fyp final report e

90
1 CN4118R: B.Eng. Dissertation Semester 1 AY 2010-2011 Coal Gasification for Clean Energy: A Simulation Study of the Downer and the Solids Distributor. Submitted in Partial Fulfillment for the degree in Bachelor of Engineering, National University of Singapore By Jayadev S Marol U070448E Supervisor: Professor Wang Chi-Hwa Date of Submission: 3 rd January 2011

Upload: cunbai-lu

Post on 03-Oct-2014

191 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: FYP Final Report E

1

CN4118R: B.Eng. Dissertation

Semester 1 AY 2010-2011

Coal Gasification for Clean Energy: A Simulation

Study of the Downer and the Solids Distributor.

Submitted in Partial Fulfillment for the degree in Bachelor of Engineering,

National University of Singapore

By

Jayadev S Marol

U070448E

Supervisor: Professor Wang Chi-Hwa

Date of Submission: 3rd January 2011

Page 2: FYP Final Report E

ACKNOWLEDGEMENTS

Firstly, I would like to express my sincere gratitude to my supervisor, Professor Wang

Chi-Hwa for providing me with the golden opportunity to work on this project and

uncovering my interest in multiphase flows. He has been a great source of motivation and

I would like to thank him for providing me with valuable ideas and suggestions during

the monthly meetings.

Secondly, I am highly indebted to my assigned mentor, Dr Cheng Yongpan who has

patiently helped me with my modeling and related queries. I would also like to extend my

acknowledgement to Dr Eldin Lim for the healthy discussions and guidance on my

project. Thanks to all others who were part of Professor Wang Chi-Hwa’s research group

for helping me whenever I needed their assistance. It was a wonderful experience

working with them.

I would also like to thank my parents for providing me with the necessary moral support

and encouragement without which the completion of this thesis may not have been

possible.

Page 3: FYP Final Report E

1

Summary

Hydrodynamic simulation of the gas-solid flow in the downer was carried out using both

the Eulerian-Eulerian and Eulerian-Lagrangian models. In using the Eulerian-Eulerian

appraoch, solids were modeled as pseudo-fluid using the Kinetic Theory of Granular

Flow and the main focus was to investigate the most suitable drag closure for various

flow conditions. Three different drag closures by Wen &Yu, De Felice and Matsen were

tested. Firstly, the axial distribution of the solids concentration in the downer was

simulated and compared with available experimental data in literature. The commonly

used Wen & Yu’s drag closure gave simulation results that were comparable with

experimental data under high superficial gas velocity flow conditions but the solids

holdup values were severely over-predicted at low gas velocity. Matsen’s drag closure

was found to give a much better solid holdup prediction compared to the other two drag

closures under low superficial gas velocity. Secondly, the radial distribution of the solids

concentration was compared. The nature of the radial solid holdup profile predicted by

Matsen’s drag closure was also different compared to the other two drag closures. Wen &

Yu’s and De Felice’s drag closure predicted a maximum concentration at the wall, similar

to the experimental results by Cao and Weinstein (2000). Matsen’s drag closure predicted

that the peak of the solids holdup at the wall gradually moves towards the center with the

magnitude of the peak decreasing in the fully developed region of the downer. These

simulation results are consistent with experimental results by Zhang et al (1999).

Simulation results using the Eulerian-Lagrangian method were consistent with the

Eulerian-Eulerian model with the Wen & Yu’s drag closure.

Page 4: FYP Final Report E

2

As the flow in the downer is assisted by gravity, there is short contact time between the

phases in the downer (Cheng, Wu, Zhu, Wei, & Jin, 2008). This short contact time

imposes a demand on the downer inlet design to enable good mixing of the phases. Thus

two inlet designs have been proposed and consequently the sand and coal flow patterns

are investigated in efforts to innovate new inlet designs which provide better mixing.

Page 5: FYP Final Report E

3

Contents Page

Summary ............................................................................................................................. 1

Chapter 1: Introduction ................................................................................................... 5

Objective ............................................................................................................................. 7

Chapter 2: Literature review of the downer .................................................................... 8

2.1 The flow structure in the downer .............................................................................. 9

2.2 The Axial solids concentration distribution profile. ................................................ 10

2.3 Correlations to predict the solids concentration in the fully developed region of the downer. .......................................................................................................................... 11

2.4 The radial solids concentration distribution profile ................................................ 12

Chapter 3: Modeling the hydrodynamics of the downer .............................................. 16

3.1.1 Eulerian–Eulerian method .................................................................................... 17

3.1.2 Equations used in the Eulerian-Eulerian model ................................................... 18

3.2 Eulerian-Lagrangian method ................................................................................... 25

3.2.1 Equations used in Eulerian- Lagrangian Method ................................................. 25

Chapter 4: Procedures for Simulation ........................................................................... 27

4.1 Geometry and Meshing ........................................................................................... 27

4.2 Operating conditions and boundary conditions ....................................................... 28

4.3 Solution Procedures................................................................................................. 30

Chapter 5: Simulation results & Validation of the Eulerian-Eulerian Model .............. 32

5.1 Wen & Yu’s Drag Closure ...................................................................................... 32

5.1.1 Axial distribution of the solids concentration ................................................... 32

5.1.2 Axial distribution of the solids velocity ........................................................... 37

5.1.3 Effect of particle diameter, particle density and downer diameter on model simulation. ................................................................................................................. 38

5.2 Improvements to the model using various drag correlations .................................. 41

5.3 De Felice’s drag closure .......................................................................................... 42

5.4 Matsen’s drag closure .............................................................................................. 43

5.5 Radial distribution of solids concentration .............................................................. 46

Chapter 6: Validation of the Eulerian-Lagrangian model ............................................ 49

6.1 Residence time of particles . ................................................................................... 49

Page 6: FYP Final Report E

4

6.2 Axial velocity distribution of particles. ................................................................... 51

6.3 Radial velocity distribution of particles .................................................................. 53

Chapter 7: Solids distributor and Inlet design of the downer ....................................... 55

7.1 Proposed Inlet Designs ............................................................................................ 59

7.2 Modeling Approach and simulation conditions ...................................................... 60

7.3 Simulation results .................................................................................................... 63

7.3.1 Axial Solid distribution .................................................................................... 63

7.3.2 Radial Solid distribution ................................................................................... 66

Chapter 8: Conclusion .................................................................................................. 69

Chapter 9: Recommendations and Future Work .......................................................... 71

References ......................................................................................................................... 73

Nomenclature ....................................................................................................................... i

List of Figures .................................................................................................................... iii

List of Tables ...................................................................................................................... v

I. Appendix A : Axial solids velocity distribution profiles ............................................ vi

II. Appendix B: Experimental Data for the downer solid holdup for the Gs=253 kg/m2s by Guan et al (2010) ........................................................................................................ viii

III. Appendix C: Comparison of the average solids hold up for the two inlet arrangements with Ug=20 m/s. ........................................................................................... ix

IV. Appendix D: Radial distribution of the solids at various axial positions for the two inlet arrangements. .............................................................................................................. x

Tangential arrangement ............................................................................................... x

Normal arrangement .................................................................................................. xii

Page 7: FYP Final Report E

5

Chapter 1: Introduction

Coal is and in the foreseeable future will be a considerable source of fuel for power

generation but there has been increasing need for clean coal power generation and a

constant search for processes that have higher efficiency (Hanson.S, Patrick, &

Walker.A, 2002). Thus instead of conventional coal fired power plants, combined-cycle

fluidized-bed gasification systems are now emerging technologies that offer a promising

clean way to convert coal into electricity, hydrogen and other valuable energy products

(Guan, Chihiro, Ikeda, Yu, & Tsutsumi, 2009). In the current project, a Triple-bed

Combined Circulating Fluidized (TCFB) bed system is being considered for the coal

gasification process and the setup of the system is shown in the following figure 1.1.

Figure 1.1: Triple bed Circulating Fluidized Bed (Guan G. , Chihiro, Ikeda, Yu, & Tsutsumi, 2009).

As shown above, the triple-bed combined circulating fluidized bed is mainly composed

of a downer, a bubbling fluidized bed and a riser. The coal is rapidly pyrolyzed in the

downer first and the obtained gas and tar are separated from the char using a gas-solids

Page 8: FYP Final Report E

6

separator. The char then enters the bubbling fluidized bed (BFB) to be gasified with

steam (Guan G. , Chihiro, Ikeda, Yu, & Tsutsumi, 2009). The unreacted char can then be

channeled to the riser to be combusted with air. The produced heat from the combustion

can then be carried by inert solid medium such as sand and circulated into the downer and

BFB to provide the heat needed for pyrolysis and gasification process (Guan G. , Chihiro,

Ikeda, Yu, & Tsutsumi, 2009) .The cyclone is placed after the riser to separate the solids

from the air and the solids then enter the solids distributor to ensure that solids are well

distributed before they enter the downer (Guan, Chihiro, Ikeda, Yu, & Tsutsumi, 2009).

Essentially in a triple bed reactor, the pyrolysis reaction is carried out in the downer, the

gasification reaction in the BFB and char combustion in the riser. This method of

compartmentalizing the various reactions into various specific reactors helps to improve

the overall coal gasification efficiency.

Page 9: FYP Final Report E

7

Objective

The purpose of the research group is to model the flow in the triple bed circulating bed

which would help to study the flow patterns and to optimize the process. The research is

still in the initial stages and thus the objective of this thesis is to study the flow in the

downer and the solids distributor component of the TCFB system. Numerical simulations

of the downer hydrodynamics were conducted to predict the solids concentration and the

velocity profiles and the results have been validated with the experimental data available

from literature and from the experimental work of Guan et al, our partner research group

from University of Tokyo. Eulerian-Eulerian and Eulerian-Lagrangian models have been

used to model the hydrodynamics of the downer system. In the Eulerian-Eulerian model,

which has been used to a greater extent in this thesis, the effect of various drag closures

has been studied. Once a model with decent predictive capabilities has been established,

the model could then be used for optimization purposes.

Furthermore when conducting a primary study on various designs of the inlet structures,

it is neither efficient nor economical to study the flow fields experimentally. Therefore

this thesis also aims to illustrate that numerical simulation can be used as powerful tool to

study flow behaviors in the various geometries before making huge experimental

investments. Essentially, the effect of tangential inlet design and the normal inlet design

on the sand and coal holdup in the downer has been studied in this thesis using the

Eulerian- Eulerian Model.

Page 10: FYP Final Report E

8

Chapter 2: Literature review of the downer

Fluidization technique has been developed for more than several decades and previously

in conventional gas-solids flows, the particles are suspended by up flowing gas streams,

against the flow of gravity, such as in bubbling fluidized beds, turbulent fluidized bed and

risers (Cheng, Wu, Zhu, Wei, & Jin, 2008). Though the up flowing gas streams do

provide some benefits such as better inter-phase contact, it also leads to some setbacks

such as heterogeneous flow structure and significant back mixing of the phases (Cheng,

Wu, Zhu, Wei, & Jin, 2008). The overall performance of fluidized beds approaches that

to a continuous stirred tank reactor and limits improvement in some specific processes.

Thus the concept of a downer reactor was proposed and has attracted much attention in

the industry which can be seen by the numerous patents owned by major oil companies.

In a downer reactor, the gas and solids move downwards co-currently, in the direction of

gravity. This allows for a much more uniform gas-solid flow with less gas-solid back

mixing in the downer system (Ropelato, Meier, & Cremasco, 2005). Thus the flow

regime in the downer rector approaches that of a plug –flow reactor (Lehner & Wirth,

1999), (Qi, Zhang, & Zhu, 2008). Furthermore as the flow is now assisted by gravity, the

solids would be flowing at high velocity and this leads to lower residence time of the

components in the reactor (Jian & Ocone, 2003). These properties of the downer are

essentially beneficial for short contact time processes such as solids waste pyrolysis,

high-selectivity fluidized catalytic cracking, flash pyrolysis of coal and biomass where

intermediate products are favored (Qi, Zhang, & Zhu, 2008).

Page 11: FYP Final Report E

9

2.1 The flow structure in the downer

The flow structure can be divided into three sections according to the pressure profile in

the downer. At the entrance, the solid particles are accelerated by gravity and gas drag,

causing the pressure in the flow direction to drop (Liu, Luo, Zhu, & Beeckmans, 2001).

As the particle velocity increases and becomes equal to the gas velocity, the gas drag

acting on the particles become zero (Wang, Bai, & Jin, 1992). The pressure gradient at

this point becomes minimum and the pressure gradient is zero (Wang, Bai, & Jin, 1992).

The section from the inlet to this point marks the first acceleration section of the downer

(Wang, Bai, & Jin, 1992). After this section, the particles will still be accelerating due to

gravity and the particle velocity will exceed that of the gas velocity. The direction of the

gas drag becomes upward and the pressure increases gradually in the flow direction

(Johnston, Lasa, & Zhu, 1999 ). This stage is called the second acceleration stage and the

pressure gradient is greater than zero. In the third section, the velocity difference

between the particles and the gas velocity continues to increase until the drag force

becomes equal to the gravitational force. The particles will stop accelerating and particle

velocity will level off (Wang, Bai, & Jin, 1992). This constant velocity section is also

termed as the fully developed region (Liu, Luo, Zhu, & Beeckmans, 2001). The pressure

gradient is positive and constant as pressure continuously increases in the direction of the

flow (Wang, Bai, & Jin, 1992). The typical pressure profile of the downer is shown in

figure 2.1 below.

Page 12: FYP Final Report E

10

Figure 2.1: Pressure profile in a downer for Gs=202 kg/m2s and Ug=5 m/s.

2.2 The Axial solids concentration distribution profile.

Studies carried out have shown that the gas and solids flow is more uniform in the

downer then in the riser. The particle acceleration in the first two sections of the downer

results considerable dilution of the solids concentration and the solid holdup eventually

reaches the constant value in the fully developed region (Bolkan, Berruti, Zhu, & Milne,

2003). A typical solid concentration distribution profile in the downer is shown below in

figure 2.2.

Figure 2.2 : Solids concentration distribution profile in the downer for Gs =202 kg/m2s and Ug=5 m/s.

Page 13: FYP Final Report E

11

2.3 Correlations to predict the solids concentration in the fully developed region of the downer.

Previously, most of the correlations to predict the solid hold up in the fully developed

region of the downer were based on the “terminal solids concentration, ε’s , where

𝜀𝑠′ = 𝐺𝑠𝜌𝑔�𝑈𝑔+𝑈𝑡�

(1)

The equation above is based on the assumption that there is no particle agglomeration and

that of a uniform dispersion of particles in the downward gas flow (Qi, Zhang, & Zhu,

2008)

However many experimental results have showed that particle-clustering phenomenon

exists in the fully developed region of the downer and it cannot be neglected. Qi et al

(2008) considered the effects of the particle properties and various operating conditions

with different downer diameters to propose the following correlation,

𝜀𝑠∗ = 0.125 � 𝐺𝑠𝜌𝑝�𝑈𝑔+𝑈𝑡�

� � 𝑈𝑔�𝑔𝑑𝑝

�0.25

𝐴𝑟0.15 (2)

The predictions of the correlation above fitted well with experimental data obtained from

literature for low density downers (Qi, Zhang, & Zhu, 2008). For high-density downers

(εs > 0.07) the following correlation proposed by Guan et al (2010) could be used to

predict the solid concentrations in the fully developed region.

𝜀𝑠∗ = 0.104 (𝐺𝑠

𝜌𝑝�𝑈𝑔𝑑 + 𝑈𝑡�)0.56(

𝑈𝑔𝑑 + 𝑈𝑡

�𝑔𝐷)0.14𝐴𝑟0.155 (3)

Page 14: FYP Final Report E

12

2.4 The radial solids concentration distribution profile

There is yet to be a universal agreement on the nature of the radial profile of the solids

phase in the downer (Vaishali, Roy, & Mills, 2008). Different research groups have

presented different nature of radial solid hold up profiles. The experimental results by the

FLOTU group (Bai et al 1992; Wang et al 1992) reveal that the solids concentration

exhibits a peak near the wall region. In contrast, Cao and Weinstein (2000) claimed that

downer exhibits a maximum concentration at the wall itself. Experimental results by

Zhang et al (1999) seem to suggest that the initially the solids concentration is the

maximum at the wall and as the L/D ratio increases, the peak of the solid concentration

moves gradually towards the center with the magnitude of the peak decreasing.

The figure 2.3 below shows the radial solids concentration distribution as presented by

Wang et al (1992).

Figure 2.3 : Radial solids concentration profile (Wang, Bai, & Jin, 1992).

The figure above reveals that the radial concentration in the downers is generally uniform

but an annular region of high solids concentration exists near the wall of the downer. The

solids concentration increases with the increasing solids flux at all radial positions but the

increment is larger in the annular dense region (Wang, Bai, & Jin, 1992). When the gas

Page 15: FYP Final Report E

13

velocity increases at fixed solids flux, the radial solids concentration is said to become

more uniform (Wang, Bai, & Jin, 1992).

Wang et al (1992) have attributed the nature of the radial solids concentration above to

the minimization of the energy loss in a gas-solid suspension flow. In the center region,

the gas velocity is relatively high and thus the drag force acting on the solid particles is

larger (Kimm, Berruti, & Pugsley, 1996). This motivates the particles to move away from

center towards the wall region in order to lose less energy (Wang, Bai, & Jin, 1992),

(Kimm, Berruti, & Pugsley, 1996). Likewise the friction between the gas-solid

suspension and the wall causes the particles to move away from the wall region in order

to avoid losing more energy (Kimm, Berruti, & Pugsley, 1996). As a result of these two

opposing trends, an annular region of high solids concentration near the wall with a

uniform concentration at the center is formed. (Wang, Bai, & Jin, 1992).

In contrast to the experimental results from Wang et al (1992), Cao and Weinstein (2000)

claimed that downer exhibits a maximum concentration at the wall. The figure 2.4 below

shows the radial solid concentration profile obtained in their experiments.

Figure 2.4: Radial solids concentration profile (Cao & Weinstein, 2000).

Page 16: FYP Final Report E

14

A possible reason for the difference in the radial solid holdup profiles obtained could be

attributed to the different measuring equipment used by Cao and Weinstein as compared

to Wang et al (1992). An optical fiber solid concentration probe was used by Wang et al

(1992) whereas an X-ray imaging system was used by Cao and Weinstein (2000) to

measure the radial solids concentration profile. Nevertheless the solids fraction measured

away from the wall show similar profiles in most of the works and it is only the

concentration at the wall that is not in agreement.

Zhang et al (1999) did a study of the radial profiles of the solid holdup under 11 different

operating conditions and they measured the radial solids distribution using optic fiber

solid concentration probe at 8 different axial positions. The results obtained are presented

in figure 2.5 below (Zhang, Zhu, & Bergougnou, 1999).

Figure 2.5 : Radial solids concentration profile, (Zhang, Zhu, & Bergougnou, 1999).

Page 17: FYP Final Report E

15

From the experimental results above, it can be seen that the radial solid hold up is

initially fluctuating due the ‘solids distributor’s effect at about 0.020 m ( (Zhang, Zhu, &

Bergougnou, 1999). Slightly below the entrance at about 0.5 m, the solid concentration

tends to peaks at the wall. However as the L/D ratio increases, the radial profiles start to

become more uniform. The peak of the solids holdup seems to gradually move towards

the center with the magnitude of the peak decreasing (Zhang, Zhu, & Bergougnou, 1999).

Thus the experimental results of the Zhang et al (1999) might seem to suggest that the

solids concentration peaks at the wall when the flow is still in the developing zone and

further down the downer, the peak tends to shift towards the center of the wall. The

results also indicate that the nature of the solids holdup is not fixed throughout the

downer.

Page 18: FYP Final Report E

16

Chapter 3: Modeling the hydrodynamics of the downer

Numerical methods have been broadly used to study particle–fluid flow in the recent

years. Modeling the gas-solids flow in the downer system is essentially a multiphase flow

problem. The main constraint that lies in the modeling of the downer reactor is the large

separation of scales (Hoef, Annaland, Deen, & Kuipers, 2008). The flow structure which

is in the order of meters is influenced by the interactions of the gas and solid particles that

are well below the millimeter scale (Hoef, Annaland, Deen, & Kuipers, 2008) .

In modeling the multiphase flow, the dynamics of each of the phase can be can modeled

via either considering the phase as a collection of discrete particles that obey Newton’s

law that requires a Lagrangian approach or via treating the solid phase as a continuum

that is governed by Navier-Stokes type equation which requires Eulerian approach (Hoef,

Annaland, Deen, & Kuipers, 2008). The hydrodynamics in the downer can thus be

simulated using the Eulerian- Eulerian model or the Eulerian-Lagrangian model. The

main difference between these two models depends on the treatment of the solid phase

which is treated either as a continuum phase or as a discrete particle.

Numerical simulations can be carried out using computational fluid dynamics software.

ANSYS FLUENT is one such commercial software that contains the broad physical

modeling capabilities needed to model multiphase flow, turbulence, heat transfer, and

reactions for various industrial applications. FLUENT will be used to model and analyze

the flow and performance of the downer systems for both the Eulerian-Eulerian approach

and the Eulerian-Lagrangian approach.

Page 19: FYP Final Report E

17

3.1.1 Eulerian–Eulerian method

In the Eulerian-Eulerian approach, both the gas phases and the solid phase are allowed to

exist at the same point and at the same time forming an interpenetrating continuum

(Vaishali, Roy, & Mills, 2008).

Figure 3.1: Modeling the interaction between solid and gas phase (Vaishali, Roy, & Mills, 2008).

As shown in Figure 3.1, modeling the downer system needs to take into account the

interactions within and between the flow fields as well as the fluctuations flow fields of

each phase (Vaishali, Roy, & Mills, 2008). The interaction between particle mean motion

and the gas mean motion is incorporated by the drag force correlations. The relation

between the gas fluctuating motion and the gas mean motion is modeled using the

appropriate κ-Є turbulence models. Kinetic Theory of Granular Flow is used to relate the

interaction between the random particle fluctuating motion and the mean particle motion.

In this theory, solid-phase stresses are described in a manner similar to the stresses in

dense-gas kinetic theory whereby the fluctuating kinetic energy of solid is represented by

the term ‘granular temperature’(Θs) (Cheng, Wei, Guo, & Yong, 2001), (Vaishali, Roy, &

Mills, 2008). Other solid phase transport properties such as the solid phase pressure and

solid stresses are also described in terms of granular temperature. (Vaishali, Roy, &

Page 20: FYP Final Report E

18

Mills, 2008). One possible drawback of this approach is that the predictive ability of the

model depends very much on the correctness and tuning of the closures proposed for

indeterminate terms.(Cheng, Wei, Guo, & Yong, 2001). In the present work, the

interaction between the fluctuating fields of the gas phase and solid phase is not

considered as it is expected to be a correlation of a much lower order as compared to the

other three interactions (Vaishali, Roy, & Mills, 2008).

3.1.2 Equations used in the Eulerian-Eulerian model

Continuity Equation

𝜕(𝜀𝑘𝜌𝑘)𝜕𝑡

+ ∇. (𝜀𝑘𝜌𝑘𝑢𝑘����⃗ ) = 0 (4) 𝑘 = 𝑓 𝑓𝑜𝑟 𝑓𝑙𝑢𝑖𝑑𝑘 = 𝑠 𝑓𝑜𝑟 𝑠𝑜𝑙𝑖𝑑

Conservation of momentum

For fluid phase

𝜕(𝜀𝑓𝜌𝑓𝑢𝑓����⃗ )𝜕𝑡

+ ∇. �𝜀𝑓𝜌𝑓𝑢𝑓����⃗ .𝑢𝑓����⃗ � = −𝜀𝑓∇p + ∇.𝑇�𝑓 + 𝜀𝑓𝜌𝑓�⃗� + 𝐾𝑠𝑓�𝑢𝑠����⃗ − 𝑢𝑓����⃗ � (5)

Note that in the equation above p is pressure shared by all the phases and Ksf is the gas-

solid momentum exchange co-efficient.

𝑇�𝑓 is the fluid phase stress-strain tensor which takes the following form

𝑇�𝑓 = 𝜀𝑓µ𝑓�∇𝑢𝑓����⃗ + ∇𝑢𝑓����⃗𝑇� + 𝜀𝑓 �𝜆𝑓 −

23

µ𝑓� ∇.𝑢𝑓����⃗ 𝐼 ̿ (6)

Where µf and λf is the fluid shear and bulk viscosity.

For solid phase

𝜕(𝜀𝑠𝜌𝑠𝑢𝑠����⃗ )𝜕𝑡

+ ∇. (𝜀𝑠𝜌𝑠𝑢𝑠����⃗ .𝑢𝑠����⃗ ) = −𝜀𝑓∇p − ∇ps + ∇.𝑇�𝑠 + 𝜀𝑠𝜌𝑠�⃗� + 𝐾𝑠𝑓�𝑢𝑓����⃗ − 𝑢𝑠����⃗ � (7)

𝑇�𝑠 is the solid phase stress-strain tensor which takes the following form

Page 21: FYP Final Report E

19

𝑇�𝑠 = 𝜀𝑠µ𝑠�∇𝑢𝑠����⃗ + ∇𝑢𝑠����⃗𝑇� + 𝜀𝑠 �𝜆𝑠 −

23

µ𝑠� ∇.𝑢𝑠����⃗ 𝐼 ̿ (8)

Where µs and λs is the solids shear and bulk viscosity.

Compared to the fluid phase momentum equation, it can be seen that there is an extra

solid pressure term, ps, in the equation above. Details can be found in the paragraphs that

follow.

Constitutive equations

The gas-solid momentum exchange co-efficient, Ksf

The interaction of prime importance in the downer reactions is that of the mean flow field

of the gas phase and the mean flow fields of the solids phase which is stated as the ‘drag’

interaction in figure 3.1. The drag force in the downer system depends on the slip

velocity (absolute difference between the mean gas phase velocity and solid phase

velocity) and the local solids concentration (Vaishali, Roy, & Mills, 2008). There has

been several momentum exchange coefficient that have been proposed based on

experiments and fine scale simulations (Vaishali, Roy, & Mills, 2008). Three of such

momentum exchange coefficients are shown below.

Page 22: FYP Final Report E

20

Table 1: Various gas-solid momentum transfer coefficients

Reference Gas-solid momentum exchange coefficient, Ksf

Wen & Yu’s closure (1966) 𝐾𝑠𝑓 =

34𝐶𝐷

𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�µ𝑔

𝜀𝑓−2.65 (9)

Where

𝐶𝐷 =24

𝜀𝑓𝑅𝑒𝑝�1 + 0.15(𝜀𝑓𝑅𝑒𝑝)0.687� (10)

𝑅𝑒𝑝 =𝜌𝑔𝑑𝑝�𝑢𝑠 − 𝑢𝑓�

µ𝑓 (11)

Matsen’s closure (1982)

𝐾𝑠𝑓 = 0.006475𝐶𝐷𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�

µ𝑔𝜌𝑔𝜌𝑚𝑖𝑥

𝜀𝑠−0.586 (12)

Where

𝐶𝐷 =24

𝜀𝑓𝑅𝑒𝑝�1 + 0.15(𝜀𝑓𝑅𝑒𝑝)0.687� (13)

Di Felice’s closure (1994)

𝐾𝑠𝑓 =34𝐶𝐷𝜀𝑓2𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�𝜀𝑓−𝜂 (14)

Where

𝐶𝐷 =1𝜀𝑓

(0.63 + 4.8�1𝑅𝑒𝑝

)2 (15)

𝜂 = 3.7 − 0.65𝑒(− �1.5−log�𝑅𝑒𝑝�

2�2 ) (16)

The solid pressure term, ps.

For granular flows in the compressible regime (where the solids volume fraction is less

than its maximum allowed value), a solids pressure is calculated independently and used

for the pressure gradient term,∇ps , in the solids/ granular phase momentum equation

Page 23: FYP Final Report E

21

(equation 7). ( ANSYS FLUENT, 2006) (Lun, B., J., & Chepurniy, 1984), (Cheng, Wei,

Guo, & Yong, 2001).

𝑝𝑠 = 𝜀𝑠𝜌𝑠𝛩𝑠 + 2𝜌𝑠(1 + 𝑒𝑠𝑠)𝜀𝑠2𝑔𝑜,𝑠𝑠𝛩𝑠 (17)

The solids pressure equation above consists of the kinetic term and a second term due to

particle collisions. The term ess refers to the coefficient of restitution for particle-particle

collisions which is assigned to be 0.9 and the term go,ss refers to the radial distribution

function which is a correction factor that modifies the probability of collisions between

particles when the solid granular phase becomes dense ( ANSYS FLUENT, 2006). This

function may also be interpreted as the non-dimensional distance between spheres and it

takes the following form for one solids phase ( ANSYS FLUENT, 2006), (Cheng, Wei,

Guo, & Yong, 2001).

𝑔𝑜,𝑠𝑠 = �1 − (𝜀𝑠

𝜀𝑠,𝑚𝑎𝑥)13�−1

(18)

Where εs,max is the maximum packing limit of the particles which is assigned to be 0.63.

The solids shear viscosity and bulk viscosity term

The solids stress tensor contains shear and bulk viscosities arising from particle

momentum exchange due to translation and collision. The solids shear viscosity term is

comprised of the collisional, kinetic and frictional parts as shown in the equation below

(Gidaspow, 1994)

µ𝑠 = µ𝑠,𝑘𝑖𝑛 + µ𝑠,𝑐𝑜𝑙 + µ𝑠,𝑓𝑟𝑖𝑐 (19)

The frictional component, µ𝑠,𝑓𝑟𝑖𝑐, neglected in this work.

Page 24: FYP Final Report E

22

The expression for kinetic viscosity term,µ𝑠,𝑘𝑖𝑛, is derived by (Syamlal, Rogers, &

O’Brien, 1993) to be

µ𝑠,𝑘𝑖𝑛 = 𝜀𝑠𝑑𝑠𝜌𝑠�𝛩𝑠𝜋6(3 − 𝑒𝑠𝑠)

�1 +25

(1 + 𝑒𝑠𝑠)(3𝑒𝑠𝑠 − 1)𝜀𝑠𝑔𝑜,𝑠𝑠� (20)

The collisional part of the viscosity, µ𝑠,𝑐𝑜𝑙, is modeled as follows (Syamlal, Rogers, &

O’Brien, 1993)

µ𝑠,𝑐𝑜𝑙 =45𝜀𝑠𝑑𝑠𝜌𝑠𝑔𝑜,𝑠𝑠(1 + 𝑒𝑠𝑠)(

𝛩𝑠𝜋

)12 (21)

The bulk viscosity, 𝜆𝑠, term appearing in equation 8 has the following form as described

by (Lun, B., J., & Chepurniy, 1984)

𝜆𝑠 =43𝜀𝑠𝑑𝑠𝜌𝑠𝑔𝑜,𝑠𝑠(1 + 𝑒𝑠𝑠)(

𝛩𝑠𝜋

)

12

(22)

The granular temperature term

The granular temperature for the solids phase is proportional to the kinetic energy of the

random motion of the particles. The transport equation derived from kinetic theory of

granular flow and takes the following form (Ding & Gidspow, 1990).

32�𝜕(𝜀𝑠𝜌𝑠𝛩𝑠)

𝜕𝑡+ ∇. (𝜀𝑠𝜌𝑠𝑢𝑠����⃗ 𝛩𝑠)� = �−𝑝𝑠𝐼 ̿+ 𝜏�̿��:∇𝑢𝑠����⃗ + ∇. �𝑘𝛩𝑠∇𝛩𝑠� − 𝛾𝛩𝑠 + 𝛷𝑓𝑠 (23)

Where

�−𝑝𝑠𝐼 ̿+ 𝜏�̿��:∇𝑢𝑠����⃗ refers to the generation of energy by the solids tensor.

𝑘𝛩𝑠∇𝛩𝑠 refers to the diffusion of energy (𝑘𝛩𝑠 being the diffusion coefficient) which under

the Syamlal model has the following form (Syamlal, Rogers, & O’Brien, 1993).

𝑘𝛩𝑠∇𝛩𝑠 =15𝜀𝑠𝑑𝑠𝜌𝑠�𝛩𝑠𝜋4(41 − 33𝛹)

(1 +125𝛹2(4𝛹 − 3)𝜀𝑠𝑔𝑜,𝑠𝑠 +

1615𝜋

(41 − 33𝛹)𝛹𝜀𝑠𝑔𝑜,𝑠𝑠 (24)

Page 25: FYP Final Report E

23

Where

𝛹 =12

(1 + 𝑒𝑠𝑠) (25)

𝛾𝛩𝑠 refers to the collisional dissipation of energy and takes the following form derived by

Lun et al (1984).

𝛾𝛩𝑠 = 12(1 − 𝑒𝑠𝑠2)𝑔𝑜,𝑠𝑠

𝑑𝑠√𝜋𝜌𝑠𝜀𝑠2𝛩𝑠

32 (26)

and

𝛷𝑓𝑠 refers to the energy exchange between the fluid phase and the solid phase represented

by

𝛷𝑓𝑠 = −3𝐾𝑠𝑓𝛩𝑠 (27)

Thus in applying the equations, a value for granular temperature term, 𝛩𝑠, is needed. It

can be done by either assuming a constant granular temperature when the system is dense

or by algebraic formulation of the transport equations by neglecting the diffusion and

convection term ( ANSYS FLUENT, 2006). Algebraic formulation method to determine

the granular temperature term was used in this thesis.

κ-Є turbulence model

In order to account for the turbulent fluctuations in the gas–mean motion, dispersed κ -Є

turbulence model is adopted.

𝛿(𝜀𝑓𝜌𝑓𝜅𝑓)𝛿𝑡

+ ∇. �𝜀𝑓𝜌𝑓𝑢𝑓����⃗ 𝜅𝑓� = ∇.�𝜀𝑓µ𝑡,𝑓𝜎𝜅

∇𝜅𝑓� + 𝜀𝑓𝐺𝑘,𝑞 − 𝜀𝑓𝜌𝑓Є𝑓 + 𝜀𝑓𝜌𝑓П𝜅𝑓 (28)

Page 26: FYP Final Report E

24

𝛿(𝜀𝑓𝜌𝑓Є𝑓)𝛿𝑡

+ ∇. �𝜀𝑓𝜌𝑓𝑢𝑓����⃗ Є𝑓�

= ∇.�𝜀𝑓µ𝑡,𝑓𝜎Є

∇Є𝑓� + 𝜀𝑓Є𝑓𝜅𝑓

(𝐶1Є𝜀𝑓𝐺𝑘,𝑞 − 𝐶2Є𝜌𝑓Є𝑞 + 𝜀𝑓𝜌𝑓ПЄ𝑓 (29)

Where κ is turbulent kinetic energy and Є is the dissipation rate.

The source terms П𝜅𝑓 and ПЄ𝑓 represent the influence of the dispersed sand and coal

phase on the continuous air phase. The term 𝐺𝑘,𝑞 represents production of the turbulent

kinetic energy and the term µ𝑡,𝑓refers to turbulent viscosity. 𝜎Є and 𝜎𝜅 are the turbulent

Prandtl numbers for Є and κ respectively. 𝐶1Є and 𝐶2Є are constants in the κ-Є turbulence

model taking the values 1.44 and 1.92 respectively ( ANSYS FLUENT, 2006).

Thus in summary, the Eulerian –Eulerian model set up is based on the following

1) A single pressure is shared by all the phases

2) Momentum and continuity equations are solved for each phase.

3) Granular temperature (solids fluctuating energy) can be calculated for each solid

phase.

4) Solid-phase shear and bulk viscosity are evaluated by applying kinetic theory of

granular flow.

5) Various types of Inter phase drag coefficients are available to account for the

interaction between the mean flow field of the gas phase and the solids phase

6) κ- Є turbulence model is applied to account for the turbulent fluctuations of the gas

mean velocity.

Page 27: FYP Final Report E

25

3.2 Eulerian-Lagrangian method

In the Eulerian-Lagrangian approach, the solid phase is treated as discrete particles and is

modeled by calculating the path of each individual particle with the Newton’s second law

(Cheng, Wei, Guo, & Yong, 2001). The advantage of using this approach is that each

particle’s trajectory can be displayed exactly. However since large number of trajectories

are need in order to determine the average behavior of the system, this approach can be

computationally expensive.

3.2.1 Equations used in Eulerian- Lagrangian Method

The fluid phase is treated as a continuum by solving the time-averaged Navier-Stokes

equations as presented in the Eulerian- Eulerian model (equations 4 and 5 ), while the

dispersed phase is solved by tracking a large number of particles in the flow-field. Only

equations used for the motion of particles are listed below.

𝑑𝑢𝑠𝑑𝑡

= 𝐹𝑑�𝑢𝑓 − 𝑢𝑠� + 𝑔𝑥 �𝜌𝑠 − 𝜌𝑓𝜌𝑠

� (30)

The equation above is written for the x-coordinate and can be extended to other co-

ordinates likewise.

𝐹𝑑�𝑢𝑓 − 𝑢𝑠� is the drag force per unit particle mass and Fd takes the following form

𝐹𝑑 =18µ𝜌𝑠𝑑𝑠

2𝐶𝑑𝑅𝑒𝑝

24 (31)

Page 28: FYP Final Report E

26

Two –way turbulence coupling

Similar to the Eulerian-Eulerian method, the standard κ-Є turbulence model is used to

account for the turbulent fluctuations in the gas–mean motion. While the continuous

phase always impacts the discrete phase, it is also possible to incorporate the effect of the

discrete phase trajectories on the continuum in the FLUENT software. This two-way

coupling is accomplished by alternately solving the discrete and continuous phase

equations until the solutions in both phases have stopped changing ( ANSYS FLUENT,

2006).

Page 29: FYP Final Report E

27

Chapter 4: Procedures for Simulation

FLUENT 6.3 and/or FLUENT 12 was used for all the simulations in this thesis. For small

or medium sized jobs that require less than 30 minutes to compute, the simulations were

run on a laptop with Windows Vista 32-bit dual core processor and 4 gigabyte RAM. For

large jobs (especially for unsteady state Eulerian- Lagrangian and Eulerian-Eulerian

models), parallel computing was done in a high performance computing portal to speed

up computation time.

4.1 Geometry and Meshing

In the first part of the thesis, a two-dimensional model of a downer with an internal

diameter of 0.1 m and a length of 9.3 m was used to simulate a two phase flow (a solid

phase and a fluid phase). The two-dimensional geometry was created in GAMBIT which

is a preprocessor to FLUENT. The model was formed via bottom-up approach whereby

vertices were first created and the relevant vertices were joined to form edges. The edges

were finally linked to form a face before the geometry is meshed.

Meshing involves the discretization of the model into smaller volumes and is a crucial for

the finite volume method to be accurate. The smaller the volume the more accurate the

results would be but at the cost of more computational time. Thus there is a trade-off

between accuracy and computational time. A simple meshing analysis was done to

minimize computational time and maximize accuracy. With that analysis, a grid size of

15 (radial) x 750 (axial) was deemed sufficient. The figure 4.1 below shows part of the

layout of the meshed geometry. It is oriented horizontally for better viewing of the

meshes.

Page 30: FYP Final Report E

28

Figure 4.1 : Layout of the meshed geometry of the downer.

4.2 Operating conditions and boundary conditions

The meshed geometry was then exported to FLUENT. The boundary and operating

conditions were then introduced. Since the predicted solids concentration and particle

velocity were to be compared with the experimental data conducted by Bolkan et al

(2003), the particle properties were applied as presented in the journal. The table below

shows the particle properties and the operating conditions used in the simulation.

Table 2: Operating conditions for the 2D model

Operating Conditions Value

Pressure (Pa) 101325 at the outlet

Gravity (m2/s) 9.81 downwards

Gas properties

Density (kg/m3) 1.225

Viscosity (Pa.s) 1.7894 x 10-5

Particle Properties

Density (kg/m3) 1500

Shape Sphere

Diameter (µm) 67

Downer Properties

Length (m) 9.3

Diameter (m) 0.1

Page 31: FYP Final Report E

29

Boundary conditions

The following figure below shows the boundary conditions stated at respective sections

of the model.

Figure 4.2 : Boundary conditions for the 2D Model.

Wall boundary condition

For the wall boundary condition when using the Eulerian-Eulerian approach, a no-slip

condition was specified for the fluid phase and for the solids phase, a shear force is stated

which takes the following form,

𝜏𝑠 = −𝜋6 √

3Ϛ𝜀𝑠

𝜀𝑠,𝑚𝑎𝑥𝜌𝑠𝑔𝑜,𝑠𝑠�𝛩𝑠�𝑢𝑠����⃗ ‖ (33)

Where �𝑢𝑠����⃗ ‖ particle slip velocity parallel to the wall and ζ represents the specularity

coefficient between the particle and the wall. As used by Vaishali et al (2008), a

specularity co-efficient of 0.5 was used.

Page 32: FYP Final Report E

30

For the wall boundary condition when using the Eulerian-Lagrangian approach, a no slip

condition was specified for the fluid phase. For the solids phase, the particles were

allowed to ‘reflect’ of the wall.

Velocity inlet condition

For the velocity inlet condition when using the Eulerian-Eulerian approach, the

magnitude and the direction of the velocity together with the volume fraction each of the

phases is stated.

For the velocity inlet condition when using the Eulerian-Lagrangian approach, the

magnitude and the direction of the velocity for the fluid phase is stated. For the solid

phase, the particles are allowed to be ‘trapped’ in the region. To state the value of the

mass flux for solids particles, “Interaction with Continuous Phase” function was enabled

under the discrete phase model and the particles were allowed to be injected from the top

surface.

Pressure outlet condition

For the pressure outlet condition when using the Eulerian-Eulerian approach, a uniform

gauge pressure of zero was stated.

For the velocity condition when using the Eulerian- Lagrangian approach, gauge pressure

of zero was stated and the discrete particles were allowed to be released and this was

indicated with the ‘escape’ condition.

4.3 Solution Procedures

The pressure–velocity coupled SIMPLE solver method was used in the iteration for the

convergence of the solution. The convergence criteria were usually set to 0.001 for all the

Page 33: FYP Final Report E

31

terms. To obtain more accurate results for two-dimensional steady-state models, smaller

convergence criteria of 10-5 was used. The second order UPWIND implicit differencing

scheme for the convective terms and the second-order implicit time integration method

was used to solve the motion equation of the fluid. The default under-relaxation

parameter values were used during the iteration process.

Steady-State or Transient model

Generally steady sate solver was used in the Eulerian-Eulerian approach. However at

times, it is not possible to achieve convergence using steady-state solver. Thus unsteady-

state solver with a time-step of 0.0025 was used to iterate for a time period of 5 to10

seconds to compare the simulated results with the experimental data.

Page 34: FYP Final Report E

32

Chapter 5: Simulation results & Validation of the Eulerian-Eulerian Model

For the first part of the thesis, the simulation results were compared with the

experimental data as presented by Bolkan et al (2003) to validate the Eulerian-Eulerian

model. Axial distribution of the solids holdup and the solids velocity are compared for

various flow conditions. Wen & Yu’s Drag closure is used in the initial simulations.

5.1 Wen & Yu’s Drag Closure

5.1.1 Axial distribution of the solids concentration

Figure 5.1: Simulation results for superficial gas velocity of 3.7 m/s.

Figure 5.1 above compares the simulation results obtained for fixed superficial gas

velocity of 3.7m/s under three different solids flux conditions (Gs =49 kg/m2s, 101

Page 35: FYP Final Report E

33

kg/m2s and 194 kg/m2s). Area weighted average is used to compute the mean solid

concentration at any axial position. The simulation results reveal a similar trend as the

experimental results. For all the three solids flux conditions, once the solids phase enters

the downer, acceleration of the particles causes dilution of the solid holdup. For a fixed

gas velocity, a higher solids flux would also result in a higher average solid holdup at any

axial position.

However the simulated average solid holdup values are severely over predicted compared

to the experimental data. For example, for solids flux of 49 kg/m2s, the simulated average

solids concentration at the fully developed region is about 0.0083 while the experimental

data gives a value of about 0.0055. Considerable over-prediction is also observed for the

other two solids flux scenarios. In addition, the path length taken for the solid phase to

achieve a ‘fully developed’ flow is much smaller than that compared to the experimental

data. The possible reasons for these observations are that at low superficial velocity, the

drag between the solids and the air phase is significant and the effects of particle

clustering are not effectively accounted for in the model.

Page 36: FYP Final Report E

34

Figure 5.2: Simulation results for superficial gas velocity of about 7 m/s.

Figure 5.2 above compares the simulation results obtained for a fixed superficial gas

velocity of about 7 m/s under three different solids flux conditions (Gs =49 kg/m2s, 101

kg/m2s and 208 kg/m2s). The model’s predicted solids concentration in the fully

developed region is in better agreement with the experimental data at a higher superficial

gas velocity. For example, for the solids flux of 49 kg/m2s, the simulated average solids

concentration in the fully developed region is about 0.0044 while the experimental result

is about 0.0039.

However, the experimental data shows a much gradual decreases in the solids

concentration along the downer while simulation results reveal a rather steep drop. Thus

the simulated length for the solids to attain fully developed flow is much shorter than the

experimental data

Page 37: FYP Final Report E

35

Figure 5.3: Simulation results for superficial gas velocity of about 10 m/s.

Figure 5.3 above compares the simulation results obtained for a fixed superficial gas

velocity of about 10 m/s under three different solids flux conditions (Gs =49 kg/m2s, 102

kg/m2s and 205 kg/m2s). It further validates that the model predicts the solid

concentration well under high superficial gas velocity. This is possibly because at higher

gas velocity, the particles attain a higher speed and are less likely to form clusters.

From observing figures 5.1, 5.2 and 5.3 it can be seen that for a fixed solids flux,

increasing the superficial gas velocity lowers the solid concentration. At a higher

superficial gas velocity, solid particles attain a higher speed and this causes further

dilution of the solids concentration.

Page 38: FYP Final Report E

36

From comparing all the simulation results above with the experimental data, it can be

seen that the model is able to predict the solids concentration distribution profile well

when a high superficial gas velocity is used. The model tends to overestimate the solid

concentration under low gas velocity and this is partially due to inability of the model to

fully account for the significant particle clustering effect at low gas velocity. Thus

improvements to the model should be made for more accurate predictions under low gas–

velocity flow conditions. Improvements were made to model by applying other drag

closures. De Felice’s and Matsen’s drag closure were tested and the latter seems to be

able to improve the model’s solid holdup prediction at low superficial gas velocity. The

results obtained for the other two closures are presented in sections 5.3 and 5.4.

Page 39: FYP Final Report E

37

5.1.2 Axial distribution of the solids velocity

Figure 5.4: Simulation results for solids flux of about 50kg/m2s with varying Ug.

The figure 5.4 above compares the simulated solids velocity under the three various

superficial gas velocities (3.7 m/s, 7.3 m/s and 10.1 m/s). The superficial gas velocity

tends to affect the velocity of the particles significantly.

The trend observed for the solids velocity distribution in the downer can be explained as

follows. Upon entering the downer, the particles will accelerate under the influence of

gravity and the gas drag force, causing them to pick up speed. As the speed of particles

becomes larger than the gas velocity, the gas drag becomes upward and this force starts to

oppose the gravitational force. Here the particles will be gaining speed but at a slower

rate. Once the drag force equals to that of the gravitational force, the particles will stop

Page 40: FYP Final Report E

38

accelerating and particle velocity will start to level off. (Wang, Bai, & Jin, 1992),

(Johnston, Lasa, & Zhu, 1999 ).

Though the simulation predicts a similar trend of the solids velocity as that of the

experimental measurements qualitatively, the values are severely under-predicted for low

superficial gas velocity condition. This is related to the observation made earlier that the

predicted solids holdup concentration are over -predicted at low gas velocity. Since

𝐺𝑠 = 𝜌𝑠𝜀𝑠𝑢𝑠 , when the model over estimates the solids concentration, it has to under

estimate the solid velocity in order to satisfy the mass conservation equation stated above.

Thus it becomes imperative that the model results for the solids velocity are linked to the

solid concentration results. If improvements are made to the model so that it is able to

better predict the solids concentrations for low gas velocity, the results for solids velocity

would tally with experimental data as well.

Similar observations were made when comparing the simulation results with the

experimental data for solids flux of about 100 kg/m2s and 200 kg/m2s with varying

superficial gas velocity. The plots obtained are presented in Appendix A.

5.1.3 Effect of particle diameter, particle density and downer diameter on model simulation.

From studying the plots above, it can be seen that the superficial gas velocity affects the

model’s accuracy more than the solids gas flux. In this section three other parameters that

are suspected to be influential are investigated of their effects on the model’s accuracy.

The three other parameters to be studied are particle diameter, particle density and

downer diameter. The equation proposed by Qi et al (2008) to predict the solids

composition in the fully developed region of the downer would be used to compare with

the results obtained by the model for various scenarios.

Page 41: FYP Final Report E

39

𝜀𝑠∗ = 0.125 �𝐺𝑠

𝜌𝑝�𝑈𝑔𝑑 + 𝑈𝑡���

𝑈𝑔𝑑�𝑔𝑑𝑝

�0.25

𝐴𝑟0.15 (2)

Thus in the next two graphs, a plot of εs*/ εs is plotted where εs* is the calculated solids

concentration in the fully developed region of the downer using equation (2) proposed by

Qi et al (2008). εs refers to the simulated solids concentration in the fully developed

region using the model. Thus when the value of εs*/ εs is closer to 1, it would indicate

that the model is in good agreement with the calculated value.

Figure 5.5: Model Comparison for varying Particle Diameter.

Figure 5.6: Model Comparison for varying Particle Density.

Page 42: FYP Final Report E

40

Figure 5.5 and 5.6 compares the model’s predictive accuracy for varying particle

diameter and particle density respectively. The two graphs reveal that the model is able to

predict the solids concentration in the fully developed region more accurately under

higher particle diameter and particle density. As particle size or density increases, clusters

are more prone to become discrete particles under higher gas velocity (Qi, Zhang, & Zhu,

2008). Thus the model being able to predict solids concentration more accurately for

increasing particle diameter and/or density with increasing gas velocity maybe related to

the model’s inability to fully account for the particle clustering phenomena.

By observing that the downer diameter term does not appear in equation (2), it can be

realized that the downer diameter does not have an influence on the solids concentration

in the fully developed region of the downer. The model reveals a similar relation as well.

It can be seen from table 3 that for varying the downer diameter from 0.05 to 0.1m and

keeping all other parameters unchanged, the 𝜀𝑠 values obtained are relatively constant.

Table 3: Model results for varying downer diameter.

Downer Diameter, m Gs, kg/m2s Ug, m/s ρp, kg/m3 dp, µm εs

0.05 49 3.7 1500 67 0.0082

0.1 49 3.7 1500 67 0.0083

0.25 49 3.7 1500 67 0.0084

0.5 49 3.7 1500 67 0.0084

Page 43: FYP Final Report E

41

5.2 Improvements to the model using various drag correlations

From the simulation results thus far, it has been established that the model prediction of

the solids concentration and solids velocity is good agreement to the experimental data

under high superficial gas velocity flow condition. However the model tends to

overestimate the solids concentration under low superficial gas velocity and this is

partially due to the inability of the model to fully account for the significant particle

clustering effect. Improvements to the model should be made so that more accurate

predictions can be made under low gas velocity scenarios.

Vaishalli et al (2008) have stated that gas-solid dispersed flow in the downer is complex

involving multiple modes of momentum transfer (as shown in figure 3.1). However gas-

solids’ drag is the most dominating interaction (Vaishali, Roy, & Mills, 2008). It has also

been found that considerable amount of ‘drag reduction’ occurs at the cluster formation

which results in higher slip velocity and thus cause a lower solids concentration

(Vaishali, Roy, & Mills, 2008). However the current Wen & Yu drag’s closure used in

the model is unable to account this phenomenon.

In efforts to try and improve the model under low superficial gas velocity, De Felice’s

drag closure and Matsen’s drag closure were tested and the results obtained are presented

section 5.3 and 5.4. Details and equations of the drag closures have already been

presented in Chapter 3. As these drag closures were not available in ANSYS FLUENT,

they were coded under User Defined Functions (UDF). Since it has been shown earlier

that the solids concentration and the solids velocity predictions are related by the

continuity equation, it is sufficient to ensure that the improved model is able to predict

Page 44: FYP Final Report E

42

the solids concentration well under low superficial velocity in the following

investigations.

5.3 De Felice’s drag closure

Figure 5.7: Simulation results using De Felice's drag closure for Ug=3.7 m/s.

From the figure above, it can be seen that the results obtained by using De Felice’s drag

closure are very similar to the Wen & Yu’s drag closure (figure 5.1). The solids

concentration profile under low superficial gas velocity is still a severe over- prediction

for the three solids flux scenarios. Thus it can be concluded that De Felice’s momentum

exchange co-efficient is in the same range as the Wen and Yu’s and it still not able to

lower the ‘gas-solids drag’ under particle clustering place. Vaishali et al (2008) have also

showed in their simulation study that the De Felice’s gas-solid momentum exchange co-

efficient is similar to the Wen & Yu’s gas-solid momentum exchange co-efficient.

Page 45: FYP Final Report E

43

5.4 Matsen’s drag closure

Figure 5.8: Simulation results using Matsen's Drag closure for Ug=3.7 m/s.

Figure 5.8 above shows that the simulated results using Matsen’s drag closure above

gives a much better fit to the experimental data under low gas velocity conditions. It is

also worth noting that the path length taken for the solids phase to achieve fully

developed flow is comparative to the experimental data. Thus figure 5.8 seems to suggest

that the Matsen’s drag closure is able to give a much better fit to the experimental data

under low superficial gas velocity. Vaishali et al (2008) have also showed in their

simulation study that compared to Wen & Yu’s and De Felice’s drag closure, Matsen’s

drag closures is better able to predict the solids concentration under low gas velocity.

Matsen’s drag closure predicts the slip velocity around five times that of the single

terminal velocity and this allows it to account for the ‘drag reduction’ that occurs at

Page 46: FYP Final Report E

44

cluster formation, eventually enabling the model to predict a lower solids concentration

(Vaishali, Roy, & Mills, 2008) .

Table 4: Comparison of various Drag coefficients

Comparing the momentum transfer expressions for the three drag closures above, it can

be seen that the nature of the Matsen’s drag co-efficient is different compared to the other

two drag closures. The solids concentration term in the Matsen’s drag closure is raised to

the power of negative 0.586 and this allows for a much lower momentum transfer co-

efficient with an increase in solids concentration. Furthermore while the initial constant

term is 0.75 for the De Felice’s and Wen & Yu’s drag closure, Matsen’s has the initial

constant term of 0.006475. These two factors enable the Matsen’s drag closure to account

for considerable amount of drag reduction at the cluster place and this finally results in

the better solids concentration prediction under low solids velocity scenarios (Vaishali,

Roy, & Mills, 2008).

To further validate the model with Matsen’s drag closure, further simulations under low

gas velocity in the range of 0.5 to 3 m/s were carried out. The simulations were

Wen & Yu’s Closure

𝐾𝑠𝑓 =34𝐶𝐷

𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�µ𝑔

𝜀𝑓−2.65 (9)

De Felice’s Closure 𝐾𝑠𝑓 =

34𝐶𝐷𝜀𝑓2𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�𝜀𝑓−𝜂 (14)

𝜂 = 3.7 − 0.65𝑒(− �1.5−log�𝑅𝑒𝑝�

2�2 ) (16)

Where

Matsen’s Closure

𝐾𝑠𝑓 = 0.006475𝐶𝐷𝜀𝑓𝜀𝑠𝜌𝑔�𝑢�𝑠 − 𝑢�𝑓�

µ𝑔𝜌𝑔𝜌𝑚𝑖𝑥

𝜀𝑠−0.586 (12)

Page 47: FYP Final Report E

45

compared with the experimental results obtained by Guan et al (2010) recently. The

detailed experimental results are presented in Appendix B.

Figure 5.9: Comparing simulation results under low Ug , Gs= 253 kg/m2s.

The plot above shows that the simulation results using Matsen’s drag closure is a better

fit to the experimental results than using Wen & Yu’s drag closure under low superficial

gas velocity. It can also be seen that since the solids concentration is very low, the

difference between the experimental results and the simulation results using Wen & Yu’s

drag closure is very significant. For example, at a superficial gas velocity of 1m/s, the

experimental solids concentration is about 0.02 whereas the predicted solids

concentration using Wen & Yu’ drag closure is about 0.075 which is 3.5 times more than

the experimental result.

Thus in conclusion, it has been shown that the commonly used Wen and Yu’s drag

correlation is not able to predict the solids concentration well under low gas velocity

scenarios. De Felice’s drag closure also overestimates the solids concentration under low

superficial gas velocity. Due to the different nature of the Matsen’s drag expression, it

seems to give a much better prediction of the solids concentration under low gas velocity

Page 48: FYP Final Report E

46

scenarios. Furthermore, Masen’s drag closure is also able to predict the path length taken

for the flow to be fully developed much better than other two drag closures.

5.5 Radial distribution of solids concentration

The radial distribution for the solid concentration in the downer also varies with the

different drag closures. The application of the Johnson-Jackson boundary condition at the

wall with the Matsen’s drag closure seem to produce results similar to the experimental

data obtained by Zhang et al (1999) where the nature of the radial solid concentration

along the axial direction of the downer differs. Applying Wen &Yu’s and De Felice’s

drag closure produces radial solid hold up profile similar to experimental data obtained

by Cao and Weinstein where the peak of the solids concentration is seen at the wall.

Figure 5.10: Radial solids hold up profile, Matsen’s drag closure (Gs=49 kg/m2s and Ug= 3.7 m/s).

Figure 5.10 presents the radial solid holdup distribution using the Matsen’s drag closure.

Initially the solids concentration is highest at the wall. As the length of the downer

increases, the peak of the solids concentration in the annulus gradually moves towards the

center. It can also be seen that the peak of the solids concentration is decreasing and a

Page 49: FYP Final Report E

47

more uniform solids concentration at the fully developed region of the downer. The

results obtained are similar to that experimental results obtained by Zhang et al (1999).

Figure 5.11: Radial solids hold up profile, Wen & Yu’s drag closure (Gs=49kg/m2s and Ug= 3.7m/s).

Figure 5.11 presents the radial solid holdup distribution using the Wen & Yu’s drag

closure. It can be seen that results obtained are similar to the experimental results

obtained by Cao and Weinstein (2000) where the peak is observed at the wall itself.

Furthermore in comparison with the radial profile of the Matsen’s drag closure, it can be

seen that local radial peak observed in Wen & Yu’s drag closure is not distinctively

larger than the average radial solids concentration. For example in figure 5.11, the

maximum local radial solid concentration is about 0.0092 while the average solids

concentration is about 0.0084 at 1m from the entrance of the downer. However in figure

5.10, it can be seen that the solids the maximum local radial solid concentration is about

0.018 while the average solids concentration is about 0.0055 at 1m from the entrance of

the downer. Thus it can be been seen that the Wen & Yu’s drag closure predicts a more

even radial solids concentration distribution than the Matsen’s drag closure where the

solids concentration at the peak is about three times more than the average radial solids

Page 50: FYP Final Report E

48

concentration. There has already been work published where high density peak near the

wall is 2-3 times the cross sectional average solids fraction (Zhang, Qian, Yu, & Wei,

2002) which is in accordance to the radial profile predicted by Matsen’s closure .

Figure 5.12: Radial solids hold up profile, De Felice’s drag closure (Gs=49kg/m2s and Ug= 3.7m/s).

Figure 5.12 presents the radial solid holdup distribution under two different operating

conditions using the De Felice’s drag closure. Again, similar to the Wen & Yu’s drag

closure, the local radial peak observed at the wall is not as distinctively larger than the

average radial solids concentration.

Comparing the radial profiles by the different drag coefficients, Matsen’s drag closure

seems to give a radial solid holdup distribution that is different compared to the Wen &

Yu’s and De Felice’s drag closure. As there is yet to be a universal agreement on the

radial solid hold up profiles, more experimental work and study is needed to verify the

radial soilds holdup profile in the downer. However it is important to note that it has

already be established in the earlier section that the Matsen’s drag closure is able to better

predict the average axial solids concentration under low gas velocity.

Page 51: FYP Final Report E

49

Chapter 6: Validation of the Eulerian-Lagrangian model

Eulerian-Lagrangian approach was also used to model the hydrodynamics of the downer.

However Eulerian-Lagrangian approach is computationally more expensive as a large

number of solids particles are needed to be tracked. The procedure, equations and

boundary conditions used for simulation have been described in chapter 4.

Compared to the Eulerian- Eulerian approach, the advantages is that each of the particle’s

trajectory can be displayed exactly and thus the residence time of the individual particles

can be computed. However as the Eulerian- Lagrangian model is computationally more

expensive, more simulations were done using the Eulerian- Eulerian method in this

thesis. Nevertheless simulation results for the Eulerian- Lagrangian model is presented

for two operating conditions and is compared with the Eulerian- Eulerian results in this

chapter.

6.1 Residence time of particles

Figure 6.1: Particle residence time for Gs=49 kg/m2s and Ug=3.7 m/s.

Page 52: FYP Final Report E

50

Figure 6.2: Particle residence time for Gs=205 kg/m2s and Ug=10.1 m/s.

Figures 6.1 and figure 6.2 illustrates the particle residence time for two different

operating conditions. The plots also reveal that the particles in the downer exhibit a rather

uniform residence time as stated in the literature review. In figure 6.1, the residence time

of the particles under the operating condition of solids flux of 49 kg/m2s and superficial

gas velocity of 3.7 m/s ranges from 2.5 to 2.75 seconds. The particles nearer to the wall

possess lower velocity and thus they have a slightly longer residence time than the

particles in the center. Likewise from figure 6.2, the residence time of the particles under

the operating condition of solids flux of 205 kg/m2s and superficial gas velocity of

10.1m/s ranges from 0.95 to 1.1 second. The superficial gas velocity is an important

parameter that affects the residence time of the particles in the downer. Under high

superficial gas velocity, the solid particles will attain a higher velocity and flow through

the downer faster, thus having a lower residence time.

Page 53: FYP Final Report E

51

6.2 Axial velocity distribution of particles

Figure 6.3: Particle velocity distribution for Gs=49 kg/m2s and Ug=3.7 m/s.

Figure 6.2 displays the particle velocity profiles under low gas velocity as the particles

move along the downer. It can be seen that the particles attain an almost constant velocity

in the fully developed region of the downer. The particles in the center attain a velocity of

about 4.3 m/s while the particles near the wall attain a velocity of about 3.3 m/s. While

experimental results from Bolkan et al shows that the average particle velocity is about

6m/s for similar operating conditions, it can thus be seen that the Eulerian- Lagarangian

approach also under estimates the particle velocity under low gas velocity like the

Eulerian- Eulerian approach using the default Wen & Yu’s drag closure .

Page 54: FYP Final Report E

52

Figure 6.4: Particle velocity time for Gs=205 kg/m2s and Ug=10.1 m/s.

Figure 6.4 displays the particle velocity profile under higher gas velocity as the particles

move along the downer. Here the particles velocity profile tends to agree better with the

experimental results present by Bolkan et al (2003) which states an average solids

velocity of 11m/s in the fully developed region. Thus like the Eulerian- Eulerian model,

the current Eulerian–lagrangian model is also able to predict the solids properties well

under high superficial gas velocity but unable to account for the more significant particle

clustering effect under low superficial gas velocity. Thus in order to apply the Euerlian-

Lagrangain approach under low gas velocity, improvement to the model is needed to

enhance its predictive ability.

Page 55: FYP Final Report E

53

6.3 Radial velocity distribution of particles

Figure 6.5: Comparison of radial solid’s velocity profile using the two approaches.

The left contour plot in figure 6.5 displays the radial solids velocity profile in the fully

developed region using the Eulerian-Lagrangian approach while the right plot represents

the results obtained via the Eulerian-Eulerian approach for the solids flux of 49 kg/m2s

and superficial gas velocity of 3.7 m/s. Both model display similar nature of radial solids

velocity profile where the particles travel at a faster velocity in the center than near to the

wall. The values of the solids velocity in the center is also in the same range. However

the major difference is that under Eulerian-Eulerian approach, the solids velocity near the

wall tends to zero while under the Euerlian-Lagrangian approach it tends to about 3.2

m/s. Since there is yet to be a universal agreement on the radial solids velocity profile,

more experimental data and study is needed in this area.

In conclusion, it can be seen that the results obtained by the Eulerian-Lagrangian

approach are in good agreement to the Eulerian –Eulerian approach using the Wen &

Page 56: FYP Final Report E

54

Yu’s drag closure. The simulation results tend to agree well with available experimental

data by Bolkan et al (2003) under high superficial gas velocity but do not tally well under

low gas velocity. Radial velocity profiles are also generally similar to results obtained by

Euerlian- Eulerian approach with a slight exception near wall region.

Page 57: FYP Final Report E

55

Chapter 7: Solids distributor and Inlet design of the downer

As the downer aims to serve as a quick-contact reactor, the short-contact time between

the phases poses stringent demand on the solids distributor design (Cheng, Wu, Zhu,

Wei, & Jin, 2008). Primarily, the inlet distributor of the downer should enable uniform

distribution of phases, quick acceleration of the solids and excellent control of gas-solids

mixing (Cheng, Wu, Zhu, Wei, & Jin, 2008). Since the downer performance is very much

dependent on the inlet design, much effort has been put in the design of solids

distributors. A research was first done to find the various solids distributor inlet

geometries available in literature.

Figure 7.1: Solids Inlet Geometry 1 (Cheng, Wu, Zhu, Wei, & Jin, 2008).

The figure above shows a simple and one of the earliest solids distributor design whereby

the solids flow from the riser top is not separated and directly enters the downer through a

900 sharp bend. Though this design is easy to construct, it does not allow uniform

distribution of the solids in the downer (Cheng, Wu, Zhu, Wei, & Jin, 2008). As such this

structure is not currently used in practice.

Page 58: FYP Final Report E

56

Figure 7.2: Solids Inlet Geometry 2. (Cheng, Wu, Zhu, Wei, & Jin, 2008).

The figure above shows a more recent distributor design. Solids are fluidized uniformly

above the downer inlet and flow through several tubes into the downer. Gas is introduced

through the ring slots around the tubes. This design is commonly used as it enables for an

independent operation of gas flow rate for the downer and riser components and solids

flow rate can also be varied by adjusting the bed height (Cheng, Wu, Zhu, Wei, & Jin,

2008).This type of distributor can also be easily scaled up (Cheng, Wu, Zhu, Wei, & Jin,

2008). The solids distributor used in the pilot plant setup by Guan et al in the University

of Tokyo employs this design.

Figure 7.3: Solids Inlet Geometry 3. (Cheng, Wu, Zhu, Wei, & Jin, 2008).

Page 59: FYP Final Report E

57

A unique type of inlet structure designed by Lehner and Wirth (1999) is shown above.

The main feature of the structure consists of two concentric pipes, which are located in

the center of the distributor (Cheng, Wu, Zhu, Wei, & Jin, 2008). Gas flows through the

inner tube. The solids are fed to a fluidized bed with a screw feeder. The overflowing

solids from the fluidized bed will flow into the annular gap which is surrounded by the

primary air tube. A diffuser connects the outer pipe and the downer, where the solids and

the gas are further allowed to mix well (Cheng, Wu, Zhu, Wei, & Jin, 2008).

Figure 7.4: Solids Inlet Geometry 4. (Briens, Mirgain, & Bergougnou, 1997).

Briens et al (1997) designed a downer inlet equipped with eight jet nozzles to supply the

superficial gas velocity as shown in the figure above. The eight jet nozzles can be

oriented independently to improve the gas–solids mixing and contact. The bottom of

Page 60: FYP Final Report E

58

Figure 7.4 shows how the nozzles can be angled to induce a swirl and how the nozzles

could be inclined to hit the solids jet near its top or bottom of the mixing chamber

(Cheng, Wu, Zhu, Wei, & Jin, 2008). This form of inlet design provides flexibility in

controlling the early contact between the phases

Figure 7.5: Solids Inlet Geometry 5. (Cheng, Wu, Zhu, Wei, & Jin, 2008).

Figure 7.5 above shows a slightly different inlet structure design adopted by Muldowney

et al. The main motivation for this design was based on the idea that mixing is more

effective upflow while the reactions are still preferred in downflow (Cheng, Wu, Zhu,

Wei, & Jin, 2008). Therefore the reactants can be introduced into the downer at an angle

tilted upwards so that the reactants will initially be flowing upwards for a short period of

time and this enables good mixing of the phases before they start flowing downwards and

reactions occur in the downer.

Page 61: FYP Final Report E

59

Figure 7.6: Solids Inlet Geometry 6. (Zhao & Takei, 2010).

Figure 7.6 above shows the side and top view of the solids distributor designed by Tong

Zhao and Masahiro Takei to provide for a uniform solid distribution in the downer. As

shown in the diagram above, the distributor consists of one annular solid inlet and five air

nozzles, which include a center nozzle and four well-distributed side nozzles. For the four

side air nozzles, the angle between the centerline of the center nozzle and the side nozzle

is 45° (Zhao & Takei, 2010). This ensures that the supplied air not only has a velocity

component in the axial direction, but also a velocity component in the radial direction.

This is believed to assist in the radial mixing of the solids.

7.1 Proposed Inlet Designs Based on the literature review above, it can be seen that the distributor design does affect

the flow pattern in the initial stages of the downer. In this thesis, a primary study is

conducted to compare the flow patterns between a tangential inlet structure and a normal

inlet structure. The goals of proposing these inlet designs is aimed towards innovating

new flow patterns and contacting mechanisms that would be enable for a better mixing of

the coal and sand phase. This numerical simulation would also assist in making some

primary investigations before indulging in expensive experimental investments.

Page 62: FYP Final Report E

60

a) Tangential Arrangement b) Normal Arrangement

Figure 7.7: The two different inlet structures to be studied.

The two different inlet structures to be studied are shown in figure 7.7 below. In the left

arrangement, all the four nozzles are tangential to the downer while in the right

arrangement, the four nozzles are normal to the downer. In the both downer structures,

sand particles would be introduced from the top while the coal particles would be

introduced from the nozzles. To assist the coal flow in the nozzles, compressed air is also

introduced in the nozzles are high speed. Mixing between the sand the coal in the downer

is crucial so that heat transfer can occur efficiently. Thus the purpose of this part of the

thesis is to study the coal and sand distribution in the developing region of the downer in

the two different structures. 7.2 Modeling Approach and simulation conditions

In this part of the thesis, a three-dimensional downer with the two different inlet

structures was created to simulate the three phase flow. The geometries were created in

Page 63: FYP Final Report E

61

the GAMBIT using the top-bottom approach whereby the volumes were created first

before meshing the edges. Eulerian-Eulerian approach was then used in FLUENT to

simulate the three phase flow with air, sand and coal being the three distinct phases. The

equations used in simulate the flow is similar to the equations present in chapter 3.1.2.

However since a three phase flow is being modeled in this section, there would be two

equations for the solid phase, one for coal and one for sand respectively. Modeling three

phase flow also introduces the solid-solid momentum exchange co-efficient which can be

described according to the following equation.

Solid-solid momentum exchange co-efficient

𝐾𝑠𝑐 =3(1 + 𝑒𝑠𝑐) �𝜋2 + 𝐶𝑓𝑟,𝑠𝑐

𝜋28 � 𝜀𝑠𝜌𝑠𝜀𝑐𝜌𝑐(𝑑𝑠 + 𝑑𝑐)2𝑔𝑜,𝑠𝑐

2𝜋(𝜌𝑠𝑑𝑠3 + 𝜌𝑐𝑑𝑐

3)|𝑢�𝑠 − 𝑢�𝑐|

In the equation above the subscript s refers to the sand phase while the subscript c refers

to the coal phase.𝐶𝑓𝑟,𝑠𝑐refers to the coefficient of friction between the sand phase and

coal phase which is assumed to be 0 in the numerical simulation. 𝑒𝑠𝑐 refers to the sand

and coal phase restitution coefficient with a assigned value of 0.9.

Table 5: Geometrical and simulation conditions for the 3D model

Diameter of downer, D 100 mm

Diameter of nozzles, 25 mm

Length of downer, L 2000 mm

Diameter of sand particle, 80 µm

Diameter of coal particle, 0.2 mm

Density of sand particle, 2600 kg/m3

Page 64: FYP Final Report E

62

Density of coal particle, cρ 1500 kg/m3

Density of air, gρ 1.225 kg/m3

Dynamic viscosity of air, gµ 1.79 kg/(m.s)

Inlet sand fraction, sε 0.279

Inlet coal fraction, cε 0.4

Restitution coefficient, esc 0.9

Gravitational acceleration, g 9.81 m/s2

Sand mass flux, sG 350 kg/m2s

Coal mass flux, cG 35 kg/m2s

Table 5 above shows the geometrical and simulations conditions used in this simulation.

Wen & Yu’s solid-gas momentum exchange co-efficient has been used in this simulation

as it has been proven earlier that it is able to predict the solids holdup well under high

superficial gas velocity. As in the earlier Eulerian-Eulerian simulations, the dispersed κ-ε

turbulence model is applied

Boundary conditions

Sand fraction at the top inlet of the downer is introduced uniformly in the radial direction,

as well as the coal fraction at the nozzles’ inlet. The ratio of solid mass flux of coal

particles over sand particles is fixed at 0.1 so as to allow for sufficient heat transfer from

the sand to the coal particles. A uniform air velocity of 12 m/s is applied at inlet of nozzle

to supply sufficient energy to push the coal particles through the horizontal sections of

the inlet nozzles. A uniform air velocity of 5m/s is also supplied from the top inlet.

Page 65: FYP Final Report E

63

Constant pressure boundary condition is applied at the outlet of downer. No-slip

boundary condition is applied at the wall for all the three phases.

Solution Scheme

The pressure–velocity coupled SIMPLE solver method was used in the iteration for the

convergence of the solution. The convergence criteria were set to 0.001 for all the terms.

The first order UPWIND implicit differencing scheme for the convective terms and the

first-order implicit time integration method was used to solve the motion equation of the

fluid. The default under-relaxation parameter values were used during the iteration

process. Steady–state model was used.

7.3 Simulation results

7.3.1 Axial Solid distribution

Figure 7.8 : Axial Distribution of the sand holdup in the downer.

0 0.5 1 1.5 20.01

0.015

0.02

0.025

0.03

0.035

Axial distance of the downer

Ave

rage

San

d ho

ldup

Normal Arrangement

Tangential Arrangement

Page 66: FYP Final Report E

64

Figure 7.8 above shows the axial distribution of the sand holdup for both arrangements of

the downer. Both arrangements reveal a decrease in the sand holdup along axial distance

of the downer. This is expected as the particles are accelerating under the influence of the

gravity. Since the sand holdup is yet to be constant, it can be seen that the flow is still in

the developing region for the both arrangements. The sand concentration is seen to be

generally in the same range for both the inlet structures. On a closer inspection of figure

7.8, it can be seen that in the initial section of the downer, the sand holdup in the normal

arrangement is slightly higher than the tangential arrangement. In the second section, at

about 1.0 m to 1.75 m of the downer, the average sand holdup in the tangential

arrangement is higher. To ensure that this phenomenon does not occur just for this flow

scenario, the model was simulated with a superficial gas velocity of 20 m/s at the nozzles.

The sand holdup profile for the flow conditions are presented in figure III.1 (Appendix

C). The nature of the graph is also similar to the above figure. However, it seems to

suggest that at higher velocity, the difference in flow structure between tangential and

normal arrangement is reduced.

Figure 7.9 : Axial Distribution of the coal holdup in the downer.

Page 67: FYP Final Report E

65

Figure 7.9 above reveals the axial distribution of the coal holdup in the downer. It can be

seen that the average coal holdup downer is rather low .This could be attributed to the

fact that a high gas velocity of 12 m/s is applied in the nozzle which allows the coal

particles to attain a high velocity and this leads to considerable dilution of the coal

concentration in the downer. Similar to the sand hold up distribution, the normal

arrangement has a higher concentration in the first section of the downer while the

tangential arrangement has a higher concentration in the second section of the downer. A

similar observation is made in figure III.2 (appendix C) for a higher superficial gas

velocity of 20 m/s at the nozzle.

As a higher solid holdup tends to improve the heat transfer from sand to coal, more

efforts are needed to study the sand concentration under various flow scenarios for the

both inlet arrangements in order to exploit the condition.

Page 68: FYP Final Report E

66

7.3.2 Radial Solid distribution

Figure 7.10: Radial distribution of the sand concentration in the downer.

From figure 7.10 above, it can be seen that the sand holdup near the entrance of the

downer (z=0.1 m) is similar for both the inlet arrangements as sand particles are flowing

from the similar conditions from the top inlet. Near the outlet (z=1.75 m), the sand

particles are more uniformly distributed for the tangential arrangement than the normal

arrangement. In the normal arrangement, it can be seen that the sand particles concentrate

more in the center and at the nozzle section while the sand holdup near the wall is quite

low. This thus seems to suggest that the high superficial gas velocity tends to influence

the flow of the sand particles. Near the outlet the sand holdup near the center is still

Page 69: FYP Final Report E

67

higher than that near the wall for both arrangements but the sand distribution in tangential

arrangement is more uniform.

Figure 7.11: Radial distribution of the coal holdup in the downer.

From figure 7.11, the coal holdup distribution is expected to be different in the inlet

region of the downer due to the different ways that they are fed into the downer. In the

normal arrangement, the coal particles are injected from the nozzles into the center of the

downer. Hence the coal holdup is higher near the center of the downer. In the tangential

arrangement, coal particles are injected tangentially along the wall. Thus the coal holdup

Page 70: FYP Final Report E

68

near the wall is higher than the center. Near the outlet (z= 1.75 m), similar observation is

made where coal holdup is concentrated in the center region for the normal arrangement.

The coal holdup in the tangential arrangement is rather uniform though it can be seen that

the wall region still has a slightly higher coal concentration than the center.

Figures 7.10 and 7.11 only show the radial solids holdup profile at two axial positions.

The figures in Appendix D reveal the radial solids holdup at various axial positions.

Thus from studying both figures 7.10 and 7.11 and figures in Appendix D, it can be seen

that in the developing region the sand and coal particles tend to concentrate at the center

for the normal inlet configuration while in the tangential arrangement, coal and sand are

more uniformly distributed in the cross section. Since both the coal and sand particles

seem to concentrate to the center in the center, it might increase the chances for the coal

and sand particles to collide and mix more often. Better mixing of the coal and sand

particles would allow for a better heat transfer. However, it is important to quantify the

mixing between the coal and sand particles with the introduction of a mixing index.

Mixing index would also enable for better comparison between the two inlet structures

and this would be done in the future work.

It is also important to note that the flow is only simulated for the developing region for

both inlet arrangements. This is the cause for the inlet configurations to affect the flow

pattern of the coal and sand particles. It is believed that the in the developed region, the

inlet arrangement should have little influence in the radial coal and sand holdup

distribution and this will be studied in the future research.

Page 71: FYP Final Report E

69

Chapter 8: Conclusion

In this thesis, hydrodynamic simulation of the gas-solid flow in the downer was carried

out using both the Eulerian-Eulerian and Eulerian-Largarian computational fluid

dynamics models. In using the Eulerian-Eulerian approach, the κ-Є turbulence model

with the Kinetic Theory of Granular flow was applied to model the multiphase flow.

Initially, the axial distribution of the solids concentration and velocity was simulated and

validated for the Eulerian-Eulerian model with Wen & Yu’s drag closure. It was found

that the model compared well with literature data under high superficial gas velocity but

failed to account for the particle clustering effect under the low gas velocity. As clusters

are more prone to become discrete particles for larger diameter and density, the model

had better predictive ability when larger particle size and higher particle density was

used. Simulation results showed that the diameter of the downer was found to have

negligible effect on the solids concentration distribution. In efforts to improve the model

under low gas velocity two other drag closures, Matsen’s and De Felice’s drag closures

were tested. It was found that Matsen’s Drag closure was better able to predict the solid’s

concentration under low gas velocity and the simulation results agreed well with

experimental data. The difference in the nature of the Matsen’s drag closure also caused

the radial solid concentration profile to be different compared to Wen & Yu’s and De

Felice’s drag closure. Thus it can be concluded that in using the Eulerian-Eulerian model,

the Matsen’s drag closure is better suited model the downer reactor under low gas

velocity.

The Eulerian- Lagrangian approach also produced simulation results comparable to the

Eulerian-Eulerian model under Wen & Yu’s drag closure. The current Eulerian-

Page 72: FYP Final Report E

70

Lagrangian model is also not able to account for the particle clustering effect under low

gas velocity as the particle’s axial velocity distribution were an underestimation

compared to the experimental data.

In the last section of the thesis two inlet structures proposed in efforts to improve the

mixing between the sand and coal phase. The sand and coal holdup distribution in the

downer were compared for the normal and tangential inlet arrangement. In the

developing region of the downer, the sand and coal particles tend to concentrate at the

center for the normal inlet structure while in the tangential arrangement coal and sand are

more uniformly distributed the cross section. The high superficial gas velocity introduced

at the nozzles also tends to influence the flow of sand particles in the downer.

Page 73: FYP Final Report E

71

Chapter 9: Recommendations and Future Work

While this work indicates promising results in modeling the flow structure in the downer

reactor, clearly more experimental validation is necessary for the radial solids

concentration distribution. Eulerian-Eulerian model with the Matsen’s drag closure has

been found to be give results that are comparable to the experimental data. More

numerical simulations under various flow conditions may be needed to further validate

the model. Once the model’s solid holdup prediction is in good agreement to the

experimental data, the energy equation and the pyrolysis reaction can be incorporated

into the model for a more detailed study and optimization of the pyrolysis process.

The current model only encompasses the k-Є turbulence model for the gas phase. It is

recommended to incorporate the kp turbulence model for the particle phase in the future

work in efforts to improve the model. More details about the kp can be found from Cheng

et al (1999).

In order to improve the Eulerian-Lagrangian model, it is recommended to incorporate the

‘Discrete Random Walk’ model in FLUENT which would account for dispersion of the

particles due to turbulence in the fluid phase. However, adding this feature would further

increase the computational expense and convergence would be more difficult to achieve.

A mathematical model based on the energy-minimization and multi-scale (EMMS)

principle was developed to describe the hydrodynamics in the fully developed region of a

downer reactor and has been used successfully to predict local solid concentration and

gas-solid velocities by Li et al (2004). As this is a much simpler approach compared to

Page 74: FYP Final Report E

72

the Eulerian-Eulerian method (Li, Lin, & Yao, 2004). simulations could be could also be

tried using EMMS model and compared with experimental results.

To improve the tangential and normal inlet structure models, a specially designed solids

distributor could be incorporated at the top of the downer, in which 13 tubes are arranged

in the distributor as shown in the figure 9.1 below. This distributor would further enable

uniform distribution of the sand particles in the downer. Eulerian- Eulerian simulation of

the downer with the solids distributor is currently being carried out to compare with the

current simulation results presented in the thesis. Mixing index would be introduced to

Mixing index would be introduced for a better comparison of the coal and sand mixing in

for the two inlet arrangements. Validation of the simulation results with experimental

work is also necessary.

Figure 9.1 : Inlet structures with the specially designed solids distributor.

Page 75: FYP Final Report E

73

References

ANSYS FLUENT. (2006, November 30). FLUENT 6.3 user's guide.

Bolkan, Y., Berruti, F., Zhu, J., & Milne, B. (2003). Modelling circulating fluidized bed

downers. Powder Technology , 85-100.

Briens, C., Mirgain, C., & Bergougnou, M. (1997). Evaluation of Gas-Solids Mixing

Chamber through cross correlation and Hurst's Analysis. AIChE Journal , 1469-1479.

Cao, C., & Weinstein, H. (2000). Characterization of Downflowing High Velocity

Fuidized Beds. AIChE Journal , 515-522.

Cheng, Y., Guo, Y., Wei, F., Jin, Y., & Lin, W. (1999). Modeling the hydrodynamics of

downer reactors based on kinetic theory. Chemical Engineering Science , 2019-2027.

Cheng, Y., Wei, F., Guo, Y., & Yong, J. (2001). CFD simulation of hydrodynamics in the

entrance region of a downer. Chemical Engineering Science , 1687-1696.

Cheng, Y., Wu, C., Zhu, J., Wei, F., & Jin, Y. ( 2008). Downer reactor: From

fundamental study to industrial application. Powder Technology 183 , 364–384.

Deng, R., Wei, F., i Liu, T., & Jin, Y. (2001). Radial behavior in riser and downer during

the FCC process. Chemical Engineering and Processing , 259-266.

Ding, J., & Gidspow, D. (1990). A bubbling fluidization model using kinetic-theory of

granular flow. AIChE Journal , 523-538.

Felice, R. (1994). The the voidage function for fluid-particle interaction systems .

International Journal of Mutliphase Flow , 153-159.

Gidaspow, D. (1994). Multiphase flow and fluidization-continuum and kinetic theory

descriptions. Boston: Academic Press.

Guan, G., Chihiro, F., Ikeda, M., Yu, N., & Tsutsumi, A. (2009). Flow behaviors in a

high solid flux circulating fluidized bed composed of a riser, a downer and a bubbling

fluidized bed. Tokyo.

Page 76: FYP Final Report E

74

Guan, G., Chihiro, F., Yu, N., Tsutsumi, A., Ishizuka, M., & Suzuki, Y. (2009).

Downwawrd gas-solids flow characterization in a high-density downer reactor. Tokyo.

Hanson.S, Patrick, J., & Walker.A. (2002). The effect of coal particle size on pyrolysis

and steam gasification. FUEL , 531-537.

Hoef, M. v., Annaland, M. v., Deen, N., & Kuipers, J. (2008). Numerical Simulation of

Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy. Annual Review of

Fluid Mechanics , 47-70.

Jian, H., & Ocone, R. (2003). Modelling the hydrodynamics of gas-solid suspensio in

downers. Powder Technology , 73-81.

Johnston, P., Lasa, H. d., & Zhu, J.-x. (1999 ). Axial flow structure in the entrance region

of a downer fluidized bed : Effects of the distributor design. Chemical Engineering

Science , 2161-2173.

Kimm, N., Berruti, F., & Pugsley, T. (1996). Modeling the Hydrodynamics of downflow

gas-solids reactors. Chemical Engineering Science , 2661-2666.

Lehner, P., & Wirth, K.-E. (1999). Characterization of the flow pattern in a downer

reactor. Chemical Engineering Science , 5471-5483.

Li, S., Lin, W., & Yao, J. (2004). Modelling the hydrodynamics of the fully developed

region in a downer reactor. Powder Technology , 73-81.

Liu, W., Luo, K.-B., Zhu, J.-X., & Beeckmans, J. (2001). Characterization of high-

density gas–solids downward fluidized flow. Powder Technology , 27-35.

Lun, C. K., B., S. S., J., J. D., & Chepurniy, N. (1984). Kinetic theories for granular flow-

inelastic particles in Couette-flow and slightly inelastic particles in a general flow field.

Journal of Fluid Mechanics , 223-256.

Qi, X.-b., Zhang, H., & Zhu, J. (2008). Solids concentration in the fully developed region

of circulating Fluidized bed downers. Powder Technology , 417-425.

Page 77: FYP Final Report E

75

Ropelato, K., Meier, H. F., & Cremasco, M. A. (2005). CFD study of the gas-solid

behaviour in downer reactors : An Eulerian- Eulerian Approach. Powder Technology ,

179-184.

Syamlal, M., Rogers, W., & O’Brien, T. J. (1993). MFIX documentation: volume 1,

theory guide. National Technical Information Service: Springfield.

Vaishali, S., Roy, S., & Mills, P. L. (2008). Hydrodynamic simulation of gas-solids

downflow reactors. Chemical Engineering Science , 5107-5119.

Wang, Z., Bai, D., & Jin, Y. (1992). Hydrodynamics of cocurrent downflow circulating

fluidized bed (CDCFB). Powder Technology , 271-275.

Zhang, H., Zhu, J.-X., & Bergougnou, M. (1999). Hydrodynamics in downfow fuidized

beds (1): solids concentration profiles and pressure gradient distributions. Chemical

Engineering Science , 5461-5470.

Zhang, M., Qian, Z., Yu, H., & Wei, F. (2002). The near wall dense ring in a large-scale

down-flow criculating fluidized bed. Chemical Engineering Journal , 161-167.

Zhao, T., & Takei, M. (2010). Discussion of the solids distribution behavior in a downer

with new designed distributor based on concentration images obtained by electrical

capacitance tomography. Powder Technology , 120-130.

Page 78: FYP Final Report E

i

Nomenclature

𝐴𝑟 Archimedes Number

𝐶𝑓𝑟,𝑠𝑐 coefficient of friction between the sand phase and coal phase

𝐶1Є, 𝐶2Є Constants in the

𝐶𝐷 Drag coefficient

𝐷 downer diameter

𝑑𝑝 particle diameter

𝑒𝑠𝑠 Particle-particle restitution co-efficient

𝑒𝑠𝑐 Sand- coal particle restitution co-efficient

𝑔 Acceleration due to gravity

go,ss radial distribution coefficient

Gs Solids flux

𝐺𝑘,𝑞 production of turbulent kinetic energy

𝐼 ̿ Identity matrix

𝐾𝑠𝑓 Gas-solid momentum exchange coefficient

𝐾𝑠𝑐 Solid –solid momentum exchange coefficient

L Length of downer

k diffusion coefficient

κ turbulent kinetic energy

𝑝 Pressure

ps solids pressure

Re Reynolds number

𝑇�𝑓 fluid phase stress-strain tensor

𝑇�𝑠 solids phase stress tensor

𝑢𝑓 Fluid velocity

𝑢𝑠 Solids velocity

Ug Superficial gas velocity

𝑈𝑡 Terminal particle velocity

Page 79: FYP Final Report E

ii

Greek symbols

εc Coal holdup

εs Solid holdup : Sand holdup

εs,max Maximum packing limit (0.63)

Є Dissipation rate

𝛾𝛩𝑠 Collisional dissipation of energy

λf Fluid bulk viscosity

λs Solids bulk viscosity

𝜌𝑐 Coal density

𝜌𝑓 Fluid density

𝜌𝑔 Gas density

𝜌𝑚𝑖𝑥 Mixture density

µf Fluid shear viscosity

µs Solids shear viscosity

µ𝑠,𝑐𝑜𝑙 Solids collisonal viscosity

µ𝑠,𝑓𝑟𝑖𝑐 Solids frictional viscosity

µ𝑠,𝑘𝑖𝑛 Solids kinetic viscosity

µ𝑡,𝑓 Turbulent viscosity

𝜎Є Turbulent prandtl number, dissipation rate

𝜎𝜅 Turbulent prandtl number , turbulent kinetic energy

𝛩𝑠 Granular temperature

ζ Specularity coefficient

τ Shear stress

ПЄ𝑓 source term caused by influence of solid phase on turbulent kinetic energy

П𝜅𝑓 source term caused by influence of solid phase on turbulent kinetic energy

Page 80: FYP Final Report E

iii

List of Figures

Chapter 1

Figure 1.1: Triple bed Circulating Fluidized Bed (Guan G. , Chihiro, Ikeda, Yu, &

Tsutsumi, 2009). ................................................................................................................. 5

Chapter 2

Figure 2.1: Pressure profile in a downer for Gs=202kg/m2s and Ug=5m/s. ...................... 10

Figure 2.2 : Solids concentration distribution profile in the downer for Gs =202 kg/m2s

and Ug=5m/s. .................................................................................................................... 10

Figure 2.3 : Radial solids concentration profile (Wang, Bai, & Jin, 1992). .................... 12

Figure 2.4: Radial solids concentration profile (Cao & Weinstein, 2000). ...................... 13

Figure 2.5 : Radial solids concentration profile, (Zhang, Zhu, & Bergougnou, 1999). .... 14

Chapter 3

Figure 3.1: Modeling the interaction between solid and gas phase (Vaishali, Roy, &

Mills, 2008). ...................................................................................................................... 17

Chapter 4

Figure 4.1 : Layout of the meshed geometry of the downer. ............................................ 28

Figure 4.2 : Boundary conditions for the 2D Model. ........................................................ 29

Chapter 5

Figure 5.1: Simulation results for superficial gas velocity of 3.7 m/s. ............................. 32

Figure 5.2: Simulation results for superficial gas velocity of about 7 m/s. ...................... 34

Figure 5.3: Simulation results for superficial gas velocity of about 10m/s. ..................... 35

Figure 5.4: Simulation results for solids flux of about 50kg/m2s with varying Ug. .......... 37

Figure 5.5: Model Comparison for varying Particle Diameter. ........................................ 39

Figure 5.6: Model Comparison for varying Particle Density. .......................................... 39

Figure 5.7: Simulation results using De Felice's drag closure for Ug=3.7 m/s. ................ 42

Figure 5.8: Simulation results using Matsen's Drag closure for Ug=3.7 m/s. ................... 43

Page 81: FYP Final Report E

iv

Figure 5.9: Comparing simulation results under low Ug , Gs= 253 kg/m2s ....................... 45

Figure 5.10: Radial solids hold up profile, Matsen’s drag closure (Gs=49 kg/m2s and Ug=

3.7 m/s). ............................................................................................................................ 46

Figure 5.11: Radial solids hold up profile, Wen & Yu’s drag closure (Gs=49 kg/m2s and

Ug= 3.7 m/s). .................................................................................................................... 47

Figure 5.12: Radial solids hold up profile, De Felice’s drag closure (Gs=49 kg/m2s and

Ug= 3.7 m/s). .................................................................................................................... 48

Chapter 6

Figure 6.1: Particle residence time for Gs=49 kg/m2s and Ug=3.7 m/s. ............................ 49

Figure 6.2: Particle residence time for Gs=205 kg/m2s and Ug=10.1 m/s. ...................... 50

Figure 6.3: Particle velocity distribution for Gs=49 kg/m2s and Ug=3.7 m/s. .................. 51

Figure 6.4: Particle velocity time for Gs=205 kg/m2s and Ug=10.1 m/s. .......................... 52

Figure 6.5: Comparison of radial solid’s velocity profile using the two approaches. ...... 53

Chapter 7

Figure 7.1: Solids Inlet Geometry 1 (Cheng, Wu, Zhu, Wei, & Jin, 2008). ..................... 55

Figure 7.2: Solids Inlet Geometry 2. (Cheng, Wu, Zhu, Wei, & Jin, 2008) ..................... 56

Figure 7.3: Solids Inlet Geometry 3. (Cheng, Wu, Zhu, Wei, & Jin, 2008). .................... 56

Figure 7.4: Solids Inlet Geometry 4. (Briens, Mirgain, & Bergougnou, 1997). ............... 57

Figure 7.5: Solids Inlet Geometry 5. (Cheng, Wu, Zhu, Wei, & Jin, 2008). .................... 58

Figure 7.6: Solids Inlet Geometry 6. (Zhao & Takei, 2010)............................................. 59

Figure 7.7: The two different inlet structures to be studied. ............................................. 60

Figure 7.8 : Axial Distribution of the sand holdup in the downer. ................................... 63

Figure 7.9 : Axial Distribution of the coal holdup in the downer. .................................... 64

Figure 7.10: Radial distribution of the sand concentration in the downer. ....................... 66

Figure 7.11: Radial distribution of the coal holdup in the downer. .................................. 67

Chapter 9

Figure 9.1 : Inlet structures with the specially designed solids distributor. ...................... 72

Page 82: FYP Final Report E

v

Appendix

Figure I.1: Simulation results for solids flux of about 100 kg/m2s with varying Ug. ........ vi

Figure I.2 : Simulation results for solids flux of about 200 kg/m2s with varying Ug. ...... vii

Figure II.1 : Experimental data for Gs=253 kg/m2s (Guan et al 2000)............................ viii

Figure III.1 : Axial distribution of the sand holdup in the downer with Ug=20 m/s. ......... ix

Figure III.2 : Axial distribution of the coal holdup in the downer with Ug=20 m/s. ......... ix

Figure IV.1 : Radial sand holdup at various axial positions (Tangential). ......................... x

Figure IV.2: Radial coal holdup at various axial positions (Tangential). .......................... xi

Figure IV.3 : Radial sand holdup at various axial positions (Normal). ............................ xii

Figure IV.4 : Radial coal holdup at various axial positions (Normal). ............................ xiii

List of Tables

Table 1: Various gas-solid momentum transfer coefficients. ........................................... 20

Table 2: Operating conditions for the 2D model. ............................................................. 28

Table 3: Model results for varying downer diameter........................................................ 40

Table 4: Comparison of various Drag coefficients ........................................................... 44

Table 5: Geometrical and simulation conditions for the 3D model .................................. 61

Page 83: FYP Final Report E

vi

I. Appendix A: Axial solids velocity distribution profiles

a) Comparison of simulation results for solids flux of 100 kg/m2s

Figure I.1: Simulation results for solids flux of about 100 kg/m2s with varying Ug.

Page 84: FYP Final Report E

vii

b) Comparison of simulation results for solids flux of 200 kg/m2s

Figure I.2 : Simulation results for solids flux of about 200 kg/m2s with varying Ug.

Page 85: FYP Final Report E

viii

II. Appendix B: Experimental Data for the downer solid holdup for the Gs=253 kg/m2s by Guan et al (2010)

Figure II.1 : Experimental data for Gs=253 kg/m2s (Guan et al 2000).

It is important to note that the simulation results were compared with the average solid

holdup under the ‘seal’ columns. The experiments were conducted on a circulating bed.

The results under the ‘seal’ columns were taken when the superficial air velocity from the

riser was sealed off from the downer. Therefore the solid concentration values under the

‘seal’ results were used for comparison so that effect of riser gas velocity is not affected.

This would be a better comparison with the simulation results as just the downer was

modeled in this thesis. It was found that Matsen’s drag closure agree well with the

experimental results as compared to the Wen & Yu’s drag closure . De Felice’s drag

closure was already proven to produce results similar to Wen & Yu’s correlation earlier

and thus it was not tested in section 5.4.

Page 86: FYP Final Report E

ix

III. Appendix C: Comparison of the average solids hold up for the two inlet arrangements with Ug=20 m/s.

Figure III.1 : Axial distribution of the sand holdup in the downer with Ug= 20 m/s.

Figure III.2 : Axial distribution of the coal holdup in the downer with Ug= 20 m/s.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.005

0.01

0.015

0.02

0.025

0.03

0.035

Axial Distance of the Downer

Ave

rage s

and hold

up

Tangential ArrangementNormal Arrangement

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 25

6

7

8

9

10

11

12

13x 10-4

Axial Distance of the Downer

Ave

rage

coa

l hol

dup

Tangential arrangementNormal Arrangement

Page 87: FYP Final Report E

x

IV. Appendix D: Radial distribution of the solids at various axial positions for the two inlet arrangements.

Tangential arrangement

Figure IV.1 : Radial sand holdup at various axial positions (Tangential).

Page 88: FYP Final Report E

xi

Figure IV.2: Radial coal holdup at various axial positions (Tangential).

Page 89: FYP Final Report E

xii

Normal arrangement

Figure IV.3 : Radial sand holdup at various axial positions (Normal).

Page 90: FYP Final Report E

xiii

Figure IV.4 : Radial coal holdup at various axial positions (Normal).