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Hydrodynamic and scale-up studies of spouted beds He, Yan-Long 1995

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HYDRODYNAMIC AND SCALE-UP STUDIES OF SPOUTED BEDS By Yan-Long He B.A.Sc, East China Institute of Technology, 1982 M.A.Sc, The University of British Columbia, 1990 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February 1995 ©Yan-Long He, 1995 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. (Signature) Department oiCM***c«* z W < H e e r - t > V L . The University of British Columbia Vancouver, Canada Date (j/UAoz, /jjr DE-6 (2/88) Abstract The scaling relationships proposed by Glicksman (1984) for fluidized bed scale-up have been modified to provide a full set of scaling parameters for spouted bed scale-up. A force balance for particles in the annulus region leads to addition of two non-dimensional parameters, the internal friction angle (<p) and the loose packed voidage (s0) to the original Glicksman scaling relationships. Experimental verification of the full set of modified scaling parameters was conducted, first in a series of small spouted beds, then in larger columns up to 0.914 m in diameter, and finally in a pair of high temperature (500 °C) beds. Both viscous and inertial forces were important for the conditions investigated so that no simplifications could be made to the full set of scaling parameters. It is -demonstrated that the full set of modified scaling parameters is valid for spouted beds when all dimensionless parameters are matched between the prototype and model beds. A fibre optic probe was used to measure voidage profiles in spouted beds of diameter 0.152 m. The voidage in most of the annulus was found to be somewhat higher than the loose-packed voidage and increased with increasing spouting gas flow rate, contrary to usual assumptions. The voidage decreased with height in the core of the fountain for low spouting gas flow rates, but first increased with height and then decreased towards the top of the fountain at higher gas flow rates. Radial profiles of local voidage were roughly parabolic in the lower portion of the spout and blunt in the upper portion. The same fiber optic probe was also used to measure spout diameters based on significantly higher counts of output electric pulses in the spout region than in the annulus. The flat wall of semi-cylindrical spouted bed columns was found to cause considerable distortion of spout shapes which became approximately semi-elliptical. The often-used McNab (1972) equation was found to underestimate the spout diameters in a full-column, with an average deviation of 35.5%. A second fibre optic probe system was used to measure profiles of vertical particle velocities in the spout and fountain regions. In addition, a fibre optic image probe was employed to measure particle velocity profiles in the annulus. In the spout, radial profiles n of vertical particle velocities were near Gaussian in shape. Particle velocities along the spout axis in a half-column were 70% lower than in a full-column of the same diameter as the half-column under identical operating conditions. In the half column, particle velocities adjacent to the front plate were approximately 24% lower than a few millimeters away for the conditions studied. In the annulus region, there was a 28% difference between particle velocities adjacent to the column wall and those only 2 mm away. Measurements of pressure profiles and gas flow distributions in the annulus were carried out, while the influence of elevated pressures on bed hydrodynamics was also examined. in Table of Contents Page Abstract Table of Contents iv List of Tables ix List of Figures x Acknowledgement xvi Chapter 1: Introduction 1 Chapter 2: Scale-up Studies of Spouted Beds 4 2.1 Scale-up of Fluidized Beds Using Similarity Principle 4 2.1.1 Glicksman's scaling relationships (1984) 5 2.1.2 Horio's similarity rule (1986) 8 2.1.3 Experimental investigations 9 2.2 Considerations for Spouted Beds 11 2.3 Experimental Verification of the Scaling Relationships 14 2.3.1 Bed and particle parameters and operating conditions 14 2.3.2 Experimental equipment and particulate materials 16 2.3.3 Measurement methods 20 2.4 Results and Discussion 21 iv 2.4.1 Scaling tests in smaller columns 21 2.4.2 Scaling tests in larger columns and high temperature columns 25 2.5 Conclusions 33 Chapter 3: Voidage Profiles 34 3.1 Previous Work 34 3.1.1 Measurements of voidage profiles in spouted beds 34 3.1.2 The fiber optic probe technique 3 5 3.1.3 Applications of fiber optic probes for measuring voidage in fluidized 36 beds 3.2 Apparatus and Instrumentation in the Present Work 39 3.2.1 Apparatus 39 3.2.2 Instrumentation: probe, calibration and validation 41 3.3 Results and. Discussion 49 3.3.1 Voidage in the annulus 49 3.3.2 Voidage profiles in the fountain 51 3.3.3 Voidage profiles in the spout 53 3.4 Conclusions 59 Chapter 4: Spout Shapes and Diameters 60 4.1 Experimental 60 4.1.1 Apparatus and particulate materials 60 4.1.2 Fibre optic voidage probe and image probe 61 4.2 Results and Discussion 62 4.2.1 Validation of the fibre optic voidage probe 62 4.2.2 Spout diameters in the half-column 64 4.2.3 Spout diameters in the full-column 67 v 4.3 Conclusions 70 Chapter 5: Particle Velocity Profiles 71 5.1 Previous Work 71 5.1.1 Available techniques for particle velocity measurement 71 5.1.2 Measurements of particle velocities in spouted beds 73 5.1.3 Correlation method with fiber optic probe 74 5.1.4 Previous fiber optic probes 74 5.1.5 Devices for light detection and signal analysis 76 5.1.6 Previous results obtained using fiber optic technique 77 5.1.7 Half columns vs full columns 77 5.1.8 Solids flow patterns in the annulus of spouted beds 79 5.2 Experimental 80 5.2.1 Apparatus and particulate materials 80 5.2.2 Fibre optic probes and their calibration 80 5.3 Results and Discussion 86 5.3.1 Particle velocities in the spout 86 5.3.2 Particle velocities in the fountain 92 5.3.3 Particle velocities in the annulus 95 5.3.4 Solids mass flows in the spout and annulus 98 5.4 Conclusions 101 Chapter 6: Pressure Gradients and Gas Flow in the Annulus 103 6.1 Previous Work 103 6.1.1 Pressure gradients in the annulus 103 6.1.2 Gas flow distribution in the annulus 104 6.1.3 Theoretical models for predicting gas velocities in the annulus 106 vi 6.2 Experimental 108 6.2.1 Apparatus and particulate materials 108 6.2.2 Measurement techniques 109 6.3 Results and Discussion 110 6.3.1 Longitudinal pressure gradients and voidage profiles in the annulus 110 6.3.2 Pressure drop versus velocity relationships for loose-packed beds 112 6.3.3 Gas flow distributions in the annulus 115 6.3.4 Effect of U/Ums on local superficial gas velocities in the annulus 118 6.4 Conclusions 122 Chapter 7: Spouting at Elevated Pressure 125 7.1 Experimental 125 7.1.1 The pressurized rig 125 7.1.2 Measurement techniques 126 7.2 Results and Discussion 128 7.2.1 Minimum spouting velocity 128 7.2.2 Maximum spoutable bed height 130 7.2.3 Spout shape and diameter 132 7.2.4 Fountain height 13 4 7.2.5 Pressure gradient in the annulus 136 7.2.6 Regime map and spoutability 136 7.3 Conclusions 139 Chapter 8: Conclusions and Recommendations 143 9.1 Conclusions 143 9.2 Recommendations for Further Work 146 vn Nomenclature 147 References 150 Appendix 158 Vlll List of Tables Page Table 2.1: Experimental studies of Glicksman's scaling relationships for 10 fluidized beds. Table 2.2: Comparison of dimensions, properties and dimensionless groups in 15 experimental tests. The gas was air in all cases. Table 2.3: Comparison of dimensions, properties and dimensionless groups in 17 experimental tests. The gas was air in all cases. Table 2.4: Properties of particulate materials. 20 Table 2.5: Maximum spoutable bed depths for seven tests in small columns. 22 •Table 2.6: Fountain heights for the seven cases outlined in Table 2.2. 24 Table 2.7: Fountain heights for cases outlined in Table 2.3. 27 Table 3.1: Experimental measurements using the fiber optic probe technique. 39 Table 3.2: Average voidage values and corresponding standard deviations for 49 a 95% confidence interval in the annulus for U/Ums=\.l, 1.2 and 1.3. Table 5.1: Various methods for measuring particle velocities. 72 Table 5.2: Previous experimental utilization of the fiber optic technique. 78 Table 5.3: Typical measured velocities and corresponding standard 82 deviations. Table 6.1: Properties of particulate materials. 109 Table 6.2: Values of constants k, and k2 obtained by curve fitting compared 115 with values calculated from the Ergun (1952) equation. Table 6.3: Experimental values of annulus gas velocities and extrapolated 117 UaHnr Table 7.1: Properties of Particulate Materials. 126 Table 7.2: Experimental average spout diameters and values predicted from 134 the McNab (1972) equation. ix List of Figures Page Figure 1.1: Schematic diagram of a spouted bed. Arrows indicate direction of 2 solids movement. Figure 2.1: Schematic diagram showing overall equipment layout for four 18 separate columns. Figure 2.2: Dimensionless spout diameters as a function of dimensionless height 23 for smaller columns. Conditions are given in Table 2.2. Figure 2.3: Longitudinal pressure profiles in the annulus for columns of 26 diameter 76 and 152 mm, with conditions given in Table 2.2. Figure 2.4: Dimensionless spout diameters as a function of dimensionless height 28 for cases outlined in Table 2.3. Figure 2.5: Longitudinal pressure profiles in the annulus for columns of 29 diameter 152 and 914 mm with conditions given in Table 2.3. Figure 2.6: Dimensionless dead zone boundaries as a function of dimensionless 31 height for cases outlined in Table 2.3. Figure 2.7: Longitudinal pressure profiles in the annulus for high temperature 32 beds. Figure 3.1: Prevailing configurations of reflective optical probes (Krohn, 1986) 35 Figure 3.2: (a) Schematic diagram of measuring system, (b) Calibration method 36 for particle concentration (Matsuno et al., 1983). Figure 3.3: Typical fiber optic probes used by previous authors: (a) Morooka et 38 al. (1980), (b) Matsuno et al. (1983), (c) Boiarski (1985), (d) Nakajima et al. (1990), (e) Kato et al. (1990), (f) Reh and Li (1990). Figure 3.4: Experimental setup. 40 Figure 3.5: Photographs of the fiber optic system and fiber optic probes. 42 Figure 3.6: Block diagram of the fiber optic system, Model PC-3. 43 x Figure 4.5. Spout shapes in the full-column for three different gas flow rates. 69 #=0.325 m. Figure 5.1: Typical fiber optic probes used by previous authors, (a) Oki et al. 75 (1975), (b) Ohki and Shirai (1976), (c) Oki et al. (1977), (d) Ishida et al. (1980), (e) Patrose and Caram (1982), (f) Benkrid and Caram (1989). Figure 5.2: Block diagram of the fiber optic and signal processing units of the 77 measurement system employed by Randelman et al. (1987). Figure 5.3: Particle streamlines in the annulus: (a) wheat, £>c=0.292 m, 79 #=0.876 m, Z>/=35.3 mm, U/Ums=\.\, from a half column (Lim and Mathur, 1978); (b) "universal" streamlines predicted by the kinematic model of Benkrid and Caram (1989). Figure 5.4: Photograph of the fiber optic system used to measure particle 81 velocities. Figure 5.5: Fibre optic probe for particle velocity measurements in the spout 83 and fountain regions. Figure 5.6: Block diagram of the signal processing units for the fiber optic 84 system. Figure 5.7: Typical distribution of particle velocities detected by the fibre optic 85 system in the full column. z=0.218 m, r=0.01 mm (in the spout region), #=0.325 m, C//7JOT/=1.1. Figure 5.8: Fibre optic image probe for determining particle velocities in the 87 annulus region. Figure 5.9: Axial profiles of vertical particle velocities along the axis of full- 88 column (black symbols) and half-column (open symbols). #r=0.695 m, #=0.325 m. Figure 5.10: Radial profiles of vertical particle velocities in the spout of the full- 90 column. Figure 5.11: Radial profiles of vertical particle velocities in the spout of the 91 half-column. Figure 5.12: Comparisons of particle velocity profiles in the spout of the full- 93 column and the half-column with identical operating conditions for xn Figure 5.13: Radial profiles of particle velocities in the fountain of the full- 94 column for U/Um =1.3 and HF=0.31 m. Figure 5.14: Boundary between the fountain core and the downflow region in 96 the full-column for U/Um—1.3 and HF=0.37 m obtained from radial positions in Figure 5.13 where particle velocity is zero. Top surface is from photographic images. Figure 5.15: Radial profiles of downward vertical particle velocities in the 97 annulus of the full-column. Figure 5.16: Solids mass flow in the spout of the full-column. #=0.325 m. 99 Figure 5.17: Solids mass flow in the annulus of the full-column. #=0.325 m. 100 Figure 6.1: Pressure gradient in the annulus. Dc=0.11 m, Z),=14.6 mm, d -2.5 104 mm, U/Um~l, glass beads (Grbavcic et al., 1976). Figure 6.2: Effect of bed depth on air velocity in a spouted bed annulus. 105 £>c=0.152 m, Dj=19.0 mm, U/Um=l.l (Epstein et al., 1978). Figure 6.3: Effect of spouting air velocity on the superficial gas velocity in the 105 annulus. Dc=0.152 m, Df=l9.0 mm (Lim, 1975). Figure 6.4: Schematic diagram of the static pressure probe. 110 Figure 6.5: Longitudinal pressure gradients in the annulus at U/Um = 1.1. I l l Figure 6.6: Effect of static bed height on voidage profiles in the annulus at 113 U/U„, =1.1. Figure 6.7: Calibration curve of pressure gradient vs. superficial gas velocity for 114 a packed bed of glass beads (d' =1.41 mm). Figure 6.8: Gas velocity profiles in the annulus at U/Um =1.1 based on 116 measured local voidages and pressure gradients. Figure 6.9: Annulus gas velocity profile compared with equations in the 119 literature where an extrapolated value of UaHm has been employed instead of Unif. Glass beads, d=lAl mm, #=0.475 m, U/Um=l.l. Figure 6.10: Effect of spouting gas velocity on longitudinal pressure gradients 120 in the annulus for the 1.41 mm dia. glass beads. #=0.325 m. xiii Figure 6.11: Effect of spouting gas velocity on voidage profiles in the annulus 121 for the 1.41 mm dia. glass beads. H=0.325 m. Figure 6.12: Effect of spouting gas velocity on superficial gas velocities in the 123 annulus for the 1.41 mm dia. glass beads. #=0.325 m. Figure 7.1: Influence of pressure on minimum spouting velocity: comparison 129 between experimental values (given by points) and predictions from the Mathur and Gishler (1955) equation (given by lines) for H=0.135 m. Figure 7.2: Experimental maximum spoutable bed height (points) as a function 131 of pressure compared with predictions from McNab and Bridgwater (1977) equation (lines). Figure 7.3: Variation of spout diameter with pressure for three different 133 particulate materials. i7=0.135 m, U/Um=1.2. Figure 7.4: Effect of bed pressures on fountain heights for three different 135 particulate materials. i/=0.135 m, U/Um—1.2. Figure 7.5: Influence of bed pressure on longitudinal pressure profile in the 137 annulus for the smaller glass beads, rf =1.09 mm, #=0.135 m, U/Um =1.2. Figure 7.6: Regime map for the smaller glass beads at ambient pressure. 138 P=101.3 kPa, ^=1.09 mm. Figure 7.7: Influence of bed pressure on regimes. Smaller glass beads, P=239.3 140 kPa, flfp=1.09mm. Figure 7.8: Influence of bed pressure on regimes. Smaller glass beads, P=342.7 141 kPa, Jp=1.09mm. Figure A. 1: Calibration curve of output signal from the fiber optic system vs. 160 solids volume fraction for glass beads (d^l.41 mm)/water systems. Figure A.2: Calibration curve of pressure gradient vs. superficial gas velocity in 161 a packed bed of glass beads (dp=2.lS> mm). Figure A.3: Calibration curve of pressure gradient vs. superficial gas velocity in 162 a packed bed of polyethylene particles (^ =3.38 mm). Figure A.4: Influence of bed pressure on longitudinal pressure profile in the 163 annulus for the larger glass beads. d=2.18 mm, i/=0.135 m, U/Um =1.2. xiv Figure A. 5: Influence of bed pressure on longitudinal pressure profile in the 164 annulus for the steel balls. d=l.09 mm, #=0.135 m, U/Ums-\2. xv Acknowledgment I would like to express my sincere gratitude to Professors J. R. Grace and C. J. Lim for their experienced and distinguished supervision which played a very important role in the completion of this study. I am also very grateful to Professor S-Z. Qin for his contribution to the instrumentation. I am very thankful to Professor N. Epstein for providing valuable papers and to Drs. J. Zhu and K. S. Lim for their help throughout the program. Thanks are also due to the staff of the Department of Chemical Engineering Workshop and Stores for their invaluable assistance. Finally, I am grateful to my family, Jenny, Nina and my parents, for their continued encouragement, support and understanding. xvi Chapter 1 Introduction Spouted beds are used as fluid-solid contactors for various physical and chemical processes involving coarse particles. For general reviews, see Mathur and Epstein (1974) and Epstein and Grace (1984). Figure 1.1 illustrates a spouted bed schematically. The bed is made up of three distinct regions: a dilute core called the spout, a surrounding annular dense region called the annulus, and a dilute fountain region above the bed surface. Solid particles are carried up rapidly with the fluid (usually gas) in the spout to the fountain and fall down onto the surface of the annulus by gravity. In the annulus, the particles move slowly downward and, to some extent, inward as a loose packed bed. Fluid from the spout leaks outwards into the annulus and percolates through the moving packed solids there. These solids are re-entrained into the spout over its entire height. 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 countercurrent percolation of fluid. The systematic cyclic movement of the fluid and solids leads to effective fluid/solids contact for many practical operations. Spouted beds have been used in a number of industrial applications. Examples of such applications include drying of granular materials, cooling of fertilizers, solids blending, food processing, charcoal activation, coal combustion and gasification. Some other applications that have not been used on an industrial scale, but which appear to be feasible based on bench scale operation, include shale pyrolysis and thermal cracking of petroleum. Although many equations based on small-scale vessels (Dc<0.3 m) are available for predicting the hydrodynamic properties of spouted beds, there is still considerable uncertainty with respect to suitable scale-up criteria. Most existing equations do not work 1 FOUNTAIN BED SURFACE SPOUT-ANNULUS INTERFACE ANNULUS SPOUT CONICAL BASE FLUID INLET Figure 1.1: Schematic diagram of a spouted bed. Arrows indicate direction of solids movement. 2 well for larger columns. Recently, some experimental data have been obtained in considerably larger columns, up to 1.1 m in diameter (Fane and Mitchell, 1984; Green and Bridgwater, 1983; Lim and Grace, 1987; He et al., 1992). However, no fully reliable models or equations for large columns have been developed due to lack of sufficient data. Scale-up studies of spouted beds are of great importance. Moreover, there is a paucity of experimental data obtained in full columns in which such hydrodynamic properties as particle velocity profiles, voidage profiles, and spout diameters have been determined. Knowledge of those properties is of fundamental importance for understanding the hydrodynamics of spouted beds and for spouted bed modeling and design. The primary objectives of the present thesis project have included: (a) an investigation to see whether the scahng relationships proposed by Glicksman (1984) for fluidized bed scale-up can be adapted to spouted bed scale-up; (b) accurate measurement of voidage profiles and spout diameters with a fiber optic system; (c) accurate determination of particle velocity profiles by using fiber optic probes; (d) obtaining pressure profiles and gas flow distributions in the annulus; and (e) a study of the influence of elevated pressures on bed hydrodynamics. Since six independent topics have been studied in the present work and different experimental equipment as well as different solids materials were employed for individual topics, the related hterature reviews and descriptions of experimental apparatus and procedures are given in individual chapters rather than in one single chapter, as a convenience to readers. 3 Chapter 2 Scale-up Studies of Spouted Beds Although many equations based on small-scale vessels (Dc<0.3 m) are available for predicting the hydrodynamic properties of spouted beds, there is still considerable uncertainty with respect to suitable scale-up criteria. Most existing equations do not work well for larger columns. Recently, some experimental data have been obtained in considerably larger columns, up to 1.1 m in diameter (Fane and Mitchell, 1984; Green and Bridgwater, 1983; Lim and Grace, 1987; He et al., 1992). However, no fully reliable models or equations for large columns have been developed due to lack of sufficient data. Scale-up studies of spouted beds are therefore of great importance. The primary objective of the present work is to examine whether the scaling relationships proposed by Glicksman (1984) for fluidized bed scale-up can be adapted to spouted bed scale-up. 2.1 Scale-up of Fluidized Beds Using Similarity Principle The principle of similarity is often used in obtaining experimental data to represent large-scale complex flow phenomena, e.g. to calculate wind loads on buildings and to design ship hulls. The basic concept is that if two flow fields are geometrically similar and are operated with identical values of all important independent non-dimensional parameters, then the dependent non-dimensional variables must also be identical at corresponding locations (Bisio and KabeL 1985). This simple hydrodynamic principle applies also to fluidized beds. Prescriptions of dimensioiiless groups to characterize the dynamics of fluidized beds can be traced back at least as far as Romero and Johanson (1962). In order to develop proper scaling relationships for a cold model of a hot fluidized bed, four dimensioiiless similarity groups, a Froude number, a Reynolds number, the ratio of solid to fluid densities, and the ratio of particle to vessel diameters, are important as derived by Broadhurst and Becker (1973) based on the Buckingham Pi Theorem. These 4 groups were later tested experimentally by Fitzgerald et al. (1984). Recently, theoretical analysis of the scaling relationships was reported by Glicksman (1984), and experimental verification of the scaling relationships has been investigated by a number of research groups. Meanwhile, a new similarity rule for bubbling beds and a scaling law for circulating fluidized beds have been developed by Horio et al. (1986, 1989). 2.1.1 Glicksman's scaling relationships (1984) To use Glicksman's (1984) scaling relationships, it is desirable to gain insight into their derivation. The governing equations in fluidized beds of spherical particles may be written (Jackson, 1971): The conservation of mass for fluid is div(sU)=0 (2.1) The conservation of mass for particles is div[(l-s)v] = 0 (2.2) The equation of motion of the fluid can be written, + 7pfgs+gradp+fi(U-v) = 0 (2.3) where /? is an interaction coefficient. The corresponding equation for the particles is + 7psg(l-e)-/3(U-v)=0 (2.4) In the above equations the fluid is assumed to be incompressible for simplicity. All inter-particle forces, particle-to-particle collisions as well as electrostatic forces are omitted for simplicity. In order to nondimensionalize the above equations, the following dimensionless quantities are used, Pfl dU dt + U-gradU P.(l-*) dv_ dt + v -gradv 5 U U p dp (2.5) The nondimensional form of the continuity equations and the equations of motion for the fluid and the particles can then be shown to be simply, div(sU') = 0 (2.6) div[(l-e)v'] = 0 (2.7) EL Ps dt 7 + (U'-7')U' l£L&e+V Ps & (l-s) dv' 7+(v ' -V')v ' JL.Ui(S'-r)=o PP ) PSU fid, + J^L(l-£)-dZZ(U'-v')=0 (2.8) (2.9) U2 * " pJJ From equations (2.6)-(2.9) and bed geometric similarity, the controlling non dimensional parameters can be identified as Pdp p gdp Pj H Dc , particle size distribution, and bed geometry. (2.10) PJJ3 Psu2' u2' P/ d; dp For non-spherical particles, the sphericity <f>s needs to be added. In Equation (2.10) the second group, p/psU2, can be ignored when the fluid velocity is small compared to the sonic velocity or the absolute pressure does not change enough to influence the thennodynamic properties of the fluid. The coefficient /? in the first group can be related to other bed properties through the Ergun equation if the particles form a loosely packed bed, given that pp-v\ = Ap/H. Hence, ^A_l5Qs(l-sf n | 175(1-s)pfp'~v'\si (2.11) P.U J PsU<i>sdp ips The dimensionless group including (3 is a function of the particle Reynolds number (Re = pfUdpjp), the particle sphericity <f>s, the voidage s and the ratio of fluid to particle densities. When Re is 4 or lower, the inertia term can be omitted and (j3dp/psU) is only a 6 function of (psUdp/ju), s and <j>s; the density of the fluid is then unimportant. When the Reynolds number is 400 or greater, the viscous term can be ignored and (JMp/psU) is only a function of pf/ps, s, and (f>s. If the voidage is very large, the following equation can be used, P.V 4 p, U In this case there are also viscous and fluid inertia dominated regimes for Reynolds numbers below about 3 and above 1000 respectively. The nondimensional drag is a function of the same dimensionless parameters as found above when using the Ergun (1952) equation. Viscous Limit: (Re < 3) For Re < 3, the density of the gas is unimportant and the governing parameters become —f-, —i-£—, —, —£-, <j>, particle size distribution, and bed geometry. (2.13) U ju dp dp Inertial Limit: (Re > 1000) At high particle Reynolds numbers the viscous drag forces between the particle and the gas are negligible compared to the inertia forces. The fluid viscosity is then unimportant and the governing parameters become —f, — , —, —-, </>s, particle size distribution, and bed geometry. (2.14) U ps dp dp Intermediate Region: (3 > Re < 1000) In this region both viscous and inertial forces are important. No simplification can be made to the number of governing parameters, i.e. 7 =-£-, Q-Z—, %-, —, —2-, <f>s, particle size distribution, and bed geometry." (2.15) U2 ju ps dp dp Recently, Glicksman et al. (1993) explored a new set of simplified scaling relationships by reworking the governing equations of motion for the particles and the fluid together with various drag relationships. However, those drag relationships are not valid for spouted beds. These simplified scaling relationships are therefore not discussed further in the present work. 2.1.2 Horio's similarity rule (1986) Horio (1986) developed a similarity rule for bubbling fluidized beds based on the governing equations of bubbles and interstitial gas dynamics developed by Horio et al. (1983). With a scale factor defined as m = ^L=AL = i (2.16) H2 Dc2 dp2' he derived the condition for geometrically similar bubble coalescence as U>-Umfl = MU2-Umf2) (2.17) The corresponding condition for a geometrically similar flow field around a bubble and for similar bubble splitting is U^=JnUmf2 (2-18) This similarity rule requires fewer controlling conditions than Glicksman's. However, Horio's similarity rule is only valid for bubbling fluidized beds. For turbulent beds, fast beds and spouted beds, etc., a new rule has to be developed individually. Horio et al. (1989) developed another scaling law for circulating fluidized beds. Meanwhile, Glicksman (1988) showed that his original parameters reduce to those of Horio (1986) when Re is low ( < 4), a condition which is unlikely to be applicable in spouted beds. * Note that one can also use Re in place of the second group since it is simply the product of the second and third groups. Therefore, in this chapter, only Ghcksrnan's scaling relationships are examined after extending them to apply to spouted beds. 2.1.3 Experimental investigations Nicastro and GKcksman (1984) used a 0.61 m x 0.61 m atmospheric fluidized bed combustor (AFBC) operating at 1098 °K and a properly scaled 0.15 mx0.15 m cold model bed to test GHcksman's scaling relationships. Ahnstedt and Zakkay (1990) carried out experiments in a pressurized fluidized bed combustor (PFBC) at 1143 °K and 0.79 MPa as well as in a cold model bed scaled to match the hot bed. Several research groups have also sought to verify GHcksman's scaling relationships experimentaUy (e.g. Newby and Keairns, 1986; Zhang and Yang, 1987; Roy and Davidson, 1988; GHcksman et al., 1991; Chang and Louge, 1992; and GHcksman et al., 1993). Table 2.1 Hsts the bed dimensions and experimental conditions used by these workers. In these comparisons most authors measured pressure fluctuations using pressure transducers, bubble activity using capacitance probes, or bubble patterns and sizes using photography. Taken together, the results indicate that: • With appropriate scaling, good agreement is achieved in most cases between scaled beds. • Without matching the scaling parameters, the characteristics of the model and the prototype differ substantiaUy. • Successful modelling cannot be achieved by simply using the same bed material in a geometricaUy similar apparatus of different size. • hi some cases similarity has been reasonable even when certain conditions were relaxed. For example, a pair of dimensionless groups was sufficient for similarity when Re < 30 (Horio et al, 1986a). 9 Table 2.1: Experimental studies of Glicksman's scaling re Reference Nicastro and Glicksman(1984) Fitzgerald et al. (1984) Newby and Keairns (1986) Zhang and Yang ,(1987) Roy and Davidson (1988) Almstedt and Zakkay (1990) Glicksman et al. (1991) Chang and Louge (1992) Glicksman et al. (1993) Large-scale bed 0.61 m x 0.61 mAFBC, 1098 °K, 1 atm 1.38 m x 1.38 mAFBC, 1600 °F, 1 atm 0.36 m x 0.15 m cold bed, 298 °K, 101 kPa 0.915 m x 0.019 m 2-D cold bed, 298 % latm (1). £>c=0.135mFBC, 1023 °K, 1 bar (2). DC=0.2S m fluidized bed, 288 °K, 1 bar ZV=0.78mPFBC, 870 °C, 0.79 MPa 0.152mx0.152mCFBC, 870 °C, 1 atm £>c=0.32, 0.46 and 1 m CFBCs, 1120 °K\ la tm (1). 0.152 m x 0.152 m CFBC, 870 °C, 1 atm (2). 0.66 m x 0.66 m CFBC, 800 °C, 1 MPa ationships for fluidized beds. Sub-scale bed 0.15mx0.15m cold model, 298 °K, 1 atm 0.46 m x 0.46 m cold model, 100 °F, 1 atm 0.18 m x 0.075 m cold model, 298 °K\ 280 kPa 0.305 m x 0.013 m 2-D cold model, 2 9 8 % latm (1). £>c=0.045 m cold model, 288 °K, 1 bar (2). Dc=0.1 m cold model, 288 °K, 6 bar £^=0.394 m cool model, 27 °C, 0.24 MPa 0.034 m x 0.034 mCFB, 20 °C, 1 atm Dc=0.20 m CFB, 288 °K\ 1 atm (1). 0.034 m x 0.034mCFB, 20 °C, 1 atm (2). 0.13 m x 0.13rn CFB, 20 °C, 0.1 MPa (3). 0.04 m x 0.04 m CFB, 20 °C, 0.1 MPa 10 2.2 Considerations for Spouted Beds Although fluidized beds and spouted beds share many common features, there are also significant differences. Most notably, the annulus of a spouted bed constitutes a moving bed with countercurrent flow between solids and fluid, while the solids in fluidized beds appear to be in more random motion fully supported by the gas. There is substantial particle-particle contact in the annulus region of spouted beds, so that the rheological characteristics of the dense phase may play a more important role than in fluidized beds, where dense phase rheology is commonly ignored. Therefore, before the dimensionless groups proposed by Glicksman (1984) can be used to scale up spouted beds, the detailed phenomena throughout a spouted bed should be examined. While equation (2.3), the equation of motion for the fluid, can be applied to spouted beds as a first approximation for smooth spherical particles, more attention needs to be focused on interparticle stresses in the annulus region where particles are in contact with each other. The equation governing the motion of the particles (equation 2.4) can be written, P.(\-e) hv -gradv dt + TPsg(l-s)-/3(U-v)-divE=0 (2.19) where E„ is the effective stress tensor for the particle phase. If we define dimensionless quantities as in Glicksman's (1984) work and introduce a dimensionless effective stress tensor, i.e. 0' = y v = 1 v = dpv, f = ~t, E; = - i - (2.20) U U dp gpsdp equation (2.19) can be nondimensionalized as {1-8) dv' 7+(v'-V')v' dt + J^(l-s)-^(U'-v')-p-(V-E'p) = 0 (2.21) 11 Fortunately the non-dimensional coefficient in front of the stress term, gdJU2, is simply the Froude number, which has aheady been included in the Ghcksman (1984) scaling relationships. Several previous workers (McNab and Bridgwater, 1974, 1979; Benkrid and Caram, 1989; Krzywanski et al., 1989) have attempted to apply the principles of soil mechanics to derive effective stress relationships for spouted beds. They assumed that the solid particles in the annulus can be represented as a rigid plastic in a quasi-static critical condition. The law of mechanical similarity (Sokolovskii, 1965) states that in geometrically similar regions, if the values of the internal friction angle (cp), the non-dimensional coefficient of cohesion, and the loose packed voidage (s0) are identical, the equivalent stresses at corresponding points are similar if they are similar at the boundaries. Particles in spouted beds are almost always larger than 1 mm in diameter, meaning that cohesive forces can be neglected, bearing in mind that granular materials are considered cohesive only when the solid particles are smaller than about 100 [im in size. Therefore, there are only two additional non-dimensional numbers, <p and e0, which need to be considered for mechanical similarity in the annulus of spouted beds. The controlling non-dimensional parameters for spouted beds can therefore be identified as §L P6E ?L K A , u>' M ' p/ d; a; ^%s°> particle size distribution, and bed geometry. (2.22) In spouted beds other factors may also need to be considered. Ghcksman (1984) was justified in assuming ^compressibility of the gas because the fluid velocity in fluidized beds is small compared to the sonic velocity so that the absolute pressure does not change enough to influence appreciably the thermodynamic properties of the fluid. However, the inlet gas velocity can be as high as 80 m/s for large spouted beds, about 20% of the sonic speed, which means that there can be significant compressibility of the gas. Therefore, if 12 scaling relationships which assume incompressibility are applied to spouted beds, significant errors may occur near the inlet. In spouted beds, upward moving particles in the spout collide with the interface between spout and the annulus and against each other within the spout (Lefroy and Davidson, 1969) and in the fountain region, as well as at the top surface of the annulus. For over-developed fountains, particles also colhde with the column wall. Electrostatic forces are also ignored and may be important in some systems, although they can be diminished in practice by using anti-static agents. Neglecting these factors is bound to lead to some deviations, but the fact that they tend to be appreciable in limited regions suggests that the dimensionless groups adopted may be sufficient as a first approximation. The Reynolds number {Re-pjdJJIju) in spouted beds is usually of order 100 (Epstein and Levine, 1978). For large columns, the Reynolds number (based on particle diameter and relative velocity) can be as high as 3000 in the spout. In the annulus the gas velocity increases with increasing vertical distance from the inlet, and flow may change from viscous to inertial. Given the Re range, it is not possible to eliminate terms by assuming high or low Re. Hence the complete set of governing parameters given in (2.22) are used in the present work. In spouted beds the following criteria are important for stable spouting: Dtjdp < 25-30 (2.23) De/D, > 3 -12 (2.24) H<Hm (2.25) The first criterion was proposed by Chandnani and Epstein (1986) based on experimental data on a small column and fine particles and extended to a 0.91 m diameter column by Lim and Grace (1987). Equation (2.24) was proposed by Mathur and Epstein (1974) based on experience with small columns. Application of the third criterion can be difficult as available equations tend to overestimate Hm by wide margins in large columns (He, 1990). 13 2.3 Experimental Verification of the Scaling Relationships 2.3.1 Bed and particle parameters and operating conditions The strategy for verifying the scaling relationships started with a rough conceptual design of a large-scale or elevated temperature unit, defining the probable range of operating conditions, the particle characteristics and main features of the vessel. A practical sub-scale model was then designed by selecting the unit characteristic dimensions, and selecting the particle size, particle material, and spouting gas to satisfy equality of the dimensionless groups in (2.22). Some iterations were usually required to find a suitable gas and particle combination, and the fluid pressure and temperature in the sub-scale model might need to be varied. Meanwhile the three additional criteria, Equations (2.23)-(2.25), were kept in mind throughout. Test conditions for cold spouted beds are summarized in Table 2.2. Case A in Table 2.2 Usts the conditions for tests in a 0.152 m diameter column with glass beads of mean diameter 2.18 mm and with air at room temperature and atmospheric pressure. In case B, we employed 1.09 mm steel shot, with bed dimensions half those in case A and bed pressure increased to 312 kPa to match all the dimensionless groups in (2.22). Cases A and B were designed to study the validity of the scaling relationships. In order to examine the influence of each dimensionless group on similarity, one or more group was purposely mismatched in cases C to G. For example the Reynolds number and Froude number were not matched for cases C and D respectively. Mismatched dimensionless groups are shown in bold. Run C was designed to test also the error in attempting to scale up spouted beds by varying only the dimensions, i.e. achieving geometric similarity only, while using the same gas at the same temperature and pressure. In case G, sand was used instead of glass beads to examine the influence of particle sphericity and internal friction angle (<p). In case E, two groups rather than three may be considered to be not matched since 14 Table 2.2: Comparison of dimensions, properties and dimensionless groups in experimental tests. The gas was air in all cases. Condition/Run Dc(m) Dj (mm) L(m) H(m) T(°K) P(kPa) Particles dp (mm) Ps (kg/m3) pf(kg/m3) ju (x 105) U(m/s) DJD, D/dp H/Dn ts <PO £0 D/dp P/Pf Re-pdpU/ju UVzd PsdpU/v(x 10-3) A 0.152 19.1 1.14 0.323 298 101 glass 2.18 2400 1.21 1.81 1.08 8 8.7 2.1 1 26 0.41 69.9 1994 157 54.5 313 B 0.076 9.5 1.14 0.16 298 312 steel 1.09 7400 3.71 1.81 0.75 8 8.7 2.1 1 28 0.42 69.9 1995 168 52.6 334 C 0.076 9.5 1.14 0.16 298 101 glass 1.09 2450 1.21 1.81 0.74 8 8.7 2.1 1 27 0.42 69.9 2029 54 51.2 109 D 0.076 9.5 1.14 0.16 298 101 glass 1.09 2450 1.21 1.81 2.15 8 8.7 2.1 1 27 0.42 69.9 2029 157 432.2 317 E 0.076 9.5 1.14 0.16 298 312 glass 2.18 2400 3.71 1.81 1.06 8 4.4 2.1 1 26 0.41 35.0 648 474 52.5 307 F 0.076 9.5 1.14 0.16 298 101 glass 2.18 2400 1.21 1.81 1.12 8 4.4 2.1 1 26 0.41 35.0 1994 161 57.6 324 G 0.152 19.1 1.14 0.323 298 101 sand 2.18 2490 1.21 1.81 1.11 8 8.7 2.1 0.88 38 0.44 69.9 2068 163 58.7 333 15 the scaling parameters in (2.22) include Ud^pJju rather than the Reynolds number, Udppf/ju. The Reynolds number, however, is used in the following discussion for convenience, while the group Udppsl ju appears at the bottom row in Tables 2.2 and 2.3 as a reference. The conditions employed in columns of larger scale and in beds operated at elevated temperature are shown in Table 2.3. Runs H, I, J and K were designed to examine the scaling relationships for a 0.914 m diameter column, while runs L and M were designed to study the validity of the scaling relationships for operation at elevated temperatures. 2.3.2 Experimental equipment and particulate materials Figure 2.1 is a schematic diagram of the experimental set-up. It consisted of a pressurized shell (1.6 m height and 0.305 m I.D., built by earlier workers in this department) section I, a high temperature column section II and an ambient temperature and atmospheric pressure section III. The four columns used in the experiments covered in Tables 2.2 and 2.3 with diameters 0.914, 0.152, 0.076 and 0.051 m were all semi-cylindrical in cross-section. Ideally these experiments would have been conducted in fully cylindrical columns but this would have restricted the number of dependent variables that could have been compared. Except for the high temperature column, which was steel with quartz windows, the columns were made of Plexiglas. Runs B, E, I, K and M in Tables 2.2 and 2.3 were carried out in section I in Figure 2.1. The columns of diameter 0.051, 0.076 and 0.152 m were placed inside the pressurized shell to enable them to be operated at high pressures. Runs A, C, D, F, G and J were conducted in section III under ambient temperature and atmospheric pressure. The largest column of diameter 0.914 m for Run H was described previously (He et al., 1992), while the high temperature unit for Run L was previously employed by Zhao et al. (1987) and Ye et al. (1992). The pressure vessel was equipped with four pairs of facing windows, through which the entire spouted bed column could be illuminated and observed. The building 16 Table 2.3: Comparison of dimensions, properties and dimensionless groups in experimental tests. The gas was air in all cases. Condition/Run Dc(m) Dj (mm) L(m) H(m) T(°K) P(kPa) Particles dp (mm) Ps (kg/m3) /y(kg/m3) ju(x 105) U(m/s) DJD, D/dp H/Dr <t>s <P(°) So Dc/dp PjPf Re-pdpU/ju U2/zd„ pd„U/M(xW) H I J K L M 0.914 0.152 0.152 0.152 88.9 14.8 14.8 14.8 3.60 1.14 1.14 1.14 2.00 0.33 0.33 0.33 298 298 298 298 101 243 101 243 PS* sand sand sand 3.25 0.54 0.54 1.80 1020 2490 2490 2490 1.21 2.90 1.21 2.90 1.81 1.81 1.81 1.81 0.756 0.31 0.32 0.57 10.3 10.3 10.3 10.3 27.4 27.4 27.4 8.2 2.19 2.19 2.19 2.19 0.87 0.88 0.88 0.88 40 41 41 39 0.44 0.45 0.45 0.44 281 282 282 85 845 859 2059 859 164 26.2 11.3 161 18.0 18.1 19.3 18.4 138 22.5 23.3 138 0.152 0.051 19.1 6.4 1.16 1.14 0.30 0.10 773 298 101 135 glass steel 2.18 0.73 2400 7400 0.52 1.61 3.31 1.81 2.47 1.41 8 8 8.7 8.7 1.97 1.96 1 1 26 29 0.41 0.42 70 70 4586 4597 85 91 285 279 391 419 * PS - polystyrene 17 00 Exhaust Section II Section III Figure 2.1: Schematic diagram showing overall equipment layout for four separate columns. compressed air flow entered the column at ambient temperature through a pair of rotameters. At the top of the vessel, air passed through a filter before leaving through the exhaust pipe. The rig could be operated at pressures up to 445 kPa with building air. A pressure relief valve, set at 400 kPa, was installed at the top of the pressure vessel for safety reasons. The system was first pressurized to a desired pressure and then the flow rate through the inside spouted bed was adjusted by a rotameter and a bypass valve to obtain stable spouting. For the high temperature column in section II, air was heated by cylindrical electrical heaters mounted on the outside of stainless steel pipes which carried air to the column. This heating system was capable of maintaining operating bed temperatures up to 800°C with proper insulation. Details of the high temperature unit have been provided by Wu et al. (1987). The particulate materials used in this study included 1.09 mm and 2.18 mm diameter glass beads, 0.73 mm and 1.09 mm diameter steel shot, 3.25 mm volume diameter polystyrene particles, and 0.54 mm, 1.80 mm and 2.18 mm mean diameter sand. Properties of these materials are given in Table 2.4. Particle diameters were obtained by sieving, except for the polystyrene particles where measurements with a caliper were taken of 20 particles chosen at random. Particles were closely sized by choosing particles in only one 4V2 sieve interval, e.g. 2.0 to 2.36 mm for the 2.18 mm diameter particles. Particle densities were determined by the water displacement method. The glass beads and steel shot were spherical, while the polystyrene particles were nearly elliptical cylinders. The sand particles were less regular. The sphericity of the polystyrene particles was determined by measuring the dimensions of 20 randomly chosen particles with a microscope to estimate their surface areas and volumes. The sphericity of sand was determined by inserting the measured values of Umr and smr into the Ergun (1952) equation. Internal friction angles were determined by measuring the angle to the horizontal within the vessel after discharging solid particles from a two-dimensional vessel of width 305 mm and 19 thickness 25.4 mm through a slot orifice of width 25.4 mm at the centre of the horizontal base. Table 2.4: Properties of particulate materials Material Glass beads Glass beads Steel shot Steel shot Sand Sand Sand Polystyrene dp (mm) 2.18 1.09 1.09 0.73 2.18 1.80 0.54 3.25 * (kg/m3) 2400 2450 7400 7400 2490 2490 2490 1020 s0 0.41 0.42 0.42 0.42 0.44 0.44 0.45 0.44 A 1 1 1 1 0.88 0.88 0.88 0.87 9 (°) 26 27 28 29 38 39 41 40 2.3.3 Measurement methods Minimum spouting velocities were measured by observing the beds through the front windows. The gas flowrate was first increased to a value above the minimum spouting condition and then decreased slowly until spouting ceased. The gas flowrate at which the fountain just collapsed was taken as the minimum spouting flowrate. The maximum spoutable bed height was determined by increasing the bed height in steps until stable spouting could not be obtained at any gas flowrate. The corresponding loose-packed bed height was taken as Hm. The spout diameter and the fountain height were determined by a video camera, with a rule attached to each of the half-columns as a reference. Pressure taps were fitted at 50 mm or 100 mm vertical intervals along the curved wall of each of the half-columns, beginning near the inlet, to measure the overall pressure 20 drop and the pressure gradient in the annulus. The overall pressure drop was determined by a pressure transducer (Model PX242-005G-5V, Omega) connected to a pressure tap located just above the inlet orifice. The measured values were then corrected to account for any venturi effect (Mathur and Epstein, 1974). The pressure gradient in the annulus was measured by seven differential pressure transducers (Model PX163-005D-5V, Omega). For the elevated pressure tests, the entire pressure measurement system was placed inside the pressurized vessel. Output electrical signals were brought out through two power lead glands (Model PL-18-A-10, Conax Co.) and then fed to a computer by an A/D converter so that output signals could be recorded automatically using a Labtech Notebook (Version 5.0) package. Prior calibration of pressure transducers was conducted with a micromanometer (Model MM-3, Flow Corp. of Cambridge, Mass.). 2.4 Results and Discussion 2.4.1 Scaling tests in smaller columns In order to evaluate the validity of the scaling relationships in spouted beds, seven series of tests were conducted in smaller columns in which maximum spoutable bed depths, spout shapes and diameters, fountain heights, and longitudinal pressure profiles in the annulus were all measured. Table 2.2 provides a summary of the scaling test conditions. Table 2.5 presents maximum spoutable bed depths, Hm, for seven cases, corresponding to those summarized in Table 2.2. Hm values are non-dimensionalized to compare the results more clearly. As anticipated from the theory, there was excellent agreement between the prototype bed (case A) and the model bed (case B) where all dimensionless parameters in (2.22) were matched as closely as possible for the two runs. The results for cases C and D (which are the same because these two differ only in superficial velocity) deviates from case A by 21%. This indicates that successful scaling 21 cannot be achieved by varying only the column and particle dimensions. The result for case E, in which the density ratio and D/dp ratio were mismatched, also deviates from the result for case A, although the difference is less than 10%. In case F, the dimension ratio (D/d) was altered and there is an appreciable difference in #„/D c . The substantial difference between the results of cases G and A with sand and glass beads respectively illustrates the significant influence of particle sphericity and internal angle of friction on similarity. Table 2.5: Maximum spoutable bed depths for seven tests in small columns. Case* A B C,D E F G Column diameter A; (mm) 152.4 76.2 76.2 76.2 76.2 152.4 (mm) 396 195 240 180 170 660 Hn/Dc 2.60 2.56 3.15 2.36 2.24 4.33 Deviation (%) _ -1.5 21.2 -9.2 -13.9 66.5 * For other conditions, see Table 2.2. Figure 2.2 shows spout diameter as a function of height for the seven cases outlined in Table 2.2. Near similarity was again achieved when all dimensionless groups in (2.22) were matched (cases A and B). Spout diameters for case C were smaller than in A, presumably because the Reynolds number in case C was much lower. Spout diameters for case D were considerably larger than in A, emphasizing the importance of the Froude number. Case F in which the Dr I d„ ratio was mismatched and case E where several groups were not the same as in case A again deviated significantly from the results for case A. On the other hand, cases G and A gave relatively close agreement, even though 22 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 Dimensionless radius (2R/D_) Figure 2.2: Dimensionless spout diameters as a function of dimensionless height for smaller columns. Conditions are given in Table 2.2. 23 the particle sphericities and internal friction angles differed significantly. This is consistent with the theoretical model of Bridgwater and Mathur (1972), who considered a force balance and solid stresses in the annulus based on the principles of hopper flow of solids and concluded that the spout diameter depends only on the gas mass flow rate, column diameter and particle bulk density, with sphericity and internal friction angle not influencing spout shapes. Table 2.6: Fountain heights for the seven cases outlined in Table 2.2. Case A B C D E F G Bed height, H(mm) 325 160 160 160 160 160 325 Fountain height, HF (mm) 135 59 40 250 84 45 300 Dimensionless fountain height, Hp/Dc 0.89 0.78 0.53 1.56 1.11 0.59 1.97 Deviation (%) _ -13 -41 +75 +24 -34 +122 Table 2.6 summarizes fountain heights for the seven cases outlined in Table 2.2. Similarity with case A was again closest with the properly scaled case B. Lack of equality between any of the dimensionless parameters in (2.22) resulted in disagreement between the prototype bed (case A) and the mismatched model bed (cases C, D, E, F, and G). The largest discrepancy was between cases G and A, implying that fountain heights are very sensitive to particle shape, hi order to explain this phenomenon, particle velocities at several locations in the annulus region were checked. It was found that downward particle 24 velocities in case G were on average 27% lower than corresponding particle velocities in case A. The irregular sand used in G likely supports higher local effective stresses in the annulus, resulting in turn in lower particle velocities in the annulus. Based on conservation of mass, the downward solids flow in the annulus must equal the upward solids flow in the spout at any given level. Therefore, the voidage in the spout must be higher in case G than in A, bearing in mind that spout diameters were nearly the same for both cases as shown in Figure 2.2. According to the theoretical model of Grace and Mathur (1978), fountain height depends on the spout voidage at the bed surface level. The much higher fountain in case G is therefore consistent with the reduced solids circulation rate. Figure 2.3 presents dimensionless longitudinal pressure profiles for the seven cases corresponding to Table 2.2. Close correspondence between measured results clearly existed between cases A and B, with greater deviations occurring for the other five cases where one or more of the dimensionless parameters listed in (2.22) was not matched. The above results indicate that the scaling relationships in (2.22) are valid for small-scale spouted beds. All dimensionless groups in (2.22), except the ps Ipf ratio, have been individually verified to be important and, therefore, none of the groups can be omitted from the full set of scaling parameters. Solids particle internal friction angles and sphericities affect the maximum spoutable depth, fountain height and longitudinal pressure profiles. Not surprisingly, particle-particle interaction forces cannot be ignored in spouted bed scale-up studies. 2.4.2 Scaling tests in larger columns and high temperature columns The validity of the scaling parameters in (2.22) was also investigated using the 914 mm diameter column and the high temperature column of diameter 152 mm. Measurements again included spout diameters, fountain heights and longitudinal pressure profiles in the annulus. Maximum spoutable bed depths were also measured in the high temperature column, but could not be determined in the 914 mm column because not 25 1.0 0.8 0.6-0.4 •S 0.2-Q 0.0 0 Xlt?^ i. • ^^t^*^S5e ^^•VeFx.->st»r*« NtO — ^^* -• i H •. *» <.• * ^ ^is v*> ^ssS "S \ XvC Case ^ • — • -.....±. , ,, , \ / X —-a-— o ~ A--i i A B C D E F G * „ : & : 1 1 1 1 1 -V \\v. X\V\\ N A V V °X>\\. H* .0 0.2 0.4 0.6 0.8 1.0 Dimensionless vertical level, z/H Figure 2.3: Longitudinal pressure profiles in the annulus for columns of diameter 76 and 152 mm, with conditions given in Table 2.2. 26 enough polystyrene particles were available. The scaling test conditions for these tests are summarized in Table 2.3. As discussed above, the particle internal friction angle and sphericity can significantly influence hydrodynamics of spouted beds. The particles were carefully selected for cases I, J and K to match the scaling parameters in (2.22) as closely as possible. However, it was not possible to operate at a high enough pressure to allow all of the relevant groups to be matched. Olivine sand was chosen for cases I, J and K Microscopic inspection showed that the sand particles were more rounded than the polystyrene particles. Measured fountain heights, spout diameters and longitudinal pressure profiles for cases H to K are shown in Table 2.7, Figure 2.4a and Figure 2.5, respectively. Except for a 24% deviation in H/Dc, there is reasonable agreement between cases H and I, in which only the Reynolds number could not be matched. Comparisons of results for cases J and K, in which the density ratio together with the Reynolds number, and the dimension ratio were altered, respectively, with results from case H gave unsatisfactory agreement. Both viscous and inertial forces are important, and therefore no simplifications are permissible to the full set of scaling parameters. Case H I J K L M Table 2.7: Bed height, H(m) 2.00 0.33 0.33 0.33 0.30 0.10 Fountain heights for Fountain height, HF (m) 3.15 0.40 0.24 0.31 0.180 0.065 2ases outlined in Table 2.3. Dimensionless fountain height, Hp/Dc 3.45 2.63 1.58 2.04 1.18 1.27 Deviation (%) --24 -54 -41 -+8 27 "(D CO CO _CD c o "co c E b 0.0 0 0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 Dimensionless radius (2R /D ) Figure 2.4: Dimensionless spout diameters as a function of dimensionless height for cases outlined in Table 2.3. 28 CO CL < I Q . CD Z3 CO CO CD CO CO 0) c O "co c CD E b 1 .u 0.8 0.6 0.4 0.2 n n ••••. x* \ . \ \ \ \ Case —•— H • - - • - - | • ...A... J I . I . I . i • 1 --\ V -• V \ \ \ \ * vx 1 " 1 0 0 0.2 0.4 0.6 0.8 1.0 Dimensionless vertical level, z/H Figure 2.5: Longitudinal pressure profiles in the annulus for columns of diameter 152 and 914 mm with conditions given in Table 2.3. 29 A notable finding was that a dead zone on the bottom of the annulus, which was previously observed only in large columns (Green and Bridgwater, 1983; Lim and Grace, 1987; He et al., 1992), was also observed in the 0.152 m diameter column for cases I and J. The dead zone boundaries corresponding to cases H, I and J are shown in Figure 2.6. It is seen that there was again closer agreement between case H and case I. No dead zone was observed for case K Verifications of the scaling parameters in (2.22) were also conducted using the high temperature column by comparing cases L and M in Table 2.3. All dimensionless parameters in the 1/2 scale bed (case M) were chosen to match those in the high temperature bed (case L). Experimental fountain heights, spout diameters and longitudinal pressure profiles are shown in Table 2.7, Figure 2.4b and Figure 2.7 respectively. The coincidence of the hot and cold results suggests that the scaling parameters in (2.22) are sufficient for hydrodynamic similarity. For the series of tests in high temperature beds, maximum spoutable bed depths were also measured. Hm values from cases L and M were 0.34 m and 0.13 m respectively, corresponding to non-dimensionalized {H^D^) values of 2.23 and 2.56, a deviation of only 15%. The above results indicate that the modified scaling parameters in (2.22) are valid for spouted bed scale-up. This finding may be of considerable importance to simulate the behaviour of large-scale spouted beds using scaled down models operating at room temperatures since most commercial applications of spouted beds involve large columns operating at elevated temperatures so that experimental investigation of such beds is both expensive and complicated. On the other hand, most experimental investigations have been made in small vessels with air at room temperatures. The scaling method outlined here provides a means of testing the applicability of these results. 30 N CD "<D SZ V) (/) 0 c o "if) c 0 Q o O 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless radius (2RD/DC) Figure 2.6: Dimensionless dead zone boundaries as a function of dimensionless height for cases outlined in Table 2.3. 31 CO Q_ < I CL i Q . CD v_ CO CO CD i _ CL CO CO 0 c g 'co c E b 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless vertical level, z/H Figure 2.7: Longitudinal pressure profiles in the annulus for high temperature beds. 32 2.5 Conclusions The scaling relationships proposed by Glicksman (1984) for fluidized bed scale-up have been modified to provide a full set of scaling parameters for spouted bed scale-up. By analysis of the force balance on particles in the annulus region of a spouted bed, two additional non-dimensional parameters, the internal friction angle {(p) and the loose packed voidage (s0 ), have been added to the original scaling relationships, while the remaining non-dimensional parameters are identical to those in the Glicksman scaling relationships. Experimental verifications of the full set of modified scaling parameters, subject to the three criteria in equations (2.23), (2.24) and (2.25), have been conducted in columns of different size at atmospheric and elevated temperatures and pressures. It has been demonstrated that the full set of modified scaling parameters are valid for spouted beds when all dimensionless parameters are matched between a prototype and a model bed. Both viscous and inertial forces are important and, therefore, no simplifications can be obtained to the full set of scaling parameters. Successful scaling cannot be achieved by varying only bed and particle dimensions. Particle internal friction angles and sphericities have significant influence on the maximum spoutable depth, fountain height and longitudinal pressure profiles; particle-particle interaction forces cannot be ignored in spouted bed scale-up. A dead zone was observed not only in the 0.914 m diameter column, but also in the 0.152 m diameter column with a proper combination of bed geometiy, solid particles and operating conditions. 33 Chapter 3 Voidage Profiles 3.1 Previous Work 3.1.1 Measurements of voidage profiles in spouted beds The voidage in the annulus of spouted beds is usually assumed to be constant and equal to the loose-packed voidage for the particulate material (Mathur and Gishler, 1955; Thorley et al., 1959; Mathur and Epstein, 1974). On the other hand, Thorley et al. (1959) noted slight differences in voidage in different parts of the annulus. This was also observed by Grbavcic et al.(1976) using a water spouted bed. Further measurements are needed. In the fountain region, a y-ray technique has been used to measure the vertical voidage profile (Waldie et al., 1986). This technique is only able to determine the vertical profile of the cross-sectional average voidage in the fountain. A more advanced technique is needed to measure the local voidage profile in the fountain region. A calculation method has been frequently used to determine spout voidages (e.g. Mathur and Gishler, 1955; Lim and Mathur, 1974; Day et al., 1987), based on the fact that the downward solids flow in the annulus under steady state operating conditions equals the upward solids flow in the spout at any bed level and on the assumption (see above) that the annulus voidage equals the loose-packed voidage. The voidage in the spout is estimated by measuring downward particle velocities at the column wall and upward velocities in the spout of a half-column spouted bed with a high speed cine camera. This method is clearly unable to calculate the radial voidage distribution in the spout. Moreover, wall effects reduce the reliability of the data. 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 (3-ray absorption (Elperin et al., 1969). The piezoelectric technique requires simultaneous particle velocity 34 measurements, while the capacitance probe and P-ray absorption technique were used only in two-dimensional spouted beds. 3.1.2 The fiber optic probe technique Recently fibre optic probes have been used to measure local voidages in fluidized beds (e.g. Morooka et al., 1980; Matsuna et al., 1983; Nakajima et al, 1990). In the present work, this technique is applied to spouted beds. Krohn (1982, 1986) classified fiber optic sensors into five types: intensity-modulated, transmissive, reflective, microbending and intrinsic. Here we are only interesting in the reflective type because all sensors for measuring local bed voidages in fluidized beds have been based on this concept. O 25 50 75"" 100' 125 150 175 200 Distance (0.001 Inch) (A) Ou tpu t v s . D i s t a n c e Figure 3.1: Prevailing configurations of reflective optical probes (Krohn, 1986) Previous reflective optical probes have been reviewed by Krohn (1986) as shown in Figure 3.1. The concept is shown in Figure 3. IB. The sensor is comprised of two bundles of fibers or a pan of single fibers. One bundle of fibers transmits hght to a reflecting target, while the other bundle traps reflected hght and transmits it to a detector. The intensity of 35 the detected light depends on how far the reflecting target is from the fiber optic probe. Figure 3.1 A shows the detected light intensity versus distance from the target. The accuracy depends on the probe configuration: a hemispherical probe has more dynamic range, but less sensitivity when compared to a random probe (Figure 3.1C). A fiber pah-probe further expands the dynamic range. A single fiber used in conjunction with a beam splitter to separate the transmitted and the received beams eliminates the front slope. Reflective optical probes are especially attractive for broad sensor use due to accuracy, simplicity and potential low cost. Further details are given by Krohn (1982, 1986). D.C. Regulator nr Ught source Ught detector Voltage integrator Micro computer I Sieve i Particles . Optical probe 7777777777777777 * (a) (b) Figure 3.2: (a) Schematic diagram of measuring system (b) Calibration method for particle concentration (Matsuno et al., 1983). 3.1.3 Applications of fiber optic probes for measuring voidage in fluidized beds The basic principle underlying the fiber optic voidage probe is that the intensity of back-scattered light from particles depends on the particle concentration. Illuminating light projected from the tip of an optical fiber is partly reflected by the swarm of particles in the vicinity of the optic fiber (Figure 3.2a), and the reflected light is then guided to the light-36 detector where it is converted to electrical pulses according to the light intensity. After integration for a definite time, the integrated value is recorded in a microcomputer. As no method for direct conversion of integrated electrical signals to bed voidage or particle concentration exists, a calibration method has been used by a number of authors (e.g. Matsuno et aL, 1983; Boiarski, 1985; Nakajima et al., 1990): particles are allowed to fall freely at their terminal velocity after having travelled a certain distance. For example, as shown in Figure 3.2b, particles from a sieve at a sufficient height are made to fall uniformly by vibrating the sieve. The particle concentration can be varied by changing the weight of particles on the sieve and also by using sieves of different apertures. The particle concentration is calculated by where AW is the cumulative weight of particles sampled on the cross-sectional area S within time At, and Ut is the terminal velocity of particles at the given concentration. Knowing the particle mean diameter, density and terminal velocity, one can easily calculate the local voidage. The calibration curve is plotted as voidage versus integrated voltage. Some typical fiber optic probes employed by previous authors are shown in Figure 3.3. The probes used by Matsuno et al. (1983), Nakajima et al. (1990) and Kato et al. (1990) shown in Figures 3.3b, d and e, respectively, are essentially the same. Each fiber optic probe consists of a pair of parallel optic fibers, one from the fight source and the other connected to the light-receiver. The probe shown in Figure 3.3c is covered with a glass window to seal it from liquid media. In addition to the parallel configuration, a crossed configuration fiber optic probe has been studied by Reh and Li (1990) as shown in Figure 3.3f. This crossed configuration is strongly recommended by the authors to improve the spatial resolution of the reflective optical measurements. The probe employed 37 by Morooka et al. (1980) is shown in Figure 3.3a. The authors used this probe to measure local particle velocities and then to calculate the local holdup of solid particles. to photomultiplier Epoxy resin ass 10 -1.5 mm K H c ::::v;: « -ii (• m from light source to receiver stainless steel pipe of 1.5 mm O.D. b a >r=€ w *— Laser beam Holder Overlap Zone Stainless pipe Optical fiber d _ Fiber „ „ __ . B holder* i C o v e r HResm ~*to phototransistor © T i> 6 mm <J> 10 mm - , T • . , „•„.;„„ T ^— T /^7-x ^ mm 1 Light emitting _ I r - i - ^ r ^ o x 2 Photo-transistor L-Re^f © 3 Acrylic pipe 4 Aluminum pipe (a) CROSSED Tube <(» 6.0 mm, Fiber d> 1.0 mm Glass Window 0.4 mm (b) PARALLEL e f Figure 3.3: Typical fiber optic probes used by previous authors: (a) Morooka et al. (1980), (b) Matsuno et al. (1983), (c) Boiarski (1985), (d) Nakajima et al. (1990), (e) Kato et aL (1990), (f) Reh and Li (1990). The fiber optic technique has been used to measure local bed voidages in three dimensional fluidized beds. Table 3.1 summarizes some references and what was measured. In the present work, the fiber optic probe technique is applied to fully three-dimensional spouted beds. 38 Table 3.1: Experimental measurements using the fiber optic probe technique Reference Morooka et al. (1980) Matsuno et al. (1983) Boiarski(1985) Nakajima et al. (1990) Kato et al. (1990) Reh and Li (1990) Baietal. (1990) Unit used Fluidized bed Fluidized bed Polystyrene microspheres suspension in water Turbulent fluidized bed Circulating fluidized bed Fluidized beds Cocurrent downflow fast fluidized bed Parameter measured Radial solid concentration profile Local particle concentration Cell concentration Bubble fraction and voidage Particle holdup distribution Voidage Radial profiles of local solid concentration, particle velocity 3.2 Apparatus and Instrumentation in the Present Work 3.2.1 Apparatus Most of the experiments were carried out in a fully cylindrical plexiglas column of inside diameter 152 mm and height 1.4 m with a 60° conical base shown in Figure 3.4. A few experiments were also performed in a half-column, having the same diameter as the full-column. An inverted conical stabilizer, 55 mm in diameter and 45 mm high, was installed at the top of the column to prevent the spout and fountain from swaying. Observation indicated that the stabilizer did not appreciably change the fountain height and shape. The stabilizer was removed for measurements at the two highest levels. 39 m Fountai Spout Annulu V Air Stabilizer Fibre Optic Probe PC-3 I A/D Convertei Microcomputei Figure 3.4: Experimental setup. 40 Eighteen holes, each with fittings, were drilled at 50 mm vertical intervals along the column wall, beginning near the bottom. The fiber optic probe could be inserted in any of the holes and traversed radially to measure voidage profiles. A plate with orifice of 19.1 mm diameter at the base provided the inlet for both columns. The voidage was measured using a fibre optic probe technique. Closely sized glass beads of mean diameter 1.41 mm and density 2503 kg/m^ were used as the particles. The spouting fluid was air at room temperature. The minimum spouting velocity, Ums, for a bed height of 0.325 m was 0.54 m/s and 0.56 m/s for full and half columns respectively. 3.2.2 Instrumentation: probe, calibration and validation The fiber optic system, model PC-3 shown in Figure 3.5, was developed by the Institute of Chemical Metallurgy of the Chinese Academy of Science. Figure 3.6 shows the principle of the fiber optic system. The system is similar to those employed previously (see Figure 3.2 and section 3.1.3), except that there is a dual light-way referential light autoadjustable system to maintain long-term stability and eliminate drift due to variations of ambient temperature, light source and electronic parts. The system adjusts itself before each sampling to keep the system in its initial status. With the system there is a menu-driven data acquisition and control software package for easy operation. The software includes such features as graphical and tabular display of real-time data, and datalogging to printer or disk for further data analysis. Figure 3.7 presents a typical sample of a sampling waveform curve obtained for a spouted bed. The present work appears to be the first to report measurements of voidage using a fibre optic probe for such large particles. A relatively large probe of 4 mm ID. shown in Figure 3.8, which could cover at least several particles on the probe tip, was required. Within the probe thousands of optical fibers, each 16 u,m in diameter, were arranged in 41 Figure 3.5: Photographs of the fiber optic system and fiber optic probes. 42 ' Optical Fibers * . . .A. . . . . . r i Light : Wedge r On-Off Light Switch < — * -Light Source High Voltage Adjustment 1 ' Photo-Multipher Fiber Optic i Prob — * • A/D Converter , t Amphfier & Auto-Check — ^ e Micro-Computer Figure 3.6: Block diagram of the fiber optic system, Model PC-3. 43 TIME(s) Figure 3.7: A sampling waveform curve obtained in a spouted bed. Full-column, H=0.325 m, U/Ums=1.2. 44 Fibre bundle Side view Figure 3.8: Fibre optic probe schematic. 45 an array in which the fibers acting as light projectors alternated with fibers acting as light receivers. Previous experimental findings (Matsuno 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 fiber optic probe. In the present work, the linear relationship was checked by immersing the probe in a liquid-solids fluidized bed for voidages less than 0.75 and a well stirred beaker for voidages greater than 0.75, with details described in the Appendix. In these tests, the liquid was tap water and the particles were 1.41 mm glass beads. As shown in Figure A. 1 of the Appendix, the calibrations from both systems were very linear over the entire voidage range of interest. Therefore, an in-situ calibration curve was obtained by putting the probe in an empty column 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 large probe led to a substantial drop-off of signal with distance as shown in Figure 3.9 obtained by fixing the probe outside the column and then moving a flat plate with glass beads glued to its face to and fro in front of the tip. By increasing the light source voltage, there was less influence of remote particles, as shown by the solid circles. Because the signal is a strong function of particle concentration, the data in Figure 3.9 only represent one possible case. The probe was also tested with the same two light sources in a spouted bed. The results are shown in Figure 3.10. It is seen that the readings with two light sources are almost the same, with the largest deviation less than 3%. Thus the effect of light source voltage may be neglected. In the present work the light source voltage for all measurements was set at 3.56 V, which corresponded to the adjusted light source voltage. For each data point in this chapter, the sampling frequency was set at 1004 per second and the sampling interval was 30 s. Each voidage value given is an average value for such intervals. The standard deviation between intervals was within 0.0072 in the annulus and 0.0097 in the spout for mean values of 0.38 to 0.54 and 0.62 to 1.0, respectively. 46 CO c CD £2 D) "D 0 «+-» O 0 « + -0 s _ 0 > • — jcg 0 Original Light Source (2.34 volts) Adjusted Light Source. (3.56 volts) 0 3 6 9 12 15 Distance from probe tip (mm) Figure 3.9: Signal intensity measured by probe as a function of distance for a flat plate with attached glass beads of mean diameter 1.41 mm and for two different light sources. 47 1.0 0.9 0.8-r-°~^X 0.7 0 CT> CO o 0.6 > 0.5 0.4 0.3 1 1 1 1 1 1 1 Original Light Source *-••—* •*••«-•--•• Fountain region -+'- \ Zp=0.045 m Adjusted Light Source Spout z=0.168m Original Light Source / Annulus Adjusted Light Source 0 10 20 30 40 50 60 70 80 Radial distance from spout axis (mm) Figure 3.10: Comparison of voidage measurements within a spouted bed and in the fountain above the bed with two different light sources. Data indicated by triangles were obtained in the fountain at Zp=0.045 m; data denoted by squares and circles were taken in the spout and the annulus at z=0.168 m with H=0.325 m and U/U =1.2. 48 3.3 Results and Discussion 3.3.1 Voidage in the annulus The experimental values of voidage in the annulus for three different gas flow rates appear in Figure 3.11. The voidage in the annulus is seen to increase with increasing superficial gas velocity. The average voidage values in the annulus for U/Ums=\.\, 1.2 and 1.3 are, respectively, 2.5%, 4.9% and 11.6% higher than the loose-packed voidage of 0.412. The averaged voidage values from Figure 3.11 and corresponding standard deviations for a 95% confidence interval are listed in Table 3.2. Note that it is unlikely (95%) confidence) that the average voidage in the annulus lies below the loose-packed ..voidage, 0.412. The above findings demonstrate that the common assumption that the voidage in the annulus is constant and equal to the loose-packed voidage is not accurate. Consequently, measurement techniques, models and findings based on this assumption are open to question. For example, one common method of measuring annulus gas velocities in the cylindrical portion of a spouted bed involves determination of static pressure gradients along the annulus using a differential pressure probe or pressure taps along the column wall. The measured pressure gradients are then converted into gas velocities using the pressure drop versus velocity relationship obtained from loose-packed fixed beds. The data determined by this method will therefore underestimate the actual gas velocities in most of the annulus because a higher gas velocity is needed to give the same pressure gradient for a higher voidage. Table 3.2: Average voidage values and corresponding standard deviations for a 95% confidence interval in the annulus for U/Ums=l.l, 1.2 and 1.3. u/ums 1.1 1.2 1.3 sample average s 0.421 0.432 0.460 standard deviation (SD) 0.00093 0.00103 0.00435 critical point t.025 2.010 2.011 2.009 population mean e=s ±t025SD 0.421 ±0.0019 0.432 + 0.0021 0.460 + 0.0087 49 0 CD CO •D o > 0.55 0.501-0.45 0.40 0.35 0.55 0.50 0.45 2 0.40 0.35 0.55 0.50 0.45 0.40 0.35 4 I * I I • M • • + X U/Um s=1.3 • • t I • X 6.412 (loose-packed) U/U =1.2 ' ms * * • * * 0.412 (loose-packed) i r U/U =1.1 ms .4.I.J....I...X....I....X..I I I. *+ 0.412 (loose-packed) • 0,318 • 0.268 * 0.218 • 0.168 • 0.118 + 0.083 x 0.053 * 0.022 0 10 20 30 40 50 60 70 80 Radial distance from spout axis (mm) Figure 3.11: Voidage profiles in the annulus. Full-column, H=0.325 m. 50 Theoretical models describing gas flow in the annulus, such as the Mamuro-Hattori (1968) model, the model of Grbavcic et al.(1976) and the Epstein-Levine (1978) model, are also based on the assumption that the voidage in the annulus is equal to the loose-packed bed voidage. Some modification again appears to be necessary. The important observation of Grbavcic et al.(1976) that for a given fluid-solid combination and column geometry the annulus fluid velocity at any bed level is independent of bed depth may be in error since the static pressure gradient measurement method was employed to determine the gas velocity. The conclusion that increasing the spouting gas velocity actually decreases the net gas flow through the annulus (Epstein et al., 1978) may also be in question. Gas velocities in the annulus need further study. Figure 3.11 also reveals that there is a denser region in the annulus near the interface with the spout in which the voidage is somewhat lower than the loose-packed bed value. This probably results from the forces acting on the region, such as drag due to gas crossflow, the weight of particles in the annulus, the shear stress of gas and upward-moving particles in the spout and shear stress due to downward-moving particles in the annulus. 3.3.2 Voidage profiles in the fountain Solids concentration profiles in the fountain for U/Ums=\.\, 1.2 and 1.3 are shown in Figure 3.12. It is seen that the solids concentration is higher in the core region and decreases gradually with increasing radial distance. It is also apparent that solids concentration is quite sensitive to the spouting gas flow rate and decreases significantly with increasing spouting gas flow rate. In the core region of the fountain, the solids concentration for U/Ums=\.\ increases with height, consistent with predictions from the theoretical model of Grace and Mathur (1978). In their model, the voidage is assumed to reach the loose-packed voidage at the top of a fountain. In Figure 3.12 the lowest voidage 51 1 1 E „* LL N . <*> E II co CO . - E O 3 " 3 X ' ' LO ^ -CO O 5 i LO o> CM O : * i <: LO J^" CM O • LO CD T — o 1 1 1 I 1 ! i LO ^t P \ ^ -<—•- - " ' • •• i i i LO LO * * X co Tf 'it' ' -O O B » # X * ° V MMC * 1 y/si/ /• 1 ^"V' /Vi / -^ J i • ' ^M |C • • <?*•# • •' * » • . • * ' . * ' * • * * — 4 " i ' » * ) ( ' • ' 1 00 o CD O -3-o CM • . CM T— II CO •1 E LO CM - E o 3 3 . II X » i -f-• • - ^ H 1 -^— V^ •L " • i _r^-• ; • ' • • -^4> • i i i i — -1/ .•• i » « • /•'••' / . * • ^->>' - ^ v ? - * ^ • *X A M • <•' _ - - - ' ' ^ « < 1 — ^ 1 1 1 1 00 o CD O O CNJ (3-0 52 value is 0.57, compared with the loose-packed voidage of 0.412. However, this value was measured 5 mm below the top of the fountain; the voidage at the very top of the fountain could not be determined because the fountain tended to sway when the stabilizer was not in place. The question of whether or not the loose-packed voidage is reached at the top therefore requires further investigation. The solids concentration in the core region for both U/Ums=\.2 and U/Ums=l.3 first decreases with increasing height to some extent and then increases towards the fountain top. This may arise from radial spreading of particles at different levels and from particle deceleration. In order to compare the present data with the results of Waldie et al. (1986), the vertical profiles of the cross-sectional average voidage in the fountain were calculated and are shown in Figure 3.13. The cross-sectional voidage generally increases with height except at the fountain top where there is a slight decrease in voidage. The general trend is similar to that obtained by Waldie et al.(1986). If the results in Figure 3.13 are compared with the theoretical model of Grace and Mathur (1978), as in the work of Waldie et al. (1986), an improper conclusion arises because the model only predicts the voidage profile in the 'central core', i.e. along the axis of the fountain. If the average voidage, fountain height and fountain shape are known, the total volume of solid particles in the fountain can be estimated. For U/Ums=l.3, the particles in the fountain constitute 8.9% of the total particles in the bed. This suggests that contacting between solids particles and the gas in the fountain region cannot be ignored in some applications, e.g. for chemical reactions, cooling of fertilizer pellets, and drying of solid particles. 3.3.3 Voidage profiles in the spout Radial profiles of voidage at different levels in the spout for three gas velocities, U/Unls=l.\, 1.2 and 1.3, are presented in Figure 3.14. Increasing gas flow rate causes the local voidage to increase in the entire spout region. For each of the three values of U/Ums, 53 CD c? 100 o 8,0.95 CO s _ CD ™ 0.90 CO c o 0 CO CO CO 2 0.80 O ' 1 \ \ \ i 1 \ \ \ \ \ A i > u/u = ms i 1 i u/u = ms • U/U = ms = 1.1 1 =1.3 -=1.2 I 0 100 200 300 400 Vertical distance above bed surface (mm) Figure 3.13: Vertical profiles of the cross-sectional average voidage in the fountain. Full-column, H=0.325 m. 54 CO CO E * X' • • « • • A / / / : \ i x J • • « • I N - * • •>< I • • • 41 00 T -CO T • 1 i CO CD CN 9 • i i i i oo T — CN 9 -4 00 CD T — o i i i 00 T -x— O i i i i • CO oo o 9 + i i 1 CO LO o o 1 X 1 1 CN CN O o' 1 1 ^_ • II to - £ 3 • 3 / 1 * — i * X X / -K— • i < i • i ^^=^Sk r / • • • • + / /• < \ i • • < • • + / / : / / ,- i i :: / / 1 • ' • ' « » • < L -*£ | 1 , T-• • ^ ^ 1 . i . i . 05 O 00 O O CD O d XT CD 96BP|OA CO o 55 the local voidage decreases with increasing height and with increasing radial distance, except in the region near the top of the spout, where there exists a somewhat denser zone surrounding the spout axis. This denser zone is most noticeable for U/Ums=l.l and 1.2 and almost disappears for U/Ums=l.3. The denser central zone is probably associated with radial movement of solid particles and particle-particle collisions in the spout. It is notable that a central denser zone was predicted for some conditions recently by Krzywanski (1992). The denser central zone also exists in the fountain region as one can see from Figure 3.12. From Figure 3.14 it is also seen that in the lower portion of the spout the radial profiles of local voidage are roughly parabolic with a maximum at the spout axis while more blunt profiles are found at greater heights. As shown in Figure 3.15, the cross-sectional average voidage decreases monotonically with height. The spouting gas flow rate has more influence on the voidage in the upper portion of the spout than in the lower part. Voidages were also measured in the half-column in order to examine the effect of bed geometry on voidage profiles. The results in the half-column and in the full-column with identical operating conditions are compared in Figure 3.16. In the half-column, the probe was inserted from the curved wall at right angles to the front face, except for the point closest to the face where the probe was inserted parallel to the front plate. Although the local voidage in the half-column is lower than in the full-column, the overall voidage profiles are quite similar in the two cases. In the half column the voidage on the spout axis near the top of the spout is lower than near the interface between the spout and the annulus, which is an indication of a wall effect on voidage. One must therefore be cautious about half-column results, especially near the front face, although the difference is small enough that qualitative and semi-quantitative results can be inferred for most purposes. 56 0 CO CO -g "o > 0 G) 03 s — 0 > CO "co c o • M H W t ts 0 CO I CO CO o 4 — o 0.9 0.8-0.7-0.6 1 1 1 1 • T \ A ^ "^k x-:-. \ v i i i i i i U/U =1.3 ms • U/Um =1.2 ms U/U =1.1 ms -. 0 50 100 150 200 250 300 350 Vertical distance from the inlet (mm) Figure 3.15: Vertical profiles of the cross-sectional average voidage in the spout. Full-column, H=0.325 m. 57 1.0 0.9 0.8 0.7 CD ^ 0 . 6 a — . I I -o > 0.5 0.4 0.3-0.2 Half-column Full-column - j L J L-- • •— 0.268 #,; • 0 218 W \ " \ ---•--0.168 r -—•---0.118 —4—0.083 ^—0.053 -*~—0.022 _ j ' i • 30 30 20 10 0 10 20 Radial distance from spout axis (mm) Figure 3.16: Comparison of voidage profiles in the spout in a half column and in a full column with identical operating conditions. H=0.325 m, U/Ums=l .2. 58 3.4 Conclusions A fibre optic probe has been used to measure voidage profiles in spouted beds. A relatively large probe, compared with those employed in fluidized beds, was used in view of the relatively large particles. Even larger probes could be used for particles larger than 3 mm in spouted bed applications. The present work appears to be the first systematic study of voidage profiles in the annulus. It has been found that, except for a restricted region near the spout-annulus interface, the voidage in the annulus is higher than the loose-packed voidage and that it increases with increasing spouting gas flow rate. The common assumption that the voidage in the annulus is constant and equal to the loose-packed voidage for the particular material is therefore in error, especially with increasing gas flow. This finding needs to be considered when modelling gas flow in the annulus or when measuring gas velocities in the annulus. It has also been found that there is a denser region in the annulus near the spout interface in which the voidage is even lower than the loose-packed bed voidage. In the fountain voidage varies widely. At its core, voidage decreases with height for low U/Ums, while at higher gas velocities, it first increases with height and then decreases towards the top of the fountain. In one case for U/Ums-1.3, 8.9% of the solid particles are found in the fountain at any time. In the spout region, it has been found that the local voidage decreases with increasing height and with increasing radial distance from the spout axis. The radial profiles of local voidage are roughly parabolic in the lower portion of the spout, but are rather blunt at higher levels. There exists a somewhat denser zone surrounding the spout axis near the spout top, which extends into the fountain region. There are minor differences in bed voidage between a semi-cylindrical (half-column) and fully cylindrical column. 59 Chapter 4 Spout Shapes and Diameters Knowledge of the spout diameter and shape is of fundamental importance for understanding the hydrodynamics of spouted beds and for spouted bed modelling and design. Spout shape measurements have usually been made by visual observation through the flat transparent face of semi-cylindrical (e.g. Mathur and Gishler, 1955; Thorley et al., 1959; McNab, 1972) or two-dimensional (Goltsiker, 1967; VolpiceUi et al., 1967) columns. However, the flat face of a semi-cylindrical column may cause distortion of the spout. Only Mikhailik (1966) using a piezoelectric probe made parallel measurements in half and full cylindrical columns. However, no data were reported for the half cylindrical column and the full-column and half-column were of different diameters (94 and 140 mm, respectively). The question of whether the flat face of half-columns affects spout shape is therefore unresolved. Moreover, there is a paucity of spout diameter data obtained in full-columns. In the present work, spout diameters have been determined in a full-column and in a half-column with a fiber optic probe to examine the effect of the flat face in a half-column on spout shapes and compare experimental results with predictions from models in the literature. 4.1 Experimental 4.1.1 Apparatus and particulate materials Parallel measurements of spout diameters were carried out in the fully cylindrical Plexiglas column of inside diameter 152 mm and height 1.4 m with a 60° conical base and in the half-column, having the same diameter and shape as the full-column. The set-up for 60 each column is shown schematically in Figure 3.4 of Chapter 3. An inverted conical stabilizer, 55 mm in diameter and 45 mm high, was installed at the top of each column to prevent the spout and fountain from swaying. Observations indicated that the stabilizer did not appreciably change the fountain height and shape. Eighteen holes were drilled at 50 mm vertical intervals along the column wall, beginning near the bottom. The fiber optic probe could be inserted in each of the holes and traversed radially to measure spout diameters. A plate with an orifice of circular or semi-circular form and 19.1 mm diameter was installed at the base to provide the inlet for the two columns. Glass beads of diameter 1.41 mm and density 2503 kg/w? were used as the particles as in Chapter 3. The spouting fluid was air at room temperature. The minimum spouting velocity, Ums, for a bed height of 0.325 m was 0.54 m/s. 4.1.2 Fibre optic voidage probe and image probe The fiber optic voidage probe used to determine the interface between the spout and the annulus (spout diameter) was previously employed to measure voidage profiles in Chapter 3. It is shown in Figure 3.8. Within the probe thousands of optical fibers, each 16 (am in diameter, were arranged in a bundle with fibers acting as light projectors alternating with fibers acting as light receivers. The illuminating light from the tips of the light projectors was partially reflected by the swarm of particles in the vicinity of the optic fibers, and the reflected light was then guided to a photomultiplier where it was converted to electric pulses proportional to the light intensity. The electric voltage signals were fed to a microcomputer whose software was written to allow the output electric signals to be displayed. Spout diameters can be measured based on the fact that particle velocities in the spout are much higher than in the annulus. This causes the counts of electric output signal pulses to be significantly higher in the spout region than in the annulus. Experimental 61 results near the spout-annulus interface, firstly from the spout region and then from the annulus region, are shown in Figure 4.1(a) and Figure 4.1(b), respectively. It is seen that there is a sharp transition in the signal when the probe is moved only 1 millimeter. The average radius of the two positions can be taken as the spout-annulus boundary at that bed level. With the aid of the fiber optic probe the radiuses of the spout could be measured with a precision of 1 mm. The fiber optic voidage probe was 4 mm I.D. and 5 mm O.D. with a length of 0.3 ra la the half-column, the probe was inserted horizontally parallel to the flat wall at different levels closest to the wall and observations indicated that its presence did not appreciably distort the spout-annulus boundary when the probe was gradually moved inward. In order to verify the measurement method, an image probe, used to measure particle velocity profiles in the annulus region as discussed in Chapter 5, was also employed. The fiber optic image probe transmitted images from the interior of bed to a video camera as shown in Figure 5.8. The images on the outlet tip of the probe were enlarged by lenses. When the probe was traversed radially from the column wall to the spout, vertical particle velocities went through zero. The corresponding radial positions at different bed levels delineate the boundary between the spout and the annulus. 4.2 Results and Discussion 4.2.1 Validation of the fibre optic voidage probe Two different experimental approaches were made to verify the readings from the fiber optic probe. The first experiment was carried out in the half-column. Spout diameters at various bed levels were easily determined by visual observations through the flat transparent wall. At the same time, the fiber optic probe was used to determine the spout diameter by inserting it horizontally parallel to the front flat wall for the points closest to 62 1.0 0.8 —i 1 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 r In the Spout (a) J i I i I i I i I i I i I i I i L </> 0.2 (/) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 o 1.0 0.4 0.2 • i • i > i In the Annulus T — i — | — i — | — i — | — i — | — i — r (b) -i I i I i I ' i I i I i I i I i L 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 4.1. Output signals from the fiber optic system. Full-column, H=0.325 m, U/Ums=1.1. (a) In the spout at r=20 mm; (b) in the annulus at r=21 mm. 63 the wall. The measured spout diameters are compared in Figure 4.2(a). It is seen that there is excellent agreement between the fiber optic probe measurements and observations through the front face, with an average deviation of only 2.7%. The second experiment was conducted in the full-column with the image probe and the fiber optic probe. Results obtained by the two techniques are shown in Figure 4.2(b). The agreement is again found to be excellent, with an average deviation of only 3.4%. 4.2.2 Spout diameters in the half-column In order to investigate the effect of the flat wall on spout shapes, measurements were carried out simultaneously at the flat wall by observations and along a radial plane 90 degrees to the flat wall using the fiber optic voidage probe. The experimental values of spout radii for three different gas flow rates appear in Figure 4.3. The spout diameters determined by observations expanded considerably in the region immediately above the entrance orifice, narrowed slightly further up the column and then diverged again near the bed surface. This shape is similar to findings in a large spouted bed (He et al., 1992). However, the spout diameters measured by the fiber optic probe at 90 degrees to the flat wall diverged along the column, which is similar to one of the five spout shapes classified by Mathur and Epstein (1974). Furthermore, there was a considerable difference between the readings at the flat wall and at 90 degrees to the flat wall. Average deviations for data taken in the two different planes by the two methods for U/Ums=l.l, 1.2 and 1.3 were 30.0%, 27.5% and 28.0%, respectively. The flat wall had more effect on spout shapes in the. upper part of the column than in the lower part. It must be mentioned that the front flat face was always perfectly vertical for all measurements. Predictions from the well-known spout diameter equation of McNab (1972) are in good agreement with data observed from the flat walL with a deviation less than 15%. However, the predictions underestimate the spout diameters determined by the fiber optic voidage probe at 90° to the front face, with errors up to 38%. It should be noted that the 64 E N 400 350 300 250 200 150 100 - i — i — i — i — r Half-column o Observation v Voidage Probe so 50-0 07 400 350 300 250 200 150 100 50 — i — i — i — | — i — i — i — i — | — i — i — i — r Full-column • Image Probe v Voidage Probe B7 \ I i i i i _ r t i i i i_—I—i i i__i 0 10 20 30 r (mm) (a) 0 K7 i i • • r*fr i i i JL—L_i i i i 0 10 20 r (mm) (b) 30 Figure 4.2. Experimental spout diameters measured by fiber optic voidage probe, front observations and image probe at various bed levels for H=0.325 m, U/Ums=1.2: (a) Half-column; (b) Full-column. 65 350 • Observations from front flat face • Probe measurements from rear curved wall at 90° to front face - i — i — i — i — | — i — i — i — i — I — i — i — i — r U/Um =1.1 ms 300-250 200 150 100 50 0 i i ; • i i * • • • • • i wi*-1 I ' i I i i i i i i — i — i — | — i — i — i — i — [ — r ~ ~ i — i — r -U/U =1.2 ms • « I I .« • • • • • • • * i i m* ' • • i I • • • I • ' • • I ' ' ' • U/U =1.3 ms • .* I I • • • i i mr"i i i i i i i i i i 0 10 20 30 0 10 20 30 0 10 20 30 Radial distance from spout axis (mm) Figure 4.3. Spout shapes for three different gas flow rates in the half-column. H=0.325 m. McNab equation is based on regression of 107 data points all from half-columns and visual observations. Li order to examine the effect of the flat wall on cross-sectional spout shapes, measurements were also conducted at three different levels and at angles of 0, 45, 90, 135 and 180 degrees to the flat wall. Some typical results for three different gas flow rates are shown in Figure 4.4. It is seen that horizontal cross-sectional spout shapes are rather similar to semi-ellipses, with the areas of these semi-ellipses increasing with increasing gas flow rate. These experimental findings indicate that the flat wall of semi-cylindrical spouted beds distorts spout shapes significantly. The conventional observation method using half-columns does not provide accurate experimental data. Caution must therefore be exercised when using spout diameter data from half-columns to model and design fun-columns. It has already been shown that the front face of half-columns can cause major changes in particle velocity in different angular planes (Rovero et al., 1985). It is also shown in Chaper 5 that particle velocities along the spout axis in a half-column are 70% lower than in a full-column under identical operating conditions. 4.2.3 Spout diameters in the full-column Spout diameter measurements in the full-column were carried out using the fiber optic voidage probe from opposite directions at nine different levels. Figure 4.5 shows measured spout diameters for three different gas flow rates. The results were found to be essentially symmetric so that measurements for the cylindrical bed could be reduced to a single radial plane. The spout diameters for each of the three gas flow rates expanded sharply immediately above the entrance orifice, narrowed slightly further up the column and then diverged again near the bed surface. Spout diameters increased with increasing gas flow rate, with more influence in the upper part of the bed than in the lower part. Spout diameters remained nearly constant along the height except in the region 67 30 20 10 — • — ' — ' — ' — 1 — ' — ' — ' — ' — i — ' — ' — ' — • — 1 — ' — ' — ' — ' r- ' ' ' l •' > • z=0.318 m . - " - " i r - - -/ ''/ Xv* \ [f " U/|Jms=1-1 \ \ \ . 1 | // • U/U =1.2 \ \ \ // ms u f • U/Ums=1.3 \ ' £ 20 30 20 10 0 10 ' 20 r (mm) 30 Figure 4.4. Effects of the half-column flat wall on cross-sectional spout shapes at three levels. Half-column, H=0.325 m. 68 E N 350 300-250 -200 150 100 50 • I — i — i — i — i — i — i — i — i -U/U =1.1 ms U/U =1.2 ms U/U =1.3 ms M4 . i : i : i *)f 'I * * 0 30 <r* 0 j ' * ' ' 30 r (mm) Figure 4.5. Spout shapes in the full-column for three different gas flow rates. H=0.325 m. 69 immediately above the entrance orifice and in the region near the bed surface. It is therefore a reasonable approximation for these conditions to assume a constant spout diameter except at the bottom when doing modelling work. The experimental data have again been compared with predictions from the McNab (1972) equation. It is found that the equation underestimates the average spout diameters, with an average deviation of 35.5%. Since the McNab (1972) equation is based on half-column data and there are significant differences between data from full and half columns, this equation must be modified for full-columns. 4.3 Conclusions A fiber optic probe, which was previously employed to measure voidage profiles, has been used to measure spout diameters in half-column and in full-column spouted beds of the same diameter and particles. The technique has been vahdated by comparing the results with observations in the half-column and by readings from an image probe in a full-column. It has been found that the flat wall of the semi-cylindrical column distorts spout shapes significantly. The conventional measurement technique involving visual observation in half-columns cannot provide accurate experimental data. Caution is therefore required when using spout diameter data from half-columns for modelling and design of full-colurnus. The McNab (1972) equation underestimates the spout diameters in a full-column, with an average deviation of 35.5%. 70 Chapter 5 Particle Velocity Profiles 5.1 Previous Work 5.1.1 Available techniques for particle velocity measurement The available techniques for measuring local velocities of sohd particles in fluidized and spouted beds can be classified into five categories. The first uses a small obstacle to detect a drag force exerted on it by the flow of sohd particles (Heertjes et al., 1971; Botterill and Bessant, 1976). The second involves measurement of the rate of heat transfer by sohd particles (Marsheck and Gomezplata, 1965). The third is a tracer method (Van Velzen et al., 1974; Waldie and Wilkinson, 1986). The fourth utilizes laser-doppler anemometry, based on the difference between the frequencies of an incident laser light beam and light scattered by moving particles (Birchenough and Mason, 1976; Levy and Lockwood, 1983; Boulos and Waldie, 1986). The fifth is based on statistical correlation of the optically observed movement of particles (Oki et al., 1975; Oki and Shirai, 1976; Ishida et al., 1980; Patrose and Caram, 1982; Randehnan et al., 1987; Benkrid and Caram, 1989). These five techniques and some references are summarized in Table 5.1. For the drag force method the variation of the force measured as the strain of a small object inserted into the flow depends not only on the velocity of particles but also on their voidage. It may also depend on the characteristics of the particles. To measure the velocity, the effect of the variation of both the porosity and that of the particle characteristics on the force must be known. These statements are also vahd for the heat transfer method. These methods are indirect methods in which the measured signals cannot be related directly to the velocity; instead, the measured signals must be calibrated to the velocity. This may seriously constrain the practical applicability of these techniques. On the other hand, the tracer method, laser-doppler anemometry and statistical correlation 71 Table 5.1: Various methods for measuring particle velocities Method I. Drag force method H Heat trasfer method IH Tracer method IV. Laser-doppler anemometiy V Correlation method Principle 1. Conversion of mass flow rate variation into the variation of the strain of a small object 2. Conversion of mass flow rate variation into the rotation rate of a small impeller Conversion of mass flow rate variation into the variation of heat transfer rate 1. Measurement of a track of radioactive isotope tracer 2. Measurement of a track of a magnetized marker tracer Measurement of frenquency (Doppler-Shift) and the optical geometry Statistical determination of the transit time of particles between two fixed points Detector Piezoelectric crystal transducers Rotation rate to frequency conversion device Digital counter Thermister Integrator Scintillation counter Search coils Photo-multiplier Optic fiber Light detector References Heertjes et al. (1970) Botterill & Bessant (1976) Marsheck & Gomezplata (1965) Van Velzen et al. (1974) Waldie & Wilkinson (1986) Birchenouh & Mason (1976) Levy & Lockwood (1983) Boulos & Waldie (1986) Oki et al. (1975) Oki & Shirai (1976) Ishida et al. (1980) Patrose & Caram (1982) Benkrid & Caram (1989) 72 method are direct methods in which the measured value can be related directly to the velocity. The radioactive tracer technique appears to be unable to measure the radial profile of particle velocities, while the magnetized marker particle and search coils technique do not give good spatial resolution and can only be used in the spout of a spouted bed. Laser-doppler anemometry (L.D.A.) is restricted to particle velocities in the spout and fountain of a semi-cylindrical spouted bed or in the fountain of three-dimensional beds. 5.1.2 Measurements of particle velocities in spouted beds Starting with one of the earliest reports on spouted beds (Mathur and Gishler, 1955), cine-photography and a stopwatch have been the most frequently used techniques for measuring particle motion in spouted beds. Most work has been carried out in semi-cylindrical columns. Some more advanced techniques, such as a piezoelectric probe (Gorshtein and Soroko, 1964), a radioactive tracer technique (Van Velzen et al., 1974), and a magnetized marker particle with search coils (Waldie and Wilkinson, 1986), have also been employed in full columns to measure particle velocities. Each technique has inherent limitations. For example, wall effects debase the reliability of data from photographic techniques, while other techniques are not well suited to the measurement of radial profiles. A fiber optic probe technique, originally employed to measure particle velocities in fluidized beds (e.g. Oki et al., 1975; Oki and Shirai, 1976; Patrose and Caram, 1982), was used to measure particle velocities in the annulus of spouted beds by Randelman et al.(1987) and Benkrid and Caram (1989). This technique is extended in the present work. Hence correlation of fiber optic probes is considered further in the following sections. 73 5.1.3 Correlation method with fiber optic probe A fiber optic probe used for particle velocity measurement measures light reflected into two contiguous fibers at the tip of an muminated probe, as shown schemetically in Figure 5. If. The time delay, tab, between the two signals is then determined. With the fibers at an effective separation, Laj„ the particle velocity, v, is simply v=4*A* (5-i) The signals are detected with two photomultiplier tubes and the signals from the photomultipliers are then fed to a cross correlation analyzer. The cross-correlation function generated by the analyzer is displayed on an oscilloscope and the transit time corresponds to the maximum of the cross-correlation function. 5.1.4 Previous fiber optic probes Some typical fiber optic probes employed by previous authors are shown in Figure 5.1. The fiber optic probe used by Oki et al. (1975), shown in Figure 5. la, consists of a pair of bundles of small optical fibers. One fiber bundle is used to illuminate individual particles and the other to detect the light reflected by particles. The fibers are small enough to be able to detect the reflected light from individual particles. The probe used by Oki et al. (1977), shown in Figure 5.1c, is capable of measuring the diameter of a moving particle. Details of the fiber optic probe used by Oki and Shirai (1976) are shown in Figure 5.1b. A fiber in the center of three fibers is used to illuminate the moving individual particles, while two other fibers, A and B, are used to detect light reflected from the surfaces of these particles. The fiber optic detector employed by Ishida et al. (1980) is shown in Figure 5. Id. Probe A consists of a bundle of seven fibers, while B has three fibers. For probe A, light delivered by the central fiber is reflected from the surface of particles and received by the peripheral fibers marked 1 through 6. Probe B is used to detect bubbles. The probes used by Patrose and Caram (1982) and Benkrid and Caram (1989) appear in Figures 5. le and f, respectively. These two probes are similar to that shown in Figure 5. lb 74 e #* projector receiver A probe C receiver!? t " ^ * B projector- " ^ •light M reflected X light tight beam light (rom source signal A ^ signal B pulse TO P h o t o - { r o n \ [I]1"! source v ' P h o t o -m u l t i p l i e r (B) Receiver of Reflected Light Light (rom Source To Light Detectors -' '" , Light . . . , . ' from Light Recoveryy yf/^ ^> S o u r M Optical Fiber Thin Copper Plate Light Projec 0.6"-IJ9 mm T V?J~ \r/-"'"' k— I —< , 1.6-2.1 , mm to 0 : Projector f5 1 - 8 : Receiver SIGNAL -c PARTICLE TRAJECTORY RECEIVING FIBER X LIGHT IN - + C -•SIGNAL A(0 -c=-T RECEIVING FIBER A. CENTRAL ILLUMINATION ',EFFECTIVE < I,GEOMETRIC SIGNAL B(t) SIGNAL Ad) 'tfefoj -cr-c~ B(t) Light o i^ B. EXTERNAL ILLUMINATION e INEFFECTIVE > I,GEOMETRIC Aft) Optical Hypodermic Fiber Encasing f Particle Figure 5.1: Typical fiber optic probes used by previous authors, (a) Oki et al. (1975), (b) ObJki and Shirai (1976), (c) Oki et al. (1977), (d) Ishida et al. (1980), (e) Patrose and Caram (1982), (f) Benkrid and Caram (1989). 75 except for the definition of the distance between the two receiving fibers. In Figures 5.1a, b, c and d, the distance between the two detecting points is taken as the actual distance between the receiving fibers. However, in the cases of Figures 5.1e and f, the corresponding distance is an "effective distance" which differs slightly from the geometric distance and is obtained by calibrating the probe on a rotating disk at known angular velocities. The light source used by Oki et al. (1975, 1977) was a tungsten lamp, while that employed by Patrose and Caram (1982) and Benkrid and Caram (1989) was a laser light source. The other authors did not report their light sources. 5.1.5 Devices for light detection and signal analysis A typical block diagram of a signal processing unit is shown in Figure 5.2. The light signal received by an optic fiber is converted into an electric signal. A phototransistor in conjunction with an amplifier circuit, which is inexpensive and suitable as a high-intensity light source, has been used by Ishida et al. (1980), while photomultipliers have been used by other authors (Oki et al., 1975; Oki and Shirai, 1976; Oki et al., 1977; Patrose and Caram, 1982; Randelman et al., 1987; Benkrid and Caram, 1989). The signals from the photomultipliers are fed to a correlation and probability analyzer (often called a correlator). The cross-correlation function generated by the analyzer is displayed on a chart recorder or oscilloscope, and the transit time is read from the maximum of the cross-correlation function, ®AB(T) = ±gA(t)B(t + T)dt (5.2) with Ts » TBWi, where Ts is the sampling time. 76 PHOTO HUTIPLIER A PHOTO MULTIPLIER B FIBER OPTIC PROBE CROSS CORRELATION ANALYZER DIGITAL STORAGE OSCILLOSCOPE ILLUMINATOR CROSS CORRELATION OUTPUT EUNCTION Figure 5.2: Block diagram of the fiber optic and signal processing units of the measurement system employed by Randelman et al. (1987). 5.1.6 Previous results obtained using fiber optic technique The fiber optic technique has been used to measure local particle velocities in three dimensional fluidized beds and spouted beds. Table 5.2 summarizes some references and experimental results. Though some authors, e.g. Oki et al. (1975, 1977), reported few or even no experimental data, they did provide detailed discussions of the technique. 5.1.7 Half columns vs full columns Semi-cylindrical columns have been used to measure particle velocities in spouted beds because they are believed to accurately represent the behavior of a full column. However, Day et al. (1987) used tracer particles to measure the particle velocity in the annulus and found that particles two particle diameters from the wall moved faster than particles adjacent to the wall. Randelman et al. (1987) measured particle velocity profiles 77 in the annulus using a fiber optic technique in half and full columns and concluded that velocities were much higher in full beds than in half beds. He et al. (1992) observed dead zone boundaries in a 0.91 m diameter column and found that readings from the front flat plate and rear column wall were quite different. It is clear that it is best to make measurements in fully cylindrical columns whenever possible. The question of whether or not the flat plate affects the particle velocity in the spout region has not been investigated previously. Table 5.2: Previous experimental utilization of the fiber optic technique Reference Oki et al. (1975) Oki&Shirai(1976) Oki etal. (1977) Ishida et al. (1980) Patrose & Caram (1982) Randelman et al. (1987) Benkrid & Caram (1989) Bai et al. (1990) Unit used Rotating cylindrical bed of particles Fluidized bed High solid loading equipment Fluidized bed at high temperature Fluidized bed Spouted bed Spouted bed Downflow fast fluidized bed Properties measured Size of moving particles, particle velocities. Distributions of particle velocities, distributions of bubble velocities. Particle velocities. Vertical profile of particle velocities, vertical profile of bubble velocities. Particle velocities (few data), distribution of particle velocities. Particle velocity profile in the annulus. Particle velocity profile in the annulus. Radial particle velocity profile. 78 5.1.8 Solids flow patterns in the annulus of spouted beds It is generally believed that particles in the annulus move vertically downward and radially inward, describing approximately parabolic paths (Mathur and Epstein, 1974), illustrated by the stream lines in Figure 5.3(a). On the other hand, Randehnan et al.(1983) and Benkrid and Caram (1989) used a fiber optic technique to measure particle velocities in the annulus of a full column and concluded that a plug flow zone existed in the upper part of the annulus. Except in the bottom region, there was no entrainment across the interface of the spout, as shown in Figure 5.3(b). It is apparent that further investigation of solids trajectories and velocities in the annulus is required. 0.5 r-5 o.i Top of bed -, Run 3 Run 5 - Run 6 0 0.1 0.5 R' - r/Rw (a) (b) Figure 5.3: Particle streamlines in the annulus: (a) wheat, Dc=0.292 m, H=0.876 m, Di=35.3 mm, U/Ums=l.l, from a half column (Lim and Mathur, 1978); (b) "universal" streamlines predicted by the kinematic model of Benkrid and Caram (1989). 79 5.2 Experimental 5.2.1 Apparatus and particulate materials Most of the experiments were carried out in the fully cylindrical Plexiglas column of inside diameter 152 mm and height 1.4 m, which was employed to measure voidage profiles in Chapter 3, as shown schematically in Figure 3.4. A few experiments were also performed in the half-column, having the same diameter, base angle and orifice diameter as the full-column. An inverted conical plastic funnel, 55 mm in diameter and 45 mm high, was again installed as a stabilizer at the top of the full-column to prevent the spout and fountain from swaying. Observations indicated that the stabilizer did not appreciably change the fountain height and shape. The stabilizer was removed for measurements taken at the two highest levels in the fountain. There were eighteen holes along the column wall at 50 mm vertical intervals, beginning near the bottom. The fiber optic probe and the image probe could be inserted in any of the holes and traversed radially to measure particle velocity profiles. The same glass beads of mean diameter 1.41 mm and density 2503 lcg/m^, which were employed to measure voidage profiles in Chapter 3, were used as the particles. The calculated terminal settling velocity for the glass beads was 8.6 m/s The spouting fluid was also air at room temperature. All results reported here were for a static bed depth of 0.325 m. For this height, the minimum spouting velocities, Ums, were 0.54 m/s and 0.56 m/s for the full and half columns, respectively, while the bed pressure drops were 3.00 kPa and 3.15 kPa for the full and half column, respectively. The measured maximum spoutable bed depth, Hm, was 0.518 m. 5.2.2 Fibre optic probes and their calibration Particle velocities in the spout and the fountain regions were measured using a fibre optic system, Particle Velometer PV-3 shown in Figure 5.4, developed by the Institute of Chemical Metallurgy of the Chinese Academy of Science, China. A fibre optic probe of 80 Figure 5.4: Photograph of the fiber optic system for measuring particle velocities. 81 diameter 3 mm and length 600 mm was specially designed and developed for the spout and fountain in the present work. As shown schematically in Figure 5.5, light is reflected into two contiguous fibers of diameter 0.6 mm at the tip of an illuminated probe and the time delay between the two signals is then determined. With the fibers separated by a known distance, the particle velocity can be calculated. A typical block diagram of the signal processing units is shown in Figure 5.6. The light signals received by each of the optical fibers is converted into an electric signal by a photomultiplier. Traditionally the electric signals generated by the two photomultipliers are fed to a correlation and probability analyzer, and then the transit time is read from the maximum of the cross-correlation function as described in Section 5.1.5. In the present work, however, the electric signals generated by the two photomultipliers A and B are fed to peak detectors, and then the transit time ( r^ ) is determined by the time delay between peaks A and B. The transit time is fed to a microcomputer by an A/D convenor. Software was written by Prof. S. Qin, the developer of the Particle Velometer PV-3 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. Figure 5.7 shows a typical particle velocity distribution obtained in the full column spouted bed. Each velocity value reported in the present work is an average of more than 4,000 sampled velocity data. Typical results of measured velocities (averaged over the sampling interval) and corresponding standard deviations along the axis of spout and fountain regions for U/Um =1.3 are listed in Table 5.3. The effective distance between the receiving fibres is slightly different from the geometrical distance (Patrose and Caram, 1982; Benkrid and Caram 1989). In order to Table 5.3: Typical measured velocities anc z(m) Velocity (m/s) Standard deviation 0.681 0.15 0.06 0.668 0.72 0.27 0.568 1.48 0.42 corresponding 0.368 2.98 0.74 0.268 3.39 0.81 standarc 0.168 4.29 1.05 deviations. 0.118 5.34 1.24 0.053 6.44 1.35 82 £ (t-fyj Fiber Optic Probe Signal B Signal A/~\ Figure 5.5: Fibre optic probe for particle velocity measurements in the spout and fountain regions. 83 Optical Fibers Fiber Optic Probe A B Photo-Multiplier Photo-Multiplier — • » — * > Amplifier Amplifier — » • -* -Peak Detector Peak Detector Micro-Comt )UtC jr — • — • TAB ' ' Tr)tpi-far»*» Figure 5.6: Block diagram of the signal processing units for the fiber optic system. 84 Figure 5.7: Typical distribution of particle velocities detected by the fibre optic system in the full column. z=0.218m, r=0.01 mm (in the spout region), H=0.325 m, U/Ums=l.l. 85 obtain the effective distance for the probe used in this work, a single particle was fixed at the end of a piece of metal rod which was rotated by a DC motor. The speed of the particle could be varied by adjusting the angular speed of the motor. The particle velocity determined by using an oscilloscope and the transient time x measured by the fiber optic system were used to calculate the effective distance between the receiving fibres. The average effective distance was found to be 0.82 mm, while the actual distance between the receiving fibres was 1.06 mm. A different optical probe was employed to measure particle velocity profiles in the annulus region. Thousands of optical fibers, each of diameter 16 u,m, were arranged in an array, with fibers acting as light projectors alternating with fibers which transmit the image. The probe was 9 mm ID and 10 mm OD. In order to minimize interfere caused by the probe, the front tip was a vertical 9 mm by 4 mm rectangle. The fibre optic image probe transmitted images from the interior of the bed to a video camera as shown in Figure 5.8. The images on the outlet tip of the probe were enlarged by lenses. By playing back the video cassette frame by frame, the transit time for a particle traveling a known distance could be determined and the velocity could then be calculated. 5.3 Results and Discussion 5.3.1 Particle velocities in the spout Figure 5.9 shows the longitudinal particle velocity profiles on the axis of the spout for both the full-column and the half-column. It is seen that particles are rapidly accelerated to a maximum near the inlet orifice and then gradually decelerate until they reach the top of the bed. The particle velocities are higher over the entire height as the gas flowrate is raised. The measured longitudinal particle velocity profiles are similar in shape to previous experimental results (Mathur and Gishler, 1955; Thorley et al., 1959; Mathur and Epstein, 1974; Lim and Mathur, 1978). However, peak velocities are reached in a shorter distance than indicated by previous results summarized by Mathur and Epstein (1974). 86 Enlargement T . , . Lenses L l § h t i n Video \ Camera A -^ Image out Probe i i • i—i .1 '2 TV Monitor View of/ the Tip > \il a OO H 3 mm Figure 5.8: Fibre optic image probe for determining particle velocities in the annulus region. 87 C/) E o o > _0 O • M M n CO DL 8 7 -6 -1 -0 ' I • - / \ T/^ \ V • V L»-.\ t •ft * \ v '• * \ 1 ', \ V I Wb *v 1 •<>. " \ \ M \*V &°%x *\ III "-J *Jk • Bk ill * \ x !:: \ '• \ 1" \ N "v f \ 0 \ < ^ 11 * * • Spout Region n ' 1 « — i • • i i i i i i l *V 1 i S a -• ^  ' « I ^ ! i i i i ' ! i , o , ° , • * ^ X * • i • U/U =1.3 ms U/Um =1.2" ms U/Um =1.1 ms --V. Fountain x " Regi • i on \ _ _ . — i — . — ) t 0.0 0.2 0.4 0.6 0.8 1.0 z/H T Figure 5.9: Axial profiles of vertical particle velocities along the axis of full-column (black symbols) and half-column (open symbols). HT=0.695 m, H=0.325 m. 88 In order to examine the effect of bed geometry on particle velocity profiles, the fall-column and the half-column were operated under identical conditions. In the half-column, the probe was inserted horizontally parallel to the front flat plate for the point closest to the plate. In Figure 5.9, although the overall particle velocity profiles for both columns are quite similar in shape, the local particle velocities in the half-column are much lower, approximately 70% of the corresponding velocities in the full-column. This suggests that a half-column cannot accurately represent the behavior of a full-column with respect to particle velocities in the spout, so that previously reported experimental data obtained using cine-photography with a half-column are likely inaccurate. Radial profiles of vertical particle velocities in the spout of the full-column at three different gas flow rates are shown in Figure 5.10. The radial profiles are more complex than reported by previous workers (Lefroy and Davison, 1969; Gorshtein and Mukhlenov, 1967). The local particle velocities first increase near the inlet and then decrease with height, except near the boundary between the spout and the annulus. The velocity also decreases with increasing radial distance, except near the top of the spout where the maximum is no longer at the spout axis. This shift in the position of the maximum is most noticeable for the two lower gas flow rates. It almost disappears for the highest gas flow rate, but shows up in the fountain region as noted below. This shift has been predicted by Kraywanski (1992) and arises due to radial movement of particles and particle-particle collisions in the spout. From Figure 5.10 it is also noted that increasing gas flow causes the local particle velocity to increase throughout the entire spout. Radial profiles of vertical particle velocities in the spout were also measured in the half-column at the same three superficial gas velocities. The probe was inserted from the curved wall at right angles to the front face, except for the point closest to the face where the probe was installed parallel to the front plate. The corresponding results are presented in Figure 5.11. Note that the particle velocities closest to the front plate are approximately 89 1 CM ^ II to E . 3 "-"-« 3 1 *y/ £-& •— 1 1 1 Try*i<r -v—< • • i i •' f -•>& ^mjrtm M'm^w^" r**""" > ' o CO o CM . o T -T — II CO - £ 3 * • • — • , • 3 -i E •» N i oo T ~ CO o • 1 00 CD CM d • <8G--tik-00 T -CM d < < r 00 CD T~ d • •BJK -+"' • +± 00 T — v— d • CO 00 o d + ^SZr*'^' • ' , * * — T CO in o d X 5 ^ *•' • i CM CM o d * rr?&££ PmF * f ** \ <• • 1 jgj^JJ frt^p •traTiK -CO LO 00 CM 0 O c 05 CO o o oo TJ 03 o TJ CM 0 5 a: o o <D h E CO X 03 3 O CL CO O 3 o a CO ID .a oo • »•* -*-> o o > <D O i ex o tf-i o to o V-i OH 13 * •—I HH (S/LU) A}j00|8A 9|0j}JBd 90 16 >n Particle velocity (m/s) ro GO en o -a> Lf\ i—' & P D-EL ^ o B CD CO O s. o *o & o cT 3 >—* o o bi S1 CD on O s o CD 13* fcL ^ o o p 73 0) Q . H M * CD Q. 0)' r—K 0) 3 o CD —+1 —"J o 3 0) "O o C/) ^^-^ 3 3 s— ' ro o CO o o o ro o CO o o — • * o N") O CO O • ™ J^fr*^ • r^*-1 • > p «^ i s4 - ^ ^ .«*••-* o o ho hO i *ZJ-^ P f " X o o en CO + o o 00 CO • o _ k _ v 00 """:+ < o _ A O) 00 • o ro — V 00 1 • o ro (j) 00 • o CO — X oo i N 3 --c . c 3 -CO II — i . _x • • 1*1, •-X.VI -X^, CT> c c 3 CO II ro 1 -•tZ&^zz^&W^* WL^ i M >.—•*—i—••as i **s5g=— i > * > * $/ > J*^ . .-«'" • i i i -c . c 3 -CO II CO 24% lower than the peak values a few millimetres away from the plate surface. This is an indication that the front plate of the half-column exerts a significant influence on particle velocities. The wall effect no doubt arises from the no-slip condition on the gas and particle-wall friction. Radial profiles of particle velocities in the half-column and in the full-column with identical operating conditions are compared in Figure 5.12. The particle velocities in the half-column are very different from those in the full-column. One must therefore be cautious about half-column results, at least when using them to obtain quantitative data to be employed for modeling and design of fully cylindrical spouted beds. 5.3.2 Particle velocities in the fountain Radial profiles of vertical particle velocities in the fountain of the full-column are plotted in Figure 5.13 for U/Ums=l.3. For this condition, the fountain was overdeveloped, i.e. the outermost particles bounced off the column wall. Similar results as some previously reported observations from photographic techniques (Mathur and Epstein, 1974) can be seen in Figure 5.13. In the core region particles decelerate until they attain zero velocity at the top of the fountain and then rain down in the surrounding region. In the core region particle velocities decrease with increasing radial distance from the axis except near the bed surface, where the peak particle velocities are about 10 mm from the axis. This is consistent with the results within the spout shown in Figure 5.10. In the surrounding region, the downward particle velocities increase monotonically with increasing radial distance. From the semi-theoretical model of Grace and Mathur (1978), HF = 446 VonMX Ps (5.3) 2£ ps-pf 92 30 20 10 0 10 20 30 Radial distance from spout axis (mm) Figure 5.12: Comparisons of particle velocity profiles in the spout of the full-column and the half-column with identical operating conditions forU/Ums=1.2. 93 zF, m _ -2.0 0 10 20 30 40 50 60 70 80 Radial distance from spout axis (mm) Figure 5.13: Radial profiles of particle velocities in the fountain of the full-column for U/Um =1.3 and HF=0.37 m. 94 The particle velocity on the axis at the bed surface, v0max, is available from Figure 5.10, while the spout voidage at the bed surface, s0, can be obtained from Chapter 3. The calculated fountain heights based on these values for U/Ums=l.l, 1.2 and 1.3 are 0.14, 0.19 and 0.35 m, respectively, while the corresponding experimental values, determined with the stabilizer removed, are 0.15, 0.23 and 0.37 m. The agreement between the predicted values and experiment is therefore good. The points where the curves in Figure 5.13 cross the zero velocity line give the coordinates of the boundary between the fountain core and the fountain outer downflow region. These coordinates and the top surface of the fountain are plotted in Figure 5.14. It is seen that the fountain core expands sharply near the bed surface and then gradually contracts with increasing height. This is contrary to the assumption (Hook et al., 1992) that the fountain core spreads outward along the entire height of the fountain. The experimental results provide useful information for fountain region modeling. However, the results in Figures 5.13 and 5.14 pertain to a single operating condition. More experiments are needed to give more quantitative information on the fountain. 5.3.3 Particle velocities in the annulus As described above, radial profiles of vertical particle velocities in the annulus were determined with a separate optical probe which transmited images. The measurements were made at 2 mm radial intervals near the column wall and near the boundary between the spout and the annulus, where particle velocity gradients were high. In the middle region of the annulus, measurements were taken at 5-mm intervals. Radial profiles of vertical particle velocities for three different gas flow rates are shown in Figure 5.15. In the cylindrical part of the bed (solid symbols), vertical particle velocities decrease with decreasing height due to solids cross-flow from the annulus to the spout. On the other hand, in the lower conical region (open symbols) vertical particle velocities increase with decreasing height, due to the reduction in cross-sectional area for 95 T 1 1 r T r <D O u m T3 CD X) <D > O H <D O Q Core - (Upflow) Region 0.0 Top Surface of Fountain Downflow \ Region % c E o • • • O 0 10 20 30 40 50 60 70 80 Radial distance from spout axis (mm) Figure 5.14: Boundary between the fountain core and the downflow region in the full-column for U/Ums=l .3 and HF=0.37 m obtained from radial positions in Figure 5.13 where particle velocity is zero. Top surface is from photographic images. 96 35 -20 40 60 800 20 40 60 80 0 20 40 60 Radial distance from spout axis (mm) Figure 5.15: Radial profiles of downward vertical particle velocities in the annulus of the full-column. downwards particle motion. Increasing the gas flowrate increases vertical particle velocities in the entire annulus region. The fibre optic image probe allowed accurate determination of the boundary between the spout and the annulus in the full-column. These points correspond closely to the radial positions where particle velocities equal zero in Figure 5.15. The effect of the column wall on particle velocities in the annulus is evident in the experimental data. In the cylindrical part of the column, vertical particle velocities show very sharp gradients near the column wall, with particle velocities adjacent to the wall approximately 28% lower than only 2 mm away and 49% lower than 6 mm from the wall. These findings are again a strong indication that data obtained at the wall do not give appropriate indications of particle velocities in the annulus. One must be cautious about data taken from either a curved or a flat wall using cine-photography or visual observation/stopwatch techniques. 5.3.4 Solids mass flows in the spout and annulus With the particle velocity profiles available in the present work, spout diameters in Chapter 4 and the voidage profiles measured in Chapter 3, one can compute the upward moving solids mass flow in the spout and the downward moving solids mass flow in the annulus using the Newton-Cotes integration method. i.e. W, = 27tp frsvs(l-f)rdr (spout) (5.4) S ' JO and W =-2npA va(l-£)rdr (annulus) (5.5) The solids mass flow rates in the spout and in the annulus calculated in this manner are presented in Figures 5.16 and 5.17 for three different gas flow rates. The solids flow rates for both the spout and the annulus continue to decrease with decreasing bed level due to solids cross-flow, AW/Az, from the annulus to the spout. The change of slopes are 98 0.0*-1 1 ' 1 -— . _ • ' • • * > •.-' 'S ' > • ' ' / :'f/ ~ '^ r •J 11 i 1 * X • <. <* ^ * S^ CD o O «4— O Q_ O i — i .•* ' -* • I 1 .••••"• . ' « x ^^u • • • i 1 i ' • • - - - " ' * ^ — — -— • _ -U/Ums=1.3 U/U =1.2 ms U/Um =1.1 ms i i • 0.0 0.2 0.4 0.6 0.8 1.0 z/H Figure 5.16: Solids mass flow in the spout of the full-column. H=0.325 m. 99 0.6 0.5 -0.4 0.3 -0.2 -0.1 -0.0 • I 1 1 1 1 • I 1 • U/U =1.3 11 IO • U/U =1.2 ,,...-•' ms .•-. • . ' u/ums=i.i •.•• - -• ••••",? \^r * mm — .«'", ' • • ' • ' / ' v ' ' '^H tjK y I I • 1 1-• .x^ 'J^ • CD C o O M— O Q. O • i . i . i . 0.0 0.2 0.4 0.6 0.8 z/H 1.0 Figure 5.17: Solids mass flow in the annulus of the full-column. H=0.325 m. 100 sharper in the conical core region than in the cylindrical part, showing that cross-flow from the annulus to the spout is higher in the basal region. The experimental results support earlier findings (Mathur and Gishler, 1955; Thorley et al., 1959; Mathur and Epstein, 1974; Lim and Mathur, 1978) that particles enter the spout over its entire height, and are contrary to the conclusion (Randelman et al., 1987; Benkrid and Caram, 1989) that a plug flow zone exists in the upper part of the annulus. Based on the law of conservation of mass, the downward solids flow in the annulus must equal the upward solids flow at any given level. The results in Figure 5.16 and in Figure 5.17 are in good agreement, with most deviations less than 9%; a somewhat larger difference (19%) appears in the conical base region. The favorable agreement indicates that the three fibre optic systems employed in this chapter and in Chapter 3 are reliable and accurate. 5.4 Conclusions A fibre optic probe system has been used successfully to measure vertical particle velocity profiles in the spout and the fountain of a half-column and a full-column spouted bed. In addition, a fibre optic image probe has been employed to measure vertical particle velocities in the annulus of the full-column and to determine the spout-annulus interface in the full-column. In the spout region, the radial profiles are not parabolic as reported by some previous workers (Lefroy and Davison, 1969; Gorshtein and Mukhlenov, 1967). Near the top of the spout in the full-column, particle velocities reach a maximum away from the spout axis, and this also occurs in the fountain region for high gas flows. Vertical particle velocities on the axis of the half-column are substantially lower than in the full-column under identical operating conditions. In the half-column, particle velocities at the front plate are substantially lower than a few millimeters away, i.e. the flat plate strongly affects 101 particle velocities. One must therefore be cautious about data obtained using semi-cylindrical columns. Detailed local particle velocities measured in the fountain of the full-column allow the boundary between the fountain core and the surrounding downflow region to be determined. The fountain core expands near the bed surface and then gradually contracts with height. The semi-theoretical equation due to Grace and Mathur (1978) gave good predictions of fountain heights for the full-column. Particle velocities in the annulus measured using a fibre optic image probe increase with height in the cylindrical part of the bed. However, particle velocities increase with decreasing height in the lower conical region. The column wall has a strong influence on particle velocities in the annulus. Hence data obtained by observing particle motion at the outer wall tend to be misleading as indicators of particle velocities elsewhere in the annulus. The upward solids mass flow in the spout and the downward solids mass flow in the annulus have been calculated by numerical integration based on measured local voidage and particle velocity measurements. These solids mass flows match well at different bed levels. The results indicate that particles are transferred from the annulus over the entire spout/anuulus interface. 102 Chapter 6 Pressure Gradients and Gas Flow in the Annulus Detailed knowledge of the gas flow distribution in spouted beds is important in ascertaining the effectiveness of gas-solids contact. The vertical gas velocity in the annulus of a spouted bed generally increases with increasing bed level. The increase is more rapid in the lower part of the annulus than in the upper part, and the longitudinal gas velocity gradient approaches zero near the top of a deep bed. In small columns (De<0.3 m) no measurable radial gradients exist across the annulus in the cylindrical part of the annulus (Lim, 1975), while in larger columns there exists a slight decrease in gas velocity towards the column wall in the cylindrical part of the annulus (Lim and Grace, 1987; He et al., 1992). Near the gas inlet (in the conical base region), the local superficial gas velocity decreases with increasing radial distance (Lim, 1975). 6.1 Previous Work 6.1.1 Pressure gradients in the annulus Vertical static pressure gradients have often been measured with a differential pressure probe inserted into the annulus of spouted beds from the top of a column or using pressure taps installed along the column wall (e.g. Mathur and Gishler, 1955; Thorley et al., 1959; Grbavcic et al., 1976; Epstein et al., 1978). The measured pressure gradients can be used to provide, by integration, pressure profiles along the cylindrical portion of the annulus. Grbavcic et al. (1976) reported that for a given solid material and spouting fluid in a column of fixed geometry, the measured pressure gradient at any level in the annulus is independent of bed height as shown in Figure 6.1. This important observation was first reported casually by Thorley et al. (1959) and corroborated later by Epstein et al. (1978). 103 z(cm) Figure 6.1: Pressure gradient in the annulus. Dc=0.11 m, Dj=14.6 mm, dp=2.5 mm, U/Ums=l, glass beads (Grbavcic et al., 1976). 6.1.2 Gas flow distribution in the annulus The assumption that the annulus of a spouted bed is essentially a loose-packed bed (Mathur and Gishler, 1955) has been accepted by all workers in this field so far. This is a key assumption for estimating gas velocity in the annulus from pressure gradient data and for any theoretical description of the annulus gas flow. One common method of measuring annulus gas velocities in the cylindrical portion of a spouted bed involves determination of static pressure gradients along the annulus using a differential pressure probe or pressure taps along the column wall as described in the previous section. The measured pressure gradients are then converted into gas velocities using a pressure drop versus velocity calibration curve obtained from loose-packed fixed beds. With this method, Grbavcic et al. (1976) found that for a given fluid-solid combination and column geometry the annulus fluid velocity at any bed level is independent of bed depth, as shown in Figure 6.2. Lim (1975) noticed that 104 E o 80 60 40 2 0 0 1 9 8° A 8 ft D 1 1 • • S aA A 1 i A A A g* i o A 1 • o * o A A A 1 1 o A 1 A 1 A * 0 • e o D A A 1 1 A A A Solids Wheat Polystyrene 1 1 A A A _ H, cm 15.2 30.5 45.7 63.5 _ 30.5 45.7 ' 90.1 1 0 10 20 30 40 50 60 70 80 z , cm Figure 6.2: Effect of bed depth on air velocity in a spouted bed annulus. Dc=0.152 m, Di=19.0 mm, U / U ^ l . l (Epstein et al., 1978). 160 140'-1 2 0 -100 80 60 40 20 U/U„ Glass beads 1.1 1.3 Wheat 1.1 1.3 Polystyrene 1.1 1.3 I . 10 20 30 40 50 Figure 6.3: Effect of spouting air velocity on the superficial gas velocity in the annulus. Dc=0.152m,D~19.0mm(Lim, 1975). 105 increasing the spouting gas velocity actually decreases the net gas flow through the annulus, as shown in Figure 6.3. As discussed in Chapter 3, however, the voidage in the annulus of spouted beds has been found to be somewhat higher than the loose-packed voidage, and it increases with increasing spouting gas flow rate. Therefore, the important observation of Grbavcic et al. (1976) and the conclusion of Epstein et al. (1978) may be in question. Li the present work, parallel measurements of voidage profiles and pressure gradients were carried out to study the distribution of gas flow in the annulus. 6.1.3 Theoretical models for predicting gas velocities in the annulus Mamuro-Hattori (1968) model The first and one of the most successful derivations of the longitudinal fluid velocity profile in the annulus of a spouted bed was made by Mamuro and Hattori (1968). This model is based on a force balance on a differential height dz of the annulus. With the assumption that fluid flow in the annulus is governed by Darcy's law, and with boundary conditions: (1) at z = 0, (2) atz=H„v (3) at z = Hm, they obtained, Ua=0 ua= UaHm= Umf -dp/dz = (-dp/dz)mf= umf mf f 1-= (PS-P)0-3 sJs (6.1) Modifications of Grbavcic et al. (1976) The Mamuro-Hattori (1968) model has been extended by Grbavcic et al. (1976) to beds of height less than the maximum spoutable height, Hm. The starting point is the new boundary condition that the pressure gradient or gas velocity at any given level in the 106 annulus is independent of total bed height. Their result for annulus gas velocity, corresponding to Equation (6.1), is Ua = l-{\-(z/HJ}3 Um i-{i-(H/Hm)}3 Grbavcic et al. (1976) showed this to be in better agreement with experimental data than Equation (6.1). Modifications of Epstein and Levine (1978) The Reynolds number (Re =pfdpU I ju) in spouted beds is usually of order 100, which is almost two orders of magnitude in excess of the Reynolds number for which the Darcy's law is normally applicable. Therefore, Epstein and Levine (1978) reworked the theory of Mamuro and Hattori using the Ergun (1952) equation instead of the Darcy's law leading to: Hm a where 1-7 /- JI + 2Y) K In z-Trr + -V3 \ tan —;=- + — (1 + 7+72)1 7 2 1 \ S ) 2 (6.3) and Y = -{(v+y)/Q-y)Yn (6.4b) y = UJUmf, 7 7 = | - - A - + 2 (6.4c) Lefroy-Davidson (1969) method Lefroy and Davidson (1969) proposed an empirical equation for predicting the longitudinal fluid distribution in the annulus, 107 u. = sin r U aHm "" ' (6.5) V 2#m J Epstein et al. (1978) recommended that Equation (6.5) be modified to U, TTT U aHm 7CZ sin V 1HmJ (6.6) in which the flow regime index n for the loose-packed moving bed annulus varies from unity (Darcys law) at the bottom of the annulus to a maximum possible value of 2 (for inviscid flow) at z = Hm. 6.2 Experimental 6.2.1 Apparatus and particulate materials Parallel measurements of pressure gradients and voidage profiles were carried out in the annulus of the fully cylindrical Plexiglas column of inside diameter 152 mm described in Chapter 3 and shown schematically in Figure 3.4. A horizontal plate with an orifice of 19.1 mm diameter was installed at the base to provide the inlet. Three different particulate materials, each having a relatively narrow size distribution and nearly spherical particles, were employed in the experiments. They were glass beads of diameter 1.41 mm, glass beads of diameter 2.18 mm, and polyethylene particles of diameter 3.38 mm. The properties of these particulate materials are listed in Table 6.1. The sizes of glass beads were determined by sieving, while the dimensions of 20 polyethylene particles chosen at random were measured using calipers. Voidages and particle densities were determined by the water displacement method. The maximum spoutable heights and minimum fluidization velocities were measured experimentally. The spouting fluid was air at ambient temperature and atmospheric pressure. 108 Table 6.1: Properties of particulate materials Material Glass beads Glass beads Polyethylene dp (mm) 1.41 2.18 3.38 Ps (kg/m3) 2503 2403 926 £mf 0.412 0.408 0.380 A 1.0 1.0 0.96 Umf (m/s) 0.798 1.082 0.766 (m) 0.518 0.395 0.518 6.2.2 Measurement techniques Voidage profiles in the annulus were measured using the fiber optical system described in Chapter 3. The fiber optic probe was inserted in each of the holes along the column wall. The voidage at each level in the annulus was measured along the center of the annulus, i.e. half-way between the column wall and spout-annulus interface. Annulus gas velocity measurements were provided by a static pressure probe shown in Figure 6.4. The probe consists of two concentric stainless steel tubes of 3.1 and 6.4 mm O.D., respectively. One end of each tube was closed. Two sets of four holes (each 0.8 mm in diameter) were drilled, one set near the closed end of the small tube and the other on the corresponding end of the outer tube, as indicated in Figure 6.4. The two sets of holes were spaced 18 mm apart. The static pressure probe was inserted into the annulus from the top (closed end down) and placed approximately half-way between column wall and spout-annulus interface. Static pressure drops were then measured with a micromanometer (Model MM-3, Flow Corp. of Cambridge, Mass.) filled with a fluid (butanol) of specific gravity 0.827 g/cm3. The accuracy of the micromanometer was a pressure drop of ± 0.1 mm H 20. The measured pressure gradients were converted into gas velocities using pressure drop versus velocity relationships for loose-packed beds, discussed further below. 109 4 Holes each, 0.8 mm dia. 1370 mm ^=Z t / 3.1 mm O.D. 6.4 mm O.D. t o micromanometer Figure 6.4: Schematic diagram of the static pressure probe. 6.3 Results and Discussion 6.3.1 Longitudinal pressure gradients and voidage profiles in the annulus In order to examine the influence of static bed height on local static pressure gradients in the annulus, pressure gradients were measured for different bed heights with three different types of solid particles. Figure 6.5 shows that the local static pressure gradient in the annulus increased with z and that the increase was more rapid in the lower portion of the bed. Figure 6.5 also shows that pressure gradients obtained in beds of different depths with other conditions (material, Dc, Dh and U/Ums) held constant coincided with each other. This means that the pressure gradient at a given level was independent of bed depth, consistent with the Grbavcic et al. (1976) results. Parallel measurements of longitudinal voidage profiles in the annulus, corresponding to the static pressure gradients shown in Figure 6.5, were carried out using the fiber optic probe. Typical results are presented in Figure 6.6. It is seen that at any given level, the local voidage was somewhat higher in a deeper bed than in a shallow bed 110 0.0 0.1 0.2 0.3 0.4 0.5 Vertical distance from orifice, z (m) Figure 6.5: Longitudinal pressure gradients in the annulus at U/U =1.1. ms 111 of the same material. The average differences between two heights for the small glass beads, large glass beads and polyethylene particles were 2.6%, 1.2% and 2.1%, respectively. The results are at variance with the conclusion that for a given fluid-solid combination and column geometry the annulus fluid velocity at any level is independent of bed depth. In addition, voidages are consistently somewhat higher than smf. Gas velocities based on the static pressure gradient method must therefore underestimate actual gas velocities in the annulus because a higher gas velocity is needed to give the same pressure gradient for a higher voidage. 6.3.2 Pressure drop versus velocity relationships for loose-packed beds In order to determine the air flow through the annulus, a pressure drop versus superficial gas velocity curve for a loose-packed bed of the small glass beads (dp=l.4l mm, sm^0Al2) was obtained experimentally using a 0.152 m I.D. fluidization column. The calibration curve is given in Figure 6.7. Since voidages in the annulus of a spouted bed have been found to be higher than the corresponding loose-packed voidages, calibration curves corresponding to higher values of voidage are required. With the assumption that the Ergun (1952) equation is still applicable to beds of higher voidage values ( £>0.412), pressure drop versus superficial gas velocity curves for higher voidage values were obtained by solving the Ergun equation: dp with/} and/2 given by < y „ } = /P + f2W (6.7) f^Ky—?^-= 150^ —ff- (6.8a) f2 = k 2 0 ^ = l75PfV **) ( 6 8 b ) 112 0.45 0.44 0.43 0.42 0.41 CO ^ 0.40 CD W 0.39 h 'o > 0.38 0.37 0.36 0.35 "o ° o • • D €mf 0.34 • • 'mf D V A * • V A * • O A V • o o o _ o • V s * * * * * * * dp H solids (mm) (rn) glass beads 1.41 0.325 glass beads 1.41 0.475 glass beads 2.18 0.225 glass beads 2.18 0.375 polyethylene 3.38 0.325 polyethylene 3.38 0.483 i i i i i 0.0 0. Vertical 1 0.2 0.3 0.4 0.5 distance from orifice, z (m) Figure 6.6: Effect of static bed height on voidage profiles in the annulus at U/Ums=l. 1. From top to bottom the voidages at minimum fluidization are for the 1.41 mm glass beads, 2.18 mm glass beads and polyethylene particles, respectively. 113 05 1.3 1.2 1.1 1.0 0.9 0.8 o p CD > C/3 CU 05 0.7 0.6 CD "o CD Q. C/) S 0.5 0.4 0.3 0.2 0.1 0.0 ' : — • : ; : • — — -*-!-/ / -/-/ / / /. '" ft'/.'? ... Jrtif. f : i • • ; ' .* / /•? 6 : \ 1 / / . s / •/o' i [ • • ./" * • • / * •' • y y •' y •.' y A>'\, o .. <" ' ' ; • • /-' : ^ • s' s' • . ' '. * s / IS ,0. ..... - • ' -1 : y?v fry 4® / *Sb - < # • • s' S- - • •-'• • -V i ! •-"'- - - '• e # . ; . . . . i 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Pressure gradient (mmH20/mm) 1.4 Figure 6.7: Calibration curve of pressure gradient vs. superficial gas velocity in a packed bed column with glass beads (d =1.41 mm). 114 Table 6.2: Values of constants k1 and k2 obtained by curve fitting compared with values calculated from the Ergun (1952) equation. Material Glass beads Glass beads Polyethylene d P (mm) 1.41 2.18 3.38 kj 0.1494 0.0605 0.0258 cal. 0.1394 0.0583 0.0263 deviation 6.7% 3.6% -1.9% k2 0.1634 0.1036 0.0649 k2 cal. 0.1533 0.0991 0.0666 deviation 6.2% 4.3% -2.7% where constants kj and k2 were evaluated using experimental data for the loose-packed bed (£my=0.412). Fitted values of kj and k2 are listed in Table 6.2. The calculated pressure drop versus superficial gas velocity curves for higher voidage values of the small glass beads are presented in Figure 6.7. Calibration curves of pressure drop versus superficial gas velocity were also obtained for packed beds of the 2.18 mm glass beads and the polyethylene particles. These curves are provided in Figures A. 2 and A. 3 of the Appendix, and corresponding fitted values of kl and k2 are given in Table 6.2. Note that the fitted k values are close to values calculated from the Ergun (1952) equation. 6.3.3 Gas flow distributions in the annulus Pressure gradients in Figure 6.5 with the corresponding voidage profiles in Figure 6.6 were converted to interstitial (or relative) gas velocities by using the calibration curves for all three materials. Superficial gas velocities were obtained with subtraction of annulus particle velocities from interstitial gas velocities, s(ua-va). Resulting superficial gas velocities in the annulus are shown as a function of bed level in Figure 6.8. At any given level, the local superficial gas velocity is seen to have been higher in a deep bed than in a shallow bed of the same material. The average deviations for the small glass beads, large glass beads and polyethylene particles were 7.7%, 3.8% and 7.4%, respectively. The results suggest that the finding of Grbavcic et al. (1976) that for a given fluid-solid combination and column geometry the annulus fluid velocity at any level is independent of bed depth is open to question since this finding was predicated on the assumption that voidage in the annulus is equal to the voidage of a loose-packed bed of the same material. 115 CO E o o CD > CO 03 D) "(5 • mmmm o »+— CD Q_ C/) v A V A X X o o D I -V V A O • • o • o D • 8 ft o • o • * o * * -1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 Vertical distance from orifice, z (m) D O A V • solids glass beads glass beads glass beads glass beads polyethylene polyethylene dP H (mm)(m) 1.41 0.325 1.41 2.18 2.18 3.38 3.38 0.475 0.225 0.375 0.325 0.483 Figure 6.8: Gas velocity profiles in the annulus at U/Ums=l. 1 based on measured local voidages and pressure gradients. 116 In order to compare the experimental superficial gas velocities in the annulus with existing equations in the literature, it is important to determine Uajjm. While this could not be measured experimentally, it is possible to extrapolate the Ua data obtained at heights only a little below Hm to Uafjm. The experimental Ua values together with the values of Uaffm obtained by extrapolation for the three materials appear in Table 6.3. Hm and Umf, other key parameters in the existing equations in the literature, were determined experimentally and are listed in Table 6.1. Table 6.3: Experimental values of annulus gas velocities and extrapolated Uaffm. z(m) 0.022 0.053 0.083 0.118 0.168 0.218 0.268 0.318 0.368 0.418 0.468 Extrapolated UaHm (m/s) Ua (m/s) Small glass beads 0.354 0.537 0.562 0.618 0.651 0.733 0.771 0.807 0.833 0.856 0.865 0.870 Large glass beads 0.307 0.659 0.747 0.796 0.905 0.985 1.033 1.067 1.098 1.116 Polyethylene 0.207 0.405 0.527 0.591 0.657 0.703 0.723 0.751 0.777 0.800 0.807 0.817 117 In Figure 6.9 the experimental derived annulus gas velocities for the 1.41 mm diameter glass beads with H-0A75 are compared to the predictions of Equations (6.1), (6.2), (6.3), (6.5) and (6.6). The correlation of Lefioy-Davidson (1969) underpredicts Ua by a considerable margin. However the modified Lefroy-Davidson equation due to Epstein et al. (1978) with n=2 shows a better agreement in the conical base portion. The Mamuro-Hattori (1968) model, Epstein-Levine (1978) equation and the Grbavcic et al. (1976) equation give a better agreement in the cylindrical portion. In the above comparisons the experimental value of Uajjm has been employed in these equations instead of Umf as recommended by Epstein and Levine (1978). The above results suggest that the assumed sa for these models should be modified to give better predictions. 6.3.4 Effect of U/U^ on local superficial gas velocities in the annulus In order to examine the effect of spouting gas velocity on superficial gas velocities in the annulus, static pressure gradients and voidage profiles in the annulus were measured with identical operating conditions with the smaller glass beads at two different spouting gas velocities, U/Ums=l.l and U/Ums=l.3. The measured pressure gradients are shown in Figure 6.10, while the corresponding voidage profiles are presented in Figure 6.11. It is seen that at any bed level the pressure gradient at U/Um/=1.3 is slightly lower than at U/Ums=l.l. This is consistent with the results of Lim (1975) shown in Figure 6.3 if the voidage in the annulus is assumed to be equal to the loose-packed voidage. However, the voidage for U/Ums=\3 was found to be significantly higher than at U/Ums=\.\ at any level as shown in Figure 6.11. Therefore, the conclusion that increasing the superficial gas velocity causes a decrease in the net gas flow through the annulus may be untrue. 118 1.0 0.9 -^ s C/) £ > * •+-» o o 0 > CO 03 O) CO O t CD Q. - i CO 0.8 0.7 0.6 0.5 0.4 0.3 0? 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 Vertical distance from orifice, z (m) Figure 6.9: Annulus gas velocity profile compared with equations in the literature where an extrapolated value of UaHm has been employed instead of U f Glass beads, d =1.41 mm, H=0.475 m, U/U =1.1. ' p ' ' ms 119 1.4 1.2 ^ 1.0 E E O CM X E E, N JO GL 0.4 0.8 0.6 i 0.2 0.0 U/Ums=1.1 U/Ums=1.3 0.0 0.1 0.2 0.3 0.4 0.5 Vertical distance from orifice, z (m) Figure 6.10: Effect of spouting gas velocity on longitudinal pressure gradients in the annulus for the 1.41 mm dia. glass beads. H=0.325 m. 120 0.50 0.49 0.48 0.47 GO o °-46 •g 0.45 "o TK ° - 4 4 O 5 0.43 0.42 0.41 0.40 U/Ums=1.1 U/Ums=1.3 0.0 0.1 0.2 0.3 0.4 0.5 Vertical distance from orifice, z (m) Figure 6.11: Effect of spouting gas velocity on voidage profiles in the annulus for the 1.41 mm dia. glass beads. H=0.325 m. 121 Pressure gradients in Figure 6.10 with the corresponding voidage profiles in Figure 6.11 were converted to superficial gas velocities using the calibration curves shown in Figure 6.7. The results are presented in Figure 6.12. The annulus gas velocities at U/Ums=1.3 are seen to be significantly higher than at U/Ums=\.\, with an average deviation of 17.4%. This result is contrary to the previously reported result (Lim, 1975) that increasing the spouting gas velocity causes a decrease in the net gas flow through the annulus and is at odds with the common assumption that all the fluid flow in excess of that required for minimum spouting goes into the spout. The present results suggest that increasing the spouting gas velocity causes an increase of voidage in the annulus which in rum allows more gas to leak into the annulus. 6.4 Conclusions Parallel measurements of pressure gradients with a differential pressure probe and voidage profiles in the annulus with a fiber optic system have been carried out to study gas flow distributions in the annulus. The important observation of Grbavcic et al. (1976) that for a given fluid- solid combination and column geometry the annulus pressure gradient at any bed level is independent of bed depth was corroborated by the present experimental data. However, the voidage in the annulus was found to be higher than the loose-packed voidage for the same material, contrary to the common assumption that voidage in the annulus is constant and equal to the loose-packed voidage. Pressure drops versus superficial gas velocities for beds with voidage higher than the loose-packed voidage were calibrated by applying the Ergun (1952) equation, which made it possible to estimate superficial gas velocities in the annulus using the static pressure gradient method for voidages higher than the loose-packed voidage. 122 1.2 c/) 1.1 1.0 0.9 0.8 o o CD > CO CO 03 O • i — CD Q. r n 0.7 0.6 0.5 0.4 0.3 0.2 U/Ums=1.1 U/Ums=1.3 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 Vertical distance from orifice, z (m) Figure 6.12: Effect of spouting gas velocity on superficial gas velocities in the annulus for the 1.41 mm dia. glass beads. H=0.325 m. 123 The local superficial gas velocity in the annulus was found to be higher in deep beds than in shallow beds of the same materials. This result is contrary to the conclusion (Grbavcic et al., 1976) that for a given fluid-solid combination and column geometry the annulus fluid velocity at any level is independent of bed depth. All theoretical models and equations in the literature underpredict the superficial gas velocities in the annulus. Modifications of the voidage assumed in the annulus are needed for those models. Increasing the spouting gas velocity was found to increase the net gas flow through the annulus. This effect is beheved to be caused by the increase of voidage in the annulus with increasing flow of the spouting gas. 124 Chapter 7 Spouting at Elevated Pressure Gas spouting at ambient conditions has been extensively studied. Many equations and models are available for predicting hydrodynamic parameters at room temperature and ambient pressure. In recent years, these equations have been tested and modified with experimental data obtained from spouted beds at elevated temperatures (e.g. Wu et al, 1987; Zhao et al , 1987; Ye et al, 1992). However, knowledge of spouting at elevated pressures is relatively unknown, with few published articles on the subject. A multistage spouted bed was used by Madonna et al. (1961), who stated that the overall bed pressure was higher due to contraction of gas at the entrance to each stage. A pressurized gasification process (combining a spouted bed and a fluidized bed) has been used by British Coal Corporation (Arnold et al, 1991) at pressures up to 20 bar and by Air Products and Chemicals Incorporation (Tsao et al., 1994) at pressures up to 16 bar. The emphasis in this work has been mainly on applications. The hydrodynamics, on the other hand, have not been studied. The present work focuses on obtaining experimental data at elevated pressures and exarrdning the validity of existing equations under these conditions. 7.1 Experimental 7.1.1 The pressurized rig The pressurized spouted bed rig is described in Chapter 2, and is shown schematically in Figure 2.1. A semi-cylindrical spouted bed column, built from Plexiglas, was placed in the cylindrical steel vessel which was part of a circulating air loop. The pressurized vessel was equipped with four pairs of facing windows, through which the entire spouted bed column could be illuminated and observed. The spouted bed column had a semi-cylindrical cross-section with an inner diameter of 76.2 mm and a height of 125 1.14 m and was furnished with a 60° conical base. A semi-circular plate of 9.5 mm diameter was used as the inlet orifice. The building compressed air flow under ambient temperature entered the bed through a pair of rotameters and passed through a filter before going to the exhaust pipe and to the recirculation line. The rig could be operated at pressures of up to 445 kPa with building air. A pressure relief valve, set at 400 kPa, was installed on top of the pressurized vessel for safety. When operating at atmospheric pressure the loop was simply opened. Three different particulate materials were used in this study. Properties of these particulate materials are summarized in Table 7.1. Particle diameters were obtained by sieving and particle densities were determined by the water displacement method. All particles were spherical and closely sized. Table 7.1: Properties of Particulate Materials Material Glass beads Glass beads Steel balls dp (mm) 1.09 2.18 1.09 Ps (kg/m3) 2445 2403 7401 smf 0.425 0.408 0.434 * 1.0 1.0 1.0 7.1.2 Measurement techniques The system was first pressurized to a desired pressure value and then the flow rate through the inside spouted bed was adjusted by a rotameter and a bypass valve to obtain stable spouting. 126 The minimum spouting velocity was measured by observing the bed through the front windows. The gas flowrate was first increased to a value above the minimum spouting condition and then decreased slowly until spouting ceased. The gas flowrate at which the fountain just collapsed was taken as the minimum spouting flowrate. The maximum spoutable bed height was determined by increasing the bed height by steps until stable spouting could not be obtained at any gas flowrate. The corresponding loose-packed bed height was taken as Hm. The spout diameter and the fountain height were determined by a video camera with a ruler attached to the half-column as a reference. Eighteen holes were drilled at 50 mm vertical intervals along the curved wall of the half-column, beginning near the inlet. Pressure taps were fitted in each of the holes to measure the overall pressure drop and the pressure gradient in the annulus. The overall pressure drop was determined by a pressure transducer (Model PX242-005G-5V, Omega) connected to a pressure tap located above the inlet orifice. The measured values were then corrected to account for any venturi effect (Mathur and Epstein, 1974). The pressure gradient in the annulus was measured by seven differential pressure transducers (Model PX163-005D-5V, Omega). Since these pressure transducers were unable to resist high pressures, the entire pressure measurement system was placed inside the pressurized vessel. Output electric signals were brought out through two power lead glands (Model PL-18-A-10, Conax Co.) and then fed to a computer by a A/D converter so that output signals could be recorded automatically using a Labtech Notebook (Version 5.0) package. Prior calibration of pressure transducers was conducted with a micromanometer (Model MM-3, Flow Corp. of Cambridge, Mass.). When deterrrnning the hydrodynamic regimes, the gas flow rate was first increased to a value far above the minimum spouting condition and then decreased gradually to zero while mamtaining bed height constant. The jet entered either a spouting regime or a bubbling-slugging regime, depending on whether the bed height was above or below Hm. 127 7.2 Results and Discussion 7.2.1 Minimum spouting velocity The experimental values of minimum spouting velocities for three different particulate materials are shown in Figure 7.1. Ums was found to decrease with increasing pressure (or fluid density), which is consistent with most empirical correlations (see Mathur and Epstein, 1974). The influence of pressure on Ums was found to be more significant for the larger glass beads and the heavy steel balls than for the smaller glass beads. One possible explanation may be the different Reynolds numbers for the three kinds of particles. In spouted beds the Reynolds number (Re=pdpU/fJ) usually is of order 100 (Epstein and Levine, 1978) and flow in the annulus may change from the viscous region to the inertial region. In general, Ums is partly related to the spouting vessel geometry and partly to the minimum fluidization velocity, Umf, for the given material, i.e. Ums=F(UmJ. However, at low and high Reynolds numbers, minimum fluidization velocity has the following limits (Grace, 1986): gcPAp Umf oc —E— (viscous limit, i.e. low Re) (7.1) \gd Ap Umf « J * (inertial limit, i.e. high Re) (7.2) When the Reynolds number is low, the fluid density is unimportant, which is the case for the smaller glass beads (ite=43~91). On the other hand, at high particle Re the viscous drag forces between the particles and the fluid are negligible compared to the inertial forces and Ums then depends on the fluid density. This is the case for the larger glass beads and the steel balls (ite=233~448). For a given bed height, Ums decreases with increasing pressure (or fluid density) according to the Mathur-Gishler (1955) equation: 128 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 • A • A • A • A • A • x s o o o o A • A • A Steel balls (1.09 mm) • Glass beads (2.18 mm) o Glass beads (1.09 mm) 0 100 200 300 400 Pressure (kPa) Figure 7.1: Influence of pressure on minimum spouting velocity: comparison between experimental values (given by points) and predictions from the Mathur and Gishler (1955) equation (given by lines) for H=0.135 m. 129 u. \P'\ LA J 1/3 \2gH{p-pf) V Pf (7.3) Comparisons between the experimental data and Ums values predicted by the Mathur-Gishler (1955) equation are also given in Figure 7.1. It was found that the Mathur-Gishler equation underpredicted Ums by about 50% and 39.5% for the steel balls and the larger glass beads, respectively. The deviation decreased to around 26% for the smaller glass beads. Ums is proportional to p'0-362 for the steel balls and the larger glass beads, while the dependence was of the order of A : 0 - 2 1 8 for the smaller glass beads, indicating that the exponent on p in equation (7.3) should have different values for particles of different Reynolds numbers. These findings also indicate that the pressure dependence of Ums is weaker for lower Reynolds number. 7.2.2 Maximum spoutable bed height The maximum spoutable bed height has been characterized in the literature (Mathur and Epstein, 1974; Littman et al., 1977) as corresponding to choking of the spout, development of slugging at the top of the spout, or fluidization of the annulus. In the present work, pulsation of the spout-annulus interface and choking of the bed near the bed surface constituted the spout termination mechanism for all measurements. The effect of pressure on rrmximum spoutable bed heights for three different types of particles are shown in Figure 7.2. It is clear that Hm increased with increasing pressure so that the region of spoutability was greater at higher bed pressure. The experimental data • * are compared with the McNab and Bridgwater (1977) semi-theoretical equation: # = d p _ lA 2/3 [7001 [Ar\ [V£ 35.9xl0~Mr - 1 (7.4) It is seen that equation (7.4) consistently overestimates Hm for the steel balls and the smaller glass bead, with errors up to 36.5% and 35.6% respectively. However, 130 0.40 0.35 0.30 -0.25 -0.20 -0.15 -0.10 --A , * , * D ,. O A • -O-A ,••' D _--O i .-"" . - A - " A A A A'" A A - ^ • n o D ° ° - - — o - " "" o o Steel balls (1.09 mm) — Glass beads (2.18 mm) Glass beads (1.09 mm) I . I . 0 100 200 300 Pressure (kPa) 400 Figure 7.2: Experimental maximum spoutable bed height (points) as a function of pressure compared with predictions from McNab and Bridgwater (1977) equation (lines). 131 predictions from equation (7.4) lie below the experimental values for the larger glass beads, with an average deviation of-10.3%. The deviations between the predicted and experimental values tend to be greater at high bed pressures. The deviations are partly due to the fact that equation (7.4) is based on the Mathur-Gishler (1955) equation for minimum spouting velocity which has already been shown to give large errors for high pressure beds in the previous section and partly due to a different mechanism of spout termination, i.e. choking/instability of the spout rather than fluidization of the annulus. 7.2.3 Spout shape and diameter Figure 7.3 shows the effect of pressure on spout shapes and spout diameters for three different particles. The spout diameters for all cases expanded sharply immediately above the entrance orifice, narrowed slightly further up the column and then diverged again near the bed surface. Spout diameters increased with increasing bed pressure for all three types of particles. This trend is qualitatively predicted by the often-used empirical equation of McNab (1972): D. = 2.0 ^ 0 . 4 9 r-v 0.68 041 A (7.5) The average experimental spout diameters and the corresponding results predicted from the McNab (1972) equation are summarized in Table 7.2. The deviations between the predicted and experimental Ds values increase with increasing pressure, with the largest error up to 65.5 % for the larger glass beads at P=342.7 kPa. However, the McNab (1972) equation gave good predictions for beds at ambient pressure (P=101.3 kPa). Meanwhile, Ds was found to be proportional to G°-61-0.66 for ^c s t e e j bans an (j faQ larger glass beads and to G0-73 for the smaller glass beads, instead of G0-49 in equation (7.5). These results indicate that the McNab (1972) equation is not suitable at elevated bed pressures. 132 150 120 O • i—i O .9 90 o r*-< o o > 60 30 0 1 r — i — i — i -Steel balls (1.09 mm) 0 P.kPa 4 • 1 1 1 1 j - 1 1 1—1 1 T — T ™ i r . Glass beads . (2.18 mm) , . , / ' * r •'A i * A i i ii -<4 • r I , « : A -• u M' 4' t i l l * L * f J 1 1 1 1 1 I 1 1 — Glass beads (1.09 mm) f f 4 /,* / • 15 0 10 15 0 Spout radius (mm) 15 Figure 7.3: Variation of spout diameter with pressure for three different particulate materials. H=0.135 m, U/Ur Table 7.2: Experimental average spout diameters and values predicted from the McNab (1972) equation. Pressure (kPa) 101.3 239.3 342.7 Steelballs(1.09mm) Ds Expt'l (mm) 19.12 20.69 21.90 Ds Pred. (mm) 17.28 22.55 24.90 Dev. (%) -9.6 9.0 13.7 Glass beads (2.18 mm) Ds Expt'l (mm) 20.85 22.26 23.67 Ds Pred. (mm) 26.40 34.96 39.18 Dev. (%) 26.6 57.1 65.5 Glass beads (1.09 mm) Ds Expt'l (mm) 16.52 17.81 18.84 Ds Pred. (mm) 16.46 22.84 25.48 Dev. (%) -0.4 28.2 35.2 7.2.4 Fountain height Experimental fountain heights for three different particles are presented in Figure 7.4. All observed fountain shapes were nearly parabolic and fountain heights increased with increasing pressure. The smaller glass beads gave higher fountains, while the larger glass beads and the heavy steel balls produced relatively lower fountains. This trend is consistent with the Grace and Mathur (1978) theoretical model. Higher pressures cause an increase in gas density which will lead to increased drag. Since drag initially retards particles entrained above the bed surface and then acts upwards once the particles have slowed down below the local gas velocity, the influence of pressure depends on which of these factors is more important. 134 ^^ E «4—» O) 0 sz "05 • 4 — » c 13 O LL 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0 Glass beads (1.09 mm) Glass beads (2.18 mm) Steel balls (1.09 mm) t* 100 200 300 Pressure (kPa) 400 Figure 7.4: Effect of bed pressures on fountain heights for three different particulate materials. H=0.135 m, U/Ums=1.2. 135 7.2.5 Pressure gradient in the annulus The influence of bed pressure on the longitudinal pressure profiles in the annulus for the smaller glass beads is shown in Figure 7.5. For the given fluid-solid combination and column geometry the longitudinal pressure profile in the annulus was found to be independent of bed pressure. Measurements of longitudinal pressure profiles in the annulus for both the larger glass beads and the steel balls provided similar results shown in Figures A.4 and A.5 in the Appendix. The longitudinal pressure gradient in the annulus of a fully spouted bed at any level is governed by the Ergun (1952) equation: W d*i dpi a K } One possible explanation of the insensitivity to pressure is that when the bed pressure was increased, /^-increased and the voidage and gas velocity in the annulus decreased, which in turn produced a constant p/l-sJU^/s3 in the inertial term of equation (7.6). Actually the voidage in most of the annulus has been found (Chapter 3 and 6) to be somewhat higher than the loose-packed voidage and increases with increasing spouting gas flow rate. 7.2.6 Regime map and spoutability Figure 7.6 shows a regime map for a bed of the smaller glass beads. Five fairly distinct flow regimes were observed: (1) static bed, (2) steady spouting, (3) incoherent spouting, (4) bubbling, and (5) slugging. In the incoherent spouting region, steady spouting could not be achieved and the spout diameter in the upper part of the bed appeared to shrink and expand in a periodic manner. The spout, however, was observed to be still continuous in this region. When the bed height exceeded the maximum spoutable bed height, spouting could not be obtained by any means. In the bubbling regime the upper 136 1.0O* 0.8-Q_ 5> 0.6 -CL I CL ± 0.4-0.2-0.0 '''a. P, kPa D 101.3 o 239.3 A 342.7 I . I , I • I ' \ _l . \ . A 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless vertical level, z/H Figure 7.5: Influence of bed pressure on longitudinal pressure profile in the annulus for the smaller glass beads. dp=1.09 mm, H=0.135 m, U/Ums=1.2. 137 0.30 0.28 h 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 Static Bed P=101.3kPa_ A, Slugging Incoherent Spouting Steady Spouting 0.0 0.4 0.8 1.2 1.6 2.0 Superficial gas velocity (m/s) 2.4 Figure 7.6: Regime map for the smaller glass beads at ambient pressure. P=101.3kPa,dp=1.09mm. 138 portion of the bed became a bubbling bed with small bubbles, while in the slugging region bubble sizes were greater than 0.6DC. In order to examine the influence of pressure on regimes, measurements were also conducted at two elevated pressures. The regime maps for the smaller glass beads at P=239.3 kPa and P=342.7 kPa are presented in Figure 7.7 and Figure 7.8 respectively. It is clear that increasing pressure resulted in a larger steady spouting area and a higher Hm. In other words, spoutability could be increased by increasing bed pressure. The above regime maps have many similarities with previous regime maps reviewed by Mathur and Epstein (1974). However, in the present work incoherent spouting only occurred at bed heights close to Hm. Another difference was that slugging was never observed for H<Hm. 7.3 Conclusions Experiments have been carried out at pressures up to 345 kPa to investigate the influence of absolute pressure on key hydrodynamic parameters of spouted beds. The most notable findings are as follows: (1) The minimum spouting velocity was found to decrease with increasing pressure, consistent with most empirical correlations. The Mathur-Gishler (1955) equation gave unsatisfactory agreement. (2) The maximum spoutable bed height increased with increasing bed pressure. The McNab and Bridgwater (1977) equation consistently overestimated Hm for large or heavy particles and underestimated Hm for small particles. The deviations between the predicted and experimental values were greater at high pressures. (3) Spout diameters were found to increase with increasing pressure. Although the McNab (1972) equation gave good predictions at ambient pressure, it gave poor predictions at elevated pressures, with the largest error up to 65.5 %. 139 0.30 0.28 0.26-0.24-| T 0.22 -^ 0.20 -© 0.18 •o 0.16 CD CQ 0.14 0.12 0.10 0.08 Static Bed • i P=239.3 kPa_ Slugging flncoheren Steady Spouting 0.0 0.4 0.8 1.2 1.6 2.0 Superficial gas velocity (m/s) 2.4 Figure 7.7: Influence of bed pressure on regimes. Smaller glass beads, P=239.3kPa, d =1.09 mm. 140 0.30 0.28 0.26 0.24 -^0.22 ^ 0 . 2 0 0 0.18 -D 0.16 CD CD 0.14 0.12 0.10 h 0.08 Static Bed 0.0 0.4 Incoherent Spouting Steady Spouting 0.8 1.2 1.6 2.0 2.4 Superficial gas velocity (m/s) Figure 7.8: Influence of bed pressure on regimes. Smaller glass beads, P=342.7kPa, dp=1.09mm. 141 (4) For a given fluid- solid combination and column geometry, the longitudinal pressure profile in the annulus was virtually independent of bed pressure. (5) Five fairly distinct flow regimes were observed. The region of spoutabihty can be increased by increasing the absolute pressure. 142 Chapter 8 Conclusions and Recommendations 9.1 Conclusions The scaling relationships proposed by Glicksman (1984) for fluidized bed scale-up have been modified to a full set of scaling parameters for spouted bed scale-up. A force balance for particles in the annulus region of a spouted bed leads to the addition of two non-dimensional parameters, the internal friction angle {(p) and the loose-packed voidage (s0) in the original Glicksman scaling relationships. Experimental verifications of the full set of modified scaling parameters were conducted, first in a series of small spouted beds, then in larger columns up to 0.914 m in diameter, and finally in a pair of high temperature (500 °C) columns. Both viscous and inertial forces were important for the conditions investigated so that no simplifications could be obtained to the full set of scaling parameters. The full set of modified scaling parameters was shown to be required for spouted bed scaling, with all dimensionless parameters matched between the prototype bed and a model bed. For example, a dead zone at the bottom of the annulus was observed not only in the 0.914 m diameter column, but also in a scaled 0.152 m diameter column. Successful scaling could not be achieved by varying only the bed and particle dimensions. Internal angles of particle friction and sphericities significantly influence the maximum spoutable depth, fountain height and longitudinal pressure profiles, showing that particle-particle interactions cannot be ignored in spouted bed scale-up. Accurate measurement of voidage profiles in the fountain, spout and annulus of spouted beds was conducted with a fibre optic probe system. The voidage in most of the annulus was found to be somewhat higher than the loose-packed voidage and increased with increasing spouting gas flow rate, contrary to early findings or assumptions. There is a denser region in the annulus adjacent to the spout boundary where the voidage was a little lower than the loose-packed bed voidage. In the core of the fountain, the voidage 143 decreased with height for low spouting gas flow rates, consistent with the model of Grace and Mathur (1978); however, at higher gas flow rates, the voidage first increased with height and then decreased towards the fountain top. The radial profiles of local voidage were roughly parabolic in the lower portion of the spout and blunt in the upper portion. The fiber optic probe used to measure voidage profiles was also employed to determine spout diameters in a half-column and in a full-column based on the significantly higher counts of output electric pulses in the spout region relative to the annulus. The flat wall of semi-cylindrical spouted bed columns was found to cause considerable distortion of spout shapes, these becoming approximately semi-elliptical. Caution must therefore be exercised when using spout diameter data from half-columns for spouted bed modelling and design. The often-used McNab (1972) equation was found to underestimate spout diameters in the full-column, with an average deviation of 35.5%. Accurate determination of particle velocity profiles in the spout and the fountain of a half-column and a full-column spouted bed was carried out with another fibre optic probe system. In addition, a fibre optic image probe was employed to measure vertical particle velocity profiles in the annulus of the full-column. In the spout, radial profiles of vertical particle velocities resembled Gaussian distributions. Particle velocities along the spout axis in the half-column were 70% lower than in the full-column under identical operating conditions. In the half column, particle velocities adjacent to the front plate were approximately 24% lower than a few millimeters away. The fountain core expanded suddenly near the bed surface and then gradually contracted with height. The model of Grace and Mathur (1978) gave good predictions of fountain heights for the full-column. In the annulus region, there was a 28% difference between particle velocities adjacent to the column wall and those only 2 mm away. The integrated upward solids mass flow in the spout and the downward solids flow in the annulus matched well at different bed levels. Parallel measurements of pressure gradients with a differential pressure probe and voidage profiles in the annulus with the fiber optic system have been carried out to study 144 gas flow distributions in the annulus. The observation of Grbavcic et al. (1976) that for a given fluid- solid combination and column geometry the annulus pressure gradient at any bed level is independent of bed depth was corroborated by the present experimental data. Calibration curves of pressure drops versus superficial gas velocities for beds of voidage higher than the loose-packed voidage were obtained by applying the Ergun (1952) equation, making it possible to estimate superficial gas velocities in the annulus using the static pressure gradient method. The local superficial gas velocity in the annulus was found to be higher in a deep bed than in a shallow bed of the same material, contrary to the conclusion (Grbavcic et al., 1976) that for a given fluid-solid combination and column geometry the annulus fluid velocity at any level is independent of bed depth. All theoretical models and equations in the literature were found to underpredict superficial gas velocities in the annulus. It was also discovered that increasing the spouting gas velocity increases the net gas flow through the annulus. Experiments were carried out in a pressurized spouted bed column of diameter 76.2 mm at pressures up to 345 kPa. Three different types of solids particles were investigated with mean particle sizes in the 1.0 - 2.2 mm range. The minimum spouting velocity was found to decrease with increasing pressure. Comparison of the experimental results for minimiuTi spouting velocity with the Mathur-Gishler (1955) equation gave unsatisfactory agreement. Maximum spoutable bed height and spout diameters increased with increasing bed pressure. The McNab and Bridgwater (1977) equation consistently overestimated Hm for large or heavy particles and underestimated Hm for small particles, with the deviations between the predicted and experimental Hm values tending to be greater at high bed pressures. Although the McNab (1972) equation gave good predictions of average spout diameters for beds at ambient pressure, it give poor predictions for elevated pressures, with errors up to 65.5 %. For a given fluid-solid combination and column geometry the longitudinal pressure profile in the annulus was found to be independent of bed pressure. 145 Five flow regimes could be distinguished. Spoutability could be improved by increasing the overall bed pressure. 9.2 Recommendations for Further Work • The full set of scaling parameters for spouted bed scale-up should also apply to scale up spout-fluid beds. Experimental verifications of the corresponding modified scaling parameters could be conducted with the two geometrically similar spout-fluid beds available in this lab, i.e. the 0.152 m diameter column used previously by Sutanto et al. (1985) and the 0.914 m diameter spout-fluid bed employed in the work of He (1990). • Voidage profiles in the annulus of spouted beds should be investigated for a wider variety of fluid-solid combinations and column geometry using the fiber optic system. A mathematical model would be desirable for predicting voidage profiles in the annulus. • The experimental particle velocity profiles should be compared with theoretical models in the literature to test their validity for predicting solids circulation rates in full column spouted beds. Detailed measurements of particle velocity profiles in the conical base region should also be carried out. These would be helpful for understanding solids mixing patterns near the inlet and to elucidate the mechanism of dead zone formation at the bottom of the annulus. • Further measurements of spout diameters in full column spouted beds should be conducted to provide more data which could then be used to replace or modify the McNab (1972) equation, thereby providing better predictions of spout diameters in full columns. 146 Nomenclature a = Dimensioiiless constant defined by Equation (6.3a) ( Ar = Archimedes number, dp3(ps-pJp^//j? ( - ) CD = Drag coefficient ( - ) dp = Particle diameter (m) Dc = Inside diameter of column (m) Dj = Diameter of inlet orifice (m) Ds = Average spout diameter (m) ^P = Mean value of effective stress tensor for particle phase f} = Constant defined by Equation (6.8a) (kg/m3s) f2 = Constant defined by Equation (6.8b) (kg/m4) g = Acceleration due to gravity (m/s2) G = pJJ, mass flux of fluid (kg/m2.s) H = Bed height (m) Hp = Fountain height (m) Hm = Maximum spoutable bed depth (m) HT = Total bed height from inlet to fountain top ( m ) kj = Constant defined by Equation (6.8a) (kg/m3s) k2 = Constant defined by Equation (6.8b) (kg/m4) 7 = Unit vector in vertical direction ( - ) L = Length of column (m) p - Annulus fluid pressure (Pa) P = Overall bed pressure (Pa) PJJ ~ Annulus fluid pressure at bed surface (Pa) r = Radial coordinate (m) rs = Spout radius (m) 147 R = Column radius (m) RD = Dead zone radius, (m) Re = Reynolds number, pdpU/ju ( - ) Rs = Spout radius (m) t = Time (s) T = Temperature (°K) Ts = Sampling time (s) U = Superficial gas velocity (m/s) Ua = Superficial gas velocity in the annulus at any level (m/s) UQH = Superficial gas velocity in the annulus at z = H (m/s) ^aHm = Superficial gas velocity in the annulus at z = Hm (m/s) Umf = Minimum fluidization velocity (m/s) Ums = Minimum spouting velocity (m/s) U - Fluid velocity (m/s) ua = Interstitial gas velocity in the annulus at any level (m/s) vomax = Particle velocity along axis at bed surface ( m/s ) va = Vertical particle velocity in annulus ( m/s ) vs = Vertical particle velocity in spout ( m/s ) v = Particle velocity (m/s) Ws = Solids mass flow ( kg/s) AWS = Change of solids mass flow (kg/s) y =UJUmf (-) Y -Quantity in Equation (6.3) defined by Equation (6.4a) ( - ) z = Vertical coordinate measured from inlet orifice (m) zp - Vertical coordinate in the fountain measured from bed surface Az = Vertical height interval ( m ) 148 Greek letters P = Fluid-particle interaction coefficient ( k g / m 3 s ) APg = Overall spouted bed pressure drop (Pa) P Tr . , volume of b e d - v o l u m e of particles . . 6 = Voidage, - ( - ) volume of bed emf = Bed voidage at minimum fluidization ( - ) s0 - Spout voidage at bed surface ( - ) s0 = Loose packed voidage ( - ) 77 = Flow regime parameter defined by Equation (6.4c) ( - ) // = Fluid viscosity (kg/m.s) Pfo = Bulk density of solids in loose-packed condition (kg/m3) pf = Fluid density (kg/m3) p s = Particle density (kg/m3) Ap = (ps-pj) (kg/m3) </)s = Sphericity of particles ( - ) r = Time delay ( s ) TAB = Transit time between fibers A and B ( s ) (p = Internal friction angle of particle phase ( °) Superscript = Dimensionless variable ( - ) 149 References Almstedt, A.E. and V. 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Davidson, "Similarity between Gas-Fluidized Beds at Elevated Temperature and Pressure", in Fluidization VI, ed. J.R. Grace, L.W. Shemilt and M.A. Bergougnou, Engineering Foundation, New York, pp. 293-300 (1988). Sokolovskii, V.V., "Statics of Granular Media", Pergamon Press, Oxford.(1965). Thorley, B., J.B. Saunby, K.B. Mathur, and G.L. Osberg, "An Analysis of Air and Solid Flow in a Spouted Wheat Bed", Can. J. Chem. Eng., 37, 184-192 (1959). Tsao, T.R., E.P. Holley, J.J. Lewnard, G. von Wedel, K.W. Richardson, J.D. McClung, W.F. Domeracki and T.E. Lippert, "Commercialization of the Second Generation 156 Pressurized Circulating Fluid Bed Combustion Process", Personal communication (1994). Tung, Y., J. Li and M. Kwauk, "Radial voidage profiles in a fast fluidized bed", in Fluidization '88 Science and Technology, M. Kwauk and D. Kunii, eds, Science Press, Beijing, pp. 139-145 (1988). Van Velzen D., H.J. Flamm, H. Langenkamp and A. Casile, "Motion of Solids in Spouted Beds", Can. J. Chem. Eng. 52, 156-161 (1974). Volpicelli, G., G. Raso and L. Massimilla, "Gas and Solid-Flow in Bidimensional Spouted Beds", Proc. International Symp. on Fluidization, ed. A.A.H. Drinkenburg, Netherlands Univ. Press, Amsterdam, pp. 123-133 (1967). Waldie, B. and D. Wilkinson, "Measurement of Particle Movement in a Spouted Bed Using a New Microprocessor Based Technique", Can. J. Chem. Eng. 64, 944-949 (1986). Waldie, B., D. Wilkinson and T.G.P. McHugh, "Measurement of Voidage in the Fountain of a Spouted Bed", Can. J. Chem. Eng. 64, 950-953 (1986). Werther, J, E.-U. Hartge and D. Rensner, "Measurement techniques for gas-solid fluidized-bed reactors", Int. Chem. Eng. 33, 18-27 (1993). Wu, S.W.M., C.J. Lim and N. Epstein, "Hydrodynamics of Spouted Beds at Elevated Temperatures", Chem. Eng. Comm., 62, 251-268 (1987). Zhang, M.C. and R.Y.K. Yang, "On the Scaling Laws for Bubbling Gas-Fluidized Bed Dynamics", Powder Technol., 51, 159-165 (1987). Yamazaki, H., K. Tojo and K. Miyanami, "Measurement of local solids concentration in a suspension by an optical method", Powder Technol., 70, 93-96 (1992). Ye, B., CJ. Lim and J.R. Grace, "Hydrodynamics of Spouted Bed and Spout-Fluid Beds at High Temperatures", Can. J. Chem. Eng., 70, 840-847 (1992). Zhao, J., CJ. Lim and J.R. Grace, "Flow Regimes and Combustion Behaviour in Coal-Burning Spouted and Spout-Fluid Beds", Chem. Eng. Sci., 42, 2865-2875 (1987). 157 Appendix 158 Calibrations of the Fiber Optic Probe for the Voidage Measurements As no method for direct conversion of output electrical signals to bed voidage or particle concentration exists, a calibration method has been used by a number of authors (e.g. Matsuno et al., 1983; Boiarski, 1985; Nakajima et al., 1990). Some experimental findings (Matsuno 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 fiber optic probe. On the other hand, Tung et al. (1988) found that relationship was non-linear for FCC particles. Recently, Lischer and Louge (1992), Yamazaki et al. (1992) and Werther et al. (1993) independently carried out calibrations with various particles and discovered that particle size has a strong influence on the linearity, with there being a linear relationship between volumetric particle concentration and the output signal for particles greater than 200 jiim. In the present work, glass beads of 1.41 mm in diameter were used. Therefore, it is reasonable to expect a linear relationship between (1-s) and voltage for the fiber optic voidage probe used in this work. Calibrations using the same glass beads (dp=1.41 mm) were conducted by immersing the probe in a liquid-solids fluidized bed (Dc=100 mm, L=1.5 m) for voidages less than 0.75 and a well stirred beaker ( 1000 ml) for voidages greater than 0.75. In these tests, the liquid was tap water. As shown in Figure A.l, the calibrations from both systems are very linear over the entire voidage range of interest. Therefore, an in-situ calibration curve was obtained by putting the probe in an empty column 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. 159 0.7 0.6 0.5 0.4 • From solid-liquid fluidized bed • From a beaker where particles are uniformly distributed in water 0.0 0.1 0.2 0.3 0.4 0.5 Volume fraction of particles 0.6 Figure A. 1: Calibration curve of output signal from the fiber optic system vs. solids volume fraction in glass beads (d =1.41 mm) and water systems. 160 1.3 1.2 1.1 1.0 -w 0.9 E J 0.8 "o -2 07 (D w > $ 0.6 1 0.5 i= Q. 0.4 3 CO 0.3 0.2 0.1 0.06 ' : • • • • • / * : / . . . . . . . / . _ ?;<? l.Y/ i.'Q : /.'y •./:// - bA "" [Q \ } • bl '. / ' t\ i i , / . • \ / / •y,p // j : : / ' / '•' ' / •' '/ 7. ;.... i 1 • / ' / ' • / : • ' '' ' '/ i 1 ... p / \ ,'' • ^ * : • ^ 0 r&t-* ! & ._ i_ . , , , 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Pressure gradient (mmH20/mm) Figure A.2: Calibration curve of pressure gradient vs. superficial gas velocity in a packed bed column with glass beads (dp=2.18 mm). 161 CO 0.9 0.8 0.7 0.6 8 0.5 CD > CO a o.4 03 'o iz CD Q. 3 C7) 0.3 0.2 0.1 0.06 1 i - : ••// ! :' / r 1 \ rh i 1 , ; / / / //o • V -/ / ; ; —r1-:..'../ '// / \ i 1 \ / / / / / ' 0 : . y. . .: / : ; i \ / • / < O •'-y / i . . . CV >cv -i 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Pressure gradient (mmH20/mm) Figure A.3: Calibration curve of pressure gradient vs. superficial gas velocity in a packed bed column with polyethylene particles (d =3.38 mm). 162 LOftr T r -, 1 r 0.8 "6. < x CL i CL 0.6 0.4 0.2-0.0 -P, kPa • 101.3 o 239.3 A 342.7 . I i I i A \ \ \ j , 1 , J. 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless vertical level, z/H Figure A.4: Influence of bed pressure on longitudinal pressure profile in the annulus for the larger glass beads, d =2.18 mm, H=0.135 m, U/Ums=1.2. 163 1.0ft CL X CL i CL 0.0 0.2 0.4 0.6 0.8 1.0 Dimensionless vertical level, z/H Figure A.5: Influence of bed pressure on longitudinal pressure profile in the annulus for the steel balls, d =1.09 mm, H=0.135 m, U/Ums=1.2. 164 

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