Post on 03-Oct-2014
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CN4118R: B.Eng. Dissertation
Semester 1 AY 2010-2011
Coal Gasification for Clean Energy: A Simulation
Study of the Downer and the Solids Distributor.
Submitted in Partial Fulfillment for the degree in Bachelor of Engineering,
National University of Singapore
By
Jayadev S Marol
U070448E
Supervisor: Professor Wang Chi-Hwa
Date of Submission: 3rd January 2011
ACKNOWLEDGEMENTS
Firstly, I would like to express my sincere gratitude to my supervisor, Professor Wang
Chi-Hwa for providing me with the golden opportunity to work on this project and
uncovering my interest in multiphase flows. He has been a great source of motivation and
I would like to thank him for providing me with valuable ideas and suggestions during
the monthly meetings.
Secondly, I am highly indebted to my assigned mentor, Dr Cheng Yongpan who has
patiently helped me with my modeling and related queries. I would also like to extend my
acknowledgement to Dr Eldin Lim for the healthy discussions and guidance on my
project. Thanks to all others who were part of Professor Wang Chi-Hwa’s research group
for helping me whenever I needed their assistance. It was a wonderful experience
working with them.
I would also like to thank my parents for providing me with the necessary moral support
and encouragement without which the completion of this thesis may not have been
possible.
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Summary
Hydrodynamic simulation of the gas-solid flow in the downer was carried out using both
the Eulerian-Eulerian and Eulerian-Lagrangian models. In using the Eulerian-Eulerian
appraoch, solids were modeled as pseudo-fluid using the Kinetic Theory of Granular
Flow and the main focus was to investigate the most suitable drag closure for various
flow conditions. Three different drag closures by Wen &Yu, De Felice and Matsen were
tested. Firstly, the axial distribution of the solids concentration in the downer was
simulated and compared with available experimental data in literature. The commonly
used Wen & Yu’s drag closure gave simulation results that were comparable with
experimental data under high superficial gas velocity flow conditions but the solids
holdup values were severely over-predicted at low gas velocity. Matsen’s drag closure
was found to give a much better solid holdup prediction compared to the other two drag
closures under low superficial gas velocity. Secondly, the radial distribution of the solids
concentration was compared. The nature of the radial solid holdup profile predicted by
Matsen’s drag closure was also different compared to the other two drag closures. Wen &
Yu’s and De Felice’s drag closure predicted a maximum concentration at the wall, similar
to the experimental results by Cao and Weinstein (2000). Matsen’s drag closure predicted
that the peak of the solids holdup at the wall gradually moves towards the center with the
magnitude of the peak decreasing in the fully developed region of the downer. These
simulation results are consistent with experimental results by Zhang et al (1999).
Simulation results using the Eulerian-Lagrangian method were consistent with the
Eulerian-Eulerian model with the Wen & Yu’s drag closure.
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As the flow in the downer is assisted by gravity, there is short contact time between the
phases in the downer (Cheng, Wu, Zhu, Wei, & Jin, 2008). This short contact time
imposes a demand on the downer inlet design to enable good mixing of the phases. Thus
two inlet designs have been proposed and consequently the sand and coal flow patterns
are investigated in efforts to innovate new inlet designs which provide better mixing.
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Contents Page
Summary ............................................................................................................................. 1
Chapter 1: Introduction ................................................................................................... 5
Objective ............................................................................................................................. 7
Chapter 2: Literature review of the downer .................................................................... 8
2.1 The flow structure in the downer .............................................................................. 9
2.2 The Axial solids concentration distribution profile. ................................................ 10
2.3 Correlations to predict the solids concentration in the fully developed region of the downer. .......................................................................................................................... 11
2.4 The radial solids concentration distribution profile ................................................ 12
Chapter 3: Modeling the hydrodynamics of the downer .............................................. 16
3.1.1 Eulerian–Eulerian method .................................................................................... 17
3.1.2 Equations used in the Eulerian-Eulerian model ................................................... 18
3.2 Eulerian-Lagrangian method ................................................................................... 25
3.2.1 Equations used in Eulerian- Lagrangian Method ................................................. 25
Chapter 4: Procedures for Simulation ........................................................................... 27
4.1 Geometry and Meshing ........................................................................................... 27
4.2 Operating conditions and boundary conditions ....................................................... 28
4.3 Solution Procedures................................................................................................. 30
Chapter 5: Simulation results & Validation of the Eulerian-Eulerian Model .............. 32
5.1 Wen & Yu’s Drag Closure ...................................................................................... 32
5.1.1 Axial distribution of the solids concentration ................................................... 32
5.1.2 Axial distribution of the solids velocity ........................................................... 37
5.1.3 Effect of particle diameter, particle density and downer diameter on model simulation. ................................................................................................................. 38
5.2 Improvements to the model using various drag correlations .................................. 41
5.3 De Felice’s drag closure .......................................................................................... 42
5.4 Matsen’s drag closure .............................................................................................. 43
5.5 Radial distribution of solids concentration .............................................................. 46
Chapter 6: Validation of the Eulerian-Lagrangian model ............................................ 49
6.1 Residence time of particles . ................................................................................... 49
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6.2 Axial velocity distribution of particles. ................................................................... 51
6.3 Radial velocity distribution of particles .................................................................. 53
Chapter 7: Solids distributor and Inlet design of the downer ....................................... 55
7.1 Proposed Inlet Designs ............................................................................................ 59
7.2 Modeling Approach and simulation conditions ...................................................... 60
7.3 Simulation results .................................................................................................... 63
7.3.1 Axial Solid distribution .................................................................................... 63
7.3.2 Radial Solid distribution ................................................................................... 66
Chapter 8: Conclusion .................................................................................................. 69
Chapter 9: Recommendations and Future Work .......................................................... 71
References ......................................................................................................................... 73
Nomenclature ....................................................................................................................... i
List of Figures .................................................................................................................... iii
List of Tables ...................................................................................................................... v
I. Appendix A : Axial solids velocity distribution profiles ............................................ vi
II. Appendix B: Experimental Data for the downer solid holdup for the Gs=253 kg/m2s by Guan et al (2010) ........................................................................................................ viii
III. Appendix C: Comparison of the average solids hold up for the two inlet arrangements with Ug=20 m/s. ........................................................................................... ix
IV. Appendix D: Radial distribution of the solids at various axial positions for the two inlet arrangements. .............................................................................................................. x
Tangential arrangement ............................................................................................... x
Normal arrangement .................................................................................................. xii
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Chapter 1: Introduction
Coal is and in the foreseeable future will be a considerable source of fuel for power
generation but there has been increasing need for clean coal power generation and a
constant search for processes that have higher efficiency (Hanson.S, Patrick, &
Walker.A, 2002). Thus instead of conventional coal fired power plants, combined-cycle
fluidized-bed gasification systems are now emerging technologies that offer a promising
clean way to convert coal into electricity, hydrogen and other valuable energy products
(Guan, Chihiro, Ikeda, Yu, & Tsutsumi, 2009). In the current project, a Triple-bed
Combined Circulating Fluidized (TCFB) bed system is being considered for the coal
gasification process and the setup of the system is shown in the following figure 1.1.
Figure 1.1: Triple bed Circulating Fluidized Bed (Guan G. , Chihiro, Ikeda, Yu, & Tsutsumi, 2009).
As shown above, the triple-bed combined circulating fluidized bed is mainly composed
of a downer, a bubbling fluidized bed and a riser. The coal is rapidly pyrolyzed in the
downer first and the obtained gas and tar are separated from the char using a gas-solids
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separator. The char then enters the bubbling fluidized bed (BFB) to be gasified with
steam (Guan G. , Chihiro, Ikeda, Yu, & Tsutsumi, 2009). The unreacted char can then be
channeled to the riser to be combusted with air. The produced heat from the combustion
can then be carried by inert solid medium such as sand and circulated into the downer and
BFB to provide the heat needed for pyrolysis and gasification process (Guan G. , Chihiro,
Ikeda, Yu, & Tsutsumi, 2009) .The cyclone is placed after the riser to separate the solids
from the air and the solids then enter the solids distributor to ensure that solids are well
distributed before they enter the downer (Guan, Chihiro, Ikeda, Yu, & Tsutsumi, 2009).
Essentially in a triple bed reactor, the pyrolysis reaction is carried out in the downer, the
gasification reaction in the BFB and char combustion in the riser. This method of
compartmentalizing the various reactions into various specific reactors helps to improve
the overall coal gasification efficiency.
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Objective
The purpose of the research group is to model the flow in the triple bed circulating bed
which would help to study the flow patterns and to optimize the process. The research is
still in the initial stages and thus the objective of this thesis is to study the flow in the
downer and the solids distributor component of the TCFB system. Numerical simulations
of the downer hydrodynamics were conducted to predict the solids concentration and the
velocity profiles and the results have been validated with the experimental data available
from literature and from the experimental work of Guan et al, our partner research group
from University of Tokyo. Eulerian-Eulerian and Eulerian-Lagrangian models have been
used to model the hydrodynamics of the downer system. In the Eulerian-Eulerian model,
which has been used to a greater extent in this thesis, the effect of various drag closures
has been studied. Once a model with decent predictive capabilities has been established,
the model could then be used for optimization purposes.
Furthermore when conducting a primary study on various designs of the inlet structures,
it is neither efficient nor economical to study the flow fields experimentally. Therefore
this thesis also aims to illustrate that numerical simulation can be used as powerful tool to
study flow behaviors in the various geometries before making huge experimental
investments. Essentially, the effect of tangential inlet design and the normal inlet design
on the sand and coal holdup in the downer has been studied in this thesis using the
Eulerian- Eulerian Model.
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Chapter 2: Literature review of the downer
Fluidization technique has been developed for more than several decades and previously
in conventional gas-solids flows, the particles are suspended by up flowing gas streams,
against the flow of gravity, such as in bubbling fluidized beds, turbulent fluidized bed and
risers (Cheng, Wu, Zhu, Wei, & Jin, 2008). Though the up flowing gas streams do
provide some benefits such as better inter-phase contact, it also leads to some setbacks
such as heterogeneous flow structure and significant back mixing of the phases (Cheng,
Wu, Zhu, Wei, & Jin, 2008). The overall performance of fluidized beds approaches that
to a continuous stirred tank reactor and limits improvement in some specific processes.
Thus the concept of a downer reactor was proposed and has attracted much attention in
the industry which can be seen by the numerous patents owned by major oil companies.
In a downer reactor, the gas and solids move downwards co-currently, in the direction of
gravity. This allows for a much more uniform gas-solid flow with less gas-solid back
mixing in the downer system (Ropelato, Meier, & Cremasco, 2005). Thus the flow
regime in the downer rector approaches that of a plug –flow reactor (Lehner & Wirth,
1999), (Qi, Zhang, & Zhu, 2008). Furthermore as the flow is now assisted by gravity, the
solids would be flowing at high velocity and this leads to lower residence time of the
components in the reactor (Jian & Ocone, 2003). These properties of the downer are
essentially beneficial for short contact time processes such as solids waste pyrolysis,
high-selectivity fluidized catalytic cracking, flash pyrolysis of coal and biomass where
intermediate products are favored (Qi, Zhang, & Zhu, 2008).
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2.1 The flow structure in the downer
The flow structure can be divided into three sections according to the pressure profile in
the downer. At the entrance, the solid particles are accelerated by gravity and gas drag,
causing the pressure in the flow direction to drop (Liu, Luo, Zhu, & Beeckmans, 2001).
As the particle velocity increases and becomes equal to the gas velocity, the gas drag
acting on the particles become zero (Wang, Bai, & Jin, 1992). The pressure gradient at
this point becomes minimum and the pressure gradient is zero (Wang, Bai, & Jin, 1992).
The section from the inlet to this point marks the first acceleration section of the downer
(Wang, Bai, & Jin, 1992). After this section, the particles will still be accelerating due to
gravity and the particle velocity will exceed that of the gas velocity. The direction of the
gas drag becomes upward and the pressure increases gradually in the flow direction
(Johnston, Lasa, & Zhu, 1999 ). This stage is called the second acceleration stage and the
pressure gradient is greater than zero. In the third section, the velocity difference
between the particles and the gas velocity continues to increase until the drag force
becomes equal to the gravitational force. The particles will stop accelerating and particle
velocity will level off (Wang, Bai, & Jin, 1992). This constant velocity section is also
termed as the fully developed region (Liu, Luo, Zhu, & Beeckmans, 2001). The pressure
gradient is positive and constant as pressure continuously increases in the direction of the
flow (Wang, Bai, & Jin, 1992). The typical pressure profile of the downer is shown in
figure 2.1 below.
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Figure 2.1: Pressure profile in a downer for Gs=202 kg/m2s and Ug=5 m/s.
2.2 The Axial solids concentration distribution profile.
Studies carried out have shown that the gas and solids flow is more uniform in the
downer then in the riser. The particle acceleration in the first two sections of the downer
results considerable dilution of the solids concentration and the solid holdup eventually
reaches the constant value in the fully developed region (Bolkan, Berruti, Zhu, & Milne,
2003). A typical solid concentration distribution profile in the downer is shown below in
figure 2.2.
Figure 2.2 : Solids concentration distribution profile in the downer for Gs =202 kg/m2s and Ug=5 m/s.
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2.3 Correlations to predict the solids concentration in the fully developed region of the downer.
Previously, most of the correlations to predict the solid hold up in the fully developed
region of the downer were based on the “terminal solids concentration, ε’s , where
𝜀𝑠′ = 𝐺𝑠𝜌𝑔�𝑈𝑔+𝑈𝑡�
(1)
The equation above is based on the assumption that there is no particle agglomeration and
that of a uniform dispersion of particles in the downward gas flow (Qi, Zhang, & Zhu,
2008)
However many experimental results have showed that particle-clustering phenomenon
exists in the fully developed region of the downer and it cannot be neglected. Qi et al
(2008) considered the effects of the particle properties and various operating conditions
with different downer diameters to propose the following correlation,
𝜀𝑠∗ = 0.125 � 𝐺𝑠𝜌𝑝�𝑈𝑔+𝑈𝑡�
� � 𝑈𝑔�𝑔𝑑𝑝
�0.25
𝐴𝑟0.15 (2)
The predictions of the correlation above fitted well with experimental data obtained from
literature for low density downers (Qi, Zhang, & Zhu, 2008). For high-density downers
(εs > 0.07) the following correlation proposed by Guan et al (2010) could be used to
predict the solid concentrations in the fully developed region.
𝜀𝑠∗ = 0.104 (𝐺𝑠
𝜌𝑝�𝑈𝑔𝑑 + 𝑈𝑡�)0.56(
𝑈𝑔𝑑 + 𝑈𝑡
�𝑔𝐷)0.14𝐴𝑟0.155 (3)
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2.4 The radial solids concentration distribution profile
There is yet to be a universal agreement on the nature of the radial profile of the solids
phase in the downer (Vaishali, Roy, & Mills, 2008). Different research groups have
presented different nature of radial solid hold up profiles. The experimental results by the
FLOTU group (Bai et al 1992; Wang et al 1992) reveal that the solids concentration
exhibits a peak near the wall region. In contrast, Cao and Weinstein (2000) claimed that
downer exhibits a maximum concentration at the wall itself. Experimental results by
Zhang et al (1999) seem to suggest that the initially the solids concentration is the
maximum at the wall and as the L/D ratio increases, the peak of the solid concentration
moves gradually towards the center with the magnitude of the peak decreasing.
The figure 2.3 below shows the radial solids concentration distribution as presented by
Wang et al (1992).
Figure 2.3 : Radial solids concentration profile (Wang, Bai, & Jin, 1992).
The figure above reveals that the radial concentration in the downers is generally uniform
but an annular region of high solids concentration exists near the wall of the downer. The
solids concentration increases with the increasing solids flux at all radial positions but the
increment is larger in the annular dense region (Wang, Bai, & Jin, 1992). When the gas
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velocity increases at fixed solids flux, the radial solids concentration is said to become
more uniform (Wang, Bai, & Jin, 1992).
Wang et al (1992) have attributed the nature of the radial solids concentration above to
the minimization of the energy loss in a gas-solid suspension flow. In the center region,
the gas velocity is relatively high and thus the drag force acting on the solid particles is
larger (Kimm, Berruti, & Pugsley, 1996). This motivates the particles to move away from
center towards the wall region in order to lose less energy (Wang, Bai, & Jin, 1992),
(Kimm, Berruti, & Pugsley, 1996). Likewise the friction between the gas-solid
suspension and the wall causes the particles to move away from the wall region in order
to avoid losing more energy (Kimm, Berruti, & Pugsley, 1996). As a result of these two
opposing trends, an annular region of high solids concentration near the wall with a
uniform concentration at the center is formed. (Wang, Bai, & Jin, 1992).
In contrast to the experimental results from Wang et al (1992), Cao and Weinstein (2000)
claimed that downer exhibits a maximum concentration at the wall. The figure 2.4 below
shows the radial solid concentration profile obtained in their experiments.
Figure 2.4: Radial solids concentration profile (Cao & Weinstein, 2000).
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A possible reason for the difference in the radial solid holdup profiles obtained could be
attributed to the different measuring equipment used by Cao and Weinstein as compared
to Wang et al (1992). An optical fiber solid concentration probe was used by Wang et al
(1992) whereas an X-ray imaging system was used by Cao and Weinstein (2000) to
measure the radial solids concentration profile. Nevertheless the solids fraction measured
away from the wall show similar profiles in most of the works and it is only the
concentration at the wall that is not in agreement.
Zhang et al (1999) did a study of the radial profiles of the solid holdup under 11 different
operating conditions and they measured the radial solids distribution using optic fiber
solid concentration probe at 8 different axial positions. The results obtained are presented
in figure 2.5 below (Zhang, Zhu, & Bergougnou, 1999).
Figure 2.5 : Radial solids concentration profile, (Zhang, Zhu, & Bergougnou, 1999).
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From the experimental results above, it can be seen that the radial solid hold up is
initially fluctuating due the ‘solids distributor’s effect at about 0.020 m ( (Zhang, Zhu, &
Bergougnou, 1999). Slightly below the entrance at about 0.5 m, the solid concentration
tends to peaks at the wall. However as the L/D ratio increases, the radial profiles start to
become more uniform. The peak of the solids holdup seems to gradually move towards
the center with the magnitude of the peak decreasing (Zhang, Zhu, & Bergougnou, 1999).
Thus the experimental results of the Zhang et al (1999) might seem to suggest that the
solids concentration peaks at the wall when the flow is still in the developing zone and
further down the downer, the peak tends to shift towards the center of the wall. The
results also indicate that the nature of the solids holdup is not fixed throughout the
downer.
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Chapter 3: Modeling the hydrodynamics of the downer
Numerical methods have been broadly used to study particle–fluid flow in the recent
years. Modeling the gas-solids flow in the downer system is essentially a multiphase flow
problem. The main constraint that lies in the modeling of the downer reactor is the large
separation of scales (Hoef, Annaland, Deen, & Kuipers, 2008). The flow structure which
is in the order of meters is influenced by the interactions of the gas and solid particles that
are well below the millimeter scale (Hoef, Annaland, Deen, & Kuipers, 2008) .
In modeling the multiphase flow, the dynamics of each of the phase can be can modeled
via either considering the phase as a collection of discrete particles that obey Newton’s
law that requires a Lagrangian approach or via treating the solid phase as a continuum
that is governed by Navier-Stokes type equation which requires Eulerian approach (Hoef,
Annaland, Deen, & Kuipers, 2008). The hydrodynamics in the downer can thus be
simulated using the Eulerian- Eulerian model or the Eulerian-Lagrangian model. The
main difference between these two models depends on the treatment of the solid phase
which is treated either as a continuum phase or as a discrete particle.
Numerical simulations can be carried out using computational fluid dynamics software.
ANSYS FLUENT is one such commercial software that contains the broad physical
modeling capabilities needed to model multiphase flow, turbulence, heat transfer, and
reactions for various industrial applications. FLUENT will be used to model and analyze
the flow and performance of the downer systems for both the Eulerian-Eulerian approach
and the Eulerian-Lagrangian approach.
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3.1.1 Eulerian–Eulerian method
In the Eulerian-Eulerian approach, both the gas phases and the solid phase are allowed to
exist at the same point and at the same time forming an interpenetrating continuum
(Vaishali, Roy, & Mills, 2008).
Figure 3.1: Modeling the interaction between solid and gas phase (Vaishali, Roy, & Mills, 2008).
As shown in Figure 3.1, modeling the downer system needs to take into account the
interactions within and between the flow fields as well as the fluctuations flow fields of
each phase (Vaishali, Roy, & Mills, 2008). The interaction between particle mean motion
and the gas mean motion is incorporated by the drag force correlations. The relation
between the gas fluctuating motion and the gas mean motion is modeled using the
appropriate κ-Є turbulence models. Kinetic Theory of Granular Flow is used to relate the
interaction between the random particle fluctuating motion and the mean particle motion.
In this theory, solid-phase stresses are described in a manner similar to the stresses in
dense-gas kinetic theory whereby the fluctuating kinetic energy of solid is represented by
the term ‘granular temperature’(Θs) (Cheng, Wei, Guo, & Yong, 2001), (Vaishali, Roy, &
Mills, 2008). Other solid phase transport properties such as the solid phase pressure and
solid stresses are also described in terms of granular temperature. (Vaishali, Roy, &
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Mills, 2008). One possible drawback of this approach is that the predictive ability of the
model depends very much on the correctness and tuning of the closures proposed for
indeterminate terms.(Cheng, Wei, Guo, & Yong, 2001). In the present work, the
interaction between the fluctuating fields of the gas phase and solid phase is not
considered as it is expected to be a correlation of a much lower order as compared to the
other three interactions (Vaishali, Roy, & Mills, 2008).
3.1.2 Equations used in the Eulerian-Eulerian model
Continuity Equation
𝜕(𝜀𝑘𝜌𝑘)𝜕𝑡
+ ∇. (𝜀𝑘𝜌𝑘𝑢𝑘����⃗ ) = 0 (4) 𝑘 = 𝑓 𝑓𝑜𝑟 𝑓𝑙𝑢𝑖𝑑𝑘 = 𝑠 𝑓𝑜𝑟 𝑠𝑜𝑙𝑖𝑑
Conservation of momentum
For fluid phase
𝜕(𝜀𝑓𝜌𝑓𝑢𝑓����⃗ )𝜕𝑡
+ ∇. �𝜀𝑓𝜌𝑓𝑢𝑓����⃗ .𝑢𝑓����⃗ � = −𝜀𝑓∇p + ∇.𝑇�𝑓 + 𝜀𝑓𝜌𝑓�⃗� + 𝐾𝑠𝑓�𝑢𝑠����⃗ − 𝑢𝑓����⃗ � (5)
Note that in the equation above p is pressure shared by all the phases and Ksf is the gas-
solid momentum exchange co-efficient.
𝑇�𝑓 is the fluid phase stress-strain tensor which takes the following form
𝑇�𝑓 = 𝜀𝑓µ𝑓�∇𝑢𝑓����⃗ + ∇𝑢𝑓����⃗𝑇� + 𝜀𝑓 �𝜆𝑓 −
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µ𝑓� ∇.𝑢𝑓����⃗ 𝐼 ̿ (6)
Where µf and λf is the fluid shear and bulk viscosity.
For solid phase
𝜕(𝜀𝑠𝜌𝑠𝑢𝑠����⃗ )𝜕𝑡
+ ∇. (𝜀𝑠𝜌𝑠𝑢𝑠����⃗ .𝑢𝑠����⃗ ) = −𝜀𝑓∇p − ∇ps + ∇.𝑇�𝑠 + 𝜀𝑠𝜌𝑠�⃗� + 𝐾𝑠𝑓�𝑢𝑓����⃗ − 𝑢𝑠����⃗ � (7)
𝑇�𝑠 is the solid phase stress-strain tensor which takes the following form
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𝑇�𝑠 = 𝜀𝑠µ𝑠�∇𝑢𝑠����⃗ + ∇𝑢𝑠����⃗𝑇� + 𝜀𝑠 �𝜆𝑠 −
23
µ𝑠� ∇.𝑢𝑠����⃗ 𝐼 ̿ (8)
Where µs and λs is the solids shear and bulk viscosity.
Compared to the fluid phase momentum equation, it can be seen that there is an extra
solid pressure term, ps, in the equation above. Details can be found in the paragraphs that
follow.
Constitutive equations
The gas-solid momentum exchange co-efficient, Ksf
The interaction of prime importance in the downer reactions is that of the mean flow field
of the gas phase and the mean flow fields of the solids phase which is stated as the ‘drag’
interaction in figure 3.1. The drag force in the downer system depends on the slip
velocity (absolute difference between the mean gas phase velocity and solid phase
velocity) and the local solids concentration (Vaishali, Roy, & Mills, 2008). There has
been several momentum exchange coefficient that have been proposed based on
experiments and fine scale simulations (Vaishali, Roy, & Mills, 2008). Three of such
momentum exchange coefficients are shown below.
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Table 1: Various gas-solid momentum transfer coefficients
Reference Gas-solid momentum exchange coefficient, Ksf
Wen & Yu’s closure (1966) 𝐾𝑠𝑓 =
34𝐶𝐷
𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�µ𝑔
𝜀𝑓−2.65 (9)
Where
𝐶𝐷 =24
𝜀𝑓𝑅𝑒𝑝�1 + 0.15(𝜀𝑓𝑅𝑒𝑝)0.687� (10)
𝑅𝑒𝑝 =𝜌𝑔𝑑𝑝�𝑢𝑠 − 𝑢𝑓�
µ𝑓 (11)
Matsen’s closure (1982)
𝐾𝑠𝑓 = 0.006475𝐶𝐷𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�
µ𝑔𝜌𝑔𝜌𝑚𝑖𝑥
𝜀𝑠−0.586 (12)
Where
𝐶𝐷 =24
𝜀𝑓𝑅𝑒𝑝�1 + 0.15(𝜀𝑓𝑅𝑒𝑝)0.687� (13)
Di Felice’s closure (1994)
𝐾𝑠𝑓 =34𝐶𝐷𝜀𝑓2𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�𝜀𝑓−𝜂 (14)
Where
𝐶𝐷 =1𝜀𝑓
(0.63 + 4.8�1𝑅𝑒𝑝
)2 (15)
𝜂 = 3.7 − 0.65𝑒(− �1.5−log�𝑅𝑒𝑝�
2�2 ) (16)
The solid pressure term, ps.
For granular flows in the compressible regime (where the solids volume fraction is less
than its maximum allowed value), a solids pressure is calculated independently and used
for the pressure gradient term,∇ps , in the solids/ granular phase momentum equation
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(equation 7). ( ANSYS FLUENT, 2006) (Lun, B., J., & Chepurniy, 1984), (Cheng, Wei,
Guo, & Yong, 2001).
𝑝𝑠 = 𝜀𝑠𝜌𝑠𝛩𝑠 + 2𝜌𝑠(1 + 𝑒𝑠𝑠)𝜀𝑠2𝑔𝑜,𝑠𝑠𝛩𝑠 (17)
The solids pressure equation above consists of the kinetic term and a second term due to
particle collisions. The term ess refers to the coefficient of restitution for particle-particle
collisions which is assigned to be 0.9 and the term go,ss refers to the radial distribution
function which is a correction factor that modifies the probability of collisions between
particles when the solid granular phase becomes dense ( ANSYS FLUENT, 2006). This
function may also be interpreted as the non-dimensional distance between spheres and it
takes the following form for one solids phase ( ANSYS FLUENT, 2006), (Cheng, Wei,
Guo, & Yong, 2001).
𝑔𝑜,𝑠𝑠 = �1 − (𝜀𝑠
𝜀𝑠,𝑚𝑎𝑥)13�−1
(18)
Where εs,max is the maximum packing limit of the particles which is assigned to be 0.63.
The solids shear viscosity and bulk viscosity term
The solids stress tensor contains shear and bulk viscosities arising from particle
momentum exchange due to translation and collision. The solids shear viscosity term is
comprised of the collisional, kinetic and frictional parts as shown in the equation below
(Gidaspow, 1994)
µ𝑠 = µ𝑠,𝑘𝑖𝑛 + µ𝑠,𝑐𝑜𝑙 + µ𝑠,𝑓𝑟𝑖𝑐 (19)
The frictional component, µ𝑠,𝑓𝑟𝑖𝑐, neglected in this work.
22
The expression for kinetic viscosity term,µ𝑠,𝑘𝑖𝑛, is derived by (Syamlal, Rogers, &
O’Brien, 1993) to be
µ𝑠,𝑘𝑖𝑛 = 𝜀𝑠𝑑𝑠𝜌𝑠�𝛩𝑠𝜋6(3 − 𝑒𝑠𝑠)
�1 +25
(1 + 𝑒𝑠𝑠)(3𝑒𝑠𝑠 − 1)𝜀𝑠𝑔𝑜,𝑠𝑠� (20)
The collisional part of the viscosity, µ𝑠,𝑐𝑜𝑙, is modeled as follows (Syamlal, Rogers, &
O’Brien, 1993)
µ𝑠,𝑐𝑜𝑙 =45𝜀𝑠𝑑𝑠𝜌𝑠𝑔𝑜,𝑠𝑠(1 + 𝑒𝑠𝑠)(
𝛩𝑠𝜋
)12 (21)
The bulk viscosity, 𝜆𝑠, term appearing in equation 8 has the following form as described
by (Lun, B., J., & Chepurniy, 1984)
𝜆𝑠 =43𝜀𝑠𝑑𝑠𝜌𝑠𝑔𝑜,𝑠𝑠(1 + 𝑒𝑠𝑠)(
𝛩𝑠𝜋
)
12
(22)
The granular temperature term
The granular temperature for the solids phase is proportional to the kinetic energy of the
random motion of the particles. The transport equation derived from kinetic theory of
granular flow and takes the following form (Ding & Gidspow, 1990).
32�𝜕(𝜀𝑠𝜌𝑠𝛩𝑠)
𝜕𝑡+ ∇. (𝜀𝑠𝜌𝑠𝑢𝑠����⃗ 𝛩𝑠)� = �−𝑝𝑠𝐼 ̿+ 𝜏�̿��:∇𝑢𝑠����⃗ + ∇. �𝑘𝛩𝑠∇𝛩𝑠� − 𝛾𝛩𝑠 + 𝛷𝑓𝑠 (23)
Where
�−𝑝𝑠𝐼 ̿+ 𝜏�̿��:∇𝑢𝑠����⃗ refers to the generation of energy by the solids tensor.
𝑘𝛩𝑠∇𝛩𝑠 refers to the diffusion of energy (𝑘𝛩𝑠 being the diffusion coefficient) which under
the Syamlal model has the following form (Syamlal, Rogers, & O’Brien, 1993).
𝑘𝛩𝑠∇𝛩𝑠 =15𝜀𝑠𝑑𝑠𝜌𝑠�𝛩𝑠𝜋4(41 − 33𝛹)
(1 +125𝛹2(4𝛹 − 3)𝜀𝑠𝑔𝑜,𝑠𝑠 +
1615𝜋
(41 − 33𝛹)𝛹𝜀𝑠𝑔𝑜,𝑠𝑠 (24)
23
Where
𝛹 =12
(1 + 𝑒𝑠𝑠) (25)
𝛾𝛩𝑠 refers to the collisional dissipation of energy and takes the following form derived by
Lun et al (1984).
𝛾𝛩𝑠 = 12(1 − 𝑒𝑠𝑠2)𝑔𝑜,𝑠𝑠
𝑑𝑠√𝜋𝜌𝑠𝜀𝑠2𝛩𝑠
32 (26)
and
𝛷𝑓𝑠 refers to the energy exchange between the fluid phase and the solid phase represented
by
𝛷𝑓𝑠 = −3𝐾𝑠𝑓𝛩𝑠 (27)
Thus in applying the equations, a value for granular temperature term, 𝛩𝑠, is needed. It
can be done by either assuming a constant granular temperature when the system is dense
or by algebraic formulation of the transport equations by neglecting the diffusion and
convection term ( ANSYS FLUENT, 2006). Algebraic formulation method to determine
the granular temperature term was used in this thesis.
κ-Є turbulence model
In order to account for the turbulent fluctuations in the gas–mean motion, dispersed κ -Є
turbulence model is adopted.
𝛿(𝜀𝑓𝜌𝑓𝜅𝑓)𝛿𝑡
+ ∇. �𝜀𝑓𝜌𝑓𝑢𝑓����⃗ 𝜅𝑓� = ∇.�𝜀𝑓µ𝑡,𝑓𝜎𝜅
∇𝜅𝑓� + 𝜀𝑓𝐺𝑘,𝑞 − 𝜀𝑓𝜌𝑓Є𝑓 + 𝜀𝑓𝜌𝑓П𝜅𝑓 (28)
24
𝛿(𝜀𝑓𝜌𝑓Є𝑓)𝛿𝑡
+ ∇. �𝜀𝑓𝜌𝑓𝑢𝑓����⃗ Є𝑓�
= ∇.�𝜀𝑓µ𝑡,𝑓𝜎Є
∇Є𝑓� + 𝜀𝑓Є𝑓𝜅𝑓
(𝐶1Є𝜀𝑓𝐺𝑘,𝑞 − 𝐶2Є𝜌𝑓Є𝑞 + 𝜀𝑓𝜌𝑓ПЄ𝑓 (29)
Where κ is turbulent kinetic energy and Є is the dissipation rate.
The source terms П𝜅𝑓 and ПЄ𝑓 represent the influence of the dispersed sand and coal
phase on the continuous air phase. The term 𝐺𝑘,𝑞 represents production of the turbulent
kinetic energy and the term µ𝑡,𝑓refers to turbulent viscosity. 𝜎Є and 𝜎𝜅 are the turbulent
Prandtl numbers for Є and κ respectively. 𝐶1Є and 𝐶2Є are constants in the κ-Є turbulence
model taking the values 1.44 and 1.92 respectively ( ANSYS FLUENT, 2006).
Thus in summary, the Eulerian –Eulerian model set up is based on the following
1) A single pressure is shared by all the phases
2) Momentum and continuity equations are solved for each phase.
3) Granular temperature (solids fluctuating energy) can be calculated for each solid
phase.
4) Solid-phase shear and bulk viscosity are evaluated by applying kinetic theory of
granular flow.
5) Various types of Inter phase drag coefficients are available to account for the
interaction between the mean flow field of the gas phase and the solids phase
6) κ- Є turbulence model is applied to account for the turbulent fluctuations of the gas
mean velocity.
25
3.2 Eulerian-Lagrangian method
In the Eulerian-Lagrangian approach, the solid phase is treated as discrete particles and is
modeled by calculating the path of each individual particle with the Newton’s second law
(Cheng, Wei, Guo, & Yong, 2001). The advantage of using this approach is that each
particle’s trajectory can be displayed exactly. However since large number of trajectories
are need in order to determine the average behavior of the system, this approach can be
computationally expensive.
3.2.1 Equations used in Eulerian- Lagrangian Method
The fluid phase is treated as a continuum by solving the time-averaged Navier-Stokes
equations as presented in the Eulerian- Eulerian model (equations 4 and 5 ), while the
dispersed phase is solved by tracking a large number of particles in the flow-field. Only
equations used for the motion of particles are listed below.
𝑑𝑢𝑠𝑑𝑡
= 𝐹𝑑�𝑢𝑓 − 𝑢𝑠� + 𝑔𝑥 �𝜌𝑠 − 𝜌𝑓𝜌𝑠
� (30)
The equation above is written for the x-coordinate and can be extended to other co-
ordinates likewise.
𝐹𝑑�𝑢𝑓 − 𝑢𝑠� is the drag force per unit particle mass and Fd takes the following form
𝐹𝑑 =18µ𝜌𝑠𝑑𝑠
2𝐶𝑑𝑅𝑒𝑝
24 (31)
26
Two –way turbulence coupling
Similar to the Eulerian-Eulerian method, the standard κ-Є turbulence model is used to
account for the turbulent fluctuations in the gas–mean motion. While the continuous
phase always impacts the discrete phase, it is also possible to incorporate the effect of the
discrete phase trajectories on the continuum in the FLUENT software. This two-way
coupling is accomplished by alternately solving the discrete and continuous phase
equations until the solutions in both phases have stopped changing ( ANSYS FLUENT,
2006).
27
Chapter 4: Procedures for Simulation
FLUENT 6.3 and/or FLUENT 12 was used for all the simulations in this thesis. For small
or medium sized jobs that require less than 30 minutes to compute, the simulations were
run on a laptop with Windows Vista 32-bit dual core processor and 4 gigabyte RAM. For
large jobs (especially for unsteady state Eulerian- Lagrangian and Eulerian-Eulerian
models), parallel computing was done in a high performance computing portal to speed
up computation time.
4.1 Geometry and Meshing
In the first part of the thesis, a two-dimensional model of a downer with an internal
diameter of 0.1 m and a length of 9.3 m was used to simulate a two phase flow (a solid
phase and a fluid phase). The two-dimensional geometry was created in GAMBIT which
is a preprocessor to FLUENT. The model was formed via bottom-up approach whereby
vertices were first created and the relevant vertices were joined to form edges. The edges
were finally linked to form a face before the geometry is meshed.
Meshing involves the discretization of the model into smaller volumes and is a crucial for
the finite volume method to be accurate. The smaller the volume the more accurate the
results would be but at the cost of more computational time. Thus there is a trade-off
between accuracy and computational time. A simple meshing analysis was done to
minimize computational time and maximize accuracy. With that analysis, a grid size of
15 (radial) x 750 (axial) was deemed sufficient. The figure 4.1 below shows part of the
layout of the meshed geometry. It is oriented horizontally for better viewing of the
meshes.
28
Figure 4.1 : Layout of the meshed geometry of the downer.
4.2 Operating conditions and boundary conditions
The meshed geometry was then exported to FLUENT. The boundary and operating
conditions were then introduced. Since the predicted solids concentration and particle
velocity were to be compared with the experimental data conducted by Bolkan et al
(2003), the particle properties were applied as presented in the journal. The table below
shows the particle properties and the operating conditions used in the simulation.
Table 2: Operating conditions for the 2D model
Operating Conditions Value
Pressure (Pa) 101325 at the outlet
Gravity (m2/s) 9.81 downwards
Gas properties
Density (kg/m3) 1.225
Viscosity (Pa.s) 1.7894 x 10-5
Particle Properties
Density (kg/m3) 1500
Shape Sphere
Diameter (µm) 67
Downer Properties
Length (m) 9.3
Diameter (m) 0.1
29
Boundary conditions
The following figure below shows the boundary conditions stated at respective sections
of the model.
Figure 4.2 : Boundary conditions for the 2D Model.
Wall boundary condition
For the wall boundary condition when using the Eulerian-Eulerian approach, a no-slip
condition was specified for the fluid phase and for the solids phase, a shear force is stated
which takes the following form,
𝜏𝑠 = −𝜋6 √
3Ϛ𝜀𝑠
𝜀𝑠,𝑚𝑎𝑥𝜌𝑠𝑔𝑜,𝑠𝑠�𝛩𝑠�𝑢𝑠����⃗ ‖ (33)
Where �𝑢𝑠����⃗ ‖ particle slip velocity parallel to the wall and ζ represents the specularity
coefficient between the particle and the wall. As used by Vaishali et al (2008), a
specularity co-efficient of 0.5 was used.
30
For the wall boundary condition when using the Eulerian-Lagrangian approach, a no slip
condition was specified for the fluid phase. For the solids phase, the particles were
allowed to ‘reflect’ of the wall.
Velocity inlet condition
For the velocity inlet condition when using the Eulerian-Eulerian approach, the
magnitude and the direction of the velocity together with the volume fraction each of the
phases is stated.
For the velocity inlet condition when using the Eulerian-Lagrangian approach, the
magnitude and the direction of the velocity for the fluid phase is stated. For the solid
phase, the particles are allowed to be ‘trapped’ in the region. To state the value of the
mass flux for solids particles, “Interaction with Continuous Phase” function was enabled
under the discrete phase model and the particles were allowed to be injected from the top
surface.
Pressure outlet condition
For the pressure outlet condition when using the Eulerian-Eulerian approach, a uniform
gauge pressure of zero was stated.
For the velocity condition when using the Eulerian- Lagrangian approach, gauge pressure
of zero was stated and the discrete particles were allowed to be released and this was
indicated with the ‘escape’ condition.
4.3 Solution Procedures
The pressure–velocity coupled SIMPLE solver method was used in the iteration for the
convergence of the solution. The convergence criteria were usually set to 0.001 for all the
31
terms. To obtain more accurate results for two-dimensional steady-state models, smaller
convergence criteria of 10-5 was used. The second order UPWIND implicit differencing
scheme for the convective terms and the second-order implicit time integration method
was used to solve the motion equation of the fluid. The default under-relaxation
parameter values were used during the iteration process.
Steady-State or Transient model
Generally steady sate solver was used in the Eulerian-Eulerian approach. However at
times, it is not possible to achieve convergence using steady-state solver. Thus unsteady-
state solver with a time-step of 0.0025 was used to iterate for a time period of 5 to10
seconds to compare the simulated results with the experimental data.
32
Chapter 5: Simulation results & Validation of the Eulerian-Eulerian Model
For the first part of the thesis, the simulation results were compared with the
experimental data as presented by Bolkan et al (2003) to validate the Eulerian-Eulerian
model. Axial distribution of the solids holdup and the solids velocity are compared for
various flow conditions. Wen & Yu’s Drag closure is used in the initial simulations.
5.1 Wen & Yu’s Drag Closure
5.1.1 Axial distribution of the solids concentration
Figure 5.1: Simulation results for superficial gas velocity of 3.7 m/s.
Figure 5.1 above compares the simulation results obtained for fixed superficial gas
velocity of 3.7m/s under three different solids flux conditions (Gs =49 kg/m2s, 101
33
kg/m2s and 194 kg/m2s). Area weighted average is used to compute the mean solid
concentration at any axial position. The simulation results reveal a similar trend as the
experimental results. For all the three solids flux conditions, once the solids phase enters
the downer, acceleration of the particles causes dilution of the solid holdup. For a fixed
gas velocity, a higher solids flux would also result in a higher average solid holdup at any
axial position.
However the simulated average solid holdup values are severely over predicted compared
to the experimental data. For example, for solids flux of 49 kg/m2s, the simulated average
solids concentration at the fully developed region is about 0.0083 while the experimental
data gives a value of about 0.0055. Considerable over-prediction is also observed for the
other two solids flux scenarios. In addition, the path length taken for the solid phase to
achieve a ‘fully developed’ flow is much smaller than that compared to the experimental
data. The possible reasons for these observations are that at low superficial velocity, the
drag between the solids and the air phase is significant and the effects of particle
clustering are not effectively accounted for in the model.
34
Figure 5.2: Simulation results for superficial gas velocity of about 7 m/s.
Figure 5.2 above compares the simulation results obtained for a fixed superficial gas
velocity of about 7 m/s under three different solids flux conditions (Gs =49 kg/m2s, 101
kg/m2s and 208 kg/m2s). The model’s predicted solids concentration in the fully
developed region is in better agreement with the experimental data at a higher superficial
gas velocity. For example, for the solids flux of 49 kg/m2s, the simulated average solids
concentration in the fully developed region is about 0.0044 while the experimental result
is about 0.0039.
However, the experimental data shows a much gradual decreases in the solids
concentration along the downer while simulation results reveal a rather steep drop. Thus
the simulated length for the solids to attain fully developed flow is much shorter than the
experimental data
35
Figure 5.3: Simulation results for superficial gas velocity of about 10 m/s.
Figure 5.3 above compares the simulation results obtained for a fixed superficial gas
velocity of about 10 m/s under three different solids flux conditions (Gs =49 kg/m2s, 102
kg/m2s and 205 kg/m2s). It further validates that the model predicts the solid
concentration well under high superficial gas velocity. This is possibly because at higher
gas velocity, the particles attain a higher speed and are less likely to form clusters.
From observing figures 5.1, 5.2 and 5.3 it can be seen that for a fixed solids flux,
increasing the superficial gas velocity lowers the solid concentration. At a higher
superficial gas velocity, solid particles attain a higher speed and this causes further
dilution of the solids concentration.
36
From comparing all the simulation results above with the experimental data, it can be
seen that the model is able to predict the solids concentration distribution profile well
when a high superficial gas velocity is used. The model tends to overestimate the solid
concentration under low gas velocity and this is partially due to inability of the model to
fully account for the significant particle clustering effect at low gas velocity. Thus
improvements to the model should be made for more accurate predictions under low gas–
velocity flow conditions. Improvements were made to model by applying other drag
closures. De Felice’s and Matsen’s drag closure were tested and the latter seems to be
able to improve the model’s solid holdup prediction at low superficial gas velocity. The
results obtained for the other two closures are presented in sections 5.3 and 5.4.
37
5.1.2 Axial distribution of the solids velocity
Figure 5.4: Simulation results for solids flux of about 50kg/m2s with varying Ug.
The figure 5.4 above compares the simulated solids velocity under the three various
superficial gas velocities (3.7 m/s, 7.3 m/s and 10.1 m/s). The superficial gas velocity
tends to affect the velocity of the particles significantly.
The trend observed for the solids velocity distribution in the downer can be explained as
follows. Upon entering the downer, the particles will accelerate under the influence of
gravity and the gas drag force, causing them to pick up speed. As the speed of particles
becomes larger than the gas velocity, the gas drag becomes upward and this force starts to
oppose the gravitational force. Here the particles will be gaining speed but at a slower
rate. Once the drag force equals to that of the gravitational force, the particles will stop
38
accelerating and particle velocity will start to level off. (Wang, Bai, & Jin, 1992),
(Johnston, Lasa, & Zhu, 1999 ).
Though the simulation predicts a similar trend of the solids velocity as that of the
experimental measurements qualitatively, the values are severely under-predicted for low
superficial gas velocity condition. This is related to the observation made earlier that the
predicted solids holdup concentration are over -predicted at low gas velocity. Since
𝐺𝑠 = 𝜌𝑠𝜀𝑠𝑢𝑠 , when the model over estimates the solids concentration, it has to under
estimate the solid velocity in order to satisfy the mass conservation equation stated above.
Thus it becomes imperative that the model results for the solids velocity are linked to the
solid concentration results. If improvements are made to the model so that it is able to
better predict the solids concentrations for low gas velocity, the results for solids velocity
would tally with experimental data as well.
Similar observations were made when comparing the simulation results with the
experimental data for solids flux of about 100 kg/m2s and 200 kg/m2s with varying
superficial gas velocity. The plots obtained are presented in Appendix A.
5.1.3 Effect of particle diameter, particle density and downer diameter on model simulation.
From studying the plots above, it can be seen that the superficial gas velocity affects the
model’s accuracy more than the solids gas flux. In this section three other parameters that
are suspected to be influential are investigated of their effects on the model’s accuracy.
The three other parameters to be studied are particle diameter, particle density and
downer diameter. The equation proposed by Qi et al (2008) to predict the solids
composition in the fully developed region of the downer would be used to compare with
the results obtained by the model for various scenarios.
39
𝜀𝑠∗ = 0.125 �𝐺𝑠
𝜌𝑝�𝑈𝑔𝑑 + 𝑈𝑡���
𝑈𝑔𝑑�𝑔𝑑𝑝
�0.25
𝐴𝑟0.15 (2)
Thus in the next two graphs, a plot of εs*/ εs is plotted where εs* is the calculated solids
concentration in the fully developed region of the downer using equation (2) proposed by
Qi et al (2008). εs refers to the simulated solids concentration in the fully developed
region using the model. Thus when the value of εs*/ εs is closer to 1, it would indicate
that the model is in good agreement with the calculated value.
Figure 5.5: Model Comparison for varying Particle Diameter.
Figure 5.6: Model Comparison for varying Particle Density.
40
Figure 5.5 and 5.6 compares the model’s predictive accuracy for varying particle
diameter and particle density respectively. The two graphs reveal that the model is able to
predict the solids concentration in the fully developed region more accurately under
higher particle diameter and particle density. As particle size or density increases, clusters
are more prone to become discrete particles under higher gas velocity (Qi, Zhang, & Zhu,
2008). Thus the model being able to predict solids concentration more accurately for
increasing particle diameter and/or density with increasing gas velocity maybe related to
the model’s inability to fully account for the particle clustering phenomena.
By observing that the downer diameter term does not appear in equation (2), it can be
realized that the downer diameter does not have an influence on the solids concentration
in the fully developed region of the downer. The model reveals a similar relation as well.
It can be seen from table 3 that for varying the downer diameter from 0.05 to 0.1m and
keeping all other parameters unchanged, the 𝜀𝑠 values obtained are relatively constant.
Table 3: Model results for varying downer diameter.
Downer Diameter, m Gs, kg/m2s Ug, m/s ρp, kg/m3 dp, µm εs
0.05 49 3.7 1500 67 0.0082
0.1 49 3.7 1500 67 0.0083
0.25 49 3.7 1500 67 0.0084
0.5 49 3.7 1500 67 0.0084
41
5.2 Improvements to the model using various drag correlations
From the simulation results thus far, it has been established that the model prediction of
the solids concentration and solids velocity is good agreement to the experimental data
under high superficial gas velocity flow condition. However the model tends to
overestimate the solids concentration under low superficial gas velocity and this is
partially due to the inability of the model to fully account for the significant particle
clustering effect. Improvements to the model should be made so that more accurate
predictions can be made under low gas velocity scenarios.
Vaishalli et al (2008) have stated that gas-solid dispersed flow in the downer is complex
involving multiple modes of momentum transfer (as shown in figure 3.1). However gas-
solids’ drag is the most dominating interaction (Vaishali, Roy, & Mills, 2008). It has also
been found that considerable amount of ‘drag reduction’ occurs at the cluster formation
which results in higher slip velocity and thus cause a lower solids concentration
(Vaishali, Roy, & Mills, 2008). However the current Wen & Yu drag’s closure used in
the model is unable to account this phenomenon.
In efforts to try and improve the model under low superficial gas velocity, De Felice’s
drag closure and Matsen’s drag closure were tested and the results obtained are presented
section 5.3 and 5.4. Details and equations of the drag closures have already been
presented in Chapter 3. As these drag closures were not available in ANSYS FLUENT,
they were coded under User Defined Functions (UDF). Since it has been shown earlier
that the solids concentration and the solids velocity predictions are related by the
continuity equation, it is sufficient to ensure that the improved model is able to predict
42
the solids concentration well under low superficial velocity in the following
investigations.
5.3 De Felice’s drag closure
Figure 5.7: Simulation results using De Felice's drag closure for Ug=3.7 m/s.
From the figure above, it can be seen that the results obtained by using De Felice’s drag
closure are very similar to the Wen & Yu’s drag closure (figure 5.1). The solids
concentration profile under low superficial gas velocity is still a severe over- prediction
for the three solids flux scenarios. Thus it can be concluded that De Felice’s momentum
exchange co-efficient is in the same range as the Wen and Yu’s and it still not able to
lower the ‘gas-solids drag’ under particle clustering place. Vaishali et al (2008) have also
showed in their simulation study that the De Felice’s gas-solid momentum exchange co-
efficient is similar to the Wen & Yu’s gas-solid momentum exchange co-efficient.
43
5.4 Matsen’s drag closure
Figure 5.8: Simulation results using Matsen's Drag closure for Ug=3.7 m/s.
Figure 5.8 above shows that the simulated results using Matsen’s drag closure above
gives a much better fit to the experimental data under low gas velocity conditions. It is
also worth noting that the path length taken for the solids phase to achieve fully
developed flow is comparative to the experimental data. Thus figure 5.8 seems to suggest
that the Matsen’s drag closure is able to give a much better fit to the experimental data
under low superficial gas velocity. Vaishali et al (2008) have also showed in their
simulation study that compared to Wen & Yu’s and De Felice’s drag closure, Matsen’s
drag closures is better able to predict the solids concentration under low gas velocity.
Matsen’s drag closure predicts the slip velocity around five times that of the single
terminal velocity and this allows it to account for the ‘drag reduction’ that occurs at
44
cluster formation, eventually enabling the model to predict a lower solids concentration
(Vaishali, Roy, & Mills, 2008) .
Table 4: Comparison of various Drag coefficients
Comparing the momentum transfer expressions for the three drag closures above, it can
be seen that the nature of the Matsen’s drag co-efficient is different compared to the other
two drag closures. The solids concentration term in the Matsen’s drag closure is raised to
the power of negative 0.586 and this allows for a much lower momentum transfer co-
efficient with an increase in solids concentration. Furthermore while the initial constant
term is 0.75 for the De Felice’s and Wen & Yu’s drag closure, Matsen’s has the initial
constant term of 0.006475. These two factors enable the Matsen’s drag closure to account
for considerable amount of drag reduction at the cluster place and this finally results in
the better solids concentration prediction under low solids velocity scenarios (Vaishali,
Roy, & Mills, 2008).
To further validate the model with Matsen’s drag closure, further simulations under low
gas velocity in the range of 0.5 to 3 m/s were carried out. The simulations were
Wen & Yu’s Closure
𝐾𝑠𝑓 =34𝐶𝐷
𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�µ𝑔
𝜀𝑓−2.65 (9)
De Felice’s Closure 𝐾𝑠𝑓 =
34𝐶𝐷𝜀𝑓2𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�𝜀𝑓−𝜂 (14)
𝜂 = 3.7 − 0.65𝑒(− �1.5−log�𝑅𝑒𝑝�
2�2 ) (16)
Where
Matsen’s Closure
𝐾𝑠𝑓 = 0.006475𝐶𝐷𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�
µ𝑔𝜌𝑔𝜌𝑚𝑖𝑥
𝜀𝑠−0.586 (12)
45
compared with the experimental results obtained by Guan et al (2010) recently. The
detailed experimental results are presented in Appendix B.
Figure 5.9: Comparing simulation results under low Ug , Gs= 253 kg/m2s.
The plot above shows that the simulation results using Matsen’s drag closure is a better
fit to the experimental results than using Wen & Yu’s drag closure under low superficial
gas velocity. It can also be seen that since the solids concentration is very low, the
difference between the experimental results and the simulation results using Wen & Yu’s
drag closure is very significant. For example, at a superficial gas velocity of 1m/s, the
experimental solids concentration is about 0.02 whereas the predicted solids
concentration using Wen & Yu’ drag closure is about 0.075 which is 3.5 times more than
the experimental result.
Thus in conclusion, it has been shown that the commonly used Wen and Yu’s drag
correlation is not able to predict the solids concentration well under low gas velocity
scenarios. De Felice’s drag closure also overestimates the solids concentration under low
superficial gas velocity. Due to the different nature of the Matsen’s drag expression, it
seems to give a much better prediction of the solids concentration under low gas velocity
46
scenarios. Furthermore, Masen’s drag closure is also able to predict the path length taken
for the flow to be fully developed much better than other two drag closures.
5.5 Radial distribution of solids concentration
The radial distribution for the solid concentration in the downer also varies with the
different drag closures. The application of the Johnson-Jackson boundary condition at the
wall with the Matsen’s drag closure seem to produce results similar to the experimental
data obtained by Zhang et al (1999) where the nature of the radial solid concentration
along the axial direction of the downer differs. Applying Wen &Yu’s and De Felice’s
drag closure produces radial solid hold up profile similar to experimental data obtained
by Cao and Weinstein where the peak of the solids concentration is seen at the wall.
Figure 5.10: Radial solids hold up profile, Matsen’s drag closure (Gs=49 kg/m2s and Ug= 3.7 m/s).
Figure 5.10 presents the radial solid holdup distribution using the Matsen’s drag closure.
Initially the solids concentration is highest at the wall. As the length of the downer
increases, the peak of the solids concentration in the annulus gradually moves towards the
center. It can also be seen that the peak of the solids concentration is decreasing and a
47
more uniform solids concentration at the fully developed region of the downer. The
results obtained are similar to that experimental results obtained by Zhang et al (1999).
Figure 5.11: Radial solids hold up profile, Wen & Yu’s drag closure (Gs=49kg/m2s and Ug= 3.7m/s).
Figure 5.11 presents the radial solid holdup distribution using the Wen & Yu’s drag
closure. It can be seen that results obtained are similar to the experimental results
obtained by Cao and Weinstein (2000) where the peak is observed at the wall itself.
Furthermore in comparison with the radial profile of the Matsen’s drag closure, it can be
seen that local radial peak observed in Wen & Yu’s drag closure is not distinctively
larger than the average radial solids concentration. For example in figure 5.11, the
maximum local radial solid concentration is about 0.0092 while the average solids
concentration is about 0.0084 at 1m from the entrance of the downer. However in figure
5.10, it can be seen that the solids the maximum local radial solid concentration is about
0.018 while the average solids concentration is about 0.0055 at 1m from the entrance of
the downer. Thus it can be been seen that the Wen & Yu’s drag closure predicts a more
even radial solids concentration distribution than the Matsen’s drag closure where the
solids concentration at the peak is about three times more than the average radial solids
48
concentration. There has already been work published where high density peak near the
wall is 2-3 times the cross sectional average solids fraction (Zhang, Qian, Yu, & Wei,
2002) which is in accordance to the radial profile predicted by Matsen’s closure .
Figure 5.12: Radial solids hold up profile, De Felice’s drag closure (Gs=49kg/m2s and Ug= 3.7m/s).
Figure 5.12 presents the radial solid holdup distribution under two different operating
conditions using the De Felice’s drag closure. Again, similar to the Wen & Yu’s drag
closure, the local radial peak observed at the wall is not as distinctively larger than the
average radial solids concentration.
Comparing the radial profiles by the different drag coefficients, Matsen’s drag closure
seems to give a radial solid holdup distribution that is different compared to the Wen &
Yu’s and De Felice’s drag closure. As there is yet to be a universal agreement on the
radial solid hold up profiles, more experimental work and study is needed to verify the
radial soilds holdup profile in the downer. However it is important to note that it has
already be established in the earlier section that the Matsen’s drag closure is able to better
predict the average axial solids concentration under low gas velocity.
49
Chapter 6: Validation of the Eulerian-Lagrangian model
Eulerian-Lagrangian approach was also used to model the hydrodynamics of the downer.
However Eulerian-Lagrangian approach is computationally more expensive as a large
number of solids particles are needed to be tracked. The procedure, equations and
boundary conditions used for simulation have been described in chapter 4.
Compared to the Eulerian- Eulerian approach, the advantages is that each of the particle’s
trajectory can be displayed exactly and thus the residence time of the individual particles
can be computed. However as the Eulerian- Lagrangian model is computationally more
expensive, more simulations were done using the Eulerian- Eulerian method in this
thesis. Nevertheless simulation results for the Eulerian- Lagrangian model is presented
for two operating conditions and is compared with the Eulerian- Eulerian results in this
chapter.
6.1 Residence time of particles
Figure 6.1: Particle residence time for Gs=49 kg/m2s and Ug=3.7 m/s.
50
Figure 6.2: Particle residence time for Gs=205 kg/m2s and Ug=10.1 m/s.
Figures 6.1 and figure 6.2 illustrates the particle residence time for two different
operating conditions. The plots also reveal that the particles in the downer exhibit a rather
uniform residence time as stated in the literature review. In figure 6.1, the residence time
of the particles under the operating condition of solids flux of 49 kg/m2s and superficial
gas velocity of 3.7 m/s ranges from 2.5 to 2.75 seconds. The particles nearer to the wall
possess lower velocity and thus they have a slightly longer residence time than the
particles in the center. Likewise from figure 6.2, the residence time of the particles under
the operating condition of solids flux of 205 kg/m2s and superficial gas velocity of
10.1m/s ranges from 0.95 to 1.1 second. The superficial gas velocity is an important
parameter that affects the residence time of the particles in the downer. Under high
superficial gas velocity, the solid particles will attain a higher velocity and flow through
the downer faster, thus having a lower residence time.
51
6.2 Axial velocity distribution of particles
Figure 6.3: Particle velocity distribution for Gs=49 kg/m2s and Ug=3.7 m/s.
Figure 6.2 displays the particle velocity profiles under low gas velocity as the particles
move along the downer. It can be seen that the particles attain an almost constant velocity
in the fully developed region of the downer. The particles in the center attain a velocity of
about 4.3 m/s while the particles near the wall attain a velocity of about 3.3 m/s. While
experimental results from Bolkan et al shows that the average particle velocity is about
6m/s for similar operating conditions, it can thus be seen that the Eulerian- Lagarangian
approach also under estimates the particle velocity under low gas velocity like the
Eulerian- Eulerian approach using the default Wen & Yu’s drag closure .
52
Figure 6.4: Particle velocity time for Gs=205 kg/m2s and Ug=10.1 m/s.
Figure 6.4 displays the particle velocity profile under higher gas velocity as the particles
move along the downer. Here the particles velocity profile tends to agree better with the
experimental results present by Bolkan et al (2003) which states an average solids
velocity of 11m/s in the fully developed region. Thus like the Eulerian- Eulerian model,
the current Eulerian–lagrangian model is also able to predict the solids properties well
under high superficial gas velocity but unable to account for the more significant particle
clustering effect under low superficial gas velocity. Thus in order to apply the Euerlian-
Lagrangain approach under low gas velocity, improvement to the model is needed to
enhance its predictive ability.
53
6.3 Radial velocity distribution of particles
Figure 6.5: Comparison of radial solid’s velocity profile using the two approaches.
The left contour plot in figure 6.5 displays the radial solids velocity profile in the fully
developed region using the Eulerian-Lagrangian approach while the right plot represents
the results obtained via the Eulerian-Eulerian approach for the solids flux of 49 kg/m2s
and superficial gas velocity of 3.7 m/s. Both model display similar nature of radial solids
velocity profile where the particles travel at a faster velocity in the center than near to the
wall. The values of the solids velocity in the center is also in the same range. However
the major difference is that under Eulerian-Eulerian approach, the solids velocity near the
wall tends to zero while under the Euerlian-Lagrangian approach it tends to about 3.2
m/s. Since there is yet to be a universal agreement on the radial solids velocity profile,
more experimental data and study is needed in this area.
In conclusion, it can be seen that the results obtained by the Eulerian-Lagrangian
approach are in good agreement to the Eulerian –Eulerian approach using the Wen &
54
Yu’s drag closure. The simulation results tend to agree well with available experimental
data by Bolkan et al (2003) under high superficial gas velocity but do not tally well under
low gas velocity. Radial velocity profiles are also generally similar to results obtained by
Euerlian- Eulerian approach with a slight exception near wall region.
55
Chapter 7: Solids distributor and Inlet design of the downer
As the downer aims to serve as a quick-contact reactor, the short-contact time between
the phases poses stringent demand on the solids distributor design (Cheng, Wu, Zhu,
Wei, & Jin, 2008). Primarily, the inlet distributor of the downer should enable uniform
distribution of phases, quick acceleration of the solids and excellent control of gas-solids
mixing (Cheng, Wu, Zhu, Wei, & Jin, 2008). Since the downer performance is very much
dependent on the inlet design, much effort has been put in the design of solids
distributors. A research was first done to find the various solids distributor inlet
geometries available in literature.
Figure 7.1: Solids Inlet Geometry 1 (Cheng, Wu, Zhu, Wei, & Jin, 2008).
The figure above shows a simple and one of the earliest solids distributor design whereby
the solids flow from the riser top is not separated and directly enters the downer through a
900 sharp bend. Though this design is easy to construct, it does not allow uniform
distribution of the solids in the downer (Cheng, Wu, Zhu, Wei, & Jin, 2008). As such this
structure is not currently used in practice.
56
Figure 7.2: Solids Inlet Geometry 2. (Cheng, Wu, Zhu, Wei, & Jin, 2008).
The figure above shows a more recent distributor design. Solids are fluidized uniformly
above the downer inlet and flow through several tubes into the downer. Gas is introduced
through the ring slots around the tubes. This design is commonly used as it enables for an
independent operation of gas flow rate for the downer and riser components and solids
flow rate can also be varied by adjusting the bed height (Cheng, Wu, Zhu, Wei, & Jin,
2008).This type of distributor can also be easily scaled up (Cheng, Wu, Zhu, Wei, & Jin,
2008). The solids distributor used in the pilot plant setup by Guan et al in the University
of Tokyo employs this design.
Figure 7.3: Solids Inlet Geometry 3. (Cheng, Wu, Zhu, Wei, & Jin, 2008).
57
A unique type of inlet structure designed by Lehner and Wirth (1999) is shown above.
The main feature of the structure consists of two concentric pipes, which are located in
the center of the distributor (Cheng, Wu, Zhu, Wei, & Jin, 2008). Gas flows through the
inner tube. The solids are fed to a fluidized bed with a screw feeder. The overflowing
solids from the fluidized bed will flow into the annular gap which is surrounded by the
primary air tube. A diffuser connects the outer pipe and the downer, where the solids and
the gas are further allowed to mix well (Cheng, Wu, Zhu, Wei, & Jin, 2008).
Figure 7.4: Solids Inlet Geometry 4. (Briens, Mirgain, & Bergougnou, 1997).
Briens et al (1997) designed a downer inlet equipped with eight jet nozzles to supply the
superficial gas velocity as shown in the figure above. The eight jet nozzles can be
oriented independently to improve the gas–solids mixing and contact. The bottom of
58
Figure 7.4 shows how the nozzles can be angled to induce a swirl and how the nozzles
could be inclined to hit the solids jet near its top or bottom of the mixing chamber
(Cheng, Wu, Zhu, Wei, & Jin, 2008). This form of inlet design provides flexibility in
controlling the early contact between the phases
Figure 7.5: Solids Inlet Geometry 5. (Cheng, Wu, Zhu, Wei, & Jin, 2008).
Figure 7.5 above shows a slightly different inlet structure design adopted by Muldowney
et al. The main motivation for this design was based on the idea that mixing is more
effective upflow while the reactions are still preferred in downflow (Cheng, Wu, Zhu,
Wei, & Jin, 2008). Therefore the reactants can be introduced into the downer at an angle
tilted upwards so that the reactants will initially be flowing upwards for a short period of
time and this enables good mixing of the phases before they start flowing downwards and
reactions occur in the downer.
59
Figure 7.6: Solids Inlet Geometry 6. (Zhao & Takei, 2010).
Figure 7.6 above shows the side and top view of the solids distributor designed by Tong
Zhao and Masahiro Takei to provide for a uniform solid distribution in the downer. As
shown in the diagram above, the distributor consists of one annular solid inlet and five air
nozzles, which include a center nozzle and four well-distributed side nozzles. For the four
side air nozzles, the angle between the centerline of the center nozzle and the side nozzle
is 45° (Zhao & Takei, 2010). This ensures that the supplied air not only has a velocity
component in the axial direction, but also a velocity component in the radial direction.
This is believed to assist in the radial mixing of the solids.
7.1 Proposed Inlet Designs Based on the literature review above, it can be seen that the distributor design does affect
the flow pattern in the initial stages of the downer. In this thesis, a primary study is
conducted to compare the flow patterns between a tangential inlet structure and a normal
inlet structure. The goals of proposing these inlet designs is aimed towards innovating
new flow patterns and contacting mechanisms that would be enable for a better mixing of
the coal and sand phase. This numerical simulation would also assist in making some
primary investigations before indulging in expensive experimental investments.
60
a) Tangential Arrangement b) Normal Arrangement
Figure 7.7: The two different inlet structures to be studied.
The two different inlet structures to be studied are shown in figure 7.7 below. In the left
arrangement, all the four nozzles are tangential to the downer while in the right
arrangement, the four nozzles are normal to the downer. In the both downer structures,
sand particles would be introduced from the top while the coal particles would be
introduced from the nozzles. To assist the coal flow in the nozzles, compressed air is also
introduced in the nozzles are high speed. Mixing between the sand the coal in the downer
is crucial so that heat transfer can occur efficiently. Thus the purpose of this part of the
thesis is to study the coal and sand distribution in the developing region of the downer in
the two different structures. 7.2 Modeling Approach and simulation conditions
In this part of the thesis, a three-dimensional downer with the two different inlet
structures was created to simulate the three phase flow. The geometries were created in
61
the GAMBIT using the top-bottom approach whereby the volumes were created first
before meshing the edges. Eulerian-Eulerian approach was then used in FLUENT to
simulate the three phase flow with air, sand and coal being the three distinct phases. The
equations used in simulate the flow is similar to the equations present in chapter 3.1.2.
However since a three phase flow is being modeled in this section, there would be two
equations for the solid phase, one for coal and one for sand respectively. Modeling three
phase flow also introduces the solid-solid momentum exchange co-efficient which can be
described according to the following equation.
Solid-solid momentum exchange co-efficient
𝐾𝑠𝑐 =3(1 + 𝑒𝑠𝑐) �𝜋2 + 𝐶𝑓𝑟,𝑠𝑐
𝜋28 � 𝜀𝑠𝜌𝑠𝜀𝑐𝜌𝑐(𝑑𝑠 + 𝑑𝑐)2𝑔𝑜,𝑠𝑐
2𝜋(𝜌𝑠𝑑𝑠3 + 𝜌𝑐𝑑𝑐
3)|𝑢�𝑠 − 𝑢�𝑐|
In the equation above the subscript s refers to the sand phase while the subscript c refers
to the coal phase.𝐶𝑓𝑟,𝑠𝑐refers to the coefficient of friction between the sand phase and
coal phase which is assumed to be 0 in the numerical simulation. 𝑒𝑠𝑐 refers to the sand
and coal phase restitution coefficient with a assigned value of 0.9.
Table 5: Geometrical and simulation conditions for the 3D model
Diameter of downer, D 100 mm
Diameter of nozzles, 25 mm
Length of downer, L 2000 mm
Diameter of sand particle, 80 µm
Diameter of coal particle, 0.2 mm
Density of sand particle, 2600 kg/m3
62
Density of coal particle, cρ 1500 kg/m3
Density of air, gρ 1.225 kg/m3
Dynamic viscosity of air, gµ 1.79 kg/(m.s)
Inlet sand fraction, sε 0.279
Inlet coal fraction, cε 0.4
Restitution coefficient, esc 0.9
Gravitational acceleration, g 9.81 m/s2
Sand mass flux, sG 350 kg/m2s
Coal mass flux, cG 35 kg/m2s
Table 5 above shows the geometrical and simulations conditions used in this simulation.
Wen & Yu’s solid-gas momentum exchange co-efficient has been used in this simulation
as it has been proven earlier that it is able to predict the solids holdup well under high
superficial gas velocity. As in the earlier Eulerian-Eulerian simulations, the dispersed κ-ε
turbulence model is applied
Boundary conditions
Sand fraction at the top inlet of the downer is introduced uniformly in the radial direction,
as well as the coal fraction at the nozzles’ inlet. The ratio of solid mass flux of coal
particles over sand particles is fixed at 0.1 so as to allow for sufficient heat transfer from
the sand to the coal particles. A uniform air velocity of 12 m/s is applied at inlet of nozzle
to supply sufficient energy to push the coal particles through the horizontal sections of
the inlet nozzles. A uniform air velocity of 5m/s is also supplied from the top inlet.
63
Constant pressure boundary condition is applied at the outlet of downer. No-slip
boundary condition is applied at the wall for all the three phases.
Solution Scheme
The pressure–velocity coupled SIMPLE solver method was used in the iteration for the
convergence of the solution. The convergence criteria were set to 0.001 for all the terms.
The first order UPWIND implicit differencing scheme for the convective terms and the
first-order implicit time integration method was used to solve the motion equation of the
fluid. The default under-relaxation parameter values were used during the iteration
process. Steady–state model was used.
7.3 Simulation results
7.3.1 Axial Solid distribution
Figure 7.8 : Axial Distribution of the sand holdup in the downer.
0 0.5 1 1.5 20.01
0.015
0.02
0.025
0.03
0.035
Axial distance of the downer
Ave
rage
San
d ho
ldup
Normal Arrangement
Tangential Arrangement
64
Figure 7.8 above shows the axial distribution of the sand holdup for both arrangements of
the downer. Both arrangements reveal a decrease in the sand holdup along axial distance
of the downer. This is expected as the particles are accelerating under the influence of the
gravity. Since the sand holdup is yet to be constant, it can be seen that the flow is still in
the developing region for the both arrangements. The sand concentration is seen to be
generally in the same range for both the inlet structures. On a closer inspection of figure
7.8, it can be seen that in the initial section of the downer, the sand holdup in the normal
arrangement is slightly higher than the tangential arrangement. In the second section, at
about 1.0 m to 1.75 m of the downer, the average sand holdup in the tangential
arrangement is higher. To ensure that this phenomenon does not occur just for this flow
scenario, the model was simulated with a superficial gas velocity of 20 m/s at the nozzles.
The sand holdup profile for the flow conditions are presented in figure III.1 (Appendix
C). The nature of the graph is also similar to the above figure. However, it seems to
suggest that at higher velocity, the difference in flow structure between tangential and
normal arrangement is reduced.
Figure 7.9 : Axial Distribution of the coal holdup in the downer.
65
Figure 7.9 above reveals the axial distribution of the coal holdup in the downer. It can be
seen that the average coal holdup downer is rather low .This could be attributed to the
fact that a high gas velocity of 12 m/s is applied in the nozzle which allows the coal
particles to attain a high velocity and this leads to considerable dilution of the coal
concentration in the downer. Similar to the sand hold up distribution, the normal
arrangement has a higher concentration in the first section of the downer while the
tangential arrangement has a higher concentration in the second section of the downer. A
similar observation is made in figure III.2 (appendix C) for a higher superficial gas
velocity of 20 m/s at the nozzle.
As a higher solid holdup tends to improve the heat transfer from sand to coal, more
efforts are needed to study the sand concentration under various flow scenarios for the
both inlet arrangements in order to exploit the condition.
66
7.3.2 Radial Solid distribution
Figure 7.10: Radial distribution of the sand concentration in the downer.
From figure 7.10 above, it can be seen that the sand holdup near the entrance of the
downer (z=0.1 m) is similar for both the inlet arrangements as sand particles are flowing
from the similar conditions from the top inlet. Near the outlet (z=1.75 m), the sand
particles are more uniformly distributed for the tangential arrangement than the normal
arrangement. In the normal arrangement, it can be seen that the sand particles concentrate
more in the center and at the nozzle section while the sand holdup near the wall is quite
low. This thus seems to suggest that the high superficial gas velocity tends to influence
the flow of the sand particles. Near the outlet the sand holdup near the center is still
67
higher than that near the wall for both arrangements but the sand distribution in tangential
arrangement is more uniform.
Figure 7.11: Radial distribution of the coal holdup in the downer.
From figure 7.11, the coal holdup distribution is expected to be different in the inlet
region of the downer due to the different ways that they are fed into the downer. In the
normal arrangement, the coal particles are injected from the nozzles into the center of the
downer. Hence the coal holdup is higher near the center of the downer. In the tangential
arrangement, coal particles are injected tangentially along the wall. Thus the coal holdup
68
near the wall is higher than the center. Near the outlet (z= 1.75 m), similar observation is
made where coal holdup is concentrated in the center region for the normal arrangement.
The coal holdup in the tangential arrangement is rather uniform though it can be seen that
the wall region still has a slightly higher coal concentration than the center.
Figures 7.10 and 7.11 only show the radial solids holdup profile at two axial positions.
The figures in Appendix D reveal the radial solids holdup at various axial positions.
Thus from studying both figures 7.10 and 7.11 and figures in Appendix D, it can be seen
that in the developing region the sand and coal particles tend to concentrate at the center
for the normal inlet configuration while in the tangential arrangement, coal and sand are
more uniformly distributed in the cross section. Since both the coal and sand particles
seem to concentrate to the center in the center, it might increase the chances for the coal
and sand particles to collide and mix more often. Better mixing of the coal and sand
particles would allow for a better heat transfer. However, it is important to quantify the
mixing between the coal and sand particles with the introduction of a mixing index.
Mixing index would also enable for better comparison between the two inlet structures
and this would be done in the future work.
It is also important to note that the flow is only simulated for the developing region for
both inlet arrangements. This is the cause for the inlet configurations to affect the flow
pattern of the coal and sand particles. It is believed that the in the developed region, the
inlet arrangement should have little influence in the radial coal and sand holdup
distribution and this will be studied in the future research.
69
Chapter 8: Conclusion
In this thesis, hydrodynamic simulation of the gas-solid flow in the downer was carried
out using both the Eulerian-Eulerian and Eulerian-Largarian computational fluid
dynamics models. In using the Eulerian-Eulerian approach, the κ-Є turbulence model
with the Kinetic Theory of Granular flow was applied to model the multiphase flow.
Initially, the axial distribution of the solids concentration and velocity was simulated and
validated for the Eulerian-Eulerian model with Wen & Yu’s drag closure. It was found
that the model compared well with literature data under high superficial gas velocity but
failed to account for the particle clustering effect under the low gas velocity. As clusters
are more prone to become discrete particles for larger diameter and density, the model
had better predictive ability when larger particle size and higher particle density was
used. Simulation results showed that the diameter of the downer was found to have
negligible effect on the solids concentration distribution. In efforts to improve the model
under low gas velocity two other drag closures, Matsen’s and De Felice’s drag closures
were tested. It was found that Matsen’s Drag closure was better able to predict the solid’s
concentration under low gas velocity and the simulation results agreed well with
experimental data. The difference in the nature of the Matsen’s drag closure also caused
the radial solid concentration profile to be different compared to Wen & Yu’s and De
Felice’s drag closure. Thus it can be concluded that in using the Eulerian-Eulerian model,
the Matsen’s drag closure is better suited model the downer reactor under low gas
velocity.
The Eulerian- Lagrangian approach also produced simulation results comparable to the
Eulerian-Eulerian model under Wen & Yu’s drag closure. The current Eulerian-
70
Lagrangian model is also not able to account for the particle clustering effect under low
gas velocity as the particle’s axial velocity distribution were an underestimation
compared to the experimental data.
In the last section of the thesis two inlet structures proposed in efforts to improve the
mixing between the sand and coal phase. The sand and coal holdup distribution in the
downer were compared for the normal and tangential inlet arrangement. In the
developing region of the downer, the sand and coal particles tend to concentrate at the
center for the normal inlet structure while in the tangential arrangement coal and sand are
more uniformly distributed the cross section. The high superficial gas velocity introduced
at the nozzles also tends to influence the flow of sand particles in the downer.
71
Chapter 9: Recommendations and Future Work
While this work indicates promising results in modeling the flow structure in the downer
reactor, clearly more experimental validation is necessary for the radial solids
concentration distribution. Eulerian-Eulerian model with the Matsen’s drag closure has
been found to be give results that are comparable to the experimental data. More
numerical simulations under various flow conditions may be needed to further validate
the model. Once the model’s solid holdup prediction is in good agreement to the
experimental data, the energy equation and the pyrolysis reaction can be incorporated
into the model for a more detailed study and optimization of the pyrolysis process.
The current model only encompasses the k-Є turbulence model for the gas phase. It is
recommended to incorporate the kp turbulence model for the particle phase in the future
work in efforts to improve the model. More details about the kp can be found from Cheng
et al (1999).
In order to improve the Eulerian-Lagrangian model, it is recommended to incorporate the
‘Discrete Random Walk’ model in FLUENT which would account for dispersion of the
particles due to turbulence in the fluid phase. However, adding this feature would further
increase the computational expense and convergence would be more difficult to achieve.
A mathematical model based on the energy-minimization and multi-scale (EMMS)
principle was developed to describe the hydrodynamics in the fully developed region of a
downer reactor and has been used successfully to predict local solid concentration and
gas-solid velocities by Li et al (2004). As this is a much simpler approach compared to
72
the Eulerian-Eulerian method (Li, Lin, & Yao, 2004). simulations could be could also be
tried using EMMS model and compared with experimental results.
To improve the tangential and normal inlet structure models, a specially designed solids
distributor could be incorporated at the top of the downer, in which 13 tubes are arranged
in the distributor as shown in the figure 9.1 below. This distributor would further enable
uniform distribution of the sand particles in the downer. Eulerian- Eulerian simulation of
the downer with the solids distributor is currently being carried out to compare with the
current simulation results presented in the thesis. Mixing index would be introduced to
Mixing index would be introduced for a better comparison of the coal and sand mixing in
for the two inlet arrangements. Validation of the simulation results with experimental
work is also necessary.
Figure 9.1 : Inlet structures with the specially designed solids distributor.
73
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i
Nomenclature
𝐴𝑟 Archimedes Number
𝐶𝑓𝑟,𝑠𝑐 coefficient of friction between the sand phase and coal phase
𝐶1Є, 𝐶2Є Constants in the
𝐶𝐷 Drag coefficient
𝐷 downer diameter
𝑑𝑝 particle diameter
𝑒𝑠𝑠 Particle-particle restitution co-efficient
𝑒𝑠𝑐 Sand- coal particle restitution co-efficient
𝑔 Acceleration due to gravity
go,ss radial distribution coefficient
Gs Solids flux
𝐺𝑘,𝑞 production of turbulent kinetic energy
𝐼 ̿ Identity matrix
𝐾𝑠𝑓 Gas-solid momentum exchange coefficient
𝐾𝑠𝑐 Solid –solid momentum exchange coefficient
L Length of downer
k diffusion coefficient
κ turbulent kinetic energy
𝑝 Pressure
ps solids pressure
Re Reynolds number
𝑇�𝑓 fluid phase stress-strain tensor
𝑇�𝑠 solids phase stress tensor
𝑢𝑓 Fluid velocity
𝑢𝑠 Solids velocity
Ug Superficial gas velocity
𝑈𝑡 Terminal particle velocity
ii
Greek symbols
εc Coal holdup
εs Solid holdup : Sand holdup
εs,max Maximum packing limit (0.63)
Є Dissipation rate
𝛾𝛩𝑠 Collisional dissipation of energy
λf Fluid bulk viscosity
λs Solids bulk viscosity
𝜌𝑐 Coal density
𝜌𝑓 Fluid density
𝜌𝑔 Gas density
𝜌𝑚𝑖𝑥 Mixture density
µf Fluid shear viscosity
µs Solids shear viscosity
µ𝑠,𝑐𝑜𝑙 Solids collisonal viscosity
µ𝑠,𝑓𝑟𝑖𝑐 Solids frictional viscosity
µ𝑠,𝑘𝑖𝑛 Solids kinetic viscosity
µ𝑡,𝑓 Turbulent viscosity
𝜎Є Turbulent prandtl number, dissipation rate
𝜎𝜅 Turbulent prandtl number , turbulent kinetic energy
𝛩𝑠 Granular temperature
ζ Specularity coefficient
τ Shear stress
ПЄ𝑓 source term caused by influence of solid phase on turbulent kinetic energy
П𝜅𝑓 source term caused by influence of solid phase on turbulent kinetic energy
iii
List of Figures
Chapter 1
Figure 1.1: Triple bed Circulating Fluidized Bed (Guan G. , Chihiro, Ikeda, Yu, &
Tsutsumi, 2009). ................................................................................................................. 5
Chapter 2
Figure 2.1: Pressure profile in a downer for Gs=202kg/m2s and Ug=5m/s. ...................... 10
Figure 2.2 : Solids concentration distribution profile in the downer for Gs =202 kg/m2s
and Ug=5m/s. .................................................................................................................... 10
Figure 2.3 : Radial solids concentration profile (Wang, Bai, & Jin, 1992). .................... 12
Figure 2.4: Radial solids concentration profile (Cao & Weinstein, 2000). ...................... 13
Figure 2.5 : Radial solids concentration profile, (Zhang, Zhu, & Bergougnou, 1999). .... 14
Chapter 3
Figure 3.1: Modeling the interaction between solid and gas phase (Vaishali, Roy, &
Mills, 2008). ...................................................................................................................... 17
Chapter 4
Figure 4.1 : Layout of the meshed geometry of the downer. ............................................ 28
Figure 4.2 : Boundary conditions for the 2D Model. ........................................................ 29
Chapter 5
Figure 5.1: Simulation results for superficial gas velocity of 3.7 m/s. ............................. 32
Figure 5.2: Simulation results for superficial gas velocity of about 7 m/s. ...................... 34
Figure 5.3: Simulation results for superficial gas velocity of about 10m/s. ..................... 35
Figure 5.4: Simulation results for solids flux of about 50kg/m2s with varying Ug. .......... 37
Figure 5.5: Model Comparison for varying Particle Diameter. ........................................ 39
Figure 5.6: Model Comparison for varying Particle Density. .......................................... 39
Figure 5.7: Simulation results using De Felice's drag closure for Ug=3.7 m/s. ................ 42
Figure 5.8: Simulation results using Matsen's Drag closure for Ug=3.7 m/s. ................... 43
iv
Figure 5.9: Comparing simulation results under low Ug , Gs= 253 kg/m2s ....................... 45
Figure 5.10: Radial solids hold up profile, Matsen’s drag closure (Gs=49 kg/m2s and Ug=
3.7 m/s). ............................................................................................................................ 46
Figure 5.11: Radial solids hold up profile, Wen & Yu’s drag closure (Gs=49 kg/m2s and
Ug= 3.7 m/s). .................................................................................................................... 47
Figure 5.12: Radial solids hold up profile, De Felice’s drag closure (Gs=49 kg/m2s and
Ug= 3.7 m/s). .................................................................................................................... 48
Chapter 6
Figure 6.1: Particle residence time for Gs=49 kg/m2s and Ug=3.7 m/s. ............................ 49
Figure 6.2: Particle residence time for Gs=205 kg/m2s and Ug=10.1 m/s. ...................... 50
Figure 6.3: Particle velocity distribution for Gs=49 kg/m2s and Ug=3.7 m/s. .................. 51
Figure 6.4: Particle velocity time for Gs=205 kg/m2s and Ug=10.1 m/s. .......................... 52
Figure 6.5: Comparison of radial solid’s velocity profile using the two approaches. ...... 53
Chapter 7
Figure 7.1: Solids Inlet Geometry 1 (Cheng, Wu, Zhu, Wei, & Jin, 2008). ..................... 55
Figure 7.2: Solids Inlet Geometry 2. (Cheng, Wu, Zhu, Wei, & Jin, 2008) ..................... 56
Figure 7.3: Solids Inlet Geometry 3. (Cheng, Wu, Zhu, Wei, & Jin, 2008). .................... 56
Figure 7.4: Solids Inlet Geometry 4. (Briens, Mirgain, & Bergougnou, 1997). ............... 57
Figure 7.5: Solids Inlet Geometry 5. (Cheng, Wu, Zhu, Wei, & Jin, 2008). .................... 58
Figure 7.6: Solids Inlet Geometry 6. (Zhao & Takei, 2010)............................................. 59
Figure 7.7: The two different inlet structures to be studied. ............................................. 60
Figure 7.8 : Axial Distribution of the sand holdup in the downer. ................................... 63
Figure 7.9 : Axial Distribution of the coal holdup in the downer. .................................... 64
Figure 7.10: Radial distribution of the sand concentration in the downer. ....................... 66
Figure 7.11: Radial distribution of the coal holdup in the downer. .................................. 67
Chapter 9
Figure 9.1 : Inlet structures with the specially designed solids distributor. ...................... 72
v
Appendix
Figure I.1: Simulation results for solids flux of about 100 kg/m2s with varying Ug. ........ vi
Figure I.2 : Simulation results for solids flux of about 200 kg/m2s with varying Ug. ...... vii
Figure II.1 : Experimental data for Gs=253 kg/m2s (Guan et al 2000)............................ viii
Figure III.1 : Axial distribution of the sand holdup in the downer with Ug=20 m/s. ......... ix
Figure III.2 : Axial distribution of the coal holdup in the downer with Ug=20 m/s. ......... ix
Figure IV.1 : Radial sand holdup at various axial positions (Tangential). ......................... x
Figure IV.2: Radial coal holdup at various axial positions (Tangential). .......................... xi
Figure IV.3 : Radial sand holdup at various axial positions (Normal). ............................ xii
Figure IV.4 : Radial coal holdup at various axial positions (Normal). ............................ xiii
List of Tables
Table 1: Various gas-solid momentum transfer coefficients. ........................................... 20
Table 2: Operating conditions for the 2D model. ............................................................. 28
Table 3: Model results for varying downer diameter........................................................ 40
Table 4: Comparison of various Drag coefficients ........................................................... 44
Table 5: Geometrical and simulation conditions for the 3D model .................................. 61
vi
I. Appendix A: Axial solids velocity distribution profiles
a) Comparison of simulation results for solids flux of 100 kg/m2s
Figure I.1: Simulation results for solids flux of about 100 kg/m2s with varying Ug.
vii
b) Comparison of simulation results for solids flux of 200 kg/m2s
Figure I.2 : Simulation results for solids flux of about 200 kg/m2s with varying Ug.
viii
II. Appendix B: Experimental Data for the downer solid holdup for the Gs=253 kg/m2s by Guan et al (2010)
Figure II.1 : Experimental data for Gs=253 kg/m2s (Guan et al 2000).
It is important to note that the simulation results were compared with the average solid
holdup under the ‘seal’ columns. The experiments were conducted on a circulating bed.
The results under the ‘seal’ columns were taken when the superficial air velocity from the
riser was sealed off from the downer. Therefore the solid concentration values under the
‘seal’ results were used for comparison so that effect of riser gas velocity is not affected.
This would be a better comparison with the simulation results as just the downer was
modeled in this thesis. It was found that Matsen’s drag closure agree well with the
experimental results as compared to the Wen & Yu’s drag closure . De Felice’s drag
closure was already proven to produce results similar to Wen & Yu’s correlation earlier
and thus it was not tested in section 5.4.
ix
III. Appendix C: Comparison of the average solids hold up for the two inlet arrangements with Ug=20 m/s.
Figure III.1 : Axial distribution of the sand holdup in the downer with Ug= 20 m/s.
Figure III.2 : Axial distribution of the coal holdup in the downer with Ug= 20 m/s.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.005
0.01
0.015
0.02
0.025
0.03
0.035
Axial Distance of the Downer
Ave
rage s
and hold
up
Tangential ArrangementNormal Arrangement
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 25
6
7
8
9
10
11
12
13x 10-4
Axial Distance of the Downer
Ave
rage
coa
l hol
dup
Tangential arrangementNormal Arrangement
x
IV. Appendix D: Radial distribution of the solids at various axial positions for the two inlet arrangements.
Tangential arrangement
Figure IV.1 : Radial sand holdup at various axial positions (Tangential).
xi
Figure IV.2: Radial coal holdup at various axial positions (Tangential).
xii
Normal arrangement
Figure IV.3 : Radial sand holdup at various axial positions (Normal).
xiii
Figure IV.4 : Radial coal holdup at various axial positions (Normal).