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Heat transfer processes in Rotary kilns Barr, Peter Vernon 1986

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HEAT TRANSFER PROCESSES IN ROTARY KILNS by PETER VERNON BARR B.Sc. The University of New Brunswick, 1971 M.Sc. The University of New Brunswick, 1973 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 Chemical Engineering) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1986 © Peter Vernon Barr, 1986 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a llowed without my w r i t t e n p e r m i s s i o n . Department of ^ ^ ( ^ n ^ c ' c ^ t o ^ ^ t A ^ - T S A p . The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 D a t e i i ABSTRACT An experimental i n v e s t i g a t i o n of rotary k i l n heat transfer processes was car r i e d out and a u n i f i e d heat transfer model developed to describe the i n d i v i d u a l processes and t h e i r i n t e r a c t i o n . A 0.406 m ID by 5.5m re f r a c t o r y lined p i l o t k i l n f i r i n g natural gas was u t i l i z e d for a series of 23 heat transfer t r i a l s . Limestone, petroleum coke and two Ottawa sands were heated using a wide range of f i r i n g rates while r o t a t i o n rate, k i l n i n c l i n a t i o n , k i l n loading and bed depth were held nearly constant. The bed material was i n the r o l l i n g mode for a l l t r i a l s . Measurements were made to obtain the net heat transfer rates for the bed material, the freeboard gas, the r e f r a c t o r y wall and, unique to the study, the heat flux at the inside wall surface as a function of circ u m f e r e n t i a l p o s i t i o n . H i g h r a t e s of net heat input to the bed m a t e r i a l , Q^ > which occurred very near to the k i l n entrance, were found to decline quickly • * with a x i a l d i s t a n c e and, f o r an i n e r t bed, the r a t i o of Q, to Q , the D S S rate of energy loss through the k i l n w a l l , tended toward the r a t i o of the exposed bed surface area to the exposed wall surface area. At the onset of the limestone c a l c i n a t i o n r e a c t i o n Q, i n c r e a s e d s h a r p l y without a D corresponding increase i n Q . Over the f u l l y instrumented portion of the S S k i l n , which extended from 1.32m to 5.0m, the rate of heat transfer from the covered wall to the bed, Q , , was < 30% of the rate to exposed bed i i i surface from the freeboard. With an i n e r t bed the net exchange Q , was cw+cb found to decline with a x i a l distance and negative values were encountered beyond the k i l n mid-point. The onset of bed c a l c i n a t i o n reversed this t r e n d and p o s i t i v e v a l u e s of Q , were always recorded i n the cw+cb c a l c i n a t i o n zone. The temperature of the bed material and the insi d e wall surface were found to be closely-coupled and the actual temperature difference could not be determined due to the l i m i t a t i o n s of the measuring technique. The onset of bed c a l c i n a t i o n was always characterized by s i g n i f i c a n t increases i n both the net heat input rate to the bed material and the amount of temperature c y c l i n g at the insi d e wall surface. A zone-type r e a l gas model was developed for the r a d i a t i v e heat exchanges i n the freeboard and the r e s u l t s presented i n the form of r a d i a t i v e heat transfer c o e f f i c i e n t s . For the p i l o t k i l n , f i r i n g at 10% excess a i r , the c o e f f i c i e n t for r a d i a t i v e heat transfer from the freeboard gas to the exposed wall or bed surfaces was calculated to range from 2 15 ->• 55 W/m K f o r gas temperatures from 800 1800 K. Model predictions for a prototype k i l n of 4 m ID indicated an increase i n the gas to surface r a d i a t i o n by a factor ~ 3. The c o e f f i c i e n t s for r a d i a t i v e exchange among the freeboard surfaces i n the p i l o t k i l n were s i g n i f i c a n t l y larger than for the gas to surface exchange while, i n the prototype, they were of comparable magnitude. For the i n e r t bed t r i a l s ^the convective component of the freeboard surface i v heat f l u x was c a l c u l a t e d by subtracting the c a l c u l a t e d r a d i a t i v e contribution from the net surface f l u x . Convection to the exposed bed surface was found to be enhanced r e l a t i v e to the exposed wall surface although less than reported previously. C o e f f i c i e n t s for heat transfer between the covered wall and covered bed were shown to be s i g n i f i c a n t l y reduced i n a r e f r a c t o r y l i n e d k i l n r e l a t i v e to an unlined metal drum. A f i n i t e d i f f e r e n c e model of the r e f r a c t o r y and bed material, incorporating the derived heat transfer c o e f f i c i e n t s , was v e r i f i e d using the p i l o t k i l n data and extended to examine the r e l a t i o n s h i p e x i s t i n g among the heat trans f e r processes at any k i l n c r o s s - s e c t i o n . Both the close-coupling of the p i l o t k i l n bed and wall temperatures and the high rate of net bed heat input occurring near the k i l n entrance and i n the presence of a c a l c i n i n g bed were explained by the u n i f i e d model. Model predictions were obtained for a 4m ID prototype k i l n and aspects of k i l n thermal performance i d e n t i f i e d which have important repercussions for the operation of rotary k i l n s . V TABLE OF CONTENTS Abstract i i Table of Contents v L i s t of Tables i x L i s t of Figures x Nomenclature x v i i Acknowledgements x x i i i Chapter 1 Introduction 1 Chapter 2 L i t e r a t u r e Review ^ 2.1 Radiation i n the Freeboard Region 7 2.1.1 Emissive C h a r a c t e r i s t i c s of Gases 8 2.1.2 Calculation of Freeboard Radiation H 2.2 Convection i n the Freeboard 2 0 2.2.1 Convection to the Exposed Wall Surface 2 0 2.2.2 Convection to the Exposed Bed Surface 2 4 2.3 Covered Wall/Bed Heat Transfer 2 8 2.3.1 E f f e c t i v e Thermal Conductivity of a Packed Bed 3 0 2.3.2 Surface Film C o e f f i c i e n t 3 8 2.3.3 Covered Wall/Bed Heat Transfer Models 4 1 v i 2.4 P a r t i c l e Motion Within the Bed Material 4 5 2.4.1 Transverse Bed Motion 4 7 2.5 Flow Conditions i n the Freeboard Gas 5 2 Chapter 3 Scope of the Present Work 5 8 Chapter 4 The P i l o t K i l n F a c i l i t y 5 9 4.1 General Description 5 9 4.2 Instrumentation 6 2 4.2.1 Gas Temperature Thermocouples 6 5 4.2.2 Bed Temperature Thermocouples 6 9 4.2.3 Wall Refractory Temperature Thermocouples .... 7 0 4.2.4 Solids Material Measurements 7 2 4.2.5 Additional Freeboard Gas Measurements 7 3 4 . 3 Solids Feed Materials 7 3 Chapter 5 P i l o t K i l n T r i a l s 7 6 Chapter 6 Heat Transfer Models 7 9 6.1 Evaluation of Net Heat Transfer Rates for the Bed Material and Freeboard Gas 8 0 6.2 Heat Flux Calculation for the K i l n Wall 8 3 6.2.1 Heat Loss C a l c u l a t i o n i n the Wall Steady-State Layer 8 3 6.2.2 Heat Flux C a l c u l a t i o n i n the Wall Active Layer 8 5 v i i 6 .3 Estimation of Temperature Rise for P a r t i c l e s at the Exposed Bed Surface 9 0 6.4 Radiative Heat Transfer i n the Freeboard 9 5 6.4.1 The Freeboard Gas Emi s s i v i t y / Absorptivity Models 9 6 6.4.2 Radiative Heat Transfer from the Freeboard Gas to the Exposed Bed and Wall Surfaces .... 1 0 3 6.4.3 Radiative Heat Transfer Among the Freeboard Surfaces 1 1 2 6.4.4 Accuracy of the Radiation Model 1 3 3 6.5 A Unified Model for Heat Transfer of a K i l n Cross-Section 1 3 5 Chapter 7 Results and Discussion 1 3 9 ; 7.1 Results from the P i l o t K i l n T r i a l s 1 3 9 7.1.1 The Inert Bed T r i a l s 1 4 0 7.1.2 The Calc i n a t i o n T r i a l s 1 5 3 7.2 Convective Heat Transfer i n the Freeboard 1 6 2 7 .3 Heat Transfer Between the Covered Wall and Bed 1 7 0 7.4 Temperature Rise for P a r t i c l e s on the Bed Surface ... 1 7 9 7.5 Results from the Freeboard Radiation Model 1 8 2 7.5.1 Radiative Exchange Between the Freeboard Gas and Exposed Bed and Wall Surfaces 1 8 4 7.5.2 Radiative Exchange Between the Exposed Bed and Wall Surfaces 1 9 3 v i i i 7.5.3 Radiative Exchange Between Areas on the Exposed Wall 1 9 6 7.6 Application of the U n i f i e d Heat Transfer Model 1 9 9 7.6.1 Model Results for the P i l o t K i l n 2 0 1 7.6.2 Model Predictions for the Prototype Rotary K i l n 2 1 6 Chapter 8 Conclusions 2 2 4 Chapter 9 Recommendations for Future Work 2 2 9 References 2 3 0 Appendix ( I ) Response of the Bed Temperature Thermocouples 2 36 Appendix ( I I ) Computer Flow Charts 2 4 2 Appendix ( I I I ) Results from the P i l o t K i l n T r i a l s 2 4 7 Appendix ( I V ) K i l n Energy Balance 2 7 1 LIST OF TABLES i x Table 2.1 Expressions proposed for the freeboard gas to surface heat transfer c o e f f i c i e n t 19 Table 2.2 Expressions proposed for the covered wall to covered bed heat transfer c o e f f i c i e n t ^ Table 4.1 Relevant physical properties 74 Table 5.1 Summary of run conditions 7 7 Table 6.1 Composition of natural gas used for the p i l o t k i l n t r i a l s 97 Table 6.2 Values of e x t i n c t i o n c o e f f i c i e n t s for cl e a r - p l u s - t h r e e -gas e m i s s i v i t y approximations 9 7 Table 7.1 A comparison of model predictions with measurements from the p i l o t k i l n 2 0 4 Table 7.2 Conditions applicable to the prototype k i l n simulation 217 Table IV. 1 Results from the k i l n energy balance 275 X LIST OF FIGURES F i g . 1.1 Rotary K i l n schematic 2 F i g . 1.2 Basic paths and processes for k i l n heat transfer 4 F i g . 2.1 Approximation of r e a l gas t o t a l emissivity using multiple gray gases ( a f t e r Hottel and Sarofim) 9 F i g . 2.2 Showing the n e g l i g i b l e influence of a x i a l gas temperature gradients on gas to k i l n wall heat f l u x ( a f t e r Gorog) .... 16 F i g . 2.3 Showing the rapid decline i n exposed bed to wall view factors with a x i a l p o s i t i o n ( a f t e r Gorog) 17 F i g . 2.4 Showing the e f f e c t of r o t a t i o n rate on convection to the exposed wall and bed surfaces ( a f t e r Tscheng) 2 3 F i g . 2.5 Predicted vs. experimental values of gas to exposed bed Nusselt Number (af t e r Tscheng) 2 7 F i g . 2.6 V a r i a t i o n of e f f e c t i v e thermal conductivity with void f r a c t i o n ( a f t e r M e s s i e r and Elan) 3 2 F i g . 2.7 Heat transfer paths i n a stagnant packed bed ( a f t e r Yagi and Kunii) 3 3 F i g . 2.8 The orthorhombic unit c e l l of Wakao and Kato 3 6 F i g . 2.9 E f f e c t i v e thermal conductivity of the orthorhombic l a t t i c e structure ( a f t e r Wakao and Kato) 3 7 F i g . 2.10 Boundary conditions assumed for covered wall/covered bed heat transfer models 42 x i F i g . 2.11 Bed motion showing the shape of the bed active layer 4 8 F i g . 2.12 Flow patterns of double-concentric jets i n long c y l i n d r i c a l chambers ( a f t e r Chedaille) 5 3 F i g . 4.1 The p i l o t k i l n f a c i l i t y 6 0 F i g . 4.2 Thermal conductivity of LWR24 61 F i g . 4.3 P i l o t k i l n burner region ( d e t a i l ) 6 3 F i g . 4.4 C a l i b r a t i o n curve for the gas flow o r i f i c e plate 6 4 F i g . 4.5 Schematic diagram of thermocouple c i r c u i t s 6 6 F i g . 4.6 A x i a l locations of k i l n thermocouples 6 7 F i g . 4.7 Cross-section of the k i l n showing the thermocouple i n s t a l l a t i o n s 6 8 F i g . 4.8 Wall temperature measurement probe ( d e t a i l ) 71 F i g . 6.1 Determination of net heat transfer rates from f i r s t law analysis 31 F i g . 6.2 The wall active and steady-state layers 8 4 F i g . 6.3 Energy balance for an elemental volume of the wall (per unit a x i a l length) , 8 7 F i g . 6.4 F i n i t e difference model nodal configuration for the wall a c t i v e layer 8 8 F i g . 6.5 Assumed motion of p a r t i c l e s at the exposed bed surface .... 9 1 x i i F i g . 6.6a An elemental volume of a s p h e r i c a l bed p a r t i c l e 9 3 F i g . 6.6b Boundary c o n d i t i o n s f o r p a r t i c l e s r o l l i n g down the exposed bed surface 9 4 F i g . 6.7a T o t a l gas e m i s s i v i t y f o r P u n n = 2 ( a f t e r H o t t e l ) 9 8 F i g . 6.7b T o t a l gas e m i s s i v i t y f o r P„ ~/P__ = 1 ( a f t e r H o t t e l ) 9 9 F i g . 6.8 Temperature v a r i a t i o n of the gas e m i s s i v i t y weighting c o e f f i c i e n t s 1 0 1 F i g . 6.9 Temperature v a r i a t i o n of the gas a b o s r p t i v i t y weighting c o e f f i c i e n t s 1 0 2 F i g . 6.10 R a d i a t i v e exchange among volume and surface zones w i t h i n the k i l n freeboard 1 0 4 F i g . 6.11 R a d i a t i v e exchange between a surface zone and a gas zone .. 1 0 5 F i g . 6.12 R a d i a t i o n from a gas volume to surface area w i t h one * i ^ 1 0 9 r e f l e c t i o n F i g . 6.13 R a d i a t i o n between surface areas with one and two PI 1 0 9 r e f l e c t i o n s F i g . 6.14 Gas and surface zoning i n the p i l o t k i l n 1 1 1 F i g . 6.15 D i r e c t r a d i a t i v e exchange between two gray surfaces 1 1 3 F i g . 6.16 D i r e c t s p e c i f i c exchange f a c t o r s f o r the p i l o t k i l n (4 p l o t s ) 1 1 6 x i i i F i g . 6.17 Direct s p e c i f i c exchange factors for the prototype k i l n (4 plots) 1 2 0 F i g . 6.18 Radiation between surfaces with one and two r e f l e c t i o n s ( d e t a i l ) 1 2 5 F i g . 6.19 S p e c i f i c surface to surface exchange area for one r e f l e c t i o n ( p i l o t k i l n -2 plot s ) 1 2 8 F i g . 6.20 S p e c i f i c surface to surface exchange area for one r e f l e c t i o n (prototype k i l n - 2 plots) 1 3 0 F i g . 6.21 S p e c i f i c surface to surface exchange area for two r e f l e c t i o n s ( p i l o t k i l n ) 1 3 2 F i g . 7.1 K i l n a x i a l temperature p r o f i l e s ( i n e r t bed t r i a l ) \k-2 F i g . 7.2 Mean gas-surface temperature differences ( i n e r t bed t r i a l ) 1 4 5 F i g . 7.3 Net heat transfer rates ( i n e r t bed t r i a l ) 1 4 6 F i g . 7.4 Covered wall to bed heat Input as a f r a c t i o n of gas plus exposed wall input ( i n e r t bed t r i a l ) 1 4 8 F i g . 7.5 Average values of surface heat fluxes ( i n e r t bed t r i a l ) ... 149 F i g . 7.6 Range of inside wall temperature (i n e r t bed t r i a l ) 1 5 1 Fi g . 7.7 Circumferential v a r i a t i o n of heat f l u x into the wall surface ( i n e r t bed t r i a l ) 1 5 2 F i g . 7.8 K i l n a x i a l temperature p r o f i l e s ( c a l c i n a t i o n t r i a l ) 1 5 5 F i g . 7.9 Mean gas-surface temperature differences ( c a l c i n a t i o n t r i a l ) 1 5 6 x i v F i g . 7.10 Net heat transfer rates ( c a l c i n a t i o n t r i a l ) 1 5 7 F i g . 7.11 Covered wall to bed heat input as a f r a c t i o n of gas plus exposed wall input ( c a l c i n a t i o n t r i a l ) 1 5 8 F i g . 7.12 Average values of surface heat fluxes ( c a l c i n a t i o n t r i a l ) 1 5 9 F i g . 7.13 Range of inside wall temperature ( c a l c i n a t i o n t r i a l ) .... 1 6 0 F i g . 7.14 Circumferential v a r i a t i o n of heat f l u x into the wall surface ( c a l c i n a t i o n t r i a l ) 1 6 1 F i g . 7.15 Convection to the exposed wall surface 1^5 F i g . 7.16 Comparison of gas to exposed wall convection with the f l a t plate c o r r e l a t i o n 1 6 7 F i g . 7.17 Convection to the exposed bed surface 1 6 8 F i g . 7.18a Covered wall to bed heat input as a f r a c t i o n of gas plus exposed wall input ( i n e r t bed t r i a l s ) 1 7 2 F i g . 7.18b Covered wall to bed heat input as a f r a c t i o n of gas plus exposed wall input ( c a l c i n a t i o n t r i a l s ) 1 7 3 F i g . 7.19a Covered wall/covered bed heat transfer c o e f f i c i e n t s (T - 1200K) 1 7 7 F i g . 7.19b Covered wall/covered bed heat transfer c o e f f i c i e n t s (T = 450K) 1 7 8 F i g . 7.20 Temperature r i s e for p a r t i c l e s during exposure to the k i l n freeboard (model predictions) 1 8 1 XV F i g . 7.21 Thermal resistance model for heat transfer through the k i l n wall 1 8 6 F i g . 7.22 Gas to surface r a d i a t i v e c o e f f i c i e n t for the p i l o t k i l n . 1 8 7 F i g . 7.23 Showing the n e g l i g i b l e e f f e c t of a x i a l gas temperature gradients ( p i l o t k i l n ) 1 8 9 F i g . 7.24 Radiative heat transfer c o e f f i c i e n t s from the freeboard gas ( p i l o t k i l n ) 1 9 0 F i g . 7.25 Radiative heat transfer c o e f f i c i e n t s from the freeboard gas ( p i l o t k i l n ) 1 9 1 F i g . 7.26 Radiative heat transfer c o e f f i c i e n t s from the freeboard gas (prototype k i l n ) 1 9 2 F i g . 7.27 Bed to wall surface heat transfer c o e f f i c i e n t s for the p i l o t k i l n 1 9 5 F i g . 7.28 Wall to wall surface heat transfer c o e f f i c i e n t s for the p i l o t k i l n 1 9 8 F i g . 7.29 V a r i a t i o n of net heat transfer rates with T - T , ws eb o ( p i l o t k i l n ) 2 0 9 F i g . 7.30 V a r i a t i o n of the net heat transfer components with T - T . ( p i l o t k i l n ) 2 1 0 ws eb o F i g . 7.31 V a r i a t i o n of average temperature and temperature c y c l i n g at the ins i d e wall surface with T - T ( p i l o t k i l n ) 2 1 2 ws eb o F i g . 7.32 V a r i a t i o n of a x i a l temperature gradients with T - T , 2 1 3 ws eb o x v i F i g . 7.33 V a r i a t i o n of net heat transfer rates with T - T , ws eb o (prototype k i l n ) 2 20 F i g . 7.34 V a r i a t i o n of the net bed heat transfer components with T - T , (prototype k i l n ) 2 2 1 ws eb o F i g . 7.35 V a r i a t i o n of average temperature and temperature c y c l i n g at the inside wall surface with T w g - T (prototype k i l n ) 2 2 2 o F i g . 1.1 Signal obtained from the bed temperature thermocouples ( t y p i c a l ) 2 3 8 F i g . 1.2 V a r i a t i o n of the pseudo-time constant with time at 3 leves of bed temperature 2 3 9 F i g . 1.3 V a r i a t i o n of the pseudo-time constant with temperature for a contact time of 6 seconds 2 AO F i g . II.1 Flow chart for the p i l o t k i l n data analysis and c a l c u l a t i o n of net heat transfer rates ('FILE') 2 4 3 F i g . II.2 Flow chart for the c a l c u l a t i o n of surface/surface r a d i a t i v e heat transfer ('KSS') 2 4 4 F i g . II.3 Flow chart for the c a l c u l a t i o n of surface/gas r a d i a t i v e heat transfer ('KSG') 2 4 5 F i g . II.4 Flow chart for the u n i f i e d heat transfer model at a k i l n cross-section (»WALL2') 2 4 6 F i g . IV.1 Linear f i t of the steady-state energy loss through the k i l n r e f r a c t o r y w a l l l 2 7 3 x v i i NOMENCLATURE a Gas a b s o r p t i v i t y weighting c o e f f i c i e n t -A Area (m 2) c P Constant pressure s p e c i f i c heat (kJ/kgK) c p Molar constant pressure s p e c i f i c heat (kJ/Mole K) d P P a r t i c l e diameter (mm) D K i l n inside diameter (m) D e Equivalent diameter (m) °H Hydraulic diameter (m) e Gas emissivity weighting c o e f f i c i e n t -E 2 Black-body emissive power (W/m K) g 2 Gr a v i t a t i o n a l a c c e l e r a t i o n (m/Sec ) h 2 Average heat transfer c o e f f i c i e n t (W/m ) h c 2 Heat transfer c o e f f i c i e n t for conduction (W/m K) R h 2 Heat transfer c o e f f i c i e n t for r a d i a t i o n (W/m K) h f 2 Heat transfer c o e f f i c i e n t across surface f i l m (W/m K) h s h 2 Heat transfer c o e f f i c i e n t at k i l n s h e l l (W/m K) H Molar enthalpy (kJ/Mole) H. fo Molar enthalpy of formation (kJ/Mole) k Thermal conductivity (W/mK) be Bed e f f e c t i v e thermal conductivity (W/mK) k s Thermal conductivity of the p a r t i c l e material (W/mK) k g Thermal conductivity of a gas (W/mK) k wo Thermal conductivity of wall r e f r a c t o r y extrapolated to 0 K (W/mK) x v i i i K Gas a b s o r p t i v i t y c o e f f i c i e n t (cm ^ atm L ) a L o c a l l y defined length (m) X cw Covered wall length (m) A ew Exposed wall length (m) L Radiation path length (cm) OR o v e r a l l length of condict (m) L m Radiation mean beam length f o r a gas volume (m) L s Distance t r a v e l l e d by p a r t i c l e s on the bed surface On) m Revolutions of p a r t i c l e while on bed surface (-) • m Entrainment rate of confined jet (Kg/sec) • m g 2 Mass f l u x of freeboard gas (Kg/M sec) H P Mass flow of primary jet (Kg/sec) M s Mass flow of secondary jet (Kg/sec) N Total number of hypothetical gray gas components (- ) n Rotation rate (Rev/sec) • n Molar flow (Mole/sec) P Gas p a r t i a l pressure (atm) P Gas t o t a l pressure (atm) • q Heat f l u x (kW/m2) Q Heat transfer rate (kW) Q Heat transfer rate per unit of a x i a l k i l n length (kW/m) • Q Steady-state heat transfer rate through the k i l n wall (kW/m) ss r Radius from k i l n axis (m) r^ Primary j e t radius (m) r Secondary j e t radius (m) s r Radius of k i l n s h e l l surface (m) sh r Radius of inside wall surface (m) ws x i x ss Direct surface to surface r a d i a t i v e exchange area (m ) — -2 ss S p e c i f i c surface to surface r a d i a t i v e exchange area (m ) 2 sg D i r e c t surface to gas r a d i a t i v e exchange area (m ) 2 gs Direct gas to surface r a d i a t i v e exchange area (m ) t Time (sec) t. Thickness of bed active layer (m) b t Contact time (sec) c At Time i n t e r v a l (sec) T Temperature (K) T Temperature of the inside wall surface at point of emergence from o under the bed (K) T Temperature of the inside wall surface at point of immersion under w s l the bed (K) T Temperature of proposed surface layer of bed material adjacent to the covered wall (m) T/C Abbreviation for thermocouple (-) U Primary jet v e l o c i t y (m/sec) P U Secondary jet v e l o c i t y (m/sec) s OR V e l o c i t y of p a r t i c l e s on bed surface (m/sec) 3 V Volume (m ) 3 CV Control volume (m ) X Thickness of the proposed surface layer of bed material adjacent to the covered wall (m) Z A x i a l k i l n coordinate (m) Greek Gas etnissivity (-) OR 2 Thermal d i f f u s i v l t y (m /sec) 2 E f f e c t i v e thermal d i f f u s i v l t y of bed (m /sec) Angle subtended by s o l i d s surface (radians) OR C o e f f i c i e n t term for the r e f r a c t o r y thermal conductivity (-) Wavelength (nm) L o c a l l y defined angle (radians) 2 Kinematic v i s c o s i t y (m /sec) E m i s s i v i t y -8 2 4 Stephan-Boltzman Constant 5.67x10 (W/m K ) 3 Density (kg/m ) OR Surface r e f l e c t i v i t y (-) Transmissivity (-) Pseudo time constant of decay (sec) Degree of s o l i d f i l l (%) Void f r a c t i o n of bed material (-) Angular k i l n coordinate (radians) xxi Subscripts b Bed c Convective component cb Covered bed surface cw Covered wall surface eb Exposed bed surface ew Exposed wall surface fb Freeboard (en mass) fbg Freeboard gas (en mass) fbs Freeboard surfaces (en mass) g Gas R Radiative component s Surface (general) sh S h e l l ss Steady-state w Wall ws Inside Wall surface Dimensionless Numbers Ar Archimedes Number Be Becket Number hV Bi Blot Number -.—r k A s Ct Craya-Curtet Number Fo Fourier Modulus a t ( — ) Diameter Nusselt Number 7^ -k g hz Entrance Length Nusselt Number ^ — g 4od T 3 Radiative Nusselt Number „- 1 ^, \-,— (2/e-l)k 6 Radiative Nusselt Number 2/E-0.264 Peclet Number RePr v Prandtl Number — a Diameter Reynolds Number v UZ Entrance Length Reynolds Number — Du Rotational Reynolds Number — v Thring-Newby Number x x i i i ACKNOWLEDGEMENTS "It i s an old maxim of mine that, when you have excluded the impossible, whatever remains, however improbable, must be the truth" Sherlock Holmes/ACD. I would l i k e to extend my sincerest thanks to my supervisors, Dr. J.K. Brimacombe and Dr. A.P. Watkinson, for without t h e i r enthusiasm, guidance and (occasional) coercion, t h i s thesis could not have been completed. F i n a n c i a l support for the research was provided by Alcan and i s most g r a t e f u l l y acknowledged. I am also indebted to Mr. Patrick Wenman for his physical assistance, timely advice and knack of getting things done. - 1 -CHAPTER 1 INTRODUCTION The e s s e n t i a l components of a rotary k i l n are shown i n F i g . 1.1. They consist of an i n c l i n e d metal c y l i n d e r , u s u a l l y r e f r a c t o r y l i n e d , r o t a t i n g about i t s l o n g i t u d i n a l axis on trunions. A granular or s l u r r y m a t e r i a l , fed into the elevated end, forms a bed (or burden) which moves continuously through the k i l n due to the combined e f f e c t s of r o t a t i o n and g r a v i t y . Gas flowing i n the freeboard, e i t h e r co-current or counter-current to the bed, exchanges energy with the bed m a t e r i a l . A flame may be present i n the freeboard. The net energy exchange can be from bed to gas or vice-versa and the bed material may remain i n e r t throughout i t s residence time or may undergo endothermic or exothermic chemical reactions. Rotary k i l n s f i n d a p p l i c a t i o n i n many areas of the chemical and m e t a l l u r g i c a l i n d u s t r i e s . They are v e r s a t i l e , being capable of handling a range of p a r t i c l e sizes simultaneously and are noted for uniformity of product when c o r r e c t l y operated. In addition d i r t y f u e l s can be u t i l i z e d without serious product contamination. Common ap p l i c a t i o n s include c a l c i n i n g , reducing, roasting, and s i n t e r i n g with product temperatures ranging up to about 1600 K. Despite widespread usage, k i l n design and operation remains more an art than a science. In terms of energy consumption, the cost of i n e f f i c i e n c y can be high. A large lime k i l n can consume an equivalent - 2 -F i g . l - 1 R o t a r y k i l n s c h e m a t i c -3-of 400,000 barrels of o i l per year. An improvement i n thermal e f f i c i e n c y of 1% would y i e l d annual savings of ~ $140,000 i n reduced f u e l costs. To s i m p l i f y the de s c r i p t i v e process and since i t i s the more common s i t u a t i o n , the bed material w i l l be considered the net r e c i p i e n t of energy from the freeboard gas. Energy exchange within a rotary k i l n occurs p r i m a r i l y as heat transfer, the work input to drive the r o t a t i o n being n e g l i g i b l y small. This heat transfer occurs v i a the paths and processes i l l u s t r a t e d i n F i g . 1.2. The freeboard gas transmits energy to the exposed wall and bed surface by r a d i a t i o n and convection, while simultan-eously a r a d i a t i v e exchange i s set-up between these two exposed surfaces. The r o t a t i o n of the k i l n causes a transient response within a thin layer at the inside wall surface so that, i n addition to conducting energy to the surroundings, the wall acts as a regenerator. Once entering the bed material, energy i s d i s t r i b u t e d by heat transfer and by advection due to the motion of p a r t i c l e s within the bed. In large k i l n s at high temperatures d i r e c t r a d i a t i o n from the freeboard gas i s the largest Input to the bed material followed i n uncertain order of importance by contributions from the exposed w a l l , and covered wall plus convection from the gas. K i l n design implies the c a p a b i l i t y of c o r r e c t l y s i z i n g the unit required to carry out the process concerned for a given maximum material feed rate. It i s s e l f evident that heat transfer to the bed w i l l c ontrol the heating rate for in e r t dry bed material but i t has also been established to be the rate l i m i t i n g factor for limestone c a l c i n a t i o n ^ ^ as - 4 -( 1 ) Gas t o e x p o s e d bed ( r a d i a t i o n + c o n v e c t i o n ) ( 2 ) E x p o s e d w a l l t o e x p o s e d bed ( r a d i a t i o n ) ( 3 ) C o v e r e d w a l l / c o v e r e d bed ( r a d i a t i o n + c o n v e c t i o n + c o n d u c t i o n ) ( 4 ) Gas t o e x p o s e d w a l l ( r a d i a t i o n + c o n v e c t i o n ) ( 5 ) S h e l l t o s u r r o u n d i n g s ( r a d i a t i o n + c o n v e c t i o n ) ( 6 ) E x p o s e d w a l l t o e x p o s e d w a l l ( r a d i a t i o n ) F i g . 1 . 2 B a s i c p a t h s and p r o c e s s e s f o r k i l n h e a t t r a n s f e r w e l l as i r o n ore r e d u c t i o n w i t h i n an SL/RN k i l n . The h e a t i n g of material to reaction temperature may require a considerable portion of the k i l n , estimated at 70% of the k i l n length i n the instance of the SL/RN ( 3 ) p r o c e s s . To c a r r y out the thermal design requires knowledge of the c o e f f i c i e n t terms r e l a t i n g each heat transfer process to the appropriate temperature d r i v i n g force. Numerous heat transfer models for rotary k i l n s which presuppose the a v a i l a b i l i t y of the required heat transfer c o e f f i c i e n t s have appeared i n the l i t e r a t u r e . ^ 4 D e s p i t e an obvious need f o r more r e s e a r c h to (18") support such models , remarkably few studies into s p e c i f i c aspects of (19-25) the heat t r a n s f e r problem have been published. No Investigation, supported by empirical data and considering simultaneously a l l the processes of F i g . 1.2, has yet been made a v a i l a b l e . The current study, undertaken to improve t h i s u n s a t i s f a c t o r y s i t u a t i o n , was c a r r i e d out i n four stages: ( i ) A s e r i e s of heat transfer t r i a l s were c a r r i e d out using the UBC p i l o t k i l n f a c i l i t y , which enabled the d i r e c t c a l c u l a t i o n of the net rate of energy loss by the freeboard gas, the net rate of energy input to the bed material and, unique to t h i s study, the net energy f l u x across the inside wall surface. r 6 -( i i ) A s o p h i s t i c a t e d r a d i a t i o n heat transfer model was developed to p r e d i c t r a d i a t i v e heat transfer c o e f f i c i e n t s for the freeboard (gas to exposed wa l l , gas to exposed bed, exposed wall to exposed bed, exposed wall to exposed wall) i n both the p i l o t k i l n and a prototype k i l n having a scale-up f a c t o r of 10:1. ( i i i ) Using a f i n i t e d i f f e r e n c e representation of the r e f r a c t o r y wall and granular bed material, a u n i f i e d model for heat transfer at any k i l n c r o s s - s e c t i o n was developed and v e r i f i e d using the data from ( I ) . The necessary heat transfer c o e f f i c i e n t s were obtained from ( i i ) . ( i v ) U t i l i z i n g the u n i f i e d model to Investigate the complex i n t e r a c t i o n among the heat transfer processes ( F i g . 1.2), aspects of the p i l o t k i l n data were explained and predictions made for the prototype k i l n . In a d d i t i o n , c o e f f i c i e n t s for convective heat transfer from the gas to the exposed wall and bed material were derived from the p i l o t ( 22 ) k i l n d a t a f o r c o m p a r i s o n to t h o s e of a r e c e n t s t u d y -7-CHAPTER 2 LITERATURE REVIEW In a rotary k i l n , energy from the freeboard gas i s tra n s f e r r e d to the k i l n wall and bed material by both r a d i a t i v e and convective heat exchange. The subsequent d i s t r i b u t i o n of t h i s energy i s of v i t a l importance to the s a t i s f a c t o r y operation of the k i l n , the goal being to maximize the net amount received by the bed and minimize the amount l o s t through the r e f r a c t o r y w a l l . Therefore the r a d i a t i v e exchange among the exposed wall and bed surfaces and the combined conductive, convective and r a d i a t i v e exchange between the covered wall and bed material must be characterized. This i n turn requires an understanding of bed motion since i t plays a key r o l e i n these secondary exchanges. In a d d i t i o n , some understanding of the freeboard gas flow conditions encountered within rotary k i l n s i s required, due to the coupling of the heat transfer problem to the flow f i e l d . 2 . 1 Radiation i n the Freeboard Region The freeboard region of a rotary k i l n forms an enclosure f i l l e d with the emitting/absorbing mixture of gases r e s u l t i n g from the combustion process and, i n many instances, the chemical reaction within the bed mat e r i a l . The c a l c u l a t i o n of r a d i a t i v e heat transfer within the freeboard involves f i r s t adequately simulating the emissive/absorptive c h a r a c t e r i s -t i c s of the gas mixture and then Incorporating the r e s u l t s into a r e a l i s t i c geometric model. 2.1.1 Emissive C h a r a c t e r i s t i c s of Gases In the absence of a luminous flame or s i g n i f i c a n t concentration of p a r t i c u l a t e s , H^O (vapour) and CC^ account f o r most of the emission/ absorption within the freeboard gas, other emitting species such as CO and SO^, normally being present i n n e g l i g i b l e concentrations. Although a l l gases which emit thermal r a d i a t i o n do so only over d i s c r e t e wavelength bands (and are termed r e a l gases), the concept of a gray gas, absorbing a l l wavelengths equally, i s often introduced to reduce the computational e f f o r t inherent i n gas r a d i a t i o n a n a l y s i s . For such a hypothetical gas, K i r c h o f f ' s Law (e = a) i s v a l i d for a l l wavelengths i n s t e a d of being r e s t r i c t e d to monochromatic r a d i a t i o n only (e = a..). K A. To take p a r t i a l advantage of the s i m p l i f i c a t i o n allowed by a gray gas assumption, yet avoid the large error normally associated with doing ( 26 ) so, H o t t e l demonstrated that the r a d i a t i v e c h a r a c t e r i s t i c s of a r e a l gas (or mixture of r e a l gases) could be c l o s e l y matched by a weighted summation of a s u f f i c i e n t number of gray gases as shown i n F i g . 2.1. (27) As d e t a i l e d i n Hottel and Sarofim the t o t a l gas em i s s i v i t y can be approximated by N e s I e n{l-exp(-K npL)} (2.1) n=l where N denotes the number of hypothetical gray gas components being assumed and e are the emissivity weighting c o e f f i c i e n t s . The e x t i n c t i o n - 9 -F i g . 2 . 1 A p p r o x i m a t i o n m u l t i p l e g r a y of r e a l gas t o t a l e m i s s i v i t y u s i n g g a s e s ( a f t e r H o t t e l and S a r o f i m ) - 1 0 -c o e f f i c i e n t K^= 0 i s incorporated to simulate the wavebands over which the gas i s r a d i a t i v e l y c l e a r . After choosing a gas temperature, one set of both and K n v a l u e s can be obtained by f i t t i n g the e m p i r i c a l t o t a l e m i s s i v i t y data for the actual mixture of gases to the form of eq. 2.1. A l l temperature dependence i s then assigned to the weighting c o e f f i c i e n t s and th e i r v a r i a t i o n with gas temperature obtained by f i t t i n g to the gas t o t a l e m i s s i v i t y data over the necessary temperature range. S i m i l a r l y , gas a b s o r p t i v i t y for black (or gray) body r a d i a t i o n i s represented by N a = I a n{l-exp(-K npL)} (2.2) n=l where are the a b s o r p t i v i t y weighting c o e f f i c i e n t s . Total gas absorp-t i v i t y for black body r a d i a t i o n , a function of both the temperature of the gas and of the emitting surface, can be obtained from t o t a l e missivity data using the r e l a t i o n s h i p T c T a(T T s, pL) = (^) e ( T ^ P L ^ ) (2.3) s g with 0.45 < c < 0.65, the exact value depending on the gas mixture concerned. Again a l l temperature dependence i s assigned to the weighting c o e f f i c i e n t s but f i t t i n g i s necessary over a range of both (absorbing) gas temperature and (emitting) surface temperature. - 1 1 -In p r a c t i c e most of the d i f f i c u l t y i n f i t t i n g gas t o t a l e m i s s i v i t y data using eq. 2.1 and eq. 2.3 occurs at small values of pL. Thus for very large enclosures as few as two gray gas components may be s a t i s f a c -tory while for smaller enclosures four or more might be necessary. S i n c e only gray gases are incorporated in the model, = and the a b s o r p t i v i t y of the gas for i t s own r a d i a t i o n i s equal to ' i t s e m i s s i v i t y at that gas temperature. 2.1.2 C a l c u l a t i o n of Freeboard Radiation The most complex heat transfer problem i n the freeboard occurs when the gas and surface temperature d i s t r i b u t i o n s are not known. The zone (28) method of Hottel and Cohen , incorporating a weighted gray gas emissiv-i t y model, provides a rigorous means to obtain a s o l u t i o n but only If the flow and combustion f i e l d s for the freeboard gas are known. This l a t t e r requirement presents a formidable obstacle and the only complete zone (13) model for the rotary k i l n freeboard i s that of Jenkins and Moles which was obtained by assuming plug flow downstream of the r e c i r c u l a t i o n region (Section 2.5) and extrapolating gas concentration data to estimate the combustion f i e l d . Predictions of wall and gas temperature p r o f i l e s were shown to be In reasonable agreement with experimental data but few other d e t a i l s were presented . Although such models show considerable promise, at present they have several l i m i t a t i o n s : ( i ) A lack of r e l i a b l e general models for the flow and combustion f i e l d s . ( i i ) The computational complexity r e s t r i c t s t h e i r general usage and hence development. ( i i i ) The freeboard does not represent the complete heat transfer problem. The transient response of the r e f r a c t o r y wall surface and heat trans f e r between the covered wall and bed (Section 2.3) as well as heat transfer within the bed material i t s e l f (Section 2.4) must be incorporated to obtain a complete k i l n heat transfer model. The zone method i s a sequence of modules for the c a l c u l a t i o n of progressively more d i f f i c u l t r a d i a t i v e heat transfer problems. A complete (27) d e s c r i p t i o n of the method i s provided by , but for the purpose of the current study a b r i e f discussion of d i r e c t r a d i a t i v e exchange i s s u f f i c i e n t . To begin the c a l c u l a t i o n procedure the enclosure, which i s assumed to be formed from gray d i f f u s e surfaces, i s subdivided into a s u f f i c i e n t number of zones, both gas and surface, such that each can reasonably be considered to be Isothermal with uniform pro p e r t i e s . U t i l i z i n g a weighted gray gas emissivity model, the r a d i a t i v e exchange between zone pa i r s , for each gray gas component n, next must be evaluated. v For the pair of surface zones and A^ (see F i g . 6.16) the di r e c t exchange area ( s j s ^ ) n * s defined by E . Cos, 0 . Cos 9 . QA ^ A = ~n2~ I I h 1 dA.dA, (2.4a) n A.->- A. II ' ' 2 n i->-i i i j l . . r. . A i A j ^ = E . (s .s.) J.n j i ' n (2.4b) where i s the radiant energy leaving A. that w i l l be incident on A without impinging on any other enclosure surface. For a black enclosure with known zone temperatures a complete d e s c r i p t i o n of surface/surface and gas/surface r a d i a t i v e heat transfer i s provided by N QA -*-A =1 (S.S.) (E.-E.) (2.5a) \A..-«-A. L 1 i i n i i / n J i n=l J V A = I < V l > n < V V n <2'5b> k i n=l where g^s^denotes the gas to s u r f a c e d i r e c t exchange area (see F i g . 6.13) and V represents a gas volume zone. -14-The net r a d i a t i o n to surface zone i n such a black enclosure i s R Q i , = l, V, iS3S^n < W n ^k Si>n < V E l » n <2'6> net n=l j=l J J k=l where J and K represent the t o t a l number of surface and gas zones re s p e c t i v e l y . The a p p l i c a t i o n of eq. 2.6 to gray walled enclosures w i l l r e s u l t i n values of Q which are too large by a factor < — — r . For R 1 Z net e n c l o s u r e s with s u r f a c e e m i s s i v i t i e s e g < 0.9 a means of accounting for r e f l e c t e d energy, such as ray t r a c i n g , can reduce t h i s e r r o r s u b s t a n t i a l l y . (29) Gorog used a modified r e f l e c t i o n method i n combination with a weighted gray gas emissivity model to carry out a t h e o r e t i c a l study of r a d i a t i v e heat transfer i n the freeboard of a rotary k i l n . The r a d i a t i v e heat fluxes to elements on the exposed wall dA and exposed bed dA , were ew eb calculated by d i v i d i n g the freeboard into a number of a x i a l s l i c e s e xtending i n both d i r e c t i o n s from dA and dA , and t r a c i n g the rays ew eb ° J emitted by the gas volume zones and the wall and bed surface zones u n t i l they reach e i t h e r dA or dA , . Values of net surface heat input were ew eb v obtained by making the summations Qj» = I Q J A + I Q v J A + I Q J A - e , dA , E (2.7) dA , L ew^ -dA , L xeb->dA , L xg>dA , eb eb eb eb eb eb eb Q J A = I Q J » + ! < ! , , , + J Q j . - e dA E (2.8) xdA L xew*-dA L xeb->dA L xg->dA ew ew ew v ' ew ew ew ew -15-The net rate of heat transfer from the freeboard gas was also calculated Q = e L A E - 7 Q - I Q , " I Q (2.9) g 8 m g g ew*g eb->g L xg->g where L i s the mean beam le n g t h of the gas and A i s the t o t a l area of m g the bounding surface. (23 ) Gorog et a l c i t e d some p a r t i c u l a r l y u s e f u l c o n c l u s i o n s r e s u l t i n g from the model: ( i ) Radiation from the freeboard gas to the r e f r a c t o r y wall and bed surface i s l o c a l i z e d by the poor t r a n s m i s s i v i t y of the gas for i t s own r a d i a t i o n . Therefore a x i a l gas temperature gradients have n e g l i g i b l e influence ( F i g . 2.2) and for the same reason r e f l e c t e d gas r a d i a t i o n can be neglected. ( i i ) Because the view factors between the wall and bed surface decline quickly with a x i a l distance ( F i g . 2.3) v i r t u a l l y a l l the wall r a d i a t i o n reaching the bed surface originates less than one k i l n diameter away (and vice versa). Therefore wall and surface a x i a l temperature gradients may also be neglected. Unfortunately less rigorous r e l a t i o n s h i p s for the c a l c u l a t i o n of ra d i a t i o n i n the freeboard have most often been employed. The most basic r e l a t i o n s h i p can be obtained by assuming a gray freeboard gas r a d i a t i n g to - 1 6 -F i g . 2 . 2 Showing th e t e m p e r a t u r e f l u x ( a f t e r n e g l i g i b l e i n f l u e n c e of a x i a l g r a d i e n t s on gas t o k i l n w a l l Gorog), gas h e a t -17-F i g . 2 . 3 Showing t h e r a p i d view f a c t o r s w i t h d e c l i n e i n e x p o s e d bed t o w a l l a x i a l p o s i t i o n ( a f t e r G o r o g ) -18-a gray, isothermal bounding surface. The problem i s thus reduced to that of two i s o t h e r m a l gray bodies and the solu t i o n i s r e a d i l y a v a i l a b l e ^ 3 ^ cn 4 ™ 4 A ovT T. > g ( g - A J Q = i ( 2 a ° ) g*A — + — - 1 8 *« \ where A i s the surface area bounding the gas. By s t i l l r e quiring the bounding surface to be isothermal but drop-ping the gray gas assumption, an a l t e r n a t i v e r e l a t i o n s h i p i s suggested by< 2 7> ( £ A g + 1 ) 4 4 V A ; A g - + - a ( £ g T g " A V A } ( 2 ' N ) 8 S S with a being used to i n d i c a t e that the gas a b s o r p t i v i t y i s to be g 8 e v a l u a t e d at the temperature of the bounding surface. For e > 0.80 the g error associated with eq. 2.11 i s stated to be under 10% with the p r o v i s o that T and T. must d i f f e r by at least several hundred Kelvin g A • g degrees. A summary of expressions which have been u t i l i z e d to calculate r a d i a t i v e exchange between the freeboard gas and exposed bed and wall surfaces i s presented i n Table 2.1. -19-TABLE 2.1 Expressions proposed f o r the freeboard gas to surface r a d i a t i v e heat transfer c o e f f i c i e n t Reference „h . W/m2K Rg*A g Comments (2) 4 4 o(e T - . a T ) g g A g g A g T - T. Similar to Eq. 2.11 (4),(5),(8) T ~ T, 8 A g Gray gas s i m i l a r to Eq. 2.10 (6) r p 4 4 $ . g g.Ag i> = Overa l l r a d i a t i o n exchange factor (9) 23 •* 113 Author's estimate (12) / 0 *' A [ T ( Z ) 4 - T (Z,0) 4] 9 8 g 8 g exp <£'= Over a l l r a d i a t i o n interchange factor (32) 4 4 *< Tg " TA g> 1- + -L.-1 8 A g Eq. 2.11 T = Average r a d i a t i n g ® gas temperature - 2 0 -2.2 Convection i n the Freeboard Convective heat transfer, i n p a r a l l e l with gas r a d i a t i o n , occurs between the freeboard gas and i t s bounding surfaces, the exposed wall and exposed bed mat e r i a l . At low temperatures, convection i s the dominant energy transport process but at moderate or high temperatures i t s r e l a t i v e importance i s less c e r t a i n . Downstream of any r e c i r c u l a t i o n and i n the absence of marked asymmetry due to buoyancy or geometrical e f f e c t s (Section 2.5), the s i t u a t i o n resembles that developing pipe flow for which numerous c o r r e l a t i o n s of the forms NuD= f ( R e D , Pr, £) (2.12) or Nuz= f ( R e z , Pr) are a v a i l a b l e . However an a d d i t i o n a l complication arises due to the fundamentally d i f f e r e n t surfaces presented to the the freeboard gas by the (hydrodynami-c a l l y ) smooth, impermeable r e f r a c t o r y wall and the porous, tumbling layer of granular bed mat e r i a l . 2.2.1 Convection to the Exposed Wall Surface F o r t u r b u l e n t d e v e l o p i n g flow i n sho r t pipes (2 < L/D < 20) H K r e i t h ^ 3 ^ recommends the Dittus-Boelter c o r r e l a t i o n .-21-Nu7 = 0.023 [ l + ( ^ r ) ° ' 7 ] Re n °* 8 P r ° ' 3 3 (2.13) DH L °H (31) w h i l e f o r somewhat longer pipes (10 < L/D < 400) K r e i t h and Black v ' n suggest D 0 , 0 5 5 Nu~ - 0.036 (-f) Re n °* 8 P r ° * 3 3 (2.14) DH L °H (24) a r e s u l t chosen by to calculate wall convection i n a t h e o r e t i c a l study of rotary k i l n heat t r a n s f e r . For a 0.406 m ID p i l o t k i l n f i r i n g natural gas, Watkinson and (32) Brimacombe c a l c u l a t e d convection to the exposed wall surface using „ 0.4334 D N U [ ) = 1.26 (Re D Pr ^ ) (2.15) H H and found i t to account for < 10% of the measured wall heat f l u x over the temperature range encountered (> 700 K). At Re = 2000, representative of H 2 the p i l o t k i l n t r i a l s , values of h ~ 2 •*• 3 W/m K were obtained. I t v c g»ew was noted that gas r a d i a t i o n would increase with k i l n s i z e , due to increased beam lengths, while the e f f e c t of scale-up would be to reduce the role of convection to the exposed wall s t i l l further since according 0 1t- . n-0.13 - " ' >, •"•"»•-to eq. 2.15 h a D •- . - . ;-c g->ew - 2 2 -(33) 2 Wes et a l recorded h ~ 5 W/m K using a i r i n an empty metal c g»ew & v 3 drum equipped with a x i a l l y aligned f l i g h t s . A near doubling of the a i r flow and Re^ (2500 -> 4500) enhanced h by only 4% i n d i c a t i n g Nu„ a D ' c g+ew 3 3 D Re^^"^ 7. The s m a l l exponent could be due to flow conditions peculiar to the apparatus (Section 2.5). (22) Tscheng c a r r i e d out an extensive series of convection t r i a l s i n a 0.191m ID x 2.44m k i l n using heated a i r i n the freeboard to eliminate 2 gas r a d i a t i o n . Values of h ~ 2->-9 W/m K were obtained over the range ° c g>ew 6 1600 < Re^ < 7800. Regression analysis was used to obtain the c o r r e l a t i o n i c/ ^  0.575 „ -0.292 .„ Nu. = 1.54 Re^ Re (2.16) D D a) g*ew although: as can be seen from F i g . 2.4, the actual e f f e c t of r o t a t i o n a l Reynolds number Re^ may be questioned. The Re^ dependence of eq. 2.16 can be observed to l i e i n the midrange of the e a r l i e r c o r r e l a t i o n s . Although the s i t u a t i o n was one of developing flow, data from only a short test s e c t i o n were used to o b t a i n eq. 2.16 and no c o r r e l a t i o n f o r Nu was CJ developed. Since, at k i l n operating temperatures, convection probably accounts for < 10% of the t o t a l exposed wall surface heat f l u x , the use of any established c o r r e l a t i o n for developing pipe flow should introduce n e g l i g i -ble error to k i l n heat transfer c a l c u l a t i o n s . The use of eq. 2.16, derived from actual k i l n data, may require the addition of a factor for entrance length, while i t should be noted that eqs. 2.13 to 2.15 predict average values of Nu^ over the entrance region. -23-£1 * JC o K ID O* o> •E 8 6 i I r Fill A 6.5% o I 1.0% IT) N O CP •E I 0.8 0.61 0.4 K 0.2' 0.4 A A 4 J I L o ^ 8 N< O N v. J L Rotation rate (rpm) F i g . 2 . 4 Showing t h e e f f e c t o f r o t a t i o n r a t e on c o n v e c t i o n t o the e x p o s e d w a l l and bed s u r f a c e s ( a f t e r T s c h e n g ) 2.2.2 Convection to the Exposed Bed Surface The r e l a t i v e importance of convection at the exposed bed surface i s considerably less c e r t a i n than at the exposed w a l l . Most e a r l i e r (4 5 34) s t u d i e s ' ' a p p l i e d pipe flow c o r r e l a t i o n s at the bed surface as w e l l as the w a l l surface. S p e c i f i c values of ^ g ^ . ^ ranging upward from 2 (12 ) 1.5 W/m K have been invoked, o f t e n without reported j u s t i f i c a t i o n . (19) Friedman and Marshall c a r r i e d out extensive t r i a l s i n a rotary heat exchanger using a i r and various sands. Although i n t e r n a l f l i g h t s were used for most experiments, a test series was performed varying, i n addition to the gas and s o l i d s flows, the number of f l i g h t s . Without 2 i n t e r n a l f l i g h t s , values of 19 < ^ g ^ g ^ < 35 W/m K were obtained with no discernable Re^ dependence. F l i g h t s were found to enhance convective heat transfer considerably, by a factor of 2 for a single f l i g h t up to a factor of 5 with 8 f l i g h t s i n place. S i g n i f i c a n t l y , neither p a r t i c l e size (150 •*• 2300(a) nor r o t a t i o n r a t e (3 •*• 20 rpm) had any c l e a r e f f e c t on c ng^. e^» contrary to what might be expected i f the bed surface played a l i m i t i n g r o l e i n the heat transfer process. 2 (33) Values of h , ~ 77 W/m K were r e p o r t e d by u s i n g potato starch of unspecified p a r t i c l e size at a drum r o t a t i o n rate of 3 rpm. However, the drum was equipped with a x i a l l y aligned f l i g h t s which l i m i t s the g e n e r a l i t y of the r e s u l t s . Re^ was again found to have n e g l i g i b l e influence but h . was observed to increase l i n e a r l y with r o t a t i o n rates c g+eb from 3 •> 6 rpm which prompted the conclusion that transient heat -25-trans f e r might be a factor at the bed surface. The maximum value reported was h . = 160 W/m2K. c g->-eb (32) 2 In the p i l o t k i l n experiments values of 120 < c h g > e b < 240 W/mK were reported and convection to the exposed bed surface was thought to account f o r up to 80% of the net heat transfer to the bed. The convective c o n t r i b u t i o n was obtained by dif f e r e n c e according to = „ Q , + Q , + Q , + „Q ^ (2.17) x b n e t R g+eb c g+eb xcw*cb R^ew*eb The net input to the bed, was calculated from measurements of a x i a l net bed and gas temperature gradients using f i r s t law a n a l y s i s . Both Q c w^. c b and 'Q . were assumed to be n e g l i g a b l y s m a l l , w h i l e _Q , was Rxew-»-eb R^g-*eb (22) c a l c u l a t e d by means of eq. 2.10. The experimental study reported by (35) Tscheng and Watkinson i s the most thorough to date r e l a t i n g to the subject. A f t e r considering the data i t was concluded that h - f(Re_ , Re , n) (2.18) c g*eb v D ' or ' where D g i s the equivalent diameter calculated from the f r a c t i o n n of the k i l n cross s e c t i o n occupied by the bed material. The c o r r e l a t i o n (2.19) - 2 6 -was obtained by regression analysis and the re s u l t s plotted as per F i g . 2.5. As with eq. 2.16, proposed for the exposed wall, eq. 2.19 was obtained from a short test section and i s e s s e n t i a l l y a l o c a l value only. Again the data do not strongly j u s t i f y the i n c l u s i o n of Re ( F i g . 2.4). co As was the case for the exposed wall, eq. 2.19 implies a dec l i n i n g r o l e for convection to the exposed bed material with increasing k i l n diameter. S e v e r a l important r e s u l t s r e g a r d i n g h . were common to the c g+eb experimental studies. ( i ) h , considerably exceeded h c g>eb c g-»-ew ( i i ) P a r t i c l e s i z e d i d not s i g n f l c a n t l y influence h , at least for c g*eb p a r t i c l e to k i l n diameter r a t i o s i n the order of 1% or l e s s . ( i i i ) K i l n r o t a t i o n rate played either a minor or at most inconclusive r o l e . The r e s u l t s of would appear to be the most r e l i a b l e a v a i l a b l e i n d i c a t i n g that h , ~ 10 h . The observed convective enhancement c g->eb c g->ew was att r i b u t e d to the combined e f f e c t s of a larger true surface area at the bed surface and movement of the uppermost p a r t i c l e layers r e l a t i v e to the i n t e r s t i t i a l gas. For the l a t t e r an a d d i t i o n a l factor, which could not be evaluated from the theory, was required by the model. The actual (35) area of the porous bed s u r f a c e has been estimated to be about twice the chord length although further suggestions that advection by p a r t i c l e s i n the bed surface might reduce bed thermal resistance would seem i n v a l i d -27-Predicted N u g < e b F i g . 2 . 5 P r e d i c t e d vs e x p e r i m e n t a l v a l u e s o f gas t o ex p o s e d bed N u s s e l t Number ( a f t e r T s c h e n g ) - 2 8 -s i n c e no temperature g r a d i e n t s i n t o the bed m a t e r i a l were noticed and h , has been shown to be at most a weak f u n c t i o n of r o t a t i o n rate, c g->eb Enhancement of heat transfer by s t a t i c surface roughness has been ( 3 6 ) the s u b j e c t of numerous i n v e s t i g a t i o n s . Dipprey and Sabersky performed an extensive experimental study of heat and momentum transfer i n smooth and rough tubes with f u l l y developed flow and concluded that surface roughness could enhance convective heat transfer by a factor of 2 -> 3 at most. The data supported the explanation of surface protrusions penetrating the molecular d i f f u s i o n layer adjacent to the surface. A (37) s i m i l a r enhancement l i m i t was observed by Sugawara and Sato f o r developing a i r flow over roughened f l a t p lates. Other studies have confirmed these r e s u l t s . Assuming that once the f u l l y rough surface condition i s achieved no further increase i n the convective c o e f f i c i e n t i s possible by s t a t i c roughness, the s i g n i f i c a n t l y large enhancement factors measured at the non-static exposed bed surface must be a t t r i b u t a b l e to the (22) p a r t i c l e motion perhaps by the mechanism described by 2.3 Covered Wall/Bed Material Heat Transfer The r o t a t i o n of the k i l n wall surface sets up a transient heat exchange between the covered wall and the adjacent granular bed material. This s i t u a t i o n i s common to spouted and packed beds, s t i r r e d bed contact heaters and rotary k i l n s , although In this l a s t instance, the problem i s made less complex by the fact that the i n t e r s i t i t a l gas i s not flowing -29-through the bed and i n most cases the bed material adjacent to the wall rotates as a r i g i d body with the wall (Section 2.4). The c a l c u l a t i o n of covered wall/bed material heat transfer requires that the thermal resistance of the bed material, plus any addition thermal resistance occurring at the in t e r f a c e , be c o r r e c t l y evaluated. In addi-t i o n , a r e a l i s t i c transient heat transfer model Is necessary and the correct i n i t i a l and boundary conditions must be established. Heat transfer within a granular material occurs by conduction, convection and r a d i a t i o n . However the material i s usually assumed to behave as a continuum (quasi-homogeneous) and the combined e f f e c t of a l l three heat t r a n s f e r processes expressed as an e f f e c t i v e thermal conductivity k^ e which must be evaluated either e m p i r i c a l l y or from one of the many t h e o r e t i c a l models a v a i l a b l e . In the region of contact between a wall and a granular material, the continuum model breaks down and a f i l m or contact resistance i s i n t r o -duced to model the actual heat transfer processes. Thus heat transfer between the k i l n wall and the bed material can be considered to occur by convection across a thin gas f i l m at the i n t e r -face, according to q = h.(T - T . ) ^ f ws^ cb (2.20) - 3 0 -followed by conduction into the bed material, for which * = kbe f < 2- 2 1> For a planar continuum material, i n the absence of mass flow, heat generation or work e f f e c t s , conservation of energy requires that (38) the d e r i v i a t i o n being g e n e r a l l y a v a i l a b l e , eg. . For pl a n a r one dimensional conduction with constant thermal conductivity eq. 2.22 reduces to | I = k _ ^ T 3 at cp 9 X 2 (39) A n a l y t i c a l s o l u t i o n s to eq. 2.23 have been obtained f o r a number of common i n i t i a l and boundary conditions. More recently,numerical techniques such as f i n i t e differences have come into general use to allow for the sol u t i o n of the conduction equation i n one, two or three dimen-sions f o r any set of i n i t i a l and boundary conditions. 2.3.1 E f f e c t i v e Thermal Conductivity of a Packed Bed The e f f e c t i v e thermal conductivity k^ e of a stationary packed bed, without gas flow, can be anticipated to be a function of at least the following: -31-k b e = f n ( k g , k g, G, T) (2.24) where G i s a complex function of geometry, which includes the variables of p a r t i c l e s i z e and shape, void f r a c t i o n , gas pressure, etc. The heat exchange process involves conduction, through p a r t i c l e s and i n t e r s t i t i t a l gas, r a d i a t i o n between adjacent p a r t i c l e s and beyond v i a openings i n the l a t t i c e structure and possibly natural convection of the i n t e r s i t i t a l gas. The very complex nature of the geometry function has confined t h e o r e t i c a l studies of the problem to regular p a r t i c l e shapes (usually spherical) arranged i n some s p e c i f i e d l a t t i c e s tructure. Extension of the r e s u l t s to random arrangements of i r r e g u l a r p a r t i c l e s has been through the introduc-t i o n of various empirical shape factors or accommodation c o e f f i c i e n t s . D i e s s l e r and E i a n ^ 0 ^ proposed that i n the absence of s i g n i f i c a n t r a d i a t i v e e f f e c t s , porosity was the only s i g n i f i c a n t geometrical factor and obtained the semiempirical r e s u l t s shown by F i g . 2.6 where ^ = f n ( i - , 0 ) (2.25) g g (41) Schotte extended the r e s u l t s by i n c l u d i n g a r a d i a t i v e term. Radiation across a p a r t i c l e layer was assumed to consist of two components i n p a r a l l e l ( F i g . 2.7), one through the i n t e r p a r t i c l e void spaces and a second i n series with conduction through the p a r t i c l e s . The e f f e c t i v e thermal conductivity due to r a d i a t i o n , calculated using F i g . 2 . 6 V a r i a t i o n of e f f e c t i v e t h e r m a l c o n d u c t i v i t y w i t h v o i d f r a c t i o n ( a f t e r D i e s s l e r and E i a n ) . - 3 3 -1. Heat t r a n s f e r t h r o u g h t h e s o l i d . 2. Heat t r a n s f e r t h r o u g h t h e c o n t a c t s u r f a c e o f s o l i d . 3. Heat t r a n s f e r between a d j a c e n t s u r f a c e s by r a d i a t i o n and c o n v e c t i o n t h r o u g h t h e gas f i l m . 4. R a d i a n t h e a t t r a n s f e r between v o i d s p a c e s . F i g . 2 . 7 Heat t r a n s f e r p a t h s i n a s t a g n a n t packed bed ( a f t e r Y a g i and K u n i i ) - 3 4 -1 - 0 + 0 4 c r e d T 3 (2.26) R be 1_ 1 " w " p k s 4 a e d T 3 P was then added to the r e s u l t from F i g . 2.6. Although continuing to be based on the heat transfer paths shown i n F i g . 2.7 t h e o r e t i c a l models for pr e d i c t i n g k^ g have s t e a d i l y increased i n both s o p h i s t i c a t i o n and complexity. (42) (43) Ya g i and K u n i i v and K u n i i and Smith v ' considered i n d e t a i l r a d i a t i o n and conduction across the thin wedge of gas near the contact points between spherical p a r t i c l e s to obtain the expression K (AL/d )(2-e) Nu (AL/d ) (1-0) m 0 [ l + 2 SL] + 2 ( 2 . 2 7 ) g p + 0(i-o 1 . 2(1-0) (d IX ) + Nu R l d k s where: Nu R^ = r a d i a t i v e Nusselt number (2.28) 4 a T 3d _ P ( 2 / e - l ) k o AL = average thickness of a p a r t i c l e layer JL = t h i c k n e s s of a s l a b of bed material which o f f e r s the same thermal D resistance as the p a r t i c l e . X = t h i c k n e s s of a s l a b of s t a t i o n a r y f l u i d which o f f e r s the same v J thermal resistance as the f l u i d i n the region of p a r t i c l e contact. -35-For spherical p a r t i c l e s , t h e o r e t i c a l expressions were derived to evaluate AL, JL and I . ' b v (44) Wakao and Kato employed a f i n i t e d ifference conduction model to analyse the orthorhombic unit c e l l of spherical p a r t i c l e s (0 = 0.395) shown i n F i g . 2.8. By defining another r a d i a t i v e Nusselt number N UR2 " ( 2/ e - 0.264^ ( 2 ' 2 9 ) s the r e s u l t s plotted i n F i g . 2.9 were obtained (for the single value 0 =0.395). (45) Schlunder i n t r o d u c e d the f a c t that as the thickness of the wedge of gas adjacent to the p a r t i c l e contact point becomes of the same order as the mean free path of the gas molecules, the gas no longer behaves as a continuum. I n c l u d i n g this e f f e c t , Bauer and S c h l u n d e r ^ ^ derived a complex r e l a t i o n k D e = fn{k , k , T,k, , k , d . 0, ck , C,, , f(e )} (2.30) k " * l , V g ' R be ' ge ' p' v* Y k ' Form' v c'pr > where: k^ e = equivalent thermal conductivity of a very t h i n gas layer. (b^  = r e l a t i v e flattened p a r t i c l e surface contact area. C„ = p a r t i c l e shape factor Form v e = p a r t i c l e s i z e d i s t r i b u t i o n function. -36-1. Heat t r a n s f e r through the s o l i d . 2. Heat t r a n s f e r through the c o n t a c t s u r f a c e of s o l i d . 3. Heat t r a n s f e r between adjacent s u r f a c e s by r a d i a t i o n and c o n v e c t i o n through the gas f i l m . A. Radiant heat t r a n s f e r between v o i d spaces. F i g . 2 . 8 The orthorhombic u n i t c e l l of Wakao and Kato -37-Fig.2.9 E f f e c t i v e thermal l a t t i c e s t r u c t u r e c o n d u c t i v i t y ( a f t e r Wakao of the orthorhombic and Kato) - 3 8 -(47 48) I t i s e v i d e n t from these r e s u l t s and from others ' t h a t detailed consideration of the fundamental heat transfer processes e n t a i l s the introduction of geometry dependent variables which are amenable to t h e o r e t i c a l treatment only for the simplest of p a r t i c l e shapes and l a t t i c e structures. (49) Vortmeyer i n a survey of the a v a i l a b l e models for c a l c u l a t i o n (44) of k, recommended that of as the most t h e o e r e t i c a l l y rigorous, but i n be a comparison of the r e s u l t s from various models found generally good agreement. However i n comparing predicted r e s u l t s to the measurements of (47 ) Beveridge and Haughey , obtained from alumina spheres ( d p « 6mm, e » 0.7), a l l the models were somewhat high unless the assumed emi s s i v i t y values were reduced to a value of 0.5. (49) From the r e s u l t s of the choice of model used to c a l c u l a t e k^ g would seem a r b i t r a r y . I t was noted that a l l a v a i l a b l e empirical datarare for small values of NuT 'R2-2.3.2 Surface Film C o e f f i c i e n t As long ago as 1949 Hatta and Maeda made use of a wall f i l m c o e f f i c i e n t of heat transfer i n analyzing t h e i r data for heat transfer i n (52) p a c ked b e d s . Y a g i and K u n i i found that f o r p u r e l y r a d i a l heat transfer through a packed bed, the thermal resistance increased s i g n i f i -cantly near the walls even when the Peclet number for f l u i d flow through the bed went to zero. They proposed that the f i l m c o e f f i c i e n t must consist of two additive components, one being independent of Pe. - 3 9 -( 5 3 ) Schwartz and Smith showed the void f r a c t i o n near a wall surface to be larger than i n the core of the packed bed due to the less intimate contact possible between p a r t i c l e s and a f l a t surface than among p a r t i c l e s . As shown i n F i g . 2 . 6 e f f e c t i v e thermal conductivity i s se n s i -t i v e to void f r a c t i o n which i n part accounts for the increased resistance near the w a l l . ( 5 4 ) S u l l i v a n and Sabersky i n e v a l u a t i n g four d i f f e r e n t granular materials proposed the simple empirical r e l a t i o n h f - £ / (2.31) P and calculated C ~ 0.085 for s p h e r i c a l p a r t i c l e s . R i c h a r d and Rahaven^^^ analyzed data of numerous authors and suggested v a r i a b l e C was rela t e d to porosity according to C = 5 . 1 6 0 5 * 0 6 ( 2 . 3 2 ) though the data does not appear to bear out th i s r e l a t i o n s h i p . S c h l u n d e r p r e s e n t e d a complex model for heat transfer at the wall, based on consideration of spheres contacting a f l a t surface. Central to this model i s the fact that i n the very thin wedges of gas very near to a contact point the thermal conductivity of the gas tends to zero - 4 0 -as the gap approaches the mean free path of the molecules. The model was subsequently improved and i s given by Mollekopf and M a r t i n ^ a s k h, = fh + (1-f) S — + ,-h . (2.33) f w p / d ~ + Z P where: h = wall to p a r t i c l e heat transfer c o e f f i c i e n t , wp 2 k 0.5d = & {f i + L±A) i n f i + P-l - 1} r U 0.5d J ^ I + 6 J ' P P „h , = r a d i a t i v e wall to bed heat transfer c o e f f i c i e n t . R wb 4 a T 3 ! - + ! - - i e e w s f = wall surface coverage factor (stated to have a value of 0.8). 1 = modified mean free path of molecules. 9 f l 2 IIRT k f l y ' / M P(2C f - R/M) y = accommodation c o e f f i c i e n t (stated to be i n the range 0.8 < y 0.9). 6 = sum of surface roughness heights for both surfaces. M = molecular weight of the gas R = universal gas constant In t h i s model h^ i s a f u n c t i o n of temperature due to both i t s e f f e c t on ra d i a t i v e heat transfer and on gas molecule mean free path. In dealing ( 4 5 ) with non-spherical p a r t i c l e s , Schlunder suggests , on the basis of i t s successful a p p l i c a t i o n , the assumption of point contact with zero surface roughness. 2.3.3 Covered Wall/Bed Heat Transfer Models Only a handful of empirical studies s p e c i f i c a l l y r e l a t e d to covered wall/bed heat transfer i n a rotary k i l n have appeared i n the l i t e r a t u r e and a l l have been for low temperatures i n uninsulated metal drums. Although the r e s u l t s may be of l i m i t e d usefulness i n the current study., the attendant data arethe best currently a v a i l a b l e . In an i n v e s t i g a t i o n into the heating of potato starch and yellow (33) d e x t r i n e u s i n g a 0.6m ID x 9m s t e e l drum Wes et a l assumed the boundary and i n i t i a l conditions shown i n F i g . 2.10a: ( i ) Constant temperature isothermal w a l l . ( i i ) Constant temperature isothermal core of bed material. ( i i i ) I n i t i a l l y uniform bed temperature. ( i v ) N e g l i g i b l e thermal resistance at the i n t e r f a c e . The r e s u l t i n g s o l u t i o n to the conduction eq. 2.23 i s the f a m i l i a r penetration theory r e s u l t T - r x,t b T ^ = e r f f 1 <2-34> w - b _,<x t 2/ be c from which i t i s e a s i l y shown that -42-•w Txp = Tb x^O \>0 T^- T w ^ T» (a ) Wes et al (33) 1 wl VO Tx?0=Twl 0<x<x =TD xw,<x wl te=0 T0ftc=Tw T*>c= Twl 0^x<x w | (b) Wachters a Kramers ( 2 0 ) ! AT, 1c=0 Tx>0= Tb x>0 tc>0 T 0 f t=VAT f Taj ,*C=T|, (c) Lehmberg et al (21) F i g . 2 . 1 0 Boundary c o n d i t i o n s assumed f o r c o v e r e d w a l l / b e d heat t r a n s f e r . - 4 3 -Eq. 2.35 was stated to adequately correlate the data although the b o u n d a r y c o n d i t i o n T = T has been g e n e r a l l y c o n s i d e r e d 3 o , t w e 3 c ( 58 ) u n r e a l i s t i c . The fact that the drum was equipped with a x i a l l y aligned f l i g h t s may account for s a t i s f a c t o r y r e s u l t s being obtained using eq. 2.35. Wachters and K r a m e r s ^ ^ , h e a t i n g sand of unspecified s i z e i n a 0.152m ID x 0.475m copper drum without i n t e r n a l s , found eq. 2.35 to con-siderably overestimate heat transfer c o e f f i c i e n t s . Instead they proposed the boundary condition i l l u s t r a t e d i n F i g . 2.10b, also without introducing the f i l m c o e f f i c i e n t at the w a l l . To obtain a sol u t i o n to eq. 2.23 i t was assumed, without any j u s t i f i c a t i o n , that the average temperature of the wall layer was constant. By introducing two dimensionless variables be constant / 0 * = = = Bi Fo (2.36) h , /not, t l o c a l l o c a l cw*cb be c X 6 = w A (2.37) 2 Ax, t be c a functional r e l a t i o n s h i p between <J> and dimensionless wall layer depth 6 was obtained. For a "thick" wall layer (6 > 2) (b i s nearly constant and 2 k b e h = ! _ 6 > 2 (2.38) c w * c b 3/iIaTT" be c - 4 4 -while for a " t h i n " wall layer ( 6 < 0.6) i s a l i n e a r function of 6 and 2 k h - — 6 < 0.6 (2.39) cw*cb (1+2 6 ) /Tla. t be c Reducing the wall layer thickness increases n C W L > c ^ , a n d i n the l i m i t (6 = 0) eq. 2.39 i s reduces to eq. 2.35. By adjusting the r a t i o T w ^ / T b o and the wall layer thickness X a reasonable f i t to the data was obtained using eq. 2.38 (thick layer) for r o t a t i o n rates < 10 rpm and eq. 2.39 ( t h i n layer) for rate > 10 rpm. (21) Lehmberg et a l included a f i l m resistance between the wall and bed material. The assumed boundary and i n i t i a l conditions are shown by (39) F i g . 2.10c. The s o l u t i o n to eq. 2.23, obtained fronr , provided the r e s u l t 2 h , cw+cb / k b e C p b p b ,2 . kbe r r h f x c f ,a, t k, / be c be e r f c ( ^ - a b e t c ) - l]} (2.40) se Values of ^ c w > c b were obt a i n e d experimentally by heating sand of four d i f f e r e n t average p a r t i c l e sizes (0.16 •> 1.0 mm) along with soda (0.14mm) i n a r o t a t i n g s t e e l cylinder (0.25m ID x 0.60m). -45-No empirical data for covered wall/bed heat exchange at temperatures s u f f i c i e n t l y high for r a d i a t i o n to play a s i g n i f i c a n t r o l e have yet appeared. In the absence of any tested c o r r e l a t i o n s the evaluation of h cw->cb for use i n rotary k i l n modelling has been haphazard. A summary of some expressions used i s provided by Table 2.2. (35) (20 21 33) Tscheng and Watkinson u t i l i z e d the data from ' ' t o obtain the c o r r e l a t i o n h , I cw->cb cw Nu , = -. cw*cb k, be 2 Q 0.3 = 11.6 [SLA) (2.41) a, be Unfortunately eq. 2.41 must be r e s t r i c t e d to r e l a t i v e l y low temperatures and c a r r i e s the a d d i t i o n a l requirement that a » a, (isothermal w a l l ) . w b 2.4 P a r t i c l e Motion Within the Bed Material The s a t i s f a c t o r y operation of a rotary k i l n requires not only that energy must reach the bed material surface by the external heat transfer processes but that i t must penetrate into the bed and be uniformly d i s t r i -buted. This i n t e r n a l energy transport occurs by conduction, convection and ra d i a t i o n through the bed and by advection of the bed p a r t i c l e s . An understanding of bed motion i s e s s e n t i a l to an understanding of the r e l a t i v e importance of these i n t e r n a l energy transport mechanisms. -46-TABLE 2.2 Expressions proposed f o r the covered w a l l to covered bed heat transf e r c o e f f i c i e n t Reference hcw/cb < W / l A > Comments (2) 550 ( C f b g ) ° - 5 6 7 5 h , c g->-eb G = Mass fl u x of freeboard gas (5) 226.8 Author's estimate (6) 4p, C , d « ** ^b pb p (l/o>) $ = Heat p e n e t r a b i l i t y c o e f f i c i e n t <£'= Empirical burden mixing c o e f f i c i e n t (9) 74 -> 142 Author's estimate (16),(24) 11.6 k, 2a 0.3 be <-nr 8-\ cw be Eq. 2.41 (12) 41 Author's estimate - 4 7 -The bed motion can be divided into two components: ( i ) Motion i n the a x i a l d i r e c t i o n due to k i l n i n c l i n a t i o n . ( i i ) Motion i n the plane transverse to the axis due to k i l n r o t a t i o n . Although ( i ) i s c e r t a i n l y of importance;since i t determines p a r t i -c l e residence times, i t i s ( i i ) which influences the transverse d i s t r i b u -t i o n of energy through p a r t i c l e mixing. 2.4.1 Transverse Bed Motion (59) F o l l o w i n g the d e s c r i p t i o n of Rutgers the transverse bed motion originates with p a r t i c l e s at the wall being c a r r i e d along by f r i c t i o n with the r o t a t i n g wall surface. This motion i s transferred without slippage to successive layers of the bed so that some portion of the bed material rotates as a r i g i d body about the k i l n axis at the same angular rate as the k i l n w a l l . Although other modes have.been c l e a r l y identified^°^ only the r o l l i n g bed shown by F i g . 2.11 w i l l be considered for th i s study. Such a bed w i l l consist of e s s e n t i a l l y two regions. ( i ) A core zone with p a r t i c l e s moving as a r i g i d body with the k i l n w a l l . T h i s has been r e f e r r e d to as the plug flow r e g i o n ^ * ^ despite the fact that, k i l n i n c l i n a t i o n being orders of magnitude less than the s t a t i c angle of repose for the bed material, p a r t i c l e s within t h i s region w i l l have zero a x i a l v e l o c i t y . - 4 8 -Bed active layer Plug flow region F i g . 2 . 1 1 Bed m o t i o n showing t h e shape of t h e bed a c t i v e l a y e r -49-( i i ) A zone adjacent to the freeboard gas cons i s t i n g of p a r t i c l e s moving i n a d i r e c t i o n e s s e n t i a l l y p a r a l l e l to the exposed bed surface. This w i l l be termed the bed active layer. In this region vigorous transverse mixing of the p a r t i c l e s can occur near the exposed surface. H e n e i n ^ 6 0 ^ used the 0.4m ID x 5.5m UBC p i l o t k i l n along with batch rot a t i n g cylinders (0.4m ID and 1.0m ID) to study the transverse bed motion of several materials which included sand and limestone. The t r a n s i t i o n 2 to r o l l i n g bed was found to be a function of a Froude number — — , % f i l l s g and a s i n g l e e m p i r i c a l term 0G the s l i p p i n g angle for the bed material. The r o t a t i o n rate required for t r a n s i t i o n from slumping to r o l l i n g mode was observed to decline with increasing bed depth. By sighting through a plexiglas end plate, the bed active layer could be observed to have the shape shown i n F i g . 2.11. The maximum thickness at midchord was found to increase with p a r t i c l e s i z e , r o t a t i o n r a t e and bed depth. For deeper beds ( t ^ / d p > 40) the maximum thickness of the active layer was < 10% of the bed depth. (21) Lehmberg et a l performed a s e r i e s of t r i a l s to determine the i n t e n s i t y of p a r t i c l e mixing i n the bed active layer using a 0.31m ID x 0.3m batch rotating c y l i n d e r . The reported shape and thickness of the -5.0-bed active layer was i n good agreement with . Colored tracer p a r t i c l e s i n i t i a l l y placed at the lower end of the i n c l i n e d bed surface were observed to be uniformly mixed into the bed a f t e r < 4 passes through the bed active layer i n d i c a t i n g vigorous but not complete mixing within the layer for each pass. T r i a l s using hot tracer p a r t i c l e s i n j e c t e d into the bed at the base of the bed i n c l i n e were also c a r r i e d out. By measuring the decay i n p a r t i c l e temperature each time the p a r t i c l e s returned to the i n j e c t i o n region, a time constant for the decay was calculated and found to decline slowly with r o t a t i o n rate. Complete mixing was again achieved a f t e r the fourth pass through the bed active layer. (22) Tscheng measured the v e l o c i t y of p a r t i c l e s within the bed active layer and found the chordwise v e l o c i t y to decrease i n an approximate l i n e a r manner from a maximum at the free surface. The v e l o c i t y at the bed surface exceeded the wall surface c i r c u m f e r e n t i a l v e l o c i t y by a factor of about s i x . In developing a semi-empirical model to predict residence time, Mu ( 61) and Perlmutter also adopted the two region model. By considering some f r a c t i o n of the material entering the bed active layer to be p e r f e c t l y mixed and the remainder to pass through without mixing (bypass), a mathematically workable model was obtained. Calculated values of bypass were i n the range 0.85 •> 0.93 i n d i c a t i n g somewhat less vigorous mixing than the previous examples. -51-For sodium bicarbonate p a r t i c l e s (50 100a) colored tracer tests r e p o r t e d b y ^ 2 0 ^ showed a tendency for p a r t i c l e s i n a thin layer adjacent to the wall to p r e f e r e n t i a l l y return to the wal l , although few d e t a i l s were given. The bed active layer was taken to consist of two separate well mixed layers without s i g n i f i c a n t mixing between the l a y e r s . P e a r c e ^ ^ also recognized that complete mixing would not occur with a single pass through the bed active layer and introduced a mixing e f f e c -tiveness c o e f f i c i e n t which was estimated to l i e i n the range 0.5 •> 1.0. ( 62) Numerous studies of transverse mixing had defined mixing c o e f f i c i e n t s based on d i f f u s i o n analogies or s t a t i s t i c a l techniques but none have found (63 64) widespread a p p l i c a t i o n . Macauly and Donald ' concluded from experi-mental data that transverse mixing i s at least two orders of magnitude fa s t e r than a x i a l mixing. C h a t t e r j e e et a l ^ " ^ c a r r i e d out segregation tests i n a 0.3m ID x 2m c y l i n d e r . A uniform mixture of coal and ir o n ore of the same p a r t i c l e s i z e range -6+3 and i n proportion 3:7 by weight was used as feed. No a x i a l segregation was observed but segregation i n the transverse plane was quite pronounced, the ir o n ore tending to form a kidney within the bed. Although the p o s s i b i l i t y of bed material segregation, p a r t i c u l a r l y when the feed material has a wide p a r t i c l e size d i s t r i b u t i o n , i s generally acknowledged, no detai l e d studies of the problem appear to be a v a i l a b l e . 2.5 Flow Conditions i n the Freeboard Gas In most f i r e d rotary k i l n s the f u e l and primary a i r enter the f r e e -board as a jet centered on the k i l n a x i s . Secondary a i r i s supplied to the annulus surrounding the f u e l and primary a i r jet but with an average v e l o c i t y about an order of magnitude l e s s . In addition, the d i s t r i b u t i o n of the secondary a i r i s often biased by the shape of the supply duct. Chedaille et a l ^ 6 6 ^ i d e n t i f i e d two common sit u a t i o n s for concentric jets issuing into long c y l i n d r i c a l enclosures. For the f i r s t case, which i s t y p i c a l of a boiler-type burner, the primary (central) and secondary (annular) jets have v e l o c i t i e s of the same order and 'occupy a r e l a t i v e l y small f r a c t i o n of the chamber cross-section. For the second case which i s more c h a r a c t e r i s t i c of rotary k i l n s the secondary flow, with v e l o c i t y an order of magnitude less than the primary j e t , occupies nearly a l l the a v a i l a b l e annular area. For both cases four flow zones along the furnace, as depicted by F i g . 2.12, were noted ( i ) The primary and secondary jets combine to form, or for the second case the primary jet alone forms, a single s e l f - p r e s e r v i n g free jet and entrainment of surrounding material begins. This occurs over several primary jet nozzle diameters for the primary jet alone and over a somewhat longer distance for the combining j e t s . B o i l e r - t y p e burner I- Zone X Zone XX ZoneTJJ. Zone L Y • Z o o Reverse flow region K i l n - t y p e burner F i g . 2 . 12 Flow p a t t e r n s o f d o u b l e - c o n c e n t r i c j e t s c y l i n d r i c a l chambers ( a f t e r C h e d a i l l e ) i n l o n g -54-( I i ) The single jet expands i n the manner of a free jet entraining material which i s of r e l a t i v e l y low v e l o c i t y , either pure r e c i r c u -lated material (case one) or a mixture of secondary a i r and r e c i r -culated material (case two). ( i i i ) The expanding jet approaches the chamber wall and viscous e f f e c t s cause departure from free jet behaviour. The downstream flow peaks w e l l b e f o r e the point Z ^ where the j e t expands to the s o l i d boundary. ( i v ) Beyond Z , at which the w a l l boundary l a y e r b e g i n s , the flow develops as i t would along a pipe with non-uniform entrance v e l o c i t y . assumed that u n t i l reaching the wall the behaviour was that of a free jet and Hinze's formula for the entrainment rate T h r i n g and Newby (67) f o r such axisymmetric enclosed jet flows, - 1) (2.42) plus the u n i v e r s a l j e t spreading angle, which y i e l d s = 4.5 R (2.43) would be applica b l e . For case two i t was noted that, the mass av a i l a b l e i n the secondary being known, the p o s i t i o n by which a l l of i t would be e n t r a i n e d (Z^ of F i g . 2.12) could be c a l c u l a t e d by eq. 2.43. A j e t s i m i l a r i t y parameter was proposed based on the calculated Z /Z r a t i o Zn M + M r T h - / - - ( - E (2.44) 0 0 M S P For Th > 1 the entrainment requirement i s s a t i s f i e d by the secondary flow and no r e c i r c u l a t i o n occurs. For Th < 1 the r e c i r c u l a t i o n rate was r e p o r t e d as 0.5 -* 1.0 times that of the free jet passing from Z to Z J K 6 o oo C 6 8 ) Craya and C u r t e t by si m p l i f y i n g the axisymmetric equations of motion, and introducing empirical r e s u l t s as necessary, deduced the relevant s i m l a r i t y parameter for case two with constant density, to be Ct Ct = ± - 1.5(a)2 + 0.579 ^ M , (2.45) 4 ^ (2r ID) P where: U p = V e l o c i t y of primary stream U g = V e l o c i t y of secondary stream q = II(U -U )r 2 P s P Q = n U g(R-6*) 2 + q * The boundary l a y e r displacement t h i c k n e s s 6 can usually be neglected. 2r (69) For p p < 0.05 which covers many s i t u a t i o n s , Curtet demonstrated that -56-1/2 Th Ct ' 5 1 (2.46) B e c k e r et a l a p p l i e d mass and momentum c o n s e r v a t i o n to a control volume which included the exit plane of the nozzle plus an a r b i t r a r y boundary extending downstream to derive the s i m i l a r i t y parameter where: (2.47) Moles et a l applied cold modelling techniques to study the flow within c o a l - f i r e d cement k i l n s , a f t e r f i r s t surveying data on 39 i n d u s t r i a l units which were found to operate within the range 0.35 < Th < 0.80 ( i . e . low to moderate r e c i r c u l a t i o n ) . The r e s u l t s confirmed Ct or Th as u s e f u l i n d i c a t o r s of r e c i r c u l a t i o n l e v e l s although the flow was markedly asymmetric due to the configuration of the secondary a i r i n l e t ductwork. The r e c i r c u l a t i o n vortex at the top of the c y l i n d r i c a l f i r i n g section was observed to be considerably stronger and larger i n extent than that at the bottom, d e f l e c t i n g the jet downward. A noteworthy conclusion was the importance of incorporating the i n l e t ducting into physical flow models. I t was r e p o r t e d that axlsymmetric r e c i r c u l a t i o n patterns were established i n a 0.225m diameter by 0.630m long cold furnace model, but over the range of Th < 0.31 for which r e s u l t s were presented, the jet did not penetrate to the wall and the r e c i r c u l a t i o n extended over the f u l l model length (5.6R). The a d d i t i o n a l complication of buoyancy e f f e c t s must also be (72) c o n s i d e r e d when d e a l i n g with burning f u e l j e t s . Beer recommends the use of a modified Froude number, or Archimedes number, defined by 2 g r s ( T g - T j J 2 T s g Ar = S g S (2.48) U T where T g i s the temperature of the f u l l y combusted gases while T g i s that of the secondary a i r . Buoyancy e f f e c t s have been shown to be s i g n i f i c a n t ^ 7 3 ^ for Ar > 0.01. -58-CHAPTER 3 SCOPE OF THE PRESENT WORK In a rotary k i l n , the net rate of heat transfer from the freeboard gas to the k i l n burden depends upon the i n t e r a c t i o n of a l l the processes and paths Introduced i n Chapter 1. These component processes are not unique to the rotary k i l n and have been the subject of numerous studies. However, investigations r e l a t i n g s p e c i f i c a l l y to heat transfer i n rotary k i l n s have either focussed on Individual processes, such as r a d i a t i o n or convection, or when a broader perspective has been adopted, have f a i l e d to incorporate r e a l i s t i c models for a l l the heat transfer paths and processes shown i n F i g . 1.2. No study has yet appeared which adequately describes the complex i n t e r a c t i o n of the heat transfer processes occurring at a rotary k i l n c ross-section. It was the objective of the present work to provide t h i s d e s c r i p t i o n by: ( i ) Developing a deta i l e d model, incorporating a l l the transport proceses i n a r e a l i s t i c manner, f o r heat t r a n s f e r at a cross-section of rotary k i l n . ( i i ) Obtaining measurements of heat transfer rates i n the UBC p i l o t k i l n to allow v e r i f i c a t i o n of the mathematical model. In addition to the net rates of heat transfer to the bed and through the k i l n w a l l , which have previously been measured, the net surface heat f l u x at the inside wall, as a function of cir c u m f e r e n t i a l p o s i t i o n , was to be obtained. CHAPTER 4 THE PILOT KILN FACILITY 4.1 General Description For the experimental portion of th i s research, the UBC p i l o t k i l n , i l l u s t r a t e d i n F i g . 4.1 was u t i l i z e d . This f a c i l i t y has been i n service for several years and seen use i n numerous i n d u s t r i a l tests as well as (74) h e a t t r a n s f e r t r i a l s . P r i o r to commencement of the study, an extensive refurbishing was car r i e d out and ad d i t i o n a l instrumentation incorporated. The c y l i n d r i c a l r o t a t i n g portion, comprising three sections of 0.609m ID s t e e l pipe (6 mm wall) flanged together and r i d i n g on two sets of s t e e l r o l l e r s , was l i n e d with 3mm of Fibrefrax 970 paper followed by 90mm of P l i b r i c o P l i c a s t LWR 24 castable r e f r a c t o r y . F i g . 4.2 depicts the manufacturer's conductivity data for the l i n i n g material while measured values of density and s p e c i f i c heat for LWR 24 are included i n Table 4.1. K i l n length i s 5.5m with an ID of 0.406 + 0.005m. Power for k i l n r o t a t i o n was provided by an e l e c t r i c motor and variable speed gearbox with a chain and sprocket f i n a l d r i ve. The granular s o l i d s material was fed from an overhead storage hopper v i a a variable speed belt conveyor to a c o l l e c t o r and discharge chute. A dam was i n s t a l l e d at the feed-end of the k i l n , providing an opening of 0.21m ID, to prevent s p i l l - b a c k of s o l i d s material while an ad d i t i o n a l small dam of 0.35m ID was i n s t a l l e d at the s o l i d s discharge-end to promote uniform a x i a l s o l i d s bed depth. No preheating of the feed material was provided. 4 Fig.4.1 The pilot kiln facility -61-F i g . 4 . 2 T h e r m a l c o n d u c t i v i t y o f LWR 24 F i r i n g was by natural gas with a burner arrangement as shown i n F i g . 4.3. Primary a i r was supplied by 8 nozzles equally spaced around a c i r c l e of radius 75mm and concentric with the 30mm ID gas supply pipe. Secondary a i r was introduced through 8 equally spaced nozzles, also concentric with the gas supply duct, but on a 150mm radius c i r c l e . The i n s t a l l a t i o n of the secondary a i r nozzles was to eliminate,severe r e c i r c u -l a t i o n problems encountered on i n i t i a l t r i a l s (Section 2.5). Combustion a i r was supplied at ambient temperature. Metering of the natural gas supply was by means of an o r i f i c e plate c a l i b r a t e d against a po s i t i v e displacement gas meter. The c a l i b r a t i o n curve,,along with i t s t h e o r e t i c a l counterpart, i i s shown i n F i g . 4.4. Combustion a i r supply was monitored by an uncalibrated ASTM standard o r i f i c e p late. Primary combustion a i r was subsequently bled from the combustion a i r supply and metered through a 3 rotameter. Total a v a i l a b l e a i r supply was 0.06 m /sec. (130 scfm). 4.2 Instrumentation A basic prerequisite was to i n s t a l l instrumentation s u f f i c i e n t to carry out o v e r a l l mass and energy balances for the k i l n . However the primary consideration was to i n s t a l l a d d i t i o n a l Instrumentation to enable de t a i l e d c a l c u l a t i o n of heat fluxes at various a x i a l locations along the k i l n . To a t t a i n these objectives a t o t a l of 80 thermocouples were incorp-orated, 66 being located with the rotating k i l n body. Error l i m i t s of standard thermocouple wire were considered acceptable, a fact which, combined with the large number of thermocouples involved and the high rate of f a i l u r e encountered i n service, dictated against thermocouple c a l i b r a t i o n . -6.3-Primary air Secondary air Natural gas Solids dam m m \\\\\\\\\\\\\\\ Seal Secondary air Primary ' air • Gas Secondary air F i g . 4 . 3 P i l o t k i l n b u r n e r r e g i o n ( D e t a i l ) . Flow (l/s) - 7 9 --6-5-Thermocouple outputs were logged by means of a 4 channel chart recorder and the b i a s i n g feature u t i l i z e d , as r e q u i r e d , to i s o l a t e and magnify p l o t s of t r a n s i e n t s i g n a l s . Recorder c a l i b r a t i o n was checked r o u t i n e l y although no adjustments were r e q u i r e d . The s i g n a l s from thermocouples r o t a t i n g w i t h the k i l n were routed to the recorder v i a one of 4 p a i r s of copper s l i p r i n g s , each s l i p r i n g being 30mm wide. Vacuum f l a s k c o l d j u n c t i o n s were mounted on the r o t a t i n g o k i l n body and m a i n t a i n e d at 0 C using a crushed ice/water mixture which was w e l l s t i r r e d by the k i l n r o t a t i o n . Thermocouple s e l e c t i o n was v i a one of 4 thermocouple grade switches a l s o mounted on the r o t a t i n g body. F i g . 4.5 i l l u s t r a t e s a t y p i c a l thermocouple c i r c u i t . L o c a tion of thermocouples i s d e t a i l e d i n F i g . 4.6. A more d e t a i l e d d e s c r i p t i o n of instrumentation f o l l o w s . 4.2.1 Gas Temperature Thermocouples Gas temperatures were obtained using s h i e l d e d s u c t i o n thermocouples at 8 a x i a l l o c a t i o n s ( F i g . 4.6). Each thermocouple was designed ( F i g . 4.7) so as to s l i d e r a d i a l l y a l l o w i n g measurements to be obtained at any r a d i u s , though i n p r a c t i c e the maximum was determined by bed depth since immersion w i t h i n the bed caused clogging of s u c t i o n l i n e s . Vacuum was provided by a fan u n i t , r o t a t i n g w i t h the k i l n body, connected to each thermocouple v i a 12mm copper tubing with a shut-off valve incorporated. Thermocouples were Type S Pt-10% Pt Rh formed from 31 gauge wire (0.33mm) wi t h s u i t a b l e compensating wire lea d i n g to the c o l d j u n c t i o n and -66-Slip Cu r i ! l i . Cu Recorder Type 'S* comp wire Ice r both i 41 i Cu Cu Switch P t l iP t IO%Rh Y Junction Type 'S ' T / c Cu Cu Recorder Slip ring sr Ice r both J Cu Cu Switch Alumel Chromel Y Junction Type V T / c F i g . 4 . 5 S c h e m a t i c d i a g r a m o f t h e r m o c o u p l e c i r c u i t s . ± 1.0 2.0 A D G P 4.0 3.0 Kiln length (m) Gas temp suction T.C. Bed temp T.C. Shell temp T.C. Wall probe T.C. 5.0 5.5 FigA.6 A x i a l l o c a t i o n s o f k i l n t h e r m o c o u p l e s -68 & thermocouple (typeK) F i g . 4 . 7 C r o s s - s e c t i o n of t h e k i l n t h e r m o c o u p l e l o c a t i o n s showing the -69-copper c i r c u i t r y f o l l o w i n g . Based on a measured gas v e l o c i t y ~ lOm/sec i n the suc t ion l i n e s , the thermocouple junct ion temperature was estimated to be w i th in 25 K of the true gas temperature and to lag by about 4 seconds. The l a rges t measuring e r rors occurred in the hot test regions of the k i l n where the s h i e l d temperature was only about mid-way between the wa l l and gas temperature. The time constant for thermocouple s i g n a l decay was ~ 6 seconds. 4 .2 .2 Bed Temperature Thermocouples Measurement of s o l i d s bed temperature was v i a 12 bare thermocouples at f i xed a x i a l l o c a t i o n s ( F i g . 4.6) again with allowance for r a d i a l move-ment. Due to the r o t a t i o n of the thermocouples with the k i l n body, a t rans ien t response was obtained as each junct ion a l ternated between the freeboard and the bed m a t e r i a l . Although the k i l n could be stopped momentari ly, the response of the thermocouples wi th in the bed was too slow to obtain the bed temperature without p o s s i b l y d i s t u r b i n g the bed e q u i l i b r i u m . Bed temperatures were instead ca lcu la ted by s o l v i n g the lumped capaci ty response e q u a t i o n ^ 3 ^ t T T / C ~ T b t — = e x p ( - ^ - ) (4.1) oLT/C  lb  t m f o r the t r u e bed tempera ture T , , . S i n c e the bed m a t e r i a l and b t = °° c thermocoup le j u n c t i o n were not in e q u i l i b r i u m x was not constant with tm t i m e . Va lues of the pseudo time constant T were obtained from a s e r i e s tm of plunge tes ts as descr ibed in Appendix ( I ) . -70-Type S thermocouples formed from 31 gauge wire were employed in the hottest third of the ki l n while Type K chromel-alumel thermocouple made from 22 gauge (0.7mm) wire were used over the remainder. In each case double bore alumina sheathing was utilized to route the bare wire portion of the circuit through holes drilled in the kiln wall and to support the junction (Fig. 4.7). 4.2.3 Wall Refractory Temperature Thermocouples To enable accurate measurement of the cyclical wall surface temperature and to obtain radial profiles of the steady state deep wall temperatures a special wall probe shown in Fig. 4.8 was designed. Probes were cast from LWR refractory, to exactly match the thermal characteristics of the wall, using silicon rubber molds. Thermocouples were accurately located at depths of 0, 12.7, 44.5 and 76.2mm by means of a j i g which was removed immediately after pouring of the refractory. Sufficient material was poured to cover the surface thermocouples to a depth of about 2mm. After curing at room temperature for 12 hours, this surplus layer was carefully f i l e d away until the surface thermocouples could f i r s t be seen. The probes were then fired in an oven following the refractory manufacture's recommended schedule. The truncated wedge shape was chosen to disturb the one dimensional wall heat flux as l i t t l e as possible. After f i r i n g the probes were inserted into matching openings cast into the k i l n wall, covered by 3mm of Fibrefrax 970 paper, and capped by a 6mm section of steel plate with screw tabs to hold the probe firmly in position. The resulting installation provided a very close thermal match to the kiln wall. -71-Surface temp to cold junction Fig.4 . 8 W a l l t e m p e r a t u r e measurement p r o b e ( D e t a i l ) . - 7 2 -Probe thermocouples were Type K made from 22 gauge (0.7mm) wire with the exception of the surface thermocouples of probes i n s t a l l e d i n the hottest region of the k i l n which were Type S formed from 31 gauge wire. Aft e r fusion, the junctions were f i l e d to an approximate spherical shape only about 1.5 times the wire diameter i n order to minimize thermal i n e r t i a . The junction leads were placed at the junction bed depth ( i . e . along isotherms) for a distance of about 25 wire diameters to eliminate measurement errors due to heat conduction along the wire. To obtain s h e l l temperatures, 10 Type K thermocouples were set into small holes d r i l l e d to a depth of about 6mm into the s t e e l s h e l l . Since the thermal resistance of the s h e l l was less than 1% of the t o t a l wall resistance, i t was assumed to be r a d i a l l y isothermal. 4.2.4 Solids Material Measurements The supply rate of s o l i d s material was obtained by two methods. The primary means was by c l e a r i n g the accumulated material from the k i l n discharge hopper, located under the f i r i n g box, at i n t e r v a l s of time and weighing the material c o l l e c t e d . For i n e r t feed material the feed rate was equated to the discharge rate, while for materials having undergone chemical reaction, the feed rate was calculated a f t e r i n c l u s i o n of the appropriate reaction formula(e). As a secondary means the bel t feeder was ca l i b r a t e d for each material but for a l l t r i a l s the feed rate was taken to be that obtained by d i r e c t weighing of the k i l n discharge. - 7 3 -For reacting materials, sampling ports located at i n t e r v a l s along the k i l n length were u t i l i z e d to c o l l e c t bed material for subsequent chemical a n a l y s i s . 4.2.5 Additional Freeboard Gas Measurements As a check on the d i r e c t measurement of combustion a i r flow, gas samples withdrawn from the region immediately upstream of the gas di s c h a r g e by means of a large syringe were analysed for CO^ concentration using a gas chromatograph. However a l l freeboard gas flows reported are based on the measured flows of natural gas and combustion a i r . Although considered highly desirable to do so, gas v e l o c i t i e s with-i n the k i l n were not q u a n t i t a t i v e l y measured for lack of a suitable technique. Very poor o p t i c a l access precluded tracer techniques while the ava i l a b l e dynamic pressure head, f a l l i n g within the range 0.006 < Ap < 0.6mm H 20 ( 9 x l 0 ~ 7 < Ap < 9 x l 0 ~ 5 p s i ) was i n s u f f i c i e n t f o r p i l o t tube t e s t s . An unsuccessful attempt was made using a p i t o t tube and d i f f e r e n t i a l pressure transducer ( s e n s i t i t i v y ~ 0.7mm ^ 0 ) . 4.3 Solids Feed Materials T r i a l s were ca r r i e d out using Ottawa sand of two size ranges, limestone and petroleum coke. Material bulk thermophysical properties, along with 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 , are l i s t e d i n Table 4.1. With the T a b l e 4.1 Relevant Physical Properties Sand (Fine) Sand (Coarse) Limestone Pet.Coke LWT24 (Refractory) k w/mK 0.268 0.268 0.692 0.400 0.400 Pbulk kg/m3 1520 1460 1680 775 1334* Pparticle kg/m3 2627 2627 - - -C p @ 700K kJ/KgK 1.085 1.085 1.137 1.549 1.130 1000K 1.160 1.160 1.298 1.762 1.269 1300K 1.195 1.195 1.452 1.892 1.409 a @ 700K m /sec 1.63 x 10" -7 1.63 x 10~7 3.62 x 10" -7 3.33 x 10' -7 2.65 x 10"7 1000K 1.52 x 10" -7 1.52 x 10~7 3.17 x 10" -7 2.93 x 10' -7 2.36 x 10"7 1300K 1.48 x 10" -7 1.48 x 10"7 2.84 x 10" -7 2.73 x 10" -7 2.13 x 10"7 Part.Size -20 + 50 - 6 + 12 -6 + 18 - 6 + 1 7 0 N/A Dist. > 96% > 92% > 90% > 90% Measured - 7 5 -exception of the petroleum coke, the p a r t i c l e s i z i n g of each material was t i g h t l y grouped. The coarse sand and limestone had a k i l n to p a r t i c l e diameter r a t i o ~ 160 and the f i n e sand ~ 400. Ottawa sand was used for the majority i n e r t material t r i a l s since i t s properties are best documented and, for the converse reason, petroleum coke was used for only a few t r i a l s . -76-CHAPTER 5 PILOT KILN TRIALS A series of 23 heat transfer t r i a l s were performed on the p i l o t k i l n , the run conditions being summarized i n Table 5.1. In each instance the k i l n was f i r e d at low heat, without r o t a t i o n , overnight to allow pre-heating and the actual t r i a l conditions of f i r i n g , s o l i d s material feed and r o t a t i o n rate i n t i t i a t e d about 6 AM. After about 6 hours, weighing of the s o l i d s discharge at i n t e r v a l s of time and the monitoring of several wall surface thermocouples were begun and continued for about 2 hours to ensure the steady-state condition was achieved. Thermocouple cold junctions were then iced and a complete set of T/C output data recorded, beginning with the gas suction units and proceeding through wall and s h e l l T/C's to the so l i d s temperature T/C's. Gas temperatures at several r a d i i were recorded, the largest being at about 25mm above the exposed bed surface. The transient output from the wall surface T/C's were recorded at higher chart speeds, 50 or 100 vs. 20mm/ min., with biasing to give reasonable amplitude. P r i o r to recording outputs from the 11 ro t a t i n g bed temperature T/C's a small alumina scoop, inserted through an opening i n the f i r i n g box and incorporating a single T/C, was used to obtain the so l i d s material temperature as i t t r i c k l e d over the exit dam. Output from the remaining bed temperature T/C's was obtained with the k i l n r o t a t i o n momentarily stopped and the T/C's immersed i n the bed. C o l l e c t i o n and weighing of the s o l i d s material discharge was T a b l e 5.1 Summary of Run Conditions GAS AIR FEED RUN (SCFM) PRIM/SEC MAT/RATE COMMENTS (SCFM) (KG/HR) TH01 1.75 20/40 CS/62.0 LT/LF 02 2.15 35/86 CS/62.0 LT/HF 03 3.00 37/86 CS/62.0 MT/HF 04 4.18 37/91 CS/62.0 HT/HF 05 1.45 20/42 FS/58.0 LT/LF 06 1.90 30/62 FS/62.0 LT/MF 07 2.20 39/91 FS/63.0 LT/HF 08 4.23 40/85 FS/65.0 HT/HF 09 5.35 40/91 FS/64.0 HT/HF 10 " 0.95 20/42 PC/33.0 LT/LF 11 1.40 30/63 PC/33.0 MT/MF 12 1.92 40/86 PC/33.0 MT/MF 13 3.15 40/84 PC/34.0 HT/HF 14 3.8 35/65 LS/36.0 MT/MF 1.0 RPM 15 2.0 25/65 LS/40.0 LT/MF 16 4.05 35/65 LS/45.0 MT/MF 17 2.2 21/81 _LS/45.0 LT/MF 18 6.0 39/40 LS/50.0 HT/HF 1.0 RPM 19 4.9 39/36 LS/50.0 HT/MF 20 5.05 38/16 LS/42.0 HT/LF 21 5.5 36/54 LS/55.0 HT/MF 22 5.5 31/62 LS/47.0 HT/MF 23 5.2 37/16 LS/58.0 HT/LF KEY: CS - COARSE SAND FS - FINE SAND LS - LIMESTONE PC - PETROLEUM COKE LT - LOW TEMP. MT - MODERATE TEMP. HT - HIGH TEMP. LF - LOW FLOW MF - MODERATE FLOW HF - HIGH FLOW ALL RUNS AT 1.5 RPM EXCEPT AS NOTED. -78-discontinued just p r i o r to the f i r s t s t o p - k i l n measurement. To complete the run a flue gas sample was drawn from the v i c i n i t y of the gas discharge for composition analysis (dry basis) on the chromatograph. If limestone was the feed material, samples were drained from the sample ports for subsequent analysis to determine the f r a c t i o n a l c a l c i n a t i o n at each port a x i a l l o c a t i o n . The t o t a l time required for data c o l l e c t i o n was about 1.5 hours. - . 7 9 -CHAPTER 6 HEAT TRANSFER MODELS Numerous mathematical heat transfer models, each f a l l i n g into one of two categories according to purpose, were required during the course of t h i s research: (i) Models necessary to convert the pilot k i l n data into net heat transfer rates for the bed material, the freeboard gas and the refractory wall (Sections 6.1 and 6.2). ( i i ) Models to enable the prediction of net heat transfer rates through the calculation of their component processes and to form the elements for a larger unified heat transfer model at a cross-section of k i l n (Sections 6.3 to 6.5). The models f a l l i n g into the f i r s t category were incorporated into a general data analysis program, which performed a variety of additional tasks including the conversion of raw thermocouple emf data, the curve f i t t i n g necessary to obtain continuous temperature profiles and the organization of results into printed and plotted output. A flow chart is attached as Appendix (II). Conversion of thermocouple output data was by means of polynomial curves obtained from regression analysis (least squares) of the Type K and Type S standard thermocouple tables. The maximum allowed f i t t i n g error was + 0.25% (roughly + 3 Kelvin degrees). -80-A l l a x i a l temperature p r o f i l e s were also obtained by l i n e a r regression analysis using the UBC l i b r a r y routine DOLSF, while inside wall surface temperatures were f i t t e d to cubic splines using the l i b r a r y routine DSPLFT. 6.1 Evaluation of Net Heat Transfer Rates for the Bed Material and Freeboard Gas Assuming steady-state steady-flow conditions, without s i g n i f i c a n t work, k i n e t i c energy or p o t e n t i a l energy e f f e c t s , the f i r s t law for a control volume i s given by Q = £(hH)_ , - X(nH)_ ^ . (6.1) c vn e t L Leaving L V 'Entering v ' Assuming uniform conditions at any k i l n cross section, the a p p l i c a t i o n of eq. 6.1 to the unit a x i a l length control volumes of freeboard gas and bed material shown i n F i g . 6.1, y i e l d s N g dT _ dn Q =1 (n c -j—**• + H. -j-^ "} (6.2a) cv 1 p i dz i dz v ' g i-1 N b dT _ dn C -I {n. c . - j — + H, -r-J-} (6.3a) c v b ^ j pj dz j dz ' where N g and N^ represent the number of species present i n the gas and bed respe c t i v e l y and Q denotes the rate of heat transfer per unit k i l n length. K n H ) . . Qy leaving gas r 4 -I (hH) 4 — . r ^ entering I /////// ~1 c v bed _ J I ( n H ) # . CV — entering C v b e d leaving F i g . 6 . 1 D e t e r m i n a t i o n o f n e t h e a t t r a n s f e r r a t e s from f i r s t law a n a l y s i s -82-Gas samples drawn from the k i l n at a distance of 0.7m downstream from the f i r i n g box showed v i r t u a l l y the same composition as samples taken from the gas discharge, i n d i c a t i n g a very short flame. For Inert bed material t h i s allows s i m p l i f i c a t i o n of eq. 6.2a and 6.3a to the forms Q = I n.c , (6.2b) cv I p i dz v ' g 1=1 N b _ dT, For the limestone t r i a l s i t i s e a s i l y shown from the c a l c i n a t i o n equation CaC0 3 -*• CaO + C0 2 (6.4) that, at any a x i a l l o c a t i o n , d ACaO d A C 0 2 d ACaC0 3 dz dz dz df nCaC0 3 dz (6.5) where n C a £ 0 denotes the molar feed rate of CaCO^ into the k i l n . Enthalpy values were c a l c u l a t e d ^ 7 " ^ from _ _ T _ H = H- + / c dT (6.6) f ° 298 P and s p e c i f i c heats were obtained f r o m v -83-The net rate of heat transfer from the gas was calculated using eq. 6.2 while the net rate of heat transfer to the bed was calculated by means of eq. 6.3. The values of axial temperature gradients were calculated by the regression routine but the fractional calcination curves were plotted by hand and the required gradients obtained visually. 6.2 Heat Flux Calculation for the Kiln Wall Following the suggestion o f ^ 7 ' 2 ^ the k i l n wall was treated as two distinct regions (Fig. 6.2): (i) The thin layer near the inside surface within which temperature cycling occurs due to the k i l n rotation. This w i l l be referred to as the wall active layer. ( i i ) The remaining wall refractory and shell where temperatures are steady with time. This w i l l be termed the wall steady-state layer. 6.2.1 Heat Loss Calculation in the Wall Steady-State Layer Conduction in the wall steady-state layer was assumed to be in the dT dT w w radial direction only since i t was observed that — > 50 - 7 5 ™ • -84 W S A L Wall active layer S S L Wall steady state layer .6.2 The w a l l a c t i v e and s t e a d y - s t a t e l a y e r s - 8 5 -The thermal conduc t i v i t y data for the wal l r e f r a c t o r y ( F i g . 4.2) was f i t t e d by the simple l i n e a r curve k = k (1 + ST ) (6.7) w w ^ w o (28) The steady-state one-dimensional conduction equation T - T • W W Q = 2n k [ l + | ( T - T )] ~ (6.8) ss W o 1 w 2 l n ( r 2 ' r i ) was used to c a l c u l a t e the rate of energy loss through the s teady-s ta te w a l l l a y e r . At e a c h w a l l probe p o s i t i o n th ree v a l u e s of Q were ss c a l c u l a t e d by p a i r i n g values from the buried thermocouples (at depths of 12.7 , 44.0, 76.2mm r e s p e c t i v e l y ) and the r e s u l t i n g heat t ransfer rates averaged to obtain Q s s A value of average i n s i d e wal l surface was back -ca lcu la ted from eq. « 6.8 by i n s e r t i n g Q and the r e s u l t i n g value used to check the surface s s temperature r e s u l t s . 6.2.2 Heat Flux C a l c u l a t i o n i n the Wall Act ive Layer As i n the s teady-s ta te l ayer ,conduc t ion i n the wall active layer was assumed to be one dimensional s ince i t was observed that - 8 § -dT dT ws s ws I T > " d e " ( 6 > 9 a ) dT dT An energy balance on the elemental volume of wal l of uni t a x i a l l eng th , shown i n F i g . 6.3 y i e l d s the r e s u l t c fi dV | i = (k rd0 | i ) - ( k r d Q J l ) (6.10) pw^ w o t ' -w a r ; . d r v w 3r y dr v ' r + 2 ~ r ~ To evaluate the heat flux> :eq.6vlO was f i r s t replaced.by - i t s^equivalent forward-time centre-space (FTCS) f i n i t e d i f f e rence approximations using the network shown in F i g . 6.4. For node i at time step j the equation to be s a t i s f i e d i s c P AV. r .+ r . . . w 1 f T - T 1 - k f 1 f T - T ) 1 i , j + l i,r wi ^ 2 > ^ i + l . j + l i , j + l j A0 A r +r k w i (Ti,j+r Vi.j+i) <6-n> the a p p l i c a b l e boundary condi t ions be ing: T i A = T „ c < 0 > j - 1 J (6.12a) i , J ws l n ( r / r ) r i - l , j - T I , j • %s 2 H k T J - 1 * J (6.12b) wl where T i s the measured i n s i d e wa l l surface temperature, ws - 8 7 -Qr-dr = (K w r d 0 a j ) r _ d r 2 ar I F i g . 6 . 3 E n e r g y b a l a n c e f o r an e l e m e n t a l ( p e r u n i t a x i a l l e n g t h ) volume of t h e w a l l - 8 8 -A0 TT u - i t . c : Boundary conds: T , j for j=l,J Qss ( rx - rT_,) T U "4-1,1 K ( r r * r r _ , )A0 / 2 = constant F i g . 6 . 4 F i n i t e a c t i v e d i f f e r e n c e model n o d a l c o n f i g u a t i o n f o r t h e w a l l l a y e r - 8 9 -Since the k i l n was operated at e q u i l i b r i u m , the r a d i a l temperature at any f i x e d p o i n t ( r , Z , 0) i n the w a l l must be independent of t ime. T h e r e f o r e a t any p o i n t ( r , Z ) , m o v i n g w i t h the w a l l , the r a d i a l temperature p r o f i l e must be the same at the beginning and end of each k i l n r e v o l u t i o n : < T i , l>REV = < T i ,J>REV- l 1 = 1 * 1 (6.13) A f te r input t ing an approximate i n i t i a l r a d i a l temperature p r o f i l e the required i n i t i a l cond i t ion was obtained by i t e r a t i v e l y approaching the requirement of eq . 6.13 u n t i l s a t i s f y i n g the c o n d i t i o n < T i , l> " < T i ,J> max < 10 i=l->I -5 (6.14) The r e s u l t i n g temperature p r o f i l e was found to be independent of the i n i t i a l p r o f i l e . Using a l i n e a r f i r s t approximation, convergence normally required < 50 i t e r a t i o n s . Subject to these boundary and i n i t i a l c o n d i t i o n s , the f i n i t e d i f f e r e n c e equations 6.11 were solved for one complete k i l n revo lu t ion and the ins ide wal l surface heat f lux obtained using k (T - T . ,) WS WS 1 , j / ^  i r \ q = >±- (6.15) ws. r l n ( r , / r ) i ws 1 ws -90-The node spacing was increased moving i n the r a d i a l d i r e c t i o n and a s u f f i c i e n t number used so that one a d d i t i o n a l node resulted i n max < 0.01%. S i m i l a r l y the time i n t e r v a l was chosen such that one a d d i t i o n a l time step resulted i n < 0.01%. For an assumed active layer t h i c k -ness of 20mm, 100 s p a c i a l nodes and 100 times steps were employed. The c a l c u l a t i o n for the wall active layer were ca r r i e d out by the k i l n data analysis program as per the flowsheet of Appendix I I . 6.3 Estimation of Temperature Rise for P a r t i c l e s  at the Exposed Bed Surface P a r t i c l e s at the surface of the bed active layer can undergo b r i e f but intense heat transfer from the freeboard. Because estimates of p a r t i c l e Biot number indicated values of Bi > 0.1 a model of surface p a r t i c l e transient response was developed. P a r t i c l e s for the model were assumed to be s p h e r i c a l , having the diameter of the average bed p a r t i c l e s i z e , and to r o l l down the exposed s u r f a c e an average d i s t a n c e L g at v e l o c i t y U g as shown i n F i g . 6.5. U g Such p a r t i c l e s would r o t a t e M r e v o l u t i o n s at a r a t e of n d p revolutions/sec. and be on the surface t seconds where s F i g . 6 . 5 Assumed m o t i o n of p a r t i c l e s a t t h e e x p o s e d bed s u r f a c e - 9 2 -2U u = - (6.16b) P t s = ^ (6.16c) s Transient r a d i a l conduction was assumed wi th in each p a r t i c l e . A heat balance for the elemental volume dV of F i g . 6.6a y i e l d s a s i m i l a r r e s u l t to eq. 6.10 c p dV | £ " O r 2 Cosyd0dy | ? ) _ d r - (k r 2 Cosydedy f^l dr 1 7 , pp"p o t ^ p 1 1 d r ; r + j - v p ' ' brJr~Y~ (6.17) The temperature response of the r o l l i n g surface p a r t i c l e was c a l c u l a t e d by r e p l a c i n g eq . 6.17 by the equivalent FTCS nodal express ion . AV. (T. . , , - T . ,) r .+ r . . . i i t j + l i , j ' = , i , _ , a p CosyAyA9At 1 2 > 1 i + i , j + l i , j + l J r +r - ( - H r ^ (Ti,j+r T i - i , j + i ) < 6 - 1 8 > and so lv ing the r e s u l t i n g set of nodal equations subject to the boundary and i n t i a l condi t ions descr ibed below. As shown in F i g . 6.6b, the outside p a r t i c l e surface was assumed to be subjected to uniform heat f l u x while exposed to the freeboard and to be ad iaba t ic while fac ing in to the bed. At the p a r t i c l e centre the r a d i a l -93-Axls of particle rolling motion F i g . 6 . 6 a An e l e m e n t a l volume o f a s p h e r i c a l bed p a r t i c l e --94-Q=QP. Usp= rpcj I.C. Tp uniform at time to when particle moves to bed surface BjC.'s r=0 t >t0 dTp =0 r=r p t = t p Q r p =QP exp r Kexp • = tp Q r p = 0 Kcov  F i g . 6 . 6 b Boundary c o n d i t i o n s f o r p a r t i c l e s f a l l i n g down t h e e x p o s e d bed s u r f a c e -95-temperature gradient was set equal to zero . At the ins tant of sur fac ing each p a r t i c l e was assumed to be iso thermal . A g r i d of 50 s p a c i a l nodes and 50 time steps per p a r t i c l e r e v o l u t i o n was used for a l l c a l c u l a t i o n s . Increasing both values by a f a c t o r of two resu l ted i n < 2% change i n the f i n a l surface temperature. Rad ia l temperature p r o f i l e s were ca lcu la ted at a standard value for angle o y of 45 but f i n a l r a d i a l temperature p r o f i l e s were only weakly dependent upon the choice of y . 6.4 Rad ia t ive Heat Transfer i n the Freeboard In the freeboard region r a d i a t i v e heat exchange occurs between the gas volume and i t s bounding s u r f a c e s , the i n s i d e wal l and exposed bed. A d d i t i o n a l r a d i a t i v e exchanges occur between area elements on the ins ide wa l l and other areas on both the wal l and exposed bed sur face . No d i r e c t exchange e x i s t s between an area on the exposed bed surface and other areas on that s u r f a c e . (27 ) Based on the method of a zone type, r e a l gas, r a d i a t i v e heat t rans fe r model of the freeboard region was developed to c a l c u l a t e the r a d i a t i v e heat f lux d i s t r i b u t i o n around i t s per iphery , at one a x i a l p o s i t i o n , for any given gas and surface temperature d i s t r i b u t i o n . Each component of r a d i a t i v e heat f lux was c a l c u l a t e d separate ly to al low d e t a i l e d ana lys is of i t s r e l a t i v e importance. 6.4.1 The Freeboard Gas Em i s s i v i t y / A b s o r p t i v i t y Models To simulate the emissive c h a r a c t e r i s t i c s of the freeboard gas, a clear-plus-three-gray-gas model was developed following the procedure (27) given i n . The composition of the natural gas f u e l used for a l l t r i a l s i s given by Table 6.1. Complete combustion of the f u e l gas r e s u l t s i n the p a r t i a l pressure r a t i o PH.O — — « 2 (6.19) >co2 for the products of combustion. For the limestone c a l c i n a t i o n t r i a l s the CC>2 evolved from the bed resulted i n a more nearly equimolal r a t i o PH_0 — — » 1. (6.20) - c o 2 Plots of the freeboard gas t o t a l e m i s s i v i t y , derived from the (27) empirical data i n , are shown i n Fi g s . 6.7 and 6.7b. The gas t o t a l e missivity data was f i t t e d to the form of eq. 2.1 e(T , pL) = I e [l-exp(-K pL)] (2.1) g n=l - 9 7 -TABLE 6.1  COMPOSITION OF NATURAL GAS USED FOR  THE PILOT KILN TRIALS (from supplier) Component % By Volume CH^ Methane 9 4 . 8 7 C 2H 6 Ethane 2 . 6 9 CgHg Propane 0 . 7 5 C^H^Q Butane 0 . 2 5 N 2 1 . 2 1 Miscellaneous 0 . 2 3 TABLE 6.2 VALUES OF EXTINCTION COEFFICIENTS FOR CLEAR-PLUS-THREE-GRAY-GAS E M I S S I V I T Y , APPROXIMATIONS Gray Gas Number K pH 20 / PC0 2~ 2 (cm-atm) ^  K pH 20 / pC0 2" 1 (cm-atm) 1 0 0 2 0.01061 0.01837 3 0.0984 0.1903 4 0.9843 1.6568 1 1—I M i l l - 1 I I I I I I 1 1—I I III I—I | 0.1 E CD (/) a 0.0 V 1 1 I I I I 111 I I I I I I I ll J I I I I I II 0.1 10 Pressure path length (Ft-atm) F i g . 6 . 7 a T o t a l gas e m i s s i v i t y f o r P H 2o/pcO = 2 ( a f t e r H o t t e l ) Pressure path length ( Ft-atm) F i g . 6 . 7 b T o t a l gas e m i s s i v i t y f o r pjj O/VQQ =1 ( a f t e r H o t t e l ) - 1 0 0 -A gas temperature of 1388 K, r e p r e s e n t a t i v e of the c a l c i n a t i o n t r i a l s , was chosen to o b t a i n the e x t i n c t i o n c o e f f i c i e n t s , K f o r the equimolal H„0:C0„ n ^ 2 2 c a s e . S i n c e the i n e r t bed t r i a l s were co n s i d e r a b l y c o o l e r , the K values n were e v a l u a t e d a t a gas t e m p e r a t u r e of 833 K f o r the 1.95:1 (R^ChCC^) freeboard gas mixture. The e x t i n c t i o n c o e f f i c i e n t values obtained are summarized i n Table 6.2. The temperature v a r i a t i o n of the e m i s s i v i t y weighting c o e f f i c i e n t s , e^, o b t a i n e d by f i t t i n g t h e gas t o t a l e m i s s i v i t y f o r o t h e r gas t e m p e r a t u r e s w h i l e r e t a i n i n g the o r i g i n a l v a l u e s , i s shown by F i g . 6.8. To complete the r a d i a t i v e model of the freeboard gas, the a b s o r p t i v i t y of the gas f o r gray r a d i a t i o n was simulated u t i l i z i n g the two r e l a t i o n s h i p s 4 <z(T ,T pL) = I a [ l - e x p ( - K pL] (2.2) S 8 n=l n n T 0.55 T = (f 8-) e ( T s , p L ^ - ) (2.3) s g to c a l c u l a t e the v a r i a t i o n , with e m i t t i n g surface temperature, of the gas a b s o r p t i v i t y w e i g h t i n g c o e f f i c i e n t a ( a t f i x e d a b s o r b i n g gas n temperature). The r e s u l t s of t h i s procedure are shown on F i g . 6.9. -101-F i g . 6 . 8 T e m p e r a t u r e v a r i a t i o n o f g a s e m i s s i v i t y w e i g h t i n g c o e f f i c i e n t s . - 1 0 2 -600 1000 1400 1800 Emitting surface temperature K F i g . 6 . 9 T e m p e r a t u r e v a r i a t i o n o f t h e gas a b s o r p t i v i t y w e i g h t i n g c o e f f i c i e n t s . -103-By c a r e f u l l y ad just ing a l l the parameters, e m i s s i v i t y / a b s o r p t i v i t y models of the freeboard gas were obtained with an accuracy of bet ter than + 5% for pL > 1.2 cm atm. 6.4.2 Radia t ive Heat Transfer From the Freeboard Gas to the Exposed Bed To c a l c u l a t e the r a d i a t i v e exchange between a s u r f a c e area (which i s for the moment required to be r a d i a t i v e l y black) on the exposed bed or r e f r a c t o r y w a l l and the volume of freeboard gas V \ , shown in F i g . 6 . 1 0 , the s u r f a c e to gas d i r e c t exchange a rea S ^ S ^ > for each gray gas component, must be evaluated for use i n eq . 2.5b Values of s^g^ were obtained i n a unique manner. Refer r ing to F i g . 6 .11, p e n c i l of beams emitted by the elemental area dA^ (forming a part of A^) i s seen to t raverse the volume V.. The beam p ie rces at two points forming the areas dA^ and d A ^ ' . Assuming the beam i s of small d ivergence, both areas w i l l form the same s o l i d angle centred on dA and Wall Surfaces 4 \t V = I ( s . g .) (E - E .) L . v i r n v i i ; n j n=l J J (2.5b) dA . Cos 9 . dA' Cos 9 . 1 _ (6.21) -104-F i g . 6 . 1 0 R a d i a t i v e e xchange among volume and s u r f a c e z o n e s w i t h i n t h e k i l n f r e e b o a r d - 1 0 5 Finite Volume V; Pencil of beams from A Finite surface A; dA 11 R a d i a t i v e e x c h a n g e between a s u r f a c e zone and a gas zone -106-The r a d i a t i v e energy reaching dA^ i s given by n^dA dA .. dA.CosQ. i—1 = £ d A i C o s 9 1 — - n Ti->j (6.22) n i r . . while that reaching dA^ w i l l be n^dA -»-dA* dA'. Cos9 . E,. * n d A i C 0 s 9 i J , 2 <6'23> n b i r ' . The excess of r e s u l t 6.23 over 6.22 must be the amount absorbed from the p e n c i l by d V \ . Inc luding eq . 6.21 th is y i e l d s the r e s u l t n x d A ^ d V . i 1 = -L f Q - Q 1 E., E, ^ dA.-fdA'. ^dA.+dk.) n i n i i j i j 1 dA^CosGi = - d A . C o s G , ' — 1 ^ f x * - T . .) (6.24) TC i I 2 ^ni->j n i - > j ; r i j Replacing the elemental areas dA^ and dA^ by smal l but f i n i t e areas AA^ and AA.. a l l o w s a c l o s e a p p r o x i m a t i o n of s ^ g j by c a r r y i n g out the summations necessary to obta in -107-1 cose c o s e . where A, Is used to denote a l l the surfaces of V. over which beams from A, i 3 I can e x i t . This method of c a l c u l a t i n g sg values, although somewhat cumber-some i n d e s c r i p t i o n , was e a s i l y programmed and yielded demonstrably correct r e s u l t s at a s i g n i f i c a n t saving i n computation time over the (27) technique suggested by , p a r t i c u l a r l y when V impinges on A^ ,. Since only gray component gases are used, r e c i p r o c i t y can be invoked and <«J 8l )n = ( S i g j > n ( 6 ' 2 6 ) The net r a d i a t i v e heat f l u x from the freeboard volume Vj to the b l a c k surface A^ can be calculated using eq. 6.25 to evaluate ( s ^ 8 ^ ) n f ° r each gray gas component ->• <V. ->• A L i n-1 S i g j Vn (6.27) - 1 0 8 -For a freeboard made up e n t i r e l y of black surfaces eq. 6.27 provides a rigorously correct expression for the r a d i a t i v e exchange between the gas volume V\ and the surface area A^, of F i g . 6.10. However the bounding surfaces i n the freeboard possess e m i s s i v i t i e s < 1 so that, i n a d d i t i o n to d i r e c t exchange, V and A^, i n t e r a c t r a d i a t i v e l y v i a r e f l e c t i o n ( s ) from other surface elements. This s i t u a t i o n i s i l l u s t r a t e d f o r the simplest case of a single r e f l e c t i o n by F i g . 6.12. (27 ) F o r dark g r a y e n c l o s u r e s (e > 0.75) H o t t e l s t a t e s that n e g l i g i b l e e r r o r w i l l r e s u l t i f the factor (e g+ l ) / 2 i s used to account f o r r e f l e c t e d energy where e g represents the average surface emissivity. Thus for the freeboard eq. 6.27a can be replaced by v : A, 2 -Jr- \ < si*i>n ( E r V n <6-27b> . 1 1 i n=l J In fact the influence of r e f l e c t e d gas r a d i a t i o n on the r a d i a t i v e f l u x at the freeboard surfaces should remain r e l a t i v e l y small even at moderate surface e m i s s i v i t i e s due to the poor transmissivity of an (23) e m i t t i n g gas f o r i t s own r a d i a t i v e bands. Gorog et a l showed that, even i n the p i l o t k i l n , t y p i c a l l y > 80% of r e f l e c t e d gas r a d i a t i o n leaving a surface i s reabsorbed by the freeboard gas without impinging on another surface and concluded that r e f l e c t i o n e f f e c t s could safely be ignored i n dealing with gas emissions. R e c a l l i n g that transmissivity i s given by F i g . 6 . 1 3 R a d i a t i o n between s u r f a c e a r e a s w i t h one and two r e f l e c t i o n s - 1 1 0 --K pL x = e n (6.28) n v ' i t i s evident that, at the much longer path lengths c h a r a c t e r i s t i c of i n d u s t r i a l k i l n s , the role of i n d i r e c t gas/surface r a d i a t i o n w i l l be further reduced for most ap p l i c a t i o n s . To apply eq. 6.27b, the k i l n freeboard was subdivided into zones centred on a unit length circumferential s t r i p of exposed wall and bed surface as shown by F i g . 6.14. Taking advantage of symmetry, exchange area c a l c u l a t i o n s were necessary for only one a x i a l d i r e c t i o n from the unit circumferential s t r i p . The h a l f volume of freeboard gas was subdivided into 152 zones, 38 at each of four a x i a l positions while the unit s t r i p was divided into 20 zones, 6 being on the bed surface. The net surface heat flux at any zone on the unit s t r i p was obtained by summing eq. 6.27b for a l l the gas zones e + 1 4 152 <fb£A« = -V- I I <S±HK <V Vn <6'29> 6 i i n=l 1=1 J Using eq. 6.29 for i = 1*20 the c i r c u m f e r e n t i a l v a r i a t i o n of gas to exposed bed ( i = l-»-6) and exposed wall ( i = 7->20) surface heat flux was obtained, the r e s u l t s being converted into terms of a l o c a l r a d i a t i v e gas/surface heat transfer c o e f f i c i e n t RWA± = f n ( 0 ' W V P C V H 2 ° ' °' F i U ) (6.30) - 1 1 1 -Y I I I I z, z 2 z 3 z 4 F i g . 6 . 1 4 Gas and s u r f a c e z o n i n g i n t h e p i l o t k i l n - 1 1 2 -The c a l c u l a t i o n of gas /sur face r a d i a t i v e exchange in the freeboard was performed by the program "KSG" (see Appendix II for f lowchar t ) . 6.4.3 Radia t ive Heat Transfer Among the Freeboard Surfaces To c a l c u l a t e the d i r e c t r a d i a t i v e exchange between a gray surface area A^ and another gray surface area Aj as shown in F i g . 6.15 the surface to s u r f a c e d i r e c t exchange area s ^ s ^ f ° r each gray component i n the in terven ing gas must be evaluated for use i n eq . 2.5a which, when modif ied to account for the grayness of each s u r f a c e , takes on the form The d i r e c t exchange areas s . s . were o b t a i n e d a c c o r d i n g to the 4 D i r V t A 1 j n-1 = T (s.s.) (e .£ .E - e . e .E .) r,_i i j n j i i i j j ' n (6.31) normal (27) expression (6.32a) Cos9 J Cos9 . i 3 X . . AA.AA. n i+j i j (6.32b) 2 which fol lows from the de f in ing eq. 2 .4 . Aga in , s ince each component gas i s gray, r e c i p r o c i t y can be appl ied to d i r e c t exchange areas and - 1 T 3 -F i g . 6 . 1 5 D i r e c t r a d i a t i v e exchange between two g r a y s u r f a c e s -114-(6.33) The c a l c u l a t i o n of r a d i a t i v e heat transfer among the freeboard surfaces was c a r r i e d out i n a s i m i l a r manner to that of gas/surface exchange. The freeboard boundary was considered as two symmetrical regions, centred on the unit length circumferential s t r i p of exposed bed and wall surface, and subdivided into 100 zones, 20 at each of four a x i a l p o s i t i o n s . The circumferential d i s p o s i t i o n of zones was as per the unit s t r i p , 6 on the exposed bed and 14 on the exposed w a l l . The r a d i a t i v e exchange between gray surfaces occurs over a l l wavelengths, only a few of which are within the gas absorption spectra. Roughly 50% of the energy emitted by the freeboard surfaces l i e s within the r a d i a t i v e l y c l e a r bands (K^ = 0) as shown by F i g . 6.8 and for t h i s component d i r e c t surface/surface exchange i s e n t i r e l y view factor c o n t r o l l e d . For the remainder of the emitted surface energy, the p a r t i a l pressure of the freeboard gas emitting/absorbing species must also be considered. Because of the large f r a c t i o n of surface emission l y i n g within the freeboard gas clear bands, i n d i r e c t exchange can play a s i g n i f i c a n t role i n s u r f a c e / s u r f a c e r a d i a t i v e , exchange when e < 0.9. To account for s r e f l e c t e d r a d i a t i o n a ray tracing technique, in which energy emitted from a surface A i s traced u n t i l reaching surface A., was employed. j l -115-It was found useful to define the s p e c i f i c d i r e c t exchange factor -2, s^Sj (having units of length ) between A^ , and A., according to For an empty k i l n ( s j _ s j ) n w i l l be a function only of the angular and-axial separations, 9.. and AZ. , r e s p e c t i v e l y , between A. and A. (for a i j i j 1 I given k i l n diameter and gas mixture). Results from the c a l c u l a t i o n of s s f o r a 2:1 mixture of H O and CO (p = 0.26 P) are shown i n 1 j L L "2 2 F i g . 6.16 for the 0.4m ID p i l o t k i l n and i n F i g . 6.17 for a 4m ID prototype k i l n . The series of functional r e l a t i o n s h i p s ( S i S j > n , 9 l j = f n I A Z i j I < 6' 3 5> thus obtained provides a suitable basis from which to proceed with the evaluation of the contribution to the r a d i a t i v e exchange between A^ and A^ due to beams undergoing a s i n g l e r e f l e c t i o n such as from the surface A^ ( F i g . 6.13). By assuming one value of e for the wall (and hence a b s o r p t i v i t y a and r e f l e c t i v i t y p) the analysis of the problem i s much s i m p l i f i e d . Quantities derived for one, two and three r e f l e c t i o n s w i l l be denoted by s i n g l e , double and t r i p l e prime superscripts r e s p e c t i v e l y . -116-T 1 1 1 1 1 1 1 r P ( H 2 0 + C 0 2 ) = 0 -260 atii 1 1 1 1 1 1 1 1 1— 16 32 48 64 flXIRL S E P A R A T I O N - C M Fig 6.16a Direct specific exchange factor for the pilot kiln - Clear band radiation. -117-b J o CD CJ X UJ U-o" »—< o UJ Q_ L L K T ) p(H20+C02r0.260 atm Rbs.Coef. K=0.012 /cm-atm Angle B deg A 25 • 58 o90 o 123 ol55 O180 n 1 1 1 1 1 6 AXIAL*SEPARATION*- CM 64 80 Fig 6.16b Direct specific exchange factor for the pilot kiln - Gray band radiation. -118-3 P<H20+C02)= & -260 at I I flbs.Coef. K= 0.098 /cni-atm 16 i 1 r AXIA?SEPARATION*- CM 80 Fig 6.16c Direct specific exchange factor for the pilot kiln - Gray band radiation. -119-c n ^ ( H 2 0 + C 0 2 ) = 0 -260 atn RbsXoef. K= 0.984 /cnratm Angle 8 deg A 25 • 58 o n 1 1 1 1 1 6 AXIAL*SEPARATION*- CM 6 4 60 Fig 6.)6d Direct specific exchange factor for the pilot kiln - Gray band radiation. - 1 2 0 -P ( H 2 0 + C 0 2 ) = 0.260 atm flbs.Coef. K= 0.000 /cm-atm Angle B deg ^ 25 • 58 o90 O 123 ol55 O180 T 320 480 R X I f l L S E P f l R f l T I O N - C M r 640 800 Fig 6.17a Direct specific exchange factor for the prototype kiln - Clear band radiation. -121-i 1 1 1 1 1 1 1— r P(H20+C02)= 0-260 atm Angle 8 deg Fig 6,17b Direct specific exchange factor for the prototype kiln - Gray band radiation. 1 2 2 -co P ( H 2 0 + C 0 2 ) = 0-260 atm Rbs.Coef. K= 0.098 /cm-atm Angle 8 deg A 25 • 58 tee - i 1 r 1 1 160 320 480 R X I f l L S E P A R A T I O N - C M 640 Fig 6.17c Direct specific exchange factor for the prototype kiln - Gray band radiation. 800 -123-P ( H 2 0 + C 0 2 r 0 - 2 6 0 atm Abs.Coef. k> 0.984 /cffratni Angle B deg A 25 ; i 1 1 1 1 1 1 1 1 n 160 320 480 640 800 R X I f l L S E P R R R T I O N - CM Fig 6.17d Direct specific exchange factor for the prototype kiln - Gray band radiation. - 1 2 4 -I t can be seen from F i g . 6.18a, which shows the s i t u a t i o n i n more d e t a i l , that s, s . V A j "n-i* V k ^ ? \ ^ ' ( V E J > } ( 6 * 3 6 ) The combined e f f e c t of the en t i re freeboard i s obtained by summing eq. 6.36 over a l l the r e f l e c t i n g surfaces i j n=l k=l J " i x ^ j ' E < E i " E J ) } (6.37b) where s j _ S j ' *- s the s p e c i f i c exchange fac tor for one r e f l e c t i o n . For beams u n d e r g o i n g two r e f l e c t i o n s , between and A^, such as from A^ and A^ ( F i g . 6.13b) the a n a l y s i s can be e a s i l y extended. Again by cons ider ing the more d e t a i l e d d e p i c t i o n i n F i g . 6.18b i t can be seen that 4 \ \ QA': A. = l l l ^ v ^ v J V A V ^ V v 1 (6-38a) i j n=l A=l k=l J = I {s±s " A A e (E - E )} (6.38b) n=l J J J -125-(a) Direct & one reflection (b) Two reflections F i g . 6.18 R a d i a t i o n between s u r f a c e s with one and two r e f l e t i o n s ( D e t a i l ) . For the 4m ID prototype k i l n only the clear band r a d i a t i o n contributed s i g n i f i c a n t l y through the f i r s t r e f l e c t i o n due to the much longer path lengths. Results from the s p e c i f i c exchange factor c a l c u l a t i o n s for the 2:1 H-0/CO- f r e e b o a r d gas mixture (p = 0.26 P) are presented as a L L 2 2 series of p l o t s . For the p i l o t k i l n , with an assumed value of surface r e f l e c t i v i t y p = 0.30, F i g s . 6.19 and 6.20 show the v a r i a t i o n of s £ s j ' ( i . e . one r e f l e c t i o n ) with a x i a l and ci r c u m f e r e n t i a l separation of and Aj f o r each gray component of the freeboard gas ( p i l o t k i l n and prototype k i l n r e s p e c t i v e l y ) . It i s evident that only surface emissions l y i n g i n the clear and nearly clear gas absorption bands ( i . e . n = 1,2) contribute s i g n i f i c a n t l y through even one r e f l e c t i o n . Comparison with F i g . 6.16 shows that s.s.' ~ 0.1 - 0.2 s.s.. i 3 i 3 For emitted energy undergoing two r e f l e c t i o n s i n the p i l o t k i l n the re s u l t s are generally s i m i l a r ( F i g . 6.21). The importance of a l l the absorbed bands declines r e l a t i v e to the c l e a r bands as expected and values of s.s.'' ~ 0.01-0.07 s.s. are encountered. For the prototype k i l n only i 3 ± 3 emitted r a d i a t i o n i n the clear band contributed s i g n i f i c a n t l y for one and two r e f l e c t i o n s , as shown i n Fi g s . 6.20 and 6.22. For three l e v e l s of r e f l e c t i o n values of s.s'*'< 0.02 s.s. were i j i 3 obtained and unless p < 0.5 the error introduced by accounting for only two r e f l e c t i o n s w i l l be under 3%. -127-The r a d i a t i v e exchange between s u r f a c e s such as A . and A . was i J c a l c u l a t e d by combining the eqs. 6.31, 6.37 and 6.38 to obtain 4 = = = o = V j }ml { ( s i S 3 + S i S j ' + S i S j " > e <V E j » n < 6 ' 3 9 > which i s cor rec t to two r e f l e c t i o n s . The n e t s u r f a c e h e a t f l u x at any zone A^ on the u n i t l e n g t h c i r c u m f e r e n t i a l s t r i p was obtained by summing eq . 6.39 for a l l the freeboard surface zones 4 200 — — — q , , A = I I ( ( s . s . + s . s . ' + s . s . * ' ) A . e . e . ( E . - E.)} (6.40) ^fbs^Aj, 1 J i J i j j i i i j n v ' Using eq . 6.40 for i = 1>20 the c i r c u m f e r e n t i a l v a r i a t i o n heat f lux at the exposed bed ( i = l->6) and exposed wal l ( i = 7->20) surfaces due to r a d i a t i v e interchange with the freeboard boundary could be c a l c u l a t e d . The r e s u l t s were subsequently converted into the more use fu l form of r a d i a t i v e s u r f a c e / s u r f a c e heat t rans fe r c o e f f i c i e n t s (Sect ion 7 .4 ) . -128-flngle 0 deg A Q . O • 48.0 O96.0 O144.0 Reflectivity=0.300 P ( H 2 0 + c o 2 r 0-260 atm flbs.Coef.K= 0.000 /cm-atm K=0.000 _ ! j 1 1 1 1 6 RXI fiL2 SEPfiRRT I Off - CM 64 80 Fig 6J9a Specific surface to surface exchange area for one reflection (Pilot Kiln) -129-flngle 8 deg A O . O • 48.0 O96.0 O 144.0 Reflectivity=0.300 P(H20+co2r 0-260 atm Abs.Coef.K=0.Q12 /curat*! 0.098 0.984 K=0.012 K-0.Q98 1 6 RXIflL2SEPARATION* CM Fig 6.19b Specific surface to surface exchange area for one reflection (Pilot Kiln) i 1 r -130-i 1 1 1 1 r Angle 8 deg R e f l e c t ! v i t y = 0 . 3 0 0 A 0 . 0 p ( H 2 0 + c o 2 r 0 . 2 6 0 atm ° 4 8 . 0 Abs.Coef.K= 0 . 0 0 0 /cm-atm -O 9 6 . 0 0 1 4 4 . 0 F i g 6.20a S p e c i f i c su r face to sur face exchange area fo r one r e f l e c t i o n (Prototype K i l n ) -131-flngle 8 deg • 48.0 O96.0 O 144.0 Reflectivity=0.300 P ( H 2 0 + C 0 2 r 0-260 atm Abs.Coef.K=0.012 /cm-atm 0.098 0.984 K=0.Q12 800 Fig 6.20b Specific surface to surface exchange area for one reflection (Prototype Kiln) -132-flngle B deg • 45.0 O90.0 O 135.0 O180.0 Reflectivity=0.300 P(H20+C02)=0 -260 atm AbsXoef.K= 0.000 /cnratii 0.012 0.098 K=0.000 i 1 r 32 fiXIRL SEPflRflTlON - C M Fig 6.21 Specific surface to surface exchange area for two reflections (Pilot Kiln) -133-The c a l c u l a t i o n of su r face /sur face r a d i a t i v e exchange i n the freeboard was performed by the program "KSS" a f lowchart for which appears i n Appendix I I . The a n a l y s i s of r e f l e c t i o n s was c a r r i e d out by a u x i l i a r y programs REFl and REF2. To u t i l i z e the r e f l e c t i o n ana lys is r e s u l t s , the f i t t e d curves , such as those of F i g s . 6.19 to 6.21, were wr i t ten onto a storage f i l e by REFl and REF2 for subsequent use by KSS (Appendix i i ) . Only i n d i r e c t exchanges were ca lcu la ted by means of f i t t e d polynomials with d i r e c t exchanges always being evaluated for ac tua l freeboard geometry using eq. 6.32b. In t h i s way the small e r ror introduced into the s p e c i f i c exchange area c a l c u l a t i o n s by the assumption of an empty k i l n with uniform surface e m i s s i v i t y i s fur ther reduced. 6.4.4 Accuracy of the Radiat ion Model A check on the accuracy of the d i r e c t exchange area c a l c u l a t i o n s i s a v a i l a b l e by r e f e r r i n g to the de f in ing eq. 2 .5 . The emitted r a d i a t i v e e n e r g y from any s u r f a c e A on the exposed bed or w a l l to the e n t i r e s freeboard can e a s i l y be shown to be apportioned according to 4 Q A ->fb s = y E A m n s s n=l 4 * * - 7 E { (s . s c , ) + (s . g „ ) } L . n s A fbs n v A 6 f b g ' n J n=l s s (6.41) -134-where the a s t e r i s k i s used to denote exact va lues . It fo l lows from eq. 6.42 that ( S A S f b s ) n + ( S A 8 f b g ) n = A s ( 6 ' 4 2 ) s s The error in the c a l c u l a t e d values of d i r e c t exchange area for sur face A i s given by s { A s " t ( s A S f b s > n + ( S A 8fbg>J> 1 0 0 E r r n - 2 5 ( 6 . 4 3 ) s An error l i m i t of + 4% was adhered to for the i n d i v i d u a l d i r e c t exchange area c a l c u l a t i o n s . In general the la rges t errors are associa ted w i t h the l a r g e s t v a l u e s of and s i n c e net r a d i a t i v e exchange i s a funct ion of a l l values the ac tua l e r ror l i m i t s are s u b s t a n t i a l l y bet ter that + 5%. The remaining uncer ta in t i es assoc ia ted with the freeboard r a d i a t i v e exchange c a l c u l a t i o n s are those due to ( i ) E r r o r s i n the t o t a l e m i s s i v i t y da ta . ( i i ) E r r o r s attached to the gray gas assumption and the subsequent f i t t i n g procedure. ( i i i ) E r ro rs due to incomplete treatment of r e f l e c t e d r a d i a t i o n . ( i v ) Uncerta inty as to the e m i s s i v i t y of the exposed bed and wal l s u r f a c e s and i t s s p e c t r a l d i s t r i b u t i o n . -1.35-Of these uncertainties only those of ( i i ) and ( i i i ) l i e d i r e c t l y under the control of the current i n v e s t i g a t i o n and these have been reduced to well under 10%. The basic data of ( i ) have been i n use for many years and represent the best a v a i l a b l e , although the accuracy i s probably no better than 10%. The greatest uncertainty i s that of ( i v ) and for many materials, the ava i l a b l e data i s inadequate for the requirements of sophisticated modelling techniques. 6.5 A U n i f i e d Model for Heat Transfer at a K i l n Cross-section To enable deta i l e d i n v e s t i g a t i o n of the i n t e r a c t i o n among the i n d i v i d u a l heat transfer processes and also to e s t a b l i s h t h e i r r e l a t i v e importance, a u n i f i e d heat transfer model for a given k i l n cross-section was developed. Heat transfer within the k i l n wall was assumed to be i n the r a d i a l d i r e c t i o n only (Sections 6.2.1 and 6.2.2) and the f i n i t e difference approximation eq. 6.11 for the transient one-dimensional conduction eq. 6.10 u t i l i z e d to cal c u l a t e the temperature p r o f i l e through the entire wall section as a function of circumferential p o s i t i o n . The boundary c o n d i t i o n for an area element ws . on the inside wall 3 surface during i t s period of exposure to the freeboard region was where f b i denotes the t o t a l number of zones i n the freeboard region. qfb*ws R i->ws . c i-*ws j ; i ws .' J (6.48) -136-The necessary r a d i a t i v e heat transfer c o e f f i c i e n t s were obtained using the model of Section 6 .4. Convection from the freeboard gas to the exposed w a l l s u r f a c e was c a l c u l a t e d u s i n g the c o r r e l a t i o n ^ 3 ^ f o r a developing turbulent boundary layer Nu z = 0.029 R e z ° ' 8 P r ° * 3 3 (6.49) Convection to the exposed bed surface was calculated by assuming an enhancement factor of 5 ( i . e . h , = 5 h ) a value which appeared to c g+eb c g-»-ew r r (22) better f i t the p i l o t k i l n data (Section 7.2) than the r e s u l t s o f v ' which concluded h , ~ 10 h c g->eb c g+ew For the portion of each k i l n revolution which this same surface element spends covered by the bed, the conduction model was extended to include the bed material. The inner boundary condition for this extended model was established by assuming the layer of bed material contacting the wall to be i n i t i a l l y isothermal and at the same temperature as the exposed bed surface. The e f f e c t i v e thermal conductivity of the bed material was (41) e v a l u a t e d according to the f a i r l y simple model of and the contact (or f i l m ) r e s i s t a n c e was c a l c u l a t e d from eq. 2.33 based on Schlunder's model . Conditions at the k i l n s h e l l were assumed to be steady which provided the s h e l l - s i d e boundary condition h ^ " ( D h u + n , ) (T - T ) (6.50) n s h R sh c sh sh « v ' - 1 3 7 , -For convection at the k i l n s h e l l the r e s u l t NIL = 0.11 {(0.5 Re 2 + G O P r } 0 , 3 5 (6.51) D , (jj U sh recommended i n ^ 3 ^ f o r n a t u r a l c o n v e c t i o n from r o t a t i n g cylinders was u t i l i z e d . Radiation at the s h e l l was calculated from the simple . . n.(30) two-gray-body r e s u l t ( T *- T 4 ) sh 0 0 R hsh " £ s h ° T - T ( 6 ' 5 2 ) sh » For given conditions of k i l n geometry, r o t a t i o n rate, freeboard gas composition and bed and wall materials the independent variables for the model are the freeboard gas temperature and the exposed bed surface temperature. To operate the model, the c y c l i c a l behaviour of the wall r e f r a c t o r y was u t i l i z e d i n the same manner as for the wall active layer model (Section 6.2.2). Thus the temperature at any f i x e d point ( r , z, 9 ) within the wall must be independent of time. Beginning from an assumed i n i t i a l wall temperature p r o f i l e the c a l c u l a t i o n proceeds through one k i l n r e volution, the f i n a l r a d i a l temperature p r o f i l e providing the i n i t i a l condition for the subsequent re v o l u t i o n . -138-To obtain f a i r l y rapid convergence i t was found useful to carry out the c a l c u l a t i o n for about 20 i t e r a t i o n s , i n order to obtain a much better estimate of the i n i t i a l surface temperature, and then r e s t a r t the c a l c u l a t i o n from the beginning using the improved i n i t i a l condition. Using t h i s technique, and incorporating a damping factor into the co r r e c t i o n applied to obtain each new i n i t i a l condition , convergence could generally be obtained within 150 Iterations based on the convergence c r i t e r i o n T ( i , l ) - T ( i , J ) max i=l->I < 0.05 Kelvin Degrees where I represents the t o t a l number of r a d i a l wall nodes and J the t o t a l number of time steps per k i l n r e v o l u t i o n . -139-CHAPTER 7 RESULTS AND DISCUSSION The chapter i s opened by a general d i s c u s s i o n of the p i l o t k i l n t r i a l s i n which severa l notable r e s u l t s are set aside for l a t e r exp lanat ion . A t ten t ion i s then focussed on convect ion and covered wa l l / covered bed heat t rans fe r in the p i l o t k i l n before moving on to the r e s u l t s from the bed surface temperature model in Sect ion 7.4 and the freeboard r a d i a t i o n model in Sect ion 7 .5 . The chapter c loses with a d e t a i l e d d i s c u s s i o n of the r e l a t i o n s h i p among the k i l n heat t rans fe r processes stemming from the a p p l i c a t i o n of the u n i f i e d heat t ransfer model to f i r s t the p i l o t k i l n (Sect ion 7.6.2) and subsequently the la rger prototype k i l n (Sect ion 7 . 6 . 3 ) . 7.1 Resul ts from the P i l o t K i l n T r i a l s As was stated i n Chapter 3 the primary purpose of the p i l o t k i l n t r i a l s was to provide v e r i f i c a t i o n for a more general a n a l y t i c a l model of ro tary k i l n heat t rans fe r processes . The complexity of these processes , and the l i m i t a t i o n s imposed by some of the da ta , p a r t i c u l a r l y for the bed mater ia l temperature, are not conducive to obta in ing new ins igh ts from a purely empi r ica l s tudy. The r e s u l t s obtainable f a i r l y d i r e c t l y from the p i l o t k i l n data , net heat f luxes and some but not a l l of the associa ted temperature d r i v i n g f o r c e s , are not i n themselves p a r t i c u l a r l y i n s t r u c t i v e s ince the d e t a i l s - 14 " b -of the component heat fluxes are lacki n g . As w i l l become evident, the onset of an endothermic bed reaction ( i . e . limestone c a l c i n a t i o n ) brings about a s i g n i f i c a n t s h i f t i n the r e l a t i o n s h i p among the heat transfer processes occurring simultaneously at any k i l n a x i a l p o s i t i o n . The presence (or absence) of the endothermic bed reaction i s the major d i s t i n g u i s h i n g point among the t r i a l s , which were accordingly c l a s s i f i e d as being e i t h e r i n e r t bed, consisting of 16 t r i a l s using fin e sand, coarse sand, petroleum coke and limestone at low temperature, or c a l c i n i n g , c o n s i s t i n g of 6 higher temperature limestone t r i a l s . The raw data from each t r i a l , made up of the various gas, wall and bed thermocouple outputs plus the flow measurements for the combustion gas, a i r and bed material (and the a x i a l composition of the bed for the limestone t r i a l s ) , were converted into heat transfer rates by the data analysis program (Appendix II) incorporating the methods of Sections 6.1 and 6.2 In addition to the printed output the more pertinent r e s u l t s are provided by the program i n plotted form. To avoid needless r e p e t i t i o n , only two t r i a l s w i l l be discussed i n d e t a i l , one for the i n e r t bed condition and one for the c a l c i n i n g bed condition. Results from the remaining t r i a l s are given i n plotted format by Appendix ( I I I ) . 7.1.1 The Inert Bed T r i a l s For the i n e r t bed condition, t r i a l T4 w i l l be u t i l i z e d for purposes of discussion. Referring to Table 5.1, which d e t a i l s the run conditions, T4 was c a r r i e d out using the coarse sand at a gas f i r i n g rate of 1.97 3 1/sec (4.18 f t /min) under standard conditions. For the reasons outlined -141-i n Chapter 5 ( i . e . to maximize Re and to reduce d i s t o r t i o n of the freeboard gas flow by r e c i r c u l a t i o n and buoyancy e f f e c t s ) the combustion was at 215% excess a i r . For the s o l i d s feed rate of 62 kg/hr t h i s f i r i n g condition provided near maximum allowable sand e x i t temperatures. In F i g . 7.1 the a x i a l temperature p r o f i l e s are plotted. Values of freeboard gas temperature are plotted as indicated i n the figure key, for points about 2.5 cm off the bed surface and about 10 cm off the diagonally opposite wall surface. At large values of excess a i r r a d i a l gas temperature gradients were minimized, with nearly uniform r a d i a l gas temperatures occurring over most of the k i l n length. In the region of the f i r i n g box, gas temperatures were s l i g h t l y depressed near the top of the k i l n freeboard, due to the secondary a i r stream, while near to the gas discharge some thermal s t r a t i f i c a t i o n was found to develop with maximum gas temperatures occurring i n the region of the l a t t e r thermocouple p o s i t i o n . Measurements of gas temperatures closer to the wall, obtained with some d i f f i c u l t y since immersion of the suction thermocouples within the bed had to be avoided, showed only a small temperature decline (~ 10 K) i n approaching the wall surface. Poor mixing within the gas flow meant that some thermal s t r a t i f i c a t i o n developed adjacent to the bed surface, probably due to the enhanced convective loss to the bed (Section 7.2). This s t r a t i f i c a t i o n i s evident i n F i g . 7.1 from the increasing temperature difference between the measuring points at each a x i a l l o c a t i o n . Except within the i n i t i a l 1.5 m of k i l n length the bed temperature and freeboard gas temperature were found to increase (nearly) l i n e a r l y with a x i a l distance. This l i n e a r v a r i a t i o n , which i s t y p i c a l of low -142-T T T T RUN NUMBER T4 O BULK SOLIDS A INSIDE UflLL (flVG) • GRS-2.5 Ci OFF BED O GflS-10 ci OFF UflLL O <> i 1 1 1 1 1 1 1 1 r 1 AXIA POSITION (METRES? 5 Fig.7.1 Pilot kiln axial temperature profiles Inert bed trial T4 -143-temperature counter-flow heat exchangers where convection i s the dominant (12) heat t r a n s f e r mechanism, has also been predicted for high temperature rotary k i l n s . The model did not, however, indicate the much larger bed temperature gradient measured i n the entrance region (0 -> 1.5 m) of the p i l o t k i l n (item i below). Of p a r t i c u l a r importance i n F i g . 7.1 are two points r e l a t i n g to the bed temperature p r o f i l e s : ( i ) The rapid, non-linear increase i n bed temperature over the i n i t i a l 1.5 m of the k i l n . At the f i r s t bed thermocouple l o c a t i o n , only 16 cm from the point of entering the k i l n , the sand has increased nearly 200 K i n temperature despite t h i s being i n the coolest region of the k i l n . The r e s u l t s of F i g . 7.1 indicate an average net bed heat input rate over the f i r s t 1.5 m of k i l n which i s ~ 4.5 times the rate i n the remainder of the k i l n . This i n i t i a l rapid heating of the charge was observed i n a l l the t r i a l s . ( i i ) The small temperature difference between the bed material and the Inside wall temperature. Again t h i s r e s u l t i s consistent for a l l k i l n t r i a l s . Within the l i m i t a t i o n s of the technique necessary for obtaining the bed temperatures, the actual temperature difference between the bed m a t e r i a l and the w a l l s u r f a c e cannot be established. However i t can be concluded that this temperature difference i s small. -144-Although not shown i n F i g . 7.1, no measurable r a d i a l temperature gradients were found within the bed material, an absence a t t r i b u t a b l e to the close s i z i n g of the feed material and the small bed depth i n the p i l o t scale f a c i l i t y . As shown i n F i g . 7.2 the temperature d r i v i n g force for heat tr a n s f e r from the freeboard was 120 •> 180 K. The k i l n s h e l l temperatures were ~ 380 K. For the steady-state heat loss Q through the r e f r a c t o r y s s wall ( s h e l l loss) the gas to wall surface thermal resistance represents < 15% of the t o t a l thermal resistance near the burner, a value which increases to > 50% near the gas e x i t . The absence of measurable r a d i a l temperature gradients within the bed indicates that gas to exposed bed surface heat transfer i s c o n t r o l l e d by conditions i n the freeboard, at l e a s t for the vigorously mixed bed surface which i s c h a r a c t e r i s t i c of a r o l l i n g bed. This condition of n e g l i g i b l e burden-side thermal resistance (9) corresponds to the 'well mixed' bed which was found to best match previous data. The net rate of heat transfer to the bed material, per a x i a l metre of k i l n , i s provided i n F i g . 7.3 which also shows the net covered wall to bed heat transfer rate and the s h e l l loss through the r e f r a c t o r y . Denoting the number of s p e c i e s present i n the bed material by then, for an inert bed the net rate of heat input, given by n 1 1 1 1 1 1 1 r RUN NUMBER T4 O GRS-WRLL A GRS-BED i 1 1 1 1 1 1 1 1 1 — ; 1 AXIAL POSITION (METRES) 4 Fig.7.2 Mean gas-surface temperature differences -146-T T T T T T RUN NUMBER T4 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED WALL ~i 1 1 1 1 1 r 1 flXIRL POSITION ?METRES) 4 Fig . 7 . 3 Net heat t r a n s f e r r a t e s -147-i s e s s e n t i a l l y a d i r e c t funct ion of the a x i a l temperature gradient s ince the s p e c i f i c h e a t , c^ Is genera l ly a weak funct ion of temperature. Thus the near ly l i n e a r bed temperature gradient p r e v a i l i n g beyond the i n i t i a l 1.5 m of bed i s r e f l e c t e d i n the near ly uniform bed heat ing rate Q, ~ 1 b kW/m, a value wel l below the s teady-s ta te l o s s through the wal l r e f r a c t o r y , Q ~ 2 -»• 3 kW/m. C l e a r l y the heat ing e f f i c i e n c y over the s s major i ty of k i l n length i s poor. Heat t rans fe r between the covered wal l and bed i s not a major fac tor at any k i l n p o s i t i o n , as can be seen more c l e a r l y by F i g . 7.4 which shows the net exchange, i n f a c t , to be genera l ly negat ive , I .e. from the bed to the covered w a l l . The s i t u a t i o n dep ic ted , with the covered wal l to bed exchange being p o s i t i v e near the co ld end but d e c l i n i n g and eventua l ly assuming negative values beyond some a x i a l d i s t a n c e , i s t y p i c a l of the iner t bed t r i a l s . A simple s t ra igh t l i n e curve through the data points of F i g . 7.4 i s s h i f t e d upward by lower f i r i n g rates (and hence lower k i l n temperatures) but the negative slope i s always present . For t h e lowest temperature t r i a l s , v a l u e s of Q , ~ 0.4 Q . , were cw*cb xg+ew-*eb observed. For surface heat f l u x e s , the s i t u a t i o n i s that of F i g . 7 .5 . Covered wal l net heat f luxes are much less than at the exposed wal l (~ 2 2 kW/m ) which are i n turn somewhat l e s s than at the exposed bed surface (~ 2 (19 22 32 33) 3 •* 6 kW/m ). The enhancement at the bed surface i s expected » » » / and i s d iscussed fur ther i n Sect ion 7 .2 . -148-i 1 1 1 r AXIAL POSITION (METRES) 4 Fig.7.4 Covered wall to solids heat input as a fraction of gas plus exposed wall input -149-1 1 1 1 1 i 1 1 1 — RUN NUMBER T4 O TO EXPOSED SOLID SURFACE -A TO EXPOSED INSIDE UflLL oo - • TO COVERED INSIDE WALL O ( N J — o o o o FLUX i O o > A A JEflT O A A A A A (M ~ • • • • • • • o — • CM ,. 1 i i i i i 1 1 1 1 1 fiXIRL POSITION ?METRES) 4 Fig.7,5 Average values of surface heat fluxes -150-The net values of inside wall heat f l u x were obtained as described i n Chapter 6, using a f i n i t e difference model of the wall active layer w i t h the measured i n s i d e w a l l temperature T as one boundary condition and the measured steady-state s h e l l loss Q as the other. Results from ss the f i n i t e difference model indicate the active layer thickness to be ~ 1 (7 12 29) cm which i s c o n s i s t e n t with p r e d i c t e d values ' ' . Thermocouples placed 1.27 cm below the surface were i n steady-state. With transient response only to a depth of ~ 10 mm the probe surface thermocouple junction diameter ~ 1 mm became a s i g n i f i c a n t factor since the recorded output then r e f l e c t s an average for the i n i t i a l 10% of the active layer thickness. To account for t h i s averaging e f f e c t a correction factor was obtained by using the u n i f i e d heat transfer model (Section 6.5) to p r e d i c t , for the conditions at the measuring p o s i t i o n , the r a d i a l wall temperature p r o f i l e as a function of circumferential p o s i t i o n . At each circ u m f e r e n t i a l p o s i t i o n a predicted average wall temperature for the 1mm layer of re f r a c t o r y on the inside surface was calculated and subtracted from the predicted surface temperature. The r e s u l t i n g value of temperature difference was then added to the averaged temperature, measured by the thermocouple, to obtain an improved value for the inside w a l l s u r f a c e temperature T^ g at that c i r c u m f e r e n t i a l p o s i t i o n . F i g . 7.6 shows the v a r i a t i o n of the i n s i d e w a l l s u r f a c e temperature AT as a ws function of a x i a l l o c a t i o n . The thermocouple lag near the points of immersion and emersion by the bed i s s i g n i f i c a n t when the wall heat flux i s plotted as a function of ci r c u m f e r e n t i a l p o s i t i o n ( F i g . 7.7) although the net surface fluxes w i l l not be too se r i o u s l y i n error (< 20%) even without use of the temperature c o r r e c t i o n . -151-i 1 1 1 1 1 1 1 r 1 AXIAL POSITION ?METRES) 4 5 Fig . 7 . 6 Range of i n s i d e w a l l temperature -152-i 1 1 r RUN NUMBER T4 Probe 1 Z=4.89 • Exposed Covered -i 1 1 1 1 1 1 r 72.0 144.0 216.0 288.0 RNGULRR POSITION o.o 360.0 Fig . 7 . 7 C i r c u m f e r e n t i a l v a r i a t i o n of heat f l u x i n t o the w a l l s u r f a c e -153-As noted at the outset , the trends descr ibed i n the foregoing d i s c u s s i o n are general for the iner t bed t r i a l s . The most important o b s e r v a t i o n s are the c l o s e - c o u p l i n g of the bed and i n s i d e w a l l temperatures and the rap id dec l ine in bed heat ing rate beyond the i n i t i a l 1.5 m of k i l n l ength . 7.1.2 The C a l c i n a t i o n T r i a l s For the reac t ing bed cond i t ion t r i a l T20 w i l l be c i t e d , for which the gas f i r i n g rate was 2.38 1/sec at about 10% excess a i r . The l imestone feed rate was 42 kg /hr with a f i n a l f r a c t i o n a l c a l c i n a t i o n of 98%. The a x i a l temperature p r o f i l e s of F i g . 7.8 are s i m i l a r to the iner t bed case although peak freeboard temperatures are considerably greater (~ 1700 K fo r the gas) c h i e f l y due to the much smal ler secondary a i r burden. The bed mater ia l again undergoes rapid heat ing wi th in the i n i t i a l 1.5 m of k i l n and the bed and ins ide wal l temperatures are c l o s e l y l i n k e d . Thermal s t r a t i f i c a t i o n of the freeboard gas is present from the outset which r e s u l t s in a s i g n i f i c a n t l y la rger temperature d r i v i n g force for gas to wal l heat t rans fe r ( F i g . 7 .9 ) . The onset of bed c a l c i n a t i o n commences at about the k i l n midpoint , beyond which the net rate of heat input to the bed, + H j dZ dn i ( 6 . 3 a ) -154-where N, represents the number of species present in the bed m a t e r i a l , i s b dominated by the r e a c t i o n enthalpy term. The endothermic bed reac t ion thus acts as a sink for energy and the slope of the bed temperature p r o f i l e becomes i n s e n s i t i v e to the net rate of heat t rans fe r to the bed. A p lot of net input rates for the c a l c i n a t i o n t r i a l ( F i g . 7.10) provides a revea l ing comparison with the iner t bed t r i a l ( F i g . 7 .3 ) . P r i o r to the onset of c a l c i n a t i o n , the net input to the l imestone bed i s only s l i g h t l y greater than for the sand (due to the greater freeboard temperatures) and i s d e c l i n i n g . However with c a l c i n a t i o n , the net input to the bed increases sharp ly , peaking at 11 kW/m for an increase of ~ 300% over the rate immediately preceeding any r e a c t i o n . The s teady-sta te s h e l l l oss does not undergo a corresponding i n c r e a s e . With c a l c i n a t i o n , the d e c l i n e i n Q . i s ar rested and p o s i t i v e ' cw+cb r values are again recorded ( F i g . 7 .11) . Heat f lux to the exposed bed surface ( F i g . 7.12) r e f l e c t s the large values of bed heating rate in the c a l c i n a t i o n zone. Corresponding to the increased bed heat ing rate i s a marked increase i n the temperature c y c l i n g at the i n s i d e w a l l , moving from a p r e - c a l c i n a t i o n value of 6 K to peak values of 50 K ( F i g . 7 .13) . A lso accompanying the bed reac t ion are s t rongly negative l o c a l covered wal l surface heat f luxes ( i . e . q . +) as shown in F i g . 7.14. ncv>cb -155-Fig.7.8 Kiln axial temperature profiles Calcining bed trial T20 -156-T T RUN NUMBER T20 O GRS-WflLL A GflS-BED —I 1 1 1 1 r AXIAL POSITION ?METRES) 4 Fig.7.9 Mean gas-surface temperature differences - 1 5 7 -T T T T T T T RUN NUMBER T20 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL n 1 1 1 1 1 1 r 1 flXIRL POSITION (METRES) 4 Fig.7.10 Net heat t r a n s f e r r a t e s - 1 5 8 -i 1 1 1 1 1 r 1 AXIAL POSITION (METRES) 4 F i g . 7 J 1 Covered w a l l t o s o l i d s heat i npu t as a f r a c t i o n of gas p l u s exposed w a l l i npu t -159-1 1 1 1 1 i i I 1 RUN NUMBER T20 O TO EXPOSED SOLID SURFACE 8 -A TO EXPOSED INSIDE WALL • TO COVERED INSIDE UflLL — o _ C M X X — -ZD _ J 1 . o Ll_ _ 1 cx L U m o -<M o o O o -o ° o A A A A A A A A ~ o _ 1 • • • • • • • • 1 0 1 1 1 1 1 1 1 AXIAL POSH!ON 1 1 fMETRES) 1 4 1 5 5 F i g . 7 J 2 Average values of surface heat fluxes -160-i 1 — — i 1 1 1 1 1 r 1 AXIAL POSITION (METRES) 4 5 F i g . 7 J 3 Range of i n s i d e w a l l temperature -161-i 1 1 r RUN NUMBER T 2 0 Probe 1 Z=4\89 • Probe 8 Z=1.32 • Exposed X— Covered ~i r 288.0 0.0 1 1 1 1 1 72.0 144.0 216.0 ANGULAR POSITION 360.0 Fig . 7 J 4 C i r c u m f e r e n t i a l v a r i a t i o n of heat f l u x i n t o the w a l l s u r f a c e - 1 6 2 -The evidence thus points to a significant shift in the relationship among the various heat transfer processes accompanying the endothermic bed calcination reaction. The reasons for this shift can be identified using the unified heat transfer model and are discussed in Section 7.6. 7.2 Convective Heat Transfer in the Freeboard The role of convection in rotary k i l n heat transfer has not been c l e a r l y established. Various studies (Section 2.2) have indicated that convection to the exposed bed surface may be considerably more efficient than at the exposed wall surface. The most thorough investigation of (22 ) convection in rotary k i l n s i s that of i n which values of h , ~ c g-*eb (21 22) 10 h were measured. However previous investigations ' of c g-> ew freeboard convective heat transfer have been hampered by the inability to measure the covered wall/bed energy exchange. With the pilot k i l n t r i a l s this restriction has been removed. To obtain the convective heat flux at the exposed wall and bed surface the radiative contribution (calculated using the results of Section 7.5) was subtracted from the measured net surface heat fluxes. Thus for the exposed wall q = „. q - „q (7.1) cH+ew R+c^ -»-ew R^ -*ew and for the exposed bed b^ e^w*eb R^ g+eb c^w+cb q T (7.2) c V e b A e b - 1 6 3 -Although the measurement of the covered wall/bed exchange i s a s i g n i f i c a n t advance, s e v e r a l problems are a s s o c i a t e d with the determination of convective heat transfer c o e f f i c i e n t s from the p i l o t k i l n data: ( i ) The r e s t r i c t e d range of Reynolds numbers. The maximum ava i l a b l e a i r flow provided values of Re^ ~ 9000. A lower l i m i t on Re^~ 3000 was set by the necessity of avoiding any strong biasing of the flow (72 ) due to buoyancy e f f e c t s which may occur f o r Ar < 0.01. In terms of Re , a more a p p r o p r i a t e parameter for a developing flow z (see i i following), the short length of the p i l o t k i l n resulted i n 4 5 values of 10 < Re^ < 10 which corresponds to the t r a n s i t i o n range for a developing boundary layer with s i g n i f i c a n t free stream turbulence. Thus considerable scatter of the data was i n e v i t a b l e . ( i i ) The length to diameter r a t i o . For the p i l o t k i l n L/D = 13 while end e f f e c t s , p a r t i c u l a r l y the flow a c c e l e r a t i o n near the dam at the gas e x i t , render the r e l i a b l e test section somewhat shorter. This value of L/D implies a developing flow for the entire k i l n length even with the turbulent free stream conditions p r e v a i l i n g i n the burner region. ( i i i ) The i n a b i l i t y to measure precise bed surface temperatures. As w i l l be shown i n Section 7.5 the p o t e n t i a l for r a d i a t i v e exchange between the exposed wall and bed surfaces becomes s i g n i f i c a n t at higher surface temperatures. However the temperature r i s e -16.4-experienced by bed p a r t i c l e s exposed to the freeboard w i l l be small (Section 7.4) and the exposed bed surface can be assumed to be isothermal. In addition, by simultaneously considering a l l the heat transfer processes occurring at a k i l n cross-section, i t w i l l be shown i n Section 7.6 that, for an in e r t bed material, the exposed bed surface temperature must be approximately equal to the wall surface temperature at the point of exposure to the freeboard (at the same a x i a l p o i s i t i o n ) . This condition was assumed to be exactly true for the 16 i n e r t bed runs analyzed for convection. At the r e l a t i v e l y low freeboard temperatures c h a r a c t e r i s t i c of these t r i a l s the c a l c u a t e d v a l u e s of h , and h were not overly c g^ -eb c g-*ew sen s i t i v e to the bed surface temperature, generally varying < 10% when the temperature equality assumption was relaxed by + 5 K. The t r i a l s T l to T17, l i s t e d i n Table 5.1, were carried out using various materials (Table 4.1) at several freeboard temperature le v e l s for each material and subsequently analyzed for the convective component of heat transfer. The r o t a t i o n rate was maintained at 1.5 rpm except for t r i a l s T14 to T16 which were at 1 rpm. F i l l was held approximately constant (~ 12%), as was the k i l n slope. In a l l cases the bed was i n a r o l l i n g mode. Ma t e r i a l residence times under these conditions were ~ 2.5 hours. In F i g . 7.15 va l u e s of Nu , are p l o t t e d a g a i n s t Re . As a z'g->ew r e z anticipated the scatter of the data points i s considerable and no new c o r r e l a t i o n i s proposed. A comparison of the exposed wall r e s u l t s with -165-J , — - 1 - 1 1 1 1 1 I 1 J in c o ^ 4 IM ZD z c n - l 1 CO A Fine Sand • Coarse Sand O Petroleum Coke O Limestone o 10< A T^F * DA ^  *> o o o d D • • AD • -T- 1 1 1 1 1 — r 3 5 7 10» RE , Fig 7.15 Convection to the exposed wall surface - 1 6 6 -the c o r r e l a t i o n ^ 3 * ^ f or a developing turbulent boundary layer over a f l a t plate Nu v = 0.029 R e , 0 , 8 P ° * 3 3 (7.3) Z Z r i s shown by F i g . 7.16 where again considerable scatter i s evident. Eq. 7.3 can be seen to generally exceed the k i l n r e s u l t s , which can be a t t r i b u t e d to the fact that the boundary layer at the k i l n wall i s u n l i k e l y to be f u l l y turbulent. The range of convective c o e f f i c i e n t encountered, h ~ 1.5 -*• 15 ° c g*ew 2 (22) 2 W/m K, agrees w e l l with the values observed by Tscheng (2 -* 9 W/m K) which were obtained over a s i m i l a r range of Re . z At the exposed bed surface ( F i g . 7.17) somewhat larger convective c o e f f i c i e n t s were observed, again with considerable data scatter. In h 2 terms of magnitude, the values of c g*eb ~ 5 -* 20 W/m K are not too far (19) 2 from those of v ' (19 -> 35 W/m K at Re ~ 3000) but well below the r e s u l t s r e p o r t e d b y ( 3 3 ) (~ 77 W/m2K) a n d ( 3 2 ) (120 > 240 W/m2K). In the l a t t e r case the r e s u l t s do not take into account the covered wall/bed exchange and the treatment of the r a d i a t i v e contribution i s not very rigorous. F i g 7.17 may show a trend toward larger values of Nu , for the z,g^eD smaller p a r t i c l e materials, fin e sand and petroleum coke, although the (19) data do not support any d e f i n i t e conclusion. The r e s u l t s of showed -167-0.029 RE°Z 8 P R 0 - 3 3 Fig .7J6 Comparison of gas to exposed wall conv-ection with the flat plate correlation -168-1 1 1 1 1 1 1 1— A Fine Sand • Coarse Sand O Petroleum Coke A O Limestone 0 o o 0 ° * o c n -CP poo «> A *°A> • A O D A A O ° 1 j 1 1 1 1 1—r-10« 3 5 7 10« RE , Fig 7.17 Convection to the exposed bed surface -169-(22) no p a r t i c l e s i z e e f f e c t while those of i n d i c a t e d a s l i g h t inverse r e l a t i o n s h i p between c n ^ e ^ a n c* p a r t i c l e s i z e . F i g s . 7.15 and 7.17 do not indicate convection to the exposed bed surface of the p i l o t k i l n to be an order of magnitude greater than to the exposed wall surface. The mean value of Nu ~ 480 ( F i g . 7.17) i s z , g-*eb only about twice the mean value for Nu ( F i g . 7.15). This enhance-z,g->-ew 6 ' ment factor ~ 2 i s s i m i l a r to values obtained for stationary roughness (22) elements ( S e c t i o n 2.2) and w e l l below the factor ~ 10 reported by . However, i n view of the large amount of scatter exhibited by the current data, the re s u l t s must be viewed with caution. Although exact values of convective c o e f f i c i e n t s remain el u s i v e , approximate values are s u f f i c i e n t to examine the r e l a t i v e importance of gas convection versus gas r a d i a t i o n . 2 In the p i l o t k i l n , assuming median values of h ~ 5 W/m K and v c g+ew 2 h , ~ 10 W/m K, i t can be seen by r e f e r r i n g to the plots of „h , , c g+eb J R g+eb/ew i n F i g . 7.25 that convection to the exposed wall w i l l be comparable to gas ra d i a t i o n only at low emitting gas concentrations or r e l a t i v e l y low gas temperatures. However, for the exposed bed surface, convection i s always s i g n i f i c a n t , accounting for about 20% of the t o t a l gas to bed surface heat transfer even at stoichiometric gas mixtures and temperatures of 1700 K. -170-For the prototype k i l n , the ro le of convect ion i s reduced to a very minor one due to the combined e f f e c t s of longer emit t ing gas path lengths , which i n c r e a s e ^ h , , by a f a c t o r of 3 as shown i n F i g . 7.26, and the R g->-eb/ew J e ' i n v e r s e r e l a t i o n between h , . and the c h a r a c t e r i s t i c d imens ion c g> eb/ew 0.8 which i s i m p l i c i t i n c o r r e l a t i o n s of the form Nu a Re * (or any exponent < u n i t y ) . 7.3 Heat Transfer Between the Covered Wall and Bed Heat t rans fe r between the covered wa l l and the contact ing bed mate r ia l (covered bed) has genera l ly received inadequate a t t e n t i o n . It was noted b y ^ ^ that u n t i l the process was proper ly understood (and became pred ic tab le ) the mathematical model l ing of rotary k i l n heat t rans fe r could be of only l im i ted use i n the design process . However the development of r e a l i s t i c models for covered wa l l / covered bed heat t ransfer has, u n t i l now, been severe ly r e s t r i c t e d by the d i f f i c u l t y i n a c t u a l l y measuring th is exchange. For the p i l o t k i l n t r i a l s the net surface heat f lux to the ins ide wal l was obtained as a continuous funct ion of c i r c u m f e r e n t i a l p o s i t i o n by applying the f i n i t e d i f f e r e n c e model of Sect ion 6.2 to the unsteady state (ac t ive ) layer adjacent to the s u r f a c e . At each of the 8 probe a x i a l l oca t ions ( F i g . 4.6) the measured ins ide wal l surface temperature p r o f i l e , i n conjunct ion with 3 deep wal l temperatures, provided the boundary condi t ions necessary to solve for the wal l ac t i ve layer temperature d i s t r i b u t i o n and subsequently the heat f l u x d i s t r i b u t i o n . -171-In the p i l o t k i l n t r i a l s , as pointed out i n Sectio n 7.1, the i n s i d e w a l l and bed temperatures were too c l o s e l y l i n k e d to e s t a b l i s h a meaningful temperature d i f f e r e n c e . The measured heat t r a n s f e r rates between the covered w a l l and bed m a t e r i a l cannot, t h e r e f o r e , be presented i n the form of an equivalent heat t r a n s f e r c o e f f i c i e n t h , . cw*cb The r e l a t i v e importance of covered wall/bed heat exchange i n the p i l o t k i l n t r i a l s can be asc e r t a i n e d from F i g . 7.18 which p l o t s the r a t i o of heat input at the covered bed surface to the heat input at the exposed bed surface (versus k i l n a x i a l p o s i t i o n ) . For F i g . 7.18a, which shows data from the i n e r t bed t r i a l s , i t i s evident that the regenerative heat t r a n s f e r a s s ociated w i t h the i n s i d e w a l l temperature c y c l i n g can provide both p o s i t i v e and negative net inputs to the bed m a t e r i a l . However the a x i a l g r a d i e n t of Qcw^.c^/ ^g+ew+eb * S a^-ways negative and, although the covered w a l l to bed heat t r a n s f e r u s u a l l y begins with p o s i t i v e values, i t s t e a d i l y decreases with a x i a l p o s i t i o n , o f t e n becoming negative. The highest temperature t r i a l s produced the smallest p o s i t i v e and l a r g e s t negative values of Q , / Q . , e cw*cb xg+ew>eb. For the limestone c a l c i n a t i o n t r i a l s ( F i g . 7.18b), i t can be seen that a f t e r the onset of the c a l c i n a t i o n r e a c t i o n , which commences at an a x i a l p o s i t i o n of about 2.5 •* 3 m, the a x i a l gradient of Q c w > ct/Qg+ ew+eb becomes p o s i t i v e and the covered w a l l provides energy to the bed. R e c a l l i n g the r e s u l t s of Sectio n 7.1, the net heat input to the c a l c i n i n g bed was found to be much l a r g e r than f o r an i n e r t bed. Thus, although the - 1 7 2 -Inert Bed Trials A Fine Sand Trial T4 • Coarse Sand Trial T8 O Petroleum Coke Trial T13 O Limestone Trial T15 O A ^ • • O O ( X • o o A 2 v a . 6 o x o ~i 1 1 1 1 1 r 1 RXIAL POSITION ?METRES) 4 Fig 7.18a Covered wall to solids heat input as a fraction of gas plus exposed wall input -173-o T T T T in o' Calcination Trials Limestone O Trial T18 A Trial T19 • Trial T20 CDo I I LU + CD CC LD~> 5 C o LU CO X A N 8 o 8 ° 8 A CO in —i 1 1 T 1 n r AXIAL POSITION (METRES) Fig 7.18b Covered wall to solids heat input as a fraction of gas plus exposed wall input -174-regenerative contribution to the net energy input to the bed remains small i n the presence of c a l c i n a t i o n , the associated heat fluxes are much greater than those measured for the i n e r t bed. To examine the covered wall/bed heat exchange, the portion of the u n i f i e d heat transfer model (Section 6.5) r e l a t i n g to the covered wall/covered bed exchange was u t i l i z e d to c a l c u l a t e heat transfer c o e f f i c i e n t s applicable to the k i l n s i t u a t i o n . Thus the covered wall/ covered bed exchange was simulated by means of a f i n i t e difference model for transient, 1-dimensional conduction i n the wall and contacting bed m a t e r i a l which used the e f f e c t i v e bed thermal conductivity k. (evaluated be from eq. 2.33) and assumed the presence of a f i l m c o e f f i c i e n t h^ at the (41) contact between the wall and bed (evaluated using the method of ). The c a l c u l a t i o n was car r i e d out for the appropriate contact time t c . The presence of s i g n i f i c a n t temperature c y c l i n g i n ref r a c t o r y l i n e d k i l n s i s a t t r i b u t a b l e to the low thermal d i f f u s i v i t y of the refr a c t o r y r e l a t i v e to an unlined metal s h e l l ( i . e . a T i m „ . ~ 0.02 a , ). An o v e r a l l LWR24 s t e e l heat transfer c o e f f i c e n t for the exchange between the covered wall and bed can be defined by Q v , _ xcw>cb cw>cb (T - T,)A W ; ws^ b cw dT dT b fn fa , a, t ^, — ~ — , 3 — ) (7.4b) w' be, contact dr ' dr ; ' -175-where T and T t are the surface temperatures of the wall and bed at the ws^ b point of i n i t i a l contact (see F i g . 6.2). It w i l l be assumed that, for a d T b r o l l i n g bed, mixing within the bed active layer w i l l ensure that a 0* For an u n l i n e d metal k i l n k^ i s s u f f i c i e n t l y large that v i r t u a l l y a l l the thermal resistance Is on the bed side and temperature gradients i n the metal s h e l l w i l l be n e g l i g i b l e . The functional r e l a t i o n 7.4b has been derived a n a l y t i c a l l y for t h i s s i t u a t i o n under a v a r i e t y of i n i t i a l and (39) boundary conditions as summarized i n Carslaw and Jaeger In r e f r a c t o r y l i n e d k i l n s a ~ a. and the i n s i d e wall surface w be temperature w i l l vary while i n contact with the bed material. The e f f e c t of wall surface temperature v a r i a t i o n i s a reduction of the temperature difference between the wall and bed surface across the f i l m resistance. Thus values of h . w i l l be reduced i n the presence of a r e f r a c t o r y cw->cb l i n i n g . The s i t u a t i o n Is also complicated by the presence of r a d i a l dT w temperature g r a d i e n t s ^ i n the re f r a c t o r y l i n i n g at the i n i t i a l point of contact with bed material ( F i g . 6.2). If the inside wall surface temperature T w g at t h i s p o i n t exceeds the bed temperature T^ then the wall surface layer w i l l lose energy both to the bed and r a d i a l l y through the w a l l . I f however T < T, the wall surface layer receives energy from ws^ b the bed to counteract the loss through the w a l l . In the former case -176-(T^^ > T^) the bed and w a l l surface temperatures qu ick ly move together w h i l e i n the l a t t e r i n s t a n c e ( T w g < T^) the w a l l s u r f a c e temperature response i s i n h i b i t e d by heat t ransfer from the bed. These e f fec ts are shown In F i g . 7.19 which, as noted p r e v i o u s l y , was obtained using a por t ion of the u n i f i e d heat t ransfer model. The bed m a t e r i a l assumed f o r the s i m u l a t i o n s was sand (d^ = 2.5mm). In F i g . dT 7 . 1 9 a , f o r T and T v ~ 1200 K, the e f f e c t s of both -r-Z- and T v s . T^ ws b dr ws^ b are c l e a r l y ev ident . In most k i l n s i t u a t i o n s T > T, and actua l values ws^ b of h , w i l l be much l e s s than f o r the s t e e l s h e l l case (a lso F i g . cw->cb v 6 7.19a) . Model p r e d i c t i o n s f o r much lower temperature l e v e l s (T and T, ~ ws b 450 K) a r e shown by F i g . 7 . 1 9 b . Both the f i l m c o e f f i c i e n t h f and e f f e c t i v e bed thermal conduct iv i t y k^ are much reduced in the absence of any s i g n i f i c a n t r a d i a t i v e c o n t r i b u t i o n , which r e s u l t s i n considerably s m a l l e r va lues of h , . Since i t i s the usual s i t u a t i o n , only the case cw*cb J of T > T, i s shown i n F i g . 7.19b. The model p r e d i c t i o n s for the case of ws^ b r an unl ined s t e e l s h e l l can be seen to agree very we l l with the corresponding exact s o l u t i o n for conduction in a s e m i - i n f i n i t e body, which (30) (22) i s r e a d i l y a v a i l a b l e ; eg . The c o r r e l a t i o n of Tscheng 2a 0.3 nr p Nu . = 11.6 f W 1 (2.41) cw*cb J be - 1 7 7 -Contact time (s) F i g . 7 . 1 9 a C o v e r e d w a l l / c o v e r e d b e d h e a t t r a n s f e r c o e f f i c -i e n t s ( T = 1 2 0 0 K ) - 1 7 8 -300. 2 5 0 r K b e = 034 W/mK _h f = l60W/m 2 K 2 0 0 T w s , > T b Tscheng Steel shell Model K r e i t h { 3 0 ) CM E U n o JZ I 50 100 50 0 - 5 0 1 0 7.5 5.0 E E \ 8 12 16 20 24 Contact time (s) F i g . 7 . 1 9 b C o v e r e d w a l l / c o v e r e d b e d h e a t t r a n s f e r c o e f f i c -i e n t s ( T = 4 5 0 K ) -179-was derived from data for unlined metal drums but using much smaller p a r t i c l e s i z e s and somewhat over-estimates h , when extrapolated to r cw*cb r larger p a r t i c l e sizes (also F i g . 7.19b). For the calculation of heat transfer between the covered wall and bed material in refractory lined kilns the use of coefficents obtained for isothermal walls seriously overestimates the efficiency of the exchange. The results of the type shown in Fig. 7.19 for nonisothermal walls provide much better values of n c w^. c^ D u t a r e n o t 8 0 easy to generalize, being functions of (at least) the several variables in eq. 7.4b. For strongly d 2T w nonlinear i n i t i a l temperature gradients the second derivative ^— would dr 2 become an additional variable. Although temperature gradients in the bed d T b material could effect n c w > c b » t n e presence of a vigorous mixing action in the exposed bed surface layer makes the occurrence of any significant gradient unlikely. In the pilot k i l n t r i a l s no radial bed temperature gradients were discernable. 7.4 Temperature Rise for Particles on the Bed Surface In Section 6.3, a simple model was developed to estimate the temperature rise for rolling spherical particles exposed to the kiln freeboard, the variables being, in addition to the thermophysical properties, the particle diameter, the surface velocity and the surface distance travelled before re-immersion Into the bed. Although this model considerably oversimplifies the actual situation (i.e. actual particles -180-are not s p h e r i c a l , w i l l not r o l l about a s ing le f i xed axis and the energy f l u x l i n e s w i l l not be p r e c i s e l y r a d i a l ) i t f u l f i l l s i t s intended purpose of prov id ing an upper bound on the p a r t i c l e temperature r i s e . (22 ) Tscheng noted a d e a r t h of a p p l i c a b l e data i n the l i t e r a t u r e r e l a t i n g p a r t i c l e surface v e l o c i t i e s to k i l n operat ing v a r i a b l e s . Based on a f i l m study in a 0.19 m.ID l u c i t e k i l n model, a value of 0.2 m/sec was a s s u m e d at 3 r p m . The d a t a a l s o i n d i c a t e d tha t U , a ( R o t a t i o n r s u r f 1/2 r a t e ) . A s s u m i n g tha t the bed p a r t i c l e s u r f a c e v e l o c i t y w i l l be p r o p o r t i o n a l to the c i r c u m f e r e n t i a l v e l o c i t y at the k i l n wal l to the y power, then for the p i l o t k i l n at 1.5 rpm U ~ 0.2 / |4 / rTTo- ~ ° ' 2 — ( 7 -5 ) sur f 3.0 0.19 sec ' For the prototype k i l n with a sca le -up fac tor of 10, the bed p a r t i c l e surface v e l o c i t i e s would be ~ 0.6 m/sec. (22) No i n f o r m a t i o n was reported fo r the d istance t r a v e l l e d on the s u r f a c e , but assuming that p a r t i c l e s in at l eas t the f i r s t severa l layers reach the surface at some point in each c y c l e , the distance w i l l be much less than the chord length of exposed bed. For the p i l o t k i l n a value of 0.3 X . was used (0.1 m) and for the prototype 0.2 X . was chosen (0.6 m), eb eb both f igures being f e l t to be i n excess of ac tua l d i s t a n c e s . Predic ted p a r t i c l e surface temperature r i s e v s . freeboard heat f lux to the bed i s r e c o r d e d i n F i g . 7.20 for both the p i l o t k i l n (d = 2.5mm) and the prototype k i l n (d = 25 mm). P F i g . 7 . 2 0 T e m p e r a t u r e r i s e f o r p a r t i c l e s d u r i n g e x p o s u r e t o t h e k i l n f r e e b o a r d (model p r e d i c t i o n s ) - 1 8 2 -For an exposed bed s u r f a c e heat f l u x of 25 kW/m and a p a r t i c l e c o n d u c t i v i t y k g = 3.4 W/mK the p r e d i c t e d p a r t i c l e surface temperature increases are 5 K and 3 K f o r the p i l o t k i l n and prototype r e s p e c t i v e l y . From p i l o t k i l n data (and as w i l l be shown i n Sections 7.6) such large values of surface heat f l u x w i l l be associated w i t h s i g n i f i c a n t l e v e l s of i n s i d e w a l l temperature c y c l i n g , and r e l a t i v e to the v a r i a t i o n of the i n s i d e w a l l surface temperature the bed p a r t i c l e surface temperature increase during exposure to the freeboard i s small (< 10%). The f a c t that i n d i v i d u a l p a r t i c l e s at the bed surface experience only small temperature i n c r e a s e s , r e l a t i v e to the temperature c y c l i n g at the i n s i d e w a l l s u r f a c e , plus the f a c t that the surface distance t r a v e l l e d by each p a r t i c l e w i l l be only a f r a c t i o n of the exposed bed l e n g t h , means that the exposed bed may, f o r the freeboard heat t r a n s f e r c a l c u l a t i o n s , be taken as i s o t h e r m a l . 7.5 R e s u l t s From the Freeboard R a d i a t i o n Model The freeboard r a d i a t i o n model, d e t a i l e d i n Chapter 6, was u t i l i z e d to develop r a d i a t i v e heat t r a n s f e r c o e f f i c i e n t s d e s c r i b i n g each of the three b a s i c exchanges o c c u r r i n g i n the freeboard: ( i ) between the e m i t t i n g gas and area elements on the exposed bed and i n s i d e w a l l surfaces ( i i ) between area elements on the exposed bed surface and elements on the i n s i d e w a l l surface ( i i i ) between area elements on the i n s i d e w a l l s u r f a c e . -183-The introduction of a coefficient for radiative heat transfer between two surfaces, defined simply as R hl-2 R ql?2 T - T 1 J (7.6) provides a useful format for the presentation and subsequent uti l i z a t i o n of model results. However, from the discussion of Chapter 6, i t is evident that the temperatures and of the emitting bodies determine the fractional amount of emitted energy lying within the absorption bands of the intervening gas (e.g. Wien's displacement law) while the temperature of the gas in turn determines how efficiently each band is absorbed. In g e n e r a l , f o r the two bodies of eq. 7.6, Rhlt2 " f n (T1> T2» V V G ) (7.7) where P and T c h a r a c t e r i z e the pressure and temperature of the g g intervening absorbing gas and G fixes the geometry. Thus the temperature independence (or near independence) which is the hallmark of convective heat transfer coefficients is absent for their radiative counterparts. When the t o t a l pressure is approximately atmospheric, the emissivity/absorptivity of a gas mixture is primarily determined by the mixture temperature and the relative concentrations of the emitting species. Two freeboard gas mixtures have been chosen for the current work (Section 6.4.1): -184-( i ) p ^./Pprt - 2 f o r n a t u r a l gas combustion ( i i ) p n / p P n - 1 f o r n a t u r a l gas combustion plus c a l c i n a t i o n of the bed In a d d i t i o n , only two k i l n s i z e s are dealt w i t h , the 0.406m ID p i l o t k i l n and a h y p o t h e t i c a l prototype k i l n of 4.0m ID. Therefore i t i s to be i m p l i c i t l y understood that the s p e c i f i c r e s u l t s presented are f o r these p a r t i c u l a r combinations of k i l n s i z e and freeboard gas r e l a t i v e composition. 7.5.1 R a d i a t i v e Exchange Between the Freeboard Gas and Exposed Bed and Wall Surfaces At a given a x i a l l o c a t i o n w i t h i n a k i l n , the r a d i a t i v e c o e f f i c i e n t s 2 m a t e r i a l . f o r gas to exposed bed surface h R g-»-eb and gas to exposed w a l l h R g->ew w i l l vary w i t h c i r c u m f e r e n t i a l p o s i t i o n = f L ( T ( r , 9 ) , T e b ( 9 ) , P,p, % F i l l } (7.8) R g+ew = f {T ( r , 9 ) , T ( 9 ) , P,p, % F i l l } L z ew (7.9) -185-If heat transfer from the freeboard gas through the k i l n wall to the environment i s considered as a simple series connected c i r c u i t of three thermal resistances ( F i g . 7.21), the measured temperatures i n the p i l o t k i l n indicate that about 70% of the t o t a l resistance Is within the r e f r a c t o r y wall and that the remainder i s f a i r l y equally divided between the freeboard and the exterior s h e l l . The d r i v i n g force across the freeboard gas resistance was from 80-200 Kelvin degrees (K). (27) The longer mean beam lengths f o r gas r a d i a t i o n and somewhat thicker ( a l b e i t with higher thermal conductivity) r e f r a c t o r y walls t y p i c a l of i n d u s t r i a l k i l n s indicate a reduced role for the freeboard gas r e s i s -tance compared to the p i l o t k i l n . Thus a gas/wall surface temperature difference i n the order of 50-150 K can be anticipated for an operational k i l n depending on the r e f r a c t o r y thickness and conductivity. Reliable (12) (77) data are scarce but values of 200 K and 140 K have been reported and as l i t t l e as 50 K predicted. A mean temperature difference of 100 K between the freeboard gas and i t s bounding surfaces was chosen as a baseline for the r a d i a t i o n model r e s u l t s . In F i g . 7.22 the c i r c u m f e r e n t i a l v a r i a t i o n of „h and „h , i s R g->-ew R g*eb shown f o r an isothermal gas mixture, p. .= 0.26 atm, i n the p i l o t k i l n (T -T . , = 100 K). With the exception of points near the wall/bed g eb/ew interfaces the heat transfer c o e f f i c i e n t s are v i r t u a l l y independent of (23) p o s i t i o n . As noted by gas r a d i a t i o n i s a l o c a l phenomenon due to the poor transmissivity of an emitting gas for i t s own r a d i a t i o n . Thus the asymmetry introduced by the bed does not s i g n i f i c a n t l y a l t e r the l o c a l gas/surface exchange geometry except near the wall/bed i n t e r f a c e s . -186-I R = 2TrR ,AZ R h f l ^ w > n ( r t h e l l / r l ) 2 7 r K r e f A Z I 2 7 r r s h e l l A Z h t h e l l F i g . 7.21 T h e r m a l r e s i s t a n c e model k i l n w a l l f o r h e a t t r a n s f e r t h r o u g h t h e - 1 . 8 7 -—i 1 1 1 r P(H20+C02)~0 -260 atn TGas"TSurface= 1 0 0 ( K ) T c a s ^ ) O 800 A 1300 • 1800 8-I C M i H I — UJ UJ o UJ CE »—< O cr • • • • • • • • • D • • • • Q • • • A A A A A A A A A A A A A A A A " " A A ° ° o o n o ° ° ° o o o o o o o o o o <r E x p . B e d E x p . U a l l _j 1 1 1 1 1 1 r 72 144 216 268 ANGULAR P O S I T I O N - ( D E G ) 360 Fig 7.22 Gas to surface radiative coefficient for the pilot kiln. -18.8-This localization of gas radiation also accounts for the lack of dependence for „h . and „h upon axial (Fig. 7.23) and radial gas F R g->eb R g+ew temperature gradients as well as % f i l l . Therefore, in concurrence with (23) the conclusions of , variations in freeboard gas temperature can reasonably be neglected in calculating gas to bed or wall surface radiative exchange. Additionally, the model indicates that, with the proviso that results w i l l be slightly high near the wall/bed interfaces, the circumferential variation of „h .and _h for an isothermal wall R g+eb R g-»-ew and bed surface can also be ignored. Thus a single value h , , , equal K g"^ew/eD to the (nearly) uniform value present over the majority of the wall and bed surface, can be utilized when the circumferential variation of surface temperature is small. In F i g . 7.24 the v a r i a t i o n of „h , , with T - T , , e R g+ew/eb g ew/eb is indicated, again for the pilot k i l n at p,„ __ . = 0.26 atm. Provided V.H.2u -t- ^ ^2^ the surface temperature variation of the exposed bed and wall is relatively small (< 50 K), which w i l l be shown to generally be the case, negligible error can be seen to result from using averaged values for surface temperatures. F i n a l l y the v a r i a t i o n of _h , , with p / T 1 n , n n . atm is J R g+ew/eb ^H2 2 detailed in Fig. 7.25 for the pilot k i l n and 7.26 for the 4m ID prototype k i l n . Again the low transmissivity of the gas for i t s own radiation accounts for the increase in „h , . by a factor of only about three R g->ew/eb compared to a factor of ten for geometric scale. -1-8-9-1 1 1 1 P(H20+C02)=0 -260 atn TGas"TSurfaces 1 0 0 ( K J 8" i C M X is-i H »— U J UJ o UJ P a cc o cr Q £ - I A A • A TGas<K) 800 1300 1800 dTGas/dZ=+200 K/m dTGas/dZ=-200 K/m O • A • • • • A A , A A A A A A A A A A A A A A A " A A A A ^ A A A A A A A A A A A A A % 8 8 8 8 ^ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 E x p . B e d E x p . U a l l 72 T — i 1 1 r A N G U L A R * P O S I T I O N - 6 ( D E G ) ~ r — 288 360 Fig 7.23 Showing the negligible effect of axial gas temperature gradients (pilot kiln). -190-Fig/7.24 Radiative heat transfer coefficients from the freeboard gas (Pilot Kiln) -.1.91-Fig.7.25 Radiative heat transfer coefficients from the freeboard gas (Pilot Kiln) —192-T T T * . - W — I 1— 100 K P(H20+C02) a t B PH2(/'c02 O 0.330 1 A 0.260 2 A 0.260 (Eq.2.11) 2 700 900 EMITTld£°°GAS TEr^ ATURE V R L v i N . 1700 1900 Fig/7.26 Radiative heat transfer coefficients from the freeboard gas (Prototype Kiln) - 1 9 3 -A r e s u l t of p a r t i c u l a r importance from the gas ra d i a t i o n model i s the magnitude of the freeboard gas to bounding surface r a d i a t i v e c o e f f i c i e n t . F i r i n g natural gas at 10% excess a i r and allowing for a d d i t i o n a l C0 o from bed c a l c i n a t i o n ( i . e . p, 0.33 atm) a bound I ' 2 C°2 on „h , , i s given by: R g*ew/eb & 3 8 < R^ Vew/eb'^  6 0 K ( P i l o t K i l n ) 20 < R h g^. e w/ e b< 2 0 0 w/m2 K (Prototype K i l n ) As shown i n F i g . 7.25 remarkably good values for h , , can be e R g+ew/eb obtained from the simple r e l a t i o n s h i p ^ 3 ^ Q , . = A . . e w / e ^ a(e T 4 - a T . v 4 ) (2.11) g>ew/eb ew/eb 2 g g g ew/eb where again the gas a b s o r p t i v i t y a must be evaluated at the emitting surface temperature. 7.5.2 Radiative Exchange Between the Exposed Bed and Wall Surfaces Gas t r a n s m i s s i v i t y for gray (or any broad spectrum) r a d i a t i o n i s high even over long path lengths since t y p i c a l l y about 75% of such r a d i a t i o n w i l l be within the clear (K^) or only poorly absorbed (^) bands of the gas ( F i g . 6.8). In addition, since the radiant spectrum emitted by surfaces i s large, surface/surface r a d i a t i v e exchange can be s i g n i f i c a n t l y more e f f e c t i v e than gas/surface exchange for any given temperature l e v e l . -1.94-By modelling the response of exposed bed surface p a r t i c l e s to heat f l u x ( S e c t i o n 7.4), i t was shown that a r o l l i n g bed surface can be assumed to be chordwise i s o t h e r m a l . In a d d i t i o n i t w i l l be demonstrated i n Section 7.6 that the w a l l surface temperature and exposed bed surface temperature are c l o s e l y l i n k e d , a r e s u l t c l e a r l y evident i n the p i l o t k i l n t r i a l s . For two surfaces i n r a d i a t i v e exchange Rql->2 = R h l - 2 ( T l " V 4 4 a a ( T x - T 2 ) (7.10a) (7.10b) from which i t can be r e a d i l y observed that R h l - 2 a 4 4 a ( T ^ - T 2*) X - T 1 2 (7.11) At T 1 = 1500 K the RHS of eq. 7.11 w i l l d e c l i n e l i n e a r l y from 765 W/m K at T 2 = 1499 K to 728 W/m2 K at T 2 = 1450 K, a change of < 5%. Thus an e r r o r of < 5% can be a n t i c i p a t e d by assuming a f i x e d value of R^l+2 0 D t a i n e d f o r a n y v a l u e of T 2 w i t h i n the range (T^- 50) < T 2 < T^. F i g . 7.27 shows the v a r i a t i o n of „h , f o r isothermal exposed 6 R eb->-ew r w a l l and bed surfaces i n the p i l o t k i l n . The w a l l temperature i s set 50 K above bed tem p e r a t u r e and p. . = 0.26 atm. Symmetry allows (H 20 + C0 2^ p l o t t i n g of r e s u l t s f o r only one-half the period of w a l l surface exposure. The gas temperature has n e g l i g i b l e i n f l u e n c e w i t h i n i t s probable range of -195-i i 1 1 1 1 1 r P (H20+C02)=0.260 atro TSurface (Kelvin) o e e e e e o & 0.1 0.2 0.3 0 4 o F R A C T I O N O F E X P O S E D T I M E Fig 7.27 Solid to wall surface heat transfer coeff-icient for the pilot kiln -196-v a r i a t i o n . In view of the foregoing d i s c u s s i o n , F i g . 7.27 should be a c c u r a t e to w i t h i n 5% f o r T - 50 < T , <T (aside from e r r o r s associated ew eb ew w i t h the a c t u a l r a d i a t i o n model). Comparing F i g . 7.27 with F i g . 7.25 i t i s a pparent t h a t at higher temperatures the a b i l i t y of the d r i v i n g f o r c e T - T ~ 80-200 K to s u s t a i n a mean value of T s i g n i f i c a n t l y above T , g ew ew J eb i s l i m i t e d . For the prototype k i l n , surface to surface r a d i a t i v e exchange i s reduced by about 25% while gas to surface exchange i s increased by about 300%. Thus „h ( F i g . 7.26) g e n e r a l l y exceeds Jn , except at the R g^ew 6 R eb+ew ^ highest temperatures considered. 7.5.3 R a d i a t i v e Exchange Between Areas on the Exposed Wall Unlike area elements on the planar bed surface, which have no d i r e c t view of other bed surface areas, the curvature of the k i l n wall allows d i r e c t r a d i a t i v e exchange between areas on the exposed refractory w a l l . Again since the exposed wall surface emits over a l l wavelengths the interchange between wall elements p e r s i s t s over long path lengths, being e n t i r e l y view factor controlled for bands which are not absorbed by the freeboard gas. -1.9.7-The temperature c y c l i n g at the inside r e f r a c t o r y surface, which i s induced by the k i l n r o t a t i o n , has been the subject of t h e o r e t i c a l s t u d i e s ^  * . As an area on the wall surface rotates from under the bed i t commences an unsteady state r a d i a t i v e exchange with exposed bed surface and the elements of the wall (which have progressed further into the exposure period) as well as r a d i a t i v e and convective exchange with the freeboard gas. To su i t the requirements of Section 7.6, the ra d i a t i v e heat t r a n s f e r c o e f f i c i e n t ^h from the entire exposed wall ew to the R ew>ew^ area of i n t e r e s t ew^ was defined by q ew-*ew .h R ew*ew_, AT (7.12) i ew As was shown i n Section 7.5.2, n e g l i g i b l e error w i l l r e s u l t from n e g l e c t i n g n o n l i n e a r e f f e c t s p r o v i d e d AT < 50 K . However the ew c o e f f i c i e n t w i l l be a function of the shape assigned to the exposed wall temperature p r o f i l e , although fortunately the dependence i s not strong. Using the wall surface temperature p r o f i l e s measured i n the p i l o t k i l n , the v a r i a t i o n of „h shown i n F i g . 7.28 was obtained. As i n the case R ew+ew^ of exposed wall/exposed bed r a d i a t i v e exchange, the magnitude of „h R ew->ew^  can become s i g n i f i c a n t l y l a r g e r than _h i n the p i l o t k i l n . The 6 J e R g+ew^ ^ v longer path lengths i n the prototype r e s u l t i n a reduction of about 25% i n h R ew*ew^ -198-• i i i P(H20+C02r0 -260 atm Tsurface (Kelvin) O700 A 950 • 1200 O1450 O1700 T T — i r FRACTION OF EXPOSED TIME ~ ~ i — 0.8 0.0 0.2 1.0 Fig 7.28 Wall to wall surface heat transfer coeff-icient for the pilot kiln -199-The r a d i a t i v e exchange between surface elements such as ew^ and the remainder of the freeboard r e f r a c t o r y w i l l play a r o l e i n the o v e r a l l heat transfer process through i t s influence on the exposed wall surface temperature p r o f i l e . The e f f e c t w i l l be one of increasing the rate of temperature r i s e for f r e s h l y exposed areas at the expense of areas nearing the end of exposure which may tend to s t i f l e wall surface temperature c y c l i n g . 7.6 A p p l i c a t i o n of the U n i f i e d Heat Transfer Model The i n t e r a c t i o n among the heat transfer processes occurring at a k i l n cross-section was investigated using the u n i f i e d heat transfer model of Section 6.5. It w i l l be r e c a l l e d that, for given conditions of k i l n geometry (which i s understood to include the thermophysical properties of the bed material and wall r e f r a c t o r y ) and freeboard gas composition, only two independent temperatures are required to carry out the c a l c u l a t i o n : ( i ) The freeboard gas temperatures. As was shown In Section 7.5, both a x i a l and r a d i a l gas temperature gradients may be neglected without s i g n i f i c a n t e r r o r . ( i i ) The exposed bed surface temperature. For the r o l l i n g bed condition the temperature r i s e for p a r t i c l e s during exposure to the freeboard was estimated i n Section 7.4 to be < 5 K . I t w i l l be assumed that t h i s p a r t i c l e temperature r i s e i s much less than the increase i n the exposed wall surface temperature and that the exposed bed - 2 - 0 0 -surface can be regarded as being isothermal. In addition, i t i s assumed that the vigorous mixing of p a r t i c l e s within the tumbling surface layer w i l l ensure a r a d i a l l y isothermal bed layer near the point of i n i t i a l contact with the w a l l . The heat transfer model was applied both to the 0.406 ID p i l o t k i l n and the hypothetical 4m ID prototype k i l n . The freeboard r a d i a t i v e heat transfer c o e f f i c i e n t s have been described i n Section 7.5. Convection to the exposed r e f r a c t o r y wall was calculated using the f l a t plate c o r r e l a -t i o n (eq. 7.3) while convection to the exposed bed surface was calculated by assuming h , = 5 h which i s a compromise between the factor ~ c g->eb c g*ew (22) 10 determed by and the factor ~ 2 indicated by the p i l o t k i l n t r i a l s . For the prototype k i l n the role of convection i s s u b s t a n t i a l l y reduced wi t h cQg^.e|j ~ 0*05 ^Qg^gb being t y p i c a l of the model r e s u l t s (assuming a convective enhancement factor of f i v e ) . At the k i l n s h e l l the r e s u l t Nu^ = 0.11 {(0.5 Re 2 + G O P r } ° * 3 5 (7.13) D CO t) recommended i n ^ 3 ^ f o r n a t u r a l c o n v e c t i o n from r o t a t i n g cylinders was u t i l i z e d . Radiation at the s h e l l was calculated from the simple two gray .(30) body r e s u l t ( T s h 4 " T-> R hsh = £ s h 0 (T . - T ) ( 7 * 1 4 ) sh °° -201-Heat t rans fe r between the covered wal l and bed was ca lcu la ted w i t h i n the m o d e l , r a t h e r than from the v a l u e s of h , presented in cw+cb Sect ion 7.4, i n order to u t i l i z e a more exact r a d i a l wa l l temperature p r o f i l e at the point of immersion under the bed. 7.6.1 Model Resul ts for the P i l o t K i l n In present ing the p i l o t k i l n t r i a l r e s u l t s (Sect ion 7.1) three p a r t i c u l a r l y s a l i e n t items were noted: ( i ) A f te r very rap id heating wi th in the i n i t i a l 1.5 m of k i l n length , the net heat input to the bed mater ia l dec l ined and eventual ly ( for the i n e r t bed) l e v e l l e d out at a value wel l below the rate of loss through the k i l n wal l r e f r a c t o r y . ( i i ) Over the 75% of k i l n length with f u l l inst rumentat ion , the bed temperature and k i l n wal l temperature were c l o s e l y - c o u p l e d . ( i i i ) At the onset of the c a l c i n a t i o n r e a c t i o n the net heat input rate to the bed mater ia l increased d r a m a t i c a l l y . The reasons for each of these observed phenomena are access ib le us ing the u n i f i e d heat t ransfer model. -202-For each p i l o t k i l n t r i a l the freeboard gas temperatures are r e a d i l y a v a i l a b l e but exact values of the exposed bed surface temperature are not . Thus at each probe a x i a l l o c a t i o n for which the experimental ly der ived heat f luxes are a v a i l a b l e , the a p p l i c a t i o n of the model requires the i n s e r t i o n of severa l bed surface temperatures to obta in the best match of the da ta . Guidance i n the choice of temperatures i s a v a i l a b l e by r e f e r r i n g to F i g s . 7.7 and 7.14 which p lo t the c i r c u m f e r e n t i a l v a r i a t i o n of wa l l surface heat f l u x . For example at probe p o s i t i o n #5 for the ine r t bed t r i a l T4 ( F i g . 7.7) the wal l heat f lux just p r i o r to emergence from 2 t h e bed q , ~ 500 W/m . The f i l m c o e f f i c i e n t f o r heat t r a n s f e r cb+cw between the covered wal l and bed, which i s c a l c u l a t e d by the model, has a 2 value ~ 350 W/m K. Therefore bed surface temperatures at the apex of the s lop ing exposed surface should be about 1.5 K above the wal l surface temperature at i t s point of emergence from the bed, the l a t t e r value being a v a i l a b l e from the measurements. A summary of the r e s u l t s obtained from the a p p l i c a t i o n of the heat t ransfer model to 20 d i f f e r e n t k i l n l o c a t i o n s , se lec ted to span the range of mater ia ls and temperatures encountered in the t r i a l , i s provided in Table 7 .1 . At each k i l n l o c a t i o n the model p r e d i c t i o n s obtained using the measured freeboard gas temperatures (one for gas to exposed bed heat t rans fe r and a second for gas to exposed wa l l heat t ransfer ) i n conjunct ion with severa l assumed values of bed temperature r e l a t i v e to exposed w a l l surface temperature ( T w g - T g ^) are presented for comparison o with the measured values o f : - . 2 0 3 -( i ) Average inside wall surface temperature T ws ( i i ) Range of inside wall surface temperature per k i l n r o t a t i o n AT ws ( i i i ) Net heat transfer rate to the exposed wall surface Q ^ew ( i v ) Net heat transfer rate to the covered wall surface Q cw (v) Net steady-state loss through the r e f r a c t o r y wall Q s s ( v i ) Net heat transfer rate to the bed AT , Q and Q are perhaps the best i n d i c a t o r s of a s a t i s f a c t o r y ws ew cw data match since they are r e l a t i v e l y i n s e n s i t i v e to the precise value of the wall thermal resistance and the e f f e c t of aging on the conductivity of the p i l o t k i l n r e f r a c t o r y i s d i f f i c u l t to pr e d i c t . Both Q and T are ss ws d i r e c t l y r e l a t e d to the r e f r a c t o r y c o n d u c t i v i t y . Values of Q, at b positions where bed c a l c i n a t i o n i s present are denoted by a double a s t e r i s k . The model predictions are generally i n very good agreement with the measured values. The close-coupling of the bed and inside wall temperatures i s evident i n the model r e s u l t s , the range -6 < ( T w g - T e b ) < o +10 being ample to reproduce a l l the t r i a l r e s u l t s with the exception of Q g s (as d i s c u s s e d below). For l o c a t i o n s with bed c a l c i n a t i o n , s l i g h t d e p r e s s i o n of bed temperatures (T - T , > 0) y i e l d s the best match of ws eb o a l l the variables while for most of the Inert bed locations, a small e l e v a t i o n of assumed bed temperature (T - T , < 0) i s r e q u i r e d . ws eb n o -204-TABLE 7.1 # # TRIAL Z Tws ~ Teb T ws AT W S e^w MAT m U K K K kW/m kW/m kW/m kw/m T4 3.83 NA 920* 9.3* 2.53* +0.21* 2.74* 1.01* C.S. +2 867 11.3 2.36 -0.08 2.21 2.08 -2 880 9.7 2.31 +0.04 2.25 1.76 -4 892 8.0 2.23 +0.17 2.31 1.41 3.01 NA 861* 8.5* 2.24* +0.18* 2.32* 1.42* 0 832 10.6 2.19 -0.07 2.04 1.85 -2 843 9.0 2.13 +0.05 2.10 1.54 -4 856 7.4 2.06 +0.17 2.15 1.23 1.32 NA 735* 10.4* 1.87* -0.07* 1.80* 1.96 +2 743 10.9 1.94 -0.17 1.66 1.57 0 755 9.3 1.87 -0.06 1.72 1.30 T8 3.83 NA 916* 11.9* 2.62* +0.05* 2.68* 1.14* F.S. +2 871 12.9 2.42 -0.20 2.14 2.32 -2 895 9.6 2.28 +0.04 2.24 1.66 -4 908 7.9 2.22 +0.17 2.30 1.30 3.01 NA 841* 11.6* 2.40* +0.01* 2.40* 1.12* +2 829 12.0 2.21 -0.19 1.96 2.03 -2 852 8.8 2.09 +0.05 2.06 1.42 -4 865 7.2 2.02 +0.17 2.11 1.10 1.32 NA 712* 12.4* 1.92* -0.20* 1.72* 2.11* +4 735 11.8 1.87 -0.27 1.58 1.61 +2 745 10.3 1.81 -0.16 1.62 1.36 -2 767 7.2 1.71 +0.05 1.70 0.85 T9 3.83 NA 1036* 12.1* 3.02* +0.17* 3.20* 1.34* F.S. +2 984 15.2 3.00 -0.24 2.65 2.98 0 996 13.4 2.91 -0.10 2.69 2.59 -4 1020 9.8 2.75 0.17 2.80 1.73 3.01 NA 958* 10.7* 2.70* +0.17* 2.88* 1.40* +2 940 14.1 2.73 -0.22 2.45 2.60 0 950 12.5 2.67 -0.09 2.49 2.25 -4 973 9.0 2.52 +0.18 2.60 1.45 * Denotes experimental value C.S. Denotes coarse sand F.S. Denotes fine sand - 2 0 5 -TABLE 7.1 (Cont.) TRIAL Z Tws Q" Teb T ws A Tws e^w c^w ^ss % MAT K K K kW/m kW/m kW/m kw/m T9 1.32 NA 800* 13.6* 2.26* -0.17* 2.09* 2.04* F.S. +2 826 12.0 2.20 -0.19 1.95 1.75 0 836 10.4 2.14 -0.07 1.99 1.45 T12 383 NA 614* 4.7* 1.16* +0.09* 1.26* 0.41* P.C. +2 531 6.1 0.93 -0.12 0.79 1.18 0 547 4.6 0.87 -0.02 0.85 0.96 -3 563 2.7 0.82 +0.12 0.91 0.68 2.66 NA 570* 4.3* 0.96* +0.04* 1.02* 0.44* +2 516 5.8 0.86 -0.12 0.74 1.07 0 531 4.3 0.81 -0.01 0.80 0.86 -3 546 2.4 0.77 +0.12 0.85 0.58 1.32 NA 521* 4.9* 0.87* -0.02* 0.85* 0.53* +2 496 5.4 0.78 -0.11 0.67 0.88 0 510 4.0 0.74 -0.02 0.72 0.67 -3 527 2.0 0.69 +0.12 0.78 0.40 T18 4.39** NA 1331* 54.4* 7.34* -2.03* 5.30* 11.31* L.S. +3 1413 40.2 6.70 -1.26 5.12 8.71 +5 1391 46.5 7.02 -1.72 5.00 10.33 +10 1341 61.1 7.80 -2.81 4.71 13.80 2.30 NA 1088* 15.3* 3.66* -0.01* 3.65* 3.10* +3 1095 19.5 3.98 -0.42 3.38 3.55 0 1109 15.9 3.80 -0.16 3.46 2.68 -3 1125 12.7 3.62 +0.11 3.54 1.77 T19 3.83** NA 1213* 26.9* 5.03* -0.68* 4.33* 7.06* L.S. +3 1230 30.9 5.06 -1.09 3.80 5.18 +5 1210 36.3 5.40 -1.50 3.71 6.30 +10 1166 48.9 6.13 -2.50 3.50 8.90 2.30** NA 1047* 11.5* 3.26* +0.21* 3.17* 1.85* +3 1060 18.7 3.55 -0.42 2.98 3.03 0 1076 15.2 3.36 -0.15 3.06 2.17 -3 1092 11.6 3.16 +0.15 3.14 1.28 * Denotes experimental value ** Denotes calcining position P.C. Denotes petroleum coke L.S. Denotes limestone -206-TABLE 7.1 (Coiit.) _ TRIAL Z Tws 0~ Teb T ws A Tws e^w c^w Qss % MAT K K K kW/m kW/m kW/m kw/m T20 ** 4.39 NA 1368* 46.3* 7.62* -2.00* 5.63* 10.52* L.S. +3 1412 40.0 6.36 -1.35 4.76 8.91 +6 1377 49.7 6.90 -2.10 4.56 11.43 +10 1336 61.6 7.59 -3.03 4.35 14.27 2.30 NA 1079* 10.5* 3.67* -0.04* 3.39* 1.54* +3 1119 20.0 3.87 -0.46 3.27 3.08 0 1135 16.4 3.68 -0.17 3.34 2.11 -3 1152 12.8 3.46 +0.12 3.42 1.08 T21 4.39** NA 1181* 26.0* 4.82* -0.52* 4.31* 8.07* L.S. +3 1181 28.8 4.75 -1.01 3.57 5.97 +6 1151 36.2 5.17 -1.60 3.42 7.47 +10 1114 95.2 5.70 -2.31 3.24 9.20 1.32 NA 913* 13.4* 2.72* -0.09* 2.63* 2.68* +3 921 15.9 2.81 -0.36 2.36 2.42 0 938 12.6 2.65 -0.12 2.43 1.77 -3 956 9.2 2.48 +0.13 2.51 1.08 * Denotes experimental value ** Denotes calcining position L.S. Denotes limestone -207-An exception to the l a t t e r case occurs at Z = 1.32m which i s near enough to the entrance for some res i d u a l wall/bed i n t e r a c t i o n to s t i l l be present. The f a c t that p r e d i c t e d values of Q g g are cons i s t e n t l y about 15% below the measured values appears to be due to an increase i n the re f r a c t o r y thermal conductivity with aging. The agreement among the three e x p e r i m e n t a l values of Q , a v a i l a b l e from the three steady-state wall s s thermocouples, was generally no better than + 10% about the mean value. For the i n e r t bed t r i a l s at large excess a i r ( i . e . T4, T8, T9, T12) the predicted values of have a large convective component since c n g ^ . e | j ~ h , . Under these conditions the considerable uncertainty attached to R g->eb h . i s c a r r i e d over to values of Q, . The t r i a l s using petroleum coke c g+eb b (represented by T12 i n Table 7.1) were p a r t i c u l a r l y vulnerable since c o n d i t i o n s i n the f r e e b o a r d were such that h , considerably exceeded c g*eb „h R g+eb With the exception of convection to the exposed bed surface, the a b i l i t y of the u n i f i e d heat transfer model to simulate the i n t e r a c t i o n of the various heat transfer processes i n the p i l o t k i l n would appear to be established i n Table 7.1. For c a l c u l a t i n g the bed heating rate at low le v e l s of freeboard temperature or while f i r i n g with large values of excess a i r , an improved value of h . i s r e q u i r e d . Provided these ' v c g+eb conditions -208-are avoided, the model can now be extended to examine how the heat transfer processes occurring at an a x i a l k i l n section must i n t e r a c t , f i r s t i n the p i l o t k i l n and subsequently i n the prototype k i l n . To allow quantitative analysis a 0.406 m.ID k i l n , r o t a t i n g at 1.5 rpm, and f i r i n g natural gas at 2.5 1/sec (10% excess a i r ) w i l l be considered. For the coarse sand a feed rate of 50 kg/hr w i l l give ~ 12% o o f i l l . Two l e v e l s of f r e e b o a r d gas temperature (1050 K and 1550 K) were chosen and the c a l c u l a t i o n s c a r r i e d out over the range - 2 0 < T - T , < ws eb o 50 K . Resulting from these simulations are the very informative series of plots beginning with F i g . 7.29 which shows the v a r i a t i o n of the net rates of heat input to the wall and bed. To achieve rapid heating of the bed, i t i s evident that the bed temperature must be depressed below the p r e v a i l i n g w a l l s u r f a c e temperature ( i . e . T w s - T g^ > 0). At the higher o gas temperature a swing of only 20 K i n the value of T - T , (from -10 ws eb o K to +10 K ) raises the net input to the bed from 0 kW/m to +10 kW/m. A more subtle e f f e c t shown by F i g . 7.29 i s the decline i n the loss through the r e f r a c t o r y wall with increasing amounts of bed temperature depression. Thus, i f the bed temperature could be held below the wall temperature, a very e f f i c i e n t k i l n would r e s u l t . -209-F i g . 7 . 2 9 V a r i a t i o n o f n e t h e a t t r a n s f e r r a t e s w i t h T ( P i l o t K i l n ) W S o - 2 1 0 -1 I I 1 1 f Tg(°K) 1550 1050 F i g . 7 . 3 0 V a r i a t i o n o f t h e n e t b e d h e a t t r a n s f e r c o m p o n e n t s w i t h T - T • ( P i l o t K i l n ) ws e b o - 2 1 1 -In F i g . 7.30 the v a r i a t i o n of the component processes which make up the net bed i n p u t are p r e s e n t e d . F o r d e p r e s s e d bed temperatures the freeboard gas, exposed wal l and covered wal l a l l provide heat input to the bed and high heat ing rates can be ach ieved. As the bed temperature i s e l e v a t e d , the covered wal l input almost immediately becomes negative f o l l o w e d by the exposed wal l (at about -9 K for T = 1550 K) and f i n a l l y by the gas (at about -16K ). It i s evident that e leva t ion of the bed temperature, r e l a t i v e to the w a l l , w i l l decrease the net bed heating rate s i g n i f i c a n t l y . The e f f e c t of v a r y i n g T - T . o n the i n s i d e wal l temperature i s ws eb r o dramatic ( F i g . 7 .31) . As bed temperature dec l ines r e l a t i v e to the w a l l , the average i n s i d e wa l l temperature i s pushed down r e l a t i v e to the gas at a much f a s t e r r a t e . A swing of 65 K i n the v a l u e of T - T , , from ws eb' o -15 •* + 50 K , r e s u l t s in a drop of 385 K i n the average wal l surface temperature. Thus depression of the bed temperature forces down the average i n s i d e wal l temperature which provides a la rger temperature p o t e n t i a l for gas to wal l and gas to bed heat t r a n s f e r . This increased heat t rans fe r to the wal l r e s u l t s In a corresponding increase in the amount of temperature c y c l i n g (a lso F i g . 7.31) which i s i n turn r e f l e c t e d i n the increased heat input to the bed from both the exposed and covered wal l s u r f a c e s . - 2 1 2 -1 6 0 0 1 0 0 I 4 0 0 H -I 2 0 0 r — I 0 0 0 H 8 0 0 h -6 0 0 - 2 0 - 1 0 4 0 5 0 Twso T e b ( K ) F i g . 7 . 3 1 V a r i a t i o n o f a v e r a g e t e m p e r a t u r e a n d t e m p e r a t u r e c y c l i n g a t t h e i n s i d e w a l l s u r f a c e w i t h T ( P i l o t K i l n ) ws e b •213-1500 1 2 5 0 k lOOOh-^ 7 5 0 h -E 5 0 0 h -N T J \ - 2 5 0 - 5 0 0 250h-- 2 0 -10 10 20 30 40 50 T w s 0 Teb ( K ) F i g . 7 . 3 2 V a r i a t i o n o f a x i a l t e m p e r a t u r e g r a d i e n t s w i t h T - T , ( P i l o t K i l n ) ws e b y o -214-However f o r an i n e r t bed, such as sand, the a x i a l bed temperature gradient must respond d i r e c t l y to the net heating r a t e . For the flow c o n d i t i o n s being considered, the response i n terms of a x i a l temperature gradients i s qu i t e d i f f e r e n t f o r the freeboard gas and the bed as shown by F i g . 7.32. This i s not an i d e a l s i t u a t i o n s i n c e , i n t h i s case, large d T b dT i n p u t s t o t h e bed w i l l r e s u l t i n -r=— » -r^- 8- which t r a n s l a t e s i n t o ac. at, d e c l i n i n g v a l u e s of w i t h a x i a l d i s t a n c e . F i g . 7.32 does i n d i c a t e a p o s s i b l e remedy, that of simply i n c r e a s i n g the bed feed r a t e (and k i l n i n c l i n a t i o n i f % f i l l i s to be maintained) since IT - — (7.15) "b Cpb The r e s u l t s presented i n F i g s . 7.29 to 7.32 i l l u s t r a t e q uite c l e a r l y why, as reported i n Section 7.1, the bed temperatures were observed to r i s e most r a p i d l y i n the i n i t i a l 1.5 m of the k i l n f o r i t i s here that the c o l d (room temperature) m a t e r i a l i s introduced i n t o a much h o t t e r k i l n environment. This i n i t i a l r a p i d h e a t i n g , u n f o r t u n a t e l y , dTfo dT d e c l i n e s q u i c k l y due to the r e s u l t i n g mismatch, -r=— » -T=^» dZ dZ The coupling of the bed and w a l l surface temperatures, evident i n ' the p i l o t k i l n t r i a l s , i s a l s o a t t r i b u t a b l e to the imbalance between dT t dT b g ^ z and which accompanies any s i g n i f i c a n t separation i n temperature l e v e l s . The heat t r a n s f e r from the freeboard gas to the exposed w a l l and exposed bed, regardless of how i t may subsequently be r e d i s t r i b u t e d , w i l l be roughly i n the r a t i o -215-dT Q g-»ew _ 3  Qg->eb based on t h e i r r e l a t i v e a r e a s . For t h i s reason -r^- w i l l be a l l i e d more dZ c l o s e l y to the wall than to the bed. But the r a t i o of thermal resistances R •j j p— w i l l change only slowly with a x i a l p o s i t i o n i n the k i l n , meaning dT dT WS 2 t h a t ^ a ' Thus any mismatch between the bed and gas temperature gradient implies a s i m i l a r mismatch with the wall surface temperature gradient. The co r r e c t i o n e f f e c t , shown i n F i g . 7.32, i s present for both ele v a t i o n and depression of bed temperature, r e l a t i v e to the wall, and the tendency w i l l therefore always be for the two temperatures to move together with a x i a l distance unless some disturbance i s introduced. In the discussion to this point i t has been shown that very high bed heating rates, i n conjunction with reduced heat loss through the k i l n w a l l , can be achieved i f the bed temperature can be suppressed r e l a t i v e to the w a l l . However i t was also shown that the heat transfer processes between the wall and bed w i l l always tend to remove the temperature d r i v i n g f o r c e . For an i n e r t bed there i s no mechanism to i n h i b i t the wall and bed temperatures from moving together. However, with the onset of the c a l c i n a t i o n reaction the response of the bed temperature gradient to the bed heat input rate i s considerably dampened, since the enthalpy term of eq. 6.2a becomes dominant. Thus the bed temperature w i l l tend to lag -216-below the prevailing wall temperature and the sharp increases In net heat transfer to the bed observed in the pilot k i l n t r i a l s (Section 7.1) are the result. The calcining bed can be represented in the model by increasing the bed material specific heat by an order of magnitude. With calcination, the covered wall/bed heat transfer process becomes more efficient since the bed material contacting the wall surface w i l l remain nearly isothermal rather than moving toward the wall surface temperature. The increased heat transfer to the bed which accompanies the calcination reaction is attributable mostly to the tendency of bed temperature to lag below the wall temperature rather than enhanced covered wall to bed heat transfer. For the baseline operating conditions previously described, a comparison of results obtained for the actual coarse sand and a similar hypothetical sand having a specific heat 50 times larger to simulate calcination showed that, although the interaction between the covered wall and hypothetical bed material was enhanced, the net heat transfer to the bed increased by only about 10%. 7.6.2 Model Prediction for the Prototype Rotary Kiln To complete this investigation the unified heat transfer model was applied to the 4 m.ID prototype kiln for the conditions listed in Table 7.2. The two values of refractory thickness were chosen (30 cm and 15 cm) to correspond roughly with the upper and lower limits of current design practice. -217-TABLE 7.2 Conditions Applicable to  the Prototype Kiln Simulation ID (m) 4.0 T g(K) 1550 PH 20+C0 2 ( a t m ) 0.26 P H 2 0 / P C 0 2 ( _ ) 2/1 F i l l (%) 12 k (W/mK) w 0.85 @ 298K p w (kg/m3) 2000 Wall thickness Ar (m) w 0.30 solid curves 0.15 dashed curves d (mm) P 25 hf(W/m2K) 540.0 k b e (W/mK) 2.90 -218-The v a r i a t i o n of the net heat t rans fe r rates with T - T , for the ws eb o prototype k i l n i s shown in F i g . 7.33. As was observed i n the p i l o t k i l n , the net input to the bed can be seen to increase r a p i d l y with the l e v e l of bed temperature depression achieved while the s teady-s ta te s h e l l loss undergoes a small d e c l i n e . R e c a l l i n g the r e s u l t s from the freeboard r a d i a t i o n model i n Sect ion 7.5 i t i s evident tha t , r e l a t i v e to the p i l o t k i l n , heat t ransfer i n the freeboard reg ion of the prototype k i l n w i l l be character ized by s i g n i f i c a n t l y more e f f i c i e n t r a d i a t i v e heat t rans fe r from the gas, s ince gas to surface r a d i a t i v e c o e f f i c i e n t s were increased by about 300%, but only s l i g h t l y l ess e f f i c i e n t exchange among the freeboard s u r f a c e s , the reduct ion in surface to surface c o e f f i c i e n t s being only about 25%. Thus • ^g->eb P r o v ^ ^ e s a s i g n i f i c a n t l y l a rger f r a c t i o n of the net bed input for the prototype k i l n ( F i g . 7.34) than for the p i l o t k i l n ( F i g . 7 .30) . The enhancement in gas r a d i a t i o n which accompanies the sca le -up br ings a marked reduct ion in the gas s ide thermal res is tance and hence i n the temperature d i f f e rence between the gas and wal l surface ( F i g . 7 .35) . In a d d i t i o n , because the s u r f a c e / s u r f a c e exchanges are smaller r e l a t i v e to the gas /sur face exchanges the dec l ine In the average wal l surface temperature and increase in wal l temperature c y c l i n g which accompany bed temperature suppression are somewhat l ess i n the prototype k i l n (a lso F i g . 7 .35) . - 2 1 9 -A l t h o u g h the i n t e r a c t i o n among the three components Q g > e ^ » • * Q , and Q , i s al t e r e d somewhat by scale-up, the important re s u l t s ew-»-eb ew->cb r > v derived i n i t i a l l y for the p i l o t k i l n remain v a l i d : ( i ) Rapid heating of the bed material can only occur when the bed temperature i s depressed r e l a t i v e to the w a l l . The mechanisms by which t h i s can occur are s t i l l through the introduction of low temperature bed material or the onset of an endothermic bed reactio n . ( i i ) The i n t e r a c t i o n of the heat transfer mechanisms w i l l r e s u l t i n a tendency for the bed and wall surface temperature to move together with a x i a l distance a f t e r which heat transfer to the bed w i l l be almost e n t i r e l y from the freeboard gas. An important r a m i f i c a t i o n of r e s u l t ( i ) r e l a t e s to the use of i n t e r n a l devices which enhance heat transfer from the freeboard gas to the bed material. For an i n e r t bed which has reached equilibrium with the p r e v a i l i n g wall temperature, the e f f e c t of increasing gas to bed heat t r a n s f e r w i l l be to e l e v a t e the bed temperature and provoke a • • c o r r e s p o n d i n g d e c l i n e i n Q , and Q , . Thus the net heat transfer c ew*eb xw-^cb to the bed w i l l be l i t t l e changed. However for a c a l c i n i n g bed, an increase in any component of heat transfer has less tendency to elevate the bed temperature and the net bed input can show a corresponding - 2 2 0 -F i g . 7 . 3 3 . V a r i a t i o n o f n e t h e a t t r a n s f e r r a t e s w i t h T - T w s e b ( P r o t o t y p e K i l n ) 0 - 2 2 1 -i i i — i — i — r z F i g . 7 . 3 4 V a r i a t i o n o f t h e n e t bed h e a t t r a n s f e r c o mponents W l t h T w s " T e b ( P r o t o t y p e K i l n ) - 2 2 2 -1800 1600 I400h-CO 2 | y- 1200 I000H-800 - 2 0 -10 T w S ; T e b ( K ) F i g . 7 . 3 5 V a r i a t i o n o f a v e r a g e t e m p e r a t u r e a n d t e m p e r a t u r e c y c l i n g a t t h e i n s i d e w a l l s u r f a c e w i t h T ( p r o t o t y p e k i l n ) ws eb -223-increase. Also stemming from ( i ) i s the p o s s i b i l i t y that k i l n thermal e f f i c i e n c y w i l l Improve with Increasing bed mass flow by slowing the response of bed temperature a x i a l gradient to bed heating rate. The thermal resistance of the re f r a c t o r y l i n i n g has a s i g n i f i c a n t e f f e c t on the k i l n thermal performance. A reduction of wall thickness s h i f t s a larger f r a c t i o n of the t o t a l temperature po t e n t i a l to the freeboard gas. For an empty k i l n i t Is evident that any lessening i n the wall resistance w i l l r e s u l t i n more rapid cooling of the freeboard gas. The presence of the bed material does not a l t e r this basic fact but as shown i n F i g . 7.33, the net input to the bed w i l l also be s u b s t a n t i a l l y increased since the l a t t e r w i l l also move toward the inside wall temperature. The increase i n net input to the bed i s more than o f f s e t by the increased s h e l l l o s s . -r 2-2.4-CHAPTER 8 CONCLUSIONS The complex i n t e r a c t i o n among the heat transfer processes in a rotary k i l n has been investigated by means of a mathematical model which incorporates a l l the transport mechanisms and allows for t h e i r i n t e r a c t i o n u n t i l the equilibrium condition i s reached. Results from this model were i n good agreement with the heat transfer rates measured i n a 0.406 m ID p i l o t k i l n . On t h i s basis, predictions were made for a prototype 4 m ID i n d u s t r i a l rotary k i l n . By choosing T , the temperature of the i n s i d e wall surface at the o point of emergence from the bed material as a reference, the net rate of heat input to the bed material was shown to be very s e n s i t i v e to changes i n bed temperature T r e l a t i v e to T^ g . At a gas temperature of 1550 K, o the net heat input to the bed i n the p i l o t k i l n was found to increase at an average rate of 0.5 kW/m for each degree of T - T , ( F i g . 7.29) with ws eb o n e g a t i v e v a l u e s o c c u r r i n g for T - T , < -12 .K. On t h i s basis the very ws eb o high net inputs to the bed material recorded over the i n i t i a l 1.5 m ( i n p a r t i c u l a r the i n i t i a l 15 cm) of the k i l n length and i n the presence of the endothermic bed c a l c i n a t i o n reaction were explained since, only i n these regions, did a mechanism exist to suppress the bed temperature r e l a t i v e to the w a l l . The close-coupling of the bed temperature to the inside wall surface temperature, observed elsewhere in the p i l o t k i l n t r i a l s , was also explained by demonstrating that any s i g n i f i c a n t departure from this condition would tend to a l t e r the a x i a l gradient of the bed temperature p r o f i l e to restore the equality. The e s s e n t i a l f e a t u r e s of the i n t e r a c t i o n among Q , , 0 , and b xg->eb' xew*eb ^cw-»-cb w e r e f ° u n c * to remain v a l i d f o r the p r o t o t y p e k i l n although the importance of the s u r f a c e / s u r f a c e exchanges (Q , and Q ,) were r ° ^ew+eb xcw->-cb somewhat reduced owing to the enhancement in gas r a d i a t i o n accompanying the scale-up. Several important conclusions r e l a t i n g to the operation of rotary k i l n s were derived from the study: ( i ) The effectiveness of rotary k i l n s used s o l e l y for heating and cooling operations w i l l be low since the response of the a x i a l bed temperature gradient to heat transfer i s to bring the bed temperature and wall surface temperature together with a x i a l distance. Under these conditions the p o t e n t i a l l y e f f e c t i v e exchange between the burden and wall i s s t i f l e d and the r a t i o of net bed heat input to s h e l l loss w i l l tend toward the r a t i o ^eb^ew* ^ e e ^ f * c * e n c y * s H k e l y to improve with bed thoughput d T b - 1 s i n c e ,_ a (m, ) and the response of the bed temperature to the dZ b net heat input rate w i l l be dampened. - 2 2 6 -( i i ) Except i n the endothermic reaction zone, the i n s t a l l a t i o n of in t e r n a l s which Increase the heat transfer to the bed material w i l l not s i g n i f i c a n t l y enhance the net heat transfer to the bed since • * any i n c r e a s e i n Q , w i l l be o f f s e t by a decline i n both Q , g-*eb J xew*eb and Q , . cw»cb ( i i i ) Preheating of k i l n feed material should be s u f f i c i e n t for rapid reaction to proceed immediately upon entering the rotary k i l n . The r a d i a t i v e exchange between the freeboard gas and the k i l n wall surface and exposed bed surface was calculated by means of a r e a l gas, zone type model and the re s u l t s presented as r a d i a t i v e heat transfer c o e f f i c i e n t s . Values of „h , , were found to be i n s e n s i t i v e to R g->ew/eb circ u m f e r e n t i a l p o s i t i o n , owing to the poor transmissivity of the gas for i t s own r a d i a t i o n . F o r n a t u r a l gas combustion at 10% excess a i r , „h , .was calculated to be within the range R g+ew/eb 6 15 < _h , . < 55 W/m2K ( P i l o t K i l n ) R g+ew/eb , 2 25 < „h , . < 175 W/m K (Prototype K i l n ) R g-»-ew/eb J r ' for gas temperaures from 800 •*• 1800 K. In agreement with an e a r l i e r (23) study , gas r a d i a t i o n was observed to be a l o c a l i z e d phenomenon, l i t t l e affected by a x i a l and r a d i a l gas temperature gradients or % f i l l . -227-Radiative exchange c o e f f i c i e n t s between area elements on the exposed bed and inside wall surfaces and the remainder of the k i l n freeboard surfaces were calculated and found to be several times larger than the c o e f f i c i e n t f o r gas to surface exchange „h , , In the p i l o t R g>ew/eb K k i l n and of comparable magnitude to R ng^. e w/ e b * n t n e prototype k i l n (at t y p i c a l k i l n operating temperatures and c o n d i t i o n s ) . Predicted values of the c o e f f i c i e n t s for covered wall/covered bed heat t r a n s f e r , obtained using a f i n i t e d ifference model of the wall and bed material, were found to be reduced by a factor ~ 4 r e l a t i v e to p r e d i c t e d v a l u e s f o r u n l i n e d metal drums. This reduction i n h , was cw-*cb caused by the temperature of the r e f r a c t o r y surface moving toward the contacting bed surface temperature, thus reducing the p o t e n t i a l for heat t r a n s f e r . The presence of p o s i t i v e r a d i a l wall temperature gradients, dT - r — W > 0 was shown to be an important factor i n the c a l c u l a t i o n of h , dr r cw-»-cb and to r e s u l t i n c o n s i d e r a b l y smaller values for h , when, as i n the ' cw*cb ' case of rotary k i l n s , the wall surface temperature exceeds the l o c a l bed temperature at the point of i n i t i a l contact. The combined ef f e c t of the surface/surface exchanges, both In the freeboard and at the covered wall/covered bed i n t e r f a c e , w i l l be to l i n k the bed temperature c l o s e l y to the wall surface temperature, an e f f e c t which was c l e a r l y indicated in the r e s u l t s from the p i l o t k i l n t r i a l s and i l l u s t r a t e d by the predictions of the u n i f i e d heat transfer model. - 2 2 8 -In the p i l o t k i l n t r i a l s , the heat f l u x at the i n s i d e wal l surface was obtained d i r e c t l y from the measurements of the wal l surface temperature. Under t r i a l c o n d i t i o n s , the covered wal l /bed heat t ransfer was found to be considerably less than at the exposed bed sur face . For the i n e r t bed c o n d i t i o n s v a l u e s of Q , < 0 were obtained over much of cw->cb the k i l n . In the presence of bed c a l c i n a t i o n the magnitude of Q c w ^ . c ^ w a s i n c r e a s e d s i g n i f i c a n t l y and was always > 0. However Q ^ remained e } J ^cw->cb considerably below the exposed bed input which was a lso found to increase dramat ica l ly with the onset of the bed r e a c t i o n . Convective c o e f f i c i e n t s for gas to exposed wal l and exposed bed heat t r a n s f e r were c a l c u l a t e d from the p i l o t k i l n da ta . Values of h , c g->eb ~ 2 h were o b t a i n e d , thus i n d i c a t i n g somewhat l e s s c o n v e c t i v e c g+ew enhancement than prev ious ly repor ted . However, the large amount of sca t te r in the data precluded any d e f i n i t e conc lus ion to be drawn. For near s t o i c h i o m e t r i c f i r i n g on natura l gas i t was observed that h 1.0 > C g > 0.25 ( P i l o t K i l n ) R g+eb h 0.13 > c h e > 0.03 (Prototype K i l n ) R g+eb over the gas temperature range from 800 •*• 1800 °K and at representat ive f i r i n g r a t e s . From the l a t t e r resu l t i t can be seen that convection i s u n l i k e l y to provide a s i g n i f i c a n t c o n t r i b u t i o n to heat t ransfer for i n d u s t r i a l sca le rotary k i l n s . -2-29-CHAPTER 9 RECOMMENDATIONS FOR FUTURE WORK Further research could be divided into two e f f o r t s : ( i ) An experimental i n v e s t i g a t i o n of the covered wall/covered bed i n t e r a c t i o n , p a r t i c u l a r l y i n the region near the k i l n entrance, using nonrotating thermocouples to measure bed temperatures. Stationary thermocouples would enable deta i l e d mapping of bed temperatures and the assumption of n e g l i g i b l e r a d i a l bed temperature gradients proposed i n the current study could be tested. Improved bed temperatures i n conjunction with the wall temperature probes would allow c a l c u l a t i o n of covered wall/covered bed heat t r a n s f e r c o e f f i c i e n t s f o r comparison with model pre d i c t i o n s . The p i l o t k i l n f a c i l i t y could be u t i l i z e d for such a study although a d d i t i o n a l modifications would be required. ( i i ) The development of a mathematical heat transfer model for the rotary k i l n using heat transfer c o e f f i c i e n t s both from the current study and from the experimental study of ( i ) . None of the models ava i l a b l e i n the l i t e r a t u r e appear to r e a l i s t i c a l l y simulate a l l the heat transfer processes i n conjunction with tested values for the necessary c o e f f i c i e n t s . I t i s f e l t that the basis for a successful k i l n heat transfer model i s now a v a i l a b l e . - 2 3 0 -REFERENCES 1. C.N. S a t t e r f i e l d and F. Feakes, K i n e t i c s of the Thermal Decomposition of Calcium Carbonate, A.I.Ch.E. J o u r n a l , _5 ( 1 ) , pp. 115-122, (1959). 2. V. Venkateswaran and J.K. Brimacombe, "Mathematical Model of the SL/RN D i r e c t Reduction Process", Met. Trans. B, 8B, pp. 387-398, (1977). 3. K. Wilson, "The SL/RN Process at the G r i f f i t h Mine", Presented at 16th Conference of M e t a l l u r g i s t s , Vancouver, Canada, (August, 1977). 4. A. Sass, "Simulation of the Heat Transfer Phenomena i n a Rotary K i l n " , I & EC Process Design and Development, 6_ ( 4 ) , pp. 532-535, (1967). 5. J.B. R i f f a u d , B. 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Chemical Engineering 18 ( 2 ) , pp. 181-204, (1978). 47. G.S.G. Beveridge and D.P. Haughey, " A x i a l Heat Transfer i n Packed B e d s . S t a g n a n t Beds Between 20 and 750 C", I n t . J . Heat Mass Tr a n s f e r , 14, pp. 1093-1113, (1971). 48. S. Masamune and J.M. Smith, "Thermal C o n d u c t i v i t y of Beds of S p h e r i c a l P a s r t i c l e s " , I & EC Fundamentals, 2_, pp. 136-143, (1963). 49. D. Vortmeyer, "Radiation i n Packed Beds", Keynote paper KS-6, 6th I n t . Heat Transfer Conference, 6^  pp. 525-539, Toronto, Canada (1978). 50. P. Zehner and E.V. Schlunder, "Thermal C o n d u c t i v i t y of Granular M a t e r i a l s at Moderate Temperatures", Chem. Ing. Techn., 42, pp. 933-941, (1970). 51. S. Hatta and S. Maeda, "Heat Transfer i n Beds of Granular C a t a l y s t , I and I I " , Kagaku-Kikai, Chem. Eng. (Japan), 12_, 56, (1948), 13, 79, (1949). 52. S. Y a g i i and D. K u n i i , "Studies i n Heat Transfer Near Wall Surface i n Packed Beds, A.I.Ch.E. Journa l 6 ( 1 ) , pp. 97-103, (1960). 53. C.E. Schwartz and J.M. Smith, "Flow D i s t r i b u t i o n In Packed Beds, I n d u s t r i a l Engineering Chemistry ( I . E . and C.) 45_, 4, pp. 1209-1218, (1953). 54. W.N. S u l l i v a n and R.H. Sabersky, "Heat Transfer to Flowing Granular Media", I n t . J . Heat Mass Transfer 18, pp. 97-107, (1975). 55. P. Richard and G.S.V. Raghaven, " P a r t i c l e - P a r t i c l e Heat Transfer A p p l i c a t i o n s to Drying and Processing - A review,' Proc. of the F i r s t I n t . Symp. on Drying, Montreal Canada, pp. 132-140 (1978). 56. E.V. Schlunder, "Warmeubergang an Bewegte Kugelschuttungen b e i K u r z f r i s t i g e r a Kontakt", Chem. Ing. Techn. 43_, pp. 651-654, (1971). 57. N. Mollekopf and H. M a r t i n , "Zur Theorie des Warmeubergane an B e t w e g t e K u g e l s c h u t t u n g e n b e i K u r z f r i s t i g e m K o n t a k t VT-Verfahrenstechnik, 16_, pp. 701-706, (1982). 58. N. E p s t e i n and K.B. Mathur, "Heat and Mass Transfer i n Spouted Beds -A Review", Canadian Society of Chemical Engineering, 49, p. 467, (1971). - 2 3 4 -59. R. Rutgers, " L o n g i t u d i n a l Mixing of Granular M a t e r i a l Flowing through a R o t a t i n g C y l i n d e r : Part I - D e s c r i p t i v e and T h e o r e t i c a l " , Chemical Engineering Science, 20, pp. 1079-1087, (1965). 60. H. Henein, J.K. Brimacombe and A.P. Watkinson, "Experimental Study of Transverse Bed Motion i n Rotary K i l n s " , Met. Trans. B, 14B ( 6 ) , pp. 191-205, 1983. 61. J . Mu and D.D. Perlmutter, "The Mixing of Granular S o l i d s i n a Rotary C y l i n d e r " , A.I.Ch.E. J o u r n a l , 26_ ( 6 ) , pp. 928-934, (1980). 62. H. Henein, J.K. Brimacombe and A.P. Watkinson, "The Modelling of Transverse S o l i d s Motion i n Rotary K i l n " , Met. Trans. B, 14B ( 6 ) , pp. 207-220, (1983). 63. K.W. Carley-MacAuly and M.B. Donald, "The Mixing of S o l i d s i n Tumbling Mixers - I ", Chemical Engineering Science, 17, pp. 493-506, 1962. 64. K.W. Carley-MacAuly and M.B. Donald, "The Mixing of S o l i d s i n Tumbling Mixers - I I " , Chemical Engineering Science, 19_, pp. 191-199, (1964). 65. A. C h a t t e r j e e , A.V. Sathe, M.P. S r i v a s t a v a and P.K. Mukhopadhyay, "Flow of M a t e r i a l s i n Rotary K i l n s Used f o r Sponge Iron Manufacture" P a r t I - E f f e c t of Some Operating V a r i a b l e " , Met. Trans. B, 14B, pp. 375-381, (1983). 66. J . C h e d a i l l e , W. Leuckel and A.K. Chesters, Aerodynamic Studies C a r r i e d Out on Turbulent J e t s by the I n t e r n a t i o n a l Flame Research Foundation, Proc. 3rd Symposium on Flames and Industry - The Use of Models, London, (October, 1966). 67. M.W. Thring and M.P. Newby, "Combustion Length of Enclosed Turbulent Jet Flames", Proc. 4th I n t . Symposium on Combustion, (1953), pp. 789-796, Wi l l i a m s and W i l k i n s , B a l t i m o r e . 68. A. Craya and R. C u r t e t , "On the Spreading of a Confined J e t " , Comptes-rendus, Academie des Sciences, P a r i s , 241, pp. 621-622, (1955). 69. R. C u r t e t , "Confined J e t s and R e c i r c u l a t i o n Phenomena with Cold A i r Combustion and Flame", 2 ( 4 ) , pp. 383-411, (1958). 70. H.A Becker, H.C. H o t t e l and G.C. W i l l i a m s , "Mixing and Flow i n Ducted Turbulent J e t s " , Ninth Symposium ( I n t . ) on Combustion, Academic Press, London, pp. 7-20, (1963). 71. F.D. Moles, D. Watson and P.B. L a i n , "The Aerodynamics of the Rotary Cement K i l n " , J o u r n a l of the I n s t i t u t e of Fuel , pp. 353-362, (December, 1973). - 2 3 5 -72. J.M. Beer, "The Significance of Modelling", Proc. 3rd Symposium on Flames and Industry - The Use of Models, London, (October, 1966). 73. J.M. Beer, N. Chigier and K.B. Lee, "Modelling of Double Concentric Burner Jets", Ninth Int. Symposium on Combustion, Cornell University, N.Y., pp. 892-900, (1969). 74. J.K. Brimacombe and A.P. Watkinson, "Heat Transfer in a Direct Fired Rotary Kiln: I - Pilot Plant and Experimentation, Met. Trans. B, 9B, pp. 201-208, (1978). 75. G.J. Van Wylen and R.E. Sonntag, Fundamentals of Classical Thermo- dynamics, 2nd edition, Wiley, New York, N.Y., (1976). 76. Heat Transfer Data Book, General Electric Company, Corporate Research and Development, Schenectady, N.Y. (1971). 77. K.E. Peray and J.J. Waddell, The Rotary Cement Kiln, Chemical Publishing Co., N.Y. (1972). 78. Kelly, U.S. Bureau of Mines (1934). 79. Thermophysical Properties of Matter, The TPRC Data Series, Vol. 2, IFI/Plenum, N.Y. and Washington (1970). 80. Perry, J.H. (Editor in Chief), Chem. Eng. Handbook, 3rd Ed., McGraw H i l l , N.Y. (1950). APPENDIX (I) Response of the Bed Temperature Thermocouples The length of the p i l o t k i l n precluded obtaining bed temperatures by means of thermocouples inserted from the k i l n end openings. The necessity of i n s t a l l i n g the bed temperature thermocouples through the k i l n wall resulted i n transient output signals ( F i g . 1.1) as the junctions were a l t e r n a t e l y exposed to the freeboard and swept through the bed material. The time required for the thermocouples to e q u i l i b r a t e with the bed was found to be s u f f i c i e n t l y long (~ 60 + 180 sec) that the response of the bed became a factor i f the k i l n r o t a t i o n was stopped. For this reason the response of the bed thermcouples to immersion i n an isothermal mass of bed material was obtained to allow the true bed temperature to be obtained from the transient signals a c t u a l l y recorded. Neglecting temperature gradients within the junction material, the transient response ( a f t e r converting emf values to temperatures) of the thermocouple to Immersion within the bed material i s given by { C p P V dF}T/C = V l / C AT/C ( TT/C " V (1.1) f o r which, p r o v i d e d h, i s constant, the so l u t i o n (30) Is the f a m i l i a r WT/C -237-T — T t T/C b A t = exp{- —-} (1.2) where T i s the time constant of signal decay, tm The heat transfer between the bed material and the junction i s complex and h ^ ^ ^ , w i l l vary with time and, when r a d i a t i o n Is s i g n i f i c a n t , the o v e r a l l temperature l e v e l . However, i f a junction at a known i n i t i a l temperature q T^Q i s plunged into an isothermal mass of bed material then a f t e r the c o n t a c t time t a pseudo time constant T can be obtained c tm x t m TJC_ T d.3) t T/C b ln( % _ T ) olT/C Xb Although T i s not constant with time or temperature i t can be used to tm c a l c u l a t e T, when the same thermocouple i s plunged into a bed material at b approximately the same l e v e l provided the signal at the same contact time t i s employed, c Values f o r x were obtained f o r each bed m a t e r i a l at s e v e r a l tm temperature l e v e l s by plunging thermocouples into c r u c i b l e s containing about 2 Kg of the material which had been soaked overnight i n a laboratory f u r n a c e . The v a r i a t i o n of with t i s shown i n F i g . 1-2. The tm c temperature and composition of the bed, as well as p a r t i c l e s i z e , can be -238-Enters bed Time (s) F i g . I . l S i g n a l c o u p l e o b t a i n e d f r o m ( t y p i c a l ) bed t e m p e r a t u r e thermo-O Coarse sand A Fine sand o Limestone • Petroleum coke 1 1 5 10 Time (s) 20 i g . 1 . 2 V a r i a t i o n o f t h e p s e u d o - t i m e c o n s t a n t w i t h t i m e a t t h r e e l e v e l s of bed t e m p e r a t u r e 50 -240-10 9 8 - N o ~ 7 B 5 4 — exp (~bTb a b o Coarse sand 23.731 1.727 X IO"3 A Fine sand 1 8.337 1.535 X IO"3 O Limestone 19.528 1.691 X IO"3 • Pet coke 16,035 1.581 X IO"3 500 700 900 100 Bed temperature (K ) F i g . 1 . 3 V a r i a t i o n of the p s e u d o - t i m e c o n s t a n t w i t h t e m p e r a t u r e f o r a c o n t a c t t i m e of 6 s e c o n d s -241-seen to i n f l u e n c e T . At a contact time t =6 sec from immersion the tm c v a r i a t i o n of with bed temperature i s plotted i n F i g . 1.3. The true bed temperatures were obtained from the transient bed thermocouple data ( F i g . 1.1) as follows: ( i ) The l e v e l of the bed temperature was assumed to be approximately the same as the j u n c t i o n temperature at t = 6 sec. The value of T at that temperature l e v e l was then taken from F i g . 1.2 for the bed material. ( i i ) The thermocouple j u n c t i o n temperatures at t = 0 and t = 6 sec c c were obtained from the output curve F i g . 1.1. ( i i i ) Eq. 1.3 was solved for the true bed temperature T, . b N e g l i g i b l e error was incurred by assuming the bed temperature l e v e l to be equal to the j u n c t i o n temperature at t = 6 sec s i n c e T i s a c tm f a i r l y weak function of temperature. -242-APPENDIX (II) Computer Program Flow Charts To reduce bulk the major computer programs associated with the study are presented as flow charts. L i s t i n g s of the source-decks may be obtained from Dr. A.P. Watkinson of the Chemical Engineering Department at UBC. Several peripheral programs were developed for manipulation of data, curve f i t t i n g , p l o t t i n g of r e s u l t s , etc. but are not detai l e d owing to t h e i r s i m p l i c i t y . -243-(atart) read T/C emf data; f i r i n g conditions bed mat• feed rate; calcln. data; etc. convert emf data to temperatures; curve f i t axial & clrcumf. temp, profiles v a i l steady-state loss, net input to bed Probe - 1 calculate wall active layer nodal network & I n i t i a l radial temp, pr o f i l e T w(r,0) run f i n i t e d l f f . model for one rev. using fitted curve T W B& ( d T w / d r ) B B as B.C.'s calc. AT W - max T w(r,2it) - T w(r,0) rev » rev+1 Yes calc. Hm(B), 4 C W(6), 1ev(0), 4 e b etc Yes probe read radiative heat trans, coef. data (ie f i g s . 7.24-7.27) probe= probe+1 calc. radiative contribution to Qe^ & Q e v yes write temps; heat transf. results ; c ^ e v & c V e b ' generate req'd plots Fig.II.1 Flow chart f o r the p i l o t k i l n data analysis and the c a l c u l a t i o n of net heat transfer rates -"FILE" -244-read geometric variables & freeooara gas composition No Yes k-1 1-1 J-l read surface rone local temperature and gradient read values of (SjjT)^ from 'RKSG'; temp variation of gas emlss. & abs. weighting coef. from 'RPIT' (ie Figs. 6.8 & 6.9); specific exchange factors for direct +1 +2 reflections from •RREF' (ie Figs. 6.16, 6.17, 6.18) calculate coordinates of Aj relative to Ajj (SjBj)k from eq. 6.32b carry out calc'n for upstream exchanges r — i •1 1-1 1-•1 calculate net radiative exchange from eq. 6.39 carry out 8 annua tlons to reduce total zones by 4 write values (sp\) t° 'RKSS Tes / write net surface/surface exchange results 7F1 iS" I •O F i g . I I . 2 Flow chart f o r the c a l c u l a t i o n of surface/surface r a d i a t i v e heat transfer - "KSS" -245-read geometric variables & freeboard gas composition No read loca l surf. zone temp+ gas temp + gas temp grad. read values of (a^gi)^ from •RKSG*; Temp variation of gas emiss. i abs. weighting coef. from 'RFIT' (ie Figs. 6.8 & 6.9) Yes k-1 1-1 calculate coordinates of Vj relative to A^; carry out coordinate transform's & subdivide Vj to achieve std. form Fig.II.3 Flow chart for the c a l c u l a t i o n of surface/gas r a d i a t i v e heat t r a n s f e r - "KSG" -246-read geometric variables; freeboard gas composition; Tg, Twe - Teb, Reg, dp, k8, kg read fitted curves for exchange coefficients (i 'reeboard radiative Le. Tigs. 7.24-7.28) calculate hf (eq. 2.33 finite difference node wall and bee ) & kv e (eq. 2.26); radii & volumeB In material initialize radial temp, profiles In wall Tw(r,0) from eq. 6.8 for SS condition & and for the material Tfc(r, t e x p) calculate Rhg eb/ew' Rheb ew: Rhew ev±'' c hg ew ( e9- 6 - 4 9 ) : c V e b ' 5 c V e v ; h 8 h * 6.52) run wall finite diff. model for period of exp. to freeboard-obtaining T (r,6 ) w texp run wall + bed finlted using Tb(r,etexp) + T„ diff. model for t cov rr'etexp> f o r I'c* calc. ATV- max T w(r.e t e x p + c o v)- Tw(r,0) No Yes i T w < tesf; write T (r,6); T (r,e) w b Q e w, Q c w, %. Q etc. obtained from temp, results (stop) Fig.II.4 Flow chart for the u n i f i e d heat t r a n s f e r model at a k i l n c ross-section - "WALL2" -247-APPENDIX ( I I I ) R e s u l t s From The P i l o t K i l n T r i a l s T r i a l T l flxial temperature p r o f i l e "i 1 1 1 1 1 1 1 r RUN NUMBER Tl O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL 1 I I I 1 1 1 1 r 1 flxiflL P O S I T I O N FMETRES) 4 T r i a l T l Net heat t r a n s f e r r a t e s T r i a l T 2 flxial t e m p e r a t u r e p r o f i l e ~i 1 1 1 1 1 1 1 r RUN NUMBER T2 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL i r "i 1 1 1 1 1 r RUN NUMBER T3 OBULK SOLIDS A INSIDE UflLL tflVG) • GftS-2.5 ca OFF BED O GRS-IO ca OFF UflLL T 1 1 1 1 1 1 1 1 r ' flXIfil POSITION (METRES* 5 T r i a l T 3 A x i a l t e m p e r a t u r e p r o f i l e i 1 1 1 1 1 1 1 r RUN NUMBER T3 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL 1 1 1 1 1 1 1 1 1 A X I A L P O S I T I O N FMETRESI 4 T r i a l T 3 N e t h e a t t r a n s f e r r a t e s i 1 1 1 1 1 1 1 r RUN NUMBER T4 ONET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED WALL T 1 1 1 1 1 1 1 T 1 RxiflL P O S I T I O N FMETRESJ 4 T r i a l T 4 N e t h e a t t r a n s f e r r a t e s T i 1 1 1 r RUN NUMBER T5 O BULK SOLIDS A INSIDE UflLL (flVG) • GflS-2.5 ca OFF BEO O GRS-10 ca OFF UflLL T T" T r RXlfll POSITION (METRES4 T r i a l T 5 A x i a l t e m p e r a t u r e p r o f i l e i r i r RUN NUMBER T5 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROH COVERED UflLL I i 1 1 1—:—I 1 1 1 r 1 RXlflL POSITION ?METRES) 4 T r i a l T 5 N e t h e a t t r a n s f e r r a t e s T 1 1 1 1 1 1 1 1 r RUN NUMBER T6 OBULK SOLIDS A INSIOE UflLL (RVG) • GftS-2.5 ca OFF BED O GflS-10 ca OFF UflLL T 1 1 1 1 1 1 1 1 T 1 AXIAL POSITION (METRES? • T r i a l T 6 A x i a l t e m p e r a t u r e p r o f i l e T r i a l T 6 N e t h e a t t r a n s f e r r a t e s o 8. o 8. 28 T RUN NUMBER T 7 O BULK SOLIDS A INSIDE UflLL (flVG) • GflS-2.5 ca OFF BED O GAS-10 ca OFF UflLL 1 1 1 1 1 T R I -CE or UJ o_ _ 8-o 8- T 1 1 1 1 1 1 1 1 r 1 AXIAL POSITION (METRES? 5 T r i a l T7 A x i a l t e m p e r a t u r e p r o f i l e n 1 1 1 1 1 1 1 r RUN NUMBER T7 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVEREO UflLL T 1 1 1 1 1 1 1 r 1 A X I A L P O S I T I O N FMETRESJ 4 T r i a l T7 N e t h e a t t r a n s f e r r a t e s T r i a l T 8 A x i a l t e m p e r a t u r e p r o f i l e n 1 1 1 1 1 1 1 r RUN NUMBER T 8 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL T 1 1 1 1 1 1 1 T 1 R x i f i L P O S I T I O N FMETRES) 4 T r i a l T 8 N e t h e a t t r a n s f e r r a t e s T r i a l T9 flxial temperature p r o f i l e s T T RUN NUMBER T9 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED MOLL © — e e — o i 1 1 1 1 1 1 r 1 flxiRL P O S I T I O N ?METRESJ 4 T r i a l T9 Net heat t r a n s f e r r a t e s T r i a l T10 flxial temperature p r o f i l e i 1 1 1 1 1 1 1 r RUN NUMBER T10 ONET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UFLLL 1 1 1 1 1 1 1 1 1 RXIR-L POSITION ?METRES) 4 T r i a l T10 Net heat t r a n s f e r r a t e s T r i a l T i l flxial temperature p r o f i l e n 1 1 1 1 1 r 1 r RUN NUMBER T i l O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL 1 1 1 1 1 1 1 1 1 AXIAL POSITION fMETRES) 4 T r i a l T i l Net heat t r a n s f e r r a t e s T r i a l T12 A x i a l temperature p r o f i l e n 1 1 1 1 1 v"—i r RUN NUMBER T 1 2 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL -e—e- - e — e e—o -o—a-T 1 1 1 1 1 1 1 r 1 RxiflL P O S I T I O N FMETRESJ 4 T r i a l T12 Net heat t r a n s f e r r a t e s T r i a l T13 flxial temperature p r o f i l e RUN NUMBER T13 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UfiLL T 1 1 1 1 1 1 1 1 1 AXIAL POSITION ?METRES) 4 T r i a l T13 Net heat t r a n s f e r r a t e s " i i i i 1 1 1 1 1 r RUN NUMBER T14 O BULK SOLIDS A INSIDE UflLL (flVG) • GflS-2.5 ca OFF BED O GAS-10 c i OFF UflLL i 1 1 1 1 1 1 1 1 r ' RXIfit POSITION (METRES)* 5 Trial T14 Axial temperature profile in T i 1 1 1 1 1 r arm UJ u_ . COfM z cc oc t— -f— rx UJ RUN NUMBER T14 O NET INPUT TO SOLIOS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL -e—e—e- -e e ©—© - a — a — ° a B-—o i • i 1 1 r 1 1 1 1 1 — 1 RXIflL POSITION fMETRES) 4 Trial T14 Net heat transfer rates T r i a l T 1 5 flxial temperature p r o f i l e T T T T T T RUN NUMBER T 1 5 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED WALL i I n 1 r~ 1 1 1 r 1 A X I A L P O S I T I O N FMETRESJ 4 T r i a l T15 Net heat t r a n s f e r r a t e s RUN NUMBER T16 O BULK SOLIDS A INSIDE URLL (flVG) • GflS-2.5 ci OFF BED O GflS-10 ci OFF WALL ~l 1 1 1 1 1 1 1 1 r 1 RXIRL POSITION (METRES? 5 T r i a l T16 A x i a l temperature p r o f i l e T 1 1 1 1 1 1 1 r RUN NUMBER T 1 6 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL 1 1 1 1 1 1 1 1 T 5 RXIRL P O S I T I O N (METRES) 4 T r i a l T16 Net heat t r a n s f e r r a t e s RUN NUMBER T 17 O BULK SOLIDS A INSIDE UflLL (flVG) • GflS-2.5 ca OFF BED O GflS-10 ca OFF WALL 1 1 1 1 1 1 1 1 1 1— 1 AXIAL POSITION (METRES? 5 T r i a l T 1 7 flxial temperature p r o f i l e AXIAL POSITION (METRES? T r i a l T18 A x i a l temperature p r o f i l e ^ n 1 1 1 1 1 1 1 r RUN NUMBER T18 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UHLL 1 1 1 1 1 1 1 1 1— 1 AXIAL POSITION fMETRES) " T r i a l T18 Net heat t r a n s f e r rates TEMPERATURE (KELVIN) 900 1100 1300 J I I I I L 1500 JL 1700 i HEAT TRANSFER (KW/M) 5 10 15 ' ' I I L_ 20 _ l _ 25 • > 0 zo i n X T J N ) O CO 50 rn to U l . 1-1 fl ;= Z 10 z ^ -o x T J - £ - I ^ o r- o M i ' s s 3 a T 1 1 1 1 1 1 1 r T 1 1 1 1 1 1 1 1 r ' flXIfll POSlTIoS (METRES? 5 T r i a l T20 A x i a l temperature p r o f i l e s RUN NUMBER T20 ONET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL 1 RxiRL P O S I T I O N FMETRESJ 4 T r i a l T20 Net heat t r a n s f e r rates T 1 1 r T 1 1 1 r T RUN NUMBER T21 O BULK SOLIDS A INSIDE UflLL (RVG) • GflS-2.5 n OFF BED O GOS-10 ci OFF "RU-SH 1 1 1 1 1 1 1 1 1 r ° 1 AXIAL POSITION (METRES? 5 T r i a l T21 A x i a l t e m p e r a t u r e p r o f i l e «- T RUN NUMBER T 2 1 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED WRLL .—.in. 2 : -or LU U_o. co— z cc or cc LU I N> ON OO I — 1 1 1 1 1 r A X I A L P OSITION ?METRES) 4 T r i a l T21 N e t h e a t t r a n s f e r r a t e s T "T o P. o 8. UJ UJ OTo ^ 2 I— Z\ -CC or UJ o_ . RUN NUMBER T 2 2 O BULK SOLIDS A INSIDE UflLL (flVG) • GflS-2.5 c» OFF BED O GflS-10 ci OFF URLL 1 1 1 1 1 r flXIRL POSITION (METRES? T r i a l T22 flxial t e m p e r a t u r e p r o f i l e -i 1 1 1 1 1 1 1 r RUN NUMBER T 2 2 O NET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED UflLL i I 1 1 1 1 I 1 1 — 1 RXIRL P O S I T I O N ?METRES) 4 T r i a l T22 N e t h e a t t r a n s f e r r a t e s T T T T T T RUN NUMBER T23 ONET INPUT TO SOLIDS A KILN SHELL LOSS • NET INPUT TO SOLIDS FROM COVERED URLL i o I ~ i 1 1 1 1 1 r ' AXIAL POSITION fMETRES) 4 T r i a l T23 Net heat transfer rates -271-APPENDIX (Iv) K l i n Energy Balance I f the entire k i l n , including the f i r i n g box, i s considered as a cont r o l volume then conservation of energy requires that g \ s { ( A ^ l e a v i n g " < A H > e n t e r i n g ) } + ^ { * ^ l e a v i n g " ( * " e n t e r i n g ^ = - ( Q s s + Q F B ) (IV.l) where Q i s the r a t e of energy l o s s through the k i l n wall and Q.™ s s FB i s the r a t e of l o s s from the f i r i n g box. H and n denote the molar enthalpy and molar flow r e s p e c t i v e l y for the various materials crossing the k i l n boundary. By defining AE = Y {(n H). . - (n H) . } (IV.2) g L 'leaving v 'entering v ' gas AE, = 7 {n H) 1 . - (n H), . } (IV.3) bed leaving v 'leaving v ' \ = ~ ( A E g + A V ( I V * 4 ) eq. I V . l can be put into the more compact f or AE + AE, = Q (IV.5) g b X L To o b t a i n Q the values of w a l l l o s s per u n i t length were f i t t e d s s as shown i n F i g . I V . l to a s t r a i g h t l i n e and the area under the curve c a l c u l a t e d . The f i r i n g box l o s s was estimated from Q FB = W A B + R hFB ) (TFB - 2 %> (IV.6) V a l u e s f o r were d e r i v e d form the c o r r e l a t i o n (30) f o r n a t u r a l convection from v e r t i c a l f l a t p l a t e s Nu = 0.13 (GrPr) 0.33 (IV.7) and the r a d i a t i v e c o e f f i c i e n t was c a l c u l a t e d using the simple 2 gray body r e s u l t of eq. 6.52. The s u r f a c e temperature of the f i r i n g box T was FB obtained from the averaged r e s u l t of 7 thermocouples i n s t a l l e d over the s u r f a c e . Both the gaseous reactants and the bed m a t e r i a l were assumed to enter the k i l n at 298K. The gas e x i t temperature was found to be a c c u r a t e l y represented by e x t r a p o l a t i n g the a x i a l gas temperature p r o f i l e s . A small alumina scoop c o n t a i n i n g a thermocouple was used to measure the temperature of the bed m a t e r i a l f a l l i n g i n t o the hopper under the f i r i n g box. This discharge hopper was not included i n the f i r i n g box heat l o s s c a l c u l a t i o n . -273-Axial position (m) F i g . I V . 1 L i n e a r f i t o f t h e s t e a d y - s t a t e e n e r g y l o s s t h r o u g h t h e k i l n r e f r a c t o r y w a l l -274-A comparison of Q g g + Q p B with values of Q L calculated using eq. IV.5 i s provided by Table IV.1. The closure of the o v e r a l l energy balance i s g e n e r a l l y w i t h i n 10%. The tendency for Q + Q„„ to exceed Q„ can be ss FB H L accommodated within the error bounds of the t o t a l gas flow i n the freeboard. -275-TABLE IV.1 RESULTS FROM THE KILN ENERGY BALANCE TRIAL AE g kW A E b kW \ kW %h kW kW Q T kW 0.5(Q L+ Q T ) T02 -13.0 7.2 5.8 5.6 1.0 6.6 -0 .13 T04 -27.2 12.8 14.4 13.2 1.4 14.6 -0.01 T06 -12.9 5.8 7.1 6.9 1.0 7.9 -0.11 T09 -34.7 14.5 20.2 16.6 1.5 18.1 +0.1 T12 -10.3 3.3 7.0 6.1 0.8 6.9 +0.01 T14 -28.0 9.0 19.0 14.7 1.6 16.3 +0.15 T18 -60.2 41.6 18.6 21.1 1.6 22.7 -0 .19 T20 -56.4 32.8 23.6 22.1 1.6 23.7 -0.02 T22 -49.0 30.2 18.8 19.0 1.5 20.5 -0 .09 

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