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Elutriation of particles from rotary kilns Tackie, Emmanuel Nii 1987

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ELUTRIATION OF PARTICLES FROM ROTARY KILNS by EMMANUEL Nil TACKLE B.Sc.(Hons) University of Science and Technology, Ghana, 1973 M.A.Sc. University of British Columbia, Canada, 1982 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Chemical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JUNE 1987 ® EMMANUEL Nil TACKLE, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) ABSTRACT The e l u t r i a t i o n of fine materials from the solids bed in rotary k i l n s was studied in a laboratory scale steel cylinder of 0.2m in diameter and 2.4m in length. The cylinder was charged with a batch of fine alumina p a r t i c l e s having a mean size of 64jum and the average e l u t r i a t i o n rate measured at d i f f e r e n t a i r flow rates, rotational speeds and percentage of solids f i l l . A l l measurements were done at room temperature. To show the eff e c t of fines concentration and segregation in the solids bed, a binary mixture of fine alumina and coarse Ottawa sand was used. Local dust concentration p r o f i l e s were measured in the freeboard through a probe equipped with a f i l t e r . Design factors such as the geometry of the k i l n e x i t dams, were found to influence dust carryover into the cleaning equipment by accelerating the flowing gas and or obstructing the flow of solids in the gas phase. Wall roughness and imperfections also affected e l u t r i a t i o n especially at higher rotational speeds by exposing trapped fines d i r e c t l y into the flowing gas. Dust concentration measurements revealed that most of the solids in the gas phase t r a v e l l e d in sa l t a t i o n within about 2 cm above the bed surface. With the wall e f f e c t eliminated by an insert, increasing the rotational speed was i i found to exhibit a negative e f f e c t on the e l u t r i a t i o n rate. Dust concentrations were higher in the gas phase above the lower edge of the rotating bed than at the upper edge or midpoint. However, while the concentration above the rest of the bed remained f a i r l y constant with increased rotational speeds, at the lower edge of the bed i t decreased. Banding segregation occurred in the beds composed of fine and coarse p a r t i c l e s . E l u t r i a t i o n increased with the number of fine bands formed which was proportional to the concentration of fines. The location of the bands from the exit also influenced e l u t r i a t i o n . Saltating p a r t i c l e s returning to the bed close to the exit had a better chance of ejecting other p a r t i c l e s i f they landed on fine bands than they would i f they landed on coarse bands. Gas ve l o c i t y exhibited the strongest influence on e l u t r i a t i o n rate. A c o r r e l a t i o n of experimental results showed a ve l o c i t y dependence of U 6 regardless of i n i t i a l fines concentration in the bed. An entrainment mechanism has been formulated based on the c o l l i s i o n of sa l t a t i n g p a r t i c l e s on the solids bed. Subsequently, a simple mathematical model was developed to describe the influence of the operating variables on e l u t r i a t i o n . The model predictions were v e r i f i e d with the experimental data and the scanty data in the l i t e r a t u r e . The model requires knowledge of the s a l t a t i o n height and the threshold shear stress for p a r t i c l e movement. Model predictions for t y p i c a l i n d u s t r i a l k i l n s are presented. The predictions are in f a i r l y good agreement with values reported in a survey of i n d u s t r i a l k i l n operations made prior to the experimental program, given that the effect of k i l n internals was not accounted for in the model. iv Table of Contents ABSTRACT i i LIST OF TABLES - v i i i LIST OF FIGURES ACKNOWLEDGEMENTS :-x±v 1 . INTRODUCTION 1 1 . 1 General 1 1.2 Industrial Dusting Problems 4 2. LITERATURE REVIEW 11 2.1 Introduction 11 2.2 Solids Flow Patterns 11 2.3 Solids Segregation Patterns 16 2.4 Mechanics of entrainment 19 2.4.1 Threshold of P a r t i c l e Movement 19 2.4.2 Transport of P a r t i c l e s 22 . 2.5 Entrainment in Rotary Kilns 27 3. SCOPE OF PRESENT WORK 31 4. EXPERIMENTAL APPARATUS AND MATERIALS 33 4. 1 Apparatus 33 4.1.1 Rotating Cylinder 33 4.1.2 Dust Col l e c t i o n 42 4.2 Instruments 42 4.2.1 Velocity Measurements 43 4.2.2 Dust Sampling 44 4.3 Materials 47 5. EXPERIMENTAL PROCEDURE 52 5.1 Introduction 52 5.2 Unimodal System 53 v 5.3 Velocit y P r o f i l e and Dust Sampling 55 5.4 Bimodal System 57 5.5 Operating Range 58 6. RESULTS AND DISCUSSIONS 59 6.1 Saltation Experiment 59 6.2 Bed Behaviour 61 6.3 E l u t r i a t i o n of Fine alumina P a r t i c l e s 62 6.3.1 Effect of Rotating Wall 67 6.3.2 Effect of Exit Dam Geometry 79 6.3.3 Velocity P r o f i l e s 87 6.3.4 Isokinetic Dust Sampling 95 6.3.5 Size D i s t r i b u t i o n of Dust and Solids Bed .107 6.4 Photographic Experiments with Coloured P a r t i c l e s 110 6.5 Mechanism of Dust Pick-Up 120 6.6 E l u t r i a t i o n from a Bed containing a mixture of Sand and Alumina 122 6.7 Correlation of E l u t r i a t i o n Rates 128 7. MATHEMATICAL MODELING OF ENTRAINMENT 142 7.1 Introduction 142 7.2 Momentum and material balance 145 7.3 P a r t i c l e Trajectory 154 7.4 Ef f e c t of Bed Inclination and Rotation 161 7.4.1 Estimation of R, 161 7.4.2 Estimation of K 2 162 7.5 Model predictions 163 7.6 Comparison with experimental data 167 8. INDUSTRIAL APPLICATIONS 183 v i 8.1 Operational Implications 183 8.2 Minimum Saltation Velocity 187 8.3 Industrial Predictions 189 9. CONCLUSIONS AND RECOMMENDATIONS 198 9.1 Conclusions 198 9.2 Recommendations for Future Work 200 NOMENCLATURE 202 REFERENCES 208 APPENDIX A : CALIBRATION OF INSTRUMENTS 214 APPENDIX B : FORCES ACTING ON BED PARTICLES 223 APPENDIX C : NUMERICAL SOLUTION OF MODEL EQUATIONS 231 APPENDIX D : COMPUTER PROGRAMS 237 APPENDIX E : EXPERIMENTAL DATA 249 v i i LIST OF TABLES Page Table 1.1 Survey of i n d u s t r i a l k i l n operating conditions 6 Table 4.1 Dimensions of conical exit dam and cardboard insert 40 Table 4.2 Physical properties of s o l i d p a r t i c l e s 51 Table 6.1 Dust concentration measurements in a conical exit dam 83 Table 6.2 Typical l o c a l mean velocity measurements for isokinetic sampling 94 Table 6.3 Local dust concentration above a non-rotating bed 106 Table 6.4 Typical size of segregated bands in a bimodal bed 129 Table 6.5 Rough wall data used in co r r e l a t i o n of Equation 6.16 134 Table 6.6 Smooth wall data used in co r r e l a t i o n of Equation 6.17 136 Table 6.7 Data for the bimodal system used in corre l a t i o n of Equation 6.19 139 Table 7.1 Typical jump distance of a s a l t a t i n g p a r t i c l e 160 Table 7.2 Summary of run conditions introduced into model Equation 7.40 172 Table 7.3 Input and output parameters for predictions based on Equation 7.40 173 v i i i LIST OF FIGURES Page Figure 1.1 Essential features of a rotary k i l n 2 Figure 2.1 Types of p a r t i c l e motion in rotary k i l n s 13 Figure 2.2 Types of segregation patterns in rotary cylinders (1 8) 17 Figure 4.1 Schematic diagram of experimental apparatus 34 Figure 4.2 Photograph of apparatus and probe locations 35 Figure 4.3 Design of end boxes 37 Figure 4.4 Various k i l n exit geometries 38 Figure 4.5 Disa 55A76 steel clad hot f i l m probe 45 Figure 4.6 P i t o t - s t a t i c tube and sampling probe 46 Figure 4.7 Size d i s t r i b u t i o n of alumina p a r t i c l e s 49 Figure 5.1 Cyclone discharge size d i s t r i b u t i o n 56 Figure 6.1 Saltation experiment: Plan view of sol i d s solids bed, rpm=4,gas velocity=4m/s 60 Figure 6.2 Bed behaviour diagram 63 Figure 6.3 E l u t r i a t i o n rate versus rotational speed for d i f f e r e n t a i r v e l o c i t i e s at 5% f i l l in the presence of the exposed cylinder wall 64 Figure 6.4 E l u t r i a t i o n rate versus rotational speed for d i f f e r e n t a i r v e l o c i t i e s at 10% f i l l in the presence of the exposed cylinder wall 65 Figure 6.5 E l u t r i a t i o n rate versus rotational speed for d e i f f e r n t a i r v e l o c i t i e s at 15% f i l l in the presence of the exposed cylinder wall 66 Figure 6.6 E l u t r i a t i o n rate versus gas ve l o c i t y showing contribution due to wall rotation for a f l a t exit dam 70 Figuer 6.7 E l u t r i a t i o n rate versus rotational speed at 5% s o l i d s loading in a covered wall cylinder 71 Figure 6.8 E l u t r i a t i o n rate versus rotational speed at 10% s o l i d s loading in a covered wall cylinder 72 i x Figuer 6.9 E l u t r i a t i o n rate versus rotational speed at 15% s o l i d s loading in a covered wall cylinder 73 Figure 6.10 Wall effect at 15% f i l l 75 Figure 6.11 Wall effect at 10% f i l l 76 Figure 6.12 Wall effect at 5% f i l l 77 Figure 6.13 Ef f e c t of s o l i d s loading on e l u t r i a t i o n 78 Figure 6.14 E l u t r i a t i o n rate in a cylinder with a f l a t e x i t dam and an exposed wall 81 Figure 6.15 E l u t r i a t i o n rate in a cylinder with a f l a t e x i t dam and a covered wall 82 Figure 6.16 Influence of e x i t geometry on e l u t r i a t i o n rate at various r o t a t i o n a l speeds 84 Figure 6.17 Influence of exit geometry on e l u t r i a t i o n rate at various a i r v e l o c i t i e s 85 Figure 6.18 Photograph showing sol i d s behaviour at exit dam at higher rotational speeds 88 Figure 6.19 Velocity p r o f i l e s along the v e r t i c a l and horizontal diameters of the empty cylinder 89 Figure 6.20 Typical v e l o c i t y p r o f i l e s above solids bed at 5% f i l l 91 Figure 6.21 Typical v e l o c i t y p r o f i l e s above s l i d s bed at 10% f i l l 92 Figure 6.22 Velocity d i s t r i b u t i o n on a semi-logarithmic plot 93 Figure 6.23 Dust concentration p r o f i l e s above solids bed in a 'rough' wall experiment 96 Figure 6.24 Dust concentration p r o f i l e s above solids bed in a 'smooth' wall experiment 97 Figure 6.25 Axial dust concentration p r o f i l e above solids bed 98 Figure 6.26 Dust concentration changes at spe c i f i e d locations in a cylinder with a 'bent l i p ' exit dam, exposed wall and at 10% f i l l 100 Figure 6.27 Dust concentration changes at sp e c i f i e d locations in a cylinder with a x: -conical exit dam, exposed wall and at 5% f i l l 101 Figure 6.28 Dust concentration changes at spe c i f i e d locations in a cylinder with a 'bent l i p ' exit dam, exposed wall and at 5% f i l l 103 Figure 6.29 Dust concentration changes at spe c i f i e d locations in a cylinder with a 'bent l i p ' exit dam, covered wall and at 5% f i l l 104 Figure 6.30 Dust concentration changes at spe c i f i e d locations in a cylinder with a 'bent l i p ' exit dam, covered wall and at 10% f i l l 105 Figure 6.31 Size d i s t r i b u t i o n of co l l e c t e d dust at s p e c i f i e d locations above bed in an exposed wall cylinder 108 Figure 6.32 Effect of rotational speed on dust size d i s t r i b u t i o n at Location 2 109 Figure 6.33 Bed p a r t i c l e size d i s t r i b u t i o n at s p e c i f i e d locations 25 cm from exit dam 111 Figure 6.34 Bed p a r t i c l e size d i s t r i b u t i o n at spe c i f i e d locations 55 cm from exit dam 112 Figure 6.35 Bed p a r t i c l e size d i s t r i b u t i o n at upper edge of bed for various % f i l l s 113 Figure 6.36 Bed p a r t i c l e size d i s t r i b u t i o n at centre of bed for various % f i l l s 114 Figure 6.37 Bed p a r t i c l e size d i s t r i b u t i o n at lower edge of bed for various % f i l l s 115 Figure 6.38 Photographic time exposures of coloured bed surface in a horizontal bed at 4.21 m/s a i r v e l o c i t y 117 Figure 6.39 Photographic time exposures of coloured bed surface in an i n c l i n e d bed at 3.7 m/s a i r v e l o c i t y 118 Figure 6.40 Photographic time exposures of coloured bed surface in an i n c l i n e d bed at 4.21 m/s a i r v e l o c i t y 119 Figure 6.41 Concentration time plot for 5% i n i t i a l fines concentration in a bimodal bed 125 x i Figure 6.42 Concentration time plo t for 10% i n i t i a l fines concentration in a bimodal bed ., 126 Figure 6.43 E l u t r i a t i o n rate versus i n i t i a l fines concentration 127 Figure 6.44 Scatter plot of predicted versus observed dimensionless e l u t r i a t i o n from a uniform sized bed and exposed wall cylinder 135 Figure 6.45 Scatter plot of predicted versus observed dimensionless e l u t r i a t i o n from a uniform sized bed and covered wall cylinder 137 Figure 6.46 Scatter plot of predicted versus observed dimensionless e l u t r i a t i o n from a bimodal bed 140 Figure 7.1 Typical p a r t i c l e trajectory 146 Figure 7.2 P a r t i c l e trajectory from an inclined bed .... 146 Figure 7.3 Effect of p a r t i c l e density and gas density on model predictions, D=3.5m, N=2rpm 164 Figure 7.4 Effect of p a r t i c l e size on model predictions 165 Figure 7.5 Effect of errors onsaltation height on model predictions 166 Figure 7.6 Comparison of model predictions with experimental data points at 5% f i l l 168 Figure 7.7 Comparison of model predictions with experimental data points at 10% f i l l 169 Figure 7.8 Comparison of model predictions with experimental data points at 15% f i l l 170 Figure 7.9 Comparison of model predictions with experimental data at 1 and 3 rpm at various gas v e l o c i t i e s 174 Figure 7.10 S e n s i t i v i t y of model predictions to changes in s a l t a t i o n height 176 Figure 7.11 S e n s i t i v i t y of model predictions to changes in p a r t i c l e size 177 Figure 7.12 Sensityvity of model predictions to changes in p a r t i c l e density 178 Figure 7.13 Comparison of model predictions with experimental data for bimodal system 180 Figure 7.14 Comparison of model predictions with experimental data of Khodorov (1) 181 Figure 8.1 Velocity factor versus flow v e l o c i t y for t y p i c a l i n d u s t r i a l operations 191 Figure 8.2 Velocity factor - P a r t i c l e size correction factor 192 Figure 8.3 Velocity factor - Saltation height correction factor 193 Figure A1 Calibration curve for rotameter 216 Figure A2 Constant temperature anemometer system, Rp denotes probe resistance 217 Figure A3 Calibration curve for DISA 5A76 steel clad hot film probe.. 221 Figure B1 Force balance on a horizontal bed 224 Figure B2 Force balance on an i n c l i n e d bed 224 Figure B3 Force balance on p a r t i c l e s in a rotating bed 228 x i i i ACKNOWLEDGEMENTS I wish to express my sincere gratitude and appreciation to Dr. J. K. Brimacombe and Dr. A. P. Watkinson for their encouraging advice and useful suggestions throughout the course of this study. Special thanks to the staff of the Chemical Engineering workshop and stores for their remarkable assistance in the construction of the equipment. Discussions with fellow graduate students and other faculty members are also g r a t e f u l l y acknowledged. I am also grateful to the Natural Sciences and Engineering Research Council for f i n a n c i a l support in the form of Research Assistanship. F i n a l l y , but not the least, I wish to extend my warmest appreciation to members of my family, p a r t i c u l a r l y Marian, for their patience and support throughout the duration of th i s endeavour. x i v To my mother for her love , 2 V Chapter 1 INTRODUCTION 1.1 GENERAL D i r e c t - f i r e d rotary kilns are i n d u s t r i a l reactors employed in the thermal processing of s o l i d materials by dir e c t contact with the products of combustion of a f u e l . E s s e n t i a l l y , the i n d u s t r i a l k i l n i s a steel cylinder lined with refractory bricks on account of the elevated temperatures applied in the various processes. It is rotated about i t s axis upon suitable bearings at speeds ranging from 0.4-3rpm and is inclined at slopes varying from 0.02 to 0.06 m/m. In most operations c a r r i e d out in a continuous mode, raw material i s fed to the upper end (Figure 1.1) and travels down the k i l n by both a x i a l and circumferential motion that provide maximum exposure to contacting hot gases in cocurrent or countercurrent flow. Dams placed at various locations along the length determine the sol i d s residence time in the k i l n . In the usual case of countercurrent direct f i r i n g , fuels such as pulverised coal, atomised fuel o i l or natural gas are f i r e d through burners placed in a combustion chamber located at the lower (hot) end with the exhaust gases c o l l e c t e d in a stationary hood at the upper (feed) end. Heating of the charge is thus accomplished through 1 Flue gas End box Angle of inclination Firing hood t Product discharge F i g u r e 1.1 E s s e n t i a l f e a t u r e s of a r o t a r y k i 3 radiation from the flame and exposed k i l n wall, conduction from the k i l n refractory l i n i n g in contact with solids and by convection from the hot gases flowing over the charge. Rotary k i l n s are increasingly used in the chemical and metallurgical industries in such operations as drying and preheating, c a l c i n i n g , roasting, nodulising, fusing, incineration and reduction of ores as well as to perform certain chemical reactions. In the production of cement, the k i l n i s extensively employed to e f f e c t the chemical reaction of the s o l i d constituents at or near their temperature of fusion (1700-1900°K). The c a l c i n a t i o n of lime mud and limestone are c a r r i e d out in the pulp and paper industry and the steel industry respectively to remove v o l a t i l e constituents such as carbon dioxide or combined water by decomposition at temperatures ranging from 1300 to 1600°K. Fine materials, such as phosphate rock, agglomerate into nodules when p a r t i a l l y calcined at temperatures in the range 1500-1700°K. Also, the aluminum industry calcines petroleum coke for high quality electrode carbon at 1200-1400°K and hydrated alumina to remove water at 1500°K. In the metallurgical industry, roasting of various ores, such as copper, zinc, gold, s i l v e r etc., below their fusion point to remove sulphur and arsenic and the d i r e c t reduction of iron ore are c a r r i e d out in rotary k i l n s . In the cereal industry moistened grains are steamed and cooked or conditioned in rotary k i l n s . 4 1.2 INDUSTRIAL DUSTING PROBLEMS Dusting i s an i n t e g r a l p a r t of any r o t a r y k i l n o p e r a t i o n i n which there i s d i r e c t contact between the hot combustible gases and the s o l i d m a t e r i a l . Simultaneous with the h e a t i n g of the charge, l a r g e q u a n t i t i e s of dust may be e n t r a i n e d i n t o the gas phase. T h i s dust c o n s t i t u t e s l o s t m a t e r i a l as w e l l as an environmental hazard i f e f f e c t i v e measures are not taken fo r i t s c o l l e c t i o n . Even i f c o l l e c t e d and r e c y c l e d , dust can consume heat and r e a c t a n t s and thus impose a dead load on the process. The amount of d u s t i n g i s a complex f u n c t i o n of the o p e r a t i n g c o n d i t i o n s and s o l i d s p r o p e r t i e s such as the l i n e a r gas v e l o c i t y , p a r t i c l e s i z e d i s t r i b u t i o n and s o l i d s flow p a t t e r n . Dust may be generated by a t t r i t i o n i n the s o l i d s bed or from uncombusted products i n the case of s o l i d f u e l s . Thus d u s t i n g v a r i e s from o p e r a t i o n to o p e r a t i o n . The a l l o w a b l e degree of d u s t i n g i n an o p e r a t i o n w i l l depend on such f a c t o r s as the value of the m a t e r i a l , the cost and o p e r a t i n g d i f f i c u l t i e s of dust c o l l e c t i o n equipment and the e f f e c t of f i n e s on both gas-phase r a d i a t i o n and s o l i d s bed behaviour. In an attempt to assess the extent of d u s t i n g i n v a r i o u s o p e r a t i o n s , a survey of k i l n users i n the pulp and paper, cement and s t e e l i n d u s t r i e s i n Canada and a few i n 5 the United States and elsewhere was ca r r i e d out. The results are tabulated in Table 1.1. The actual names of operations have been replaced by codes to comply with requests for c o n f i d e n t i a l i t y . The dust i s removed customarily in cyclone c o l l e c t o r s but for expensive materials and extremely fine p a r t i c l e s , e l e c t r o s t a t i c p r e c i p i t a t o r s or bag c o l l e c t o r s may be employed either independently or in conjunction with the cyclone. Cement k i l n s usually employ e l e c t r o s t a t i c p r e c i p i t a t o r s while lime kilns use wet scrubbers often with cyclone c o l l e c t o r s . The c o l l e c t e d dust may be recycled into the process or as in iron ore roasting and reduction k i l n s , dumped as waste. Gas v e l o c i t i e s at the k i l n e x i t range from 2m/s to as high as 23.3m/s but the flow Reynolds number based on t h i s velocity in a l l the kilns surveyed i s of the order of 1x10 s. A t t r i t i o n in the so l i d s bed was found to be one of the underlying causes of dusting. For example in Operation #28,a feed material of 16 to 37.5 mm generated dusts a l l of which passed 53M. Most k i l n s also have internals ( t r e f o i l s , chain, l i f t e r s , dams and mixers) that serve to improve contact between hot gases and s o l i d p a r t i c l e s for improved heat transfer but may increase dust losses. Due to the varied sources, k i l n sizes and operations the re s u l t s of the survey did not point strongly to s i g n i f i c a n t e f f e c t s of operating variables. However there were suggestions of the influence of operating and material variables such as gas v e l o c i t i e s , 6 Table 1.1 Survey of I n d u s t r i a l K i l n O p e r a t i n g C o n d i t i o n s Operat i on Feed Material K i l n Entrained Dust Type S ize mesh(%) Rate t/day S i ze m L/D Internals Speed Slope Ret. Solids Fuel Exit gas time Loading velocity rpm deg hr % m/s Rex 10-5 Dust t/day Dust Dust Size Loading Kg/m3 (%feed) mesh(%) Or i g i n Col 1ect ing Equipment Ul t imate Use 1CSL 2CL 3CM 4CL0 5CNS 6CSM 7LSM 8LPG 9LMB 10LMB 1 1LPA 12LS 13LI 14LM 15L8R 16LS 17LGL 18LGL cement mix +170(22) cement mix -75(90) cement mix -200(81) Cement mix -200(66) cement mix -200(13) cement mix -75(82) limestone -200(60) 1imemud 1imemud 1imemud 1Imemud 1imemud 1Imemud limestone 37.5-53 1imestone 9.5-25 limestone 12.5-45 11memud 1Imemud 7505 12O0 2256 4262 768 3600 1425 288.5 77 150 210 254 453 .6 3901 544 353.3 278.4 439 5. 18 3.66 3.0 4.75 4 .88 3.05 2. 13 3.2 3.2 3.33 2.9 4.3 2.7 3.05 3.05 3.5 16.7 33.3 16.7 16.7 33.3 27 .8 28.6 20.0 26.3 16.7 25.6 35.7 25.0 14.9 23.8 26.3 chains t r e f o l I s none none chains cha1ns dams cha ins chaIns cha ins t r e f o l I s 11fters m i xers trefo i1s mixers dams dams cha i ns 2.5 2.38 1.33 2.38 2.5 1.27 2.09 2.75 3 1.72 0.67 2 3.0 1.0 2 2.0 0.75 1.33 1.49 2.5 1.2 1.79 3.0 1.0 1.79 2.0 1.0 1.79 1.75 1.0 2.3 2.0 1.0 1.5 2.0 1.3 1.79 2.5 1.72 2.09 4.0 1.13 2.09 3.0 1.28 2.09 2.0 10 10 10 10 1 . 5 1 .5 2.09 2.2 1.79 3.0 coal coal/gas bunker C coal/gas bunter C coal/gas coal/fjas gas bunker C bunker C gas bunker C gas coal coal gas gas gas 16.00 8.38 23.4 4.4 8.6 2.49 2. 15 4.4 1 .88 3.5 2. 1 6. 1 6.4 4. 17 3.5 2. 1 2.65 4. 13 1.5 4.6 0.84 2.05 3.44 1 .40 1 .74 1 . 17 2.37 1 .48 3.74 3.68 1 .04 0.5 1 . 33 1 .97 516.5 503.2 916.2 136 . 3 4.00 10.7 11.8 75.75 90. 7 254 25.83 3.8 10 20 0.053 0.08 0.07 0.03 O.OOI 0.008 0.009 0.032 0.026 0.053 0.012 0.002 0.02 0.022 6.9 11.8 25.5 9.6 1 .4 14.0 7.8 36 .0 -75(90) -200(99) -75(95) -200(91) 20.0 6.5 4.8 -200(80) 1.08 -200(88) 3.6 4 . 6 5 (98) 5 (98) feed a t t r l t I o n feed a t t r i t ion feed feed feed a t t r i t i o n feed feed feed feed feed feed feed fue1.feed a t t r i t i o n feed feed elec./prec. elec./prec. cyclone elec./prec. elec./prec. elec./prec. elec./prec. elec./prec. elec./prec. scubber scrubber elec./prec. spray chamb. scrubber spray chamb. scrubber baghouse f a b r I c / f i I t e r elec./prec. cyclone elec./prec. scrubber peabody scrubber recycled 90% recycle 10% waste recycle was te recycle waste 15% recycle 85% waste recycle recycle recycle recycle recycle recycle recycle recycle recycIed waste waste waste recuc1e recyc1e Operat io h Feed Mater ial K i l n Entrained Dust Type Size Rate 5 fze L/D Interna 1 s Speed S1 ope Ret. Sol ids Fuel Exit gas Rex10-5 Dust Oust Dust Size Or ig in Co l lect ing Ult imate 11me Loading ve loc i t y Loading Equipment Use mesh(%) t/day m rpm deg hr m/s t/day Kg/m3 (%feed) mesh(%) mm* mm mm-mm 19LT 1imeraud - 545 3 .35 25 .0 cha ins 1 .07 2.09 3.0 - bunker C 3.3 1 . 111 11 .65 0.005 2.14 - feed venturi scrubber recyc le 20LW 11metnud - 393 3 .66 27 .O cha ins 1.8 1.79 - - gas 6.5 2. 19 59.0 0.001 15.0 - feed ventur1 recyc le scubber 21LH 1Imestone 25-75 16-31.5 335 2 .44 16 .7 dams 11fters mixers 1 .0 1.79 2.5 bunker C 4.5 1 .01 cyclone waste 22LW 1imestone 12.5(67) 145. 1 2 .74 20 . 0 cha ins 1.3 2. 38 3 .0 - bunker C 3.2 0 .82 13.0 O.O08 9 . 0 - at t r i t ion scrubber recyc le 23LE 1imemud - 453.5 3 .2 25 .0 dams 1.5. 1 .79 3.5 - gas 6.6 1 .95 - - - - - scrubber waste 24LBS 1imestone 4 . 7 5 - 9 . 5 295.6 2 . 1 27 .8 none 1 .25 2.09 2.5 10 coal 4.5 0 .86 9.75 0.008 3 .3 -300(100) feed/burner attr11 ion baghouse waste 25L8S 1imestone 9 .5 -16 433.5 2 . 1 32 .3 none 1 .25 2.09 3.0 10 coal 6.5 1 .27 14.29 0.01 3 .3 -300(100) feed/burner a t t r i t i o n baghouse waste 26LBS 1imestone 4 . 7 5 - 9 . 5 295.6 2 . 1 27 .8 mixers 1 .25 2 .09 2.5 10 coal 4.5 0 .86 9.75 0.008 3 .3 -300(100) feed/burner a t t r i t ion baghouse waste 27LBS 1Imestone 9 . 5 - 1 6 . 0 433.5 2 1 32 .3 none 1.25 2.09 3.0 10 coal 6.5 1 .27 14.29 0.01 3 .3 -300(1O0) feed/burner a t t r i t ion baghouse waste 28LBS ]imestone 16-37.5 640.5 3 5 35 7 heat exchaner 1 .25 2.38 3.5 10 coal 5.67 1 .73 32.42 O.008 5. 1 -300(100) feed/burner a t t r i t i o n baghouse waste 29LS8 1Imestone 19-53 540 2 74 16 7 dams 1. 13 3 .0 3 .0 15 gas 10.66 1 .46 27 .0 0.011 22.0 -30(100) a t t r i t i o n cyclone scrubber waste 30LSB 1imestone 19-53 540 2 74 16 7 dams t r e f o i 1 s 1. 17 3 .0 3 .0 15 gas 10.66 1 46 27.0 0.011 22.0 -30(100) a t t r i t ion cyclone scrubber waste 31LSB calc ium carbonate 19-50 720 3. 35 12 5 none 1 .O 1 .79 2.0 10/20 coal/oi I 8.8 1 48 24 .0 0.004 3 .3 -200(80) fed/burner at t r11 ion cyclone scubber waste 32LSB calc ium carbonate 19-37.5 470.4 3. 05 11 . 1 dams mixers 0.9 2.09 2.5 13 coal/gas 3.9 2 43 ~ - -200(90) burner a t t r i t ion eye 1 one scrubber ac id/neut . 33L5B ca1c i um carbonate 12.5-50 960 3. 35 14. 3 1 i f t e r s 1.6 1 .79 2.0 5 coal 3.7 2 58 48 .0 0.017 5 .0 feed/burner a t t r i t i o n cyclone scrubber waste 34LSB calc ium carbonate 9 . 5 - 5 0 600 2. 74 14. 9 t r e f o i1s dams 1 .08 - 2.0 10/15 bunker C 4.9 0 75 7.52 0.014 1 .3 feed at t r11 ion cyclone scrubber waste 35LSB caIciufli carbonate 9 . 5 - 5 0 800 2. 74 14. 9 m i xers dams 1 .67 1 .79 2.0 10/15 bunker C 7.0 1 2 1 1 .56 0.014 1 .4 feed a t t r i t ion cyclone scrubber waste 360NZ i ron sand char -45(97) 960 3. 54 21 . 3 dams 0.55 2.0 3 .0 char 5.8 2. 06 55.2 0.011 5.8 -200(87) feed sett 1ing chamber baghouse hydrocyclone recyc le waste 370NM 1ron ore 9 .5 -16 168 2. 13 2 1 . 7 dams 0.45 1 .79 6.3 12/23 gas/oi1 5. 15 0. 7 1 . 74 0.001 1 .0 -400(80) feed i sok inet i c waste 380NM i ron ore coal 6 . 3 - 3 7 . 5 166.3 2. 13 2 1. 7 dams 0.47 1 .79 7.3 15/24 coal 5.2 0. 71 10.77 0.007 6.5 -400(80) feed at tr i t ion 1sok inet1c waste 8 size d i s t r i b u t i o n , type of material and rotational speed on e l u t r i a t i o n . Nevertheless, with a rate between 1% to 36% of feed, dusting appears to be a major production constraint in k i l n operation. Dust loading in the exit gas i s higher in the cement ki l n s where the feed materials are also f i n e r . Typical values as high as 0.08 kg/m3 are recorded. Higher dust loadings are also recorded in lime k i l n s with limemud feeds than those with limestone feeds which contain r e l a t i v e l y coarser material. A t t r i t i o n seems to be a s i g n i f i c a n t factor in k i l n s that process limestone. In a p a r t i c u l a r k i l n (#14) featuring l i f t e r s in addition to other internals, dust loading was as high as those recorded in cement k i l n s . A t y p i c a l s t e e l company (#16) that provided detailed c o n f i d e n t i a l data, reported entrainment of about 3.8 tonnes/day in their 353 tonnes/day lime processing k i l n . C o l l e c t i o n equipment consists of a cyclone of 78% e f f i c i e n c y and a subsequent e l e c t r o s t a t i c p r e c i p i t a t o r of 96% e f f i c i e n c y which reduce the dust loading to 0.84 tonnes/day e x i t i n g the cyclone and to 0.035 tonnes/day ex i t i n g the p r e c i p i t a t o r . Another lime k i l n i n s t a l l a t i o n (#14) which processed as much as 3901 tonnes calcium carbonate per day generates 254 tonnes/day of dust which i s c o l l e c t e d in a 12 compartment bag house with each compartment housing 240 fiberglass bags. The expense involved in the recovery of 9 fines i s no doubt very large with regard to c a p i t a l and operational cost not to mention the energy consumed in heating and cooling recycled dust. Thus for an optimum design of a rotary k i l n i n s t a l l a t i o n , knowledge of dust entrainment i s essential in addition to the heat transfer and so l i d s residence time . A thorough investigation into the causes of dust pick-up, which involves both th e o r e t i c a l and experimental work w i l l therefore be very useful in this regard. Previous studies (1,2,3) on entrainment report widely d i f f e r e n t e f f e c t s of the primary factors such as gas v e l o c i t y , which suggests the complexity of the phenomenon. While these studies were carried out under d i f f e r e n t conditions, not a l l of the c o n t r o l l i n g factors were considered so that the results are applicable only to the k i l n tested. It has been suggested (2), for example, that variation in p a r t i c l e size d i s t r i b u t i o n may be a primary cause for the discrepancies. Thus in t h i s work, a programme of experimental investigation of the various operating and material variables has been conducted. Attention has been devoted to such factors as gas v e l o c i t y , solids bed behaviour due to changes in rotational speed and % f i l l , material type and size d i s t r i b u t i o n in an attempt to understand the physical mechanism by which fine p a r t i c l e s are picked up in the k i l n . The effect of a t t r i t i o n , gas temperature and k i l n internals 10 has not been s t u d i e d . In a d d i t i o n , an attempt has been made to model entrainment mathematically, based on the f l u i d mechanics of the system and the f a c t o r s mentioned above, to understand the mechanism of entrainment and to p r e d i c t e l u t r i a t i o n r e s u l t s i n l a r g e r k i l n s . Chapter 2 LITERATURE REVIEW 2.1 INTRODUCTION K n o w l e d g e o f t h e s o l i d s f l o w p a t t e r n i s v i t a l t o t h e u n d e r s t a n d i n g o f t h e t r a n s f e r m e c h a n i s m s t h a t o c c u r i n a r o t a r y k i l n . S o l i d p a r t i c l e s a r e s u b j e c t e d t o b o t h r a d i a l a n d a x i a l m o t i o n s t h a t c o n t r o l t h e e x t e n t t o w h i c h t h e y a r e e x p o s e d t o t h e h o t g a s e s a n d a l s o t h e i r r e s i d e n c e t i m e d i s t r i b u t i o n i n t h e k i l n . C o n s e q u e n t l y , a l l t r a n s f e r p r o c e s s e s a r e a f f e c t e d by t h e e n s u i n g m i x i n g o f s u r f a c e a n d bed p a r t i c l e s . R e s e a r c h i n t o t h e o p e r a t i o n o f r o t a r y k i l n s h a s , t h e r e f o r e , l a r g e l y i n v o l v e d t h e b e h a v i o u r o f t h e s o l i d s p e r t a i n i n g t o t h e m i x i n g , r e s i d e n c e t i m e d i s t r i b u t i o n a n d h e a t t r a n s f e r . L i t t l e work h a s b e e n r e p o r t e d on e n t r a i n m e n t a n d how i t i s r e l a t e d t o t h e o p e r a t i n g c o n d i t i o n s o f t h e k i l n . 2.2 SOLIDS FLOW PATTERNS F o r v a r y i n g r o t a t i o n a l s p e e d s , H e n e i n ( 4 ) h a s g i v e n a c o n v e n i e n t summary o f t h e modes o f t r a n s v e r s e b e d b e h a v i o u r n a m e l y , s l i p p i n g , s l u m p i n g , r o l l i n g , c a s c a d i n g , c a t a r a c t i n g a nd c e n t r i f u g i n g d e p e n d i n g on s u c h v a r i a b l e s a s k i l n d i a m e t e r , % f i l l , b e d / w a l l f r i c t i o n a n d p a r t i c l e c h a r a c t e r i s t i c s . The s l u m p i n g b e d h a s been d e s c r i b e d by 11 1 2 Z a b l o t n y ( 5 ) and P e a r c e ( 6 ) a s f o l l o w s . At v e r y low speeds, i f t h e r e i s no r e l a t i v e motion between b u l k s o l i d s and the c y l i n d e r w a l l , the bed i n c l i n a t i o n i n c r e a s e s u n t i l i t reaches the s t a t i c a n g l e of repose of the s o l i d s , 0 S,whereupon a segment i s deta c h e d from the upper p a r t of the bed and slumps t o the lower e x t r e m i t y . The f i n a l bed i n c l i n a t i o n , BOC(Figure 2.1), i s lower than the s t a t i c a n g l e of repose i n which case no slumping o c c u r s u n t i l the s t a t i c a ngle i s reached a g a i n , and the p r o c e s s r e p e a t s i t s e l f . The segment of s o l i d s AOB i s d e f i n e d by a s h e a r i n g a n g l e , <j>,which has a v a l u e of 12-15° ( 5 ) . The slum p i n g f r e q u e n c y has been obse r v e d t o depend on the p h y s i c a l p r o p e r t i e s of the s o l i d s ( 5 , 7 ) and t o i n c r e a s e w i t h i n c r e a s i n g r o t a t i o n a l s p e e d ( 6 , 7 ) . T r a n s v e r s e m i x i n g i n slumping beds t a k e s p l a c e o n l y i n the slumping m a t e r i a l . I n the b u l k of the bed t h e p a r t i c l e s remain i n f i x e d c i r c u l a r t r a j e c t o r i e s . At s l i g h t l y h i g h e r r o t a t i o n a l speeds the bed e x h i b i t s a c o n t i n u o u s r o l l i n g a c t i o n . The s h e a r i n g a n g l e d i m i n i s h e s t o ze r o and a c o n t i n u o u s s o l i d s motion r e p l a c e s the p e r i o d i c s l u m p i n g . I n t h i s mode, F i g u r e 2.1, the b u l k of the s o l i d s remain i n f i x e d t r a j e c t o r i e s i n the bed, and the moving l a y e r , f e d c o n t i n u a l l y from t h e upper edge of the bed assumes a c o n s t a n t a n g l e of i n c l i n a t i o n . W i t h i n c r e a s e d r o t a t i o n a l speed, an advanced s t a g e of r o l l i n g r e f e r r e d t o as c a s c a d i n g , i s o b s e r v e d . Then, t h e s o l i d s i n the upper edge of the bed d e t a c h a t a h i g h e r e l e v a t i o n ( i n the t o p 1 3 S l u m p i n g 1 R o l l i n g 2 C a s c a d i n g 3 C a f a r a c f i n g 4 Centr i fuging Figure 2.1.Types of p a r t i c l e motion in rotary kilns(5,8) 1 4 q u a d r a n t ) such t h a t the c r o s s - s e c t i o n of the bed assumes the t y p i c a l c r e s c e n t or kid n e y shape. R u t g e r s ( 8 ) has d e s c r i b e d m i x i n g i n c a s c a d i n g beds t o be r e s t r i c t e d t o the t h i n moving l a y e r of s o l i d s on the bed s u r f a c e below which t h e r e i s a st a g n a n t c o r e of p a r t i c l e s . In the l a r g e r l ower p a r t of the bed below t h i s c o r e , p a r t i c l e s move i n f i x e d t r a j e c t o r i e s . C a r l e y - M a c a u l y and D o n a l d O ) regard e d the s o l i d s bed as composed of two r e g i o n s , an a c t i v e t o p l a y e r and a lower p a s s i v e r e g i o n . Here a g a i n , s o l i d s e n t e r t h e a c t i v e r e g i o n i n the upper p a r t of the bed where m i x i n g o c c u r s and l e a v e a t the lower p a r t i n t o the p a s s i v e r e g i o n where they move i n f i x e d t r a j e c t o r i e s . S l i p p i n g o c c u r s a t v e r y low % f i l l s or when the c y l i n d e r w a l l i s smooth and the s o l i d s have a h i g h i n t e r n a l burden f r i c t i o n . In one form of s l i p p i n g ( 8 ) , the whole bed, a f t e r a t t a i n i n g an i n c l i n a t i o n lower than the s o l i d s a n g l e of r e p o s e , s l i p s down a g a i n s t the c y l i n d e r w a l l coming t o r e s t a t a much lower i n c l i n a t i o n . The p r o c e s s r e p e a t s i t s e l f i n an o s c i l l a t o r y type of motion. L i t t l e m i x i n g of s o l i d s o c c u r s i n s l i p p i n g b e d s ( 8 , l 0 ) . C a t a r a c t i n g and c e n t i f u g i n g which i n v o l v e e r r a t i c bed b e h a v i o u r a r e n o r m a l l y not found i n r o t a r y k i l n o p e r a t i o n . With such d i v e r s e b e h a v i o u r p a t t e r n s , v a r i o u s s t u d i e s have been d i r e c t e d a t c h a r a c t e r i s i n g and measuring p e c u l i a r a s p e c t s of the bed b e h a v i o u r and r e l a t i n g them t o m a t e r i a l or o p e r a t i n g v a r i a b l e s i n a b i d t o p r e d i c t the b e h a v i o u r of the bed and i t s e f f e c t on any p r o c e s s . Such measurements as 15 the slumping frequency, the thickness of the active r o l l i n g layer, the residence time of p a r t i c l e s on the surface of the bed and the conditions under which bed behaviour changes from slumping to rolling(5,6,7,8,11,12) have been reported in the past often with contradictory results because of limited experimental data. The most recent and thorough of these investigations(7) reported measurements that confirmed that the slumping frequency increases with ro t a t i o n a l speed and i s dependent on p a r t i c l e properties (shape and size) and that the active layer thickness in a r o l l i n g bed increases with rotational speed. In addition, the studies demonstrated that the d i f f e r e n t modes of bed motion can be conveniently delineated on a bed behaviour diagram which i s a plot of bed depth versus rotational speed. Studies on the characterisation of the mixing of solids have reported a x i a l dispersion coefficients(8,13,14) which suggest that the solids t r a v e l e s s e n t i a l l y in a plug flow manner. Transverse mixing on the other hand has been shown(12,15,16,17) to be at least two orders of magnitude faster than a x i a l mixing. Dust generation w i l l be expected to accelerate with rot a t i o n a l speed. Increased slumping frequency and r o l l i n g w i l l generate vigorous p a r t i c l e mixing at the surface of the bed and t h i s w i l l be expected to increase the tendency for the p a r t i c l e to be projected into the gas phase. 16 2.3 SOLIDS SEGREGATION PATTERNS In a m u l t i p a r t i c l e feed consisting of solids with d i f f e r e n t s i z e , shape or density, segregation has been observed to occur in various patterns as shown in Figure 2.2 (8,14,17,18,19). In one form, r a d i a l segregation, smaller or denser p a r t i c l e s concentrate in a horizontal core in the bed whereas in banding segregation, alternate bands of coarse and f i n e , or l i g h t and heavy p a r t i c l e s , form along the axis of the cylinder. The t h i r d type, end longitudinal, occurs when the finer or denser p a r t i c l e s form two end bands at the end walls leaving the coarse or l i g h t e r solids in the center. Of the three mechanisms of segregation - percolation, flow and vibration (18,20,21) - percolation(22) appears to be the predominant mechanism by which segregation occurs in rotary cylinders. According to Donald and Roseman(18,20) th i s i s true as long as the average coarse-to-fine size r a t i o i s greater than 1.2 in which case r a d i a l segregation obtains. The type of a x i a l segregation that occurs w i l l depend on the angle of repose of the components of the mixture. Banding segregation is observed when the angle of repose of the smaller sized component i s greater than that of the coarse; otherwise, end longitudinal segregation i s found. Henein et al(22) have observed that while the presence of fines a f f e c t s the bed behaviour patterns, the 1 7 (I) Radial (II) Banding longitudinal Y//A y/A (111) End longitudinal Coarser or lighter solids Finer or denser solids F i g u r e 2.2.Types of s e g r e g a t i o n p a t t e r n s i n r o t a r y c y l i n d e r s ( 1 8 ) 18 flow c h a r a c t e r i s t i c s of the bed such as the s t a t i c angle of repose, shear angle and slumping frequency or the dynamic angle of repose and the active layer thickness are not s i g n i f i c a n t l y affected. They also confirmed that although most fines appear in the central core, the composition of the core was such that the solids adopt a r a d i a l configuration that minimises the t o t a l core volume. A second segregation of fines also occurred at the apex of the bed near the wall. These fine s , unable to r o l l down the bed as do the coarse p a r t i c l e s , percolate down the cylinder wall. They could e a s i l y f i l l wall imperfections and consequently be compacted into place by bed weight. The experiments of Henein et al were made over r e l a t i v e l y short periods of time to ensure that only r a d i a l segregation, which occurs from 2 to 4 orders of magnitude faster than a x i a l segregation(17,20), occurred. In i n d u s t r i a l k i l n s , those fines associated with the central core would be least exposed to the freeboard and thus would turn up as p a r t i a l l y reacted products. Fines in the second segregation core are better exposed to the freeboard by the action of the rotating wall and thus are more l i k e l y to be entrained. 19 2.4 MECHANICS OF ENTRAINMENT 2.4.1 THRESHOLD OF PARTICLE MOVEMENT The mechanism by which par t i c u l a t e materials are entrained from surfaces consisting of loosely packed grains by a flowing f l u i d i s complicated owing to the nature of the hydrodynamic forces which a r i s e from the interactions between the grains and the f l u i d that l i f t s the p a r t i c l e s . F l u i d forces can be i d e n t i f i e d as shear, l i f t and a combination of these due to the turbulent eddies. In any turbulent shear flow past a plane s o l i d boundary three major flow regimes - the viscous sublayer, the turbulence-generation layer, or buffer layer and the outer region or core-region - can be recognised. The viscous sublayer i s the viscosity-dominated flow adjacent to the boundary. Next to t h i s i s the buffer layer in which very energetic small scale turbulence i s generated by i n s t a b i l i t y of the strongly sheared f l u i d . The broad region outside the turbulence-generation zone, the core region, occupies most of the flow cross-section. The large size turbulence eddies here are more e f f i c i e n t at transporting momentum normal to the flow d i r e c t i o n than the smaller eddies nearer to the boundary. For a bed of p a r t i c l e s subjected to a steady turbulent flow of f l u i d , the magnitude of the f l u i d forces acting on the grains w i l l thus depend on the flow regimes preva i l i n g at the boundary. If the grains are small compared to the size of the viscous sublayer, that i s d is such that 20 the boundary Reynolds number u rdp / t> < 5, the action of the viscous forces results in a drag which acts on the entire hydrodynamically smooth surface. For larger boundary Reynolds numbers in the range 30-70, the p a r t i c l e s protrude into the turbulence generation layer and shed eddies. The drag force becomes greater because of the contribution, in addition to skin f r i c t i o n , of form drag as a consequence of fore and a f t - pressure differences for each p a r t i c l e . However, even the viscous sublayer i s no longer regarded as laminar and steady. Studies on the c h a r a c t e r i s t i c pattern of eddy motion and eddy structure near the boundary in a turbulent shear flow past a s o l i d wall by Kline et al(23), Corino and Brodkey(24), Wallace(25) and Of fine and Kline(26) have shown that turbulent flow involves a quasi-deterministic pattern of movements of f l u i d parcels in a process c a l l e d bursting. Thus the surface layers of the s o l i d bed of granular p a r t i c l e s would be subjected to f l u i d forces which are randomly varying in time and space. P a r t i c l e s may be moved by the drag exerted by a passing eddy or by hydrostatic pressure r e s u l t i n g from the unequal v e l o c i t y d i s t r i b u t i o n caused by the eddy or mean flow. For a bed of cohesionless particles(where adhesion forces are n e g l i g i b l e ) , the component of gravity force r e s i s t i n g entrainment w i l l vary depending on the l o c a l packing that determines the d i r e c t i o n of easiest movement. Thus there i s no c r i t i c a l stage at which bed p a r t i c l e s are 21 suddenly placed in motion en masse. Grass(27) reported that grain movement took place only when the d i s t i n c t l y random d i s t r i b u t i o n of shear stresses due to f l u i d flow overlaps with the d i s t r i b u t i o n of c r i t i c a l shear stresses of the bed p a r t i c l e s . Early t h e o r e t i c a l analysis(28,29) assumed that the average grain w i l l start to move when the f l u i d forces are strong enough to just rotate the grain about the pivot produced by grains lying beneath i t , in the downstream d i r e c t i o n . Thus the c r i t e r i o n for the threshold conditions were derived based on the equality of opposing moments of the average tangential drag force and the r e s i s t i v e g r a v i t a t i o n a l force(see Appendix B) as —2- =H (2.1) ?s dp where 0 is a function of the boundary Reynolds number and p a r t i c l e geometry. Thus, p a r t i c l e entrainment i s a function of both the temporal mean drag, or the shear v e l o c i t y , rather than of the average v e l o c i t y and of the intensity of turbulence that acts to agitate the p a r t i c l e s , putting them into suspension or reducing t h e i r c r i t i c a l shear stress. On an i n c l i n e d bed, as in a rotary cylinder, the threshold conditions can be shown to s a t i s f y Equation 2.1 above.(Appendix B) 22 2.4.2 TRANSPORT OF PARTICLES Above the c r i t i c a l shear, p a r t i c l e s are transported in three major modes depending on their size and the flow strength: s a l t a t i o n , in which the p a r t i c l e s ejected from the surface f a i l to go into suspension but move in d i s t i n c t t r a j e c t o r i e s under the influence of a i r resistance and gravity that returns them into the bed, either to rebound on s t r i k i n g the surface or to embed themselves in i t and eject other particles;suspension flow, in which small p a r t i c l e s are held in suspension by the v e r t i c a l component of turbulent eddies and; surface creep, involving p a r t i c l e s that r o l l or s l i d e on the surface of the bed under the influence of f l u i d drag or impact of returning p a r t i c l e s . These have been the results of early experimental observations in wind tunnels by Bagnold(28), Chepil(30) and Zingg(31). The r e l a t i v e proportions of the material that move in these respective modes depend on the c h a r a c t e r i s t i c s of the bed material and on the hydrodynamic regimes pr e v a i l i n g at the flow boundary. A substantial fraction(28) of the moveable material i s usually transported as bed load( p a r t i c l e s in s a l t a t i o n and surface creep) in beds composed of naturally occurring aggregates. However, the nature of the forces acting on the bed and how t h i s a f f e c t s p a r t i c l e pick up above the threshold, is s t i l l unclear. Measurements of the ve l o c i t y p r o f i l e above 23 the s a l t a t i o n layer in wind tunnels(28,31,32,33) reveal a logarithmic velocity d i s t r i b u t i o n of the form = 5.751og - +C0 (2.2) U T k 0 where k is roughly the height of the s a l t a t i o n layer. It follows, by analogy with the aerodynamic behaviour of s o l i d roughness that the s a l t a t i o n layer behaves as an aerodynamic roughness of height proportional to the thickness of the layer(34). In their motion r e l a t i v e to the flow, the s a l t a t i n g p a r t i c l e s offer resistance to the flow and shed wakes which are introduced into the main flow. The t o t a l shear stress exerted on the s t a t i c bed might, therefore, be expected to depend on the nature of the interaction between the f l u i d and the s a l t a t i n g p a r t i c l e s . Bagnold(28) recognised two d i f f e r e n t situations, the f l u i d threshold (as discussed in Section 2.4.1), which i s the condition under which grain movement i s f i r s t detectable on an i n i t i a l l y stationary surface and the impact threshold, which i s the condition under which s a l t a t i o n , o r i g i n a l l y in progress, would just be maintained. His measurements and those of Chepil(35) indicate the value, |3, a measure of the ra t i o of the hydrodynamic stress to p a r t i c l e s p e c i f i c weight, to be _ 2 of the order 10 at the f l u i d threshold. At the impact threshold, they found |3, a slowly varying function of the boundary Reynolds number, to be smaller, with a value of 0.0064. They attributed the difference to be the effect of 24 the impact of p a r t i c l e s returning from s a l t a t i o n . However, turbulent fluctuations in both pressure and skin f r i c t i o n , also might be present. Consequently, theories of sediment transport have been based on two d i f f e r e n t viewpoints. The b a l l i s t i c models favoured by Bagnold(28,34,36,37,38) assume the impact of s a l t a t i n g p a r t i c l e s to be the c o n t r o l l i n g factor in entrainment and transport. Here, once s a l t a t i o n has begun, the transfer of momentum from the free stream to the s t a t i c bed is acomplished by c o l l i s i o n of returning p a r t i c l e s with bed surface p a r t i c l e s . On the other hand, the f l u i d l i f t models(39,40,41) assume the f l u i d l i f t and drag to be the c o n t r o l l i n g forces. The e f f e c t of impacting p a r t i c l e s i s regarded as constituting a stress component on the bed. Above the f l u i d threshold, the aerodynamic forces are capable of projecting p a r t i c l e s into the f l u i d , the effect of p a r t i c l e impact serving only to increase the l i f t c o e f f i c i e n t . Thus correction factors were introduced(39), for instance, to account for grain impact in Einstein's(41) stochastic bed load function based on f l u i d l i f t alone. Consequently, several formulae have been proposed for the rate of transport of bed load p a r t i c l e s (28,34,36,37,38,39,41,42). Notable among these are the transport theory of Bagnold(28,36,37). He developed his theory based on the notion that the rate of work done in transporting the p a r t i c l e s i s equal to the "input power" 25 from the flow times an e f f i c i e n c y factor. P a r t i c l e s in sa l t a t i o n receive horizontal impulse from the f l u i d flow which they transfer to the bed on impact to eject other p a r t i c l e s . Bagnold assumed the transformation of t h i s f l u i d thrust to be accomplished by a mechanism similar to that acting between s o l i d surfaces s l i d i n g past each other and thus expressed the f l u i d thrust in terms of the submerged weight of the p a r t i c l e and the tangent of the angle of f r i c t i o n or f r i c t i o n c o e f f i c i e n t . For the weight of p a r t i c l e s M moving over a unit area of bed, the mean reactive stress acting on the bed, thus, w i l l be: f x = M tana (2.2) and consequently the rate of work i s f v T J = MU tana (2.3) Hence the energy statement becomes R = MU = f u( — E _ ) (2.4) & P x Utana i e . transport rate per unit bed width = available power times e f f i c i e n c y . The necessary consequence of t h i s model i s that the f l u i d borne shear stress exerted on the bed i s n e g l i g i b l e , f a l l i n g below the value at the threshold where no s a l t a t i o n can be sustained. Owen(34) and Yalin(42) had 26 recognised t h i s and introduced the impact threshold as a li m i t i n g condition for the control of p a r t i c l e concentration in their s a l t a t i o n models. However, their assumptions of the i n i t i a l p a r t i c l e s a l t a t i o n v e l o c i t y and f l u i d flow in the sal t a t i o n layer, which are not in agreement, have not received much recognition. Other sediment transport models have been discussed by Yalin(43) and Raudkivi(44) which indicate a general T dependence of entrainment on the factor, — — , or the . . 7 s d p f r i c t i o n v e l o c i t y . Suspension i s an advanced stage of p a r t i c l e movement which occurs when the root mean square of the v e r t i c a l component of turbulence is approximately equal to the p a r t i c l e s e t t l i n g v e l o c i t y . Various models also have been proposed as discussed by Yalin(43) and Raudkivi(44) to describe the d i s t r i b u t i o n of p a r t i c l e s in suspension based on the concept of d i f f u s i o n , energy considerations and on a s t a t i s t i c a l mechanics approach. The di f f u s i o n approach which has received much attention assumes that turbulent agitation i s s u f f i c i e n t to disperse p a r t i c l e s that d r i f t downward under the action of gravity. Early treatment by Rouse(45) showed the p a r t i c l e d i s t r i b u t i o n to be dependent on the factor, Ut/UTj3/<=Z. Since /3=1 as assumed by Rouse, and K=0.4, then Ut/Ur=1 corresponding to Z=2.5 i s the l i m i t above which suspension would be concentrated in a zone very close to the 27 bed. The condition Ut/UT<1 has been confirmed a n a l y t i c a l l y by Sumer(46) and experimentally by Francis(47) as the c r i t e r i o n for suspension to occur. Thus, while a s a t i s f a c t o r y a n a l y t i c a l approach to entrainment has not been achieved, the significance of the shear v e l o c i t y , which i s a measure of the shear stress and the turbulence intensity, i s c l e a r . 2.5 ENTRAINMENT IN ROTARY KILNS Very l i t t l e has been done on the entrainment of fines in rotary k i l n s . Friedman and Marshall(48) pioneered an extensive experimental study on dusting in rotary dryers equipped with f l i g h t s but could not develop a general cor r e l a t i o n c i t i n g the complexity of the process as a cause. Khodorov(1) analysed the dynamics of entrainment by dimensional analysis and the application of the Bernoulli Equation and continuity equation to the turbulent eddies that hold the p a r t i c l e s in suspension. He i d e n t i f i e d the flow Froude group, U /(gD), the dimensionless s e t t l i n g v e l o c i t y , Ut/U, and n 0, a size d i s t r i b u t i o n parameter, as factors a f f e c t i n g entrainment at constant rotational speed and holdup. Assuming a Stokes' regime s e t t l i n g , he replaced d ^ g p the v e l o c i t y group by —£ 2 a n d 28 obtained from experiments, a functional r e l a t i o n s h i p of the form K U V/ 2 PD 5/ 4( 1 - X ) r s „ 3/2,3n ( 2 - 5 ) Pp d p n 0 This equation might not adequately predict entrainment since i t does not account for p a r t i c l e s in s a l t a t i o n . Li(2) considered the rate of entrainment to be made up of a fines a v a i l a b i l i t y function, ND/V, and a f l u i d dynamic function f ( n 0 , U t u ) I e , in a general entrainment equation of the form L r s = KLN/Vr^f(n 0,u t,u ) I edL (2.6) In the physical model of L i , leading to the a v a i l a b i l i t y function, most of the fines that percolate through the coarse bed are assumed to s e t t l e f i n a l l y on coarse p a r t i c l e s that form the bottom layer of the bed such that the eventual cascading at the upper edge of t h i s bottom layer exposes the fines to the freeboard. Assuming the f l u i d dynamic function to be equivalent to Khodorov's model, Li(3) obtained a combined entrainment equation in which he introduced a factor to account for the fact that gas ve l o c i t y influences entrainment in a manner dependent on fines concentration. However, from experimental tests in a petroleum coke ca l c i n e r , L i obtained an empirical correlation in which not only the re l a t i o n between r g and U d i f f e r e d from that of Khodorov, but also the f l u i d dynamic function was made up 29 e s s e n t i a l l y of a function of gas Reynold's number and p a r t i c l e terminal v e l o c i t y . The Li c o r r e l a t i o n showed r g a U^'^. From the results of the work of Friedman and Marshall (48), L i (3) pointed out that the entrainment rate did not always follow Khodorov's 4th power r e l a t i o n with the gas v e l o c i t y . Since the concentration of entrainable fines is dependent on both the size d i s t r i b u t i o n of the feed material and the gas velocity, the power rel a t i o n of entrainment rate to the gas v e l o c i t y w i l l vary with the size d i s t r i b u t i o n of the feed material. The petroleum coke of L i , on a cumulative weight percentage-logarithmic plot, i s characterised by a slope of 0.7 as compared to that of Khodorov's sand of 7.7, hence the smaller exponent (0.5) for his entrainment r e l a t i o n with gas v e l o c i t y . Miller(49) has recently reported values of the v e l o c i t y exponents between 2.97 and 1.23 for materials of size d i s t r i b u t i o n characterised by slopes ranging from 4.55 to 3.15 in that order. The behaviour of the bed as the r o t a t i o n a l speed i s increased and the solids motion changes through slumping, r o l l i n g and cascading, might be expected to a f f e c t the manner in which p a r t i c l e s are picked up over the entire bed surface. The edge entrainment model of L i which was coupled with Khodrov's suspension model cannot adequately describe the o v e r a l l dusting process. Furthermore, for multi-sized p a r t i c l e s material, d i f f e r e n t types of segregation patterns (Section 1.3) might play an important role and the effect of 30 fines concentration on bed behaviour could complicate matters. Thus, further experiments to investigate the basic mechanism of entrainment in rotary kilns and the effect of fines concentration and i t s attendant segregation problems as well as bed behaviour are desirable. The dependence of entrainment on flow Reynolds number(3) or flow Froude number(1) is not consistent with other studies of a related phenomenon of sediment transport(Section 1.4). It i s believed that the c h a r a c t e r i s t i c s of the r e l a t i v e motion of grains in a f l u i d are more s i g n i f i c a n t than the c h a r a c t e r i s t i c s of the f l u i d flow. Thus the e f f e c t of p a r t i c l e Reynolds number and or Froude number must be considered. Chapter 3 SCOPE OF PRESENT WORK The objective of t h i s work has been to conduct a systematic experimental programme that i s currently lacking in the l i t e r a t u r e , to study the fundamental factors that influence entrainment. Owing to the complex nature of the problem, i n i t i a l work was confined to s i m p l i f i e d conditions that w i l l enable the basic understanding of the mechanisms operating. Subsequently, based on the success of t h i s mechanism, more complex situations were to be investigated to offer an improved understanding of the various aspects of the problem due to the diverse conditions of rotary k i l n operation as evidenced in Table 1.1. For t h i s study, an unheated model k i l n with no internals was used. However the flow Reynolds number was such that flow patterns were similar to those of i n d u s t r i a l rotary k i l n s . The f i r s t part of the experiments involved solids of narrow size d i s t r i b u t i o n to eliminate the e f f e c t of segregation patterns. Emphasis was placed on the influence of gas v e l o c i t y , bed behaviour due to changes in rotational speed and the degree of f i l l of the so l i d s charge on the rate of e l u t r i a t i o n . The second part of the study focussed on beds composed of p a r t i c l e s of various sizes to examine the effect of fines concentration and segregation patterns. 31 32 In order to interpret the re s u l t s of the experiments e f f e c t i v e l y , for p r a c t i c a l applications and design purposes, an attempt was made to model the system mathematically from a mechanistic point of view and to develop scale-up c r i t e r i a for i n d u s t r i a l applications. Chapter 4 EXPERIMENTAL APPARATUS AND MATERIALS 4.1 APPARATUS A schematic representation of the experimental apparatus used to make measurements of the e l u t r i a t i o n process i s shown in Figure 4.1. A p i c t o r i a l view also can be seen in Figure 4.2. The system consisted primarily of two major sections, a rotating steel cylinder and a cyclone dust c o l l e c t i o n unit. It has been designed for batch operation to avoid the large quantities of materials that would be required for continuous operation. Also, the d i f f i c u l t y involved in measurements made in a continuous feeding where bed p a r t i c l e segregation cannot be controlled i s not encountered under batch conditions. 4.1.1 ROTATING CYLINDER The rotating cylinder was constructed of seamless, cold-drawn mild steel pipe of 0.203m inside diameter and 2.44 m length made up of three segments of 0.914 m, 0.61 m and 0.914 m length respectively. These segments were held together by metal rings (5 x 1.9 cm) and set screws. This arrangement was intended for easy variation of the cylinder length by removal of a segment and also easy access to the inner wall to roughen the surface. The L/D r a t i o of 12 is 33 A Anemometer B Blower C Cyclone D- D u s i hopper E Exit end box F Filler H Honeycomb HP SP 1 Hot film probe Sampling probe Inlet end box K Rotating cylinder 0 Orifice plate R Rotameter K V Vocuum pump Figure 4.1 Schematic diagram of experimental apparatus. THE QUALITY OF THIS MICROFICHE IS HEAVILY DEPENDENT UPON THE QUALITY OF THE THESIS SUBMITTED FOR MICROFILMING. UNFORTUNATELY THE COLOURED ILLUSTRATIONS OF THIS THESIS CAN ONLY YIELD DIFFERENT TONES OF GREY. LA QUALITE DE CETTE MICROFICHE DEPEND GRANDEMENT DE LA QUALITE DE LA THESES SOUMISE AU MICROFILMAGE. MALHEUREUSEMENT, LES DIFFERENTES ILLUSTRATIONS EN COULEURS DE CETTE THESES NE PEUVENT DONNER QUE DES TEINTES DE GRIS. Figure 4.2: Photograph of apparatus and probe locations. 36 s l i g h t l y shorter than most i n d u s t r i a l k i l n s . The rotating cylinder f i t s into two end boxes of d i f f e r e n t design (see Figure 4.3) sealed with graphite packing to a clearance of about 0.8mm. The end box at the gas i n l e t was constructed of a 0.23 m diameter by 0.15 m length s t e e l cylinder. This was f i t t e d with a honeycomb packing composed of hexagonal c e l l s 10 cm long made from 0.15 mm walled hexagonal tubes with 10 mm p i t c h . The honeycomb served to streamline the intake a i r maintaining the d i r e c t i o n of flow p a r a l l e l to the cylinder axis and also to break up any unexpected large eddies that might reach the intake. The a i r outlet end box was constructed from perspex material of 0.348 m diameter and 0.17 m length with a dusty a i r bottom take-off pipe of 0.102 m diameter. Both end boxes were equipped with dams of various sizes and shapes to retain the s o l i d s at various loadings. As shown in Figure 4.4 the ring plates were designed with outside diameters equal to that of the cylinder to enable dir e c t attachment to i t . The f l a t dams were shaped to the same form as the cross-section of the bed. To avoid s o l i d s s p i l l a g e they were made bigger to provide extra height (1.0-1.5 cm) above the bed. The plates of various sizes depending on the degree of f i l l , were held stationary in the flange arrangement in the end boxes and their faces padded with foam material to seal off the s o l i d s . Conical dams, with the larger end designed to f i t Gas exit end box F i g u r e 4 . 3 : D e s i g n of end boxes . Ring dam Bent l ip dam Conical dam F i g u r e 4.4 V a r i o u s k i l n e x i t g e o m e t r i e s 39 into the inside diameter of the cylinder were also used. The included angle was 20°,10° less than that of some i n d u s t r i a l k i l n s , to ensure a smooth t r a n s i t i o n of the a i r flow from the cylinder to the truncated end of the cone whose dimensions for various degrees of f i l l are shown in Table 4.1. The conical dams f i t t e d snugly into the cylinder (Figure 4.4) and rotated with i t such that the extreme ends of the bed were held up by the slanting sides of the internal face. The la s t dam geometry was the bent l i p dam. Es s e n t i a l l y , the protruding end of the f l a t dam, discussed above, was bent over to dip into the bed thus offering l i t t l e resistance to both a i r flow and the movement of pa r t i c l e s and at the same time containing the s o l i d beds within the cylinder at a l l rotational speeds. The open end of the perspex end box was covered with a perspex plate, 0.457 m diameter and 19mm thickness designed to hold two metal probes: a sampling probe and a pitot-tube or hot f i l m probe as shown in Figure 4.3. These probes pass through holes in a s l i d e that runs through a slot cut diametrically on one side of the end plate. A s l i t , 10 mm x 50mm cut in the s l o t , permits the insertion of probes into the k i l n through the holes. The end plate can be rotated in s i t u such that the probes traverse the whole cross-sectional area of the cylinder since they can be moved diametrically as well with every motion of the s l i d e that c a r r i e s them. T a b l e 4.1 40 Dimens ions of c o n i c a l e x i t dam and c a r d b o a r d i n s e r t (cm) Con i ca1 dam I n s e r t %f i l l e 1 b a m t 5 8 . 1 5 11.40 1 1 . 60 2 .0 7. 5 2 . 0 1 0 7 .06 17.5 1 7 . 90 3 . 1 0 7. 5 2.0 1 5 6 .0 23.80 24 . 1 3 4 .20 7 . 5 2 .0 41 The cylinder s i t s on eight metal r o l l e r s supported on thrust bearings and i s driven through a chain-and-sprocket arrangement by a Graham variable-speed drive and motor of 1/2 HP. The whole assembly i s mounted on a steel-channel frame whose slope i s adjustable to a desired i n c l i n a t i o n for solids discharge. To ensure a high f r i c t i o n a l c o e f f i c i e n t between the inner walls of the cylinder and the solids bed that w i l l prevent s o l i d s slippage, the walls were roughened with some of the alumina p a r t i c l e s used in the experiment. The walls were f i r s t coated with enamel paint and, while wet, sprinkled with fine alumina. The cylinder was rotated and excess alumina was allowed to f a l l off the walls while the remainder dried on the walls with the paint. However, because of a preliminary observation of the effect of the rough wall on entrainment, a cardboard insert was provided to cover the exposed cylinder wall in some experimental runs. The tube insert, of s l i g h t l y smaller size than the cylinder, (Table 4.1), was cut open a x i a l l y such that the exposed wall of the cylinder extending from the upper edge of the bed to a location very close to the lower edge of the bed was covered and not accessible to the gas flow. The cardboard insert was supported by the stationary end boxes such that i t remained in space as the cylinder turned around i t . Its position was, however, adjustable to accommodate the changing i n c l i n a t i o n of the bed at higher rotational speeds. 42 4.1.2 DUST COLLECTION Air was pulled through the system by means of a high pressure Dayton exhaust cen t r i f u g a l blower driven by a 2HP motor through belt-and-pulley arrangements. The blower was connected to two cyclones operating in p a r a l l e l through 0.102 m diameter metal sheet duct-work such that the system operated on the open c i r c u i t , suction configuration of a wind tunnel. Air enters the k i l n by the honeycomb i n l e t , leaves by the opposite end box, through the cyclones, where i t s dust content i s removed, and into the exhaust blower. The cyclones were constructed of galvanised sheet metal, each with 0.203 m diameter, and were capable of removing dust p a r t i c l e s down to I O M ^ at 98 - 9 9 % e f f i c i e n c y discharging through a i r t i g h t connections into a common receiving hopper. 4.2 INSTRUMENTS Measurements were made through the access provided in the perspex end plate attached to the gas exit end box that permitted insertion of probes into the cylinder in a dir e c t i o n p a r a l l e l to the axis. Thus the problem of having to enter the rotating wall was avoided. However measurements were limited to short distances into the k i l n to avoid sagging of the probes. Local v e l o c i t y and dust concentration measurements were made with probes carried by the s l i d e that 43 moved diametrically in the s l o t in the end plate and whose movements were measured on graduations made on the end plate. The end plate was held in position by sp e c i a l l y designed clamps (Figure 4.3) that could be relaxed to enable i t s rotation. Thus the probes could be positioned at any location on the k i l n cross-section by a combination of tr a n s l a t i o n a l and angular motion. 4.2.1 VELOCITY MEASUREMENTS Average v e l o c i t y values were calculated from measurements made with an o r i f i c e meter with radius taps, i n s t a l l e d in the discharge l i n e of the blower. The pressure drop was measured with a water manometer. For l o c a l v e l o c i t y measurements a DISA 55A01 anemometer was used in conjunction with a special DISA 55A76 Steel Clad Probe. The usual hot-wire and hot-film probes were considered to be quite unsuitable for t h i s purpose because heat transfer from the wire or fi l m was l i k e l y to depend strongly on the presence of the s o l i d s . Fine p a r t i c l e s adhere to the wire or f i l m and are continually removed by abrasion and redeposition re s u l t i n g in appreciable fluctuations in measurements (50). In the case of the hot-wire, there is a danger of damage by p a r t i c l e s in the a i r or chance l i g h t contact with the wall. The 55A76 Probe was selected since only mean ve l o c i t y measurements were 44 needed and because of i t s robust construction as compared to the usual wire and f i l m probes. The non-directional probe, shown in Figure 4.5 i s comprised of a nickel sensor wound round a c y l i n d r i c a l former and enclosed in a s t a i n l e s s steel tube 1.1 mm dia. x 6 mm long attached with a thin layer of A r a l d i t e . As shown in Figure 4.5, the st a i n l e s s steel tube i s insulated from the 4 mm dia. x 125 mm long stai n l e s s steel support tube by a p l a s t i c section. The probe has a meter long cable ending in a demountable BNC connector that i s coupled to the 4mm probe cable of the anemometer. A special p i t o t s t a t i c tube designed to permit insertion into the k i l n in the same manner as the anemometer probe was used for c a l i b r a t i o n . The head of the pitot-tube was the e l l i p s o i d a l nose design b u i l t to B.S.I, s p e c i f i c a t i o n s . Figure 4.6 shows the detailed dimensions. The pressure drop across the pitot-tube was measured by a d i f f e r e n t i a l micro-manometer using the n u l l method and which has a s e n s i t i v i t y of 0.0051 mm of n-Butyl alcohol. 4.2.2 DUST SAMPLING Sampling of the gas phase was accomplished with the sampling probe (Figure 4.6) of 9.5mm diameter attached to a 8.0 mm steel tube that could be inserted into the k i l n Figure 4.5: DISA 55A76 steel clad hot f i l m probe. 3 mm F i g u r e 4.6: P i t o t - s t a t i c tube and s a m p l i n g p r o b e . 47 through the same l o c a t i o n as the p i t o t - t u b e employed f o r c a l i b r a t i o n and p a r a l l e l to the s t e e l c l a d probe such that the e n t i r e c r o s s - s e c t i o n of the k i l n could be t r a v e r s e d . The sampling tube c o u l d be moved at r e g u l a r i n t e r v a l s along the k i l n a x i s up to a d i s t a n c e h a l f the k i l n l e n g t h . I s o k i n e t i c sampling was ensured s i n c e l o c a l v e l o c i t i e s were measured p r i o r to sampling with the s t e e l c l a d probe. Other elements of the sampling t r a i n were a SARTORIUS GmbH i n - l i n e f i l t e r h older c o n t a i n i n g f i l t e r paper on a s i n t e r e d s t e e l holder to t r a p p a r t i c l e s , a GAST vacuum pump to draw the sample and a Matheson (605) rotameter to measure the i s o k i n e t i c sampling r a t e . 4 . 3 MATERIALS Fine alumina powder obtained from the K i t i m a t p l a n t of Alcan Canada L t d . was used f o r the bulk of the experiments. The s i z e d i s t r i b u t i o n of the alumina, as shown i n F i g u r e 4.7, was narrow compared to r o t a r y k i l n feeds and thus experiments i n v o l v i n g alumina alone were regarded as a one component system. As w i l l be shown the d i s t r i b u t i o n was s u f f i c i e n t l y narrow that there was no d i f f e r e n c e between m a t e r i a l e l u t r i a t e d and that remaining i n the bed. Ottawa sand of very narrow d i s t r i b u t i o n (0.6 mm - 0.85 mm) was used as the coarse component in a second set of experiments i n v o l v i n g a two-component system where the f i n e alumina component was the only e n t r a i n a b l e m a t e r i a l under the 48 experimental conditions. The p a r t i c l e size analysis of the alumina was undertaken by both standard sieves and the computerised 'electrozone' Coulter counter system supplied by P a r t i c l e Data Laboratories. Sieve analysis was convenient for large samples obtained from bulk feed charge whilst the small sample requirement of the electrozone system, 0.1 to 200 mg, was p a r t i c u l a r l y suitable for small dust samples such as that obtained i s o k i n e t i c a l l y in the freeboard of the k i l n . The mean p a r t i c l e s i z e , the Sauter mean, was calculated from the sieve analysis results which are l i s t e d in Table 4.2 using the relationship 1 d_ = (4.1). P K x ^ d ^ ) Here x^ represents the f r a c t i o n of the material in size i n t e r v a l i , and dpi; the arithmetic mean of the mesh dimensions of the two sieves that define the fracti o n i . The loose packed bulk density of the materials was measured in beakers of known volumes. Excess solids were poured into the beakers, l e v e l l e d and then weighed. The fixed-cone method was also employed in the measurement of the angle of repose of the alumina material. A s u f f i c i e n t quantity was c a r e f u l l y poured to p i l e on a f l a t surface through a funnel placed very close to the surface to avoid uneven d i s t r i b u t i o n of the discharge. The slopes of the poured p i l e s were then mean size "- 62.3 /u 10 30 50 70 90 110 Particle size LI F i g u r e 4 . 7 : S i z e d i s t r i b u t i o n of a l u m i n a p a r t i c l e s . 50 measured. Measurements of the p a r t i c l e density using the displaced volume technique in a pycnometer gave values (3200 kg/m3) far below the 3970-3990 kg/m3 quoted in standard references (51,52) presumably because of the porous nature of the material. The physical c h a r a c t e r i s t i c s of the materials used are reported in Table 4.2. 51 Table 4.2 Physical properties of s o l i d p a r t i c l e s Alumina Ottawa sand P a r t i c l e density (Kg/m3) 3990 (51) 2627 Bulk density (Kg/m3) 950 1344 Mean p a r t i c l e size (jum) 64.31 790 Angle of repose 30° 31° Sieve analysis, Alumina p a r t i c l e s ve Interval P a r t i c l e Weight diameter (jum) (Mm) 180-150 165 1 .06 150-125 137.5 2.80 125-106 115.5 6.02 106-90 98 9.90 90-75 82.5 20.87 75-63 69 1 7.26 63-53 58 26.36 53-45 49 6.04 45-38 41.5 7.55 38-0.0 1 9 2.13 Chapter 5 EXPERIMENTAL PROCEDURE 5.1 INTRODUCTION A l l experiments were carr i e d out with the sol i d s bed in batch mode. The behaviour of the. s o l i d s , either slumping, r o l l i n g or cascading, has been found (7) to be dependent solely on the rotational speed (or Froude number) and bed depth, or fraction of so l i d s loading for a pa r t i c u l a r material. Also for i n d u s t r i a l k i l n s operating in the continuous mode, changes in operating variables such as feed rate, bed i n c l i n a t i o n and rotational speed have been observed to cause changes in the bed p r o f i l e or average retained volume of the k i l n (7,48,53,54,55,56,57,58,59), resul t i n g in the occurrence of d i f f e r e n t types of bed motion along the k i l n length. Thus, in order to reduce the large number of variables and to control the eff e c t of bed behaviour, i t was advantageous to resort to batch operation. In t h i s case, only the ro t a t i o n a l speed and bed depth were varied experimentally giving r i s e to the same bed behaviour patterns that would occur in continuous operation" under a given set of operating variables. Batch operation also has the added advantage of requiring a smaller volume of solids and elimination of the time required for the solids discharge to reach a steady state. Moreover, a x i a l segregation in a continuous operation due to so l i d s a x i a l 52 53 motion could af f e c t any measurements based on a simple so l i d s plug flow model. A l l e l u t r i a t i o n measurements were also made in the batch mode, c o l l e c t i n g entrained dust over short time intervals to determine the average rate. Local entrainment rate determination would have required measurements of the a x i a l concentration p r o f i l e involving r a d i a l mixed mean concentration of the so l i d s . Thus point measurements of concentrations across the k i l n at an a x i a l location would be necessary to evaluate the mixed mean. Such measurements are very d i f f i c u l t and tedious e s p e c i a l l y since there was irregular s o l i d s d i s t r i b u t i o n r a d i a l l y in the gas phase (Section 6 . 3 . 4 ) . It was also not possible to employ the usual technique of varying the gas flow rate and measuring exit solids concentration changes in the gas because the process i t s e l f was fundamentally dependent on the f l u i d v e l o c i t y . Furthermore, because the bulk of the dust travels very close to the bed surface, any attempt to sample close to the bed had the ris k of sampling the bed i t s e l f . 5.2 UNIMODAL SYSTEM The experimental procedure involving the narrowly sized alumina p a r t i c l e s i s described here. An accurately weighed quantity of sol i d s to f i l l a predetermined volume fraction of the cylinder was ca r e f u l l y placed in the cylinder to 54 cover the f u l l length. To do t h i s , the material was f i r s t placed in a 10.16 cm ABS pipe that had been cut open a x i a l l y along a chord. The pipe was then inserted into the cylinder and rotated to discharge the material through the cut-away s l i c e . The procedure was carr i e d out in two stages. Each stage involved half the t o t a l material inserted successively through the opposite ends of the cylinder. The feeding pipe, thus, was charged to cover 1.22 m of i t s 1.52 m length to f a c i l i t a t e the manual transfer into the cylinder. The end boxes carrying the exit dams were then fixed in place and the horizontal cylinder rotated for a period to ensure a uniform bed p r o f i l e . The a i r system was then turned on; and the a i r flow was measured by the ca l i b r a t e d o r i f i c e meter (see Appendix A) and controlled by a notched b u t t e r f l y valve in the discharge l i n e . Entrained dust c o l l e c t e d in the cyclone discharge hopper was weighed at time i n t e r v a l s . Two hoppers, a solids discharge valve, and an intermediate hopper permitted the c o l l e c t i o n of the fractions without stopping the process. The time intervals ranged from 3 minutes to 20 minutes depending on the operating conditions. About the same time was allowed for the system to be steady. Since only i n i t i a l rates were required, a maximum of two fractions were obtained in some cases so that a run lasted anywhere from 9 minutes to one hour. E l u t r i a t i o n rates were constant over time after the i n i t i a l waiting period. Typical time measurements have been reported in Appendix E. The cyclones were capable of removing p a r t i c l e s of size in the 55 whole range of the feed size d i s t r i b u t i o n as shown in Figure (5.1). The amount of p a r t i c l e s less than 10am that go through the cyclone i s n e g l i g i b l e . Measurements of o v e r a l l cyclone e f f i c i e n c y gave values, over the flow rates employed, of 98 - 99%. The r e p r o d u c i b i l i t y of t h i s technique was good (Section 6.3).The cylinder was discharged by removing the end boxes, adjusting the i n c l i n a t i o n and commencing rotation. Two sets of experiments were performed. One set involved measurements in which the cylinder wall was exposed to the gas flow and referred to as exposed wall or rough wall experiments. In the other set, the effect of the rough wall was isolated by the use of the cardboard insert described in Section 4.1.1. Measurements made in t h i s set were referred to as covered wall or smooth wall experiments. 5.3 VELOCITY PROFILE AND DUST SAMPLING Transverse v e l o c i t y p r o f i l e s were measured l o c a l l y in a direc t i o n perpendicular to the surface of the rotating bed at various a i r flow rates. Local v e l o c i t i e s were measured with the DISA 55A76 Steel Clad Probe whose positions were recorded on the graduations on the perspex end box flange that c a r r i e d i t . These locations were well above the salt a t i o n layer where the p a r t i c l e concentration was r e l a t i v e l y high such that measurements were not grossly Figure 5.1 Cyclone disharge size d i s t r i b u t i o n 57 a f f e c t e d by the presence of the p a r t i c l e s . In some cases, i s o k i n e t i c sampling of dust was conducted at these l o c a t i o n s to e v a l u a t e the dust c o n c e n t r a t i o n p r o f i l e above the bed. I s o k i n e t i c sampling a l s o was c a r r i e d out i n some runs at s e l e c t e d l o c a t i o n s c l o s e to the bed s u r f a c e at the upper end, the middle and lower end of the r o t a t i n g bed. L o c a l v e l o c i t i e s were measured at these p o s i t i o n s and the i s o k i n e t i c sampling r a t e determined based on these v e l o c i t i e s as w e l l as the area of the sampling probe. The i n - l i n e f i l t e r holder equipped with a pre-weighed f i l t e r paper was connected to the sampling tube and the sampling r a t e set on the rotameter i n the sampling t r a i n . The sampling tube was i n i t i a l l y purged with compressed a i r to c l e a n i t of any d e p o s i t from p r e v i o u s use. The sampling pump was then turned on to commence sampling. The sampling time v a r i e d from 5 to 10 minutes depending on the o p e r a t i n g c o n d i t i o n and the l o c a t i o n . Sampled dust was c a r e f u l l y t r a n s f e r r e d , together with the f i l t e r paper, i n t o a pre-weighed weighing d i s h . 5 .4 BIMODAL SYSTEM The procedure was the same as that f o r the unimodal system except i n the manner i n which feed m a t e r i a l was charged i n t o the c y l i n d e r . The la r g e d i f f e r e n c e i n s i z e between the coarse and f i n e m a t e r i a l s d i d not permit 58 thorough manual mixing of the two components s i n c e the f i n e m a t e r i a l tended to p e r c o l a t e t o the bottom of any c o n t a i n e r in which the mixing was done. Thus, i n order to ensure uniform d i s t r i b u t i o n of f i n e s i n the mixture, the measured q u a n t i t y of coarse m a t e r i a l was fed i n t o the c y l i n d e r and the c y l i n d e r r o t a t e d long enough to o b t a i n uniform bed depth. The f i n e alumina p a r t i c l e s were then spread u n i f o r m l y along the l e n g t h of the feed p i p e and i n t r o d u c e d a x i a l l y to the lower edge of the coarse bed. The bed was then r o t a t e d to promote l a t e r a l mixing of the two components. For the mixture of s o l i d s having d i f f e r e n t s i z e and d e n s i t y , the average bulk d e n s i t y was computed as "m = x1^b1 + X2"b2 ( 5 ' 1 ) where x r e p r e s e n t s mass f r a c t i o n and pj^and are i n d i v i d u a l component bulk d e n s i t i e s . 5.5 OPERATING RANGE The c y l i n d e r was operated at r o t a t i o n a l speeds of up to a maximum of 13 rpm with s o l i d s percent l o a d i n g of 5, 10 and 15 such that the bed was e i t h e r i n a slumping or r o l l i n g mode. Average a i r v e l o c i t i e s ranged from 2.5 m/s to 4.2 m/s. These v a l u e s are comparable to the v e l o c i t y of 3.5 m/s t y p i c a l of i n d u s t r i a l alumina k i l n s . At these v e l o c i t i e s the flow Reynolds number was above 10" f o r rough dynamic s i m i l a r i t y with i n d u s t r i a l k i l n s that operate at Reynolds number of the order of 10 5 (Table 1.1). Chapter 6 RESULTS AND DISCUSSIONS 6.1 SALTATION EXPERIMENT Preliminary experiments were conducted to determine the predominant mode in which entrained p a r t i c l e s are transported. In these experiments the solids bed was composed of both fine entrainable alumina p a r t i c l e s and coarse sand p a r t i c l e s . I n i t i a l l y , the alumina fines occupied 61 cm of the cylinder length from the gas i n l e t end and coarse Ottawa sand (0.6-0.85mm) occupied the rest of the k i l n length as shown in Figure 6.1. The system was l e f t to run with a i r flow for about 4 1/2 hrs after which v i s i b l e patches of fines were observed at regular intervals of 23-30 cm at the upper edge of the bed which suggested that the fine p a r t i c l e s were "hopping" along the bed. To check i f these observations were not due to the occurrence of banding segregation, a fresh charge of p a r t i c l e s was rotated for about 5 hrs without a i r flow. No such patches were observed confirming the transport of fines by a i r in the previous experiment. To also check i f banding segregation did occur once p a r t i c l e s had been transported to the coarse bed by the a i r , a previously mixed charge of fine and coarse p a r t i c l e s was introduced into the k i l n . A few seconds l a t e r , a l l the fines were observed to segregate r a d i a l l y to the upper edge of the bed before subsequently segregating into small 59 60 F i n e Coarse Air » * O 0 „ / » 0 0 o • • <» 0 o t t -*| o. 6 1 m 1 . 8 3 m ( a ) I n i t i a l bed configuration Air 6 * » ° o o • ( b) A f t e r 4.5 hours of dusting Air a a * a 0 0 O • 0 0 ( c ) F i n a l bed c o n f i g u r a t i o n Figure 6.1 Saltation experiment: Plan view of bed, rpm=4, gas velocity=3.7 m/s 61 patches. These patches eventually spanned the width of the bed to form segregated bands. Entrained p a r t i c l e s , therefore, returned to the bed in sal t a t i o n landing at various locations on the coarse bed but were soon segregated into bands. The formation of the bands started from the upstream end and increased in number towards the exit with time. It appears, therefore, that the i n i t i a l patch or band formed as a consequence of entrainment from the i n i t i a l bed of fines and subsequently redeposited on the coarse bed. Successive bands were formed from entrainment from previously formed fine p a r t i c l e bands. The experiment was repeated with a batch of titanium-iron concentrate p a r t i c l e s (63-150M) and alumina of lesser density than the titanium-iron p a r t i c l e s but of comparable size d i s t r i b u t i o n ; and the same phenomenon was observed. 6.2 BED BEHAVIOUR In the absence of any model for the prediction of the bed behaviour of fine materials such as the alumina used, visu a l observations of the bed behaviour pattern were made in the cylinder over a range of rotational speeds and % f i l l . The results are presented in a t y p i c a l bed-behaviour diagram (7), as shown in Figure 6.2, which i s a plot of bed depth versus rotational speed and on which the t y p i c a l bed motion modes slumping, t r a n s i t i o n and r o l l i n g - have been 62 l a b e l l e d . The b o u n d a r i e s i n d i c a t e d s e r v e o n l y as a gu i d e s i n c e the v i s u a l judgement of bed motion was s u b j e c t t o human e r r o r . Over t h e range of rpm c o v e r e d , the bed was m o s t l y i n the r o l l i n g regime. P r e d i c t i o n s from the bed b e h a v i o u r model of Henein et al. (7) and from s i m i l a r a n a l y s i s p r e s e n t e d i n Appendix B, i n d i c a t e t h a t f o r the p h y s i c a l p r o p e r t i e s of the a l u m i n a , and c y l i n d e r s i z e , c a s c a d i n g can o n l y occur at r o t a t i o n a l speeds of about 60 rpm. S u b s e q u e n t l y , a l l e x p e r i m e n t s were c a r r i e d out i n the slump i n g and r o l l i n g regimes w h i c h , i n any event a re t y p i c a l of i n d u s t r i a l o p e r a t i n g c o n d i t i o n s . 6 . 3 ELUTRIATION OF FINE ALUMINA PARTICLES The e f f e c t of the p r i m a r y f a c t o r s such as k i l n r o t a t i o n a l speed, gas v e l o c i t y and degree of f i l l on e l u t r i a t i o n was i n v e s t i g a t e d h e r e . At a p a r t i c u l a r v e l o c i t y and degree of f i l l , average e l u t r i a t i o n r a t e s were measured f o r v a r i o u s r o t a t i o n a l speeds. T y p i c a l r e s u l t s c a r e shown i n F i g u r e s 6.3 t o 6.5 where the average v e l o c i t y * i s seen t o v a r y from 2.5 to 3.7 m/s. Over t h e r o t a t i o n a l speeds c o v e r e d the bed b e h a v i o u r v a r i e d from s l u m p i n g t o r o l l i n g f o r a l l degrees of f i l l of 5, 10, and 15%. From th e s e p l o t s e l u t r i a t i o n i s seen t o i n c r e a s e markedly w i t h i n c r e a s i n g gas v e l o c i t y and l e s s so w i t h r o t a t i o n a l speed and pe r c e n t a g e f i l l . A l t h o u g h o v e r a l l r a t e s were measured, the v a l u e s o b t a i n e d w i l l be v e r y c l o s e t o t h e i n i t i a l e n t r a i n m e n t r a t e 0.05 0.04 0.03 0.02 0.01 • \ O A^ l 1 j^mo OA A - \ 1 -• • • co \A A A A A A S = slumping T = transit ion R = ro l l ing A 0 6 R P M 8 10 12 F i g u r e 6.2 Bed behaviour diagram F i g u r e 6.3 E l u t r i a t i o n r a t e v e r s u s r o t a t i o n a l speed f o r d i f f e r e n t a i r v e l o c i t i e s a t 5% f i l l i n the p r e s e n c e of the exposed c y l i n d e r w a l l 65 F i g u r e 6.4 E l u t r i a t i o n r a t e v e r s u s r o t a t i o n a l speed f o r d i f f e r e n t a i r v e l o c i t i e s at 1 0 % f i l l i n the p r e s e n c e of the exposed c y l i n d e r w a l l 66 Figure 6.5 E l u t r i a t i o n rate versus r o t a t i o n a l speed for d i f f e r e n t a i r v e l o c i t i e s at 15% f i l l in the presence of the exposed cylinder wall 67 s i n c e d u s t c o n c e n t r a t i o n m e a s u r e m e n t s a s w i l l be d i s c u s s e d l a t e r i n S e c t i o n 6.3.4 d i d n o t c h a n g e v e r y much o v e r most o f t h e c y l i n d e r l e n g t h . I n o t h e r w o r d s , s t e a d y s t a t e c o n d i t i o n s were a t t a i n e d o v e r most o f t h e c y l i n d e r l e n g t h . The mass o f f i n e s e l u t r i a t e d o v e r a p e r i o d o f t i m e was v e r y s m a l l c o m p a r e d t o t h e t o t a l q u a n t i t y o f s o l i d s i n t h e b e d . F o r e x a m p l e , i n Run B13, 38.8g o f m a t e r i a l were c o l l e c t e d o v e r 4 m i n u t e s i n t e r v a l f r o m a 5% f i l l b e d o f 3.74kg mass. A l s o i n Run B68, 8 5 . 3 k g of f i n e s were c o l l e c t e d o v e r t h e same p e r i o d o f t i m e i n a 10% f i l l b e d o f t w i c e t h a t o f t h e 5% f i l l . M e a s u r e m e n t s made were v e r y r e p r o d u c i b l e w i t h d e v i a t i o n s o f u n d e r 5%. F i g u r e s 6.8 a n d 6.9 show t y p i c a l s c a t t e r o f t h e d a t a . I n F i g u r e 6.3 t o 6.5, t h e s o l i d s l i n e s r e p r e s e n t t h e b e s t f i t s t o t h e e x p e r i m e n t a l d a t a t o t h i r d o r d e r p o l y n o m i a l s . 6 . 3 . 1 EFFECT OF ROTATING WALL I t was o b s e r v e d i n t h e p r e l i m i n a r y e x p e r i m e n t s t h a t a s t h e r o t a t i n g w a l l p a s s e s f r o m u n d e r n e a t h t h e b e d , i t c a r r i e s f i n e p a r t i c l e s t r a p p e d i n c r e v i c e s on t h e r o u g h w a l l . T h e s e p a r t i c l e s w e r e o b s e r v e d t o f a l l b ack o n t o t h e bed u n d e r t h e a c t i o n o f g r a v i t y t h r o u g h t h e f r e e b o a r d . T h i s f l o w o f s o l i d s i n c r e a s e d w i t h r o t a t i o n a l s p e e d . When t h e gas f l o w was t u r n e d o n , t h e s e p a r t i c l e s became e n t r a i n e d b e f o r e t h e y r e a c h e d t h e b e d . The i n s e r t d e s c r i b e d i n C h a p t e r 4 t h u s p e r m i t t e d t h e s t u d y o f t h e i n f l u e n c e o f t h e w a l l . W i t h t h e 68 insert in place p a r t i c l e s f a l l i n g off the rough wall, were trapped on the outer surface of the cardboard in the region between the insert and the inner surface of the cylinder wall and thus were not entrained in the gas. Therefore, the whole bed was in contact with the gas except in the region between the k i l n wall and the upper edge of the bed. E l u t r i a t i o n from this part of the bed was termed edge entrainment by L i (2). In L i ' s model, fine p a r t i c l e s that percolate to the bottom of the bed are eventually c a r r i e d up by the rotating wall to the upper edge of the bed where they get entrained. With th i s arrangement, the effect of the rotating wall could be observed as the difference between the entrainment curve for the case when the cylinder wall was exposed and that when covered or "smoothened" with the in s e r t . I n i t i a l measurements with a f l a t exit dam are presented in Figure 6.6 where a t h i r d curve, representing entrainment from the exposed wall when the sol i d s bed was covered, i s shown. The bed was covered over i t s t o t a l length and width with polyethylene material secured to both stationary end boxes. When the wall was covered, no s i g n i f i c a n t entrainment occurred at a i r v e l o c i t i e s below 3 m/s. Actually, no physical movement of bed p a r t i c l e s was observed on the stable bed u n t i l a i r v e l o c i t i e s reached values of about 2.5 - 2.7 m/s. The threshold v e l o c i t y was estimated at 2.62 m/s. On the other hand, with the wall exposed, entrainment at 69 v e l o c i t i e s as low as 1.5 m/s was measured. The difference between the two curves appeared to increase with increase in gas v e l o c i t y . The observed increase however, was greater than the quantity entrained from the bare wall when the bed was covered. This suggested a complex interaction of the p a r t i c l e s f a l l i n g from the wall with the pick-up mechanism. This w i l l be explained in the l i g h t of further experiments in Section 6.5. These results do not correspond to the 'bent l i p ' experiments shown e a r l i e r in Figures 6.3 to 6.5. With the i s o l a t i o n of the edge entrainment, the set of experiments carried out under similar conditions gave e l u t r i a t i o n rates due solely to pick up by the gas. As shown in Figures 6.7-6.9, the entrainment p r o f i l e s are d i f f e r e n t . The s o l i d l i n e s represent t h i r d order polynomial f i t to the data. The curves, unlike those of the 'rough wall' (Figures 6.3-6.5) show a decline in entrainment with increased rotational speed at low rotational speeds followed by an increase in entrainment. In the case of the 5% f i l l , the decline occurred over a wide range of rotational speeds and at a l l v e l o c i t i e s . This phenomenon which i s obviously obscured by the ef f e c t of the wall in the case of the rough wall experiments, w i l l later be explained (Section 6.5) by the mechanism of entrainment. In L i ' s model (2), surface entrainment or 'smooth wall' entrainment would be negligible since a l l fines are entrained by the edge entrainment mechanism. In the case of the 10% and 15% f i l l s , the 70 16.0 Average Velocity (m/s) F i g u r e 6 . 6 E l u t r i a t i o n r a t e v e r s u s gas v e l o c i t y s h o w i n g c o n t r i b u t i o n due t o w a l l r o t a t i o n f o r a f l a t e x i t dam F i g u r e 6.7 E l u t r i a t i o n r a t e v e r s u s r o t a t i o n a l speed at 5% s o l i d s l o a d i n g i n a c o v e r e d w a l l c y l i n d e r J 72 0 3 6 9 12 RPM Figure 6.8 E l u t r i a t i o n rate versus r o t a t i o n a l speed at 1 0 % s o l i d s loading in a covered wall c y l i n d e r Figure 6.9 e l u t r i a t i o n rate versus r o t a t i o n a l speed at 15% s o l i d s loading in a covered wall cylinde 74 moderate increase at higher rotational speeds (9-12), i s thought to be due to the influence of the exit dam at this rpm range (see Section 6.3.2). A crossplot of e l u t r i a t i o n rate versus average a i r v e l o c i t y at d i f f e r e n t rotational speeds obtained from the rough and smooth wall experiments (Figures 6.3-6.9), gives a clearer i l l u s t r a t i o n of the effect of the wall as shown in Figures 6.10-6.12. At higher a i r v e l o c i t i e s , the rough wall mechanism designated ' r ' , becomes indistinguishable from the smooth wall mechanism designated 's' for a l l degrees of f i l l . Obviously as the a i r flow increases, considerably more p a r t i c l e s are entrained from the surface and the contribution from the wall becomes n e g l i g i b l e . However, at constant a i r v e l o c i t y the wall effect becomes very s i g n i f i c a n t as rotational speed increases which i s understandable. In Figure 6.13, the moderate increase in entrainment with % f i l l at constant a i r flow and rotational speed might be attributed in part to the corresponding r e l a t i v e increase in bed surface area bearing in mind that the t o t a l entrainment includes p a r t i c l e s in surface creep. The chord lengths measured were 0.121 m, 0.145 m, and 0.165 m for the 5, 10 and 15% f i l l beds respectively. 75 2.2 2.6 3 3.4 3.8 Average Velocity(m/s) Figure 6.10 Wall e f f e c t at 15% f i l l : rpm rough wall smooch wall 11 • • 6 o • 3 A -f-76 2.2 2.6 3 3.4 3.8 4.2 Average Velocity (m/s) Figure 6.11 Wall e f f e c t at 10% f i l l : rpm rough wall smooth wall 11 • • 6 0 • 3 A +-77 3 28.0 h 24.0 h 20.0 h 16.0 3 cd o 12.0 cd 8.0 h 4.0 h 0.0 2.6 3 3.4 3.8 4.2 Average Velocity(m/s) F i g u r e 6.12 W a l l e f f e c t a t 5% f i l l : rpm rough w a l l smooth w a l l 11 • • 6 O • 3 A + Figure 6.13 E f f e c t of solids loading on entrainment 79 6.3.2 EFFECT OF EXIT DAM GEOMETRY The t o t a l length of the k i l n was regarded as the test section because of the l i m i t a t i o n s outlined in Chapter 5, Section 5.1. It therefore became necessary to assess and minimise the effect of the i n l e t / e x i t dam geometry on dust pick-up. Four dam geometries were considered as shown in Figure 4.4. The ring plate of same outside diameter as that of the cylinder was perfect to contain the s o l i d s . The inside diameter, which varied depending on the degree of f i l l however, caused s i g n i f i c a n t contraction and expansion of the gas flow with i t s attendant c i r c u l a t i o n and eddy formation as indicated by preliminary v e l o c i t y measurements. Also the accelerated flow due to the reduction in flow area could not be related to the average v e l o c i t y in the bulk of the k i l n . Therefore, the ring dam was abandoned in favour of the f l a t plate of the same shape as the cross-section of the bed. With the f l a t plate dams, a i r flow acceleration at the exits was thereby reduced considerably since the dam heights were just s l i g h t l y (~1.5 cm) above that of the bed, o f f e r i n g p r a c t i c a l l y uniform flow area along the length of the cyl i n d e r . Typical average e l u t r i a t i o n rates, measured with the f l a t dam are shown in Figures 6.14 and 6.15 for both rough and smooth wall at various degrees of f i l l . However, i t was observed that the excess height of the dam above the bed surface (dam l i p ) affected the rate of entrainment. See for example, the overlap in Figures 6.14 and 6.15 where the 80 10% dam l i p was higher. Under similar conditions, entrainment in a 10% f i l l bed of larger surface area i s expected to be higher at a l l rotational speeds and a i r v e l o c i t i e s than from a 5% f i l l bed. P a r t i c l e s t r a v e l l i n g close to the bed in s a l t a t i o n and those in surface creep could not follow the change in d i r e c t i o n due to the presence of the l i p and thus were trapped and deposited in the bed at the e x i t . The bed depth thus increased at the exit as more and more p a r t i c l e s a r r i v e from upstream. Dynamic equilibrium was established between bed height and entrainment rate after some time. Measurements made with t h i s dam geometry were, thus, very unreliable and could not be related to the changing height of the dam l i p . Conical dams with the larger end designed to f i t into the inside diameter of the k i l n were then employed. The conical dams were not much better than the rings. As shown in Figures 6.16 and 6.17, e l u t r i a t i o n rates were very high especially in the conical section where the flow was accelerated. This was confirmed by an increase in dust concentration measured at various heights above the bed at diff e r e n t locations close to the large end of the conical exit through to locations close to the smaller end, the in l e t to the end box, as shown on Table 6.1. Also, since the bed depth was uniform and there were no obstructions at the exit as in the case of the f l a t dam, solids in surface creep were e a s i l y swept into the discharge end box. 8 1 0 3 6 9 1 2 RPM Figure 6.14 E l u t r i a t i o n rate in a cylinder with a f l a t exit dam and an exposed wall 82 0.0 I ' ! 1 ! 1 ! 1 1 0 3 6 9 12 RPM Figure 6.15 E l u t r i a t i o n rate in a cylinder with a f l a t exit dam and a covered wall 83 Table 6.1 Dust Concentration Measurements in Conical Dam (mg/litre) D i s t a n c e from gas e x i t (cm) H e i g h t above bed 5. 5cm 2. 5cm 1 . 8cm 1 . 2cm Average v e l o c i ty (m/s) 0.0 25.0 1 . 42 1 .27 2.13 2.12 3.24 2.82 26.70 9.69 2.6 ( 1 5 % F I L L ) 0.0 20.0 55.0 0.30 0.30 0.24 0.96 0.90 0.82 2.06 ( 5 % F I L L ) 84 Figure 6.16 Influence of exit geometry on e l u t r i a t i o n rates at various rotational speeds. 85 F i g u r e 6.17 I n f l u e n c e of e x i t geometry on e l u t r i a t i o n r a t e at v a r i o u s a i r v e l o c i t i e s 86 With the bent l i p dam, the flow area was not r e s t r i c t e d at the exit to cause a i r flow acceleration and a l l obstruction to the movement of p a r t i c l e s in surface creep was removed. Velocity p r o f i l e s were thus uniform a x i a l l y throughout the length of the cylinder and average entrainment rates r e f l e c t e d the rates of p a r t i c l e s t r a v e l l i n g in a l l modes: suspension, s a l t a t i o n and surface creep, as already discussed in Section 6.3 and shown in Figures 6.3-6.5. However, in the case of the 10% and 15% soli d s loading, at higher rotational speeds (>6rpm), s o l i d s at the upper half of the leading edge of the bed rode a l i t t l e higher on the slanting surface of the dam than the remaining part of the leading edge as shown in Figure 6.18. Consequently, the higher entrainment at th i s point of the dam, due to accelerated flow, could upset the t o t a l rate. This could explain the increase in entrainment at higher(>6) rpm under the covered wall conditions as mentioned in Section 6.3.1. The 'bent l i p ' exit dam geometry was, on the whole, ideal for the purposes of the experimental measurements. However, as indicated in Figures 6.16 and 6.17, the influence of the exit geometry on entrainment with respect to flow v e l o c i t y and rotational speed indicates the f l a t dam to be more e f f e c t i v e at reducing entrainment because of the obstruction i t of f e r s to the movement of p a r t i c l e s very close to the bed at the e x i t . Consequently, the higher the excess height of dam above the bed the less entrained dust is car r i e d over into the c o l l e c t i o n unit. The 87 conical dam enhances entrainment because of the flow acceleration and subsequent higher dust pick-up which i s apparently what pertains in most i n d u s t r i a l k i l n s . 6.3.3 VELOCITY PROFILES Local mean ve l o c i t y p r o f i l e s were measured in the empty cylinder and also above the s o l i d s bed at various a i r flow rates at about 190 cm downstream of the honeycomb straightener. Measurements upstream of this point could not be made because of the inadequate length of the steel clad probe. Flow beyond th i s point was assumed to show l i t t l e change although the cylinder length was inadequate for the establishment of f u l l y developed flow which i s t y p i c a l of i n d u s t r i a l k i l n s . The velocity p r o f i l e s measured along the v e r t i c a l and horizontal diameters of the empty cylinder are presented in Figure 6.19. Although the p r o f i l e s did not show exact symmetry about the cylinder axis due probably to entrance e f f e c t s , they were reasonably f l a t over the flow Reynolds numbers covered. It was not intended to measure turbulence fluctuations and i n t e n s i t i e s in the flow f i e l d owing to the presence of fine p a r t i c l e s . However, a few were attempted as mentioned below to v e r i f y their influence on entrainment. These measurements were designed in an attempt to see i f the dust loading results were due to large differences in l o c a l turbulence i n t e n s i t i e s . 89 T — i — : — f Velocity (m/s) Figure 6.19 V e l o c i t y p r o f i l e s along the v e r t i c a l and horizontal diameters of the empty cylinder 90 Mean v e l o c i t y p r o f i l e s were also made at various locations in a plane normal to the bed surface and above the sa l t a t i n g layer to minimise interference by s a l t a t i n g p a r t i c l e s that were usually confined to distances within 2.5 cm above the bed. Figures 6.20 and 6.21 show t y p i c a l v e l o c i t y p r o f i l e s that were reasonably f l a t . On semi-logarithmic plots (Figure 6.22) these p r o f i l e s approximate straight l i n e s . However attempts to estimate the f r i c t i o n v e l o c i t y from the slopes of these l i n e s , as described by Equation (2.2), did not prove r e l i a b l e . Other mean vel o c i t y measurements were made at selected locations, designated 1, 2 and 3 for the purposes of isokinetic dust sampling (section 6.3.4). Typical values at these locations are shown in Table 6.2. In a few cases, l o c a l turbulence levels were estimated from measurements of RMS values (Appendix A) at these locations to assess the eff e c t of l o c a l turbulence i n t e n s i t i e s on l o c a l dust pick-up. Velocity measurements at Location 3, for example, were consistently lower and ro t a t i o n a l speeds of the k i l n had no effect on any measurements. Also the turbulence le v e l s appeared to be lowest at location 3, although the values at the other locations were not grossly d i f f e r e n t . The levels measured were s i g n i f i c a n t l y lower than expected le v e l s of about 10% due to the high time constant of the probe, designed to measure mean v e l o c i t i e s . 9 1 Figure 6.20 Typical v e l o c i t y p r o f i l e s above solids bed at 5% f i l l 92 Velocity (m/s) Figure 6.21 Typical velocity p r o f i l e s above s o l i d s bed at 10% f i l l 93 Figure 6.22 Velocity d i s t r i b u t i o n on semi-logarihtmic plot T a b l e 6.2 T y p i c a l L o c a l Mean V e l o c i t y and % t u r b u l e n c e l e v e l s (Average v e l o c i t y = 3.7 m/s) L o c a t ion RPM 1 2 3 m/s % m/s % m/s % 1 3. 92 2.7 3.96 2.7 3.61 2.6 6 3.84 2.7 3. 96 2.7 3.61 2 . 5 10 3.92 2 . 5 3.96 2.6 3.57 2.3 * Probe p o s i t i o n s 2 cm above bed 95 6 .3 .4 ISOKINETIC DUST SAMPLING Simultaneous with the l o c a l mean velocity measurements is o k i n e t i c sampling of dust was done at selected lo c a l positions to determine dust concentrations in the freeboard in an attempt to ident i f y the r e l a t i v e degree of dust pick-up in lo c a l areas of the bed. Consequently, coupled with a knowledge of the behaviour of the bed at these locations, i t was hoped to formulate a mechanism by which entrainable fines leave the bed into the gas phase in rotary k i l n s . The f i r s t of these measurements i s shown in Figure 6.23 that i l l u s t r a t e s t y p i c a l concentration p r o f i l e s in the same plane as the v e l o c i t y p r o f i l e s , normal to the bed. Most of the entrained p a r t i c l e s travel very close to the bed, within about 2 cm, presumably in s a l t a t i o n . Above t h i s height, the dust concentration f a l l s to very low values consisting of very fine p a r t i c l e s that are held in suspension. The concentration p r o f i l e was not affected by the condition of the exit dam geometry and rotating wall, as evidenced by Figures 6.23 and 6.24 obtained under d i f f e r e n t wall conditions, 'rough' and 'smooth' respectively, and d i f f e r e n t exit geometries (Figure 6.23). The a x i a l dust concentration d i s t r i b u t i o n , measured a x i a l l y at heights of about 2.0 cm above the bed, is shown in Figure 6.25. Thus there i s l i t t l e change in dust concentration at least within the l a s t meter 96 Bent Lip 2.92m/s 0.00 0.03 0.06 0.09 Height Above Bed (m) Figure 6.23 Dust concentration p r o f i l e s above sol i d s bed in a 'rough' wall experiment 97 Figure 6.24 Dust concentration p r o f i l e s above s o l i d s bed in a 'smooth' wall experiment 98 0.15 0.10 0.05 5%fill, Rough wall Vel=2.92m/s 0 0.3 0.6 0.9 Distance from Exi t (m) 1.2 F i g u r e 6.25 A x i a l dus t c o n c e n t r a t i o n p r o f i l e 2cm above the c e n t r e of the s o l i d s bed 99 of bed length to the gas exit suggesting steady state conditions. Measurements also were made in a transverse direction with respect to the cylinder axis. Typical locations representing the top edge, the central part and the lower edge of the bed along a bed width were chosen for these measurements. As mentioned above, these locations have been designated 1, 2 and 3 respectively. To relate dust concentrations to the transverse behaviour of the bed, measurements were made at various rotational speeds at heights ~2 cm above the bed. Under exposed cylinder wall conditions, concentrations at location 1 were higher than those at locations 2 and 3 at higher rotatonal speeds and increase monotonically with r o t a t i o n a l speeds (Figure 6.26). At lower rpm's, location 3 exhibited higher dust concentrations but thi s dropped steadily as rpm was increased, while at location 2, dust pick-up remained lower and increased s l i g h t l y at higher rpm to approach the value at location 3. The change in concentration at location 1 with rpm was unaffected by changes in exit dam geometry, as shown in Figure 6.27, for a conical dam and by changes in degree of f i l l , as in Figure 6.28 for 5% f i l l . The r e l a t i v e magnitudes of the dust concentration at these locations confirm the strong influence of the rotating wall on the average rate of entrainment, referred to e a r l i e r as edge entrainment (Section 6.3.1). 1 0 0 F i g u r e 6.26 Dust c o n c e n t r a t i o n changes at s p e c i f i e d l o c a t i o n s i n a c y l i n d e r w i t h a 'bent l i p ' e x i t dam,exposed w a l l and at 1 0 % f i l l 101 Figure 6.27 Dust concentration changes at s p e c i f i e d locations in a cylinder with c o n i c a l exit dam,exposed wall and at 5% f i l l 102 Under covered wall conditions where the influence of the cylinder wall was eliminated, dust pick-up at location 1 was reduced markedly and, in fact, dropped below that at locations 2 and 3 as shown in both Figures 6.29 and 6.30 obtained at dif f e r e n t degrees of f i l l . Dust concentrations at locations 2 and 3, though higher than that at location 1 declined with rpm in the same fashion as for the rough wall condition at the same locations. Again so l i d s loading had no effect on the p r o f i l e s . Unlike location 1 (for rough wall), t h i s decline in dust concentration at locations 2 and 3 was inconsistent with the bed behaviour or sol i d s flow patterns. As r o t a t i o n a l speed i s increased, solids slump or r o l l down the bed at increasing speeds and number such that the subsequent chaotic movements and c o l l i s o n s are expected to enhance entrainment. Apparently even over a stable bed (no rotation), dust concentrations at Locations 2 and 3 were s t i l l higher, as can be seen in Figures 6.29 and 6.30, irrespective of the fact that mean v e l o c i t i e s and turbulence levels were lower at location 3 (Section 6.3.3). More isok i n e t i c sampling was performed over a non-rotating bed at various bed orientations to reveal how sensitive dust pick-up was to bed i n c l i n a t i o n . As shown in Table 6.3, dust concentrations were reasonably uniform over the bed surface when horizontal. With the bed inclined at an angle close to the dynamic angle of repose of the material (30°), dust concentrations at Locations 2 and 3 increased, 1 0 3 F i g u r e 6.28 D u s t c o n c e n t r a t i o n c h a n g e s a t s p e c i f i e d l o c a t i o n s i n a c y l i n d e r w i t h 'bent l i p ' e x i t dam,exposed w a l l and a t 5 % f i l l Figure 6.29 Dust concentration changes at sp e c i f i e d locations in a cylinder with 'bent l i p 1 exit dam,covered wall and at 5% f i l l 1 05 F i g u r e 6.30 D u s t c o n c e n t r a t i o n c h a n g e s a t s p e c i f i e d l o c a t i o n s i n a k i l n w i t h 'bent l i p ' e x i t dam a n d c o v e r e d w a l l a t 10% f i l l 1 06 T a b l e 6.3 L o c a l Dust C o n c e n t r a t i o n s on a N o n - R o t a t i n g Bed a t 5% f i l l and 3.7m/s gas v e l o c i t y . H o r i z o n t a l I n c l i n e d bed pa r 11y bed i n c l i n e d bed L o c a t i o n (30°) (15-20°) L e f t R i g h t q u a d r a n t q u a d r a n t m g / l i t r e m g / l i t r e mg/1i t r e m g / 1 i t r e 1 0.84 0.4 0.30 0.21 2 0.62 1.18 1.18 0.65 3 0.90 3.92 4.03 3.08 1 07 the increase being higher at Position 3 regardless of the location of the bed, whether in the lower l e f t or lower right quadrant of the cross-section of the cylinder. Dust concentrations at Location 1, however, either dropped, or were unchanged depending on the l o c a l v e l o c i t y . At an intermediate i n c l i n a t i o n (15-20°) the increase in dust concentrations at locations 2 and 3 was moderate. 6 .3 .5 SIZE DISTRIBUTION OF DUST AND SOLIDS BED Although the alumina material consisted of a very narrow d i s t r i b u t i o n of p a r t i c l e sizes, analysis of the dust and bed samples was essential to study any possible e f f e c t of size segregation on the l o c a l dust pick-up and how t h i s i s related to the observed changes discussed in Section 6.3.4. The computerised electrozone p a r t i c l e analyser, supplied by P a r t i c l e Data Laboratories, Ltd. which employs the coulter-counter technique, was used for these analyses. The size d i s t r i b u t i o n of dusts c o l l e c t e d by i s o k i n e t i c sampling at the various locations i s shown in Figure 6.31. Finer dust i s observed at Location 1 because at the wall, r e l a t i v e l y fine p a r t i c l e s are c a r r i e d up by the action of the wall and exposed to the gas (edge entrainment). Dust collected at Location 3 appeared s l i g h t l y larger than those at the centre of the bed. This pattern, however, was not supported by solids bed size d i s t r i b u t i o n at these locations 1 08 Figure 6.31 Size d i s t r i b u t i o n of c o l l e c t e d dust at s p e c i f i e d locations above bed in a c y l i n d e r with an exposed wall 109 Figure 6.32 E f f e c t of rpm on dust si z e d i s t r i b u t i o n at location 2 110 as shown in Figures 6.33-6.34. Moreover, the r e l a t i v e magnitude of the dust concentrations (Figures 6.29 and 6.30) could not be explained by the dust size d i s t r i b u t i o n pattern at these positions. Also Figure 6.32 shows that the dust size d i s t r i b u t i o n at any location did not change much with rotational speed as is shown for Location 2. The size d i s t r i b u t i o n of the bed did not also depend on the % f i l l , transverse location, nor a x i a l location (Figures 6.33-6.37). Therefore i t appears that segregation on the surface of the bed had no effect on dust pick-up. This i s l i k e l y because l i t t l e segregation, i f any, took place in a bed of such a narrow size d i s t r i b u t i o n and had no s i g n i f i c a n t influence on the dust d i s t r i b u t i o n pattern. 6 . 4 PHOTOGRAPHIC EXPERIMENTS WITH COLOURED PARTICLES In a f i n a l attempt to investigate the mechanism by which the dust concentration in the gas increases down the bed in an inclined bed but remains more uniform in a horizontal bed, a series of photographs of the bed surface was made. Quantities of coloured bed material were placed a x i a l l y at the lower edge, centre and upper edge of the bed. The a i r flow was resumed without rotation and changes in the behaviour and quantity of the coloured material against the background of white bulk bed material were photographed at time i n t e r v a l s . The process was repeated for both inclined 111 10 30 50 70 90 110 P a r t i c l e s i z e \J F i g u r e 6.33 Bed p a r t i c l e s i z e d i s t r i b u t i o n at s p e c i f i e d l o c a t i o n s 25cm from the e x i t dam 1 1 2 F i g u r e 6.34 Bed p a r t i c l e s i z e d i s t r i b u t i o n a t s p e c i f i e d l o c a t i o n s 55cm f r o m t h e e x i t dam Figure 6.35 Bed p a r t i c l e size d i s t r i b u t i o n at upper edge of bed for various % f i l l s 1 1 4 Figure 6.36 Bed p a r t i c l e size d i s t r i b u t i o n at centre of bed for various % f i l l s 1 1 5 10 30 50 70 90 110 P a r t i c l e s i z e p F i g u r e 6.37 Bed p a r t i c l e s i z e d i s t r i b u t i o n at the lower edge of bed f o r v a r i o u s % f i l l s 116 and horizontal beds at various a i r v e l o c i t i e s . The r e s u l t s are shown in a series of photographs in Figures 6.38-6.40. It became apparent from the exposures that c o l l i s i o n of returning p a r t i c l e s on the bed was responsible for the enhanced entrainment from the surface of the bed. P i t t i n g of the bed surface by returning p a r t i c l e s scoured away coloured p a r t i c l e s leaving irregular depressions and ridges. On the horizontal bed these ridges and depressions occurred uniformly over the bed surface. However on the i n c l i n e d bed they were confined to the lower edge and the centre. L i t t l e or no change occurred to the p a r t i c l e s placed at the upper edge in the case of the in c l i n e d bed. Also on the i n c l i n e d bed, p a r t i c l e s in surface creep did not move p a r a l l e l to the f l u i d flow d i r e c t i o n but at an angle to i t towards the lower edge of the bed. As the normal force on a p a r t i c l e s i t t i n g on the inclined bed decreases due to increase in f l u i d l i f t (but not s u f f i c i e n t to l i f t i t ) , the f r i c t i o n a l force r e s i s t i n g i t s movement down the slope decreases. The p a r t i c l e , u n t i l projected into the f l u i d thus i n i t i a l l y moves under the action of the resultant g r a v i t a t i o n a l force and f l u i d drag down the slope. Therefore at i t s i n i t i a l departure from the bed, the p a r t i c l e has a normal and a transverse (down the incline) component of v e l o c i t y . F i g u r e 6.38 P h o t o g r a p h i c time exposures of c o l o u r e d bed s u r f a c e i n a h o r i z o n t a l bed a t 4.21m/s a i r f l o w 120 6.5 MECHANISM OF DUST PICK-UP The mechanism of e n t r a i n m e n t i n r o t a r y k i l n s w i l l be d e s c r i b e d here i n view of the e x p e r i m e n t a l f i n d i n g s p r e s e n t e d i n t h i s c h a p t e r . F i n e bed m a t e r i a l s are p r o j e c t e d i n t o the gas phase by t h r e e dominant mechanisms. The rough r o t a t i n g w a l l causes f i n e p e r c o l a t e d m a t e r i a l underneath the s o l i d s bed t o be c a r r i e d up above the bed t h u s g i v i n g them a b e t t e r exposure t o the f l o w i n g gas. As they a r e c a r r i e d h i g h e r up, t h e s e p a r t i c l e s f a l l i n t o the f r e e b o a r d , under g r a v i t a t i o n a l f o r c e and become e n t r a i n e d . F l u i d l i f t due t o asymmetric d i s t r i b u t i o n of s t a t i c p r e s s u r e around the p a r t i c l e , or t u r b u l e n t e d d i e s can a l s o cause p a r t i c l e s t o be e n t r a i n e d . However t h i s mechanism i s l e s s e f f e c t i v e than the c o l l i s i o n of r e t u r n i n g p a r t i c l e s on the s o l i d bed. In t h e absence of the e f f e c t of the r o t a t i n g w a l l ('smooth w a l l ' ) , f l u i d l i f t and t u r b u l e n t e d d i e s a r e c e r t a i n l y i m p o r t a n t i n i n i t i a t i n g e n t r a i n m e n t . However once p a r t i c l e s a r e e n t r a i n e d the f l u i d f l o w i n the r e g i o n c l o s e t o the bed i s m o d i f i e d by the p r e s e n c e of the e n t r a i n e d p a r t i c l e s c a u s i n g a r e d u c t i o n i n the f l u i d shear s t r e s s and t h u s f l u i d l i f t on the s u r f a c e of the bed. Subsequent e n t r a i n m e n t i s t h e r e f o r e e f f e c t i v e l y a c c o m p l i s h e d by the impact of s a l t a t i n g p a r t i c l e s on the bed. T h i s can be seen i n the e xposures i n F i g u r e s 6.39 and 6.40 where p a r t i c l e e n t r a i n m e n t a t the upper edge of the bed 121 i s found to be almost non-existent compared to the rest of the surface which is subjected to intense p a r t i c l e c o l l i s i o n s . This result is an excellent experimental confirmation of the b a l l i s t i c models of sediment transport put forward by Bagnold (28,36,37) and others(30,31). Here the impact of p a r t i c l e s in sal t a t i o n are perceived to be most important in co n t r o l l i n g entrainment and transport. Theories which assume f l u i d l i f t and drag as the c o n t r o l l i n g factors (39,40,41) cannot be j u s t i f i e d in the l i g h t of the present observations. In the rotary k i l n , because of the i n c l i n a t i o n of the bed and the i n i t i a l motion of so l i d s down the slope, the p a r t i c l e trajectory has a ve l o c i t y component down the bed. The trajectory i s such that the p a r t i c l e s c o l l i d e with the bed displaced some distance transverse to their o r i g i n a l p o s i t ion. P a r t i c l e s projected from the upper edge of the bed w i l l therefore return to a location closer to the centre of the bed and those from the centre of the bed w i l l impact the bed very close to the lower edge. Since c o l l i s i o n s enhance entrainment, successive c o l l i s i o n s down the bed w i l l cause an increase in dust concentrations further down the bed. This explains the higher dust concentration measurements made at Location 3. 1 22 In a m u l t i p a r t i c l e system where complete r a d i a l segregation of fines occurs, (Section 2.3), the predominant mode of entrainment w i l l be edge entrainment due to the rotating wall since c o l l i d i n g p a r t i c l e s w i l l be unable to eject coarser p a r t i c l e s . When banding segregation occurs surface entrainment by c o l l i s i o n w i l l be s i g n i f i c a n t . However entrainment could be d r a s t i c a l l y minimised and unsteady because of the interspersed bands of coarse material. Saltating p a r t i c l e s that land on coarse bands are l i k e l y to be embedded since they do not possess enough momentum to eject p a r t i c l e s larger than themselves. The l o c a l dust concentration w i l l , therefore, appear to be low over the coarse bands and high over the fine bands. The ove r a l l dusting in an i n d u s t r i a l k i l n w i l l not only depend on the fines concentration but also depend on the location of the fine bands. Bands located close to the exit dam w i l l enhance dusting as entrained dust i s e a s i l y c a r r i e d over into the end box. Beds with end longitudinal segregation (section 2.3) w i l l be in thi s category. The influence of the rotating wall could also be enhanced by c o l l i s i o n on the bed closer to the top edge by p a r t i c l e s released from the wall. 6.6 ELUTRIATION FROM A BED CONTAINING A MIXTURE OF SAND AND  ALUMINA Most i n d u s t r i a l k i l n s are fed with material composed of naturally occurring aggregates; thus the objective of thi s 123 part of the work was to study the e f f e c t of fines concentration on entrainment. Several experiments were car r i e d out at degrees of f i l l of 5% and 10% for controlled fines concentrations of 15%, 10% and 5%. As expected, because of the large differences in size of the components (section 4.3), the banding type of segregation occurred in a l l the experiments with the number of bands increasing with the fines concentration. The bands were very d i s t i n c t and stable, especially in the case of the 10% f i l l . In the case of the 5% f i l l , the band widths tended to be wider at the upper edge of the bed and sometimes featured a depression with the coarser materials on both sides. Attention was p a r t i c u l a r l y placed on the 10% f i l l experiments covering three v e l o c i t y levels of 2.74, 3.47 and 3.74 m/s and three ro t a t i o n a l speeds of 1, 3 and 6 rpm a l l in the slumping and r o l l i n g regimes similar to the uniform material experiments. In these runs the concentration of fines in the bed with time was calculated from the i n i t i a l composition of the bed and the mass of fines e l u t r i a t e d . Typical fines concentration/time changes are shown in Figures 6.41 and 6.42. I n i t i a l attempts to f i t the results to f i r s t - o r d e r k i netics were not very successful. Thus in l i n e with other experimental work on e l u t r i a t i o n in f l u i d i z e d beds (60,61,62), a kinetic model of the form (63) 1 dWr _ R_ = = K r (Wf/W,)n (6.1) S T dt r 1 t 124 was assumed where T i s the width of a bed of t o t a l weight Wt and fines weight such that the fines weight fraction = Wf — . Thus W t R_ = - 1 = K r ( C f ) n (6.2) s Tdt r t This implies that the s p e c i f i c rate of entrainment i s a function of fines concentration. For a power function, K r defines a rate constant which w i l l be a function of operating conditions. Extracting the i n i t i a l rates from the i n i t i a l slopes of the concentration/time plots (Figures 6.41 and 6.42), the order n, obtained from a log-log plot of rate versus i n i t i a l concentration, Figure (6.43), ranged between 1.2 to 1.35. This s l i g h t v a r i a t i o n might be due to the re l a t i v e location of the extreme fine bands in the respective beds. The control of the band location was not possible regardless of the extreme care exercised in placing the s o l i d s in the cylinder (Section 5.4) to ensure uniform d i s t r i b u t i o n of the fines. In a l l experiments, measurements of the band widths were made before the start of each entrainment test with a metal s t r i p about 1.5 m long and 3 cm wide. One face of t h i s s t r i p had a red paper s t r i p of the same size glued on. Before use, t h i s red side was smeared with a thin layer of adhesive such that when the metal s t r i p was placed on the bed lengthwise and the thin edge pressed into the bed, the 1 25 0.051 T 1 1 1 1 i P 0.050 *5J 0.049 \ Cj" 0.048 0.047 0.046 0.045 rpm = 6 Velocity = 3.47m/s 10 20 30 40 50 60 T i m e (min). F i g u r e 6.41 C o n c e n t r a t i o n time p l o t s f o r 5% i n i t i a l f i n e s c o n c e n t r a t i o n i n a bimodal bed 1 26 0.101 0.097 0 rpm = 6 Velocity = 3.47m/s 10 20 30 40 T i m e (min). 50 60 F i g u r e 6.42 C o n c e n t r a t i o n time p l o t f o r 10% i n i t i a l f i n e s c o n c e n t r a t i o n i n a b i m o d a l bed 1 2 7 Figure 6.43 Elutration rate versus i n i t i a l fines concentration 128 white f i n e bands l e f t impressions a g a i n s t the red background which were measured o u t s i d e the k i l n . The procedure was done from both ends of the bed to ensure measurements of a l l bands. As r e p o r t e d on Table 6.4, the band s i z e s were not the same, however t h e i r number was always p r o p o r t i o n a l to the f i n e s c o n c e n t r a t i o n . The average s i z e of the coarse bands was 85cm f o r the 5%, 55cm f o r the 10% and 25cm f o r the 15% f i n e s c o n c e n t r a t i o n . 6 .7 CORRELATION OF ELUTRIATION RATES From c o n s i d e r a t i o n s of the i n t e r a c t i n g f o r c e s a c t i n g on the bed of p a r t i c l e s , Appendix B, the e l u t r i a t i o n r a t e can be s a i d to depend on the f o l l o w i n g v a r i a b l e s ; r S = R S ' T = f ( r ' P p ' P , M ' d p ' g ' R ' X'"' X> = F ( U r , p p , p, u, d p , g, R, X, co, X) (6.3) where X i s the % f i l l and X i s the angle of repose of the m a t e r i a l . Dimensional a n a l y s i s leads to the f o l l o w i n g r e l a t i o n s h i p ; s = F ( _ L , _T_ , , J 2 , I £ , X f x) (6.4) pU TD 2 gdp v g D where D=2R. The f r i c t i o n v e l o c i t y U r can be r e p l a c e d by the average Table 6 . 4 Typical Size of Segregated Bands in a Bimodal Bed. RUN L o c a - Number of f i n e bands t i o n from e x i t 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 (cm) (cm) TO 3 .7 4.3 4 .5 4.3 60 5.0 7.3 6.0 6.2 3 .0 4.2 7.0 3.1 25 5.3 7.0 5.2 5.2 6.7 6.8 4.7 4.3 5.0 6 .6 4.2 20 1.8 3.8 6.2 6.1 7 .2 9 .0 5.4 5.2 4.1 4 .4 4.0 3 .9 50 3 .9 6.5 7.3 7.3 3 .6 7 .0 3 .8 2.8 82 3.9 5.3 4.8 7.0 S19 0.05 S25 0.10 S27 0.15 S32 0.15 534 0.10 535 0.05 1 3 0 v e l o c i t y through the following relationship; fpU 2 8 p U2 = — — ( 6 . 5 ) — = f D = /8/f ( 6 . 6 ) and therefore U r d p o ^ £ v »tD and P U T 2 pU : ?s dp 7 s f D 2 d p But UD d 0 fD - f< - ' r 2 ) f D and ( 6 . 7 ) ( 6 . 8 ) Ud D UD d D —-B = — . - E ( 6 . 9 ) Also, from considerations of force balance (Appendix B), the dimensionless relationship takes the form; r_ pU2 UD CJ 2D D s = $( r _ , , — f X,X) ( 6 . 1 0 ) pUD2 7 s d p v g d r 131 where 7_ = (p_ - p)g. In Equation (6.10), the density r a t i o , t> p Pn/Pr does not appear independently because the o v e r a l l entrainment i s not influenced by acceleration of individual p a r t i c l e s in s a l t a t i o n . In the present experiments, the only entrainable material was alumina; thus the la s t term, X, and the scale r a t i o , °/dp, were not changed. Also introducing the s p e c i f i c rate, R g = r s/T, where T is the width of the bed, the % f i l l term, X, can be eliminated. The ultimate dimensionless groups thus become: R q pU 2 pUD ' s p UD v g D (6.11) The f i r s t term on the R.H.S. i s a density modified Froude number which i s the r a t i o of the hydrodynamic force and the gravitational force on the p a r t i c l e . The second term represents the flow Reynolds number which characterises the structure of the flow close to the bed which could be either laminar or turbulent depending on the value of th i s group. The t h i r d term is the rotational Froude number which i s an indication of the r e l a t i v e importance of the cent r i f u g a l and gravitational forces acting on the p a r t i c l e . The la s t term is the scale r a t i o which accounts for the fact that flow Reynolds number instead of the p a r t i c l e Reynolds number i s being used. Replacing 4> in Equation (6.11) with a power function we have: R. pUD = C pU2 X UD y CJ2D z . ?s dp V g D w (6.12) 1 32 The exponents x, y, z and w, and the constant C were then determined empirically by f i t t i n g with the experimental data using the least-squares method. The vel o c i t y r a t i o U/Ut, i s uniquely dependent on the f i r s t two groups as shown below and therefore need not be present. C D = — ( 6 . 1 3 ) D 3pU2 therefore U 3C n pU2 — = v/( — - ) (6.14) U t 4 ?s dp But since C D is a function of the p a r t i c l e Reynolds number then U UcL pU2 — = * ( — B , ) (6.15) U T v 7 s d p I n i t i a l estimates indicated that the rough wall data best f i t t e d the dimensionless equation when the flow Reynolds number and the scale r a t i o are replaced by the i r equivalent, the p a r t i c l e Reynolds number as shown in Equation (6.9). However, since only gas v e l o c i t y was varied in the experiment, the groups containing the gas v e l o c i t y term were combined for subsequent c o r r e l a t i o n . This leaves two dimensionless groups in the co r r e l a t i o n for the dimensionless e l u t r i a t i o n rate, one for the v e l o c i t y and the other for the r o t a t i o n a l speed term. These groups inevitably 1 33 c o n t a i n parameters which have not been v a r i e d i n the e x p e r i m e n t s and hence the exponents on t h o s e parameters have not been v e r i f i e d . The rough w a l l d a t a ( T a b l e 6.5) thus y i e l d the f o l l o w i n g e q u a t i o n pUD = 0.423 pU> 5.05 " CJ2D 0. 1 44 7 e d 2 L ' S p J g (6.16) The r e g r e s s i o n c o e f f i c i e n t f o r the above a n a l y s i s , R 2, was 0.9 and the s c a t t e r p l o t of the p r e d i c t e d r a t e , r.h.s of E q u a t i o n (6.16) i n comparison t o the e x p e r i m e n t a l l y o b t a i n e d r a t e , l . h . s of same e q u a t i o n , i s shown i n F i g u r e ( 6 . 4 4 ) . The f i r s t term i s the r a t i o of the d e n s i t y m o d i f i e d Froude number and the p a r t i c l e Reynolds number. The o v e r a l l dependence on the gas v e l o c i t y , which appears i n two g roups, i s R s a U 6. The a n a l y s i s f o r the smooth w a l l d a t a ( T a b l e 6.6) y i e l d e d the f o l l o w i n g power f u n c t i o n pUD = 0.13 5.29 " co2D -0.055 7 d 2 L 's p J g (6.17) w i t h a r e g r e s s i o n c o e f f i c i e n t of 0.883 and a s c a t t e r p l o t as shown i n F i g u r e ( 6 . 4 5 ) . The r o t a t i o n of the w a l l shows a s l i g h t n e g a t i v e i n f l u e n c e as the rough w a l l i s c o v e r e d i n t h i s c a s e . However the o v e r a l l exponent on the f l o w v e l o c i t y 6 29 i s of the o r d e r of 6 i.e.Rg a U . In the bimodal system, the r a t e , R g, was c o r r e l a t e d as above w i t h the c o n c e n t r a t i o n i n t r o d u c e d as an a d d i t i o n a l term. Thus 1 34 T a b l e 6.5 Rough w a l l data used in c o r r e l a t i o n of E q u a t i o n 6 .16. RUN RPM U R s B01 3 2.60 0.00015 B02 6 2.60 0.00034 B04 1 2.60 0.00013 B05 3 3.04 0.00055 B06 1 3.04 0.00048 B07 6 3.04 0.00083 B09 3 3.38 0.00114 B1 1 6 3.38 0.00145 B1 2 1 3.38 0.00111 B1 3 3 3.70 0.00169 B1 4 6 3.70 0.00183 B1 5 1 3.70 0.00177 B1 6 9 3.70 0.00215 B1 7 1 1 3.70 0.00227 B18 3 3.38 0.00106 B1 9 9 3.38 0.00136 B20 6 3.38 0.00115 B21 1 3.38 0.00115 B22 1 1 3.38 0.00152 B23 3 2.92 0.00036 B24 9 2.92 0.00072 B25 1 2.92 0.00036 B26 6 2.92 0.00057 B27 1 1 2.92 0.00092 B28 1 1 2.61 0.00058 B29 6 2.61 0.00030 B30 3 2.61 0.00018 B31 9 2.61 0.00048 B32 1 2.61 0.00015 B33 6 2.58 0.00029 B35 1 2. 58 0.00011 B36 3 2.58 0.00016 B38 6 3.03 0.00072 B40 1 3.03 0.00054 B4 1 3 3.03 0.00055 B43 3 3.43 0.00115 B44 1 3.43 0.00115 B46 6 3.43 0.00135 1 35 Figure 6 .44 Scatter plot of predicted versus observed dimensionless entrainment from a uniform sized bed fexposed wall k i l n Table 6.6 Smooth wall data used in co r r e l a t i o n RUN RPM U R, B48 3 4.13 0.00293 B49 1 4.13 0.00314 B50 9 4.13 0.00276 B51 1 1 4.13 0.00276 B52 6 4.13 0.00275 B53 1 3 4.13 0.00279 B54 6 3.70 0.00120 B55 1 1 3.70 0.00138 B56 3 3.70 0.00136 B57 1 3.70 0.00171 B58 9 3.70 0.00127 B59 1 1 3.04 0.00036 B60 6 3.04 0.00028 B61 9 3.04 0.00032 B62 1 3.04 0.00044 B63 3 3.04 0.00029 B64 3 4.11 0.00263 B65 1 4.11 0.00281 B67 6 4.11 0.00283 B69 3 3.70 0.00178 B69A 3 3.70 0.00181 B70 6 3.70 0.00194 B70A 6 3.70 0.00195 B73 1 3.70 0.00186 B73A 1 3.70 0.00193 B74 3 3.10 0.00049 B74A 3 3.10 0.00051 B77 6 3.10 0.00072 B78 1 3.10 0.00072 B79 1 3.70 0.00212 B80 3 3.70 0.00203 B8 1 6 3.70 0.00223 B84 3 3.38 0.00129 B84A 3 3 . 38 0.00122 B85 1 3.38 0.00143 B86 6 3.38 0.00143 B89 3 2.87 0.00033 B89A 3 2.87 0.00025 B90 1 2.87 0.00040 B90A 1 2.87 0.00038 B91 6 2.87 0 . 00040 1 37 Figure 6.45 Scatter plot of predicted versus observed dimensionless entrainment from a uniform sized bed and covered wall pUD = C pU2 X [ u d p ] y " co2D " . ?s dp . V g 1 38 (6.18) Using regression analysis and combining the f i r s t two terms on the right hand side as before, the experimental data shown in Table 6.7 yielded a best f i t of the form: R, pUD = 4.15 pUp 5.5 co2D . ' s p . g 0.36 r 1 .28 L f (6.19) with a regression c o e f f i c i e n t of 0.93 and a scatter plot shown in Figure 6.46 From Equation (6.2) and (6.19), Kr= 4.15pUD pUi> 5.5 " CJ2D 0.36 7 d 2 L ' s p . g (6.20) Thus the rate constant, Kr, increases with both gas v e l o c i t y and rotational speed. For the multiple regression analysis, the above power functions were l i n e a r i z e d by taking the logarithm of both sides of the equation. In this case, the logarithms of the dimensionless groups on the r.h.s represented the independent variables with the exponents as corresponding c o e f f i c i e n t s . The equations a r i s i n g from the least square analysis were then solved simultaneously by numerical technique to evaluate the values of the exponents. In another analysis involving the Froude group and Reynolds group as separate groups, the p a r t i c l e (density modified) 1 39 Table 6.7 Data for the bimodal system used in co r r e l a t i o n of Equation 6.19 RUN C, RPM U Rs S32 15 1 3.47 0.000083 S33 10 1 3.47 0.000057 S40 5 1 3.47 0.000022 S34 10 3 3.47 0.000110 S35 5 3 3.47 0.000042 S41 15 3 3.47 0.000221 S36 5 6 3.47 0.000090 S37 15 6 3.47 0.000461 S39 10 6 3.47 0.000277 S19 5 3 2.70 0.000011 S18 15 3 2.70 0.000035 S17 10 3 2.70 0.000021 S20 10 6 2.70 0.000033 S21 15 6 2.70 0.000069 S22 5 6 2.70 0.000018 S24 5 3 3.74 0.000074 S25 10 3 3.74 0.000164 S26 15 3 3.74 0.000302 S27 15 6 3.74 0.000559 S28 10 6 3.74 0.000234 S29 5 6 3.74 0.000122 S30 1 5 1 3.74 0.000157 S31 10 1 3.74 0.000103 S32 5 . 1 3.74 0 .000044 Figure 6.46 Scatter plot of predicted versus observed dimensionless entrainment from a bimodal bed 141 Froude number which characterizes the r a t i o of f l u i d force on the p a r t i c l e to i t s weight was the predominant factor in a l l the c o r r e l a t i o n s . The influence of the Reynolds number which characterizes the flow structure near the bed was weaker especially in the case of the unimodal system. For a flow which i s h y d r a u l i c a l l y rough with respect to the coarse component in a bimodal system, the entrainable fines could fi n d themselves s i t t i n g in the 'laminar sublayer' between the coarse p a r t i c l e s . Hence the flow Reynolds number w i l l also be important. However these conclusions are subject to further experimental v e r i f i c a t i o n in which the effect of changes in the f l u i d and p a r t i c l e properties are studied. The scale r a t i o which characterizes the influence of the flow depth did not appear in any of the co r r e l a t i o n s . P a r t i c l e transport as discussed above were confined to regions close to the bed. Contrary to the correlations of Khodorov (1) and L i (3) the flow Froude number was not found useful. The corresponding dimensional cor r e l a t i o n which involve only the parameters varied in the experiments are : Rough wall R s = 1.39 x 10~ 6 . u 6 * 0 5 . c o 0 ' 2 8 8 (6.21) Smooth wall R c = 0.345 x 10" 6 . u 6 ' 2 9 . c j ~ 0 - 1 1 (6.22) Bimodal R s = 3.65 x 10~ 6 . U 6' 5 . c j ° - 7 2 C f 1 - 2 8 (6.23) Chapter 7 MATHEMATICAL MODELING OF ENTRAINMENT 7.1 INTRODUCTION In t h i s chapter, a mathematical model of the transport of dust in the freeboard, based on the experimental observations discussed in Chapter 6 w i l l be presented. The most important operating conditions which aff e c t the transport of p a r t i c l e s examined are the gas flowrate and the rotational speed. As a preliminary analysis, the eff e c t of the rotating wall w i l l not be considered. The model i s then tested against the experimental data obtained with the k i l n wall covered. However i t should be applicable to k i l n operations at low rot a t i o n a l speeds where the roughness effect is n e g l i g i b l e . The experimental observations indicate that c o l l i s i o n of s a l t a t i n g p a r t i c l e s with the bed surface i s the most important factor that governs p a r t i c l e pick-up. F l u i d l i f t i s c e r t a i n l y i n f l u e n t i a l in i n i t i a t i n g the s a l t a t i o n and turbulent fluctuations of both pressure and skin f r i c t i o n might also play a role. However, the c o l l i s i o n of returning p a r t i c l e s thereafter constitutes an e f f i c i e n t mechanism for the transfer of f l u i d momentum to the bed. On impact, a p a r t i c l e may rebound or eject other p a r t i c l e s and embed i t s e l f in the surface of the bed. The ov e r a l l effect i s a 1 4 2 143 reduction in the horizontal component of momentum and a gain in the v e r t i c a l or normal component of momentum of the p a r t i c l e . Thus for successive undiminished s a l t a t i o n events, the f l u i d must restore the horizontal v e l o c i t y of the p a r t i c l e by imparting an equivalent impulse during the sal t a t i o n time. Consequently, when the fluid-borne shear stress f a l l s below the impact threshold, the f l u i d w i l l be unable to sustain the s a l t a t i o n and returning p a r t i c l e s on impact w i l l merely expend energy to set surface p a r t i c l e s into surface creep motion and sa l t a t i o n w i l l eventually die out. Thus following Owen (34), the impact threshold can be regarded as the l i m i t i n g condition c o n t r o l l i n g the number of p a r t i c l e s engaged in s a l t a t i o n . Since the t o t a l rate of momentum transfer, or shear stress, i s constant throughout the sa l t a t i o n layer (34), a very good estimate of the transport rate within i t can be obtained from momentum and material balances. A complicating factor, however, i s that the presence of the p a r t i c l e s a l t e r s the ve l o c i t y d i s t r i b u t i o n of the f l u i d in the sal t a t i o n layer. The i n i t i a l p a r t i c l e v e l o c i t y depends on the motion of the interacting p a r t i c l e s before and after c o l l i s i o n and the forces of inter a c t i o n , a l l of which are unknown. Therefore in the absence of any knowledge of the i n i t i a l p a r t i c l e v e l o c i t y and f l u i d v e l o c i t y d i s t r i b u t i o n in the s a l t a t i o n layer, some reasonable estimates are necessary. The i n i t i a l v e l o c i t y of the p a r t i c l e i s 1 44 calculated from a knowledge of the average s a l t a t i o n height which i s i t s e l f estimated from measurements of dust concentration p r o f i l e , ( S e c t i o n 6.3.4, Figures 6.23 and 6.24) and the equation of motion. The f l u i d v e l o c i t y in the sa l t a t i o n layer is taken as the average v e l o c i t y . Velocity p r o f i l e s measured near the bed have values close to the average value (Figure 6.20 and 6.21). The analysis is also confined to bed-load transport only, involving p a r t i c l e s in s a l t a t i o n . As discussed elsewhere (Section 6.3.4), the concentration of sol i d s in suspension farther away from the bed was small under the conditions studied and was neglected. The i n i t i a l analysis considers entrainment from a f l a t horizontal stable bed; effe c t s of i n c l i n a t i o n and rotation are included via correction factors. Furthermore, the treatment i s based on the following assumptions: 1. Bed p a r t i c l e s are uniform in size and shape and are nearly spherical. 2. P a r t i c l e s are transported in s a l t a t i o n . In th i s mode, p a r t i c l e s are transported in a series of i d e n t i c a l steps regardless of location and time. 3. A steady exchange of p a r t i c l e s exists between the bed material and those in the s a l t a t i o n layer. 4. Returning p a r t i c l e s either bounce back or eject fresh p a r t i c l e s , the tangential momentum and excess kinetic energy of the incident p a r t i c l e being absorbed in 145 surface creep. The o v e r a l l picture i s then simply a steady transport of f l u i d momentum to the bed surface via the salt a t i n g p a r t i c l e s . A t y p i c a l p a r t i c l e trajectory based on the observations of Bagnold (28) and Chepil (30), as shown in Figure 7.1, has an i n i t i a l v e r t i c a l upward r i s e and a f i n a l f a l l i n c l i n e d at an angle depending on the terminal velocity of the p a r t i c l e and gas v e l o c i t y . A p a r t i c l e in sal t a t i o n may receive i t s i n i t i a l momentum from the impact of a returning p a r t i c l e or from the turbulent v e l o c i t y f i e l d or f l u i d l i f t . The i n i t i a l impulse, which i s shortlived, determines the i n i t i a l v e l o c i t y of the s a l t a t i n g p a r t i c l e . In Figure 7.1 the streamwise d i r e c t i o n i s represented by the x-axis while the y-axis represents the v e r t i c a l d i r e c t i o n . For a stable f l a t and horizontal bed, conditions in the transverse z-direction are assumed invariant so that the system s i m p l i f i e s to a two-dimensional case. 7.2 MOMENTUM AND MATERIAL BALANCE The general momentum equation applies to both the f l u i d phase and the particulate phase in which U and V are the conjugate components of f l u i d v e l o c i t y and U n, V those of the p a r t i c l e v e l o c i t y . For two-dimensional flow, the equation of motion for the particulate phase can be written Figure 7.2 P a r t i c l e trajetory from an i n c l i n e d bed. 147 a s (64) 3U_ 3U_ 9TJ n n( — P + U — P + V — P ) = _ ( u-U n) + n g Y ( 7 . 1 ) 9t p 9x P 9y T P x f o r t h e x - d i r e c t i o n a n d 9V. n( „ 9V„ 9V„ n — £ + U _ - ^ + V _ — P ) = - ( V - V ) + n g v ( 7 . 2 ) 9t P 9x P 9y T P y f o r t h e y - d i r e c t i o n . The f i r s t a n d s e c o n d t e r m s on t h e R.H.S. o f E q u a t i o n s ( 7.1) a n d ( 7 . 2 ) a r e t h e d r a g f o r c e s a n d g r a v i t a t i o n a l f o r c e s r e s p e c t i v e l y w h i l e r i s t h e r e l a x a t i o n t i m e f o r momentum t r a n s f e r f r o m f l u i d t o p a r t i c l e g i v e n by 3 C D p | U „ | F o r S t o k e s ' f l o w t h i s r e d u c e s t o r=—B-J2 ( 7 . 4 ) 1 8M I n b o t h E q u a t i o n s ( 7 . 1 ) and ( 7 . 2 ) , t h e e f f e c t s o f a p p a r e n t mass, B a s s e t f o r c e a n d d i f f u s i o n h a v e been n e g l e c t e d . F o r t h e f l u i d p h a s e , t h e momentum e q u a t i o n ( f r o m a c o n s i d e r a t i o n o f t h e c o n t i n u i t y e q u a t i o n ) s i m p l i f i e s t o ( 6 5 ) 9U 9U 9U 9P 9 9U p ( — + u — + v — ) = - — + — (-pu'v' + M — ) + p g v 3t 9x 9y 9x 9y 9y x 1 48 nun + -2- (U -U) (7.5) T P for the x-direction and 9V 9V 9V 9P 9 9V p( — + U — + V — ) = - — + — (-pu'v' + M — ) + P Q „ 9t 9x 9y 9y 9x 9x y m^ n + ( V - V ) (7.6) T ^ for the y-di r e c t i o n . 9 For a flow that is steady ( — = 0) on average, and 9t g independent of distance along the stream ( — =0), and 9x since the mean flow i s one-dimensinal (V =0), Equations (7.1) and (7.5) reduce to dU n n nV_ = - (U-U_) (7.7) dy T and dP d r f m_n — + -2- (U -U) (7.8) dx dy T P where dU T F =ii — -pu'v', i e . f l u i d shear stress in the presence of £ dy p a r t i c l e s . Note that u' and v' are turbulent fluctuations of U and V. Equation (7.8) reduces to the single-phase 1 49 turbulent flow case when n=0 and the single-phase laminar flow case when n=u'=v'=0. Substitution of Equation (7.7) into equation (7.8) yiel d s dP d r f dU_ — = — - " mDn V — 2 (7.9) dx dy P P ay But dP/dx = dr T/dy i . e . the horizontal pressure gradient balances the t o t a l v e r t i c a l gradient of shearing stress. Therefore: dTm d r f dU_ = — - " m n V — £ (7.10) dy dy P P dy and d r T = d r f - mpn V pdU p r T = r f + r s (7.11) where r g i s the shear stress due to the presence of the p a r t i c l e s , i s the fluid-borne stress and T t the t o t a l shear stress due to f l u i d flow and p a r t i c l e impact. The general momentum balance in the x-direction thus reduces to the simple form: TT " r f = r s = " m p n V p U P ( 7 , 1 2 ) to be coupled with the solids continuity equation to follow. 150 In the s a l t a t i o n l a y e r , the p a r t i c l e number d e n s i t y c o n s i s t s of upgoing p a r t i c l e s n , and downgoing p a r t i c l e s n 2 , i . e . n = n , + n , (7.13) For s teady c o n d i t i o n s , c o n t i n u i t y r e q u i r e s tha t the v e r t i c a l f l u x (mass r a t e of p a r t i c l e s per u n i t h o r i z o n t a l area) i s c o n s t a n t . Thus the v e r t i c a l f l u x a t any p o i n t upwards or downwards must e q u a l tha t at the bed s u r f a c e , i e V p 1 n 1 = V p l 0 n l 0 V P 2 n 2 = V p 2 0 n 2 0 ( 7 ' 1 4 ) where the v e l o c i t y components of a t y p i c a l p a r t i c l e at a d i s t a n c e y from the bed s u r f a c e are U p 1 , V p 1 i n the upgoing p a r t ( F i g u r e 7.1) of the t r a j e c t o r y and U p 2 , V p 2 i n the downgoing p a r t and the s u b s c r i p t 0 denotes the s u r f a c e of the bed . A l s o at the s u r f a c e of the bed, f o r a s teady exchange of p a r t i c l e s between the bed m a t e r i a l and those in s a l t a t i o n , c o n t i n u i t y of v e r t i c a l f l u x y i e l d s V p 1 0 n l 0 = _ V p 2 0 n 2 0 (7.15) where the n e g a t i v e s i g n denotes a change in d i r e c t i o n of the downward f l u x . From E q u a t i o n s (7.14) and (7.15) 151 Vp1 n1 = ~ Vp2 n2 = V p l O n l O = ~ Vp20 n20 and V p l O n l O V pi n. V p l O n l O V. (7.16) p2 The horizontal or streamwise flux however, varies with y and is made up of flux of upgoing p a r t i c l e s and downgoing p a r t i c l e s . The mass flux per unit bed width, G,in the horizontal d i r e c t i o n i s thus given by (34) G = ; o m P ( n 1 U P l + n 2 U p 2 ) d Y u vp1 vp2 = m n l 0V 1 f J ; ( J B i - ^ 2 ) d y (7.17) P 1 0 P 1 U o v p l v p 2 In Equation (7.12), U and V represent the net v e l o c i t y of upgoing and downgoing p a r t i c l e s i . e . U p - U P 1 + Up2 V p = V p l " Vp2 ( 7 ' 1 8 ) At the bed surface, p a r t i c l e s leave in a di r e c t i o n normal to 152 the surface, and U p 1Q = 0 (see Figure 7.1); thus Equation (7.12) reduces to T t - r f = m p n 2 0 V p 2 0 U p 2 0 = m p n l 0 V p l 0 U p 2 0 (7.19) Substituting Equation (7.19) into (7.17) G = -2—1 J ( - E l - - B l ) d y (7.20) UP 2 0 0 V P 1 Vp2 The value of the fluid-borne shear stress depends on the quantity of p a r t i c l e s engaged in s a l t a t i o n . Following Owen (34) and Yal i n (42), the l i m i t i n g value of i s assumed to be r Q , the f l u i d stress at the impact threshold. Therefore r T - T F = K 0 ( T T - T 0) (7.21 ) where K 0 i s a proportionality constant with values ranging between 0 and 1. For the steady conditions under which the experiments were conducted, in which dust entrainment reached an optimal value for most part of the cylinder length, (see Section 6.3.4), K 0 w i l l be nearly equal to 1. Therefore r f = T q and Equation (7.20) becomes G = T-^lo ; h ( Hr2i _ ZB2 ) d y ( 7 . 2 2 ) UP 2 0 0 Vp1 V P 2 This is the t o t a l mass flux of p a r t i c l e s per unit width over a horizontal stable bed across a v e r t i c a l plane 153 perpendicular to the f l u i d stream. The term r T - TQ represents that part of the t o t a l shear stress on the bed due to the impact of the sa l t a t i n g p a r t i c l e s . The remaining term containing the vel o c i t y components of the s a l t a t i n g p a r t i c l e s i s hereby referred to as the ve l o c i t y factor, V f. On an i n c l i n e d bed, not the whole bed surface i s subjected to p a r t i c l e bombardment and e l u t r i a t i o n has been observed to f a l l with rotational speed at least in the slumping and r o l l i n g regimes studied. To correct for the effect of bed i n c l i n a t i o n and the eff e c t of rotation on entrainment, two factors R, and K2 are introduced into Equation (7.22) to give G = K,K2 J ( - £ 1 - J?2 )dy = K l K 2 ( r T - r 0 ) V f (7.23) Up20 0 V P 1 Vp2 The values of K, and K 2 w i l l be determined in a following section. T t can be estimated from the rel a t i o n s h i p 1 r T = - f p U 0 2 (7.24) 1 8 where f i s the f r i c t i o n factor and U 0 i s the average v e l o c i t y . The impact threshold shear stress, T 0, can be estimated s i m i l a r l y i f the v e l o c i t y at the threshold i s known. Otherwise i t can be estimated from the empirical relationship of Bagnold (28) and Chepil (35) as(Section 2.4.2) 154 r 0 = 0.0064? d (7.25) b p The f r i c t i o n factor f, can also be obtained from the Moody f r i c t i o n diagram or i t s equivalent correlation 1 D 9.28 — - 21og — = 1.14 - 2log(1 + ) (7.26) / f d p Re/f(d p/D) 7.3 PARTICLE TRAJECTORY The ve l o c i t y factor, , in Equation (7.23) can be estimated from a solution of Equations (7.1) and (7.2) describing the p a r t i c l e motion. Under the conditions imposed on the system, i.e . steady developed flow, Equation (7.1) reduces to Equation (7.7) (Section 7.2) and (7.2), reduces s i m i l a r l y to Equation 7.27 dV„ V-V„ V —2 = 2 + g (7.27) p dy r * then since V = 0 dV_ V_ V —2 = - _E + g (7.28) p dy r y The nature of r in Equations (7.7) and (7.28) depends on the drag c o e f f i c i e n t on the p a r t i c l e s (Section 7.2). Assuming no p a r t i c l e - t o - p a r t i c l e interaction of the s a l t a t i n g p a r t i c l e s , the drag c o e f f i c i e n t of flow around the p a r t i c l e s , C D, in the intermediate range was taken to be that given by the 155 correlation of S c h i l l e r and Naumann obtained from Table 5.1 (66) of the form C n = — (1 + 0.15Re 0* 6 8 7) u Re (7.29) such that Equations (7.7) and (7.28) assume the form dU dt dV dtL, U-LV ( U - l L j dy dV. dt dy P - |U 0.687 RI E = v D ^ = - Ws> - | u R | 0 - 6 8 7 + g where r , =—^P-—P 18M p d 1 , 3 1 3 *' = G.3?3 U.687 2.7M and |UR| = (U-U p) 2 + V p 2 0.5 (7.7a) (7.28a) 156 Separating the trajectory into the upward and downward components of motion, Equations (7.7a) and (7.28a) become for the upward motion dU n 1 du . U-u . (U-U . ) | U R 1 | 0 * 6 8 7 — P - i = v_. — E l = 21 + P 1 ' R 1, ' (7.30) dt, P1 dy, Ti r2 dv n 1 dv n 1 V n 1 V ,|U R 1| 0' 6 8 7 —21 = v_. —21 = - -21 - Pi 1 R1 ' - 7 (7.31) dt, P 1 dy, r , r 2 9 and for the downward motion dU_, dU_, U-U_, (u -u„ , ) |U D,| 0' 6 8 7 __P2 = v —P-2- = 21 + p2 ' R2l (7.32) dt 2 P^ dy 2 r, r 2 ^ . V p 2 g E l . - ! ^ - V l " R 2 l ° - 6 8 7 ( 7 . 3 3 ) d t 2 P 2 dy 2 r, r 2 9 where 7 q = ( ^  )g = g v (7.34) 9 pp y Equations (7.30) and (7.31), (7.32) and (7.33) have been solved using numerical methods with the following i n i t i a l conditions: for Equations (7.30) and (7.31), at y, = 0 (refer to Figure 7.1) UP 1 - U P 1 0 - 0 V p l = V p l 0 (7.35) The i n i t i a l p a r t i c l e v e l o c i t y , v p i r j ' w a s n o t e a s Y t 0 estimate a n a l y t i c a l l y in the absence of any knowledge of the forces of interaction in a c o l l i s i o n which is not one 1 57 dimensional. It was, therefore, deduced from experimental measurements of the average sa l t a t i o n height, h , i t s e l f estimated from dust concentration p r o f i l e measurements (Section 6.3.4). Noting that at the top of the trajectory, y!=h, V p 1= 0 = v p i h ' vplO w a s obtained from a solution of Equation (7.31) that s a t i s f i e d the above conditions by t r i a l and error. For Equations (7.32) and (7.33) at y 2 = h-y, = 0, Up2 = Up2h = Up1h V p 2 = Vp1h - 0 ( 7 - 3 5 )  up1h c o u l d b e obtained from a solution of Equation (7.30) at y,=h. Thus at any location, y=y 1 f v e l o c i t y components of the upgoing and downgoing p a r t i c l e s were evaluated. A detailed description of the solutions to Equations (7 . 30 )-(7 . 33 ) is presented in Appendix C. For an average alumina p a r t i c l e of size 64M and terminal v e l o c i t y 0.41 m/s obtained from standard c a l c u l a t i o n techniques(66), as outlined in Appendix C, solution of the above equations and subsequent evaluation of Equation (7.22) are presented here. Under the conditions of the experiment, p (25°C) = 1.196 kg/m3 M = 1.8215 x 10" 5 N s/m2 Therefore for a p a r t i c l e density of 3990 kg/m3 158 T, =0.0498 s T 2 =0.1239 s Then, for an average s a l t a t i o n height, h =0.02 m and average flow v e l o c i t y , U = 3.7 m/s, solution of Equations (7.30) (7.33) with the boundary conditions outlined above gives t y p i c a l values of the p a r t i c l e v e l o c i t y as: i n i t i a l v e r t i c a l v e l o c i t y , v p i n = 1.125 m/s f i n a l horizontal v e l o c i t y , U p 2n = 3.62 m/s f i n a l v e r t i c a l v e l o c i t y , V p 2 n = 0.32 m/s Sim i l a r l y , the velocity component of the p a r t i c l e at any location could be determined. Subsequently, the integral in equation 7.22 was evaluated numerically using the adaptive Simpson's method which gave a value of 0.425. Then the velo c i t y factor, V f = 0.425/3.62 s At the average velocity of 3.7 m/s, Trp (from Equations 7.24 and 7.26) = 0.046 N/m2 At the threshold velocity of 2.62 m/s (Section 6.3.1) r 0 = 0.0246 N/m2 159 Thus for a horizontal stable (no rotation) bed, the entrainment rate per unit bed width, given by Equation (7.22) is thus evaluated as G = (T T - T q) V f = (0.046-0.0246) x 0.425/3.62 = 0.0025 kg/m.s The horizontal distance t r a v e l l e d by the p a r t i c l e at the end of the s a l t a t i o n could also be obtained from a double integration of Equation (7.7) with respect to time over the t o t a l time of s a l t a t i o n . An approximate value can however be obtained from a Stokes' regime motion as x = U(t - 7,(1 - e~ t / TM) (7.36) For a sa l t a t i o n height of 2.0 cm, t y p i c a l horizontal jump distance at the end of the s a l t a t i o n for various mean flow v e l o c i t i e s are shown in Table (7.1). The sa l t a t i o n period t = t, + t 2 in Equation (7.36) was obtained from the solutions of Equations (7.30) - (7.33). 160 Table 7.1 Typical jump distance of a s a l t a t i n g p a r t i c l e Average gas veloc i ty m/s 276 3.0 4.0 5.0 6.0 7.0 8.0 P a r t i c l e jump distance cm 1978 29.7 39.6 49.5 59.4 69.3 79.2 161 7.4 EFFECT OF BED INCLINATION AND ROTATION 7 . 4 . 1 ESTIMATION OF K , On an i n c l i n e d bed, the i n i t i a l upward v e l o c i t y of the p a r t i c l e can be resolved into components normal and p a r a l l e l to the in c l i n e d surface. The p a r t i c l e t r a j e c t o r y , with respect to the normal ve l o c i t y component, i s similar to the two-dimensional case shown in Figure (7.1) and described by Equations (7 . 30)-(7.33) but with 7 replaced by 7 Cos0 where y y 6 i s the bed i n c l i n a t i o n , equal to the dynamic angle of repose of the s o l i d s . However, owing to i t s v e l o c i t y component in the transverse d i r e c t i o n , the p a r t i c l e is displaced a distance OB (Figure 7.2) at the end of the trajectory. Since c o l l i s i o n of s a l t a t i n g p a r t i c l e s with the solids bed has been observed to play a major role in the entrainment of p a r t i c l e s , R, w i l l be expected to be a function of the f r a c t i o n of the t o t a l bed area that i s bombarded by the s a l t a t i n g p a r t i c l e s . This expectation i s j u s t i f i e d from the photographic experiments discussed in Section 6.3.6. The p a r t i c l e trajectory in the transverse d i r e c t i o n is given as in Equation (7.31) (assuming one-dimensional motion) as dw 1 .687 w (7.37) P dz 1 62 On a stable inclined bed, the i n i t i a l transverse v e l o c i t y , , of the p a r t i c l e i s assumed to be zero i . e . at z = 0, wp = WpQ = 0. However, in a slumping/rolling bed, the i n i t i a l transverse v e l o c i t y w i l l be close to the o r i g i n a l v e l o c i t y of the p a r t i c l e in the passive region of the bed i . e . at z = 0,Wp = WpQ = 7TNR/30. With this as the i n i t i a l condition, the transverse displacement of the p a r t i c l e , z = OB (Figure 7.2) is obtained from a numerical solution of Equation ( 7 . 3 7 ) . The f r a c t i o n of the bed width affected by c o l l i s i o n i s then estimated as T-OB Ki = (7 .38) T where T i s the t o t a l width of bed which is a function of % f i l l . As rpm increases, K, decreases. C o l l i s i o n on the bed could only take place at distances beyond OB down the inclined bed measured from the upper edge of the bed. 7.4 .2 ESTIMATION OF K? At the same time, dust concentration at the lower edge of the bed was observed to f a l l with increased rpm (Section 6 . 3 . 5 ) . P a r t i c l e s in t h i s section of the bed, close to the rotating wall, experience a cen t r i f u g a l force, imparted by the rotation as they enter the passive region of the bed. Fewer p a r t i c l e s are therefore ejected, or the height of salt a t i o n of individual p a r t i c l e s i s reduced, as the i n i t i a l 163 p a r t i c l e velocity of ejection i s diminished by the v e l o c i t y toR in the opposite sense into the passive region imparted by the rotation. The bed at t h i s lower edge appears to be "folded" back into the passive region. The o v e r a l l dust pick-up w i l l therefore be expected to f a l l by a factor of: V. K- pi 0 VP 1 0 + " R (7.39) The complete form of equation 7.23 w i l l thus be G = T-z V pi 0 VP 1 0 + " R ( r T " T o } U P20 h U n 1 U n ? ; ( _P_L - _ 2 l ) d y V pi V. p2 (7.40) 7.5 MODEL PREDICTIONS The overa l l predictions of the model i l l u s t r a t i n g the ef f e c t of d i f f e r e n t parameters are presented in Figures (7.3) - (7.5). A t y p i c a l i n d u s t r i a l k i l n of 3.5 m diameter operating at a rotational speed of 2 rpm was selected for the estimation of the parameters in the model. The shear stress was obtained from Equations (7.24) and (7.26). The threshold shear stress , r Q was estimated from Equation (7.25). For p a r t i c l e s of d i f f e r e n t densities, the model Equation (7.40), predicts as expected, higher values of the e l u t r i a t i o n rate (G = R g) per unit bed width, for l i g h t e r p a r t i c l e s . However, as shown in Figure (7.3), the effect of 1 6 4 U o (m/s) F i g u r e 7.3 E f f e c t of p a r t i c l e d e n s i t y and gas d e n s i t y on model p r e d i c t i o n s . D = 3.5 m, N = 2 rpm. 165 CO 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.00-1 0.003 0.002 0.001 0.000 30 h = 2.0cm p9 - 3000 k g / m 3 p - 0.679 k g / m 3 U = 8.0 m/s U = 6.0 m/s U = 4.0 m/s 50 70 90 d (M) 110 F i g u r e 7.4 E f f e c t of p a r t i c l e s i z e on model p r e d i c t i o n s . 166 0.010 0.008 U u = 6.0m/s p°r - 3000 k g / m 3 p'= 0.679 k g / m ' CO 0.006 - 0.004 0.002 d = 50 fj. 0.000 0.5 1 1.5 2 2.5 3 3.5 4 h (cm) 4.5 F i g u r e 7.5 E f f e c t of assumed v a l u e of s a l t a t i o n h e i g h t on model p r e d i c t i o n s . 167 p a r t i c l e density i s also influenced by the physical properties of the gas such as i t s density which affects the shear stress (Equation 7.24) and the relaxation times T, and T 2 . At the same gas v e l o c i t y , p a r t i c l e s of the same density are entrained more e a s i l y in a denser f l u i d than in a less dense f l u i d . The effect of p a r t i c l e size i s shown in Figure (7.4) where larger p a r t i c l e s exhibit greater resistance to entrainment because of greater mass. In Figure (7.5), the effect of the assumed value of the s a l t a t i o n height i s shown. The entrainment of finer p a r t i c l e s predicted by the model i s seen to be more sensitive to changes to s a l t a t i o n height than coarser p a r t i c l e s . 7.6 COMPARISON WITH EXPERIMENTAL DATA Th»e model predictions based on Equation (7.40) are compared to the experimental data in Figures 7.6-7.8 to i l l u s t r a t e the effect of rotational speed and a i r v e l o c i t y at various % f i l l s on dust pick-up. Only data for the "smooth wall", bent-lip configuration were considered since the effect of the wall roughness had not been accounted for in the development of the model. Also, experimental data obtained beyond 6 rpm for the cases of 10 and 15 % f i l l were excluded from the comparisons because of the apparent influence of the exit dam as discussed in Section 6.3.2 at these rotational speeds. Over the range tested, the model predictions exhibit very good agreement with the 1 6 8 28.0 24.0 h 20.0 12.0 u 3 8.0 4.0 0.0 1 1 %F111=5 1 • 4.13m /s — • • _ — 3.70m /s — _ o - o O • 3.04m /s o (J -A A 1 A 1 A 1 A i 0 6 RPM 12 F i g u r e 7 . 6 C o m p a r i s o n o f model p r e d i c t i o n s w i t h e x p e r i m e n t a l d a t a p o i n t s a t 5 % f i l l . 169 F i g u r e 7.7 Comparison of model p r e d i c t i o n s wi th e x p e r i m e n t a l data p o i n t s at 10% f i l l . 1 70 28.0 h %Fill=15 24.0 20.0 3.70m/s • 16.0 3.38m/s •ri 12.0 o o 8.0 4.0 2.87m/s .A. A A 0.0 0 4 RPM 6 8 F i g u r e 7.8 C o m p a r i s o n o f m o d e l p r e d i c t i o n s w i t h e x p e r i m e n t a l d a t a p o i n t s a t 15% f i l l . 171 experimental data. The deviation from the predicted values of the experimental data f a l l within 10% except in the case of the 5% f i l l at 3.7 m/s where the deviation reached about 30%. The s l i g h t minimum exhibited by most experimental data could be attributed to the s l i g h t e f f e c t of the exit dam. Data for higher rotational speeds have been excluded from the comparisons. Model predictions at 2 rpm for various a i r v e l o c i t i e s are shown in Figure 7.9 where experimental data at 1 and 3 rpm have been presented for comparison. Although s a l t a t i o n height was maintained at 2.0 cm for a l l v e l o c i t i e s , the agreement i s seen to be very good since the effe c t of the exit dam i s neg l i g i b l e at these ro t a t i o n a l speeds. In applying the model, the only f i t t i n g parameters introduced were the sa l t a t i o n height, h, the bed width, T, which varied with % f i l l , and the shear stress, T T, estimated from the f r i c t i o n factor obtained from the flow Reynolds number and the flow roughness factor, Equation (7.26). The impact threshold, r Q , was the same at 0.0246 N/m2 in a l l cases. Table 7.2 shows values for various experimental conditions. Table 7.3 shows some t y p i c a l input data and corresponding outputs where the sa l t a t i o n height, h, was marginally adjusted to r e f l e c t the changes in v e l o c i t y . The effect of errors in the selected parameters are shown in Figures (7.10)- (7.12) for density, p a r t i c l e size and sa l t a t i o n height. These have been presented in the form of correction factors C^, C p and respectively to the base case described above. E l u t r i a t i o n appears to be more Table 7.2 Summary of run c o n d i t i o n s i n t r o d u c e d i n t o model e q u a t i o n 7.40 Runs nos. % f i l l Bed Average Re shear w i d t h a i r v e l . X 1 0 " 4 s t r e s s (m) (m/s) (N/m 2) B48-B53 5 0.121 4.13 5.31 0.0556 B54-B58 5 0.121 3.70 4.76 0.046 B59-B63 5 0.121 3.04 3.96 0.0318 -B64-B67 10 0.145 4.11 5.09 0.053 B69-B70 10 0.145 3.70 4.58 0.046 B73-B78 10 0.145 3.10 3.84 0.033 B79-B81 1 5 0. 1 65 3.70 4.39 0.0471 B84-B86 1 5 0.165 3.38 4.01 0.040 B 8 9 - B 9 1 1 5 0. 1 65 2.87 3.40 0.0296 1 73 T a b l e 7 . 3 I n p u t and O u t p u t p a r a m e t e r s f o r p r e d i c t i o n s b a s e d on E q u a t i o n 7.40 X (%) 5 10 1 5 T (m) 0 . 1 2 1 0 . 1 4 5 0 . 1 6 5 U Q (m/s) 4 . 1 3 3 . 7 0 2 . 8 7 Trp (N/m2) 0 . 0 5 5 6 0 . 0 4 6 0 . 0 2 9 6 r Q (N/m2) 0 . 0 2 4 6 0 . 0 2 4 6 0 . 0 2 4 6 h (m) 0 . 0 2 2 0 . 0 2 0 0 . 0 1 8 V p i 0 (m/s) 1 . 2 3 1 . 1 2 5 0 . 9 4 2 U p 2 0 (m/s) 4 . 0 6 3 . 6 2 2 . 7 9 N (rpm) 0 . 0 3 . 0 6 . 0 K, 0 . 81 0 . 8 4 2 0 . 8 6 3 K 2 1 . 0 0 0 . 9 7 2 0 . 9 3 7 INTEGRAL 0 . 5 0 2 0 . 4 2 5 0 . 3 2 9 r g (Kg/min) 0 . 0 2 2 0 6 0 . 0 1 7 1 0 0 . 0 0 3 6 2 F i g u r e 7.9 Comparison of model p r e d i c t i o n s w i th e x p e r i m e n t a l d a t a at 1 and 3 rpm at v a r i o u s v e l o c i t i e s . 1 75 sensitive to changes in p a r t i c l e s i z e . A change of 10% in the predicted rate can be accomplished with only 6% change in p a r t i c l e size. However, for the same change, 8.5% change in p a r t i c l e density or 12.5% error in the measurement of the saltation height w i l l be necessary. A 50% error in the estimation of the s a l t a t i o n height w i l l show only about 30% change in the predicted rate. The same error in p a r t i c l e size w i l l predict e l u t r i a t i o n rates about 60% higher or lower.. Although the analysis and the experiments have been confined to the slumping and r o l l i n g bed behaviours, which is what pertains in rotary k i l n operation, no s i g n i f i c a n t changes are expected to occur when the bed i s cascading. The quantity of solids in transport i s controlled by the l i m i t imposed by the impact threshold. Any excess s o l i d s introduced into the flow when the residual f l u i d shear i s at the impact threshold value, w i l l be immediately re-deposited from the gas phase except at locations very close to the exit where these s o l i d s w i l l be swept into the end box by the flow. Thus any increase in entrainment due to the ef f e c t of a cascading bed or increased wall roughness w i l l be confined to areas close to gas exit section of the k i l n . The present model should therefore be applicable to i n d u s t r i a l situations as discussed in the next chapter where there are no internals or excessive evolution of gases from the charge to offset the conditions imposed on the model. The excellent 1 76 0.5 1 1.5 2 2.5 3 3.5 4 4.5 h (cm) Figure 7.10 S e n s i t i v i t y of model predictions to changes in sa l t a t i o n height. Figure 7.11 S e n s i t i v i t y of model predictions to changes p a r t i c l e size. 0.8 1 ' 1 1 ! 1 J 1 1 I • I 3200 3400 3600 3800 4000 4200 4400 P P (kg/m 3) Figure 7.12 S e n s i t i v i t y of model predictions to changes p a r t i c l e density. 179 agreement of the model with the experimental data also suggests that the transverse dust concentration p r o f i l e over the inclined bed does not influence the behaviour of the p a r t i c l e s in s a l t a t i o n . P a r t i c l e s in s a l t a t i o n interact with the f l u i d in the same way regardless of bed i n c l i n a t i o n . In order to apply the model to bimodal experiments, K r in Equation (6.2) w i l l be defined as equal to G in Equation (7.40). Thus R s = G , C f 1 * 2 8 A plot of R s i s shown in Figure 7.13 where the experimental data at 3 rpm are also shown for comparison. The agreement i s very good. Comparison of the model predictions to the experimental data of Khodorov (1) i s shown in Figure 7.14. Khodorov's experiments were made with sand p a r t i c l e s of mean size, 530M, in a small scale cylinder of same size as that in t h i s experiment. In comparing his data, two s a l t a t i o n heights of 1 cm and 2 cm were considered. Khodorov's sand of size about ten times the size of the alumina used in t h i s experiment w i l l probably jump to a height considerably less than the 2 cm average estimated here. However, as shown in Figure 7.5 and also in Figure 7.14, e l u t r i a t i o n rate i s less sensitive to changes in s a l t a t i o n height for larger p a r t i c l e s . The 180 10 1 0 - l , • • , 2 3 4 5 6 U (m/s) F i g u r e 7.13 Comparison of model p r e d i c t i o n s with experimental data f o r bimodal system. 181 F i g u r e 7.14 Comparison of model p r e d i c t i o n s wi th e x p e r i m e n t a l da ta of Khodorov ( 1 ) . 182 model also indicates that the threshold v e l o c i t y of Khodorov's p a r t i c l e i s about 4.5 m/s below which there could be no more entrainment. However, Khodorov measured entrainment at 3.57 m/s and 4.13 m/s probably due the to effect of wall imperfections or r e s t r i c t i o n s at the gas exit which he did not account for. Above the threshold, his data agree very well with the predictions of the model for the s a l t a t i o n heights assumed. Chapter 8 INDUSTRIAL APPLICATIONS 8.1 OPERATIONAL IMPLICATIONS Obviously, a study of t h i s duration could not cover a l l the numerous and complex conditions that a f f e c t dusting in rotary k i l n operation. However certain fundamental deductions can be made, in general, about the operational conditions and design to reduce dusting s i g n i f i c a n t l y in the various i n s t a l l a t i o n s . The most important observations regarding the mechanics of entrainment made in this study are that 1. Most of the entrained dust travels very close to the bed. 2. The c o l l i s i o n of returning p a r t i c l e s with bed surface p a r t i c l e s i s very important in enhancing entrainment. Any operational and design modifications aimed at reducing entrainment should therefore be made with these factors in mind. The most important factors a f f e c t i n g dusting in commercial rotary k i l n operation are the design of the a i r discharge end box and the configuration of the exit dam that retains the solids in the k i l n to prevent s p i l l a g e into the end box. Restrictions at t h i s end of the k i l n , for example, 183 184 the introduction of large feed chutes (as in counter-current operations) w i l l cause higher flow v e l o c i t i e s that w i l l favour higher dusting. Conical exits or steeply sloping exit dams and smaller end box designs w i l l cause accelerated flows such that entrained dusts and p a r t i c l e s in surface creep w i l l be quickly swept into the dust c o l l e c t i o n units. On the other hand, higher exit dams, f l a t dams with extra l i p heights especially at the gas exit end, w i l l prevent the majority of the dust that travels in s a l t a t i o n and surface creep from being c a r r i e d over into the end box. This w i l l be p a r t i c u l a r l y useful for kilns processing extremely fine materials such as cement and alumina where p a r t i c l e c o l l i s i o n w i l l be e f f e c t i v e over the entire bed surface to promote dusting. Most k i l n s , as seen from the survey (Table 1.1), also have internals. These internals (chains, f l i g h t s , t r e f o i l s , dams and mixers) offer better gas solids contact, often in the drying zone where material movement i s d i f f i c u l t (with wet feeds), by l i f t i n g material into the d i r e c t path of the hot gases. Although the use of internals cannot be avoided in most operations, their location could be extended further away from the feed end into the k i l n . Typical s a l t a t i o n distances presented in Table (7.1) give useful guide for the estimation of the location of internals. Bigger p a r t i c l e s w i l l have shorter s a l t a t i o n t r a v e l distance. By this design, entrained dust re s u l t i n g from the intimate contact would 185 have s u f f i c i e n t time to s a l t out of the gas phase before reaching the e x i t . This i s p a r t i c u l a r l y useful for feeds in which large quantities of coarse materials are present. Returning p a r t i c l e s , in th i s case, are l i k e l y to land on bed surface regions composed of segregated coarse p a r t i c l e s which are too large to be ejected; therefore the a r r i v i n g p a r t i c l e s become embedded. Wet feeds introduced in counter-current operations w i l l also s i g n i f i c a n t l y 'scrub' the dusty gas to recover some fines before the e x i t . In k i l n s without internals, higher wall roughness and cracks in k i l n refractory l i n i n g s could also cause excessive dusting problems especially at higher rpm. It is recommended that where possible, the roughness factor, defined here as the r a t i o of size of wall imperfections and size of the mean p a r t i c l e , be kept below 1 to ensure minimum e f f e c t . In operations that process fine materials and those in which r a d i a l segregation of the fines i s predominant, wall imperfections w i l l be very c r u c i a l to dusting control. In cases where longitudinal segregation occurs, the location of the segregated fines with respect to the gas exit dam w i l l be c r u c i a l . It i s desirable to maintain these fines farther away from the e x i t . One method might be to introduce recycled dust farther into the k i l n away from the feed chute via another i n s t a l l e d fines chute to maintain subsequent segregation away from the e x i t . If a t t r i t i o n i s a major source of fines as observed in the survey (for some cases), 186 reduction of k i l n internals and operation at lower solids percent f i l l s might help reduce a t t r i t i o n l e v e l s . One way of shortening chain section for example, w i l l be by proper f i l t r a t i o n of mud from wet scrubbers to reduce drying load. In some i n s t a l l a t i o n s (67, 68), f i l t r a t i o n of feed and the use of e l e c t r o s t a t i c p r e c i p i t a t o r s to produce dry recycle dust for reduced feed moisture, has been r e l i a b l e in t h i s regard. F i n a l l y , i f the gas v e l o c i t y could be reduced below the threshold conditions, dusting w i l l be decreased considerably but the gas load also depends highly on energy requirements. Thus a knowledge of the minimum velocity at which entrainment w i l l cease w i l l be b e n e f i c i a l for an optimum design of flow conditions. As discussed in Section 2.4.1 i t is d i f f i c u l t to define a c r i t i c a l stage at which p a r t i c l e s w i l l be entrained as conditions on the same bed w i l l vary from place to place depending on packing c h a r a c t e r i s t i c s , turbulent conditions and flow regimes. However, for a general guide, average conditions w i l l s u f f i c e . The most widely accepted such condition in sediment transport i s the impact threshold of Bagnold (28). Zenz (69) has also given a graphical method for m u l t i p a r t i c l e systems. The equation of Bagnold w i l l be used in the next section to estimate minimum sa l t a t i o n v e l o c i t i e s . It must be mentioned that visual estimation of alumina used in t h i s experiment gave values comparable to Bagnold's predictions (see below). 187 The ef f e c t of temperature could not be studied and i s recommended for further studies. Local temperature changes w i l l c e r t a i n l y affect l o c a l gas v e l o c i t i e s and evolution of gas from the charge in the heating zone w i l l influence l o c a l packing and thus pick-up. 8.2 MINIMUM SALTATION VELOCITY The threshold conditions according to Bagnold (28) and others for flow in the hydrodynamically rough regime i s s a t i s f i e d by therefore or and T ° = 0.0064 y d_ 's p r 0 = 0.0064 7 s d p f pU2 = 0.00647cdr, 8 & p 8(0.00647 Q) d n U2= 2 fp U = U m i n = 0.226/ ( ^ 2 ) (8.1) min £ p When the Reynolds number in a flow system exceeds about 10", the flow pattern and f r i c t i o n factor become substantially independent of Reynolds number (70). Thus for a known 188 roughness factor, the f r i c t i o n factor can be obtained without any serious error due to the unknown Reynolds number. For the alumina p a r t i c l e s used 7 S = 39118 N/m3 d p = 64M dp/D = 0.0003 p (air at room temperature) = 1.196 kg/m3 and the f r i c t i o n factor f = 0.024 and thus Umin = 2 - 1 1 m / s This compares f a i r l y well with the 2.62 m/s measured for the same p a r t i c l e s in th i s experiment (Section 6.3.1). For any ve l o c i t y above such threshold values, the extent of dusting could then be predicted from the model equation presented in Chapter 7 or the correlations in Chapter 6. The prediction of the threshold ve l o c i t y in an i n d u s t r i a l k i l n however, would be a very major undertaking because of the complicated flow patterns in the k i l n . Gas jets from the supply fans and flame jets would create a very turbulent non-uniform flow f i e l d . Larger scale eddies capable of moving p a r t i c l e s into suspension would be present such that the threshold conditions would be far lower than that predicted above. 189 8.3 INDUSTRIAL PREDICTIONS Examination of Equations (6.16) and (6.17) i n d i c a t e s that the most important f a c t o r s t hat a f f e c t entrainment are the flow v e l o c i t y , p a r t i c l e s i z e , and w a l l roughness. The k i l n s i z e has l i t t l e e f f e c t . T h i s i s not s u r p r i s i n g s i n c e as was shown in the present experiment most of the p a r t i c l e s t r a v e l very c l o s e to the bed i n s a l t a t i o n . In cases where the flow i s such that a s u b s t a n t i a l p a r t of the dust i s t r a n s p o r t e d i n suspension, the e f f e c t of diameter might be s u b s t a n t i a l . The i n f l u e n c e of k i l n s i z e w i l l be through i t s e f f e c t on the s c a l e of t u r b u l e n c e . Larger eddies of t u r b u l e n c e c o n t a i n much more energy than s m a l l e r ones and are more capable of s e t t i n g p a r t i c l e s i n t o suspension. Thus s i n c e these equations were obtained from experimental data i n a k i l n of a s i n g l e s i z e , any p r o j e c t i o n s to l a r g e r diameter should be subjected to f u r t h e r experimental v e r i f i c a t i o n . For alumina k i l n s and k i l n s p r o c e s s i n g e q u i v a l e n t f i n e - g r a i n e d m a t e r i a l , Equation (7.40) from the model may be employed d i r e c t l y to p r e d i c t entrainment r a t e s . In a t y p i c a l alumina k i l n producing about 350 tons of c a l c i n e d alumina per day, the gas v e l o c i t y at the e x i t was estimated as 3-4 m/s (71). In a p p l y i n g Equation (7.40), the only unknown f a c t o r w i l l be the average s a l t a t i o n h e i g h t , h, which in t h i s case can be taken as 2 cm s i n c e the flow v e l o c i t y f a l l s 190 in the range measured in the present experiments. The bed width, T, w i l l be a function of solids percent loading and k i l n size which w i l l vary with the type of i n s t a l l a t i o n . The c a l c u l a t i o n w i l l follow the same procedure outlined in Appendix C. Certainly, corrections should be made for wall roughness, internals and exit dam configuration. However at very low rpm the roughness e f f e c t i s n e g l i g i b l e and the model should apply to alumina k i l n s without int e r n a l s . For a convenient application of the model, values of the v e l o c i t y factor, , for t y p i c a l i n d u s t r i a l materials, alumina, limestone and cement have been computed for t y p i c a l i n d u s t r i a l operating conditions. These have been presented graphically as shown in Figure 8.1 for a p a r t i c l e size of 75iim and sa l t a t i o n height of 2 .0 cm. The v e l o c i t y factor appears to be independent of f l u i d v e locity but dependent on p a r t i c l e size and s a l t a t i o n height. Therefore, correction factors for variation in p a r t i c l e size and s a l t a t i o n height have also been presented in Figures 8.2 and 8.3 to make Figure 8.1 applicable to operations with d i f f e r e n t s o l i d s i z e s . Thus to apply Equation ( 7 . 4 0 ) , i t i s only necessary to estimate the t o t a l shear stress and the threshold shear stress. For i n d u s t r i a l k i l n s operating at very low rot a t i o n a l speeds of 1-3 rpm, t y p i c a l values of K, and K 2 are 0.994 and 0.988 respectively. Therefore K, and K 2 can be assumed equal to 1. 1 9 1 0.25 0.24 h 0.23 0.22 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.13 h = 2.0cm d p = 75 jum pr = 1521 kg/W pf = 2650 kg/m 1 p = 3990 kg/m J 6 8 10 U (m/s) 12 14 Figure 8. 1 industr i a l V e locity factor versus flow v e l o c i t y for t y p i c a l operations 1 9 2 Figure 8.2 V e l o c i t y factor - p a r t i c l e size correction factor 1 93 0-5 1 1.5 2 2.5 3 3.5 4 4.5 h (cm) Figure 8.3 V e l o c i t y factor - s a l t a t i o n height correction factor 194 Considering a t y p i c a l alumina k i l n (71), the e l u t r i a t i o n rate can be estimated from Equation (7.40) as follows. The k i l n considered has a diameter of 3.5 m and the soli d s loading i s 10%. The rotational speed i s 2 rpm and the gas exit temperature i s 250° C. Then from Table 1-5a (52), the bed width i s given by T = R x 1.45 = 1.75 x 1.45 = 2.537 m At t h i s temperature, the gas properties are p = 0.679 kg/m3 v = 4.037 x10" 5 m2/s For p a r t i c l e properties similar to that used in t h i s experiment and for a gas v e l o c i t y , U = 4.0 m/s, the flow Reynolds number is estimated as 3.4 x 10 5. The r e l a t i v e roughness, dp/D, assumed to be t y p i c a l of the whole internal surface of the k i l n i s 0.0000183. From Equation (7.26), the f r i c t i o n factor, f = 0.01426 and from Equation (7.24) and (7.25) Trp = 0.0194 N/m2 r 0 = 0.016 N/m2 From Figures 8.1 and 8.2 195 V f = 0.151 s Cp = 1 - 1 0 Therefore from Equation (7.40) Rs = (0.0194 - 0.016) x 0.151 x 1.10 = 0.000562 kg/m.s r s = T x Rs = 0.00143 kg/s = 123.8 kg/day For a gas ve l o c i t y of 5.5 m/s, f = 0.0135 and r T = 0.0347 N/m2. Thus R s = (0.0347 - 0.016) x 0.151 x 1.1 = 0.00311 kg/m.s r s = 0.00788 kg/s = 680 kg/day For a t y p i c a l cement k i l n operating at a gas exit temperature of 1160° C such as that in Operation 2CL in Table 1.1, 7 S = 14914 N/m3 U = 8.38 m/s p = 0.2515 kg/m3 v = 201 x 10" 6 m2/s T = 1.83 x 1.45 = 2.653 m Then for a p a r t i c l e size of 90M, f = 0.0166, T t = 0.0366 N/m2, r Q = 0.0086 N/m2, V f = 0.2220 s, C = 0.93. Therefore 1 96 R s = 0.00578 kg/m.s r = 0.00578 x 2.654 kg/s = 1.36 tonnes/day For a s a l t a t i o n height of 3.5 cm, C n = 1.5 and r g = 2.04 tonnes/day. S i m i l a r l y f o r a limestone k i l n o p e r a t i n g at t y p i c a l gas e x i t temperature of 677° C (Operation 25LBS, Table 1.1) 7 S = 25985 N/m3, U = 6.5 m/s, p = 0.2707 kg/m3, v = 179 x 10~^ m 2/s, and T = 1.523 m. Then f o r a p a r t i c l e s i z e of 75n and s a l t a t i o n height of 3 cm, f = 0.0192, r T = 0.0274 N/m2, r c = 0.012 N/m2, V f = 0.182 s, C h = 1.37, and R s = 0.0038 kg/m.s and r g = 505 kg/day. In commercial k i l n s p r o c e s s i n g wet feed as i n alumina k i l n s , the d r y i n g zone i s pro v i d e d with i n t e r n a l s f o r the purpose of c a r r y i n g the feed along and dropping i t i n t o the hot gas stream. In alumina k i l n s , such i n t e r n a l s as paddles or G o l d b e r g - s p i r a l s (71) promote e x c e s s i v e dust c a r r y - o v e r i n t o the end box. I t i s not s u r p r i s i n g that even f o r a w a l l shear s t r e s s of 0.019 N/m2 d u s t i n g i s f a r g r e a t e r than can be p r e d i c t e d by the models which have not accounted f o r the e f f e c t of i n t e r n a l s . 1 97 The c o r r e l a t i o n of Equation (6.16) cannot be s t r i c t l y applied to i n d u s t r i a l conditions since the ef f e c t of other parameters such as p a r t i c l e density and gas properties had not been considered. The use of i t must therefore be viewed as a projection only , subject to further experimental v e r y f i c a t i o n . For the alumina k i l n , asuming room temperature conditions for the gas, ? s d p 2 5.05 = 0.0187 u 2 D 0.1 44 = 0.549 Then R s = 0.423 x 1.196 x 4.0 x 3.5 xO.0187 x 0.549 kg/m.s = 0.0727 kg/s.m r s = 0.0727 x 2.54 = 0.185 kg/s = 15.96 tonnes/day For a production capacity of 350 tons/day, t h i s i s 4.56% of feed. Comparison of these predictions with the dust outputs reported in Table 1.1 show good agreement granting that most kiln s have internals that promote excessive dust. Chapter 9 CONCLUSIONS AND RECOMMENDATIONS 9.1 CONCLUSIONS The e l u t r i a t i o n rate of fines from the solids bed in rotary k i l n s has been experimentally studied and the influence of such operating variables as gas flow rate, ro t a t i o n a l speed and s o l i d percent f i l l have been examined. Experiments were primarily c a r r i e d out with fine alumina p a r t i c l e s of narrow size d i s t r i b u t i o n and l o c a l dust and v e l o c i t y measurements in the freeboard were made. From the results of the experiments, an entrainment mechanism based on the c o l l i s i o n of s a l t a t i n g p a r t i c l e s with the bed has been proposed. Design factors, such as the geometry of the k i l n exit dams, were found to influence dust carryover into the cleaning equipment. Wall roughness also affected entrainment by especially exposing trapped fines to the gas at higher rotational speeds. An increase of rotational speed, by i t s e l f , (excluding wall effect) exhibited a negative e f f e c t on entrainment in the slumping and r o l l i n g bed studied. This was demonstrated by the f a l l in dust concentration in the gas above the lower edge of the bed where p a r t i c l e s enter the passive region. An increase in s o l i d percent f i l l increased e l u t r i a t i o n marginally and is thought to be related to the corresponding moderate increase in bed surface area. Gas v e l o c i t y exhibited the strongest 198 199 influence on e l u t r i a t i o n and in a correlation established showed a vel o c i t y dependence of U e. A mathematical model has been developed to describe the influence of operating variables. It f i t s the experimental data reasonably and was applied to scale k i l n based on an estimated sa l t a t i o n height of p a r t i c l e s . The model was based on the influence of the c o l l i s i o n of sa l t a t i n g p a r t i c l e s on e l u t r i a t i o n and requires knowledge of the s a l t a t i o n height. It assumes p a r t i c l e s in suspension to be n e g l i g i b l e and accounts for p a r t i c l e s in s a l t a t i o n and surface creep. Under conditions where gas flow and p a r t i c l e size are such that the p a r t i c l e s are transported in suspension, the predictions of the model might be inadequate. In other experiments involving coarse Ottawa sand and fine alumina, fines concentration in the bed mixture and segregation patterns were found to influence entrainment strongly. Banding segregation occurred in a l l cases and the number of fine bands was proportional to the concentration of f i n e s . The entrainment was observed to be dependent on the location of the bands from the e x i t . When the bands were farther from the e x i t , a portion of the entrained dust was salted out onto the coarse bands before i t reached the exit thus diminishing the ov e r a l l entrainment. A kinetic model of the form of Equation (6.2) f i t t e d the data reasonably well with a rate constant given by the correlation of Equation 200 ( 6 . 2 0 ) . Further work w i l l be r e q u i r e d i n t h i s area as mentioned i n the f o l l o w i n g s e c t i o n . 9.2 RECOMMENDATIONS FOR FUTURE WORK The b a s i c mechanism and the i n f l u e n c e of primary o p e r a t i n g and design f a c t o r s on entrainment i n r o t a r y k i l n s has been s t u d i e d i n t h i s p r o j e c t . However, more work needs to be done c o n s i d e r i n g the d i v e r s e o p e r a t i n g c o n d i t i o n s , type and p h y s i c a l p r o p e r t i e s of m a t e r i a l s processed, i n r o t a r y k i l n s . I t i s recommended that f u t u r e work be made i n the f o l l o w i n g areas. 1. More work be made on bimodal and e v e n t u a l l y m u l t i p a r t i c l e system st u d y i n g s p e c i f i c a l l y the e f f e c t of a l l other forms of s e g r e g a t i o n and the i n f l u e n c e of t h e i r l o c a t i o n i n the k i l n . In t h i s regard, wet feed or completely coarse m a t e r i a l c o u l d be placed to cover d i f f e r e n t lengths of the downstream end of the k i l n to vary the l o c a t i o n of the nearest f i n e and e n t r a i n a b l e band. The behaviour of the segregated p a t t e r n s i n i n c l i n e d continuous k i l n o p e r a t i o n and how t h i s a f f e c t s dust c a r r y o v e r should a l s o be examined. 2. The e f f e c t of gas temperature and gas e v o l u t i o n from the bed i n hot experiments c o u l d a l s o be examined i n the f u t u r e . 3. K i l n i n t e r n a l s , e x i t geometry and l i n i n g roughness should a l s o be s t u d i e d f o r q u a n t i t a t i v e assessment of 201 t h e i r i n f l u e n c e on e n t r a i n m e n t . Large e d d i e s i n i n d u s t r i a l k i l n s would be v e r y e f f e c t i v e i n b r i n g i n g p a r t i c l e s i n s u s p e n s i o n . A study of t h e e f f e c t of k i l n s i z e might throw some l i g h t on t h i s and a d d i t i o n a l m o d e l l i n g of suspended p a r t i c l e s c o n s i d e r e d . Of p a r t i c u l a r i n t e r e s t w i l l be a s t u d y of k i l n s i z e or t u r b u l e n c e l e v e l s on the t h r e s h o l d c o n d i t i o n s . . 4. F i n a l l y , s t u d i e s must be conducted t o i n v e s t i g a t e the c o n d i t i o n s t h a t f a v o u r l e s s a t t r i t i o n i n beds composed of c o a r s e and e r o d i b l e m a t e r i a l s . The i n f l u e n c e of k i l n i n t e r n a l s on a t t r i t i o n s h o u l d be g i v e n s p e c i a l a t t e n t i o n . M o d i f i c a t i o n s and r e f i n e m e n t s c o u l d then be made t o the b a s i c model d e v e l o p e d i n Chapter 7 i n t h e l i g h t of the above recommendations t o p e r m i t i t s a p p l i c a b i l i t y t o v a r i o u s complex o p e r a t i o n s . NOMENCLATURE A 2 B B, C C D D, D 2 D e d P E E 0 E RMS F f f f T O r i f i c e area Constant, defined in Equation A4 Slope of output voltage/velocity curve Constant, defined in Equation 6.12 Constant, defined in Equation A1 Constant, defined in Equation 2.2 O r i f i c e discharge c o e f f i c i e n t Drag Co e f f i c i e n t Weight fr a c t i o n of fines Density correction factor P a r t i c l e size correction factor Saltation height correction factor K i l n diameter Pipe diameter O r i f i c e diameter Equivalent diameter of freeboard P a r t i c l e diameter Bridge output voltage Bridge output voltage at no flow Root mean square voltage fluctuations Component of f l u i d stress transfered to the bed via s a l t a t i n g p a r t i c l e s Functional rel a t i o n s h i p Functional relationship Darcy f r i c t i o n factor F r i c t i o n factor defined in Equation 6.6 nr kg/kg m m m m m V V V N/m: 202 203 g g y h Hi k K K 0 K, K 2 K r 1 L m p M n 0 n n N N RC P Pi P 2 q R„ Gravitational acceleration External force in the x-direction External force in the y-direction Height of sal t a t i o n layer Limit of integration Turbulent intensity Equivalent roughness height Proportionality constant, Equation 2.5 Proportionality constant, Equation 7.21 Correction factor for bed i n c l i n a t i o n Correction factor for bed rotation E l u t r i a t i o n rate constant D i f f e r e n t i a l pressure Lenght of K i l n Mass of a p a r t i c l e Mass of p a r t i c l e s per unit bed area Size d i s t r i b u t i o n parameter Number p a r t i c l e concentration Order of kinetic model Rotational speed Rotational speed at r o l l i n g cascading boundary F l u i d pressure Upstream s t a t i c pressure Downstream s t a t i c pressure Volumetric rate of discharge Spe c i f i c e l u t r i a t i o n rate m/s2 N N m m m kg/s m m m kg kg/m 2 m"3 rpm rpm N/m3 Pa Pa m3/s kg/s m 204 r E l u t r i a t i o n rate kg/s R Kiln radius m R Q Probe operating resistance ohm R T Probe resistance at ambient temperature ohm R Bridge arm resistance ohm T Width of bed m T a Ambient temperature °C T Q Probe operating temperature °C U T F r i c t i o n v e l o c i t y m/s U t P a r t i c l e terminal v e l o c i t y m/s Uy Local f l u i d v e l o c i t y at distance y above bed m/s U R Resultant r e l a t i v e v e l o c i t y m/s U Local f l u i d v e l o c i t y in the x-direction m/s U Average s u p e r f i c i a l f l u i d v e l o c i t y in freeboard m/s u' Turbulent v e l o c i t y fluctuation in the x-direction m/s Up Local p a r t i c l e v e l o c i t y in the x-direction m/s Up1 Local upwards p a r t i c l e velocity in the x-drection m/s Up2 Local downwards p a r t i c l e v e l o c i t y in the x-direction m/s V Local f l u i d v e l o c i t y in the y-direction m/s v' Velocity fluctuation in the y-direction m/s Vp Local p a r t i c l e v e l o c i t y in the y-direction m/s V . Local upwards p a r t i c l e velocity 205 in the y-direction m/s Local downwards p a r t i c l e v e l o c i t y in the y-direction m/s V Bed hold-up volume per unit cylinder length m3/m Wf Weight of fines kg Wp Local p a r t i c l e v e l o c i t y in the z-direction m/s Wfc Total weight of material kg w Local f l u i d v e l o c i t y in the z-direction m/s w Exponent of scale r a t i o , Equation 6.12 X Volume fr a c t i o n of s o l i d bed m3/m3 x Distance m x Exponent of Froude's group in power function x^ Mass fr a c t i o n of material on sieve i kg/kg y Distance m z Distance m Z Factor defined as Ut/UT/3/c 206 Greek l e t t e r s a Direction of movement ° 0 Function of boundary Reynold's number as defined in Equation 2.1 0 Ratio of thraot to pipe diameter 8 Bed i n c l i n a t i o n ° X Angle of repose ° M F l u i d v i s c o s i t y Ns/m2 M S C o e f f i c i e n t of f r i c t i o n v F l u i d kinematic v i s c o s i t y m2/s p F l u i d density kg/m3 Ps S o l i d density kg/m3 P J D 1 Component 1 bulk density kg/m3 P ] O 2 Component 2 bulk density kg/m3 * Functional r e l t i o n s h i p K Karman constant T Relaxation time s T 0 C r i t i c a l shear stress N/m2 T f Shear stress due to f l u i d flow N/m2 T S Shear stress due to s o l i d impact N/m2 T T Total shear stress due to f l u i d flow and s o l i d impact N/m2 CJ Angular speed of rotation rad/s. <j> Shape factor 7 Sp e c i f i c submerged weight of p a r t i c l e . N/m3 7 Angular measure of so l i d s loading 0 S u b s c r i p t s P s f 0 h 1 2 p a r t i c l e s o l i d f l u i d bed s u r f a c e top of t r a j e c t o r y upward t r a j e c t o r y downward t r a j e c t o r y REFERENCES 1. Khodorov, E.I., "Entrainment of Materials from Rotary Kilns", Khim. Prom.,416 (1961). 2. L i , K.W., "Entrainment in Rotary Cylinders", AIChE J.20 ,1031 (1974). 3. L i , K.W., "Application of Khodorov's and L i ' s Entrainment Equations to Rotary Coke Calciners", AlChe J.20,1017 (1974). 4. Henein, H., "Bed Behaviour in Rotary Cylinders with Application to Rotary Ki l n s " , Ph.D. Thesis, University of B r i t i s h Columbia, Canada (1980). 5. Zablotny, W.W., "The Movement of the Change in Rotary Kil n s " , I n t l . Chem. Eng.5, 360 (1965). 6. Pearce, K.W., "A Heat Transfer Model for Rotary Ki l n s " , J. Inst, of Fuel, pp. 363, Dec. 1973. 7. 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C h e p i l , W.S., "Dynamics of Wind E r o s i o n I I I : The Transport C a p a c i t y of the Wind", S o i l S c i . 6 0 , 475 (1945). 34. Owen, P.R., " S a l t a t i o n of Uniform Grains i n A i r " , J . F l u i d Mech.20, 225 (1964). 35. C h e p i l , W.S., "Dynamics of Wind E r o s i o n I I : I n i t i a t i o n of S o i l Movement", S o i l Sci.6Cj(5), 397 (1945) . 36. Bagnold, R.A., "The Flow of C o h e s i o n l e s s Grains i n F l u i d s " , Proc. Roy. Soc. London,A249, 235 (1956) . 37. Bagnold, R.A., "The Nature of S a l t a t i o n and of Bed Load Transport i n Water",Proc. Roy. Soc. London.A.332,473 (1973). 38. R e i z e s , J.A., "Numerical Study of Continuous S a l t a t i o n " , A.S.C.E., J . Hyd. Div.104, 1405 (1978). 39. Kdib, A.A., "A F u n c t i o n of Sand Movement by Wind", Univ. C a l i f . , B e r k e l y , Hyd. Eng. Lab., T e c h n i c a l Report HEL-2-12, p. 91 (1965). 40. White, B.R. and S c h u l t z , J . 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F r a n c i s , J.R.D., " E x p e r i m e n t s on t h e M o t i o n o f S o l i t a r y G r a i n s a l o n g t h e Bed o f a W a t e r S t r e a m " , P r o c . Roy. S o c , L o n d o n 332, 443 ( 1 9 7 3 ) . 48. F r i e d m a n , S . J . a n d M a r s h a l l , W.R., " S t u d i e s i n R o t a r y D r y i n g , P a r t I , H o l d u p a nd D u s t i n g " , Chem. Eng. P r o g r . 4 5 ( 8 ) , 483 ( 1 9 4 9 ) . 49. M i l l e r , T.N., " E n t r a i n m e n t i n R o t a r y K i l n s " , B.A.Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h C o u m b i a , C a n a d a , 1 9 8 3 . 50. B o o t h r o y d , R.G. a n d G o l d b e r g , A.S., " M e a s u r e m e n t s i n F l o w i n g Gas S o l i d s S u s p e n s i o n s I I " , B r i t . Chem. Eng. J_5(3) ,357( 1 970) 51. W e a s t , R . W . ( E d i t o r ) , Handbook o f C h e m i s t r y a n d P h y s i c s ( 5 6 t h E d i t i o n ) CRC P r e s s 1974 52. P e r r y , J.H. a n d C h i l t o n , C.H., ( E d i t o r s - i n - C h i e f ) C h e m i c a l E n g i n e e r ' s Handbook 5 t h E d . p.3-6,1973 53. B a y a r d , R.A., "New F o r m u l a D e v e l o p e d f o r K i l n T i m e " , Chem. M e t . E n g . 5 2 , 1 0 0 ( 1 9 4 5 ) 54. Saeman, W.C., " P a s s a g e o f S o l i d s t h r o u g h R o t a r y K i l n s " , Chem. E n g . P r o g . 4 7 ( 1 0 ) , 5 0 8 ( 1 9 5 1 ) 55. P i c k e r i n g , R.W.,Feakes, F. a n d F i t z g e r a l d , M.L., "Time f o r P a s s a g e o f M a t e r i a l t h r o u g h R o t a r y K i l n s " , J . A p p l . C h e m . H 1 ) , A 7 ( 1 9 5 1 ) 56. V a r e n t s o r , P.V., Y u f a , M.S., "The Movement o f Bed o f S o l i d s P a r t i c l e s i n R o t a r y K i l n s " , I n t l . Chem. Eng. J_( 1 ) ,88( 1961 ) 212 57. Kramers, H. and Crockewit, P., "The Passage of Granular Solids through Inclined Rotary Kilns", Chem. Eng. Sci.1(6),259(1952) 58. S u l l i v a n , I.D., Maier, C.G. and Ralston, D.C. "Passage of Solids P a r t i c l e s through Rotary Cylinder Ki l n s " , U.S. Bureau Mines. Tech. Rep. no. 384(1927) 59. Vahl, L. and Kingma, W.G., "Transport of Solids through Horizontal Rotary Cylinders" Chem. Eng. Sci.1(6),253(1952). 60. Osberg, G.L. and Charlesworth, D.H., " E l u t r i a t i o n in a Fl u i d i z e d Bed",Chem. Eng. Prog.47(11),566(1951). 61. Wen, C.Y. and Hashinger, R.F., " E l u t r i a t i o n of S o l i d P a r t i c l e s from a Dense-Phase F l u i d i z e d Bed", AIChE J.6(2), 221(1960) 62. Leva, M., " E l u t r i a t i o n of Fines from F l u i d i z e d Systems", Chem. Eng. Prog.£7( 1 ),39(1951). 63. Kunii, D. and Levenspiel, 0., F l u i d i z a t i o n Engineering, p 312, John Wiley and sons Inc.,New York,1969 64. Kl i n z i n g , G. E., Gas-Solid Transport,p 74, McGraw-Hill, New York,1981 65. Hinze, J. 0.,Turbulence,An Itroduction To Its Mechanism and Theory,p 19,McGraw-Hi11,New York,1959 66. C l i f t , R., Grace, J . R., Weber, M. E.,Bubbles,Drops,and Pa r t i c l e s , p 111,Academic Press,New York,1978 67. Lime K i l n Improvement Seminar, CPPA, P a c i f i c Coast,University of B r i t i s h Columbia,June 13 1984 68. Lewko, L., "Benefits of Pr e c i p i t a t o r Dry Dust Injection into the Lime Kiln",Pulp Paper Can,85(3):T52-56(1984) 69. Zenz, F. A.,"Conveyability of Materials of Mixed P a r t i c l e Size",I&EC Fundamentals3_( 1), 65(1964) 70. Johnstone, R. E.,Thring, M. W.,Pilot PLants,Models,and Scale-Up Methods in Chemical Engineering,p115, McGraw-Hill ,New York,1957 71. Hejja, A. A., "Rotary Kilns in the Metallurgical Industry" Research Report no.1,Department of Metallurgy, University of 213 Witwatersrand,Johannesberg, 1976 72. Ower, E. and Pankhurst, R. C.,The Measurement of Ai r Flow ,p 32,Pergamon Press, Oxford,1977 73. A.S.M.E Research Committee on F l u i d Meters, F l u i d MetersTheory and Application, 6th. Ed.,1971 74. Bradshaw, P., An Introduction to Turbulence and Its Measurement, p116, Pergamon Press,1971 75. Simons, D. B and Senturk, F.,Sediment Transport Technology, Water Resources Publications, Colorado 1977. 76. Cross, M., "The Transverse Motion of Solids Moving Through Rotary KiIns",Powder Tech. 22, 187(1979) 77. Henein ,H., Brimacombe, J . K. and Watkinson, A. P., "The Modeling of Transverse Solids Motion in Rotary K i l n s " , Metall. Trans. J_4B, 207(183) APPENDIX A : CALIBRATION OF INSTRUMENTS A1 PITOT-STATIC TUBE,ORIFICE PLATE AND ROTAMETER The p i t o t - s t a t i c tube described in Chapter 4 was used to c a l i b r a t e the steel clad hot f i l m probe. The working equation for a p i t o t tube i s given as U = Cv/21 = C/2AP/p A1 where the value of C ranges between 0.98 and 1.0 (52). For the s p e c i f i c a t i o n s used for th i s design, the value of C = 1 (72). The impact pressure was measured by the micromanometer model MM3 supplied by Flow Corporation. With butyl alcohol of S.G. 0.8166 as manometric f l u i d , the unit could measure pressure differences as high as 413.69 N/m2 with a s e n s i t i v i t y of 0.005 mm of Butyl alcohol. The o r i f i c e meter which was located in the discharge leg of the blower was used to measure mean a i r v e l o c i t i e s . It was designed to the recommendations of the A.S.M.E. report on f l u i d meters (73). The square-edged radius taps type was incorporated into the 0.1016 m diameter discharge duct. With the blower discharge capacity of between .073m3/s and 0.165m3/s, the Reynolds number based on the o r i f i c e diameter and v e l o c i t y was between 7 x 105 and 18 x 10 5. Thus the c o e f f i c i e n t of discharge including the v e l o c i t y of approach factor given as K 214 215 was obtained from the data of Spitzglass, Figure 5-17 in Perry (52) as 0.81. The weight rate of flow of a i r was calculated from the working equation w = qp = 0.81 A2v/ 2p(P 1-P 2) A3 where A 2 i s the area of o r i f i c e and 0 = D^D, = 0.81. The rotameter, Matheson type 605, used in the iso k i n e t i c sampling was calibrated against gas meters at room temperature as given in Figure A1. A2 CALIBRATION OF THE STEEL CLAD PROBE WITH THE PISA 55A01  CONSTANT TEMPERATURE ANEMOMETER A2.1 PRINCIPLE The p r i n c i p l e of measurement i s based on the convective heat loss from an e l e c t r i c a l l y heated probe to the flow. In the constant temperature anemometer, amplifiers are employed to keep the probe temperature and hence i t s resistance nearly constant such that measurement of the amount of power required to keep the temperature constant i s a measure of the cooling applied by the flow. Figure A2 shows a schematic of a constant temperature anemometer system. The probe or transducer forms one arm of a Wheatstone bridge c i r c u i t , the other variable arm consisting of three resistance decades. 216 20.0 1 ' ! : ! ' • i 2 7 12 17 22 Flow rate (1/min) F i g u r e A1 C a l i b r a t i o n c u r v e f o r r o t a m e t e r . F i g u r e A2 C o n s t a n t t e m p e r a t u r e anemometer system, Rp denot probe r e s i s t a n c e 218 The bridge i s fed by an amplifier whose input i s a feedback of the bridge output, signal, a measure of the imbalance caused by the convective cooling of the probe. The resu l t i n g loop system forms a control device by which the instrument automatically adjust i t s e l f to a certain probe temperature depending on the resistance decade setting. The heat loss due to the flow is a function of the difference in temperature between the probe and the f l u i d , the physical properties of the f l u i d , the dimensions and physical properties of the probe and the f l u i d flow v e l o c i t y . In i t s convenient form based on the works of King and others, the relati o n s h i p takes the form (74) E 2 = E£ + B U 0 , 5 (A4) which i s useful in obtaining the vel o c i t y from bridge output voltage. E and E Q are bridge voltages at any flow v e l o c i t y and at zero flow v e l o c i t y respectively. E Q i s a function of temperature. Therefore, c a l i b r a t i o n s are only suitable for measurements at temperatures at which they were made. Changes in temperature was allowed for as mentioned below. A2.2 MEASUREMENTS The c a l i b r a t i o n involved setting the resistance decades and hence the operating temperature of the probe and measuring the output voltage for a known flow v e l o c i t y . The anemometer was checked and set according to the operating 219 procedure and the resistance decades set for a predetermined operating temperature. I n i t i a l l y , the recommended formula, 0 .65 R_ = Rm + 10.4 (T 0 - T_) A5 o i 1 Q 0 o a where R T = t o t a l probe + leads resistance at ambient temperature T & was used. This required a chosen temperature T Q less than the maximum permissible of 1 0 0 ° C to be used to calculate the decade setting, R Q , the operating resistance. Thus the ambient temperature had to be known. For the laboratory setting in which the experiments were conducted, separate monitoring of ambient temperature was d i f f i c u l t and sometimes unreliable since the probe location was not e a s i l y accessible. The overheat r a t i o mode of operation was thus adopted. For a probe resistance of 10.4 ohms at 2 0 ° C an overheat r a t i o of 1 :1.33 gave operating temperatures safely below the maximum. In which case, to allow for any possible ambient temperature fluctuations, the probe resistance was checked each time before use and the operating decades re-set as required instead of measuring ambient temperature with a mercury-in-glass thermometer at locations farther away from the probe. For the same reason, the bridge output voltage for zero ve l o c i t y , E Q , was measured before each use. From equation A 4 , ( E 2 - E 2) a U 0* 5 and thus the same ca l i b r a t i o n curve was used for a l l temperature ranges ( 2 0 - 2 5 ° ) C provided the resistance decades were re-set and Eo measured each time. The voltage at zero flow velocity was 220 measured without removing the protective open ended cover of the probe and with no a i r flow. Calib r a t i o n was accomplished in the k i l n with the p i t o t - s t a t i c tube described in Chapter 4. Both the probe and the p i t o t tube were supported in the end plate of the discharge end box of the k i l n . The v e l o c i t y measurements were made at the same location in the k i l n with f i r s t the p i t o t tube and then with the probe when the pit o t tube had been moved away by the f a c i l i t y in the end plate described in section 4.2.1. The output voltage was measured by a d i g i t a l voltmeter connected through an external connection provided on the anemometer for accurate readings. The res u l t i n g c a l i b r a t i o n curve shown in Figure A3 is seen to have a better f i t to a straight l i n e in the range of v e l o c i t i e s measured. Regression analysis gave B = 57 V 2/s^'^ The percentage of turbulence was estimated from Epj^g, E and E 0 as %Turbulence = 100 B,U dE where B, = — dU From equation A4, >2_ 4E E 2 - E 2 B, = ^ A7 Therefore 221 Figure A3 Calibration curve for DISA 55A76 s t e e l clad hot f i l m probe. 222 4E %Turbulence = E R M S —100 A 8 E 2 — E ' J0 APPENDIX B : FORCES ACTING ON BED PARTICLES A rigorous analysis of the forces acting on a bed of loose grains in the boundary of a flowing f l u i d i s very d i f f i c u l t for reasons mentioned in section 1.4.1. With some si m p l i f i c a t i o n s , however, the analysis could be c a r r i e d out ( 7 5 ) to define an average condition of entrainment and more importantly i d e n t i f y the factors that strongly influence p a r t i c l e entrainment. In a rotating cylinder, the rotation makes the analysis more complex. Extra forces are introduced and the behaviour of surface p a r t i c l e s i s changed. In this section an attempt w i l l be made to i d e n t i f y these forces and how they af f e c t p a r t i c l e entrainment from the bed. Beginning with a force balance on a single p a r t i c l e on a stable f l a t bed, the analysis i s s i m p l i f i e d by considering an average p a r t i c l e subjected to average f l u i d forces. On a bed composed of cohesionless p a r t i c l e s , the onset of p a r t i c l e movement occurs when the combined l i f t and drag forces produced by the f l u i d flow exceed the r e s i s t i v e g r a v i t a t i o n a l force. The forces act on the p a r t i c l e as shown in Figure B1 where a is the d i r e c t i o n of easiest movement. The submerged weight of the p a r t i c l e FQ i s given by 223 F i g u r e B2 F o r c e b a l a n c e on an i n c l i n e d b e d . 225 F Q = C,d£ ( p p " p) g (B1) where i s a form c o e f f i c i e n t and d D the c h a r a c t e r i s t i c d i a m e t e r of the p a r t i c l e . The drag f o r c e F D i s a l s o g i v e n by FD " r o C * d P < B2> where TQ i s the average boundary shear s t r e s s and C 2, a form c o e f f i c i e n t dependent on the boundary Reynolds number. The average l i f t f o r c e c o u l d be e x p r e s s e d as F L = C L C 3 d P P \ - <B3) where C L i s the l i f t c o e f f i c i e n t , U the v e l o c i t y of the f l o w c l o s e t o the bed and C 3 a form c o e f f i c i e n t of a r e a of the p a r t i c l e normal t o the f l o w and a l s o dependent on boundary Reynolds number. Fp i s the f r i c t i o n a l f o r c e . S i n c e the f o r c e s a r e not c o i n c i d e n t , the e q u i l i b r i u m c o n d i t i o n s w i l l be the e q u a l i t y of moments about the p i v o t ( 2 9 ) . Thus U 2 a ^ ^ P p - p) g dp s i n a - a, C L C 3 d ^ p — s i n a = a 2 C 2 r 0 d ^ Cosa (B4) where a 1 f a 2 a r e moment arms of the r e s p e c t i v e f o r c e s . N o t i n g t h a t r 0 = p U 2 r and assuming U = C«U T i . e . the f l o w v e l o c i t y a t the g r a i n l e v e l i s p r o p o r t i o n a l t o the shear v e l o c i t y , e q u a t i o n B4 reduces t o 226 IS - Ii = P (B5) ( p p - p) g dp a ^ C s / C ^ a 2CotaC 2/C, where C 5 = C 3 C 4 / 2 and M s a function of p a r t i c l e geometry and boundary Reynolds number. Thus when C L = 0 , higher values of T q i s required to move the p a r t i c l e . In a rotary k i l n , the bed i s in c l i n e d crosswise to the flow. On a stable bed, the forces on the p a r t i c l e w i l l be as shown in Figure B2, where flow i s in a di r e c t i o n normal to the paper. Notice FQ has been resolved into components perpendicular and p a r a l l e l to the i n c l i n e and F R i s the resultant of the drag and the component of FQ down the i n c l i n e . At the onset of movement, moments of a l l forces about the pivot ,P, give U 2 a i C ^ p p - p) g d 3p cost? sina - a, C L C 3 d^p — sina = a, F R cosa (B6) where F R = ( F 2 D + ( F G s i n 0 ) 2 ) 1 / 2 In a rotating bed, the situation i s complicated by the introduction of ce n t r i f u g a l forces due to rotation which act on p a r t i c l e s just before they leave the passive region at the upper half of the bed or enter i t at the lower part of the bed. The effect of t h i s on entrainment can be viewed for 227 the sake of s i m p l i c i t y , in the context of i t s effect on the behaviour of the bed. Thus analysis of the forces acting on the bed due to rotation in the absence of f l u i d flow w i l l be considered. Other forces acting on p a r t i c l e s in a rotating bed have been i d e n t i f i e d as g r a v i t a t i o n a l and f r i c t i o n a l in previous analysis by Davies (11) and Cross (76). A recent analysis reported by Henein (77) was based on the mechanics of r i g i d bodies, treating the whole bed as a r i g i d body. However since i t is the entrainment of i n d i v i d u a l p a r t i c l e s which is of concern here, the following treatment w i l l be confined to single p a r t i c l e s on the surface of the bed. Consider a p a r t i c l e P, s i t t i n g on the bed surface PC in c l i n e d at an angle 8 to the horizontal as shown in Figure B3. 7 is the angular measure of the % f i l l , F N normal force, F c centrifugal force , F Q = Mg and F p f r i c t i o n a l force Resolving these forces p a r a l l e l and normal to the bed surface we have F F + F c s i n7 = Mg sine? (B7) F c + MG COS0 = F N (B8) At the point of movement, F P = M G F N where M s i s the c o e f f i c i e n t of f r i c t i o n between the p a r t i c l e and those underneath i t . Eliminating F P and F N , equations B7 and B8 y i e l d 228 F i g u r e B3 F o r c e ba lance on p a r t i c l e s in a r o t a t i n g bed 229 M S ( F C c o s i + mpgcose) + F C sin7 = mpg sine (B9) and mpg sine - mpgMs cose = F c sin7 + M S F C C O S 7 (B10) But F~ = rn C J 2 R C p Therefore mpg sine - m pgM s cose = m pcj 2 R(sin7 + M S C O S 7 ) and sine - M s cose = co2 R ( ( M S C0S7 + sin7))/g (B1 1 ) Thus the resultant bed i n c l i n a t i o n 9 i s a function of the rotational Froude number, % f i l l and f r i c t i o n c o e f f i c i e n t or angle of repose for that matter. It i s evident from equation C10 that an increase in either the rpm or the radius of the k i l n w i l l cause an increase in the angle 6 and the p a r t i c l e w i l l not move u n t i l i t i s c a r r i e d further around in the dir e c t i o n of rotation. At a constant rotational speed, the p a r t i c l e nearer the centre of the k i l n w i l l be moved e a r l i e r when d i s smaller than that at P. Accordingly (77) when the resultant bed i n c l i n a t i o n places the outermost p a r t i c l e P in the upper quadrant, the i n i t i a l v e l o city w i l l be directed away from the k i l n wall in a cascading mode of behaviour. The projection of p a r t i c l e s 230 into the freeboard w i l l thus enhance p a r t i c l e pick-up. On the other hand, a reverse action with an adverse ef f e c t on entrainment would be occurring at the extreme lower end of the bed. At the rolling/cascading boundary, defined by the condition that places P on the abscissa (77) : 7 + 6 = 90° M s = tanX where X = 30° i s the angle of repose of the s o l i d p a r t i c l e s . At a % f i l l of 5, 7 = 36°. Equation B11 in terms of 7 becomes C O S 7 - M S s i n 7 = cjj|c R ( ( M S C O S 7 + s i n 7))/g (B12) from equation B12, the rotational speed N R^ at the rolling/cascading boundary i s estimated as N R £ = 30co/7r = 64. Thus for the range of rotation at which the experiments were car r i e d out the bed behaviour was either slumping or r o l l i n g . APPENDIX C :  NUMERICAL SOLUTION OF MODEL EQUATIONS In e v a l u a t i n g the i n t e g r a l i n E q u a t i o n 7.40, i t was n e c e s s a r y t o s o l v e E q u a t i o n s (7.30-7.33) f o r the v e l o c i t y components of the p a r t i c l e i n b o t h p a r t s of the t r a j e c t o r y which form the terms i n the i n t e g r a l a t any l o c a t i o n , y, above the bed. E q u a t i o n s (7.30-7.33) were s o l v e d by i n t e g r a t i n g n u m e r i c a l l y u s i n g the Runge-Kutta d i f f e r e n t i a l e q u a t i o n s o l v i n g t e c h n i q u e . For the i n t e g r a t i o n t o be a c c o m p l i s h e d c o n c u r r e n t l y i n E q u a t i o n ( 7 . 4 0 ) , a s t a n d a r d n u m e r i c a l i n t e g r a t i o n t e c h n i q u e was used. In t h i s c a s e , the A d a p t i v e Simpson's method was used. In t h e i r f u l l form, E q u a t i o n s (7.30-7.33) can be w r i t t e n a s : V P1 V. P1 V p2 V P 2 d u p 1 . . °-UPI • U- UP' dy i T 1 7-2 d vP i . . - !EI - !EI ' dy. T 1 d uP 2 . . U " U P 2 + U"°P2 d y 2 r 2 d VP 2 . . - ZEI - ! E 2 " d y 2 T 1 T2 ( U - U p 1 ) 2 + Vpf 0.344 ( u - u p 1 ) 2 + V p 2 0.344 ( U - U p 2 > 2 + V P 2 0.344 ( u - u p 2 ) 2 + V p | 0.344 (CI ) (C2) (C3) (C4) The f o l l o w i n g boundary c o n d i t i o n s a p p l y t o E q u a t i o n s (C1-C4): At y , = 0 , 231 232 At y,=h, " U P 1 0 V P ' - Vp10 " ° P 2 0 Vp2 = Vp20 UP1 " ° P1h VP1 = V P 1 h " U p 2 h = 0 p1h Vp2 " Vp2h = 0 For the upgoing p a r t of the t r a j e c t o r y , Equations (C1) and (C2) were s o l v e d simultaneously and f o r the downgoing p a r t Equations (C3) and (C4) were s o l v e d s i m u l t a n e o u s l y . In Equation (C2), V P L = 0 at the top of the t r a j e c t o r y , i . e . at y, = h. T h e r e f o r e the value of the i n i t i a l p a r t i c l e v e r t i c a l v e l o c i t y , V P 1 Q , was determined from Equations (C1) and (C2) by t r i a l end e r r o r , i n t h i s case the b i s e c t i o n method was used. F i r s t , V P 1 Q was a s s i g n e d a value and s i n c e U p 1Q = 0 Equations (C1) and (C2) were s o l v e d with these i n i t i a l c o n d i t i o n s f o r the f i n a l value of V P 1 over the i n t e r v a l 0 h, where h i s a predetermined height of the s a l t a t i o n l a y e r . If the c a l c u l a t e d value V was not equal to zero, another i n i t i a l v a lue f o r V P 1 Q was assumed and the procedure repeated f o r the same s o l u t i o n i n t e r v a l u n t i l the f i n a l v e l o c i t y was c l o s e enough to zero by an assigned e r r o r . With ths value of V p i f j ' the v e l o c i t y at increments of he i g h t s between y, = 0 and y, = h were f o r m a l l y obtained by s o l v i n g 233 Equations (C1) and (C2). The v e l o c i t y components of the p a r t i c l e i n the downward motion was then determined at the same height increments but i n the downwards d i r e c t i o n by a p p l y i n g the Runge-Kutta d i f f e r e n t i a l e quation s o l v i n g technique to Equations (C3) and (C4). The i n i t i a l values i n t h i s case were the f i n a l v a l u e s from the s o l u t i o n of Equations (C1) and (C2). Hence, at s e v e r a l d i s c r e t e h e i g h t s y = Y i = h - y 2 , the v e l o c i t y components V p 1 , U p 1 and V p 2 , U p 2 were determined. Consequently, i n the numerical e v a l u a t i o n of the i n t e g r a l i n Equation (7.40), the r e s p e c t i v e terms of the i n t e g r a n d were r e a d i l y obtained at these h e i g h t s . At i n t e r m e d i a t e h e i g h t s , the v e l o c i t y components were obtained by c u b i c s p l i n e i n t e r p o l a t i o n at the a p p r o p i a t e i n t e r v a l . The i n t e g r a t i o n was however c a r r i e d out to an upper l i m i t h,, very c l o s e to h, the s a l t a t i o n h e i g h t , s i n c e the i n t e g r a n d was indeterminate at h, i e . (h-h,) = 10" 5. The t r a n s v e r s e d i s t a n c e t r a v e l l e d by the p a r t i c l e , z = OB, ( F i g u r e 7.2) at the end of the s a l t a t i o n was estimated from a s o l u t i o n of Equation (7.37) u s i n g the same t e c h i n i q u e . F i r s t , Equations (C1) and (C2) were s o l v e d i t e r a t i v e l y i n the time domain f o r the time at which the p a r t i c l e ' s f i n a l h o r i z o n t a l v e l o c i t y was U p 2Q a s determined above. With t h i s s a l t a t i o n time, Equation (7.37) was s o l v e d i n the time domain to determine the p a r t i c l e s t r a n s v e r s e v e l o c i t y , w , at the end of t h i s time. Then, Equation (7.37) 234 was solved again, t h i s time in the space domain, z, and i t e r a t i v e l y , to determine the distance over which the transverse v e l o c i t y was equal to w . The computer program hr for the above analysis i s presented in Appendix D. In a t y p i c a l c a l c u l a t i o n , consider the sa l t a t i o n trajectory for a l l the runs in which the average gas vel o c i t y was 3.7m/s for p a r t i c l e and a i r properties as follows: (9=30° d p=64 M Pp=3990 kg/m3 p(25°C)=1.196 kg/m3 7gCos0=8.49 N/m3 M(25°C)=1.8215 x 10~ 5 N/m s ^(equation 7.28) = 0.049846 r 2(equation 7.28) = 0.12393 h=0.02 m At the top of the trajectory, y, = h, Vp1 = 0 Equations (C1) and (C2) give V p i o a s 1« 1 25m/s and Vp 2g as 3.62 m/s. The subsequent integration over the sal t a t i o n height y i e l d s a value of 0.425 for the integral in Equation (7.40). 235 PARTICLE TERMINAL VELOCITY CALCULATION For a p a r t i c l e of s i z e = 64 x 10~ 6 m, d e n s i t y = 3990 kg/m 3 the t e r m i n a l v e l o c i t y , U T, i n a i r of d e n s i t y = 1.196 kg/m 3 and v i s c o s i t y = 1.8215 x 10~^ N.s/m 2, i s e s t i m a t e d by the f o l l o w i n g method ( 6 6 ) . 4d 3 g p ( p -p) N n = — E E D 3M 2 4 (64 x 1 0 ~ 6 ) 3 x 1.196 (3990 - 1.196) x 9.807 3 x (1.8215 x10 b ) 3Pr, 2U n 3 = 49.287 = -P T u 4 ( p p - p ) g M 3(1 . l 9 6 ) 2 x U r r 3 = =t = 1.506 Urp3 4(3990-1.196)X9.807 x 1.8215 x 10 b T From the c o r r e l a t i o n t a b u l a t e d i n Appendix B ( 6 6 ) , T h e r e f o r e l o g N D 1 / 3 = l o g K u ] / 3 N D 1 / / 3 = 3.66 l o g N D 1 / 3 = 0.5642 l o g N n 1 / 3 = -0.332 N D 1 / 3 = 0.46558 N D = 0.109 and 1 . 5 0 5 6 U T 3 = 0.1009 U T = 0.406 m/s. APPENDIX D : COMPUTER PROGRAMS C THIS PROGRAM EVALUATES THE HORIZONTAL FLUX, G, OF PARTICLES C IN THE SALTATION LAYER AS GIVEN BY EQUATION 7.40. C IT EVALUATES THE INTEGRAL TERM AND COMPUTES VALUES FOR KI AND K2 C PARTICLE VELOCITIES: C VP10 = INITIAL UPWARD VELOCITY C VP1 = UPWARD VELOCITY, VZO = INITIAL TRANSVERSE VELOCITY C UP1H =STREAMWISE VELOCITY AT TOP OF SATATION LAYER C VP20 = FINAL DOWNWARD VELOCITY C TAOI,TAU2,RELAXATION TIMES AS IN EQUATION OF MOTION,DG-GRAVITATI C ONAL ACCEL., U = FLUID VELOCITY, D=CYLINDER DIAMETER C SHST = TOTAL SHEAR STRESS ,PST = IMPACT THRESHOLD C RHOP = PARTICLE DENSITY, RHO = FLUID DENSITY C DP = PARTICLE SIZE, UM = FLUID VISCOCITY, W=BED WIDTH C c IMPLICIT REAL*8(A-H,0-Z) DIMENSION RPM(60) ,G(60) ,W2(50) ,UU2(50) COMMON/BLKA/VP1(50),UP1(50),VP2(50),UP2(50) COMMON/BLKB/TAU1,TAU2,U,DG COMMON/BLKC/DX,M,JJ,VP 10,UP2 0,VZO,VZ COMMON/BLKD/RE,DE COMMON/BLKE/N,NM COMMON/BLKF/X(21),7(21) EXTERNAL FUNC,FTT,FRIC,F77,FZZ DATA A,BfVA,VF,EPS2/0.ODO,1.9999D-2,0.9D0,1.5D0,1.OD-5/ DATA D,PST,W/0.203DO,0.0246DO,0.121D0/ DATA RHOP,RHO,DP,UM/3990.D0,1.196D0,0.O0OO64D0,0.0000182D0/ DE-D/DP M-2 N-21 T1«=DP**2.D0 T2»DP**1.313D0 T3«UM**0.313D0 T4«RHO**0.687D0 TAU1=RHOP*T1/(18.D0*UM) TA02=RHOP*T2/(2.7D0*T3*T4) PI-4.D0*DATAN(1.DO) EPS3= t.D-4 EPS1=1.D-5 DG-9.807*0.866*(RHOP-RHO)/RHOP HH-2.0D-2 TI=0.1D0 TF-1.5D0 ZF»0.05DO NM-N-1 U=3.7D0 X(1)=A DX=(HH-A)/NM DO 25 1=2,N IM-I-1 25 X(I)=X(IM)+DX DT1=2.D-2 DX1=2.D-1 RE=U*D*RHO/UM C C FIND VP 10 FROM ASSUMED SALTATION HEIGHT BY TRIAL AND ERROR C C JJ=1 CALL INSRCH(FYY,VA,VF,DX1 ,EPS 1 ,VR) 237 238 IF(VR.GE.VF) GO TO 29 VP10=VR WRITE(6,11)VP10 11 FORMAT(IX,'INITIAL VERTICAL VELOCITY=',F10.6) C C DETERMINE PARTICLE'S UPWARD VELOCITY COMPONENTS C CALL RKT(VP10,0.0D0,VP1,UP1) UP1H=UP1(N) VP1H=VP1(N) WRITE(6,22)UP1H 22 FORMATt1X,'HORIZONTAL VELOCITY AT h=',F10.6) C C DETERMINE PARTICLE'S DOWNWARDS VELOCITY COMPONENTS C JJ=2 CALL RKT(VP1H,UP1H,W2,UU2) VP20=W2(N) DP20=UU2(N) WRITE(6,12)VP20 12 FORMATt1X,'FINAL VERTICAL VELOCITY=',F1 0.6) WRITE(6,13)UP20 13 FORMAT(1X,'FINAL HORIZONTAL VELOCITY=',F10.6) C C MATCH DOWNWARD VELOCITIES TO CORRESPONDING UPWARD DISTANCES C DO 14 I=1,N NN-N-Q-1 ) VP2(I )=W2(NN) 14 UP2(I)=UU2(NN) C C EVALUATE THE INTEGRAL TERM IN FLUX C CALL SIMPtFUNC,A,B,EPS2,AREA,NP) WRITE(6,15)AREA,EPS2,NP 15 FORMATtIX,'AREA=1 ,F10.6,2X, 'EPS=',F10.6/5X,'NPOINT=',18) C C ESTIMATE SHEAR STRESS, SHST C CALL INSRCH(FRIC,0.01 DO,0.04DO,2.OD-4,EPS 1,FR) FAC=FR SHST=RHO*FAC*U**2/8.DO G1=(SHST-PST)/UP20 WRITE(6,44) 44 FORMAT(IX,'RPM',6X,'K1',8X,'K2',8X,'ELUTRIATION RATE') C C EVALUATE TOTAL SALTATION TIME, TS C CALL INSRCH(FTT,TI,TF,DT1,EPS3,TR) IF(TR.GE.TF) GO TO 29 TS=TR C C COMPUTE TRANSVERSE DISTANCE TRAVELLED, ZB C C C GENERATE ROTATIONAL SPEEDS C M=1 DO 41 1=1,10 239 41 RPM(I)=I GENERATE RPM DO 4 2 1=1,10 C C ESTIMATE INITIAL TRANSVERSE VELOCITY ,VZO C VZO=PI*0.1016*RPM(IJ/30.D0 C C EVALUATE K1 C JJ=1 DX=TS/NM CALL RNZ(VZO,0.0D0,VZ) JJ=2 CALL INSRCH(FZZ , 0.001D0,ZF,0.004D0,EPS3,ZB) IF(ZB.GE.ZF) GO TO 29 TK1=(W-ZB)/W C C EVALUATE K2 C TK2=VP10/(VZO+VP10) c C EVALUATE HORIZONTAL FLUX C G(I)=G1*TK1*TK2*AREA*W*60.D0 WRITE(6,43)RPM(I),TK1,TK2,G(I) 43 FORMAT(1X,F4.1,2X,F6.4,4X,F6.4,11X,F8.6) 42 CONTINUE GO TO 32 29 WRITE(6,31 ) 31 FORMAT(IX,'ITERATION FAILED') 32 STOP END C C SUBROUTINE INSRCH(F,XI,XF,DX3,EPS,XT) C THIS PROGRAM USES THE BISECTION METHOD TO FIND THE ROOT OF A FUNCTION IMPLICIT REAL*8(A-H,0-Z) X1=XI Y1=F<X1) 10 X2=X1+DX3 IF(X2.GT.XF) GO TO 50 Y2=F(X2) IF(Y1*Y2.LE.0.0D0)GO TO 20 X1=X2 Y1=Y2 GO TO 10 20 IF(Y2.EQ.0.0D0)GO TO 50 30 X3=(X1+X2)/2.D0 IF(DABS((X3-X1)/X3).LT.EPS)GO TO 60 Y3=F(X3) IF(Y1*Y3.LE.0.0D0)GO TO 40 X1=X3 Y1=Y3 GO TO 3 0 40 X2=X3 Y2=Y3 GO TO 3 0 50 X3=X2 60 XT=X3 RETURN END SUBROUTINE RUNG(XX1,XX2,YB) IMPLICIT REAL*8(A-H.O-Z) DIMENSION YOU) ,Y1 (4) COMMON/BLKC/DX,M,JJ,VP 10,UP20,VZO,VZ COMMON/BLKE/N,NM EXTERNAL Fl,FT1 YO(1)=XX1 YO(2)=XX2 DO 21 1=2,N IF(JJ.EQ.I) CALL RKCC(F1,DX,YO,Y1) IF(JJ.EQ.2) CALL RKCC(FT1,DX,YO,Y1) DO 18 J=1,M 18 YO(J)=Y1(J) 21 CONTINUE IF(JJ.EQ.I) YB=Y1(1) IF(JJ.EQ.2) YB=Y1(2) RETURN END SUBROUTINE RNZ(XX1,XX2,YB) IMPLICIT REAL*8(A-H,0-Z) DIMENSION YO(4),Y1(4) COMMON/BLKC/DX,M,JJ,VP10,UP20,VZO,VZ COMMON/BLKE/N,NM EXTERNAL FZ1,FZ2 YO(1)=XX1 YO(2)=XX2 DO 21 I=2,N IF(JJ.EQ.I) CALL RKCCtFZI,DX,YO,Y1) IF( JJ.EQ.2") CALL RKCC(FZ2,DX,YO,Y1) DO 18 J=1,M 18 YO(J)=Y1(J) 21 CONTINUE YB-Y1(1) RETURN END SUBROUTINE RKT(XX1,XX2,YV1,YU1) IMPLICIT REAL*8(A-H,0-Z) DIMENSION YOU) ,Y1 (4) ,YV1 (50) ,YU1 (50) COMMON/BLKC/DX,M,JJ,VP 10,UP2 0,VZO,VZ COMMON/BLKE/N,NM EXTERNAL Fl,F2 YO(1)=XX1 YO(2)=XX2 YV1(1)=XX1 YU1(1)=XX2 DO 2 0 I = 2,N IF(JJ.EQ.1)CALL RKCC(F1,DX,YO,Y1) IF(JJ.EQ.2)CALL RKCC(F2,DX,YO,Y1) DO 10 J=1,M 10 YO(J)=Y1(J) YV1(I)=Y 1 ( 1 ) YU1(I)=Y1 (2) 2 4 1 20 CONTINUE RETURN END C C C SUBROUTINE RKCC(F,D2X,VYO,VY1) IMPLICIT REAL*8(A-H,0-Z) DIMENSION VYOU) ,VY1 (4) ,YYO(4) ,YY1 (4) COMMON/BLKC/DX,M,JJ,VP 10,UP2 0,VZO,VZ EXTERNAL F NINT=50 DO 15 J=1 ,M 15 YYO(J)= VYO(J) DXX=D2X/NINT DO 20 1=1,NINT CALL RK4(F,YYO,YY1,DXX) DO 18 J=1 ,M 18 YYO(J)=YY1(J) 20 CONTINUE DO 17 J=1 ,M 17 VY1(J)=YY1(J) RETURN END C C C c SUBROUTINE RK4(F,Y,Y1,DDX) IMPLICIT REAL*8(A-H,0-Z) REAL*8 K1(4),K2(4),K3(4),K4(4) DIMENSION Y(4),Y1(4),YY(4) COMMON/BLKC/DX,M,JJ,VP 10,UP20,VZO,VZ COMMON/BLKE/N,NM DO 10 J=1 ,M 10 K1(J)=DDX*F(J rY) DO 20 K=1 ,M 20 YY(K)=Y(K)+K1(K)/2.D0 DO 30 J=1 ,M 30 K2(J)=DDX*F(J,YY) DO 40 K=1 ,M 40 YY(K)=Y(K)+K2(K)/2.D0 DO 50 J=1 ,M 50 K3(J)=DDX*F(J,YY) DO 60 K=1,M 60 YY(K)=Y(K)+K3(K) DO 70 J=1 ,M 70 K4(J)=DDX*F(J,YY) DO 80 J=1 ,M 80 Y1(J)=Y(J) +(K1(J)+2.D0*K2(J)+2.D0*K3(J)+K4(J))/6.D0 RETURN END C FUNCTION EVALUATES INTEGRAND FROM VELOCITY COMPONENTS USING C SPLINE INTERPOLATION C DOUBLE PRECISION FUNCTION FUNC(YY) IMPLICIT R E A L * 8 ( A - H , 0 - Z ) COMMON/BLKA/VP1(50),UP 1 ( 5 0 ) , V P 2 ( 5 0 ) , U P 2 ( 5 0 ) COMMON/BLKE/N,NM 242 COMMON/BLKF/X(21) ,Y(21) EXTERNAL FF DO 10 I=1,N 10 Y d )=VP1(I) CALL SPLINE V1=FF(YY) DO 11 1=1,N 11 Y(I)=UP1(I) CALL SPLINE U1=FF(YY) DO 12 1=1,N 12 Y(I)=VP2(I) CALL SPLINE V2=FF(YY) DO 13 1=1,N 13 Y(I)=UP2(I) CALL SPLINE U2=FF(YY) RAT1=U1/V1 RAT2=U2/V2 FDNC=RAT1+RAT2 RETURN END C C CUBIC SPLINE INTERPOLATION ROUTINE C SUBROUTINE SPLINE IMPLICIT REAL*8(A-H,0-Z) COMMON/BLKE/N,NM COMMON/BLKF/X(21),Y(21) COMMON/BLKG/Q(20),R(21),S(20) DIMENSION H(20),A(21),B(21),C(21),D(21),TAB(101,20) C C FORM DIVIDED DIFFERENCE TABLE FOR A CUBIC POLYNOMIAL C FOR THE SET OF DATA C MM-N-3 JMAX=10 IF(JMAX.GT.N) JMAX=N DO 10 I=1,N TAB(I,1)=Y(I) 10 CONTINUE DO 30 J=2,JMAX JM-J-1 NN-N-JM DO 20 1=1,NN IP- I + J M TAB(I,J) = (TAB(I + 1 , J M ) - T A B ( I , J M ) ) / ( X ( I P ) - X ( I )) 20 CONTINUE 30 CONTINUE A4=TAB(1,4) B4=TAB(MM,4) C C CALCULATE H(I ) C DO 50 1=1,NM 50 H(I)=X(I + 1 )-X(I ) C C COEFFICIENTS OF TRIDIAGONAL EQUATIONS C 243 B(1)="H(1) C(1)=H(1) D( 1 )=3.*H(1)*H(1)*A4 DO 60 1=2,NM IP-I+1 IM-I-1 A(I)=H(IM) B(I)=2.*(H(IM)+H(I)) C(I)=H(I) 60 D ( I ) = 3 . * ( ( Y ( I P ) - Y ( I ) ) / H ( I ) - < Y ( I ) - Y ( I M ) ) / H ( I M ) ) A(N)=H(NM) B(N)=-H(NM) C(N)=0.D0 D(N)=-3.*H(NM)*H(NM)*B4 C C CALL THOMAS ALGORITHM TO SOLVE TRIDIGONAL SET C CALL TDMA(A,B,C,D,R,N) C C DETERMINE Q(I) AND S(I) C DO 70 1=1,NM IP-I+1 Q ( I ) = ( Y ( I P ) - Y ( I ) ) / H ( I ) - H ( I ) * ( 2 . * R ( I ) + R ( l P ) ) / 3 . 70 S ( I ) = ( R ( I P ) - R ( I ) ) / ( 3 . * H ( I ) ) RETURN END C C SUBROUTINE TDMA(A,B,C,D,X,N) IMPLICIT REAL*8(A-H,0-Z) DIMENSION A(N),B(N),C(N),D(N),X(N),P(21),Q(21) NM-N-1 P(1)=-C(1)/B(1) Q(1)=D(1)/B(1) DO 10 1=2,N IM-I-1 DEN=A(I)*P(IM)+B(I) P(I)=-C(I l/DEN 10 Q(I)=(D(I)-A(I)*Q(IM))/DEN X(N)=Q(N) DO 20 11=1,NM I=N-II 20 X(I)=P(I)*X(I+1)+Q(I) RETURN END C C FUNCTION EVALUATES VELOCITY COMPONENT AT ANY HEIGHT BY SPLINE C INTERPOLATION C DOUBLE PRECISION FUNCTION FF(Z) IMPLICIT REAL*8(A-H,0-Z) COMMON/BLKE/N,NM COMMON/BLKF/X(21),Y(21) COMMON/BLKG/Q(20),R(21),S(20) 1 = 1 IF(Z.LT.X(1)) GO TO 30 IF(Z.GT.X(NM)) GO TO 20 J=NM 10 K=(I+J)/2 IF(Z.LT.X(K)) J=K IF(Z.GE.XtK)) I=K IFCJ.EQ.I+1) GO TO 30 GO TO 10 20 I=NM 30 DX=Z-X(I) FF«Y(I)+DX*(Q(I)+DX*(R(I)+DX*S(I))) RETURN END C C EQUATION OF UPWARD MOTION WITH RESPECT TO HEIGHT C DOUBLE PRECISION FUNCTION F1(I,YR) IMPLICIT REAL*8(A-H,0-Z) DIMENSION YR(4) COMMON/BLKB/TAU1,TAU2,U,DG IF(I.EQ.1) GO TO 11 IF(I.EQ.2) GO TO 12 11 VT1 = 1/TAU1 VT2=(U-YR(2))**2+YR(1 )**2 VT3=VT2**0.344D0 VT4=VT3/TAU2 VT5«DG/YR( 1 ) FI--VT1-VT4-VT5 RETURN 12 VT1=(U-YR(2))/(YR(1)*TAU1) V T 2=(U-YR(2))/(YR(1)*TAU2) VT3=(U-YR(2))**2+YR(1)**2 VT4=VT3**0.344D0 F1-VT1+VT2*VT4 RETURN END C C EQUATION OF DOWNWARD MOTION WITH RESPECT TO HEIGHT C DOUBLE PRECISION FUNCTION F2(I,YR) IMPLICIT REAL*8(A-H,0-Z) DIMENSION YR(4) COMMON/BLKB/TAU1,TAU2,U,DG IF(I.EQ.1) GO TO 13 IF(I.EQ.2) GO TO 14 13 VT1=1/TAU1 VT2=(U-YR(2))**2+YR(1)**2 VT3=VT2**0.344D0 VT4=VT3/TAU2 VT5=DG/YR(1) F2=-VT1-VT4+VT5 RETURN 14 VT1 = (U-YR(2))/(YR(1)*TAU1 ) VT2=(U-YR(2))/(YR(1)*TAU2) VT3=(U-YR(2))**2+YR( 1 )**2 VT4=VT3**0.344DO F2=VT1+VT2*VT4 RETURN END DOUBLE PRECISION FUNCTION FYY(YY) IMPLICIT REAL*8(A-H,0-Z) 245 CALL RUNG(YY,O.DO,YBB) FTY=YBB RETURN E N D C C C DOUBLE PRECISION FUNCTION FTT(TT) IMPLICIT REAL*8(A-H,0-Z) COMMON/BLKC/DX,M,JJ,VP 10,UP2 0,VZO,VZ COMMON/BLKE/N,NM DX-TT/NM CALL RUNG(VP10,0.D0,TTB) FTT=UP20-TTB RETURN E N D C C EQUATION OF MOTION WITH RESPECT TO TIME C DOUBLE PRECISION FUNCTION FT 1(I,TH) IMPLICIT REAL*8(A-H,0-Z) DIMENSION TH(4) COMMON/BLKB/TAUI,TAU2,U,DG IF(I.EQ.1) GO TO 11 IFCI.EQ.2) GO TO 12 11 VT1=TH(1)/TAU1 VT2=(U-TH(2))**2+TH(1)*TH(1) VT3=VT2**0.344D0 VT4«TH{1)*VT3/TAU2 VT5=DG FT1=-VT1-VT4-VT5 RETURN 12 VT1=(U-TH(2))/TAU1 VT2=(U-TH(2))/TAU2 VT3=(U-TH(2))**2+TH(1)*TH(1) VT4=VT3**0.344D0 FT1=VT1+VT2*VT4 RETURN END C C C C FRICTION FACTOR CORRELATION C DOUBLE PRECISION FUNCTION FRIC(XX) IMPLICIT REAL*8(A-H,0-Z) COMMON/BLKD/RE.DE R1=RE*(DSQRT(XX))/DE R2=(9.28/R1)+1 FRIC=1/(DSQRT(XX))- 2 *DLOG10(DE)- 1 .14+ 2*DLOG10(R2) RETURN END C C DOUBLE PRECISION FUNCTION F Z 1(I,XX) IMPLICIT REAL*8(A-H,0-Z) DIMENSION XX (4) COMMON/BLKB/TAUI,TAU2,U,DG VT1= XX( 1 )/TAU1 VT2=XX(1)**1.687D0/TAU2 FZ1=DG*0.577D0-VT1-VT2 RETURN END DOUBLE PRECISION FUNCTION FZ2(I,XX) IMPLICIT REAL*8(A-H,0-Z) DIMENSION XX(4) COMMON/BLKB/TAUI,TAU2,U,DG VT1=1/TAU1 VT2=XX(1)**0.687D0/TAU2 VT3=DG*0.577D0/XX(1) FZ2=VT3-VT1-VT2 RETURN END DOUBLE PRECISION FUNCTION FZZ(XX) IMPLICIT REAL*8(A-H,0-Z) COMMON/BLKC/DX,M,JJ,VP10,UP2 0,VZO,VZ COMMON/BLKE/N,NM DX-XX/NM CALL RNZ(VZO,0.D0,RB) FZZ=VZ-RB RETURN END 247 C NUMERICAL INTEGRATION USING THE ADAPTIVE SIMPSONS TECHNIQUE C SUBROUTINE SIMP(F,A,B,EPS,SUM,N) IMPLICIT REAL*8(A-H,0-Z) DIMENSION H(20),TOL(20),SR(20),XR(20) DIMENSION F1(20),F2(20),F3(20),F4(20),F5(20) IMAX=20 N-3 SUM=0.D0 X1=A C C SET STRIP WIDTH AND TOLERANCE FOR EACH LEVEL C H(1)=(B-A)/2.D0 TOL(1)=20.D0*EPS DO 10 I=2,IMAX IM-I-1 H(I)=H(IM)/2.D0 TOL(I)=TOL(IM)/2.D0 10 CONTINUE C C CALCULATE INITIAL AREA S USING TWO STRIPS C XR(1)=A+2.D0*H(1) Fl(1)=F(A) F3(1)=F(A+H(1)) F5(1)=F(B) S-H(1)*(F1(1)+4.D0*F3(1)+F5(1))/3.D0 1 = 1 C C RECALCULATE SL AND SR UNTIL SL+SR-S<TOL C 20 N=N+2 F2(I)=F(X1+H(I)/2.D0) F4(I)=F(X1+3.D0*H(I)/2.D0) SL=H(I)*(F1(I)+4.D0*F2(I)+F3(I))/6.D0 SR(I)=H(I)*(F3(I)+4.D0*F4(I)+F5(I))/6.D0 IF(DABS(SL+SR(I)-S).LT.TOL(I))GO TO 30 C C IF SL+SR-S >TOL,INCREASE LEVEL AND SUBDIVIDE LEFT STRIP C IM»I 1=1 + 1 IF(I.GT.IMAX)GO TO 60 S-SL Fl(I)=F1(IM) F3(I)=F2(IM) F5(I)=F3(IM) XR(I)=X1+2.D0*H(I) GO TO 20 C C IF SL+SR-S <TOL, ADD SL+SR ONTO S AND LOCATE CORRECT LEVEL C 30 SUM=SUM+SL+SR(I) X1=X1+2.D0*H(I) DO 40 J=I,I IF(DABS(X1-XR(J)).LT.H(IMAX)/2.D0)GO TO 50 40 CONTINUE 50 I=J IF(I.EQ.1)RETURN 248 IM-I-1 S-SR(IM) FI (I ) =F3(IM) F3(I)=F4(IM) F5(I)=F5(IM) GO TO 20 60 WRITE(6,70)X1 70 FORMAT(IX,'WARNING- INTEGRATION FAILS BETOND X=',F7.4) 60 RETURN END APPENDIX E : EXPERIMENTAL DATA 250 EXPERIMENTAL DATA FLAT DAM CONFIGURATION RUN %FI LL RPM AVE.VEL ELUTRIATION RATE m/s g/min ROUGH WALL F01 05 3 1.51 0.210 F2 05 3 1.51 0.270 F3 05 3 2.06 0.320 F4 05 3 2.06 0.330 F20 05 3 2.72 1 . 170 F2I 05 3 2.87 2.860 F22 05 3 2.97 3.260 F23 05 3 3.24 9.660 F7 05 3 3.62 11.410 F8 05 3 3.62 11.580 'H WALL F1 1 05 3 2.45 0.060 FI 3 05 3 3.52 1 . 180 F14 05 3 3.52 2.730 FI 5 05 3 3.4 3 2.140 F16 05 3 3.92 6.300 F17 05 3 4.15 9.100 : E D B E D F26 05 3 2.70 0. 185 F27 05 3 3.58 0.660 F28 05 3 4.50 1 .290 F29 05 3 5.25 2.710 F30 05 3 5.48 2.810 WALL F31 05 1 3.70 5.580 F32 05 3 3.70 5.700 F33 05 5 3.70 5.560 F34 05 7 3.70 6.020 F35 05 9 3.70 6.920 F36 05 1 1 3.70 7.940 F37 05 1 3 3.70 9.220 F38 10 1 3.70 4.400 F39 1 0 3 3.70 4.220 F40 l 0 5 3.70 6.240 F4 1 1 0 7 3.70 7.200 F4 2 10 9 3.70 9.230 251 SMOOTH WALL F43 10 1 4.43 3.910 F44 10 3 4.43 3.110 F45 10 5 4.43 4.210 F46 10 7 4.43 4.700 F47 10 9 4.43 6.010 F48 10 1 1 4.43 7.970 F49 20 1 4.43 13.290 F50 20 3 4.43 14.480 F5 1 20 5 4.43 14.820 F52 20 7 4.43 17.240 F53 20 9 4.43 20.800 F54 20 1 1 4 .43 23.850 F55 05 1 4.43 4.350 F56 05 3 4.43 3.520 F57 05 5 4.43 3.750 F58 05 7 4.43 3.500 F59 05 9 4.43 3.950 F60 05 1 1 4.43 4.460 F61 05 1 5 4.43 4.980 CONICAL DAM CONFIGURATION RUN %FILL RPM ROUGH WALL C01 05 3 C02 05 1 C02A 05 1 C03 05 5 C04 05 7 C05 05 9 C05A 05 9 C06 05 1 1 C06A 05 1 1 C07 05 13 COS 05 1 5 C09 05 1 CIO 05 5 CI 1 05 9 C12 05 3 C13 05 7 C14 05 1 C15 05 3 C16 05 1 C16A 05 1 C17 05 3 C18 05 9 C18A 05 9 C19 05 5 C20 05 3 C21 05 2 C22 05 1 C22A 05 1 C23 05 3 C24 05 5 C25 05 7 C25A 05 7 C26 05 1 3 C27 05 1 1 C28 10 1 C29 10 3 C30 10 9 C31 10 7 C32 10 5 C33 10 1 1 C34 10 3 C35 10 9 C36 10 1 C37 10 5 C38 1 0 1 AVE.VEL ELUTRIATION RATE m/s g/min 1 .60 3.20 1 .60 1 .86 1 .60 2.17 1 .60 3.51 1 .60 3.81 1 .60 3.16 1 .60 3.15 1 .60 3.82 1 .60 3.66 1 .60 4.62 1 .60 4.99 2.06 2.90 2.06 5.35 2.06 5.70 2.06 5.25 2.06 5.79 2.06 6.32 2.06 7.24 2.97 13.61 2.97 13.60 2.97 16.12 2.97 26.92 2.97 26.33 2.97 20.61 2.97 19.38 2.97 16.42 2.61 7.85 2.61 7.49 2.61 10.95 2.61 11.95 2.61 1 4.35 2.61 14.14 2.61 17.97 2.61 16.19 1 .59 5. 27 1 .59 7.58 1 .59 9.02 1 .59 8.81 1 .59 8.60 1 .59 10.14 2.1 1 16.30 2.1 1 21 .27 2.11 23.27 2.11 18.82 2.11 10.31 253 C39 10 3 2.58 22.50 C40 10 9 2.58 32.52 C4 1 10 1 2.58 15.68 C42 10 1 1 2.58 33.28 C43 10 6 2.58 28.25 C44 1 5 9 1 .58 25.42 C45 15 6 1 .58 21 .40 C46 15 3 1 .58 17.54 C47 15 1 1 .58 1 1 .69 C48 1 5 9 2.06 72. 18 C49 15 6 2.06 59.32 C50 1 5 3 2.06 45.48 C51 1 5 1 2.06 33.38 C52 15 6 2.60 94.92 C53 1 5 3 2.60 81 .80 C54 15 1 2.60 64. 12 WALL C55 05 3 1 .79 2.84 C56 05 9 1 .79 2.37 C57 05 1 1 1 .79 2.15 C58 05 1 1 .79 2.32 C59 05 13 1 .79 2.12 C60 05 6 1 .79 2.10 C61 05 3 2.10 3.77 C62 05 9 2.10 3.92 C63 05 13 2. 10 5.03 C64 05 1 1 2.10 4.56 C65 05 6 2.10 3.71 C66 10 3 1 .65 6.26 C67 10 6 1 .65 5.27 C68 10 1 1 .65 4.50 C69 10 9 1 .65 5.58 C70 10 1 1 1 .65 5.52 C71 10 3 2.14 12.90 C72 10 1 2.14 9.75 C73 10 9 2.14 15.58 C74 10 6 2.14 15.66 C75 10 2 2.14 11 .68 C76 10 4 2. 14 13.93 C77 10 1 1 2.14 15.57 C78 10 6 1 .62 16.13 C79 1 0 3 1 .62 16.09 C80 1 0 1 1 .62 10.09 C81 10 9 1 . 62 19.57 254 BENT LIP CONFIGURATION RUN % F I L L RPM ROUGH WALL BO t i5 3 B02 15 6 B03 15 9 B04 15 1 B05 15 3 B06 15 1 B07 15 6 BOB 15 9 B09 1 5 3 BIO 1 5 9 Bl 1 1 5 6 Bl 2 15 1 B13 05 3 Bl 4 05 6 B15 05 1 B16 05 9 B17 05 1 1 B18 05 3 B19 05 9 B20 05 6 B21 05 I B22 05 1 1 B23 05 3 B24 05 9 B25 05 1 B26 05 6 B27 05 1 1 B28 05 1 1 B29 05 6 B30 05 3 B31 05 9 B32 05 1 B33 10 6 B34 10 9 B35 10 1 B36 10 3 B37 10 1 1 B38 10 6 B39 l 0 9 B40 l 0 1 B4 1 10 3 B42 10 1 1 B43 10 3 B44 '0 1 B45 10 1 1 B46 1 0 6 B47 10 9 AVE.VEL ELUTRIATION RATE m/s g/min 2.60 1 .49 2.60 3.32 2.60 6.00 2.60 1 .25 3.04 5.42 3.04 4.75 3.04 8.21 3.04 1 1 .69 3.38 1 1 .25 3.38 18.35 3.38 14.36 3.38 10.94 3.70 12.37 3.70 13.40 3.70 12.97 3.70 15.70 3.70 16.62 3.38 7.75 3.38 9.93 3.38 8.42 3.38 8.40 3.38 11.12 2.92 2.63 2.92 5.27 2.92 2.65 2.92 4.20 2.92 6.76 2.61 4.27 2.61 2.17 2.61 1 .35 2.61 3.51 2.61 1.11 2.58 2.48 2.58 4.02 2.58 0.99 2.58 1 .35 2.58 5.27 3.03 6.29 3 .03 9.91 3.03 4.72 3.03 4.78 3.03 11.54 3.43 10.03 3.43 9.98 3.43 17.90 3.43 11.71 3.43 14.84 SMOOTH WALL B48 05 3 4.13 21.48 B49 05 1 4.13 23.0 1 B50 05 9 4.13 20.21 B51 05 1 1 4.13 20.20 B52 05 6 4.13 20. 14 B53 05 13 4.13 20.45 B54 05 6 3.70 8.78 B55 05 1 1 3.70 10.06 B56 05 3 3.70 9.94 B57 05 1 3.70 12.54 B58 05 9 3.70 9.28 B59 05 1 1 3.04 2.67 B60 05 6 3.04 2.05 B6 1 05 9 3.04 2.36 B62 05 1 3.04 3.25 B63 05 3 3.04 2.14 B64 1 0 3 4.11 22.88 B65 10 1 4.11 24.46 B67 10 6 4.11 24.66 B66 10 1 1 4.11 27.73 B68 10 9 4.11 26.54 B69 10 3 3.70 15.51 B69A 10 3 3.70 15.72 B70 10 6 3.70 16.84 B70A 10 6 3.70 16.97 B7 3 10 1 3.70 16.22 B73A 10 1 3.70 16.78 B7 1 10 1 1 3.70 19.99 B72 10 9 3.70 18.40 B72A 10 9 3.70 19.16 B7 4 10 3 3.10 4.22 374A 10 3 3.10 4.44 B77 10 6 3. 10 6.30 B78 10 1 3.10 6.24 B76 1 0 9 3.10 7.09 B75 10 1 1 3.10 7.98 B79 1 5 1 3.70 20.97 B80 1 5 3 3.70 20.09 B8 1 15 6 3.70 22.07 B82 1 5 9 3.70 24.38 B82A 1 5 9 3.70 24.23 B83 1 5 1 1 3.70 28.20 B84 1 5 3 3.38 12.82 B84A 15 3 3.38 12.10 B85 1 5 1 3.38 14.13 B86 1 5 6 3.38 14.14 B87 1 5 9 3.38 16.94 B88 1 5 1 1 3.38 19.91 B89 1 5 3 2.87 3.24 B89A 1 5 3 2.87 2.45 B90 15 1 2.87 3.97 B90A 1 5 1 2.87 3.79 B9 I 1 5 6 2.87 3.96 B92 15 9 2.87 6.31 B93 1 5 l 1 2.87 7.55 256 BIMODAL SYSTEM 10% F I L L RUN CONC. RPM AVE.VEL ELUTRIATION RATE m/s g/min S32 15 1 3.47 0.722 S33 10 1 3.47 0.496 S40 5 1 3.47 0.191 S34 10 3 3.47 0.957 S35 5 3 3.47 0.371 S4 1 15 3 3.47 1 .923 S36 5 6 3.47 0.783 S37 15 6 3.47 4.01 1 S39 10 6 3.47 2.410 S19 5 3 2.70 0.096 S 1 8 15 3 2.70 0.304 S 1 7 10 3 2.70 0.179 S20 10 6 2.70 0.287 S21 15 6 2.70 0.600 S22 5 6 2.70 0.158 S24 5 3 3.74 0.644 S25 10 3 3.74 1.427 S26 15 3 3.74 2.624 S27 15 6 3.74 4.863 S28 10 6 3.74 2.036 S29 5 6 3.74 1 .061 S30 1 5 1 3.74 1 .366 S3 1 1 0 1 3.74 0.896 S32 5 1 3.74 0.383 5 % F I L L S 1 2 2.5 3 3.02 0.0700 SI 3 1 5 3 3.02 0.3111 SI 1 10 3 3.02 0.2400 TYPICAL DUST MEASUREMENTS WITH TIME Time s t a r t e d Time s t o p p e d Dust R a t e (min) (min) (g) ( g / m i n ) Run C02: % f i1 1 =l5, rpm=5, U=1.6 m/s l.O 11.0 19.78 1.98 11.0 21.0 22.18 2.29 21.0 31.0 21.69 2.17 31.0 41.0 18.65 1.86 41.0 51.0 17.85 1.78 Run C03: % f i11 = 5, rpm=5, U=1.6 m/s 1.0 11.0 29.28 2.93 11.0 21.0 33.04 3.30 21.0 31.0 32.06 3.20 31.0 41.0 35.09 3.51 Run C17: % f i l l = 5 , rpm=5, U=2.97 m/s 1.0 4.0 45.67 15.22 4.0 - 7 . 0 47.13 15.71 7.0 10.0 46.89 15.63 10.0 13.0 48.37 16.12 Run C21: % f i 1 1 = 5, rpm=5, U=2.6l m/s 1.0 4.0 34.77 11.59 4.0 7.0 35.69 11.90 7.0 10.0 35.86 11.95 10.0 13.0 35.81 11.94 Run B O l : % f i11=15, rpm=3, U=2.61 m/s 1.0 11.0 12.34 1.23 11.0 21.0 14.26 1.43 21.0 31.0 14.87 1.49 31.0 41.0 15.59 1.56 Run 313: % f i 1 1 = 5 , rpm=3, U=3.7 m/s 1.0 4.0 35.10 11.70 4.0 7.0 37.12 12.37 7 . 0 10 . 0 38 .39 12.96 Run B44: % f i 11 =10, rpm=6, U=3.43 m/s 1.0 4.0 27.81 9.27 4.0 7.0 29.94 9.98 Run B54: % f i l l = 5 , rpm=6, u"=3.68 m/s 1.0 4.0 24.92 8.31 4.0 7.0 26.35 8.78 Run B68: % f i11=10, rpm=11, U=4.11 m/s 1.0 4.0 81.55 27.18 4.0 7.0 85.33 28.18 Run B75: % f i l l = 1 0 , rpm=11, U=3.10 m/s 1.0 6.0 38.09 7.62 6.0 11.0 39.88 7.98 Run B82: % f i l l = 1 5 , rpm=9, U=3.7 m/s 1.0 4.0 72.15 24.05 4.0 7.0 73.15 24.38 Run B88: % f i l l = 1 5 , rpm=11, U=3.38 1.0 4.0 59.06 19.68 4.0 7.0 59.74 19.91 

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