverage are a l l important hydrodynamic parameters tha t a f f e c t the heat t r a n s f e r between the g a s - s o l i d s suspens ion and the w a l l . In order to e s t i m a t e these hydrodynamic p a r a m e t e r s , s e v e r a l measurements were c a r r i e d out i n a c o l d model c i r c u l a t i n g f l u i d i z e d b e d . As these exper iments have a l r e a d y been d e s c r i b e d i n d e t a i l i n Chapter 3, o n l y a c o n c i s e summary of the r e l e v a n t r e s u l t s i s p r e s e n t e d h e r e . The double heat t r a n s f e r probe exper iments p r e s e n t e d i n S e c t i o n 3 .3 .2 suggest t h a t there e x i s t s a " c h a r a c t e r i s t i c " r e s i d e n c e l e n g t h at the w a l l f o r s t r a n d s in the downflowing a n n u l u s . T h i s i m p l i e s tha t a f t e r i t s f o r m a t i o n , a s t r a n d would f a l l a long the w a l l f or a c h a r a c t e r i s t i c l e n g t h b e f o r e d i s i n t e g r a t i n g and be ing d i s p e r s e d . Among the three proposed d e f i n i t i o n s of t h i s l e n g t h d i s c u s s e d i n S e c t i o n 3 . 3 . 2 , the i n t e g r a t e d average l e n g t h , a ^ n t / i s used i n the model s i n c e i t i s the most c o n v e n t i o n a l d e f i n i t i o n and i s a l s o very s i m i l a r to another proposed l e n g t h , a 0 ^ . At any r a t e , as shown i n S e c t i o n 4.3 below, the model i s found not to be o v e r l y s e n s i t i v e to v a r i a t i o n s i n t h i s l e n g t h . Hence, we o b t a i n L from E q . 3.8 as 0 596 L = a. . = 0.0178 P B ' ^ D (4.1) m t susp v ' Both the double probe exper iments i n S e c t i o n 3 .3 .2 and the h i g h speed c inematography r e s u l t s i n S e c t i o n 3 . 3 . 3 suggest that there e x i s t s a r a t h e r wide d i s t r i b u t i o n of f a l l i n g v e l o c i t i e s for the s t r a n d s . The average f a l l i n g v e l o c i t y of the s t r a n d s , however, i s not i n f l u e n c e d s i g n i f i c a n t l y by suspens ion d e n s i t y -106-and i s g i v e n i n S e c t i o n 3 . 3 . 3 as U s = 1.26 m/s (4.2) T h i s v a l u e i s of the same order of magnitude as w a l l v e l o c i t i e s de termined or suggested by o t h e r s ( e . g . , G l i c k s m a n , 1988; Hartge et a l . , 1988; G e l d a r t , 1989; Tsuo , 1989). Hence, t h i s v a l u e w i l l be assumed to a p p l y i n a g e n e r a l way u n t i l f u r t h e r d a t a become a v a i l a b l e i n the f u t u r e . The c a p a c i t a n c e probe s i g n a l s , o b t a i n e d s i m u l t a n e o u s l y wi th the i n s t a n t a n e o u s heat t r a n s f e r s i g n a l s i n S e c t i o n 3 . 3 . 3 , c o n t a i n u s e f u l hydrodynamic i n f o r m a t i o n about the annulus l a y e r . F i g u r e 4.1 i s a c u m u l a t i v e f requency d i s t r i b u t i o n p l o t of the c a p a c i -tance probe s i g n a l s (see F i g u r e 3 . 1 8 ) , i n which the c u m u l a t i v e time f r a c t i o n of w a l l coverage by a s t r a n d of vo idage e i s p l o t t e d a g a i n s t (1-e) f o r four c r o s s - s e c t i o n a l a r e a - a v e r a g e d suspens ion d e n s i t i e s . F i g u r e s 3.18 and 4.1 both i n d i c a t e c l e a r l y that f a s t f l u i d i z e d beds , u n l i k e b u b b l i n g f l u i d i z e d beds , do not possess two d i s c r e t e and d i s t i n c t phases ( e . g . , a u n i f o r m low voidage dense phase (or emuls ion) and a h i g h voidage d i l u t e phase (or b u b b l e ) ) , at l e a s t above the t u r b u l e n t p r i m a r y zone. I n s t e a d , the f a s t bed c o n s i s t s of wide d i s t r i b u t i o n s o f vo idages which vary wi th the t ime-averaged and c r o s s - s e c t i o n a l a r e a -averaged suspens ion d e n s i t y . In order to c h a r a c t e r i z e the vo idage d i s t r i b u t i o n s for the s t r a n d s , the c u m u l a t i v e frequency d i s t r i b u t i o n p l o t s shown i n F i g u r e 4.1 are each d i s c r e t i z e d a c c o r d i n g to the scheme shown i n F i g u r e 4 .2 . The d i f f e r e n t time F i g u r e 4.1 Cumulat ive time f r a c t i o n of w a l l coverage by s t r a n d s with voidage € versus 1 - e at four d i f f e r e n t suspension d e n s i t i e s . Cum. f 1 - C 2 1 " c 3 1 " e 4 1 " e 5 ure 4.2 D i s c r e t i z a t i o n scheme for the c u m u l a t i v e time f r a c t i o n of w a l l coverage p l o t s i n F i g u r e 4 . 1 . -109-f r a c t i o n s of w a l l coverage f^, f^, e t c . , c o r r e s p o n d i n g to d i f f e r e n t va lues of ( 1 - e ) , are a d j u s t e d such tha t area A^ = area A 2 , A 3 = A 4 , and so on . The r e s u l t i n g va lues of f and c o r r e s p o n d -ing (1-e) va lues f o r four d i f f e r e n t suspens ion d e n s i t i e s are t a b u l a t e d i n Tab le 4 . 1 . The t ime f r a c t i o n of w a l l c o v e r a g e , f , i s then p l o t t e d a g a i n s t suspens ion d e n s i t y at s i x d i f f e r e n t v a l u e s of vo idage i n F i g u r e 4 . 3 . T h i s f i g u r e p r o v i d e s a c o n v e n i e n t way of e s t i m a t i n g the time f r a c t i o n of w a l l coverage c o r r e s p o n d i n g to d i f f e r e n t vo idages f o r a wide range of suspens ion d e n s i t i e s . 4 .2 .2 Model F o r m u l a t i o n As i n b u b b l i n g f l u i d i z e d bed heat t r a n s f e r , i t seems r e a s o n a b l e to model heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d bed as the sum of p a r t i c l e c o n v e c t i v e t r a n s f e r due to p a r t i c l e s brought from the bu lk to the s u r f a c e , gas c o n v e c t i v e t r a n s f e r due to gas t r a v e l l i n g a long the s u r f a c e , and r a d i a t i v e t r a n s f e r between the s u r f a c e and the g a s - s o l i d s s u s p e n s i o n . S ince the r a d i a t i v e component, which becomes s i g n i f i c a n t at h i g h t e m p e r a t u r e s , has been t r e a t e d i n S e c t i o n 2 . 3 . 2 , o n l y the p a r t i c l e c o n v e c t i v e and gas c o n v e c t i v e components are d e a l t wi th i n depth h e r e . In view of r ecen t work on c i r c u l a t i n g f l u i d i z e d bed hydrodynamics summarized i n the above s e c t i o n , we propose the f o l l o w i n g heat t r a n s f e r mode l , i l l u s t r a t e d g r a p h i c a l l y i n F i g u r e 4 .4 : F i r s t , the s o l i d s f low p a t t e r n i n the column i s mode l l ed as a c o r e - a n n u l u s s t r u c t u r e such t h a t p a r t i c l e s move up the cen ter -110-Time F r a c t i o n s of W a l l Coverage f o r S trands of D i f f e r e n t Voidages at Four Suspens ion D e n s i t i e s . TABLE 4.1 Susp. D e n s i t y 15.3 28.1 32.0 46.7 (kg/m 3 ) 1 - e Time F r a c t i o n of W a l l Coverage , f 0.0 0.525 0.271 0.232 0.050 0.1 0.423 0.581 0.547 0.421 0.2 0.041 0.116 0.157 0.326 0.3 0.011 0.023 0.047 0.139 0.4 0.0 0.009 0.017 0.050 0.5 0.0 0.0 0.0 0.014 Sum 1.0 1.0 1.0 1.0 F i g u r e 4.3 Time f r a c t i o n of w a l l coverage versus suspens ion d e n s i t y f o r s i x d i f f e r e n t s t r a n d v o i d a g e s . - 1 1 2 -Wall Annulus Core 0 'w 1 T * T, 0 a m m • p - m - * j m F i g u r e 4.4 I l l u s t r a t i o n of the proposed heat t r a n s f e r model for c i r c u l a t i n g f l u i d i z e d beds . -113-of the column in a dilute core and down along the column wall in a dense annulus layer of thickness 5. The net solids flux between the core and the annulus is assumed to be zero, with the solids flux in either direction denoted by m. Both m and 6 are assumed to be independent of height. In view of this, the present model is more like l y to apply to heat transfer surfaces located in the more developed upper portion of the fast fluidized bed risers above the lower turbulent primary zone than in the more rapidly developing regions. Particles are assumed to be evenly dispersed in the core which has a uniform temperature T . In the annulus, particles are assumed to congregate into various dense structures resembling waves, strands, or streamers. These are denoted here simply as "strands." The strands are assumed to have a distribution of voidages as shown in Figure 4 . 3 . In addition, these strands are assumed to continuously form, move downward along the wall surface, and fi n a l l y disintegrate, similar (albeit in a more orderly manner) to what is observed visually in the cold model circulating fluidized bed. At the top of the heat transfer surface on the wall (position Z0 in Figure 4 . 4 ) , a strand is formed with voidage e at the temperature T^ (which is assumed equal to the bulk tempera-ture T ) and comes into contact with the wall. The wall is c assumed to be isothermal at a constant temperature T . This assumption is valid since the limiting heat transfer resistance in a circulating fluidized bed is on the suspension side and not on the coolant side. The strand then travels down along the surface to position Z.. at a fa l l i n g velocity U for a length L, -114-the c h a r a c t e r i s t i c r e s i d e n c e l e n g t h at the w a l l , b e f o r e the s t r a n d d i s i n t e g r a t e s . I t i s r e c o g n i z e d tha t there e x i s t s a wide range of f a l l i n g v e l o c i t i e s f o r the s t r a n d s as d i s c u s s e d i n S e c t i o n s 3 .3 .2 and 3 . 3 . 3 . However, i n order to s i m p l i f y the model and keep the c a l c u l a t i o n s to a manageable l e v e l , we ignore the d i s t r i b u t i o n of f a l l i n g v e l o c i t i e s and assume that a l l s t r a n d s f a l l at a u n i f o r m v e l o c i t y of 1.26 m/s . At any r a t e , a n a l y s i s i n S e c t i o n 4.3 below shows t h a t the model i s not o v e r l y s e n s i t i v e to v a r i a t i o n s i n the f a l l i n g v e l o c i t y . The r e s i d e n c e t ime , t , of each p a r t of the s t r a n d at the s u r f a c e i s t h e r e f o r e where L and U s are g i v e n by E q s . 4.1 and 4 . 2 , r e s p e c t i v e l y . Dur ing t h i s p e r i o d of c o n t a c t , heat i s conducted from the i s o t h e r m a l w a l l i n t o the s t r a n d (or v i c e v e r s a i f the bed i s h o t t e r than the s u r f a c e , as i n a c o m b u s t o r ) . I t seems reasonab le to t r e a t t h i s t r a n s f e r i n terms of unsteady heat c o n d u c t i o n from an i s o t h e r m a l s u r f a c e to a homogeneous s e m i - i n f i n i t e medium, wi th an e f f e c t i v e thermal c o n d u c t i v i t y and a thermal w a l l c o n t a c t r e s i s t a n c e at the i n t e r f a c e . D i r e c t i o n of t h i s heat t r a n s f e r i s assumed to be h o r i z o n t a l from the w a l l i n t o the s t r a n d . Any t r a n s f e r i n the v e r t i c a l d i r e c t i o n i s i g n o r e d h e r e . The o v e r a l l heat t r a n s f e r c o e f f i c i e n t between the s u r f a c e and the s t r a n d , d e f i n e d as r t = L / U r ' s (4.3) h = q / ( T - T ) o ^s w a (4.4) -115-where q i s the r a t e of heat t r a n s f e r per u n i t area between the S s u r f a c e and the s t r a n d , can then be w r i t t e n h Q = l / ( l / h w + l / h e ) (4.5) Here h i s the w a l l c o n t a c t heat t r a n s f e r c o e f f i c i e n t , and h i s w e the e f f e c t i v e heat t r a n s f e r c o e f f i c i e n t f o r unsteady heat t r a n s f e r i n t o a homogeneous s e m i - i n f i n i t e medium from a c o n s t a n t temperature w a l l . M i c k l e y and F a i r b a n k s (1955) who proposed the o r i g i n a l packet theory s o l v e d the unsteady heat t r a n s f e r e q u a t i o n and o b t a i n e d the f o l l o w i n g e x p r e s s i o n for h g at any i n s t a n t t a f t e r exposure of the packet to the w a l l : h e = V k e P p C P P ( 1 - e ) / 7 r t ( 4 - 6 > where k i s the e f f e c t i v e thermal c o n d u c t i v i t y of the s emi -e J i n f i n i t e medium, and p and c are the d e n s i t y and the s p e c i f i c P PP heat c a p a c i t y of the s o l i d p a r t i c l e s r e s p e c t i v e l y . The e f f e c t i v e thermal c o n d u c t i v i t y , k , in E q . 4.6 can be e s t i m a t e d from the e x p r e s s i o n proposed by G e l p e r i n and E i n s t e i n (1971) : k = k e g g - e n i - W k A n + 0 . 2 8 * a - 6 3 < W " ' 1 8 g p * ^ (4.7) f o r p a r t i c l e s wi th d iameter l e s s than 0 . 5 - 0 . 7 mm and k / k <=5000 P g where k and k are the thermal c o n d u c t i v i t i e s of the p a r t i c l e s P g -116-and gas r e s p e c t i v e l y . R e s u l t s from E q . 4.7 are a lmost i d e n t i c a l wi th those from the k Q e x p r e s s i o n g i v e n by K u n i i and Smith (1960) over the range of i n t e r e s t , i . e . 0.4<e<=1.0. There has been much heated d i s c u s s i o n on the a p p r o p r i a t e n e s s of u s i n g the packet theory to d e s c r i b e heat t r a n s f e r i n b u b b l i n g f l u i d i z e d beds . Whi le the o r i g i n a l M i c k l e y and F a i r b a n k s model (Eq. 4.6) has been shown to g i v e good a p p r o x i m a t i o n s for medium to long c o n t a c t t i m e s , i t o v e r p r e d i c t s the e x p e r i m e n t a l d a t a f o r s h o r t c o n t a c t t imes s i n c e h g i n E q . 4.6 approaches i n f i n i t y when t tends to z e r o . T h i s s h o r t c o m i n g , however, was l a t e r r e c o g n i z e d and r e c t i f i e d by other r e s e a r c h e r s , m a i n l y by i n t r o d u c i n g a thermal c o n t a c t r e s i s t a n c e between the packet of emuls ion and the w a l l . Baskakov et a l . (1973), f or example, showed tha t f i n i t e heat t r a n s f e r c o e f f i c i e n t s can be o b t a i n e d at a l l t imes by adding a t h i n gas f i l m between the w a l l and the p a c k e t . A l though the e x i s t e n c e of a t h i n gas f i l m between the g a s -s o l i d s emuls ion and the w a l l i s c o n s i d e r e d by some to be f i c t i -t i o u s , the thermal c o n t a c t r e s i s t a n c e due to the w a l l can be j u s t i f i e d . G o r e l i k (1967), Kubie and Broughton (1975), Ozkaynak and Chen (1980) a l l suggested tha t the vo idage of the packet i n the w a l l r e g i o n i s d i f f e r e n t from tha t for the r e s t of the p a c k e t . A l s o , Sch lunder (1980) argued tha t when a p e r f e c t sphere i s i n c o n t a c t wi th a p e r f e c t l y f l a t w a l l , heat i s t r a n s f e r r e d mos t ly through a t h i n gas gap, whose t h i c k n e s s near the r e g i o n of the c o n t a c t p o i n t i s l e s s than the mean f r e e path of gas mole -c u l e s . Decker and Gl i cksman (1981), on the o ther hand, suggested t h a t due to the n o n - i d e a l c o n t a c t s u r f a c e s between the p a r t i c l e -117-s u r f a c e and the w a l l , i . e . , a s p e r i t i e s on the s u r f a c e s of p a r t i c l e s , there are many g a s - f i l l e d r e g i o n s between c o n t a c t p o i n t s throughout the c o n t a c t r e g i o n . Hence, whi l e the a c t u a l c o n t a c t r e s i s t a n c e at the w a l l can take on d i f f e r e n t forms, the use of a t h i n gas f i l m can be j u s t i f i e d on p h y s i c a l grounds as w e l l as f o r mathemat i ca l c o n v e n i e n c e . For very s h o r t c o n t a c t t i m e s , heat does not u s u a l l y p e n e t r a t e i n t o the packet for a depth of more than one or two p a r t i c l e d i a m e t e r s . In t h i s c a s e , the use of a cont inuum concept i n the packet t h e o r y i s c a l l e d i n t o doubt . B o t t e r i l l and W i l l i a m s (1963) argued that i t i s more a p p r o p r i a t e to c o n s i d e r heat t r a n s f e r i n t o the f i r s t l a y e r of p a r t i c l e s at the w a l l . T h i s was l a t e r extended to two p a r t i c l e s , as d i s c u s s e d by B o t t e r i l l and But t (1968). I t i s i n t e r e s t i n g to note that a t h i n gas f i l m between the w a l l and the f i r s t p a r t i c l e i s needed to o b t a i n good agreement wi th e x p e r i m e n t a l d a t a . A l though heat t r a n s f e r to a s e r i e s of p a r t i c l e s i s c o n c e p t u a l l y s u p e r i o r to the cont inuum approach of the packet theory for s h o r t c o n t a c t t i m e s , i t shou ld be noted that l a b o r i o u s and t ime-consuming n u m e r i c a l methods are needed to s o l v e the g o v e r n i n g e q u a t i o n s . Even the s i m p l i f i e d v e r s i o n of B o t t e r i l l ' s model proposed by Gabor (1970), based on a l t e r n a t e s l a b s of gas and s o l i d , r e q u i r e s a c o m p l i c a t e d n u m e r i c a l s o l u t i o n t e c h n i q u e . In c o n t r a s t , the packet theory o f f e r s s imple c l o s e - e n d e d s o l u t i o n s . Even f o r very s h o r t c o n t a c t t i m e s , n o t w i t h s t a n d i n g a l a c k of r i g o r o u s j u s t i f i c a t i o n , the packet theory c o u p l e d wi th a w a l l thermal c o n t a c t r e s i s t a n c e has been shown ( G l o s k i et a l . , 1984) to p r o v i d e good agreement wi th - 1 1 8 -experimental data. As the contact time of the packet at the wall increases, the penetration depth of heat also increases. As Eq. 4.6 is derived from unsteady heat conduction into a semi-infinite medium, i t is necessary to establish that the penetration distance does not exceed the thickness of the annulus in the model. By solving the equation for transient heat conduction from an isothermal wall into a homogeneous semi-infinite strand with a wall contact thermal resistance, the following temperature profile in the strand can be obtained: T-T 1 = (1 - erf (x/2Jat) ) (4.8) T -T 1 + h /h w c e' w Here x is the heat penetration distance into the strand and 0!=k /p c (1-e) is the effective thermal dif f u s i v i t y of the e *p pp J strand. Figure 4.5 plots the 95% penetration distance (i.e., the distance from the wall at which (T-T )/(T -T )=0.05) against the vertical distance travelled by a typical strand of 250 fim sand along the heat transfer surface at 1.26 m/s for four different strand voidages. The wall contact heat transfer coefficient, h , ^ w used for this figure is obtained from Eq. 4.18 derived later, with n=2.5. With the exception of l-e=0.1, the 95% penetration distances do not exceed 1 mm in a l l cases, even when the strands f a l l along the wall for 1.5 m. For l-e=0.1, the 95% penetration distance only exceeds 1 mm i f the strand f a l l s further than 1 m. Hence, i t is justifiable to use Eqs. 4.5 and 4.6 here to model F i g u r e 4.5 95% heat p e n e t r a t i o n d i s t a n c e versus v e r t i c a l d i s t a n c e t r a v e l l e d by a t y p i c a l s t r a n d of 250 jxm sand at 1.26 m/s for four d i f f e r e n t s t r a n d v o i d a g e s . - 1 2 0 -the heat t r a n s f e r between the w a l l and the s t r a n d s . The amount of heat t r a n s f e r r e d per u n i t a r e a to a s t r a n d i n t h the i vo idage i n t e r v a l , Q s ^ r d u r i n g the time of c o n t a c t from p o s i t i o n s to Z^ i s g i v e n by dt (4.9) which , by u s i n g E q s . 4.4 and 4 . 5 , can be expres sed as s i f f c r T - T / —2— \J 1/h + 1 dt (4.10) l / h w + l / h e E q u a t i o n 4.10 can be i n t e g r a t e d by s u b s t i t u t i n g h Q from E q . 4.6 to g i v e ' S I 2(T - T ) w a c 2 A . 1/h c + (1/h ) l n ' w w 1/h + c ' w (4.11) where c i s g i v e n by 7 T t c = k p c ( l - e . ) e P PP x (4.12) S ince f^ corresponds to the f r a c t i o n of time d u r i n g which the s u r f a c e i s covered by a s t r a n d of voidage e^  as g i v e n i n F i g u r e 4 . 3 , the amount of heat t r a n s f e r r e d per u n i t area to a l l s t r a n d s from Z . to Z-. can be found by summation for a l l s t r a n d s , that i s , 0 1 -121-Qt - Z ( f i . Q 8 i ) (4.13) During the fraction of time when the surface is covered with gas only (i.e., e = l ) , heat transfer between the wall and the annulus is assumed to be that of particle-free, steady state, fully developed convection from gas in a column. For the length L from position to Z^, the average heat transfer coefficient between the surface and the bed (core) is given by At position Z^, after the strands have left the surface and disintegrated, the gas and the particles in the annulus are assumed to be mixed well and attain a new "mixing cup" temperature T^. Assuming that the thickness of the annulus is much smaller than the column width, we can estimate T"^  from a heat balance on a l l a strands as they travel downwards in the annulus from Za to Z.: Z^. Since the temperature of the annulus only changes at Z^ where the heated strands are mixed together, T in this f i r s t 0 interval is equal to T . The average voidage of the annulus, e , can be obtained from h. = Q./t (T -T ) t t' r x w c' (4.14) Q. + 2mc t (T -T ) = O c 5(1-6 )(T1-T0) t pp rv c a' "p pp a' v a a' (4.15) a e = I (f . . e.) a l l (4.16) -122-E q u a t i o n 4.15 can t h e r e f o r e be r e a r r a n g e d to express as T l - V C P P + T a ' P p 8 < l - V - 2 m V + 2 m t r T c ( 4 1 ? ) P p 8d-e,) Now, new s t r a n d s at the temperature are formed at and move down a long the w a l l at v e l o c i t y U f o r a l e n g t h L b e f o r e s they d i s i n t e g r a t e at Z^. S i m i l a r to the p r e v i o u s s t e p , t o t a l heat conducted i n t o the annulus from Z^ to can be e s t i m a t e d 0 1 from E q s . 4.11 and 4.13 by r e p l a c i n g T by T . The annulus then 3 c l 2 a t t a i n s a new temperature T at Z~ a f t e r the s t r a n d p a r t i c l e s are a z d i s p e r s e d and w e l l mixed wi th o ther annulus p a r t i c l e s . S i m i l a r l y , 2 0 the temperature T can be e s t i m a t e d from E q . 4.17 wi th T a a r e p l a c e d by T ^ . T h i s p r o c e s s i s assumed to be repeated for the a whole l e n g t h of the heat t r a n s f e r s u r f a c e on the column w a l l . T o g e t h e r , E q s . 4 .11 , 4 .13 , and 4.17 summarize the above mode l . The L - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t a long the s u r f a c e i s g i v e n by E q . 4 .14 . A s imple BASIC computer program, w r i t t e n f o r p e r f o r m i n g the model c a l c u l a t i o n s , i s l i s t e d i n Appendix 5. 4 .3 C O M P A R I S O N O F M O D E L W I T H E X P E R I M E N T A L R E S U L T S The model f ormula ted i n the above s e c t i o n has three unknown v a r i a b l e s : the t h i c k n e s s of the annulus 5, the s o l i d s f l u x between the annulus and the core m, and the w a l l c o n t a c t heat t r a n s f e r c o e f f i c i e n t h . The f i r s t two v a r i a b l e s w i l l be used as w f i t t i n g parameters of the model whi l e h w i l l be de termined -123-e m p i r i c a l l y below. A c c o r d i n g to the assumptions of the mode l , s t r a n d s f a l l a long the w a l l from the top of the heat t r a n s f e r s u r f a c e (Z^) for a r e s i d e n c e l e n g t h L to Z^ (Z^+L). The l e n g t h of L i s found to v a r y wi th the a r e a - a v e r a g e d suspens ion d e n s i t y as shown i n F i g u r e 3 . 1 7 . For the range of suspens ion d e n s i t i e s c o n s i d e r e d h e r e , 3 which i s 10-60 kg/m , L v a r i e s from about 0.1 to 0.2 m. For heat t r a n s f e r s u r f a c e s wi th l e n g t h s l e s s than L , t h e r e i s no s t r a n d d i s p e r s i o n and no renewal of c o n t a c t of each i n d i v i d u a l s t r a n d as i t t r a v e l s a long the s u r f a c e . The model can then be s i m p l i f i e d to the case of a s i n g l e c o n t a c t , and the parameters m and 5, which e n t e r o n l y at the end of each i n t e r v a l of l e n g t h L , do not have to be c o n s i d e r e d . T h i s i s the case for d a t a from Basu and Nag (1987), Kobro and B r e r e t o n (1986), and the i n s t a n t a n e o u s heat t r a n s f e r s tudy d i s c u s s e d i n Chapter 3. S i m i l a r to the p r a c t i c e i n b u b b l i n g f l u i d i z e d bed heat t r a n s f e r , the c o n t a c t r e s i s t a n c e between the w a l l and the s t r a n d can be expres sed as the r e s i s t a n c e o f f e r e d by a gas gap of t h i c k n e s s d / n such tha t P d / n 1/h = — £ (4.18) w k 9 The l o c a l t ime-averaged heat t r a n s f e r c o e f f i c i e n t s o b t a i n e d wi th the i n s t a n t a n e o u s heat t r a n s f e r probe i n Chapter 3 are used to f i t the c o n t a c t r e s i s t a n c e expressed i n E q . 4 .18 . The middle heat t r a n s f e r c o e f f i c i e n t s o b t a i n e d i n F i g u r e 3.11 are compared -124-with the model at three v a l u e s of n as shown i n F i g u r e 4 . 6 . The data from the midd le p o s i t i o n are more a p p r o p r i a t e f o r the p r e s e n t model s i n c e they were o b t a i n e d i n the more deve loped p o r t i o n of the f a s t f l u i d i z e d bed r i s e r away from the bottom and the t o p . I t i s apparent from F i g u r e 4.6 tha t n=2.5 g i v e s the bes t f i t to the heat t r a n s f e r c o e f f i c i e n t d a t a . I t i s i n t e r e s t -ing to note that n i s commonly between 4 to 12 when da ta o b t a i n e d for b u b b l i n g f l u i d i z e d beds are f i t t e d (Decker and G l i c k s m a n , 1981; Saxena and Gabor , 1981) . The s m a l l e r v a l u e of n found here suggests t h a t the c o n t a c t r e s i s t a n c e i n c i r c u l a t i n g f l u i d i z e d beds between the w a l l s u r f a c e and the s t r a n d s i s b i g g e r than that i n c o n v e n t i o n a l b u b b l i n g f l u i d i z e d beds . T h i s i s r easonab le s i n c e one would expect the f o r c e s p r e s s i n g the dense phase (emulsion) a g a i n s t the w a l l i n b u b b l i n g beds to be s t r o n g e r than those p r e s s i n g the s t r a n d s a g a i n s t the w a l l i n c i r c u l a t i n g beds . The va lue of n=2.5 i s used f o r a l l the f o l l o w i n g model p r e d i c t i o n s . The model i s compared wi th the d a t a of Basu and Nag (1987) i n F i g u r e 4.7 for two p a r t i c l e s i z e s , 87 and 227 fim. The f i g u r e shows tha t e x c e l l e n t agreement i s o b t a i n e d wi th the da ta f o r the 227 t^m p a r t i c l e s . The mode l , however, o v e r p r e d i c t s the da ta f o r the 87 fim p a r t i c l e s . S i m i l a r l y , the d a t a of Kobro and B r e r e t o n (1986) are compared wi th the model i n F i g u r e 4.8 for two p a r t i c l e s i z e s , 170 and 250 fim. Whi le the model aga in o v e r p r e d i c t s the da ta i n both c a s e s , the d i s c r e p a n c y i s somewhat s m a l l e r for the 170 fim p a r t i c l e s than that for the 250 fim p a r t i c l e s . -125-F i g u r e 4.6 Comparison of model p r e d i c t i o n wi th the e x p e r i m e n t a l data from F i g u r e 3.11 for three d i f f e r e n t n . -126-F i g u r e 4.7 Comparison of model p r e d i c t i o n with the e x p e r i m e n t a l data of Basu and Nag (1987) for two p a r t i c l e s i z e s . -127-400 £ 300 200h 100r-R susp , kg/rrv Figure 4.8 Comparison of model prediction with the experimental data of Kobro and Brereton (1986) for two particle sizes at T =25 C susp -128-For the longer heat transfer surfaces used in experiments described in Chapter 2, the length of the surface exceeds the characteristic residence length of the strands obtained from Figure 3.17. This suggests that there would be strand dispersion and renewals of strand contact. Hence, the parameters m and 5 start to play a role in the model prediction. The effect of different characteristic residence lengths of strands is shown in Figure 4.9 which compares predicted local heat transfer coefficient profiles along the membrane wall surface for four different values of L. The model predictions are calculated with m=0.05 kg/m .s and 5=1 mm. These choices for m and 5 are discussed later in this chapter. Figure 4.9 shows that the predicted local heat transfer coefficient drops rapidly as the strands travel along the wall surface for a length L. This i n i t i a l portion, before any renewal occurs (i.e., for Z<L) is independent of L. When the old strands are dispersed (after each interval of length L) and the new strands come into contact with the wall, the local heat transfer coefficient shows sudden increases, then rapidly drops from the higher values. As L increases, the frequency of contact renewals decreases. In the limit that L becomes very large, i t can be seen from Figure 4.9 that there are no renewals in strand contact and the local heat transfer coefficient profile becomes that for a single (i.e., non-renewed) strand contact. It is significant that the model prediction gives the best agreement with experimental data at very large L. This point is discussed further below. The experimental data is for T =407 C. Radiation at this susp -129-400 F i g u r e 4.9 P r e d i c t e d v a r i a t i o n s i n l o c a l heat t r a n s f e r c o e f f i -c i e n t a long membrane w a l l s u r f a c e for four d i f f e r e n t L . m=0.05 k g / m 2 . s ; 5=1 mm. C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l da ta from F i g u r e 2.19 wi th U=7.5 m/s , d =241 fim, P 0 1 1 0 „ = 54 k g / m 3 , T__ = 407 C . susp susp -130-temperature i s l i k e l y to be s m a l l and i s i g n o r e d i n the model c a l c u l a t i o n . To s i m p l i f y the p r e s e n t a t i o n of the p r o f i l e s i n F i g u r e 4 . 9 , the l o c a l heat t r a n s f e r c o e f f i c i e n t s are averaged and c a l c u l a t e d from E q . 4.14 f o r each segment of L a long Z and p l o t t e d a g a i n s t Z . F i g u r e 4.10 shows a p l o t of the L - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t a g a i n s t Z f o r d i f f e r e n t v a l u e s of L . I t i s apparent t h a t the model p r e d i c t i o n s are not o v e r l y s e n s i t i v e to v a r i a t i o n s i n L , but t h a t i n c r e a s i n g L above the va lues o b t a i n e d from the two-probe exper iments i n Chapter 3 a g a i n r e s u l t s i n improved agreement wi th the e x p e r i m e n t a l d a t a . The i n f l u e n c e of d i f f e r e n t f a l l i n g v e l o c i t i e s of the s t r a n d s on the L - a v e r a g e d model p r e d i c t i o n s i s shown i n F i g u r e 4 . 1 1 . As e x p e c t e d , a h i g h e r f a l l i n g v e l o c i t y r e s u l t s i n h i g h e r p r e d i c t e d heat t r a n s f e r c o e f f i c i e n t s due to a s h o r t e r c o n t a c t time f o r the s t r a n d s at the w a l l . For the v e l o c i t y range of 1-2 m/s , i t can be seen from F i g u r e 4.11 t h a t the p r e d i c t i o n s are aga in not o v e r l y s e n s i t i v e to v a r i a t i o n s i n the f a l l i n g v e l o c i t y . The L - a v e r a g e d p r e d i c t i o n s of the model for d i f f e r e n t combinat ions of m and 5 are compared with e x p e r i m e n t a l da ta for the membrane w a l l (from F i g u r e 2.19) i n F i g u r e 4 .12 . The p r e d i c t e d p r o f i l e s show tha t the model i s l e s s s e n s i t i v e to v a r i a t i o n s i n m but q u i t e s e n s i t i v e to v a r i a t i o n s i n 5. I t can be seen from F i g u r e 4.12 tha t the bes t f i t g i v e n by the model 2 w i t h i n the l i m i t e d range i n v e s t i g a t e d i s for m=0.05 kg/m .s and 5=1 mm. It i s apparent that b e t t e r agreement would be a c h i e v e d i f 5 were chosen even s m a l l e r . However, an annulus t h i c k n e s s of 1 mm appears to be a l r e a d y s m a l l e r than r e p o r t e d v a l u e s . For -131-F i g u r e 4.10 In f luence of s t r a n d ' s r e s i d e n c e l e n g t h , L , on the p r e d i c t e d v a r i a t i o n s in L - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l s u r f a c e . m=0.05 kg /m^.s ; 5=1 mm. C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l data wi th same e x p e r i m e n t a l c o n d i t i o n s as i n F i g u r e 4 . 9 . -132-400 CN * £ 300-200 J 100-F i g u r e 4.11 In f luence of s t r a n d ' s f a l l i n g v e l o c i t y , U s , on the p r e d i c t e d v a r i a t i o n s i n L - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l s u r f a c e . S o l i d l i n e s : p e r i o d i c renewals of s t r a n d c o n t a c t (Eq. 4 . 1 ) ; m=0.05 k g / m 2 . s ; 5=1 mm, Broken l i n e s : no renewal of s t r a n d c o n t a c t . C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l data wi th same e x p e r i m e n t a l c o n d i t i o n s as in F i g u r e 4 . 9 . -133-400r £ ^300 200 m = 0.5 100 o o o o o o o 0.4 0.8 1.2 1.6 m F i g u r e 4.12 Comparison of p r e d i c t e d v a r i a t i o n s in L - a v e r a g e d heat t r a n s f e r c o e f f i c i e n t a long membrane w a l l s u r f a c e ( s o l i d l i n e s ) with e x p e r i m e n t a l data for two d i f f e r e n t m and 5. Broken l i n e : no renewal of s t r a n d c o n t a c t . C i r c l e s c o r r e s p o n d to e x p e r i m e n t a l data wi th same e x p e r i m e n t a l c o n d i t i o n s as i n F i g u r e 4 . 9 . -134-example, an annulus t h i c k n e s s of 5-10 mm can be i n f e r r e d from the da ta of Monceaux et a l . (1986) f o r a 144 mm diameter co lumn. S i m i l a r l y , an annulus t h i c k n e s s i n the order of 5-15 mm i n a 152 mm diameter column can be i n f e r r e d from the r e s u l t s o b t a i n e d by both B r e r e t o n (1987) and Rhodes e t a l . (1988). Recent e r o s i o n probe r e s u l t s o b t a i n e d by Grace e t a l . (1989b) i n the p i l o t - s c a l e u n i t d e s c r i b e d i n Chapter 2 a l s o suggest a t h i c k n e s s of 12-20 mm. I t i s apparent from F i g u r e 4.12 tha t a l though the model does g i v e the r i g h t order of c o e f f i c i e n t magnitude and p r e d i c t a c o r r e c t t r e n d of heat t r a n s f e r c o e f f i c i e n t , i t f a i l s to p r e d i c t the r a p i d drop in c o e f f i c i e n t s measured a long the membrane w a l l , u n l e s s 5 i s a l lowed to s h r i n k even f u r t h e r or L i s a l l owed to become very l a r g e . T h i s d i s c r e p a n c y can be r e a d i l y e x p l a i n e d by the p h y s i c a l c o n f i g u r a t i o n of the membrane w a l l s u r f a c e . As a l r e a d y d i s c u s s e d i n S e c t i o n 3 . 3 . 2 , the membrane w a l l s u r f a c e d i f f e r s from a smooth s u r f a c e i n t h a t i t o f f e r s some p r o t e c t i o n for the s t r a n d s such tha t they can move a long the membrane w a l l s u r f a c e for a much longer l e n g t h wi thout be ing d i s p e r s e d p r e m a t u r e l y . T h i s i m p l i e s tha t E q . 4 . 1 , o b t a i n e d for a smooth w a l l , w i l l p r o b a b l y not a p p l y w e l l to a membrane w a l l s u r f a c e . R a t h e r , the c h a r a c t e r i s t i c r e s i d e n c e l e n g t h of the p r o t e c t e d s t r a n d s shou ld approach the l e n g t h of the membrane w a l l . T h i s seems to be the case i n F i g u r e 4.12 where the broken c u r v e , o b t a i n e d by assuming the s t r a n d s to be i n c o n t a c t wi th the s u r f a c e over the whole l e n g t h of membrane w a l l , shows much improved agreement wi th the e x p e r i m e n t a l p r o f i l e . The remaining d i f f e r e n c e s between the da ta and the broken curve are p r o b a b l y -135-due to the f a c t tha t the f i n ( f l a t ) p a r t s of the membrane w a l l , where the q u a l i t a t i v e exper iment d e s c r i b e d i n S e c t i o n 3 . 3 . 2 i n d i c a t e s the p a r t i c l e c o n t a c t to be most f r e q u e n t , are l e s s e f f e c t i v e as t r a n s f e r s u r f a c e s than the tube (curved) p a r t s (Bowen et a l . , 1989) because of the i n c r e a s e d d i s t a n c e r e q u i r e d f o r heat c o n d u c t i o n . The v a r i a t i o n s of average heat t r a n s f e r c o e f f i c i e n t wi th suspens ion d e n s i t y f o r the membrane w a l l are compared wi th the model i n F i g u r e 4 .13 . Agreement wi th the data g e n e r a l l y improves when a s m a l l e r annulus t h i c k n e s s i s used i n the mode l . In a d d i -t i o n , agreement wi th the da ta seems to be b e t t e r at low suspen-s i o n d e n s i t i e s . However, the bes t agreement, i s a g a i n o b t a i n e d i f the s t r a n d s are assumed to s t a y at the membrane w a l l s u r f a c e for i t s e n t i r e l e n g t h as shown by the broken curve i n F i g u r e 4 .13 . The da ta of F e u g i e r e t a l . (1987) o b t a i n e d wi th a 0.95 m long heat t r a n s f e r s u r f a c e for three d i f f e r e n t p a r t i c l e s i z e s are compared with the model (m=0.05 kg/m . s , 5=1 mm) i n F i g u r e 4 .14 . No d e t a i l s on the heat t r a n s f e r s u r f a c e c o n f i g u r a t i o n were g i v e n by the a u t h o r s . Whi le e x c e l l e n t agreement wi th the 95 [im p a r t i c l e s i s o b t a i n e d , the model o v e r p r e d i c t s the da ta f o r 215 and 625 [im p a r t i c l e s . On the o ther hand , i f the s t r a n d s are assumed to r e s i d e at the w a l l f o r the whole l e n g t h o f the heat t r a n s f e r s u r f a c e , improved agreement i s o b t a i n e d wi th both 215 and 625 [im p a r t i c l e s , wh i l e agreement i s worse for the s m a l l e s t p a r t i c l e s . As shown i n the membrane w a l l c a s e , i t i s important to know the c o n f i g u r a t i o n of the heat t r a n s f e r s u r f a c e s at the column -136-susp F i g u r e 4.13 Comparison of model p r e d i c t i o n with e x p e r i m e n t a l data for the membrane w a l l from F i g u r e 2.14 with T S U S p = 4 1 0 C . S o l i d l i n e s : p e r i o d i c renewals of s t r a n d c o n t a c t (Eq. 4 . 1 ) ; m=0.05 k g / m ^ . s . Broken l i n e : no renewal of s t r a n d c o n t a c t . -137-F i g u r e 4.14 Comparison of model p r e d i c t i o n wi th the e x p e r i m e n t a l data of F e u g i e r et a l . (1987) f o r t h r e e p a r t i c l e s i z e s . Curves a : p e r i o d i c renewals of s t r a n d c o n t a c t (Eq. 4 . 1 ) ; m=0.05 k g / m 2 . s ; 5=1 mm. Curves b : no renewals of s t r a n d c o n t a c t . -138-w a l l and i t s e f f e c t on l o c a l s o l i d s f low p a t t e r n s i n order to make c o r r e c t p r e d i c t i o n s of heat t r a n s f e r c o e f f i c i e n t i n any § co lumn. So f a r i n t h i s t h e s i s , we have attempted to a p p l y one se t of measured l o c a l hydrodynamics i n our smooth c o l d model column (summarized i n S e c t i o n 4 .2 .1) i n the proposed model to p r e d i c t heat t r a n s f e r r e s u l t s f o r a wide range of columns used i n d i f f e r e n t s t u d i e s . I t i s c e r t a i n l y p o s s i b l e t h a t the l o c a l hydrodynamics i n v a r i o u s equipment may d i f f e r s u b s t a n t i a l l y from those o b t a i n e d i n our co lumn. T h i s may w e l l e x p l a i n some of the l a c k of agreement wi th e x p e r i m e n t a l da ta of o ther workers . However, even wi th t h i s l i m i t a t i o n , r easonab le agreement i s o b t a i n e d between model p r e d i c t i o n s and e x p e r i m e n t a l r e s u l t s from a wide range of s t u d i e s , a l t h o u g h with some tendency , as wi th our own d a t a , to o v e r p r e d i c t i o n . I t i s perhaps f i t t i n g to add here that the use of P S U S p a s the independent v a r i a b l e i n the p r e s e n t model p r e d i c t i o n s i s a c h o i c e of convenience s i n c e a l l heat t r a n s f e r r e s u l t s (from p r e v i o u s workers and those i n t h i s t h e s i s ) show s t r o n g c o r r e l a -t i o n wi th P S U S p even at d i f f e r e n t h e i g h t s , a l t h o u g h with some T h i s p o i n t was demonstrated d r a m a t i c a l l y at one p o i n t when the exper iments d e s c r i b e d i n Chapter 3 were be ing c a r r i e d o u t . I n a d v e r t e n t l y , the probe was i n s t a l l e d at 9 0 ° to i t s u s u a l o r i e n t a t i o n , i . e . , w i th the wires c o n n e c t i n g the p l a t i n u m f i l m to the e l e c t r i c a l c i r c u i t at the top and bottom r a t h e r than at the s i d e s . The measured heat t r a n s f e r c o e f f i c i e n t s were about 30% lower than those determined p r e v i o u s l y under i d e n t i c a l c o n d i t i o n s , presumably due to the f a c t that the top w i r e , which p r o t r u d e d about 0.1 mm from the s u r f a c e , d e f l e c t e d p a r t i c l e s away from the probe s u r f a c e as they descended. Note that t h i s e x p e r i e n c e a l s o suggested tha t heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d bed u n i t s may be s e n s i t i v e to the roughness of the t r a n s f e r s u r f a c e . -139-e x c e p t i o n s as i n F i g u r e 3 . 1 1 . In r e a l i t y , p i s r e l a t e d to a 1 susp whole se t of hydrodynamic parameters such as s u p e r f i c i a l gas v e l o c i t y , s o l i d s c i r c u l a t i o n r a t e , p a r t i c l e d e n s i t y , p a r t i c l e s i z e d i s t r i b u t i o n , gas d e n s i t y and v i s c o s i t y , as w e l l as column e x i t geometry, which appear i n E q . 1.1 but do not appear e x p l i c i t l y i n the mode l . These parameters are i n d i r e c t l y accounted for i n the model through the v a r i a b l e p . A l though ^ "susp ^ the s i g n i f i c a n t c o r r e l a t i o n between h and p has been ^ ' s u s p demonstrated to be somewhat f o r t u i t u o u s , as d i s c u s s e d i n S e c t i o n 3 . 3 . 1 , use of P s u g p serves to decouple heat t r a n s f e r from the hydrodynamics . The p r e l i m i n a r y r e s u l t s from the model p r e s e n t e d here are e n c o u r a g i n g , though more r e s u l t s are needed to v e r i f y tha t p i s ab le to account f o r , on i t s own, a wide v a r i a t i o n ' susp i n hydrodynamic and geometr ic v a r i a b l e s . Compared with the e x i s t i n g model of Basu and Nag (1987) or Subbarao and Basu (1986), the p r e s e n t model i s more r e a l i s t i c and c o r r e s p o n d s b e t t e r to what i s observed p h y s i c a l l y . Whi le both models make use of the packet t h e o r y , the s i m i l a r i t y between the two models s tops at E q s . 4.5 and 4.6 in t h i s t h e s i s . A major weakness i n the Basu and Nag model i s tha t t h e i r e x p r e s s i o n for the r e s i d e n c e time of s t r a n d s at the w a l l i s d e r i v e d from the d o u b t f u l concept of t r e a t i n g v o i d r e g i o n s i n a f a s t bed as gas bubbles i n a b u b b l i n g bed grown to t h e i r maximum s t a b l e s i z e s . Another major d i f f e r e n c e between the two models i s tha t the p r e s e n t model p r e d i c t s s u c c e s s f u l l y the e f f e c t of heat t r a n s f e r s u r f a c e l e n g t h on the heat t r a n s f e r c o e f f i c i e n t measured. T h i s i s not the case for the Basu and Nag mode l . -140-The model of S e k t h i r a e t a l . (1988) a l s o f a i l s to account for the e f f e c t of heat t r a n s f e r s u r f a c e l e n g t h . Moreover , s i n c e t h e i r model i s based on heat t r a n s f e r to s i n g l e p a r t i c l e s , the p a c k i n g of p a r t i c l e s at the w a l l s u r f a c e i s c r i t i c a l to the model p r e d i c t i o n s . T h i s i n f o r m a t i o n i s , at b e s t , d i f f i c u l t to determine e x p e r i m e n t a l l y i n a c i r c u l a t i n g f l u i d i z e d bed . A l s o , the S e k t h i r a e t a l . model i s l i k e l y to underes t imate the heat t r a n s f e r c o e f f i c i e n t for long r e s i d e n c e t imes s i n c e on ly heat t r a n s f e r to the f i r s t l a y e r of p a r t i c l e s i s i n c l u d e d i n the m o d e l . To c o n c l u d e , heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds has been mode l l ed by r e c o g n i z i n g the importance of s t r a n d s i n the annulus of an o v e r a l l c o r e - a n n u l u s f low s t r u c t u r e . Heat i s assumed to be t r a n s f e r r e d between the s u r f a c e and the s t r a n d s by t r a n s i e n t c o n d u c t i o n , wi th a w a l l c o n t a c t r e s i s t a n c e which i s f i t t e d e m p i r i c a l l y . The s t r a n d s are assumed to t r a v e l down the w a l l f or a f i x e d d i s t a n c e b e f o r e b r e a k i n g up , m i x i n g w e l l wi th o ther annulus p a r t i c l e s , and r e f o r m i n g aga in at the s u r f a c e . The vo idages and the r e s p e c t i v e t ime f r a c t i o n s of w a l l coverage of s t r a n d s at the w a l l have been e s t i m a t e d based on e x p e r i m e n t a l v a l u e s . The r e s u l t i n g model can account f o r both the i n f l u e n c e of heat t r a n s f e r s u r f a c e l e n g t h as w e l l as the p a r t i c l e s i z e e f f e c t . I t g i v e s r e a s o n a b l e agreement wi th a wide range of p u b l i s h e d e x p e r i m e n t a l d a t a . However, the i n t e r i o r c o n f i g u r a t i o n of heat t r a n s f e r s u r f a c e i s c l e a r l y i m p o r t a n t . The e f f e c t of the i n t e r i o r geometry on the f low p a t t e r n of p a r t i c l e s must be taken i n t o account for non-smooth s u r f a c e s l i k e membrane w a l l to g i v e improved agreement wi th e x p e r i m e n t a l r e s u l t s . -141-CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 5.1 CONCLUSIONS T h i s t h e s i s r e p r e s e n t s an attempt to e l u c i d a t e the heat t r a n s f e r p r o c e s s i n c i r c u l a t i n g f l u i d i z e d beds . To accompl i sh t h i s g o a l , we approached the problem from two f r o n t s . F i r s t , a wide range of e x p e r i m e n t a l d a t a was o b t a i n e d from a p i l o t - s c a l e c i r c u l a t i n g f l u i d i z e d bed combustor as d e t a i l e d i n Chapter 2. At the o u t s e t of t h i s s t u d y , there was a severe l a c k of heat t r a n s f e r d a t a f o r c i r c u l a t i n g f l u i d i z e d beds , e s p e c i a l l y for systems at e l e v a t e d t e m p e r a t u r e s . T h i s was f u r t h e r compounded by wide s c a t t e r among the d a t a a v a i l a b l e t h e n . Not o n l y was t h i s p e r p l e x i n g to r e s e a r c h e r s , but i t a l s o e s s e n t i a l l y l i m i t e d the d e s i g n of c i r c u l a t i n g f l u i d i z e d bed r e a c t o r to a c o s t l y e m p i r i c a l p r o c e s s . The s t r o n g i n f l u e n c e of the a r e a - a v e r a g e d suspens ion d e n s i t y on average heat t r a n s f e r c o e f f i c i e n t i n c i r c u l a t i n g f l u i d i z e d beds r e p o r t e d e a r l i e r i s conf i rmed by our r e s u l t s i n Chapter 2. In a d d i t i o n , our r e s u l t s a l s o show a r e l a t i v e l y weak i n f l u e n c e of the s u p e r f i c i a l gas v e l o c i t y . R a d i a t i o n i s found to be an important f a c t o r at suspens ion temperatures over 400 C . R e s u l t s a l s o show tha t i t i s r easonab le and p r a c t i c a l to t r e a t the heat t r a n s f e r i n c i r c u l a t i n g f l u i d i z e d beds by s e p a r a t i n g the t o t a l heat t r a n s f e r c o e f f i c i e n t i n t o three s epara te but a p p r o x i -mate ly a d d i t i v e components, namely, the gas c o n v e c t i v e component, the p a r t i c l e c o n v e c t i v e component, and the r a d i a t i v e component. -142-More i m p o r t a n t l y , the v e r t i c a l l e n g t h of heat t r a n s f e r s u r f a c e i s shown to be an important parameter due to the p r e d o m i n a n t l y downflowing l a y e r of p a r t i c l e s at the column w a l l . E a r l i e r seemingly d i s c r e p a n t e x p e r i m e n t a l da ta are r e c o n c i l e d by t a k i n g i n t o account the e f f e c t of the heat t r a n s f e r s u r f a c e l e n g t h . Second, i n p a r a l l e l wi th the e f f o r t of Chapter 2, the heat t r a n s f e r mechanisms i n c i r c u l a t i n g f l u i d i z e d bed were s t u d i e d i n a t r a n s p a r e n t c o l d model u n i t . Ins tantaneous and s imul taneous l o c a l measurements were o b t a i n e d u s i n g m i n i a t u r e i n s t a n t a n e o u s heat t r a n s f e r probes and a c a p a c i t a n c e p r o b e . R e s u l t s i n Chapter 3 show that the sudden peaks i n measured heat t r a n s f e r c o e f f i -c i e n t are d i r e c t l y caused by the a r r i v a l s of p a r t i c l e s t r a n d s at the probe s u r f a c e , c o n f i r m i n g the important r o l e p l a y e d by s o l i d p a r t i c l e s i n the heat t r a n s f e r p r o c e s s . T h i s h e l p s to e x p l a i n the s t r o n g i n f l u e n c e of a r e a - a v e r a g e d suspens ion d e n s i t y on l o c a l heat t r a n s f e r c o e f f i c i e n t a long the co lumn. Moreover , the d i f f e r e n t c h a r a c t e r i s t i c s i n the heat t r a n s f e r c o e f f i c i e n t t r a c e s measured at d i f f e r e n t p o s i t i o n s a long the column suggest tha t d i f f e r e n t hydrodynamics are at work t h e r e . T h i s f u r t h e r i m p l i e s tha t the r e l a t i v e l y s i m i l a r v a r i a t i o n s of t ime-averaged heat t r a n s f e r c o e f f i c i e n t wi th suspens ion d e n s i t y observed at three d i f f e r e n t v e r t i c a l column p o s i t i o n s are f o r t u i t o u s , due to a p r o b a b l e c o u n t e r - b a l a n c i n g of d i f f e r e n t c o n t r o l l i n g f a c t o r s . In a d d i t i o n , c r o s s - c o r r e l a t i o n r e s u l t s o b t a i n e d from two heat t r a n s f e r probes suggest that there e x i s t s a c h a r a c t e r i s t i c r e s i d e n c e l e n g t h for s t r a n d s i n the w a l l l a y e r . A r a t h e r wide range of s t r a n d f a l l i n g v e l o c i t i e s was measured wi th an average -143-v e l o c i t y of 1.26 m / s . With the c o m p l e t i o n of the above two s t u d i e s , and wi th the emerging consensus on hydrodynamics among r e s e a r c h e r s , a heat t r a n s f e r model for c i r c u l a t i n g f l u i d i z e d beds i s proposed i n Chapter 4. The o v e r a l l f low s t r u c t u r e of the bed i s assumed to be c o r e - a n n u l u s , wi th a d i l u t e upf low core and a dense downflow annulus w a l l l a y e r . P a r t i c l e s i n the annulus are assumed to congregate i n t o waves of s t r a n d s wi th d i f f e r e n t v o i d a g e s . These s t r a n d s are f u r t h e r assumed to undergo a r e p e a t i n g p r o c e s s of f o r m a t i o n , movement down a long the w a l l , and f i n a l l y d i s i n t e g r a -t i o n and m i x i n g wi th other annulus p a r t i c l e s . Dur ing the p e r i o d of c o n t a c t , heat i s t r a n s f e r r e d between the w a l l and the s t r a n d s by t r a n s i e n t heat c o n d u c t i o n i n t o a s e m i - i n f i n i t e medium wi th a w a l l c o n t a c t r e s i s t a n c e . Both the voidage and time f r a c t i o n of w a l l coverage of the s t r a n d s were e s t i m a t e d from e x p e r i m e n t a l measurements. The r e s u l t i n g model g i v e s r e a s o n a b l e agreement wi th a wide range of p u b l i s h e d d a t a . The agreement w i th da ta from non-smooth heat t r a n s f e r s u r f a c e ( e . g . , membrane wal l ) i s , however, improved when the e f f e c t of such a s u r f a c e on the f low p a t t e r n of p a r t i c l e s i s taken i n t o a c c o u n t . 5.2 RECOMMENDATIONS FOR FUTURE WORK The bu lk of the p r e s e n t work concerns heat t r a n s f e r s u r f a c e s l o c a t e d at the w a l l of the co lumn. Whi le t h i s i s the most common and by f a r the most important area f o r l o c a t i n g heat t r a n s f e r s u r f a c e s , some des igns a l s o u t i l i z e a d d i t i o n a l t r a n s f e r s u r f a c e s -144-suspended i n s i d e the co lumn. I t i s not c l e a r whether the r e s u l t s and c o n c l u s i o n s o b t a i n e d here can a p p l y to those suspended i n t e r n a l s u r f a c e s . There should be f u t u r e work to s tudy and c h a r a c t e r i z e the d i f f e r e n c e s and s i m i l a r i t i e s i n c i r c u l a t i n g f l u i d i z e d bed heat t r a n s f e r between these two k i n d s of t r a n s f e r s u r f a c e . F u r t h e r m o r e , an i n t e r e s t i n g i n d i r e c t o b s e r v a t i o n from F i g u r e 4.12 i s that a v e r t i c a l membrane w a l l , which i s commonly used i n c o m m e r c i a l - s c a l e b o i l e r s , a l t h o u g h s e n s i b l e i n terms of m i n i m i z i n g tube e r o s i o n and p a r t i c l e a t t r i t i o n p r o b l e m s , i s a c t u a l l y not a very e f f i c i e n t heat t r a n s f e r s u r f a c e c o n f i g u r a t i o n s i n c e i t promotes l i t t l e p a r t i c l e r e n e w a l , as demonstrated by the r a p i d drop i n the l o c a l heat t r a n s f e r c o e f f i c i e n t p r o f i l e . Indeed, as suggested by the model p r e d i c t i o n s i n F i g u r e 4 .12 , i f the renewal r a t e of p a r t i c l e s (or s t rands ) i s i n c r e a s e d , h i g h e r heat t r a n s f e r c o e f f i c i e n t s can be o b t a i n e d . Thus , f u t u r e work shou ld study ways of promot ing renewal of p a r t i c l e s to membrane w a l l s u r f a c e s . I t should a l s o i n v e s t i g a t e the d e s i g n of more e f f i c i e n t heat t r a n s f e r s u r f a c e s . -145-NOMENCLATURE separation distance between two heat transfer probes, (m) length defined in Figure 3 . 16 , (m) length defined in Figure 3 . 16 , (m) length defined in Figure 3 . 16 , (m) 2 area of heat transfer probe, (m ) 2 areas defined in Figure 4 . 2 , (m ) vertical length of heat transfer surface, (m) Biot number of membrane wall f i n , (=h.w /k^S^) variable in Eq. 4.12 specific heat capacity of particles, (J/kg.K) surface-volume mean particle size, (/tm) average diameter between sieves, (jU.m) emissivity of heat transfer surface emissivity of suspension time fraction of wall coverage by strand time fraction of wall coverage by strand in i voidage interval wall coverage time fractions defined in Figure 4 2 acceleration due to gravity, (9.81 m/s ) 2 solids circulation flux, (kg/m .s) time-averaged length-averaged heat transfer coefficient, (W/m2.K) effective heat transfer coefficient for strand, (W/m2.K) 2 gas convective component of h, (W/m .K) -146-h^ - i n s t a n t a n e o u s heat t r a n s f e r c o e f f i c i e n t , (W/m .K) h - o v e r a l l heat t r a n s f e r c o e f f i c i e n t between w a l l and s t r a n d , (W/m 2 .K) 2 h - p a r t i c l e c o n v e c t i v e component of h , (W/m .K) 2 nr a d - r a d i a t i v e component of h , (W/m .K) h - heat t r a n s f e r c o e f f i c i e n t between w a l l and core averaged over l e n g t h L , (W/m 2 .K) 2 h w - w a l l c o n t a c t heat t r a n s f e r c o e f f i c i e n t , (W/m .K) 2 h^ - l o c a l heat t r a n s f e r c o e f f i c i e n t , (W/m .K) h z - heat t r a n s f e r c o e f f i c i e n t averaged over the l e n g t h of t r a n s f e r s u r f a c e from Z = 0 to Z=Z, (W/m 2 .K) I - e l e c t r i c c u r r e n t through probe c i r c u i t , (A) k g - e f f e c t i v e thermal c o n d u c t i v i t y of s t r a n d , (W/m.K) - thermal c o n d u c t i v i t y of membrane w a l l f i n , (W/m.K) k - thermal c o n d u c t i v i t y of gas , (W/m.K) k - thermal c o n d u c t i v i t y of p a r t i c l e s , (W/m.K) P L - c h a r a c t e r i s t i c r e s i d e n c e l e n g t h of s t r a n d at w a l l , (m) 2 m - s o l i d s f l u x f r o m / t o core t o / f r o m a n n u l u s , (kg/m .s) n - parameter i n E q . 4.18 P - p r e s s u r e , (kPa) q - i n s t a n t a n e o u s power d i s s i p a t e d by heat t r a n s f e r p r o b e , (W) q = - r a t e of heat t r a n s f e r per u n i t area between w a l l and s t r a n d , (W/m2) Js t i l Q . - heat t r a n s f e r r e d per u n i t area to s t r a n d i n i " S I •1 3 Q 2 - secondary a i r f l o w r a t e , (m / s ) voidage i n t e r v a l f or l e n g t h L , (J /m 2 ) Q - heat t r a n s f e r r e d per u n i t area to a l l s t r a n d s for l e n g t h L , ( J /m 2 ) 3 Q, - p r i m a r y a i r f l o w r a t e through d i s t r i b u t o r , (m / s ) -147-cross-correlation coefficient maximum cross-correlation coefficient parameter defined in Figure 3.16 reference electrical resistance, (Q) electrical resistance of heat transfer probe, {Q) standard deviation of instantaneous heat transfer coefficient, (W/m^ .K) time, (s) residence time of strand at wall, (s) temperature, (K) average temperature of annulus for length L, (K) temperatures of annulus at positions Z_, Z.., Z„ respectively, (K) temperature of core, (K) outlet water temperature of heat transfer surface, (K) temperature of heat transfer probe, (K) temperature of heat transfer surface, (K) temperature of gas-solids suspension, (K) temperature of wall surface, (K) superficial gas velocities above and below secondary air inlet respectively, (m/s) average falling velocity of strand, (m/s) voltages before and after heat transfer probe respectively, (V) half-width of membrane wall f i n , (m) heat penetration distance into strand, (m) weight fraction of particles with average size d ^  distance from tube axis to axis of column, (mm) -148-h a l f - w i d t h of co lumn, (mm) h e i g h t of column above d i s t r i b u t o r , (m) p o s i t i o n a l ong membrane w a l l measured downward from i t s t o p , (m) p o s i t i o n s a long w a l l s u r f a c e d e f i n e d i n F i g u r e 4 .4 , (m) e f f e c t i v e thermal d i f f u s i v i t y of s t r a n d , ( = V p p c p p ( l - e ) ) , ( m 2 / s ) t h i c k n e s s of a n n u l u s , (mm) t h i c k n e s s of membrane w a l l f i n , (m) t o t a l p r e s s u r e drop over co lumn, (kPa) vo idage of s t r a n d average vo idage of annulus t h i vo idage i n t e r v a l of s t r a n d vo idages d e f i n e d i n F i g u r e 4.2 3 p a r t i c l e d e n s i t y , (kg/m ) suspens ion d e n s i t y at a g i v e n l e v e l averaged over column c r o s s - s e c t i o n , (kg/m 3 ) -8 2 4 S t e f a n - B o l t z m a n n c o n s t a n t , (5.672 x 10 W/m . 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Fundamenta l s , 3, 324-328 (1964). -156-APPENDIX 1 Sample Calculations and Error Estimation of Suspension-to-Surface Heat Transfer Coefficient from Membrane Wall Let h0 be the hi be the u 0 be the be the Ai be the ro be the r i be the w be the Q be the Tin be the Tout be the Tsusp be the p be the cp be the Sr be the k be the *t be the h.t. coefficient based on outside area, 4 tubes, 4 W/m.K @40 C) or, Rate of heat transferred Rate of heat from suspension into = absorbed by cooling water cooling water U A (T - (T +T. )/2) = pc Q(T -T. ) (Al.l) o ov susp v out i n " ' ^ p v out in' v ; which can be rearranged to give pc Q T , - T. U - ?LE_ 2«t IB ( A 1 . 2 ) o A T - (T .+T. )/2 o susp out in Substituting Ts u s p=860±l C, Tq u t=65.3±0.1 C, Tin=10±0.1 C, Ao=0.314±0.016 m-S Q=1.25xl0"4±4.8xl0-7 m3/s into Eq. A1.2 gives ri - (992. 2)(1. 25x10 4)(4175) 65. 3-10 _ ,2 Uo 07314 860-75.3/2 ~ 1 1 0'9 W / m 'K -157-Us ing the e r r o r e s t i m a t i o n procedure suggested by Holman (1984), i t can be shown t h a t the e x p e r i m e n t a l u n c e r t a i n t y i n U i s about 5% f o r the t y p i c a l c o n d i t i o n s g i v e n above. ( The c o n v e c t i v e heat t r a n s f e r c o e f f i c i e n t i n s i d e c o o l i n g t u b e s , h^ , can be o b t a i n e d from S l e i c h e r and Rouse (1975): Nu = 5 + 0.015 Re m P r n (A1.3) where Now m = 0.88 - 0.24/(4 + Pr) (A1.4) n = 0.333 + 0.5 exp(-0 .6 Pr) (A1.5) Re = pQ/27T^ri = (992.2) (1.25x10 )/21T(658X10 D ) (0.00695) = 4316.4 • Pr = C p / i / k = (4175) (658x l0~ D ) / ( 0 .633 ) = 4.34 m = 0.88 - 0 .24/(4+4.34) = 0.851 n = 0.333 + 0.5 e x p ( - 0 . 6 ( 4 . 3 4 ) ) = 0.370 I t f o l l o w s from E q . A1.3 t h a t Nu = h i ( 2 r i ) / k = 5 + 0 . 0 1 5 ( 4 3 1 6 . 4 ) w , O D ( 4 . 3 4 ) W , J / = 37.0 Thus , h . = N u . k / 2 r i 1 = (37.0) (0 .633) /2(0 .00695) = 1686.0 W / m 2 . K The three c o e f f i c i e n t s (h , h . , U ) are r e l a t e d by v o l o 2 l n ( r / r . ) 1 + - + (A1.6) U A h.A. 27TkJ_ h A o o 1 I t o o where Ai = 27Tri AQ = 27Tr0 -158-E q . A1.6 can be r e a r r a n g e d to g i v e 1 1 1 r I n ( r / r . ) o h U h . l r . l o o 1 1 0.01065 0.00695 ln (0 .01065 /0 .00695) 14 .4 /0 .01065 110.9 1686.0 2 = 0.007793 m K/W The s u s p e n s i o n - t o - s u r f a c e heat t r a n s f e r c o e f f i c i e n t i s t h e r e f o r e T h i s c o e f f i c i e n t i s based on a s i m p l i f i e d geometry of a complete tube wi thout f i n s . In r e a l i t y , the geometry (with f i n s and o n l y about h a l f the tube exposed) i s more complex. An e s t i m a t e of the e r r o r i n v o l v e d i n u t i l i z i n g the s i m p l i f i e d geometry can be o b t a i n e d from Model 2 of Bowen et a l . (1989). For the above c o n d i t i o n s , t h i s l eads to hQ=142 W/m^.K, which d i f f e r s by 11% from the above v a l u e . Another source of u n c e r t a i n t y i s i n u t i l i z i n g the S l e i c h e r and Rouse e q u a t i o n to c a l c u l a t e the i n s i d e heat t r a n s f e r c o e f f i c i e n t , e s p e c i a l l y i n the range of Re between 4000 and 10000. Even i f the va lue of h^ were i n e r r o r by 20%, i t can be shown tha t the e r r o r i n h Q i s l e s s than 3% for the t y p i c a l c o n d i t i o n s g i v e n above. -159-APPENDIX 2 Tabulation of Experimental Heat Transfer Coefficient Data A. Section 2.2 (Membrane Walls) (U/L - Upper/Lower surface) d P (fin) T susp (C) out (C) U (m/s) ° 1 (m/s) V Q 1 G s 2 (kg/m .s) P ' susp (kg/m 3 ) h (W/m 2 .K u 188 386 35 5.0 5.0 0.0 9.3 35.2 L 188 410 36 5.0 5.0 0.0 - 14.1 37.3 U 188 260 34 4.0 4.0 0.0 - 14.5 35.8 U 188 266 35 4.1 4.1 0.0 - 15.7 44.0 U 188 181 29 4.6 1.9 1.5 7.0 16.1 43.7 • 188 319 37 4.4 4.4 0.0 — 18.3 44.9 U 188 177 29 4.6 1.9 1.5 7.9 18.5 48 .8 U 188 259 36 3.9 3.9 0.0 - 20.2 51.7 U 188 327 37 4.4 4.4 0.0 - 20.5 49. 3 L 188 349 34 6.2 5.7 0.1 13.8 25.0 43.4 U 188 333 34 6.2 5.7 0.1 13 .8 25. 4 51.2 U 188 284 33 4.5 4.1 0.1 10. 5 28.8 54.0 U 188 312 38 4.3 4.3 0.0 - 30 .6 61.4 L 188 272 37 4.0 4.0 0.0 - 30.9 52.3 U 188 191 34 4.3 4.3 0.0 - 32.1 63.7 L 188 276 39 4.1 4.1 0.0 - 37.6 60.2 L 188 186 31 4.6 1.9 1.5 7.0 37.2 60.2 L 188 333 42 4.4 4.4 0.0 - 38.1 69.2 L 188 340 44 4.4 4.4 0.0 - 40.7 87.2 U 188 282 36 4.9 4.4 0.1 15.9 41.2 68.4 U 188 309 37 6.0 5.5 0.1 17.4 41.5 72.1 U 188 198 27 4.4 4.4 0.0 - 42.9 64.0 u 188 275 36 4.7 4.3 0.1 15.8 43.7 76.6 L 188 182 31 4.6 1.9 1.5 7.9 48 . 0 65.6 L 188 293 36 4.5 4.1 0.1 10.5 54.6 83.8 L 188 267 44 3.9 3.9 0.0 - 55.9 114.1 L 188 318 39 6.0 5.5 0.1 17.4 56.3 88 . 4 L 188 196 37 4.3 4.3 0.0 - 60.2 91.7 • 188 298 39 5.7 5.2 0.1 27.3 63.6 93.4 U 188 187 33 5.6 2.9 1.0 27.5 69.9 87.6 U 188 306 41 5.9 5.3 0.1 37.7 75. 5 114.2 U 188 262 37 6.7 5.0 0.4 46.6 76 . 1 104. 2 L 188 270 37 6.7 5.0 0 . 4 46.6 79 . 3 98.9 L 188 313 43 5.9 5.3 0.1 37.7 86.3 150.2 L 188 305 41 5.7 5.2 0.1 27.3 87 . 4 137.0 U 188 297 42 5.8 5.3 0.1 39.6 8 7: 4 117.7 L 188 289 43 4.9 4.4 0.1 15.9 89.6 155.9 L 188 202 41 4.4 4.4 0.0 - 106.2 130.1 -160-d P (Atm) T susp (C) out (C) U (m/s) U l (m/s) Q 2 / Q L G s 2 (kg/m .s) p •susp (kg/m 3 ) h (W/m 2 .K u 188 253 38 6.6 4.8 0.4 62.5 109.4 120.1 u 188 240 38 6.5 4.7 0.4 68.7 114.6 135.3 L 188 302 47 5.8 5.3 0.1 39.6 122.3 191.8 L 188 259 41 6.6 4.8 0.4 62.5 123.6 157.1 L 188 190 37 5.6 2.9 1.0 27.5 127.4 172.4 L 188 319 53 4.3 4.3 0.0 - 130.9 239.5 L 188 281 45 4.7 4.3 0.1 15.8 132.2 202.0 L 188 245 44 6.5 4.7 0.4 68.7 171.5 250.7 U 356 363 35 4.8 4.8 0.0 - 10.8 41.0 U 356 404 34 5.2 5.2 0.0 - 12.7 29. 3 U 356 373 34 4.7 4.7 0.0 - 13.9 37.3 U 356 390 35 5.0 5.0 0.0 — 14.6 33.6 U 356 379 35 4.8 4.8 0.0 - 14.9 37.9 U 356 380 34 4.8 4.8 0.0 - 15. 2 42.3 U 356 351 34 4.6 4.6 0.0 - 15.3 31.7 L 356 408 38 4.8 4.8 0.0 - 17.6 34.9 L 356 435 36 5.2 5.2 0.0 - 21.1 40.9 L 356 418 37 5.0 5.0 0.0 - 23.3 44.1 L 356 398 38 4.7 4.7 0.0 - 23.8 41.7 L 356 402 39 4.8 4.8 0.0 - 25.2 45.7 L 356 429 38 6.4 6.4 0.0 - 26 .8 41. 9 U 356 409 38 6.4 6.4 0.0 - 28.4 40.8 u 356 385 37 6.1 6.1 0.0 - 29.0 60.5 u 356 345 34 5.8 5.8 0.0 - 30.2 58 .7 u 356 367 37 5.9 5.9 0.0 - 31.7 66.2 L 356 401 40 4.8 4.8 0.0 - 33.9 56.4 u 356 404 38 6.3 6.3 0.0 - 34.2 49.5 u 356 398 37 6.1 6.1 0.0 - 38.0 44.6 u 356 374 38 6.0 6.0 0.0 - 38 .1 57.0 L 356 368 39 4.6 4.6 0.0 - 38 . 5 71.1 L 356 415 40 6.3 6.3 0.0 - 50. 5 99.4 L 356 354 40 5.8 5.8 0.0 - 64.8 101.2 L 356 379 40 5.9 5.9 0.0 - 64.8 81.1 L 356 382 47 6.0 6.0 0.0 - 88.6 165.3 B . S e c t i o n 2.3 (Tube) (G not determined) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ g d T T p susp out u L Q 2 / Q x y / y o (fim) (C) (C) (m/s) (m/s) susp h (kg/m 3 ) (W/m 2 .K) 241 877 48 8.6 4.3 1.0 0.92 51.4 176.8 241 883 40 8.6 4.3 1.0 0.92 18.8 135.9 -161-d P T susp out U ° 1 V Q 1 y / y 0 O •susp h (C) (C) (m/s) (m/s) (kg/m 3 ) (W/m 2 .K 241 883 46 8.6 4.3 1.0 0. 92 26.1 165.3 241 879 54 8.6 4.3 1.0 0.92 60.4 201.5 241 875 51 8.6 4.3 1.0 0.92 68.6 191.8 241 870 54 8.6 4.3 1.0 0.92 60.4 201.8 241 887 45 8.6 4.3 1.0 0.92 41.6 158.6 241 886 52 8.6 4.3 1.0 0.92 49.0 191.9 241 883 37 8.6 4.3 1.0 0.92 11.4 122. 3 241 875 38 8.6 4.3 1.0 0.92 6.5 131.5 241 706 28 7.4 3.8 0.9 0.92 19.6 109.4 241 690 26 7.4 3.8 0.9 0.92 9.8 96.6 241 708 27 7.4 3.8 0.9 0.92 15.5 104.8 241 701 33 7.4 3.8 0.9 0.92 36.7 136.9 241 694 35 7.4 3.8 0.9 0.92 45.7 146.5 241 697 25 7.4 3.8 0.9 0.92 1.6 93.0 241 708 27 7.4 3.8 0.9 0.92 11. 4 102.3 241 708 27 7.4 3.8 0.9 0.92 12.2 102.6 241 699 34 7.4 3.8 0.9 0.92 46.5 145.6 241 699 35 7.4 3.8 0.9 0.92 44.9 145.7 241 700 33 7.4 3.8 0.9 0.92 39.2 143.1 241 696 32 7.4 3.8 0.9 0.92 34.3 135.6 241 596 23 6.6 3 . 5 0.9 0.92 21. 2 100.0 241 586 30 6.6 3 . 5 0.9 0 .92 40.8 124.4 241 588 31 6.6 3.5 0.9 0.92 49.0 125.7 241 590 34 6.6 3.5 0.9 0.92 57.1 147.5 241 590 33 6.6 3.5 0.9 0.92 65.3 142.6 241 588 32 6.6 3.5 0.9 0.92 40.8 130.8 241 581 25 6.6 3.5 0.9 0.92 24 . 5 91.3 241 588 29 6.6 3.5 0.9 0.92 35.1 116.3 241 580 24 6.6 3 . 5 0.9 0.92 12.2 84.1 299 367 32 6.5 5.5 0.2 0.92 18 . 0 68.4 299 321 33 6.5 5.5 0.2 0.92 32.7 78.1 299 316 31 6.5 5.5 0.2 0.92 34.3 79.1 299 303 34 6.5 5.5 0.2 0.92 36.7 77. 3 299 405 33 6.5 5.5 0.2 0.92 3.3 45.6 299 358 33 6.5 5.5 0.2 0.92 18.0 63.0 299 369 32 6.5 5.5 0.2 0 . 92 18.0 65.9 299 378 31 6.5 5.5 0.2 0.92 17.1 66.7 299 373 34 6.5 5.5 0.2 0.92 25.3 73.1 299 390 31 6.5 5.5 0.2 0.92 16. 3 67. 3 299 376 33 6.5 5.5 0.2 0.92 24.5 75.5 299 380 30 6.5 5.5 0.2 0.92 26 .1 68.6 299 382 31 6.5 . 5.5 0.2 0.92 23.7 72.4 299 386 34 6.5 5.5 0.2 0.92 26 . 9 78.7 299 399 35 6.5 5.5 0.2 0.92 4.1 44.1 299 427 32 6.5 5.5 0.2 0.92 4.1 50.6 299 426 35 6.5 5.5 0 . 2 0.92 4.9 44.6 299 369 30 6.5 5.5 0.2 0.92 37.5 86.1 299 361 32 6.5 5.5 0.2 0.92 35.9 86.8 -162-d P fim) T susp (C) T 4. out (C) U (m/s) U l (m/s) Q 2 / Q l y / y Q "susp (kg/m 3 ) h (W/m 2 .K 299 361 34 6.5 5.5 0.2 0.92 28.6 82.4 299 337 32 6.5 5.5 0.2 0.92 44.9 92.2 299 320 33 6.5 5.5 0.2 0.92 44.1 91.1 299 364 33 6.5 5.5 0.2 0.92 20.4 73.9 299 368 31 6.5 5.5 0.2 0.92 19.6 74.3 299 344 30 6.5 5.5 0.2 0.75 31.0 74.0 299 346 32 6.5 5.5 0.2 0.75 28.6 71.4 299 345 31 6.5 5.5 0.2 0.75 24. 5 63.6 299 350 31 6.5 5.5 0.2 0.75 18.8 62.4 299 356 34 6.5 5.5 0.2 0.75 27.8 79.3 299 365 32 6.5 5.5 0.2 0.75 20.4 63.3 299 369 33 6.5 5.5 0.2 0.75 19.6 60.6 299 342 35 6.5 5.5 0.2 0.75 6.5 41.8 299 339 34 6.5 5.5 0.2 0.75 3.3 47.7 299 357 33 6.5 5.5 0.2 0.75 4.1 45.2 299 309 33 6.5 5.5 0.2 0.75 36.7 76.2 299 292 •31 6.5 5.5 0.2 0.75 40.8 71.6 299 281 34 6.5 5.5 0.2 0.75 54. 7 90.4 299 342 35 6.5 5.5 0.2 0.75 30.2 66. 2 299 318 32 6.5 5.5 0.2 0.75 38.4 67.6 299 305 33 6.5 5.5 0.2 0.75 44.1 73.7 299 355 31 6.5 5.5 0 . 2 0. 50 18 .8 61.8 299 362 32 6.5 5.5 0.2 0. 50 22.9 63.0 299 363 31 6.5 5.5 0.2 0. 50 24. 5 70. 3 299 363 34 6.5 5.5 0.2 0. 50 20.4 63.1 299 326 32 6.5 5.5 0.2 0.50 40.8 74.1 299 291 33 6.5 5.5 0.2 0. 50 46.5 75.7 299 274 33 6.5 5.5 0.2 0.50 52.2 96.1 299 269 35 6.5 5.5 0.2 0.50 43.3 77.2 299 320 34 6.5 5.5 0.2 0.50 17.1 63.5 299 403 34 6.5 5.5 0.2 0. 50 3.3 50.8 299 416 32 6.5 5.5 0.2 0.50 3.3 50. 5 299 423 34 6.5 5.5 0.2 0. 50 2.4 47. 4 299 283 29 6.5 5.5 0.2 0.50 39.2 69.2 299 362 30 6.5 5.5 0.2 0.0 24.5 67.7 299 373 32 6.5 5.5 0.2 0.0 4.1 45.8 299 376 31 6.5 5.5 0.2 0.0 3.3 47. 3 299 368 34 6.5 5.5 0.2 0.0 10.6 54.4 299 362 32 6.5 5.5 0.2 0.0 11.4 50.3 299 312 33 6.5 5.5 0.2 0.0 42.4 72.2 299 302 31 6.5 5.5 0.2 0.0 36.7 69.7 299 280 29 6.5 5.5 0.2 0.0 56.9 76.3 299 266 28 6.5 5.5 0.2 0.0 53 .1 81.0 299 279 29 6.5 5.5 0.2 0.0 29. 4 68.5 299 282 30 6.5 5.5 0.2 0.0 36.7 77.3 299 346 33 6.5 5.5 0.2 0.0 28.6 65.8 227 864 36 9.3 5.5 0.7 0.92 31.8 135. 9 227 837 37 9.3 5.5 0.7 0.92 43.3 145.7 -163-d P T susp out U U l V Q 1 y/yQ O 'susp h fim) (C) (C) (m/s) (m/s) (kg/m 3 ) (W/m 2 .K 227 851 42 9.3 5.5 0.7 0.92 58.0 170.9 227 847 41 9.3 5.5 0.7 0.92 50.6 170.8 227 857 42 9.3 5.5 0.7 0.92 57.1 174.3 227 852 44 9.3 5.5 0.7 0.92 53.1 176.0 227 844 41 9.3 5.5 0.7 0.92 33.5 163.5 227 856 46 9.3 5.5 0.7 0.92 65.3 186.0 227 843 41 9.3 5.5 0.7 0.92 44.1 160.8 227 848 43 9.3 5.5 0.7 0.92 50.6 178.6 227 855 43 9.3 5.5 0.7 0.92 52.2 178.4 227 847 41 9.3 5.5 0.7 0.92 34.3 166.8 227 844 42 9.3 5.5 0.7 0.92 39.2 166.3 227 847 41 9.3 5.5 0.7 0.92 45.7 163.2 227 846 41 9.3 5.5 0.7 0.92 44.1 161. 3 227 860 34 9.3 5.5 0.7 0.92 11.4 126.3 227 855 33 9.3 5.5 0.7 0.92 7.3 119. 3 227 844 38 9.3 5.5 0.7 0.92 26.1 142.5 227 834 39 9.3 5.5 0.7 0.92 39. 2 156.5 227 837 38 9.3 5.5 0.7 0.92 31.8 152.8 227 843 -38 9.3 5.5 0.7 0.92 28 .6 150.8 227 836 39 9.3 5.5 0.7 0.92 30.2 155.6 227 833 39 9.3 5.5 0.7 0.92 28 .6 159.0 227 851 31 9.3 5.5 0 . 7 0 .92 1.6 111.6 227 853 31 9.3 5.5 0.7 0.92 4.9 118.8 227 837 31 9.3 5.5 0.7 0 .92 11.4 114.8 227 850 42 9.3 5.5 0.7 0.75 62.0 175.6 227 853 42 9.3 5.5 • 0.7 0.75 65.3 173.3 227 855 40 9.3 5.5 0.7 0.75 61.2 159.5 227 857 44 9.3 5.5 0.7 0.75 65.3 176.6 227 857 43 9.3 5.5 0.7 0.75 51.4 177.5 227 859 43 9.3 5.5 0 . 7 0.75 66. 9 175.1 227 853 37 9.3 5.5 0.7 0.75 26.1 140.8 227 868 32 9.3 5.5 0 . 7 0.75 9.8 116.5 227 849 32 9.3 5.5 0.7 0.75 35.9 147.7 227 852 38 9.3 5.5 0.7 0.75 49.0 149.0 227 854 39 9.3 5.5 0.7 0.75 38.4 157 . 7 227 851 38 9.3 5.5 0.7 0.75 53.9 149.9 227 850 37 9.3 5.5 0.7 0.75 28.6 141. 3 227 848 37 9.3 5.5 0.7 0.75 24.5 148 .1 227 850 39 9.3 5.5 0.7 0.75 50.6 164.4 227 849 40 9.3 5.5 0.7 0.75 62.0 165. 3 227 856 32 9.3 5.5 0.7 0.75 1.6 121.4 227 882 35 9.3 5.5 0 . 7 0.75 11.4 129.6 227 853 34 9.3 5.5 0.7 0.75 8 . 2 131.2 227 850 31 9.3 5.5 0 . 7 0.75 11.4 119.4 227 851 37 9.3 5.5 0.7 0.75 31.0 144.6 227 854 35 9.3 5.5 0.7 0.75 31.0 139.4 227 858 35 9.3 5.5 0.7 0.75 27.8 135. 5 227 845 36 9.3 5.5 0.7 0.50 19.6 143.2 -164-d P T susp out U ° 1 V Q 1 y / y 0 1 susp h (C) (C) (m/s) (m/s) (kg/m 3 ) (W/m 2 .K; 227 846 38 9.3 5.5 0.7 0.50 34. 3 154.6 227 850 37 9.3 5.5 0.7 0.50 32.7 147.6 227 850 36 9.3 5.5 0.7 0.50 23.7 141.2 227 852 38 9.3 5.5 0.7 0.50 44.9 152.1 227 859 38 9.3 5.5 0.7 0.50 28.6 150.1 227 860 38 9.3 5.5 0.7 0.50 34.3 150.5 227 855 43 9.3 5.5 0.7 0.50 57.1 180.9 227 858 42 9.3 5.5 0.7 0.50 71.0 173.6 227 861 44 9.3 5.5 0.7 0.50 66.1 185.8 227 864 45 9.3 5.5 0.7 0.50 73.5 189.1 227 865 46 9.3 5.5 0.7 0.50 63.7 189.8 227 864 44 9.3 5.5 0.7 0.50 54/7 178.5 227 865 43 9.3 5.5 0.7 0.50 65.3 178.8 227 864 41 9.3 5.5 0.7 0.50 52.2 162. 2 227 867 35 9.3 5.5 0.7 0. 50 1.6 128.8 227 852 38 9.3 5.5 0.7 0.50 8.2 150.7 227 875 37 9.3 5.5 0.7 0. 50 16.3 139.4 227 866 39 9.3 5.5 0.7 0. 50 2.4 152.4 227 864 41 9.3 5.5 0.7 0.0 8.2 156.1 227 868 38 9.3 5.5 0.7 0.0 2.4 141.4 227 857 38 9.3 5.5 0.7 0.0 4.1 143.5 227 860 39 9.3 5 . 5 0.7 0.0 3.3 145.6 227 850 38 9.3 5.5 0.7 0.0 4.9 140.4 227 851 39 9.3 5.5 0.7 0.0 29.4 147.7 227 851 45 9.3 5.5 0.7 0.0 49.0 176.2 227 864 40 9.3 5.5 0.7 0.0 20.4 151.0 227 862 39 9.3 5.5 0.7 0.0 19.6 146.8 227 849 40 9.3 5.5 0.7 0.0 10.6 153.7 227 861 45 9.3 5.5 0.7 0.0 57.1 173.1 227 862 42 9.3 5.5 0.7 0.0 44.1 160.5 227 864 46 9.3 5.5 0.7 0.0 46.5 181.1 227 865 48 9.3 5.5 0.7 0.0 68.6 189.1 227 864 43 9.3 5.5 0.7 0.0 42.4 164.5 227 865 50 9.3 5.5 0.7 0.0 66.9 202.7 227 866 48 9.3 5.5 0.7 0.0 80.8 191.5 227 864 50 9.3 5.5 0.7 0.0 78.4 200. 3 227 865 50 9.3 5.5 0.7 0.0 77.5 203.5 -165-C. Section 2.3 (Membrane Wall) (G not determined) s d T T . U U, Q _ / Q , p h p susp out 1 v 2 ' 1 "susp (fim) (C) (C) (m/s) (m/s) (kg/m 3 ) (W/m 2 .K) 222 876 50 9.5 4.8 1.0 47.4 138.7 222 907 58 9.5 4.8 1.0 59.7 160.0 222 880 50 9.5 4.8 1.0 40.9 138.3 222 875 47 9.5 4.8 1.0 33.2 128.2 222 878 52 9.5 4.8 1.0 49.7 145.7 222 877 51 9.5 4.8 1.0 44.6 143.2 222 863 43 9.5 4.8 1.0 16.1 115.6 222 874 54 9.5 4.8 1.0 60.7 156.3 222 886 58 9.5 4.8 1.0 69.8 166.5 222 893 53 9.5 4.8 1.0 54.4 147.3 222 873 43 9.5 4.8 1.0 4.1 116. 2 222 869 48 9.5 4.8 1.0 35.0 130.1 222 835 41 9.5 4.8 1.0 10.2 111.2 222 829 44 9.5 4.8 1.0 21.0 126.3 222 837 36 9.5 4.8 1.0 1.9 94.7 222 694 36 8.7 5.9 0.5 52.0 121.0 222 698 41 8.7 5.9 0.5 70.4 144.6 222 689 39 8.7 5.9 0 . 5 67.0 139.1 222 689 38 8.7 5.9 0.5 59.0 127.8 222 687 37 8.7 5.9 0.5 53.1 126.7 222 665 34 8 . 7 5.9 0.5 40.0 117.1 222 686 37 8.7 5.9 0.5 55.0 122.7 222 691 38 8.7 5.9 0.5 65.0 129.6 222 669 27 8.7 5.9 0.5 3.0 83.6 222 612 22 8.7 5.9 0.5 2.6 71.5 222 628 31 8.7 5.9 0.5 36.7 111.2 222 666 29 8.7 5.9 0.5 17.0 94.6 222 698 38 8.7 5.9 0.5 52.0 128.4 222 718 38 8.7 5.9 0.5 40 .0 124 .0 222 721 37 8.7 5.9 0.5 46.0 119.8 222 686 27 8.7 5.9 0.5 11.4 85.1 241 379 26 7.4 6.2 0.2 57.8 112.2 241 402 19 7.4 6.2 0.2 25.1 71.2 241 395 22 7.4 6.2 0.2 31.0 88 . 2 241 395 22 7.4 6.2 0.2 30.2 86.1 241 396 23 7.4 6 . 2 0 . 2 38.3 88.2 241 428 18 7.4 6.2 0 . 2 3.1 57.0 241 435 17 7.4 6 . 2 0.2 5.9 52. 2 241 443 16 7.4 6.2 0.2 2.5 47.7 241 416 18 7.4 6.2 0.2 10.0 58 .7 241 407 27 7.4 6.2 0.2 53.3 105.0 241 411 25 7.4 6.2 0.2 47.9 97.2 -166-D. S e c t i o n 3.3 (Instantaneous Heat T r a n s f e r Probe) (Q2/Q1=0-0; 0=7 m/s; dp=171 fim; Ts u s p=35 C; Tp b=83 C) Y G O h s s "susp (m) ( k g / m 2 . s ) (kg/m 3 ) (W/m 2 .K) (W/m 2 .K) 0.84 54.7 94.7 356.4 38.4 0.84 56.7 91.4 352.4 41.6 0.84 58.7 137.1 416.8 42.8 0.84 58.8 143.1 424.4 44. 5 0.84 59.0 154.3 423.5 41.2 0.84 58.5 146.4 422.6 42.6 0.84 59.6 152.4 423.2 42.8 0.84 60. 2 184.1 438 .3 32.2 0.84 60.1 179.5 439.4 41.0 0.84 53.7 74.9 308.1 42.1 0.84 51.9 81.5 323. 3 39.7 0.84 52.9 84.8 338 .6 37.3 0.84 5.1.2 90.1 351.4 34.2 0.84 51.9 92.7 344.7 38.7 0.84 52.6 113.9 362.2 39.2 0.84 54.1 106.6 358 .1 43.1 0.84 55.8 130.5 383.2 42.8 0.84 57.2 130.5 390.2 40.6 0.84 56.3 132.5 393.5 42.7 0.84 0.0 0.0 111.7 8 . 3 0.84 0.0 0.0 110.9 8.4 0.84 2.5 0.7 105.8 7.7 0.84 6.7 4.0 103.6 7.2 0.84 7.8 4.0 102.8 7.4 0.84 11.8 7.3 157.4 17.4 0.84 12.0 8.6 176.5 19.7 0.84 38 .6 38 . 4 236. 1 19.5 0.84 40.0 40. 4 225. 3 21.6 0.84 44. 3 56.3 253.5 32.5 0.84 43.2 57.0 260.7 32.5 0.84 35.5 39.7 234.3 24 .1 0.84 31.8 27.2 237.4 22.2 0.84 30.4 29.1 235.4 21.7 4.04 35.4 10.6 117.7 8.5 4.04 33.8 11.8 122.0 7.8 4.04 37.5 15.0 129. 7 9.5 4.04 38 . 4 17 .1 130.7 8 . 7 4.04 44. 1 19.7 155.7 11.6 4.04 43. 1 19.4 146.8 10.6 4.04 49.0 28 . 9 193.0 21.4 4.04 48 . 5 30.6 186.8 17.9 4.04 52. 5 37.7 229.9 29.4 4.04 51.6 36.8 207 .8 28.5 4.04 59.1 43.3 253 .3 30.8 -167-Y G O h s s • susp (m) ( k g / m 2 . s) (kg/m 3 ) (W/m 2 .K) (W/m 2 .K 4.04 58.8 45.0 261.0 35.3 4.04 62.8 49.8 276.3 33.7 4.04 59.0 52.4 277.4 34.0 4.04 67.5 60.6 296.3 35.8 4.04 59.8 58.3 291.1 36.6 4.04 34.6 15.6 142.3 12.2 8.61 27.1 30.5 232.4 19.8 8.61 26.7 31.8 238.7 17.2 8.61 32.2 37.1 240.7 18.3 8.61 31.1 41.7 254.1 20.0 8.61 35.0 45.7 245.4 17.6 8.61 35.9 45.0 249.2 17.1 8.61 39.7 54.3 258.5 22.3 8.61 41.0 53.7 255.4 21.7 8.61 40.8 59.0 274. 2 24.2 8.61 45.1 64.9 279.6 23.2 8.61 45.9 67.6 272.9 22.9 8.61 46.7 71.5 289.0 24.7 8.61 50.7 96.7 349.3 34.0 8.61 50.1 102.7 352.7 32.9 8.61 58.8 120.6 366.7 34.6 8.61 55.7 117.9 372.5 32.8 8.61 60.0 124.5 400 . 7 37.5 8.61 60.6 125.2 402.6 37.0 8.61 65.2 138 . 4 420 . 7 41.9 8.61 65.7 141.1 440.8 39.2 8.61 47.5 70.2 305.7 29.5 8.61 48.2 68 . 2 312.0 29.8 8.61 27.2 32.5 245.6 18.0 8.61 27.0 30.5 238 . 7 19.5 8.61 15.3 23.2 219.2 15.5 8.61 15.8 . 21.9 227.5 16.5 8.61 8.9 11.3 215.7 11.9 8.61 8.8 11.3 214.0 9.9 8.61 10.7 17.2 240.4 16.5 8.61 10.9 16.6 240.4 14.9 8.61 51.3 82.1 337 . 3 31.5 8.61 50.1 82.1 333.6 31.3 -168-APPENDIX 3 FORTRAN Computer Program for Controlling the  Temperature of the Instantaneous Heat Transfer Probe $STORAGE:2 PROGRAM ULOG10X2 IMPLICIT INTEGER (A-Z) INTEGER* 4 I I , D A T A M A X , K K , L L , N N REAL*4 P 0 , P S , V 0 , V 0 1 , V I , V l l , V 2 , V 2 1 , V S , V S 1 , R P R O B E , R R E F , R R S E T , + K P , E R , A 0 , B 0 , A 1 , B 1 , A 2 , B 2 DIMENSION ITIME(9000) , IVV1(9000) , IVV2(9000) CHARACTER*12 FNAME C C THIS PROGRAM IS USED FOR LOGGING HEAT TRANSFER DATA AND STORE C THEM IN AN UNFORMATTED F I L E . VOLTAGE LOGGING IS UNIPOLAR. C LOGGING AND STORAGE OF DATA ARE DONE SEPARATELY. C PROBE RESISTANCE CONTROLLER IS PROPORTIONAL. C C C INITIALIZATION AND DATA INPUT C CHAN0=1 CHAN1=2 CHAN2=10 VI1 = 0 VI2 = 0 ER=0.0 TIMNUM=0 RREF=1.7115 A0=-1.326819496E-1 B0=1.060733867 Al=3.997577679E-2 B1=9.993961936E-1 A2=5.43066587E-3 B2=1.352162785E-1 WRITE(*,10) 10 F O R M A T ( / , ' DATA STORAGE F I L E N A M E : 1 , \ ) R E A D ( * , 2 0 ) FNAME 20 FORMAT(A12) O P E N ( 3 , F I L E = FNAME,STATUS= 1 NEW1 ,FORM='UNFORMATTED 1) W R I T E ( * , 3 0 ) 30 F O R M A T ( / , ' NUMBER OF DATA POINTS (MAX=9000) : 1 , \ ) R E A D ( * , 4 0 ) D A T A M A X 40 FORMAT ( 1 7 ) WRITE(*,50) 50 F O R M A T ( / , ' CONTROLLER G A I N : ' , \ ) R E A D ( * , 6 0 ) KP 60 FORMAT(F10.2) - 1 6 9 -WRITE(*,70) 70 F O R M A T ( / , ' RESISTANCE SET POINT:' , \ ) READ(*,80) RRSET 80 FORMAT(F10.5) WRITE(*,90) 90 FORMAT(/ , ' DELAY F A C T O R : ' , \ ) READ(* , * ) NN WRITE(*,110) 110 F O R M A T ( / , ' STEADY STATE OUTPUT VOLTAGE READ(*,120) VS 120 FORMAT(F10.5) C C DATALOGGING AND CONTROL C PS=VS*VS VS1=A0+B0*VS VIS=NINT(409.5*VS1)-2048 CALL INIT CALL DAOUT(CHAN0, VIS) CALL TIMST(TIMNUM) DO 13 0 11 = 1,DATAMAX SUM1=0 SUM2=0 DO 121 KK=1,NN LL = KK 121 CONTINUE DO 125 JJ=1,10 CALL ADIN(CHAN1,VII) CALL ADIN(CHAN2,VI2) SUM1=SUM1+VI1 125 SUM2=SUM2+VI2 CALL TIMRD(TIMNUM,TIME) CALL TIMST(TIMNUM) ITIME(II)=TIME IVV1(II)=SUM1 IVV2(II)=SUM2 Vl=SUMl/4096 .0 V2=SUM2/4096.0 V11=A1+B1*V1 V21=A2+B2*V2 RPROBE=(V11-V21)*RREF/V21 ER=RRSET-RPROBE P0=PS+KP*ER I F ( P 0 . L T . l . E - 8 ) P0=0.0 V0=SQRT(P0) I F ( V 0 . G T . 9 . 9 ) V0=9.9 I F ( V 0 . L T . 1 . 0 ) V0=1.0 V01=A0+B0*V0 VI0=NINT(V01*409.5)-20 48 CALL DAOUT(CHAN0,VI0) 130 CONTINUE -170-C C RESET AND DATA STORAGE C CALL DAOUT(CHAN0,VIS) CALL DISI DO 140 II=l f DATAMAX I V V 1 ( I I ) = I V V 1 ( I I ) / 1 0 I V V 2 ( I I ) = I V V 2 ( I I ) / 1 0 WRITE (3) I I , ITIME(II) , I W l ( I I ) , I W 2 ( I I ) 140 CONTINUE CLOSE(3) STOP END -171-APPENDIX 4 Estimation of Error Caused by the Protective Plastic Film Let hg be the apparent heat transfer coefficient measured, and h be the real heat transfer coefficient, r h and h are related by a r J l/ha = 1/h + Film Thermal Resistance (A4.1) where Film Thickness F i l m Thermal R e s i s t a n c e = Film Thermal Conductivity Now, film thickness = 10 [im or 10 ^ m (measured) and film thermal conductivity = 0.195 W/m.K (assumed to be similar to plexiglas, and obtained from Kreith and Black, 1980) Therefore, from Eq. A4.1, h = l/( l / h - 10-5/0.195) (W/m2.K) (A4.2) r a Hence, h =253 W/m2.K i f h =250 W/m2.K (Error = 1%) r a hr=408 W/m2.K i f hg=400 W/m2.K (Error = 2%) -172-APPENDIX 5 BASIC Computer Program for Model Calculations 5 CLEAR 10 DIM E ( 6 ) , F ( 6 ) , K ( 6 ) , Q ( 6 ) , T ( 2 ) 20 TW=50 30 TC=410 40 DP=241E-6 50 L=1.59 60 H0=10 70 B l=DP/2 .5 80 V=1.26 90 KP=0.582 100 RP=2650 110 CP=800 120 INPUT "M=";M 130 INPUT "THICK=";TK 140 INPUT "DENSITY=";RS 142 J=RS/10 143 ON J GOSUB 600,700 ,800 ,900 ,1000,1100 144 IF RS=54 THEN GOSUB 1200 150 EA=0 160 FOR 1=0 TO 5 170 EA=EA+E(I)*F(I) 180 NEXT I 190 LS=0.017775*RS~0.59607 210 IF LS>L THEN LS=L 220 T1=0 230 T2=LS/V 240 Q(0)=H0*(TW-TC)*(T2-T1) 250 Z=LS/2 260 T(0)=TC 270 TF=(TW+T(0))/2 280 KG=0.024243+6.06886E-5*TF 290 FOR 1=0 TO 5 295 K1=E(I)*(1-KG/KP) 296 K2=KG/KP+0 .28*(1 -E(I ) )* (0 .6 3*(KP/KG)"0.18) 300 K(I)=KG*(1+K1/K2) 310 NEXT I 320 A=TW-T(0) 330 B=B1/KG 340 FOR 1=1 TO 5 350 C = S Q R ( P I / ( K ( I ) * R P * C P * E ( I ) ) ) 360 Q1=C*(SQR(T2)-SQR(Tl) ) 37 0 Q2 = B*LOG( (B+C*SQR(Tl) )/(B+C*SQR(T2) ) ) 380 Q(I)=2*A*(Q1+Q2)/C~2 390 NEXT I 400 QT=0 410 FOR 1=0 TO 5 - 1 7 3 -420 QT=QT+Q(I)*F(I) 430 NEXT I 440 HT=QT/(TW-TC) / (T2-T1) 450 PRINT "Z=";Z 460 PRINT "H=";HT 470 G1=QT/CP+T(0)*(TK*RP*EA-2*M*(T2-T1))+2*M*TC*(T2-T1) 480 T( l )=G1/ (TK*RP*EA) 490 T(0)=T(1) 500 Z=Z+LS 510 GOTO 270 600 E(0) = 0. 0 :F (0) =0. 665 610 E(l) = 0. 1 :F (1) =0. 305 620 E(2) = 0. 2 :F (2) = 0. 023 630 E(3) = 0. 3 :F [3) =0. 007 640 E(4) = 0. 4 :F (4) = 0. 0 650 E(5) = 0. 5 :F (5) = 0. 0 660 RETURN 700 E(0) = 0. 0 :F (0) = 0. 423 710 E(l) = 0. 1 :F (1) = 0. 498 720 E(2) = 0. 2 :F k2) = 0. 062 730 E(3) = 0. 3 :F r3) = 0. 014 740 E(4) = 0. 4 :F k4) = 0. 003 750 E(5) = 0. 5 :F (5) =0. 0 760 RETURN 800 E(0) = 0. 0 :F k 0 ) = 0. 242 810 E(l) = 0. 1 :F (1) = 0. 576 820 E(2) = 0. 2 :F 2) = 0 . 133 830 E(3) = 0. 3 :F 3) = 0 . 037 840 E(4) = 0. 4 :F 4) = 0. 012 850 E(5) = 0. 5 :F [5) = 0. 0 860 RETURN 900 E(0) = 0. 0 :F 0) = 0. 111 910 E(l) = 0 . 1:F (1) = 0. 523 920 E(2) = 0. 2 :F 2) = 0. 242 930 E(3) = 0. 3 :F 3) = 0. 088 940 E(4) = 0. 4 :F 4) = 0. 030 950 E(5) = 0. 5 :F (5) = 0. 006 960 RETURN 1000 E(0) = 0. 0 :F 0) = 0. 032 1010 E(D = 0. 1 :F (1) = 0. 347 1020 E(2) = 0. 2 :F 2) = 0. 369 1030 E(3) = 0. 3 :F 3) = 0. 170 1040 E(4) = 0. 4 :F 4) = 0. 063 1050 E(5) = 0. 5 :F [5) =0. 019 1060 RETURN 1100 E(0) = 0. 0 :F 0) = 0. 001 1110 E(l) = 0. 1 :F (1) = 0. 046 1120 E(2) = 0. 2 :F 2) = 0 . 515 1130 E(3) = 0. 3 :F 3) = 0. 279 1140 E(4) = 0. 4 :F 4) = 0. 119 1150 E(5) = 0. 5 :F 5) = 0. 040 1160 RETURN 1200 E(0) = 0. 0 :F(0) = 0. 013 1210 E ( l ) = 0 . 1 : F ( 1 ) = 0 . 2 4 3 1220 E(2)=0 .2 :F(2)=0 .425 1230 E(3)=0 .3:F(3)=0 .210 1240 E(4)=0 .4:F(4)=0 .083 1250 E(5)=0 .5:F(5)=0 .026 1260 RETURN 

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