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Influence of Particle Shape and Bed Height on Fluidization

Permanent Link: http://ufdc.ufl.edu/UFE0045621/00001

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Title: Influence of Particle Shape and Bed Height on Fluidization
Physical Description: 1 online resource (72 p.)
Language: english
Creator: Liao, Lingzhi
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: geldart's-group -- minimum-fluidization-velocity -- nonspherical-particles -- sphericity -- voidage
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Fluidized beds have been widely used in industry. The minimum fluidization velocity is not only a crucial factor for reaction design; it is also an important index for process control. Compared to other parameters, the effects of bed voidage and particle sphericity on minimum fluidization velocity are obscure and difficult to predict. Therefore, the present work investigates thefluidization behavior of particles with different sphericity. It is found that as the sphericity decreases, the bed voidage increases. Increasing the particledensity and initial bed height causes the voidage to decrease due to the strong compression in the bed. The decrease in the voidage can lead to a decrease in the minimum fluidization velocity. Channeling appears in the fluidization process of flakes that have a sphericity of less than 0.6, even when the flakes are characterized as Group B particles. Additionally, channeling becomes more significant as the sphericity decreases. This cohesive fluidization behavior of flakes can be better described by the redefining the particlediameter Dp as the ratio of volume to surface area. In addition, a modification of the boundary between Geldart’s Groups A and C is proposed.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Lingzhi Liao.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Curtis, Jennifer S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045621:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045621/00001

Material Information

Title: Influence of Particle Shape and Bed Height on Fluidization
Physical Description: 1 online resource (72 p.)
Language: english
Creator: Liao, Lingzhi
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: geldart's-group -- minimum-fluidization-velocity -- nonspherical-particles -- sphericity -- voidage
Chemical Engineering -- Dissertations, Academic -- UF
Genre: Chemical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Fluidized beds have been widely used in industry. The minimum fluidization velocity is not only a crucial factor for reaction design; it is also an important index for process control. Compared to other parameters, the effects of bed voidage and particle sphericity on minimum fluidization velocity are obscure and difficult to predict. Therefore, the present work investigates thefluidization behavior of particles with different sphericity. It is found that as the sphericity decreases, the bed voidage increases. Increasing the particledensity and initial bed height causes the voidage to decrease due to the strong compression in the bed. The decrease in the voidage can lead to a decrease in the minimum fluidization velocity. Channeling appears in the fluidization process of flakes that have a sphericity of less than 0.6, even when the flakes are characterized as Group B particles. Additionally, channeling becomes more significant as the sphericity decreases. This cohesive fluidization behavior of flakes can be better described by the redefining the particlediameter Dp as the ratio of volume to surface area. In addition, a modification of the boundary between Geldart’s Groups A and C is proposed.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Lingzhi Liao.
Thesis: Thesis (M.S.)--University of Florida, 2013.
Local: Adviser: Curtis, Jennifer S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045621:00001


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1 INFLUENCE OF PARTICLE SHAPE AND BED HEIGHT ON FLUIDIZATION By LINGZHI LIAO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCI ENCE UNIVERSITY OF FLORIDA 2013

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2 2013 L ingzhi Liao

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3 To my m om and d ad

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4 ACKNOWLEDGMENTS I would like to express my gratitude to my advisor Prof Jennifer S. Curtis for teach ing me how to be a researche r, guid ing me with patience and encourag ing me all the time. I am also gr ateful to my dear parents for supporting me, loving me and trusting in me unconditionally I would also like to acknowledge my committee member D r. K evin Powers for his instruction and suggestions. Additionally my thank s go to my colleague s Yu Guo, Casey LaMarche, Sarah Mena, Poom Buncha Deepak Rangrajan and Henna Tangri for offering to help with my research and for sharing their experience ; to my friends, Jie Han, Dan Mao, Yang Song, and Linli Hu, for taking care of me and backing me up ; and to Jim Hinnant, Dennis L. Vince, Shirley A. Kelly, Deborah D. Sandoval, Carolyn Miller, and all the officers who helped me. My special thanks are extended to Santiago A. Tavares Claire Eder and Dr. Seymour S. Block for their generous help in improving my thesis.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 TABLE OF CONTENTS ................................ ................................ ................................ .. 5 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 NOMENCLATURE ................................ ................................ ................................ ........ 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 12 2 BACKGROUND ................................ ................................ ................................ ...... 14 Minimum Fluidization Velocity ................................ ................................ ................. 15 Key Parameters That Affect Minimum Fluidization Velocity ................................ .... 17 Diameter of Particle ................................ ................................ .......................... 17 Sphericity of Particle ................................ ................................ ......................... 17 Voidage at Minimum Fluidization ................................ ................................ ...... 17 Fluid Properties ................................ ................................ ................................ 18 Correlations fr om the Literature Used to Predict Minimum Fluidization Velocity ..... 18 S implification of the Ergun Equation ................................ ................................ 18 Modification of the Carman Kozeny Equation ................................ .................. 19 Combination of Dimensionless Terms ................................ .............................. 19 Literature Data for Minimum Fluidization Ve locity and Sphericity ........................... 20 Previous Correlation between Voidage and Sphericity ................................ ........... 20 Objectives of This Study ................................ ................................ ......................... 21 3 EXPERIMENTAL METHODS ................................ ................................ ................. 31 Experimental Materials ................................ ................................ ........................... 31 Density ................................ ................................ ................................ ............. 31 Size ................................ ................................ ................................ .................. 31 Sphericity ................................ ................................ ................................ .......... 32 Voidage ................................ ................................ ................................ ............ 32 Determination of Experimental Minimum Fluidization Velocity ................................ 33 Experimental Apparatus ................................ ................................ ................... 33 Experimental Procedure ................................ ................................ ................... 33

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6 4 RESULTS AND DISCUSSION ................................ ................................ ............... 44 Experimental Results for U mf mf ................................ ................................ ...... 44 Explanation for Voidage Range ................................ ................................ .............. 44 Narrowing of Voidage Range Due to Increse in Sphericity ............................... 44 Factors Accounting for the Voidage Range ................................ ...................... 45 Influence of Bed Height on Voidage and Minimum Fluidization Velocity .......... 46 Comparison of Experimental Re mf and Theoretical Re mf ................................ ......... 46 Fluidization Behavior of Flakes ................................ ................................ ............... 47 Effect of Channeling on Minimum Fluidization Velocity ................................ .... 48 New Definition to Describe D p for Flakes ................................ .......................... 48 5 CONCLUSION AND FUTURE WORK ................................ ................................ .... 62 Conclusion ................................ ................................ ................................ .............. 62 F uture Work ................................ ................................ ................................ ............ 62 APPENDIX: FLUIDIZATION AND DEFLUIDIZATI ON CURVES OF FLAKES .............. 64 LIST OF REFERENCES ................................ ................................ ............................... 69 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 72

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7 LIST OF TABLES Table page 2 1 Prediction correlation of minimum fluidization velocity ................................ ........ 23 2 2 Literature Data for U mf mf ................................ ................................ ............ 24 2 3 mf ................................ ................................ ......................... 27 3 1 Physical Properties of tested materials ................................ ............................... 33 4 1 U mf mf data for particles with close particle net volume ............................... 50 4 2 U mf mf data for particles with different particle net volume .......................... 51 4 3 Comparison of Experimental Re mf and Re mf from Carman Kozeny equation ..... 52

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8 LIST OF FIGURES Figure page 2 1 A comparison of the sphericit y of common 3D objects ................................ ....... 29 2 2 ................................ ............... 29 2 3 Publish ed data and correlation on effect of sphericity on voidage ...................... 30 2 4 Sphericity versus aspect ratio for cylinder s and square cuboid s ....................... 30 3 1 ................................ .......................... 36 3 2 Microscope pictures of spheres ................................ ................................ .......... 37 3 3 Microscope pictures of cylinder s and cubes ................................ ....................... 38 3 4 Microscope pictures of sharp particles ................................ ............................... 39 3 5 Microscope pictures of flakes ................................ ................................ ............. 40 3 6 Fluidization and defluidization curve of glass spheres 400 600 ................... 42 3 7 Fluidization and defluidization loop of polyamide cylinders 380*380 ........... 42 3 8 Schematic diagram of Fluidized Bed GUN T CE 220.. ................................ ........ 43 4 1 Literature data and experimental data of sphericity versus voidage ................... 53 4 2 Spheres packing.. ................................ ................................ ............................... 54 4 3 Force analysis of single particle with different density in fluidized bed ............... 55 4 4 Force analysis of single particle with different bed height in fluidized bed .......... 56 4 5 Fluidization and Defluidization curve and minimum fluidizaiton veloicity of glass spheres 400 600 m at different particle total volume (initial bed height). ................................ ................................ ................................ ........................... 56 4 6 Influence of Bed Height on Voidage. ................................ ................................ .. 57 4 7 Influence of Bed Height on minimum fluidization velocity ................................ .. 57 4 8 Fluidization and Defluidization curve of Hexagonal Flakes 1120*180 ......... 58 4 9 Fluidization behavior of flakes ................................ ................................ ............ 59 4 10 Channeling and cracks of flakes ................................ ................................ ......... 60

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9 4 11 Influence of channeling on minimum fluidization velocity ................................ .. 61 4 12 ................... 61 A 1 Fluidization and defluidization curve s for plastic square flakes 780*190 ..... 64 A 2 Fluidization and defluidization curve s for plastic hexagonal flakes 1120*180 at different initial bed height ................................ ................................ ......... 65 A 3 Fluidization and defluidization curve s for plastic hexagonal flakes 1120*100 ................................ ................................ ................................ ..................... 66 A 4 Pressure drop versus air flow rate for plastic diamond flakes 1500*50 ....... 67 A 5 Pressure drop versus air flow rate for plastic rectangular flakes 1550*300*40 m ................................ ................................ ................................ ..................... 68

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10 NOMENCLATURE A Cross area of fluidized bed, cm 2 A p Surface area of particles, m 2 A r Archimedes number, dimensionless D in Inner d iameter of cylinder test vessel, cm D p Particle diameter, m D v Equivalent volume diameter, m g Gravitational acceleration, m/s 2 g c Standard gravitational acceleration, 9.806 m/s 2 H initial Initial height of fluidized bed, cm H mf Height of fluidized bed at minimum fluidization cm m p Mass of particles, g ( P) Pressure drop, mm in w ater Re Reynolds number, dimensionless Re mf Reynolds number at minimum fluidization, dimensionless U mf Minimum fluidization velocity, m/s V p Volume of particles, m 3 Greeks Voidage of fluidized bed, dime nsionless m Voidage of fluidized bed at minimum fluidization dimensionless f Density of fluid, g/cm 3 p Density of particles, g/cm 3 Sphericity of particles, dimensionless Viscosity of fluid, kg/m/s

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11 Abstract of Thesis Presented to the Graduate Scho ol of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science INFLUENCE OF PARTICLE SHAPE AND BED HEIGHT ON FLUIDIZATION By Lingzhi Liao May 2013 Chair: Jennifer S. Curtis Major: Chemical Engineering Flui dized bed s ha ve been widely used in industry T he minimum fluidization velocity is not only a crucial factor for reaction design ; it is also an important index for process control. Compared to other parameters, t he effect s of bed voidage a nd particle sphericity on minimum fluidization velocity are obscure and difficult to predict. Therefore, the present work investigates the fluidization behavior of particles with different sphericity It is found that as the sphericity decreases, the bed v oidage increases. I ncreasing the particle density and initial bed height causes the voidage to decrease due to the strong compression i n the bed. The decrease in the voidage can lead to a decrease in the minimum fluidization velocity Channeling appear s in the fluidiz ation process of flakes that have a sphericity of less than 0.6 even when the flakes are characterized as Group B particles A dditionally, c hanneling becomes more significant as the sphericity decreases. This cohesive fluidization behavior of flakes can be better described by the redefining the particle diameter D p as the ratio of volume to surface area. In addition, a modification of the boundary between Geldart s Group s A and C is proposed.

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12 CHAPTER 1 INTRODUCTION O ver the last century, f luid ized beds have been rapidly developed and popularized in industry. For coal combustion, mineral, and metallurgical processes, fluidized bed combustion s stand out due to its capability of operating at a continuous stage, providing homogeneous thermal distri bution not only inside the fluidized bed but also between materials and their container and enhanc ing contact opportunities between solid and fluid materials. For coal gasification, nuclear power plants, water and waste treatment and other chemical react ions, fluidized bed s br ing advantages such as their uniform mixture of materials and large contact area which lead to effective and efficient chemical reactions and heat transfer. T h e catalytic cracking process is another of the earliest application s of fluidized bed. However, there are some uncertain factors that have hindered the design, optimization, and scale up of fluidized beds. O ne of the uncertain factors is the operation temperature for a gas solid system. Studies have shown that in addition to i ts influence on gas properties, temperature could also affect voidage at minimum fluidization, the minimum fluidization velocity, and the minimum bubbling velocity [1] To eliminate the influence of temperature on gas p roperties, Wen Ching Yang [2] proposed using Archimedes number to replace particle diameter while using dimensionless density to replace particle density, which is defined as the ratio of the difference between par ticle density and fluid density to the fluid density. Wall effect is another controversial element: it exerts a direct influence on the pressure drop of fluidized beds. The ratio of the test vessel diameter to the particle diameter is the main variable use d to indicate the sever ity of the wall effect. M oreover, the influence of wall effect on pressure

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13 drop varies at different flow regimes [3, 4] T he influence of wall effect also varies based on a d ifference in particle shape [4] The way size distribution affect s fluidization is unknown, as well In industr ies particles are seldom monodisperse ; additionally, the size distribution of particles varies from one ty pe to another. D. Gauthier etc. [5] and C. Lin etc. [6] st udied four classifications of mixtures at room temperature and high temperature respectively. The four classificati ons of mixtures were a binary mixture, a uniform distribution, a narrow cut, and a Gaussian distribution. It was concluded that the mean diameter of particles was insufficient to represent polydisperse particles and that different mixture s could lead to d ifferent behaviors in fluidized beds. Large size distribution may also result in the particles entrainment in fluidized beds. Moreover other factors, such as inter particle forces, the fluidized bed s shape and size, and the materials used in the fluidiz ed bed, can also influence fluidization to a certain extent. However, those effects have only been qualitatively generalized; the research failed to produce a clear and quantitat ive description T hus, a rigorous and accurate prediction is not available for fluidized beds.

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14 CHAPTER 2 BACKGROUND A packed bed is a column filled with packing materials. Liq ui d or gas can flow through a packed bed to achieve separation or reactions. F or sufficiently low flow rates the fluid passes through the void space between particles without disturbing them. This case is referred to as a fixed bed At higher flow rates, the drag forces generated by the pressure difference acting on the particles can exceed the gravitational force and lift up the particles. However, when the bed of particles expands, the drag force drops because of a reduction in the fluid velocity in the void spaces. Th is result s is a highly dynamic state that we refer to as fluidization. When fluidizing solid particles in a packed bed, there is a pressure d rop across the unit that causes energy losses. Several researche r s have expressed concern s about the relationship between the energy losses and the properties of fluid s and solids, and equations describing this relationship have been derived based on theor etical analysis and experimental data. The most widely accepted equations are the Carman Kozeny equation, the Burke Plummer equation and the Ergun e quation. [7] It is commonly believed that for a laminar flow, with low Reynolds numbers t hat is up to 10 where the viscous energy losses dominate the Carman Kozeny equation is valid as shown below (Eq. 2 1) ( 2 1 ) w here ( P) is the frictional pressure drop across a bed depth H U i s the superficial flui d velocity, is the viscosity of fluid and D v are the sphericity and the equivalent volume diameter of packing materials is the voidage of the pack ed bed and g c is the

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15 standard gravitational acceleration In addition, the diameter of non spherical particles is assumed to be described as the equivalent volume diameter times the sphericity of particles. As the fluid velocity increase s the flow is no longer a laminar flow and become s turbulent with high er Reynolds numbers (Greater than 2000) T he kine tic energy losses caused by changing channel cross section and fluid flow direction are the main contributor to the pressure drop. In this case the Burke Plummer equation as shown below (Eq. 2 2) has to be taken into consideratio n. ( 2 2 ) w here f is the density of fluid A ssuming that the viscous losses and the kinetic energy losses are additive and simultaneous the pressure drop in entire region from laminar to turbulent, can be obtain ed using the Ergun e quation as s hown below (Eq. 2 3 ) whic h is the summation of Eq.2 1 and 2 2. ( 2 3 ) Minimum Fluidization Velocity W ith the incre as e in fluid velocity, the drag force can become sufficient to balance the gravity of the solids. This dynamic equilibrium occurs at a minimum fluidization velocity and is known as incipient fluidization Once this minimum fluidization velocity is reached the fluidized bed is formed.

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16 W hen fluidization is about to occur the pressure drop no longer depend s on the fluid velocity and stay s constant at a certain range, which can be expressed as follows (Eq. 2 4 ). ( 2 4 ) w m is the voidage of packed bed at minimum fluidization and p is the density of particles T he substitution of Eq. 2 4 into the Ergun e quation (Eq. 2 3) gives Eq. 2 5 shown below, which lead to a quadratic equation for the minimum fluidization velocity (U mf ). ( 2 5 ) In order to sim plify the form of the Ergun e quation at incipient fluidiz ation, two dimensionless numbers (Archimedes Number (Ar) and Reynolds Number (Re)) have been introduced. Th e A rchimedes Number (Ar) is the ratio of the gravitational forces to the viscous force s as shown in Eq. 2 6. ( 2 6 ) The Reynolds Number (Re mf ) which is defined as the ratio of inertial forces to viscous forces at incipient fluidization, as shown in Eq. 2 7. ( 2 7 ) When substituting Ar ( Eq. 2 6) and Re mf (Eq. 2 7) into the Ergun Equation at incipient fluidization ( Eq. 2 5) Eq. 2 8 shown below is obtained.

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17 ( 2 8 ) When solving for the minimum fluidization velocity using Eq. 2 8, a problem that arised when trying to get values for the sphericity and voidage at minimum fluidization m Key Parameter s T hat A ffect Minimum Fluidization Velocity Diameter of Particle E quivalent volume diameter is defined as the diameter of a sphere that has the same volume as the particle. S urface to volume diameter i s defined as the diameter of a sphere that has the same surface area to volume ratio as the particle Sphericity of Particle S phericity is an important measure that describe s how round a particle is. I t is defined as the ratio of the surface area of a sph ere with the same volume as the given particle to the surface area of the particle itself as described in Eq. 2 9. (2 9) A s phere has sphericity of 1. S ome regular shape particles have a fixed value of sphericity, as show n in Figure 2 1 [8] However most particles do not have a regular shape and the ir sphericity is affected by other parameters, such as aspect ratio. Voidage at Minimum Fluidization Voidage is defined as the ratio of the volume of interspace between particles to the volume of packed b ed as shown in Eq. 2 10. V oidage at minimum fluidization has the same definition ex cept both volumes are obtained at incipient fluidization. (2 10)

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18 Fluid Properties The v iscosity and density of the fluid exert inf luence on the minimum fluidization velocity as well In the case of air, its viscosity and density are dependent on the environmental temperature and humidity Correlations f rom the Literature Used to Predict Minimum Fluidization Velocity Researchers hav e devised solutions t o th e problem of finding an d m Some of these adaptions include simplifications to the Ergun equation, modifications to the Carman Kozeny equation and the combination of dimensionless terms. A brief description for these three approaches follows. S implification of the Ergun Eq uation The first form of prediction correlation is based on the Ergun e quation at incipient fluidization. Researchers replaced the coefficient s and on the Ergun equation with two constants based o n fit ting the literature data to proposed equations In other word s this method simplifie s Eq. 1 8 into Eq. 2 11 as shown below: ( 2 11 ) w here C 1 and C 2 are constants. U mf can now be obtained simply by so lving quadratic equation 2 11 The most famous correlation solving C 1 and C 2 is [9] as shown below (Eq. 2 1 2 ). (2 12) However, this form of predictive correlation entailed relatively large error of 30 40%, and is only valid for limited conditions. Besides, the assumed relati onships

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19 and are not valid for all and m O ther scientists used the same method and found different values for the constants A summary of their findings is shown in Table 2 1. Modification of the Carman Kozeny Equation The second option is a modification of the Carman Kozeny e quation at incipient fluidization. As shown below, Eq. 2 1 3 is the original form of the Carman Kozeny e quation at incipient fluidization. ( 2 1 3 ) A s before, Researchers [10, 11] made the same a ssumption that was s hown in the first method they replac ed the coefficient with a constant. Additionally they changed the linear relationship between Ar and Re mf into an exponential relationship. The general form of this method is shown in Eq. 2 1 4 ( 2 1 4 ) w here a and b are constant. This form of predicti ve correlation has the same problem as the first form. Moreover, the modification of the relationship from linear to exponential is not supported by theory. Combination of Dimensionless Terms F or this case, Researchers summarized the factors related to minimum fluidization velocity, grouped them into dimensionless terms, and assembled these terms tog ether based on literature data. R. Coltters and A.L. Rivas [12] even specialize d the coefficient according to different materials particle size, particle density, particle

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20 shape, and different gas They also emphasized the importance of the properties of the particle surface in U mf prediction. This metho d is more experimentally based and cannot be explained theoretically. Literature Data for Minimum Fluidization Velocity and Sphericity Literature data for minimum fluidization velocity, voidage and sphericity are listed in Table 2 2 and Table 2 3 along with density and diameter informatio n Because particle shape is one of the main factor s of study, most literature data presented were chosen from non spherical particles. Figure 2 2 showed the particles Geldart s classification of literature data Previ ous Correlation between Voidage and Sphericity F. Benyahia etc. [13] studied the relationship between voidage and sphericity, and summarized their relationship as stated in Eq. 2 1 5 ( 2 1 5 ) This e qua tion is only v alid for 0.42 < < 1.0. The extra term related to wall effect has been eliminated. H. Hartman etc. worked out another equation to describe voidage and sphericity (Eq. 2 1 6 ) by fitting the literature data ( 2 1 6 ) In addition, one of the assumptions mad e by Wen and Yu, which has been proven more accurate [14] also describes the relationship between voidage and sphericity. A s illustrated in Figure 2 3 it can be concluded that as sphericity increases, voidage decre ases. However, the relation between voidage and sphericity cannot be expressed precisely with a function, as each value of sphericity corresponds to more than one value of voidage.

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21 Objectives of This Study Because the coefficient s in the Ergun e quation and the Carman Kozeny e quation are obtained from experimental data, we have reason to believe these coefficient s are not perfectly accurate. Nevertheless, the basic form at of these equations has been theoretically prove n and is convincing. In order to estimat e the minimum fluidization velocity with more reliability and less difficulty, we propose to use the Carman Kozeny e quation and replace the term and the constant preced ing this term with a function of In this way, we can save the effort of findin g m which is hard to estimate without doing an experiment. This is true because m needs to be experimentally acquired at minimum fluidization velocity and if an experiment need s to be conducted, then ther e is no need to work on prediction correlation. In order to make this modification, we need to study the relationship between voidage and sphericity and examine why the voidage range exist s identifying the parameters that affect voidage. N one of existing correlations discussed for this situation are taken into consideration. T he goal of this study is to determine the possible parameters that affect voidage of particles with the same sphericity. F or particles with a sphericity of close to 1, their shape is quite uniform. H owever, for cylinders, the sphericity maximizes to 0.87 when the aspect ratio is equal to 1 and then sphericity drops with either an increasing or a decreasing aspect ratio. A s shown in Figure 2 4, cylinders with aspect ratio of 0.2 and 5 share a n identical sphericity of 0.7, b ut one of them is a flat disk while the other is a long cylinder. The shape difference becomes more severe as sphericity decreases.

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22 T he objectives of th is study are as follows: To analyze the mechanism of fluidizati on of spherical and non spherical particles and to understand the effect s of voidage T o investigate the effects of particle properties and fluidized bed parameter s on the voidage and minimum fluidization velocity T o study the fluidization behavior and void age of flakes for a better understanding of the fluidization of low sphericity particles

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23 Table 2 1. Prediction correlation of minimum fluidization velocity Authors Prediction Correlations P. Bourge o is, P. Grenier [1 5] J.F. Richardson, M.A.D.S. Jeromino [16] D.C. Chitester, R.M. Kornosky, L.S. Fan, J.P. Danko [17] J. Reina, E. Velo, L. Puigjaner [18]

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24 Table 2 2 Literature Data for U mf and mf Author Materials p (kg/m 3 ) d p s ( ) U mf (m/s10 2 ) mf ( ) S.K. Gupta, V.K. Agarwal, S.N. Singh, et al [19] Iron ore tailings 2551 24.15 0.67 8.34 0.565 Zinc slime 2748 18.15 0.59 6.78 0.63 Pre hydrocyclo ne uranium tailings 2830 18.62 0.54 7.83 0.654 Post hydrocyclone uranium tailings 2677 16.68 0.47 5.73 0.686 Fly ash 1622 108 0.83 2.51 0.59 Z.Lj. Arsenijevic, Z.B. Grbavcic, R.V. Garic Gaulovic, F.K. Zdanski [20] Crushed Stone 2712 2 000 0.72 723 0.471 Crushed Stone 2712 241 0 0.697 775 0.467 Crushed Stone 2712 273 0 0.734 813 0.471 A.W. Nienow, P.N. Rowe, L.Y.L Cheung [21] Copper shot 886 0 550 1 4 9.5 Copper shot 8860 461 1 45.1 Copper shot 8860 273 1 19.5 Copper shot 8860 115 1 4.2 Copper shot 8860 97 1 2.9 Copper shot 8860 70 1 2.3 Copper powder 8860 461 0.56 44.8 Copper powder 8860 273 0.56 16.5 Copper powder 8860 195 0.56 13.5 Bronze shot 854 0 388 1 31.5 Bronze shot 8540 273 1 19.5 Bronze shot 8540 231 1 18 Bronze shot 8540 114 1 5.6 Steel shot 744 0 388 1 35.2 Steel shot 7440 324 1 26.7 Steel shot 7440 273 1 22.8 Steel shot 7440 138 1 18.1

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25 Table 2 2 Continu ed Author Materials p (kg/m 3 ) d p s ( ) U mf (m/s10 2 ) mf ( ) A.W. Nienow, P.N. Rowe, L.Y.L Cheung [21] Ballotini 295 0 550 1 24 Ballotini 2950 461 1 20.3 Ballotini 2950 3 88 1 18.7 Ballotini 2950 273 1 7.2 Ballotini 2950 231 1 4.3 Ballotini 2950 165 1 3.2 Quartz Glass 2650 273 0.63 9.8 Quartz Glass Quartz Glass 2250 388 0.69 11.5 Quartz Glass 2250 324 0.69 10.7 Quartz Glass 2250 273 0.69 6.6 Sodium perborate 2130 726 0.7 27.4 Carbon 1930 388 0.7 10.8 Carbon 1930 324 0.7 9.7 Carbon 1930 195 0.7 3.4 Sugar 1590 649 0.5 22.4 Sugar 1590 461 0.5 9 Sugar balls 1490 928 1 28.3 Polystyrene spheres 1 05 0 649 1 13.5 Polysty rene spheres 1 05 0 550 1 12.6 Polystyrene spheres 1 05 0 273 1 3.2 Polystyrene spheres 1 05 0 231 1 2.3 N.S. Grewal, S.C. Saxena [22] Silicon carbide 3220 178 0.67 3 9 0.495 Silicon carbide 3240 362 0.67 15 6 0.49 Alumina 4015 259 0.64 10 4 0.51 Silica sand 2670 167 0.81 2 7 0.44 Silica sand 2670 451 0.84 15 1 0.41 Silica sand 2670 504 0.88 22 0.42 Glass beads 2490 265 1 5 9 0.4 Glass beads 2490 357 1 10 6 0.4 Glass beads 2490 427 1 16 3 0.405 Lead glass 4450 241 1 9 3 0.4 Dolomite 2840 312 0.6 11 8 0.54 Dolomite 2840 293 0.635 10 5 0.525

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26 Table 2 2 Continu ed Author Materials p (kg/m 3 ) d p s ( ) U mf (m/s10 2 ) mf ( ) D.S. Povrenovic, Dz.E. Hadzismajlovi c, Z.B. Grba vcic, D. V. Vukovic, H. Littman [23] Glass spheres 2400 4 000 1 1 71 0.42 Glass spheres 2482 5 000 1 1 87 0.43 Glass spheres 2482 6 000 1 2 08 0.44 Hollow plastic spheres 529 10 000 1 1 27 0.54 Dried peas 1275 5 000 1 1 4 0 0 .44 CaCO 3 2600 2 4 00 1 1 15 0.42 Plastic chips 936 3 6 00 0.85 91 0.48 R. Solimen e, A. Marzocchella, P. Salatino [24] Silica Sand 2600 125 ~0.8 2 3 Silica Sand 2600 328 ~0.8 11 1 Silica Sand 2600 333 ~0.8 11 3 Silica Sand 2600 510 ~0.8 19 7 B. Liu, X. Zhang, L. Wang, H. Hong [25] Plasticine 1476 7000 1 195 4 0.39 Plasticine 1476 7125 0.85 178 6 0.335 Plasticine 1476 7012 0.8 17 5. 1 0.369 Pl asticine 1476 7019 0.7 173 3 0.382 Plasticine 1476 6940 0.8 155 2 0.47 Plasticine 1476 7012 0.6 156 8 0.428 Plasticine 1476 7043 0.6 197 4 0.448 Plasticine 1476 7000 0.6 168 2 0.512 J. Reina, E. Velo, L. Puigjaner [26] Forest 621 1 14 0 0.69 25 0.47 Demolition 759 1 48 0 0.35 32 0.56 Slot machines 529 1 63 0 0.24 34 0.7 Furniture 621 1 57 0 0.32 33 0.62 Palettes 505 1 69 0 0.33 26 0.65 Van Heerden et. al. [27] Carborundum 3180 82 0.92 1.13 0.471 Carborundum 3180 94 0.95 1.48 0.471 Carborundum 3180 95 0.94 1.5 0.471 Carborundum 3180 117 0.83 2.19 0.496 Carborundum 3180 162 0.9 4.56 0.487 Carborundum 3180 192 0.99 5.82 0.476 Carborundum 318 0 225 1 7.09 0.475 Iron oxide 5180 92 0.88 2.43 0.494

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27 Table 2 3 Literature Data for mf Author Materials p (kg/m 3 ) d p s ( ) U mf (m/s10 2 ) mf ( ) M. Leva [28] S harp sand 50 0.67 0.60 S harp sand 70 0 .67 0.59 S harp sand 100 0.67 0.58 S harp sand 200 0.67 0.54 S harp sand 300 0.67 0.50 S harp sand 400 0.67 0.49 R o und sand 50 0.86 0.56 R o und sand 70 0.86 0.52 R o und sand 100 0.86 0.48 R o und sand 200 0.86 0.44 R o und sand 300 0.86 0.42 Anthracite coal 50 0.63 0.62 Anthracite coal 70 0.63 0.61 Anthracite coal 100 0.63 0.60 Anthracite coal 200 0.63 0.56 Anthracite coal 300 0.63 0.53 Anthracite coal 400 0.63 0.51 Fischer Tropsch catalyst 100 0.58 0.58 Fischer Tropsch catalyst 200 0.58 0.56 Fischer Tropsch catalyst 300 0.58 0.55 G.G. Brown. et al. [29] Spheres 5511.8 1 0.3781 0.468 Glass sph eres 5308.6 1 0.412 L ead shot, uniform size 6350 1 0.375 0.375 0.397 0.415 0.421 L ead shot, uniform size 1473.2 1 0.363 0.373 0.374 0.375 L ead shot, uniform size 3073.4 1 0.370 0.383 0.390

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28 Table 2 3 Continu ed Author Materials p (kg/m 3 ) d p s ( ) U mf (m/s10 2 ) mf ( ) G.G. Brown. et al. [29] C elite cylinders 6781.8 0.877 0.361 0.365 0.372 0.455 0.457 0.461 Celite Spheres 5511.8 1 0.3784 0.468 Berl saddles 50038 0.314 0.780 35052 0.297 0.785 25019 0.317 0.750 14986 0.296 0.758 11988.8 0.342 0.710 9906 0.329 0.694 B erl saddles 25400 0.370 0.725 B erl saddles 12700 0.370 0.7125 0.761 N ickel saddles 3352.8 0.1 40 0.931 3289.3 0.140 0.935 R aschig rings 50038 0.260 0.853 35052 0.262 0.835 25019 0.272 0.826 9906 0.420 0.655 R aschig rings 25400 0.391 0.707 R aschig rings 9779 0.531 0.554 0.620 G lass rings 5791.2 0.4 11 0.67 6934.2 0.370 (0.314) 0.72 9842.5 0.294 0.80 11976.1 0.254 0.845 MgO Granules 4775.2 0.735 0.426 0.434 0.513 Flint sand 284.48 0.925 0.385 Glass beads 693.42 1.0 0.391 NaCl 139.7 0.837 0.465

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29 Fig ure 2 1 A comparison of the sphericit y of common 3D objects [8] Figure 2 2 Particle Geldart s Classification of literature data

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30 Figure 2 3 Published d ata and correlation on effe ct of sphericity on voidage Figure 2 4 Sphericity versus aspect ratio for cylinder s and square cuboid s

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31 CHAPTER 3 EXPERIMENTAL METHODS Experimental Materials In order to s tudy the fluidization behavior of particles with different shap e s 1 8 particl es with different sphericit ies ranging from 0.24 to 1.0, w ere tested in this study. S ome materials such as polyamid cylinders, glass spheres, and flakes, appear well defined and uniform in shape, while others such as crushed glass, ovaline, aluminum oxi de, and sands, are irregular ly shape d Physical properties of the materials are listed in Table 3 1, and Figure 3 1 show s that all tested particles belong to Geldart s group B Density Density data for all materials were measured with the water displacemen t method Size Polyamid cylinders and cubes, polycarbonate cylinders and plastic flakes were manufactured with specific dimensions and a relatively narrow size distribution. However other materials like glass spheres, polystyrene spheres, crushed glass, ovaline, aluminum oxide and sands varied in their dimensions and had a relatively wide size distribution so they were sieved manually to achieve a relatively narrow size distribution All materials w ere photographed with an optical microscope Olympus B X60 digital camera with SPOT insight using different magnific ation lens es, and were simultaneously analyzed by ImageJ. Figure 3 2 shows microscope pictures of the spheres. M icroscope pictures of the cylinders and cubes can be seen in Figure 3 3 Figure 3 4 show s microscope pictures of the sharp particles. Figure 3 5 contains

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32 microscope pictures of the flakes .For round and sharp particles ( with a sphericity of over 0.7), size was also measured by obtaining the equivalent circular area diameter as measured b y a BECKMAN COULTER RapidVUE Particle Shape and Size Analyzer Sphericity Glass spheres, polystyrene spheres, polyamid cylinders and cubes, polycarbonate cylinders and plastic flakes are manufactured with a well defined shape. However crushed glass, ova line, aluminum oxide and sands are not specially manufactured and have irregular shapes For those materials with a well defined shape, the sphericity was calculated based on the condition To achieve the perfect condition, cylinders and cub es were considered to have an aspect ratio equal to 1 and flakes were considered as square s rectangle s regular diamond s or regular hexagon s Also all the particles were treated as monodisperse, which means that they were of a uniform size. For those pa rticles without a well defined shape, the sphericity was determined by a BECKMAN COULTER RapidVUE Particle Shape and Size Analyzer Voidage Voidage at minimum fluidization was calculated based on the following equation (Eq. 3 1) ( 3 1 ) w here m p is the weight of the particles, H mf is the height of the fluidized bed at minimum fluidization, p is the particle density and A is the cross area of the fluidized bed. S imilarly, the height of the static bed was used to calculate the voidage of the static bed 0

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33 Determination of Experimental Minimum Fluidization Velocity Experimental minimum flu idization velocity was determined by measuring the pressure drop across a bed of particles. As an example, t ake the experimental data for glass spheres 400 600 m : a s diagrammed in Figure 3 6 the pressure drop increase d with air flow rate until the bed ex pand ed and increase d the porosity ( blue line ). As the air flow rate was further increased, the pressure drop attain ed a maximum value that wa s independent of air flow rate For the fluidization curve of cohesive particles, the value of pressure drop reac he d a peak and then f ell off slightly (as shown in Figure 3 7 ) T his can be expalained, because the frictional force must be overcome before a rearrangement of particles can take place. If the process is reversed, the defluidization line can be obtained (r ed line) To experimentally identify the minimum fluidization point, a linear function is fitted to the data in the defluidization step before they reach a constant value (as shown in figure 3 6). This line will intersect the constant value of pressure dro p for the bed at the minimum fluidization point. Experimental Apparatus The air part of GUNT CE 220 Fluidized Bed Formation as shown in Figure 3 8 was used to test minimum fluidization velocity. The inner diameter of the air cylinde r vessel is 4 4 c m, and the air flow rate was adjusted and measured by an AAB PurgeMaster A6142C301BNA0DAS with a range of 0 32 L/min. Experimental Procedure Before fluidizing the particles, t he weight of particles filling the fluidized bed, the initial bed height, the room tempe rature and humidity w ere measured Then the air flow rate meter was changed at 1 L/min increments until the pressure drop did not varied significantly. At this point, the pressure drop, the flow rate, and the bed height were

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34 recorded. These data belongs t o the blue line in figure 3 6. To obtain the defluidization line, shown red in figure 3 6, the flow rate was decreased at the same rate of 1 L/min, and the pressure drop recorded at each point. As an example, t he fluidization and defluidization loop of pol yamide cylinders i s illustrated in Figure 3 7

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35 Table 3 1. Physical Properties of tested materials Material Shape D imension ( ) d ev ( ) p (g/ c m 3 ) Glass Sphere s 212 300 250 5 1 2.5 0.02 Glass Sphere s 400 6 00 533 8 1 2.4 0.08 Polystyrene Spheres 200 400 242 7 1 1.05 0.04 Polystyrene Spheres 400 600 480 9 1 1.05 0.03 Polycarbonate Cylinder 500 *500 (D*H ) 624 7 0.874 1 2 0.02 Polyamid Cylinder 380 *380 (D*H) 451 6 0.874 1.1 0.03 Polyamid Cylinder 500 *500 (D*H) 670 8 0.874 1.1 0.03 Polyamid Cube 500 *500*500 723 6 0.806 1.1 0.03 Ovaline Irregular 212 300 339 6 0.76 3.4 0.09 Sand irre gular 212 300 281 7 0.75 2.6 0.04 Aluminum Oxide Irregular 212 300 373 5 0.74 3.9 0.06 Glass Irregular 212 300 347 9 0.7 2 2.7 0.05 Glass Irregular 400 600 630 10 0.72 2.1 0.02 Plastic Suqare Flake 780*190 604 2 0.63 1.2 0.04 Plasti c Hexagonal Flake 1120*180 654 3 0.60 1.3 0.05 Plastic Hexagonal Flake 1120*100 538 3 0.46 1.3 0.03 Plastic Daimond Flake 1500*50 571 5 0.32 1.4 0.02 Plastic Rectangular Flake 1550*300*40 328 1 0.24 1.4 0.02

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36 Figure 3 1. Geldart s G roup of experimental particles

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37 A B C D Figure 3 2. Microscope pictures of spheres A) Glass Spheres 212 300 B) Polystyrene Spheres 200 400 C) Glass Spheres 400 600 and D) Polystyrene Spheres 425 600

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38 A B C D Figure 3 3 Microscope pictures of cylinders and cubes A) Polyamid Cylinders 380*380 B) Polyamid Cylinders 50 0*500 C) Polycarbonate Cylinders 500*500 and D) Polyamid Cubed 500*500*500

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39 A B C D Figure 3 4 Microscope pictures of sharp particles A) Ovaline 212 300 B) Sand 212 300 C) Aluminum Oxide 212 300 and D) P Crushed Glass 212 300

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40 A B C D E F Figure 3 5 Microscope pictures of flake s A) and B) Plastic Square Flakes 780*190 C) and D) Plastic Hexagonal Flakes 1120*180 E ) and F ) Plastic Hexagonal Flakes 1120*100

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41 A B C D Figure 3 5 Continu ed A) and B) Plastic Rectangular Flakes 1550*300*40 D) Plastic Diamond Flakes 1500*50

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42 Figure 3 6 Fluidization and defluidization curve of glass spheres 400 600 Figure 3 7 Fluidization and defluidization loop of polyamide cylinders 380*380

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43 A B Figure 3 8 Schematic diagram of Fluidized Bed GUN T CE 220. A) Schematic layout B) Picture of Fluidized Bed GUNT CE 220 (Source: http://www.gunt.de/static/s3316_1.php?p1=0&p2=&pN=search;Volltext;ce%2 0220 A ccessed March 20 1 3 ) 1 .) Table support with panel ; 2 .) Bypass valve for air with sound absorber ; 3 .) Rotameter for air with needl e ; 4 .) Single tube manometer for differential air pressure ; 5 .) Swith for diaphragm compressor ; 6 .) Test vessel for air ; 7 .) Air filter ; 8 .) Scale ; 9 .) Water overflow ; 10 .) Fixing for the upper Sintered plate ; 11 .) Test vessel for water ; 12 .) Bleed/vent va lve ; 13 .) Two tube manometer for water pressure ; 14 .) Switch for diaphragm pump ; 15 .) Rotameter for water with needle valve; 16 .) Bypass valve for water ; 17 .) Water supply ; 18 .) 20 .) Sintered plate (not visible) ; 19 .) 21 .) Distribution chamber ; 22 .) Air supply Further components behind the cover ( not visible ) include : 23 .) Supply tank for water with drain tap and safety valve ; 24 .) Diaphragm pump ; 25 .) Compressed air reservoir with safety valve ; 26 .) Diaphragm compressor

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44 CHAPTER 4 RESULTS AND DISCUSSI ON Experimental Results for U mf and mf Table 4 1 show s the experimental results for minimum fluidization velocity and voidage at the minimum fluidization of 16 particles with total particle volume close to 100 cm 3 ( with initial bed height around 10 cm) A dditionally, Figure 4 1 includes the experimental and literature data for voidage and sphericity. Explanation for Voidage Range Voidage was calculated using the theoretical definition. F or particles with a fixed dimension and shape, the packing patterns b ecame the main factor influenc ing voidage. T ak ing spheres as an example, in a packed bed, for the densest and loosest packing patterns ( illustrated in figure 4 2 ) the voidage can be calculated a t 0.27 and 0.48 respectively. Figure 4 2 also show s the dense st and loosest packing patterns against the wall, and the voidage s are 0. 40 and 0.4 8 respectively. Consequently, different packing patterns of particles can result in different voidage s The same conclusion applies for the non spherical particles. Narrowin g of Voidage Range Due to Increse in Sphericity W hen it comes to voidage, random packing has been emphasized so that the influence of particle packing patterns can be ignored This policy is more effective for particles with a higher sphericity. For instan ce, with a fixed packing pattern no matter how much a sphere was rotated, the voidage of particles in a packed bed or fluidized bed would remain constant Nevertheless, the orientation of particles with a lower sphericity could significantly affect voidag e. A small change in packing patterns could

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45 cause a relatively large difference in voidage. This explain s why the voidage range is relatively wider for lower sphericity than it is for higher sphericity. Factors Account ing for the Voidage Range Although the voidage range indicate s the trend of a change in voidage due to sphericity, this range m ight result in some error T he following parameters may account for the range: different roughness and cohesion of particles which can result in different friction f orce s and aggregation s different size and wall effect Different samples of the same material may share the same shape but those with a larger diameter correspond to lower voidage different particle density D enser particles tend to form a denser packing pattern in fluidized bed s as shown in figure 4 3 different bed height s L arger bed height s tend to form a denser packing pattern in fluidized bed s as shown in figure 4 4 different shape s. E ven with same sphericity the shape can differ b ased on differ ent aspect ratio s Using sphericity alone to describe the shape of particle s is evidently in sufficient. For example, in cylinder s and square cuboid s sphericity increases and then decreases as aspect ratio increases. In other word s any aspect ratio (other than an aspect ratio equal to 1 ) can always find another aspect ratio that is its own reciprocal and has the same sphericity, as shown in Figure 2 4 To provide a visual a disk with a large surface could have the same sphericity as a very long cylinder. H owever, despite having the same sphericity, the flakes and cylinders have different voidage s and behave differently in fluidized bed s

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46 Influence of Bed Height on Voidage and Minimum Fluidization Velocity The data in Table 4 2 show the influence of differe nt bed height s and particle densit ies on voidage. As shown in Figure s 4 5 4 6 and 4 7 it can be concluded that v oidage decreases as total particle volume increases when H initial /D in <5, and an increase in total particle volume can cause a decrease in U m f H owever this trend weakened as H initial /D in increase d, and this could be explained by Janssen s Equatio n. When bed height increases to a certain point, the vertical forces acting on a particle in a fixed position w ill no longer change. Comparison of Ex perimental Re mf and Theoretical Re mf T h e experimental Re mf was calculated based on its definition, as shown in Eq. 2 7 by substituting experimental U mf A dditionally, according to experimental Re mf da ta, all Re mf are smaller than 10. Hence, it can be impl ied that they lie in the laminar regime and that the Carman Kozeny equation is the best one to apply T hrough rewrit ing the Carman Kozeny e quation by substituting the Archimedes number and chang ing the sequence the theoretical method used to calculate Re m f can now be expressed as follow s (Eq. 4 1): (4 1) As shown in table 4 3, the theoretical Re mf are larger than th ose taken from the experiment, ranging from 1.1 to 3.6 times larger In order to explain the difference, some parameters of particles and t he experimental environment were checked. A dmittedly, the temperature and humidity of the environment affect the air properties and the sphericity of particles which contributes to the theoretical Re mf However, the difference

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47 caused by air density, visco sity, sphericity, and wall effect is relatively small compa red to the existing difference. H alf of the tested particles have size range s bigger than 100 m as measured by sieving. However, the equivalent volume diameter measured by the BECKMAN COULTER Rap idVUE Particle Shape and Size Analyzer is beyond the size range of the particles. C alculating the Re mf for minimum diameter and maximum diameter both experimentally and using Eq. 4 1 the Re mf were more consisten t at the minimum diameter values For cylin ders and cubes the D min was extracted from the average length of each edge, which can be also referred to as the average sieve diameter. Because Re mf were more consistent at smaller diameters the smaller particles exert ed a larger influence on minimum fl uidization than the larger particles T he smaller particles reached a dynamic steady state first T herefore, the smaller particles were drawn to move upward more readily than the larger particles due to their lower gravitational force, but the smaller part icles were resisted by the larger particles above them. Consequently those smaller particles helped to form a looser packing pattern and increased the voidage at minimum fluidization, which led to a smaller minimum fluidization than expected based on the Re mf calculated using the average diameter Fluidization Behavior of Flakes An interesting phenomenon appear ed in the fluidization and defluidization process: when the air flow rate was increased or decreased to slightly below minimum fluidization velocity small channels appeared against the wall or inside the packed bed where voidage is relatively high. Air tend ed to pass through the packed bed th r ough void s with lower resistance. S pheres or particles with a sphericity of close to 1 ha d higher mobility i n the packed or fluidized bed as compared to particles with low

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48 sphericity. Once a channel appear ed particles with higher mobility c ould react and move quickly to clear channels away. F or spheres, those processes happened almost simultaneously without any noticeable channels. On the contrary for flakes with very low sphericity, due to poor mobility, the channels w ould remain in place or even continue expanding O f course, the mobility of particles is not only related to particle shape but also to the roug hness of the particle surface. As illustrated in Figure 4 8, during the fluidiz ation of flakes in a fluidized bed, channeling was observed when the air flow rate was slightly below the minimum fluidization velocity. However, this phenomenon bec a me more obv ious as the sphericity of flakes decrease d A s shown in Figure 4 9 the pictures w ere taken before minimum fluidization whe n channeling appeared for plastic square flakes and hexagonal flakes It is evident that the plastic hexagonal flakes 1120*100 with a sphericity 0.46, which is lower than the sphericity of the other two flakes, have more apparent channels. P lastic diamond and rectangular flakes with low sphericit ies (0.24 and 0.36 respectively ) c ould not be fluidized because deep channel s and even cracks appeared as the air flow rate increased a s shown in Figure 4 1 0 Effect of Channeling on Minimum Fluidization Velocity When Ar versus Re mf is plotted with experimental and literature data, as shown in Figure 4 1 1 flakes can be easily differen tiated from other particles because they have a much larger Re mf when Ar is constant Because Re mf is directly related to U mf channeling account s for the large U mf New Definition to Describe D p for Flakes I f the particle diameter D p i s defined as the equ ivalent volume diameter, then the flakes will fall in the Group B region. H owever, channel s and cracks belong to the

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49 fluidization behavior of Geldart s Group C particles B u t if D p is redefined as the ratio of the volume over the surface area of flakes, th e flakes drop to the Group A and C region s A s shown in Figure 4 1 2 the boundary area of Group A and C may move to a larger D p region. T he redefinition of D p as the ratio of the volume over the surface area of flakes keep s the units consistent and also di fferentiate s flakes from long cylinders with the same sphericity. Even though long cylinders w ere not tested in this research, it is believed that they behave differently in a fluidized bed due to their large differences in shape. However, this new method of defin ing D p may not work for large flakes because D p will be too high, and therefore they will not fall into the newly defined Group C category. However, experiments with these flakes have not been performed, so it is not known if they will behave as Gr oup A or Group C spherical particles

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50 Table 4 1. U mf and mf data for particles with close particle net volume Material Weight (g) Total Particle Volume (cm 3 ) U mf STD (m/s) 0 ( ) mf STD ( ) Glass Spheres 212 300 m 192.8 78.69 0.0413 0.00 02 0.44 0 0.446 0.00 5 Glass Spheres 400 600 m 237.15 95.24 0.15 6 0.001 0.414 0.41 7 0.00 3 Polystyrene Spheres 200 400 m 100.2 95.43 0.0238 0.00 07 0.039 0.444 0.00 5 Polystyrene Spheres 4 25 600 m 98.04 93.37 0.0888 0.0006 0.42 6 0.43 2 0.0005 Poly carbonate Cylinders 500*500 m 114.7 95.58 0.0841 0.003 0.448 0.452 0.003 Polyamid Cylinders 380*380 m 98.5 87.17 0.0943 0.0008 0.499 0.503 0.0009 Polyamid Cylinders 500*500 m 101.83 90.1 2 0.089 1 0.0005 0.44 1 0.445 0.002 Polyamid Cubes 500 *500 *500 m 97.6 86.37 0.13 2 0.002 0.46 4 0.47 4 0.0007 Ovaline 212 300 m 261.4 76.88 0.0700 0.001 0.551 0.556 0.003 Sand 212 300 m 242.2 91.74 0.0444 0.001 0.531 0.536 0.002 Aluminum Oxide 212 300 m 260.4 66.77 0.0943 0.001 0.531 0.535 0.0009 Crushed Galss 212 300 m 200.9 80.36 0.0536 0.0005 0.538 0.542 0.004 Crushed Galss 400 600 m 183 82.81 0.224 0.009 0.544 0.550 0.001 Plastic Square Flakes 780*190 m 99.27 82.73 0.2 0.009 0.550 0.561 0.002 Plastic Hexagonal Flakes 1120*180 m 97.11 74.7 0 0.173 0.001 0.559 0.568 0.0005 Plastic Hexagonal Flakes 1120*100 m 68.93 53.02 0.242 0.002 0.719 0.727 0.005

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51 Table 4 2 U mf and mf data for particles with different particle net volume Material Weight (g) Total Partic le Volume (cm 3 ) U mf STD (m/s) 0 ( ) mf STD ( ) Glass Spheres 400 600 m 148.85 59.7 8 0.161 0.000 6 0.438 0.446 0 237.15 95.24 0.15 6 0.001 0.414 0.41 7 0.00 3 349.6 140.4 0.153 0.000 6 0.400 0.401 0.002 Polystyrene Spheres 4 25 600 m 50.32 47.92 0.0901 0.000 3 0.46 6 0.46 7 0.001 98.04 93.37 0.0888 0.0006 0.42 6 0.43 2 0.0005 142.87 136. 1 0.0886 0.0002 0.41 5 0.418 0.0009 Polyamid Cylinders 500 *500 m 51.88 45.91 0.0925 0.0008 0.479 0.483 0.0005 101.83 90.1 2 0.089 1 0.0005 0.44 1 0.445 0.002 202.98 179.6 0.088 1 0.0006 0.412 0.41 9 0.003 Polyamid Cubes 500 *500*500 m 54.1 47.8 8 0.142 0.00 5 0.49 2 0.508 0.00 5 97.6 86.37 0.13 2 0.002 0.46 4 0.47 4 0.0007 194.6 172.2 0.11 9 0.002 0.43 4 0.4 40 0.002 281.2 248. 9 0.118 0.00 3 0.42 4 0.43 1 0.00 3 401.45 355. 3 0.118 0.001 0.41 8 0.425 0.00 2 Hexagonal Flakes 1120 *180 m 47.91 36.85 0.171 0.0009 0.589 0.59 6 0 97.11 74.7 0 0.173 0.001 0.559 0.568 0.0005 189.84 146.0 0.17 3 0.0008 0.539 0.5 50 0.00 2

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52 Table 4 3 Comparison of Experimental Re mf and Re mf from Carman Kozeny equation Material D v ( m ) Experimental Carman Kozeny Equation Re mf (D v ) Re mf (D min ) Re mf (D max ) Re mf (D v ) Re mf (D min ) Re mf (D max ) Glass Spheres 212 300 m 250 0.64 0.54 0.77 1.12 0.68 1.93 Glass Spheres 400 600 m 533 5.18 3.89 5.83 8.52 3.60 12.15 Polystyrene Spheres 200 400 m 242 0.36 0.30 0.59 0.43 0.24 1.93 Polystyrene Spheres 4 25 600 m 480 2.66 2.35 3.32 3.00 2.08 5.85 Polycarbonate Cylinders 500*500 m 624 3.27 2.83 6.79 4.40 Polyamid Cylinders 380*380 m 451 2.65 2.35 3.69 2.58 Polyamid Cylinders 500*500 m 670 3.72 3.11 7.50 4.40 Polyamid Cubes 500*500*500 m 723 5.95 5.25 10.18 5.75 Ovaline 212 300 m 339 1.48 0.92 1.31 5.39 1.32 3.73 Sand 212 300 m 281 0.78 0.59 0.83 1.98 0.85 2.41 Aluminum Oxide 212 300 m 373 2.19 1.25 1.76 6.63 1.22 3.45 Crushed Galss 212 300 m 347 1.16 0.71 1.00 3.39 0.77 2.19 Crushed Galss 400 600 m 630 8.79 5.58 8.37 18.97 4.86 16.39 Plasti c Square Flakes 780*190 m 604 7.53 7.76 Hexagonal Flakes 1120*180 m 654 7.05 10.14 Hexagonal Flakes 1120*100 m 538 8.11 11.07

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53 Figure 4 1 Literature data and experimental data of sphericity versus voidage

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54 A B C D Figure 4 2. Spheres packing A) densest packing in packed bed B) Loosest packing in packed bed C) densest packing against the wall and D) loosest packing against the wall (Source: http://www.earth360.com/math_spheres.html Last accessed March 20 1 3).

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55 A B C D Figure 4 3 Force analysis of single particle with different density in fluidized bed A) force analysis of single particle in fluid ized bed B) particles with smaller density formed a looser packing C) force analysis of single particle in fluidized bed and D) particles with larger density formed a denser packing.

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56 A B Figure 4 4 Force analysis of single pa rticle with different bed height in fluidized bed A) force analysis of single particle in fluidized bed B) particles with larger bed height formed a denser packing. Figure 4 5 Fluidization and Defluidization curve and minimum fluidizaiton veloicit y of glass spheres 400 600 m at different particle total volume ( initial bed height)

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57 Figure 4 6 Influence of Bed Height on Voidage Figure 4 7 Influence of Bed Height on minimum fluidization velocity

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58 Figure 4 8 Fluidization and Defl uidization curve of Hexagonal Flakes 1120*180

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59 A B C Figure 4 9 Fluidization behavior of flakes A) channeling of plastic square flakes 780*190 B) channeling of plastic hexagonal flakes 1120*180 and C) channeling of plastic hexagonal flakes 1120*100

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60 A B Figure 4 1 0 Channeling and cracks of flakes A) channeling of plastic diamond flakes 1500*50 and B) channeling and cracks of plastic rectangular flakes 1550*300*40 m

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61 Figur e 4 1 1 Influence of channeling on minimum fluidization velocity Figure 4 1 2 Redefine D p for flakes and boundary for Geldart s Group A and C

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62 CHAPTER 5 CONCLUSION AND FUTURE WORK Conclusion B ased on the fluidized bed experiment performed for parti cles with different shape s densit ies and dimension s fluidization behavior was investigated and classified. I n the process of seeking to explain voidage range, particle density and initial bed height w ere taken into consideration. T he main finding s of th is work can be summarized as follows: When H initial /D in < 5, as the total particle volume increases, the voidage decreases, causing a decrease in U mf Flakes with a volume/surface area ratio of properties F uture Work I t is believed that the fluidization behavior of flakes and e long ated particles is quite different from that of spheres when the sphericity is l ess than a certain value H owever, in this study, we have only tested flakes with a sph e ricity of 0.24 to 0.63 and a thickness of 40 m to 180 m. Therefore, we are not sure whether the channeling behavior of flakes is due to shape, thickness or the roughness of the surface A better knowledge of this interesting behavior may give us a deeper understanding of the flu idized bed mechanism. F uture work on the fluidization behavior of flakes c ould focus on the following points: To study flakes of different densities and sizes in order to better determine the D p of flakes and the boundary n fluidized bed s To explore the effect s o f the surface roughness of flakes on the cohesive fluidization behavior

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63 To investigate the fluidization behavior of elongated cylinders with low sphericity and to examine the difference s between flakes and cylinders

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64 APPENDIX FLUIDIZATION AND DEFLUIDIZATION CURVES OF FLAKES Figure A 1 Fluidization and defluidization curve s for plastic square flakes 780*190

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65 Figure A 2 Fluidization and defluidization curve s for plastic hexagonal flakes 1120*180 at diff erent initial bed height.

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66 Figure A 3 Fluidization and defluidization curve s for plastic hexagonal flakes 1120*100

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67 Figure A 4 Pressure drop versus air flow rate for plastic diamond flakes 1500*50

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68 Figure A 5 Pressure drop versus a ir flow rate for plastic rectangular flakes 1550*300*40 m

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69 LIST OF REFERENCES [1] H. Xie, D. Geldart, Fluidization of FCC powders in the bubb le free regime: effect of types of gases and temperature, Powder Technol 82 (1995) 269 277. [2] W. Yang, Modification and re interpretation of Geldart's classification of powders, Powder Technol 171 (2007) 69 74. [3] R. Di Felice, L.G. Gibilaro, Wall effec ts for the pressure drop in fixed beds, Chemical Engineering Science 59 (2004) 3037 3040. [4] B. Eisfeld, K. Schnitzlein, The influence of confining walls on the pressure drop in packed beds, Chemical Engineering Science 56 (2001) 4321 4329. [5] R.P. Chhabra, Estimation of the minimum fluidization velocity for beds of spherical particles fluidized by power law liquids, Powder Technol 76 (1993) 225 228. [6] C. Lin, M. Wey, S. You, The effect of particle size distribution on minimum fluidization vel ocity at high temperature, Powder Technol 126 (2002) 297 301. [7] Martin Rhodes, Introduction to particle technology, 2nd ed., John Wiley & Sons, Ltd, Chichester, England, 2008. [8] T. Li, S. Li, J. Zhao, P. Lu, L. Meng, Sphericities of non spherical objec ts, Particuology 10 (2012) 97 104. [9] C.Y. Wen, Y.H. Yu, A generalized method for predicting the minimum fluidization velocity, AIChE J. 12 (1966) 610 612. [10] M. Hartman, O. Trnka, K. Svoboda, Fluidization characteristics of dolomite and calcined dolomi te particles, Chemical Engineering Science 55 (2000) 6269 6274. [11] H.J. Subramani, M.B. Mothivel Balaiyya, L.R. Miranda, Minimum fluidization B powders, Exp. Therm. Fluid Sci. 32 (2007) 166 173. [12] R. Coltters, A.L. Rivas, Minimum fluidation velocity correlations in particulate systems, Powder Technol 147 (2004) 34 48. [13] F. Benyahia, K.E. O'Neill, Enhanced Voidage Correlations for Packed Beds of Various Particle Shapes and Sizes, Particulate Scien ce & Technology 23 (2005) 169 177. [14] A. Delebarre, Revisiting the Wen and Yu Equations for Minimum Fluidization Velocity Prediction, Chem. Eng. Res. Design 82 (2004) 587 590.

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70 [15] P. Bourgeois, P. Grenier, The ratio of terminal velocity to minimum fluid ising velocity for spherical particles, The Canadian Journal of Chemical Engineering 46 (1968) 325 328. [16] Anon, V elocity voidage relations for sedimentation and fluidization Chemical engineering science (1979) 1419 1422. [17] D.C. Chitester, R.M. Korno sky, L. Fan, J.P. Danko, Characteristics of fluidization at high pressure, Chemical Engineering Science 39 (1984) 253 261. [18] J. Reina, E. Velo, L. Puigjaner, Predicting the minimum fluidization velocity of polydisperse mixtures of scrap wood particles, Powder Technol 111 (2000) 245 251. [19] S.K. Gupta, V.K. Agarwal, S.N. Singh, V. Seshadri, D. Mills, J. Singh, C. Prakash, Prediction of minimum fluidization velocity for fine tailings materials, Powder Technol 196 (2009) 263 271. [20] Z.L. Arsenijevic, Z. B. Grbavcic, R.V. Garic Grulovic, F.K. Zdanski, Determination of non spherical particle terminal velocity using particulate expansion data, Powder Technol 103 (1999) 265 273. [21] A.W. Nienow, P.N. Rowe, L.Y. Cheung, A quantitative analysis of the mixing of two segregating powders of different density in a gas fluidised bed, Powder Technol 20 (1978) 89 97. [22] N.S. Grewal, S.C. Saxena, Comparison of commonly used correlations for minimum fluidization velocity of small solid particles, Powder Technol 26 ( 1980) 229 234. [23] D.S. Povrenovi, D.E. Had?ismajlovi, ?.B. Grbav?i?, D.V. Vukovi?, H. Littman, Minimum fluid flowrate, pressure drop and stability of a conical spouted bed, The Canadian Journal of Chemical Engineering 70 (1992) 216 222. [24] R. Solimen e, A. Marzocchella, P. Salatino, Hydrodynamic interaction between a coarse gas emitting particle and a gas fluidized bed of finer solids, Powder Technol 133 (2003) 79 90. [25] B. Liu, X. Zhang, L. Wang, H. Hong, Fluidization of non spherical particles: Sph ericity, Zingg factor and other fluidization parameters, Particuology 6 (2008) 125 129. [26] J. Reina, E. Velo, L. Puigjaner, Predicting the minimum fluidization velocity of polydisperse mixtures of scrap wood particles, Powder Technol 111 (2000) 245 251. [27] C.C. Xu, J. Zhu, Prediction of the Minimum Fluidization Velocity for Fine Particles of various Degrees of Cohesiveness, Chem. Eng. Commun. 196 (2009) 499 517.

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71 [28] M. Leva, Fluidization, McGraw Hill, New York, 1959. [29] G.G.b.1. Brown, Unit operation s, Wiley, New York, 1950.

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72 BIOGRAPHICAL SKETCH Lingzhi Liao was born and rais ed in Hunan, in the People s Republic of China. She attended Centre South University where she received a B achelor s in Chemical Engineering and Technology. After graduating, she continued her Masters studies at the University of Florida At the University of Florida, Lingzhi has held the s ocial c hair position in the Graduate Association of Chemical Engineers (GRACE), an d won the Graduate Student Council s award of Outstanding Organization of the year.