li thesis.pdf

8/15/2019 LI Thesis.pdf

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Student name: Li Li

Student ID: 211712508

Supervisor: Subrat Das

Fluidized bed had been used in many

industrial application. Such as fluidized

bed reactor and fluidized bed

combustion. The efficiency of the

fluidized bed is significantly depend on

the drag coefficient, heat transfer

coefficient and other factors. In this

study, simulation will be used to study

this parameters and effect on fluidized

performance.

Simulation

study of gas-

solids

fluidized bedAn eulerian–eulerian

approach

Deakin University


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ContentsAcknowledgment .................................................................................................................................... 3

1 Introduction .......................................................................................................................................... 4

2 Project objective and deliverable ......................................................................................................... 5

2.1Objective ........................................................................................................................................ 5

2.2 Deliverable .................................................................................................................................... 5

3 Specific project aim ............................................................................................................................. 5

4 Project benefits and implications ......................................................................................................... 6

4.1 Project benefits .............................................................................................................................. 6

4.2 Project implication ........................................................................................................................ 6

5 Literature review .................................................................................................................................. 7

5.1 Theory of fluidization ................................................................................................................... 7

5.2 Particles in fluidised bed ............................................................................................................... 8

5.2.1 Particle types .............................................................................................................................. 9

5.3 Fluidization ................................................................................................................................... 9

5.3.1 Fluidized phases ..................................................................................................................... 9

5.3.2 Fluidized bed type ................................................................................................................ 10

5.3.3Minimum fluidization velocity ............................................................................................. 10

5.4 Heat transfer in fluidized bed ...................................................................................................... 12

5.4.1 Heat transfer theory .............................................................................................................. 12

5.4.2Active particles ..................................................................................................................... 13

5.5 Computational Fluid Dynamics .................................................................................................. 14

5.5.1 Introduction of Computational Fluid Dynamics .................................................................. 14

5.5.2 Advantage of Computational Fluid Dynamics ..................................................................... 14

5.5.4 Application of Computational Fluid Dynamics ................................................................... 15

5.5.5 Operation process of Computational Fluid Dynamics ................................................... 16

5.5.6 Eulerian model approach in Computational Fluid Dynamics ........................................ 17 6 Methodology ...................................................................................................................................... 19

6.1Use CFD to modeling heat transfer in gas fludized bed .......................................................... 19

6.2 Use CFD to simulate a fluidized bed reactor and study its heat transfer ................................ 22

7 Result and discussion ......................................................................................................................... 27

7.1 Use CFD to modeling heat transfer in gas fludized bed ............................................................. 27

7.1.1Overall characteristics of heat transfer .................................................................................. 27

7.1.2 Different gas superficial velocity VS heat transfer coefficient ............................................ 28

7.1.3 Different particle size VS heat transfer coefficient .............................................................. 28


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Acknowledgment

There are many people for me to thanks to finish my final year project. Although their role is

different, equally important .Firstly, Dr Subrat Das he carried me all the way from begin to the

end. He support with my project with his time and patience. He had given lots of ideals during

the work process. I would also need to give thanks to all my family members, without their

support in lift I not done this.


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1 Introduction

Fluidized bed is normally consist of mixture of solid particle materials and fluid with two phase

in one state. It is one of the most widely used modern technologies that increase the production

efficient of many physical and chemical industrial process. Some industrial process include but

not limit to cracking and reforming of hydrocarbons (oil), carbonization and gasification of

coal, ore roasting.

Fluidization is the process of solid particles convert from static solid -state to dynamic fluid –

state by supply gas or liquid into the solid particles system. When supply liquid or gas into

pack of solid particles (granular material) pressure drop will occurs due fluid drag force on

these particles. When the velocity of fluid reach certain point the fluid drag force will equal or

exceed the gravitational force of these granular materials in the system and particles in the

system no longer rest on each other. This is the point of fluidization. The fluidized solid

particles have three main characterises that used in indusial production: fluidized solid particles

are easy to transfer between reactors; the temperature in the fluidization system is uniform; the

excellent heat transfer in the fluidization system. The application of fluidization is fluidized

bed and can be used for several purposes such as separating mixed solid particles; reactor for

chemical reaction and operating transfer mass and heat in the system. (B.Bhandari 2006)

It is a simulation and experimental based project that aim to determinant characterises of five

different granular material particle when they are fluidised. A theoretical evaluation will be

made before hands to determent these characterises. These parameter are the minimum

fluidized velocity of each granular material, pressure during fluidization of these granular

material, coefficient of heat transfer when implant heat resource in the fluidised bed. After

these a simulation software will be used, namely ANSYS computational fluid dynamics .which

not only able to indicate the aiming parameter but also can observe the situation of the

fluidization. In the end experiment will be conducted to determent weather the data match the

theoretical calculations.


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2 Project objective and deliverable

2.1Objective

The objective of this project is to understand the fluidization characteristics of differentgranular material. And know how to predict the outcome of certain material based on its

proprieties. In order to optimize fluidized bed process for this kind of material.

2.2 DeliverableAnalysis and study characteristics of 5 different granular particles in fluidized bed by simulate

fluidization of these particles in CFD and perform fluidization experiment to obtain

experimental data. And compare the result from simulation and experiment. Before star any

simulation or experiment an evaluation will be made based on the theories of Fluidization.

These following data are need to be collect from simulation and experiment:The minimum velocity of gas flow in the fluidized cause fluidization of these five granular

materials,

Pressure drop in the fluidized bed during the fluidization of these five particles.

The pressure distribution in the fluidized bed of these 5 material in each stage of fluidization;

The loosening speed of these 5 materials in fluidized bed in each stage of fluidization;

The coefficient of heat transfer in fluidized bed for these 5 materials. There are two section

need to consider for this: the speed of particles vs heat transfer and depth of mass vs heat

transfer.

3 Specific project aim

The aim of this project is to study the fluidization characteristics of 5 different granular material

by using simulation software and performing experiment. There are some key factors that focus

on this project: the pressure drop, the pressure distribution in the fluidized bed, the loosening

speed and coefficient of heat transfer in the fluidization system. The design of fluidized bed

will require quantitative knowledge of fluidized bed heat transfer characteristics and fluid.

Therefore this project is necessary for helping establish the optimization of fluidized bed

process with different material.


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4 Project benefits and implications

4.1 Project benefits

The main knowledge been practice in this project is heat transfer and fluid mechanic. This project also require some study on fluidized, as it is a new developing technology. By going

through this project some key parameter that effect on fluidization which include the shape of

particles in the fluidized bed, the density and shape of the particles. This project would also

involve use software to simulate the performance of fluidization of 5 particles in different stage.

(CFD) It would require some technical assistance from project supervisor on how to use

ANSYS computational fluid dynamics (CFD). Instruction from technician is need also need

on how to operate fluidized bed in laboratory room. Some risk and hazard during experiment

also need to be ware for safety reason

4.2 Project implicationThis project is the study of characterises of fluidization when 5 different materials used in the

fluidized bed. The study not only study about the fluidized stage of fluidization but also every

stage of the fluidization. While there are some factors or parameters need to consider in this

study. How will different particles effect on the pressure lost during fluidization; the

relationship between properties of particle(material) and loosening speed ; as well as how

will the particle effect on the coefficient heat transfer .


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5 Literature review

5.1 Theory of fluidization

When passing gas or liquid (fluid) through a pack of granular material in cylinder a pressuredrop will occurs due to drag force add on these particle by passing fluid. These granular

material will become fluidized when the drag force is equal or greater than the gravitational

force of the particles. At this point of fluidization the velocity of fluid namely “minimum

fluidising velocity”. If continue increase the fluid velocity, the pressure drop however would

not gain significantly. In the case of this, the fluidised bed will expand. (J.A.M.Kuipers 8 March

2005)

When fluidization occus Particles become

fluidized solid and fluid are mixtrued in highdrgree and high coefficient of heat transfer. It

can be used in many area such as dry moist

paricles, combustion reactor,calcination .

The temperature in the fluidized bed are

uniformed distributed , so it is a fine

environment for heat treating heat sensitive

material .

(at point of vmt is fluidization point) (fig 1 )

as shown , the particle on the right the drag force is larger than

gravertasional force(fig 2a and fig 2b)

However , fluidied bed requrie dust control and treatment to maintain its opreation condition .It

will increase cost more than capotal cost and run fluidied bed as shown :

Advantage Disadvantage

Fine gas-solid mass transfer(excellent

contact ion)

Require dust control and treatment

Fine coefficient of heat transfer Difficult to scale up due to complex

hydrodynamic

Uniform temperature distributed Attrition of catalyst particles

Low pressure drop Broad residence time distribution of gas andsolid


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Able to carry high volumes fluid(S.L.Petro 2007)(Table 1)

5.2 Particles in fluidised bed

As in any case of

fluidization, it

always connect to

particulate solid

particle. These solid

particle are normally

consist ofmechanical mixture

(Fig 3)

Multitude of solid particle. Some natural solid particle are originate from many long-term

natural processes: heated, cooled , thermal dilated, coiled , chopped up change of atmospheric ,

erased by sea waves . Some solid particles are also been produce from technological process

such as grinded milled, evaporation m, crystallized sprayed and dried. In addition, some

particle just from organic origin: seed of plant. (2011 Fluidized bed)

But most solid particle in the fluidized bed are commonly consist of particle with large range

of shape and size. Because the non-organic particle that in the nature are most likely have wide

range of shape and size. However by certain manufacture process it is possible to unify the size

and shape of these non-uniform particles. The organic solid particle in the natural are normally

uniformed which mean they have the same size and shape. In this project, all particles been

used in the simulation and experiment are have same shape and size.

Beside the effect of fluidized bed parameter itself and external environment, the particles’

geometrical, physical and aerodynamically are the main parameter which cause different

characteristic of fluidized bed. (2011 Fluidized bed)

They are

The true density of particle ;

Particle density in the fluidized bed with gas ( the porosity in the bed is negligible)

The bulk density of the particle ( mass per unit mass in the fixed fluidized bed)

porosity of particle in the fluidized bed (the really particle volume in the fix fluidized bed)

the average equivalent particle or known as the characteristic dimension of

the shape of particles,

particle size distribution — probability distribution of particle distribution due to their size,


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The terminal of velocity — when the force on the particle are in equilibrium. (2011 Fluidized

bed)

5.2.1 Particle typesBase on the size of different particles, Geldart had create a classification for all particles to

gain understanding of fluidized bed activities. The particle with diameter of 20 - 100 μmand density less than 1.4g/cm3 is Geldart A. This kind of particles are easily fluidized and

very intensity bed activity. Particle with larger size from 40 to 500μm and greater density

from 1.4 to 4.5g/cm3. Sands is the typical particle for Geldart B, bubble can observed when

fluidized. Due to the small diameter of Geldart C particles, they are hardly fluidized due

cohesive force within each particles. They size from 20 to 30μm .The largest particles are

Geldart D particles, their diameter normally over 600μm. (Jonas A. England, 2011)

5.3 Fluidization

When the particle in the fluidised bed are fluidized, it is caused by sufficient gas velocity to

break up through the bed in vertical direction. In the fixed bed state, the particles in the bed

are rest on one another with many contacting point with forces applied on them.

(Gravitational force of particle by weight). The force on the particles are been speared in all

directions on the contact point on the particles.

When the bed reach its minimum velocity, the solid particle would be in state of equilibrium,

the gravity drag force are equal, in the result of this, they will floating, and moving. The

contacting duration of each particles would be reduce significantly and the force of them

are completely small and weak, then these particle will in state of fluidization.

In this state, the movement of particles are always in chaotic, and increasing velocity couldincreasing particles distance as well as bed high .The pressure drop in this state across the

bed is constant and equal to bed weigh. It can be obtained be reach minimum fluidization

velocity in the bed. (2011 Fluidized bed)

5.3.1 Fluidized phasesFluidized bed can be classified by the number of phase it have. Such as a bed with more than

one solid phase is a multiphase system. The figure 4 on the left is a typical example of

multiphase fluidized bed. In this bed there are two solid phase particles sand and biomass with

three type of particle defend by its

particles diameter .Figure 5b showsthat, bed with one single phase the

relationship between superficial

gas velocity and pressure drop in

the bed until it reach the minimum

fluidization velocity is

linear .However the relationship

for multiphase system is not linear

related. It is difficult to predict the

minimum fluidization velocity for

multiphase (Jonas A. England,

2011)


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(fig4)

(Fig 5a and Fig 5b)

5.3.2 Fluidized bed typeThere are two type of fluidized bed based on observation of bed expand activity. One of know

as bubbling fluidized bed (BFBs). While the gas superficial velocity is exceed minimum

fluidization velocity of this bed, bubble would formed at the bottom of bed. These bubble like

structure can assist with the mixture condition and increase efficiency of fluidized.

While gas superficial velocity keep increase after bubbling stage, Solid particles in the bedwould carried out by gas flow in the bed and back to bed due to gravity. It is known as

Circulating fluidized bed. CFD can provide very heat transfer and chemical reaction between

gas and solid particles due to long constant time. (Jonas A. England, 2011)

5.3.3Minimum fluidization velocityThe most commonly used method to determent the transition phase fluidized from fixed bed

to fluidization stage is by observing and measure the pressure drop across the bed as function

of fluid velocity . As been shown below a curve of characteristic shape of bed of pressure VS

velocity. (2011 Fluidized bed)

By plotting the relationship between the pressure drop and the superficial gas velocity candetermine whether a fluidized bed is fluidized. When gas pump into fluidized bed through

granular material, particles in bed would experience drag force and buoyancy force due to

pressure. The pressure drop in the bed is proportion to superficial gas velocity. When pressure

drop is high enough to cause drag force and buoyancy force balance gravitational force of

granular material. At this point, granular material is fluidized and in an equilibrium stage

pressure drop become constant cross the bed even further increase gas velocity.

(Brian Y Lattimer, 2012)


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When minimum fluidization velocity is

reached, the pressure drop and gas velocity

curve will bended and pressure drop did not

change even velocity increase.

(Fig 6)

Minimum fluidization velocity and pressure drop are key for characterizing and understanding

operation and design of fluidized beds. By performing experiment or using related correlation

pressure drop can obtained.

The most simple form of pressure drop cross bed is :

mgΔP=

A

The pressure drop cross the bed can be calculated by

b mf ΔP =(1- )( ) s g b gH

The Voids fraction defines

1 sg

Since the pressure drop is propositional to the gas velocity the pressure drop, and it knows as

Ergun relation can be written as:

22* *

b b3 2 3

150(1 ) 1.75(1 )ΔP =H * * *

( * ) *

g g g g b

s p s p

u v v H

d d

When let equation 1 and equation 2 are equal the minimum fluidization velocity can be written

as following expression:

2 0.5* *Re (33.7 0.049 ) 33.7 p mf g mf g

d v Ar u


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Where the expression of Ar can be written as

2* *

2

* ( ) p g s g

q

g d Ar

u

Where the parameter in the above equation:

∆Pb is the pressure drop cross fluidized bed;

Hb is the bed height;

ϵf is packed bed porosity ;

ρp is density of solid particles;

ρg is the density of fluid, in this case, it is the density of gas;

g is gravitational acceleration ;

∅S is the shape factor of particles which cannot experimentally obtained, it need to be obtain

from data base;Ar and Remf are the Archimedes number and a modified Reynolds number;

vf is minimum fluidization velocity ;

d is diameter of the solid particles.

The minimum fluidization velocity can be express as

2 2.

.

( ) ( ) ( )*

150 1

s s s s mf g mf

g mf g

d U

u

Where Re


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same as the temperature of particle in the fluidized bed when it escape from bed. This

observation show that the particle have great heat exchange ability with gas when fluidized.

This intensive heat transfer is because the solid particle in the bed have very large specific heat

transfer surface (3000 to 45000 m2/m3), even outweigh the defect of small heat transfer

coefficient (6-25 W/m2°C) of solid particles. The large heat capacity of solid particle is another

parameter that cause the small temperature difference between gas and solid particles.

The coefficient of heat transfer of solid particle between heating source in the fluidized bed can

be calculated as (2011 Fluidized bed)

2* ( * * )

* p

b

k cd

w

Where

dp is particle diameter;

wb is the average air speed in the fluidized bed

ρ ∗ c ∗ φ are the density, heat capacity and conductivity of gas.

5.4.2Active particles

1. Ignore the small heat transfer coefficient of gas to particle, the gas and solid particles

temperature are equal even it is very close to distribution plate. With the distance of five

times of solid particles diameter, the difference of

temperature will decrease around 100 times. Just in seconds,

the gas temperature in the bubble will turn to the same

temperature as solid particle temperature. The equalization

of temperature even can happen with distance as far as 10mm.

In the case of a fluidized bed has chemical reaction, the active

solid particle react with the gas in the fluidized bed and

release heat to the fluidized system which is a complex process. The active particle been heated up by contact with


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heat source in the bed. Simultaneously, evaporation ounces as well. The efficient of this

initial process are completely relay on the heat transfer of solid particle and bed. When

reaction started, the particle temperature rise up and have process of reverse heat exchange

to the system. This chemical reaction process is governed by mass transfer. (The reaction

surface of particle between gases in the bed). The mass transfer mechanisms of fluidized

bed system toward to particle is depend on molecular diffusion and transport

convention.as result of most active particles are inhabit the emulsion phase, so mass

transfer increase with increase of size of inert bed material . (2011 Fluidized bed)

(Fig 7)

2. The two parameter that govern the mass transfer mechanisms are: packages of particle that

contact with fresh gas from external environment, and the movement of these packages are

determent by bubble flow in the bed; the other is the velocity of percolate pass by emulsion

with velocity of vmf .

5.5 Computational Fluid Dynamics

5.5.1 Introduction of Computational Fluid Dynamics Computational Fluid Dynamics is a simulation system that can predict heat transfer,

fluid flow behaviour, and mass transfer or any other fluid related activity and

parameter. All the simulations were done by computer solve mathematical equations

that correlate to parameter or fluid activity. The computer based simulations can

perform millions of calculations and predict behaviours of fluid that interested in

engineers and scientist .Most of the simulations can only allow them to study the

phenomena but not accurate predication. Navier-stokes equation is a typical

governing equation that used in CFD simulation. This equation can be modified to a

more simple form by removing viscosity to yield the Euler equations. Additional

simplify can be done if necessary down to Potential equations by the same method.

(S’Kumar Pandey 2010)

In most simulation cases, CFD would been given boundary conditions and specific geometry

to solve complex nonlinear governing equations to linear form results. The result include but

not limit to heat transfer coefficient, temperature, pressure moist condition. The simulation

can allow engineers to study phenomena, design new product, and improve the performance

of existing design.

5.5.2 Advantage of Computational Fluid DynamicsCFD had been designed and develop for many decades to assist with problem solving in their

design with simulation and predict result rather than physical testing with equipment and

operating conditions. They can obtain information from a complex cases with complex

boundary conditions. It is also been widely used in industrial area and research file becauseof the following advantage of a CFD:

(Park. 2009)


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Low cost, high efficiency: The cost for performing simulation is relatively than real

experiment. The cost for obtaining and operating physical equipment is expansive

when obtain vital design data. However, the cost in simulation can be significantly

decreased.

Flexibility: it is easy to change the parameter without change any of them in real lift.

It can allow researchers and engineers repeat simulation forever until meet their

expectation

Fast – The simulation can normally perform millions of calculations in as short time

without experiment. It can give engineers advantage in time when test their design

performance.

Wide range in information: The CFD simulation can provide engineers the fluid

hydrodynamics or any other related parameters in different region of the operating

system. Unlike experiments in real life, limit of region can be studied.

Can simulate fluid cases in real life: Most fluid problem or fluid related problem can

be experimental solved. However, some case may not able or easy to obtain such

condition. CFD simulation can use governing equation to provide theoretically result

in any conditions Reliable: CFD can provide result that match with the experimental closely .Coding

and program are improving rapidly, it will be more reliable in the future.

5.5.3 Limitation of Computational Fluid Dynamics

Although CFD simulation can provide perfect engineering and researching base with its

advantages , some limitation still need to be considered and resolved in the future study

(Bakker.2002)

Physical models- CFD simulation require real life physical model to process its task (such as

heat exchanger, fluidization, turbulence, etc.). The accuracy of CFD result is depend on the

physical model it based on.

Numerical errors-CFD simulation is using numerical method to solving governing

equations, so numerical errors are exist. (Errors cannot be resolve only can be minimize)

Round-off error: it is due to the finite word size provide by computer. Another one is

truncation error, it is caused by the numerical model been used (appropriate numerical model

can minimize this error).

Boundary conditions-CFD is based in real physical model, appropriate boundary conditions

are necessary for the simulation to obtain accurate result.

5.5.4 Application of Computational Fluid Dynamics

CFD not only can be used to simulate blood flow in blood veins, so biomedicine

engineers also can use it to study circulatory and respiratory system in human or

animal body .


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Due to the high temperature and difficulty in visual exam of liquid steel, it is hard to

perform quality control. However CFD can be used to simulation the flow of liquid

steel in the vessels and improve the quality of steel products.

In glass industry control and measure the flow quantities is a difficult task, but with

the simulation done by CFD all the manufacture process can be evaluate and

optimized.

Marine engineers also use CFD to study occasion actives such as weather, occasion

flow.

CFD can be used to simulate the flow behaviour and performance in any flow related

equipment, so designers can analysis their designs for chemical industry. The

equipment like Fluidized bed, heat exchanger and stirred tank. (S’Kumar Pandey

2010)

5.5.5

Operation process of Computational Fluid DynamicsFor the convince of user who are new to CFD simulation software, most CFD software onmarket would provide them with the simulation process done by experience users present

with their interfaces and result of simulations. Any CFD simulations have three main

elements to process. (S’Kumar Pandey 2010)

1 Pre-processing

2. Solver

3. Post – processing

5.5.5.1 Pre-ProcessingIn this process CFD operator uses its means to transform the flow problem into an

appropriate form and can be understand by solver. The most common tools such as TGRID,

DM, and GAMBIT. Pre-process including the following steps:

Built the geometry for the flow system or simulation environment

Create appreciate mesh for the geometry and divide into many smaller with no

overlapping sub-system

Define suitable boundary condition and continuum conditions for the simulation

(gravitational force, pressure, etc.)

The flow problem like flow viscosity, heat transfer, pressure would be with non-linear govern

equations and calculate in each cell. The prediction accuracy is significantly depend on the

number of cells in the mesh. With smaller mesh the more accurate the solution will be.

(S’Kumar Pandey 2010)

5.5.5.2 SolverIt the process which calculated the govern equations and produce predicted data result for

next step. The govern fluid equations would be solved by FLUENT with finite-volume

method. So FLUENT is able to simulate with many different physical models, such as

laminar or turbulent, compressible or incompressible, viscous or inviscid etc. The fluid


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govern equation are non-linear and coupled, the solver will continue perform calculation in

iteration loop until a liner solution is obtained. (Bakker, 2002) The following are the main

step in solver stage:

Use simple function to estimate the flow related unknown variables.

Substituted the estimated unknown variables into the govern equation of flow andcalculation in next stage

Perform mathematical manipulations and obtain the result data.

5.5.5.3 Post-ProcessingIn the final step CFD will analysis and interpret obtained data to visual images or animations

show how will the flow behaviour. The obtained data can also be export and process by other

post processing software such as TechPlot, Ensight, and Fieldview. (Bakker. 2002).The

following are the main step for post-processing. (S’Kumar Pandey 2010)

Display the simulation system with mesh or geometry

Give all related properties related contour plot

Contour plot of all the properties

Vector plots

2D &3D surface plots

X-Y plots with different properties

Analysis particles activity

Create convergence for simulation.

Evaluated manipulation

Create animations

5.5.6 Eulerian model approach in Computational Fluid Dynamics

The most commonly used model in solving multiphase model in FLUENT IS Eulerian model.In each phase of the simulation a set of continuity and momentum will be solved. The

pressure and exchange coefficient are used to couple flow related govern equations. The

couple method or patterns are depend on the phases which they are in. For example, in gas-

solid fluidized bed, the manner of handle gas phase is different from mixture phase. The flow

kinetic theory in fluidized bed is used to obtain granular flows properties such as temperature

viscosity, pressure, temperature and so on. Moreover, the type of mixture model can also

determine the momentum. The function in FLUENT' can be self-define and customized to

calculate momentum exchange with their own manner. Eularian model is design to calculate

equations in a sinter penetrating continuum phase rather than a complex mixture phase. The

identical particles in the system with respect particle properties (such as density and size). Insuch manner and apply suitable boundary conditions and jump conditions to each phase


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interactions, the balance of energy, momentum can be built in each phase. (Painet al., 2001).

For Eularian multiphase model, the solid phase momentum balance cannot obtained without

assumptions or certain averaging techniques. Because in solid phase no equation is available

for approximate resultant continuum and some parameter is lacking (normal stress, viscosity).

Eularian multiphase model has wide range of applications such as fluidized bed in this

project, suspensions of particles and bubble columns. (S’Kumar Pandey 2010)


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6 Methodology

6.1Use CFD to modeling heat transfer in gas fludized bed

6.1.1 Theory and equationsAn Eulerian-Eulerian multiphase gas-solids fluidized was built to modeling the hydrolytic and

heat transfer coefficient. The pressure and viscosity are determined by fine particle flow

kinetic theory while the model for gas phase turbulence is a sub mesh scale. (R’Yusuf, Moren,

2005)

The heat transfer coefficient in this simulation is determined by energy balance equation in

each phase of the fluidized bed. The energy balance is showed as below:

Gas phase energy balance

* ,* *( ) ( ) (* * * ) j j

g g j g g g s v s g g

j

g g h h u k

T

t xa T T

x x

Solid phase energy balance

* * ** *( ) ( (* ) ) j j

s s s js g s s

j s s s v sh h u k

T

t xa T T

x x

Where

,

R

T

n p n n

T

h C dT To simplify to energy balance equations, the expression of heat transfer coefficient of

interphase volumetric and thermal conductivity that take effect are required.

Thermal conductivity in gas phase

Due to the presence of other phase in the phase study in, the effective thermal conductivity is

different to its microscopic thermal conductivity. An expression were introduced based on the

model of Zehner and Schluender can be written as:

, (1- 1( ))

gm

g l g

g

k K

)((1 ω ( ) )* 1 ω gm

s g

s

k K a C


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Where

2

2 1 10.5( 1)

1 (1 ) 1

a b a bC In b

a b ba b

b a a

Where

3ω 7.26*10

sm

gm

k a

k

The effective thermal conductivity would also effect by its turbulent components in this

phase even the sub-mesh scale turbulence is obtained .So the sub thermal conductivity can be

determined by following expression:

, , s s coll s kimk k k

Where the turbulent components thermal conductivity is:

,

* .

0.7 g tur

tur p g

k C

Where the constant turbulent number Prandtl is 0.7

Thermal conductivity in solid phase

While use kenotic theory of granular flow to calculate the thermal conductivity in the solid

phase can be shown as the expression of temperature of granule particles in the bed.

Hunt had introduce a new mechanics model to calculate effective thermal conductivity based

on the particles movement and neglecting particle collection:

3

2

1

2* , * * *

0

Θ

32

s p s dp s

ck

g

Where go is the expression radial distribution.

In this case the particle collisions is unelectable, so the thermal conductivity for solids phase

should consist of both particle collision and granular flow kenotic theory, so the expression

can be written as:


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, , s s coll s kimk k k

The thermal conductivity contributed by collisions is introduced by Gelperin and Einstein is

0.180.63 ), (

,

*

1(1 )

0. (1 )28 gm

sm

gm s

sm s coll

s k k

im sm

g

k s

m

k

k k

k

k k

Heat transfer coefficient in interphase

The heat transfer coefficient of interphase volumetric is the intermedium of the energy

balance equation for these two phases

v 6 1α g gp

pd

Where gp is determined by the heat transfer coefficient of gas particle in the bed

2

1 1* 2 0.2 0.73 3(7 10 5 ) *(1 0.7 Re * ) (1.33 2.4 1.2 )*

gp p g g p g g p

gm

a d Pr Re Pr

k

6.1.2 CFD model simulation set upIn this case study, the subject is the heat transfer given by an immersed vertical tube in thefluidized bed. This fluidized bed is known as Winder system, it is a bed with diameter of 0.2m

and the bed height is variable depend on the solids particles volume fraction and many

immersed tube with different in length. In this simulation, the system is simplified to a 2D

fluidized bed 0.1m in wide with a constant temperature near by the inlet jet .Some boundary

conditions were set as below. The temperature at the minimum velocity is 298K and the

pressure within the bed was 1bar. In both phase, they been set to have no slip. The courant

criterion is used to calculate the time step. The material thermal properties are shown in the

table below, (R’Yusuf, Moren, 2005)

In this simulation, a very fine mesh is necessary to place perpendicular to the wall heat sourceto determine the temperature gradients near the wall. While the distance from the wall is

increased, the mesh size is increase as well. From research, it is suggest that: for the most

accurate result, the cell need to be divide to sub-cell till a mesh dependent result is observed.

The research also state that with 7 sub-cell with size of 7.812*10-5 is the most appropriate one.

In this simulation, there were 26*50 computational cells used to calculate the average heat

transfer coefficient:

w w

g g g s s s

t w b

k T k T

x x

a T T


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(Table 2)

(Fig 8)

6.2 Use CFD to simulate a fluidized bed reactor and study its heat

transfer

6.2.1 Theory and equationsThis case study can be used in industrial fluidized simulation as the averaged equations

involved in Eulerian multiphase model. Different hydrodynamic equations would be applied

respect to its phase.There some boundary conditions and assumptions need to be made before the simulation:

The gas phase of the fluidized is in ideal condition and incompressible

the fluidized bed is built in a 2D model and not symmetric

assume not heat transfer exist between different solids phase of the bed the heat flux produced by solids particles is assume to be constant

In this case study a set of equations were introduced to imply the heat transfer and drag force

in each phase related with apocopate term. The viscosity and stress are governed by granular

temperature which change with time passing and bed height. The solid and gas phase equations

were developed by using Eularian – multiphase model with standard method. The solids volume

fraction and gas volume fraction should sum up equal to one. (Y’ Behjat, 2007)

1

2

1 g s

εg+∑

2=1 s=1

This equation can be further divide into solid and gas phase as:


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( ) 0

( ) 0

g g

g g g

s s

s s s

vt

vt

The momentum equation of gas and solid phase can be express as:

( ) *σ

( ) *σ

g g g g g g g g gs g g

s s s s s s s s gs s s

v v v f

v

t

t

g

v v f g

The interaction force between solid and gas is represent by f gs, it is determined by the transferof momentum between these two phases. In this case, in order to simplify the simulation, only

take the effect of drag and buoyancy force. So f gs can be express as below:

gs s g gs s g f P F v v

Fgs is the drag force coefficient which need to experimentally obtain. Two approach bad been

developed to calculate drag force coefficient in different stage of the fluidization.

The first stage is while at begin, the solids volume is highest and Ergun equation is needed.

While the second stage the volume fraction of gas and solids are in equilibrium, so gas volume

and Reynolds number are used to determine the thermal velocity .The Syamlal – :

O'Brien drag model in second phase is calculated by thermal velocity as below expression.

2

3 Re( ) ( ) | |

4

s g g gs s s g

r p r

F CD v vv d v

Where vra is2 20.5( 0.06 [(0.06 Re ) 0.12 Re (2 ) 0.12 (2 ) )])r av A Re B A A Rea B A A

Gidaspow had also introduce a model to calculate the drag force coefficient

While ε g>0.8

While ε g≤0.8

2.65

2

2* *

* ( )

3| | *

4

( )150 1.75 | |

s g g g s s g g

p

s g s g g s g

g p p

F CD v vd

u F v v

d d


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Some similarity can be seen from the equations above and further research suggest that the

equation to calculate thermal momentum can be simplified as below:

0

2

αβ αβ

2αβ * * β* β β αβ

3 3* β * β

3(1 )( * )2 8 ( ) | |

2 ( ( ) ( ) )

f

s s s s s p p s g

s p s p

e C

F d d g v vd d

Where g0αβ is the distribution factor and can be determined by:

02

2β

αβ

β 1

1 3=

( )

p p s

g g p p p

d d g

d d d

There two stress in the fluidized bed so for different solid volume fraction the stress can be

express as:

-

-

p p s s

v v s s

P I

P I

*

*

g g

g g

Granular temperature can be determined by the granular energy and increase while temperature

rise. Different solid particles movement have different granular energy. So granular

temperature can directly reflect the bed activity .And granular temperature is a different parameter form solid phase temperature. The following equation is for determine granular

energy:

3 3

( ) ( ) σ :2 2

s s s s s s s g v v qt

Although, a granular energy equation was develop, the granular temperature is still an unknown

parameter. Research suggest that with the theoretical explanation of the suspension of solids

particles with multi-size. In addition, based on the granular particle flow theory, the mixture

particle properties is equal to granular properties (temperature). The granular temperature

equation below is based on the assumption of the local granular energy is overrun and ignore

the effect of gas diffusion and conversion. (Y’ Behjat, 2007)

2 2 2 21 * * * *1 4 2 3 2

4

( ) [ ( ) 4 ( ( ) 2 * ( ))][ ]

2

s s s s s s

s

K tr D K tr D K K tr D K tr D

K

The internal gas energy balance equation can be written as temperature of gas


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2

1

( * ) g g pg g g g g rg C T v T H H t

The thermal conductivity in solid phase is consist of direct contact conduction and gas wages

trapped in solid particle indirect conduction. In this simulation the heat conductivity is ignore

as it is very small. So the heat diffusion is negligible in this one and the solid phase thermal

conductivity has expression below:

*( * ) * s s s p s s s s s s rs sC T v T k T H H t

The different in solid phase and gas phase of its temperature is known as the heat transfer

between these two phases:

0

( ) g g s g H T T The expression of the relationship between heat transfer coefficient and Nusselt number can be

written as:

* *0

2

6 g s g

p

k Nu

d

It is assume that the particle and gas porosity range is from 0.35 to 1 and the Reynolds number

is considerable high, so Nusselt number can be written as1 1

2 0.2 2 0.73 3(7 10 5 )(1 0.7 Re Pr ) (1.33 2.4 102 ) Re *Pr g g g g Nu

Consideration for boundary conditions

Some values of variables are need to be apply and use through the entire of the simulation.

The simulation start with a fixed bed (solid particles have zero velocity) and the superficial gas

velocity is uniformed through the bed. (Same in each spot of bed) The initial temperature of

both gas and solid particle were set to 380K. The wall inlet is heated up with constant

temperature and constant velocity. The bed is operate in a constant pressure in atmosphere

The gas velocity consider to be vertical with not horizontal vectors. The expression below this

the equation of vertical gas velocity given by gas jet.

* , max ,

,

*0

6

* 3

s s s w

t w

s s

u vv

n g

6.2.2 CFD model simulation set upThe main contribute equation in this simulation would be solved by a, method called Semi-

Implicit Method for Pressure Linked equation (SIMPLE), it is designed for Eularian multiphasesimulation by discrete pressure linked equations. This method can divide all related parameters


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into finite controllable variables. Such as the solid volume fraction, granular kinetic flow and

mixture phase density. The simulation would study the center of the mesh point of the bed

based on these parameters. The velocity of the bed was calculate on the cross over mesh of the

bed with controlled solid volume surface. The condition in the bed is constant and do not

interact with outside environment. The grid size for this simulation is 55*200 to ensure right

answer and each mesh can be investigate independently. (Y’ Behjat, 2007)

(Table 3)


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7 Result and discussion

7.1 Use CFD to modeling heat transfer in gas fludized bed7.1.1Overall characteristics of heat transferA freely bubble fluidized bed experiment was processed to analysis the heat transfer coefficient

with in it .In the one of experiment, the inlet jet was set near the heated wall as it been simulated

to study to study the relationship between heated wall’s heat transfer coefficient and

hydrodynamic. At inlet jet, the superficial velocity of gas is 1.2m/s and cause forming of bubble

in the wall vicinity. The thermal conductivity at solid phase was obtained by Kuipers model.

The figure below had shown the rise and formation of bubble in the bed with contours. Also

shows the time takes bubble leave bed is 1 second. It also shows the volume fractions of solid

phases and heat transfer activities at bed height of 0.15m respect to temporal variation .Becausethe solids particles bed were contact with the heated wall at the beginning, so the initial heat

transfer coefficient is at the highest point. Initially, the heat transfer coefficient is very high as

the bed comes in contact with the heated wall. (R’Yusuf, Moren, 2005)

(Fig 9)

(Fig 10)


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7.1.2 Different gas superficial velocity VS heat transfer coefficientThe graph below had shown the heat transfer coefficient take effect by the gas velocity at inlet.

The particle of the fluidized bed is 400μm . Due to unpredictable bed activity at begin of thesimulation, the data was record 3 second after simulation started. The average heat transfer

coefficient result was from last 2 second of the simulation. The graph shown the heat transfer

coefficient was rising up with the increase of gas superficial velocity. The experimental and

simulation suggest the similar trend for heat transfer coefficient. (M ‘Hamzehei,2009) As seen

in the figure, the heat transfer coefficient increases with gas velocity up to a certain point before

levelling down. Both simulations and experiments conform to this trend. The value is different

is because the simulation is a modified 2-D fluidized bed, but in real life is 3D. Furthermore,

it is necessary to simulated more model with longer period to revive more reliable result.

(Fig 11)

7.1.3 Different particle size VS heat transfer coefficientThe graph below had shown heat transfer coefficient two particles with different size in a

fluidized bed while increase their gas superficial velocity. The Fig. 6 shows the trend of heat

transfer coefficient against gas superficial velocity for two type particle different in size. Both

for experimental and simulated result at a given gas superficial velocity, the smaller particle

tend higher than larger particle. (R’Yusuf, Moren, 2005) It is because the smaller particle size

the larger contact area with the environment, in result this, the heat transfer coefficient is higher.

For reason for difference in value of perdition and simulation is stated in first discussion the

quantitative difference between predictions and measurements persist due to reasons cited

before. Even though, the simulation result follow the similar trend as the experimental result.


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(Fig 12)


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7.2 Use CFD to simulate a fluidized bed reactor and study its

heat transfer

7.2.1 Overall discussion of the result

In order to show the simulation can predict the correct tend of the bed activity , the simulationresult were necessary to compare with experimental data from literature research .As the figure

13 show below as set of experimental data and simulation data were compared base on the bed

expansion vs time period. (Y’ Behjat, 2007)Two model of simulations had been compare with

the experimental data and the graph suggest that Syamlal-O'Brien and Gidaspow have 7.7%

and 10. % difference for time vs bed expansion ratio

Both simulation model had given right trend of bed expansion ratio vs gas superficial velocity

however the result given by Syamlal – O'Brien model is more close to the experimental result.

However, it does not necessary mean Syamlal – O'Brien is better than another, it is because it is

more suitable to this kind of simulation.

In figure 14 is the result of experiment and simulation on the solid particle viodage on cross

section against time. At gas velocity of 0.38m/s. both simulation and experiment were startrecording after 5 to 10 second as the bed activity was not obvious. The graph suggest that in

either simulation or experiment the bubble had merge in the middle of the bed and move up to

bed surface. However difference still can be found between experimental results on the solid

volume fractions. Gidaspow simulation model shows higher error in predict bubble activity,

thus Syamlal – O'Brien summation model is more appropriate to predict hydrodynamic in this

case.

(Fig 13)


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(Fig 14)

7.2.2 Particles distributions and

hydrodynamic simulationThis discussion is about solids particle activity

while they all uniform distrusted in the bed with

constant gas velocity pump into the bed.

(Vg=0.38m/s). These activity was predicted by

two drag force model .The colours in a t=1s

suggest the bed high was increased while bubble

can be observed. The bed high then drop while

bubble left the bed. From graph a, b, c, d suggest

that when bubble was formed at the bottom of

the bed was very small and became bigger

bubble while rise to top of bed. In the result of

bed wall defect and contact with other bubble in

the bed, the target bubble looks stretched. Both

simulation model had given similar result. (Y’

Behjat, 2007)

The graph in figure 16 suggest that when inlet

jet speed is 38cm/s volume fraction of solid

phases were different because of particle . (M

‘Hamzehei,2009)The particles with much larger

diameter tend to expand more at bottom of the

bed and less intensive bed activity near top of

bed. Furthermore, reactor with bimodal

particles has greater bed expansion when

mono-dispersed particles was used in the

reactor. (Fig 15)


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(Fig 16)

7.2.3 Simulation of heat transfer in fluidized reactorThe discussions in this part is about the heat

exchange between solid phase and gas

phase .while gas pump into bed with constant

velocity. The heat transfer coefficient of these

two referring phases were analyzed while

polymerization reaction is the heat and

hydrodynamic source .Two different bed reactor

were investigated with same initial bed height

0.4mThe polymerization reaction had cause the

temperature increase in reactor. However,

temperature is not uniform distrusted, at the top

of bed highest temperature can be observed from

the figure 17 a. Inversely, figure 17b shows the

gas temperature is more uniform distributed by

the observation of less hot spot.

Simulation results for the reactor with. Figure

18 has shown the effect of gas superficial velocity on bed temperature .The trend of the graph

suggest that bed with higher gas superficial velocity, bed tend to have higher heat zone due to

frequent heat exchange between these two phases. Furthermore, this graph had also show thatthe temperature at bed height of 0.6m is almost constant that is due to in solid phase, particles

rarely reach these height. (Y’ Behjat, 2007)

In figure 19, it had shown the influence of inject gas superficial velocity on heating zone of

solid phase. The trend suggest that the higher heat transfer coefficient in solid phase can be

obtained by increase gas superficial velocity similar as figure 18. In the result of that however,

the solid phase would have less temperature, as more heat exchange merge during this period

and particles loss heat to gas. A temperature peak of solid phase can be observed at bed height

of 0.55m. It is result of large solid volume fraction in that area with higher contacting area


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(Fig18) (Fig19)


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8 Conclusions

8.1 Use CFD to modeling heat transfer in gas fludized bed

In this simulation, an Eulerian multiphase modeling is used to simulate 2-D bubbling fluidized bed to study different factor effect on heat transfer coefficient. The solids volume fraction and

bed hydrodynamics near the vicinity of the wall can effect on the heat transfer coefficient

significantly .Two solids thermal conductivity models were used in the simulation. The result

suggests that bed with higher gas superficial velocity or smaller particles can obtain much

higher heat transfer coefficient. (R’Yusuf, Moren, 2005)The result value of simulation is fair,

as difference can be found when compare to experimental result. Further research and

simulation is necessary to predict the heat transfer coefficient in the fluidized bed with 3D

modeling. So the capability of the simulation software can be fully developed and more

accurate result is expected.

8.2 Use CFD to simulate a fluidized bed reactor and study its

heat transferA 2D fluidized bed was built to simulation the model of transfer coefficient and

hydrodynamic .the first stage research suggest that Eulerian multiphase is the most appropriate

simulation approach for this project study . The Eulerian multiphase approach consist of solid-

gas phase equations and momentum equations. A compare was done between simulated result

and experimental result of bed expansion vs time. The result graph shows the simulation model

can predict the bed activity quite well.

It also successfully predict that the formation of bubble is at the bottom of the bed and these

bubble would travel to the top of bed with other bubble to form one bigger bubble.

The predictions made by Syamlal – O'Brien and Gidaspow model have very similar outcome.

However, Syamlal – O'Brien has more closed result experimental result.

The fluidized bed with larger particle diameter tend to have larger volume fraction of solid

phase at the bottom of the bed and few at top of bed.

Furthermore, also can observed the fluidized bed with mono-particles tend to have less bed

expansion and activity when compare to bimodal particles

At last the analysis result of hydrodynamic behavior in solid and gas phases shows the

temperature has significant change when closer to the reactor due to the heat source in the bed


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9 Reference

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Appendix A

Table of figure

Figure number Figure page DescriptionFigure 1 7 Gas velocity vs pressure

drop

Figure 2(a,b) 7 Force experienced by solid

particle

Figure 3 8 Particles in fluidization

Figure 4 9 Multiphase fluidization

indication

Figure 5 10 Single phase vs multiphase

Figure 6 11 Gas velocity vs pressure

drop

Figure 7 13 Bubble in fluidized bedFigure 8 16 Set up for CFD gas fluidized

bedFigure 9 20 Solid Volume fraction graphFigure 10(a,b) 20 Solid volume fraction

against timeFigure 11 21 effect of gas velocity on

heat transfer coefficientFigure 12 21 Effect of particle size on

heat transfer coefficientFigure 13 22 Bed expansion vs gas

velocityFigure 14 22 bed expansion vs bed

heightFigure 15 23 Volume fraction in

reactor bedFigure 16 23 Solid volume fraction vs

bed heightFigure 17(a,b) 24 Reactor bed

hydrodynamic Vs bed

heightFigure 18 24 Heat transfer coefficient

VS timeFigure 19 24 Heat transfer coefficient

VS bed height


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Symbols and units


41/41

Bibliography

Bubble-Wall interaction for asymmetric injection of jets in solid- gas fluidized bed

CFD modelling of heat and mass transfer of fluidized bed dryer

CFD Modeling of Heat Transfer in Gas Fluidized Beds

CFD modeling of hydrodynamic and heat transfer in fluidized bed reactors

CFD simulation of pharmaceutical particle drying in a bubbling fluidized bed reactor

Comparison of fluidized bed flow regimes for steam methane reforming in membrane

reactors: A simulation study

Computational study of heat transfer in bubbling fluidized bed with Geldart A powder.

Comparison of fluidized bed flow regimes for steam methane reforming in membrane

Reactors a simulation study

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