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CFD MODELLING OF THE HYDRODYNAMICS OF SCRAP TYRE
IN A FLUIDIZED BED REACTOR
Thesis
By
JOHN JAIRO ORTIZ MARTINEZ
Submitted to the Office of Graduate Studies of
Universidad de Los Andes
In partial fulfillment of the requirements for the degree of
M.SC. CHEMICAL ENGINEERING
December 2015
Major Subject: Chemical Engineering
CFD modelling of the hydrodynamics of scrap tyre in a fluidized bed reactor
Copyright 2015, John Jairo Ortiz Martinez
CFD MODELLING OF THE HYDRODYNAMICS OF SCRAP TYRE
IN A FLUIDIZED BED REACTOR
Thesis
By
JOHN JAIRO ORTIZ MARTINEZ
Submitted to the Office of Graduate Studies of
Universidad de Los Andes
In partial fulfillment of the requirements for the degree of
M.SC. CHEMICAL ENGINEERING
Approved by:
Chair of committee, Rocio Sierra Ramirez, Ph. D.
Committee Members, Watson Lawrence Vargas, Ph. D.
Gerardo Gordillo Ariza, Ph. D
Omar López Mejía, Ph. D.
Head of Department, Oscar Alvarez Solano, Ph. D.
December 2015
Major Subject: Chemical Engineering
i
ABSTRACT
CFD modelling of the hydrodynamics of scrap tyres in a fluidized bed reactor (December 2015)
John Jairo Ortiz Martínez, Universidad de los Andes, Colombia
Advisors: Rocío Sierra Ramírez, Ph. D. Omar López Mejía, Ph. D.
Fluidization is one of the most promising technologies to transform waste materials (biomass,
plastics and end-of-life tyres) into useful products via thermochemical processes. This
technology has been investigated computationally using CFD as a tool for the design of the
reactor. Most literature regarding CFD techniques focus on the fluidization of biomass particles.
However, there are very few computational studies regarding the fluidization of scrap tyre
particles. The composition and density of these particles affects significantly the dynamics inside
a fluidized bed reactor. In this work, the dynamics of tyre particles in a fluidized bed were
investigated both numerically and experimentally. The applied methodology consisted in two
different approaches: a 2D approach, where bubble characteristics where analyzed and a 3D
approach, where pressure drop was compared. An Eulerian-Eulerian approach with two different
drag models was used for the computational model. The results show that the Eulerian-Eulerian
approximation does not predict well the behavior of tyre particles in a fluidized bed reactor.
Bubble diameter and rise velocity are highly overpredicted while the bed expansion is
underpredicted. On the other hand the pressure drop from the computational model seems to fit
well the experimental findings above the minimum fluidization velocity. Nonetheless the
pressure drop below the minimum fluidization velocity is not well predicted. The discrepancy
may be attributed to the fact that tyre particles are classified as Geldart A particles and hence, the
ii
dynamics are more complex and cannot be well predicted using a standard Eulerian-Eulerian
approach.
iii
RESUMEN
Modelamiento en CFD de la dinámica de la fluidización de partículas de llanta (Diciembre 2015)
John Jairo Ortiz Martínez, Universidad de los Andes, Colombia
Advisors: Rocío Sierra Ramírez, Ph. D. Omar López Mejía, Ph. D.
La fluidización es uno de las tecnologías más prometedoras para transformar material de desecho
(biomasa, plástico y llantas) en compuestos útiles por medio de procesos termoquímicos. La
dinámica computacional se ha utilizado como herramienta para la investigación de este proceso,
en especial para el diseño optimo del reactor. Gran parte de la literatura relacionada con
dinámica computacional está enfocada en la fluidización de partículas de biomasa. En
consecuencia, los estudios concernientes a la fluidización de llanta son muy limitados. Sin
embargo se ha encontrado que la composición y densidad de las partículas de llanta afectan
significativamente el comportamiento dentro del reactor de lecho fluidizado. En este trabajo se
investigó la dinámica de la fluidización de partículas de llanta tanto experimental como
numéricamente. La metodología aplicada consistió en dos diferentes acercamientos: un
acercamiento en dos dimensionas para analizar las características de las burbujas y un
acercamiento en tres dimensiones donde se compararon los perfiles de caída de presión. Para el
modelo computacional se utilizó la aproximación Euleriana-Euleriana con dos modelos de
arrastre distintos. Los resultados muestran que la aproximación Euleriana-Euleriana no predice
correctamente el comportamiento de las partículas de llanta en un lecho fluidizado. El diámetro y
velocidad de ascenso son sobre predichos por el modelo computacional mientras la expansión de
la cama presenta valores inferiores a los observados experimentalmente. Por otro lado la caída de
presión es similar para velocidades superiores a la mínima velocidad de fluidización. Sin
iv
embargo para velocidades inferiores, el modelo computacional es incapaz de predecir la caída de
presión. La discrepancia entre los resultados se debe posiblemente al hecho de que las partículas
de llanta se encuentran clasificadas como partículas Geldart A. La dinámica que presentan estas
partículas es más compleja y no puede ser predicha correctamente bajo la aproximación
Euleriana-Euleriana.
v
ACKNOWLEDGEMENTS
I would like to thank my family and friends for the love, belief, and support they have
provided me throughout my life, especially to my mother, Patricia Martinez. She gave me much
love and support, and thanks to my brother Fernando for always believing in me. I would also
want to thank many of my friends who guide and encourage me in this project.
I would to express my deepest gratitude to Dr. Rocío Sierra for her guidance and
unconditional support throughout this work. Thank you for all the appreciation and patience
during my graduate study. I would like also to thank to all my fellow graduate students for all
their support and help.
vi
NOMENCLATURE
Abbreviations
BSD Bubble size distribution
CCD Charged Coupled Device
CFD Computational Fluid Dynamics
CFB Circulating Fluidizing Bed
DCS Differential Scanning Calorimetry
DIA Digital Image Analysis
DTG Differential Thermo Gravimetry
ECT Electrical Capacitance Tomography
FFT Fast Fourier Transform
GDT Gamma Computed Tomography
KTGF Kinetic Theory of Granular Flow
MFIX Multiphase Flow with Interphase eXchanges
PC-SIMPLE Phase-Coupled Semi-Implicit Method for Pressure Linked Equations
PET Positron Emission Tomography
PSD Particle Size Distribution
QUICK Quadratic Upwind Interpolation for Convective Kinematics
SIMPLE Semi-Implicit Method for Pressure Linked Equations
TFM Two Fluid Model
TCSM Three Component Simulation Model
TGA Thermo Gravimetry Analysis
UDF User Defined Function
XCT X-ray Computed Tomography
Roman Symbols
vii
A Transversal Area (m2)
Ar Archimedes Number (-)
𝐴𝑏 Bubble Area (pixel2)
c Copula joint probability density function (-)
𝐶𝜑 Copula bivariate Archimedean function (-)
𝐶𝑑,𝑜𝑟 Orifice Drag Coefficient (-)
𝐶𝑑 Drag Coefficient (-)
𝑐𝑖 Contribution of reaction i (-)
𝐷𝑏 Bubble Equivalent Diameter (pixel)
𝑑𝑜𝑟 Orifice diameter (m)
𝐷𝑝 Particle Diameter (𝜇𝑚)
𝑑𝑡 Tube diameter (m)
E Activation Energy (J/mol)
𝑒𝑠𝑠 Restitution coefficient (-)
F Cumulative Probability function (-)
g standard gravity (m/s2)
𝑔0,𝑠𝑠 Radial distribution coefficient (-)
H Bed Height (m)
𝐻0 Initial Bed Height (m)
I Stress Tensor Identity Matrix (-)
𝐼2𝐷 Second invariant of the deviatoric stress tensor (-)
𝑘0𝑖 Pre-exponential factor (-)
𝐾𝑔𝑠 Gas-solid Interphase Coefficient (-)
𝑁𝑃 Number of points (inside bubble) (-)
𝑁𝑜𝑟 Number of orifices per area (#/m2)
𝑝 Pressure (Pa)
viii
𝑝𝑠 Solid Pressure (Pa)
R Universal Gas Constant (J/mol-K)
𝑅𝑒𝑠 Reynolds Number of solid phase (-)
Remf Particle Reynolds Number at minimum fluidization (-)
T Temperature (°C)
t time (s)
Th Threshold Value (-)
𝑢𝑖 Uniformed distributed marginal variable (-)
𝑈𝐶 Terminal Velocity (m/s)
𝑈𝑔 Superficial Gas Velocity (m/s)
𝑈𝑚𝑏 Minimum Bubbling Velocity (m/s)
𝑈𝑚𝑓 Minimum Fluidization Velocity (m/s)
𝑢𝑜𝑟 Orifice velocity (m/s)
𝑈𝑇𝑟 Transport Velocity (m/s)
𝑣𝑖 Velocity field of phase i (m/s)
�⃗�𝑠,𝑤 Particle slip velocity (m/s)
𝑉𝑡 Volatile percentage in time t (-)
𝑉∞ Ultimate attainable volatile yield (-)
W Bed Weight (kg)
X Total mass loss (-)
𝑋𝑖 Mass loss of component i (-)
𝑥𝑐 X-coordinate of Centroid (-)
𝑦𝑐 Y-coordinate of Centroid (-)
Greek Symbols
𝛼 Under relaxation factor (-)
𝛽 Heating rate (°C/min)
ix
𝜌𝑠 Solid Density (kg/m3)
𝜌𝑔 Gas Density (kg/m3)
∆𝑝 Pressure Drop (Pa)
휀𝑠 Solid Fraction (-)
휀𝑔 Gas (void) Fraction (-)
휀𝑚𝑓 Void Fraction at minimum fluidization (-)
𝜇𝑖 Shear Viscosity of phase i (kg/m-s)
𝛷𝑠 Sphericity Factor (-)
𝜆𝑖 Bulk Viscosity (kg/m-s)
𝜃 Parameter for Archimedean copula function (-)
𝛩𝑠 Granular Temperature (m2/s2)
𝜙𝑔𝑠 Transfer rate of kinetic energy (kg/s3-m)
𝑘𝛩𝑠 Diffusion coefficient of granular energy (kg/m-s)
𝛾𝛩𝑠 Collision dissipation of energy (kg/s3-m)
휀𝑠,𝑚𝑎𝑥 Maximum solid fraction (-)
𝜏 Kendall-tau correlation parameter (-)
�̅�𝑖 Tensor of viscous stresses (Pa)
𝜑 Specularity coefficient (-)
x
TABLE OF CONTENTS
ABSTRACT ...................................................................................................................................................... i
RESUMEN ..................................................................................................................................................... iii
ACKNOWLEDGEMENTS ........................................................................................................................... v
NOMENCLATURE ....................................................................................................................................... vi
TABLE OF CONTENTS ............................................................................................................................... x
LIST OF FIGURES ...................................................................................................................................... xii
LIST OF TABLES ...................................................................................................................................... xiii
1. Introduction ......................................................................................................................................... 1
1.1. Problem Statement ............................................................................................................................. 1
1.2. Objectives ............................................................................................................................................... 3
2. State of the art ..................................................................................................................................... 4
2.1. Fluidization ................................................................................................................................................. 4
2.1.1. Fluidization beds .............................................................................................................................. 4
2.1.2. Fluidization regimes ....................................................................................................................... 5
2.1.3. Material classification ..................................................................................................................... 7
2.1.4. Minimum fluidization velocity .................................................................................................... 8
2.1.5. Gas holdup and velocity measurements............................................................................... 10
2.2. Waste tyre pyrolysis ............................................................................................................................ 13
2.2.1. Waste tyre reaction scheme ...................................................................................................... 14
2.2.2. Types of Pyrolysis ......................................................................................................................... 18
2.2.3. Pyrolysis reactors.......................................................................................................................... 20
2.2.4. Key parameters of the tyre pyrolysis process ................................................................... 21
2.3. Mathematical modelling of the hydrodynamics of gas/solid fluidization ...................... 25
2.3.1. Eulerian-Eulerian approach using KTGF ............................................................................. 26
2.3.4. Kinetic theory of granular flow ................................................................................................ 29
3. Methodology ..................................................................................................................................... 32
3.1. Experimental setup .............................................................................................................................. 32
3.1.1. Pseudo 2D setup ............................................................................................................................ 33
3.1.2. Electrostatic charge reduction ................................................................................................. 34
xi
3.1.3. 3D Setup ............................................................................................................................................ 34
3.1.4. Pressure drop versus superficial velocity curve ............................................................... 36
3.1.5. Direct visualization ....................................................................................................................... 37
3.1.6. Copula bivariate ............................................................................................................................. 38
3.2. Computational study ............................................................................................................................ 41
3.2.1. Two/three dimensional case .................................................................................................... 41
3.2.2. PC-SIMPLE algorithm .................................................................................................................. 42
3.2.4. Initial and boundary conditions .............................................................................................. 43
3.2.5. User defined function implementation ................................................................................. 44
4. Results and discussion .................................................................................................................. 45
4.1. Parametric study .............................................................................................................................. 45
4.2. Bubble characteristics .................................................................................................................... 48
4.3. Pressure drop versus superficial velocity .............................................................................. 54
4.4. Frequency analysis .......................................................................................................................... 57
5. Conclusions and recommendations ......................................................................................... 60
Bibliography .............................................................................................................................................. 62
APPENDIX A: MATLAB CODE FOR FINDING BUBBLE PROPERTIES ................................... 68
APPENDIX B: UDF IMPLEMENTATION IN ANSYS....................................................................... 70
xii
LIST OF FIGURES
Figure 1. Schematic of a fluidized bed reactor [16]. ................................................................................................... 5
Figure 2. Different fluidization regimes as a function of gas superficial velocity [16]. ............................................. 7
Figure 3. Geldart’s classification of particles [12]. ..................................................................................................... 8
Figure 4. Pressure drop vs superficial gas velocity for uniform sized sand [11]........................................................ 9
Figure 5. Greyscale image (left), grey intensity histogram (middle) and threshold image (right) [22]................. 11
Figure 6. Typical product yield from pyrolysis [44]. ................................................................................................. 19
Figure 7. Heating rate effect on pyrolysis [2] ........................................................................................................... 24
Figure 8. Multi-level approach for modelling gas-solid fluidization [60]. ............................................................... 25
Figure 9. Transport mechanisms for solid particles: Frictional, collisional and kinetic [61]. ................................ 29
Figure 10. Pseudo 2D model. ..................................................................................................................................... 34
Figure 11. Three dimensional model. ....................................................................................................................... 35
Figure 12. Snapshots of the two dimensional fluidized bed. .................................................................................... 37
Figure 13. Digital image analysis, from left to right: 1. Original Image, 2. Filtered image, 3. Connectivity analysis,
4. Final image with each bubble identified. ............................................................................................................... 38
Figure 14. Microscopic image of tyre particles. ....................................................................................................... 44
Figure 15. Time-averaged solid volume fraction profiles, Gidaspow (left), Levenspiel (right). ............................. 46
Figure 16. Time-averaged velocity profiles at Z = 5cm, Gidaspow (left), Levenspiel (right). ................................ 47
Figure 17. Instantaneous void fraction contours for the Gidaspow (top) and Haider-Levenspiel (bottom) model.
..................................................................................................................................................................................... 48
Figure 18. Bubble size distribution ........................................................................................................................... 49
Figure 19. (left) Diameter evolution as a function of bed height (experimental). (right) random simulation of
10000 points using weighted Frank’s copula. ........................................................................................................... 50
Figure 20. Probability density distribution for different equivalent bubble diameters. (top left) 𝐷𝑏 = 0.5 𝑐𝑚,
(top right) 𝐷𝑏 = 1 𝑐𝑚, (bottom left) 𝐷𝑏 = 1 𝑐𝑚 and (bottom left) 𝐷𝑏 = 4 𝑐𝑚. .................................................... 51
Figure 21. Equivalent bubble diameter as a function of bed height. ...................................................................... 52
Figure 22. Equivalent bubble diameter as a function of bubble diameter. ............................................................. 52
Figure 23. Measured pressure drop at z = 10 cm, U = 0.3 m/s. ................................................................................ 54
Figure 24. Experimental pressure drop versus superficial velocity curves. ............................................................. 55
Figure 25. Three dimensional isosurfaces at void fraction of 0.3 and void fraction contours at four consecutive
time instants. .............................................................................................................................................................. 56
Figure 26. Comparison of experimental and simulated pressure drop for H = 10 cm. ........................................... 57
Figure 27. Normalized power spectrum density of experimental (top left) and computational results, U = 0.2
m/s (top right), U = 0.3 m/s (bottom left), U = 0.4 m/s (bottom right). ................................................................... 59
xiii
LIST OF TABLES
Table 1. Model constants from literature. ................................................................................................... 17 Table 2. Reactors and product yield of waste tyre pyrolysis ............................................................... 22 Table 3. Archimedean Copula function and Kendall-tau parameter. .............................................. 40 Table 4. Preliminary distribution plate design. ........................................................................................ 36 Table 5. Simulation parameters. ..................................................................................................................... 42 Table 6. Cases considered in the parametric study. ................................................................................ 45
1
1. Introduction
1.1. Problem Statement
About 1.5 billion new tires are produced worldwide each year and consequently just as many
would eventually become end-of-life tires. This means that more than 3.3 million metric tonnes of
waste tires are discarded annually, which represent a significant portion of the total solid waste
stream [1]. Tire management is a difficult task as tires are not biodegradable and can last several
decades without signification degradation. They are designed to withstand severe mechanical
stresses as well as harsh climatic conditions [2]. As a consequence, the disposal and recycling of
scrap tires becomes a difficult task. On the other hand, improper management may present risk to
public health and the environment. Waste pneumatic tires are ideal habitats for rodents and
mosquitos that transmit the yellow fever and dengue. This is particularly important for tropical and
subtropical regions [3]. Besides, piled tires are prone to heat retention and hence, they increase the
risk of fire incidents. Once ignited, the flames are difficult to control and put out. In addition, they
can burn for months, generating all kind of potentially harmful components (smoke, oil, organic,
leachate, etc.) that affect the quality of soil, water and air [3, 4]. For these reasons, waste tire
disposal has become a major environmental concern, especially in areas of large population and
highly industrialized countries.
Different strategies have been proposed to solve the problem concerning waste tire disposal. Scrap
tires contain high volatile compounds with moderate sulfur and low ash contents [2]. Also, its
heating value is greater than coal or biomass, which makes it an ideal material for .thermochemical
processes such as combustion, pyrolysis and gasification [5]. In the pyrolysis process, organic
material within the tire is thermally degraded to produce oil, non-condensable gas and solids. The
oily liquid is rich in hydrocarbons and can be used as a fuel substituent or chemical feedstock [1].
The solid residue is a carbonaceous solid which may be used directly as solid fuel or upgraded to
produce activated carbon and/or carbon black [6]. The gas product is rich in light hydrocarbons
and is normally employed in situ to supply the energy requirements of the process due to its high
heating value [2, 5, 7]. In addition, the process emits low amounts of contaminants to the
environment with no hazardous emissions [7]. The tyre pyrolysis has demonstrated promising
results at both laboratory and pilot-plant scale using diverse technologies.
Fluidization is one of the most promising technologies for thermochemical processes as it offers
several advantages over conventional ones. These advantages include improved mass and heat
2
transfer due to particle mixing, isothermal conditions, lower temperature requirements and the
possibility of continuous operation [8]. However the gas-solid dynamics that occur during
fluidization are still not understood. Furthermore the behavior of materials like biomass, tyre or
plastics under fluidization remains virtually unexplored. Understanding the phenomena that
occurs during fluidization is an integral component for efficient operation of thermochemical
processes.
In this study a computational approach using CFD (Computational Fluid Dynamics) is used to model
the fluidization of scrap tyre particles. A small-scale 2D and 3D fluidized bed cold models were
constructed to validate the computational results. The two dimensional model was used to compare
bubble properties while the three dimensional was used to compare the pressure drop. For the
simulations two drag coefficient models were compared: The Gidaspow model [9] and the Haider-
Levenspiel model [10]. The last model was of particular interest as it considers the effect of
sphericity of particles on the drag force. The results show that the dynamics of tyre particles in a
fluidized bed reactor cannot be well-predicted using standard Two-Fluid Models (TFM). Bubble
diameter and rise velocity are overpredicted whereas bed expansion is under predicted with these
drag models. Furthermore bubble diameter probability distribution shows that bubbles from the
experiments presented restricted growth caused probably due to Van der Waals cohesive forces.
On the other hand mean pressure drop estimated from simulations has good agreement with
experimental findings at superficial gas velocities above the minimum fluidization velocity;
nonetheless the minimum fluidization velocity curve cannot be well estimated. The discrepancy
between computational and experimental results can be attributed to the properties that tyre
particles exhibit. These particles behave like Geldart A particles which present special
considerations that must be addressed before attempting to simulate them with TFM.
3
1.2. Objectives
General objective
Study the hydrodynamics of tyre particles in a fluidized bed using computational fluid dynamics
and compare with experimental results.
Specific objectives
Design and develop a pseudo 2D and 3D cold-model of a fluidizing bed reactor.
Model two dimensional fluidized bed behaviour using CFD.
Compare the results of the 2D computational model with the 2D cold model via
direct visualisation.
Model three dimensional fluidized bed behaviour using CFD.
Compare the three dimensional computational model with the observed behaviour
on the experimental setup.
4
2. State of the art
2.1. Fluidization
2.1.1. Fluidization beds
Fluidization is a phenomenon that occurs when a fluid passes vertically through a bed of packed
solid particles. If the flowrate is high enough, the drag force of the fluid surpasses both the
gravitational and frictional forces of the particles and they will be suspended by the incoming gas
(or liquid). In this scenario the particles behave like a fluid with a characteristic density, this is
known as fluidized bed. Most of the important industrial applications of fluidization use gas/solid
systems and thus, this research will focus on these systems.
There are many designs for fluidized bed reactor on gas/solid systems, each with its own
advantages and drawbacks. However, there are general features that most reactors have: plenum,
distributor, bed region and a riser. The plenum, or windbox is where the gas enters the reactor and
its function is to generate a constant pressure distribution. The fluid then passes through a
distributor (aerator) that ensures a nearly uniform distribution of gas flow. Several distributors
designs have been proposed for fluidized beds, example of these designs are: perforated or
multiorifice plates, tuyeres and caps distributors, pipe grids and spargers [11, 12]. Above the
distributor is the bed region where the solids particles rest initially and once the gas passes through
the distributor, fluidization happens. It should be noted that directly above the distributor, usually
there is a mesh screen that prevents backflow of granular material. The riser is located above the
bed region and contains the particles that ejected from the bed. Depending on the application, the
riser would be open to the atmosphere or connected to other equipment.
The hydrodynamics of the solid particles in a fluidized bed depends greatly on the design of the
fluidized reactor. Particularly the distributor has an important effect on the hydrodynamics and
hence, numerous studies have been published on this account [13-15]. On the other hand, several
authors consider that the gas plenum is not relevant if the ratio between bed pressure drop and
grid pressure drop is high enough. Nonetheless, Litz developed correlations on the minimum
plenum height based on the gas inlet location and geometry of the fluidized bed [14].
5
Figure 1. Schematic of a fluidized bed reactor [16].
2.1.2. Fluidization regimes
Gas solid fluidization has several regimes depending on the operation conditions of the fluidized
bed. Grace et al. [17] gives an overview of the common regimes and their characteristics. There are
at least seven regimes: fixed bed, expanded bed, bubbling fluidization, slugging fluidization,
turbulent fluidization, fast fluidization and pneumatic conveying.
Fixed bed: At low gas velocities, the fluid simply flows through the particles without segregation of
the particles and therefore bed height and volume fraction remain constant. The pressure drop
increases and the movement of particles are limited to small-scale vibrations.
Expanded bed: when the velocity increases to the minimum fluidization velocity (𝑈𝑚𝑓), the
particles moves apart and the bed expands in volume, lowering the volume fraction. The pressure
drop reaches its maximum value. The drag and buoyant forces counterbalance the frictional and
gravitational forces of the particles. This regime is the transitional regime between fixed and
fluidized bed [18].
6
Bubbling fluidization: As velocity increases, bubbles start to form at the bottom of the bed region
and coalesce as they go upward through the reactor but the bed volume does not increase further.
The minimum velocity to reach this regime is called minimum bubbling velocity (𝑈𝑚𝑏). For solid
particles with low density and low particle diameter (Geldart A particles), there is an intermediate
regime between minimum bubbling and fluidization velocity known as particulate or homogeneous
fluidization [12]. Nonetheless, most gas/solid fluidization beds start to bubble as soon as it reaches
the minimum fluidization velocity and thus 𝑈𝑚𝑓 ≅ 𝑈𝑚𝑏.
Sluggish fluidization: When the bed height to bed diameter ratio is large enough, large bubbles
begin to form and spread across the column, these large bubbles are called slugs. The criteria to
identify this slugs is if the bubble grows up 50 % of the column diameter [17]. The particle diameter
determines the shape and behavior of the slugs, for fine particles the slugs are well formed and flow
upward until the bubble reaches the surface of the bed. For coarse particles the slugs are formed
but they disappear before reaching the surface.
Turbulent fluidization: When the gas velocity surpasses the terminal velocity of the particles (𝑈𝐶),
the movement of solids becomes chaotic and the upper bed surface is indistinguishable. This
regime is determined experimentally as the moment where the pressure fluctuations reach a
maximum. This maximum is a function of the initial bed height [11, 17].
Fast fluidization: At higher velocities, a transport velocity is reached (𝑈𝑡𝑟). At this point the
boundaries of the bed disappear and entrainment becomes significant. Particles are carried upward
by the incoming gas and then descend as clusters along the outer walls.
Pneumatic conveying: if the velocity is increased further, the particles are carried away with the gas
as a dilute phase. Fast fluidization and pneumatic conveying are characteristic of circulating
fluidized beds (CFB) and transport reactors [12].
This research is focused on the bubbling regime since is one of the typical operations of
conventional fluidized beds. It should be noted that different bed material, flow conditions and
reactor geometry and design affects each regime independently.
7
Figure 2. Different fluidization regimes as a function of gas superficial velocity [16].
2.1.3. Material classification
The behavior of the solid particles depends upon the solid properties: mean size diameter, bulk
density, particle size distribution (PSD), cohesiveness, etc. Geldart (1973) gives a standard
classification of uniformed particles based on the difference between solid and gas density (𝜌𝑠 −
𝜌𝑔) and the mean particle size. This classification is valid for air at ambient conditions [9].
Group A (aerated): particles with low particle density (< 1400 𝑘𝑔
𝑚3) and small mean diameter. The
principal characteristics of these particles are the expansion after reaching the minimum
fluidization velocity and the intermediate regime that exists before reaching the minimum bubbling
velocity in which the particles do not produce bubbles.
Group B (bubbling): particles with mean diameters and density within a specific range.
40 𝜇𝑚 < 𝑑𝑝 < 400 𝜇𝑚 and 1400 𝑘𝑔
𝑚3 < 𝜌𝑠 < 4000 𝑘𝑔
𝑚3. These particles form bubbles immediately
after reaching minimum fluidization velocity and the bed expansion is not large at atmospheric
pressure.
8
Figure 3. Geldart’s classification of particles [12].
Group C (cohesive): this group constitutes particles that are difficult to fluidize at normal
conditions. These materials exhibit interparticle forces stronger than the drag force exerted by the
gas and hence, they tend to lift as a plug [8]. These particulates are not usually used for
conventional fluidization unless mechanical vibrators or stirrers are used.
Group D (spoutable): particles that are very large or very dense belong to this group. Bubbling
fluidization of these particles is difficult since the bubbles rise slower than the incoming gas.
Therefore, spouting is common occurrence for these particles.
2.1.4. Minimum fluidization velocity
One of the most important parameters for designing and analyzing a fluidized bed reactor is the
minimum fluidization velocity. This parameter sets the lower limit to the gas flowrate and is a key
parameter in the CFD modelling of the process [19]. The minimum fluidization velocity is
determined experimentally by measuring the pressure drop across the bed at a high superficial gas
velocity where the bed is totally fluidized and decreasing it smoothly until there is no gas flow. The
value of minimum fluidization velocity is the gas velocity when the pressure drop equals the weight
of the bed. This comes as a result of the equilibrium of drag forces of the gas versus the
gravitational and frictional forces of the particulate material.
9
Figure 4. Pressure drop vs superficial gas velocity for uniform sized sand [11].
Hilal et al. [19] studied the effect of bed diameter, distributor and inserts on the minimum
fluidization velocity. The results show that bed diameter and geometry have an impact on 𝑈𝑚𝑓 with
decreased velocity at bigger diameters and increased velocity with higher number of holes in a
distribution plate. In addition Felipe et al. [20] used the standard pressure fluctuation to accurate
calculate the minimum fluidization for Geldart B and A particles. It was shown that both differential
and absolute pressure measurements were appropriate to estimate 𝑈𝑚𝑓 . In addition the plenum
chamber is the most adequate place to take pressure measurements since there are no problems
with probe plugging and offering similar results to probes above the distributor. Finally Escudero
[16] studied the effect of bed material and bed height on the minimum fluidization velocity in a
cylindrical reactor. He found that the H/D relation does not affect significantly the 𝑈𝑚𝑓 since the
velocity remained constant for all the range. However, the bed material affects the minimum
velocity as the density of the material increases so does 𝑈𝑚𝑓 . Therefore to fluidize high density
material, a higher velocity is required and a larger pressure drop is expected as the mass of the bed
increases.
On the other hand a mathematical model for 𝑈𝑚𝑓 is possible to obtain if one assumes uniformed
sized spherical particles and no significant frictional forces at the wall. The momentum balance can
be written as:
∆𝑃𝑓𝑟/𝐻0⏟ 𝑑𝑟𝑎𝑔
= (1 − 휀𝑚𝑓)(𝜌𝑠 − 𝜌𝑔)𝑔⏟ 𝑏𝑢𝑜𝑦𝑎𝑛𝑐𝑦
(1)
Where the frictional pressure force is calculated using Ergun correlation [9].
10
∆𝑃𝑓𝑟
𝐻0= 150
(1 − 휀𝑚𝑓)2
휀𝑚𝑓2
𝜇𝑈𝑚𝑓
(𝛷𝑠𝑑𝑝)2
⏟ 𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑡𝑒𝑟𝑚
+ 1.751 − 휀𝑚𝑓
휀𝑚𝑓3
𝜌𝑔𝑈𝑚𝑓2
𝛷𝑠𝑑𝑝⏟ 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑡𝑒𝑟𝑚
(2)
Combining both equations, the general equation for 𝑈𝑚𝑓 for isotropic spherical particles is:
1.75
휀𝑚𝑓3𝛷𝑠
(𝑑𝑝𝑈𝑚𝑓𝜌𝑔
𝜇)
2
+150(1 − 휀𝑚𝑓)
휀𝑚𝑓3𝛷𝑠
2 (𝑑𝑝𝑈𝑚𝑓𝜌𝑔
𝜇) =
𝑑𝑝3𝜌𝑔(𝜌𝑠 − 𝜌𝑔)𝑔
𝜇2
(3)
Or in terms of particle Reynolds number and Archimedes number [21].
1.75
휀𝑚𝑓3𝛷𝑠
(𝑅𝑒𝑝,𝑚𝑓)2+150(1 − 휀𝑚𝑓)
휀𝑚𝑓3𝛷𝑠
2 (𝑅𝑒𝑝,𝑚𝑓) = 𝐴𝑟 (4)
𝑅𝑒𝑓,𝑚𝑓 =
𝑑𝑝𝑈𝑚𝑓𝜌𝑔
𝜇
(5)
𝐴𝑟 =
𝑑𝑝3𝜌𝑔(𝜌𝑠 − 𝜌𝑔)𝑔
𝜇2
(6)
2.1.5. Gas holdup and velocity measurements
One of the most common methods to analyze bubble behavior in a 2D fluidized bed is direct
visualization. This approach is noninvasive, straightforward, and allows real time measurements of
bubble diameter, center of mass, velocity and mean particle motion. In this method, video
recordings with a CCD camera are used to capture the fast movement of particles. Digital image
analysis is then used to examine each image and obtain important information about the bubble
dynamics such as [22]:
(1) Bed average expansion as function of time. (2) Gas holdup as function of time. (3) Distribution of bubble equivalent diameters as function of distance from the distributor. (4) Bubble aspect ratio. (5) Number of bubbles as function of the distance from the distributor. Busciglio [23] provides a detailed description of the application of DIA (Digital Image Analysis) to
the study of fluidized beds. The method follows these steps:
1. Image crop: certain sections of the image are omitted to focus the analysis on the fluidized
bed only.
11
2. Threshold: The original greyscale image is converted into a binary one, making it suitable
for further analysis. This procedure assigns a value of pixel luminescence to the binary
image 𝑔(𝑥, 𝑦) depending on the pixel luminescence observed in the greyscale image 𝑙(𝑥, 𝑦).
𝑔(𝑥, 𝑦) = {1, 𝑖𝑓 𝑙(𝑥, 𝑦) ≥ 𝑇ℎ 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(7)
Figure 5. Greyscale image (left), grey intensity histogram (middle) and threshold image (right) [22].
The threshold value has to be carefully chosen to identify correctly the bubble phase and
separate it from the dense phase. Nonetheless, Busciglio stated that threshold values
ranging from 0.4-0.8 will not affect bubble measurements in a significant manner.
3. Index: Each individual region (bubbles) is identified employing connectivity analysis. The
Image Processing Toolbox of MatLab has all of the methods (as functions) needed for this
identification.
4. Filter: False bubbles and peripheral voids arising from the bubble dynamics and particle-
wall interactions have to be excluded from the statistical analysis.
5. Bubble properties: The area, equivalent diameter and centroid coordinates for each bubble
are computed using the following equations:
12
Area:
𝐴𝑏 =∑𝑏(𝑥𝑗,𝑦𝑗)
𝑁𝑝
𝑗=1
= ∫∫𝑏(𝑥, 𝑦)𝑑𝑥𝑑𝑦
(8)
Equivalent diameter:
𝑑𝑏 = √4𝐴𝑏𝜋
(9)
(9) Centroid coordinates:
𝑥𝑐 = ∫∫𝑥 𝑏(𝑥, 𝑦)𝑑𝑥𝑑𝑦 𝐴𝑏⁄
(10)
𝑦𝑐 = ∫∫𝑥 𝑏(𝑥, 𝑦)𝑑𝑥𝑑𝑦 𝐴𝑏⁄
(11)
𝑁𝑜𝑡𝑒: Scaling factors are used to convert pixel values into distances and areas
Busciglio et al. [22] developed a fully automated and robust program using MatLab® that performs
a frame-by-frame analysis and measures bubble properties in a 2D fluidized bed. By comparing
bubble diameter, aspect ratio and velocity with correlations found in literature, the authors
confirmed the applicability of this methodology and proposed it as a tool for validation of CFD
simulations. Shen et al. [24] applied digital image analysis in a bubbling fluidized bed with Geldart B
particles to obtain time average data from which bubble density, bubble velocity and bubble
diameter can be calculated. The authors also derived equations for the bubble rise velocity and bed
height as a function of gas velocity and particle diameter. In this work the bubble rise velocity was
calculated based on the methodology presented by Asegehegn et al. [25].
13
2.2. Waste tyre pyrolysis
This investigation is part of a bigger research regarding the application of gas/solid fluidization on
waste tyre pyrolysis. Accordingly, the following section gives a literary review of pyrolysis of scrap
tyre, the types of pyrolysis, key factors influencing the reaction and the advantages of using
fluidization for this kind of process.
Pyrolysis is the thermal degradation of organic compounds at high temperatures (> 200°C) in an
oxygen-free environment. In this process the volatile organics are decomposed to gases and liquids,
which can be used as fuel substituent or for the extraction of useful bio-chemicals [2, 26]. On the
tyre pyrolysis, there is also a solid residue that consists mainly of carbon black and the mineral
matter present initially in the tyre. This char is a suitable material for the production of activated
carbon or a smokeless fuel [27, 28]. According to Aylón [29] this thermochemical process seems to
be a promising alternative for waste treatment as it converts solid wastes into high calorific fuels,
chemicals or other valuable by-products with minor environmental impact.
In general, the pyrolysis involves the addition of heat in an inert ambient to break chemical bonds,
which allows the organic material within the tyre to decompose and vaporize. When a feedstock is
heated under those conditions, several reactions such as dehydration, dehydrogenation, cracking,
isomerisation and aromatisation take place [2]. As the process products have a wide broad
compositional range, extending from olefins to coke, the optimal operating conditions would
depend on the type of feedstock as well as the main target of the process.
Amongst the thermochemical treatments, pyrolysis shows attractive advantages overall since its
products are manageable and then valorised depending on the final objective of the plant. The
liquid fuel, one of the main products, can be handled, storage and transported with relatively ease.
Moreover, the volume of the non-condensable gases from a pyrolysis plant is less than the volume
from a combustion process and hence, there is a diminution of gas production [2]. In addition, it is
remarkable that:
This process allows the separation of impurities from fuel before its combustion. Up to 70%
of the original sulphur content remained in the solid char rather than being released as gas
[6]. While the hazardous emissions of alkali and heavy metals are reduced and even avoided
by retaining the metals within the solid residue. The temperature range of a conventional
pyrolysis reactor (250°C- 500°C) does not allows the metals to volatize, Conesa [30]
14
investigated the influence of temperature on the pyrolysis process, Metal contents of the
char were reported similar at 450°C and 700°C.
Minimal air pollution emission from pyrolysis units is expected due to the fact that most of
the gaseous product is burned within the process. The primary emission sources are
fugitive sources and equipment leaks [2]. Furthermore, the low levels of oxygen within the
process inhibit the formation of dioxins and furans. Values of 0.021 and 0.015 pg/g for
dioxins and furans respectively have been reported [1].
The solid residue contains up to 90% of carbon contents that could be used for several
purposes, one of which is as a substitute carbon black. If technological advances permit a
large-scale production of substitute carbon black, it would imply a major CO2 emission
reduction. The amount of CO2 produced per mass of carbon black ranges from 0.5 to 3.5
kg/kg tyre. Tyres and rubber products are the main end-use applications and accounts
approximately 90% of the carbon black market [2].
Nevertheless, there are some technological problems that must be solved for large-scale application
of the process. Currently, it is limited to a laboratory/pilot plant scale and mainly for research
purposes with few commercial applications [1]. One of the main problems is the poor quality of the
heterogeneous carbon-rich solid by-product [6]. It must be upgraded prior commercialization.
Another remarkable issue arises when trying to achieve an even temperature distribution through
the reactor. It has become a technological bottleneck for industrial applications and discourages
both economic and technical feasibility [2]. Furthermore, the economic viability of the process is
very sensitive as it clearly depends on the utilization of all three by-products, especially the liquid.
Tyre liquid fuel must compete with crude oil derivatives at current market conditions [7].
2.2.1. Waste tyre reaction scheme
Most studies related to the scrap tyre kinetics use techniques that relies almost exclusively on
thermal analysis, such as thermogravimetry (TGA), differential thermogravimetry (DTG) or
differential scanning calorimetry (DCS) [31]. Moreover, the Arrhenius model is commonly used
among researchers in the kinetic analysis of tyre degradation.
Different approximations have been proposed to correlate data from the thermogravimetric
analysis. However, there are two distinct approaches when applying the models to experimental
data. The most popular approach is the modelling of thermal decomposition of each main
component separately, where each component represent a peak in a TGA curve. This approach is
15
known as multistage decomposition model. The other model is the assumption of a 1-step
mechanism, where a single peak is represented with a set of kinetic parameters [32].
Several published models in literature for both approaches together with operating conditions and
calculated kinetic parameters are detailed below:
Zabaniotou et al [33] assumed a 1-step mechanism, first-order kinetic model, for modelling flash
pyrolysis of scrap tire particles using a helium as carrier gas at atmospheric pressure. The following
equation describes the proposed model.
𝑑𝑉𝑖𝑑𝑡
= 𝑘0𝑖 ∙ 𝑒−𝐸𝑖𝑅𝑇 ∙ (𝑉∞ − 𝑉𝑖) (13)
Where 𝑉𝑖 is the percentage of volatile in time t, 𝑉∞ is the ultimate attainable volatile yield, 𝑘0𝑖 is the
pre-exponential factor and 𝐸𝑖 is the activation energy. Using an integral approach, they also
proposed the following equation:
𝑉𝑖 = 𝑉
∞ ∙ [1 − exp (−𝑅𝑇2
𝐸𝛽∙ exp (−
𝐸
𝑅𝑇)] (14)
According to the authors, this model predicts fairly well the total weight loss of tyre particles for
temperatures below 550°C. However, at higher temperatures secondary reactions occur and the
first-order kinetic model does not fit adequately.
Seneca et al. [34] performed thermogravimetric analysis to scrap tyres under inert atmosphere for
a wide range of heating rate (5 to 900 K/min). From analysis of Arrhenius plots, they concluded
that pyrolysis cannot be represented as a single reaction pathway. They further observed that
radial non-uniformities of temperature, overall volatile pressure and concentrations are
inconsequent at moderate heating rates (5, 10, 20 and 100 K/min). Nonetheless at higher heating
rates, heat and mass transfer limitations may occur, which might enhance secondary reactions
between the volatiles and char.
Aylon et al. [29] modelled the overall tyre decomposition considering four independent
components: Additives (non-polymeric material added during tyre fabrication), a first polymeric
material (polybutadiene or styrene-butadiene), a second polymer (natural butadiene) and a solid
residue (carbon black with mineral matter used as reinforcing material). The general kinetic law for
each reaction is:
16
𝑑𝑋𝑖𝑑𝑡
= 𝑘0𝑖 ∙ 𝑒−𝐸𝑖𝑅𝑇 ∙ (1 − 𝑋𝑖)
𝑛 (15)
As each component reacts independent of other components, the overall conversion rate is
represented as the sum of all parallel reactions:
𝑑𝑋
𝑑𝑡=∑𝑐𝑖
𝑑𝑋𝑖𝑑𝑡
𝑁
𝑖=1
= ∑𝑐𝑖
𝑁
𝑖=1
𝑘0𝑖 ∙ 𝑒−𝐸𝑖𝑅𝑇 ∙ (1 − 𝑋𝑖)
𝑛 (16)
Where N is the number of parallel reactions occurring simultaneously and 𝑐𝑖 is the contribution of
each reaction to the total mass loss. Using non-linear regression methods, they calculated the
kinetic parameters. Finally this model was compared with experimental results in a fixed bed
reactor, which gave a fairly good correlation between the data and hence, the applicability of this
model was confirmed.
Several authors [35-38] have considered the kinetic parameters (activation energy and pre-
exponential factor) of the tyre decomposition to be dependent on the heating rate, particle size and
reactor pressure. They have employed a kinetic model known as “three (or more) component
simulation model (TCSM)”, which is similar to Aylon’s kinetic model as it considers rubber as a
composite made of elastomers, fabric, oil and other components [39]. On the other hand, other
researchers [37, 39, 40] state the importance of incorporating heat and mass transfer equations
into the kinetic model due to the fact that heat transfer effects should not be neglected, especially
under high heating rates. As a consequence, several integrated models have been reported in
literature.
Cheung et al. [37] attempt the integration between the mass loss kinetics, the exothermic reactions
and heat for a large tyre particle. Using this simulation the authors developed a multi-stage
operation strategy which saved up to 17% of energy usage despite longer completion times.
Integrated models help to understand the mechanisms that limit the tire pyrolysis rate, which is
important for the development of industrial pyrolysis units from the point of view of process
control, economics and product quality. Furthermore, these kinetics models promote the
improvement of existing pyrolysis applications as different heat and mass transfer strategies can be
studied and hence, reactor designs can be optimized. However, the heat and mass transfer that
occurs between the tyre particle and the flowing fluid (nitrogen, steam, evolved gases, or a
combination of the latter) have a huge impact in the continuous process and affect the overall rate
17
[41]. Consequently, it is important to connect the transport phenomena with existing kinetic
models.
Table 1. Model constants from literature.
Reference Condition 𝐸𝑎(𝑘𝑗/𝑚𝑜𝑙) A (1/min) Zabaniotou et al. [33] 𝛽: 70 − 90 𝐾/𝑠
P.S. : 425-500 μm 65.6 5.10
Aguado et al. [31] 98.6 7.35𝑥104
Aylón [29] 𝛽: 5 − 40 °𝐶/𝑚𝑖𝑛 P.S.: 0.4-0.6 mm
Additives: 70 Polymer 1: 212 Polymer 2: 265
Additives: 1.0𝑥104 Polymer 1: 8.2𝑥1014 Polymer 2: : 3.2𝑥1017
Leung and Wang [35] 𝛽: 10 °𝐶/𝑚𝑖𝑛 P.S. : 0.355-0.425 mm Three-Component simulation model
Component 1: 52.5 Component 2: 164.5 Component 3: 136.1
Component 1: 2.0𝑥104 Component 2: 6.3𝑥104 Component 3: 2.3𝑥104
Quek et al. [40] 𝛽: 10 °𝐶/𝑚𝑖𝑛 P.S.: 1 mm
Oil: 43 NR: 207 SBR: 152 BR: 215
Oil: 7.7𝑥102 NR: 1.7𝑥1016 SBR: 6,0𝑥108 BR: : 2.7𝑥1011
Lee et al. [42] 𝛽: 2,5,10,20 °𝐶/𝑚𝑖𝑛
Additives: 69.73 Rubber: 118.04 Cyclized rubber: 128.93
Additives: 4.6𝑥106 Rubber; 5.0𝑥108 Cyclized rubber: 1.2𝑥109
Mazloom et al.[28] Thermal pyrolysis Catalytic pyrolysis
𝑘1: 5.9𝑥103
𝑘2: 2.0𝑥103
𝑘3: 0.00 𝑘4: 2.9𝑥10
3 𝑘1: 5.6𝑥10
5 𝑘2: 6.5𝑥10
3 𝑘3: 3.5𝑥10
3 𝑘4: 1.2𝑥10
4 𝑘5: 4.6𝑥10
3
𝑘1: 2.0 𝑥10−2
𝑘2: 1.4𝑥10−2
𝑘3: 2.9𝑥10−3
𝑘4: 5.1𝑥10−3
𝑘1: 0.51 𝑘2: 1.06 𝑘3: 1.94 𝑘4: 5.13 𝑘5: 1.28
Cheung et al. [37] 𝛽: 5,10,15,20 °𝐶/𝑚𝑖𝑛 P.S.: 2.5 cm
Reaction 1: 69.73 Reaction 2: 88.02 Reaction 3a: 118.04 Reaction 3b: 103.95 Reaction 3c: 128.93
Reaction 1: 4.6𝑥106 Reaction 2: : 2.5𝑥108 Reaction 3a: 5.0𝑥108 Reaction 3b: : 5.4𝑥108 Reaction 3c: 1.2𝑥109
Olazar et al. [43] Tire to intermediate: 46.1 Tire to gas: 63.1 Tire to liquid: 40.1 Tire to aromatics: 89.3 Intermediate to aromatics: 36.3 Intermediate to tar: 14.1 Intermediate to char: 20.5
Tire to intermediate: 6.8𝑥10 Tire to gas: 3.5𝑥10−7 Tire to liquid: 1.3𝑥10 Tire to aromatics: 5.3𝑥103 Intermediate to aromatics: 5𝑥10−1 Intermediate to tar: 2.4𝑥10−3 Intermediate to char: 4.8𝑥10−1
Table 1 reports kinetic models from several authors. There are remarkable differences between the
reported values of activation energies and pre-exponential factors for the proposed models. These
differences could be attributed to several causes, such as: diverse tyre composition (different level
of vulcanization, diverse additives, other polymers, etc.), inconsistent operating conditions
18
(Temperature range, heating rate, particle size, vapour residence time, etc.) and the use of different
kinetic models to explain the peaks in the thermograms [31].
2.2.2. Types of Pyrolysis
Pyrolysis can be classified according to the operating conditions: the heating rate, the pressure and
temperature. Most authors suggest a general simple classification as slow, fast or flash pyrolysis
depending on the heating rate and vapour residence time. However, due to technological advances
and better understanding of the process, special types of pyrolysis can also be found on literature:
hydro, catalytic and vacuum pyrolysis (based on the environment) microwave or plasma pyrolysis
(based on the heating system) [2].
The slow pyrolysis is characterised by low temperatures and heating rates as well as long residence
times for both solid and vapour phases. Typical product yield on this mode are char: 35% wt, liquid:
30 % wt and gas 35% wt, with gas residence times in the order of hours to days [44]. Longer
residence times lead to secondary reactions between the volatiles and charred material, yielding
more coke, tar and thermally stable products. The main objective of the slow pyrolysis is char
production and thus, this process is also termed as carbonisation.
Contrary to slow pyrolysis, fast pyrolysis involves high heating rate with short residence time for
vapor phase. Heat and mass transfer process, phase transition phenomena and chemical kinetics
play a crucial role within the reactor. One critical consideration of the process is the temperature
control, which must be in optimal levels to minimize charcoal formation and vapor cracking. On the
other hand, the rapid quenching of volatiles favors the formation of liquid products as the
condensation inhibits the breakdown of higher molecular weight species into non-condensable gas
product [44]. As a matter of fact, fast pyrolysis have been used as a route for liquid fuel production
with several types of feedstock (usually around 50-60% wt for rubber feedstock) [2].
19
Figure 6. Typical product yield from pyrolysis [44].
The essential features of a fast pyrolysis process for producing liquids are [45] :
- High heating rate with large heat transfer rate at the particle interface, which requires small
particle sizes (< 3mm) as rubber tires have poor thermal conductivity.
- Accurate temperature control around 500°C to maximize liquid yield.
- Short vapor residence times to minimize secondary reactions.
- Fast char removal to reduce cracking of vapors.
- Rapid cooling of the volatiles to obtain the liquid fuel product.
Flash or ultra-pyrolysis implies the thermal cracking under conditions of high temperature
(between 450 and 600°C), very short reaction time (much less than 500ms), higher heating rate
(greater than 1000°C/s) and rapid product quenching. Aguado et al. [31] studied tyre flash
pyrolysis in a fast heating micro reactor (with a heating rate up to 20,000K/s) with an exceptionally
small residence time (below 100ms), which minimizes most secondary reactions.
In order to increase or upgrade the yield or some properties of liquid products, catalytic processes
have been proposed. Williams et al. [46] investigated the tyre pyrolysis using zeolite catalysts (Y-
type and ZSM-5) in a fixed bed reactor. The results showed over 50 wt% of single ring aromatics,
such as benzene, toluene and xylenes in the liquid fraction. Likewise, other researchers [6] have
found enhancement of the volatiles yield and the liquid fuel properties using expanded perlite
catalyst.
20
2.2.3. Pyrolysis reactors
Different types of reactors have been used for pyrolysis of waste tyres; examples include fixed bed,
screw kiln, rotary kiln, entrained and fluidised bed. Table 2 shows diverse pyrolysis reactors tested
for research purposes with reported oil, gas and char yields. Fluidized and entrained beds are
mostly used for fast pyrolysis whilst fixed bed reactors are associated with slow pyrolysis.
Nonetheless, it is possible to achieve fast pyrolysis with fixed bed reactors by adjusting the heating
rate and gas residence time. Due to the desire for a continuous process, the investigations are
performed in rotary kilns, moving bed screw reactors and fluidised beds. This type of reactors has
the advantage of continuous and direct feeding of the hot reactor.
The most common application for fixed bed reactors is in laboratory experiments as they are easy
to construct and operate. Diez et al. [47] used a 40 cm long, 7 cm in diameter, quartz tube reactor.
The heating rate varied from 5 to 60 °C/min, under a steady nitrogen flow of 200 ml/min. Berrueco
et al. [48] used an externally heated fixed bed reactor. The stainless reactor is 5.5 cm in diameter
and 40 cm in height, under a fixed heating rate of 15 °C/min and a nitrogen flowrate of 0.4 l/min.
large batch reactors system processing 1 tonne of shredded waster tire have reported lower liquid
yields than smaller fixed reactors [1]. There are heat transfer limitations for such a large volume of
tyres contained within the fixed bed reactor. Therefore higher residence times and non-uniform
temperature profile are expected from the reactor.
Fluidised bed pyrolysis of tyres has been extensively investigated by Kaminsky and co-workers [49-
51]. They reported similar oil yield at laboratory scale (30.2 wt% with a throughput of 1 kg/h) and
pilot plant scale (30.9 wt% with a throughput of 200 kg/h). The fluidized beds were heated
indirectly to temperature range between 500 and 780 °C via radiant heat tubes within the bed of
quartz sand. Dai et al. [52] used a circulating fluidised reactor (CFB) to evaluate the particle size
temperature and gas residence time effect on fast pyrolysis. They reported a maximum oil yield of
52 wt% at 450 °C that decreased strikingly to 30 wt% at 810 °C with an increased gas yield from 15
to 40 wt%. Furthermore, they showed a slightly decrease of oil yield with longer residence time.
From 51 wt% at 1 s residence time to 48 wt% at 5 s residence time for a reactor temperature of
500 °C. One of the main advantages of a fluidised bed over a fixed bed reactor is the isothermallity,
which allows the operation at a specific temperature and even autothermal pyrolysis. Another
advantage is the gas velocity versatility, which reduce the residence time and permits the pyrolysis
of scrap tyre mixtures with other feedstock such as plastic, coal or biomass [31].
21
Several other reactor designs have been proposed for pyrolysis of tyres. Examples of these
investigations include: moving bed reactors [53], spouted beds [43], vacuum pyrolysis and drop
tube [1]. The spouted bed is a type of fluidized bed reactor which presents the following
characteristics: isothermal operation, high heat transfer rate, low gas residence time that reduce
secondary reactions, better sand-solid interaction that typical fluidized reactors, minimum
agglomeration due to vigorous bed movement. For this kind of reactor, products yield for oil of
about 62 wt%, 35 wt% for char and 3 wt% for gas were reported [54]. They also studied the
influence of zeolite catalyst on gas and liquid composition. On the other hand, Aylon et al.
[5]compared the performance of a screw kiln reactor with a static fixed bed reactor. They reported
maximum oil yields of 48.4 wt% and 56.4 wt% for the screw kiln and fixed bed reactor respectively.
They attributed the conversion difference to faster heating rates and longer gas residence times of
the moving bed reactor. Finally, vacuum pyrolysis has become relevant in recent years because of
the advantages associated with lower residence times of volatiles and inert gas flow rate: lower,
energy requirements for the overall process, simpler apparatus for volatile condensation: increased
oil yield and better control of its composition. This last feature is particularly important for
improving the liquid product as fuel substituent and the quality of the solid residue as carbon black.
Since volatile carbonization by secondary reactions is reduced, the surface properties of the
charred material are similar to commercial carbon black.
2.2.4. Key parameters of the tyre pyrolysis process
Temperature has a significant effect on the conversion and product yield. For this reason it is
considered as the governing variable of the tyre pyrolysis. However there are other variables
involved in the process such as particle size, heating rate and superficial velocity of the inert gas.
These variables play an important role on the occurrence of secondary reactions and residence
time and hence, influence the gas, liquid and solid composition and distribution.
22
Table 2. Reactors and product yield of waste tyre pyrolysis [1]
Reactor Experimental Conditions Maximum oil yield
Temperature (°C) Oil (wt %)
Char (wt %)
Gas (wt %)
Fixed bed, batch Temperature: 400-700 °C 500 40.26 47.88 11.86
Fixed bed, batch Temperature: 500-1000 °C Heating rate: 1200 °C/min
500 58.0 37.0 5.0
Fixed bed, batch Temperature: 900 °C Heating rate: 2 °C/min Tyre mass: 1000000 g
950 20.9 40.7 23.9
Fixed bed, batch Temperature: 350-600 °C Heating rate: 5-35°C/min
400 38.8 34.0 27.2
Fixed bed, batch, internal fire tubes
Temperature: 375-575 °C Tyre mass: 750 g
475 55 36 9
Moving screw bed Temperature: 375-575 °C Mass flowrate: 3.5 -8.0 kg/h
600 48.4 39.9 11.7
Rotary kiln Temperature: 375-575 °C Throughput: 4.8 kg/h
550 38.12 49.09 2.39
Vacuum, conical spouted bed
Temperature: 425-500 °C Vacuum: 50 kPa
500 ~60 ~34 ~4
Rotary kiln Temperature: 450-650 °C Throughput: 12-15 kg/h
500 45.1 41.3 13.6
Fluidised bed Temperature: 740 °C Throughput: 1 kg/h Tyre powder
740 30.2 48.5 20.9
Fluidised bed Temperature: 750-780 °C Throughput: 30 kg/h Tyre pieces
750 31.9 38.0 28.5
Fluidised bed Temperature: 700 °C Throughput: 200 kg/h Whole tyre
700 26.8 35.8 19
Fluidised bed Temperature: 450-600 °C Throughput: 0.2 kg/h Tyre granules
450 55.0 42.5 2.5
Circulating fluidised bed
Temperature: 375-575 °C Throughput: 4.8 kg/h
450 ~52 ~28 ~15
Conical spouted bed Temperature: 400-700 °C 500 ~62 ~35 ~3
Vacuum Temperature: 485-550 °C Batch(80-180 kg) and continuous
520 45 36 6
Vacuum Temperature: 500 °C Pilot scale semi continuous
500 56.5 33.4 10.1
Vacuum Temperature: 450-600 °C Batch(100 kg)
550 47.1 36.9 16
Drop tube reactor Temperature: 450-1000 °C Throughput: 0.03 kg/h
450 37.8 35.3 26.9
23
2.2.4.a. Temperature
Gas fraction increases with temperature due to powerful thermal cracking occurring at high
temperatures. Therefore, a decrease of long chain hydrocarbons in favor of light hydrocarbons (C1-
C4) and H2 is expected [55]. Nevertheless, Gas composition and yield is very sensitive to secondary
reactions such as heterogeneous reactions involving the inorganic compounds of tyre and thermal
cracking. For this reason, the reported values of gas composition, calorific value and yield are quite
dissimilar among the literature [2].
The yield of pyrolytic liquid is almost stable at temperatures below 500°C with a subsequent
decrease at higher temperatures. This result is attributed to secondary reactions that rise the gas
fraction at expense of liquid fraction [6]. In general, most volatiles are released at temperatures
around 450°C-500°C. However lower temperatures (< 375°C) have been reported for catalytic
systems [56]. On the other hand, liquid composition is strongly dependent on temperature. High
pyrolysis temperatures promote the formation of conjugated bonds and aromatics in the tyre
liquid, therefore, enhance its properties as a fuel substituent. In contrast, lower temperatures favor
olefin and diolefinic hydrocarbons production which may have negative effects in gasoline. These
compounds tend to polymerize and form gums that could damage engine fuel systems [2].
Temperature slightly reduces the solid fraction due to the secondary reaction between carbon
black and CO2 and decomposition of inorganic material within the char. Nevertheless, char yield is
linked to many factors such as reactor size, heat transfer efficiency, heating rate and vapor
residence time. As a consequence, the effect of temperature on char yield is not analyzed
individually but depending on operation conditions within the reactor. The specific surface of the
char shows a significant increase at high temperatures and heating rates.
2.2.4.b. heating rate
For a given temperature, the heating rate (°C/min) has a great effect on the conversion of volatiles
and char. Generally speaking, high heating rates reduce the solid fraction and enhance the amount
of volatiles released from the tire particle. In TGA, a shift to higher temperatures of the weight loss
profile is observed. Therefore, the degradation rate of pyrolysis and the maximum volatilization
temperature range is affected by the heating rate [2]. However, fast heating rates could promote
secondary reactions that increase the gas fraction while reducing the liquid fraction. Moreover, long
chain components are produced in a very short time, which leave the reactor before further
cracking or decomposition [57]. This result is not favourable to both quantity and quality of
24
produced oil. This phenomenon is not observed at moderate heating rates. The heating rate is one
of the most studied parameters in the pyrolysis due to its influence on product yield, completion
time and energy requirements of the process. In addition, Senneca et al. [58] found that increasing
the heating rate lead to a more uniform radial distribution of temperature and pressure within the
particle.
Figure 7. Heating rate effect on pyrolysis [2]
2.2.4.c. Particle size
The effect of particle size has not been studied extensively due to the general presumption that
small tire particles have no significant limitations in mass and heat transfer and present a high
conversion grade. This assumption can be justified when experiments are conducted at high
heating rates [58]. Nevertheless, there is a trade-off between the required energy and pyrolysis
time. A small particle size can complete the pyrolysis process in a short time but it requires more
energy compared to a larger particle size [59]. In addition, depending on operating conditions, a
small particle size can lead to a fast devolatilization and hence, secondary reactions.
25
2.3. Mathematical modelling of the hydrodynamics of gas/solid fluidization
One of the principal difficulties to create a reliable mathematical model of fluidization is the
complexity of the dense gas-particle behaviour and lack of understanding of the phenomena that
occurs within the reactor. Particularly the nature of forces related to particle-particle interaction
(collision forces), gas-particle interaction (drag forces) and particle wall interactions (frictional
forces) [60]. In addition, bubbles characteristics (size, number, velocity, etc.) affect significantly the
heat and mass transfer processes, the mixing and segregation of particles and even the overall
conversion. Therefore the behaviour of bubbles should be considered before understanding the
hydrodynamics of a fluidized bed.
There are two approximations to model the behaviour of a gas-solid fluidized bed: the continuum
(Eulerian) model and the discrete (Lagrangian) model. On the discrete model, the motion of
particles is tracked individually and considers the effect of particle-particle collision as well as
particle gas interaction. Collisions between particles can be modelled using the hard sphere or soft
sphere approach, depending on the physical properties. Also, certain properties such as gas
pressure, gas viscosity and thermal conductivity are calculated from statistical methods [60]. The
main advantage of this model is the level of detail obtained; particularly with particle-particle
interactions. Although this approach can be applied at any length scale, it has been mainly used for
small-scale applications up to 𝑂(105) particles. Computing times and memory availability are the
two main restrictions for larger applications [61].
Figure 8. Multi-level approach for modelling gas-solid fluidization [60].
On the other hand the continuum model, known as Eulerian-Eulerian approximation, assumes that
each phase is interpenetrating and interacts with each other. By this approach, the discrete
properties of each particle are replaced by local average values in order to formulate integral
26
momentum, mass and energy balances for a control volume that contains both phases. Therefore
these equations resemble Navier-Stokes equations; however the continuum model requires closure
models to describe the rheology of the gas and the solid phases [62].
The main idea of multi-scale modeling is that the required closure models are obtained from more
detailed models such as Lattice-Boltzmann or the Carman-Kozeny approximation [60]. Nonetheless,
most successful closure models are based on the Kinetic Theory of Granular Flow (KTGF) which is
analogous to the kinetic theory for dense gases. Using KTGF, it is possible to develop closure
equations that account for solid pressure, solid viscosity, and radial distribution among other
required properties. The advantage of KTGF is the underlying understanding of particle-particle
interactions [62]. Moreover, these equations consider the dissipation of kinetic energy due to
inelastic particle collisions, surface friction and elastic deformation of particles by introducing
certain parameters like granular temperature, restitution coefficient and specularity coefficient.
The Eulerian-Eulerian approach using granular kinetic theory has proven successful on predicting
key aspects of the fluidized bed: pressure-drop, bed-expansion, voidage profiles and bubble
behavior [8, 61-68]. The balance between computational costs, reasonable agreement with
experimental data, level of detail and range of applicability is perhaps, the major advantage of this
approach. The Eulerian-Eulerian approximation is the most common method for fluidized bed
simulations in engineering applications.
2.3.1. Eulerian-Eulerian approach using KTGF
The following conservative equations apply for dispersed multiphase flows. An Eulerian model for
the mass and momentum equations is applied using kinetic theory of granular flow for the
consideration of solids fluctuation energy. The conservation equations for the general multiphase
flow can be found in [9, 21].
2.3.1.1. Mass balance
Reynolds transport theorem applied to an arbitrary volume gives the well-known continuity
equations for the gas and solid phases:
Gas phase:
𝜕(휀𝑔𝜌𝑔)
𝜕𝑡+ ∇ ∙ (휀𝑔𝜌𝑔𝑣𝑔) = 0
(17)
Solid phase:
27
𝜕(휀𝑠𝜌𝑠)
𝜕𝑡+ ∇ ∙ (휀𝑠𝜌𝑠𝑣𝑠) = 0
(18)
By definition, the summation of volume fractions of all phases must be one.
휀𝑔 + 휀𝑠 = 1 (19)
2.3.1.2. Momentum balance
The second law of Newton states that “the rate of change of momentum of a system is equal to the
sum of forces acting on the system”. In a fluidised-bed, the forces acting on the system are as
follows: viscous forces ∇ ∙ �̅�𝑖 , the body force 휀𝑖𝜌𝑖𝑔, the static pressure force 휀𝑖 ∙ ∇𝑝, the solid
pressure force ∇𝑝𝑠 and the interphase force 𝐾𝑔𝑠(𝑣𝑔 − 𝑣𝑠).
Gas phase:
𝜕(휀𝑔𝜌𝑔𝑣𝑔)
𝜕𝑡+ ∇ ∙ (휀𝑔𝜌𝑔 𝑣𝑔⃗⃗⃗⃗⃗ 𝑣𝑔⃗⃗⃗⃗⃗) = −휀𝑔 ∙ ∇𝑝 + ∇ ∙ �̅�𝑔 + 휀𝑔𝜌𝑔𝑔 + 𝐾𝑔𝑠(𝑣𝑔 − 𝑣𝑠)
(20)
Solid phase:
𝜕(휀𝑠𝜌𝑠𝑣𝑠)
𝜕𝑡+ ∇ ∙ (휀𝑠𝜌𝑠 𝑣𝑠⃗⃗⃗⃗ 𝑣𝑠⃗⃗⃗⃗ ) = −휀𝑠 ∙ ∇𝑝 − ∇𝑝𝑠 + ∇ ∙ �̅�𝑠 + 휀𝑠𝜌𝑠𝑔 + 𝐾𝑔𝑠(𝑣𝑔 − 𝑣𝑠)
(21)
The term �̅�𝑖 is the stress tensor; if one assumes that both phases behave like Newtonian fluids then
the term �̅�𝑖 is expressed as [9]:
�̅�𝑖 = 휀𝑖𝜇𝑖(∇𝑣𝑖 + ∇𝑣𝑖
𝑇) + 휀𝑖(𝜆𝑖 −2
3𝜇𝑖)∇ ∙ 𝑣𝑖𝐼
(22)
Where 𝜇𝑖 and 𝜆𝑖 are the shear and bulk viscosity of phase i which come from the kinetic theory of
granular flow. The term I represents the dimensionless stress tensor identity matrix.
2.3.1.3. Drag coefficient
One of the most dominant forces in fluidization is the interphase momentum force. This force
couples the gas and solids momentum equations by considering the drag forces exerted on the solid
by the incoming gas. In general, the drag force is calculated as a product of the drag coefficient (𝐶𝑑),
the slip velocity (|𝑣𝑔 − 𝑣𝑠|) and certain parameters of the fluidized material (particle diameter, gas
density, etc.). Several models to estimate the drag coefficient have been reported in literature [9, 61,
68, 69]. However various studies have shown that the drag models predict similar values of
pressure drop, axial velocity, bed expansion and bubble characteristics [8, 62, 63, 68]. In this
research the Gidaspow model was chosen for its prediction capacity, range of applicability and
needless adjustment [61, 63, 68].
28
The gas-solid interphase coefficient (𝐾𝑔𝑠) is calculated using the following expressions [9].
𝐾𝑔𝑠 =
3
4𝐶𝑑휀𝑠𝜌𝑔|𝑣𝑔 − 𝑣𝑠|
𝑑𝑠휀𝑔−2.65 for 휀𝑔 > 0.8
(23)
𝐾𝑔𝑠 = 150
휀𝑠2𝜇𝑔
휀𝑔𝑑𝑠2 + 1.75
휀𝑠𝜌𝑔|𝑣𝑔 − 𝑣𝑠|
𝑑𝑠for 휀𝑔 < 0.8
(24)
Where the drag coefficient is given by
𝐶𝑑 =
24
휀𝑔𝑅𝑒𝑠[1 + 0.15(휀𝑔𝑅𝑒𝑠)
0.687]
(25)
𝑅𝑒𝑠 =
𝑑𝑠𝜌𝑔|𝑣𝑔 − 𝑣𝑠|
𝜇𝑔
(26)
It should be noted that tyre particles are nonspherical particles and hence, a correction in the drag
coefficient model is essential to take this aspect into account. Haider and Levenspiel [10]
developed an equation for the drag coefficient for nonspherical particles by adjusting experimental
data from different particle geometries to the following equation.
𝐶𝑑 =
24
𝑅𝑒𝑠(1 + 𝐴𝑅𝑒𝐵) +
𝐶
1 +𝐷𝑅𝑒𝑠
(27)
Where
𝐴 = exp(2.3288 − 6.4581𝛷 + 2.4486𝛷2) (28)
𝐵 = 0.0964 + 0.5565𝛷 (29)
𝐶 = exp(4.905 − 13.8944𝛷 + 18.4222𝛷2 − 10.2599𝛷3) (30)
𝐷 = exp(1.4681 + 12.2584𝛷 − 20.7322𝛷2 + 15.8855𝛷3) (31)
𝛷 =
𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒
𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑠𝑝ℎ𝑒𝑟𝑒 𝑤𝑖𝑡ℎ 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑣𝑜𝑙𝑢𝑚𝑒
(32)
Other authors have proposed more sophisticated correlations for the drag coefficient [70, 71].
These correlations consider particle orientation and volumetric shape factors for calculating drag
forces. For this reason, they are well suited for Eulerian-Lagrangian and Lattice-Boltzmann
simulations where discrete particle geometry is considered. However for the Eulerian-Eulerian
approach, where the particles are modelled as a fluid, is not possible to implement them properly.
29
2.3.4. Kinetic theory of granular flow
As mentioned before, expressions for shear and bulk viscosities for the solid phase come from the
kinetic theory of granular flow. Solid bulk viscosity represents the particle’s resistance against
compression and is given by Lun et al. [64]:
𝜆𝑠 =4
3휀𝑠𝜌𝑠𝑑𝑠𝑔0,𝑠𝑠(1 + 𝑒𝑠𝑠)√
𝛩𝑠𝜋
(33)
Shear viscosity considers the tangential forces due to particle interactions and is given as:
𝜇𝑠 = 𝜇𝑠,𝑐𝑜𝑙 + 𝜇𝑠,𝑘𝑖𝑛 + 𝜇𝑠,𝑓𝑟𝑖 (34)
Where 𝜇𝑠,𝑐𝑜𝑙 represents the collisional contribution for the shear viscosity.
𝜇𝑠,𝑐𝑜𝑙 = 4
5휀𝑠𝜌𝑠𝑑𝑠𝑔0,𝑠𝑠(1 + 𝑒𝑠𝑠)√
𝛩𝑠𝜋
(35)
The kinetic contribution 𝜇𝑠,𝑘𝑖𝑛 is given by Gidaspow model [9].
𝜇𝑠,𝑘𝑖𝑛 =10𝜌𝑠𝑑𝑠√𝛩𝑠𝜋
96휀𝑠𝑔0,𝑠𝑠(1 + 𝑒𝑠𝑠)[1 +
4
5휀𝑠𝑔0,𝑠𝑠(1 + 𝑒𝑠𝑠)]
2 (36)
Finally the frictional contribution 𝜇𝑠,𝑘𝑖𝑛 is given by Schaeffer’s model [61]:
𝜇𝑠,𝑓𝑟𝑖 =𝑃𝑠sin (𝜙𝑔𝑠)
2√𝐼2𝐷 (37)
Figure 9. Transport mechanisms for solid particles: Frictional, collisional and kinetic [61].
According to the kinetic theory of granular flow, the drag force induced by the gas causes a velocity
profile in the solid particles. In a fully developed flow, the highest velocity for the gas phase is
30
expected in the axis of the reactor while the minimal velocity is likely found near the wall. However,
the kinetic energy of the particles dissipates over time due to collisions between particles, friction
between particles and inelastic deformation. As a result, particles move randomly and an average
approximation is needed then, to estimate the effect of this randomness in the solid velocity profile.
The instantaneous particle velocity is decomposed in two velocities, the local average velocity and a
random velocity [62]. This random fluctuating velocity is measured introducing a variable known
as granular temperature, which is defined as one third of the mean square of the random velocity
component of the velocity, 𝑣′[9].
𝛩𝑠 =1
3⟨𝑣′⟩2 (38)
The distribution of granular temperature is computed using an additional conservation equation
for the random kinetic energy.
3
2
𝛿
𝛿𝑡(휀𝑠𝜌𝑠𝛩𝑠)⏟
𝑛𝑒𝑡 𝑐ℎ𝑎𝑛𝑔𝑒
+3
2∇ ∙ (𝜌𝑠휀𝑠 𝑣𝑠⃗⃗⃗⃗ 𝛩𝑠)⏟ 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛
= ∇ ∙ (𝑘𝛩𝑠∇𝛩𝑠)⏟ 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛
+ (−𝑝𝑠𝐼 + �̅�𝑠): ∇ ∙ 𝑣𝑠⃗⃗⃗⃗⏟ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛
− 𝛾𝛩𝑠⏟ 𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑖𝑜𝑛
+ 𝛷𝑔𝑠⏟𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒
(39)
The terms at the left side represent the net change of granular temperature inside the control
volume and the convective contribution of the local averaged velocity. The first term at the right
side represent the diffusion of random kinetic energy, the second term represent the generation
term due to local acceleration of particles [62], the third term is the dissipation of energy due to
particle-particle collision and the last term represent the exchange of energy between the phases.
There are many models for the diffusion coefficient of granular energy 𝑘𝛩𝑠. Nevertheless, in this
simulation only the Gidaspow correlation is used [61].
𝑘𝛩𝑠 =150𝜌𝑠𝑑𝑠√𝛩𝑠𝜋
384 ∙ (1 + 𝑒𝑠𝑠)𝑔0,𝑠𝑠[1 +
6
5휀𝑠𝑔0,𝑠𝑠(1 + 𝑒𝑠𝑠) + 2𝜌𝑠𝑑𝑠휀𝑠
2(1 + 𝑒𝑠𝑠)𝑔0,𝑠𝑠√𝛩𝑠𝜋] (40)
The solid pressure represents the normal force due to particle-particle interaction. This term helps
with the numerical stability of the overall model.
𝑃𝑠 = 휀𝑠𝜌𝑠𝛩𝑠 + 2𝜌𝑠(1 + 𝑒𝑠𝑠)휀𝑠2𝑔0,𝑠𝑠𝛩𝑠 (41)
The dissipative term is calculated using Lun’s model [72].
𝛾𝛩𝑠 =12(1 − 𝑒𝑠𝑠
2)𝑔0,𝑠𝑠
𝑑𝑠√𝜋𝜌𝑠휀𝑠
2𝛩𝑠3/2
(42)
31
The term 𝛷𝑔𝑠 represents the exchange of energy between the phases due to frictional forces
between the gas and the particles [62].
𝜙𝑔𝑠 = −3𝐾𝑔𝑠𝛩𝑠 (43)
The term 𝑒𝑠𝑠 is the coefficient of restitution between particles. It represents the mean kinetic
energy left after collision of particles and is a function of mechanical properties of the solid particle
and the collisional speed. One the assumptions of a CFD model are that the coefficient of restitution
remains constant during the simulation, which is approximately true for quasi-elastic collisions
[61].
Finally the term 𝑔0,𝑠𝑠 is the radial distribution for the solid phase and may be interpreted as the
probability of a binary collision. This term prevents from reaching unrealistic values of the solid
volume fraction. Ding and Gidaspow [9] developed an empirical model to estimate the radial
distribution.
𝑔0,𝑠𝑠 = [1 − (휀𝑠
휀𝑠,𝑚𝑎𝑥)
1/3
]
−1
(44)
32
3. Methodology
3.1. Experimental setup
For this research, two types of cold-model reactors were developed: A pseudo-2D model and a 3D
model. Section 3.1.1 describes the main features considered in the design of the pseudo 2D reactor.
Section 3.1.2 explains how the 3D model was designed and constructed. The pseudo 2D model is
used to observe directly the dynamics of tyre particles under fluidization and compare the results
with a computational model. Bubble formation and velocity fields of the dense phase are of
particularly interest for the comparison between experimental and computational models. The 3D
model is used as a prototype where to operate the fluidized bed reactor at different conditions of
inlet velocity, materials and bed height, then select the appropriate operating conditions for the
reactor and design a functional fluidized bed reactor.
There is one important issue that was observed during the construction of both models. The first
trials on the systems showed maldistribution of the gas, with only local fluidization of particles but
no homogenous fluidization. The maldistribution of gas resulted in unreliable readings of pressure
and unusual bubble behavior, especially near the wall of the reactor. Most authors overlook this
issue and do not give too many details about how the reactors were constructed, particularly the
system below the fluidized bed (e.g. the distribution plate and the windbox). It is important to
design correctly the fluidization system and ensure that enough pressure drop from the air
distribution system is attained. According to Kunii and Levenspiel [11], the pressure drop from the
air distribution system should be between 20-40% of the minimum expected pressure drop from
the fluidized bed. The authors give a simple methodology to design perforated plates for a fluidized
bed.
1. Determine the required pressure drop of the distributor based on the operating conditions
of the fluidized bed or using the criteria, 20-40% of overall pressure drop.
2. Calculate the vessel Reynolds number 𝑅𝑒 = 𝑢0𝑑𝑡𝜌𝑔 𝜇⁄ and select the corresponding value
for the orifice coefficient 𝐶𝑑,𝑜𝑟. The values of the orifice coefficient may be found in
literature [11].
3. Determine the gas velocity through the orifice using the following equation.
𝑢𝑜𝑟 = 𝐶𝑑,𝑜𝑟 (
2∆𝑝𝑑𝜌𝑔
)
1/2
(45)
Ensure that the ratio 𝑢0/𝑢𝑜𝑟 be less than 10%.
33
4. Based on the geometry, decide the number of orifices per area of distributor 𝑁𝑜𝑟 or the
orifice diameter 𝑑𝑜𝑟 . Then calculate the other variable based on the following equation.
𝑢0 =𝜋
4𝑑𝑜𝑟2 𝑢𝑜𝑟𝑁𝑜𝑟 (46)
The tyre particles used in this study were prepared using a sieve shaker several times to obtain a
particle size of 400-500 μm range. The particle size showed a normal distribution. The fines that
may have remained from the sieving process were eliminated by fluidizing the particles at a high
superficial gas velocity, until no significant amount of fines was observed at the gas outlet.
3.1.1. Pseudo 2D setup
There are several difficulties when studying bubble behavior inside a fluidized bed, especially in a
three dimensional one. Specialized methods and equipment are required for visualization.
Examples of these methods include: gamma computed tomography (GDT), X-ray computed
tomography (XCT), X-ray radiography, electrical capacitance tomography (ECT) and positron
emission tomography (PET). However due to technical and economical limitations, it was not
possible to use any of these methods and instead, we opted for a direct visualization method. For
this reason a two dimensional reactor was designed and created. By studying bubble behavior on
the 2D fluidized bed, we can estimate several key parameters for the simulation (e.g. specularity
coefficient, restitution coefficient) and compare the drag coefficient models. The 2D reactor was
constructed in acrylic with a cross sectional area of 10x2.5 cm and a height of 50 cm. The
distributor plate consisted on 88 holes of 2 mm, square distribution, 1 mm pitch which gives an
open area of 0.96%. A 60 mesh screen is fixed over the plate to avoid lodging problems on the
orifices or the windbox. The measured pressure drop was above 25% of the expected pressure
drop. The windbox is 7 cm tall and has two 1/8 in threaded fittings where the air enters the reactor.
Additionally small polyethylene pellets (2 mm) were introduced in the windbox to achieve a
uniform air distribution, the windbox was filled to ¾ of its capacity to avoid clogging from the
pellets if completely filled. Square (5 x 15 cm) flanges are placed at the top of the windbox and the
bottom of the bed chamber to connect the sections together. Each flange have four 0.635 cm (1/4
in) ID threaded holes located at the back, front and sides of the reactor.
34
Figure 10. Pseudo 2D model.
3.1.2. Electrostatic charge reduction
Electrostatic charge build up in a fluidized bed is an important issue at laboratory and industrial
scale. In the case of insulating particles like tyre or biomass, the charge is principally due to
triboelectric charging. In this process, friction and eventual separation of insulating particles causes
a net electric charge on the particles [76]. Triboelectric charging depends on many factors such as
particle size, particle material and surface properties and thus, it is unpredictable and hard to
control. One of the main problems with electrostatic charge in a fluidized bed is the accumulation
of particles in the wall. The particles that adhere to the wall form a sheet of overlaying particles.
This causes wall fouling and decreases the overall conversion in the reactor [77]. For both 2D and
3D cold model reactor, copper tape is used to reduce electrostatic build up in the reactor. The
copper tape is connected to ground via copper wires. In addition a small amount of salt is also used
in the 2D reactor as it improves visualization as it reduces electrostatic charge on the front wall.
3.1.3. 3D Setup
The reactor is made in acrylic and consists of two main sections: the bed chamber and the windbox.
The bed chamber is 50 cm tall and 10 cm diameter. Four ¼ in threaded fittings were installed at 10,
20, 30 and 40 cm from the bottom. These fittings are used as pressure measurements points. A 2 cm
particle injection port was installed at the top of the reactor. This port also serves as the exit point
35
for the gas phase during operation. Both sections are connected using circular flanges (12.5 cm O.D)
located at the top of the windbox and bottom of the 3D model. The flanges have six 0.635 cm (1/4
in) ID threaded holes evenly spaced around the center of the flange. Silicone adhesive was used to
ensure that no air could escape from the side of the reactor.
The distribution plate is located under the bed chamber and consists of 100 holes 1 mm diameter, 1
mm pitch in a triangular distribution. The diameter and number of holes were estimated based on
the methodology proposed by Kunii and Levenspiel [11]. A 60 mesh screen is fixed over the plate to
avoid lodging problems on the orifices or the windbox.
On the other hand, three different configurations for the windbox were tested to overcome the
nonuniformity issue. A conical geometry of 15 cm tall with 0.9525 cm diameter at the bottom and
10 cm diameter at the top, a cilndrical geometry of 20 cm tall and 10 cm diameter with an 0.9525
cm opening at the center of the plenum and a cilndrical geometry of 10 cm tall and 10 cm diameter
filled with 1.27 cm diameter glass marbles. Visual inspection showed that the third geometry
provided the most uniform gas flow of all the considered geometries. The marbles ensure that local
effects of air input due to plenum geometry are neglected before reaching the distribution plate.
Figure 11. Three dimensional model.
The pressure drop was measured with the differential pressure manometer Extech HD755. The low
range of the sensor made it suitable to capture the expected low pressure drop.
36
Table 3. Preliminary distribution plate design.
Parameter Value
Inlet
Pipe Diameter (m) 0.093 Pipe Area (𝑚2) 6.793𝑥10−3
Volumetric Flow (L/min) 30
Volumetric Flow (𝑚3/s) 5𝑥10−4
Superficial Velocity (m/s) 0.304
Perforated plate
Re 448.5
𝐶𝑑𝑜𝑟 0.610
Orifice velocity 10.11
% Open area 0.728
Orifice Diameter (m) 0.001
Orifice Area (𝑚2) 7.854𝑥10−7
Nor (#/𝑚2) 9271
Nor 63
3.1.4. Pressure drop versus superficial velocity curve
The pressure drop versus superficial velocity curve was determined at three different bed heights
(5, 8 and 10 cm) using the following measurement procedure. The tyre particles are fluidized at the
maximum velocity allowed by the compressor, which was 6.5 SCFM (184 Lpm). Once the system
reached a steady state condition, pressure data is acquired each second with the Extech pressure
manometer and transfer to a computer via USB connection. The pressure data was averaged over a
ten minute time span which was found out to sufficiently enough for measurements purposes. Then
the air flow rate was decreased by 0.5 SCFM by manually closing the air regulator. When the system
reaches a new steady condition (which takes about 30 seconds) the process is repeated until
reaching 0 SCFM which concluded the experimental run. The trials started by weighing the tyre
particles needed for the specific bed height and then, running the experiment. Once finished the
additional mass required to reach the new bed height was weighted and introduced to the reactor.
No significant amount of mass is lost during the fluidization. Once all the experimental runs were
carried out, the procedure is repeated without material in the bed chamber to estimate the
pressure drop produced solely by the reactor. The windbox, marbles and distribution plate display
a significant pressure drop. The pressure drop obtained from the empty reactor is then subtracted
from the pressure drop data obtained from the experimental runs.
37
3.1.5. Direct visualization
The bubbles characteristics of the two dimensional model were visualized using a high speed
camera (Photon Fastcam 1024PCI) placed at 5 cm from the reactor. This ensured that the behavior
of the whole bed could be observed and hence, a complete analysis of the overall bed was possible.
Three high intensity sets of lights were carefully located on the back side of the reactor. This
illumination was essential to enhance image contrast as well as to discriminate properly the bubble
phase from the moving particles. In addition a blank sheet of paper was placed behind the back wall
of the reactor to increase image contrast. It was observed that bubbles were easier to identify when
using this method. Video recording began 10 minutes after the fluidization started to ensure that
the reactor had reached a steady state and avoid that any transient behavior was measured. On the
other hand, the device used allows the capture of image at an incredibly fast rate, however the
image contrast and brightness deteriorated as the frame rate increased. A rate of 60 fps was chosen
to obtain reliable data with good image quality. According to Busciglio [23], the frame rate must be
chosen depending on the time scale of the bubbling phenomena.
Figure 12. Snapshots of the two dimensional fluidized bed.
Once the images were obtained, they were processed and analyzed using an in-house routine in
MatLab. Particularly the Image Processing Toolbox was widely employed. In the Appendix A a
section of the routine used is presented. Bubble identification was possible because light coming
from the back of the reactor passes through them while light cannot pass through the solid phase.
Once the images were processed, bubbles were represented as white areas. The methodology used
in this work was similar to the one presented by Busciglio [22]. The steps used for the digital image
analysis can be found in section 2.1.5. There is one important consideration regarding image
analysis that should be mentioned. The recirculation of particles inside the bubbles may produce
images that appear as a smaller bubble followed by a constellation of smaller bubble or produce
black zones inside the bubble which can be falsely interpreted as smaller bubbles or even two
38
bubbles. Thus the filtering of false bubbles is crucial to DIA in order to avoid false data interfering
with the statistical analysis.
Figure 13. Digital image analysis, from left to right: 1. Original Image, 2. Filtered image, 3. Connectivity analysis, 4. Final image with each bubble identified.
A similar DIA methodology was applied to the two dimensional simulations in order to compare the
experimental with the computational results. Computational images were obtained at a rate of 100
fps. A total of 2500 frames where analyzed from each simulation while 1000 frames where
analyzed from the 2D cold model. It was found that this amount of images was enough for statistical
analysis of bubble characteristics. From DIA bubbles properties like diameter, rise velocity and
aspect ratio can be adquired for each time step.
3.1.6. Copula bivariate
The digital image analysis produces a considerable amount of raw data related to some bubble
properties. This information must be treated statistically to analyze it properly. Most authors
compare the mean value of some bubble property with bed height and observe a pattern, which is
related to the fluidization phenomena. An example is the increase of bubble diameter and bubble
rise velocity along bed height. However there is an intrinsic issue when applying this method as the
variance is not considered in the analysis; the data presents a wide range that augments along bed
height. Bubble phenomena like mixing, segregation and coalescence is not investigated properly
when only considering the mean value in the analysis. In contrast, the probability distribution of
bubble properties give a more accurate description as bubble phenomena is in principle
probabilistic. During the realization of this work, it was observed that a multivariate probability
39
distribution results in a better mathematical description of the distribution of bubble diameter
along bed height. In this work three statistical analysis were performed, bubble frequency
distribution, mean value of bubble diameter and bubble rise velocity and the multivariate
probability distribution of bubble diameter versus bed height. The mean value analysis was mainly
used to compare the results with literature whereas the multivariate probability distribution was
used to study a different methodology for investigating bubble phenomena. The following section
explains the multivariate probability distribution function used in this work.
A copula is a multivariate parametrically specified probability distribution produced from the
marginal distribution of each random variable [73]. Their main advantage is the easiness when
trying to express and estimate the joint probability distribution. It also allows the separation
between the behavior of each random variable (marginal) and the dependency that may exists
between the variables. In this work, the focus is on bivariate copulas because that statistical
analysis for the 2D case considers only two random variables: bubble diameter and bed height.
The Sklar’s theorem states that the joint cumulative probability distribution of two random
variables 𝐹(𝑥1, 𝑥2) with cumulative density functions 𝐹𝑗(𝑥) = 𝑃(𝑋𝑗 ≤ 𝑥). There exists a copula C
such as [74]:
𝐹(𝑥1, 𝑥2) = 𝐶(𝐹1(𝑥1), 𝐹2(𝑥2)) (47)
Is both functions F and C are differentiable, then the joint probability density function (pdf) f
satisfies
𝑓(𝑥1,𝑥2)
𝑓(𝑥1)𝑓(𝑥2)= 𝑐(𝐹1(𝑥1), 𝐹2(𝑥2)) (48)
Where c is the probability density function of the copula distribution. This implies that the copula
pdf is the probability distribution of the dependency between variables. Furthermore, it can be also
interpreted as the correction needed to transform the independent probability distribution into a
joint probability distribution.
One of the most popular families of copulas for two random variables is the Archimedean copula,
which has the form:
𝐶𝜑(𝑢1, 𝑢2) = 𝜑(𝜑(𝑢1) + 𝜑(𝑢2)) (49)
40
Where 𝜑 is the generator function of the Archimidean copula 𝐶𝜑(𝑢1, 𝑢2) and 𝑢𝑖 is the uniformed
distributed marginal variable.
𝑢𝑖 = 𝐹(𝑥𝑖), 𝑢𝑖~𝑈(0,1) (50)
The generator describes the dependency structure between the random variables and is generally
presented as a univariate function with parameter θ. The most common Archimidean copulas are
the Frank, Gumbel and Clayton copulas. An attractive feature of these copulas is that dependency
measurements can be obtained easily from them as a function of the parameter θ. One of these
dependency measurements is the Kendall’s-tau ((𝜏), which is a non-parametric measure of the
correlation between random variables. Table 3 summarizes the copula function, the generator
function and the relationship between 𝜃 and 𝜏.
Table 4. Archimedean Copula function and Kendall-tau parameter.
Copula Copula function Relationship between 𝜃 and 𝜏 Equation
Gumbel exp (−[(−ln (𝑢1))𝜃 + (−ln (𝑢2))
𝜃]1/𝜃) 𝜃 =
1
(1 − 𝜏)
(51)
Frank −1
𝜃ln [1 +
(exp(−𝜃𝑢1) − 1) (exp(−𝜃𝑢2) − 1)
(exp(−𝜃) − 1)] 𝜏 = 1 −
4
𝜃+4
𝜃2∫
𝑡
exp(𝑡) − 1𝑑𝑡
𝜃
0
(52)
Clayton (𝑢1−𝜃 + 𝑢2
−𝜃 − 1)−1/𝜃
𝜃 =2𝜏
1 − 𝜏
(53)
These three archidimidean copulas are distinguished by the way they capture tail dependence. The
Clayton copula captures lower tail dependence while Gumbel copula captures upper tail
dependence. Frank copula is symmetric and hence, it does not show tail dependence. For all three
copulas, the parameter 𝜃 is estimated via maximum likelihood method [75].
It is worthwhile to note that most copula families present symmetry with respect of the diagonal
line along the unit square while the experimental data show asymmetric behavior in transformed
space. Then a special class of Archimedean copula is necessary to describe correctly the
dependence between variables is given by [75]:
𝐶𝜃,𝑤1,𝑤2(𝑢1, 𝑢2) = 𝑢11−𝑤1𝑢2
1−𝑤2𝐶𝜃(𝑢𝑖𝑤1, 𝑢2
𝑤2) (54)
Where 𝑤1 and 𝑤2 are weight parameter ranging from 0 to 1. In this work the weight parameters
were found to be 𝑤1 = 0.8,𝑤2 = 1.
41
3.2. Computational study
In this study, isothermal simulations assuming no reaction were performed using FLUENT 15.0 and
the Eulerian-Eulerian model described in section 2.3. Two dimensional computational models were
simulated and compared with the results obtained from the pseudo 2D setup experimental model.
Both drag coefficient models were compared in order to determine which model best fits the
experimental data. On the other hand, a preliminary parametric study was performed in order to
study the effect of specularity coefficient and restitution coefficient on three key variables: solid
phase volume fraction, pressure drop and solid phase velocity. From the parametric study,
numerical values for the restitution and specularity coefficient were obtained and a drag coefficient
model was chosen. These results were then used in a 3D simulation. The pressure fluctuations
estimated in the 3D simulation were compared with the ones obtained in the 3D model. In addition,
grid independence studies were carried out using the first drag model (Gidaspow model) to
estimate the required mesh in each case. Additionally all computational models presented the same
discretization schemes; a first order scheme was used for the temporal component of the equations
while a second order upwind scheme was implemented for the spatial discretization and
momentum equations. The quadratic upwind interpolation for convective kinematics scheme
(QUICK) was chosen for the volume fraction and granular temperature equations [8]. These
discretization schemes were chosen to achieve convergence on most time steps in a reasonable
computational time while avoiding computational problems such as numerical instabilities and
false diffusion. The simulation time in all cases was 30 seconds and time-averaged from 5 to 30
seconds in even spaced time intervals.
3.2.1. Two/three dimensional case
Two scenarios were evaluated in order to compare the results of different simulation drag models:
The Gidaspow model and the Haider-Levenspiel model. A time step of 0.0005s with 100 iterations
per step was chosen for the two-dimensional simulations whereas a time step of 10−5𝑠 was used
for the three dimensional case. The volume domain for the two dimensional case was discretized
with 8000 rectangular cells, it was found that a finer mesh did not change significantly the results
on pressure drop, void fraction and axial velocity. The three dimensional scenario was discretized
with 22840 hexagonal cells considering the exhaustive computational time taken for simulation.
Table 5 shows the additional parameters considered for the simulations. It is worth noting that the
values of restitution coefficient and specularity coefficient were chosen based on the preliminary
parametric study.
42
Table 5. Simulation parameters.
Symbol Property Unit Value Reference/Comment
𝜌𝑠 Solid density Kg/m3 950 Scrap tyre particles
𝜌𝑔 Gas density (20°C) Kg/m3 1.251 Air
𝜇𝑔 Gas viscosity (20°C) Kg/m-s 1.78𝑥10−5 Air
𝐷𝑝 Mean particle diameter 𝜇m 0.425 Experimental value
𝑒𝑠𝑠 Restitution coefficient - 0.9 𝜑 Specularity coefficient - 0.25
εg0 Initial bed voidage - 0.57 Calculated [17]
𝐷𝑡 Reactor diameter m 0.100 𝐻𝑡 Reactor height m 0.500 𝐻0 Initial bed height m 0.100
𝑈0 Superficial gas velocity m/s 0.30 Minimum fluidization
velocity
𝛥𝑡 Time step s 10−4 2D scenario
Convergence criteria - 1𝑥10−3
3.2.2. PC-SIMPLE algorithm
The convergence criterion for all simulation was 10−4 for each considered scaled residual. The
phase coupled SIMPLE (PC-SIMPLE) algorithm was applied for the pressure-velocity coupling. This
method is an extension of the SIMPLE (Semi-Implicit Method for Pressure Linked Equations)
method for multiphase flows. The linearized momentum equations are solved coupled by phases
using a block algebraic multigrid scheme; it solves a vector equation formed by the velocities of all
phases simultaneously [63]. The pressure correction equation incorporates total volume continuity
equations (instead of mass continuity equations) and interfacial coupling terms. According to
Ansys®, this algorithm is robust and suitable for Eulerian-Eulerian simulations [78].
The following steps are the main operations of the PC-SIMPLE algorithm [61].
1. Initialize the pressure field, the velocity field, solid volume fraction and granular
temperature.
2. Calculate the physical properties and exchange coefficients.
3. Evaluate the velocity field of both phases based on the current pressure field (𝑃𝑔∗).
4. Apply the pressure correction equation (𝑃𝑔,) for the fluid phase.
5. Update the pressure field considering under-relaxation factors. 𝑃𝑔 = 𝑃𝑔∗ + 𝛼𝑝𝑔𝑃𝑔
,
6. Calculate the velocity corrections (𝑣𝑔′⃗⃗⃗⃗⃗) from 𝑃𝑔
, and update the velocity field for the fluid
phase. 𝑣𝑔⃗⃗⃗⃗⃗ = 𝑣𝑔∗⃗⃗⃗⃗⃗ + 𝑣𝑔
′⃗⃗⃗⃗⃗
43
7. Compute the pressure gradients (𝛿𝑃𝑖
𝛿 𝑖) that will be used on the solid volume fraction
correction equation.
8. Evaluate the solid volume fraction equation (휀𝑠′)
9. Update the solid volume fraction. 휀𝑠 = 휀𝑠∗ + 𝛼𝑣𝑓휀𝑠
,
10. Estimate the solid velocity correction (𝑣𝑠′⃗⃗ ⃗⃗ ) and update the solid velocity field 𝑣𝑠⃗⃗⃗⃗ = 𝑣𝑠
∗⃗⃗⃗⃗⃗ + 𝑣𝑠′⃗⃗⃗⃗
11. Evaluate the solid pressure.
12. Compute any additional transport variable (temperature, turbulence property, etc.)
13. Calculate all the scaled residuals of the discretized equations and check for convergence. If
the convergence criterion is not met then go to step 2 with the updated transport variables
(velocity, pressure, solid volume fraction, etc.) and repeat the process.
3.2.4. Initial and boundary conditions
The initial condition for all scenarios was at minimum fluidization, with zero velocity for the solid
phase, an initial bed height of 0.15m and a bed voidage of 0.42. The inlet condition was a superficial
velocity boundary condition for the gas phase at 3𝑈𝑚𝑓. The minimum fluidization velocity was
estimated with Ergun’s equation. The pressure outlet boundary condition was established at the
outlet. The freeboard was high enough to ensure a fully developed flow for the gas phase. The wall
boundary condition for the gas phase velocity was zero (no-slip condition). A partial slip condition
was set for the tangential velocity of the solid phase [79].
�⃗�𝑠,𝑤 = −
6𝜇𝑠휀𝑠,𝑚𝑎𝑥
√3𝛩𝑠𝜌𝑠휀𝑠𝜑𝑔0,𝑠𝑠
𝛿�⃗�𝑠,𝑤𝛿𝑛
(55)
The boundary condition for granular temperature at the wall is [61]:
𝛩𝑠,𝑤 = −𝑘𝑠𝛩𝑠𝑒𝑠𝑠,𝑤
𝛿𝛩𝑠,𝑤𝛿𝑛
+√3𝛩𝑠
3𝜌𝑠휀𝑠𝜑𝑔0,𝑠𝑠𝑣𝑠2
6𝑒𝑠𝑠,𝑤휀𝑠,𝑚𝑎𝑥
(56)
Where �⃗�𝑠,𝑤 is the particle slip velocity, 𝑒𝑠𝑠,𝑤 is the restitution coefficient at the wall, 𝜑 is the
specularity coefficient and 휀𝑠,𝑚𝑎𝑥 is maximum volume fraction due to packing. According to
Armstrong [80], low values of the specularity coefficient underpredict the axial velocity of particles
near the wall. In addition, Loha et al. [81] studied the effect of the wall boundary conditions with
different specularity coefficient values. The authors showed that the pressure drop, time-averaged
axial velocity and granular temperature do not change significantly at high values. However, values
below 0.1 presented huge deviations from experimental findings.
44
3.2.5. User defined function implementation
The implementation of an Eulerian-Eulerian simulation in Fluent only has drag models for spherical
particles. Therefore a C routine code had to be written to implement the Haider & Levenspiel model
on the simulation. Readers interested in creating their own customized functions in Ansys Fluent
are encouraged to read Ansys UDF manual [82]. The complete code used for the Haider &
Levenspiel simulation can be found in Appendix B.
Microscopic images of tyre particles were acquired to calculate the average sphericity. Digital
Image Analysis (DIA) was used to estimate the surface area of the particle and calculate the
minimum circle that can be circumscribed (convex hull circle) around the particle. The ratio
between the surface areas is the degree of sphericity. A total of 100 particles were analyzed, which
was assumed to be sufficient for statistical analysis. The average value of sphericity for the tyre
particles was 0.6264. Figure 3.5 shows an example of the procedure conducted to calculate the
sphericity of each particle. The blue line represents the contour of the particle which was obtained
with the active contour algorithm. The green dot is the centroid of the particle. The red line is the
minimum bounding circle around the particle. This circle was found using the MatLab code
provided by John D’Errico [83].
Figure 14. Microscopic image of tyre particles.
45
4. Results and discussion
4.1. Parametric study
Eight cases with three factors were considered for the parametric study, these factors are the drag
coefficient model, the restitution coefficient and the specularity coefficient. Table 6 shows the
considered cases as well as the mean average pressure drop obtained in each scenario.
Table 6. Cases considered in the parametric study.
Case study Drag coefficient model 𝑒𝑠𝑠 𝜑 Mean average drop (Pa)
Case 1 Gidaspow 0.9 0.25 386.66 Case 2 Gidaspow 0.9 0.5 380.24 Case 3 Gidaspow 0.7 0.25 385.61
Case 4 Gidaspow 0.7 0.5 386.95 Case 5 Levenspiel 0.9 0.25 388.12 Case 6 Levenspiel 0.9 0.5 388.96 Case 7 Levenspiel 0.7 0.25 385.98
Case 8 Levenspiel 0.7 0.5 386.70
The average pressure drop does not present a significant change for all the considered cases; the
maximum change is approximately 2% of the maximum pressure drop. This implies that the
restitution coefficient and specularity coefficient has no significant effect on the pressure drop for
the range studied. In the work of Lohah et al. [81] it was reported that only extremely low values of
the specularity coefficient (near zero) may have a significant on the pressure drop. However, the
pressure drop did not change significantly even for large specularity values. On the other hand, the
negligible effect of the restitution coefficient can be attributed to the low inlet velocity used for the
simulation. According to Cloete [84] only at high velocities a moderate impact of the restitution
coefficient on the pressure drop is observed. In addition the drag coefficient model did not show
any effect on the pressure drop, this comes as consequence of the similarity between the drag
coefficient models.
Figure 4.1 shows the profile of mean solid fraction versus axial direction for all cases considered.
The overall behavior is an increase of solid fraction up to 4 cm above the distributor and then an
almost linear decrease of the dense volume fraction until it reaches zero at a height of
approximately 15 cm. There are slightly minor differences at low heights, particularly at the
inflexion point, nonetheless the overall solid volume profiles are very similar for all cases. Thus
both parameters do not have a significant effect on the bed expansion of the fluidized bed. The fact
46
that neither the pressure drop or bed expansion are affected by both parameters results may be
seen as a positive remark. The experimental procedures to estimate these parameters are not
trivial and usually have some degree of uncertainty. Consequently simulations that are not greatly
affected by the value of these parameters are easier to simulate. In addition, the observed
insensitivity can be attributed to the flow regime. Cloeter [84] showed that for bubbling
fluidization, the effect of both parameters is almost negligible whereas for fast fluidization the
impact became important particularly for narrow geometries.
Figure 15. Time-averaged solid volume fraction profiles, Gidaspow (left), Levenspiel (right).
Figure 4.2 shows the mean axial velocity versus the radial position at 5 cm from the distribution
plate. All velocity profiles have a common trend with the lowest velocities near the walls of the
reactor and highest velocities at the center. This comes as a result of the recirculation of solids inside
the reactor. The solid phase move upwards at the center of the reactor, where the resistance due to
friction is lower and once it reaches the bed surface, it moves downward along the reactor walls. A
similar behavior of the velocity profiles is observed in the work of Laverman et al [85]. The authors
also report the formation of two vortices at the top half of the reactor, which are the solid
recirculation zones in the reactor. The specularity coefficient has a moderate effect on the axial
velocity, at 0.25 the velocity near the center is slightly higher for the Gidaspow model. An increase of
roughly 12% is observed near the center, whereas the restitution coefficient has a negligible effect on
the velocity and will not discussed further. Except for the first case (𝑒𝑠𝑠 = 0.9, 𝜑 = 0.25) both drag
models coefficient models predict the same average axial velocity profile. It is worth noting that the
Haider-Levenspiel model predicts a certain degree of asymmetric behavior, which may rise from
considering non-spherical particles.
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0 0,2 0,4
Hei
ght
(m)
Solid volume fraction
ess = 0.9, ϕ = 0.25 ess = 0.9, ϕ = 0.5 ess = 0.7, ϕ = 0.25 ess = 0.7, ϕ = 0.5
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
0,5
0 0,2 0,4
Hei
ght
(m)
Solid volume fraction
ess = 0.9, ϕ = 0.25 ess = 0.9, ϕ = 0.5 ess = 0.7, ϕ = 0.25 ess = 0.7, ϕ = 0.5
47
Figure 16. Time-averaged velocity profiles at Z = 5cm, Gidaspow (left), Levenspiel (right).
From the previous results it can be stated that both parameters have little effect on key variables
(pressure drop, bed expansion and axial velocity. Therefore the uncertainty of not knowing exactly
the values of these parameters does not affect significantly the simulation results. This is a
remarkable result since previous studies have concluded differently [86-88]. Considering the
fluidization regime, it may be reasonable to conclude that the importance of fluid particle
interaction is of greater importance than particle-particle and particle wall interaction. On the other
hand, the drag coefficient models showed a similar trend for all three variables. This suggest that
the sphericity correction incorporated in the Haider-Levenspiel model does not affect greatly the
results. Since this model was developed from the Gidaspow model, the basic assumption regarding
the model may have a greater influence than the sphericity correction. More robust models are
necessary to ensure that the sphericity of particles is considered in the drag model. The numerical
values chosen for the restitution coefficient and specularity coefficient are 0.9 and 0.25
respectively. Further studies are required to determine if other parameters (particle, density,
particle size, initial void fraction) affect the simulation results.
-0,43
-0,33
-0,23
-0,13
-0,03
0,07
0,17
0,27
0 0,02 0,04 0,06 0,08 0,1
Tim
e a
vera
ged
axi
al v
elo
city
(m
/s)
X position (m)
ess = 0.9, ϕ = 0.25
ess = 0.9, ϕ = 0.5
ess = 0.7, ϕ = 0.25
ess = 0.7, ϕ = 0.5
-0,40
-0,30
-0,20
-0,10
0,00
0,10
0,20
0,30
0 0,02 0,04 0,06 0,08 0,1
Tim
e a
vera
ged
axi
al v
elo
city
(m
/s)
X position (m)
ess = 0.9, ϕ = 0.25
ess = 0.9, ϕ = 0.5
ess = 0.7, ϕ = 0.25
ess = 0.7, ϕ = 0.5
48
4.2. Bubble characteristics
Figure 17. Instantaneous void fraction contours for the Gidaspow (top) and Haider-Levenspiel (bottom) model.
49
Figure 18. Bubble size distribution
Figure 4.4 shows the bubble size distribution (BSD) obtained from the experimental and
computational data. The apparent trend between the simulations and experimental bubble
distribution is quite similar. However, the Gidaspow model presents a local maxima at a bubble
diameter slightly bigger than the one obtained experimentally. In addition the experimental BSD
exhibits a larger concentration of bubbles at small diameters (≈1 cm). This result can be attributed
to the limitations of two-dimensional simulation as they only consider a slice at the center of the
reactor, leaving behind some bubbles from the analysis [86], especially the small bubbles that are
produced near the distributor [22]. Different authors have reported similar bubble diameter
distributions for other fluidized bed materials [23, 66, 67]. Even though the models slightly differ in
bubble frequency, the observed trend is quite similar. Thus it can be stated that both drag functions
predict BSD in a similar manner. , Figure 4.5 shows the distribution obtained from randomly
generated 10000 points following the weighted Frank’s copula distribution. The probability
distribution captures correctly the bubble diameter tendency to grow along bed height and hence,
frank’s copula can describe the dependency between bubble diameter and bed height. The Kendall-
tau parameter was found to be 0.2421 which implies that there is a weak correlation between the
two variables. This result can be attributed to the wide distribution of bubble diameter and bubble
mixing and segregation. On the other hand bubble diameter evolution from the simulations behave
similarly to the experimental results, with increased variability along the bed height. The Kendall-
tau parameters for the Gidaspow and Levenspiel model were 0.3163 and 0.2140 respectively.
50
Figure 19. (left) Diameter evolution as a function of bed height (experimental). (right) random simulation of 10000 points using weighted Frank’s copula.
In general the experimental data show the typical increase in bubble diameter as it moves upwards
the reactor. Likewise the variability of data is rising along the bed height, as a result of coalescence,
splitting and nucleation phenomena [23]. Several authors have reported the same wide distribution
for different fluidization bed conditions [22, 67, 89]. The copula bivariate was used to estimate the
joint probability distribution using formula 46. Figure 4.6 displays the joint probability distribution
based on the experimental data and simulation models. From the simulation joint probability
distributions it can be stated that the probability concentrates primarily at low heights (< 5 cm)
with small diameters (0.5 cm). At higher bed heights, the probability decreases until reaching the
maximum bed expansion. The probability distribution from the experimental data at small
diameters (0.5 and 1 cm) shows a broader probability in a wider spectrum of bed heights. This
implies that implies that bubble growth rate may be lower for the experimental setup when
compared with simulations. This result may be attributed to the cohesive effect of Van der Waals
forces and/or electrostatic build up that inhibited bubble growth. In addition it was observed that
splitting of bubbles did not happen frequently on the experimental trials. For higher bubble
diameters, the probability is negatively skewed towards the maximum the bed expansion. This is an
expected result since larger bubbles are expected due to bubble growth along the bed and mixing
phenomena. Nonetheless, the probability of finding large bubbles is larger on the simulations than
on the experimental, especially for the Gidaspow model. In addition both simulations underpredict
bed expansion, the estimated experimental bed expansion was 17.2 cm. while the simulations
predict a bed expansion of 13.3 cm (Gidaspow) and 12.4 cm (Levenspiel).
0
1
2
3
4
5
6
7
8
0 5 10 15 20
Mea
n D
iam
eter
(cm
)
Height (cm)
Raw data
0
1
2
3
4
5
6
7
0 5 10 15 20
Mea
n D
iam
eter
(cm
)
Height (cm)
Frank's copula
51
Figure 20. Probability density distribution for different equivalent bubble diameters. (top left) 𝐷𝑏 = 0.5 𝑐𝑚, (top right) 𝐷𝑏 = 1 𝑐𝑚, (bottom left) 𝐷𝑏 = 1 𝑐𝑚 and (bottom left) 𝐷𝑏 = 4 𝑐𝑚.
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0 5 10 15 20
Pro
bab
ilit
y d
ensi
ty d
istr
ibu
tio
n
Bed height (cm)
Levenspiel
Gidaspow
Experimental
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0 5 10 15 20
Pro
bab
ilit
y d
ensi
ty d
istr
ibu
tio
n
Bed height (cm)
Levenspiel Gidaspow Experimental
0
0,005
0,01
0,015
0,02
0,025
0,03
0,035
0,04
0 5 10 15 20
Pro
bab
ilit
y d
ensi
ty f
un
ctio
n
Bed height (cm)
Levenspiel Gidaspow Experimental
0
0,002
0,004
0,006
0,008
0,01
0,012
0 5 10 15 20
Pro
bab
ilit
y d
ensi
ty f
un
cito
n
Bed height (cm)
Levenspiel Gidaspow Experimental
52
Figure 21. Equivalent bubble diameter as a function of bed height.
As mentioned before, the simulation and the experimental data showed the same trend of
increasing bubble diameter as the bed height rises. However there is a discrepancy between the
mean bubble diameters predicted by the simulation and the experimental data. As figure 4.7 shows,
both models overpredict mean bubble diameter at low heights and present a maximum bubble
diameter well below the experimental bed height. This comes as a consequence of the inability of
the model to predict accurately the bed expansion. Nevertheless the maximum bubble diameter
predicted by the Gidaspow model is close to the experimental value. According to Hulme [67] the
choice of volume fraction cutoff value is important since it defines the bubble boundary. High cutoff
values (> 0.3) overpredict bubble diameter especially at low heights. Most authors use a cutoff
value of 0.3 which was also used for this work [23-25]. But Hulme uses a value of 0.2 which seems
to fit the experimental more accurately.
Figure 22. Equivalent bubble diameter as a function of bubble diameter.
0
0,5
1
1,5
2
2,5
3
0 5 10 15 20
Mea
n B
ub
ble
Dia
met
er (
cm)
Height (cm)
Gidaspow
Levenspiel
Experimental
20
25
30
35
40
45
50
0,5 1,5 2,5 3,5 4,5 5,5 6,5
Bu
bb
le r
ise
velo
city
(cm
/s)
Bubble diameter (cm)
Experimental Gidaspow Levenspiel
53
As seen in Figure 4.8, the bubble rise velocity was examined at averaged bubble diameters. It is
evident that the velocities obtained from the experimental and simulations differ from each other.
The bubble rise velocity profile predicted by the Gidaspow model is approximately 20 cm/s faster
than the experimental velocity. On the other hand, the Levenspiel model seems to fit better the
experimental data. The nonsphericity of particles may have added additional drag force which
would result in lower velocities. Nonetheless the model still presents considerable deviations from
the experimental data at bubble diameter between 2 and 4 cm. The reason of these deviations is
unclear but the wider particle size distribution from the experimental work may have contributed
to the discrepancy [67]. As a conclusion, the Gidaspow and Levenspiel model are quite similar and
thus, predict the same behavior for the fluidized bed. However particle sphericity does affect the
bubble rise velocity and velocity profiles. This implies that any successful drag coefficient model
applied for nonspherical particles like biomass, plastics or tyre particles should consider this effect.
Additionally, the discrepancy between experimental and computational results can be attributed to
the following analysis. Considering that tyre particles present low density (950 kg/m3) with small
particle size (420 μm), they are in the transition state between Geldart A and Geldart B particles.
Wang [90] reported that Standard Eulerian model fails to predict the hydrodynamics of fluidized
beds for Geldart A particles. Mesoscale structures (bubbles/clusters) have different length and time
scales that cannot be fully captured by the simulations due to computational limitations. Normally
coarse grids are used to reduce the computational time but they fail to resolve for all the
spatiotemporal structures and the bed expansion is not predicted correctly [91]. In addition
standard drag coefficient models neglect the inter-particle cohesive effect due to Van der Waals
forces as well as the effect of mesoscale structures on the drag force [63, 90, 92]. Wang [90] gives a
state-of-the-art review of the most used strategies to overcome this issue. Among them there are
two main strategies that may be applied to bubbling fluidization of tyre particles. The use of scaling
factors and modification to the drag force correlation based on the experimental minimum
bubbling velocity. Both strategies attempt to modify the drag correlation model in order to fit the
experimental data. As explained by Ye et al. [93] even though scale factors may yield better results
regarding solid fraction and axial velocities; this method is case-sensitive and hence, its range of
applicability is limited to each specific scenario. Likewise the modification of the drag correlation
model presents certain limitations when applied for different bed materials [90]. For these reasons
the application of Euler-Lagrangian models to accurately predict the hydrodynamics of a fluidized
bed is highly desirable even at the expense of computational cost. Moreover the comparison
between the 2D experimental and simulation presents a special difficulty regarding similitude. The
54
experimental and computational model have indeed geometric similitude. However the kinematic
similitude is questionable for several reasons: first the air distribution inside the experimental
model is not completely uniform. There are small dead zones at the inlet particularly near the
reactor walls where bubble growth is inhibited. Furthermore the inlet velocity is measured before
the windbox so the velocity at the distribution plate is uncertain. Second the extra dimension of the
pseudo two dimensional model affects the overall behavior inside the reactor. This comes from the
observation that solid flow pattern differs from the front to the back of the reactor. Considering that
the kinematic similitude remains unproven, the dynamic similitude is not obtained. A correction to
the velocity computed from the simulation is essential as the kinematic and dynamic similitude are
not obtained.
4.3. Pressure drop versus superficial velocity
The minimum fluidization velocity was determined experimentally using the procedure presented
in Section 3.1.4 for three different bed heights (5, 8 and 10 cm). Three experimental runs were
performed for each bed height to provide better estimation of the pressure drop. It was observed
that small variations on the experimental conditions influences the absolute pressure drop
measured by the sensor (although the pressure drop remained unaffected). As seen in Figure 4.9
the pressure drop exhibits a sinusoidal waveform at sufficient long times. The origin of this
waveform is not known since this behavior was also observed when the bed height is empty. It may
be an effect of the gas passing through the marbles or the oscillations caused by the compressor. It
should be pointed out that the frequency of the waveform changed when the system was restarted.
Figure 23. Measured pressure drop at z = 10 cm, U = 0.3 m/s.
150
170
190
210
230
250
270
290
310
330
350
0 200 400 600 800 1000 1200 1400 1600
Pre
ssu
re d
rop
(P
a)
Time (s)
55
Figure 4.10 shows the pressure drop versus superficial velocity at three different bed heights. At
low velocities the pressure drop is virtually the same for all three cases. But for higher velocities the
pressure drop increases significantly for the larger beds. During the experiments, it was observed
than the fluidization started at a superficial velocity around 0.3 m/s. At this stage the first bubbles
started to rise to the surface and the bed surface expanded notably. However the maximum bed
expansion was obtained at a velocity of 0.36 m/s, when the bed surface changes rapidly and
bubbles rise to the surface in a constant manner. This leads to the conclusion that the fluidization
presented two regimes, the first one was likely to be the intermediate homogeneous regime,
characteristic to Geldart A particles, where the drag force counterbalance the gravitational and
frictional forces. The second regime was the bubbling regime, where bed expansion ceases, bubbles
form and move upward to the bed surface. Therefore the velocity value of 0.3 and 0.36 would be the
minimum fluidization velocity and minimum bubbling velocity respectively. On the other hand,
According to Kunii & Levenspiel [11], the expected pressure drop is 𝑊 𝐴𝑡⁄ , at which point it is said
that all solids eventually fluidize. The measured pressure drop is close to this value for each bed
height. The discrepancy between the values can be attributed to the wide distribution of particle
size during the experimental setup. Figure 3.5 shows microscopic images of tyre particles used for
the experiments. It is clear that most scrap tyre particles presented a cylindrical shape with a length
many times larger than its width. It is suspected that the width was short enough for the particles
to pass through the coarsest sieves but with an overall particle size larger than the mesh used in the
sieve.
Figure 24. Experimental pressure drop versus superficial velocity curves.
0
50
100
150
200
250
300
350
400
0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40
Pre
ssu
re d
rop
(P
a)
Superficial gas velocity (m/s)
H = 5 cm
H = 8 cm
H = 10 cm
W/At (5 cm)
W/At (8 cm)
W/At (10 cm)
56
In addition three dimensional simulations were used to estimate the pressure drop using only the
Gidaspow model since both drag models predict similar values of mean pressure drop. The mean
pressure drop obtained from the simulation is quite similar to the theorical value expected from a
fluidized bed which is 399.8 Pa. Furthermore the simulated and calculated pressure drop is
relatively close to the experimental value at a fluidized state. The simulated and experimental
pressure drop present a difference of approximately 5%. It is worthwhile to notice that the
distribution plate may produce gas jets and particle agglomeration (which may also increase due to
electrostatic build up). These dead zones causes that not all particles are fluidized which decreases
the measured pressure drop [8]. Additionally the 3D simulations were run at different initial
superficial gas velocities in order to obtain the pressure drop versus velocity curve.
Figure 25. Three dimensional isosurfaces at void fraction of 0.3 and void fraction contours at four consecutive time instants.
As observed in Figure 4.12, the simulated pressure drop from the simulations did not change
significantly at different inlet velocities. According to Taghipour [63] pressure drop cannot be
estimated at velocities below the minimum fluidization velocity since the dominant forces in a
unfluidized bed are interparticle and frictional forces. These forces are not well predicted in the
standard Eulerian-Eulerian model. Furthermore Teaters [8] reports that FLUENT does not have the
capacity of predicting correctly the pressure drop in a unfluidized bed. The author performed a
parametric study in the unfluidized regime, changing five key parameters: Solids packing limit,
frictional viscosity model, frictional packing limit, drag model and packed bed model. It was
57
concluded that none of these parameters affect significantly the pressure drop in a unfluidized bed
regime and thus, “FLUENT does not capture the complex physics of a densely packed bed as is
characteristic of the unfluidized regime” [8]. On the other hand, other authors [8, 68, 94] have
used the MFIX (Multiphase Flow with Interphase eXchanges) code to accurately estimate the
pressure drop in an unfluidized bed regime. A major difference between FLUENT and MFIX is the
inclusion of a solid-solid momentum exchange term in the momentum balance of the solids, which
depends on the restitution coefficient, frictional coefficient between particles and radial
distribution function. For future works regarding fluidization using the Eulerian-Eulerian model, it
would be advisable to consider different CFD codes and their applicability in the problem at hand.
Figure 26. Comparison of experimental and simulated pressure drop for H = 10 cm.
4.4. Frequency analysis
Pressure drop from the experimental and three dimensional simulations was analyzed using the
Fast Fourier Transform (FFT), which allows the data to be analyzed in the frequency domain.
Power spectrum densities are used to identify dominant frequencies that are related to bubbling
phenomena inside the fluidized bed reactor. Looking at Figure 4.13 the discrepancies between
experimental and computational data are notorious. The experimental power spectrum shows a
peak at the lowest frequency possible, which was around 0.58 mHz. This can be attributed to the
low frequency sinusoidal wave formed during the experimental trials (see figure 4.9). Moreover the
sample rate of the pressure sensor was not fast enough to fully capture the dominant frequencies of
the fluidized beds. Therefore signal aliasing caused that most dominant frequencies to be aliased in
the low frequency bins, which explains the high peak. According to Ommen [95] sampling rate
0
50
100
150
200
250
300
350
400
450
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40
Pre
ssu
re d
rop
(P
a)
Superficial gas velocity (m/s)
Experimental
3D Simulation
58
should be at least 20 Hz considering that most of energy density is below 10 Hz. On the other hand
the simulated power spectrum densities present a pattern where the largest peaks are located at
low frequencies (below 10 Hz). Power density seems to spread at larger frequencies as the velocity
increases. As pointed out by Lirag & Littman [96], the frequency is related to bubble coalescence,
which in turn depends on inlet velocities. Higher velocities lead to faster ascending bubbles, which
would eventually coalescence at the bed surface. Finally the highest peaks obtained from the
simulations were compared to the natural frequency of the bed, which is given by [89]:
𝑓𝑒 =
1
𝜋√𝑔
𝐻𝑚𝑓 (55)
The natural frequency of the bed is 3.15 Hz for the bed considered in this work. The dominant
frequency for the simulations were 2.0568, 4.6 Hz and 3.13 at U = 0.2, 0.3 and 0.4 m/s respectively.
All the frequency values are close to the theoretical value however the highest velocity showed the
closest agreement to this value. Nonetheless it remains a matter of study the applicability of
equation 55 for gas-solid fluidization for Geldart A particles.
59
Figure 27. Normalized power spectrum density of experimental (top left) and computational results, U = 0.2 m/s (top
right), U = 0.3 m/s (bottom left), U = 0.4 m/s (bottom right).
60
5. Conclusions and recommendations
The hydrodynamics of scrap tyre particles in a fluidized bed in two and three dimensions was
investigated using computational fluid dynamics and compared with experimental data. In order to
accomplish this two experimental cold models were constructed: a pseudo two dimensional model,
where the characteristics of bubbles could be examined properly and a three dimensional cold
model in which the pressure drop was measured at different velocities and bed heights. The
commercial software ANSYS Fluent was used to simulate the gas solid fluidization using an
Eulerian-Eulerian model the kinetic theory of granular flow. The two dimensional simulations were
used to compare two drag coefficient models: the Gidaspow model and the Haider-Levenspiel
model. It was concluded that neither of these drag models could accurately model the
hydrodynamics of tyre particles since the particle behave like Geldart A particles. By comparing
bubble frequency, bubble diameter, bed expansion and bubble rise velocity it was determined that
both models overpredict both bubble diameter and bubble rise velocity while underpredicting bed
expansion. Only bubble frequency appears to be comparable with the experimental findings. In
addition the joint probability density distribution was estimated using bivariate copulas. It was
observed that the correlation between bubble diameter and bed height is relatively low due to wide
distribution of bubble diameter along bed height. In addition bubble diameter distribution at low
diameters (1 cm) is broader in the experiments than in the simulation. This may be due to cohesive
forces by Van der Waals forces or electrostatic build that prevented bubbles to grow properly. On
the other hand the mean pressure drop from three dimensional simulations calculated is close to
the experimental measurements at fluidized state which is encouraging. Nevertheless the minimum
fluidization velocity could not be predicted properly using three dimensional simulations. The lack
of prediction can be attributed to an intrinsic issue regarding standard Eulerian-Eulerian models to
model gas-solid fluidization with Geldart A particles. Drag coefficient modifications are needed to
improve the capacity of prediction of these models. Particularly to correct for the intermediate
homogeneous regime observed for Geldart A particles. In addition it was observed that the
inclusion of nonsphericity in the drag model did not improve significantly the prediction capacities
of the models, although the bubble rise velocity seems to yield better results when considering
particles as nonspherical. Furthermore it was observed that the restitution coefficient and
specularity coefficient do not have a significant effect on the simulation. At bubbling regime it
seems that the bubbling phenomena is dominated primarily by gas-particle interaction. Further
studies are required to study the behavior of the parameters at different regimes. Finally in-house
developed code using Matlab was developed to capture the most relevant bubble characteristics
61
like bubble diameter and bubble velocity. This digital image analysis technique can be used as post-
processing tool for both experimental and computational works regarding bubble characterization
For future work, it is suggested the use of more sophisticated drag coefficient models to fully
capture the dynamics of gas-solid fluidization. These models should be especially tuned to Geldart A
particles and especially for low density particles. An alternative is the use of Euler-Lagrangian
models that reported successful results for these kind of particles [90]. One is most important
consideration would be the equilibrium between accurate results and computational time.
Furthermore the use of other codes such as MFIX should be compared with the commercial ANSYS
Fluent as it has been reported than other CFD codes are capable of predicting pressure drop in
unfluidized state[8]. The use of turbulence models should also be considered especially for three
dimensional simulations as turbulence is a three dimensional phenomena in itself. On the other
hand Particle Image Velocimetry is an interesting option to measure the solid phase velocity in the
bed and compare the results with simulations. As reported by Laverman, better results can be
obtained if PIV measurements are combined with image analysis. Finally a pressure sensor with a
faster sample rate would be appropriate to compare pressure fluctuations and dominant frequency
from the experimental and computational findings. In this way a full CFD model that correctly
predicts the hydrodynamics of a gas-solid fluidized bed could be obtained.
62
Bibliography
[1] P. T. Williams, "Pyrolysis of waste tyres: A review," Waste Management, vol. 33, pp. 1714-1728, 8// 2013.
[2] J. D. Martínez, N. Puy, R. Murillo, T. García, M. V. Navarro, and A. M. Mastral, "Waste tyre pyrolysis – A review," Renewable and Sustainable Energy Reviews, vol. 23, pp. 179-213, 7// 2013.
[3] U. N. E. Programme, "Revised technical guidelines on environmentally sound management of used tyres ", Brazil2008.
[4] A. Gulzad, "Recycling and pyrolysis of scrap tire," Slovak University of Technology in Bratislava Bratislava2011.
[5] E. Aylón, A. Fernández-Colino, M. V. Navarro, R. Murillo, T. García, and A. M. Mastral, "Waste Tire Pyrolysis: Comparison between Fixed Bed Reactor and Moving Bed Reactor," Industrial & Engineering Chemistry Research, vol. 47, pp. 4029-4033, 2008/06/01 2008.
[6] N. Antoniou and A. Zabaniotou, "Features of an efficient and environmentally attractive used tyres pyrolysis with energy and material recovery," Renewable and Sustainable Energy Reviews, vol. 20, pp. 539-558, 4// 2013.
[7] R. Murillo, A. Aranda, E. Aylón, M. S. Callén, and A. M. Mastral, "Process for the Separation of Gas Products from Waste Tire Pyrolysis," Industrial & Engineering Chemistry Research, vol. 45, pp. 1734-1738, 2006/03/01 2006.
[8] L. Teaters, "A Computational Study of the Hydrodynamics of Gas-Solid Fluidized Beds," Master in Sciences, Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2012.
[9] D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Chicago, Illinois: Academic Press, Inc., 1994.
[10] A. Haider and O. Levenspiel, "Drag coefficient and terminal velocity of spherical and nonspherical particles," Powder Technology, vol. 58, pp. 63-70, 5// 1989.
[11] D. Kunii and O. Levenspiel, Fluidization Engineering, 2nd ed ed. Stoneham, MA: Butterworth-Heinemann, 1991.
[12] N. P. Franka, "Visualing fluidized bed with X-rays," Master of Science, Mechanical Engineering, Iowa State University, Ames, Iowa, 2008.
[13] J. M. Paiva, C. Pinho, and R. Figueiredo. (2004, The influence of the distributor plate on the bottom zone of a fluidized bed approaching the transition from bubbling to turbulent fluidization. Chemical Engineering Research and Design 82, 25-33.
[14] B. Abdelgawad, "Design of a gas-solid fluidized bed reactor at high temperature and high pressure," Master in Sciences, Chemical Engineering, Université de Montréal, Montreal, 2013.
[15] M. Wormsbecker, T. S. Pugsley, and H. Tanfara, "The Influence of Distributor Design on Fluidized Bed Dryer Hydrodynamics," in The 12th International Conference on Fluidization - New Horizons in Fluidization Engineering, Brooklyn, USA, 2007, pp. 815-822.
[16] D. Escudero Guevara, "Bed height and material density effects on fluidized bed hydrodynamics " Master of Science, Mechanical Engineering, Iowa State University, Ames, Iowa, 2010.
[17] J. R. Grace, B. Leckner, J. Zhu, and Y. Cheng, "Fluidized beds," in Multiphase Flow Handbook, C. Crowe, Ed., ed Boca Raton, FL: Taylor & Francis Group, 2006, pp. 292-385.
[18] L. C. González Susatama, "Construcción de una planta piloto para secado de café por lecho fluidizado," Master in Sciences, Ingenieria Agricola, Universidad Nacional de Colombia, Bogotá, Colombia, 2014.
63
[19] N. Hilal, M. T. Ghannam, and A. M. Z. (2001, Effect of Bed Diameter, Distrubutor and Inserts on Minimum Fluidization Velocity. WILEY-VCH Verlag GmbH, 24, 161-165.
[20] C. A. S. Felipe and S. C. S. Rocha, "Prediction of minimum fluidization velocity of gas–solid fluidized beds by pressure fluctuation measurements — Analysis of the standard deviation methodology," Powder Technology, vol. 174, pp. 104-113, 5/25/ 2007.
[21] K. Papadikis, "Computational modelling of the fast pyrolysis of biomass in bubbling fluidised bed reactors," Doctor of Philosophy, School of Engineering & Applied Science, Aston University, Birmingham, 2009.
[22] A. Busciglio, G. Vella, G. Micale, and L. Rizzuti. (2008, Analysis of the bubbling behaviour of 2D gas solid fluidized beds Part I. Digital image analysis technique. 140, 398-413.
[23] A. Busciglio, G. Vella, and M. Giorgio, "Measurement of Multiphase Flow Characteristics Via Image Analysis Techniques: The Fluidization Case Study," in Hydrodynamics: Theory and model, Z. Jinhai, Ed., ed: InTech, 2012, p. 318.
[24] L. Shen, F. Johnsson, and B. Leckner, "Digital image analysis of hydrodynamics two-dimensional bubbling fluidized beds," Chemical Engineering Science, vol. 59, pp. 2607-2617, 7// 2004.
[25] T. W. Asegehegn, M. Schreiber, and H. J. Krautz, "Investigation of bubble behavior in fluidized beds with and without immersed horizontal tubes using a digital image analysis technique," Powder Technology, vol. 210, pp. 248-260, 7/10/ 2011.
[26] K.-L. Lam, A. O. Oyedun, K.-Y. Cheung, K.-L. Lee, and C.-W. Hui, "Modelling pyrolysis with dynamic heating," Chemical Engineering Science, vol. 66, pp. 6505-6514, 12/15/ 2011.
[27] A. Gulzad, "Recycling and pyrolysis of scrap tire," Slovak University of Technology Bratislava2011.
[28] G. Mazloom, F. Farhadi, and F. Khorasheh, "Kinetic modeling of pyrolysis of scrap tires," Journal of Analytical and Applied Pyrolysis, vol. 84, pp. 157-164, 2009.
[29] E. Aylón, M. S. Callén, J. M. López, A. M. Mastral, R. Murillo, M. V. Navarro, et al., "Assessment of tire devolatilization kinetics," Journal of Analytic and Applied Pyrolysis, vol. 74, pp. 259-264, 2005.
[30] J. Conesa, I. Martin-Gullón, R. Font, and J. Jauhiainen, "Complete Study of the Pyrolysis and Gasification of Scrap Tires in a Pilot Plant Reactor," Environmental Science & Technology, vol. 38, pp. 3189-3194, 2004.
[31] R. Aguado, M. Olazar, D. Vélez, M. Arabiourrutia, and J. Bilbao, "Kinetics of scrap tyre pyrolysis under fast heating conditions," Journal of Analytic and Applied Pyrolysis, vol. 73, pp. 290–298, 2005.
[32] A. Quek and R. Balasubramanian, "Mathematical modeling of rubber tire pyrolysis," Journal of Analytical and Applied Pyrolysis, vol. 95, pp. 1-13, 2012.
[33] A. Zabaniotou, J. Lagoudakis, T. E., and G. Stavropoulos, "Energetic Utilization of Used Tires," Energy Sources, vol. 24, pp. 843-854, 2002.
[34] O. Senneca, P. Salatino, and R. Chirone, "A fast heating-rate thermogravimetric study of the pyrolysis of scrap tyres," Fuel, vol. 78, pp. 1575–1581, 1999.
[35] M. Juma, Z. Koreňová, J. Markoš, J. Annus, and Ľ. Jelemenský, "Pyrolysis and combustion of scrp tyre," Petroleum & Coal, vol. 48, pp. 15-26, 2006.
[36] M. Olazar, R. Aguado, D. Vélez, M. Arabiourrutia, and J. Bilbao, "Kinetics of Scrap Tire Pyrolysis in a Conical Spouted Bed Reactor," Industrial Engineering Chemical Research, vol. 44, pp. 3914-3925, 2005.
[37] K.-Y. Cheung, K.-L. Lee, K.-L. Lam, C.-W. Lee, and C.-W. Hui, "Integrated kinetics and heat flow modelling to optimise waste tyre pyrolysis at different heating rates," Fuel Processing Technology, vol. 92, pp. 856-863, 2011.
64
[38] J. F. González, J. M. Encinar, J. L. Canito, and J. J. Rodríguez, "Pyrolysis of automobile tyre waste. Influence of operating variables and kinetics study," Journal of Analytical and Applied Pyrolysis, vol. 59, pp. 667–683, 2001.
[39] B. Lah, D. Klinar, and B. Likozar, "Pyrolysis of natural, butadiene, styrene–butadiene rubber and tyre components: Modelling kinetics and transport phenomena at different heating rates and formulations," Chemical Engineering Science, vol. 87, pp. 1 - 13, 2013.
[40] A. Quek and R. Balasubramanian, "An algorithm for the kinetics of tire pyrolysis under different heating rates," Journal of Hazardous Materials, vol. 166, pp. 126–132, 2009.
[41] B. Lah, D. Klinar, and B. Likozar, "Pyrolysis of natural, butadiene, styrene–butadiene rubber and tyre components: Modelling kinetics and transport phenomena at different heating rates and formulations," Chemical Engineering Science, vol. 87, pp. 1-13, 1/14/ 2013.
[42] K. L. Lee, K. Y. Cheung, K. L. Lam, and C. W. Hui, "Optimization of Multi-Stage Waste Tyre Pyrolysis Process," in 20th European Symposium on Computer Aided Process Engineering, Ischia, Naples, 2010.
[43] M. Olazar, G. Lopez, M. Arabiourrutia, G. Elordi, R. Aguado, and J. Bilbao, "Kinetic modelling of tyre pyrolysis in a conical spouted bed reactor," Journal of Analytic and Applied Pyrolysis, vol. 81, pp. 127–132, 2008.
[44] A. V. Bridgwater, "Review of fast pyrolysis of biomass and product upgrading," Biomass and Bioenergy, vol. 38, pp. 68 - 94, 2012.
[45] D. Meier, B. Van de Beld, A. V. Bridgwater, D. C. Elliott, A. Oasmaa, and F. Preto, "State-of-the-art of fast pyrolysis in IEA bioenergy member countries," Renewable and Sustainable Energy Reviews, vol. 20, pp. 619-641, 2013.
[46] P. T. Williams and A. J. Brindle, "Fluidised bed pyrolysis and catalytic pyrolysis of scrap tyres," Environmental Technology, vol. 24, pp. 921-929, 2003.
[47] C. Díez, O. Martínez, L. F. Calvo, J. Cara, and A. Morán, "Pyrolysis of tyres. Influence of the final temperature of the process on emissions and the calorific value of the products recovered," Waste Management, vol. 24, pp. 463-469, 2004.
[48] C. Berrueco, E. Esperanza, F. J. Mastral, J. Ceamanos, and P. García-Bacaicoa, "Pyrolysis of waste tyres in an atmospheric static-bed batch reactor: Analysis of the gases obtained," Journal of Analytic and Applied Pyrolysis, vol. 74, pp. 245-253, 2005.
[49] W. Kaminsky and C. Mennerich, "Pyrolysis of synthetic tire rubber in a fluidised-bed reactor to yield 1,3-butadiene, styrene and carbon black," Journal of Analytical and Applied Pyrolysis, vol. 58–59, pp. 803-811, 4/1/ 2001.
[50] W. Kaminsky, M. Predel, and A. Sadiki, "Feedstock recycling of polymers by pyrolysis in a fluidised bed," Polymer Degradation and Stability, vol. 85, pp. 1045-1050, 9// 2004.
[51] W. Kaminsky, C. Mennerich, and Z. Zhang, "Feedstock recycling of synthetic and natural rubber by pyrolysis in a fluidized bed," Journal of Analytical and Applied Pyrolysis, vol. 85, pp. 334-337, 5// 2009.
[52] X. Dai, X. Yin, C. Wu, W. Zhang, and Y. Chen, "Pyrolysis of waste tires in a circulating fluidized-bed reactor," Energy, vol. 26, pp. 385-399, 2001.
[53] E. Aylón, A. Fernández-Colino, R. Murillo, G. Grasa, M. V. Navarro, T. García, et al., "Waste tyre pyrolysis: Modelling of a moving bed reactor," Waste Management, vol. 30, pp. 2530-2536, 12// 2010.
[54] M. Olazar, R. Aguado, M. Arabiourrutia, G. Lopez, A. Barona, and J. Bilbao, "Catalyst Effect on the Composition of Tire Pyrolysis Products," Energy & Fuels, vol. 22, pp. 2909-2916, 2008.
[55] M. Suhanya, M. Thirumarimurugan, and T. Kannadasan, "Recovery of oil from waste tyres using pyrolysis method: a review," International Journal of Research in Engineering & Technology, pp. 81-90, 2013.
65
[56] S. Karthikeyan, C. Sathiskumar, and R. Srinivasa, "Effects of process parameters on tire pyrolysis: a review," Journal of Scientific & Industrial research, vol. 71, pp. 309-315, 2012.
[57] Q. Cao, L. E. Jin, W. R. Bao, and Y. K. Lu, "Factors Influencing the Quality of Pyrolytic Oil from Used Tires," Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, vol. 30, pp. 833-841, 2008/03/27 2008.
[58] O. Senneca, P. Salatino, and R. Chirone, "A fast heating-rate thermogravimetric study of the pyrolysis of scrap tyres," Fuel, vol. 78, pp. 1575-1581, 10// 1999.
[59] A. Oyedun, K.-L. Lam, M. Fittkau, and C.-W. Hui, "Optimisation of particle size in waste tyre pyrolysis," Fuel, vol. 95, pp. 417-424, 5// 2012.
[60] M. A. van der Hoef, M. Ye, M. van Sint Annaland, A. T. Andrews, S. Sundaresan, and J. A. M. Kuipers, "Multiscale Modeling of Gas-Fluidized Beds," in Advances in Chemical Engineering. vol. Volume 31, B. M. Guy, Ed., ed: Academic Press, 2006, pp. 65-149.
[61] M. Hamzehei, "Study of Hydrodynamics and Heat Transfer in the Fluidized Bed Reactors," in Heat Transfer: Mathematical Modelling, Numerical Methods and Information Technology, A. Belmiloudi, Ed., ed. Ahvaz, Iran: Intech, 2011, pp. 332-382.
[62] T. W. Asegehegn, M. Schreiber, and H. J. Krautz, "Numerical Simulation of Dense Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model," in Computational Simulations and Applications, ed. Cottbus, Alemania: Intech, 2011, pp. 235-258.
[63] F. Taghipour, N. Ellis, and C. Wong. (2005, Experimental and computational study of gas-solid fluidized bed hydrodynamics. Chemical Engineering Science 60, 6857–6867. Available: http://www.researchgate.net/profile/Naoko_Ellis/publication/235997787_Experimental_and_computational_study_of_gassolid_fluidized_bed_hydrodynamics/links/0046351e9efa4176f8000000.pdf
[64] Y. Behjat, S. Shahhosseini, and S. H. Hashemabadi, "CFD modeling of hydrodynamic and heat transfer in fluidized bed reactors," International Communications in Heat and Mass Transfer, vol. 35, pp. 357-368, 3// 2008.
[65] N. Xie, F. Battaglia, and S. Pannala, "Effects of using two- versus three-dimensional computational modeling of fluidized beds: Part I, hydrodynamics," Powder Technology, vol. 182, pp. 1-13, 2/15/ 2008.
[66] B. Halvorsen, "An Experimental and Computational Study ofFlow Behaviour inBubbling Fluidized Beds," Doctor in Engineering, Department of Technology, The Norwegian University of Science and Technology, Porsgrunn, Norway, 2005.
[67] I. Hulme, E. Clavelle, L. van der Lee, and A. Kantzas, "CFD Modeling and Validation of Bubble Properties for a Bubbling Fluidized Bed," Industrial & Engineering Chemistry Research, vol. 44, pp. 4254-4266, 2005/06/01 2005.
[68] M. Deza, N. P. Franka, T. J. Heindel, and F. Battaglia, "CFD Modeling and X-Ray Imaging of Biomass in a Fluidized Bed," Journal of Fluids Engineering, vol. 131, pp. 111303-111303, 2009.
[69] J. Lundberg, "CFD study of a bubbling fluidized bed," Master in Sciences, Faculty of Technology, Telemark University College, Porsgrunn, Norway, 2008.
[70] A. Hölzer and M. Sommerfeld, "New simple correlation formula for the drag coefficient of non-spherical particles," Powder Technology, vol. 184, pp. 361-365, 6/2/ 2008.
[71] G. H. Ganser, "A rational approach to drag prediction of spherical and nonspherical particles," Powder Technology, vol. 77, pp. 143-152, 11// 1993.
[72] C. K. K. Lun, S. B. Savage, D. J. Jeffrey, and N. Chepurniy, "Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield," Journal of Fluid Mechanics, vol. 140, pp. 223-256, 1984.
66
[73] M. Mahfoud and M. Massmann. (2012, Bivariate Archimedean copulas:an application to two stock market indices. 39. Available: http://www.few.vu.nl/nl/Images/werkstuk-mahfoud_tcm243-277460.pdf
[74] P. Bloomfield, "Copulas," in Statistics and Financial Risk, ed. Raleigh, North Carolina: North Carolina State University, 2013.
[75] K. Goda, "Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands," Structural Safety, vol. 32, pp. 112-123, 3// 2010.
[76] K. Dong, Q. Zhang, Z. Huang, Z. Liao, J. Wang, and Y. Yang, "Experimental Investigation of Electrostatic Reduction in a Gas–Solid Fluidized Bed by an in Situ Corona Charge Eliminator," Industrial & Engineering Chemistry Research, vol. 53, pp. 14217-14224, 2014/09/17 2014.
[77] D. Song, F. Salama, and P. Mehrani, "Study of Electrostatic Charging in Gas-Solid Fluidized Bed Polyethylene Reactors," in ESA Annual Meeting on Electrostatics, Cocoa beach, FL, 2013
[78] I. Ansys, "Fluent user guide, version 15.0," ed.
[79] T. Li and S. Benyahia, "Revisiting Johnson and Jackson boundary conditions for granular flows," AIChE Journal, vol. 58, pp. 2058-2068, 2012.
[80] L. M. Armstrong, K. H. Luo, and S. Gu, "Two-dimensional and three-dimensional computational studies of hydrodynamics in the transition from bubbling to circulating fluidised bed," Chemical Engineering Journal, vol. 160, pp. 239-248, 5/15/ 2010.
[81] C. Loha, H. Chattopadhyay, and P. K. Chatterjee, "Euler-Euler CFD modeling of fluidized bed: Influence of specularity coefficient on hydrodynamic behavior," Particuology, vol. 11, pp. 673-680, 12// 2013.
[82] I. ANSYS. (2009). Ansys Fluent 12.0: UDF manual. Available: http://orange.engr.ucdavis.edu/Documentation12.0/120/FLUENT/fludf.pdf
[83] J. D'Errico, "A suite of minimal bounding objects," Version 2 ed: The MathWorks, Inc., 2012. [84] S. Cloete, J. Cloete, S. T. Johansen, and S. Amini, "The parametric sensitivity of fluidized bed
simulations carried out in different flow regimes," presented at the 10th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries, Trondheim, Norway, 2014.
[85] J. A. Laverman, I. Roghair, M. v. S. Annaland, and H. Kuipers, "Investigation into the hydrodynamics of gas–solid fluidized beds using particle image velocimetry coupled with digital image analysis," The Canadian Journal of Chemical Engineering, vol. 86, pp. 523-535, 2008.
[86] I. Hulme and A. Kantzas*, "Validation of Bubble Properties of a Bubbling Fluidized Bed Reactor Using CFD with Imaging Experiments," Polymer-Plastics Technology and Engineering, vol. 44, pp. 73-95, 2005/01/01 2005.
[87] J. Wang, M. A. van der Hoef, and J. A. M. Kuipers, "CFD study of the minimum bubbling velocity of Geldart A particles in gas-fluidized beds," Chemical Engineering Science, vol. 65, pp. 3772-3785, 6/15/ 2010.
[88] J. Li, "Euler-Lagrange simulation of flow structure formation and evolution in dense gas-solid flows," Ph. D, University of Twente, Enschede, Netherlands, 2002.
[89] A. Acosta-Iborra, C. Sobrino, F. Hernández-Jiménez, and M. de Vega, "Experimental and computational study on the bubble behavior in a 3-D fluidized bed," Chemical Engineering Science, vol. 66, pp. 3499-3512, 8/1/ 2011.
[90] J. Wang, "A Review of Eulerian Simulation of Geldart A Particles in Gas-Fluidized Beds," Industrial & Engineering Chemistry Research, vol. 48, pp. 5567-5577, 2009/06/17 2009.
67
[91] J. Wang, M. A. van der Hoef, and J. A. M. Kuipers, "Why the two-fluid model fails to predict the bed expansion characteristics of Geldart A particles in gas-fluidized beds: A tentative answer," Chemical Engineering Science, vol. 64, pp. 622-625, 2// 2009.
[92] S. Zimmermann and F. Taghipour, "CFD Modeling of the Hydrodynamics and Reaction Kinetics of FCC Fluidized-Bed Reactors," Industrial & Engineering Chemistry Research, vol. 44, pp. 9818-9827, 2005/12/01 2005.
[93] M. Ye, J. Wang, M. A. van der Hoef, and J. A. M. Kuipers, "Two-fluid modeling of Geldart A particles in gas-fluidized beds," Particuology, vol. 6, pp. 540-548, 12// 2008.
[94] S. K. Kanholy, "Eulerian-Eulerian Modeling of Fluidized Beds," Ph. D, Mechanical Engineering Department, Virginia Polytechnic Institute and State University Blacksburg, Virginia, 2014.
[95] J. R. van Ommen, S. Sasic, J. van der Schaaf, S. Gheorghiu, F. Johnsson, and M.-O. Coppens, "Time-series analysis of pressure fluctuations in gas–solid fluidized beds – A review," International Journal of Multiphase Flow, vol. 37, pp. 403-428, 6// 2011.
[96] R. C. Lirag and H. Littman, "Statistical study of the pressure fluctuations in a fluidized bed," Rensselaer Polytechnic Institute, Troy, New York.
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APPENDIX A: MATLAB CODE FOR FINDING BUBBLE PROPERTIES
function [Area_R,Centroids_R] = Burbujas(i,filtro,F2)
% Algoritmo de detección de burbujas % Entradas de la función: % i = Valor del segundo asociado a la imagen. % filtro = Valor para filtro de area de burbujas, si el area es menor al
filtro se desprecia dicha burbuja.
Nombre = strcat('D:\Tesis Maestria\Version Corregida
(Final)\2D_Gida_Caso1\Caso1-',num2str(i),'.bmp'); Imagen1 = imread(Nombre);
H = 754; %Altura 676-1-u L = 155; %longitud 135-1-u Xmin = 381; %Posición X - Inicial 453-1-u Ymin = 38; %Posición Y - Inicial 16-1-u
Zone = [Xmin Ymin L H]; IM1 = imcrop(Imagen1,Zone); IM2 = rgb2gray(IM1); IM3 = imadjust(IM2,[0.1 0.7],[]);
IM4 = im2bw(IM3, graythresh(IM3));
V_RGB(1,:) = [0,10]; V_RGB(2,:) = [30,F2]; V_RGB(3,:) = [160,255];
F1 = +(IM1(:,:,1) >= V_RGB(1,1) & IM1(:,:,1) <= V_RGB(1,2)); F2 = +(IM1(:,:,2) >= V_RGB(2,1) & IM1(:,:,2) <= V_RGB(2,2)); F3 = +(IM1(:,:,3) >= V_RGB(3,1) & IM1(:,:,3) <= V_RGB(3,2));
Im_bin = F1.*F2.*F3;
lnoise = 0.1; filt_images = bpass(Im_bin,lnoise); LS = im2bw(filt_images); [B,L] = bwboundaries(filt_images,'noholes'); [BW1, threshold] = edge(filt_images, 'Canny'); fudgeFactor = 0.1; BWs = edge(BW1,'Canny', threshold * fudgeFactor);
se90 = strel('line', 1, 50); se0 = strel('line', 1, 0); BWsdil = imdilate(BWs, [se90 se0]); BWdfill = imfill(BWsdil, 'holes'); BWnobord = imclearborder(BWdfill, 8);
property = regionprops(BWnobord, 'Centroid'); property2 = regionprops(BWnobord, 'Area'); property3 = regionprops(BWnobord, 'Boundingbox');
69
centroids = cat(1, property.Centroid); Area = cat(1, property2.Area); BB = cat(1, property3.BoundingBox);
Factor = 0.1/152; %m/Pixels Cont = 1;
AR = BB(:,4)./ BB(:,3);
for i = 1:length(Area) if Area(i,1) > filtro if AR(i) > 0.3 Area_2(Cont,1) = Area(i,1); Area_R(Cont,1) = Area(i,1).*Factor^2; Centroids_2(Cont,1) = centroids(i,1); Centroids_2(Cont,2) = centroids(i,2); Centroids_R(Cont,1) = centroids(i,1).*Factor; Centroids_R(Cont,2) = (H-centroids(i,2)).*Factor; Cont = Cont+1; end end end
figure, imshow(IM1) hold on for i = 1:length(B) Boundary = cell2mat(B(i,:)); plot(Boundary(:,2),Boundary(:,1),'r') hold on end
labels = cellstr(num2str([1:length(Centroids_2)]')); plot(Centroids_2(:,1),Centroids_2(:,2),'g*') text(Centroids_2(:,1),Centroids_2(:,2), labels, 'VerticalAlignment','bottom',
... 'HorizontalAlignment','right')
end
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APPENDIX B: UDF IMPLEMENTATION IN ANSYS
