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Hydrodynamic studies of spouted and spout-fluid beds Pianarosa, Denis Lorenzo 1996

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HYDRODYNAMIC STUDIES OF SPOUTED AND SPOUT-FLUID BEDS by DENIS LORENZO PIANAROSA B.Eng., McGill University, 1992 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S C H E M I C A L E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A December 1996 © Denis Lorenzo Pianarosa, 1996 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 of The University of British. Columbia Vancouver, Canada Date \?2>EZeH&ee- ff. DE-6 (2/88) Abstract Hydrodynamic experiments were conducted in a three-dimensional spout-fluid bed with a specially designed conical distributor to supply the auxiliary air. The vessel used was a cylindrical column, 0.15 m in diameter and 1.05 m high fitted with an inlet orifice plate with a diameter of 19.1 mm. Glass beads of three different mean diameters, 1.33, 1.84 and 2.53 mm, were used as bed materials. Previously developed techniques employing optical fibre sensors and instruments were used to measure local time-averaged voidage and particle velocity. Radial profiles of local voidage inside the bed were obtained for various ratios of auxiliary air flow to total air flow (Q^/QT) t 0 t n e column. Increasing the proportion of auxiliary flow at constant total flow resulted in a significant decrease in spout voidage, while little or no influence was observed in the annulus. Voidage in the annulus varied significantly from the bottom to the top of the bed. In the conical section, local voidages were consistently lower than the loose-packed voidage and consistently higher than the loose-packed voidage in the cylindrical section. The low voidage in the conical section suggests that particles are being compacted in this region. Cross-sectional average voidages in the spout decreased monotonically with height and were lower for a higher proportion of auxiliary flow but independent of particle size. Spout diameter was unaffected by the proportion of auxiliary air being supplied to the column, supporting the findings of Sutanto (1983). Both the McNab (1972) and Wu (1986) equations were found to under-predict average spout diameters by as much as 28%. In general, particle velocity decreased with increasing proportion of auxiliary flow. However, the effect was more pronounced in the spout than in the annulus. Solids mass flow rates decreased with increasing proportion of auxiliary flow. The observed increase ii in solids mass flow rates with particle size is most likely due to the higher gas velocities required for spouting. The integrated upward solids flow in the spout was consistently higher than the corresponding downward solids flow in the annulus. The discrepancy can be attributed to inherent inaccuracies in the measurement techniques and instruments used as well as physical phenomena which could not be entirely eliminated. Pressure gradients in the annulus increased with an increasing proportion of auxiliary gas, as expected. The effect of auxiliary air was greater at the bottom of the bed, and the profiles converged towards a maximum value at the top of the bed. In addition, discontinuities in the profiles were observed near the cone-cylinder junction. Superficial gas velocities in the annulus were obtained by combining the pressure gradients with measured local voidage in an equation of the form of the Ergun (1952) equation for fluid flow through a packed bed. The results were not entirely consistent, most likely due to the sensitivity of the calculation to voidage measurements which had considerable scatter. iii Table of Contents Abstract 1 1 Table of Contents iv List of Tables vii List of Figures 5 0 Acknowledgments X 1 V Chapter 1 Introduction 1 1.1 Fluid-Solid Systems 1 1.2 Fluidized and Spouted Beds 2 1.3 The Spout-Fluid Bed Technique 6 1.4 Regime Maps 8 1.5 Applications of Spout-Fluid Beds 13 1.6 Scope of Work 17 Chapter 2 Experimental Set-up 20 2.1 Apparatus 20 2.1.1 Column Design 20 2.1.2 Flow Rate Measurement 25 2.2 Particles 29 2.3 Operating Conditions 34 2.4 Instrumentation 35 Chapter 3 Voidage Profiles 37 3.1 Introduction 37 3.2 Measurement Techniques 38 3.3 Experimental Equipment: Instrumentation and Technique 40 3.3.1 Voidage Measurement 40 3.3.2 Spout Diameter 45 3.4 Results and Discussion 45 3.4.1 Voidage Profiles 45 3.4.2 Spout Shape and Diameter 55 3.5 Summary 59 iv Chapter 4 Particle Velocity Profiles and Solid Circulation Rates 60 4.1 Introduction 60 4.1.1 Particle Flow in the Spout of Spouted Beds 60 4.1.2 Particle Flow in the Annulus 62 4.1.3 Solids Circulation Rates 64 4.2 Measurement Techniques 65 4.3 Equipment and Instrumentation 66 4.3.1 Particle Velocity Measurements in the Spout 66 4.3.2 Particle Velocity Measurements in the Annulus 71 4.4 Results and Discussion 74 4.4.1 Particle Velocity Profiles in the Spout and Annulus 74 4.4.2 Solids Mass Flow Rates 80 4.4.3 Fountain Height 90 4.5 Summary 92 Chapter 5 Pressure Gradients and Gas Flow in the Annulus 94 5.1 Introduction 94 5.1.1 Pressures Gradients in the Annulus 94 5.1.2 Gas Flow in the Annulus 96 5.2 Theoretical Models for Gas Velocity in the Annulus of Spouted and Spout-Fluid Beds 98 5.3 Experimental Methods 99 5.4 Results and Discussion 102 5.4.1 Longitudinal Pressure Gradients 102 5.4.2 Gas Distribution in the Annulus 106 5.5 Summary 110 Chapter 6 Conclusions and Recommendations I l l 6.1 Conclusions I l l 6.2 Recommendations 113 Nomenclature 115 References 118 v Appendices Appendix A Rotameter Calibration Curves 124 Appendix B Calibration Curves of Pressure Gradient vs Superficial Gas Velocity 127 Appendix C Experimental Data: Voidage, Particle Velocity and Spout Diameter 129 Appendix D Experimental Data: Annular Differential Pressure Drop 159 Appendix E Computer Program Used for Calculation of Cross-Sectional Average Spout Voidage, Mass Flow Rates and Superficial Gas Velocity 166 Appendix F Computed Results of Cross-Sectional Average Spout Voidage, Mass Flow Rates and Superficial Gas Velocity 183 Appendix G Effect of Pulsating Flow through the Spout on the Calculation of Solids Mass Flow Rate 189 vi List of Tables Table 2.1: Properties of glass beads used in experiments 29 Table 2.2: Summary of spouting and auxiliary flow combinations used in experiments 35 Table 3.1: Experimental average spout diameters and values predicted from the McNab (1972) equation 58 Table 3.2: Experimental average spout diameters and values predicted from the Wu (1986) equation 58 Table 4.1: Experimental fountain heights and values predicted from the Grace and Mathur (1978) equation 92 Table 5.1: Values of kj and ^  obtained by curve fitting of experimental data compared with values calculated from Equations 5.2 and 5.3 101 Table C. 1: Experimental measurements of voidage and particle velocity. (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.22, Q A / Q T = 0 °> Qs = 0.0149 m-Vs, Q A = 0.00 m/s) 130 Table C.2: Experimental measurements of voidage and particle velocity. (dp=1.33mm,H=0.280m,U/Ums=1.20,QA/QT=0.15,Qs=0.0125m3/s, QA=0.00221m3/s) 133 Table C.3: Experimental measurements of voidage and particle velocity. (dp=1.33mm,H=0.280m,U/Ums=1.19,QA/QT=0.29,Qs=0.0103m3/s, QA=0.00417m3/s) 136 Table C.4: Experimental measurements of voidage and particle velocity. (dp=1.33mm,H=0.280m,U/Ums=1.20,QA/Qx=0.43,Qs=0.00826m3/s, QA=0.00634m3/s) 139 Table C.5: Experimental measurements of voidage and particle velocity. (dp=1.84mm,H=0.280m,U/Ums=1.23,QA/QT=0.0,Qs=0.0177m3/s, QA=0.00m3/s) 142 Table C.6: Experimental measurements of voidage and particle velocity. (dp= 1.84mm,H=0.280m,U/Ums= 1.20,Q A/Q T=0.15 ,QS=0.0147m3/s, QA=0.00260m3/s) 145 vii Table C.7: Experimental measurements of voidage and particle velocity. (dp=1.84mm,H=0.280m,U/Ums=1.23,QA/Qx=0.26,Qs=0.0123m3/s, QA=0.00430m7s) 148 Table C.8: Experimental measurements of voidage and particle velocity. (dp=1.84mm,H=0.280m,U/Ums=1.23,QA/Qx=0.39,Qs=0.0101m3/s, QA=0.00650m3/s) 151 Table C.9: Experimental measurements of voidage and particle velocity. (dp=2.53mm,H=0.280m,U/Ums=1.20,QA/Qx=0.0,Qs=0.0251m3/s, QA=0.00m3/s) 154 Table C. 10: Experimental measurements of voidage and particle velocity. (dp=2.53mm,H=0.280m,U/Ums=1.20,QA/Qx=0.43,Qs=0.0143m3/s, QA=0.0110m3/s) 156 Table C. 11: Experimental measurements of spout radius (dp=l 33mm) 158 Table C.12: Experimental measurements of spout radius (dp= 1.84mm) 158 Table C.13: Experimental measurements of spout radius (dp=2.53mm) 158 Table D. 1: Annular differential pressure drop measurements. (dp = 1.33 mm, H = 0.280 m, L V U m s = 1.22, Q A / Q T = 0.0, Q s = 0.0149 rn/s, Q A - 0.00 nY7s) 157 Table D.2: Annular differential pressure drop measurements. (dp = 1.33 mm, H = 0.280 m, TJ/U m s = 1.20, Q A / Q X = 0.15, Q s = 0.0125 mVs, Q A = 0.00221 iri/s) 157 Table D.3: Annular differential pressure drop measurements. (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.19, Q A / Q X = 0.29, Q s = 0.0103 m3/s, Q A = 0.00417 m3/s) 158 Table D.4: Annular differential pressure drop measurements. (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.20, Q A / Q X = 0.43, Q s = 0.00826 m3/s, Q A = 0.00634 m3/s) 158 Table D.5: Annular differential pressure drop measurements. (dp = 1.84 mm, H = 0.280 m, U / U m s = 1.22, Q A / Q X = 0.00, Q s = 0.0176 m3/s, Q A = 0.00 m3/s) 159 Table D.6: Annular differential pressure drop measurements. (dp = 1.84 mm, H - 0.280 m, U / U m s = 1.20, Q A / Q X = 0.15, Q s = 0.0146 m3/s, Q A = 0.00259 m3/s) 159 vm Table D.7: Annular differential pressure drop measurements. (dp = 1.84 mm, H = 0.280 m, U / U m s - 1.21, Q A / Q T = ° - 3 0 > Qs = 0.0122 m3/s, Q A = 0.00520 m3/s) 160 Table D.8: Annular differential pressure drop measurements. (dp = 1.84 mm, H = 0.280 m, U / U m s = 1.22, Q A / Q T = 0.43, Q s = 0.0101 m3/s, Q A = 0.00749 m3/s) 160 Table D.9: Annular Differential Pressure Drop Measurement. (dp = 2.53 mm, H = 0.280 m, U / U m s = 1.21, Q A / Q T = 0.0, Q s = 0.0252 m3/s, Q A = 0.00 m3/s) 161 Table D. 10: Annular differential pressure drop measurements. (dp = 2.53 mm, H = 0.280 m, U / U m s = 1.19, Q A / Q X = 0.15, Q s = 0.0211 m3/s, Q A = 0.00378 m3/s) 161 Table D. 11: Annular differential pressure drop measurements. (dp = 2.53 mm, H = 0.280 m, U / U m s = 1.20, Q A / Q T = 0.28, Q s = 0.0181 m3/s, Q A = 0.00695 m3/s) 162 Table D. 12: Annular differential pressure drop measurements. (dp = 2.53 mm, H = 0.280 m, U / U m s = 1.21, Q A / Q T = 0.43, Q s = 0.0143 m3/s, Q A = 0.0110 m3/s) 162 Table F. 1: Computed results of mass flow rates in the spout. (dp= 1.33 mm, H = 0.280 m, U / U m s = 1.2) 184 Table F.2: Computed results of mass flow rates in the annulus. (dp= 1.33 mm, H = 0.280 m, U / U m s = 1.2) 184 Table F.3: Computed results of cross-sectional average spout voidage. (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.2) 185 Table F.4: Computed results of annular superficial gas velocity. (d p= 1.33 mm, H = 0.280 m, U / U m s = 1.2) 185 Table F.5: Computed results of mass flow rates in the spout. (dp= 1.84 mm, H = 0.280 m, U / U m s - 1.2) 186 Table F.6: Computed results of mass flow rates in the annulus. (dp - 1.84 mm, H = 0.280 m, U / U m s = 1.2) 186 Table F.7: Computed results of cross-sectional average spout voidage. (dp - 1.84 mm, H = 0.280 m, U / U m s =1.2) 187 ix Table F.8: Computed results of annular superficial gas velocity. (dp = 1.84 mm, H = 0.280 m, U / U m s =1.2) 187 Table F.9: Computed results of mass flow rates in the spout. (dp = 2.53 mm, H = 0.280 m, U / U m s =1.2) 188 Table F. 10: Computed results of mass flow rates in the annulus. (dp-2.53 mm, H = 0.280 m, U / U m s = 1.2)...: 188 Table F. 11: Computed results of cross-sectional average spout voidage. (dp = 2.53 mm, H = 0.280 m, U / U m s =1.2) 188 Table F. 12: Computed results of annular superficial gas velocity. (dp = 2.53 mm, H = 0.280 m, U / U m s =1.2) 188 x List of Figures Figure 1.1: Schematic diagram of a spouted bed 3 Figure 1.2: Schematic diagram of a spout-fluid bed 7 Figure 1.3: Regime map due to Nagarkatti and Chatterjee (1974). (Particles: glass beads, p = 24\0 kg/m3, H b = 0.185 m, dp = 0.60 mm, Dj = 5.0 mm, Dc - 90 mm, fluid used: air) 9 Figure 1.4: Regime map due to Vukovic et al. (1982). (Particles: calcium carbonate, p - 2600 kg/m3, Hf) = \rc^dp=\.% mm, Dj - 15 mm, Dc = 70 mm, fluid used: air) 10 Figure 1.5: Regime map due to Sutanto et al. (1985). (Particles: polystyrene, p = 1040 kg/m3, = 0.60 m, dp = 2.9 mm, Dj = 19.1 mm, Dc= 152 mm, fluid used: air) 11 Figure 2.1: Schematic diagram of spout-fluid bed used in experiments 21 Figure 2.2: Cross-sectional view of conical subdistributor 22 Figure 2.3: Top view of conical section minus wire mesh showing distribution of holes 23 Figure 2.4: Details of the orifice plates 26 Figure 2.5: Schematic showing overall layout of experimental equipment 28 Figure 2.6: Details of differential pressure probe 30 Figure 3.1: Schematic diagram of fibre optic system used to measure local particle concentration 41 Figure 3.2: Calibration curve by He (1995) of output signal from the fibre optic system vs. solids volume fraction in glass beads (dp = 1.41 mm) and water systems 44 Figure 3.3: Output signals from the fibre optic system, (a) in the spout; (b) in the annulus 46 Figure 3.4: Radial voidage profiles at different ratios of auxiliary air flow to total air flow (QA/Qf) for smallest glass beads (dp = 1.33 mm) 47 xi Figure 3.5: Radial voidage profiles at different ratios of auxiliary air flow to total air flow (QA/Qf) f ° r intermediate glass beads {dp =1.84 mm) 48 Figure 3.6: Vertical profiles of cross-sectional average voidage in the spout (glass beads, dp = 1.33 mm, U/Ums = 1.2, H= 0.280m) 52 Figure 3.7: Vertical profiles of cross-sectional average voidage in the spout (glass beads, dp = 1.84 mm, U/Ums = 1.2, H= 0.280m) 53 Figure 3.8: Vertical profiles of cross-sectional average voidage in the spout for all three particle sizes at two values of Q^QT^^ms = !-2> #=0.280m) 54 Figure 3.9: Vertical profiles of spout radii for all three particle sizes 56 Figure 4.1: Schematic of fibre optical system for measurement of particle velocities in the spout 68 Figure 4.2: Schematic diagram of equipment used for measuring particle velocities in the annulus 72 Figure 4.3: Radial profiles of upward, vertical particle velocities in the spout {dp =1.33 mm) 75 Figure 4.4: Radial profiles of upward, vertical particle velocities in the spout {dp =1.84 mm) 76 Figure 4.5: Radial profiles of downward vertical particle velocities in the annulus {dp = 1.33 mm) 78 Figure 4.6: Radial profiles of downward vertical particle velocities in the annulus {dp= 1.84 mm) 79 Figure 4.7: Solids mass flow rate in the spout {dp = 1.33 mm) 82 Figure 4.8: Solids mass flow rate in the annulus {dp = 1.33 mm) 83 Figure 4.9: Solids mass flow rate in the spout {dp = 1.84 mm) 84 Figure 4.10: Solids mass flow rate in the annulus {dp = 1.84 mm) 85 Figure 4.11: Solids mass flow rate in the spout at two values of Q^/Qf for all particle sizes 88 xii Figure 4.12: Solids mass flow rate in the annulus at two values of QA^QT^0V A^ particle sizes 89 Figure 4.13: Fountain height vs QA^QT^0T a " particle sizes 91 Figure 5.1: Longitudinal pressure gradients in the annulus (dp =1.33 mm) 103 Figure 5.2: Longitudinal pressure gradients in the annulus (dp = 1.84 mm) 104 Figure 5.3: Longitudinal pressure gradients in the annulus (dp = 2.53 mm) 105 Figure 5.4: Superficial gas velocity profiles in the annulus for different ratios of QA/QT(dp = 1 3 3 m m ) 107 Figure 5.5: Superficial gas velocity profiles in the annulus for different ratios of QAfQj(dp =1.84 mm) 108 Figure 5.6: Superficial gas velocity profiles in the annulus for all three particle sizes at two values of QA^QT- 109 Figure A. 1: Calibration curve for central inlet rotameter 125 Figure A. 2: Calibration curve for left, auxiliary rotameter 126 Figure A 3 : Calibration curve for right, auxiliary rotameter 126 Figure B. 1: Calibration curves of pressure gradient vs superficial gas velocity in loose-packed beds 128 xin Acknowledgments I would like to thank the University of British Columbia and the Department of Chemical Engineering for providing an enriching and stimulating environment for carrying out my studies. In particular, I would like to thank the gentlemen of the workshop who have been extremely helpful throughout this project. Their expertise, knowledge and excellent craftsmanship played a very big role in this project. I would also like to thank the secretarial and store staff who have gone out of their way, on many occasions, to help me. I would like to express my sincere gratitude to Drs. Jim Lim and John Grace for the financial assistance, experience and distinguished supervision they provided which allowed me to complete this work. I am very grateful to Dr. Lim for his guidance and support. His door was always open to me and I am grateful for the encouragement and optimism he provided during difficult times. I would also like to express my appreciation to Dr. Grace for the respect and dedication he showed me and especially for his valuable insights and ideas. I am very grateful to Drs. Dingrong Bai, K. Seng Lim and Clive Brereton for their help and assistance throughout the project and especially for their willingness to put their work aside to discuss ideas and problems with my work. I would like to thank my friends and fellow students who have lent their support and made the difficult times more bearable. I am especially grateful to my best friend, Marline, who was always there for me and was an endless source of encouragement. Most of all, I would like to thank my family for their patience, support and encouragement, especially my parents who have given so much of themselves so that I may achieve my goals. xiv Chapter 1 Introduction 1.1 Fluid-Solid Systems Various techniques have been developed for assuring intimate contact between solids and fluids because of the importance of such systems throughout the chemical process industry as well as in other areas such as electric power generation, food processing, pharmaceutical manufacture and mineral processing. Fluid-solid systems are encountered in many physical processes such as drying of granular material, drying of suspensions and solutions, transportation of solids, particle coating, adsorption, absorption and filtration operations, as well as in heat exchangers, quenching, etc. (Mathur and Epstein, 1974a). In chemical processes, the solids may take part directly in the reaction, for example in carbonization of oil shale and coal, calcination of limestone and roasting of sulfide ores. The solids may alternatively be used as catalysts, as a heat carrier or to absorb a gaseous species in order to obtain better reactor performance, improved conversion or selectivity. Such systems are encountered, for example, in synthesis reactions and in cracking and reforming of hydrocarbons (Kunii and Levenspiel, 1969). In the latter part of this century, biotechnology introduced a new dimension to fluid-solid systems. The cells or microorganisms act as the solid "particles" which must interact with the fluid containing nutrients required for growth. The application of living cells to industrial and commercial uses has been very important in food processing, waste water treatment and the pharmaceutical industry for example. 1 The following is a brief background of different fluidization techniques used for fluid-solid contacting and the development of the spout-fluid bed technique. An account of previous studies done on spout-fluid beds which are not considered in this study is given. More detailed reviews of previous work in the specific areas tackled in this project are included in the introductions to the corresponding chapters. 1.2 Fluidized and Spouted Beds The fluidized bed has been extensively used for contacting solids and fluids due to its unique characteristics such as, excellent mixing resulting in uniformity of conditions including temperature within the bed, high heat and mass transfer rates and ease of transfer of solids due to their fluid-like state (Mathur and Gishler, 1955). However, fluidized beds are often ineffective in handling coarse particles of non-uniform size and shape. Above a certain particle size (typically dp > 1 mm) large bubbles form in the bed and slugging tends to occur. Under these conditions the fluid effectively bypasses the solids and agitation is inconsistent. This reduction in fluid-solid contact and agitation often makes the fluidized bed a poor system for large particles. Mathur and Gishler (1955) developed the spouted bed technique for handling particles too large for conventional fluidized beds. Originally designed for drying agricultural grains, the spouted bed has since been applied in a wide variety of operations. Figure 1.1 provides a schematic representation of a spouted bed column. It consists of a cylindrical section connected to a conical or flat-bottomed base section with a single, centrally located orifice. 2 FLUID OUTLET SPOUTING FLUID INLET Figure 1.1: Schematic diagram of a spouted bed (arrows indicate direction of flow). 3 Spouting involves contacting of solids with fluid by injecting a steady axial flow of fluid into the bed of particles through the orifice at the bottom of the bed. The spouted bed is made up of two distinct regions: a dilute core called the spout and a surrounding dense region called the annulus. When the fluid injection rate is high enough, particles are carried up through the hollowed spout within the bed of solids. These particles, after rising to a height above the surface of the bed, rain back down as a fountain onto the annulus. In the annulus the particles move downward and inward as a slowly moving packed bed. Under spouting conditions the fluid in the spout assists in supporting the surrounding annulus region and therefore must be at a higher pressure. Because of this pressure difference, fluid from the spout leaks into the annulus along the entire height of the bed. Due to the shearing action of the spout along the annulus, particles are entrained back into the spout over the entire bed height as well. The overall system thereby becomes a composite of a centrally located dilute-phase cocurrent-upward transport region surrounded by a dense-phase moving packed bed, with counter-current percolation of fluid. Mathur and Gishler (1955) identified the most important factors affecting spouting, including orifice diameter, fluid-flow rate, bed depth and particle size. They observed that for a certain particle size and column diameter there is a maximum orifice size beyond which spouting does not occur. The maximum bed depth of a certain material which can be made to spout depends not only on the inlet orifice size but also on the column diameter. Several other authors (Mathur and Epstein, 1974b; Kamiec, 1983; Green and Bridgwater, 1983; Fane 4 and Mitchell, 1984; Lim and Grace, 1987) observed that bed diameter plays a more important role than originally thought. This is particularly important if existing correlations and models are to be used for scale-up of spouted beds to commercial size. For the application to drying operations, a distinct advantage of the spouted bed system is that the low residence time of the solids in the spout allows much higher inlet gas temperatures to be used, thereby increasing the heat transfer efficiency without over-heating the solids. This characteristic is especially important for drying of agricultural grains and in the food processing industry. One disadvantage of the spouted bed is that local mixing is not as high as in a fluidized bed because most particles are moving slowly in the dense annular region. Thorley et al. (1959) predicted that only about 15% of the particles in a spouted bed are in the spout at any instant. Later observations, including those of He et al. (1995), have shown that this value is closer to 3%. Since the gas passing through the spout is not in contact with the solids in the annulus, the contacting efficiency of the system is reduced. In addition, the slow moving packed bed zone may lead to agglomeration problems, especially if the solids are sticky or tend to sinter. 5 1.3 The Spout-Fluid Bed Technique By introducing air directly into the annulus, Chatterjee (1970) found that it was possible to reduce the limitations of spouting and fluidization by superimposing the two types of systems. A schematic diagram of a spout-fluid bed is given in Figure 1.2. In addition to the injection of spouting fluid through the central orifice, auxiliary fluid is introduced through a porous or perforated distributor. This technique can result in a higher rate of circulation of solids and fluid than either spouting or fluidization alone. Compared to fluidized beds, spout-fluid beds can operate under a much wider range of fluid flow rates without succumbing to slugging or bumping which generally reduce the efficiency of the system. In addition, the technique can eliminate such undesirable effects as slugging or particle stratification by species. This is particularly useful in systems such as roasting, calcining or gasification where the particles are continuously changing in size and/or density. With respect to spouted beds, the auxiliary air increases the fluid-solid contact in the annulus. It also reduces the tendency for particles to sit for extended periods in contact with themselves or the walls of the column where agglomeration may occur. In the spout, a greater solids loading is achieved due to the higher pressure in the annulus pushing the particles toward the axis. This results in increased fluid-solid contact in the spout. Comparative studies of spout and spout-fluid bed combustors have been performed by 6 FLUID OUTLET if SPOUTING FLUID INLET FOUNTAIN A N N U L U S S P O U T DISTRIBUTOR CALMING C H A M B E R - AUXILIARY FLUID INLET - FLUID F L O W SOLIDS F L O W Figure 1.2: Schematic diagram of a spout-fluid bed (arrows indicate direction of flow). 7 Madonna et al. (1980), Lim et al. (1984), Zhao et al. (1987) and Lim et al. (1988). Both found that the addition of auxiliary air in the spout-fluid bed results in more uniform axial temperature profiles and appears to provide a useful combination of the spouted and fluidized bed. The spout-fluid bed technique also allows better control of the system by operating under a broader range of fluidizing or spouting conditions. 1.4 Regime Maps The introduction of the auxiliary flow adds another degree of freedom. Therefore different types of bed behaviour are obtained by adjusting the ratio of auxiliary air flow to spouting air flow. These different operating modes can be represented by a phase diagram or regime map. Flow regimes in spout-fluid beds have been studied by a number of authors and regime maps have been constructed (Nagarkatti and Chatterjee, 1974; Dumitrescu, 1977; Littman et al., 1976, Vukovic et al., 1982; Heil and Tels, 1983; Sutanto et al., 1985). Although significant differences exist among these, they share many common features. Differences can be attributed to variations in column design and bed material and in the terminology used to define each regime. Regime maps determined experimentally by Nagarkatti and Chatterjee (1974), Vukovic et al. (1982) and Sutanto et al. (1985) are presented in Figures 1.3, 1.4 and 1.5, respectively. Four common flow regimes can be identified from these diagrams: 8 D C CD c * N l_t_ 160 Spouting (Central) flow (Ndm /min air) Figure 1.3: Regime map due to Nagarkatti and Chatterjee (1974). (Particles: glass beads, pp = 2410 kg/m3, H = 0.185 m, dp = 0.60 mm, D, = 5.0 mm, £> c = 90 mm, fluid: air) 9 4 to O o 00 cr Vertical t ransport Jet i n fluidized bed (Fluidized bed with local spout) Spout- f luid bed (H>Hmsf) Fixed \ bed \ Spout- f luid bed (H<Hmsf) f \e \d (Q/Qmf) 0.5 Figure 1.4: Regime map due to Vukovic et al. (1982). (Particles: calcium carbonate, pp 2600 kg/m3, H = 1 m, dp = 1.8 mm, Dt = 15 mm, Dc = 70 mm, fluid: air) 10 1.6 1.4 H 1.2H 0.4 H 0.2 H Legend O Observed spout .-with aeration # Observed spout-flutdlzation Jet in fluidized bed (slugging) JFTD Spout-fluidization (SF) \ JF(II) (bubbling) \ Packed bed (P) \ ^ Spouting with aeration (SA) I 1 I ^ I 1 r~ 0.2 0.4 0.6 0.8 \ Q / Q 1.2 1.4 1.6 m f Figure 1.5: Regime map due to Sutanto et al. (1985). (Particles: polystyrene, pp = 1040 kg/m3, H = 0.60 m, dp = 2.9 mm, Dt = 19.1 mm, Dc = 152 mm, fluid: air) 11 (i) Fixed or packed bed regime: When the total flow through the bed (central flow plus auxiliary flow) is less than Umj, the particles remain motionless as in a packed bed. If the central flow is high enough, a cavity is formed above the spout inlet and the gas dissipates into the bed, forming a channel along the entire bed height. (ii) Jet in fluidized bed regime: In this case the total gas flow (QT = Q$ + QA) LS somewhat greater than that required for minimum fluidization. One finds slugging in the upper part of the bed at higher auxiliary flow rates and bubbling at lower flow rates. The spout is only partially developed in this region. (iii) Spouting with aeration regime: This regime has the appearance of a conventional spouted bed. It corresponds to relatively low auxiliary flow rates. (iv) Spout-fluidization regime: Increasing the auxiliary flow rate eventually leads to a state where the annular solids become fluidized and the spout exhibits unstable behaviour, although it breaks the surface of the bed. Zhao et al. (1987) developed a regime map for a spout-fluid bed operating at high temperatures (c. 600°C). They found that increasing the bed temperature led to a shift in the flow regime boundaries. In comparison to operation at room temperature, stable spouting disappeared at high temperatures, being replaced by pulsatory spouting, even without the addition of auxiliary air. This behaviour was also reported by Ye et al. (1992) with 12 temperatures up to 880°C. The jet-in-fluidized bed regime and slugging also appeared with less auxiliary air flow. He (1990) and He et al. (1992) investigated the hydrodynamics of spout-fluid beds in a large-diameter column (Dc = 0.91 m). In general, the results gave regime maps similar to those that previous authors obtained with much smaller columns. In contrast to the findings of Sutanto et al. (1985) where there was a bubbling regime between the packed bed and spouting-with-aeration regimes, the transition in this study was direct. It was also noted that the minimum fluid flow rate for spouting-with-aeration always exceeded the minimum spouting flow rate and that the minimum total fluid flowrate for spout-fluidization was equal to the minimum fluidization flow rate. 1.5 Applications of Spout-Fluid Beds The spout-fluid bed technique has been successfully applied in coal combustion and gasification. Increasing energy demands coupled with diminishing fuel resources have led to the development of new processes for obtaining energy from other resources. Coal, a relatively abundant natural resource in North America and some other parts of the world, has become extremely important as an alternate source of energy. Environmental standards have also become more stringent; therefore, more efficient and cleaner processes for the combustion of coal must be explored (Madonna et al., 1980). 13 In December 1980, the total world supply of coal was estimated at 717 billion tonnes (approximately 1.6xl01 3 MBtu) representing 70% of the total world fossil energy resources while natural gas and crude oil make up only 22% of available reserves (Pate and Mensinger,. 1989). However, over 70% of the energy used in North America is in the form of liquid or gas hydrocarbons, with only 20% from coal. There is an abundant source of energy in the form of coal waiting to be used. The difficulty is to use the coal in an economical and environmentally friendly way. Coal is not the only alternate source of energy available. There are also large quantities of waste materials from agricultural, industrial and domestic uses which can be used as sources of energy or feedstocks for gasification. These include municipal solid waste, wood and wood waste, paper mill refuse, peat and manure. For example, there is currently a surplus of approximately 1870 million tonnes of straw per year in the United States for which there is no attractive market (Langille and Ghaly, 1991; Ergudenler and Ghaly, 1992). Ergudenler and Ghaly (1992) predicted that straw, with its relatively low ash content and reasonably high energy content, could be an excellent source of energy. Traditionally, gasification and combustion processes have been carried out in fixed or fluidized beds. Fixed beds generally suffer from several drawbacks. They require a non-swelling, closely graded coal in order to obtain constant and uniform flow conditions in the bed and produce substantial amounts of tar (Arnold et al., 1992). The development of circulating fluidized bed combustion (CFBC) has led to distinct advantages such as improved combustion efficiency due to the recirculation of unburned particles, low S O x and N O x 14 emissions and good control of the combustion process (Zhou, 1995). However, these systems require fine particles of relatively uniform size distribution, necessitating added preparation. This added preparation increases both the cost of the coal and the impact on the environment since losses in handling the material can be significant and human exposure to dust is increased. For these reasons, particular effort has been directed toward the use of industrial grade coals and easier methods for reducing dust, S O x and N O x emissions compared with conventional coal-fired power stations. Madonna et al. (1980) performed an extensive study of fluidized, spouted and spout-fluid beds related to their application to coal combustion. They studied attrition, mixing patterns, temperature and fluid velocity profiles in all three systems and concluded that the fluidized and spout-fluid beds were more suitable for combustion since they displayed a higher mixing rate and improved air/particle contact. Zhao et al. (1987) observed more uniform axial temperature profiles in a spout-fluid bed compared to the spouted bed, indicating higher mixing rates and better air/particle contact. Chatterjee et al. (1983) studied wall-to-bed heat transfer characteristics of spout-fluid beds. Their findings showed that the maximum wall-to-bed heat transfer coefficient was 30% more than the maximum obtainable from the corresponding fluidized bed. In addition, the heat transfer coefficient in the spout-fluid bed increased with increasing particle size while the opposite was true in the fluidized bed. This suggests that the spout-fluid bed is more suitable for combustion of coarser fuels, requiring less preparation. Arnold et al. (1992) reported the 15 successful development of an air-blown spout-fluidized bed gasification process for the production of low calorific value gas. The gasifier was made to operate with two commercially available grades of coal, 12-25 mm and 0-25 mm, and achieved conversion efficiencies of up to 95%. In addition, the gasifier was operated with coals of ash content up to 40%, swelling numbers up to 8V2 and sulphur contents up to 4%, without any operational problems. An interesting system was developed for a dual distributor wheat straw gasifier by Ergudenler and Ghaly (1992). This novel approach used a primary air supply to fluidize the bed material within the main fluidizing column while a secondary air supply was used to create a jet of air which carried the bed material (alumina) and fuel (straw) to the main fluidizing column. Although it was operated as a fluidized bed, the distributor system resembles that of a spout-fluid bed system with a central air inlet and a surrounding air distributor. The spout-fluid bed with draft tube (Yang and Keairns, 1983; Berruti et al., 1988; Grbavcic et al., 1992) and the Internally Circulating Fluidized Bed (Milne et al., 1992) are further modifications of the spout-fluid bed which have been studied extensively . The draft tube is a tube or pipe installed within the bed either some distance above the spouting fluid inlet or attached directly to it, with orifices in the wall of the tube near the base in the case of an ICFB. For a draft tube which is impermeable to both solids and fluid, the most important characteristics of those systems are: 1. There is no bed height limitation; 2. the minimum spout-fluid velocity is lower in a bed with draft tube because there is no loss of gas to the 16 annulus; 3. the draft tube forces all of the particles to travel through the entire annulus section, surrounding the draft tube before reentering the spout in the entry section thereby narrowing the particle residence time distribution in both the spout and annulus. 1.6 Scope of Work The earliest studies on spout-fluid beds focused primarily on bed behaviour and fluid flow with only a rudimentary analysis of the solids circulation rate and distribution. Considering the hybrid nature of this technique, observations were often compared to correlations developed for spouted and fluidized beds and modified to obtain a new set of models. The work of Sutanto (1983) showed significant observable differences in particle circulation rates and voidage under different spout-fluid conditions. He (1990) recommended that an investigation of particle velocities in the spout and annulus be undertaken together with measurements of solids mass circulation rate in spout-fluid beds. It is the opinion of Berruti et al. (1988) that the solids circulation rate is possibly the most critical variable in predicting the performance of a spouted bed. Stocker (1987) found that the lack of experimental data on solids circulation was the last missing piece of design information to successfully model a pilot scale spout-fluid bed reactor with a draft tube used for the ultrapyrolysis of heavy oil. Quantitative measurements of voidage and particle velocities and solids circulation rates are essential in order to understand the behaviour and reveal fundamental physical laws for fluid-solid contact in spout-fluid beds. 17 This thesis investigates the hydrodynamics in a fully cylindrical spout-fluid bed using recently developed measurement techniques. The study involves measurements of local particle concentration, particle velocity and annular gas flows for different ratios of spouting to fluidizing air flow rates. Three sizes of glass beads with narrow size distributions were used for the experiments in order to investigate the effect of particle diameter on the hydrodynamics. The influence of these variables on solids circulation rate as well as on spout shape and fountain height is examined. Chapter 2 describes, in detail, the experimental equipment used throughout this research project. Details on instrumentation and experimental techniques are given in the corresponding chapters where they are used. Also included in this section is an outline of the operating conditions under which the experiments were carried out. Chapters 3 and 4 begin with a brief review of previous studies on voidage, particle velocities and solids circulation rates. Following this is a discussion of measurement techniques which have been used to carry out studies of voidage and particle velocities and a description of the techniques used in this study. Together with voidage measurements, a study of spout shape and diameter is presented in Chapter 3. Chapter 4 includes a discussion of the effects of auxiliary flow and particle size on fountain height. 18 Chapter 5 describes the method used to determine the gas flow in the annulus of the spout-fluid bed, as well as presenting results and reviewing past work on this subject. Finally, the main conclusions drawn from this work are presented in Chapter 6, together with recommendations for future studies. 19 Chapter 2 Experimental Set-up 2.1 Apparatus 2.1.1 Column Design The experiments in this study were carried out in a fully cylindrical column constructed of Plexiglas with a specially designed conical base for the injection of auxiliary air into the column as shown in Figure 2.1. The cylindrical section has an inside diameter of 152 mm and measures 900 mm in height. Sampling ports of two sizes were installed along the height of the column on opposite sides through which different probes could be passed in order to take the necessary measurements. One set of ports consisted of eighteen holes, 5 mm in diameter drilled into the wall of the cylinder. Plexiglas sleeves 25 mm in diameter with 3.2 mm (1/8 inch) NPT taps drilled into them were glued over the holes for support and fitted with 6.4 mm (1/4 inch) plastic fittings. The other set of ports consisted of nine holes, 12.5 mm in diameter with 31 mm Plexiglas sleeves, 9.5 mm (3/8 inch) NPT taps and 9.5 mm (3/8 inch) fittings. The ports were installed at 50 mm intervals, with the lowest one 40 mm above the bottom edge of the cylinder. The conical section is shown in Figure 2.2 and was designed in a similar fashion to the one used by Sutanto (1983). It consists of five layers of Plexiglas plates, machined and glued together to form a cone with five layers of calming chambers into which the auxiliary air is injected. The air makes its way into the bed through 70 openings, each 3 mm in diameter, evenly spaced over the entire conical surface (Figure 2.3). Each layer of the subdistributor is supplied by a separate auxiliary air line with its own orifice-plate flowmeter and control valve. 20 AUXILIARY FLOW LINES 12.7 mm FITTINGS SPOUT GAS INLET 23.5 mm ID 6.4 mm FITTING FIVE LAYERS OF CALMING CHAMBERS FRONT VIEW SIDE VIEW Figure 2.1: Schematic diagram of spout-fluid bed used in experiments (dimensions in mm). 21 267 152 P O R T Figure 2.2: Cross-sectional view of conical section (all dimensions in mm). 22 TOP VIEW OF CONE Distribution of holes in conical section Subdistributor Diameter at the Number of holes of Spacing between section centre of each 3 mm diameter holes (cm) section (cm) 1 4.13 7 1.85 2 6.67 10 2.09 . 3 9.13 14 2.05 4 11.6 18 2.02 5 14.0 21 2.10 Figure 2.3: Top view of conical section minus wire mesh showing distribution of holes. 23 Gas flow through each of the five layers could therefore be controlled individually. Diffusers were fabricated and placed at the outlets of each of the auxiliary air lines in order to provide uniform gas flow across the distributor openings. 75 mesh steel screen was installed over the entire inner surface of the conical section to prevent particles from entering or blocking the subdistributor chambers. Directly opposite the auxiliary air line inlets to the subdistributor are sampling ports which allow access to the conical section of the bed. Holes, 5 mm in diameter, were drilled through each section of the subdistributor, and 3.2 mm (1/8 inch) NPT taps were drilled into the outer surface. A piece of 6.4 mm (1/4 inch) nylon tubing was placed inside each port to act as a guide for the probes and prevent particles from flowing into the calming chambers. The tubing was held in place by glue and by the plastic fittings in each tap. Additional ports were also provided between the air inlets and the 5 mm ports. These were comprised of varying lengths of 12.7 mm (1/2 inch) stainless steel tubing inserted through the calming chambers to fit flush against the inside of the subdistributor wall. These were installed so that an air-tight fit was achieved at both ends of the tube, thereby avoiding any type of fittings or glue. It was originally planned to use these smaller ports for the smaller probes used in the voidage and spout particle velocity measurements, while the larger ports were to accommodate the larger probe for particle velocity measurements in the annulus. However, it turned out to be simpler to use the larger ports for all probes since it was then unnecessary to change the positions of the instruments to take the different measurements and it also allowed better consistency in placing the probes at different radial positions. A sheath made of plastic tubing was designed to fit into the large ports and permitted the smaller probes to be inserted for taking measurements. This system was necessary to create a seal which prevented air and solids from escaping. The bottom port was also used as a discharge opening to empty the bed of particles or to adjust the bed height. 24 Three orifice plates for the central air flow were machined from aluminum with inlet diameters of 12.7, 19.1 and 25.4 mm (0.5, 0.75 and 1 inches). A piece of fine wire mesh was glued to the bottom of each orifice plate to prevent particles from falling down the air-inlet pipe during shut-off. Details of the orifice plates are given in Figure 2.4. Only the mid-sized orifice was used in these experiments. The orifice plates were designed with a pressure tap through the mid-section of the plates for taking pressure measurements. However, only the absolute pressure at the bottom of the bed is required to determine the flowrate through the bed, and the taps were not used. Instead, the bottom small sample port of the conical section was employed for this purpose. An inverted plastic runnel, 55 mm in diameter and 45 mm long, attached to the end of a i m long piece of stainless steel tubing was suspended from the top of the column as a stabilizer for the fountain. The funnel had forty-three perforations each 5 mm in diameter which allowed the air to flow with minimum disturbance. The stabilizer was positioned so that the edge of the funnel came down over the top of the fountain but did not come in contact with the glass beads. 2.1.2 Flow Rate Measurement Gas flowrates are set by rotameters which were calibrated with a standard orifice flowmeter. The total auxiliary air flow is controlled by two rotameters connected in parallel each with a maximum capacity of 13 SCFM (6.14x10"3 m3/s) at 21°C and 1 atm (101.3 kPa) (Brooks Instrument Division, model# 1307D09FB1A, tube size Brooks R-9M-25-3F). The air then passes through a flow manifold constructed of PVC piping where it is split into five separate lines. Each line is equipped with a ball valve and an orifice plate, making it possible to control the flow to each section of the subdistributor individually. 25 Dimensions (mm) D (dia.) A (dia.) B (dia.) C E F G H I J (dia.) 12.7 19.1 25.4 38.1 44.4 16.8 4.3 3.3 4.6 4.6 2.0 0.8 Figure 2.4: Details of the orifice plates. 26 The central flow line is controlled by a larger rotameter with a maximum capacity of 40 SCFM (1.89xl0-2 m3/s) at 0°C and 1 atm (101.3 kPa) (King Instrument Company, model# G-03291-66). The air is supplied by the main building compressor at pressures between 40 and 55 psig (377.0 and 480.4 kPa). A pressure reducing valve was installed upstream of the rotameters in order to reduce the pressure fluctuations and maintain a relatively steady flow of air through the bed. A schematic diagram of the apparatus is shown in Figure 2.5. A system, similar to that used by Wu (1986), was set up to determine the actual air flow through the bed of particles. Pressure taps were installed before and after the rotameters in order to measure the average pressure drops across the rotameters. For the large manometer, the pressure taps were connected to a mercury differential pressure manometer (specific gravity = 13.6), while the downstream pressure tap was connected to a Bourdon gauge. The taps on the small manometers were connected to a differential manometer containing water (specific gravity =1), and the downstream pressure was measured with a Bourdon gauge connected to the flow manifold. The average pressure of the rotameters was determined by adding half the differential pressure to the downstream pressure reading, i.e. Protameter(SauSe) ~ (AProtameter)^~^Pdownstream(SauSe) (2-1) A pressure tap was installed 11 mm above the orifice plate of the column and connected to a water-filled manometer in order to measure the pressure at the bottom of the bed. The average pressure inside the bed was taken as: Pbed = PATM+P/2 (2.2) The air flow rate through the rotameter at standard conditions could be obtained from the rotameter reading and rotameter pressure. Corrections could then be made to determine the flow rate through the bed at operating conditions, i.e. Tbed and PDecj. 27 HI a: D CO CO O uj O CL 111 CL a: i t o CO CO LLI CH a. o o s •3 n cu CL, X CD <+-< O -*-» 3 O l-l > O GO C o e 0 on (N <D t-i 1 28 Differential pressure drop measurements for determining annular gas velocities were performed with the probe shown in Figure 2.6, used earlier by Wu (1986). The probe consists of a small stainless steel tube, 3.1 mm OD, inserted through a larger tube of 9.5 mm OD. The inner tube was sealed at the bottom and bent at an angle of 90°. A short piece of stainless steel tube of 3.1 mm OD was soldered perpendicularly onto a hole drilled on the outer shell in line with the bent tube and 28 mm apart Holes of 0.8 mm were drilled into the two tips. The small pressure drops were measured with an inclined U-tube manometer, at an angle of 19°, filled with fluid of specific gravity 0.827. Minimum readability was ±0.5 mm on a linear scale, corresponding to a pressure drop of ± 0.1 mm H 2 O (±1 Pa). 2.2 Particles Glass beads of three different sizes (Potters Industries, New Jersey; A-240, A-170, A-130) were used in this study as bed materials. The key properties of these materials are given in Table 2.1. Table 2.1: Properties of glass beads used in experiments. dp PP Pb s0 Urns (mm) (kg/m3) (kg/m3) (m/s) (m) 1.33 2493 1460 0.415 1 0.672 0.453 1.84 2485 1454 0.415 1 0.795 0.458 2.53 2463 1450 0.411 1 1.12 0.337 29 To inclined manometer. 3/8" (9.5 mm) 316 S S T U B E 1/8" (3.2 mm) 316 S S T U B E 1320 mm 0.8 mm holes 4 on each end 28 mm 22 mm Figure 2.6: Details of differential pressure probe. 30 The mean particle diameter of each set of glass beads was determined from sieve anaylsis as: 1 (2.3) where xt is the mass fraction of particles within an average screen aperture size of dpi. Each set of glass beads had a relatively narrow size distribution while the beads themselves were nearly spherical in shape, as verified from measurement of a number of beads from each set with calipers. The densities of the glass beads were determined by liquid displacement. A known mass of glass beads was slowly added to a 1000 ml graduated cylinder containing a known quantity of water. The increase in the level of the water was used to determine the volume of particles added. Average densities were taken from several measurements with an uncertainty of less than 1% (at a confidence level of 95%). The bulk density of the beads was determined to obtain the loose packed voidage of the beads. A graduated cylinder was partially filled with a known weight of particles. With the top end covered, the cylinder was inverted and returned quickly to its upright position. The volume was recorded and the bulk density (p^) calculated. The tests were repeated several times to obtain an average value. The loose packed voidage of the particles corresponding to the voidage in a loose packed bed was then calculated as: The maximum spoutable bed height, Hm, was determined by increasing the bed height until stable spouting could not be sustained for any gas flowrate. At this point, the corresponding loosely-packed bed height was taken as Hm. Several tests were done to ensure (2.4) 31 reproducibility. To increase the bed height, particles were poured into the bed from the opening at the top of the column. All experiments were subsequently performed with a bed height of 0.280 m. The minimum spouting velocity, Ums, for each set of particles at the specified bed height was determined following the procedure outlined by Mathur and Gishler (1955). In this procedure, the gas flowrate is first increased until stable spouting is achieved and then decreased slowly until the spout collapses. The gas flowrate at which the fountain just collapses, indicated by a sudden rise in bed pressure drop, is taken as the minimum spouting flowrate. This test was repeated three times to ensure reproducibility of the results. The superficial gas velocity was determined by dividing the volumetric flowrate by the cross-sectional area of the cylindrical section of the bed. Operation with the smallest particle size resulted in a build-up of static electricity in the column, strong enough to cause electric discharges whenever a metal part was touched. This was cause for some concern due to the electronic equipment used to take measurements. In an attempt to eliminate the static build-up on the probes, they were connected via a piece of copper wire to the air piping in order to ground the charge. This, however, only resulted in repelling the particles from the tip of the voidage probe, leading to erroneous voidage measurements. Consequently, the ground was only connected to the instrument in case of a power surge. In taking measurements of annular particle velocities it was noticed that the particles were repelled from the tip of the probe whether or not the probe was grounded. This made it difficult to obtain acceptable recordings of particle motion in the annulus. A solution was necessary to eliminate the static charge in the bed. One option was to saturate the air with water by bubbling through a column of water before passing it through the bed. This required the design and fabrication of new equipment and reorganization of the piping system and experimental equipment which would have taken some time. Another option was to add 32 an anti-static powder to the particles. Since the latter solution was the simplest, it was tried first. The product used was Larostat 519 supplied by PPG Industries Inc., of Gurnee, Illinois, USA. This product is commonly used by other researchers to control static electricity in studies of circulating fluidized beds with fine FCC particles (Issangya, 1996). The recommended dosage of 0.05% w/w was initially used. While it was very effective in eliminating static electricity, it also had very significant effects on bed properties. For example, once the powder was mixed into the solids in the bed, the height of the bed increased by approximately 20 mm. In addition, the minimum spouting velocity increased by about 10%). The particles were removed, washed and dried and placed back in the bed. The bed properties returned to their original values and the static electricity although not completely eliminated, was reduced considerably. Static electricity did not cause the same problems with the larger particles. Hence, no anti-static powder was added to the larger particles. It was still difficult to obtain clear images of the particles in the cylindrical section where the voidage is high. Because the beads are made of glass it was sometimes difficult to distinguish them from the background if the intensity of light was too high. However, a certain intensity of light is required in order to transmit the image from the tip of the probe to the camera through the fibre optic cable. To solve this problem, some particles (about 1% of the total) were coloured with blue ink, dried and placed in the bed together with the other particles. When the dark particles passed in front of the image probe, they were in sharp contrast to the surroundings and could be seen clearly on the recorded video. 33 2.3 Operating Conditions This work studies particle circulation and gas distribution under various combinations of spouting and auxiliary flows. In order to determine the appropriate flow combinations, a calibration or regime map had to be obtained for each set of particles. The range over which the experiments were carried out was between spouting of the bed with no auxiliary air to the maximum ratio of auxiliary to spouting flow rates under which a stable spout could be sustained at a constant total flow rate. The experiments were carried out at a total flow rate of 1.2 Qms (where, Qms = UmsAc) for each particle size. The spouting and auxiliary flow rates were adjusted so that the total flow of air through the bed remained constant at this value. For each size of glass beads, a calibration for the spouting and auxiliary rotameters was obtained to determine the flow through the bed of particles and set the conditions for the experiments. The spouting rotameter was first calibrated to determine the flow rate at 1.2 Qms. This was done by increasing the spouting flow rate above Qms incrementally and recording the necessary pressure readings to determine the actual flow rate through the bed. The auxiliary air was then introduced while the spouting air was decreased, again in small increments, to obtain a calibration of the rotameters under spouting with aeration. The auxiliary air was increased until stable spouting could not be achieved, representing the extreme ratio of spouting to auxiliary air flow rates to be used. Two additional points evenly spaced between the two extreme cases were selected for the experiments. Table 2.2 gives the flow combinations for each particle size. 34 Table 2.2: Summary of spouting and auxiliary flow combinations used in experiments. dp (mm) QA/QT QA (m3/s) QS (mVs) 1.33 0.00 0.0000 0.0146 0.14 0.0021 0.0125 0.28 0.0041 0.0105 0.43 0.0063 0.0083 1.84 0.00 0.0000 0.0175 0.15 0.0026 0.0149 0.29 0.0051 0.0124 0.43 0.0075 0.0100 2.53 0.00 0.0000 0.0242 0.15 0.0036 0.0206 0.29 0.0068 0.0170 0.42 0.0103 0.0140 2.4 Instrumentation Although the spout-fluid bed technique has been used in a number of applications, a better understanding of the behaviour of such systems has been hampered by both the complex hydrodynamics of two-phase, solid-fluid flow as well as a lack of suitable measurement tools required to investigate local properties in such systems. In recent years, the development of reflective optical probes has enabled measurement of local particle velocities and concentration in both dense and dilute suspensions. These probes are of particular interest to the study of two-phase systems because they can provide 35 accurate measurements of local properties inside three-dimensional structures with minimal disturbance to flow. He (1995) performed an extensive study of the hydrodynamics of spouted beds with fibre optic probes, measuring both particle velocity and concentration. The same techniques were used in this work to study the hydrodynamics in a spout-fluid bed. A static pressure probe and manometer are used to track the flow of gas through the annulus under varying operating conditions. A detailed description of each measurement technique and its calibration is given in the chapter where the corresponding measurements are presented. 36 Chapter 3 Voidage Profiles 3.1 Introduction Most studies of spouted and spout-fluid beds have assumed that the voidage in the annular region is the same as in a loose-packed bed (Mathur and Gishler, 1955). The annulus has therefore been considered to operate as an evenly distributed volume of solids. However, it has been known for some time that this is not strictly the case. For example, Thorley et al. (1959) and Grbavcic et al. (1976) observed that slight differences of voidage exist in different parts of the annulus. Eljas (1975) was able to take measurements of annular voidage in a two-dimensional bed using a y-ray absorption technique and found variations of voidage in different locations in the annulus as high as 0.1. He (1995) measured local particle concentrations in a three-dimensional spouted bed with an optical fibre probe and found that at low flow rates, the voidage in the annulus was slightly higher than the loose-packed bed voidage. In general, He's observations showed annular voidage increasing towards the axis of the bed and higher local voidages at the wall at higher flowrates. At the spout-annulus boundary, a dip in voidage was observed which sometimes fell below the loose-packed voidage. With increasing gas flow rates, the voidage in the annulus further increased above the loose-packed bed voidage. The voidage tended to increase with height reaching values well above the loose-packed voidage (30% higher) at the top of the bed for high spouting flow rates (U/U m s = 1.3). It is well known and accepted that the spout behaves like a riser in which particles are being transported upward in a dilute phase. At the bottom, where the air enters the bed, the voidage in the spout is close to unity and it then decreases with height. The voidage also varies radially across the spout, usually reaching a maximum at the spout axis. 37 3.2 Measurement Techniques An indirect method based on a solids mass balance for a bed operating at steady state has been widely used to determine spout voidage (Mathur and Gishler, 1955; Lim, 1975; Day et al., 1987). With the assumption that the voidage in the annulus is equal to the voidage in a loose-packed bed, the average spout voidage at any level can be determined by equating the downwards solids flow rate in the annulus to the upward rate in the spout. Downward particle velocities are measured at the column wall, while upward particle velocities in the spout of a half-column are measured with a high speed camera. This method has obvious limitations. First, only radial average voidage values are obtained; second, downward particle velocity measurements are not reliable due to wall effects and cannot be considered to represent the actual mean velocities in the annulus. Other techniques which have been employed to measure voidage in the spout include a piezoelectric probe (Mikhailik and Antanishin, 1967), a capacitance probe (Goltsiker, 1967), and P-ray adsorption (Elperin et al., 1969). However, these techniques are complicated and require careful calibration. Recently, reflective optical fibre probes have been used to study local properties in particulate systems. They have been used to measure both voidage and particle velocities in fluidized and circulating fluidized beds. Most recently they have been applied to the study of spouted beds (He et al., 1994; He, 1995) and conical spouted beds (Olazar et al., 1995) in which the particles are of the order of 1 mm in diameter or bigger. He (1995) used a fibre optic probe to measure voidage profiles in the fountain, spout and annulus of spouted beds. The major finding of this work was that the voidage in most of the annulus was somewhat higher than the loose-packed bed voidage and increased with increasing spouting gas flow rate. This is contrary to the widely accepted assumption that the voidage in this region is constant and equal to that in a fixed bed of loosely packed particles. 38 Consequently, theoretical models and experimental findings based on this assumption are questionable since a higher voidage in the annulus will affect the gas flow rate through this region. Voidage profiles within the spout have revealed that the local voidage decreases with height and with radial distance from the spout axis. As reported in the literature (Mathur and Epstein, 1974b; Grbavcic et al., 1976), the cross-sectional average voidage decreases monotonically with height. Radial voidage profiles were found to be parabolic in the lower portion of the spout and blunt at higher levels. A comparison of voidage profiles in the spout of full and half-columns also led to the conclusion that wall effects are present and that caution should be used when interpreting results obtained in half-columns (Benkrid and Caram, 1989; He, 1995). Olazar et al. (1995) used a somewhat different fibre optic probe set-up than He (1995), but both worked on the same principle. Olazar et al. (1995) found that there was non-uniformity in the local bed voidage both in the spout and in the annulus of conical spouted beds, especially near the gas inlet. This new information could be useful in developing improved models for gas and solids flow for rigorous reactor design. In the absence of such findings in the past, oversimplified models which assume longitudinally uniform spout diameters, radially uniform voidage profiles in the spout and isotropically uniform voidage in the annulus have been the only available tools. In this study, an updated version of the fibre optic probe used by He (1995) has been used to make an in-depth study of the voidage distribution in the spout and annulus of a spout-fluid bed. 39 3.3 Experimental Equipment: Instrumentation and Technique 3.3.1 Voidage Measurement Voidage measurements were performed with a model PC-4 fibre optic system developed by the Institute of Chemical Metallurgy of the Chinese Academy of Science, in Peking, China. A schematic diagram of the instrument is presented in Figure 3.1. The major components of the instrument are an optical fibre probe, a light source, a photo-multiplier, and an A/D converter which processes the data for analysis by computer. In addition, the instrument is equipped with a referential light auto-adjustable system to maintain signal stability and eliminate drift due to variations of ambient temperature, light source and electronic parts. The system can thus be set to adjust itself before each measurement to keep the instrument in its initial condition. The basic principle underlying fibre optic voidage measurement is that the intensity of back-scattered light from particles depends on the particle concentration. The probe is composed of two overlapping bundles of optical fibres. One bundle transmits the light to the target while the other bundle captures the reflected light and transmits it to the detector or photo-multiplier. The reflected light signals are converted to electrical signals by the photo-multiplier, with the voltage dependent on the light intensity. The integration of the electrical pulses generated from the swarm of particles in front of the probe over a certain period of time can therefore be correlated to their concentration by calibration. Since there is no direct conversion of the output electrical signal to particle concentration, the system must be calibrated. Previous experimental findings (Matsuna et al., 1983; Qin and Liu, 1982; Boiarski, 1985) have shown that there is a linear relationship between voidage and the output signal of the fibre optic probe. On the other hand, several 40 Fibre optic cables Probe High Voltage Adjustment A/D _ ^ Micro-Converter Computer A V On-Off Light Switch ^ Photo-Multiplier ^ Amplifier & ^ Auto-Check it Figure 3.1: Schematic diagram of fibre optic system used to measure local particle concentration. 41 authors (Zhou, 1995; Hong and Tomita, 1995; Issangya et al., 1996) have found that a non-linear relationship exists for fine particles of the order of 100 urn or smaller (eg. FCC particles). It has been reported by several authors that the linearity of the relationship is dependent on the size of the particles (Lischer and Lounge, 1992; Yamazaki et al., 1992; Werther et al., 1993) with the relationship being linear for particles greater than 200 pm. He (1995) and Zhou (1995) have verified the relationship between output voltage and particle concentration with the same instrument used in this study for glass beads of 1.41 mm in diameter and Ottawa sand of 213 urn in diameter, repectively. In both cases the relationship was linear. Since the particles used in this study are of similar size to those used by He (1995), it is reasonable to expect a linear relationship between particle concentration and voltage. Two methods were used to perform the calibration for the glass beads by He (1995). For voidages less than 0.75, the calibration was carried out in a liquid-solid fluidized bed. In such a system, assuming the particles are quite uniformly distributed, the voidage could be obtained from the height, H , of the expanded bed. ^ = 1 - ^ - ( 1 - ^ ) (3-1) where H 0 is the height of a loose-packed bed and e0 is the voidage of the loose-packed bed. A set of bed voidage data was obtained by changing the fluid velocity to achieve different bed heights, H . For voidages above 0.75, the fluidized bed system is not suitable for calibration because the bed surface is obscure and difficult to determine accurately. Therefore, calibrations at higher voidages were carried out in a well-stirred beaker. A known volume of solid particles was put into a beaker with a known quantity of water. The solid-liquid mixture was then stirred until the particles were uniformly distributed in the water. Different voidages 42 were achieved by varying the ratio of solids to liquid in the beaker. The result of the calibration is shown in Figure 3.2. This clearly indicates a linear relationship over the range of voidage between 0 and the value corresponding to a loose-packed bed. A linear relationship between the output signal and particle concentration was also obtained by Olazar et al. (1995) for glass beads of similar size from a calibration in air. Therefore, calibration of the instrument for these experiments was carried out by putting the probe in an empty, cylindrical container and in a slowly moving bed (equivalent to a loose-packed bed) of known voidage to obtain two widely separated values for a linear calibration. The size of the measuring volume depends on the local voidage. Zhou (1995) performed tests in which the tip of the fibre optic probe was approached with a small piece of stainless steel plate. The measuring distance was approximately 7 mm for a voidage approaching 1 and about 4 mm for a voidage of 0.9. A similar test was performed in this study in which the probe was placed in an opaque cylinder containing glass beads. The probe was slowly brought closer to the particles and at a distance of approximately 10 mm the signal increased from zero. In this work, the fibre optic probe consisted of a cylindrical section 4 mm in O.D. and 150 mm long which encased the Quartz fibres, each 16 um in diameter. At the tip of the probe, light projecting fibres and light receiving fibres were arranged in four concentric rings, in an alternating pattern. Radial profiles of voidage were taken starting from the wall inward. Each measurement was taken over a 30 second time period at a sampling frequency of 330 Hz, yielding an average voidage value. Reproducibility was checked by repeating the radial profile at least four times at selected axial positions for each particle size. 43 Volume fraction of particles Figure 3.2: Calibration curve by He (1995) of output signal from the fibre optic system solids volume fraction in glass beads (dp =1.41 mm) and water systems. 44 3.3.2 Spout Diameter The delineation of the interface between the spout and the annulus has been carried out with the voidage probe according to the method of He (1995). The interface is determined by the difference in the output signals between the spout and annulus recorded by the fibre probe as shown in Figure 3.3. When the tip of the probe is in the annulus, the corresponding signal is formed of wide peaks, due to the fact that the particles are moving at low velocity. When the tip of the probe is in the spout, the high particle velocities result in an output signal formed by sharp, narrow peaks. The point where the signal changes from one type of signal to the other corresponds to the radial position of the spout/annulus boundary. Measurements were taken along the height of the bed at radial intervals of 2 mm resulting in an experimental error of ± 1 mm. 3.4 Results and Discussion 3.4.1 Voidage Profiles Radial profiles of local voidage for two particle sizes under varying operating conditions are presented in Figures 3.4 and 3.5. In each figure, the solid symbols represent levels above the cone while open symbols are inside the cone. The top of the cone is 0.108 m above the inlet orifice. From the repetition of several profiles taken on different days, 95% confidence intervals (representing approximately two standard deviations) were established for reproducibility of measurements under the same conditions. In the centre of the spout, the reproducibility was good, with an average confidence interval below ± 5 % of the mean value. In the annulus, the deviation was higher, varying between ± 1 % and ± 2 0 % but generally still below ±5%. 45 1.0 —i 1 1 — i — i — T — i — | — i — i — i — i — i — | — • — i — i — r In the Spout 0.4 0.2 (b) j ' i i i i i i i i i i i i i • 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time (second) Figure 3.3: Output signals from the fibre optic system, (a) in the spout; (b) in the annulus. 46 s 6 m 3 '96eppA 2 3 00 47 e s 00 o CO o o 3 '86epK)A 48 O 3 II T 3 cd CD JD !» "5b CD T 3 CD CD o i — '3 "c3 -*-» o -*-» o o .2 3 O O c CD 03 « CD o CD OB CvS •a 'o > 1 3 pi IT ) c i CD u, 0 0 The greatest uncertainty in the measurements is at the spout/annulus interface, with confidence intervals in excess of ±10% and sometimes higher than ±20%. This uncertainty is due to the unstable nature of the boundary between the spout and the annulus where particles and air are constantly being exchanged between the two regions. Another factor is the difficulty in keeping the spout perfectly centered at all times. Because the stabilizer had to be moved for different operating conditions, it was impossible to place it in the exact same position every time. The stabilizer was placed over the spout rather than in the exact centre of the column. Therefore, if the spout was not in exactly the same position as in previous experiments, this would affect the voidage profiles and the relative position of the spout within the column. In the centre of the spout and in the annulus the deviation is less because gradients in voidage are much less pronounced. In general, the voidage in the spout decreases with increasing height, while the reverse is true for the annulus. This is in agreement with the observations of He (1995) and, at least for the spout voidage, agrees with theoretical models developed so far. The decrease in voidage in the spout is due to entrainment of particles from the annulus and to loss of gas to the annulus along the height of the bed. For all particle sizes, the voidage in the spout decreases with increasing values of QA^QT- The effect of auxiliary air on the spout voidage is more pronounced above the conical distributor section. In Figures 3.4 and 3.5, one can also observe an increasing difference in voidage at the axis of the column between the conical and cylindrical sections (ZC = 0.11 m) of the bed. This seems to indicate that particles are entrained into the spout mostly in the conical section due to the geometry of the walls which tend to guide the downward moving particles toward the centre. This phenomenon is probably enhanced by the introduction of auxiliary air from the wall of the cone which tends to loosen the particles in the annulus, allowing them to 49 be entrained into the spout more readily. The auxiliary air may also be pushing the particles inwards from the wall into the spout. The measured voidage in the annulus varies considerably from the bottom to the top of the bed. A range of measured values between 0.33 and 0.55 exists, the greatest variation occurring with the smallest particles. It has been proposed elsewhere (Eljas, 1975) that the low voidage observed in the conical section is due to particles realigning and compacting as they move downward and are redirected by the converging walls of the cone. Another possible explanation for these observations is an accumulation of fines or dust particles in the void spaces of larger particles. These fines may be produced by attrition of the particles from operation of the bed over long periods of time while dust may be present in the supply air. When the column was emptied to change particle sizes it was noted that fine particles had accumulated in the conical distributor between the cone surface and the steel screen. No consistent trend with increasing auxiliary air flow is evident for voidage in the annulus. However, in Figure 3.4, at the highest ratio of auxiliary air flow to total air flow, the voidage profiles in the annulus are all above the loose-packed bed voidage. This seems to indicate that a certain minimum auxiliary gas flow is required to significantly affect the annulus voidage. However, no such effect was observed for the two larger particle sizes. At no time during the experiments did the annulus appear to be fluidized. Therefore, diverting the flow of air to the annulus should only have contributed to increased aeration with little effect on voidage. Differences between these results and those of He (1995) with no auxiliary air are evident. A comparison of the left-most profile from Figure 3.4, which is operating as a spouted bed since there is no auxiliary air being injected into the bed, and the results obtained by He for the same particle size and U/Ums=\2 reveals that the local voidages in the annulus 50 in this study are higher and more scattered. In the earlier study, the voidage profiles along the height of the bed were smooth, overlapping each other almost entirely and were relatively constant across most of the annulus. In addition, the profiles were all slightly above the loose-packed bed voidage at that value of U/Ums. Only at higher flow rates did the profiles show more variation with bed height and deviate further from the loose-packed bed voidage. The problem with static electricity build-up mentioned in Chapter 2 may have caused this discrepancy. Figures 3.6 and 3.7 show axial cross-sectional average voidage profiles in the spout for dp = 1.33 mm and 1.84 mm. Although the data show some scatter, voidage decreases monotonically with height. Increasing the proportion of auxiliary air decreases the average voidage along the entire bed, with the largest decrease occurring at the top. Figure 3.8 shows the cross-sectional average voidage in the spout for the three particle sizes at the two extreme ratios of auxiliary air flow to total air flow. Particle size does not appear to have a significant influence on the average spout voidage. The profiles are in agreement with previous observations obtained with semi-cylindrical columns (Lim, 1975; Day et al., 1987). Under spouting only (Qj[/Qj = 0.0), the longitudinal profiles of average spout voidage show better agreement with the model of Lim and Mathur (1978) than with the Leffoy and Davidson (1969) model which predicts a more complex profile. 51 1.0 0.9 Q) D) 05 •g O > CD 0.8 D) CO CD > 03 O 0.7 t j CD CO CO CO O <-> 0.6 0.5 1 I 1 I • i r- 1 1 1 ' Q ^ Q T • • 0.0 • 0.15 • \ A 0.28 • ^ 1 • - -0.43 -A \ \ \ — • -\ \" - _ \ ". \ I y A •v. • i i i 1 -I . I . 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Vertical distance from orifice, z (m) Figure 3.6: Vertical profiles of cross-sectional average voidage in the spout (glass beads, dp 1.33 mm, U/Ums = 1.2, H= 0.280m). 52 1.0 T — ' — i — 1 — i — > — i — • — r 0.9 \-D) 05 •g o > CD CD CO CD > CD "CD C 0 tj CD CO 1 CO co o O 0.8 0.7 0.6 0.5 Q ^ Q T -\ \ \ A \ A . v • "•• • • -• _ TOP OF CONE I 1 - ._A T l 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Vertical distance from orifice, z (m) Figure 3.7: Vertical profiles of cross-sectional average voidage in the spout (glass beads, dp 1.84 mm, U/Ums = 1.2, //= 0.280m). 53 1.0 0.9 h 0.8 \-0.7 h d) D) •g 0.6 O > CD 0.5 D) CD 1.0 > (0 £ 0.9 g TJ CD 0.8 c/> i CO CO o 1 I 1 I 1 I 1 1 0.43 — i — 1 1 o (mm) 5 o a • o 1.33 1.84 . • o A A 2.53 1 , 1 , 1 8 • O A • o o 0.7 0.6 h 0.5 0.00 0.05 0.10 0.15 0.20 0.25 Vertical distance from orifice, z (m) 1 1 1 1 1 1 • a 1 I = 0.0 o i 1 - H o • • i . i . i i i 0.30 Figure 3.8: Vertical profiles of cross-sectional average voidage in the spout for all three particle sizes at two values of QA^QT^^ms = 1-2, / / = 0.280 m). 54 3.4.2 Spout Shape and Diameter The spout/annulus boundaries along the height of the bed are shown in Figure 3.9 for the three particle sizes under varying operating conditions. In all cases, the spout expands sharply immediately above the inlet orifice, narrows slightly near the cone/cylinder junction (zc = 0.11 m) and then diverges again near the bed surface. The profiles show increasing spout radius with particle size. This trend is in qualitative agreement with the empirical equation of McNab (1972): D. = 2.0 QOA9 £ ) 0 . 6 8 (3.2) The profiles also show that with decreasing particle size, the narrowing point part-way up the bed is more pronounced, in agreement with previous observations (Mathur and Epstein, 1974b; Lim, 1975). Spout radii are unaffected by the ratio, QA/QT- Although there appears to be a slight narrowing of the spout diameter at the highest QA^QT f ° r m e smallest particle size, this effect is not significant given the precision of the measurement technique. In addition, no such effect is present for the two larger particle sizes. Similar observations were made by Sutanto (1983). In order to develop an explanation for these observations, it is necessary to consider two factors affecting the size and shape of the spout in spout-fluid beds. First, the addition of auxiliary flow has the tendency to loosen the solids in the annulus, thereby facilitating their entrainment by the spout. This effect would tend to increase the diameter of the spout. On the other hand, by diverting part of the total flow of air to the auxiliary distributor, less air is injected through the central spouting inlet. The result is less air being available for entrainment of particles through the spout which would tend to reduce the spout diameter. 55 1 1 1 1 i i | i 1 1 - 4 - —8 - £ - » -_ M 1 I . I . i 8 o c> R cs in cs o cs 8 a o LO o 8 cs E E, O Q. 03 E £ 8 c T3 8 . 5 5 0) N CD CD CD c d ,o -a c d 3 O Q-tn <+* O J D 53 o i _ a, "cd o '•S CD > <3\ m CD 3 E (LU) SOIJUO v^oqe }i|6!9H 56 These two opposing effects, acting simultaneously, appear to cancel each other, and no significant net effect on spout diameter is observed. Sutanto (1983) also found that the McNab (1972) equation predicted the data very well if the total flow through the bed was used in the correlation. Wu (1986) tested the McNab (1972) equation at various conditions and found that although it predicted spout diameter well for air at room conditions, it was unreliable at higher temperatures and for helium at room temperature. An alternate expression Ds = 5.6 J[ i0.433 n0.583 .0.133 (Pbpfg) 0.283 (3.3) was developed based on the theoretical model of Bridgwater and Mathur (1972) and a least squares fit of Wu's data. This expression, which includes both fluid density and viscosity as parameters, not only gave better agreement with Wu's data, but it is also dimensionally correct, another advantage over the McNab (1972) equation. Experimental values of average spout diameter obtained in this work and the corresponding results predicted from the equations of McNab (1972) and Wu (1986) are summarized in Tables 3.1 and 3.2, respectively. In the present case both the McNab (1972) equation and the correlation of Wu (1987) underestimate the experimental spout diameters for all particle sizes. The largest deviations occur for the biggest particles. An equally large descrepancy was obtained by He (1995). The discrepancy is probably due to the fact that both the McNab and Wu equations are based on half-column data. 57 Table 3.1: Experimental average spout diameters and values predicted from the McNab (1972) equation. QA/QT dn = 1.33 mm dn = 1.84 mm dn = 2.53 mm DS expt'l (mm) DS pred. (mm) % dev. DS expt'l (mm) DS pred. (mm) % dev. DS expt'l (mm) D8 pred. (mm) % dev. 0.00 32.4 27.9 -13.9 37.6 30.3 -19.4 47.9 36.2 -24.4 0.15 32.9 27.7 -15.8 35.1 30.0 -14.5. 45.9 36.0 -21.6 0.28 31.1 27.5 -11.6 35.3 30.1 -14.7 45.6 36.1 -20.8 0.43 29.5 27.6 -6.4 35.9 30.3 -15.6 48.3 36.3 -24.8 Table 3.2: Experimental average spout diameters and values predicted from the Wu (1986) equation. QA/QT dn = 1.33 mm dn = 1.84 mm dn = 2.53 mm DS expt'l (mm) DS pred. (mm) % dev. DS expt'l (mm) DS pred. (mm) % dev. DS expt'l (mm) DS pred. (mm) % dev. 0.00 32.4 27.7 -14.5 37.6 29.8 -20.7 47.9 34.9 -27.1 0.15 32.9 27.5 -16.4 35.1 29.6 -15.7 45.9 34.7 -24.4 0.28 31.1 27.4 -11.9 35.3 29.7 -15.7 45.6 34.8 -23.7 0.43 29.5 27.5 -6.8 35.9 29.8 -17.0 48.3 34.9 -27.7 58 3.5 Summary A fibre optic probe was used to measure local voidage profiles inside a fully-cylindrical spout-fluid bed. Both radial and longitudinal voidage profiles were obtained under varying flow configurations ranging from spouting alone with no auxiliary aeration (QA/QT = 0-0), to a maximum ratio of auxiliary air to total air flow (QA/QT) ° f ^ 43. For all particle sizes, the voidage in the spout decreased with increasing values of QA^QT- Lower gas flow rate through the spout inlet combined with a loosening of the annulus solids with the addition of auxiliary gas flow contribute to increased solids concentration in the spout. A greater decrease in spout voidage in the cylindrical portion of the bed compared to the conical section indicates that particle entrainment occurs mostly in the lower portion of the column. Local voidage in the annulus varied significantly from the bottom to the top of the bed. Measured voidages, much lower than the loose packed bed voidage in the conical section, require further investigation. Annulus voidage profiles appeared to be independent of QA^QT, probably because the auxiliary air did not fluidize the solids in this region but merely increased aeration of the annular solids. Axial cross-sectional average voidage profiles in the spout decreased monotonically with height and were independent of particle size. The same fibre optic probe system was employed to determine the spout/annulus boundary in spout-fluid beds for all three particle sizes. In accordance with the findings of Sutanto (1983), it was found that spout shape and diameter are independent of QA/QT> probably due to counter-balancing effects of decreased flow through the spout inlet and increased aeration of the annulus. However, both the McNab (1972) and Wu (1986) equations underestimate average spout diameter by as much as 28%. 59 Chapter 4 Particle Velocity Profiles and Solid Circulation Rates 4.1 Introduction Although a number of studies on solid flows and circulation rates have been carried out in spouted beds, very little information on this subject is available for spout-fluid beds. Considering the increasing applicability and versatility of this contacting technique, more studies are required. Both Sutanto (1983) and He (1990) recommended that particle velocities and solids circulation rates be given more attention in order to gain better understanding of spout-fluid beds. A spout-fluid bed operating in the spouting with aeration regime is very similar in nature to a spouted bed. In fact, it is essentially a spouted bed with additional air injected into the annulus. Because of this similarity, it is possible to compare observations of spouted bed behaviour with the present spout-fluid beds. A short survey of previous studies on particle flow in spouted beds is presented next, followed by a summary of different measurement techniques used previously and a description of the techniques used in this work. Finally, the results of this work are presented and discussed. 4.1.1 Particle Flow in the Spout of Spouted Beds The flow of solids in the spout is influenced by the interaction between the particles and the high velocity gas jet. Mathur and Gishler (1955) carried out the first measurements of particle velocities in the spout with the use of a high speed motion picture camera in a half-column. Average spout velocities were determined at different levels along the height of the 60 bed, allowing axial profiles along the spout to be plotted. Their studies showed that the particles entering the bottom of the spout from the annulus experienced sudden acceleration as they came into contact with the air jet. After reaching a maximum velocity some distance above the fluid inlet, the particles began to decelerate and eventually came to a complete stop and reversed direction at the top of the fountain. Mathur and Gishler (1955) explained that this deceleration is due to "particles traveling up the spout transferring part of their energy to particles entering the spout from the annulus, thereby accelerating them from rest to the average particle velocity at that level." In addition, they noted that the air velocity in the spout fell sharply after entering the bed, thereby greatly reducing the lifting effect on the particles. These observations were confirmed by other authors using the same technique (Thorley et al., 1959; Mathur and Epstein, 1974b; Lim and Mathur, 1978). Radial profiles of particle velocities in the spout have most commonly been described as parabolic (Lefroy and Davidson, 1969; Lim, 1975), with particle velocities reaching a maximum at the spout axis. He et al. (1995) performed particle velocity measuements in the spout with an optical fibre probe and observed more complex patterns than previously reported. The most significant of these differences was in the shape of the radial profiles, which followed a sigmoidal shape rather than a parabola. The profiles were narrower at the bottom of the bed, with sharper velocity gradients near the gas inlet owing to the greater fluid velocities in this region. Another significant difference observed by He et al. (1995) was a shift in the position of the maximum velocity away from the spout axis at the top of the bed. This shift was also predicted by Krzywanski (1992) and arises due to radial movement of particles and particle-particle collisions in the spout. No known studies of particle velocities in the spout of spout-fluid beds have been published to date. 61 4.1.2 Particle Flow in the Annulus It is generally accepted that particles move downward and to some extent radially inward in the annulus, so that particles are constantly being entrained into the spout. Mathur and Gishler (1955) measured annular particle velocities by following coloured particles moving along the wall of the column. They observed a decrease in particle velocity from the top of the bed to the bottom, indicating that there is a steady cross-flow of solids from the annulus to the spout along the bed height. In addition, observations through the transparent, flat plate of a half-column showed that particle velocities were essentially constant between the spout and the column wall. In other words, there was no appreciable gradient of particle velocities across the annulus; therefore the velocities seen at the column wall gave a good representation of velocities elsewhere in the annulus. The cross-flow of solids has been supported by other studies (Lim, 1975; Sullivan et al., 1987). However, the latter observation of nearly uniform particle velocity across the annulus, while a valid approximation for the top portion of the bed, is not valid in the lower portion, especially in the cone or gas-entrance region (Lim, 1975). He et al. (1995) further showed that wall effects are significant and that observations made at the column wall are not representative of the behaviour in the core of the bed. They reported particle velocities at the wall to be approximately 49% lower than those measured 6 mm (approximately four particle diameters) away from the wall. This is in agreement with earlier findings of Rovero et al. (1985) who showed that particle velocities were 15 to 20% lower at the column wall compared to those obtained at the mid-point of the annulus. In general, He et al. (1995) reported that vertical particle velocities in the annulus decreased with decreasing height in the cylindrical section due to the cross-flow of solids, while in the lower conical region vertical particle velocities increased with decreasing height due to the reduction in cross-sectional area. This was also in agreement with the findings of Rovero et al. (1985). 62 Benkrid and Caram (1989) measured particle velocities in the annulus of a spouted bed using an optical fibre probe. Their observations showed a zone of solids plug flow in the upper part of the annulus where the particles moved at uniform velocity. Using a half-sectional spout-fluid bed, Sutanto (1983) measured particle velocities in the annulus under different operating conditions. Preliminary tests showed that particle velocities were lowest at the junction of the flat front face and the curved surface of the column. Sutanto (1983) concluded that this was due to wall effects caused by the convergence of the two surfaces. Consequently, measurements were taken at the mid-section of the curved surface, far from the flat face. His observations showed that the particle velocity increased with bed height because the deeper bed resulted in more solids being entrained into the spout, thereby increasing the solids circulation rate. Studies at different flow conditions revealed that the annular particle velocity increased with increasing auxiliary flow for deeper beds, while the reverse was true for the shallowest bed. The effects of auxiliary flow entry position on particle velocity were also investigated by Sutanto (1983). When auxiliary air was introduced through the lower portion of the conical distributor section, the particle velocities were lower than when the air was introduced through the upper portion of the distributor. This was attributed to a greater percentage of auxiliary flow bypassing directly into the spout when air was supplied to the bottom of the distributor. Supplying the air through the top of the distributor increased particle velocity by loosening the annular solids. In view of the dubious results obtained from observations made at the wall of the column and the scarcity of data on particle circulation in spout-fluid beds, further investigation is required. 63 4.1.3 Solids Circulation Rates Quantitative measurements of solids circulation are essential to reveal fundamental physical laws for fluid-solid contact in spout-fluid systems. Such measurements are important, for example in drying operations or for carrying out chemical reactions where precise control of the contact time between the fluid and solids is necessary. On the basis of their observations of radially uniform annular particle velocities, and using the loose-packed bed voidage to represent the voidage in the annulus, Mathur and Gishler (1955) were able to derive the downward flow of solids in the annulus. Their results showed that solids flow rate increased linearly with height above the cone or entrance region. The cross-flow rate of solids per unit height in this region was therefore constant. Similar observations were made by Thorley et al. (1959) and Lim and Mathur (1978). The maximum solids circulation rate occurred at the top of the bed. Based on measurements of particle velocities in the annulus, Benkrid and Caram (1989) concluded that the overall solid circulation in spouted beds remained constant along the height of the bed indicating that, except in the bottom region, there was no entrainment across the wall of the spout. On the other hand, He (1995), using a similar optical fibre technique, corroborated earlier findings that particles enter the spout over its entire height. Below the cylindrical section, a sharp change in the slope of the solids circulation rate with height has been reported by several groups of researchers (Mathur and Epstein, 1974b; Lim and Mathur, 1978; He et al., 1995). This indicates a greater cross-flow of solids in the cone region and explains earlier observations (Mathur and Gishler, 1955) of a continually collapsing solid-gas interface near the gas inlet. 64 4.2 Measurement Techniques Most measurements of particle velocities have been obtained by following the motion of particles along the wall of transparent vessels. Mathur and Gishler (1955) were able to determine the velocity of particles in the annulus by timing individual marked particles over a fixed distance. In order to take particle measurements in the spout, they constructed a half-sectional column with a glass plate which opened the interior of the bed to view. In this way they were able to take high speed photographs of the spout. Since particle velocities are very high in this region (of the order of meters per second), framing speeds of 2000 - 3000 s_1 were required. These techniques have been used in a number of other studies, e.g. Thorley et al. (1959), Lefroy and Davidson (1969), Lim (1975), Lim and Mathur (1978), to obtain data upon which theoretical models were either based or verified. One of the most important assumptions involved with these techniques is that the observed particle velocities at the wall are representative of those away from the wall. In other words, wall boundary effects are ignored based on early observations of Mathur and Gishler (1955) indicating that particle velocities across the annulus at a given level are nearly uniform. However, Day et al. (1987), in taking such measurements at the flat wall of the half-column, found that particles two particle diameters away from the round wall moved faster than those adjacent to the round wall. Benkrid and Caram (1989) obtained radial particle velocity profiles using an optical fibre probe and found that, while at the top of the bed the particle velocity profile is nearly flat, this is not the case in the bottom region where a large gradient exists. They also found significant differences between profiles obtained in full and half-sectional beds. Similar observations were made by Rovero et al. (1985) and He et al. (1995). A number of other techniques have been used to measure particle velocities in spouted beds, a review of which is given by Boulos and Waldie (1986). These methods include stereophotogrammetry (McNab and Bridgwater, 1979), a piezoelectric probe technique 65 (Gorshtein and Mukhlenov, 1967), radioactive tracers (Van Velzen et al. 1974), magnetic tracers (Waldie and Wilkinson, 1986) and laser-doppler anemometry (Boulos and Waldie, 1986). Each of these techniques has its own advantages and disadvantages. In general, the ideal properties of the measurement technique are simplicity (not time consuming, inexpensive and reliable) and the ability to take measurements within a three-dimensional bed. The above methods are all deficient in at least one of these characteristics. Optical fibre probes have been successfully used to measure particle velocities in both fluidized beds (e.g. Oki et al., 1975; Oki et al., 1977; Patrose and Caram, 1982; Zhou, 1995) and spouted beds (e.g. Benkrid and Caram, 1989; He et al. 1995; Olazar et al., 1995). The main advantages of this technique are that it is direct measuring so that the measured value can be related directly to the velocity; no complicated calibration method is required. The probes can be easily inserted inside the bed to take local velocity measurements. Optical fibre probes were therefore used in this work to measure particle velocities in both the spout and annulus of spout-fluid beds. 4.3 Equipment and Instrumentation 4.3.1 Particle Velocity Measurements in the Spout The optical fibre system used to measure particle velocities in the spout is shown schematically in Figure 4.1. It consists of a three-fibre probe, a signal analyzer and a computer used to process the data and display the results. The optical fibre probe and signal analyzer (Particle Velometer PV-3) were developed and built by the Institute of Chemical Metallurgy of the Chinese Academy of Science in Peking, China. 66 The probe consists of three fibres or fibre bundles. The probe is inserted horizontally into the bed with the three fibres in the tip aligned with the direction of flow of the particles. The middle fibre is used to project light to illuminate the particles. As the particles pass in front of the probe, light is reflected back to the other two fibres. The signal from each fibre is sent to photo-multipliers which convert the light signals to electrical signals. These signals are amplified and sent to peak detectors which determine the time delay, AtAC, between the two signals. The velocity is obtained by dividing the effective separation length between the fibres by the transit time between the two signals, i.e. The transit time data are sent to a microcomputer via an A/D converter. A particular advantage of this system is that since the signals are processed by the hardware (electric circuit) as opposed to a computer program, the processing time is much shorter. Software has been written to carry out the data analysis which includes calculations and determinations of the statistical distribution of particle velocities, total number of particles detected, sampling time, maximum and minimum velocities, average velocity, peak velocity and root mean square deviation. In order to use this measurement technique, the diameter of the optical fibres or fibre bundles and the separation between them must be chosen so that the dominant signals are from a single particle moving past the probe tip. In general, the diameter of the detecting fibres or fibre bundles as well as the effective distance must be similar to the diameter of the particles (Zhou, 1995). The probe consisted of a cylindrical portion, 3.7 mm in diameter and 315 mm long, which housed the delicate fibres. The tip of the probe consisted of a 10 mm long flattened section, 1.5 mm wide by 3.6 mm high. The fibres were divided into three bundles each about 1 mm in diameter. 67 o h— CL O LLI a: CD LU CO o CL CO I > CL cr: LLI N < < o o _ l LU > LU I o h -> t. cd LU _] o I-or o \-o LU < 1-LU LU CL Q cr: LU \- LU i _i X i 1 o CL (D O CL /"NT* OT i 1— h -/"NT* OT _l o _l PH' MU PH' MU o < LY. LU LU LL LL _l _l CL CL < < a: O i -o LU < h-LU LU CL Q LU < o _ i < z O CO < < o CO cr: LU V-Z) CL o o 3 o ex CD CD O a , o CD s CD <*> cd CD s CD cd o O cd s CD o t/3 CD 3 0 0 68 The effective distance between the fibres had to be determined for each probe since the effective distance is not the same as the geometric distance (Patrose and Caram, 1982; Benkrid and Caram, 1989). The calibration was carried out with the aid of an Optical Chopper supplied by Scitec Instruments. This instrument consists of a small D/C motor connected to a controller and frequency analyzer. A single particle was fixed to the end of a length of wire attached to the D/C motor. The speed of the motor and hence of the particle is adjusted by the controller. At the base of the motor is a light transmitter/detector which sends a signal to the instrument whenever the particle passes by it, and the frequency is displayed by the instrument. Knowing the distance of the particle from the centre of rotation (centre of the motor), r, and the rotational frequency, / , the tangential velocity of the particle at the end of the wire can be calculated. An oscilloscope was connected to the optical fibre system to measure the transit time, AtAC, between the two fibres, and the effective distance, lep could be determined from the equation 1^=2TT rf AtAC (4.2) The average effective distance between the receiving fibres, determined by the method described above, was found to be 1.15 mm, while the actual distance was approximately 2 mm. The large discrepancy was surprising at first. He (1995), using the same instrument with a smaller size probe and the same calibration technique, measured an effective distance which was approximately 20% smaller than the geometric distance. Zhou (1995) proposed that the difference between the effective and geometrical distances is due to the alignment of the fibres and differences in diameter of the fibre bundles. Another possible factor affecting the effective optical distance is the intensity of the light signal. A stronger light source or a more sensitive detector will detect the reflected light from particles further from the probe giving different velocity measurements than those closer to the probe. For these reasons, calibration is 69 neccessary for accurate measurement, and it is important to keep the settings constant for each calibration. Measurement of spout particle velocities were carried out with the instrument calibrated as above, i.e. with leff~ 115 mm. However, it was later discovered that the data for spout particle velocity and voidage, when applied in the Grace and Mathur (1978) equation for fountain height, underpredicted experimental measurements by a factor of two. This required further investigation. It appeared that there was error in either the voidage measurements or the particle velocity measurements. Due to the large discrepancy between the effective and geometric distances between the fibres of the particle velocity probe, the accuracy of this instrument was investigated first. The probe was tested against particles travelling at a known velocity in order to simulate the flow of particles inside the spout, as opposed to having just one particle pass the probe tip as in the calibration. Particles were dropped from a height above the probe such that they reached their terminal velocity before passing the probe. The measured velocity was significantly lower than the calculated terminal velocity (approximately 75% lower). The difference coincided with the differences between measured and calculated fountain heights. This suggested that the original calibration method was flawed and that the error was in the velocity measurements. Since no error in methodology could be found, a new calibration technique was attempted. Following the method of Benkrid and Caram (1989), the probe was calibrated using the Optical Chopper and a rotating disk with 30 slits in it which produced a stroboscopic effect simulating moving particles. The velocity read by the optical fibre probe instrument was matched to the tangential velocity of the rotating disk by adjusting the input for the effective distance between the fibres through trial and error. This method resulted in an effective distance of 1.7 mm, in closer agreement with the actual distance between the fibres and a correct measurement of the particles' terminal velocity. Therefore, the experimental data obtained previously had to be multiplied by a factor of 1.48 in order to correct for the earlier false calibration. All 70 experimental results presented in this work have been corrected in this manner. The reason for the errors in the original calibration technique is unknown. Radial profiles of particle velocities were taken at 2 mm intervals starting from the bed axis outward at different locations along the height of the bed. Each measurement was taken from a sample of at least 1024 particles. Due to the large number of measurements to be taken, in general only one measurement was taken at each point. Reproducibility was checked by repeating the measurement across the spout at least three times at selected axial positions for each particle size. Similar confidence intervals (95%) were obtained during reproducibility tests done at different bed levels and operating conditions. Therefore, they were used to represent the precision of all measurements. The instrument works best when the particle velocities are high because the light signal is narrower and the peak easily detected. At lower velocities, the signals tend to flatten out and at too low velocities the instrument is incapable of detecting the signal peaks. The range of velocities which can be detected with precision is between about 0.20 and 16.0 m/s. 4.3.2 Particle Velocity Measurements in the Annulus In the annulus, particle velocities are of the order of 0.01 m/s, which is beyond the range of capability of the instrument used for the spout velocity measurements. A different method was therefore employed to measure particle velocities in the annulus (He, 1995). An optical fibre probe was again used so that it could be inserted into the bed to take local velocity measurements at different radial locations. A schematic diagram of the apparatus is presented in Figure 4.2. The probe consists of thousands of optical fibres, each 16 um in diameter, arranged in an array with light emitting fibres alternating with light receiving fibres. The probe is significantly larger than the previous one, with a diameter of 10 mm and a length 71 E N L A R G E M E N T L E N S L I G H T IN P R O B E o m M O N I T O R V C R V I D E O M I X E R I M A G E O U T 10 mm 8 mm 4 mm F R O N T V I E W O F P R O B E T I P C O M P U T E R Figure 4.2: Schematic diagram of equipment used for measuring particle velocities in the annulus. 72 of 225 mm. The tip of the probe extends 11 mm and has a rectangular cross-section measuring 9 mm by 4 mm. The probe is large so that it can accommodate enough fibres to transmit a clear image from the tip of the probe. The images are enlarged through a lense and recorded with a video camera onto a video cassette. By playing back the video cassette frame by frame, the transit time for individual particles to travel a known distance can be determined and the velocity calculated. A Cohu Ffigh Performance CCD camera was employed to capture the images from the probe. The signals were subsequently recorded onto a video cassette using a SONY Hi-Fi VHS recorder. Measurement of particle velocities was carried out using a microcomputer with the aid of an image analysis software package, Optimas 5.1, developed by Optimas Incorporated. A Videonics digital video mixer served as an interface between the video cassette recorder and the computer. A calibration for length measurement was required to measure the distance traveled by the individual particles. The calibration was obtained by placing a ruler with precise markings in front of the probe and recording its image on tape. The image was then displayed on the computer and used for calibration. Particle velocities were then obtained by following a particle through a series of frames, counting the total number of frames it passes through, and measuring the distance traveled. Measurements were taken at radial positions from the wall of the column to the spout-annulus boundary. For each position, a recording time of one minute was used from which 15 particle velocities were measured in order to obtain a representative sample at that position. The recording frequency of the V C R is set at 30 frames per second, while the length over which particles can clearly be seen on the tip of the image probe is approximately 7 mm. The particle must be present in at least three consecutive frames in order to identify it as the same particle and make a measurement. Taking all this into consideration, the maximum particle velocity which can be measured with this technique is approximately 0.07 m/s. The 73 gap between the measurement ranges of the two techniques employed means that there is a region near the spout/annulus boundary over which reliable measurements cannot be obtained. In order to obtain values in this region, the profiles were extrapolated to the spout/annulus boundary. 4.4 Results and Discussion 4.4.1 Particle Velocity Profiles in the Spout and Annulus Figures 4.3 and 4.4 show the radial profiles of particle velocities (corrected data) in the spout at different ratios of auxiliary air to total air flow rates for two particle sizes (original, uncorrected experimental data are presented in Appendix C). The profiles have the same characteristic shape as those reported by He et al. (1995). In particular, the profiles show that a maximum velocity is reached some distance above the orifice and then decreases with height. While the particle velocities generally decrease with radial distance from the spout axis, near the top of the bed, the maximum velocity is somewhat removed from the axis. This shift away from the spout axis was also observed by He et al. (1995), and is believed to be due to radial movement of particles and particle-particle collisions in the spout (Krzywanski, 1992). Increasing the proportion of auxiliary flow reduces the local particle velocity in the spout due to a lower spout gas flow rate. The reduction in particle velocity is roughly proportional to the reduction in spout gas flow rate. In addition, the difference in local particle velocity between the bottom and the top of the bed is diminished with increasing QA/QT 74 T—1—• | • — | — ' — | — i — | — " — | — i — i — i — | — ' — | — i — | — i — r — i — r ° (S/LU) AjpoiSA e p i L i B d 75 (S/LU) AlJOO|GA 9 P ! P 2 d 76 Radial profiles of downward particle velocities in the annulus are plotted in Figures 4.5 and 4.6 for the same two particle sizes (experimental data are presented in Appendix C). In the cylindrical part of the bed (solid symbols), vertical particle velocities decrease with decreasing height due to the cross-flow of solids from the annulus to the spout, which is greater at the bottom of the column. The cross-flow of solids is greater in the lower portion of the column, because of the high voidage in the spout at that level leaving more space for incoming particles from the annulus. Since the particles can move inward as well as downward, fewer particles have to move downward and the vertical velocity of the particles is reduced. At the top of the bed, the spout voidage is lower, as is evident from the plots in Chapter 3. Hence, there is less space for particles to enter from the annulus and the particles are forced to move downward at a faster rate. In the conical section (open symbols), vertical particle velocities show the same trend near the wall. Towards the spout/annulus interface, however, the trend is reversed and the velocities increase, rather dramatically, with decreasing height. This is due to the reduction in cross-sectional area for downward moving particles. Except at the very base of the cylindrical section, the velocity profiles in this region are not flat as previously believed. Typically, the profiles show a boundary layer near the wall of the column and near the spout/annulus boundary. In between, the velocity decreases with radial distance from the spout axis. The same behaviour was reported by He et al. (1995). Just above the cone/cylinder junction, the profiles tend to be fairly flat. With an increasing proportion of auxiliary air, there is a slight decrease in particle velocities in the entire annulus region. This is most evident in the conical section of the column. 77 (j> - g c i c i o ' c i o ' c i c i 3= N • 4 • O < > > _L • ' • ' • 1 " 1 I i I i I i I o CO o CD 5 o CM in cT • ' • ' > _ l _ I 1 I 1 I 1 I 1 I 1 jj'*1 '^ 1 ' • • < H o -rn < • cP -I • I ' I • ' • o CO 1 I 1 I 1 I ' I ' I 1 I ' I o If dr D> <><<>S>- a -I I l_ o CN O CO o CD Hi o CN E E^ o Q . (/) E g CD O c CO 9 C O " O CO or CN CN (S/LUUJ) AlJ00|8A 9|0!lJBd 78 3 °0 gg b: P C 3 C » C i C i O ' C> C i • • O < > > > ><<< J I I l _ 0 J_ o 00 T T J • «4 ^ <DC9 • • J D < < -1^  O CM g S g ^ C j L g o L p o L n o L n o CM CM E 0 ) 3 o Q . C/> E (D O c 05 -4—" CO T3 "CO ~o CO a : 0 0 _ 3 3 cd CD in CD O > JD cd D-7d o CD > -a u cd C o o u o cd cd CD S-. 00 E (s/ww) AjpoieA eionJBd 7 9 4.4.2 Solids Mass Flow Rates The solids mass flow rates in the spout and annulus were calculated by combining the voidage profiles from Chapter 3 and the velocity profiles from this chapter in the following expressions: Since voidage and particle velocity are average values of measurements obtained over a certain period of time, the solids mass flow rates calculated in this manner represent time-averaged values. Equation 4.3 represents the upward moving solids mass flow in the spout while Equation 4.4 represents the downward moving solids mass flow in the annulus. The integrals were evaluated numerically using the 5-panel Newton-Cotes method and spline interpolation between data points. The spout radius, rs, was determined experimentally as described in the previous chapter. The solids mass flow rates in the spout and annulus under varying values of QA^QT along the height of the bed are presented in Figures 4.7 through 4.10 for particles ofdp= 1.33 mm and 1.84 mm (computed data are presented in Appendix F). The data show considerable scatter, particularly in the spout and for the smaller particle size. This scatter is due to experimental error and the limited precision of the instruments, compounded during the computation of the solids flow rate outlined above. For each data point there is an error associated with voidage, particle velocity and spout radius measurements. Errors in placing the probes at the right position, a spout which is not centered, as well as variations in flow (4.3) 0 (4.4) 80 rate through the bed all contribute to the overall error in the measurements. When these errors are combined in the integration, the resulting deviations can be very significant. In view of this, a sensitivity analysis was performed to see what effect voidage and particle velocity have on the final results. For the spout, the voidage has a much greater effect on the solids flow rate than particle velocity. A 5% increase in voidage results in about a 25% decrease in mass flow rate, while a 10% increase in particle velocity results in an equal increase in mass flow rate. For the annulus, the effect of experimental error is more moderate. Both voidage and particle velocity have approximately equal effects on mass flow rate. An increase in voidage or particle velocity results in a proportional decrease or increase in Ws, respectively. The calculation of the mass flow rate in the spout is very sensitive to the chosen spout radius because of the relatively small area occupied by the spout compared to the annulus. A small error in the measurement of spout radius will have a large effect on the flow rate because the radius is squared in the integration. This effect is exacerbated by the unreliable data obtained at the spout/annulus boundary. As mentioned in Chapter 3, the voidage data obtained near the boundary has the highest degree of uncertainty, of the order of 20% in certain cases. Particle velocity measurements in this region are also unreliable due to the gap which exists between the ranges of the two measurement techniques. These errors are not as crucial for the calculation of mass flow rates in the annulus because of the larger area it occupies and the more uniform profiles of voidage and particle velocity, particularly in the cylindrical section. For all cases, the calculated mass flow rates in the spout are consistently and considerably higher than those in the annulus. One possible explanation for this is that the technique for measuring particle velocities in the spout may be biased towards vertically moving particles and does not take into account particles traveling at an angle to the spout axis or particles which collide with the annulus or other particles. The measured mean particle 81 Figure 4.7: Solids mass flow rate in the spout (dp = 1.33 mm). 82 0.00 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Vertical distance from orifice, z (m) Figure 4.8: Solids mass flow rate in the annulus (dp =1.33 mm 83 Figure 4.9: Solids mass flow rate in the spout (dp = 1.84 mm). 84 Figure 4.10: Solids mass flow rate in the annulus (dp = 1.84 mm). 85 velocity, therefore, could be greater than the actual mean vertical component of particle velocity inside "the spout. Dust particles entrained in the spout may also play a role by reflecting more light to the probe and giving false readings. Another possible explanation can be found in the measurement of voidage in the spout. As mentioned in Chapter 3, the measuring volume of the voidage probe increases with increasing voidage. Therefore, in the spout, where the voidage is high, the probe may be taking more particles into account than in the annulus where the particles are more densely arranged. There may also be a significant contribution from particles in the annulus when the probe is near the spout-annulus boundary, tending to inflate the measured particle concentration. Pulsating flow of gas through the spout may also contribute to the discrepancies in mass flow rates between the spout and annulus. As the air flows through the piping system, pulses may be generated due to the compressor, the natural frequencies in the flow system or instability of the spout. The pulsating flow of gas entering the bed would cause fluctuations in the transport of solids through the bed. These fluctuations would be evident in the fountain and in the solids flow in the annulus. Fluctuations in the fountain were in fact observed, while no fluctuations were observed in the annulus. If pulsating flow was present in the spout, this would affect the calculation of the mass flow rate. In Equation 4.3 the solids circulation rate is estimated by multiplying time-averaged local particle velocity and local time-averaged particle concentration. These averages do not take into account pulses or fluctuations which may be present. By ignoring the effect of pulsating flow, the computed mass flow rates would be higher than the actual flow rates, as is evident from the analysis presented in Appendix G. Underestimation of particle velocity in the annulus could also contribute to the differences in solids flow rates. The probe used to capture the image of moving particles in 86 the annulus required that the particles pass very close to the flat front surface in order for a clear image to be recorded. Collisions with the probe and friction against the probe surface would tend to slow particles to some extent. In addition, electrostatic forces between the probe and the particles may also have an effect on particle velocity. As mentioned in Chpater 2, it was found necessary to add antistatic powder to the particles to be able to obtain a continous flow past the probe, and electrostatic effects may not have been totally eliminated. In view of the combined effects of all these factors, it is not surprising that such a large discrepancy in solids flow rates exists. Because of the scatter, each set of data was fitted by linear regression in order to extract general trends from which to compare the effects of varying proportions of auxiliary air and particle size. Although not very evident in Figures 4.7 and 4.8 for the smaller particle size, Figures 4.9 and 4.10 clearly show that with increasing QA^QT, the solids mass flow rate decreases. This is expected since with increasing QA/QT, ' e s s air l s passed through the central orifice as air is injected into the annulus, bypassing the spout. Therefore, fewer particles can be carried through the spout. The effect of particle size on the solids circulation rate can be seen in Figures 4.11 and 4.12. The solids flow rate for the two extreme values of QA/QT 0e- 0.0 and 0.43) were plotted for the three particles sizes in both the spout and annulus. The solids mass flow rate increases with particle size. This is due to the higher gas velocity required to spout the larger particles. 87 i 1 1 1 1 1 r o o ' ' i i i i i i i i i i I 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Vertical distance from orifice, z (m) Figure 4.11: Solids mass flow rate in the spout at two values of QA/QT f ° r a ^ particle sizes. 8 8 Figure 4.12: Solids mass flow rate in the annulus at two values of QA/QT^0* a ^ particle sizes. 89 4.4.3 Fountain Height Fountain heights were measured from the surface of the bed to the top of the fountain with a ruler placed against the clear wall of the column. The stabilizer was removed for these measurements. Measured fountain heights for the three particle sizes at different ratios of QA/QT are shown in Figure 4.13. The height of the fountain decreases with an increasing proportion of auxiliary air as less air is being injected through the central orifice. With a decrease in fountain height, the concentration of solids in the fountain appeared to increase while the fountain itself was well defined and more stable, not requiring the use of the stabilizer. Particle concentration within the fountain as well as fountain height and shape can have important implications in certain applications of spout and spout-fluid beds such as granulators and coating units (Waldie et al., 1986) and reactors (Grace and Mathur, 1978). In view of this, more experiments are required to examine the effects of auxiliary air on fountain characteristics. The semi-theoretical equation of Grace and Mathur (1978), 2 HF = e'046 ^L—P*— (4.5) 2g Ps-Pf predicts fountain height given the particle velocity on the axis at the bed surface, v0max, and the radial-average voidage at the bed surface, % The calculated fountain heights, based on data from Chapters 3 and 4, are compared to the measured values in Table 4.1. In general, the equation of Grace and Mathur (1978) gives fairly good predictions of fountain height, especially for the largest particle size. 90 Figure 4.13: Fountain height vs QA^QT^0V all particle sizes. 91 Table 4.1: Experimental fountain heights and values predicted from the Grace and Mathur (1978) equation. QA/QT dp = 1.33 mm dp = 1.84 mm dp = 2.53 mm HF expt'l (mm) Hp pred. (mm) % dev. Hp expt'l (mm) Hp pred. (mm) % dev. Hp expt'l (mm) Hp pred. (mm) % dev. 0.00 197 207 5.1 200 221 10.5 147 149 1.4 0.15 162 135 -16.7 125 140 12.0 96 0.28 119 97 -18.5 95 67.7 -28.7 63 0.43 94 74.4 -20.9 70 40.3 -42.4 35 34.9 -0.3 4.5 Summary The redistribution of air flow from the spout inlet to the auxiliary distributor has a more noticeable effect on particle velocity in the spout than in the annulus. In both regions, however, particle velocity decreases with increasing proportion of auxiliary air. This is due to a greater portion of gas passing through the annulus and bypassing the spout. As a result, the solids circulation rate also decreases with increasing Q^/QT • Solids mass flow rates increase with increasing particle size. However, calculated solids mass flow rates in the spout are consistently higher than those in the annulus. Possible explanations for this discrepancy include: 1) assymmetry of the spout inside the bed of particles, 2) sensitivity of the calculation of spout solids flow rate to spout diameter and difficulties in accurately measuring this value, 3) a bias in the measuring technique employed 92 for particle velocity measurements in the spout towards particles moving in the axial direction, 4) dust particles entrained in the spout, 5) inaccurate measurement of local particle concentrations in the spout due to varying measurement volume with voidage, 6) pulsating flow of gas induced by the piping system generating correlated fluctuations in particle velocity and concentration which are not considered in the computation of mass flow rates and 7) friction and electrostatic forces affecting the velocity of particles adjacent to the image probe in the annulus. Fountain height decreases with both increasing Q^/Qj and increasing particle size as predicted by the semi-theoretical model of Grace and Mathur (1978). The effect on fountain height of redistributing the air to the auxiliary distributor needs further investigation. 93 Chapter 5 Pressure Gradients and Gas Flow in the Annulus 5.1 Introduction Just as particle distribution and circulation rates are important for gas-solid contact, the fluid flow pattern plays an equally important role. Several studies of fluid flow in spout-fluid beds have been carried out (Nagarkatti and Chatterjee, 1974; Littman et al., 1974; Hadzismajlovic et al., 1983; Heil and Tels, 1983). However, since many of the studies are based on work also done on spouted beds and owing to the similarity between the two systems, fluid flow in both systems is first reviewed. 5.1.1 Pressures Gradients in the Annulus Pressure profiles in the annulus of spouted beds have been obtained from measurements of vertical static pressure gradients (Mathur and Gishler, 1955; Thorley et al., 1959; Grbavcic et al., 1976; Epstein et al., 1978). Both differential pressure probes inserted into the annulus of spouted beds from the top of the column, and pressure taps installed along the column wall have been employed. These profiles show that the pressure gradient increases with increasing height along the bed. This is due to the crossflow of gas from the spout to the annulus (the spout being at a higher pressure than the surrounding annulus). The pressure gradient variation is steeper at the bottom of the bed and levels off toward the top. Because of the exchange of gas between the spout and annulus and the loss of energy of the gas as it entrains particles, the difference in pressure between the two regions diminishes and the crossflow rate decreases with height. A further observation was made by Grbavcic et al. (1976) who reported that "for a given solid material and spouting fluid in a column of fixed geometry, the measured pressure 94 gradient at any given level in the annulus is independent of bed height." Sutanto (1983) studied overall bed pressure drop in spout-fluid beds and found it to increase with increasing auxiliary air flow. However, the overall pressure drop was always less than that for a corresponding fluidized bed. In the earliest studies of spouted beds (Mathur and Gishler, 1955; Thorley et al., 1959) it was found that radial pressure gradients were small compared to vertical gradients. While this is a valid observation in the upper section of the annulus of spouted beds, it does not hold near the gas inlet region where the area available for gas flow abruptly increases and there is considerable radial motion of particles as they are carried into the spout. For this reason, it is common for experimental measurements of gas flow patterns and pressure distributions to be restricted to the region above the conical or entry region. Rovero et al. (1983), in their attempt to model the effect of the conical-base region of spouted beds, measured static pressure in the annulus of small diameter columns (Dc = 0.08 and 0.14 m ) and obtained vertical differential pressure profiles. These profiles showed a local maximum in the cone followed by a minimum at the cone-cylinder junction for all bed depths studied. The upper part of the bed was characterized by an increase in pressure gradient, with the pressure gradient under minimum fluidization conditions providing an upper limit, as reported by all previous authors. Heil and Tels (1983) measured pressure distributions in a spout-fluid bed. They identified four flow regimes corresponding to measured spout pressure drop profiles over a range of fluidization gas velocities. However, no pressure measurements in the annulus were obtained with added fluidizing air flow. 95 In a later study, He (1990) measured radial pressure profiles in a large, half-sectional spout-fluid bed (Dc = 0.91 m). Results showed radially uniform pressure profiles in the upper cylindrical portion of the annulus, while the pressure decreased toward the column wall in the lower part of the cylindrical portion and in the conical region. 5.1.2 Gas Flow in the Annulus For the cylindrical part of the bed, the usual method for determining annular gas flow rate is from static pressure gradients. The measured pressure gradients are converted into gas velocities using a pressure drop versus velocity calibration curve obtained from loose-packed fixed beds. The underlying assumption of this method is that the void fraction in the moving annular region is the same as in the stationary loose-packed bed (Thorley et al, 1959). Using this method, and assuming that no significant radial static pressure gradients exist across the annulus (Lim, 1975), an assumption which is acceptable in the cylindrical portion of the column away from the entry region, the vertical gas velocity in the annulus of a spouted bed generally increases with increasing height (Mathur and Gishler, 1955; Thorley et al., 1959; Lim, 1975). Epstein et al. (1978), working with small cylindrical columns, were able to corroborate the finding of Grbavcic et al. (1976) that the air velocity at a given level remains the same regardless of bed depth for a given solid-fluid system and bed geometry. Furthermore, they found that the air velocity at a given level decreases with increasing spouting velocity and decreasing gas inlet diameter. A decrease in annular gas velocities towards the column wall in the cylindrical section of the column has been reported in larger columns (Lim and Grace, 1987; He et al., 1992). 96 Nagarkatti and Chatterjee (1974) measured point gas velocities across a spout-fluid bed. As expected, the fluid distribution tended to become more uniform with increasing fluidizing or auxiliary flow. Sutanto et al. (1985) observed similar behaviour and, in addition, found that the annulus gas velocity at a given level was independent of overall bed depth. The same observation was made by Grbavcic et al. (1976) and Epstein et al. (1978) in studies of spouted beds. The experiments of Sutanto et al. (1985) showed that the total flow in the annulus exceeds the auxiliary flow, indicating a net cross-flow of gas from the spout to the annulus in the cylindrical portion of the column. An analysis of fluid flow in the annulus of a spout-fluid bed of large diameter was carried out by He (1990). He found that in the conical base, the annulus superficial gas velocity increased with height, reaching a maximum in the cone region and then falling to a local minimum at the cone-cylinder junction before rising again in the cylindrical portion. This is in agreement with the findings of Rovero et al. (1983). In the above studies, the loose-packed bed voidage of the solids was used in calculating the fluid flow rate through the annulus. This assumption has been widely used because of the difficulty in obtaining actual voidage measurements, although it has been known for some time that local voidage variations may exist. For spout-fluid beds, one would expect, at least in the upper portion of the bed, that the voidage would deviate from the loose-packed bed voidage as auxiliary air increases and fluidization of the annular solids occurs. He et al. (1995) have indeed demonstrated, using an optical fibre probe technique, that the voidage in the annulus of spouted beds is greater than the loose-packed bed voidage, and that it increases with increasing gas flow. In Chapter 3, it was shown that the voidage in the annulus can be significantly higher than the packed bed voidage in the cylindrical portion of the bed, while in the conical region, the voidage tended to drop locally below this value. 97 It is clear from these studies that the fluid flow in spouted and spout-fluid beds is quite complicated, especially near the gas entry region. Past studies have focused mainly on the upper portion of the annulus where fluid and solid flows are more predictable and better understood. The entry region may well be the most important section of the bed because this is where gas first comes in contact with the solids, dictating the distribution of gas throughout the bed. Proper measurement of particle and fluid distributions is vital to understanding the contacting characteristics in spouted and spout-fluid beds. 5.2 Theoretical Models for Gas Velocity in the Annulus of Spouted and Spout-Fluid Beds The first theoretical model to describe the longitudinal fluid velocity profile and pressure drop in a spouted bed, at the maximum spoutable bed height, was developed by Mamuro and Hattori (1968). Their analysis was based on a force balance over a differential height in the annulus. The major assumption was that the upward movement of gas through the annulus is governed by Darcy's law. In addition, the model neglects friction at the spout-annulus and column wall boundaries, as well as downward solids velocities in the annulus. The annulus was considered a uniformly packed bed and the spout diameter was assumed to be constant. Rovero et al. (1983) modified the Mamuro and Hattori (1968) model for a conical-base spouted bed and developed a new model based on the vector form of the Ergun (1952) equation. Both models predicted a maximum gas velocity in the cone region and a minimum at the cone-cylinder junction, in agreement with experimental measurements. 98 A separate equation for annular gas velocity in spout-fluid beds was derived by Littman et al. (1976) based on the Mamuro and Hattori (1968) equation. The equation was based on data obtained in a liquid-phase bed which showed a linear relationship between annular and spout flow rates at the minimum spout-fluid flow rate. He (1990) and He et al. (1992) developed a model for fluid flow and pressure distribution in conical-based spout-fluid beds based on the vector form of the Ergun (1952) equation, while Day et al. (1991) did the same for a flat-bottomed bed. 5.3 Experimental Methods Pressure gradient measurements in the annulus were taken using the static differential pressure probe described in Chapter 2. The probe was inserted into the annulus from the top of the bed and placed approximately half-way between the column wall and the spout-annulus interface. Measurements were taken with the probe at the same level as the ports on the column, and an additional measurement was taken at the cone-cylinder junction where no port is present. Annulus gas velocities were calculated from differential pressure gradients according to the method described by He (1995). In order to determine the air flow through the annulus, a pressure drop versus superficial gas velocity curve for a loose-packed bed of a given material was first obtained. The calibrations were performed in the column with the bed height greater than the maximum spoutable bed height, Hm. The differential pressure probe was inserted in the centre of the column, half-way between Hm and the top of the bed. Measurements taken at different radial positions showed that there was no measurable radial variation of static pressure drop. Calibration curves were obtained for the three particle sizes used in this study and are presented in Appendix B. 99 The results of Chapter 3 have shown that the voidage in the annulus of spouted and spout-fluid beds is not equal to that of the corresponding loose-packed bed. Therefore, the calibration curves have to be adjusted for voidage. Assuming that an equation of the form of the Ergun (1952) equation is applicable to beds of voidages different from the loose-packed bed voidage (s0), a relationship between pressure drop and superficial gas velocity at different voidages could be obtained by solving the equation: 'dp\ \dz) Au + f2u2 (5.1) where x , ( i - * ) 2 ju(\-£y s K) 2 (5.2) £ z i ) = L 7 5 M z i ) f2 — ^2 1 - - -e <j>d s (5.3) The parameters fj and f2, for each particle size, were obtained by fitting the calibration curves of pressure drop versus superficial gas velocity for the loose-packed bed to the form of the Ergun equation, Equation (5.1). The constants, k} and k2, were then evaluated by inserting s0 for e in Equations 5.2 and 5.3. Since ju, pj; <j> and dp are known, predicted values oikj and k2 can be obtained from the right-hand sides of Equations 5.2 and 5.3. Experimental and predicted values of kj and k2 are listed in Table 5.1 and are in close agreement. 100 Table 5.1: Values of and k2 obtained by curve fitting of experimental data compared with values calculated from Equations 5.2 and 5.3. Particle size deviation k2 h deviation expt'l pred. expt'l pred. 1.33 mm 0.1598 0.1486 7.5% 0.1443 0.1507 -4.2% 1.84 mm 0.1025 0.0860 19% 0.1253 0.1166 7.5% 2.53 mm 0.0458 0.0475 -3.6% 0.0829 0.0879 -5.7% Replacing s, in Equation 5.1 with the local voidage in the annulus, ea, and U with U'a, the superficial gas velocity through the annulus relative to the particle, and further noting that U'a=eaua, where ua is the interstitial gas velocity in the annulus relative to the particles, Equation 5.1 can be rewritten as: dz) = KX—i^ua+k^ ^ (5.4) Combining the local voidage measurements from Chapter 3, taken at the same radial positions as the pressure drop measurements, Equation 5.4 can be solved for ua. The superficial gas velocities relative to the column were then obtained by subtracting the local downward particle velocities, from Chapter 4, from the interstitial gas velocities, i.e. Ua= 101 5.4 Results and Discussion 5.4.1 Longitudinal Pressure Gradients Longitudinal profiles of pressure gradients in the annulus were measured under varying flow conditions for all three particle sizes. The results are plotted in Figures 5.1 to 5.3. Experimental data are presented in Appendix D. All three plots show an increase in pressure drop with both height and auxiliary flow to total air flow ratio, Q^/Qj. In Figure 5.1, the apparent discontinuity in the curve for Q^QT= 0.0 suggested that further investigation near the cone-cylinder junction was necessary. In light of this, an extra measurement point was included just above the cone-cylinder junction. The curves for the two larger particle sizes, Figures 5.2 and 5.3, clearly show a discontinuity near the cone-cylinder junction. This feature has also been reported by previous authors (Rovero et al., 1983; He, 1990) in studies performed in conical-base spouted beds. The experimental results of Rovero et al. (1983) show a local maximum in the cone followed by a minimum at the cone-cylinder junction. The upper part of the bed is characterized by an increase in pressure gradient. The discontinuity observed near the cone-cylinder junction is due to the fluid flow pattern and variations in radial pressure profiles. In the cone, there is a strong radial gradient of gas flow, and hence a corresponding radial pressure gradient, due to the percolation of gas into the annulus as it enters the bed. Because of the radial component of the pressure gradient, the static pressure probe used in this work may not be suitable for measurements inside the cone. Only above the cone, once the streamlines are fully developed, nearly parallel to the bed axis and the radial pressure gradients are small, can the technique be used reliably. As seen in the figures, the point of discontinuity occurs some distance above the cone-cylinder junction and indicates that the streamlines are still in transition and not fully developed past the top of the cone. 102 Figure 5.1: Longitudinal pressure gradients in the annulus (<aL = 1.33 mm). 103 Figure 5.2: Longitudinal pressure gradients in the annulus (d„ =1.84 mm). 104 Figure 5.3: Longitudinal pressure gradients in the annulus (dp = 2.53 105 Increasing the proportion of auxiliary flow has a significant effect on the pressure drop in the annulus, with the largest influence occurring at the bottom of the bed. For the largest particle size, there is a four-fold increase in pressure drop between the two extreme values of Q^QT 0e- 0.0 and 0.43), at the bottom of the bed. This difference decreases towards the top of the bed. As the maximum spoutable bed height is approached, the pressure gradients converge to a maximum. 5.4.2 Gas Distribution in the Annulus Combining the pressure gradients with local annular voidage and particle velocities in the Ergun equation as described above, profiles of superficial gas velocity were obtained and are plotted in Figures 5.4 and 5.5 for dp = 1.33 and 1.84 mm (computed data are presented in Appendix F). Figure 5.4 shows a significant increase in annular gas velocity between simple spouting and the maximum ratio of auxiliary to total air flow. However, for the two intermediate values of Q^/Qj, the trend is inconsistent, probably due to the large amount of scatter in the data. Figure 5.5 also shows an increase in annular gas velocity with height, but again there is no consistent trend with respect to Q^/Qj. The scatter is partly due to the sensitivity of the superficial gas velocity calculation to voidage: a 5% change in the local voidage results in a 14% change in superficial gas velocity. The precision of the voidage measurement technique is within 10%, at best. Therefore, the method is prone to significant errors. In the cone, the data are quite erratic, but they appear to indicate that a local maximum is reached inside the cone followed by a minimum at the cone-cylinder junction (Figure 5.5), as observed by Rovero et al. (1983) and He (1990). However, due to uncertainty in the method used for pressure drop measurements in this region, it is 106 Figure 5.4: Superficial gas velocity profiles in the annulus for different ratios of QA^QT (d„ = 1.33 mm). 107 Figure 5.5: Superficial gas velocity profiles in the annulus for different ratios of QA/QT (dp= 1.84 mm). 108 2.0 1.6 1.2 .W 0.8 0.4 CD > 0.0 CO 0 3 o n O) 2.0 CO I 1.6 h CD Q. GO 1.2 0.8 k 0.4 1 I 1 I —•—1.33 i | i | i QA/QT=0.43 i 1 • - •- 1.84 -_ A 2.53 — M— - ' ' • . • • . 1 , 1 i . r . I 0.0 ^ 1 ' 1 1 1—X7 QA/QT=0.0 0.00 0.05 0.10 0.15 0.20 0.25 Vertical distance from orifice, z (m) 0.30 Figure 5.6: Superficial gas velocity profiles in the annulus for all three particle sizes at two values of QA^QT 109 impossible to draw any definitive conclusions as to the behaviour of gas flow in the cone from these results. Figure 5.6 compares the results for the three particle sizes at the two extreme values of QA^QT- While there appears to be an increase in annular gas velocity with particle size at QA^QT = 0-0 , this trend is not seen at QA^QT = 0-43. 5.5 Summary Longitudinal profiles of pressure gradient increase consistantly with QA^QT a n d less consistantly with particle size. Discontinuities in the profiles near the cone-cylinder junction agree with previous findings (Rovero et al. 1983; He, 1990). The discontinuity has been attributed to the geometry of the columns which have a conical base attached to a cylindrical upper section. Strong radial pressure gradients due to the gas entering through the central inlet and expanding rapidly into the annulus may also have an influence. Superficial gas velocities in the annulus increase with height as expected, but do not show any consistent trend with either QA/QT o r particle size. This is, in part, due to the sensitivity of the calculation of superficial gas velocity to local voidage measurements. 110 Chapter 6 Conclusions and Recommendations 6.1 Conclusions A study of the hydrodynamics of spout-fluid beds was carried out using previously developed techniques employing optical fibre sensors and instruments. Radial profiles of local voidage inside the bed were obtained under varying ratios of auxiliary air flow to total air flow (Q^/QT) t 0 t n e column. Increasing the proportion of auxiliary flow resulted in a significant decrease in spout voidage, while little or no influence was observed in the annulus. Voidage in the annulus varied over a wide range from the bottom to the top of the bed. In the conical section, local voidages were consistently lower than the loose-packed voidage and consistently higher than the loose-packed voidage in the cylindrical section. The low voidage in the conical section suggests that particles are being compacted together in this region. There is a dense region in the annulus near the boundary with the spout where the voidage profiles show a small depression. Cross-sectional average voidages in the spout decreased monotonically with height and were lower for a higher proportion of auxiliary flow but independent of particle size. The boundary between the spout and annulus was measured using the same optical fibre system as in the voidage measurements. Spout diameter was unaffected by the proportion of auxiliary air being supplied to the column, supporting the findings of Sutanto (1983). Both the McNab (1972) and Wu (1987) equations were found to under-predict average spout diameters by as much as 28%. Two different optical fibre systems were employed to obtain local particle velocity profiles in the spout and annulus. In general, particle velocity decreased with increasing 111 proportion of auxiliary flow. However, the effect was more pronounced in the spout than in the annulus. Solids mass flow rates decrease with increasing proportion of auxiliary flow. Increase in solids mass flow rates with particle size is most likely due to the higher gas velocities required for spouting. The integrated upward solids flow in the spout was consistently higher than the integrated downward solids flow in the annulus. The discrepancy can be attributed to inherent inaccuracies in the measurement techniques and instruments used as well as physical phenomena which could not be entirely. Overestimation of the solids flow rate in the spout could be caused by a bias in the measuring technique employed for particle velocity measurements in the spout towards particles moving in the axial direction, dust particles entrained in the spout, contribution of annular particles in measurements of voidage in the spout and pulsations in the fluid flow generating variations in particle velocity and concentration not considered in the computation of mass flow rates. Underestimation of solids flow rates in the annulus may have been caused by friction and static forces affecting the speed of particles adjacent to the image probe in the annulus. Longitudinal profiles of pressure gradients in the annulus increased with an increasing proportion of auxiliary gas, as expected. The effect of auxiliary air was greater at the bottom of the bed and the profiles converged towards a maximum value at the top of the bed. In addition, discontinuities in the profiles were observed near the cone-cylinder junction in agreement with earlier findings (Rovero et al., 1983; He, 1990). The discontinuity has been attributed to the geometry of the columns and to strong radial pressure gradients near the gas entry region of the column. Superficial gas velocities in the annulus were obtained by combining the pressure gradients with measured local voidage in an equation of the form of the Ergun (1952) equation for fluid flow through a 112 packed bed. The results were not entirely consistent, most likely due to the sensitivity of the calculation to voidage measurements which had considerable scatter. 6.2 Recommendations • An investigation of the low voidage values observed in the conical section should be carried out to determine the exact cause of these observations. • Although calibration of the concentration probe, carried out by He (1995) using glass beads in water, produced a linear relationship, calibration of the system using air as the fluid is recommended. • The interface between the spout and the annulus requires closer study to determine the forces involved at this boundary. This is necessary in order to develop more accurate models of spouted and spout-fluid beds. The development of an instrument capable of measuring particle velocities in both regions is recommended in order that particle behaviour across the boundary can be characterized. • A method for humidifying the air supplied by the building compressor is required in order to better eliminate static electricity. For example, the air supply may be bubbled through a column of water as a means of saturating it with water. • Further measurements inside three-dimensional beds are required to develop more realistic models for spout-fluid beds. For example, models are needed for fluid flow through the annulus and for spout diameter. 113 • The effects of other parameters on the behaviour of spout-fluid beds such as orifice size and bed height should be studied. In addition, tests should be carried out with a greater variety of solid-fluid combinations. • The distribution of auxiliary air flow through the sub-distributor layers should be varied as in the work of Sutanto et al. (1985) to see what effect this has on bed characteristics. 114 Nomenclature Di dp dpi Ds f fl>/2 G Hb, H BF 1± yy, Hmsf H0 kj, k2 lAC leff P PATM Pbed P downstream p 1 rotameter Q QA Qmf Qms Qs = cross-sectional area of column (m2) = column diameter (m) = orifice diameter (m) = particle diameter (m) = average screen aperture size (m) = spout diameter (m), average spout diameter in Equation 3.2 (m) = rotational frequency (Hz) = parameters in Equation 5.1 = pjU, mass flux of fluid (kg/m2-s) = bed height (m) = fountain height (m) = maximum spoutable bed height (m) = maximum stable bed height in the spout-fluid bed (m) = height of loose-packed bed (m) = constants in Equation 5.2 = true geometrical distance between optical fibres (m) = effective distance between optical fibres (m) = pressure (kPa) = atmospheric pressure (kPa) = average pressure inside the bed (kPa) = pressure downstream of rotameter (kPa) = average pressure in rotameter (kPa) - gauge pressure inside bed just above orifice (kPa) = spouting (central) fluid flow rate (m3/s) = auxiliary volumetric flow rate (m3/s) = auxiliary volumetric flow rate (m3/s at 20°C, 101.3 kPa) = minimum fluidizing flow rate (m3/s) = minimum spouting flow rate (mVs) = spouting (central) volumetric flow rate (m3/s at 20°C, 101.3 kPa) 115 QT - total volumetric flow rate through column (m3/s at 20°C, 101.3 kPa) R = linear distance between miniscae on inclined U-tube manometer (m) r = radial distance (m) Rc = column radius (m) R0 = linear distance between miniscae on inclined U-tube manometer with no pressure drop, i.e. zero reading (m) rs = spout radius (m) t = time (s) Tbed = average temperature inside bed (°C) U = superficial gas velocity (m/s) ua = interstitial gas velocity in annulus relative to particles (m/s) Ua = superficial gas velocity in annulus relative to column (m/s) U'a — superficial gas velocity in annulus relative to particles (m/s) Umj- = minimum fluidizing velocity (m/s) Ums = minimum spouting velocity (m/s) Uori = superficial gas velocity through central orifice (m/s) v0max = particle velocity on axis at bed surface (m/s) va = downward vertical particle velocity in annulus (m/s) vp = particle velocity (m/s) vs = upward vertical particle velocity in spout (m/s) Ws = solids mass flow rate (kg/s) x = mass fraction of particles (-) Z = vertical distance measured from the orifice (m) zc = height of conical section (m) 116 Greek Characters AP rotameter = pressure drop across rotameter (kPa) At AC = t i m e delay between electrical signals (s) s = voidage (-) s0 = radial-average voidage on axis at bed surface (-) sa = local voidage in annulus (-) s0 = loose-packed bed voidage (-) ss = local voidage in spout (-) (/> = particle sphericity (-) ju = viscosity (kg-m/s) pu = bulk density of particles (kg/m3) Pj- = fluid density (kg/m3) p p = particle density (kg/m3) Superscripts (over-bar) = time-averaged value ' (prime) = fluctuation about the mean 117 References Arnold, M.St.J., J.J. 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Thesis, The University of British Columbia, Vancouver (1995). 123 Appendix A Rotameter Calibration Curves 124 20 0 E 0 O O 10 0 Standard conditions: T= 20 °C, P = 101.3 kPa 0 10 Rotameter flow rate (l/s) 20 Figure A. 1: Calibration curve for central inlet rotameter. 125 7 'c/T 6 I 5 I ^ «+— 0 2 o ^ ""•—I—•—I —1—'—I— Standard conditions: I- T = 20 °C. P = 101.3 kPa O 0 _L • I • J L 0 1 2 3 4 5 6 7 Rotameter flow rate (l/s) Figure A.2: Calibration curve for left, auxiliary rotameter. i — | — i — | — i — | — i — | — i — | i — | — r ^ g i Standard conditions: • ' - T = 20 °C, P = 101.3 kPa c 5 I" E 4 h o O 3 k o * r 1 0 i l i I i ' • i • i • i 0 1 2 3 4 5 6 7 Rotameter flow rate (l/s) Figure A 3 : Calibration curve for right, auxiliary rotameter. 126 Appendix B Calibration Curves of Pressure Gradient vs Superficial Gas Velocity 127 1.2 1.0 «T 0.8 o • | 0.6 o 4z 0 CL 0.4 13 CD 0.2 0 .0G 0.0 1 1 1 1 1 Fitting Parameters 1 1 1 1 1 1 A d f i (mm) A 4 A 2.53 0.2195 0.6788 A 1.1236 -o 1.84 0.5302 • 1.33 0.7678 1.1772 --A o A A o ' O' -A O p ' -— i " i 1 1 I . I . 0.2 0.4 0.6 0.8 1.0 Pressure gradient (mml^ O/mm) 1.2 Figure B. 1: Calibration curves of pressure gradient vs superficial gas velocity in loose-packed beds. 128 Appendix C Experimental Data: Voidage, Particle Velocity and Spout Diameter 129 Table C. 1: Experimental measurements of voidage and particle velocity. (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.22, Q A / Q X - 0.0, Q s = 0.0149 m3/s, Q A = 0.00 m3/s) Particle diameter (dp) = 1.33 mm Loose-packed bed voidage (so) = 0.415 Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) = 1.22 Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.0 Spouting air flow rate (Qs) = 0.0149 m3/s Auxiliary air flow rate (QA) = 0.0000 m3/s Experiment: 130 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/- (mm) (mm/s) +/- (mm) (m/s) +/-error error error 0.011 0 0.906 0 5.02 (port #1) 3 0.932 2 5.50 6 0.947 4 5.47 8 0.951 6 5.73 11 0.925 8 1.92 13 0.845 10 1.80 16 0.630 12 1.24 18 0.406 14 0.62 0.032 0 0.906 21 38.0 3.36 0 2.96 (port #2) 4 0.925 23 36.8 1.72 2 2.95 6 0.925 26 27.3 1.35 4 2.68 9 0.909 28 21.2 1.09 6 2.27 11 0.872 30 14.0 0.59 8 1.62 14 0.800 10 0.63 16 0.546 12 0.17 19 0.418 21 0.426 26 0.433 31 0.437 0.054 0 0.874 20 29.2 1.36 0 3.37 (port #3) 2 0.858 23 25.5 1.10 2 3.50 4 0.885 25 23.2 1.90 4 3.32 7 0.881 29 16.6 0.96 6 2.74 9 0.862 34 12.2 0.76 8 2.11 12 0.820 37 10.3 0.65 10 1.48 14 0.705 40 7.5 0.58 12 0.81 130 17 0.444 42 5.2 0.42 19 0.398 24 0.418 34 0.426 39 0.437 44 0.448 0.076 0 0.848 18 19.9 1.42 0 3.42 (port #4) 5 0.863 20 19.2 0.68 2 3.45 7 0.859 25 17.5 0.96 4 2.98 10 0.832 30 15.6 0.74 6 2.53 12 0.783 35 12.9 0.59 8 1.87 15 0.627 40 10.8 0.67 10 1.15 17 0.395 45 8.4 0.50 12 0.59 22 0.376 50 6.0 0.27 27 0.388 53 5.1 0.57 32 0.392 55 4.2 0.84 37 0.395 47 0.395 52 0.399 57 0.402 0.097 0 0.858 20 12.8 0 3.23 (port #5) 6 0.866 23 13.0 2 3.19 8 0.854 25 13.2 4 2.88 11 0.820 27 11.9 6 2.38 13 0.754 30 12.2 8 1.67 16 0.612 35 11.8 10 1.04 18 0.386 40 9.9 12 0.55 21 0.382 45 9.1 23 0.400 50 7.5 28 0.408 55 6.4 38 0.420 60 5.1 48 0.416 62 4.8 58 0.408 64 3.7 63 0.408 66 3.3 66 0.408 68 0.412 0.168 0 0.816 22 7.5 0.43 0 2.33 (port #6) 4 0.808 25 10.6 0.37 2 2.16 6 0.792 30 10.4 0.42 4 1.83 9 0.766 40 10.4 0.49 6 1.60 11 0.696 50 11.1 0.65 8 1.24 14 0.538 60 11.1 0.55 10 0.68 131 16 0.386 70 11.0 0.57 12 0.33 19 0.436 73 11.2 0.52 21 0.458 76 9.4 0.56 26 0.482 36 0.458 46 0.450 56 0.436 66 0.428 71 0.424 76 0.432 0.218 0 0.774 21 7.0 1.13 0 1.75 (port #7) 4 0.762 22 11.1 0.90 2 1.60 6 0.754 25 14.2 0.59 4 1.46 9 0.735 30 13.9 0.59 6 1.21 11 0.682 35 14.4 0.55 8 0.91 14 0.597 40 13.7 0.48 10 0.76 16 0.417 50 12.9 0.54 12 0.33 19 0.483 60 12.4 0.60 21 0.493 70 13.0 0.35 26 0.497 73 12.8 0.57 36 0.483 76 12.0 0.72 46 0.471 56 0.467 66 0.463 71 0.486 76 0.532 0.268 0 0.745 23 9.6 3.55 0 1.70 (port #8) 4 0.723 25 17.0 1.33 2 1.84 6 0.715 30 17.8 1.26 4 1.72 9 0.731 35 19.0 1.13 6 1.56 11 0.696 45 16.9 0.72 8 1.29 14 0.636 55 14.4 1.07 10 1.01 16 0.488 60 13.6 0.85 12 0.75 19 0.419 65 13.9 0.85 14 0.38 21 0.571 70 13.6 0.72 26 0.533 74 13.6 0.45 36 0.514 76 11.7 0.82 46 0.529 56 0.498 66 0.498 71 0.522 76 0.544 132 Table C.2: Experimental measurements of voidage and particle velocity, (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.20, Q A / Q T = 0.15, Q s = 0.0125 m3/s, Q A = 0.00221 m3/s) Particle diameter (dp) =1.33 mm Loose-packed bed voidage (so) = 0.415 Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) =1.19 Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.15 Spouting air flow rate (Qs) = 0.0125 m3/s Auxiliary air flow rate (QA) = 0.00221 m3/s Experiment: 1333 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/-error (mm) (mm/s) +/-error (mm) (m/s) +/-error 0.032 0 0.926 17 49.6 0 3.03 (port #2) 2 0.936 19 45.2 2 3.04 4 0.929 21 36.5 4 2.82 6 0.915 23 29.4 6 2.41 8 0.893 25 23.6 8 1.93 10 0.847 27 20.2 10 1.08 12 0.758 29 12.9 12 0.68 14 0.521 14 0.33 16 0.442 15 0.13 18 0.442 20 0.446 25 0.439 31 0.421 0.054 0 0.875 16 30.8 2.27 0 3.15 (port #3) 2 0.882 18 29.6 1.43 2 2.99 4 0.879 20 25.8 1.66 4 2.53 6 0.867 22 24.2 1.32 6 2.01 8 0.848 27 17.0 0.98 8 1.31 10 0.798 37 8.3 0.51 10 0.86 12 0.681 40 6.3 0.55 12 0.48 14 0.433 42 4.0 0.48 14 0.13 16 0.361 18 0.368 20 0.372 25 0.368 30 0.376 35 0.372 133 40 0.388 44 0.376 0.076 0 0.855 17 16.2 1.51 0 3.16 (port #4) 2 0.867 20 17.4 1.01 2 3.12 4 0.871 22 16.8 1.13 4 2.81 8 0.859 24 16.2 1.50 6 2.34 10 0.829 27 14.0 0.52 8 1.75 12 0.779 37 9.7 0.72 10 1.22 14 0.649 42 7.7 0.61 12 0.82 16 0.436 49 5.2 0.31 14 0.17 18 0.367 52 4.3 0.23 20 0.387 55 2.6 0.22 25 0.405 30 0.398 40 0.405 50 0.405 55 0.409 57 0.409 0.097 0 0.849 17 9.2 0.36 0 2.50 0.617 (port #5) 2 0.853 18 10.4 0.55 2 2.64 0.431 4 0.857 19 10.6 0.68 4 2.56 0.412 6 0.853 20 11.9 0.58 6 2.25 0.265 10 0.833 25 11.5 0.87 8 1.89 0.245 12 0.795 35 10.4 0.67 10 1.31 0.039 14 0.722 45 7.8 0.42 12 0.97 0.088 16 0.521 55 5.7 0.35 14 0.52 0.020 18 0.370 63 3.0 0.25 16 0.15 0.039 20 0.370 66 2.3 0.34 25 0.396 30 0.396 40 0.400 50 0.408 60 0.392 65 0.381 68 0.362 0.168 0 0.803 20 5.8 0.46 0 2.06 (port #6) 2 0.800 22 8.7 0.63 2 1.87 4 0.792 24 9.5 0.56 4 1.66 6 0.777 30 9.6 1.09 6 1.47 8 0.754 40 10.1 0.80 8 1.12 10 0.701 50 9.6 0.71 10 0.83 12 0.573 60 9.4 1.06 12 0.46 134 14 0.433 69 8.8 1.02 14 0.13 16 0.426 73 8.5 0.68 20 0.479 76 7.5 0.50 30 0.486 40 0.479 50 0.475 60 0.463 70 0.463 76 0.463 0.218 0 0.750 22 20.6 1.88 0 1.82 (port #7) 2 0.743 24 20.7 1.36 2 1.77 4 0.739 26 15.0 0.58 4 1.65 8 0.721 30 18.3 1.26 6 1.43 12 0.638 40 17.1 1.00 8 1.16 14 0.494 50 14.0 0.96 10 0.86 16 0.410 60 15.1 0.83 12 0.69 20 0.520 69 13.4 0.70 14 0.44 25 0.524 73 13.3 0.74 16 0.13 30 0.516 76 11.3 0.87 40 0.505 50 0.490 60 0.459 70 0.463 76 0.437 0.268 0 0.709 22 8.9 0.77 0 1.50 (port #8) 2 0.694 24 20.8 1.07 2 1.56 4 0.683 26 18.2 2.01 4 1.50 8 0.701 30 19.1 1.82 6 1.34 12 0.638 40 16.5 0.88 8 1.12 14 0.535 50 16.1 0.62 10 0.91 16 0.437 60 14.5 0.79 12 0.63 18 0.437 69 14.5 0.32 14 0.37 20 0.554 73 13.8 0.75 16 0.13 22 0.501 76 14.0 0.40 25 0.508 30 0.516 40 0.524 50 0.539 60 0.532 65 0.528 70 0.508 73 0.542 76 0.630 135 Table C.3: Experimental measurements of voidage and particle velocity, (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.19, Q A / Q T = 0.29, Q s = 0.0103 m3/s, Q A = 0.00417 m3/s) Particle diameter (dP) =1.33 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) =1.19 Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.29 Spouting air flow rate (Qs) = 0.0103 m3/s Auxiliary air flow rate (QA) = 0.00417 m3/s Experiment: 1367 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/-error (mm) (mm/s) +/-error (mm) (m/s) +/-error 0.032 0 0.913 17 44.6 7.32 0 2.58 (port #2) 2 0.924 19 39.7 3.70 2 2.68 4 0.917 21 30.7 1.49 4 2.32 6 0.902 23 25.7 1.42 6 1.91 8 0.873 25 20.4 1.48 8 1.49 10 0.819 27 16.1 1.26 10 1.04 12 0.706 29 10.5 0.83 12 0.68 14 0.488 14 0.16 16 0.445 18 0.441 20 0.441 25 0.437 31 0.412 0.054 0 0.874 16 32.4 2.44 0 1.33 0.0392 (port #3) 2 0.884 18 29.1 1.17 2 1.30 0.0098 4 0.888 20 24.9 0.98 4 1.15 0.0980 6 0.881 22 20.6 0.93 6 1.01 0.0196 8 0.862 27 16.4 1.17 8 0.86 0.0294 10 0.821 32 11.2 0.89 10 0.67 0.0196 12 0.739 37 6.75 0.61 12 0.38 0.0245 14 0.523 40 4.98 0.47 14 0.15 0.0392 16 0.426 42 3.32 0.42 18 0.423 20 0.430 25 0.423 30 0.411 35 0.423 40 0.415 136 44 0.389 0.076 0 0.849 18 17.3 1.38 0 2.64 (port #4) 2 0.853 20 17.5 0.86 2 2.68 4 0.857 22 16.1 1.54 4 2.44 8 0.838 24 15.8 2.01 6 2.13 10 0.808 27 14.5 1.05 8 1.69 12 0.755 37 9.23 0.72 10 1.13 14 0.575 47 6.77 0.53 12 0.75 16 0.402 49 4.36 0.25 14 0.17 18 0.387 52 3.85 0.31 20 0.402 55 2.59 0.34 25 0.413 30 0.421 40 0.421 50 0.405 55 0.405 57 0.383 0.097 0 0.826 19 7.88 0.53 0 2.28 0.1862 (port #5) 2 0.837 20 10.1 0.63 2 2.48 0.1176 4 0.841 22 10.6 0.57 4 2.32 0.0686 6 0.841 27 10.7 0.61 6 2.11 -10 0.826 37 8.81 0.53 8 1.76 -12 0.803 42 7.03 0.37 10 1.32 0.0588 14 0.756 47 6.32 0.41 12 0.93 0.0098 16 0.605 57 4.43 0.17 14 0.52 0.0147 18 0.458 65 2.33 0.19 16 0.15 0.0392 20 0.381 68 1.44 0.22 25 0.408 30 0.416 40 0.412 50 0.404 60 0.408 65 0.400 68 0.381 0.168 0 0.777 22 5.52 0.52 0 1.74 (port #6) 2 0.770 24 8.22 0.52 2 1.59 4 0.758 26 9.17 0.79 4 1.34 6 0.747 30 9.71 0.42 6 1.09 8 0.705 40 9.62 0.28 8 0.85 10 0.599 50 9.59 0.59 10 0.48 12 0.429 60 7.95 0.49 12 0.13 137 14 0.388 69 8.48 0.71 16 0.418 73 8.59 0.56 18 0.448 76 8.77 0.74 30 0.463 40 0.467 50 0.463 60 0.471 70 0.467 76 0.467 0.218 0 0.721 24 10.7 0.50 0 1.56 (port #7) 2 0.721 26 13.4 0.81 2 1.50 4 0.713 30 14.6 0.70 4 1.34 8 0.683 40 14.4 0.63 6 1.17 10 0.641 50 13.1 0.38 8 0.88 12 0.532 60 12.8 0.60 10 0.69 14 0.429 69 12.1 0.94 12 0.43 16 0.463 73 12.3 0.45 14 0.13 20 0.467 76 10.8 0.46 25 0.490 30 0.437 40 0.441 50 0.441 60 0.459 70 0.479 76 0.467 0.268 0 0.664 26 14.2 1.13 0 1.33 0.0392 (port #8) 2 0.652 30 17.8 2.89 2 1.30 0.0098 4 0.668 40 16.4 1.57 4 1.15 0.0980 6 0.679 50 15.8 1.30 6 1.01 0.0196 8 0.664 60 16.2 0.63 8 0.86 0.0294 10 0.614 70 14.0 0.57 10 0.67 0.0196 12 0.532 73 12.8 0.41 12 0.38 0.0245 14 0.426 76 13.0 0.68 14 0.15 0.0392 16 0.406 18 0.471 20 0.467 30 0.471 40 0.486 50 0.505 60 0.479 70 0.482 73 0.505 76 0.524 138 Table C.4: Experimental measurements of voidage and particle velocity. (dp = 1.33 mm, H = 0.280 m, U / U m s = 1.20, Q A / Q T = 0.43, Q s = 0.00826 m3/s, Q A = 0.00634 m3/s) Particle diameter (dp) = 1.33 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) =1.20 Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.43 Spouting air flow rate (Qs) = 0.00826 m3/s Auxiliary air flow rate (QA) = 0.00634 m3/s Experiment: 13100 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/-error (mm) (mm/s) +/-error (mm) (m/s) +/-error 0.054 0 0.865 0.0012 18 27.6 3.44 0 2.44 0.010 (port #3) 2 0.873 0.0019 20 25.9 2.21 2 2.32 0.039 4 0.874 0.0049 22 22.9 1.23 4 1.97 0.020 6 0.861 0.0083 27 15.4 0.944 6 1.48 0.137 8 0.841 0.0090 32 9.56 0.738 8 1.09 0.010 10 0.796 0.0194 37 6.37 0.486 10 0.76 0.088 12 0.710 0.0397 40 4.42 0.454 12 0.15 0.039 15 0.510 0.0192 42 3.24 0.341 17 0.468 0.0284 20 0.472 0.0280 22 0.457 -25 0.472 0.0280 30 0.475 0.0351 35 0.462 0.0327 40 0.463 0,0513 44 0.451 0.0892 0.076 0 0.852 18 15.9 0.964 0 2.08 (port #4) 2 0.856 20 15.7 1.03 2 2.25 0.108 4 0.852 22 15.0 1.15 4 2.28 0.039 6 0.841 25 13.3 0.943 6 2.08 0.010 8 0.823 35 8.01 0.872 8 1.74 0.010 10 0.798 45 4.31 0.314 10 1.34 0.029 12 0.751 47 3.97 0.359 12 0.96 0.020 14 0.664 50 3.24 0.331 14 0.68 0.010 16 0.513 53 2.44 0.138 16 0.17 -18 0.455 20 0.459 139 25 0.470 30 0.480 35 0.470 40 0.477 45 0.463 50 0.470 57 0.491 0.097 0 0.840 19 9.03 0.669 0 1.96 0.010 (port #5) 2 0.840 20 9.6 0.546 2 2.12 0.039 4 0.837 25 11.22 0.806 4 2.12 0.059 6 0.826 35 9.39 1.01 6 2.00 0.020 8 0.811 45 5.98 0.671 8 1.73 0.069 10 0.786 55 3.69 0.222 10 1.43 0.039 14 0.673 63 1.87 0.243 12 1.00 0.020 16 0.531 66 1.26 0.228 14 0.71 0.088 18 0.466 16 0.17 -20 0.476 25 0.491 30 0.498 40 0.487 50 0.495 60 0.476 65 0.484 0.168 0 0.757 22 6.98 0.376 0 1.62 0.020 (port #6) 2 0.754 24 7.98 0.466 2 1.39 -4 0.747 26 8.24 0.355 4 1.16 0.039 6 0.729 30 8.96 0.703 6 0.99 0.049 8 0.698 40 8.50 0.363 8 0.69 0.039 10 0.601 50 7.64 0.449 10 0.37 0.382 12 0.462 60 8.19 0.497 12 0.13 -14 0.448 65 7.62 0.428 16 0.455 70 6.84 0.365 20 0.493 73 6.40 0.356 30 0.493 76 2.91 0.283 40 0.504 50 0.507 60 0.504 70 0.507 76 0.465 0.218 0 0.714 22 4.91 0.927 0 1.09 (port #7) 2 0.711 24 11.7 0.576 2 1.21 4 0.711 26 13.1 1.09 4 0.94 140 6 0.704 30 13.2 0.839 6 0.82 8 0.679 40 13.4 0.565 8 0.58 10 0.627 50 12.2 0.816 10 0.47 12 0.491 60 10.7 0.589 12 0.13 14 0.449 70 10.6 0.329 16 0.474 73 8.50 0.612 20 0.512 76 4.82 0.077 30 0.505 40 0.512 50 0.512 60 0.526 70 0.539 76 0.554 0.268 0 0.653 25 15.4 1.05 0 1.15 0.176 (port #8) 2 0.661 30 17.6 2.01 2 1.13 0.101 4 0.670 40 18.8 1.45 4 0.99 0.205 6 0.663 50 15.9 1.01 6 0.83 0.180 8 0.635 60 14.0 0.48 8 0.67 0.063 10 0.568 70 10.7 1.00 10 0.53 0.024 12 0.497 73 11.1 0.46 12 0.17 -14 0.462 76 5.21 1.02 14 0.13 -16 0.543 18 0.526 20 0.508 22 0.512 25 0.512 30 0.508 40 0.512 50 0.515 60 0.522 70 0.543 76 0.532 141 Table C.5: Experimental measurements of voidage and particle velocity, (dp = 1.84 mm, H = 0.280 m, U/U^ = 1.23, Q A / Q T = 0.0, Q s = 0.0177 m3/s, Q A = 0.00 m3/s) Particle diameter (dP) =1.84 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) = 1.23 Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.0 Spouting air flow rate (Qs) = 0.0177 m3/s Auxiliary air flow rate (QA) = 0.00 m3/s Experiment: 180 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/- (mm) (mm/s) +/- (mm) (m/s) +/-error error error 0.032 0 0.905 19 51.6 4.06 0 3.39 (port #2) 3 0.933 21 53.0 5.52 2 3.52 6 0.937 23 48.7 3.93 4 3.37 10 0.909 25 37.9 3.84 6 3.16 13 0.859 27 33.5 2.49 8 3.05 16 0.671 29 21.2 2.07 10 2.64 18 0.481 12 1.89 20 0.422 14 1.18 22 0.427 16 0.28 25 0.422 18 0.13 30 0.405 0.054 0 0.892 0.0075 18 32.9 2.53 0 3.91 (port #3) 2 0.898 0.0000 20 35.5 2.52 2 3.75 3 0.910 0.0080 22 33.0 2.34 4 3.71 4 0.906 0.0000 25 31.9 2.16 6 3.37 6 0.906 0.0080 30 22.6 1.17 8 2.65 10 0.888 0.0104 35 17.2 1.16 10 1.95 14 0.809 0.0231 40 10.2 0.90 12 1.35 16 0.683 0.0515 42 7.6 0.59 14 0.81 18 0.506 0.0712 16 0.17 20 0.419 0.0341 25 0.446 0.0329 30 0.451 0.0288 35 0.449 0.0313 40 0.434 0.0347 44 0.419 0.0247 0.076 0 0.864 0.0097 20 21.7 1.72 0 3.82 142 (port #4) 2 0.873 30 19.9 1.85 2 3.71 3 0.874 40 12.4 0.76 4 3.39 4 0.873 50 7.18 0.67 6 2.90 6 0.878 53 5.45 0.61 8 2.33 8 0.869 10 1.70 10 0.855 0.0299 12 1.06 14 0.766 0.0874 14 0.23 16 0.633 0.1741 16 0.17 18 0.458 0.0873 20 0.405 0.0747 25 0.425 0.0516 30 0.421 0.0284 40 0.422 0.0097 50 0.408 0.0031 55 0.388 0.0142 0.097 0 0.849 0.0063 20 11.3 1.28 0 3.61 (port #5) 2 0.856 0.0110 25 15.9 0.91 2 3.55 3 0.855 0.0071 30 15.5 1.33 4 3.21 4 0.858 0.0072 40 12.6 1.08 6 2.70 6 0.854 0.0062 50 9.10 0.62 8 2.09 10 0.827 0.0037 60 5.03 0.31 10 1.52 14 0.763 0.0633 63 3.81 0.75 12 0.99 16 0.551 0.0088 14 0.28 18 0.375 0.0415 16 0.25 20 0.337 0.0336 18 0.13 25 0.372 0.0648 30 0.386 0.0130 40 0.398 0.0235 50 0.405 0.0089 60 0.402 0.0182 65 0.397 0.0165 0.168 0 0.831 0.0103 22 7.91 0.32 0 2.46 (port #6) 2 0.834 0.0014 25 10.7 0.61 2 2.59 6 0.830 0.0012 30 11.9 0.98 4 2.49 10 0.810 0.0020 40 12.2 0.92 6 2.33 12 0.813 50 12.0 0.57 8 2.01 14 0.768 0.0084 60 12.3 1.00 10 1.63 16 0.699 0.0099 70 10.8 0.48 12 1.19 18 0.563 0.0294 76 10.1 0.87 14 0.91 20 0.433 0.0088 16 0.23 25 0.414 0.0099 18 0.17 30 0.452 0.0128 40 0.458 0.0117 143 50 0.462 0.0084 60 0.458 0.0052 70 0.456 0.0050 73 0.451 0.0022 76 0.461 0.0097 0.218 0 0.783 0.0122 22 10.6 0.75 0 2.11 (port #7) 2 0.781 0.0019 25 15.0 0.86 2 2.10 3 0.785 0.0076 30 16.6 0.68 4 2.00 4 0.781 0.0029 40 17.3 0.70 6 1.72 6 0.779 0.0042 50 16.1 0.40 8 1.48 10 0.763 0.0073 60 15.3 0.68 10 1.22 14 0.709 0.0140 70 15.2 0.81 12 0.97 16 0.624 0.0309 76 14.6 0.79 14 0.71 18 0.454 0.0322 16 0.17 20 0.390 0.0145 25 0.434 0.0160 30 0.458 0.0145 40 0.455 0.0062 50 0.455 0.0071 60 0.463 0.0083 70 0.476 0.0111 76 0.512 0.0142 0.268 0 0.734 22 8.51 1.55 0 1.80 (port #8) 2 0.726 25 21.6 1.71 2 1.91 4 0.697 30 21.1 1.36 4 1.85 6 0.693 40 22.0 1.85 6 1.71 10 0.702 50 18.8 0.74 8 1.45 14 0.668 60 18.5 0.79 10 1.19 16 0.643 70 16.2 0.96 12 0.88 18 0.523 76 17.0 1.14 14 0.61 20 0.448 16 0.28 25 0.423 18 0.17 30 0.445 40 0.482 50 0.477 60 0.490 70 0.519 76 0.473 144 Table C.6: Experimental measurements of voidage and particle velocity, (dp = 1.84 mm, H = 0.280 m, U/U T O = 1.20, Q A /Q T = 0.15, Q s = 0.0147 m3/s, Q A = 0.00260 m3/s) Particle diameter (dp) =1.84 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) = 1.20 Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.15 Spouting air flow rate (Qs) = 0.0146 m3/s Auxiliary air flow rate (QA) = 0.00260 m3/s Experiment: 1829 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/-error (mm) (mm/s) +/-error (mm) (m/s) +/-error 0.032 0 0.900 19 54.1 3.53 0 2.95 (port #2) 3 0.929 21 43.6 2.19 2 2.98 6 0.929 23 39.0 2.10 4 2.82 10 0.896 25 31.1 1.57 6 2.62 13 0.833 27 23.7 1.35 8 2.33 16 0.600 29 15.9 1.08 10 1.94 18 0.433 12 1.42 20 0.420 14 0.33 22 0.425 16 0.17 25 0.416 30 0.391 0.054 0 0.889 0.0017 18 33.9 3.52 0 3.31 (port #3) 2 0.898 20 37.3 2.51 2 3.31 4 0.896 0.0042 22 34.1 2.27 4 3.04 6 0.892 0.0037 25 30.0 1.13 6 2.64 10 0.860 0.0022 30 20.3 1.34 8 2.04 14 0.765 0.0550 35 13.0 0.73 10 1.32 16 0.540 0.0075 40 8.98 0.67 12 0.90 18 0.387 0.0156 42 7.22 0.72 14 0.17 20 0.380 0.0060 25 0.390 0.0014 30 0.397 0.0119 40 0.384 0.0171 42 0.370 0.0124 44 0.352 0.076 0 0.852 0.0013 19 21.8 1.38 0 3.13 (port #4) 2 0.856 20 21.7 1.82 2 3.11 145 4 0.864 0.0084 25 19.6 1.54 4 2.78 8 0.864 0.0239 30 16.5 0.88 6 2.30 10 0.840 0.0478 40 9.88 0.65 8 1.80 14 0.715 0.1819 50 5.46 0.51 10 1.22 16 0.577 0.2973 53 4.15 0.67 12 0.83 18 0.441 0.1414 14 0.17 20 0.373 0.0084 25 0.377 0.0082 30 0.397 0.0060 40 0.383 0.0039 50 0.387 0.0114 53 0.365 0.0407 0.097 0 0.840 0.0120 20 11.9 0.90 0 3.04 (port #5) 2 0.841 0.0030 25 13.7 0.80 2 3.03 4 0.849 0.0078 30 13.7 0.96 4 2.68 6 0.845 0.0038 40 10.6 0.53 6 2.30 10 0.821 0.0136 50 6.90 0.49 8 1.88 12 0.688 0.0900 60 3.98 0.45 10 1.26 14 0.556 0.1520 63 2.80 0.43 12 0.87 16 0.427 0.1048 14 0.23 18 0.430 0.0382 16 0.17 20 0.419 25 0.453 0.0320 30 0.432 0.0447 40 0.440 0.0516 50 0.403 0.0692 60 0.432 0.0487 65 0.387 0.0294 0.168 0 0.793 20 7.26 0.43 0 1.70 (port #6) 2 0.789 22 9.25 0.42 2 1.78 4 0.779 25 10.3 0.52 4 1.81 6 0.779 30 10.8 0.62 6 1.71 10 0.751 40 11.1 0.66 8 1.48 14 0.620 50 11.3 1.12 10 .1.24 16 0.466 60 10.0 0.51 12 0.99 18 0.424 70 9.82 0.51 14 0.72 20 0.395 76 7.95 0.49 16 0.17 25 0.459 30 0.477 40 0.448 50 0.462 60 0.441 70 0.448 146 76 0.441 0.218 0 0.742 20 10.5 0.65 0 1.73 (port #7) 2 0.746 22 12.7 0.78 2 1.68 4 0.746 25 13.6 1.09 4 1.59 6 0.746 30 14.8 0.81 6 1.38 10 0.723 40 14.7 0.86 8 1.11 14 0.637 50 14.0 0.56 10 0.89 16 0.524 60 13.5 0.63 12 0.68 18 0.411 70 12.9 0.67 14 0:23 20 0.423 76 12.4 1.03 16 0.13 25 0.478 30 0.450 40 0.470 50 0.470 60 0.481 70 0.450 76 0.481 0.268 0 0.669 22 11.9 1.40 0 1.52 (port #8) 2 0.667 25 16.5 1.57 2 1.54 4 0.669 30 20.6 0.97 4 1.51 6 0.684 40 19.6 0.68 6 1.35 10 0.694 50 17.2 0.88 8 1.11 14 0.609 60 15.6 0.60 10 0.86 16 0.502 70 15.4 0.43 12 0.63 18 0.449 76 14.3 0.76 14 0.33 20 0.433 16 0.13 25 0.469 30 0.490 40 0.486 50 0.490 60 0.494 70 0.526 76 0.514 147 Table C.7: Experimental measurements of voidage and particle velocity, (dp = 1.84 mm, H = 0.280 m, \J/Vm = 1.23, Q A / Q T = 0.26, Q s = 0.0123 m3/s, Q A = 0.00430 m3/s) Particle diameter (dp) =1.84 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.26 Spouting air flow rate (Qs) = 0.0123 m3/s Auxiliary air flow rate (QA) = 0.00430 m3/s 1.23 Experiment: 1857 Height (m) Radial Voidage profile position (mm) voidage +/-error Radial Particle velocity position in the annulus (mm) (mm/s) +/-error Radial Particle velocity position in the spout (mm) (m/s) +/-error 0.032 (port #2) 0 3 6 10 13 16 18 20 22 25 30 0.895 0.924 0.919 0.882 0.806 0.537 0.410 0.401 0.410 0.397 0.376 19 21 23 25 27 29 46.0 41.7 34.0 27.6 19.0 14.6 2.80 3.42 1.26 1.94 1.14 1.14 0 2 4 6 8 10 12 14 2.56 2.58 2.36 2.17 1.86 1.45 1.01 0.17 0.054 (port #3) 0 2 4 6 10 14 16 18 20 25 30 40 42 44 0.873 0.887 0.884 0.883 0.851 0.705 0.506 0.392 0.395 0.406 0.411 0.390 0.371 0.365 0.0063 0.0059 0.0021 0.0068 0.0191 0.0019 0.0242 0.0095 0.0080 0.0092 0.0054 18 20 22 25 30 35 40 42 33.0 31.3 31.4 28.1 17.9 11.0 7.04 5.06 1.97 2.41 3.24 1.84 1.13 0.85 0.70 0.51 0 2 4 6 8 10 12 14 2.82 2.70 2.43 2.06 1.54 1.04 0.74 0.17 0.076 0.870 0.0547 19 21.8 1.07120 1 2.59 148 (port #4) 2 0.902 20 20.6 0.70272 9 2 2.57 4 0.880 0.0437 25 18.1 1.39411 4 2.27 6 0.877 0.0336 30 15.6 1.02546 i 6 1.90 10 0.849 0.0050 40 8.47 l 0.80985 8 1.37 14 0.719 0.1096 50 4.15 J 0.33399 A 10 1.03 16 0:601 0.1470 53 3.68 0.38163 A 12 0.75 18 0.479 0.0318 4 14 0.17 20 0.449 0.1367 25 0.461 0.1133 30 0.460 0.1281 40 0.445 0.1296 50 0.432 0.1544 55 0.414 0.1360 0.097 0 0.837 0.0198 19 9.35 0.701 0 2.55 (port #5) 2 0.860 20 12.5 0.604 2 2.52 4 0.845 0.0203 25 12.8 1.054 4 2.25 6 0.844 0.0221 30 11.9 0.621 6 1.75 10 0.811 0.0024 40 9.29 0.601 8 1.40 14 0.670 0.1008 50 5.94 0.417 10 1.03 16 0.523 0.1045 60 3.48 0.163 12 0.74 18 0.411 0.0191 63 2.50 0.200 14 0.17 20 0.402 0.0920 25 0.424 0.0744 30 0.443 0.0691 40 0.439 0.0354 50 0.440 0.0582 60 0.434 0.0289 65 0.421 0.0324 0.168 0 0.759 18 5.27 0.455 0 1.6 (port #6) 2 0.763 20 7.95 0.322 2 1.7 4 0.759 22 9.07 0.408 4 1.6 6 0.751 25 9.41 0.553 6 1.4 10 0.708 30 10.6 0.779 8 1.2 14 0.472 40 8.74 0.508 10 1.0 16 0.417 50 9.31 0.523 12 0.7 18 0.387 60 8.35 0.601 14 0.2 20 0.442 70 8.12 0.488 16 0.1 25 0.485 76 6.63 0.436 149 30 0.459 40 0.472 50 0.459 60 0.485 70 0.442 76 0.426 0.218 0 0.694 0.0189 18 9.08 0.552 0 1.20 (port #7) 2 0.704 0.0030 20 11.5 0.468 2 1.20 4 0.705 0.0022 22 12.7 0.971 4 1.09 6 0.704 0.0030 25 13.3 0.902 6 0.98 10 0.687 0.0076 30 13.3 0.607 8 0.81 14 0.587 0.0392 40 13.3 0.871 10 0.64 16 0.486 0.0317 50 11.4 0.841 12 0.47 18 0.415 0.0055 60 11.3 0.623 14 0.13 20 0.410 0.0405 70 11.6 0.607 25 0.446 0.0387 76 10.6 0.645 30 0.447 0.0335 40 0.449 0.0327 50 0.458 0.0314 60 0.467 0.0351 70 0.466 0.0454 76 0.468 0.0344 0.268 0 0.626 20 12.0 1.01 0 1.14 (port #8) 2 0.618 22 16.9 1.05 2 1.15 4 0.613 25 18.0 1.25 4 1.12 6 0.630 30 19.3 0.83 6 0.98 10 0.618 40 16.9 1.32 8 0.79 14 0.475 50 14.2 1.00 10 0.58 16 0.445 60 12.4 0.87 12 0.28 18 0.390 70 12.7 0.60 14 0.13 20 0.433 76 10.6 0.90 25 0.449 30 0.435 40 0.445 50 0.445 60 0.471 70 0.462 76 0.471 150 Table C.8: Experimental measurements of voidage and particle velocity. (dp = 1.84 mm, H = 0.280 m, V/Vm = 1.23, Q A / Q T = 0.39, Q s = 0.0101 m3/s, Q A = 0.00650 m3/s) Particle diameter (dp) =1.84 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) = 1.23 Ratio of auxiliary air flow rate to total air flow rate (QA/QT) = 0.39 Spouting air flow rate (Qs) = 0.0101 m3/s Auxiliary air flow rate (QA) = 0.00650 m3/s Experiment: 18100 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/-error (mm) (mm/s) +/-error (mm) (m/s) +/-error 0.032 0 0.890 0.0211 17 50.9 5.63 0 2.11 (port #2) 2 0.911 0.0043 19 41.8 2 2.16 4 0.908 21 38.0 3.08 4 1.97 6 0.902 0.0121 23 27.1 2.16 6 1.70 10 0.848 0.0382 25 22.1 1.63 8 1.36 13 0.770 27 16.0 0.87 10 1.02 14 0.597 29 10.2 0.99 12 0.68 16 0.479 0.0649 14 0.17 18 0.425 0.0076 20 0.415 0.0102 24 0.399 0.0176 28 0.388 0.0294 32 0.356 0.0443 0.054 0 0.858 0.0060 18 35.5 3.12 0 2.36 (port #3) 2 0.872 0.0041 20 33.3 1.72 2 2.39 4 0.873 22 31.4 2.69 4 2.17 6 0.869 0.0010 25 26.4 1.91 6 1.78 10 0.828 0.0061 30 15.9 1.08 8 1.29 13 0.737 35 9.55 1.02 10 0.93 14 0.643 40 5.86 0.47 12 0.67 16 0.486 0.0404 42 4.32 0.29 14 0.17 18 0.401. 0.0169 20 0.398 0.0170 25 0.404 0.0117 30 0.397 0.0123 40 0.391 0.0247 42 0.364 0.0296 44 0.356 0.0149 151 0.076 0 0.831 0.0120 19 17.9 1.98 0 2.22 (port #4) 2 0.841 20 18.9 1.07 2 2.08 4 0.840 0.0015 25 17.4 0.89 4 1.88 6 0.835 0.0103 30 13.5 0.97 6 1.54 10 0.802 0.0284 40 7.85 0.71 8 1.24 14 0.652 0.1249 50 3.51 0.26 10 0.98 16 0.481 0.0801 53 2.91 0.34 12 0.67 18 0.388 0.0140 14 0.17 20 0.391 0.0509 16 0.13 25 0.403 0.0353 30 0.414 0.0360 40 0.411 0.0349 50 0.392 0.0195 53 0.394 0.0456 0.097 0 0.826 20 9.53 0.616 0 2.00 (port #5) 2 0.826 25. 11.8 0.548 2 1.99 4 0.818 30 11.1 0.729 4 1.79 6 0.814 40 8.44 0.590 6 1.52 10 0.772 50 5.71 0.348 8 1.23 14 0.554 63 2.21 0.197 10 0.96 16 0.423 66 1.04 0.195 12 0.68 18 0.369 14 0.17 20 0.387 25 0.419 30 0.419 40 0.399 50 0.411 60 0.365 65 0.380 0.168 0 0.724 18 4.72 0.355 0 1.23 (port #6) 2 0.719 20 7.10 0.433 2 1.32 4 0.719 22 8.63 0.546 4 1.32 6 0.711 25 9.49 0.691 6 1.18 10 0.669 30 9.11 0.638 8 1.03 14 0.451 40 8.21 0.463 10 0.86 16 0.405 50 7.92 0.562 12 0.62 18 0.393 60 7.69 0.412 14 0.23 20 0.414 70 7.20 0.517 16 0.13 25 0.443 76 6.67 0.586 30 0.460 40 0.458 50 0.456 152 60 0.447 70 0.451 76 0.440 0.218 0 0.660 18 8.05 0.581 0 1.02 (port #7) 2 0.664 20 11.4 0.807 2 1.03 4 0.660 22 12.9 1.041 4 1.00 6 0.664 25 12.0 0.624 6 0.87 10 0.652 30 11.7 0.869 8 0.74 14 0.515 40 10.7 0.787 10 0.58 16 0.452 50 10.3 0.768 12 0.38 18 0.419 60 9.39 0.651 14 0.13 20 0.440 70 9.90 0.545 25 0.456 76 9.25 0.692 30 0.440 40 0.460 50 0.460 60 0.471 70 0.492 76 0.479 0.268 0 0.592 20 12.7 1.32 0 0.88 (port #8) 2 0.566 22 17.4 1.08 2 0.91 4 0.566 25 17.7 1.25 4 0.90 6 0.570 30 17.1 1.45 6 0.81 10 0.583 40 16.7 1.23 8 0.66 14 0.516 50 14.6 0.88 10 0.54 16 0.454 60 11.7 0.66 12 0.28 18 0.422 70 11.8 0.71 14 0.13 20 0.426 76 12.3 0.50 25 0.441 30 0.454 40 0.422 50 0.454 60 0.449 70 0.485 76 0.485 153 Table C.9: Experimental measurements of voidage and particle velocity, (dp - 2.53 mm, H = 0.280 m, \]/Um = 1.20, Q A / Q T = 0.0, Q s = 0.0251 m3/s, Q A = 0.00 m3/s) Particle diameter (dP) = 2.53 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) = 1.20 Ratio of auxiliary air flow rate to total air flow rate (QA/QT ) = 0.0 Spouting air flow rate (Qs) = 0.0251 m3/s Auxiliary air flow rate (QA) = 0.00 m3/s Experiment: 250 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) . position position in the annulus position in the spout (mm) voidage +/- (mm) (mm/s) +/- (mm) (m/s) +/-error error error 0.076 0 0.879 25 24.0 3.11 0 3.09 0.080 (port #4) 3 0.884 28 32.2 1.71 4 3.40 0.010 6 0.894 33 32.5 1.94 8 3.08 0.216 10 0.889 38 30.2 2.27 12 2.24 0.118 15 0.855 43 23.7 2.24 14 1.67 20 0.728 48 20.0 1.89 16 1.32 0.216 25 0.366 53 13.5 1.66 18 0.85 30 0.368 20 0.62 0.010 35 0.420 40 0.422 50 0.407 55 0.387 0.168 0 0.786 0.0289 30 10.5 1.38 0 1.77 0.017 (port #6) 3 0.807 0.0071 35 17.3 0.81 2 1.89 0.017 6 0.810 0.0036 40 20.2 1.66 4 1.99 0.028 10 0.804 0.0023 50 20.1 1.52 6 1.98 0.028 15 0.780 0.0092 60 20.5 1.48 8 1.94 0.036 20 0.707 0.0177 67 20.2 1.31 10 1.82 0.040 25 0.434 0.0457 76 16.7 1.38 12 1.65 0.033 30 0.305 0.0202 14 1.43 0.052 35 0.353 0.0016 16 1.27 0.068 40 0.386 0.0164 18 1.04 0.040 50 0.405 0.0085 20 0.82 0.069 60 0.391 0.0234 22 0.63 0.030 70 0.404 0.0051 24 0.59 0.056 76 0.432 0.0115 0.268 0 0.740 0.0033 35 26.8 1.79 0 1.29 0.010 154 (port #8) 3 0.729 0.0075 40 35.0 3.79 4 1.46 0.029 6 0.717 0.0085 50 39.6 2.58 8 1.52 0.010 10 0.713 0.0093 60 35.6 2.24 12 1.42 15 0.732 0.0092 67 32.8 2.47 16 1.08 0.069 20 0.706 0.0197 76 33.6 1.91 20 0.71 0.029 25 0.573 0.0420 24 0.46 0.010 30 0.403 0.0332 26 0.45 0.049 35 0.534 0.0156 40 0.547 0.0028 50 0.557 0.0296 60 0.548 0.0266 70 0.540 0.0192 76 0.562 0.0234 155 Table C. 10: Experimental measurements of voidage and particle velocity, (dp = 2.53 mm, H = 0.280 m, U / U ^ = 1.20, Q A / Q T = 0.43, Q s = 0.0143 m3/s, Q A = 0.0110 m3/s) Particle diameter (dP) = 2.53 mm Bed height (H) = 0.280 m Ratio of superficial gas velocity to superficial gas velocity for minimum spouting (U/Ums) =1.20 Ratio of auxiliary air flow rate to total air flow rate (QA/QT ) = 0.43 Spouting air flow rate (Qs) = 0.0143 m3/s Auxiliary air flow rate (QA) = 0.0110 m3/s Experiment: 2543 Height Radial Voidage profile Radial Particle velocity Radial Particle velocity (m) position position in the annulus position in the spout (mm) voidage +/- (mm) (mm/s) +/- (mm) (m/s) +/-error error error 0.076 0 0.865 0.0328 27 12.3 1.26 0 1.52 0.029 (port #4) 3 0.879 0.0181 28 13.4 1.72 2 1.77 6 0.883 0.0166 33 15.8 1.23 4 1.88 0.049 10 0.883 0.0153 38 12.9 1.13 6 1.92 15 0.862 0.0195 43 10.9 1.06 8 1.87 0.010 20 0.773 0.0007 48 7.80 0.82 10 1.69 25 0.403 0.0132 53 5.50 0.50 12 1.50 0.049 30 0.335 0.0085 14 1.22 35 0.373 16 0.93 0.029 40 0.381 0.0309 18 0.73 50 0.352 0.0024 20 0.53 0.020 55 0.335 0.0234 0.168 0 0.706 0.0644 35 7.72 0.60 0 1.24 (port #6) 3 0.777 0.0024 40 10.6 0.58 2 1.31 6 0.766 0.0018 50 11.3 0.71 4 1.38 10 0.755 0.0018 60 12.0 1.19 6 1.38 15 0.738 0.0018 70 10.4 0.81 8 1.39 0.010 20 0.710 0.0060 76 9.44 1.09 10 1.32 25 0.603 0.0518 12 1.28 0.020 30 0.342 0.0118 14 1,14 35 0.379 0.0172 16 1.02 0.010 40 0.403 0.0060 18 0.90 50 0.408 0.0104 20 0.73 0.010 60 0.409 0.0352 22 0.59 70 0.401 0.0153 24 0.46 0.010 76 0.402 0.0313 26 0.45 0.268 0 0.664 0.0061 38 29.1 3.46 0 0.72 0.010 156 (port #8) 3 0.649 0.0008 40 33.1 2.46 2 0.76 6 0.639 0.0061 50 30.4 3.43 4 0.79 10 0.622 0.0024 60 26.2 2.58 6 0.84 15 0.624 0.0020 70 20.0 1.81 8 0.86 0.010 20 0.646 0.0063 76 17.4 1.84 10 0.89 25 0.614 0.0063 12 0.87 0.010 30 0.501 0.0016 14 0.84 35 0.485 0.0057 16 0.79 0.029 40 0.534 0.0022 18 0.70 50 0.485 0.0009 20 0.61 60 0.471 0.0191 22 0.49 70 0.492 0.0020 24 0.42 0.0098 76 0.541 0.0302 26 0.35 157 Table C. 11: Experimental measurements of spout radius (dp = 1.33 mm) Q A / Q T 0.0 0.15 0.28 0.43 Height Spout radius (m) (mm) 0.0 9.5 9.5 9.5 9.5 0.032 17.0 15.0 15.0 0.054 16.3 15.0 15.0 16.0 0.076 16.5 16.0 15.0 15.0 0.097 16.8 17.0 18.0 15.5 0.168 14.3 16.0 14.0 14.0 0.218 15.5 18.0 16.0 14.0 0.268 17.3 18.0 16.0 14.0 Table C. 12: Experimental measurements of spout radius (dP =1.84 mm) Q A / Q T 0.0 0.15 0.28 0.43 Height Spout radius (m) (mm) 0.0 9.5 9.5 9.5 9.5 0.032 18 17 17 17 0.054 18 17 17 16 0.076 18 18 18 18 0.097 19 18 18 18 0.168 20 17 18 19 0.218 19 18 18 19 0.268 20 19 18 19 Table C.13: Experimental measurements of spout radius (dP = 2.53 mm) Q V Q T 0.0 0.15 0.28 0.43 Height Spout radius (m) (mm) 0.0 9.5 9.5 9.5 9.5 0.032 29 30 29 26 0.054 24 22 23 23 0.076 24 24 24 26 0.097 24 23 22 25 0.168 26 25 25 28 0.218 27 25 24 25 0.268 28 25 26 31 158 Appendix D Experimental Data: Annular Differential Pressure Drop 159 <L> O o o o '-i <D co ^3 cd CD co N C \ t 00 h >t o\ in <N CS ' o o o o o o o o o o o o o VO o CO O o o o o © o C— © VO 00 CS Ov (N O N W h O N •*f •<*• VO vo vo © o* o © © o oo r- TJ - , - . o ^ - i -^ r «n vd o o o in •rr r~- r -h 00 00 h t-- oo oo r~-w M M iri IT) o o o o o o m W h G M O O H (N M (N T i h a N O © r-n r-* CS ^ CO "V- f- O CS Os O 5 r-n CN CN Ov r-H O r-l r-H " ! n m o M 00 O O CN CN vo oo oo oo oo oo m t> OA vo VO O O O —i CS CS o o o o o o cs <D o S i o o cd -a a cd cd > CD 60 -O CD 00 cd t-H CD CO cs *n CO C""~ CS 00 o o o VO 00 00 00 CO " O " o o o o o o o o o\ o\ oo H ifl «—i VO OV 00 O IT) >n in in vo t-~ r-o © o o o o ON I—I 00 f- CS CO ^ CO CO U-ii vdi 0 0O i - i o o\ ^ co cs cs cs cs r--t O W N (N h •^ t- oo c co co in o <—' co vo - M M M „ iri iri iri ^ vo • • • t—-o cs ^-i co cs r^ r—I r—I CS CS r-H VO Ov • ON '—' VO O O —1 r-H CS CS in in in • i — i CO vo g ^ 2; cs cs cs VO 00 00 00 00 00 in t— o> vo -—i vo o o o — cs cs o o o © o o 160 o o o -a c3 N g i n ON co oo IT) m h CN NO o o o o o o i n o o o 00 o o o o o o o o 00 r H ( \ | r H 0 \ 00 CN m NO O i n NO NO f - C- 00 o o o o o o i n co o o i n NO co "^ r i n r- r-' od t~- o o o oo i> 00 O ' t O h V I r~- in m o o ON ^ C N co o r--- o © ' 1—1 1—I r H r H fO CO i n 00 NO C~- >—i r H r H r H M N « m i n i n ^ ^ ^_ C N m' oo' C N C N co CN t~- ON >n oo co r H r H r H CN CN CO co >n • m m r-r H r H 00 cN CN CN CO NO t ON r H r H r H r H CN CN CO NO 00 OO 00 00 00 in r- ON NO H NO O O O r H CN CN O O O O O O CD O s o o . 5 1) I CN N a r H 00 NO NO 00 t \+ t O O " o o o o o o o o o o o o o o o o o o o o i n ON NO o r n c.-, o C N NO ci m r n [•"- t-~ c~- oo oo ON o o o o o o CN NO 00 NO NO O N O t> ON ON H o o o o o o o o o o o o o o o o o i n oo co i n o CN CN CO CO C N oo co m r n C N C N C N CO CO co i n t • co i n H CN CN CN CO CO >n 00 CO • 00 C N co co r H r H CO r H NO 00 00 00 00 00 m f - ON NO r n NO O O O ; H cN| CN o o o o o o 161 <L> O _ I ON ^ ^ o o C ed CO > CD co -O 0) o f CD CO c o c o o t - ^ r ^ H O N r - H i — I T — I T — i c o m c n ' — i f — i O O O O O O O - H o o o o o o o o o o o o o o o o o r - - N o o o c o r - - c o ^ r O N C S m o O r o O C N o o o o o o o o ON —< ON 00 O —1 »—< CN CN CO 00 O CO '—' '—1 •—' "—' CN CN O N O N O N T r t ~ - r ~ - O N c o O O O O O O V O O C - - 0 0 0 c s c N c s c - ~ r - m c s o o O O O O O O O T-H" CO C-- O Tt" ON NO ON o o T-* T-I cs cn co r- O 00 O O T-H ON ^ ^ ^ CN NO T - H CO T - H 5S o O r-, ID ON V • ON ^ 2 £ 2 m i n v i _ _ i n ^ • C l 00 NO O N O O O r t r t T - H ^ f N O N O O O O O C O O O O O O O O O O O T - H T - H C S C S o o o o o o o o CD o — ^ 'a « o cd s= <D a? CD cs N t - o c o t - - o o N i — oo c n o O N O N O v o i r i v o > — ' © • e s c o o ^ c o c o o o o o o o o o o o o o o o o o o © o o o o o o O C S O O C S O N C S C O - ^ -h O \ M i n t ^ O O \ i n T i - , d r m > n i n r - r - - o o © o © ' © ' © ' © o o co o o h t O N i n co co TJ-" i n i n NO ON C S ^ r - H T - H T - l T - H T - H C S C S O N o r - ^ r o o N t - - r - -o o o r - N o o o o r - r ^ c s o m r - o c s m m o © © © © o o o cs •^ j" oo o co NO i n cs >—i H cs cs co -vT m in cs r - • NO m co • -<?r oo H co • m cs ^ T - i T - i c s c s ^ ^ r m oo o co NO NO cs H H cs cs co TJ - i n N O N O 0 0 0 0 C O 0 0 0 0 0 0 c o m t > O N c o N O ^ N O O O O O T ^ T ^ C S C S o © o o o o o o 162 CD o c CD T3 o S3 CD WH CD S5 CO C N <—i 00 00 CN m 00 CN 00 CO NO o T f o o m CN O O O O o o Tt" o o oo i n o o o o o o o o o o o o o C N N O r H C O T t " C O C N N O m m N O N O N O C - - o o o o o o o o o o o o o o m O T T O N i n N O iri NO r-- oo oo o co r-H r—I r—I r—i T—t CN CN CN r - ~ < - H o r - c N o o o i n O N O m i n o o m O N C N m O N N O O O t ^ o r - o o r - H O O O O C N O O N O O O N C O r H C N c N c N c o T r ^ r m 00 C N NO O 00 ON ON <—I C N C N C O C N C O TT ON '—< C ON O '— 1 ON r H f N C N C N c o ^ - T j - f N r - H C N C N C N c o c o ^ J - m »n m r - O t - 00 • ON ON • I , — I , — i C O , — ( , — ! « / " > N O N O O O O O C O O O O O O O c o m c ~ - O N c o N O r H N O O O O O r - r H C N C N o o o o o o o o CD o c CD T3 o o <D S3 CD CD S5 P2 la PH & CN ON NO ^ m CN Tt - CN ON CO CN CO CN ~ O O " o o oo o o o o o o o o o ir> co NO r-CO NO o o o o o o o o o o o o o o c o T f o o c N O t ~ - i n 00 NO '--i *-H ^J" r—I O CN m N O t - - t - - r ~ - o o o N O N o o o o © o o o r ^ o o c o T t - ' - H O o o c o NO oo o O i—< co i n NO i — I - H C N C N C N C N C N C N t ~ - O 0 N P - ~ o i n i n r H o o c N C ~ ~ O r - T r o o r - m N o m o c o N O r H © O © O © O r n ' T t - c N t - ~ o o o r - r - ~ C N c N c o c o c o T f - T t " m m c N c o ^ O c o T r - ^ r m N o C N C O C O C O T f T T ^ N O i n • M h t~-^ CO CO CO O NO l > ON Tt" Tt - *n i n i n T T , , CN r-r oo t-- o CO CO CO Tt" m m m NO r- r-T T m m N O N O O O O O C O O O O O O O c o m t ~ - O N c o N O r H \ o O O O O; r-1 r-1 CN CN © ' © ' © ' © ' o © o © 163 C O O O O I  < a co" i i C CN CD >n C CN CD O In 3 o oo I  cd CD C O a &, O O o Q I  CD H I - . a C O C O CD In a PH _r 7d CN i—I CD O c CD -a o o T3 e cd CD CD O CN N ON 00 CN r- i n ON o o o o o m NO o o ON m i n CN NO o o o o o o - -C~- r-H i n co o o o o" o o co d^r CN t • NO ON ON O t j - O ' — N O N O O N O N ' — ' o o o o © © o o r-H NO c-^ co r—i oo t oo • r t - o n " C O N O O N C N i n ^ r ° ° r - H r - H r - H r - H C N C N r-H m ON r-H co co i n co "fr CO CN H T-H CN ON CN CN O ~ r-n' NO NO r-" r^" o C— ON ' C N NO NO 00 C N co r r m I ^ O O O C O ^ H N O O O O O C N o © ' — 1 C N co m Q Q ^ r - H r - H r - H r - H r - H r - H p °. 00 "fr t - ON 00 C N C O NO m ON O — C N co "fr m o m c N c N c N N o r - r ~ -r ^ ^ ^ r - H r - H ^ r - H r - H o o v o O r - H i n i n N O o o o d O r H ^ r o T j - i n ^ ^ r - r - H r - H r - H r - H r - H c N ^ N o r ^ c o o o o o o o C O m t - O N C O N O ' - H N O O O O O r - H r - ( C N C N o o o o © o o o CD o s i o o cd c cd cd o -o CD I H <D > cd O P< Pk CN CO 00 o o c- r - oo o "fr C O ON ON C N o m oo r - co NO o H o o o o o o o o o o o © © N O C - - O O O O N O ^ H C N O o ^ r c N o o N O O N N o c - -r o ^ i - m i n N o r ^ o o o N o o o o © o o © o r - o t ~ - O N i n i n i n ^ C N i n NO oo C N -rr r~ O O ^ r - H r - H r - H C N C N C N c N o o N o m T r o N o o ' ^ r O O r - H C O r - H O O T T m O CO CN CN r-H CO r-H- © ' v O o N O O " f r c N m r o r r ^ f - ' O ^ H C N c o ^ - m N o ^ ^ r - H r - H r - H r - H ^ H r - H O r - ^ r - H C O 0 0 N 0 C O C O r - . ^ H C N C N C N - * m N O ^ r - H r - H r - r - H r - r ^ r - H O r-H N O m r r ON <—1 1 CN CO "fr r-H r-H ^H r-H r-H CN "fr i n NO ^ t ~ - N O C O O C O C N " ^ -i r i O T - H C N c o r l - i n N O 0 > r - H r - r - H r - . r - H ^ H r - H O O N O o i n c ~ ~ N O c o m r ~ , ' o ^ H C N c o ^ r m N o ^ r - H r - H r ^ r - H r - H r - H r - H c N - ^ - N o r - c o o o o o o o c o m r - O N c o N O r - n N o 0 0 0 0 < - i i — ' C N C S o o o o o o o o 164 N? ON CD o § o o cd a cd CD SP CD p> s CO CN N CO o r-o o co i n o o o o ON ON 00 O t~-T f O O ON ON T f T f m o o o o o o o o o o o o c N t - - T f O N O N i n t - - T f C N m c o N D C N C N O N O i r > i r ) N O N O r - O O O N O N o o o o o o o o 00 00 O O t"- T f 00 T f T f m oo ON o co i n r~ '—1 •—1 '—' '—' CN CN CN CN 00 i n i n tr- in NO 00 i n t CO co t ' oo o t~- r-' ON CN ON ON t~- CO • - H c N c N c o c o T t - i n N O i n o o o c N o o o o r - T f r n c N C N c o c o T f i n N O NO rH o T f O O ' O N CO r H C N c o c o T f i n m N O r n c N C N c o c O T f i n N O r - H C O O N r - i o o o r ~ - c N C N C N C N c O T f T f i n N O c N T f N o r - - c o o o o o o o c o » n r ~ - O N c o N O ' — I N O O O O O r H r H C N C N o o o o o o o o CD o c CD o o Is .2 CO -rt -a eS C •*"< cd > ™ CD C/3 T-) CD 00 cd 1 H CD Si O CN N B T f T f CN m o o o o o CO T f o o Tt" ON NO O l > NO T f i n f - r n oo N O i n co C N o o o o o o o o o o o o © © t ~ ~ c o r H N O c o i n T f o o O r H l > O N r H O N N O t > c ~ ~ - t ~ - t ~ ~ r ~ - o o o o o N O N o © © © © o o © r H C O O N N O r H ' r J - - r J - 0 O o o rn' cN co i r i r-~- [--' C N C N C N C N C N C N C N C N r - - i > m o o o o N C N C - ^ o o r - N o o o c N O N o o r ~ C N r H O m r H C N C - ~ TT CO 00 NO CN ON NO Tt" © CO O rn' rn' O O © N O f ~ c o N o r - - N O c o i r i CO CO T f T f T f i n NO NO NO NO CN TT ON • CO IT) C O C O T f T f T f ^ N O N O , „ i n i n _ m _^ NO • co • NO • T f i n C O ^ T f ^ T f ^ N O N O r H C O r - l T f r H i n r — i r H m i n _^ ^ i n _^ • T f r- P~- i n • T f i g r T T f T f T f r n C N v o C O T f r H r H r H r n N O r H i n i n t ~ - i n c o t ~ - _ c ~ - c o -C O C O T f T f t ^ m N O ^ f C N T f N O t " - - C O 0 0 0 0 0 0 C O i n t ^ O N C O N O r H N O O O O O — i m c N C N o o o o o © o o 165 Appendix E Computer Program Used for Calculation of Cross-Sectional Average Spout Voidage, Mass Flow Rates and Superficial Gas Velocity 166 C D e n i s P i a n a r o s a C C T h i s p r o g r a m uses the d a t a f r o m the v o i d a g e a n d p a r t i c l e v e l o c i t y p r o f i l e s to C c o m p u t e s o l i d s m a s s f l o w rates i n the s p o u t a n d a n n u l u s u s i n g 5 - p a n e l N e w t o n - C o t e s C i n t e g r a t i o n a n d s p l i n e i n t e r p o l a t i o n . T h i s m e t h o d is a l s o u s e d to c o m p u t e the c r o s s -C s e c t i o n a l a v e r a g e s o f v o i d a g e a n d p a r t i c l e v e l o c i t y i n the s p o u t a l o n g the b e d . C S u p e r f i c i a l g a s v e l o c i t y i n the a n n u l u s a l o n g the h e i g h t o f the b e d is c o m p u t e d f r o m the E r g u n C e q u a t i o n b y a root f i n d i n g s u b r o u t i n e u s i n g M u l l e r ' s m e t h o d . C C I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) E X T E R N A L F U N K , F U N K 2 , F U N K M , F K E P S A , F K V P A , F A S V E L D I M E N S I O N R O O T ( l O l ) C O M M O N / B L K A / X 1 ( 4 0 0 ) , X 2 ( 4 0 0 ) , Y 1 ( 4 0 0 ) , Y 2 ( 4 0 0 ) , N 1 , N M 1 , N 2 , N M 2 C O M M O N / B L K B / Q Y 1 ( 4 0 0 ) , R Y 1 ( 4 0 1 ) , S Y 1 ( 4 0 0 ) C O M M O N / B L K C / Q Y 2 ( 4 0 0 ) , R Y 2 ( 4 0 1 ) , S Y 2 ( 4 0 0 ) C O M M O N / B L K D / X 3 (400) , Y 3 ( 4 0 0 ) , N 3 , N M 3 C O M M O N / B L K E / Q Y 3 ( 4 0 0 ) , R Y 3 (401) , S Y 3 (400) C O M M O N / E R G U N / P l , P 2 , D P D Z c set e r r o r c r i t e r i o n to b e m e t D A T A E P S , N R / 1 . D - 7 , 1 / c o p e n p r i n t f i l e a n d d a t a f i l e O P E N ( U M T = 1 2 , F I L E = 7 5 0 6 . d a t \ S T A T U S = ' u n k n o w n ' ) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c p r o p e r t i e s o f s o l i d s a n d c o n s t a n t s P I = 4 . * A T A N ( 1 . ) R H O P = 2 4 6 3 . ! k g / m 3 p a r t i c l e d e n s i t y D P = 2 . 5 3 ! ( m m ) p a r t i c l e d i a m e t e r E P S O = 0 . 4 1 1 ! l o o s e - p a c k e d - b e d v o i d a g e c enter f i t ted p a r a m e t e r s p i a n d p 2 ( for E r g u n E q . ) f o r these p a r t i c l e s P l = 0 . 2 1 9 4 9 P 2 = 0 . 6 7 8 8 6 c c c o m p u t e v o i d a g e ra t ios f l a n d f2 f o r the l o o s e - p a c k e d b e d c F 0 2 = ( l . - E P S O ) / E P S O * * 3 F 0 1 = F 0 2 * ( l . - E P S O ) c c c o m p u t e v a l u e s o f C l a n d C 2 F O R I N T E R S T I T I A L G A S V E L O C I T I E S i n the p a c k e d b e d . c C 1 = P 1 / F 0 1 C 2 = P 2 / F 0 2 c 167 c en ter d i f f e r e n t i a l p r e s s u r e d r o p f o r th is b e d l e v e l D P D Z = . 6 9 9 ! ( m m H 2 0 ) / m m ) N l = 1 4 ! n o . o f p o i n t s f o r v o i d a g e N 3 = 7 ! n o . o f p o i n t s f o r a n n . v e l o c i t y N 2 = 1 3 ! n o . o f p o i n t s f o r spt. v e l o c i t y N M 1 = N 1 - 1 N M 2 = N 2 - 1 N M 3 = N 3 - 1 c i n p u t d a t a f o r v o i d a g e a n d p a r t i c l e v e l o c i t y R E A D ( 1 2 , * ) ( X 1 ( I ) , I = 1 , N 1 ) ( rad ia l p o s i t i o n d a t a f o r v o i d ( m m ) R E A D ( 1 2 , * ) ( Y 1 ( I ) , I = 1 , N 1 ) I rad ia l v o i d a g e d a t a R E A D ( 1 2 , * ) ( X 3 ( I ) , I = 1 , N 3 ) I radia l p o s i t i o n d a t a f o r a n n . v e l . ( m m ) R E A D ( 1 2 , * ) ( Y 3 ( I ) , I = 1 , N 3 ) I radia l a n n u l a r v e l . d a t a ( m m / s ) R E A D ( 1 2 , * X X 2 ( I ) , J = 1 , N 2 ) I radia l p o s i t i o n d a t a f o r sp . v e l . ( m m ) R E A D ( 1 2 , * ) ( Y 2 ( I ) , I = 1 , N 2 ) I radia l spout v e l . d a t a (m /s ) c set i n t e g r a t i o n l i m i t s c A = X l ( l ) ( lower i n t e g r a t i o n l i m i t (centre o f b e d ) A = 0 . ( lower i n t e g r a t i o n l i m i t (centre o f b e d ) B = 2 4 . (upper int . l i m i t ( s p o u t - a n n u l u s in ter face) C = 3 0 . ( lower i n t e g r a t i o n l i m i t ( s p o u t - a n n u l u s in te r face D = 7 6 . (upper int . l i m i t (bed w a l l ) c set l i m i t s f o r l o c a l v o i d a g e f o r c a l c u l a t i n g s u p e r f i c i a l g a s v e l o c i t y . C C = 4 0 . D D = 6 0 . Q AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA C c c o m p u t e the s q u a r e o f the r a d i u s o f the a n n u l u s f o r c a l c . a r e a a v e r a g e s c R A N N 2 = D D * D D - C C * C C I (mm2) c c p r i n t ou t d a t a i n tab le f o r m a t c W R I T E ( * , 1 4 5 ) D P , Z 145 F O R M A T ( / / 1 0 x , ' D A T A A N D A N A L Y S I S F O R P A R T I C L E S O F D I A M E T E R ' , F 4 . 2 , ' m m , / 1 0 x , ' A T B E D + L E V E L # ' ,F2.0 / / / ) W R I T E ( * , 1 4 8 ) 148 F O R M A T ( ' R A D . P O S . ' , 5 X ) , V O I D ' , 1 0 X / P O S . ' , 1 0 X , ' S P V E L ' , l O X . T O S . ' , l O X . ' A N N V E L ' / / ) D O 149 i = l , 2 0 W R I T E ( * , 150)x 1 (i) ,y l ( i ) , x 2 ( i ) , y 2 ( i ) , X 3 ( I ) ,Y3 (I) 150 F O R M A T ( f 5 . 2 , 5 ( 5 x , f 9 . 5 ) ) 149 C O N T I N U E c c a r r y out s p l i n e i n t e r p o l a t i o n f o r v o i d a g e a n d v e l o c i t y d a t a 168 C A L L SPLINE(X1,Y1,N1 ,QY1,RY1,SY1) Isp l ines f o r v o i d a g e C A L L SPLINE(X2 ,Y2 ,N2 ,QY2,RY2,SY2) Isp l ines f o r spout v e l o c i t y C A L L SPLINE(X3,Y3,N3 ,QY3,RY3,SY3) Isp l ines f o r a n n u l a r v e l o c i t y c c c o m p u t e the s o l i d s f l o w r a t e i n the s p o u t c W R I T E ( * , 1 5 1 ) A , B 151 F O R M A T ( / ' T H E R A D I A L L I M I T S F O R T H E S P O U T A R E : ' , F 3 . 1 , 2 X , ' A N D \ F 5 . 2 ) C A L L A D N C ( F U M C , A , B , E P S , S U M , N P O I N T ) W R I T E ( * , * ) S U M I ( m m 3 / s ) F L O S P T = S U M * 2 . * P I * R H O P / l . d 9 W R I T E ( * , 1 6 0 ) F L O S P T 160 F O R M A T ( ' T H E S O L I D S F L O W R A T E I N T H E S P O U T IS ',F9.3,'kg/s') c c c o m p u t e the s o l i d s f l o w r a t e i n the a n n u l u s c W R I T E ( * , 1 5 2 ) C , D 152 F O R M A T ( / ' T H E R A D I A L L I M I T S F O R T H E A N N U L U S A R E : ' ,F5.2,2X,'AND ',F5.2) C A L L A D N C ( F U N K ^ , C , D 3 P S , S U M 2 , N P O r N T 2 ) WRITE (* , * )SUM2 F L O A N N = S U M 2 * 2 . * P I * R H O P / l . D 9 W R I T E ( * , 1 6 5 ) F L O A N N 165 F O P J v I A T ( ' T H E S O L I D S F L O W R A T E I N T H E S P O U T IS ' ,F9 .3 , 'kg/s') c w w w w w w w w w v w w w w w w v c c c o m p u t e s u p e r f i c i a l g a s v e l o c i t y i n the a n n u l u s u s i n g E r g u n ' s e q u a t i o n c c - ( d p / d z ) = p l x U + p 2 x U A 2 c c c o m p u t e a r e a a v e r a g e s o f v o i d a g e a n d a n n u l a r p a r t i c l e v e l o c i t y f o r the c a n n u l u s u s i n g the n e w t o n - c o t e s i n t e g r a t i o n s u b r o u t i n e c C A L L A D N C ( F K E P S A , C C , D D , E P S , S U M E P S , N P ) A V G E P S A = S U M E P S * 2 . / R A N N 2 lave , v o i d a g e i n a r m . C A L L A D N C ( F K V P A , C C , D D > E P S , S U M V P A , N P 2 ) A V G W A = S U M W A * 2 . / R A N N 2 / 1 0 0 0 . ! (m/s ) a v e . par t . v e l . i n a n n . c c c o m p u t e v o i d a g e ra t ios f l a n d f 2 w i t h the a v e r a g e v o i d a g e i n the a n n u l u s c F2=( 1. - A V G E P S A ) / A V G E P S A F 1 = F 2 * ( 1 . - A V G E P S A ) / A V G E P S A c c c o m p u t e n e w v a l u e s o f P I a n d P2 f o r e r g u n e q u a t i o n c P1=F1*C1 169 P 2 = F 2 * C 2 c c c a l l s u b r o u t i n e , m u l l e r , to s o l v e f o r U ( in terst i t ia l g a s v e l o c i t y ) c i n E r g u n E q . f o r a s ta t ionary l o o s e - p a c k e d b e d . C A L L M U L L E R (FUNKM,0.001,3.,1.D-1,NR,EPS,ROOT,IROOT) I F ( I R O O T . E Q . 0) W R I T E ( 8 , * ) ' N O R O O T S F O U N D ' A T R V E L = R O O T ( l ) ! (m/s) in ters t i t ia l g a s v e l o c i t y i n a n n u l u s c c c a l c u l a t e s u p e r f i c i a l g a s v e l o c i t y i n the a n n u l u s c c A N G S V E L = A V G E P S A * ( A I R V E L + A V G V P A ) WRITE(*,169) 169 F O R M A T ( / / / 5 x , ' R E S U L T S O F T H E C O M P U T A T I O N O F T H E S U P E R F I C I A L G A S V E L O C I T Y T H R O U G H T H E A N N U L U S A T T H I S B E D L E V E L ' ) W R I T E ( * , 1 7 0 ) A V G E P S A , A V G V P A , A r R V E L , A N G S V E L , D P D Z 170 F O R M A T ( / / 5 X , ' A V E R A G E V O I D A G E I N T H E A N N U L U S : \ F 6 . 4 / + 5 X , ' A V E R A G E P A R T I C L E V E L O C I T Y I N T H E A N N U L U S : ' , F 6 . 4 , ' m / s ' / + 5 X , T N T E R S T I T I A L G A S V E L O C I T Y : ' , F 6 . 4 , ' m / s ' / + 5 X , ' S U P E R F I C I A L G A S V E L O C I T Y : ' , F 6 . 4 , ' m / s ' / + 5 X / D I F F E R E N T I A L P R E S S U R E D R O P : ' , F 6 . 4 , ' m m H 2 0 / m m ' / ) QAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA C c c a l c u l a t e a v e r a g e s p o u t v o i d a g e a n d p a r t i c l e v e l o c i t i e s c R S P T 2 = B * B - A * A ! ( m m 2 ) w r i t e ( * , * ) b C A L L A D N C ( F K E P S A , a , b , E P S , S U M 3 , N P O I N T 3 ) A V G S P V D = S U M 3 * 2 . / R S P T 2 W R I T E ( * , 2 0 0 ) A V G S P V D 2 0 0 F O R M A T C A V E R A G E S O U T V O I D A G E = ' ,F9 .4 ) C A L L A D N C ( F A S V E L , A , B , E P S , S U M 4 , N P O I N T 4 ) A V G S P V E L = S U M 4 * 2 . / R S P T 2 / 1 0 0 0 . ! (m/s) W R I T E ( * , 2 1 0 ) A V G S P V E L 2 1 0 F O R M A T C A V E R A G E S P O U T P A R T I C L E V E L O C I T Y (m/s ) = ' , F9 .4 ) S T O P E N D ********************************* D O U B L E P R E C I S I O N F U N C T I O N F A S V E L ( X ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c f u n c t i o n c a l l e d b y s u b r o u t i n e A D N C f o r c o m p u t i n g the a r e a a v e r a g e p a r t i c l e c v e l o c i t y i n the S P O U T c 170 E X T E R N A L F Y 2 F A S V E L = F Y 2 ( X ) * 1000 . * X ! ( m m ) R E T U R N E N D $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ F U N C T I O N F Y 1 ( Z ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c s p l i n e i n t e r p o l a t i o n f u n c t i o n c a l l e d b y s u b r o u t i n e S P L I N E f o r V O I D A G E d a t a C O M M O N / B L K A / X 1 ( 4 0 0 ) , X 2 ( 4 0 0 ) , Y 1 ( 4 0 0 ) , Y 2 ( 4 0 0 ) , N 1 , N M 1 , N 2 , N M 2 C O M M O N / B L K B / Q Y 1 ( 4 0 0 ) , R Y 1 ( 4 0 1 ) , S Y 1 ( 4 0 0 ) I F ( Z L T . X l ( l ) ) T H E N 1=1 c W R I T E ( * , 5 ) Z c5 F O R M A T ( / ' W A R N T N G - ' , D 1 0 . 3 , ' IS O U T S I D E I N T E R P O L A T I O N R A N G E ' / ) E L S E I F ( Z . G T . X 1 ( N 1 ) ) T H E N I = N M 1 c W R I T E ( * , 5 ) Z E L S E 1=1 J = N 1 2 0 K = ( I + J ) / 2 I F ( Z . L T . X 1 ( K ) ) J = K I F ( Z . G E . X 1 ( K ) ) I = K I F (J . G T . 1+1) G O T O 2 0 E N D I F D X = Z - X 1 ( I ) F Y 1 = Y 1 ( I ) + D X * ( Q Y 1 ( I ) + D X * ( R Y 1 ( I ) + D X * S Y 1 ( I ) ) ) R E T U R N E N D F U N C T I O N F Y 2 ( Z ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c s p l i n e i n t e r p o l a t i o n f u n c t i o n c a l l e d b y s u b r o u t i n e S P L I N E f o r p a r t i c l e c v e l o c i t y d a t a i n the S P O U T c C O M M O N / B L K A / X 1 ( 4 0 0 ) , X 2 ( 4 0 0 ) , Y l (400) , Y 2 ( 4 0 0 ) , N 1 , N M 1 , N 2 , N M 2 C O M M O N / B L K C / Q Y 2 ( 4 0 0 ) , R Y 2 ( 4 0 1 ) , S Y 2 ( 4 0 0 ) I F ( Z . L T . X 2 ( l ) ) T H E N 1=1 c W R I T E ( * , 5 ) Z c5 F O R M A T ( / ' W A R N I N G - ' , D 1 0 . 3 , ' IS O U T S I D E I N T E R P O L A T I O N R A N G E ' / ) E L S E I F ( Z . G T . X 2 ( N 2 ) ) T H E N I = N M 2 c W R I T E ( * , 5 ) Z E L S E 171 1=1 J = N 2 2 0 K = ( I + J ) / 2 I F ( Z . L T . X 2 ( K ) ) J = K I F ( Z . G E . X 2 ( K ) ) I = K I F (J G T . 1+1) G O T O 2 0 E N D I F D X = Z - X 2 ( I ) F Y 2 = Y 2 ( I ) + D X * ( Q Y 2 ( I ) + D X * ( R Y 2 ( I ) + D X * S Y 2 ( I ) ) ) R E T U R N E N D F U N C T I O N F Y 3 ( Z ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c s p l i n e i n t e r p o l a t i o n f u n c t i o n c a l l e d b y s u b r o u t i n e S P L I N E f o r p a r t i c l e c v e l o c i t y d a t a i n the A N N U L U S c C O M M O N / B L K D / X 3 (400) , Y 3 ( 4 0 0 ) , N 3 , N M 3 C O M M O N / B L K E / Q Y 3 ( 4 0 0 ) , R Y 3 ( 4 0 1 ) , S Y 3 ( 4 0 0 ) I F ( Z . L T . X 3 ( l ) ) T H E N 1=1 C W R I T E ( * , 5 ) Z C 5 F O R M A T ( / ' W A R N I N G - ' , D 1 0 . 3 , ' IS O U T S I D E I N T E R P O L A T I O N R A N G E ' / ) E L S E I F ( Z . G T . X 3 ( N 3 ) ) T H E N I = N M 3 C W R I T E ( * , 5 ) Z E L S E 1=1 J = N 3 20 K = ( I + J ) / 2 I F ( Z . L T . X 3 ( K ) ) J = K I F ( Z . G E . X 3 ( K ) ) I = K I F (J . G T . 1+1) G O T O 2 0 E N D I F D X = Z - X 3 ( I ) F Y 3 = Y 3 ( I ) + D X * ( Q Y 3 ( I ) + D X * ( R Y 3 ( I ) + D X * S Y 3 ( I ) ) ) R E T U R N E N D D O U B L E P R E C I S I O N F U N C T I O N F U N K ( X ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c f u n c t i o n c a l l e d b y s u b r o u t i n e A D N C f o r i n t e g r a t i o n o f s o l i d s f l u x c [ ( l - e o ) * u * r ] f o r the S P O U T c E X T E R N A L F Y 1 , F Y 2 F U N K = ( 1 . - F Y 1 ( X ) ) * F Y 2 ( X ) * 1 0 0 0 . * X ! m m A 2 / s c W R I T E ( * , 150)x , fy 1 (x ) , fy2(x ) 172 c l 5 0 F O R M A T ( 3 ( 5 x , f 9 . 5 ) ) R E T U R N E N D ******************************************************** D O U B L E P R E C I S I O N F U N C T I O N F U N K 2 ( X ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c f u n c t i o n c a l l e d b y s u b r o u t i n e A D N C f o r i n t e g r a t i o n o f s o l i d s f l u x c [ ( l - e o ) * u * r ] f o r the A N N U L U S c E X T E R N A L F Y 1 . F Y 3 F U N K 2 = ( 1 . - F Y 1 ( X ) ) * F Y 3 ( X ) * 1 . * X ! m m A 2 / s c W R I T E ( * , 150 )x , fy 1 (x) , fy3 (x) c l 5 0 F O R M A T ( 3 ( 5 x , f 9 . 5 ) ) R E T U R N E N D ****************************************************************************** ****************************************************************************** D O U B L E P R E C I S I O N F U N C T I O N F K E P S A ( X ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c f u n c t i o n c a l l e d b y s u b r o u t i n e A D N C f o r c o m p u t i n g the a r e a a v e r a g e v o i d a g e i n c the A N N U L U S c E X T E R N A L F Y 1 F K E P S A = F Y 1 ( X ) * X ! ( m m ) R E T U R N E N D ****************************************************************************** ****************************************************************************** D O U B L E P R E C I S I O N F U N C T I O N F K V P A ( X ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c f u n c t i o n c a l l e d b y s u b r o u t i n e A D N C f o r c o m p u t i n g the a r e a a v e r a g e p a r t i c l e c v e l o c i t y i n the A N N U L U S c E X T E R N A L F Y 1 F K V P A = F Y 3 ( X ) * X ! ( m m ) R E T U R N E N D ****************************************************************************** ****************************************************************************** 173 F U N C T I O N F U N K M ( X ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) c c F U N C T I O N C A L L E D B Y T H E S U B R O U T I N E M U L L E R T O S O L V E F O R U I N T H E E R G U N E Q U A T I O N c C O M M O N / E R G U N / P 1 , P 2 , D P D Z F U N K M = X * ( P 1 + P 2 * X ) - D P D Z R E T U R N E N D S U B R O U T I N E A D N C ( F , A , B , E P S , S U M , N ) I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) C C T H E N E W T O N - C O T E S 4 - P A N E L M E T H O D A P P R O X I M A T E S T H E I N T E G R A L O F 4 N E I G H B O U R I N G C E Q U A L - W I D T H S T R I P S A S T H E A R E A U N D E R T H E F O U R T H - O R D E R P O L Y N O M I A L W H I C H C P A S S E S T H R O U G H T H E 5 P O I N T S ( X i , Y i ) . . . ( X i + 4 , Y i + 4 ) C R E A T E D B Y T H E I N T E R S E C T I O N S C O F T H E S T R I P L I N E S A N D T H E Y = F ( X ) C U R V E . C C C A R G U M E N T S c C A : L O W E R L I M I T O F I N T E G R A T I O N C B : U P P E R L I M I T O F I N T E G R A T I O N C S U M : T O T A L A R E A B E T W E E N L I M I T S O F I N T E G R A T I O N C N : N U M B E R O F P O I N T S U S E D T O O B T A I N T H E A R E A C X I : L . H . S . L I M I T O F I N T E G R A T I O N C H : A R R A Y O F S T R I P W I D T H S O F A T E A C H L E V E L C T O L : A R R A Y O F T O L E R A N C E F O R E A C H L E V E L U S E D T O D E C I D E I F T H E E S T I M A T E C O B T A I N E D B Y H A L V I N G 4 P A N E L S A T L E V E L i IS O F A C C E P T A B L E A C C U R A C Y C T O I N C O R P O R A T E I N T O A R E A C S R : A R R A Y O F A R E A S O F R I G H T S I D E D S T R I P S C X R : A R R A Y O F R I G H T S I D E D L I M I T O F I N T E G R A T I O N A T E A C H L E V E L C F 1 , F 2 , F 3 C F 4 , F 5 : A R R A Y S O F V A L U E S O F T H E F U N C T I O N F O R T H E 5 P O I N T S C O R R E S P O N D I N G C T O T H E F O U R T H O R D E R P O L Y N O M I A L C S : A R E A O F T H E F O U R P A N E L S U N D E R T H E C U R V E C C D I M E N S I O N H ( 2 0 ) , T O L ( 2 0 ) , S R ( 2 0 ) , X R ( 2 0 ) D I M E N S I O N F 1 ( 2 0 ) , F 2 ( 2 0 ) , F 3 ( 2 0 ) , F 4 ( 2 0 ) , F 5 ( 2 0 ) , F 6 ( 2 0 ) , F 7 ( 2 0 ) , F 8 ( 2 0 ) , F 9 ( 2 0 ) I M A X = 2 0 N = 5 S U M = 0 . D 0 174 X 1 = A C C Set s t r ip w i d t h a n d t o l e r a n c e f o r e a c h l e v e l C H ( 1 ) = ( B - A ) / 4 . D 0 T O L ( l ) = 6 0 . D 0 * E P S D O 10 I = 2 , I M A X IM= I -1 H ( I ) = H ( I M ) / 2 . D 0 T O L ( I ) = T O L ( I M ) / 2 . D 0 10 C O N T I N U E C C C a l c u l a t e i n i t i a l a r e a , S , u s i n g f o u r s t r ips C X R ( 1 ) = A + 4 . D 0 * H ( 1 ) F 1 ( 1 ) = F ( A ) F 3 ( 1 ) = F ( A + H ( 1 ) ) F 5 ( 1 ) = F ( A + 2 . D 0 * H ( 1 ) ) F 7 ( 1 ) = F ( A + 3 . D 0 * H ( 1 ) ) F 9 ( 1 ) = F ( B ) S = ( 2 . D 0 * H ( 1 ) / 4 5 . D 0 ) * ( 7 . D 0 * F 1 ( 1 ) + 3 2 . D 0 * F 3 ( 1 ) + 1 2 . D 0 * F 5 ( 1 ) + 3 2 . D 0 * F 7 ( 1 ) + 7 . D 0 * F 9 ( 1 ) ) 1=1 C C R e c a l c u l a t e S L a n d S R u n t i l S L + S R - S < T O L C 2 0 N = N + 4 F 2 ( I ) = F ( X 1 + H ( I ) / 2 . D 0 ) F 4 ( I ) = F ( X 1 + 3 . D 0 * H ( I ) / 2 . D 0 ) F 6 ( I ) = F ( X 1 + 5 . D 0 * H ( I ) / 2 . D 0 ) F 8 ( I ) = F ( X 1 + 7 . D 0 * H ( I ) / 2 . D 0 ) S L = ( H ( I ) / 4 5 . D 0 ) * ( 7 . D 0 * F 1 ( I ) + 3 2 . D 0 * F 2 ( I ) + 1 2 . D 0 * F 3 ( I ) + 3 2 . D 0 * F 4 ( I ) + 7 . D 0 * F 5 ( I ) ) S R ( I ) = ( H ( I ) / 4 5 . D 0 ) * ( 7 . D 0 * F 5 ( I ) + 3 2 . D 0 * F 6 ( I ) + 1 2 . D 0 * F 7 ( I ) + 3 2 . D 0 * F 8 ( I ) + 7 . D 0 * F 9 ( I ) ) C C I f S L + S R - S > T O L , i n c r e a s e l e v e l a n d s u b d i v i d e left s t r ip C I F ( D A B S ( S L + S R ( I ) - S ) . G T . T O L ( I ) ) T H E N I M = I 1=1+1 I F (I . L E . U M A X ) T H E N S = S L F 1 ( I ) = F 1 ( I M ) F 3 ( I ) = F 2 ( I M ) F 5 ( I ) = F 3 ( I M ) F 7 ( I ) = F 4 ( I M ) F 9 ( I ) = F 5 ( M ) X R ( I ) = X 1 + 4 . D 0 * H ( I ) G O T O 2 0 E L S E W R I T E ( * , 5 ) X I 5 F 0 R M A T ( 1 X , ' W A R N I N G - I N T E G R A T I O N F A I L S B E Y O N D X = ' , D 1 0 . 3 ) R E T U R N E N D I F C 175 C If SL+SR-S < TOL, a d d SL+SR o n t o S a n d loca te c o r r e c t l e v e l C E L S E SUM=SUM+SL+SR(I) X1=X1+4.D0*H(I) DO 30 J=I,1,-1 IF (DABS(X1-XR(J)) .LT. H(IMAX)/2.D0) T H E N I=J IF (I .EQ. 1) R E T U R N IM=I-1 S=SR(IM) F1(I)=F5(IM) F3(I)=F6(IM) F5(I)=F7(IM) F7(I)=F8(IM) F9(I)=F9(IM) GOTO 20 ENDIF 30 CONTINUE ENDIF R E T U R N E N D * * * * * * ************************************************************************ ******************************** SUBROUTINE SPLrNE(X,Y,N,Q,R,S) C C THIS SUBROUTINE USES T H E M E T H O D OF CUBIC SPLINES OF T H E F O R M : C F(X)=Y(I)+Q(I)*(X-X(I))+R(I)*(X-X(I))**2+S(I)*(X-X(I))**3 C TO I N T E R P O L A T E B E T W E E N B E T W E E N A SET OF D A T A POINTS. SELECTION B E T W E E N C N A T U R A L , C L A M P E D A N D FITTED END-CONDITIONS IS POSSIBLE. C C A R G U M E N T S : C C H : A R R A Y OF DIFFERENCES B E T W E E N E A C H SUCCESSIVE PAIR OF X i POINTS C T A B : M A T R I X OF DIVIDED DIFFERENCES FOR FITTED SPLINE M E T H O D C X D : A R R A Y OF X V A L U E S USED TO D E T E R M I N E THE DIV. DIF. C A , B , C , D : A R R A Y OF V A L U E S E N T E R E D INTO THE T D M A SUBROUTINE USED TO S O L V E C FOR T H E COEFFICIENT "R" OF THE P O L Y N O M I A L C NDPT1: FIRST END-POINT FOR SPLINE C N D P T N : L A S T END-POINT FOR SPLINE IMPLICIT R E A L * 8 (A-H,0-Z) D I M E N S I O N Q(400),R(401),S(400) D I M E N S I O N X(N),Y(N),H(400),TAB(4,4),XD(4) D I M E N S I O N A(401),B(401),C(401),D(401) C C INPUT SPLINE M E T H O D TO B E USED C NDPT1=1 GOTO 3 176 17 W R I T E ( * , 1 5 ) 15 F O R M A T ( / ' C H O O S E O N E O F T H E F O L L O W I N G S P L I N E M E T H O D S F O R ', + ' T H E F I R S T E N D - P O I N T ' , / , ' 1) N A T U R A L S P L I N E ' , / , + ' 2) C L A M P E D S P L I N E ' , / , ' 3) S P L I N E W I T H F I T T E D E N D ' , + ' P O I N T S ' / ) R E A D ( * , * ) N D P T 1 I F ( ( N D P T 1 . L T . 1) . O R . ( N D P T 1 . G T . 3)) T H E N W R I T E ( * , 1 6 ) 16 F O R M A T ( / ' I N V A L I D C H O I C E , B O N E H E A D ! P L E A S E C H O O S E A G A I N ' / ) G O T O 17 END IF 3 N D P T N = 1 G O T O 4 27 W R I T E ( * , 2 5 ) 25 F O R M A T ( / ' C H O O S E O N E O F T H E F O L L O W I N G S P L I N E M E T H O D S F O R ' , + ' T H E L A S T E N D - P O I N T ' , / , ' 1) N A T U R A L S P L I N E ' , / , + ' 2) C L A M P E D S P L I N E ' , / , ' 3) S P L I N E W I T H F I T T E D E N D ' , + ' P O I N T S ' / ) R E A D ( V ) N D P T N I F ( ( N D P T N . L T . 1) . O R . ( N D P T N . G T . 3)) T H E N W R I T E ( * , 2 6 ) 26 F O R M A T ( T N V A L I D C H O I C E , B O N E H E A D ! P L E A S E C H O O S E A G A I N ' / ) G O T O 2 7 E N D I F C C C A L C U L A T E H ( I ) C 4 N M = N - 1 D O 3 0 I = 1 , N M H ( I ) = X ( I + 1 ) - X ( I ) 30 C O N T I N U E C C D E T E R M I N E E N D - P O I N T C O N D I T I O N S F O R F I R S T E N D - P O I N T C I F ( N D P T 1 . E Q . 1) T H E N B ( l ) = l . C ( 1 ) = 0 . D ( 1 ) = 0 . E L S E I F ( N D P T 1 . E Q . 2) T H E N B ( 1 ) = 2 . * H ( 1 ) C ( 1 ) = H ( 1 ) D ( 1 ) = 3 . * ( ( ( Y ( 2 ) - Y ( 1 ) ) / H ( 1 ) ) - D 1 ) E L S E I F ( N D P T 1 . E Q . 3) T H E N C C U S E N E W T O N ' S D I V I D E D D I F F E R E N C E M E T H O D T O D E T E R M I N E T H E T H I R D D E R I V A T I V E C O F T H E T H I R D - O R E D E R P O W E R S E R I E S W H I C H P A S S E S T H R O U G H T H E F I R S T 4 P O I N T S C ( X ( 1 ) , X ( 2 ) , X ( 3 ) A N D X ( 4 ) ) . 177 c M = 4 D O 4 0 K = 1 , M X D ( K ) = X ( K ) T A B ( K , 1 ) = Y ( K ) 4 0 C O N T I N U E D O 6 0 J = 2 , M J M = J - 1 M M = M - J M D O 50 K=1 ,MM T A B ( K , J ) = ( T A B ( K + l , J I V r ; - T A B ( K ^ 50 C O N T I N U E 6 0 C O N T I N U E A 4 = T A B ( 1 , 4 ) B ( l ) = - H ( l ) C ( 1 ) = H ( 1 ) D ( 1 ) = 3 . * H ( 1 ) * H ( 1 ) * A 4 E N D I F C C D E T E R M I N E E N D - P O I N T C O N D I T I O N S F O R O T H E R E N D - P O I N T C I F ( N D P T N . E Q . 1) T H E N A ( N ) = 0 . B ( N ) = 1 . D ( N ) = 0 . E L S E I F ( N D P T N . E Q . 2) T H E N A ( N ) = H ( N M ) B(>r)=2.*H(NM) D(>0=-3.*(((Y(>0-Y(NM))/H(NM))-DN) E L S E I F ( N D P T N . E Q . 3) T H E N C C U S E N E W T O N ' S D I V I D E D D I F F E R E N C E M E T H O D T O D E T E R M I N E T H E T H I R D D E R I V A T I V E C O F T H E T H I R D - O R D E R P O W E R S E R I E S W H I C H P A S S E S T H R O U G H T H E L A S T 4 P O I N T S C ( X ( N - 3 ) , X ( N - 2 ) , X ( N - 1 ) A N D X ( N ) ) . C M = 4 D O 7 0 K = 1 , M K K = N - M + K T A B ( K , 1 ) = Y ( K K ) X D ( K ) = X ( K K ) 7 0 C O N T I N U E D O 90 J = 2 , M J M = I - 1 M M = M - J M D O 8 0 K = 1 , M M T A B ( K J ) = ( T A B ( K + 1 , J M ) - T A B ( K , J M ) ) / ( X D ( K - J M ) - X D ( K ) ) 80 C O N T I N U E 90 C O N T I N U E B 4 = T A B ( 1 , 4 ) A ( N ) = H ( N M ) B ( N ) = - H ( N M ) D ( N ) = - 3 . * H ( > I M ) * H ( N M ) * B 4 E N D I F C 178 C SPECIFY O T H E R COEFFICIENTS OF TRIDIAGONAL EQUATIONS C A(1)=0. C(N)=0. D O 100 I=2,NM IM=I-1 A(I)=H(IM) B(I)=2.*(H(Dvl)+H(I)) C(I)=H(I) D(I)=3.*(((Y(I+1)-Y(I))/H(I))-((Y(I)-Y(IM))/H(IM))) 100 C O N T I N U E C C C A L L T H O M A S A L G O R I T H M T O S O L V E TRIDIAGONAL SET C C A L L T D M A ( A , B , C , D , R , N , N M ) C C D E T E R M I N E Q(I) A N D S(I) C D O 110 I=1,NM IP=I+1 Q(I)=(Y(IP)-Y(I))/H(I)-H(I)*(2. *R(I)+R(IP))/3. S(I)=(R(IP)-R(I))/(3.*H(I)) 110 C O N T I N U E R E T U R N E N D SUBROUTINE T D M A ( A , B , C , D , X , N , N M ) IMPLICIT R E A L * 8 (A-H,0-Z) DIMENSION A(N)3(N),C(N),D(N),X(N),P(401),Q(401) P(l)=-C(l)/B(l) Q(1)=D(1)/B(1) D O 10 I=2,N IM=I-1 DEN=A(I)*P(TM)+B(1) P(I)=-C(I)/DEN Q(I)=(D(I)-A(I)*Q(IM))/DEN 10 C O N T I N U E X(N)=Q(N) D O 20I=NM,1,-1 X(I)=P(I)*X(I+1)+Q(I) 20 C O N T I N U E R E T U R N E N D C C Subroutine which uses Muller's method to search the interval XI to X F to find C the real roots of the function F(X) C SUBROUTINE MULLER(F,XI,XF,DX,NR,EPS,R,IR) 179 IMPLICIT R E A L * 8 (A-H,0-Z) DIMENSION R(NR) X1=XI Y1=F(X1) ISTART=1 C C Identify first root if F(XI)=0. C IF ( Y l .EQ. 0.D0) T H E N C A L L roEOT(F,Xl,EPS,R(l),Xl,Yl) ISTART=2 ENDIF C C Loop to find remaining roots C D O 60 I=ISTART,NR 10 JTLAG=0 C C Use incremental search to find interval [X1,X3] containing a single root C 20 X3=X1+DX IF (X3 .GT. XF) X3=XF Y3=F(X3) JT (Y1*Y3 .GT. 0.D0) T H E N IF (X3 .EQ. XF) T H E N IR=I-1 R E T U R N E L S E X1=X3 Y1=Y3 G O T O 20 ENDIF ENDIF JT (Y3 .EQ. 0.D0) T H E N C A L L IDENT(F,X3,EPS,R(I),X1,Y1) G O T O 60 ENDIF DYOLD=DABS(Y3-Yl ) C C Use linear interpolation to obtain a closer approximation of the root X2 C 30 X2=(X1*Y3-X3*Y1)/(Y3-Y1) 180 Y2=F(X2) IF (Y2 .EQ. O.DO) T H E N C A L L IDENT(F,X2,EPS,R(I),X1,Y1) G O T O 60 ENDIF C C Use Muller's method to obtain the root within the desired accuracy C C Determine the coefficients of the second order polynomial which passes C through X1.X2 and X3 C 40 DENOM=(X2-Xl)*(X3-Xl)*(X3-X2) A1=(Y1*((X2*X3**2)-(X3*X2**2))-Y2*((X1*X3**2)-(X3*X1**2)) + +Y3*((X1*X2**2)-(X2*X1**2)))/DEN0M A2=(-Yl*(X3**2-X2**2)+Y2*(X3**2-Xl**2)-Y3*(X2**2-Xl**2))/DENOM A3=(Y1*(X3-X2)-Y2*(X3-X1)+Y3*(X2-X1))/DEN0M C C Select the root of this approximating polynomial, using the quadratic formula, C which lies in the interval [XI,X3] C QRT=DSQRT((A2**2)-(4.D0*A1*A3)) X4A=(-A2+QRT)/(2.D0*A3) IF ((X4A GT. XI) A N D . (X4A .LT. X3)) T H E N X4=X4A E L S E X4B=(-A2-QRT)/(2.D0*A3) X4=X4B ENDIF Y4=F(X4) C C Check if root was fortuitously uncovered C IF (Y4 .EQ. 0.D0) T H E N C A L L IDENT(F,X4,EPS,R(I),X1,Y1) G O T O 60 ENDIF C C Check if approximate value is within EPS or else continue C IF (DABS((X4-X2)/X4) .LT. EPS) T H E N R(I)=X4 X1=X3 Y1=Y3 181 G O T O 60 ENDIF C C Check for discontinuity (JTLAG=0 on first pass with each root) C DY=DABS(Y 4-Y2) IF ((IFLAG .EQ. 3) . A N D . (DY .GT. DYOLD)) T H E N X1=X3 Y1=Y3 G O T O 10 E L S E D Y O L D = D Y IFL AG=IFL AG+1 ENDIF C C Set new values for X I , X2 and X3 for next increment to find next root C IF ((X4 .GT. XI) . A N D . (X4 .LT. X2)) T H E N X3=X2 Y3=Y2 E L S E X1=X2 Y1=Y2 ENDIF X2=X4 Y2=Y4 G O T O 40 60 C O N T I N U E IR=NR R E T U R N E N D c C Subroutine to identify X R O O T as a root of F(X)=0 and then yields new starting C values for X I (=XROOT+DX) and Y l (=F(X)) C SUBROUTINE I D E N T ( F , X R O O T , D X , R O O T , X l , Y l ) IMPLICIT R E A L * 8 (A-H,0-Z) ROOT=XROOT Xl=ROOT+DX Y1=F(X1) R E T U R N E N D ********************************************** 182 Appendix F Computed Results of Cross-Sectional Average Spout Voidage, Mass Flow Rates and Superficial Annular Gas Velocity 183 Table F. 1: Computed results of mass flow rates in the spout, (dp = 1.33 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height (m) Solids Mass Flow Rate (kg/sec) 0.268 0.653 0.628 0.526 0.413 0.218 0.432 0.606 0.576 0.332 0.168 0.448 0.513 0.388 0.341 0.097 0.438 0.510 0.510 0.522 0.076 0.454 0.429 0.440 0.488 0.054 0.456 0.360 0.262 0.287 0.032 0.200 0.307 0.318 0.011 0.312 Table F.2: Computed results of mass flow rates in the annulus. (dp = 1.33 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height Solids Mass Flow Rate (kg/sec) (m) 0.268 0.313 0.329 0.345 0.297 0.218 0.297 0.377 0.31 0.223 0.168 0.256 0.21 0.203 0.167 0.097 0.163 0.145 0.126 0.081 0.076 0.155 0.123 0.125 0.066 0.054 0.123 0.097 0.099 0.042 0.032 0.09 0.085 0.011 0.02 184 Table F.3: Computed results of cross-sectional average spout voidage. (dp = 1.33 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height Cross-Sectional Average Voidage (m) 0.268 0.708 0.618 0.615 0.587 0.218 0.713 0.619 0.622 0.647 0.168 0.732 0.664 0.651 0.649 0.097 0.841 0.739 0.762 0.737 0.076 0.846 0.784 0.751 0.767 0.054 0.866 0.808 0.843 0.835 0.032 0.908 0.848 0.849 0.011 0.02 Table F.4: Computed results of annular superficial gas velocity, (dp = 1.33 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height (m) Annular Superficial Gas Velocity 0.268 0.708 0.618 0.615 0.587 0.218 0.713 0.619 0.622 0.647 0.168 0.732 0.664 0.651 0.649 0.097 0.841 0.739 0.762 0.737 0.076 0.846 0.784 0.751 0.767 0.054 0.866 0.808 0.843 0.835 0.032 0.908 0.848 0.849 0.011 0.02 185 Table F.5: Computed results of mass flow rates in the spout, (dp = 1.84 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height Solids Mass Flow Rate (kg/sec) (m) 0.268 0.904 0.748 0.542 0.520 0.218 0.788 0.647 0.476 0.484 0.168 0.798 0.684 0.616 0.588 0.097 0.607 0.614 0.444 0.476 0.076 0.572 0.467 0.357 0.416 0.054 0.537 0.420 0.368 0.366 0.032 0.504 0.412 0.357 0.293 Table F.6: Computed results of mass flow rates in the annulus. (dp = 1.84 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height Solids Mass Flow Rate (kg/sec) (m) 0.268 0.401 0.355 0.332 0.324 0.218 0.356 0.309 0.278 0.235 0.168 0.265 0.24 0.2 0.184 0.097 0.183 0.141 0.126 0.121 0.076 0.166 0.138 0.112 0.107 0.054 0.139 0.148 0.123 0.116 0.032 0.102 0.086 0.093 0.09 186 Table F.7: Computed results of cross-sectional average spout voidag (dp = 1.84 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height Cross-Sectional Average Voidage (m) 0.268 0.685 0.647 0.586 0.566 0.218 0.738 0.702 0.684 0.626 0.168 0.795 0.738 0.667 0.632 0.097 0.832 0.767 0.775 0.712 0.076 0.846 0.839 0.848 0.786 0.054 0.880 0.870 0.853 0.824 0.032 0.912 0.887 0.870 0.867 Table F.8: Computed results of annular superficial gas velocity. (dP = 1.84 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.15 0.29 0.43 Height (m) Annular Superficial Gas Velocity 0.268 1.014 1.066 0.867 0.870 0.218 0.767 0.862 0.859 0.946 0.168 0.712 0.711 0.822 0.798 0.097 0.406 0.524 0.636 0.474 0.076 0.418 0.409 0.625 0.554 0.054 0.484 0.492 0.489 0.514 0.032 0.363 0.441 0.392 0.456 187 Table F.9: Computed results of mass flow rates in the spout, (dp = 2.53 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.43 Height Solids Mass (m) Flow Rate (kg/s) 0.268 2.085 1.997 0.168 1.897 1.850 0.076 1.259 1.006 Table F. 10: Computed results of mass flow rates in the annulus. (dp = 2.53 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.43 Height Solids Mass (m) Flow Rate (kg/s) 0.268 0.574 0.461 0.168 0.443 0.244 0.076 0.28 0.124 Table F. 11: Computed results of cross-sectional average spout voidage. (dp = 2.53 mm, H = 0.280 m, U/Ums = 1.2) Q V Q T 0.0 0.43 Height (m). Cross-Sectional Average Voidage 0.268 0.685 0.623 0.168 . 0.725 0.706 0.076 0.816 0.759 Table F. 12: Computed results of annular superficial gas velocity. (dP = 2.53 mm, H = 0.280 m, U/Ums = 1.2) Q A / Q T 0.0 0.43 Height (m) Annular Superficial Gas Velocity 0.268 1.923 1.551 0.168 0.800 0.974 0.076 0.650 0.691 188 Appendix G Effect of Pulsating Flow Through the Spout on the Calculation of Solids Mass Flow Rate 189 The presence of pulsations in the flow of air entering the bed may have a significant effect on solids circulation rates and on the calculation of solids mass flow. As explained in Chapter 4, solids mass flow rates in the spout were calculated by integrating time-averaged values of particle velocity and voidage: Ws=2npp\vs(\-ss)rdr (G.l) 0 where over-bars represent time-averaged values. However, spouted and fluidized beds are commonly subject to non-periodic or periodic fluctuations in the local flow variables. The average readings of the velocity and voidage probes used for measurements in the spout are actually obtained from highly fluctuating signals such as those shown in Figure 3.3. In the analysis of such time-varying systems, it is important to take into account the fluctuations in the measured variables (Dunn, 1980). Such an analysis is presented next for the calculation of solids mass flow rate in the spout. The instantaneous solids mass flow rate in the spout is given by 's = 2npp\vs{\-ss)rdr (G.2) where vs and ss are the instantaneous local particle velocity and voidage, respectively. The instantaneous variables may be expressed in terms of time-averaged and fluctuating components; v ,=v ,+v , ' (G.3) e.=e.+e, (G.4) where primes indicate fluctuations or deviations from the mean. Inserting Equations G.3 and G.4 into Equation G.2 and expanding gives 190 W s = J O W + vsc's+v's cs + v's c\ )rdr (G.5) o where cs = \-es is the volume fraction of particles. Taking a time-average of Equation G.5 gives _ Ri Ws = 1npt\iy,c, + vsc's + v\ cs + v\ c\)rdr (G.6) The first term in the integration is the average of a product of averages. Since the two terms in the product are independent of time vscs =vscs. The second and third terms in the integration are result in time-averages of a fluctuating component and must be zero since, by definition, the time-average of any fluctuating quantity is zero. The last term in the integration is non-zero since it does not necessarily follow that the product of two fluctuating components has a zero average. In fact, if fluctuations of voidage are correlated with fluctuations in particle velocity, the result will be a non-zero value of this term. Therefore, the time-averaged solids mass flow rate reduces to Comparing Equations G-7 and G - l , one can see that the second term in the integration has been left out in the values of Ws calculated in Chapter 4. This term may be important depending on the nature of the fluctuations. However, in order to determine the value of this term, detailed simultaneous instantaneous data must be obtained by both probes. Unfortunately, the current instruments are unable to record the instantaneous data, and even if this were possible, simultaneous measurements at the same location are currently impossible However, it is possible to deduce what effect pulsating flow would have on the fluctuating components and what effect it would have on the overall computation of solids flow rate. (G.7) 0 191 Pulsating flow is characterised by periods of high gas velocity followed by periods of lower gas velocity. Two cases may be considered. During a period of high gas velocity there is a greater throughput of gas through the spout. This results in higher instantaneous particle velocities (positive v's ) and higher voidage, or lower particle concentration (negative c's). This combination would result in a negative value for the second term in the integral of Equation G.7. During a period of low gas velocity, particle velocities in the spout would be lower (negative v 's) and the voidage would decrease (positive c 's). The result would again be a negative value for the fluctuating component in Equation G.7. For both cases, excluding the fluctuating components from the calculation of solids flow rate in the spout would result in overestimation of the flow rate, consistent with the results obtained. If the pulses were large and prominent enough, the overestimation could be significant. 192 

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