final report- environmental engineering course
TRANSCRIPT
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Introduction
Recovering Phosphorus as a non-renewable, non-interchangeable finite resource in
wastewater treatment plants is an ideal way for both cleaning water and also reusing
such a useful material. Under favorable conditions, high level of phosphates in
anaerobic digester supernatant causes struvite (MAP: MgNH4PO4.6H2O)
precipitation. One way to solve this precipitation problem, is to recovering
phosphorus from the supernatant through struvite crystallization, before it forms and
accumulates on the equipments. This process not only alleviates the formation of
unwanted struvite deposits, but also provide environmentally benign and renewable
nutrient source to the agricultural industries. Thus, the recovery of nutrients from
biological wastewater treatment plants through struvite crystallization provides an
innovative and sustainable approach for treating different wastewaters.
Fluidized-bed crystallizers (FLs) were introduced for creating large crystals that
require lower nucleation rates. FLs operate on fluidized-bed principles; that is, they
grow a mass of crystals suspended in an upward flow of supersaturated solution
through the crystallizer. The suspended crystals are allowed to grow until the
required size is achieved. The absence of a stirrer reduces both breakage of growing
crystals and nucleation. In this model, the liquid phase is assumed to flow in plug
flow pattern and the solid phase is represented by a series of equal-sized ideal mixed
beds of crystals.
Computational Fluid Dynamics (CFD) is becoming an important tool for
study of the hydrodynamic behaviour of conventional industrial crystallization
processes. This technique allows the prediction of flow patterns, local solids
concentration and local kinetic energy values, by taking into account the reactor
shape. However, there is a significant lack of studies dealing with liquid-solid
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fluidized bed crystallizers, which involve multi-particle systems. In this study [1], a
commercial CFD package, ANSYS Fluent v. 6.3, was used to complete a numerical
investigation of the hydrodynamics of the liquid-solid fluidized bed of multisize
particles struvite crystals. The simulation results were then evaluated by comparing
with the experimental investigation, using a lab-scale reactor.
The whole idea of this paper is to study hydrodynamic behavior of this process by
assuming solid particles fluidized with water without occurrence of any chemical
phenomena or any mass transfer.
In this paper, the authors try to find the distribution of particles along the bed height
by the time. The solid volume fraction profile were studied in two different time
intervals (20 s and 45 s).
Also they did the simulation with two different upflow velocities and compare the
mixing/segregation status of the bed in these two velocities. Also, the radial
distribution of solids in a specific height is studied.
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Objectives
The main goal of this term project is to simulate the same model and investigate the
same problem as they did in their work. My result will be divided in 4 different
sections:
Section 1: Intermixing/segregation behavior of solid particles
Section 2: Effect of inlet velocity change on particle distribution along the bed height
Section 3: Radial distribution of solids
Section 4: Extended results
o Mesh study (2mm*2mm), solving with finer.
o Drag models investigation: effect of different drag models.o Time step size effect (0.01 s).
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Model Development
The numerical approach, the boundary and initial conditions, as well as the
numerical procedure used in the CFD modeling, are described in this section.
Numerical approach
In this study, a multi-fluid Eulerian granular model of ANSYS Fluent v.16.2 was
used to simulate the hydrodynamics of a liquid-solid fluidized bed of struvite crystals.
In this model, the primary (liquid) and secondary (solid) phases are treated
mathematically as interpenetrating continua; conservation laws for mass and
momentum of each phase are then used to obtain a set of governing equations.
These equations are closed by providing constitutive relations, which are obtained
from empirical information or theoretical assumptions. In addition to the mass and
momentum conservation equations for the solid phase, a fluctuating kinetic energy
equation is also used to account for the conservation of solid fluctuation energy
through the implementation of the kinetic theory of granular flow. In the case of
multi-particle, fluidized bed systems, each individual solid phase (classified according
to their size) is considered as a separate secondary phase; and an equivalent number
of additional continuum and momentum equations are included to represent the
additional phases.
As the effect of different drag models are investigated in this work as extended
results, a review on three different important drag lows are considered below:
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Momentum exchange coefficients:
There are several drag laws, such as Wen and Yu (1966), Syamlal and
O'Brien (1988), Gidaspow (1994), which can explain momentum exchange between
the solid and liquid phases. All the drag laws mentioned here are empirical and
hence, their appropriateness for a particular system should be checked. In this study,
all three aforementioned drag models were examined.
Wen and Yu (1966) model:
This model is an extension of Richardson and Zaki (1954) to high void fraction ( lα
≥
0.8).
65.2687.0)Re(15.01Re
24
4
3 lv
lslls
sl
sl
lsd
uuK α
ρααα
α
--------------------------------------------(1)
where,
l
lslv
s
uud
µ
ρ
Re ----------------------------------------------------------------------------------------(2)
Gidaspow (1994) model:
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Proposing a model to cover the whole range of void fraction, Gidaspow (1994)
employed the Ergun (1952) equation in conjunction with the Wen and Yu (1966)
model:
For lα
≥ 0.8, the Wen and Yu (1966) model (Equation 17) is used, and
for lα
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22
, )2(Re012.0)Re06.0(Re306.0(5.0 X X Y X u ssssr ----------------------(6)
with
14.4
l X α ---------------------------------------------------------------------------------------------(7)
85.0
85.0
28.1
ll
l
p
l
qY
αα
αα--------------------------------------------------------------------------------(8)
The solid-solid momentum exchange coefficient imssK
has the form:
im
iimm
imimmmiiim
im ss
vsvs
ssvvssss fr ss
ss uud d
gd d C e
K
)(2
)()82
)(1(3
33
,0
22
ρρπ
ραραππ
----------------------(9)
where, Cfr is the coefficient of friction between solid phases m and i, and imsse
is the
restitution coefficient due to collisions between solid phases m and i. The restitution
coefficient takes into account the change of kinetic energy of particles when they
collide with each other. A restitution coefficient of 1 means that no energy is lost
during collision (perfect elastic collision), while a value of 0 would mean that all
kinetic energy is dissipated into heat during the collision. Rahaman and Mavinic
(2009) tested three different restitution coefficients (0.5, 0.9 and 0.95) for simulation
of the hydrodynamics of a liquid-solid fluidized bed of struvite crystals and no
variation in CFD-predicted voidage was noticed. Therefore, in this current study, a
particle-particle restitution, imsse = 0.9 was used.
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Boundary Conditions
The experimental setup is shown in Figure 1 (a), while a schematic diagram of the
computational domain is provided in Figure 1(b).
Figure 1. Schematic of (a) the experimental set-up; and (b) the computation domain
a
Pump
Tank
Flow meter
Optical fiber
probes
Manometers
Fluidized
bed
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The inlet boundary was set at the inlet section, from where liquid was continuously
injected into the reactor, and the liquid upflow (superficial) velocities were taken as
the axial liquid velocity (along the height of the column) as the inflow boundary
condition. Although a discrete distributor was used at the inlet of the reactor, a
uniform distribution of the upflow velocity is assumed in the entire set of
simulations. For simplicity, in this study, the upflow velocity is assumed to be
uniformly distributed over the entire cross-section at the inlet boundary of the
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reactor. The outlet boundary condition was held constant at atmospheric pressure.
Zero normal and tangential (i.e., no-slip) velocities for the liquid phase are assumed
at all wall boundaries. Also the solid velocity normal to the walls is set at zero. The
slip velocity between particles and the wall was obtained by equating the tangential
force exerted on the boundary and the particle shear stress close to the wall. The
granular temperature at the wall was obtained by equating the granular temperature
flux at the wall to the inelastic dissipation of energy, and to the generation of granular
energy due to slip in the wall region.
Reactor geometry and model configuration
A fluidized bed, built of Plexiglas with diameter 100 mm and height 1320 mm, was
used for this study. The liquid used in this study was water and the solids were
struvite crystals. The liquid was pumped from a tank to the reactor. A flow meter
was installed to measure the inflow rate of the liquid. The reactor was filled with
mixture of struvite crystals of different sizes (Small Size- Medium Size, Big size) with
a volume ratio of 1:1:1, in order to have a maximum packed bed height of 0.254 m.
The properties of the different sizes of struvite crystals are listed in Table 1.
Table 1. Properties of different size groups of struvite crystals and experimental
conditions
Struvite size Sieving size
(mm)
Density
(kg/m3)
Initial bed height
(mm)
Packed bed solid volume
fraction
Small 1 1541 254 0.21667
Medium 1.5 1350 254 0.21667
Big 2 1452.1 254 0.21667
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For the numerical investigation, a simulated two-dimensional (Cartesian) domain (2-
D), representing a vertical section through the diameter of the fluidized bed column
[Figure 1 (b)] was created using ANSYS Fluent v.16.2. The domain was meshed with
the grid sizes of 3×3 mm. However, in the horizontal direction, a cell growth factor
of 1.035 was applied to the computational cells to create a somewhat finer mesh
approaching both wall sides, (with a maximum cell size of 3 mm at the center) and
maximum layers of three to create finer mesh approaching both walls in order to
capture the complex flow behaviour in this region. The number of nodes created
with this mesh size was 18870 nodes.
The governing equations, explained earlier, are discretized, using the finite volume approach with an implicit second-order, upwind differencing scheme. The
discretized sets of equations, along with the appropriate initial and boundary
conditions, are solved using ANSYS Fluent v.16.2 in double precision mode. This
identical model setup was used to simulate fluidization behavior of all different size
groups of struvite crystals.
The properties of struvite crystals used in this study are listed in Table 1. Theliquid phase used for all the simulations was water with a density of 998.2 kg/m3 and
viscosity of 0.001003 Pa s. For a multi-particle system, each size group was
represented as an individual secondary phase and the liquid was considered as the
only primary phase. The simulation was run for different upflow liquid (superficial)
velocities, to simulate the bed expansion characteristics and also the solid mixing and
segregation behaviour in case of multi-particle systems. All of the simulations were
run for 60 s, with a time step of 0.001s. A summary of model settings can be found
in Table 2.
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Table 2. Summary of simulation settings (model parameters)
Geometry
Shape Cylinder Note/Unit
SizeHeight 1320 mm
Diameter 100 mm
Initial bed height 254 mm/equal weight
Particle size 1 & 1.5 & 2 mm/diameter
Mesh
Mesh size 3*3
Horizontal Cell growth 1.035 finer mesh near
both walls.
Nodes 18870
Boundary
Conditions
Outlet boundary condition pressure outlet
Inlet boundary condition Uniform velocityinlet
Wall boundary condition No slip
Gravitational acceleration 9.81 m/s2
Operation pressure 1.013*105 pa
Liquid superficial velocity 0.068 m/s
Model Equations
Viscose Model Laminar
Granular bulk viscosity Lune et al. Fixed
Frictional visosity Schaeffer Fixed
Angle of internal friction 30 degree Fixed
Granular conductivity Syamlal & O'Brien Fixed
Drag law Gidaspow
Coefficient of restitution for
particle-particle collision 0.9
Calculation Setup
Convergence criteria 0.001
Maximum iteration 20
Discretization method First order Upwind
Time step 0.001 s
The convergence criterion was set at 10-3 for all the equations and the convergences
were achieved within a maximum number of iterations (20) per time step.
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Simulation Settings
A multi-fluid Eulerian CFD model with a granular flow extension was ran on 2D
configuration. The flow considered as laminar flow and transient simulation ran up
to 60 s.
Uniform inlet water velocity and pressure outlet boundary condition was applied to
the model. Two inlet velocities of 0.068 and 0.023 m/s were selected to fluidized all
the particles without any washing away.
Parametric Investigation of some modeling parameters
The focus of this section is a parametric study of the overall bed voidage predicted.
We begin with a base case to investigate the influence of mesh size, time step size,
drag model coefficient and convergence criteria. Detailed settings for the base case
appear in table 3.
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Table 3. Characteristics of simulations for parametric studies
Simulation
NO
MeshTime step
sizeDrag Model
Inlet
velocity
Simulation
time
Resolution Nodes
1
Base case3mm*3mm 18870 0.001 Gidaspow 0.068 m/s 6 h
2 3mm*3mm 18870 0.001 Gidaspow 0.023 m/s 6 h
3 4mm*4mm 11018 0.001 Gidaspow 0.068 m/s 6 h
4 2mm*2mm 40552 0.001 Gidaspow 0.068 m/s 28 h
5 3mm*3mm 18870 0.01 Gidaspow 0.068 m/s 4 h
6 3mm*3mm 18870 0.001 Syamlal &
O'Brien 0.068 m/s 6 h
7 3mm*3mm 18870 0.001 Wen & Yu 0.068 m/s 6 h
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Results and discussion
Intermixing/segregation behavior of solid particlesThe results for section 1 (solid volume fraction study in two different interval time) is
expected to be as figure 2. As we expected, the largest particles are found to be
segregated completely at the bottom part of reactor and the other two size ranges are
mixed throughout the expanded bed height:
Figure 2. Solid volume fraction- 20 s- paper results
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Figure 2. Solid volume fraction- 45 s- paper results
The similar results for my work are presented in figure 3.
Figure 3. Solid volume fraction- 20 s
2 mm Solid 1.5 mm Solid 1 mm Solid
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Figure 3. Solid volume fraction- 45 s
As can be seen, after 20 seconds a large portion of big particles are appear at the
bottom of reactor and by the time and at time 45 s, a larger part of big solids are
confined at the bottom of bed. This trend is exactly same as the trend shown by the
paper results. At time 45s, the remaining portion of the big solid appears to be
sparsely distributed throughout the remaining height of the crystal bed while in the
paper results all the big solids are trapped at the bottom of reactor.
Effect of inlet velocity on particle distribution
The result for effect of inlet velocity on particle distribution should be as presented
in figure 4. By increasing the inlet velocity the solid volume fraction profile along the
2 mm Solid 1.5 mm Solid 1 mm Solid
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bed height will change. Wit
bed height are more unifor
Figure 4. Simulated average to
at high (0.068 m/s) and low (0.
The same result reached by
Figure 5. Simulated average toat high (0.068 m/s) and low (0.
As expected, at low upflow
terms of different size fractio
18
the lower inlet velocity the solid distrib
.
tal solid volume fractions along the bed heig
23 m/s) upflow liquid velocities, at time=45 s
y model are presented in figure 5.
tal solid volume fractions along the bed heig 23 m/s) upflow liquid velocities, at time=45 s
elocity of 0.023 m/s, the bed is reasonabl
ns of particles.
tion along the
t
, paper results.
t .
well mixed in
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Also, it is observed that at lower upflow liquid velocity, the solid volume fraction is
uniformly distributed throughout the bed and the fluidized bed height is around 0.4
m while in the paper results this height is 0.34m. On the other hand, the solid
volume fraction is found to be decreased along the bed height at a higher upflow
velocity of 0.068 m/s and the overall bed height is around 0.8 m in my model but
this amount is 0.57m in paper results. In both of models, the fluidized bed height at
high velocity is almost double compared to the bed height associated with the low
upflow liquid velocity.
Radial distribution
Expected result for radial distribution must be in agreement with the figure 6. This
figure shows the simulated time-averaged distribution of solid volume fraction, on
radial positions, at a height of 0.019m from the bottom of the reactor. As can be
seen, there is not much variation of solid volume fraction in radial direction. For
confirming the simulation predictions with the experimental results, fiber optic
voidage probe was used to measure the radial distribution of solids volume fraction.
Figure 6. Comparison of the time-averaged solid volume fractions, on radial positions, for
the simulated and experimental results- paper results.
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The radial distribution resul
there is no significant varia
interesting part is that my r
As experimental data show
more close to my model (a
0.5).
Figure 7. Comparison of the ti
Parametric Investigation
In this section, I tried to i
liquid-solid fluidized bed si
size, different drag model
parameters and the base caOverall bed voidage was cho
these parameters.
20
for my work presented in figure 7. As c
tion of solid volume fraction in radial
sult shows better agreement with experi
solid volume fraction in this height is
round 0.39) in comparison with paper
e-averaged solid volume fractions, on radia
f some modeling parameters - Extend
vestigate the effect of some important
ulation. For doing this, based on literat
s and time step size is chosen as
se ran with different settings as can be ssen as a general bed criterion that can sh
n be seen, the
direction. The
mental results.
round 0.35 is
esults (around
positions.
d results
parameters in
re[2][3], mesh
ost important
een in table 3. w the effect of
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Mesh size effect
For studying the effect of m
2*2mm and 4*4mm and th
For finer mesh, 2*2mm, th
can see in figure 8, after 45
mixed” and does not show
are in satisfactory agreement
Figure
On the other hand, running
For 60 s run, the simulatio
iteration as can be seen in fi
21
sh size 2 simulations done with two differ
results are compared below:
results show weak agreement with pape
s segregation state of different size part
ny segregation, while in 3*3 mm mesh
with paper results.
8. Solid volume fraction at time=45 s.
with this size of mesh, was much more ti
n took around 28 hours and it need a
ure 9.
ent mesh sizes,
result. As one
icles is “totally
ize, the results
e consuming.
ound 269,000
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Figure 9. Scaled residuals till time=60 s for 2*2mm grid size.
For 4*4 mm mesh size, the overall bed voidage in comparison with base case
presents closer amount with experimental results, figure 10.
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Figure 10. Compar
Drag models investigati
For investigating the effect
different drag models are c
these empirical relations, t
Gidaspow model, as expect
shows closer result to experi
in figure 11.
23
ison of overall bed voidage for different grid
n
of drag models, as discussed in earlier
osen and three different simulation ar
e best agreement with experimental res
d based on literature [4]. Also, the resu
ental data. The result for this comparis
size.
section, three
ran. Between
lt reached by
t of this work,
n is presented
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Figure 11. Comparison o
Radial distribution is chosen
difference better and seco
particles, it seems that it has
on “macro scale” paramete
volume fraction of different
claim, as shown in figure 12
24
f radial distribution of solids for different dr
for this comparison because firstly it can
ndly as drag models deal with intera
more effect on “micro scale” parameters
s such as overall bed voidage. Taking a
models ran with different drag models, c
and 13..
g models.
emphasize this
ction between
and less effect
look on solid
n confirm this
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Figure 12. Solid vol
Figure 13. Solid volume
25
me fraction at t=45 s with Wen & Yu drag
.
fraction at t=45 s with Syamlal & O'Brien dr
odel.
ag model.
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Time step size effect
For this study, a bigger tim
presented in figure 14, we
agreement with experimenta
step is more similar to pape
Figure 14. Comparis
26
step size is chosen and compared wit
can see that the bigger time step size
l results, surprisingly. Also, segregation st
result, as shown in figure 15
n of overall bed voidage for different time st
base case. As
, shows better
ate of this time
p size.
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Small solid Medium solid Big solid
Figure 15. Solid volume fraction at t=45 s with time step size= 0.01 s.
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Conclusion
An Eulerian granular multi-fluid CFD model was employed for the simulation of
chosen paper for this project and liquid-solid fluidized bed was studied. The
simulated bed expansion behaviour of mixture of different sizes of struvite crystals
was found to be consistent with the experimental results. The mixing and segregation
characteristics of liquid-solid fluidized bed of different sizes of struvite crystals,
captured by the CFD simulations, were found to follow the basic principles of
particle segregation; at steady-state, all size groups of struvite were found to be
classified according to their sizes, with the largest ones at the bottom and the smallest
ones at the top of the bed. Limited intermixing between two successive layers of
particle groups was observed. Also, the effect of grid size, time step size and different
drag models are studied as important parameters in this issue. The 4*4 mm grid size
results are close enough to experimental, whilst, is less time expensive simulation.
This conclusion is consistent with 0.01 s as time step size and Gidaspow drag model.
However, further detailed experimental investigation is needed, in order to evaluate
the simulation results.
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Reference
1. M. S. Rahaman and D. S. Mavinic, Recovering nutrients from
wastewater treatment plants through struvite crystallization: CFD
modelling of the hydrodynamics of UBC MAP fluidized-bed
crystallizer, Water Science & Technology—WST | 59.10 | 2009
2. Davarnejad et al., CFD Modeling of a Binary Liquid-Solid Fluidized
Bed, Middle-East Journal of Scientific Research 19 (10): 1272-1279,
2014.
3. Cornelissen et al, CFD modelling of a liquid–solid fluidized bed,
Chemical Engineering Science 62 -6334 – 6348, 2007.
4. Ansys Fluent user guide, v. 16.1.