Final Report- environmental engineering course

8/19/2019 Final Report- environmental engineering course

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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




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.

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Final Report- environmental engineering course