Development of Design Models for Air-gravity Fine Powder

Development of Design Models for Air-gravity

Fine Powder Transport

A thesis submitted in fulfilment of the requirements

For the award of the degree of

Doctor of Philosophy

From

THE UNIVERSITY OF NEWCASTLE

by

Hongliang DING

MEng (Zhejiang University, China)

School of Engineering

June 2017

I

Declaration

I hereby certify that the work embodied in the thesis is my own work, conducted under normal

supervision.

This thesis contains no material which has been accepted for the award of any other degree or

diploma in any university or other tertiary institution and, to the best of my knowledge and

belief, contains no material previously published or written by another person, except where due

reference has been made in the text. I give consent to this copy of my thesis, when deposited in

the University Library, being made available for loan and photocopying subject to the

provisions of the Copyright Act 1968.

(Signed) ………… …………………………………………………………….

Hongliang DING

II

Acknowledgements

Although my name is the only one that appears on the front page, I could have by no means

finished the thesis without the support from my supervisors, colleagues and family.

I would like to express my deepest appreciation to my supervisors Dr. Kenneth Williams, Bin

Chen, Professor Mark Jones and Vijay Agarwal, for their patient guidance and support during

my PhD journey. You were my primary resource when I had problems in my research. You

provided insightful discussions and constant feedback on my research and have helped hone my

skills in English writing. This experience will be invaluable for me to further my research.

I gratefully acknowledge the Chinese Scholarship Council (CSC) for providing the financial

support during my study. Moreover, I thank the University of Newcastle for providing an

additional top-up scholarship.

Acknowledgement is also given to the associate and technical staff in the workshop of TUNRA

Bulk Solids Research Associates. Particular thanks to Tony Salmon and Jed for their time and

effort on setting up the air-gravity conveyor for my research, and Mitch Gibbs for installing and

calibrating the pressure transducers. Thanks are extended to Mr. Thomas Bunn for his

generosity of supporting experimental material flyash and also for the effective discussions on

designing the air-gravity conveyor. Thanks are also given to Mr. Paul Whitworth, Eric Brooker,

Scott Brooker, Bill and Leo McFadden. Without their help and expertise, my experimental

apparatus would not have been successfully constructed, calibrated and operated. All the

members have been very supportive of experimental work during the conduct of my research.

A big “thank you” also goes to the postgraduate students in TUNRA group, Jiahe Shen, Jian

Chen, Wei Chen, Jie Guo, Nic Weightman, Jens Plinke, Ognjen Orozovic, Sam and Michael

Carr, for your wonderful company. You made my time at university much more enjoyable.

Last but not the least; I would like to express my special thanks to my family, my parents

Minghua Ding and Xiaoqin Zhang, and to my wife Yao Zhang, for their unremitting

encouragement and endless support.

Hongliang DING

18/02/2017

III

TABLE OF CONTENTS

CHAPTER 1 Introduction and Literature Review ................................. 1

1.1 Introduction of air-gravity conveyor .......................................................... 1

1.1.1 Conveying Technique ..................................................................................... 1

1.1.2 System advantages and design tolerance ........................................................ 2

1.1.3 Conveying Principles ...................................................................................... 3

1.2 The fluidisation of bulk solids...................................................................... 3

1.2.1 Flow through a fixed bed of solid particles .................................................... 5

1.2.2 Minimum fluidisation velocity ....................................................................... 7

1.2.3 Expansion of the fluidised bed ..................................................................... 10

1.3 The flow behaviour of aerated bulk solids ............................................... 12

1.3.1 Historical development ................................................................................. 13

1.3.2 Current construction and application of air-gravity conveyor ...................... 14

1.3.3 Recent research on air-gravity conveyors..................................................... 15

1.3.3.1 Vent system .................................................................................................. 15

1.3.3.2 Non-vent system ........................................................................................... 18

1.3.4 Factors influencing the flow behaviour of aerated bulk solids in air-gravity

conveyors 19

1.3.4.1 The material to be conveyed ......................................................................... 20

1.3.4.2 The width of the channel .............................................................................. 21

1.3.4.3 The channel base (porous distributor) .......................................................... 22

1.3.4.4 The inclination of the channel ...................................................................... 23

1.3.4.5 Superficial air velocity ................................................................................. 24

1.3.4.6 Material flow velocity distribution ............................................................... 26

1.4 Computational Fluid Dynamic simulation of fluidised flow ................... 28

1.4.1 Introduction of FLUENT .............................................................................. 28

1.4.2 Computational Fluid Dynamic application in gas-solid flows ..................... 29

1.5 Summary of air-gravity conveying and future development .................. 30

1.6 Objective of the thesis ................................................................................ 31

IV

1.7 Thesis overview ........................................................................................... 32

CHAPTER 2 Material properties and flow model predictions ............ 35

2.1 Introduction ................................................................................................ 35

2.2 Testing methods and powder material properties ................................... 35

2.2.1 Particle density ............................................................................................. 35

2.2.2 Loose poured bulk density ............................................................................ 36

2.2.3 Particle size and distribution ........................................................................ 36

2.2.4 Air-particle parameters ................................................................................. 37

2.2.4.1 Sand .............................................................................................................. 40

2.2.4.2 Flyash ........................................................................................................... 41

2.2.5 Material properties summarise ..................................................................... 43

2.3 Flow mode predictions ............................................................................... 43

2.4 Rheology of aerated material ..................................................................... 49

2.4.1 Experimental rig ........................................................................................... 50

2.4.2 Rheology results ........................................................................................... 51

2.4.3 Modelling the rheology of aerated materials ................................................ 52

2.4.3.1 Sand .............................................................................................................. 53

2.4.3.2 Flyash ........................................................................................................... 54

2.5 Conclusion ................................................................................................... 56

CHAPTER 3 Air-gravity conveyor rig design ....................................... 57

3.1 Introduction ................................................................................................ 57

3.2 Design and construction of the air-gravity conveyor rig ........................ 57

3.2.1 Supply hopper to conveying channel ............................................................ 58

3.2.2 Conveying channel ....................................................................................... 58

3.2.3 Conveying channel to the receiving box ...................................................... 60

3.2.4 Material return system .................................................................................. 60

3.2.5 Air supply and control .................................................................................. 60

3.2.6 Support structures ......................................................................................... 62

3.3 Instrumentation .......................................................................................... 62

V

3.3.1 Solid mass flow rate ..................................................................................... 64

3.3.2 Pressure transducers ..................................................................................... 65

3.3.3 Depth of flowing bed .................................................................................... 68

3.4 Experimental procedure ............................................................................ 68

3.4.1 Pre-start checks ............................................................................................. 69

3.4.2 Operating procedure ..................................................................................... 69

3.5 Conclusion ................................................................................................... 69

CHAPTER 4 Experimental results ......................................................... 71

4.1 Introduction ................................................................................................ 71

4.2 Experimental data analysis methods ........................................................ 71

4.2.1 Experimental pressure and mass flow rate ................................................... 71

4.2.2 Image analysis method ................................................................................. 76

4.3 Fluidised conveying of sand at vent flow condition ................................. 80

4.3.1 Flow visualization ........................................................................................ 80

4.3.2 Effect of air flow rate on sand mass flow rate .............................................. 81

4.3.3 Effect of inclination angle on sand mass flow rate ....................................... 83

4.3.4 Plenum chamber pressure ............................................................................. 83

4.3.5 Pressure drop at material layer ..................................................................... 85

4.3.6 Bed height along the channel........................................................................ 86

4.4 Fluidised conveying of sand at non-vent flow condition ......................... 87

4.4.1 Flow visualisation ......................................................................................... 87

4.4.2 Effect of air flow rate on sand mass flow rate .............................................. 88

4.4.3 Effect of inclination angle on sand mass flow rate ....................................... 89


4.4.5 Pressure at the top of the conveying channel................................................ 91


4.4.7 Bed height along the channel........................................................................ 93

4.5 Fluidised conveying of flyash at vent flow condition ............................... 94

4.5.1 Flow visualisation ......................................................................................... 94

VI

4.5.2 Effect of air flow rate on flyash mass flow rate ........................................... 95

4.5.3 Effect of inclination angle on flyash mass flow rate .................................... 96



4.5.6 Effect of mass flow rate on bed height around fluidised velocity .............. 100

4.6 Fluidised conveying of flyash at non-vent flow condition ..................... 101

4.6.1 Flow visualisation ....................................................................................... 101

4.6.2 Effect of air flow rate on flyash mass flow rate ......................................... 102

4.6.3 Effect of inclination angle on flyash mass flow rate .................................. 103

4.6.4 Plenum chamber pressure ........................................................................... 104

4.6.5 Pressure at the top of the conveying channel.............................................. 106

4.6.6 Pressure drop at material layer ................................................................... 107

4.6.7 Effect of mass flow rate on bed height around fluidised velocity .............. 107

4.7 Conclusion ................................................................................................. 109

CHAPTER 5 Modelling fluidised motion conveying based on a new

continuum approach ............................................................................... 110

5.1 Introduction .............................................................................................. 110

5.1.1 Rheology..................................................................................................... 110

5.1.2 Viscosity of fluidised material .................................................................... 112

5.2 Conservation principles and mechanics in a continuous system .......... 114

5.2.1 Conservation of mass ................................................................................. 115

5.2.2 Conservation of momentum ....................................................................... 115

5.2.3 Strain theory ............................................................................................... 116

5.3 Constitutive models of fine powder flows in a fluidised motion conveyor

118

5.3.1 Incompressible approximation ................................................................... 120

5.3.2 Fluidised motion conveying models (vent and non-vent) .......................... 121

5.3.2.1 Vent fluidised motion conveying models ................................................... 122

5.3.2.2 Non-vent fluidised motion conveying models ............................................ 130

5.4 Conclusion ................................................................................................. 137

VII

CHAPTER 6 Validation of air-gravity conveying model ................... 138

6.1 Introduction .............................................................................................. 138

6.2 Flow model validation process ................................................................ 138

6.2.1 Experimental steady flow bed height ......................................................... 138

6.2.2 Fluidised bulk density and rheology parameters ........................................ 138

6.2.3 Flow model selection .................................................................................. 139

6.2.4 Validation process ...................................................................................... 139

6.3 Validation of flow models ........................................................................ 140

6.3.1 Vent flow of sand ....................................................................................... 141

6.3.2 Non-vent flow of sand ................................................................................ 144

6.3.3 Vent flow of flyash ..................................................................................... 149

6.3.4 Non-vent flow of flyash .............................................................................. 153

6.3.5 Velocity validation for sand and flyash ...................................................... 157

6.4 Rheology-based air-gravity conveying system design protocol ............ 159

6.5 Conclusion ................................................................................................. 161

CHAPTER 7 CFD simulation on an air-gravity conveyor ................. 162

7.1 Introduction .............................................................................................. 162

7.2 Governing equations for an air-gravity conveying system ................... 162

7.2.1 Governing conservation equations ............................................................. 163

7.2.2 Kinetic theory of granular flow .................................................................. 163

7.2.3 Drag model ................................................................................................. 165

7.2.4 Turbulence model ....................................................................................... 166

7.3 Simulation conditions ............................................................................... 166

7.3.1 Geometry and boundary conditions ............................................................ 166

7.3.2 Solution procedure ...................................................................................... 167

7.4 Investigation of model parameters .......................................................... 168

7.4.1 Grid independency ...................................................................................... 169

7.4.2 Flow models (Laminar and Turbulence) .................................................... 170

7.4.3 Drag models................................................................................................ 171

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7.4.4 Specularity coefficient ................................................................................ 172

7.4.5 Coefficient of restitution ............................................................................. 174

7.5 Recommended parameters ...................................................................... 175

7.6 Verification of the model .......................................................................... 175

7.7 CFD model results of sand and flyash flow ............................................ 177

7.7.1 Sand (vent).................................................................................................. 177

7.7.1.1 Bed height along the channel for vent sand flow ....................................... 177

7.7.1.2 Centreline volume fraction and velocity along the channel for vent sand flow

178

7.7.1.3 Velocity distribution at the cross section of the channel at the location of 5

for vent sand flow ......................................................................................................... 179

7.7.1.4 CFD predicted bed height at 5 m for vent sand flow .................................. 180

7.7.2 Sand (non-vent) .......................................................................................... 181

7.7.2.1 Bed height along the channel for non-vent sand flow ................................ 181

7.7.2.2 Centreline volume fraction and velocity along the channel for non-vent sand

flow 182


for non-vent sand flow .................................................................................................. 183

7.7.2.4 CFD predicted bed height at 5 m for non-vent sand flow .......................... 184

7.7.3 Flyash (vent) ............................................................................................... 185

7.7.3.1 Bed height along the channel for vent flyash flow ..................................... 185

7.7.3.2 Centreline volume fraction and velocity along the channel for vent flyash

flow 186

7.7.3.3 Velocity distribution at the cross section of the channel at the location of 5 m

for vent sand flow ......................................................................................................... 187

7.7.3.4 CFD-predicted bed height at 5 m for vent flyash flow ............................... 188

7.7.4 Flyash (non-vent) ........................................................................................ 189

7.7.4.1 Bed height along the channel for non-vent flyash flow .............................. 189

7.7.4.2 Centreline volume fraction and velocity along the channel for non-vent sand

flow 190

IX


for non-vent flyash flow ................................................................................................ 191

7.7.4.4 CFD-predicted bed height at 5 m for non-vent flyash flow ........................ 192

7.8 Conclusion ................................................................................................. 193

CHAPTER 8 Recommended design protocol for an air-gravity

conveying system ..................................................................................... 195

8.1 Introduction .............................................................................................. 195

8.2 Recommended design protocol ................................................................ 195

8.3 Comparison between the mathematical model and the CFD model .... 197

8.4 Conclusion ................................................................................................. 200

CHAPTER 9 Conclusion and future work ........................................... 201

9.1 Conclusions ............................................................................................... 201

9.1.1 Experimental study on material properties and rheological parameters ..... 201

9.1.2 Air-gravity conveyor design ....................................................................... 201

9.1.3 Experimental study on air-gravity conveying............................................. 202

9.1.4 Fluidised motion conveying model development ....................................... 203

9.1.5 Conveying model validation ....................................................................... 203

9.1.6 CFD study on air-gravity conveying .......................................................... 204

9.2 Recommendation for future work ........................................................... 205

Reference .................................................................................................. 212

Appendices ............................................................................................... 212

10.1 Appendix A - Airslide rig drawings ........................................................ 212

10.2 Appendix B - Pressure data analysis programmes ................................ 217

10.3 Appendix C - Experimental data for air-gravity conveying of sand and

flyash 220

X

ABSTRACT

Air-gravity conveyors are widely used in industry to convey bulk materials with the advantages

of low particle velocities, low levels of particle attrition, potentially high conveying rates and

low power consumption. Most current designs are based on empirical design charts and past

experience as there have been relatively few investigations attempting to model the flow of air-

gravity conveyor systems.

Instead of empirically based methods, this thesis adopted a new continuum approach based on

fluid rheology to assess the flow performance of fine powders within air-gravity conveyors.

Meanwhile, this thesis also conducted computational fluid dynamic (CFD) numerical

simulations of an air-gravity conveying system with fluidised materials. Therefore, the objective

of this research focused on the following specific aspects: design of the air-gravity conveyor;

experimental determinations of the flow behaviour of aerated materials; theoretical modelling of

the fluidised flow conveying models based on the rheology; validation of the proposed

conveying models; and CFD simulation of the air-gravity fluidised conveying system.

Initially, experimental investigations on the basic parameters including density parameters,

particle size distribution and air-particle parameters were conducted on sand and flyash.

Essentially, a combination of a fluidisation chamber and a rotary viscometer was applied for

testing the shear stress and shear rate of fluidised materials, and then the rheology parameters

could be determined accordingly.

Secondly, the air-gravity conveyor was designed to form a circulation system for future

experimental research. Detailed drawings are presented in this thesis. Essentially, the conveying

system consists of four sections: hopper feed section, material conveying section, material

receive section and material return section. Instrumentation for measuring pressure and mass

flow rates was designed and installed in an experimental area.

Thirdly, air-gravity conveying tests were conducted on sand and flyash. The material bed

height, material mass flow rate and pressure drop were measured and analysed under vent and

non-vent condition. Based on the experimental test procedure and test programme, the effect of

air flow rate and channel inclination on the depth of flowing beds, material mass flow rate and

pressure drop along the channel were investigated and discussed.

Fourthly, a fundamental conveying model for air-gravity conveyor flows in inclined channels,

with an emphasis on the conservation of momentum taking into account the rheology of the gas-

solid mixture, was developed to predict the flow behaviour of material in air-gravity conveyors.

By inputting the rheological parameters and conveying design data, the steady flow bed height

of this air-gravity conveying system could be predicted.

XI

After that, rheology based conveying models were evaluated and validated by comparing

the steady flow bed height produced from the conveying models with the experimental

measurements. Results showed good agreements between the model predictions and

experimental observations for sand and flyash with the overall error under 30%.

Lastly, CFD has been used to simulate the air-gravity flow, where a steady, three-dimensional

fluidised granular flow is considered in a rectangular channel having frictional side walls for

different flow conditions. The results of simulated bed heights along the air-gravity channel are

discussed. The developed CFD model predicted the flow bed heights along the conveying

channel for sand and flyash quite well. Moreover, centreline volume fraction and velocity along

the channel, and velocity distribution at the cross section of the channel were also investigated,

and results showed that the CFD simulation enables the system to prediction of the fine powder

flow behaviour in an air-gravity conveying system.

XII

NOMENCLATURE

Upper Case Letters

A Cross-sectional area of the bed [m2]

Af De-aeration factor [kPa·s/m]

𝐶𝐷 Drag coefficient [-]

𝐷𝑝 Diameter of a sphere [m]

G Elasticity [-]

H Bed height [m]

𝐼 ̿ Unit tensor [-]

𝐼2D Second invariant of the deviatoric stress tensor [-]

𝐾gs Interphase exchange coefficient [-]

L length [m]

𝑁 Number of particles per unit volume [-]

P Pressure [Pa]

∆𝑃 Pressure drop [Pa/m]

𝑅𝑒 Reynolds number [-]

𝑅𝑒s Particle Reynolds number [-]

𝑆𝑏 The surface area of particles in unit volume [m2]

U Superficial velocity of the flowing fluid [m/s]

Umf Minimum fluidisation velocity [m/s]

W Bed weight [kg]

Lower Case Letters

b Channel width [m]

c Particle fluctuating velocity [m/s]

𝑏𝜌 Flow index-density function [-]

𝑑s Particle diameter (m)

𝑒s Coefficient of restitution of particle [-]

g Gravitational constant [m/s2]

g0 Radial distribution function [-]

h Packed bed of depth [m]

XIII

𝑘Θs Diffusion coefficient for granular energy [-]

𝑚𝑠 Mass flow rate of solid [kg/s]

𝑝s Solid phase pressure [Pa]

𝑟𝑎 Operating aspect ratio [-]

𝑟𝑒 Expansion ratio of the conveyed material [-]

Greek Letters

𝛼g Gas volume fraction [-]

𝛼𝑞 Volume fraction of phase q [-]

𝛼s Particle volume fraction [-]

𝛼s,max Maximum particle packing [-]

𝛾 Strain [-]

�̇� Strain rate [1/s]

𝛾𝛩s Collision dissipation of energy [m2/s2]

𝜀𝑚𝑓 Voidage at the minimum fluidization [-]

𝜀0 Voidage [-]

𝜃 The inclination angle [degree]

𝛩s Granular temperature [m2/s2]

𝜂𝜌 Consistency index-density function [-]

𝜆g Gas bulk viscosity [Pa·s]

𝜆s Solid bulk viscosity [Pa·s]

𝜇 Viscosity [Pa·s]

𝜇0 Plastic viscosity [Pa·s]

𝜇s Solid shear viscosity [Pa·s]

𝜇𝑔 Gas viscosity [Pa·s]

𝜇s,col Solid collision viscosity [Pa·s]

𝜇s,kin Solid kinetic viscosity [Pa·s]

𝜇s,fr Solid frictional viscosity [Pa·s]

𝑢𝑠 Average solids velocity along the channel [m/s]

𝜌𝑏 Bulk density [kg/m3]

𝜌𝑓 Fluidised bulk density [kg/m3]

𝜌𝑔 Gas density [kg/m3]

ρlp Loose poured bulk density [kg/m3]

𝜌𝑝 Particle density [kg/m3]

XIV

𝜌s Particle density [kg/m3]

ρt Tapped bulk density [kg/m3]

𝑣g Gas velocity [m/s]

𝑣s Solid velocity [m/s]

𝑣𝑥 Velocity at x direction [m/s]

𝑣𝑦 Velocity at y direction [m/s]

𝑣𝑧 Velocity at z direction [m/s]

𝜏 Stress [N/m2]

𝜏0𝜌 Yield stress-density function [N/m2]

�̿�g Shear stress of gas phase [N/m2]

�̿�s Shear stress of solid phase [N/m2]

Φ Permeability factor [m2/kPa·s]

∅𝑠 Sphericity [-]

𝜙gs Transfer of the kinetic energy of random

fluctuations in the particle velocity

[m2/s2]

𝜙 Angle of internal friction

[degree]

1

1 CHAPTER 1 Introduction and Literature Review

1.1 Introduction of air-gravity conveyor

Pneumatic conveying is one of the most important particulate materials handling methods

amongst the various established methods of bulk solids handling. To transport particulate

materials, the inherent advantages of pneumatic conveying systems are its cleanliness,

convenience, low cost, ease of installation and general environmental hygiene. However, these

advantages have to be balanced against some weaknesses, which include a high risk of

degradation of the particulate material, erosion of the pipeline and high power consumption

when conveying at fast velocities. In order to overcome these disadvantages, dense phase

transport appeared in the bulk solids handling industry. The ratio of particulate materials to

conveying air is greatly increased in this conveying method, which obviously reduced power

consumption and transport velocities. Unfortunately, dense phase conveying faces the problem

that it increased the tendency of the pipeline to be blocked.

Therefore, there is a need for a pneumatic system that will operate continuously at low power

consumption, with high solids flowrates and minimum risk of degradation or erosion damage.

Air-gravity conveyors meet all these conditions and have already existed for many years. They

are widely used in industries now to convey bulk materials with the advantages of low particle

velocities, low levels of particle attrition, potentially high conveying rates and low power

consumption. Powdered materials, like cement, alumina, plastic metal powders, soda ash, coal

dust, flour, resins, etc., have already been conveyed successfully in industries using these

systems. Generally, air-gravity conveyors or airslides, consist of two types of systems, vent and

non-vent. Non-vent airslides are always referred to as ‘fluidised motion conveyor’. They are all

marketed under a variety of different trade names, such as Fluidor, Whirl-Slide, Flow-Veyor

and Fluid-Slide (Woodcock and Mason, 1987).

1.1.1 Conveying Technique

Air-gravity conveyors are commonly used to transport dry particulate materials, and its

conveying technique can be regarded as an extreme form of dense phase pneumatic conveying.

Basically, a typical air-gravity conveyor consists of a rectangular granular flow channel

separated by a porous bed, and it is always inclined at a very slight angle.

Essentially, the conveying technique is used to maintain an aerated state in the bulk solid by

continuous introduction of air, from the moment that it is injected into the upper end of the

inclined channel, to the point at which it is discharged. In detail, compressed air is fed into the

lower chamber which then permeates through the media and runs the length of the channel, to

2

fluidise the particulate material. After fluidising the bed of granular material, these particulate

materials behave like a fluid and flow readily down the chute at angles much lower than the

angle of repose of the granular material.

Figure 1.1 Shows a typical air-gravity conveyor. The bulk materials flow freely down the slope

by the steady flow of air, even when the angle of inclination is very small. In order to reduce

both the inter-particulate forces, and the frictional forces between the particles and the internal

channel surfaces, the quantity of air used is kept to the absolute minimum necessary under the

condition which is sufficient to allow the material to flow (Woodcock and Mason, 1987).

Figure 1.1 Typical Air-gravity Conveyor (Mills, 1990)

1.1.2 System advantages and design tolerance

Air-gravity conveying has all the advantages of pneumatic conveying, but with few of the

disadvantages. For air-gravity flow, a particular advantage over pneumatic conveying is that the

conveying velocity is very low, around 1 m/s. Under this condition, the degradation of particles

and erosion of the conveying channel can be ignored. This is because that the particle-particle

force and the frictional force between the particle and the channel surface can be reduced by the

fluidising air, giving the air-gravity conveyor the advantages of low solid velocity with little

attrition loss, high mass flow rate and low power consumption (Klinzing et al., 1997).

Therefore, when comparing with pneumatic conveying, it needs less power requirements, and it

reduces the risk of the degradation of friable particles and erosive wear of system components

during conveying. In addition, it can avoided from disadvantages such as pipe blockage and

intermittent conveying.

3

However, it suffers from the disadvantage of downward conveying, which means that it has to

be handled under a downward angle, with the help of gravity. The downward inclination

apparently limits the air-gravity conveyor design, and the available literature shows that air-

gravity conveyors had been studied mostly using downward inclinations. That does not mean

that horizontal and upward air-gravity systems are not available; they are used in some cases of

conveyors in industry. However, a specially formed air distributor is needed for up-incline

transportation of material, which ultimately affects the basic simplicity of air-gravity conveyors

and finally results in a complicated and inefficient material handling system. Moreover, air-

gravity conveyor is sensitive to changes in the characteristics of material being conveyed. If the

material changes particle size or shape to decrease its fluidity, or if the moisture content of the

material increases, conveying problems may arise.

1.1.3 Conveying Principles

Considering the advantages that air-gravity conveyors can offer over other forms of bulk solids

handling, particularly in terms of low power consumption, air-gravity conveyors are popular in

industry. However, the study of these conveyors is not as widespread as might be expected, and

there have been few conveying investigations on air-gravity flow. In order to enable air-gravity

systems to be optimally designed, rather than over-designed, further understanding of the

phenomena involved in air-gravity conveying is necessary, and its existing drawbacks need to

be overcome.

The general principle of air-gravity conveying is very simple. It is observed that the flow of

particulate bulk solid being conveyed by an air-gravity conveyor along the conveying channel

suggests a similarity to a liquid flowing in an inclined channel. The inlet air velocity, which is

very important to pneumatic conveying systems, is not easy to correctly specify. This is because

air is compressible, and air pressure in pneumatic conveying systems is much higher than in air-

gravity conveyors. This means that to achieve and maintain a correct inlet velocity is not a

simple matter. If the velocity is too low, the material may not be conveyed at all, and the

pipeline is likely to block. If the inlet air velocity is too high the material flow rate may be

reduced, the power requirements will be excessive, and operating problems will be severe. To

maintain the liquid like state of the material, the continuous supply of air from the bottom has a

close relation to the gas fluidisation process. Therefore, the basic principles of static fluidisation

are first extended to deal with the flow of fluidised bulk particulate materials.

1.2 The fluidisation of bulk solids

Fluidisation is a process in which bulk materials are caused to behave like a fluid by

continuously feeding gas or liquid upwards through the fluidisation reactor filled with solids.

The fluidised bed behaves differently as velocity, gas and solid properties vary when the solid

4

particulates are fluidised. Commonly, there are a number of regimes of fluidization, as shown in

Figure 1.2. The first regime is that when gas flows upwards through a stationary bed of particles

and increase continually, gas flows through interstices. At this state, particles are quiescent with

a few vibrate, but retain the same height as the bed at rest. This is called a ‘fixed bed’ (Figure

1.2A).

When the gas velocity continues slowly to increase, a point will be reached where the drag force

provided by the upward moving gas equals the weight of the particles. Under this condition,

there will be a slight expansion of the bed if the bed is not restrained on its upper surface.

Meanwhile, a rearrangement of the particles happens because each particle tends to float

separately in the upward flow of fluid. This rearrangement brings the particles towards a state

corresponding to the loosest possible packing in the bed, and the voidage of the bed increases

slightly: this is the beginning point of fluidisation and is called minimum fluidisation (Figure

1.2B) with a corresponding minimum fluidisation velocity, Umf.

Further increasing the gas flow, the bed expands smoothly and homogeneously with small-scale

particle motion. The formation of fluidization bubbles sets in, and at this point, a bubbling

fluidised bed occurs, as shown in Figure 1.2C.

At greater superficial velocities, the bubbles in a bubbling fluidised bed will coalesce and grow

as they rise. Gas bubbles rise to the surface and then break through. If the ratio of the height to

the diameter of the bed is high enough, the size of bubbles may become almost the same as the

diameter of the bed. The bed surface rises and falls with regular frequency with responding

pressure fluctuation. This is called ‘slugging’ (Figure 1.2D).

If the particles are fluidised under a high enough gas flow rate, the upper surface of the bed

becomes diffused and difficult to distinguish. At the same time, a turbulent motion of solid

clusters and voids of gas of various sizes and shapes will be observed. Beds under these

conditions are called turbulent beds, as shown in Figure 1.2E.

With further increases of gas velocity, eventually the fluidised bed becomes an entrained bed in

which we have a disperse, dilute phase fluidised bed, which amounts to pneumatic transport of

bulk solids.

5

Figure 1.2 Schematic representation of fluidised beds in different regimes (Kunii and

Levenspiel, 1991)

1.2.1 Flow through a fixed bed of solid particles

Gas or other fluids flowing upwards through a supported bed of particulates can be regarded as

‘fluid flow’ through a porous medium, the difference between these two situations only

becoming evident when the fluid flow rate is high enough to cause movement of individual

particles in the bed. Zabrodsky (1966) pointed out that at this state the permeation of fluid flow

through the fixed bed corresponded to an internal flow of fluid in the interconnecting channels

between the particles, or an external flow around the particles. Keuneke (1965) gave a detailed

review of attempts to develop theoretical and semi-empirical expressions for any pressure drop

in packed and fluidised beds. Among those seeking to predict the flow behaviour in fixed beds,

Carman’s (1937) work had achieved the greatest acceptance, his extensive study had more

recently been augmented by Ergun (1952). According to their work, more and more analytical

modelling has been subsequently proposed by various authors, which then leads to expressions

for pressure drop across a fixed bed in accordance with the properties of the flowing fluid in the

bed.

Ergun (1952) had listed the variables influencing flow behaviour in fixed beds, including the

rate of fluid flow, the viscosity and density of the fluid, the closeness and orientation of packing,

and the size, shape and surface of the particles. The variable concerning the packed solids is the

voidage, expressed as:

6

𝜀0 =𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑣𝑜𝑖𝑑𝑠

𝑡𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑏𝑒𝑑 (1.1)

And the size and shape of the particles, which are conveniently achieved by defining a volume

diameter and a sphericity as follows: volume diameter, 𝐷𝑝, is the diameter of a sphere having

the same volume as the particle.

Sphericity, ∅𝑠 =

𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑝ℎ𝑒𝑟𝑒 ℎ𝑎𝑣𝑖𝑛𝑔 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒

𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 (note that ∅𝑠 < 1)

Since the volume of solid particles in a bed of unit volume is (1 − 𝜀0), we can describe the

number of particles per unit volume of the bed as

𝑁 =6(1 − 𝜀0)

𝜋𝐷𝑝3 (1.2)

and the surface area of particles in unit volume of the bed (that is, the specific surface of the

bed) is then defined as:

𝑆𝑏 = 𝑁𝜋𝐷𝑝

2

∅𝑠=6(1 − 𝜀0)

𝜋𝐷𝑝3 ∙

𝜋𝐷𝑝2

∅𝑠

Or

𝑆𝑏 =6(1 − 𝜀0)

∅𝑠𝐷𝑝

(1.3)

(It should be noted that there are many other ways of expressing particle size and the mean size

of a collection of particles of different sizes)

Various forms of the Carman-Kozeny equation for flow in packed beds is now well established

(Keuneke, 1965) and can be extended to yield various expressions for the pressure drop in

laminar flow through such beds. An alternative analysis leads to an expression for pressure drop

according to the kinetic energy of the flowing fluid and combining these gives a general

equation as:

∆𝑃𝑏ℎ=1 − 𝜀0

∅𝑠𝜀03 ∙

𝜌𝑔𝑈2

𝐷𝑝(100

𝑅𝑒𝑏+ 1.75) (1.4)

U is the superficial velocity of the flowing fluid in a packed bed of depth h, and 𝑅𝑒𝑏 is a

Reynolds number for the bed describe as:

𝑅𝑒𝑏 =2

3(∅𝑠

1 − 𝜀0)𝐷𝑝𝑈

𝑣𝑔 (1.5)

7

The Ergun’s equation can be achieved by expanding Eq.(1.4), which shows the pressure drop

across a packed bed as the sum of viscous effect (as modelled by the Carman-Kozeny equation)

and kinetic energy effect:

∆𝑃𝑏ℎ= 150

(1 − 𝜀0)2

∅𝑠2𝜀03 ∙

𝜇𝑔𝑈

𝐷𝑝2 + 1.75

1 − 𝜀0

∅𝑠𝜀03 ∙

𝜌𝑔𝑈2

𝐷𝑝 (1.6)

It is not easy to predict pressure drops in flow through packed beds, as one of the major

difficulties is the variability of voidage with particle size, shape, packing arrangement.

Meanwhile, variation of density in gas flow also causes problems in the analysis. The Ergun

equation (1.6) is just one of many correlating expressions that have been proposed. Basically,

information on the sphericity ∅𝑠 and the voidage 𝜀0 of the particulate bed is required in most of

these expressions. If this information is not available for the material concerned, it must be

determined experimentally, or estimated.

Wen and Yu (1966) developed an expression for the minimum fluidisation velocity for a range

of particle types and sizes by assuming the following approximations to holds based on

experimental data:

1−𝜀𝑚𝑓

∅𝑠2𝜀𝑚𝑓3 ≈ 11 and

1

∅𝑠𝜀𝑚𝑓3 ≈14

1.2.2 Minimum fluidisation velocity

The minimum fluidisation velocity (Umf) is the point of transition between a fixed bed regime

and a bubbling regime in a fluidised bed. Minimum fluidisation velocity is one of the most

important normalized parameters when describing the hydrodynamics in a fluidised bed (Ramos

et al., 2002).

Commonly, the minimum fluidisation velocity is obtained experimentally, and there are several

techniques reported to find the minimum fluidization velocity in a multiphase flow system.

Gupta and Sathiyamoorthy (1999) gave three different methods to measure 𝑈𝑚𝑓: (i) the pressure

drop method, (ii) the voidage method, and (iii) the heat transfer method. The first method

measures the pressure drop across the bed as a function of the superficial gas velocity. In a plot

of pressure versus superficial velocity, there is a point showing the transition between a fixed

bed regime and a bubbling regime by a constant pressure line, which is marked as the minimum

fluidisation velocity. In the voidage method, the minimum fluidisation velocity is determined

when the voidage inside the bed starts to increase due to bed expansion as the superficial gas

velocity is increased. But this method is not commonly used because it is much more difficult to

define the point at which the bed expansion starts. Finally, in the heat transfer method, the

variation of the wall heat transfer coefficient is measured as the gas velocity increases. The

point where the heat transfer coefficient increases drastically is the onset of fluidisation or the

8

minimum fluidisation velocity point. However, this method is too expensive and requires a good

experimental apparatus to measure the heat transfer data under steady-state conditions.

The phenomenon of fluidisation can best be described by a ∆𝑃/𝐿 versus U plot as shown in

Figure 1.3. Below the minimum fluidisation velocity, pressure drop across the bed can be

measured and solid particles remain at the same height. At the minimum fluidisation velocity,

all the particles are essentially supported by the gas and then a point will be reached where the

drag force provided by the upward moving gas equals the weight of the particles. The pressure

drop through the bed is then equal to the bed weight divided by the cross-sectional area of the

bed, ∆𝑃 =W/A. Further increases in gas velocity will usually not cause further increases in

pressure drop. In actual practice, however, pressure drop at minimum fluidization velocity is

actually less than W/A because a small percentage of the bed particles is supported by the wall

owing to the less than perfect design of the gas distributor, to the finite dimension of the

containing vessel, and to the possibility of channelling. At the point of minimum fluidisation,

the voidage of the bed corresponds to the loosest packing of a packed bed. The loosest mode of

packing for uniform spheres is cubic, as is 𝜀𝑚𝑓 =6−𝜋

6= 0.476. Substituting into the original

Carman equation, the following equation can be obtained:

∆𝑃

𝐿= [

72

𝑐𝑜𝑠2(𝛾)] ∙𝜇𝑈(1 − 𝜀)2

𝐷𝑝2𝜀3

(1.7)

And assuming

72

𝑐𝑜𝑠2(𝛾)= 180; 𝛾 is usually from 48 o to 51o

Then ∆𝑃

𝐿= 459

𝜇𝑈𝑚𝑓

𝐷𝑝2 (1.8)

At the point of minimum fluidisation, the pressure drop is enough to support the weight of the

particles and can be expressed as

∆𝑃

𝐿= (𝜌𝑝 − 𝜌𝑓)(1 − 𝜀𝑚𝑓) (1.9)

Combining Eq.(1.8) and Eq.(1.9) with the voidage at the minimum fluidisation 𝜀𝑚𝑓=0.476, the

minimum fluidisation velocity can be expressed as:

𝑈𝑚𝑓 = 0.00114𝑔𝐷𝑝

2(𝜌𝑝 − 𝜌𝑓)

𝜇 (1.10)

9

Figure 1.3 Pressue drop vs. fluidisation velocity plot for determination of minimum fluidisation

velocity

Zhou et al. (2008) used the pressure drop method to find and compare the minimum fluidisation

velocity of a three phase system (gas-liquid-solid) between a conical and a cylindrical fluidised

bed. They compared the experimental results of the minimum fluidisation velocity with results

achieved by using reported theoretical correlations, like the Ergun equation, as well as other

models developed by other researchers. Results agreed when using both theoretical models and

experimental procedures to get the minimum fluidisation velocity.

The minimum fluidisation velocity depends on the material properties, the bed geometry, and

the fluid properties. Sau et al. (2007) determined the minimum fluidisation velocity for a gas-

solid system in a tapered fluidised bed (conical fluidised bed) and studied the effects that bed

geometry, specifically the tapered angle, had on the minimum fluidisation velocity. They used

three different angles (4.61, 7.47, and 9.52 degrees) to observe their effects on minimum

fluidisation velocity. Results showed that as the tapered angle increased, 𝑈𝑚𝑓 also increased,

which implied a dependence of the minimum fluidisation velocity on the geometry of the

fluidised bed. Moreover, Hilal et al. (2001) analysed the effects of bed diameter, distributor, and

inserts on minimum fluidisation velocity. It was shown that both the bed diameter and the type

and geometry of the distributor affected 𝑈𝑚𝑓. Minimum fluidisation velocity values increased

with an increase in the number of holes in the distributor plate. Furthermore, with an increase in

the bed diameter, there was a decrease in the minimum fluidisation velocity. Finally, insertion

of tubes along the fluidised bed reduced the cross section area, which produced a high

interstitial gas velocity causing a decrease in 𝑈𝑚𝑓.

10

1.2.3 Expansion of the fluidised bed

With further increases of fluidisation velocity beyond the minimum fluidisation velocity, the

bed tends to expand but without any appreciable change in the pressure drop across it. Actually,

the behaviour of the fluidised bed depends upon the properties of the granular material, and as

well the fluidising medium, in other words, the ratio of their densities. Generally, where the

solids and fluid have similar densities, the bed expands uniformly and has a virtually

homogeneous structure throughout. The bed has the condition known as particulate fluidisation.

At higher superficial velocities, especially where the fluid density is much less than that of the

bed material, the structure of the bed will not be homogeneous because the fluid tends to rise

through the bed in the form of bubbles or particle-free voids. The surface of the bed becomes

similar, like a boiling liquid in appearance, and this state is known as ‘aggregative fluidisation’.

It is needed to note that not every particle can be fluidised. The behaviour of solid particles in

fluidised beds depends mostly on their size and density. Geldart (1973; 1978) carefully

observed the characteristics of the four different power types and then categorized them as

follows:

Group A is defined as ‘aeratable’ particles. In general, it includes materials of small particle size

(𝐷𝑝 < 30 𝜇𝑚) and /or low particle density (less than about 1400 kg/m3). Powders in this group

can be fluidised easily, and the bed expansion is considerable when the value of velocity stay

between the minimum fluidising velocity (𝑈𝑚𝑓) and the minimum bubbling velocity (𝑈𝑚𝑏).

After fluidisation, and shut off the fluidising velocity, these particles are relatively slow settling

in the bed. When velocities above 𝑈𝑚𝑏 , the bed bubbles freely, and at higher velocities,

axisymmetric slugging tends to occur. Further increasing of velocities, the slugging movement

is continually collapsing result in the upward flowing fluid is forced to track upwards to the top

surface of the vigorously turbulent bed.

Group B is called ‘sandlike’ particles. Including most materials in the mean particle size 40-500

𝜇𝑚 and density from 1400 to 4000 kg/m3, this group would typify the generally accepted model

of fluidised bed behaviour. For these particles, once the minimum fluidisation velocity is

exceeded, the excess gas appears in the form of bubbles. Bubbles in a bed of Group B particles

can grow to a large size.

Group C materials are ‘cohesive’, or very fine powders. Their sizes are usually less than 30𝜇𝑚,

and they are extremely difficult to fluidise because inter-particle forces are relatively large,

compared to those resulting from the action of gas. Attempting to fluidise these materials will

usually form stable channels or result in the whole bed rising as a plug, although some success

may be obtained with the help of mechanical vibrators or stirrers. Examples of Group C

materials are talc, flour and starch.

11

Group D is called ‘spoutable’ and the materials are either very large or very dense. They are

difficult to fluidise in deep beds, and their fluidisation behaviour is probably similar to powders

in Group B. Group D materials can generally be made to show the spouting phenomenon if the

gas is injected centrally in the bed. Roasting coffee beans, lead shot and some metal ores are

examples of Group D materials.

Figure 1.4 Diagram of the Geldart classification of particles (Geldart, 1973)

Geldart’s classification is clear and easy to use as displayed in Figure 1.4 for fluidisation at

ambient conditions and for velocity less than about 10𝑈𝑚𝑓. For any solid of a known density ρs

and mean particle size Dp this graph shows the type of fluidisation to be expected. It also helps

predicting other properties such as bubble size, bubble velocity, the existence of slugs etc.

Further work on comparing and clarifying the boundaries on Geldart’s chart has been done by

numerous researchers. Among them, Dixon (1979) developed a slugging diagram based on

materials’ slugging abilities in a vertical fluidisation column. Dixon argued that a material

forms either strong axisymmetric slugs, weak axisymmetric slugs, or no slugs, depending on

particle density and average particle diameter. The areas of strong axisymmetric slugs and weak

axisymmetric slugs have obvious combinations of mode of flow including fluidised dense

phase, dilute only and plug type. Molerus (1982) studied the fluidisation performance of a bulk

material instead of pneumatic conveying performance, and applied particle adhesion equations

to define the boundaries of different fluidisation classification groups based on Geldart’s chart.

Mainwaring & Reed (1987) developed a two-diagram predictive technique which incorporated

the steady state fluidisation pressure, permeability and de-aeration behaviours of the material.

Alternatively, Jones (1988) proposed a predictive chart only by relating the permeability with

de-aeration behaviours of materials under vibration. Lately, Pan (1999) substituted the particle

12

density with a loose poured bulk density value in the Geldart chart to predict the mode of flow.

More recently, a dimensionless parameters based chart was derived by Grace (2009), attempting

to more accurately categorise the material conveying mode. Chambers et al. (1998) proposed a

dimensional parameter in a diagram by utilising parameters of particle density, permeability and

de-aeration to predict mode of flow. Similarly, Fargette et al. (1996) proposed another

dimensional parameter and replaced the particle density with bulk density. Moreover, Sanchez

et al. (2003) proposed a two-parameter dimensionless diagram by considering permeability, de-

aeration rate, gravitational forces, conveying gas properties and particle size. Since a de-aeration

rate is hard to determine, based on the above work, Williams (2008) developed a diagram with

parameters of permeability and loose poured bulk density for modes of flow prediction.

Compared with basic material diagrams, similar fluidised dense phase and plug flow regions are

presented with a clear dilute phase region.

1.3 The flow behaviour of aerated bulk solids

Most free flowing particulate materials display a natural angle of repose of around 35o to 40o, as

shown in Figure 1.5a. The angle of repose will in fact depend partly upon how the heap is

formed, and there is a certain amount of disagreement as to the most reliable method of

measuring it. One method, forming a heap of the powder by pouring or by draining, tilting a box

filled with powder or rotating a horizontal cylinder half filled with powder are proposed. In

order to get such a material to flow continuously, under gravity alone, in an inclined channel it

would be necessary for the slope of the channel to be greater than about 35o, depending upon the

angle of repose and other properties like flowability of the powder, and also depending to some

extent upon the roughness of the channel surfaces, as illustrated in Figure 1.5b. Materials

exhibiting some degree of cohesiveness have angles of repose larger than the normal 35o to 40o.

Such materials often will not flow even on steeply inclined surfaces, without some form of

assistance, such as vibration of the surface.

If a powder or granular material is to move freely along a channel when the slope is much less

than the natural angle of repose, it is necessary to improve the flowability of the materials or to

reduce the frictional resistance between the bed of powder and the walls and bottom of the

channel. The introduction of air to a bulk material can provide a means of promoting flow. For

example, supporting the powder on a plate made of a suitable porous substance and allowing the

air to flow upwards through it at low velocity into the powder, can significantly reduce the

natural angle of repose (Figure 1.5b). The material will then flow continuously when the plate is

inclined at a very shallow angle. For most materials the fluidised angle of repose is between

about 2o to 6o, while for some free flowing powders this angle may be as little as 1o or even less.

This results predominantly from two reasons. One is that the air filtering through the bed of

solid particles and reduce the contact forces between them (thus perhaps causing partial

13

fluidisation of the powder). The other is that the formation of an air layer between the bed of

particles and the plate surface allows slip to take place, with a consequent sharp reduction of the

boundary shear stresses. However, it is not clear which reason is the dominant one. It seems

probable that with fine free flowing solids, which can be easily fluidised, the former effect is the

more significant, and these materials will flow satisfactorily at extremely shallow slopes.

Slightly cohesive powders, when aerated, will often flow down an inclined surface if the slope

is rather greater, perhaps around 6o to 10o. Observation of such a material suggests that the

particles are not fluidised, but move virtually as a solid mass sliding along the channel.

Figure 1.5 influence of aeration on angle of repose. (a) No aeration on horizontal pile of

material, (b) no aeration on steep incline, and (c) with aeration on shallow incline (Mills, 1990).

1.3.1 Historical development

It is not known when aeration of a bulk particulate solid was first used as an aid to conveying,

but one of the earliest relevant patents appears to have been that of Dodge in 1895, who used

air, entering an open channel through slits in the base, to transport coarse grained material. It is

interesting to note that also around the turn of the previous century the air cushion principle was

proposed for moving steel plates horizontally along a table on a series of vertical air jets

(Vollkommer, 1902).

However, significant progress in the gravity conveying of aerated powders was not made until

some thirty years later when it was found that the method provided an excellent means of

conveying cement. The German company Polysius was something of a pioneer in the

development of air-assisted gravity conveying, but was followed into the field by the Huron

Portland Cement Company of America which obtained the first British patent in 1949. Huron's

plant at Alpena, Michigan was one of the first to make extensive commercial use of this method

of conveying and employed ‘Airslides’, as they came to be called, at various stages of the

14

production process from grinding mill discharge to finished cement (Avery, 1949; Nordberg,

1949). The third organisation that played a prominent part in establishing air-gravity conveyors

was the Fuller Company which manufactured them under license from Huron and which also

held the rights to one of the main controlling British patents (Fuller, 1953). Further British

patents, mostly taken out by Huron and by the Fuller Company, indicate the gradual

development of air-assisted gravity conveying through changes to the design of the duct, feed

and take-off points, air supply, porous base material, and so on, but rarely do these patents give

any technical details on the performance of the conveyors.

Currently there are a number of different companies marketing air-gravity conveyors under a

variety of different trade names such as Airslide, Flo-tray, Gravitair, Fluidor, Whirl-Slide and

Fluid-Slide. Nevertheless, considering the advantages that they can offer over other forms of

bulk solids transport, the use of these conveyors today is not as widespread as might have been

expected. To some extent this may be the result of a lack of confidence on the part of the design

engineer.

1.3.2 Current construction and application of air-gravity conveyor

The fundamental construction of a practical air-gravity conveying installation is very simple and

indeed this is one of its main advantages over other methods of bulk solids transport. Essentially

the conveyor consists of just two U-shaped channel sections with the porous membrane

sandwiched between them. The lower channel serves as a plenum chamber to which air is

supplied at one or more points, depending upon the overall length of the conveying system.

The presence of the covered top channel renders the conveyor virtually free from problems of

dust leakage, but naturally it would also operate satisfactorily as an open channel. In this form

the device has been widely employed as flow assistors mounted at the bottom of silos, bunkers,

bulk railway wagons and lorries and so on, enabling these containers to be made with a virtually

flat base and thus having a substantially greater capacity. Where the conveyor is covered it is

necessary for the top channel to be adequately vented through suitable filters. With short

conveyors it may be sufficient to rely on the air escaping with the powder from the outlet end of

the channel and then through the vent system of the discharge hopper, if one is in use. If the

conveying system is long, or if there is a possibility of the channel outlet becoming choked with

powder, it is better to vent from two or more points between the inlet and outlet.

It is likely to prove useful to have inspection or access ports fitted at convenient positions along

the duct, especially in the region of the inlet and outlet and in other positions where blockages

may occur. Whilst it is possible to exercise some control over the flowrate of material in the

conveying duct by the use of gates or baffles, it is likely to be more satisfactory to control the

feed to the upstream end of the conveyor. Therefore, in the case of discharge from a hopper, for

15

example, flow control can be achieved by the conventional use of a rotary valve, screw feeder or

pinch valve. Where precise control of the solids flowrate is not required, flooded feed from the

hopper to the conveying duct may be satisfactory. The system is then effectively self-regulating

and with free-flowing powders there is little risk of the conveyor becoming choked, provided

that the slope of the channel and the flowrate of fluidising air are sufficient.

1.3.3 Recent research on air-gravity conveyors

Generally, there are two kinds of air-gravity conveyor systems, vent and non-vent systems.

1.3.3.1 Vent system

There is little published research into the flow of aerated powders in inclined channels. One of

the main obstacles for researchers is that they have to face the problem that the size of the air-

gravity conveyor test rig is required to be comparable to typical industrial installations. The

width of most commercially available channels is 100 mm, 120 mm and 150 mm, and it is

uncertain whether data from tests on narrower channels can reliably be extrapolated to predict

the performance of conveyors on an industrial scale. The length of a conveying channel that can

be situated in an average laboratory also tends to be limited. Whilst there may be some

theoretical justification for the use of short channels (McGuigan, 1974), there does not appear to

be any experimental evidence to confirm that uniform flow is so rapidly attained.

Additional problems are encountered when attempting to measure variables such as the depth of

the flowing bed of suspended solids, the bulk density of the bed, the velocity of the bed and so

on. In the case of "apparent viscosity" the problem is as much one of understanding and

defining the property as of measuring it. The most extensive programmes of work appear to

have been those carried out by Keuneke (1965), Qassim (1970), McGuigan (McGuigan and

Elliott, 1972; McGuigan, 1974; McGuigan and Pugh, 1976) and Pugh (1975). That of Keuneke

is especially interesting because of the number of different bulk solids investigated, which

included cement, gypsum, potash and several typical agricultural products. He studied the

fluidisation behaviour of these substances and then, using a 6 m long conveying channel,

compared their flow characteristics at different channel slopes and fluidising air flowrates. A

great deal of data is presented, mostly in graphical form, but unfortunately there is little mention

of the depth of the flowing beds of material and consequently it is not possible to build up a

comprehensive model which would allow the data to be correlated and extended.

Qassim (1970), working at Imperial College, London, restricted his investigation to 266 μm

sand flowing in a channel only 180 mm long. Despite the fact that in a short channel, fully

developed flow conditions are unlikely to be achieved, he attempted to measure the depth of the

flowing suspension at various solids mass flow rates and various channel slopes. However, he

did not show graphs of bed depth against mass flowrate and when such graphs are plotted, they

16

seem to show some remarkable inconsistencies. Qassim chose to process his data to yield shear

diagrams which largely mask these inconsistencies, and as indicated by McGuigan (1974) the

figures should be treated with some caution.

At the University of Aston a test rig based on a 3 inch long channel was developed by

McGuigan (1974) and Pugh (1975). The programme of work undertaken by McGuigan

concentrated on the apparent viscosity of the aerated sand that he used and attempted to find

some correlation between values of this property as determined in the main flow channel and by

a rotary viscometer in a small subsidiary fluidising rig. Both McGuigan and Pugh relied heavily

on shear diagrams and friction factor/generalised Reynolds number correlations in the

processing and display of their experimental data.

Muskett et al. (1973) had conveyed fluidised sand down-incline in a gravity conveyor to study

the effect of superficial air velocity on the mass flow rate of solids. They had also evaluated the

performance of a vertical baffle wall to control the flow rate of solids. Some relevant

conclusions of their study were that: (i) Solids mass flow rate increased with gate opening for

constant bed inclination angle and fluidising air velocity. (ii) Mass flow rate increased with

superficial fluidising air velocity for constant gate opening, inclination angle and conveying air

velocity. (iii) At low fluidising velocities only the top layer of particles were airflow in motion,

with the lower layer acting as an additional porous layer. As airflow increased, a critical value

was reached at which the whole bed began to flow. (iv) As inclination angle reduced, a higher

fluidising velocity was required to generate the same mass flow rate.

Consideration of research programmes involving the flow of aerated bulk solids would not be

complete without a mention of the work of Botterill and various co-workers at the University of

Birmingham (Botterill et al., 1970a; Botterill and van den Kolk, 1971; Botterill et al., 1971;

Botterill and Bessant, 1973; Botterill and Bessant, 1976). Although this work was confined to

flow in a horizontal channel in which a pressure gradient was maintained by a series of moving

paddles, many of the reported results are obviously relevant to flow in inclined channels.

Botterill et al. (1972) determined the rheological behaviour of fluidised bauxilite by using a

modified Brookfield viscometer and a closed-circuit (shape similar to one obtained by joining

two U-tubes together at their ends) open channel, which had 1.0 m test length in one of the

limbs of the circuit. They found that the fluidised bauxilite exhibits non-Newtonian flow

property and the results obtained by both the methods are comparable.

Their earlier studies (Botterill and van den Kolk, 1971; Botterill et al., 1972) found that the

effective viscosity of the fluidszed material was very sensitive to the fluidising velocity and the

bed height. When the fluidising velocity was varied from 1.25 to 2.5 Umf, the effective viscosity

was reduced by a factor of 10 (Botterill and van den Kolk, 1971). In some tests, a reduction of

17

bed height from 210 mm to 90 mm reduced the apparent viscosity by a factor of 5 (Botterill et

al., 1972). After that, Botterill and Bessant (1976) performed fluidised solids experiments in a

closed-circuit, open, horizontal, 300 mm wide channel having a porous tile distributor base. The

particles used for most experiments consisted of narrow fraction dune sand having a diameter of

200 µm and a density of approximately 2600 kg/m3. The particle flow was induced by a series

of paddles that were immersed in the bed along a straight portion of the flow channel track.

Local flow velocities over the cross-section were measured by a small turbine element having a

6 mm diameter rotor, and they established that the fluidised particulate solids show non-

Newtonian rheological behaviour. The upward fluidising air velocity in most of their

experiments was between 1.25 and 3 times Umf, the minimum fluidisation velocity for the

particles.

Botterill and Bessant (1976) measured the velocity profiles across the width of the flow at

several vertical positions for different channel aspect ratios, fluidising air velocities, and overall

material flow heights. They used two values for the fluidising air flow (1.75 Umf and 2 Umf), two

material heights (h=77 mm and 118 mm), and two channel widths (W=140 mm and 180 mm). It

was found that the basal slip velocities depended on the fluidising air flow rates. At lower air

flow rates, little or no slip appeared to occur at the bed, whereas at higher air flow rate, sand

solids shear rates there was considerable slip at the bed and a relatively small velocity gradient

in the vertical direction.

Botterill and Abdul-Halim (1979) extended the experiments of Botterill and Bessant (1976) by

using different types of particles (catalyst, sand, ash) and grain diameters for several channel

widths and heights. They assumed that the fluidised solids behaved as a power-law fluid and

calculated the velocity profile over the channel cross-section.

Ishida et al. (1980) conveyed glass beads in a 954 mm long and 39 mm wide open channel.

They measured the velocity distribution of solid particles using an optical probe in the

downward inclined channel, and attempted to categorize the flow pattern on the basis of non-

dimensional superficial air velocity (U0/Umf) and different angles of inclination of the channel.

Woodcock and Mason (1987) had systematically presented the variations of airslides used by

different researchers to convey the dry particulate materials in three types of the conveyor

inclinations, which were designed to operate at 3o-10o downward inclination.

Rao and Tharumarajan (1986) also carried out parametric investigation on an airslide of 2.5 m

length using raw meal (crushed grain-bulk density 0.91 g/cm3 and particle density 2.71 g/cm3)

as the conveyed material.

18

Hanrot (1986) experimented on fluidised alumina, which was conveyed over a horizontal

distance of 180 m and called it ‘potential fluidisation piping’.

Kosa (1988) used an open channel of 1.0 m length, which had a specially formed air distributor

plate with oblique slots, to convey polyethylene and fertilizer granules. He called it the

‘Aerokinetic Canal’, and proposed a physical model for the system.

Latkovic and Levy (1991) investigated the flow characteristics of fluidised magnetite powder in

an open channel of length 1.3 m. After that, they further extended the conveying distance to 2.3

m for minimizing the effect of entry and exit disturbances. They applied the liquid analogy and

used power-law rheological model to correlate the emulsion phase friction factor with

generalized Reynolds number. Klinzing et al. (1997) had given a systematic design procedure

for Airslides/Gravity Conveyors for downward inclined channels.

1.3.3.2 Non-vent system

Non-vent air-gravity conveyor, commonly referred as a fluidised motion conveyor, is designed

with a minor change in the constructional features of a vent system being incorporated in the

form of enclosing the conveying channel. There have been relatively few investigations of Non-

vent flows. Gupta et al. (2006) studied fly ash flow in a closed conveying channel and carried

out a parametric investigation to assess the influence of superficial air velocity, channel

inclination and valve opening on the material mass flow rate, material bed depth and plenum

chamber pressure. The increase in the valve opening increased bed height for all the conveyor

inclination angles. Also, the materials bed height decreased along the channel length in the flow

direction.

Further, Gupta et al. (2009) investigated the effect of increasing the channel length on mass

flow rate and material bed height. They predicted the performance of fluidised motion

conveying system using the equations developed by Klinzing et al. (1997), which are empirical

equations determining the width of conveying channel for an air gravity conveyor. However, the

results indicated that Klinzing et al.’s model was not valid for the design of a fluidised motion

conveying system.

Tomita et al. (2008) studied Gupta et al.’s (2006) work and proposed the possibility of fluidised

material being transported by a force other than gravity. They also introduced air vents from the

top of the channel into the horizontal conveying system and found an increase in the mass flow

rate and the height of material layer.

As there has been no theoretical or empirical correlation that could successfully predict the

performance of fluidised motion conveying, Gupta et al. (2010) developed a modified air

gravity conveyor model by adding parameters to the empirical relation in Klinzing et al.’s

19

(1997) model. A good agreement between the predicted and measured material mass flux was

achieved with the unknown parameters in the model being taken from the experimental data of

Singh et al. (1978). However, the model may not be able to give good predictions for other

fluidised motion conveying systems due to the involvement of these unknown parameters in the

model.

Ogata et al. (2012) experimentally investigated powder conveyance in a horizontal rectangular

channel using fluidising air. The powder was glass beads that are Geldart A particles, with a

mean diameter of 53 µm, a particle density of 2523 kg/m3 and a minimum fluidising velocity of

4.329 mm/s. The powder could be transported smoothly when air was supplied to the bottom of

the vessel and the air velocity at the bottom of the horizontal channel exceeded the minimum

fluidising velocity. It was found that the discharge of the powder from the vessel had significant

effect on the horizontal conveying of fluidised powder in this system.

1.3.4 Factors influencing the flow behaviour of aerated bulk solids in air-gravity

conveyors

In the above sections, it is explained how the behaviour of fluidised particulate bulk solids could

be used to advantage in air-gravity conveyors. For general purposes, it is in fact quite easy to

construct an air-gravity conveying channel, and it can be worked adequately with most bulk

solids, but if a channel is to be well designed to make the best use of available height and to

provide trouble-free operation with maximum economy, it is essential to have a good

understanding of the flow behaviour of aerated bulk solids.

The first step is to recognise the principal variables involved in conveying systems. For a given

material, the mass flowrate in an air-gravity conveying channel will depend upon the width and

inclination of the channel, the superficial velocity of the fluidising air and the depth of the

powder bed in the channel. There are other variables that should be recognised, and there of

course, a complicated inter-relationship exists amongst them. Thus, for example, the bulk

density of the materials and the superficial air velocity will affect the viscosity of the flowing

solids, as will the shear stress between the flowing powder and the internal surfaces of the

channel. Moreover, the velocity of the flowing powder would be mainly influenced by the

inclination angle, but would be affected by the bulk density and depth of the material bed.

Finally, it has to be noted that if there is any change in the nature of the conveyed powder, for

instance, the attrition of the particles, electrostatic charging or variation in moisture content, all

these relationships between variables are likely to be changed.

To properly design an experimental approach, the most valuable thing is to obtain insight into

the relationships amongst the five basic parameters: solids mass flowrate, bed depth, width and

slope of the channel and superficial air velocity. The experimental data for each material should

20

remain consistent, and then as a result, investigation into relationships between these variables,

and a correlation of the data for this material can fit well with developed physical models.

However, a survey on relevant literature reveals that there is very little direct information on

flow of fluidised material in air-gravity conveyors. Though a large amount of graphical form

data has been presented by various researchers, these data generally involve relationships

between compound parameters like modified Reynolds numbers and friction factors, so it is

difficult to study back to the raw figures. Nevertheless, all the available data have been carefully

sifted and compared.

In this section, the general factors influencing the flow behaviour of bulk materials in inclined

channels will be discussed. Valuable observations by various researchers relevant to this subject

will be summarised where they help provide understanding of the mechanism of flow.

1.3.4.1 The material to be conveyed

Almost any bulk particulate solids having good fluidising characteristics will flow easily down

an inclined surface when suitably fluidised in an air-gravity conveyor. Leitzel’s and Morrisey’s

(1971) results state that being easily fluidisable is an essential requirement for conveying in this

manner. It is in fact that many materials having slightly cohesive properties could also be

conveyed in air-gravity conveyors. Leitzel and Morrisey (1971) set an approximate limit on the

material to be conveyed by suggesting that its specification should lie within the range covered

by: Particle size distribution is 100% minus 850 𝜇𝑚, 10 to 15% minus 75 𝜇𝑚; free moisture

content is less than 1%; bulk density from 80 to 3000 kg/m3.

Generally, very cohesive materials of extremely fine particle size are unsuitable for air-gravity

conveying (Butler, 1974), because they are easy to smear over the channel surfaces and blind

the porous membrane. Clearly the flow behaviour in an inclined channel depends on the

property of the conveyed material, especially with regard to the superficial air velocity to

maintain the flow, and the minimum slope at which it could be transported. It is difficult to

define the property of material to some measurable properties which concerned with the ability

of the material to be fluidised, and also with the cohesiveness or resistance of the material to

shear. By considering coupled with the observation of similarities between flowing fluidised

solids and flowing liquids, the term viscosity or apparent viscosity can be used for fluidised

solids.

The work of Geldart in classifying bulk solids according to their fluidisation behaviour has been

discussed previously (Section 1.2.3). As shown in Figure 1.4, the chart illustrating the ranges of

Groups A, B, C and D, provides a useful guide to the suitability of powders and granular

materials for air-gravity conveying. In general, materials in Group B, which includes most

powders in the mean particle size ranges 40 to 500 μm, and density ranges 1400 to 4000 kg/m3

21

are the easiest to convey and will flow well at low inclination angles. When the supply of

fluidising air is shut off, the bed collapses rapidly and flow stops, so that there are unlikely to be

any problems with air retention.

Materials in Group A generally include powders of small particle size and/or low density. They

can be transported and should flow well in an air-gravity conveyor. However, the material may

have a tendency to continue flowing for a time after the fluidising air supply has been shut off,

because of air retention.

Group C includes cohesive powders that are difficult to fluidise satisfactorily as a result of high

inter-particle forces, electrostatic effects or high moisture content. The dividing line between

Groups C and A is very indistinct, and small-scale practical experiments must be done to assess

the suitability of doubtful materials for air-gravity conveying. However, it may be found that

apparently unsuitable materials will move continuously along an inclined channel by a

combination of flowing and sliding, provided the slope and air supply are sufficient.

Materials in Group D, with larger particle size and/or high density, can usually be conveyed in

the same manner. However, the convey system tends to require more fluidising air, so it is

suggested to convey these materials in other forms of transport, such as belt conveying, might

prove to be more suitable.

1.3.4.2 The width of the channel

The main parameter governing the capacity of an air-gravity conveyor is the channel width.

Based on the basic design data in the literature of Leitzel and Morrisey (1971), capacities are

expressed as a function only of the channel width, with little indication of how such figures

would be modified for different types of conveyed material, and for different channel inclination

angles and fluidising air flowrates.

Several authors (Chandelle, 1971; Descamps and Jodlowski, 1973; Gregoraszczuk and

Fedoryszyn, 1974) supporting the use of an expression of the form:

𝑚𝑠 ∝ 𝑏𝑥ℎ𝑦 (1.11)

It is suggested that the influence of the channel width depends on the aspect ratio at which the

channel operates from Eq.(1.11). Thus, according to Chandelle (1971), for

ℎ 𝑏 ≪ 0.5,𝑚𝑠 = 𝑏ℎ2 ⁄ ; for ℎ 𝑏 ≈ 0.5,𝑚𝑠 = 𝑏

2ℎ2 ⁄ and for ℎ 𝑏 > 0.5,𝑚𝑠 = 𝑏3ℎ⁄ . Harris

(1905) seems to imply that for the wider channels, the capacity should be more nearly

proportional to the width. However, although Harris was one of the few researchers to have

studied with channels of different widths, his range was unfortunately restricted to a maximum

width of only 67 mm.

22

For a given application, a useful preliminary estimate of the width of channel may be made by

regarding as constant the average velocity and the bulk density of the flowing suspension

(althrough both are functions of the channel slope and fluidising air velocity). The average

solids velocity would normally between 1 and 4 m/s, and the bulk density of the suspension

between 10 and 50% less than that of the material when unfluidised. Furthermore, the optimum

operating aspect ratio is around 0.5 (Chandelle, 1971) since this corresponds to the maximum

value of the hydraulic mean depth for a given cross-sectional area.

Clearly, at constant aspect ratio, channel slope and fluidising air velocity, the conveying

capacity of the channel would be proportional approximately to the square of the channel width.

Thus the width of a conveyor required to transport a mass flow rate 𝑚𝑠 of a material having

bulk density 𝜌𝑏 is given approximately by:

𝑏 = (𝑟𝑒𝑚𝑠

𝑟𝑎𝜌𝑏𝑢𝑠)12 (1.12)

where 𝑟𝑎 is the operating aspect ratio, 𝑟𝑒 is the expansion ratio of the conveyed material (that is,

the ratio of the bulk density of the unfluidised material to that of the suspension) and 𝑢𝑠 is the

average solids velocity along the channel. For many particulate bulk solid materials capable of

being transported in air-gravity conveyors, a first estimate of the width of the conveyor required

can be obtained by taking suitable average values of the quantities 𝑢𝑠, 𝑟𝑎 and 𝑟𝑒, and introducing

the particle density 𝜌𝑝 in place of the bulk density 𝜌𝑏, and thus a convenient empirical equation

may be proposed as:

𝑏 ≈ 1.6(𝑚𝑠

𝜌𝑝)12 (1.13)

where 𝑚𝑠 is the solids mass flowrate in kg/s, 𝜌𝑝 is the true density of a particle in kg/m3, giving

the width b in meters. This relationship can be used to provide a quick reference value for

determining the approximate channel width for a given application.

1.3.4.3 The channel base (porous distributor)

The channel porous base plays an important role in air-gravity conveyors, as it provides

continuous aeration of a bulk solid in an inclined channel. The requirements of this porous base

are essentially those of the gas distributor in conventional fluidisation rigs and have some

features: (1) It should provide uniform and stable fluidization. (2) It should be designed to

minimize erosion damage and attrition of bed material. (3) It should offer minimum resistance

to the flow of an aerated powder over its surface and the flow of air through it. (4) It should

prevent flow back of bed material during normal operation and on interruption of fluidisation

when the bed is shut down. (5) It should be reasonably resistant to impact damage.

23

The porous distributor obviously influences the quality of fluidisation of the conveyed material

in the channel. The way in which the quality of fluidisation is related to the pressure drop across

the distributor has been discussed in Section 1.2.2, and most of the information presented in that

Section is relevant here. However, it is known that bed flow has a significant modifying effect

on the fluidisation behaviour, particularly in suppressing bubble development in the bed.

Unfortunately, there is little published information on the flow of aerated solids on different

types of distributor. When designing an air-gravity conveyor, the aim is to keep the power

consumption to a minimum, and therefore the distributor should offer the lowest possible

resistance to air flow. Naturally the resistance has to be sufficient to provide a uniform

distribution of air into the conveyed material, not only to maintain the flow of the material but

also to ensure that flow will restart after a shutdown. This requires that a sufficient pressure-

drop exists across the distributor to guarantee that, even when a large part of it is uncovered, the

minimum fluidising velocity will still be reached in the powder remaining on the distributor. As

information is limited, it would be reasonable to use the distributor’s pressure drop data on

stationary beds for distributor comparison. Compared with stationary fluidisation, a distributor

would have a rather lower pressure drop in an air-gravity conveyor when completely covered by

the flowing powder, because the flow of the bed tends to suppress the formation of bubbles.

However, it seems difficult to restart the powder flow after shutting off the fluidising air. In

order to avoid this problem, it may be advisable to select a distributor in which the pressure

does not drop so low. Leitzel and Morrisey (1971) state that the pressure drop through the

porous medium should be greater than 50% of the total pressure drop, but this is now known to

be excessive. A more realistic proportion of the overall pressure drop is 17% to 23% as quoted

by Weber (1968).

Siemes and Hellmer (1962) demonstrated that the roughness of the channel base has an

influence on the solids flow by placing a wire grid on the top surface of the porous distributor.

They found that roughening the base of the channel in this way tended to modify the solids flow

condition by reducing the slip velocity. In effect the viscosity of the bed is increased and its

dependence on the bed depth is reduced. No other reference has been found to the effect of

roughness of the internal channel surfaces, but it seems reasonable to suppose that there is some

advantage in selecting a distributor with a smooth surface.

1.3.4.4 The inclination of the channel

The inclination angle of the channel plays an important role on the capacity of air-gravity

conveyors. The influence of the channel slope has been studied by experimental investigation,

which found that there is an optimum value of the inclination angle, which depends on the

property of any bulk solid being transported. Attempting to convey at an inclination less than

24

this optimum value will result in the depth of the material in the channel increasing excessively,

even to the point where the channel becomes completely blocked.

In most industrial applications air-gravity conveyors are installed with a slope of 2 o to 10o to

suit the plant layout, the lower limit of inclination depending upon the material being handled.

The degree of initial aeration of the conveyed powder and the nature of the porous membrane

may also influence the minimum slope that can be used. However, this optimum slope is not

easy to predict without undertaking tests with samples of the material in a small-scale model. In

general, for free-flowing materials a slope of around 3o should be sufficient, but more cohesive

substances may require a minimum of 6o to 10o for satisfactory transport.

For a constant solids mass flow rate and superficial velocity, an increase in the slope of the

channel will result in increase in the velocity of fluidised material accompanied by a decrease in

its depth. When operating at a constant aspect ratio, an increase in the channel slope would

permit an increase in the mass flowrate of solids. Most authors seem to agree that for a constant

aspect ratio and superficial air velocity the solids flowrate is likely to be proportional to the sine

of the angle of inclination of the channel (Chandelle, 1971; Descamps and Jodlowski, 1973;

Gregoraszczuk and Fedoryszyn, 1974). Experimental work with sand (Siemes and Hellmer,

1962; Muskett et al., 1973; McGuigan, 1974; Pugh, 1975) indicates that there may be a limiting

inclination angle, beyond which there will be little further increase in solids mass flowrate.

However, it is difficult to collect reliable data on the maximum solids flowrates that can be

handled by air-gravity conveyors because these tend to be very large. For a given material, there

is no effective way of predicting the minimum channel slope at which it can be conveyed. To

decide the minimum inclination, the designer either relies on past experience or tries a sample of

the powder in a small test rig. Alternatively, the designer simply allows a slope of 10o or more,

because almost any solids can be conveyed on this slope.

1.3.4.5 Superficial air velocity

Air is used as the fluidising agent to assist the flow of bulk solids in channels at shallow

inclinations, except for some special applications. For instance, in chemical processing or where

there is an explosion hazard, nitrogen and other inert gas may be used. The pressure to be

maintained in the air plenum chamber depends upon the type of porous distributor in use, the

depth of powder on the distributor, and the superficial air velocity required. Normally, the

plenum pressure would be around 2.5 to 5 kPa so that the air provider can be a simple fan or

low-pressure blower, such as a Roots-type blower.

Until now, it has not really been understood how the superficial air velocity affects the solids

flow, but an increase in the superficial air velocity can increase the solids flowrate. First, the air

flows upwards amongst the particles and fluidise them, and as a result, it reduces the contact

25

forces between particles and thus decreases the viscosity of the bed. This is similar to a

stationary fluidisation bed, and observation of such a bed should help to predict the material

flow behaviour in an air-gravity conveyor. Secondly, the increasing superficial air velocity

effectively provides a lubricating air layer between the bed of powder and the channel bottom,

and possibly also between the powder and the channel walls. Pugh (1975) and McGuigan

(1974) both reported that air flow close to the channel walls give rise to a lubricating layer of

better fluidised powder in this region, and Botterill and van der Kolk (1971) noted the presence

of a layer of air just above the surface of their porous distributor.

Fundamentally, the superficial velocity of fluidising air that would be required for satisfactory

conveying depends upon the property of this conveyed material, also the slope of the conveyor

and the mass flowrate of the bulk material to be conveyed. Thus from the fluidisation

characteristics of the material, we can know the air flow required to transport the material.

Generally, the lower the minimum fluidising velocity of the material, the less air is required to

convey it.

The relationships between the solids mass flowrate, the superficial air velocity and the channel

slope had been anticipated for a conveyor by researchers. Before the flow in the channel starts,

the superficial air velocity must be reached a certain level. For larger inclination angles, the air

velocities tend to be lower. For a given system, the solids flowrate increases rapidly when the

superficial air velocity is increased beyond the starting level, but the mass flowrate will be

restricted at the transfer point from the supply hopper to the upstream end of the channel. A

further increase in the fluidising air flow causes no appreciable change in the solids flow. There

seems to be no obvious reason for the solids mass flowrate to become restricted in the channel

itself, unless the slope of the channel is small or the aspect ratio is large. Harris (1905) and

Muskett et al (1973) both use fine sand to study air-gravity conveyors. They found that when air

flows through material, only the top layers of particles become fluidised, the remainder acting as

an additional distributor (Zabrodsky, 1966).

Values of superficial air velocity required for satisfactory conveying can vary over quite a wide

range, and it is probable that many industrial systems are operated at a higher air velocity than is

necessary. Most authorities quote around 15 to 30 mm/s (Leitzel and Morrisey, 1971; Descamps

and Jodlowski, 1973; Butler, 1974) although Descamps and Jodlowski (1973) give an example

of cement convoyed at 15 tonne/h in a 150 mm wide channel with a superficial air velocity of

only 4 mm/s. Much higher air velocities are recommended by the EEUA Handbook - from 50

mm/s up to as much as 300 mm/s for materials of low density and large particle size.

Whilst there are some differences in the values of the ratio of superficial air velocity to

minimum fluidising velocity used or recommended by the various authors, most have worked at

26

air velocities within the range 2 to 5 times 𝑈𝑚𝑓 (Siemes and Hellmer, 1962; McGuigan, 1974;

Pugh, 1975). Qassim's (1970) range of operation was restricted to 1.5 to 2.5 𝑈𝑚𝑓 as he reported

that flow was unsteady at lower or higher air velocities. For most materials tested, Keuneke

(1965) found that an air velocity between 2 and 6 𝑈𝑚𝑓 was satisfactory, but for cement and

gypsum at shallow slopes the figure had to be much greater; in the latter case, up to 30 𝑈𝑚𝑓.

Generally, experimental investigation of a granular material in a stationary fluidised bed should

determine the value of the minimum fluidising velocity 𝑈𝑚𝑓 . The optimum superficial air

velocity is likely to be between two and three times the minimum velocity at which the material

could be fluidised. At that condition, the conveyor can be operated economically without undue

risk of stoppage. For very free flowing materials on large angles, an air velocity only slightly in

excess of the minimum fluidising velocity may be sufficient, but for very fine powders up to ten

times 𝑈𝑚𝑓 may be needed. Higher air velocity is not suggested because it not only wastes

energy but also causes problems like fine particles entering the air stream after leaving the

surface of the flowing suspension. Therefore, the designer requires some knowledge of the

minimum fluidising velocity of the bulk solid to be conveyed and the air velocity at which

entrainment can begin, which corresponds approximately to the terminal velocity of the fine

particles falling in stationary air.

1.3.4.6 Material flow velocity distribution

The velocity of material flow along an inclined channel depends on the inclination of the

channel, solid mass flow rate (here is the rate of solids feed to the channel) and the superficial

velocity of the fluidising air. The roughness of the internal surface may also affect the material

flow velocity. Weber (1968) and Chandelle (1971) state that the material flow velocity in an

inclined channel is normally between 1 and 4 m/s, and Nordberg (1949) gives an example of

cement flowing in an air-gravity conveyor at about 5.4 m/s. However, of the authors who

actually measured the solids velocity under experimental conditions (Siemes and Hellmer,

1962; Shinohara et al., 1974; Pugh, 1975; Kosa, 1988) none has reported any measurement

greater than about 1.6 m/s.

It is difficult to directly measure the velocity of a flowing bed of aerated powder, especially at a

point within the bed. Small measuring probes tend to be too fragile to withstand the turbulently

flowing solid particles, while large probes cannot provide point measurements as they may

disturb the material flow. External methods using lasers or ultrasonics are good, but these

methods can only give data for the surface particles or average values for the whole cross-

section of the bed. It is also difficult to calibrate the velocity probes correctly because it is

almost impossible to provide a controlled environment that reproduces conditions similar to a

flowing fluidised bed. Keuneke (1965) tried to calibrate a velocity probe in oil but there seems

27

to be little point. Botterill and Bessant (1973) attempted to use a small annular rotating fluidised

bed to calibrate it and it may probably be the best method so far. However, even this method

was not totally reliable because of differences in the flow behaviour between the calibration rig

and the flow channel.

Perhaps the simplest method of achieving an indication of the average velocity of a bed of

moving particles is by observing the travel of a float placed on the surface of the bed (Keuneke,

1965; Botterill and Bessant, 1973; McGuigan, 1974). Mori et al (1955) provided another very

simple idea where they estimated the velocity of particles along the channel by measuring the

distance that they flow from the downstream end. Several workers (Mori et al., 1955; Siemes

and Hellmer, 1962; Shinohara et al., 1974; Pugh, 1975) have investigated the velocity profile

across the surface of the flowing bed by depositing coloured particles in a line on the moving

surface and noting their distribution after a short interval of time. By suddenly shutting off the

supply of fluidising air, Mori et al (1955) and Shinohara et al (1974) observed the distribution of

the tracer particles after the bed suddenly stopped and settled. In order to assess the validity of

the mathematical model that they had developed, Shinohara et al (1974) needed to measure the

maximum solids flow velocity under various operating conditions. The velocities that they

measured were generally in the range 0.5 to 1.2 m/s and their results showed a steady increase

in maximum solids velocity with channel inclination and with superficial air velocity. They also

observed that there was a certain air velocity where the solids velocity ceased to increase above

this air velocity. What’s more, they demonstrated that for a constant slope and constant air

velocity, the maximum solids velocity increased with increasing solids flowrate. Mori et al

(1955) had reached much the same conclusions regarding the variation of the solids flow

velocity some twenty years earlier. They also presented velocity profiles across the surface of

flowing beds of alumina and sand; with alumina they found that the velocity profile was fairly

uniform and the same trend towards a uniform profile was obvious in sand flowing in a steel

walled channel, while with glass channel walls the velocity profile was modified as a result of

sand particles adhering to the walls and therefore obstructing material slip.

Pugh (1975) and Siemes and Helimer (1962) also used coloured tracer particles on the surface

of the flowing bed, but recorded their distribution after a short interval by flash photography.

Keuneke (1965) tried the same method but found that the tracer particles tended to move in

from the sides of the channel to the middle, caused by the velocity vectors on the bed surface.

Mori et al (1955) extended the technique and then investigate the velocity distribution through

the depth of the bed by inserting a vertical band of coloured particles into the static material,

allowing it to flow for about 600 mm, and then examining the pattern of coloured particles in

the section. They found that flowing material slip at the distributor, above this zone the velocity

being fairly uniform.

28

Keuneke (1965), Botterill and Bessant (Bessant and Botterill, 1973; Botterill and Bessant, 1973;

Botterill and Bessant, 1976) developed a method using probes to investigate the variation of

velocity within the bed, instead of just at the surface. The probe Keuneke used is a wire strain-

gauge probe in which the force on the probe surface was a function of the solids flow velocity.

However, the sensor was too large (10 mm by 20 mm) for point velocity measurements, and the

procedure for calibrating the probe in flowing oil appeared questionable. Based on his study, the

variation of velocity was more significant across the flowing bed than through its depth. In

general, the velocity profiles were not parabolic and there was obvious slip at the walls and

bottom of the channel. Furthermore, the maximum velocity was not at the bed surface but at a

depth of one quarter to one half of the total depth. Mean velocities measured by Keuneke were

generally about 1 m/s, but for gypsum and for cement were somewhat slower.

A small turbine-type velocity probe was used by Botterill and Bessant (Bessant and Botterill,

1973; Botterill and Bessant, 1973; Botterill and Bessant, 1976) to determine velocity profiles in

fluidised 200 𝜇𝑚 sand flowing in a horizontal channel. The average solids velocities were only

0.1 to 0.3 m/s which were considerably slower than usual velocities in air-gravity conveyors.

They also found that the velocity distributes differently across the channel, especially with deep

beds (that is, having high aspect ratio). However, if the fluidising air velocity is reduced, a

significant variation of velocity through the depth of the bed may be developed, probably as a

result of an increase in the shear stress at the bottom of the channel.

1.4 Computational Fluid Dynamic simulation of fluidised flow

The Computational Fluid Dynamic (CFD) approach is one of the more powerful and flexible

general-purpose computational fluid dynamics software packages for modelling fluid flow and

other related physical phenomena. It offers unparalleled fluid flow analysis capabilities,

providing all the tools needed to design and optimize new fluids equipment and to troubleshoot

existing installations. It is based on fast and reliable computational methodology to provide

accurate and practical solutions for reducing risks of potential design flaws, optimizing

engineering design and provides researchers with a scientific tool.

1.4.1 Introduction of FLUENT

ANSYS FLUENT is one of the most popular computational fluid dynamics (CFD) software

packages applied to simulate fluid flow, turbulence, heat transfer, and reactions, for industrial

applications, ranging from bubble columns to oil platforms, from blood flow to semiconductor

manufacturing, from air flow over an aircraft wing to combustion in a furnace, and from clean

room design to wastewater treatment plants. With special models, this software is given the

ability to model in-cylinder combustion, aero-acoustics, turbomachinery and multiphase

systems with a broad reach. With the help of FLUENT, a wide range of phenomena can be

29

simulated, especially for the multiphase flows (mixtures of liquids/solids/gas) which are the

subject of this thesis. It can also empower a researcher to go further and faster as one optimizes

one’s product's performance.

1.4.2 Computational Fluid Dynamic application in gas-solid flows

A CFD based approach for investigating the variety of multiphase flow problems in closed

conveyors and open channels is being increasingly used. There are a number of unique

advantages of CFD. Firstly, CFD presents a means of visualizing and improving understanding

of system designs. Many devices and systems are difficult to prototype, so that the controlled

experiments are difficult or impossible to conduct. But with the help of CFD, analysis results

can show parts of the system or phenomena existing within the system that would not be

available through other means. Secondly, CFD make it possible for predicting what will happen

under a given set of conditions. Therefore, with given variables, it can provide relevant

outcomes in a short time and predict how the design will perform under a wide range of flow

conditions. Thirdly, CFD improve the efficiency of system design, and compress the design and

development cycle.

Generally, there are two fundamentally different methods used to simulate gas-solid flow in

CFD modelling according to the manner in which the particular phase is treated; the Euler-

Lagrange method and the Euler-Euler method. The Lagrange model calculates the trajectories of

individual or representative particles in the solids phase, considering the velocity, mass and

temperature history of them. It is undesirable when dispersed second phase occupies a high

volume fraction, such as liquid-liquid mixtures (Ligoure, 2000) or fluidised beds (Peirano et al.,

2002). The Euler-Euler model approach simulates the granular phase as a continuous second

fluid, which treats both continuous phases and dispersed phases as interpenetrating continua. In

this approach, the sum of phasic volume fractions is always equal to one and they are assumed

to be continuous functions of space and time.

It had been successfully simulated for gas-solid two phase flow using CFD, such as a fluidised

bed (Wang et al., 2010) and pneumatic conveying systems (Behera et al., 2013). But until

recently, very few researchers have tried to use CFD simulation to predict the flow behaviour of

air-gravity conveying.

Savage and Oger (2013) reviewed some selected experimental studies of air-gravity conveyors

and utilized a multiphase flow CFD program MFIX to describe air-gravity flows (vent airslide

flow). Their study was the first successful attempt to model airslide that considered the detailed

mechanics of fluid particles. Revisions and additions to the governing multiphase flow

equations used in the model were made, and the model compared well with experimental

velocity profiles and overall flow behaviour (Oger and Savage, 2013). However, the periodic

30

boundary conditions used in simulation meant that it could only show the steady flow state of

airslide and the bed height along the airslide flow channel could not be obtained, in their study.

Except for this study, there has been no numerical simulation on air-gravity conveying systems

being found in open literature. Since the CFD techniques are economically cheaper than the

experimental investigation, it is worthwhile to determine whether the commercially available

CFD software is enough to predict the flow behaviour of air-gravity conveyor with high

accuracy. CFD could be an effective way to study both vent and non-vent air-gravity flows.

1.5 Summary of air-gravity conveying and future development

Basically, air-gravity conveyor has a simple design which consists of a long, light-gauge steel

rectangular duct that can have a closed or open top. It is divided into two sections by a porous

membrane, the area below the membrane is the air plenum, and the area above the membrane is

the material plenum. The porous membrane allows low-pressure air to flow from the air

plenum, through the membrane, into the material plenum to fluidise the material to be

conveyed. Generally, the flow of material in air-gravity conveyors is caused by the fluidisation

air which reduces the material’s angle of repose.

From the literature discussed above, some earlier experimental studies of air-gravity conveyors

were reviewed for both vent and non-vent conveying systems. To properly study the

performance of conveying, the most valuable thing is to obtain insight to the relationships

amongst the five basic parameters: solids mass flowrate, bed depth, width and slope of the

channel and superficial air velocity. Therefore, the general factors influencing the flow

behaviour of bulk materials in air-gravity conveying was investigated, which helped establish

the mechanism of material flow.

However, there have been relatively few published research articles into the conveying

performance of aerated powders in inclined channels. One of the main difficulties for

researchers is the problem that the size of the air-gravity conveyor test apparatus needs to be

equivalent in size to typical industrial installations. Additional problems are also exist when

trying to investigate variables such as the depth of the flowing bed of suspended solids, the bulk

density of the bed, the velocity of the bed and so on. So systematic experiment are needed for

further investigating the flow of both vent and non-vent air-gravity conveyors. Thus, the bed

height along the conveying channel, and the relationship between mass flow rate, bed height

and pressure drop can be obtained. The flow pattern, the air pressure, the mass flow rate and the

bed height can be examined when the supplied airflow rate and inclination are changed.

Moreover, a suitable mathematical model to predict the performance of air-gravity flow should

be developed. As for theoretical study of the characteristics of air-gravity conveyors, few

31

successful investigations have been reported. For vent flow, a standard open channel flow

hydraulics approach based on the backwater curve was used to model the air-gravity channel

flow by Savage and Oger (2013). But their backwater analysis that used a fixed value of

Manning factor for a given channel is oversimplified. For non-vent flow, there has been no

theoretical or empirical correlation that could successfully predict the performance of fluidised

material conveying. Gupta et al. (2010) developed a modified air gravity conveyor model by

adding parameters to the empirical relation in Klinzing et al.’s (1997) model. Through

correlation between the predicted and measured material mass flux was achieved, but the model

may not be able to yield good predictions for other fluidised motion conveying systems due to

the involvement of these unknown parameters in the model.

Further, CFD simulation has proved to be an effective way to model and predict the behaviour

of gas-solid flows in fluidised bed and pneumatic conveying systems. Oger and Savage (2013)

utilized multiphase flow CFD program MFIX to describe air-gravity conveying performance

under a steady flow. Their study was the first successful attempt to model airslide, but the

periodic boundary conditions used in simulation meant that it could only show the steady flow

state of airslide and the bed height along the airslide flow channel could not be obtained in their

study. No other numerical simulation on air-gravity conveying systems has been found in open

literature. In order to enable air-gravity systems to be optimally designed, rather than over-

designed, further understanding of the phenomena involved in air-gravity conveying is

necessary. Since the CFD techniques are less expensive than other experiments, investigation on

CFD simulation on air-gravity conveyors could be an effective way to study both vent and non-

vent air-gravity flows.

1.6 Objective of the thesis

This thesis aims to study the flow behaviour of vent and non-vent air-gravity conveying

systems, and to develop the design model for an air-gravity conveyor as well. Therefore, the

designation of air-gravity conveyor should be figured out first for future experiments. In order

to construct the conveying system, drawings including feed section, conveying section, receive

section and return section have been designed for fabricating. Meanwhile, placement of support

structures and an air supply system are also need to be considered before any testing. Moreover,

pressure transducers and load cells need to be installed at pre-desired positions. After

completing the construction of the test air-gravity conveyor, the flow behaviours can be

obtained under different experimental conditions, including material mass flow rate, bed height

and pressure drop along the channel.

Also, in this thesis, rheology based air-gravity conveying models are proposed and applied to

predict the steady flow bed heights for vent and non-vent conveying systems. The fundamental

32

continuous fluid mechanics approach has been adopted. The model incorporates the rheological

characteristics of the fluidised material as well as the conveying parameters.

CFD simulation will also applied to predict the flow behaviours of air-gravity conveying

systems. Governing equations and proper models will be discussed and selected to thoroughly

simulate this conveying system. The accuracy of simulation will be validated by the

experimental results. Sand and flyash were investigated both in experiments and simulations.

1.7 Thesis overview

The flow of particulate bulk solid conveyed by air-gravity conveyors along the conveying

channel is quite similar to a liquid flowing in an inclined channel. Therefore, the fluidised

material flow can be modelled by considering the perspective of classic fluid mechanics. As the

dominant properties determining the flow performance of a liquid are its rheological properties,

the pneumatic flows can also be examined by studying its rheological performance which

reveals the fundamental correlation between the flow of the air-solids mixture and the force

which causes this deformation. Based on this assumption, to study the flow resistance of air-

gravity conveying, we can simply investigate the parameters governing its rheology. The

resistance in fluidised flow can be considered as a special type of internal friction which is in

effect amongst adjacent particles within the system, and these friction forces can be estimated

by means of a viscometer which is often used to obtain rheology of fluid. Therefore, this thesis

attempts to study bulk materials air-gravity conveying systems by using a rheology based

approach. In detail, experimental determinations of the rheological properties for fluidised

material, designation of an air-gravity conveying system, experimental study of fluidised flow,

theoretical modelling of the fluidised material flow incorporated with its rheology, validations

of the proposed conveying models and CFD study of material flow in air-gravity conveyors.

Specific work conducted is summarised below.

Firstly, Chapter 1 gives the general review of air-gravity conveyors, the fluidisation behaviour

of bulk solids and flow behaviour of aerated bulk solids. The factors influencing the flow

behaviour of aerated bulk solids in inclined channels is also introduced. A thesis overview is

incorporated as well.

Secondly, Chapter 2 provides the particle and bulk material properties for sand and flyash.

Fundamental air-particle interactions including the fluidisation behaviour for these two

materials are investigated experimentally. Moreover, experiments are conducted to determine

critical rheological parameters for aerated powder materials (sand and flyash). Due to the

different behaviours of powder materials under low and high aeration, different methods are

conducted accordingly. At low aeration, aerated powders behave like solids materials with the

yield stress dominant in determining the flow properties. Conversely, at high aeration, aerated

33

powders behave similarly to fluids. Therefore, a modified experimental method is used to

measure the viscous flow properties. The rheological properties and the bulk density are

modelled to provide quantitative measures of the rheology for the material studied. The

rheology results are subsequently become ready to be inputted into the air-gravity conveying

model derived in Chapter 6 to produce predictive bed heights profiles for conveying systems.

Thirdly, in Chapter 3, a systematic air-gravity conveyor is designed and set up. The conveying

system consists of four parts, feed system, conveying system, receive system and return system.

Detailed design drawings are presented in this Chapter and the function of each part is

illustrated as well. Then the instrumentation is discussed on installing the pressure transducers

and load cells. Calibration on these sensors is conducted for the air-gravity conveying system.

The experimental procedure also explains how the air-gravity conveyor operates.

After that, air-gravity conveying experiments with fine materials are conducted with the above

designed air-gravity conveyor in Chapter 4. The effect of airflow rate, inclination of the channel

and valve opening is investigated in relation to the material mass flow rate, pressure drop along

the channel and material bed height for both vent and non-vent air-gravity flow systems.

The rheology based air-gravity conveying model is to be derived in Chapter 5. The rheology

concept is discussed and then the constitutive governing equations of bulk material flows are

derived using the classic fluid mechanics. The steady air-gravity flowing model is developed

under steady flow state. The model incorporates the rheological characteristics of the fluidised

material as well as the conveying parameters. Also, the model can be used to predict conveying

results for further validation processes.

In chapter 6, the proposed conveying models are evaluated and validated using air-gravity flow

experimental results. Results from the rheology testing process in Chapter 4 and 5 are utilised to

produce the bed heights profile which are subsequently compared with the experimental

measurements. Good correlation is found after validation process on predicting the bed height

for an air-gravity conveying system under steady flow.

In Chapter 7, CFD models are used to simulate the air-gravity flow, where a steady, three-

dimensional fluidised granular flow is considered in a rectangular channel having frictional side

walls for different flow conditions. A Eulerian-Eulerian model that incorporates the kinetic

theory of granular flow was used to describe the air-gravity two-phase flow. The investigation

into the effects of various model parameters, i.e., grid independency, laminar/turbulence flow

models, drag models, specularity coefficient and coefficient of restitution are conducted. The

results of simulated bed heights along the air-gravity channel and the velocity cross the channel

width are discussed and verified by the measurements.

34

In Chapter 8, a standard design protocol is proposed, and comparation between mathematical

models and CFD models is discussed on sand and flyash under the conditions of vent and non-

vent flow.

Lastly, Chapter 9 presents the conclusions obtained from this air-gravity conveying research.

Additionally, an outline of future work beyond this thesis is presented.

35

2 CHAPTER 2 Material properties and flow model

predictions

2.1 Introduction

This chapter presents materials properties including particle density, bulk density, particle size

distribution and air-particle parameters for sand and flyash. Fundamental knowledge of the

materials is essential before investigating the flow behaviours in air-gravity conveying systems.

Accordingly, basic parameter testing methods and an air-particle characterisation method will

be presented in this chapter as well. The modes of flow for the materials described in this thesis

are determined using basic materials’ properties.

Two widely used industrial powder type materials, sand and flyash were studied. Sand is

utilised in the construction industry; for example, for making concrete. Flyash is the primary

coal combustion product in thermal power plants. These two materials are commonly handled

using air-gravity conveyors, especially for flyash in the power industry. Generally, the flow

mechanism of bulk materials like sand and flyash behave differently when interacting with gas.

The difference between two powder materials, is initially embedded in solids material properties

such as the particle density and particle size. Additional air-particle interacting behaviours for

different powders, including fluidisation/ aeration and pneumatic conveying, are also distinct.

The objective of this chapter is to investigate the properties of selected bulk materials and

examine the testing methods, as well as air-particle behaviours to aid the following rheology

and air-gravity conveying research.

2.2 Testing methods and powder material properties

To obtain various material properties, different testing methods and apparatuses were utilised.

In this section, different testing principles for each material property parameter are presented,

including the particle density, loose poured bulk density, the tapped bulk density, particle size

and distribution and air-particle parameters. These property parameters are presented as well.

2.2.1 Particle density

The particle density ρp is defined as the mass of an individual particle divided by the volume of

the entire particle, and it is measured using an air displacement pycnometer. The density value

will only take into account external pores in between particles. During the measurement, a bulk

material sample of known weight was placed in the chamber, and then nitrogen was fed into the

chamber to calculate the true volume of particles. Finally, the particle density could be

calculated, and it was determined by taking the average value of the density readings. The

results are given in Table 2.1.

36

Table 2.1 Particle density of materials

Materials Test 1 (kg/m3) Test 2 (kg/m3) Test 3 (kg/m3) Average particle density (kg/m3)

Sand 2717.1 2717.6 2717.4 2717.4

Flyash 2093.0 2092.8 2093.3 2093.0

2.2.2 Loose poured bulk density

Generally, the bulk density is the mass of bulk material divided by the total volume occupied by

the material. The loose poured bulk density ρlp is measured by gradually pouring the material

into a container with known mass and volume. A flat surface is obtained with no material

beyond the container top surface. The material is in a loose, non-compacted or as poured

condition, without any applied compacting force. The above procedure will effectively

minimise the compaction during the measurement process to achieve consistent and repeatable

results. Then the value of loose poured bulk density is determined by the mass of the total

material divided by the volume of the container. Three measurements were taken for each

material and the average density was calculated, as shown in Table 2.2.

Table 2.2 Tests and results for loose poured bulk density

Materials Loose poured bulk density (kg/m3)

Test 1 Test 2 Test 3 Average

Sand 1554.7 1553.0 1546.4 1551.4

Flyash 820.0 826.4 816.4 821.0

2.2.3 Particle size and distribution

The particle size is an essential parameter due to its influence on the natural force of attraction

between particles. Particle size (d0.5) and distribution were determined using the Malvern

Mastersizer 2000 model. This equipment employs the laser diffraction technique to measure the

size of particles. The measurable size range of the particle is 1- 1000 μm. Specifically, the

intensity of scattered light when a laser beam is passed through the dispersed particulate

samples is measured. Based on the amount of light scattering, the intensity values are then

analysed to produce the size and the scattering pattern. Final results were averaged by three

repeated tests. The detailed particle size distribution test results are presented in Figure 2.1 to

Figure 2.2. Both two materials analysed exhibited a single mode structure and a wide range of

size distribution. The average particle diameters for sand and flyash are summarized in Table

2.3.

37

Figure 2.1 Particle size distribution analysis of sand

Figure 2.2 Particle size distribution analysis of flyash

Table 2.3 Particle diameters of sand and flyash

Materials Average particle diameters (μm)

Sand 378.7

31.7 Flyash

2.2.4 Air-particle parameters

Except for the particle parameters discussed above, there are some air-particle parameters which

describe the gas-solid interactions as critical to predict the conveying performance of particles.

38

In detail, parameters like the fluidised bulk density, permeability, de-aeration factor and steady-

state fluidisation pressure are important and can be used to estimate the particle conveying

behaviour and flow mode. The general method to measure these parameters is derived from a

typical fluidisation test.

Figure 2.3 Schematic of the fluidisation rig.

Figure 2.3 shows the fluidisation test rig, and the Perspex chambers with an internal diameter of

70 mm was utilised. The superficial air velocity was calculated according to the volume flow

rate from a digital flow controller. A differential pressure transducer was used to record the

pressure drop across the material bed. The material bed height was determined by reading the

value off the vertical scale on the side of the chamber.

In the fluidisation test, a vertical pipe is firstly filled with the material at a designed bed height.

The air is then injected into the pipe from the bottom, the superficial air velocity was increased

from zero to the value at which the material was fully fluidised. Then the superficial air velocity

was gradually reduced to zero. Pressure gradient at each superficial air velocity was taken when

the displayed value stayed relatively steady. Bed heights were also recorded at each superficial

air velocity. Accordingly, fluidisation charts could be subsequently obtained by performing the

above tests. Figure 2.4 exemplified the idealised fluidisation charts.

39

Figure 2.4 Idealised fluidisation charts

The de-aeration test was conducted using the same configuration as for fluidisation. Based on

the pressure decay analysis, the de-aeration rate was obtained by the de-aeration test. At the

beginning of the test, the superficial air velocity increased gradually until the steady-state

fluidisation pressure was achieved. Then, the airflow was stopped using an instant shut-off

valve after the data acquisition programme started, and the pressure reading was then recorded.

The de-aeration factor, Af, was found to be in relation to the pressure unit length, ∆𝑃 𝐿⁄ , and

time, t. Using these charts, the following air-particle parameters could be determined.

(a) Fluidised bulk density

Fluidised bulk density (ρf) is determined from the apparent bulk density when a material is in

the fluidised state. In general, the fluidised bulk density is lower in value when compared with

the loose poured bulk density. The associated fluidised bulk density was calculated.

(b) Permeability

The permeability factor (Φ) is defined as the material’s ability to allow airflow to penetrate

through the packed material. It can be described as:

Φ = (𝑣𝑓

∆P 𝐿⁄)𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑓𝑙𝑢𝑖𝑑𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑝𝑜𝑖𝑛𝑡

(2.1)

where 𝑣𝑓 and ∆P 𝐿⁄ can be read from the fluidisation chart.

(c) Steady state fluidisation pressure

The steady state fluidisation pressure (∆P 𝐿⁄ )ss is defined as the specific pressure gradient value

which remains relatively constant either for increasing or decreasing the airflow. Accordingly, a

40

minimum fluidisation velocity (𝑣𝑚𝑓) is defined as the superficial air velocity at the minimum

fluidisation point.

(d) De-aeration factor

The de-aeration factor, Af, can be obtained by best fitting the experimental data to the equation

∆𝑃 𝐿⁄ = 𝐴𝑓/𝑡. Additionally, the 95% pressure decay point is considered as the fully de-aerated

point, and the de-aeration rate can be determined according to the 95% de-aeration time and

change in material bed height.

In this research, all air-particle parameters were tested three times and average values obtained.

Following the testing procedure for each particular parameter, material properties are listed

below.

2.2.4.1 Sand

The measurements for the fluidisation behaviour and de-aeration rate of sand are shown in

Figure 2.5 and Figure 2.6, respectively.

Figure 2.5 Fluidisation chart of sand

41

Figure 2.6 De-aeration of sand

As shown in Figure 2.5, initially the superficial velocity was increased from 0 mm/s to 210

mm/s gradually. It was observed that the pressure gradient in the vertical pipe increased linearly

as the superficial velocity rose from 0 mm/s to 50 mm/s. As the superficial velocity continued to

increase from 50 mm/s up to 225 mm/s, the pressure in the vertical pipe decreased first and then

stayed stable. After that, the superficial velocity was reduced from 225 mm/s to 0mm/s steadily.

The pressure was maintained at almost the same level until the superficial velocity decreased to

128 mm/s, which is the minimum fluidisation velocity in this study. The pressure then dropped

down at a steady rate as the superficial velocity decreased to 0 mm/s. The permeability of sand

was determined by the slope of superficial air velocity against pressure gradient, the value was

2.97×10-3 m2/kPa·s. Meanwhile, the fluidised bulk density of sand was determined by

measuring the fluidised bed depth, which was 1261.6 kg/m3. The de-aeration factor could be

calculated by the experimental data fitting from Figure 2.6, which is 4.2 kPa·s/m.

2.2.4.2 Flyash

The measurements for the fluidisation behaviour and de-aeration rate of flyash are shown in

Figure 2.7 and Figure 2.8, respectively.

0

2

4

6

8

10

12

14

0 1 2 3 4 5

Pre

ssu

re (

kP

a/m

)

Time (s)

De-aeration test

Af/t line

95% decay pointDe-aration Rate (s/m)

95

% D

eara

tio

n

42

Figure 2.7 Fluidisation chart of flyash

Figure 2.8 De-aeration of flyash

Initially the superficial velocity was increased steadily from 0 mm/s to 70 mm/s, as can be seen

in Figure 2.7. In the fluidisation test of flyash, channelling was observed during the initial

stages. To break down the channelling, the outside of the chamber was lightly tapped during the

test. It was found that the fluidisation occurred when the superficial velocity reached

approximately 40 mm/s, and the pressure gradient in the vertical pipe rose at a constant rate

around this superficial velocity. As the superficial velocity continued to be increased up to 70

mm/s, the value of the pressure gradient did not alter markedly. The superficial velocity was

0

1

2

3

4

5

6

0 5 10 15 20 25 30

Pre

ssure

(kP

a/m

)

Time (s)

De-aeartion test

Af/t line

95% decay pointDearation rate (s/m)

95%

Dea

rati

on

43

then decreased from 70 mm/s to 0 mm/s gradually, as shown again in Figure 2.7. It was

observed that the pressure remained at the same value while the superficial velocity reduced to

43.3 mm/s. After this point a fluctuation of pressure appeared as the superficial velocity

dropped down to 0 mm/s. The permeability factor of flyash could be obtained as 3.8×10-4

m2/kPa·s, and the fluidised bulk density of flyash was 516.7 kg/m3. The de-aeration factor could

be calculated by the experimental data fitting from Figure 2.8, which is 12.0 kPa·s/m.

2.2.5 Material properties summarise

The material properties are summarised as following:

Table 2.4 The properties of sand

Properties Value

Average Particle Diameter (d0.5) 387.7 µm

2717.4 kg/m3 Particle Density (ρp)

Loose Poured Bulk Density (ρlp) 1551.4 kg/m3

Minimum fluidisation velocity (𝑣𝑚𝑓) 128 mm/s

Fluidised Bulk Density (ρf) 1261.6 kg/m3

De-aeration factor (Af ) 4.2 kPa·s/m

Table 2.5 The properties of flyash

Properties Value

Average Particle Diameter (d0.5) 31.7 µm

2093.0 kg/m3 Particle Density (ρp)

Loose Poured Bulk Density (ρlp) 821.0 kg/m3

Minimum fluidisation velocity (𝑣𝑚𝑓) 43.3 mm/s

Fluidised Bulk Density (ρf) 516.7 kg/m3

De-aeration factor (Af ) 12.0 kPa·s/m

2.3 Flow mode predictions

In pneumatic conveying systems, an initial prediction of the flow mode is beneficial as this can

help provide clearer direction for the pneumatic conveying design process. Generally, there are

two types of predictive charts: basic particle parameter based (particle size and density) and air-

particle parameter based (permeability and de-aeration) predictive flow models. Geldart

44

(Geldart 1973) derived four distinct groups for fluidisation classification, which utilised basic

material properties of particle density and average particle diameter. It has also been extended to

predict pneumatic conveying behaviour. In dense phase pneumatic conveying, the behaviour of

the bulk solids is in many ways more important than that of individual particles.

Based on the particle property analysis, the mode of flow capability of sand and flyash used in

this study was assessed, as shown in Figure 2.9 to Figure 2.15 (Dixon 1979; Geldart 1973; Jones

and Williams 2008; Molerus 1982; Pan 1999). Boundaries between different modes of flow are

drawn to classify sand and flyash into different regions.

As can be seen from Figure 2.9 to Figure 2.15, flyash has very fine powders and a relative low

loose-poured bulk density, and it is located in the fluidised dense phase zone in all of the

prediction diagrams. Fly ash was also found to have a good air retention capability and a low

permeability value. As for sand, the prediction results show that sand belongs in the region of

the dilute phase. Sand was also found to have a poor air retention capability and a low range

permeability value. Generally, sand has a very large particle diameter and a high loose-poured

bulk density, sand powders can easily settle out while conveying due to the influence of gravity.

The sand powders which do not settle out are conveyed in the dilute phase.

Figure 2.16 to Figure 2.20 show the location of sand and flyash in the pneumatic conveying

classification diagrams based on the air-particle property analysis (Mainwaring and Reed, 1987;

Jones, 1988; Fargette et al., 1996; Chambers et al., 1998; Sanchez et al., 2003; Williams, 2008).

Both the basic and the air-particle property analysis indicated that while sand is a non-dense

phase material that cannot normally be dense-phase conveyed in traditional pipelines, fly ash

can be conveyed in the fluidised dense-phase within conventional pipelines.

Figure 2.9 Geldart fluidisation diagram showing the location of sand and flyash

100

1000

10000

10 100 1000 10000

Par

ticl

e -

Gas

Den

sity

(k

g/m

3)

Mean Particle Diameter (mm)

CC

A

B D

fluidised dense phase

plug flowunknown

45

Figure 2.10 Modified Geldart fluidisation diagram showing the location of sand and flyash

Figure 2.11 Molerus fluidisation diagram showing the location of sand and flyash

Figure 2.12 Modified Molerus fluidisation diagram showing the location of sand and flyash

100

1000

10000

10 100 1000 10000

Lo

ose

Po

ure

d B

ulk

Den

sity

(kg/m

3)



dilute only

plug flowunknown

100

1000

10000

10 100 1000 10000

Par

ticl

e D

ensi

ty (

kg/m

3)


B D

A

C

fluidised dense phaseplug flow

unknown

100

1000

10000

10 100 1000 10000

Lo

ose

-Po

ure

d B

ulk

Den

sity

(kg/m

3)



dilute only

plug flow

unknown

46

Figure 2.13 Dixon slugging diagram showing the location of sand and flyash

Figure 2.14 Modified Dixon slugging diagram showing the location of sand and flyash

100

1000

10000

10 100 1000 10000

Par

ticl

e D

ensi

ty (

kg/m

3)


strong axisymmetric

slugs

no slugging

weak axisymmetric

slugs

50 mm75 mm100 mmpipe dia.

unknown

fluidised dense

phaseplug flow

100

1000

10000

10 100 1000 10000

Lo

ose

Po

ure

d B

ulk

den

sity

(kg/m

3)


no slugging

weak axisymmetric

slugs

strong axisymmetric

slugs

50 mm75 mm100 mm

dilute only

unknownfluidised dense

phase

plug flow

47

Figure 2.15 Pan’s pneumatic conveying predictive diagram showing the location of sand and

flyash

Figure 2.16 Mainwaring and Reed’s pneumatic conveying predictive diagram showing the

location of sand and flyash

100

1000

10000

10 100 1000 10000

Lo

ose

Po

ure

d B

ulk

Den

sity

(kg/m

3)



dilute only

unknown

plug flow

0.01

0.1

1

10

100

1000

0 5 10 15 20

Per

mea

bil

ity (

m 2

/Pa.

s x

10

-6)

DP/L (Pa/m x 103)

50mm/s line of constant

fluidisation velocity

Plug flow

Dilute

phase

Fluidised dense phase

0.1

1

10

100

1000

0 5 10 15 20

Af/r

s(P

a s

m2/k

g)

DP/L (Pa/m x 103)

X=0.001 m3s/kg

Plug flow

Dilute phase

only

Fluidised dense

phase

48

Figure 2.17 Chambers’ pneumatic conveying classification diagram showing the location of

sand and flyash

Figure 2.18 Fargette’s pneumatic conveying predictive diagram showing the location of sand

and flyash

0.00001

0.0001

0.001

0.01

0.1

1

10

0.3

Nc(m

od)

Plug flow

Dilute phase

Fluidised

dense phase

0.1

1

10

100

1000

10000

100000

1000000

0.3

W

Plug flow

Dilute phase

Fluidised

dense phase

49

Figure 2.19 Sanchez’s pneumatic conveying predictive diagram showing the location of sand

and flyash

Figure 2.20 Williams’ pneumatic conveying predictive diagram showing the location of sand

and flyash

2.4 Rheology of aerated material

In this section, the experimental apparatus and testing procedure are introduced first, and then

by using this method the rheology results can be obtained. After that, the rheology of aerated

materials (sand and flyash) will be analysed.

0.1

1

10

100

0.0001 0.001 0.01 0.1 1 10

P*

Grt (x 10-3)

Plug flow

Dilute phase

Fluidised

dense phase

100

1000

10000

0.1 1 10 100 1000

'Loose-p

oure

d' bulk

density (

kg/m

3)

Permeabilty ( x 10-6 m3 s /kg)

Plug flow

Dilute phase

Fluidised dense

phase

Uknown

50

2.4.1 Experimental rig

The rheological flow properties of aerated material are dominated by its viscous response. Here

a rotary viscometer is used to measure the viscosity of aerated materials. The experimental

apparatus was designed by combining a fluidisation device with the rotary viscometer, as shown

in Figure 2.21.

For the fluidisation rig, an air flow controller was used to regulate the air mass flow rate from

50 mL/min to 30 L/min. A Perspex chamber with an internal diameter of 70 mm was utilised to

conduct the experiment. A porous membrane was installed between the air distributor and the

testing material. The material was poured into the chamber at a height of 190 mm above the

porous bed before each test. Moreover, a differential pressure transducer was used to record the

pressure drop across the material bed at a fixed distance (150 mm), and the transmitter stored

the result into the computer through a data logging device.

Figure 2.21 Schematic diagram of the testing rig combining by a fluidisation rig and a rotatory

viscometer (Chen, 2013)

The rotary viscometer used here is a coaxial-cylinders Rheomat-30 viscometer manufactured by

Contraves (Zurich, Switzerland). An electromotor with 30 rotating speed steps was used to drive

the measuring bob (Diameter: 30 mm and 46 mm) through a gear. The 30 rotating speed steps

were subdivided in geometrical progression within a range of 0.0478 ~ 350 rpm with an

increment coefficient of 1.36. The viscosity range according to the measuring system can be

from 0.001 to 1.7×107 Pa·s. The rotation was transmitted to the measuring system though a

patented cardan chuck, thus preventing the horizontal forces from affecting the driving

mechanism. Therefore, the measuring torque would not be affected by any influence caused by

the mechanical friction of the instrument. Additionally, a concentric base was placed between

51

the porous membrane and the rotating bob to minimise the lateral movement of the bob during

rotation.

Before testing the procedure, the ambient temperature was initially maintained at around 20 oC.

The material used for the rheology study was sand and flyash. As flyash may begin slugging or

channelling during fluidisation, a pre-fluidisation process was utilised to reduce this effect. That

is, a relatively high airflow was initially set to fluidise the material, after which the airflow was

gradually reduced to the desired airflow rate. At the designed airflow rate, the rotary viscometer

was turned on and the rotation speed was altered from step 15 to 30, which corresponding to the

shear rate of 0.90 s-1 to 89.8 s-1 for the 30 mm bob and 1.29 s-1 to 129.0 s-1 for the 46 mm bob.

The corresponding torque reading from the gauge at each step was then recorded to the

computer, so that the value of shear stress could be calculated based on this. Meanwhile, the bed

heights were also recorded by reading the scale value on the chamber during testing. This was a

complete rheology test process for one specific aeration level. The airflow was then set to the

next value, and the rheology test was repeated.

2.4.2 Rheology results

The relationship between shear stress and shear rate of sand were plotted in Figure 2.22. It can

be seen that the rheological behaviours showed Pseudo-plastic types for sand at tested bulk

density range. The shear stress increased with the increase of shear rate, but the increasing rate

of stress was observed to reduce during all the test process, which exhibited a shear thinning

effect. The same phenomenon was also detected in Chen’s (2013) study.

Figure 2.22 Shear diagram of sand

52

Similarly, the rheology testing for flyash was conducted under fluidised conditions, and part of

the results for the flyash are shown in Figure 2.23. Likewise, an identical Pseudo-plastic

behaviour was observed in the flyash shear diagram curves for all bulk density levels where a

shear thinning behaviour was evident.

Figure 2.23 Shear diagram of flyash

To summarise, the rheological behaviours obtained for sand and flyash were mainly due to the

complex air-solids interactions during the fluidising process. Under the fluidisation state beyond

the minimum fluidisation, the material behaved like liquid as the inter-particle bonding forces

between each particle could be ignored. There are more dynamic interactions between the air

and particles, and the void spaces between particles are large.

2.4.3 Modelling the rheology of aerated materials

To model the rheology of aerated material, an empirical approach was utilised to describe the

rheology behaviours of sand and flyash as described above. Essentially, for the Pseudo-plastic

behaviour exhibited by the aerated material, a common power-law formulation was adopted to

model its particular shear thinning effect. Therefore, each Pseudo-plastic curve could be

modelled with:

𝜏 = 𝜂𝜌�̇�𝑏𝜌 (2.2)

where ηρ is the consistency, and bρ is the flow index. A specific rheology curve could only be

defined by the two parameters together. Since the rheology of the fluid showed bulk density

dependency (Chen, 2013), both parameters showed bulk density (ρB) dependence.

53

2.4.3.1 Sand

For all the rheology testing results obtained for sand under the fluidisation state, the data were

modelled with the power-law model. For each bulk density value, the fitted values for

consistency and flow index defined by Eq.(2.2) are listed in Table 2.6. The R2 value for each

combination of these two parameters under the condition of fluidised flow was above 95%

which indicated that the Eq.(2.2) can be applied to describe the rheological phenomena of sand

under this condition.

Table 2.6 Fitted parameters of rheological curves for sand

Bulk density

(kg/m3)

Consistency

ηρ

Flow index

bρ

R2

1133.4 5.44 0.411 0.958

1157.7 5.48 0.400 0.955

1161.7 5.41 0.385 0.955

1191.5 5.62 0.342 0.952

1204.7 6.12 0.353 0.953

1229.6 6.89 0.290 0.952

1255.6 7.70 0.222 0.988

1289.7 8.24 0.161 0.973

Additionally, the results in Table 2.6 were subsequently fitted in Figure 2.24 and Figure 2.25 to

examine the correlations of the bulk density with the consistency and the flow index. In Figure

2.24, a linear correlation can be seen between the consistency and the bulk density. Therefore, a

linear line was applied to fit the testing data and the following equation was obtained:

𝜂𝜌 = 0.0202 × 𝜌𝐵 − 17.96 (2.3)

For the flow index in Figure 2.25, the best linear fit of results was used when increasing the

bulk density. Therefore, the fitting line can be defined as below:

𝑏𝜌 = −0.0017 × 𝜌𝐵 + 2.3085 (2.4)

54

Figure 2.24 Fitting of sand rheology model parameter - consistency

Figure 2.25 Fitting of sand rheology model parameter - flow index

2.4.3.2 Flyash

The power-law model fitting was also conducted based on the flyash rheology testing.

Parameter results were subsequently tabulated in Table 2.7.

Table 2.7 Model fitting parameters of rheological curves for flyash

Bulk density

(kg/m3)

Consistency

ηρ

Flow index

bρ

R2

417.6 0.180 0.634 0.966

428.4 0.164 0.665 0.968

y = 0.0202x - 17.96

0

1

2

3

4

5

6

7

8

9

10

1100 1150 1200 1250 1300

Co

nsi

sten

cy

Bulk density (kg/m3)

y = -0.0017x + 2.3085

0

0.1

0.2

0.3

0.4

0.5

0.6

1100 1150 1200 1250 1300

Flo

w i

nd

ex


55

447.2 0.256 0.569 0.945

453.6 0.280 0.540 0.952

459.7 0.290 0.561 0.962

471.9 0.245 0.596 0.970

484.9 0.400 0.495 0.963

492.2 0.387 0.509 0.965

496.3 0.395 0.484 0.943

497.1 0.374 0.531 0.952

525.3 0.480 0.535 0.951

528.5 0.545 0.444 0.953

537.9 0.542 0.443 0.951

564.2 0.699 0.382 0.957

496.3 0.395 0.484 0.966

In addition, the correlations between rheological parameters and the bulk density of flyash were

also investigated. For consistency, a linear correlation between the model fitting results and the

bulk density was observed as shown in Figure 2.26, which is:

𝜂𝜌 = 0.0035 × 𝜌𝐵 − 1.3122 (2.5)

A linear decreasing trend of the flow index when increasing the bulk density was observed in

Figure 2.27. Therefore, a linear line was modelled as:

𝑏𝜌 = −0.0016 × 𝜌𝐵 + 1.3115 (2.6)

Figure 2.26 Fitting of flyash rheology model parameter - consistency

y = 0.0035x - 1.3122

0

0.2

0.4

0.6

0.8

1

400 450 500 550 600

Consi

sten

cy


56

Figure 2.27 Fitting of flyash rheology model parameter - flow index

2.5 Conclusion

In this chapter, testing methods for particle and bulk material properties, such as the density

parameters, particle size distribution and air-particle parameters were firstly discussed. The

fluidised bulk density, permeability and steady-state fluidisation pressure were obtained through

a typical fluidisation test. These parameters for sand and flyash were then summarised in the

material data sheet. Additionally, based on the parameters of loose-poured bulk density and

particle diameter obtained above, the modes of flow for different types of materials were

classified. Flyash is in the fluidised dense phase region and sand is in the dilute only region.

The rheology study was also presented based on the viscometrical measurement and modelling

the results of sand and flyash. A combination of a fluidisation chamber and a rotary viscometer

was applied for testing the shear stress and shear rate of fluidised materials, which enabled the

investigation into the rheology of materials with respect to its bed expansion characteristics. The

fluidised materials exhibited a Pseudo-plastic type of fluidity. Moreover, based on the above

rheology testing results analyses, the rheology of fluidised bulk materials can be modelled by a

power-law method. Model parameters such as the consistency index and the flow index were

shown to have linear correlations to variations in bulk density.

y = -0.0016x + 1.3115

0

0.2

0.4

0.6

0.8

1

400 450 500 550 600

Flo

w i

ndex


57

3 CHAPTER 3 Air-gravity conveyor rig design

3.1 Introduction

The objective of this chapter is to introduce the air-gravity conveying rig design. In this section,

an investigation is made into how the system will work in terms of: feeding the material into the

channel; the continuity of flow through channels; the transfer of material from the delivery

channel to receiving box; and, its return to the main hopper. Also in this chapter, the detailed

operational procedures, air-gravity conveying visualisation and data acquisition techniques are

described.

3.2 Design and construction of the air-gravity conveyor rig

The design of the air-gravity conveyor is discussed below. The air-gravity conveying system

consists of four sections: hopper feed section, material conveying section, material receive

section and material return section. The schematic diagrams of the air-gravity conveying system

is given in Figure 3.1. The different components of the conveying system have been described

below. Also, the air supply and control system support structures will be mentioned.

Figure 3.1 Air-gravity conveying system

58

3.2.1 Supply hopper to conveying channel

A supply hopper, having the geometry of a cylinder vertical bin with a circular outlet at the

lower portion, has been used to feed the material into the channel. The main function of the

supply hopper is to store the material from the return system before testing. It is mounted on

three load cells used to measure the weight of material in the hopper and the feed mass flow

rate. Also, it is fabricated from mild steel and has a capacity of 1.5 m3 to hold approximately 2

tonnes of the sand. The material is fed from the hopper into a rectangular conveying duct, but

there is a circular inlet above the conveying channel. The circular opening is fabricated in terms

of conveniently fabricating transition pieces.

A 6 inch pneumatic butterfly valve is bolted under the hopper outlet to control the discharge of

the supply hopper. Also, another use would be to retain material in the hopper during the

process of sucking the material back to the hopper.

Behind the butterfly valve is a 6 inch manual knife gate valve. This valve is mainly designed for

the control of material feed rate into the channel with a different valve opening to the butterfly

valve, which only has the function of ‘open’ and ‘close’. A flange connector (Appendices A

Figure 10.1) is designed to link two valves, and another valve connector (Appendices A Figure

10.2) is fabricated for conveniently connecting the air-gravity conveyor inlet section.

Flexibility could be achieved by the use of a bellows or a short section of rubber. Here silver

tape was used to connect the flange connector and channel inlet. A convenient flexible section

would be immediately beneath the material feed area.

With the above design, the material in the hopper can be easily fed into the conveying channel.

Generally, it is best not to load entirely vertically onto the fluidising membrane as this may

result in severe loading forces. Here the inlet section of the channel has an angle of 5o so that the

major part of the flow is away from the membrane, rather than vertically down. Also, a steel

layer is provided under the membrane to support it.

3.2.2 Conveying channel

The basic conveying channel in our experimental study was designed into 6 meters long.

Detailed drawings can be seen in Appendices (Appendix A Figure 10.3). Two U-shaped channel

sections have been used to form a closed channel. A 3 mm porous steel layer and 5.5 mm thick

polyester layer are sandwiched between the two channel sections by using nuts and bolts. The

air-gravity conveyor was 6 meters long, and with the cross section area of 100 × 100 mm above

the air-gravity conveyor fabric (as shown in Figure 3.2). This compartment formed above the

membrane is referred to as the ‘conveying channel section’, whereas the one below it is called

the ‘plenum chamber section’ and its depth is 50 mm. Other parts of this conveyor are, in detail,

59

a 3 mm mild steel tube with 120 mm round inlet reduced to suit a 100 mm width air-gravity

conveyor (Appendix A Figure 10.4), four observation windows (75 mm × 100 mm) at 0 m, 1 m,

2 m and 5 meters, three inspection ports at 1 m, 2 m and 5 meters, 25 mm air connections and

standard discharge (Appendix A Figure 10.5).

Figure 3.2 Channel Section for Conveying System

For test purposes it would be useful to have some observation windows in the channel to

observe the behaviour of fluidised material being conveyed. Herein, four observation windows,

fabricated by using 5 mm thick Perspex sheets, are as positioned 0 m, 1 m, 2 m and 5 m along

the channel to observe the bed height, as well as the velocity along the channel via image

analysis. The windows are secured with a seal since the channels are under a slight pressure

when conducting the conveying process.

Three inspection ports (1 m, 2 m and 5 m) at the top of the channel act as a vent for the

fluidising air under vent flow conditions and for viewing purposes at non-vent flow. All the

inspection ports on each section of the conveying channel are the same with a diameter of 100

mm and a height of 100 mm. A dust collector was used to collect the dust on top of the vent to

avoid dust problems.

The air supply to the plenum chamber for fluidisation comes from an air supply system with an

air mass flow controller. Three 25 mm air connections were designed at the channel bottom to

ensure sufficient air supply, and air will enter the plenum chamber at the same time.

60

3.2.3 Conveying channel to the receiving box

Apart from the transfer of material from the supply hopper to the conveying channel, material

will have to be transferred from the channel to the receiving box. The standard discharge at the

end of the conveying channel and the receiving box are joined together with the help of a

flexible plastic tube. This tube is slipped over the collars attached to the discharge and receive

box. During the change in the inclination of the channel, the flexible tube can adjust itself.

The receiving box is designed with the size of 1500×1500×500 mm. The main functions of the

receiving box are to collect the particulate materials falling down from the standard discharge

exit, separate the gas solid mixture and measure the material mass flow rate during testing. The

receiving box is mounted on three load cells used to measure mass accumulation. It will then be

used to calculate the solid mass flow rate during each conveying test.

There are two vent ports at the top of the receiving box, one is connected to the return pipe to

make the most of the bag-type air filter on the top of the supply hopper for separation of air and

solids, and the other one was to a dust collector.

3.2.4 Material return system

To convey the material back to the hopper, a vacuum conveying system was applied for sucking

bulk particulate materials from the receiving box. Vacuum systems can be used most effectively

for the off-loading of ships and for the transfer of materials from open piles to storage hoppers,

where the top surface of the material is accessible. The suction nozzle in my return system is

designed to avoid blocking the inlet tube solidly with material, and to maintain an adequate flow

of air through the conveying line at all times. Indeed, this return system must be able to operate

continuously with the nozzle buried in the material at all times in order to maximize the material

flow rate. A bag-type air filter is located on the top of the supply hopper, so that any fines

transported can be recirculated, with no dust in the work area during the material return process.

3.2.5 Air supply and control

A rotary screw air compressor is used to supply the air with a maximum pressure capability of

700 kPa. Before feeding the air into the air-gravity conveying channel, the compressed air is

cooled and dried using a desiccant air dryer, and then flows through sonic nozzles to deliver a

constant air mass flow rate. The sonic nozzle system consists of two separate arrays of six sonic

nozzle inputs per array, as shown in Figure 3.3. Both sonic nozzle array 1 and 2 are used for the

conveying channel air supply, which enabled control and distribution of the air to give the

required air mass flow rate for the experiment.

The calibration results of the air mass flow rate for each sonic nozzle are given in Figure 3.4 and

Figure 3.5. The air mass flow rate of both the primary and secondary air supply can either be

61

pre-set or manually adjusted during the conveying process. For the experiments conducted in

this thesis, the pre-set option was used.

Figure 3.3 Picture of the two sonic nozzle arrays

Figure 3.4 Array 1 air mass flow rate calibration

y = 1.6364x + 1.8829

R² = 0.9996

0

10

20

30

40

50

60

0 5 10 15 20 25 30

Air

m

ass

flow

rat

e (g

/s)

Array 1 No.

62

Figure 3.5 Array 2 air mass flow rate calibration

3.2.6 Support structures

Support structures are designed for the air-gravity system to support the main hopper and

conveying channel. In detail, a hopper support structure and platform for supporting the main

hopper and a channel support with screw (for inclination adjustment) is drawn in Appendix A

(Figure 10.6 and Figure 10.7). The structure analysis was conducted during the design process

to ensure the structure is strong enough to support the supply hopper and conveying channel.

3.3 Instrumentation

Instrumentation for measuring pressure and mass flow rates was installed in an experimental

area (E block). The system utilised Terminal Box 4 (TB4) as well as installing new amplifiers

and a power supply. The system uses isolated current loops to generate signal data for the NI 2

× 32 channels system to minimise errors from long cable runs including voltage drop errors and

to minimise effects of electromagnetic interference (EMI) and radio frequency interference

(RFI). Cable screening and grounding is also used to minimise EMI, RFI and 50 Hz harmonic

noise that could be a problem within E block. For detail of the instrumentation see Table 3.1

below. Figure 3.6 gives details of the installation drawing.

y = 1.5439x + 2.4616

R² = 0.9998

0

10

20

30

40

50

60

0 5 10 15 20 25 30

Air

mas

s fl

ow

rat

e (g

/s)

Array 2 No.

63

Table 3.1 Instrumentation

To measure pressure along the air-gravity conveyor:

10 × Honeywell gauge transducers 0.5 PSI rated pressure

5 × Honeywell gauge transducers 1 PSI rated pressure

5 × Honeywell differential pressure transducers 1 PSI rated pressure

Mass flow rate are measured by PT load cells:

3 × 1000 kg PT load cells

3 × 500 kg PT load cells

Amplifiers and Readouts:

15 × SW signal transmitter

7 × PT 200MI panel meter

Figure 3.6 Air-gravity conveyor installation

The system was initially calibrated before installation using a Fluke 718 pressure calibrator for

the 0.5 PSI and 1 PSI transducers. During commissioning, the transducers were tested again and

any required adjustments were made. Existing precision transducer ACCUPOINT load cells

were used to measure load for the supply hopper and receiving box. Three 1000 kg load cells

were used for the supply hopper with three 500 kg load cells used for the receiving box. The

PT200MI panel indicator was initially calibrated using the mV/V input method as calibration

64

standards of 2 mV/V for each load cell were used. The calibration table can be seen in the

Appendices (Appendix A Table 10.1).

To measure the pressure along and across the conveying channel, pressure transducers were

installed on the conveying channel. The data acquisition collection used the LabVIEW software

package to record the data at an acquisition rate of 100 Hz. The data acquisition system had 64

input channels, which was sufficient for the data collection. The variations of the mass

collection in the supply hopper and receiving box, and the pressures and differential pressures

were recorded for subsequent analysis. The LabVIEW program was also used to monitor the

real-time behaviour of the system.

3.3.1 Solid mass flow rate

Three 1000 kg PT ACCUPOINT load cells were installed under the supply hopper to measure

the feed rate during the conveying process. Another three 500 kg PT ACCUPOINT load cells

were positioned under the receiving box to record the mass flow rate of the conveying material.

The material feed rate can be measured by analysing material weight loss rate on the hopper,

and the material mass flow rate can be calculated using the weight increase in the receiving box.

The calibration of load cells was done by placing a given mass of steel bricks on the hopper and

box. The results of the calibration factor for load cells were input into the data acquisition

system to derive the solids mass flow rate. The calibration curve for the load cells is shown in

Figure 3.7 and Figure 3.8, and the relationship between the voltage signal to kilogram can be

seen in Table 3.2 below.

Table 3.2 Calibration of load cells

Load cells Type Relationship (voltage transfer to kilogram)

Bin1 500 kg × 3 Bin1 (kg) = 298.44 × Bin1 (V)-0.4361

Box2 1000 kg × 3 Box2 (kg) = 300.15 × Box2 (V)-0.7318

65

Figure 3.7 Supply hopper load cells calibration

Figure 3.8 Receiving box load cells calibration

3.3.2 Pressure transducers

There are 20 pressure transducers used in my air-gravity conveying system. In detail, five 1 PSI

gauge transducers were placed at the bottom of the channel at the location of 0.5, 1.5, 2.5, 4.5

y = 298.44x - 0.4361

R² = 1

0

50

100

150

200

250

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Mas

s (

kg)

Voltage (v)

y = 300.15x - 0.7318

R² = 1

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Mas

s (

kg)

Voltage (v)

66

and 5.5 metres along the conveying channel to measure the plenum chamber pressure. Ten 0.5

PSI gauge transducers were installed at the sidewall of the channel at the location of 0.5, 1.5,

2.5, 4.5 and 5.5 metres at a height of 18 mm above the porous membrane. Moreover, five 1 PSI

differential pressure transducers were applied at the same location as above gauge transducers,

but were used to record the pressure drop from the chamber to the channel top at each location.

Similarly, all the pressure transducers were calibrated and the transfer voltage signal to kPa

value, as can be seen in Table 3.3 below. Typical calibration examples for 0.5 PSI gauge

transducer, 1 PSI gauge transducer and 1 PSI differential pressure transducer were plotted as in

Figure 3.9 to Figure 3.11.

Table 3.3 Calibration of pressure transducers

Transducers No. Type Relationship (voltage transfer to kPa)

P1 0.5 PSI P1 (kPa) = 0.3970 × P1 (V) - 0.8168

P2 0.5 PSI P2 (kPa) = 0.3687 × P2 (V) - 0.9084

P3 1 PSI P3 (kPa) = 0.6922 × P3 (V) - 0.3233

P5 0.5 PSI P5 (kPa) = 0.4424 × P5 (V) - 0.8659

P6 0.5 PSI P6 (kPa) = 0.3756 × P6 (V) - 0.8618

P7 1 PSI P7 (kPa) = 0.7049 × P7 (V) - 0.6910

P9 0.5 PSI P9 (kPa) = 0.3686 × P9 (V) - 0.8951

P10 0.5 PSI P10 (kPa) = 0.3832 × P10 (V) - 0.9144

P11 1 PSI P11 (kPa) = 0.6853 × P11 (V) - 0.3226

P13 0.5 PSI P13 (kPa) = 0.3762 × P13 (V) - 0.9261

P14 0.5 PSI P14 (kPa) = 0.3644 × P14 (V) - 0.7243

P15 1 PSI P15 (kPa) = 0.6788 × P15 (V) - 0.6398

P17 0.5 PSI P17 (kPa) = 0.4157 × P17 (V) - 0.8315

P18 0.5 PSI P18 (kPa) = 0.3856 × P18 (V) - 0.7643

P19 1 PSI P19 (kPa) = 0.7182 × P19 (V) - 0.3412

DP4 1 PSI DP4 (kPa) = 0.8634 × DP4 (V) - 1.7366

DP8 1 PSI DP8 (kPa) = 0.8630 × DP8 (V) - 1.7353

DP12 1 PSI DP12 (kPa) = 0.8658 × DP12 (V) - 1.7448

DP16 1 PSI DP16 (kPa) = 0.8682 × DP16 (V) - 1.7404

DP20 1 PSI DP20 (kPa) = 0.8666 × DP20 (V) - 1.7444

67

Figure 3.9 The typical calibration curve for the 0.5 PSI gauge pressure transducer (P1)

Figure 3.10 The typical calibration curve for the 1 PSI gauge pressure transducer (P15)

y = 0.3970x - 0.8168

R² = 0.9999

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10

Pre

ssu

re (

kP

a)

Voltage (v)

y = 0.6874x - 0.6789

R² = 0.9999

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12

Pre

ssure

(kP

a)

Voltage (v)

68

Figure 3.11 The typical calibration curve for the 1 PSI differential pressure transducer (DP4)

Pressure transducer protective boxes have also been designed to protect these sensors from

being affected by dust. The structures of the boxes were firstly draw by Solidworks and then

form STL file. After that, the STL file was read by SLIC3R to form the G-code which contains

the pathway to 3D print the structure. Finally, the structure was printed by the 3D printer using

Acrylonitrile butadiene styrene (ABS). The drawing of two kind of boxes are presented in

Appendix A (Figure 10.8 and Figure 10.9).

3.3.3 Depth of flowing bed

In order to understand the flow mechanism, visual observations were made, and some still

photographs and short movies were captured during the test run. High-speed video was used to

obtain detailed information of the solid-phase flow behaviour within the observation window of

the air-gravity conveying channel. The data obtained by high speed camera were used to

calculate the bed height through an image analysis method. A high-speed Phantom 5 video

camera with a 105 mm lens was used to capture the solid-phase flow behaviour within the air-

gravity conveying channel. The image sample rate was up to 1000 frames per second, with an

exposure time of 990 μs.

3.4 Experimental procedure

The air-gravity conveying tests were carried out on the conveying test rig. The two types of

material were transported over a range of air flow rates.

y = 0.8634x - 1.7366

R² = 1

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12

Pre

ssu

re (

kP

a)

Voltage (v)

69

3.4.1 Pre-start checks

Prior to the commencement of the first test each day, an equipment check was made to ensure

the following:

1. Pressure equipment was in a safe condition;

2. Each observation window was in a safe condition (that is, there were no obvious

cracks), and the channel connections were secure;

3. Valves were in the correct positions;

4. All the sure-locks were connected with securing pins;

5. Safety, operating, maintenance procedures were in place;

6. Pressure vessel inspection was complete and current.

3.4.2 Operating procedure

The material was conveyed back to the hopper through a vacuum conveying system firstly.

After filling the material into the supply hopper, the knife gate valve was adjusted to give the

desired opening. Then the fluidising air (with a desired value of air mass flow rate) was injected

into the plenum chamber following the pneumatic butterfly valve opening to let the material

drop down. The material from the supply hopper dropped into the conveying channel through

the feed section, and the air came up through the porous membrane to fluidise the material. The

fluidised material then flowed towards the channel discharge and then fell into the receiving

box. LABVIEW was used to record the change of mass flow rate and pressures at different

locations for the whole conveying process. 20 pressure sensors and 6 load cells were recorded

for all the conveying time to see the behaviour of this air-gravity flow system. Matlab

programmes were written to help deal with these data. Meanwhile, a high speed camera was

used to measure the bed height and velocity of conveying material through the observation

windows. The airflow control valve was turned off after the hopper become empty. This

completed one cycle of a test run.

The effect of airflow rate, inclination angle of the channel and valve opening have been

investigated in relation to the material mass flow rate, pressure drop along the channel and

material bed height for both vent and non-vent air-gravity flow systems.

3.5 Conclusion

In this chapter, the design of an air-gravity conveying rig was explained and all the parts of the

rig were fabricated based on the design drawings. The air-gravity conveying system mainly

contained four sections, namely: a hopper feed section, a material conveying section, a material

receiving section and a return section. From the analysis carried out in this chapter it would

70

appear that the complicated conveying system could be made from a number of components,

and that fabrication should not be too difficult.

Subsequently, instrumentation for measuring pressure and mass flow rates was installed in an

experimental area. The method of measuring the solid mass flow rate, pressure drop, bed height

and solid velocity were also discussed. The calibration of load cells and pressure transducers

was presented, then the calibration results were given for all these sensors. Additionally, 3D

printer was applied to print the designed pressure sensor boxes to protect them from dust.

Finally, the experimental procedure was explained and how the air-gravity conveying system

work was clearly given in this section. Following this process, an array of useable data could be

recorded and solved fluently with the help of LABVIEW and MATLAB programmes.

71

4 CHAPTER 4 Experimental results

4.1 Introduction

The design of a six-metre long air-gravity conveyor was described in last Chapter. Its flow

characteristics are now studied experimentally. The flow circuit begins with: the material being

stored in the supply hopper and discharged through a knife gate valve to the conveying channel.

The fluidised solids flow along the channel and are then collected via a receiving box on the

floor. After the materials are all conveyed to the receiving box, they are delivered back to the

supply hopper through a vacuum conveying system. The conveying tests were conducted

separately for sand and flyash to investigate the parameters of each material under vent and non-

vent conditions. The effect of air flow rate and channel inclination on the depth of flowing beds,

material mass flow rate and pressure drop along the channel were investigated and the results

are discussed in this Chapter. The superficial air velocity had been chosen to vary from the start-

up value of approximately half to twice of the minimum fluidised velocity. The inclinations of

the air-gravity conveyor were selected using three downward inclinations of 2.5o, 3.75o and 5.0o.

The knife gate valve was used to give a desired opening to control the mass flow rate of

material.

4.2 Experimental data analysis methods

In this section, the way to get the experimental pressure and mass flow rate are discussed. Then

the pressures along the channel and mass flow rate can be calculated. Also, an image analysis

method is used to analysing the video and photographs captured by a high speed camera, then

bed heights and conveying velocities can be obtained.

4.2.1 Experimental pressure and mass flow rate

The experimental procedure was provided in Chapter 3. When a sample test run was conducted

to explain how to analyse the data recorded by LABVIEW through the data acquisition system.

After filling the material in the supply hopper, the knife gate valve is adjusted to give the

desired opening before starting the test. Then the pneumatic butterfly valve opened to let

materials drop down to the conveying channel. Meanwhile, the fluidising air is injected into the

plenum chamber. The material from supply hopper dropped into the conveying channel through

the feed section, and the air coming up through the porous membrane fluidised the material.

After that, the fluidised material flowed towards the channel discharge and then fell into the

receiving box. 20 pressure sensors and 6 load cells were placed to record during all the

conveying time to see the behaviour of the air-gravity flow system. As a result, pressures at five

locations could be obtained from those pressure transducers. Load cells were placed under the

supply hopper and receiving box to investigate the mass flow rate.

72

Pressure reading from each pressure transducers and material mass flow rate from load cells can

be obtained through the data acquisition system. Figures below show the pressures at plenum

chamber, differential pressures between plenum chamber and channel top, pressures at sidewall

and the mass flow rates of receive box. As can be seen from Figure 4.1 before the start of

conveying, the pressure is zero at the plenum chamber. Once the air flow into the chamber, the

pressure increases dramatically at the beginning and then becomes stable. Note that a gradual

increase occurs ranging from 50 s to 120 s, which is caused by the acceleration of material

during the conveying process. After 120 s, the plenum pressure maintains a constant level

without irregular fluctuations until the end of test. Therefore, time between 120 s to 210 s will

be selected as a steady flow state. The mean pressure gradient is calculated by averaging the

pressure from 120 s to 210 s. The differential pressure between the bottom and channel top, and

pressure at sidewall behave similarly. And the average pressure can be obtained from 120 s to

210 s where steady flow is formed. Furthermore, the mass flow rate can be calculated from the

mass gain from the load cells weight of the receiving box versus time. To investigate the change

of mass flow rate under steady flow conditions, the time between 120 s and 210 s is chosen to

be consistent with the pressure analysis above.

Figure 4.1 Experimental measurements for the pressure at bottom, pressure at sidewall,

pressure drop between bottom and top and load cell weight.

The conveying parameters conducted for the tests are tabulated in Table 4.1 and Table 4.2 for

vent and non-vent flow of sand, Table 4.3 and Table 4.4 for vent and non-vent of flyash.

73

Table 4.1 Experimental data for vent flow of sand

No.

Air

velocity

(mm/s)

Mass

flow

rate

(kg/s)

Inclination

angle

(degree)

P_chamber

average

(kPa)

DP along the channel (kPa)

0.5m 1.5m 2.5m 4.5m 5.5m

1 58 0.63 5.00 2.471 2.448 2.498 2.456 2.469 2.495

2 72 1.32 5.00 3.154 3.082 3.086 3.082 3.073 3.086

3 85 1.68 5.00 3.488 3.340 3.436 3.444 3.428 3.330

4 96 1.72 5.00 3.946 3.818 3.840 3.854 3.831 3.787

5 106 1.76 5.00 4.387 4.281 4.261 4.292 4.272 4.251

6 127 1.70 5.00 5.135 5.082 5.133 5.094 5.098 5.132

7 140 1.70 5.00 5.719 5.657 5.714 5.674 5.685 5.700

8 96 1.48 2.50 4.197 4.351 4.353 4.361 4.351 4.377

9 106 1.11 2.50 4.652 4.662 4.669 4.668 4.665 4.684

10 127 1.52 2.50 5.635 5.683 5.703 5.715 5.694 5.732

11 96 1.56 3.75 4.184 4.126 4.091 4.129 4.095 4.069

12 106 1.53 3.75 4.602 4.530 4.534 4.537 4.519 4.479

13 127 1.69 3.75 5.510 5.451 5.472 5.483 5.463 5.455

14 72 0.30 5.00 3.508 3.146 3.225 3.338 3.368 3.332

15 85 0.30 5.00 3.923 3.633 3.677 3.784 3.780 3.776

16 96 0.30 5.00 4.028 3.973 4.024 4.001 4.002 4.034

17 106 0.30 5.00 4.383 4.334 4.391 4.360 4.367 4.401

18 117 0.30 5.00 4.906 4.609 4.615 4.657 4.681 4.666

19 127 0.30 5.00 5.241 5.119 5.114 5.125 5.105 5.121

Table 4.2 Experimental data for non-vent flow of sand

No.

Air

velocity

(mm/s)

Mass flow

rate (kg/s)

Inclination

angle

(degree)

P_chamber

average

(kPa)


0.5m 1.5m 2.5m 4.5m 5.5m

1 36 0.15 5.00 2.277 1.411 1.788 1.996 2.159 2.190

2 47 0.47 5.00 2.849 1.909 2.340 2.512 2.630 2.669

3 58 1.34 5.00 3.369 2.635 2.884 2.874 2.900 2.944

4 72 1.32 5.00 3.990 2.922 3.311 3.482 3.534 3.565

5 85 1.52 5.00 4.407 3.308 3.377 3.385 3.403 3.385

6 96 1.72 5.00 5.388 3.889 3.956 3.943 3.989 4.048

74

7 106 2.06 5.00 6.009 4.300 4.345 4.326 4.379 4.464

8 127 2.09 5.00 6.152 5.093 5.134 5.133 5.199 5.290

9 140 2.08 5.00 6.227 4.980 4.983 5.003 5.052 5.174

10 96 1.03 2.50 5.403 4.179 4.201 4.224 4.311 4.383

11 106 1.13 2.50 6.119 4.498 4.502 4.516 4.568 4.625

12 127 1.52 2.50 6.211 5.489 5.511 5.542 5.615 5.712

13 96 1.38 3.75 5.776 4.030 4.039 4.057 4.070 4.143

14 106 1.70 3.75 6.852 4.507 4.529 4.540 4.571 4.612

15 127 1.76 3.75 6.515 5.300 5.313 5.338 5.389 5.467

17 72 0.30 5.00 3.810 3.312 3.385 3.394 3.452 3.510

18 85 0.30 5.00 4.235 3.653 3.648 3.691 3.711 3.705

19 96 0.28 5.00 4.748 4.006 4.007 4.036 4.074 4.121

20 106 0.38 5.00 5.900 4.467 4.499 4.502 4.548 4.650

21 128 0.30 5.00 6.208 5.115 5.136 5.147 5.188 5.241

Table 4.3 Experimental data for vent flow of flyash

No.

Air

velocity

(mm/s)

Mass

flow rate

(kg/s)

Inclination

angle

(degree)

P_chamber

average

(kPa)


0.5m 1.5m 2.5m 4.5m 5.5m

1 13.7 0.35 5.00 0.481 0.496 0.496 0.499 0.497 0.496

2 13.7 0.95 5.00 0.510 0.519 0.540 0.535 0.532 0.514

3 13.7 2.49 5.00 0.593 0.598 0.637 0.632 0.628 0.591

4 13.7 7.34 5.00 0.698 0.758 0.750 0.742 0.739 0.741

5 24.8 0.75 5.00 0.948 0.961 0.951 0.960 0.951 0.954

6 24.8 1.41 5.00 0.968 0.983 0.973 0.980 0.971 0.974

7 24.8 3.45 5.00 1.086 1.107 1.097 1.103 1.095 1.097

8 24.8 4.26 5.00 1.132 1.154 1.140 1.145 1.135 1.136

9 36.0 0.41 5.00 1.311 1.371 1.372 1.358 1.364 1.331

10 36.0 0.88 5.00 1.336 1.392 1.393 1.384 1.385 1.367

11 36.0 2.56 5.00 1.420 1.478 1.504 1.499 1.496 1.460

12 36.0 2.97 5.00 1.459 1.521 1.521 1.510 1.512 1.514

13 42.6 0.23 5.00 1.708 1.755 1.788 1.779 1.767 1.757

14 42.6 0.54 5.00 1.722 1.778 1.797 1.789 1.777 1.775

15 42.6 2.56 5.00 1.782 1.846 1.874 1.865 1.852 1.840

16 42.6 4.92 5.00 1.940 1.999 1.984 1.981 1.970 1.973

75

17 47.1 0.22 5.00 1.825 1.857 1.892 1.886 1.879 1.854

18 47.1 0.48 5.00 1.833 1.864 1.900 1.892 1.885 1.859

19 47.1 3.41 5.00 1.933 1.971 1.961 1.961 1.956 1.953

20 47.1 8.61 5.00 2.099 2.166 2.143 2.129 2.109 1.914

21 58.0 0.21 5.00 2.357 2.443 2.450 2.445 2.436 2.448

22 58.0 0.71 5.00 2.374 2.461 2.471 2.463 2.453 2.466

23 58.0 1.23 5.00 2.398 2.494 2.498 2.493 2.480 2.489

24 58.0 3.73 5.00 2.518 2.614 2.606 2.607 2.583 2.583

25 42.6 0.39 2.50 1.758 1.773 1.761 1.776 1.768 1.771

26 42.6 0.62 2.50 1.780 1.814 1.817 1.819 1.805 1.823

27 42.6 1.38 2.50 1.826 1.858 1.868 1.870 1.856 1.869

28 42.6 1.99 2.50 1.863 1.874 1.862 1.878 1.878 1.876

29 42.6 2.69 2.50 1.872 1.902 1.888 1.903 1.895 1.896

30 42.6 0.41 3.75 1.733 1.747 1.748 1.752 1.744 1.744

31 42.6 0.65 3.75 1.756 1.760 1.764 1.762 1.763 1.759

32 42.6 0.93 3.75 1.780 1.790 1.787 1.799 1.790 1.783

33 42.6 2.64 3.75 1.832 1.847 1.845 1.849 1.841 1.840

34 42.6 2.74 3.75 1.861 1.874 1.864 1.876 1.871 1.867

35 42.6 0.36 5.00 1.714 1.765 1.792 1.783 1.771 1.765

Table 4.4 Experimental data for non-vent flow of flyash

No.

Air

velocity

(mm/s)

Mass

flow rate

(kg/s)

Inclination

angle

(degree)

P_chamber

average

(kPa)


0.5m 1.5m 2.5m 4.5m 5.5m

1 13.7 0.30 5.00 0.481 0.483 0.484 0.479 0.480 0.477

2 13.7 0.48 5.00 0.493 0.485 0.486 0.483 0.483 0.480

3 13.7 0.89 5.00 0.541 0.490 0.491 0.498 0.490 0.491

4 13.7 2.88 5.00 0.623 0.602 0.602 0.599 0.598 0.595

5 13.7 7.57 5.00 0.762 0.893 0.741 0.748 0.733 0.737

6 24.8 0.29 5.00 1.007 0.980 0.981 0.976 0.977 0.928

7 24.8 1.61 5.00 1.179 1.026 1.023 1.028 1.027 1.030

8 24.8 2.80 5.00 1.492 1.085 1.087 1.089 1.076 1.085

9 24.8 5.78 5.00 1.546 1.164 1.164 1.164 1.147 1.156

10 24.8 7.70 5.00 1.732 1.213 1.200 1.200 1.194 1.196

11 36.0 0.29 5.00 1.449 1.374 1.376 1.371 1.371 1.369

76

12 36.0 0.67 5.00 1.533 1.383 1.384 1.383 1.388 1.383

13 36.0 1.48 5.00 1.643 1.482 1.451 1.447 1.437 1.439

14 36.0 2.15 5.00 1.826 1.463 1.444 1.444 1.438 1.445

15 36.0 5.41 5.00 2.614 1.647 1.640 1.630 1.627 1.588

16 42.6 0.29 5.00 1.943 1.753 1.757 1.763 1.745 1.762

17 42.6 0.78 5.00 2.009 1.762 1.767 1.764 1.765 1.767

18 42.6 1.27 5.00 2.239 1.793 1.797 1.802 1.787 1.802

19 42.6 2.18 5.00 2.459 1.820 1.828 1.823 1.826 1.833

20 42.6 5.19 5.00 3.283 1.928 1.962 1.964 1.958 1.936

21 47.1 0.24 5.00 2.050 1.813 1.813 1.814 1.812 1.780

22 47.1 0.48 5.00 2.064 1.840 1.837 1.838 1.834 1.835

23 47.1 1.00 5.00 2.282 1.878 1.877 1.877 1.871 1.874

24 47.1 1.34 5.00 2.413 1.859 1.859 1.860 1.857 1.742

25 47.1 5.33 5.00 3.654 2.063 2.057 2.057 2.055 2.080

26 58.0 0.24 5.00 2.776 2.336 2.352 2.357 2.359 2.353

27 58.0 0.51 5.00 2.871 2.336 2.367 2.375 2.376 2.354

28 58.0 1.85 5.00 3.420 2.378 2.385 2.386 2.387 2.401

29 58.0 3.05 5.00 3.699 2.463 2.464 2.472 2.475 2.491

30 58.0 4.48 5.00 4.111 2.466 2.473 2.474 2.480 2.485

31 36.0 0.27 3.75 1.607 1.474 1.468 1.467 1.469 1.464

32 36.0 0.36 3.75 1.678 1.480 1.471 1.472 1.473 1.472

33 36.0 0.99 3.75 1.785 1.509 1.497 1.498 1.498 1.497

34 36.0 1.61 3.75 1.899 1.463 1.464 1.472 1.459 1.444

35 36.0 2.24 3.75 2.080 1.582 1.571 1.572 1.571 1.570

36 36.0 0.38 2.50 1.620 1.400 1.427 1.441 1.428 1.406

37 36.0 0.67 2.50 1.574 1.431 1.435 1.448 1.434 1.432

38 36.0 0.86 2.50 1.688 1.446 1.440 1.449 1.443 1.456

39 36.0 1.30 2.50 1.789 1.444 1.470 1.483 1.471 1.449

40 36.0 4.57 2.50 2.596 1.686 1.726 1.736 1.733 1.725

4.2.2 Image analysis method

The high speed camera was used to study the flow behaviour of the conveying material. After

analysing the video and photographs captured by high speed camera through image analysis

method, bed heights and conveying velocities can be obtained.

For the image analysis method, MATLAB programme VedioReader was used to read video

frame data from a file. After obtaining all the frame data, bed height and velocity of the

77

conveying channel can be calculated by analysing these frame data. For detailed calculation

programmes, readers are directed to Appendix B.

The picture of flowing sand can be seen below as an example of an image analysis method.

Figure 4.2 (a)-(c) present the flow characteristics of sand conveying in an air-gravity conveying

system for increasing the air velocity. The flow of sand experiences the pulsastory flow,

transition (pulsatory/non-pulsatory) and fluidised flow. At low air velocity, Figure 4.2 (a1)

shows the pulsatory flow of sand, large dune occurred during the conveying process. A multi-

dune of sand diagram can be seen in Figure 4.2 (a2) to describe the flow behaviour in the

conveying channel. Figure 4.2 (a3) shows the pressure drop between chamber and top of the

channel. The pressure trace of pulsatory flow is presented in Figure 4.2 (a3), where the pressure

fluctuations were observed. This was caused by the pulsatory flow of sand in the conveying

channel. The flow mode is dependent on air velocity and solid mass flow rate. The pressure

fluctuations only occurs when the condition is met. The observation by high speed camera and

pressure measurements during this short period have clearly shown the pulsatory flow. A

fluidised moving bed of sand was observed at higher air velocity as shown in Figure 4.2 (c1).

The steady pressure formed during the conveying of fluidised flow of sand. Figure 4.2 (b) gives

the transition area where pulsatory flow transferred to a non-pulsatory flow, where dune start to

be deformed.

78

Figure 4.2 High-speed camera visualisation of air-gravity conveying of sand

79

Figure 4.3 High-speed camera visualisation of air-gravity conveying of flyash

80

Figure 4.3 (a)-(c) present the flow characteristics for flyash conveying in an air-gravity

conveying system for different conveying air velocity. Similar to sand flow mode, pulsatory

flow of flyash was observed at lower air velocity. A typical dune of flyash with the trend of

moving forward in the observation window can be seen as shown in Figure 4.5 (a1), pulsatory

flow of flyash can be found with the accumulation of flyash in the conveying channel. While the

flysah above the conveying bed transferred to a non-pulsatory flow after increasing fluidised air

in Figure 4.3 (b1), combined with dune deformation. Figure 4.3 (c1) shows the fluidised flow

pattern of flyash observed for higher fluidised air. The pressure fluctuation is remarkably in

pulsatory flyash flow, while the pressure become stable in Figure 4.3 (c3) as the steady fluidised

flow formed. At this stage, a well fluidised state of flyash is formed and the total material bed

will slide down through the channel behave like a continuum. For the transition area, the

number of dunes and the pressure fluctuation stay between pulsatory and steady flow.

4.3 Fluidised conveying of sand at vent flow condition

The flow behaviours of fluidised sand at the vent flow condition are discussed below, including

flow visualization, effect of air flow rate and inclination angle on sand mass flow rate, plenum

chamber pressure, pressure drop at material layer and bed height along the channel.

4.3.1 Flow visualization

In this section, comments are given on different phenomena observed visually during the

testing. It has been observed that, over the range of air flow rate investigated (Figure 4.2 and

Figure 4.3), the flow of material showed a stratified bed, and a layer of air carrying insignificant

materials concentration flows above the moving material bed existed at a superficial air velocity

greater than minimum fluidisation velocity.

In detail, an initial increase in the air flow rate causes no change of material bed (Mode 1). The

same phenomenon can be shown in a fluidised bed test of a fixed bed regime. Further increase

in air flow rate built up the material bed height in all cases of conveying (Mode 2). The material

flow rate oscillations were observed as accumulation of sand in the conveying channel for a

certain period of time, followed by a sudden pulsatory flow of sand. It can be related to the

phenomenon in Bingham plastic flowing bed in that a yield shear stress has to be exceeded for

the bed to flow. After Mode 2, continually increasing the air flow rate will cause a non-

pulsatory movement of partial material bed at the top layer of the bed (Mode 3). The flow bed

height decreased and the flow accelerated after the bed starts to flow. Since the bed viscosity is

also deceasing with reduction in the bed height (Botterill and Bessant, 1976), the flow

accelerated even more. To further increase in air flow rate, a well fluidised state of sand is

formed and the total material bed slid down through the channel (Mode 4). But when the air

velocity increases even more, air bubbles would occur and come out of the sliding material bed

81

as the excess air in the channel. This characteristic is also accompanied with the vigorous

particles agitation and the upper materials behave more like dilute flow (Mode 5), and there

after the flow remains in Mode 5 with an increasing airflow rate. Table 4.5 presents the different

flow patterns observed during air-gravity conveying testing.

Table 4.5 Description of flow patterns and classification

Mode Flow description Criteria Flow regime

1 No movement of material Stationary bed Fixed bed

2

Building up of material bed height in channel

followed by start of pulsatory movement of

partial material bed from top layer and gives

extremely low mass flow rate due to length of

time intervals between two pulses

Surface shear

force-dominated

flow

Pulsatory

3 Non-pulsatory movement of partial bed of

material from top layer of bed

Combined

influence of

gravity and

shear force

Transition

(pulsatory/non-

pulsatory)

4 Steady movement of total bed of material with

occasional pulses Gravity-

dominated flow Sliding bed

5 Steady movement of total bed of material with

vigorous bubbling and particles’ agitation

4.3.2 Effect of air flow rate on sand mass flow rate

As the air flow rate significantly affects the flow behaviours of air-gravity conveying under vent

condition, the effect of this parameter is discussed below. Figure 4.4 shows the relationship

between mass flow rate of sand and superficial air velocity. From that, an increase in the air

velocity increases the material mass flow rate and then becomes stable with a further increase in

the superficial air velocity. At air velocity lower than 58 mm/s, sand could not flow along the

conveying channel. For an air velocity between 58 mm/s and 86 mm/s, the sand mass flow rate

increased with an increase in air velocity. After 86 mm/s, the mass flow rate increased slowly

and then reached a steady state which was independent of superficial air velocity. At the range

of 86 mm/s to 106 mm/s, though the material mass flow rate is trended to a steady state, obvious

pulsatory movement could be found during the flow visualisation. This indicated that good

fluidisation flow formed after the superficial air velocity of 106 mm/s.

The initial steep increase in the material mass flow rate due to the voidage enlargment caused by

the increasing air velocity. In detail, after the start of the material flow at an airflow rate lower

82

than the minimum fluidisation velocity, the distance between particles increased which enlarged

the bed voidage during the airflow rate increasing process. The viscosity of the conveying bed

decreased correspondingly (Botterill et al. 1979) which contributed more to the flow bed

acceleration. The mass flow rate saturation level being obtained at a high airflow rate, it was

because the viscosity of the conveying material did not change much with the increasing air

velocity, and most of the superfluous air vent went to the dust collector system. Therefore, the

carriage potential of the airflow rate is more effectively utilized at the initial stage than at a later

stage. For this experimental case, 106 mm/s is the optimum operating airflow rate which could

reach the maximum capacity with energy saving. Further increasing the air velocity contributes

nothing to the material mass flow rate.

Figure 4.4 Effect of the superficial air velocity on the sand mass flow rate (Vent)

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120 140 160

Mat

eria

l m

ass

flow

rat

e (k

g/s

)

Superficial air velocity (mm/s)

No flow

Pulsatory

movement

Transition

(pulsatory/non-

pulsatory)

Fluidised flow

83

4.3.3 Effect of inclination angle on sand mass flow rate

Figure 4.5 Variation of sand mass flow rate with channel inclination angle for different

superficial air velocity (Vent)

As can be seen in Figure 4.5, the sand mass flow rate increases with the increase of inclination

angle from 2.5o to 5o for a given airflow rate. The reason for this increase is that the increase of

gravitational force acts on the material at higher inclination angle. Also, Figure 4.5 shows that at

a given inclination angle 2.5o to 3.75o, the increase in the superficial air velocity increases the

sand mass flow rate. However, for the inclination of 3.75o, the increase phenomenon becomes

not obvious and when the inclination angle is increased to 5o, the sand mass flow rate is stable

around 1.72 kg/s. This is because at a higher inclination angle, the more gravity force will

contribute to the sand flow which increases the flow ability of sand. As a result, it is easier to

reach a saturation level even at lower superficial air velocity.

4.3.4 Plenum chamber pressure

For a vent air-gravity conveying system, the plenum chamber pressure equals to the total

pressure drop at cross-section of the channel as shown in Figure 4.6, that is, 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 =

∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 + ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 + 𝑃𝑡𝑜𝑝 . Where 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 is the gauge pressure at the plenum chamber,

𝑃𝑡𝑜𝑝 is the gauge pressure at the top of the channel, here 𝑃𝑡𝑜𝑝 = 0 as it is vented to atmosphere,

∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 is the pressure drop when air flows through the porous membrane and ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 is the

material layer pressure drop.

0

0.5

1

1.5

2

2.5

2 3 4 5 6

Mat

eria

l m

ass

flo

w r

ate

(kg/s

)

Inclination angle (degree)

96 mm/s

106 mm/s

127 mm/s

84

Figure 4.6 Relationship between pressures cross the conveying channel

The plenum chamber pressure is plotted in Figure 4.7 against the operating air velocity at the

material mass flow rate around 1.70 kg/s. According to the testing results from pressure

transducers, each chamber pressure is averaged by pressure measured at five locations along the

channel as there is no significant change on the chamber pressure at every air velocity.

For air flow only, it is observed that the chamber pressure exists in a liner relation when

increasing the superficial air velocity. That is to say the plenum pressure is directly dependent

on the supply of air flow rate without material in the conveying channel. The pressure drop

∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 at an air only condition can be considered as the pressure for the porous membrane

under each air velocity. When material flows in the conveying channel at a given air velocity,

the chamber pressure is higher than the air only condition. The difference between the chamber

pressure at a given velocity with or without material flow is the pressure drop for the material

layer. The value of this pressure drop is dependent on bed thickness and the bulk density of

aerated material. Higher bulk density and bed thickness will result in a higher value of pressure

drop.

85

Figure 4.7 Variation of plenum chamber pressure with different superficial air velocity (Vent)

4.3.5 Pressure drop at material layer

According to the relationship between pressures across the conveying channel (Figure 4.6), for a

vent system, ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 − 𝑃𝑡𝑜𝑝 − ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 = 𝐷𝑃 − ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 . DP is the pressure

drop between plenum chamber and the top of the channel, ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 can be measured under the

condition of air flow only. As a result, ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙, which is the material pressure drop during

testing can be obtained.

Figure 4.8 shows the pressure drop on the material layer at a location of 5 m with different

superficial air velocities. The pressure drop decrease from 700 Pa to 180 Pa with the increase of

superficial air velocity. This is caused by the lower bed height at higher airflow rate as the

pressure drop for the material layer mainly depends on its height. An increase in the superficial

air velocity was found to cause a decrease in the bed height, as shown in the figure below. The

reason for this is that the flow ability along the conveying channel was improved under a higher

superficial air velocity, material will flow quicker when compare with the condition of lower

superficial air velocity. However, at a velocity above 106 mm/s, a rapid steady flow was

established, and a further increase in the superficial air velocity had little effect on the bed

height, which remained almost constant. This is because once the well fluidisation state formed,

the spare air from bottom will vent to the vent system, so that after reaching its fluidisation

condition, increasing the superficial velocity will no longer change the bed height.

1.68 kg/s1.72 kg/s

1.76 kg/s

1.70 kg/s

1.70 kg/s

0

1

2

3

4

5

6

7

70 80 90 100 110 120 130 140 150

Pre

ssu

re (

kP

a)


With sand mass flow

Air flow only

86

Figure 4.8 Pressure drop at material layer at location of 5 m with different superficial air

velocities (85 mm/s, 96 mm/s, 106 mm/s and 127 mm/s) at the mass flow rate of 0.30 kg/s

(Vent)

4.3.6 Bed height along the channel

The bed heights along the conveying channel with different superficial air velocity are plotted in

Figure 4.9. It is observed that the bed heights decrease with increasing distance from the inlet

section at every air velocity. It is because the obvious acceleration range at the location is close

to the channel inlet. Since the bed viscosity decreases with reduction in the bed height (Botterill

and Bessant 1976), the flow is accelerating even more. This results in a lower material bed

height at the downstream location and a higher bed height at upstream location. The decreasing

trend along the channel slowly reduced at higher (117 and 127 mm/s) superficial air velocity,

which is because the steady flow state can be easily be formed at higher air velocity.

It is also observed that the increase in the airflow rate decreases the material bed heights at

every location along the channel. This is because that the material conveying velocity is higher

at a higher superficial air velocity. As a result, the bed heights at any location reduced.

However, the reduction of material bed heights become not obvious when the airflow increases

to 117 mm/s. This could cause a change in the character of material flow which occurred and

transferred to fluidised flow condition. The flow is independent of fluidising air velocity as it

has little effect on the viscosity, and the steady flow bed heights will not change anymore.

0

20

40

60

80

100

0

200

400

600

800

1000

70 80 90 100 110 120 130 140

Mat

eria

l b

ed h

eigh

t (m

m)

Pre

ssu

re d

rop

(P

a)


Material layer Pressure drop

Material bed height

87

Figure 4.9 Bed height along the channel with different superficial air velocities at material mass

flow rate of 0.3 kg/s (Vent)

4.4 Fluidised conveying of sand at non-vent flow condition

The fluidised flow of sand at the condition of non-vent are discussed here, including flow

visualization, effect of air flow rate and inclination angle on sand mass flow rate, plenum

chamber pressure, pressure at the top of the conveying channel, pressure drop at material layer

and bed height along the channel.

4.4.1 Flow visualisation

In this section, a different material flow phenomenon was observed during the testing. Similar

to vent flow of sand, the non-vent of sand flow had the flow behaviour of a stratified bed like

the flow modes in Table 4.5. Over the range of air flow rate investigated, sand showed pulsatory

movement at lower air velocity while fluidised flow appeared at air velocity around minimum

fluidisation velocity. A layer of air carrying insignificant materials concentration flows above

the moving material bed existed at the superficial air velocity larger than minimum fluidisation

velocity.

Specifically, an initial increase in the air flow rate causes no movement of the material bed

(Mode 1), and the material bed height will not change. Further increase in air flow rate, the

material bed height along the conveying channel in all the cases (Mode 2) is built up and

material is in an expend state. The accumulation of sand in the conveying channel existed for a

certain period of time, followed by sudden pulsatory flow of sand. This is because the yield

shear stress on the material has to be exceeded for the bed to flow. After that, a non-pulsatory

movement of partial material bed at the top layer of the bed (Mode 3) is observed when

0

20

40

60

80

100

0 1 2 3 4 5 6

Mat

eria

l b

ed h

eigh

t (m

m)

Location along channel length (m)

85 mm/s

96 mm/s

106 mm/s

117 mm/s

128 mm/s

88

increasing the air velocity. With a further increase in air flow rate, a well fluidised state of sand

formed and the total material bed slid down through the channel (Mode 4). But when the air

velocity increases even more, air bubbles will occur and come out of the sliding material bed as

the excess air in the channel. This characteristic is also accompanied with vigorous particle

agitation. Thereafter the flow remains in Mode 5 with an increasing airflow rate.

4.4.2 Effect of air flow rate on sand mass flow rate

Based on the visualization observed, the air flow rate significantly affects the flow behaviours

of air-gravity conveying and the effect of this parameter is discussed below.

Figure 4.10 shows the mass flow rate of sand with the increasing of superficial air velocity at a

full supply valve opening. It is found that the increase in the air velocity increases the material

mass flow rate of the air-gravity conveying system initially and thereafter is steady to a

saturation level at higher airflow rate. Combined with the phenomenon observed during the

conveying test, the flow behaviour can be divided into four sections: no flow, pulsatory

movement, fluidised flow, and dilute flow. At a velocity lower than 36 mm/s, no flow is

observed. For an air velocity between 36 mm/s and 106 mm/s, the sand mass flow rate increases

with an increase in air velocity. Above 106 mm/s, the sand flow rate reaches a steady state

which is independent of superficial air velocity. Similar behaviour was observed by Singh et al.

(1978) when testing sand in the Pneu-slide. For other angles of inclination (1o, 2o and 3o), the

critical air velocity (the air velocity above which no effect of the fluidisation level on the sand

mass flow rate is felt) appeared to be independent of inclination angle.

The initial steep increase in the material mass flow rate is due to the two reasons caused by

airflow rate (Gupta et al. 2006). Firstly, after the start of the material flow at an airflow rate

lower than the minimum fluidisation velocity, the distance between particles increases which

enlarges the bed voidage during the airflow rate increasing process. The viscosity of the

conveying bed decreased correspondingly (Botterill et al., 1979) which contributed more to the

flow bed acceleration. Secondly, the increased airflow rate increases the shear stress acting on

the upper surface of moving material bed. As for the mass flow rate saturation level being

obtained at all the high airflow rate operating situations under a given a valve opening, it is

because of the constraint posed by the inlet section with the knife gate valve opening limit. At

this stage, the carriage potential of the airflow rate is under-utilized due to unavailability of

sufficient material falling from the hopper to conveying channel. This phenomenon is also

confirmed by the observed decrease in the material bed depth at higher airflow rates and will be

discussed in the latter section. Therefore, the carriage potential of the airflow rate is more

effectively utilized at the initial stage than that at later stage. For the experimental case here, 106

mm/s is the optimum operating airflow rate which can reach the maximum capacity with energy

89

saving. Above the conveying condition of 128 mm/s (minimum fluidisation velocity in the

fluidisation test), a dilute pneumatic conveying stage can be observed. It seems obvious that the

excessive increase in the airflow rate will transform flow modes in the channel to undergo a

sequential change to finally reach the dilute pneumatic conveying. However, the studies could

not be carried out at such high airflow rates due to the dusty problem at high airflow.

Figure 4.10 Effect of the superficial air velocity on the sand mass flow rate (Non-vent)

4.4.3 Effect of inclination angle on sand mass flow rate

It is observed in Figure 4.11 that for a given airflow rate, there is a mild increase in the sand

mass flow rate from 2.5o to 5o. This is due to the fact that in the downward movement of the

material, gravity overrides the shear force to convey the material. The gravity component

corresponding to the 2.5o conveyor inclination already can effectively sweep all material falling

into the conveying channel. Further increase in the inclination angle up to 5o can cause an

increase in the material mass flow rate due to the larger gravity force component acting on the

conveying material.

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120 140 160

Mat

eria

l m

ass

flo

w r

ate

(kg/s

)


No flow

Pulsatory movement

Fluidised flow

Transition

(pulsatory/non-pulsatory)

90

Figure 4.11 Variation of sand mass flow rate with channel inclination angle for different

superficial air velocities (Non-vent)

Figure 4.11 also shows that, for a given inclination angle, the increase in the superficial air

velocity increases the sand mass flow rate. However, for inclinations of 3.75o and 5o, the sand

mass flow rate increases first and thereafter slows to a saturation level at higher air flow rate.

This is caused by the sand mass flow rate remaining the same at all the operating superficial air

velocities due to the constraint posed by the knife gate valve opening.


For a non-vent air-gravity conveying system, the pressure drop across the conveying channel

can be seen in Figure 4.6. The plenum chamber pressure is equal to the total pressure drop at the

cross-section of the channel, that is, 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 = ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 + ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 + 𝑃𝑡𝑜𝑝. Where 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟

is the gauge pressure at the plenum chamber, 𝑃𝑡𝑜𝑝 is the gauge pressure at the top of the

channel, ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 is the pressure drop when air flows through the porous membrane and

∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 is the material layer pressure drop.

The plenum chamber pressure is plotted in Figure 4.12 against the operating air velocity at

different material mass flow rates. Here each chamber pressure is averaged by pressure

measured at five locations along the channel as there is no significant change on chamber

pressure at every airflow rate. This is because the chamber is continuous and an air filled this

area so that locations along the channel do not affect the chamber pressure much.

0

0.5

1

1.5

2

2.5

2 3 4 5 6

Mat

eria

l m

ass

flo

w r

ate

(kg/s

)

Inclination angle (degree)

96 mm/s

106 mm/s

127 mm/s

91

For air flow only, it is observed that the chamber pressure exists in a liner relation for different

superficial air velocities which means that the plenum pressure is directly dependent on the

supply of air flow rate without material in the conveying channel. The pressure drop ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 at

an air only condition can be considered as the ability of pressure resistance under different air

velocities. When the air-gravity conveyor is running with material flow, the chamber pressure is

higher than the air only condition, which means that there is a material layer pressure drop in

this system. This pressure drop is dependent on bed thickness and the bulk density of aerated

material.

For a given air velocity, chamber pressure for a large mass flow rate is greater than the small

mass flow rate. The chamber pressure gradient increases with the increase in the sand mass flow

gradient. It is because a large sand mass flow rate will have greater air flow resistance offered

on to the airflow by the material bed in the conveying channel through which it comes up.

Figure 4.12 Variation of plenum chamber pressure with different superficial air velocity at

different sand mass flow rate (Non-vent)

4.4.5 Pressure at the top of the conveying channel

Figure 4.13 presents the pressure at the top of the conveying channel along the channel length

at different material mass flow rates. The value of pressure at the top of the conveying channel

is calculated by the chamber pressure and pressure drop between the chamber and the top wall.

For a given superficial air velocity, pressure at the top of the conveying channel at five locations

shows a gradually reduced trend. The existence of pressure drop along the channel validates

that, in a non-vent air-gravity flow, the driving force which causes the flow of material is not

0

1

2

3

4

5

6

7

60 70 80 90 100 110 120

Pre

ssure

(kP

a)


Sand mass flow rate (1.72 kg/s)

Sand mass flow rate (0.3 kg/s)

Air flow only

92

only the gravitational force at the flow direction but also the pressure drop along the channel.

Larger sand mass flow rates have greater top wall pressures. The pressure drops for these three

cases are 22.83 Pa/m (0.27 kg/s), 27.48 Pa/m (0.38 kg/s) and 32.78 Pa/m (2.06 kg/s). Top wall

pressure drop along the channel will be used in the future non-vent air-gravity conveying model

validation.

Figure 4.13 Pressure at the top of conveying channel along the channel length with different

sand mass flow rates under superficial air velocity of 106 mm/s (Non-vent)


According to the relationship between pressures across the conveying channel (Figure 4.6),

𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 = ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 + ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 + 𝑃𝑡𝑜𝑝 , that is to say, ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 = 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 − 𝑃𝑡𝑜𝑝 −

∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 = 𝐷𝑃 − ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟. DP is the pressure drop between the plenum chamber and the top of

the channel, and ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 can be obtained under the condition of air flow only. As a result,

∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙, which is the material pressure drop during testing, can be obtained.

Figure 4.14 shows the pressure drop on the material layer at a location of 5 m with different

superficial air velocities. The pressure drop decreases with the increase of superficial air

velocity first and then decreases slowly. This pressure drop for the conveying material layer is

mainly dependent on the material bed height and its bulk density. As the bulk density does not

change much at a fluidisation state, the pressure difference is caused by the bed height of

fluidised material. Correspondingly, the material bed height is higher at lower superficial air

velocity, and then the bed heights change little at higher superficial velocity. The bed height

change trend is quiet similar to the pressure variation trend. The reason for the change of bed

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6

Pre

ssu

re (

kP

a)


0.27 kg/s

0.38 kg/s

2.06 kg/s

93

height is because at the same mass flow rate, higher superficial air velocity will fluidise the

material better and increase the flow ability of material along the channel, which means that the

material flow velocity along the channel is higher at large superficial air velocity. Moreover,

after reaching its fluidisation, increasing the superficial velocity will no longer change the bed

height.

Figure 4.14 Pressure drop at material layer at location of 5 m with different superficial air

velocities (72 mm/s, 96 mm/s, 106 mm/s and 127 mm/s) at the mass flow rate of 0.30 kg/s

(Non-vent)

4.4.7 Bed height along the channel

In order to investigate the variation of material bed height along the conveying channel with

different operating airflow rates, the bed height was recorded by the high speed camera and then

the bed heights could be obtained by an image analysis method. Figure 4.15 gives the bed

heights at three locations along the conveying channel under different airflow supplies. It is

observed that under a given valve opening, the increase in the airflow rate decreases the material

bed heights at every location along the channel. This is because the higher shear stress on the

top surface of the conveying material developed by the higher air velocity sweeps more material

out of the channel. As a result, the bed heights at any location are reduced. However, the

reduction of material bed heights become not obvious when the airflow increases to 127 mm/s.

This could be caused by the change in the character of material flow occurring and being

transferred to fluidised flow. The flow is independent of fluidising air velocity as it has little

effect on the viscosity. After that, the flow behaves more like a dilute flow at the condition of

0

20

40

60

80

100

0

200

400

600

800

1000

60 70 80 90 100 110 120 130 140

Mat

eria

l b

ed h

eigh

t (m

m)

Pre

ssu

re d

rop

(P

a)


Material layer Pressure drop

Material bed height

94

large airflow rate (Latkovic and Levy 1991). Uniform distribution of fine particles of sand with

rapid conveying velocity is exhibited in the upper channel.

It is also clear from the figure that the bed heights decrease with increasing distance from the

inlet section. It is because that the magnitude of the shear stress is caused due to the airflow

increases along the channel length. This results in an increasing shear force, which then acts on

the top surface of material bed along the conveying direction and causes the material to

accelerate. Since the bed viscosity is also decreasing with a reduction in the bed height (Botterill

and Bessant 1976), the flow accelerates even more. This results in the lower material bed height

at the downstream location and a higher bed height at an upstream location.

Figure 4.15 Bed height along the channel with different superficial air velocity (Non-vent)

4.5 Fluidised conveying of flyash at vent flow condition

Fluidised conveying of flyash at a vent flow condition is presented in this section. Here the flow

visualization, effect of air flow rate and inclination angle on flyash mass flow rate, plenum

chamber pressure, pressure drop at material layer and effect of mass flow rate on bed height are

discussed below.


The vent flyash flow characteristics can be observed during the conveying testing. During an

initial increase in superficial air velocity, flyash can drop down from the supply hopper freely

under gravity and the first observation window will be filled up with flyash. Flyash cannot flow

under this superficial air velocity. Further increase in air flow rate builds up the material bed

0

20

40

60

80

100

0 1 2 3 4 5 6

Mat

eria

l bed

hei

ght

(mm

)


72 mm/s

85 mm/s

96 mm/s

106 mm/s

127 mm/s

95

height along the conveying channel, pulsatory flow of flyash can be found with the

accumulation of flyash in the conveying channel for a certain period of time. After that,

continual increase of the superficial air velocity will cause a non-pulsatory movement of

material bed and then a well fluidised state of flyash will be formed and the total material bed

will slide down through the channel like fluid. However, when the air velocity increases even

more, more bubbles will occur and come out of the sliding material bed, flyash in the channel

like conveyed in dilute phase flow, flyash will shelter the observation as the dilute fine flyash

conveying at a high velocity.

4.5.2 Effect of air flow rate on flyash mass flow rate

Based on the visualization observed, the superficial air velocity significantly affects the flow

behaviours of air-gravity conveyance and the effect of this parameter is discussed in this

section. Figure 4.16 presents the mass flow rate of flyash with the increasing of superficial air

velocity. An initial increase of air velocity cannot convey a full layer of static flyash drop down

from the supply hopper. Once the superficial air velocity reached to 29.3 mm/s, flaysh starts to

flow along the channel. This is because of the poor flow ability of flyash and its slow de-

aeration rate property, so flyash behaves more like a constant layer and without movement

under low air velocity, while air is enough to fluidise the flyash and it behaves like fluid and

then flows quickly along the conveying channel. Under the velocity of 29.3 mm/s, flyash can

also flow if the flyash in the supply hopper was initially fluidised by injecting some air at the

bottom of hopper to gain the property of fluid. That’s the reason flyash will flow quickly at the

velocity much smaller the minimum fluidised velocity at vent conveying system like in non-

vent conveying system.

During flyash conveying, the supply hopper feed rate was not easy to control as a constant

because of the poor flow ability of flyash. Flyash was difficult to drop down or it demonstrated

a phenomenon that a large amount of flyash collapsed suddenly from the hopper. We made use

of the slow de-aeration rate of flyash and added a little bit of air into the bottom of the hopper to

fluidise the flyash, which endowed the fluid property to flyash. Then it could flow fluently to

the conveying channel, and even be conveyed at a velocity much lower than the minimum

superficial velocity. Pulsatory and non-pulsatory movement of flyash could be observed under

the velocity of 29.3 mm/s. Above 29.3 mm/s, a well fluidised flyash flow occurred during

testing with a constant flyash material flow bed. It was found that both low and high air velocity

can reach various flyash mass flow rates.

96

Figure 4.16 Effect of the superficial air velocity on the flyash mass flow rate (Vent)

4.5.3 Effect of inclination angle on flyash mass flow rate

The effect of the flyash bed height in relation to the material mass flow rate is given in Figure

4.17 at three conveyor inclinations at the superficial air velocity of 42.6 mm/s. The flyash bed

heights were fitted to examine the correlation of mass flow rate. It reveals the increasing trend

of material bed height with increasing mass flow rate. The reason for the increase in the bed

height with increased mass flow rate is attributed to the same fluidised condition at a given

airflow velocity and inclination angle. Therefore, a linear line was applied to fit the testing data

and equations were obtained in the figure. It also shows that, for a given mass flow rate, there is

a decrease in bed height from 2.5o to 5o. The reason for this change in bed height lies in the

difference of magnitude of gravity force, once the shear stress is equal to the streamwise

gravitational component of the materials’ weight, the steady flow will be formed. Thus, it is

easy for the 2.5o conveyor to form a steady flow and the steady conveying velocity is lower than

the case of 5o.

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60

Mat

eria

l m

ass

flo

w r

ate

(kg/s

)


Vmf

Fluidised flow

No flow

Pulsatory/non-

pulsatory

97

Figure 4.17 Variation of flyash bed height with its mass flow rate at different inclination angle

(Vent)


For a vent flyash air-gravity conveying system, the pressure drop across the conveying channel

can be seen in Figure 4.6. The plenum chamber pressure equals to the total pressure drop at



channel, here 𝑃𝑡𝑜𝑝 = 0 as it is vented to atmosphere, ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 is the pressure drop when air

flows through the porous membrane and ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 is the material layer pressure drop.

The plenum chamber pressure is plotted in Figure 4.18 against the flyash mass flow rate at

different superficial air velocity. Here each chamber pressure is averaged by pressure measured

at five locations along the channel as no significant change was found along the channel

chamber. This is because the chamber is continuous and air filled this area so that locations

along the channel do not affect the chamber pressure much.

Before each test, air only testing was conducted to obtain the pressure drop on porous

membrane without a flyash flow above it. For air flow only, it is observed that the chamber

pressure exists in an increase trend with increasing superficial air velocity which means that the

plenum pressure is directly dependent on the supply of the air flow rate without material in the

conveying channel. The pressure drop ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 at an air only condition can be considered as the

y = 3.257x + 30.177

y = 5.3423x + 18.887

y = 6.6868x + 11.957

0

20

40

60

80

100

0 1 2 3 4 5 6

Hei

gh

t (m

m)

Material mass flow rate (kg/s)

2.5 degree

3.75 degree

5 degree

98

ability of pressure resistance under a different air velocity. When the air-gravity conveyor is

running with a flyash flow above it, the chamber pressure is higher than the air only condition,

which means that there is a material layer pressure drop in this system. This pressure drop is

dependent on flyash bed thickness and fluidisation condition of the aerated material.

For a given air velocity, chamber pressure for large mass flow rate is greater than the small mass

flow rate. A linear relationship can be found under a given superficial air velocity with different

flyash mass flow rates. This indicates that at each flow case flyash is in a homogeneous state,

which will result in an even increase in flyash mass flow rate.

The pressure increase rate is tabulated in Table 4.6. The chamber pressure increase rate for the

range of superficial air velocity do not change much, all the value is varied between 0.04 and

0.05 kPa·s/kg. This means that at the vent flow condition, flyash can form a fluidised flow at

each given superficial velocity and the superfluous air will vent to the vent system.


different flyash mass flow rate (Vent)

y = 0.0345x + 0.4628

y = 0.0541x + 0.9

y = 0.0513x + 1.2966

y = 0.0401x + 1.6692

y = 0.0336x + 1.8126

y = 0.0514x + 2.3302

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10

Pre

ssure

(kP

a)

Flyash mass flow rate (kg/s)

13.7 mm/s

24.8 mm/s

36.0 mm/s

42.6 mm/s

47.1 mm/s

58.0 mm/s

99

Table 4.6 Pressure increase rate at different superficial air velocity

Superficial air velocity

(m/s)

Pressure increase rate

(kPa·s/kg)

13.7 0.0345

24.8 0.0541

36.0 0.0513

42.6 0.0401

47.1 0.0336

58.0 0.0514


Based on the relationship between pressures across the conveying channel (Figure 4.6),


∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 = 𝐷𝑃 − ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟. DP is the pressure drop between plenum chamber and the top of the

channel, ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 can be obtained under the condition of air flow only. As a result, ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙,

the material pressure drop during testing can be obtained.

Figure 4.19 gives the pressure drop on the material layer at a location along the channel length

with a different flyash mass flow rate at superficial air velocity of 42.6 mm/s. The pressure drop

for flyash material layer experiences an increase at the first meter near the flyash inlet section,

then pressure drops slightly along the conveying channel. The pressure drop is not obvious and

the pressure along the channel can even be considered as constant. For the mass flow rate of

4.26 kg/s, the pressure at the last four meters keeps constant which means that the steady flow is

formed and a constant flow bed height can be seen at this condition. Meanwhile, the material

layer pressure drop increase with the increase of flyash mass flow rate, which is caused by the

higher bed height in the conveying channel.

100

Figure 4.19 Pressure drop at material layer at location along channel length with different flyash

mass flow rates at a superficial air velocity of 42.6 mm/s (Vent)

4.5.6 Effect of mass flow rate on bed height around fluidised velocity

The variation of the flyash bed height with the mass flow rate has been plotted in Figure 4.20

for three different superficial air velocities. It is observed that under a given inclination angle

and superficial air velocity, the increase in the flyash mass flow rate increases the steady flow

bed heights along the channel. This is because the same fluidisation of flyash under the same

superficial air velocity, the greater mass flow rate of flyash will lead to a higher bed height. It is

also observed that a linear correlation can be found by fitting the bed height scatters, the

detailed fitting formula can be seen in Figure 4.20. For a given mass flow rate, the bed heights

increase with the increase of airflow rate, especially for the condition of higher air velocity. This

happens due to the different fluidisation behaviour at different airflow rates for this vent air-

gravity conveying system. Obviously, it is easy to blow the flaysh up at a higher air velocity.

Therefore, the increase of bed height at higher air velocity is larger than the lower air velocity.

For vent flow system, once the well-fluidised condition formed during the conveying process,

the excessive air will go out from the up part of conveying material, not behave like another

conveying media to transport the material. This upcoming air will inflate the flyash which will

then increase the steady flow bed height of conveying layer. This is quite different from the

non-vent system, as the upcoming air has the function of material conveying, which will be

discussed in the following section.

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6

Pre

ssu

re (

kP

a)


0.75 kg/s

1.41 kg/s

3.45 kg/s

4.26 kg/s

101

Figure 4.20 Variation of flyash bed height with its mass flow rate at different superficial air

velocity (Vent)

4.6 Fluidised conveying of flyash at non-vent flow condition

Fluidised conveying of flyash in a non-vent flow condition is discussed in this section.

Following are the flow visualization, effect of air flow rate and inclination angle on flyash mass

flow rate, plenum chamber pressure, pressure drop at material layer and effect of mass flow rate

on bed height.


During the air-gravity conveying testing on flyash, different phenomenon can be observed

through the observation windows at four locations along the channel. After starting the test,

flyash can drop down freely under gravity from the supply hopper and fill up the first

observation window at the channel inlet under an initial increase in superficial air velocity.

There is no material flow along the channel. Further increase in air flow rate builds up the

material bed height during flyash conveying. Pulsatory flow of flyash can be found after the

accumulation of flyash in the conveying channel with a period of time. After that, continually

increasing the superficial air velocity will cause a non-pulsatory movement of material bed with

a slowly conveying velocity. Further increase in air velocity, a well fluidised state of flyash is

formed and the total material bed will slide down through the channel like water. However,

when the air velocity increases even more, more bubbles will occur and come out of the sliding

y = 7.9738x + 8.1735

y = 7.0652x + 10.434y = 7.6409x + 10.435

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

0 1 2 3 4 5 6

Hei

gh

t (m

m)


36.0 mm/s

42.6 mm/s

58.0 mm/s

102

material bed, flyash in the channel will behave like a diluted flow and the fine flyash will cover

all the observation window.

4.6.2 Effect of air flow rate on flyash mass flow rate

According to the visualization observed, the superficial air velocity significantly affects the flow

behaviours of air-gravity conveying and the effect of this parameter is discussed below. Figure

4.21 gives the mass flow rate of flyash with the increasing of superficial air velocity. An initial

increase of air velocity was tested for a full layer of static flyash drop down from the supply

hopper. The flyash will not flow after the first inlet of air, once the superficial air velocity

reached to 29.3 mm/s, flaysh will start to flow along the channel. As the poor flow ability of

flyash and its air retain property, flyash behave more like a constant layer and without

movement under low air velocity, while air is enough to fluidise the flyash it behaves like water

and can flow quickly along the channel. Under the velocity of 29.3 mm/s, flyash can also flow if

it is fluidised at the hopper with the property of fluid. That’s why flyash will flow quickly at the

velocity much smaller the minimum fluidised velocity. Sand tested above did not behave like

this, it will not flow until the material is well fluidised at a velocity near the minimum fluidised

velocity because of its higher air permeability and quicker de-aeration rate.

During testing on flyash, the supply hopper feed rate was difficult to control because of the poor

flow ability of flyash. Flyash will drop down with a large amount of material or without

material falling as happened during testing. To solve this problem, an initial air inlet to the

bottom of supply hopper was used to fluidise the flyash first to make it flow fluently. With this

method, flyash can be conveyed at a velocity much lower than the minimum superficial

velocity. Pulsatory and non-pulsatory movement of flyash can be observed under the velocity of

29.3 mm/s. At the velocity above 29.3 mm/s, well fluidised flyash flow occured during testing

with a constant flow bed height and fluid flow of flyash was found along the channel. Both low

and high air velocities can reach various flyash mass flow rates from low to high.

103

Figure 4.21 Effect of the superficial air velocity on the flyash mass flow rate (Non-vent)

4.6.3 Effect of inclination angle on flyash mass flow rate

The results of flyash bed height with a mass flow rate under different inclination angles were

plotted in Figure 4.22 at the air velocity of 36 mm/s. For a given inclination angle, the data were

fitted in the figure below to examine the correlations of bed height with the mass flow rate, and

a linear line was applied to fit the testing data and the following equation was obtained. This

was because once the fluidised velocity and inclination angle were given, fluidised flyash could

flow like water the fluidised state of flyash will be fromed as well. As a result, the bed height of

airslide flow would then increased linearly with the increase of mass flow rate. Also, it could be

seen in Figure 4.22 that the bed height was higher at lower inclination (2.5o), especially for the

mass flow rate smaller than 2 kg/s. This was caused by the lower gravitational force when the

inclination close to horizental. Because at this condition, it was easier to form a steady flow

velocity. Therefore, the bed height at 2.5o is higher than the bed height at 5o, which is caused by

the lower steady flow velocity at 2.5o.

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60

Mat

eria

l m

ass

flo

w r

ate

(kg/s

)


Vmf

Fluidised flow

No flow

Pulsatory/non-

pulsatory

104

Figure 4.22 Variation of flyash bed height with its mass flow rate for different inclination angle

(Non-vent)


For a non-vent air-gravity conveying system, the pressure drop across the conveying channel

can be seen in Figure 4.6. The plenum chamber pressure equals to the total pressure drop at



channel, ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 is the pressure drop when air flows through the porous membrane and

∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 is the material layer pressure drop.

The plenum chamber pressure is plotted in Figure 4.23 against the flyash mass flow rate at

different operating air velocity. Here each chamber pressure is averaged by pressure measured

at five locations along the channel as there is no significant change on the chamber pressure at

every testing. This is because that the chamber is continuous and air filled this area so that

locations along the channel do not affect the chamber pressure much.

Before each test, air only condition was applied to get the pressure drop on porous membrane

without flyash flow above it. For air flow only, it is observed that the chamber pressure exists a

liner relation for different superficial air velocity which means that the plenum pressure is

directly dependent on the supply of the air flow rate without material in the conveying channel.

The pressure drop ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 at an air only condition could be considered as the ability of pressure

y = 4.7346x + 22.033

y = 5.9577x + 19.482

y = 8.385x + 8.6846

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5

Hei

gh

t (m

m)

Material mass flow rate (kg/s)

2.5 degree

3.75 degree

5 degree

105

resistance under a different air velocity. When the air-gravity conveyor is running with material

flow, the chamber pressure is higher than the air only condition, which means that there is a

material layer pressure drop in this system. This pressure drop is dependent on bed thickness

and the bulk density of aerated material. For a given air velocity, the chamber pressure increase

with the increase of flyash mass flow rate and almost keep a liner increase for increasing mass

flow rate. This means that at each flow case flyash is on homogeneous state and behaves like a

fluid.

For a given flyash mass flow rate, the chamber pressure at a higher superficial velocity is

greater than a lower air velocity, this is because much more air come into the plenum chamber

will then definitely cause a higher chamber pressure. Also, the chamber pressure increase rate

increases with the increase in the superficial air velocity as shown in Table 4.7


different flyash mass flow rate (Non-vent)

Table 4.7 Pressure increase rate at different superficial air velocity

Superficial air velocity

(m/s)

Pressure increase rate

(kPa·s/kg)

13.7 0.0397

24.8 0.0995

y = 0.0397x + 0.4764

y = 0.0995x + 1.0107

y = 0.2306x + 1.3502

y = 0.2834x + 1.827

y = 0.3212x + 1.95

y = 0.3241x + 2.7073

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4 5 6 7 8

Pre

ssure

(kP

a)


13.7 mm/s

24.8 mm/s

36.0 mm/s

42.6 mm/s

47.1 mm/s

58.0 mm/s

106

36.0 0.2306

42.6 0.2834

47.1 0.3212

58.0 0.3241

4.6.5 Pressure at the top of the conveying channel

Figure 4.24 shows the pressure at the top of the conveying channel along the channel length at

different material mass flow rates. The value of pressure at the top of the conveying channel is

calculated by the chamber pressure and pressure drop between the chamber and the top wall.

For a given superficial air velocity, pressure at the top of the conveying channel at five locations

almost kept a constant when the flow become steady, which means a steady flow was formed

during the flyash transporting. During the testing on sand, there could be seen a slightly pressure

drop along the conveying channel. The pressure drop along the channel became negligible

because of the air pressure needed for flyash conveying was much lower than sand, which

results in no difference at the top of the channel. However, the existence air pressure at the top

of the channel will perform an additional force to assist the flyash flow accompany with the

gravitational force at the flow direction. Larger flyash mass flow rates have greater top wall

pressures, this is mostly caused by the increase in the chamber pressure because more material

is being conveyed at the channel.

Figure 4.24 Pressure at the top of conveying channel along channel length with different flyash

mass flow rates under superficial air velocity of 36.0 mm/s (Non-vent)

0

0.3

0.6

0.9

1.2

0 1 2 3 4 5 6

Pre

ssure

(kP

a)


0.29 kg/s

0.67 kg/s

1.48 kg/s

2.15 kg/s

5.41 kg/s

107


Based on the relationship between pressures across the conveying channel (Figure 4.6),


∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 = 𝐷𝑃 − ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟. DP is the pressure drop between plenum chamber and the top of the

channel, ∆𝑃𝑓𝑖𝑙𝑡𝑒𝑟 can be obtained under the condition of air flow only. As a result, ∆𝑃𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙,

which is the material pressure drop during testing can be obtained.

Figure 4.25 presents the pressure drop on the material layer at location along the channel length

with different flyash mass flow rate at superficial air velocity of 36.0 mm/s. As can be seen in

this Figure, the pressure drop for flyash material layer at lower mass flow rate (< 1 kg/s) keeps a

constant along the channel. There is almost no pressure drop along the channel. It is because

that at the lower flyash mass flow rate, the pressure needed to convey the material is low which

will result in the ignorable pressure difference along the channel. While for larger mass flow

rate, a slightly pressure drop can be found along the channel, the pressure drop at the first 2

metres changes remarkable while it becomes stable at the following channel. The material layer

pressure drop increases with the increase of flyash mass flow rate, this is caused by the higher

bed height in the channel.

Figure 4.25 Pressure drop at material layer at location along channel length with different flyash

mass flow rate at superficial air velocity of 36.0 mm/s (Non-vent)

4.6.7 Effect of mass flow rate on bed height around fluidised velocity

In order to investigate the variation of flyash bed height with mass flow rate at different

operating airflow rate, the bed height was recorded by the high speed camera and the bed

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6

Pre

ssure

(kP

a)


0.29 kg/s

0.67 kg/s

1.48 kg/s

2.15 kg/s

5.41 kg/s

108

heights were achieved by an image analysis method. Figure 4.26 gives the bed heights with

increasing mass flow rate under different airflow supply. It is observed that under a given

inclination angle and superficial air velocity, the increase in the flyash mass flow rate increases

the steady flow bed heights along the channel. Even more, a linear correlation can be found by

fitting the bed height scatters. This is because of the same fluidisation of flyash under the same

superficial air velocity. That is to say, the more mass flow rate, the higher bed height. Therefore,

the steady flow bed heights at any location increase.

Figure 4.26 Variation of flyash bed height with its mass flow rate at different superficial air

velocity (Non-vent)

For a given mass flow rate, the bed heights increase with the increase of airflow to a well-

fluidised state and then increase slightly after this superficial air velocity. This happens due to

the different fluidisation behaviour. At the velocity below the well-fluidised velocity the flyash

could slide down along the channel freely but those flyash are not fluidised perfectly, thus more

flyash deposited to the channel bottom and the flow were more like dense phase flow. When the

airflow is sufficient to fluidise the flyash, the flow becomes stable. However, at higher airflow

rate, the bed heights were almost similar with the bed height at the fluidised condition with

slightly bed increase. This is because that the incoming air contributes to the flyash flow rate at

this non-vent flow system. The incoming air should inflate the flyash more in the conveying

channel, but the higher shear stress on the top surface of the conveying material developed by

the higher air velocity and then sweeps more material out of the channel which will reduce the

y = 7.2293x + 6.846

y = 8.385x + 8.6846

y = 9.1434x + 6.4899

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0 1 2 3 4 5 6 7 8

Hei

ght

(mm

)


13.7 mm/s

36.0 mm/s

47.1 mm/s

109

bed height in theory. Therefore, the steady flow bed heights were decided by the incoming air

and the slightly increase of material bed heights become not obvious when the airflow increases

even more. This could cause by the change in the character of material flow occurred and

transferred to a dilute flow at the condition of large airflow rate. The flow was independent of

fluidising air velocity as it had little effect on the viscosity. Uniform distribution of fine parts of

flyash with rapid conveying velocity exhibited in the upper channel.

4.7 Conclusion

The air-gravity conveying test was conducted on sand and flyash, with the material bed height,

material mass flow rate and pressure drop measured and analysed under different conditions of

vent and non-vent flow. According to the experimental procedure and test programme, the

effect of air flow rate and channel inclination on the depth of flowing beds, material mass flow

rate and pressure drop along the channel was investigated and results were discussed.

The flow behaviour was discussed based on the different phenomena observed during the

testing. An initial increase in the air flow rate causes no change of material bed. A further

increase in air flow rate built up the material bed height in all the cases of conveying. The

material flow rate oscillations were observed as accumulation of conveying material in the

conveying channel for a certain period of time, followed by a sudden pulsatory flow of material.

After that, continually increasing the air flow rate will cause a non-pulsatory movement of

partial material bed at the top layer of the bed. The flow bed height decreased and the flow

accelerated after the bed starts to flow. By the further increase in air flow rate, a well fluidised

state of material was formed and the total material bed slid down through the channel. But when

the air velocity increases even more, air bubbles would occur and came out of the sliding

material bed as the excess air in the channel. This characteristic also accompanied with the

vigorous particles agitation, and the upper materials behave more like a dilute flow. Thereafter

the flow remains the same with increasing airflow rate.

It is found that the increase in the air flow rate increases the material mass flow rate of air-

gravity conveying system initially and thereafter becomes steady to a saturation level at higher

airflow rate for sand flow system. It was also found that the bed height along the channel

decreased with increasing air mass flow rate within different solid mass flow rate ranges for

sand and flyash. For a given airflow rate, pressure at the top of the conveying channel at five

locations shows a gradually reduce trend at different air flow rate. The existence of pressure

drop along the channel validates that in a non-vent air-gravity flow, the driving force causing

the flow of material is not only the gravitational force at the flow direction but also the pressure

drop along the channel. In addition, for a given material mass flow rate and inclination angle, it

is observed that the increase in the airflow rate decreases the bed height at a given location.

110

5 CHAPTER 5 Modelling fluidised motion conveying based

on a new continuum approach

5.1 Introduction

This chapter is dedicated to the discussion of the rheology concepts proposed for the study of

fluidised motion conveying. Generally, rheology is the science of deformation and flow. There

is a unique function to illustrate the relationship between an external stress and the resulting

deformation of a material, which defines the rheological characteristics of the aerated fine

powers. These characteristics can either be directly modelled based on the structure and

interactions between molecules within the material, or expressed empirically in terms of

functions. As the flow of material behaves like a fluid, viscosity has been taken from fluid to

explain the behaviour of fluidised particulate solids. However, viscosity is not a property that

can be measured directly, it has to be inferred from measurements of other quantities, which

relate specific components of the shear stress and shear rate. The derivation of the fundamental

conveying models for fluidised motion conveying has been made with an emphasis on its

rheology. In particular, 12 models for vent and non-vent fluidised motion flow based on its

rheology will be put forward in this chapter.

5.1.1 Rheology

The classical definition of rheology is the science of deformation and flow of matter. One

common factor between solids, liquids, and all materials whose behaviour is intermediate

between solid and liquid is that if we apply a stress or load on any of them they will deform or

strain. Various rheological formulations have been developed according to materials’ shear

stress and shear strain relationships. These formulations are characterised into three categories:

solids, fluids and visco-elastic materials.

According to different shear responses to the shear stresses, materials in the solids region are

often classified as rigid solids (Euclidean), linear elastic solids (Hookean) and non-linear elastic

solids. These relationships between shear stresses and shear strains are listed below:

Rigid solids: τ = 0

Linear elastic solids: 𝜏 = 𝐺𝛾 (G = constant, commonly known as the elasticity)

Non-linear elastic solids: 𝜏 = 𝐺(𝛾)𝛾

Materials behaving like fluids are also sub-classified into inviscid fluids (Pascalian), linear

viscous fluids (Newtonian) and non-linear viscous fluids (Non-Newtonian) based on various

characteristics. Likewise, the corresponding shear responses to shear stresses are:

111

Inviscid Fluid: τ = 0

Linear Viscous Fluid: 𝜏 = 𝜇 �̇� (µ = constant, commonly known as the viscosity)

Non-linear Viscous Fluid: 𝜏 = 𝜂(𝛾)̇ �̇�

For materials in the visco-elastic zone, there is a combination of both solid and fluid

characteristics 𝜏 = 𝑓(𝛾, �̇�, … ). As a result, their rheological equation contains both elasticity and

viscosity. However, in which phase the material will predominantly behave will be dependent

on the material types.

In classic fluid mechanics, the viscosity of a fluid is often referred to as the quantitative measure

of its rheology. Therefore, it can either be a linear viscous type (Newtonian), such as water and

lubricant oil, or it may behave as a non-linear viscous type (non-Newtonian), such as slurry.

For a Newtonian fluid, the shear stress has a linear relationship with the shear rate. Newtonian

fluid shear stress is defined as:

𝜏 = 𝜇𝑑𝑣

𝑑𝑦 (5.1)

where 𝜇 is the fluid viscosity, and this represents a linear correlation between the shear stress

and the strain rate for a Newtonian fluid.

For non-Newtonian fluid, like a large number of complex fluids, including those containing

very large molecules (polymers), suspensions or slurries of rigid or deformable solids matter,

the relationship between shear stress and shear rate is not directly proportional, and it cannot be

described by the Newtonian model. Since the ratio of shear stress to shear rate is not a constant,

a function is defined which is called the apparent viscosity or the viscosity function:

𝜂(�̇�) =𝜏

�̇� (5.2)

The apparent viscosity is defined by a relation between shear stress and shear rate which is

similar to the definition of the Newtonian viscosity, and materials that are modelled using Eq.

5.2 are often referred to as generalised Newtonian fluids. Some of the most common non-

Newtonian behaviours of fluids are illustrated in Figure 5.1.

112

Figure 5.1 Common shear stress – shear rate correlations

Many mathematical models have been proposed for non-Newtonian fluids, the best known

being the Bingham plastics and power-law fluids (pseudoplastic and dilatant). Bingham and

Thompson (1928) put forward a model (Eq.(5.3)) that incorporated the yield stress into the

Newtonian model based on the rheological work on mercury:

{�̇� = 0, 𝑖𝑓 𝜏 < 𝜏0𝜏 = 𝜏0 + 𝜇0𝛾,̇ 𝑖𝑓 𝜏 < 𝜏0

(5.3)

Where τ is the yield stress and 𝜇0 is the plastic viscosity. Then, a power-law relationship

(Dogadkin and Pewsner, 1931) between the shear stress and the shear rate was proposed. The

model is able to describe Newtonian, Pseudoplastic and Dilatant types of non-Newtonian fluids

based on the parameter values. This model is widely used because it can be easily fitted to the

experimental data, however, only over a limited range of shear rates:

𝜏 = 𝑚�̇�𝑛−1�̇� (5.4)

where n is the flow index and m is the consistency.

5.1.2 Viscosity of fluidised material

The behaviour of fluidised particulate solids is quite similar to ordinary liquids. To investigate

the resistance of fluidised particles, a property corresponding to viscosity has been taken from

fluid by measuring shear stress and shear rate. As viscosity is not a property that can be

measured directly, it has to be inferred from measurements of other quantities, generally shear

stress and shear rate. A considerable number of investigations have been reported in the

literature, with different approaches to measure the viscosity including rotational viscometers

(Matheson et al., 1949; Kramers, 1951; Diekman and Forsythe, 1953; Furukawa and Ohmao,

1958; Liu and Orr, 1960; Shuster and Haas, 1960; McGuigan, 1974), torsional pendulum

viscometers (Ashwin et al., 1960; Hagyard and Sacerdote, 1966), falling ball methods (Pctors

and Schmidt, 1953; Keuneke, 1965; Leont'ev and Vakhrushev, 1976), channel flow methods

113

(Siemes and Hellmer, 1962; Shinohara et al., 1974; Neuzil and Turcajova, 1977), frequency

methods (Gel'perin et al., 1966) and methods based on observations of bubble behaviour (Grace,

1970).

Among the various methods that have been employed to investigate the correlation between

viscosity and the condition of fluidisation, it appears that a Stormer-type viscometer with

hollow cylindrical rotor is the simplest with which to obtain repeatable results. Actually, there is

little significance in the absolute measurements taken with this instrument, but there is a need to

establish a standard instrument that will allow comparative tests to be made. Results from such

tests may be valuable in predicting the flow behaviour of fluidised solids in fluidised motion

conveyors, and helpful in understanding the correlation between viscosity and the fluidisation

state. Some preliminary investigation of this possibility has previously been undertaken for flow

in horizontal channels (Botterill et al., 1971).

A number of authors (Siemes and Hellmer, 1962; Shinohara et al., 1974; Neuzil and Turcajova,

1977) have taken an opposite approach, that is, they have attempted to use an air-gravity flow

channel to measure the viscosity of fluidised particulate solids. Siemes and Hellmer (1962)

based their approach on a Newtonian fluid model for flowing fluidised sand, in which the

viscosity depends only upon the superficial velocity of the fluidising air. It was found that

viscosity calculated on the basis of total slip at the channel bottom (that is, a two-dimensional

model) showed a steady increase with increasing bed depth and decreasing channel slope.

However, the viscosity showed a sharp decrease for the three-dimensional case with no slip at

the channel bottom. As a result, Siemes and Sellmer concluded that slip in fact occurred in such

a way as to give a constant viscosity at any given fluidising air velocity. Neuzil and Turcajova

(1977) also believed that an air-gravity flow channel provided the most satisfactory method of

investigating the viscosity of fluidised powders. They undertook a novel approach by attempting

to find a correlation between the dependence of the viscosity of a Newtonian liquid on

temperature, and the dependence of the viscosity of fluidised particles on the fluidising air

velocity. Although the particles used in their experiment are too large, around 500 µm

corundum, their experimental results compared quite well with the results of other workers. As

a result, they developed a somewhat complicated expression for viscosity in terms of fluidizing

air velocities. The problem in their expression is that it contained several constants that would

probably be specific to the particulate material they used and their conveying channel.

Shinohara et al. (1974) developed an empirical expression for viscosity in terms of superficial

air velocity, but the expression suffered from the same disadvantage of being specific to a single

material (in that case, fine glass beads). From their model, Shinohara et al. derived an

expression for viscosity in terms of the maximum (free surface) velocity of the flowing bed.

114

From experimental values of this easily measured quantity, they were able to study the

relationship between the viscosity and the fluidising air velocity.

In conclusion, viscosity for fluidised material is an essential parameter governing the flow

behaviour. The correlation between the viscosity of a fluidised material flowing in an inclined

channel and the property measured by more conventional viscometers in stationary fluidised

beds still needs to be further studied. Moreover, a great deal more experimental data will have to

be collected if the viscosity is to be more fully understood.

Based on the above analysis, the implication is that the viscosity function (rheological

characteristics) will vary with the composition of the fluid. In previous pneumatic conveying

studies, the rheological characteristics of aerated powders exhibited particular complexity. For

instance, the aerated powder may behave like a solid material with distinct levels of elastic

forces at zero or low aeration. However, when the aeration levels increase sufficiently with the

increase of fluidising air through the porous layer, the material then starts to lose its elasticity

and changes to a state where the airflow and particulate solids interactions dominate the

rheological behaviour. Because of the different air-solids interactions, materials inside the

pipeline are constantly switching between the different states. These two distinct behaviours are

often observed in fine powder pneumatic conveying. Therefore, once the rheology of the aerated

powder is suitably defined, it can be used to assess the performance of the pneumatic conveying

system.

To study the rheological characteristics of aerated powders, the rheology of air and solids alone

are important. Moreover, the respective air and solids proportions in such a mixture (i.e. bulk

density) is also a dominant factor. The rheological characteristics will be mainly concerned with

the experimental investigation of the rheology for aerated powders. As stated previously, this

chapter is aimed at the derivation of the fundamental conveying models for fluidised motion

conveying in an air-gravity conveyor, with an emphasis on its rheology. This will be achieved

by deriving constitutive equations for the flow system based on continuum fluid mechanics, and

this is discussed below.

5.2 Conservation principles and mechanics in a continuous system

Before modelling the fluidised motion conveying based on the rheology of conveying fluidised

material, the governing equations of the “fluid” flow are essential as the fluid will be regarded

as a continuum, namely, the mass conservation, momentum equations in three dimensions and

the strain tensor theory. Such equations provide fundamental information to understand the flow

mechanism.

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5.2.1 Conservation of mass

The mass conservation principle clearly states that the total mass of the system cannot vary

unless it is added or removed in a confined region. The density at the centre (x, y, z) of a fluid

element is denoted by ρ.

Conservation of mass:

𝜕𝜌

𝜕𝑡+𝜕(𝜌𝑣𝑥)

𝜕𝑥+𝜕(𝜌𝑣𝑦)

𝜕𝑦+𝜕(𝜌𝑣𝑧)

𝜕𝑧= 0 (5.5)

5.2.2 Conservation of momentum

Newton’s second law is utilised to derive the conservation of momentum, and it states that the

rate of change of momentum of a fluid particle equals the sum of the forces on the particle.

Consider that all of the forces acting on the fluid in Cartesian coordinates are contained within

an infinitesimal cubical element of a continuous medium. The state of stress of a fluid element

is defined in terms of the pressure and the nine viscous stress components shown in Figure 5.2.

The pressure, a normal stress denoted by P, 𝜏 is viscous stress. The usual suffix notation 𝜏𝑖𝑗 is

applied to indicate the direction of viscous stresses. The surfaces i and j in 𝜏ij indicate that the

stress component acts in j-direction on a surface normal to i-direction.

Figure 5.2 Stress components on three faces of fluid element

The velocity field can be determined using the analysis by Han (2007), based on a non-

Newtonian fluid in an enclosed rectangular channel with a constant cross-section. For a fully

developed flow, the streamwise velocity 𝑣𝑥 in the axial x-direction depended only on z and y,

and the cross channel velocity components are negligible. Then, Han’s streamwise momentum

equation can be simplified, and the x component of conservation of momentum is given by:

116

𝜌𝐷𝑣𝑥𝐷𝑡

= −𝜕𝑝

𝜕𝑥+𝜕𝜏𝑥𝑥𝜕𝑥

+𝜕𝜏𝑦𝑥

𝜕𝑦+𝜕𝜏𝑧𝑥𝜕𝑧

+ 𝜌g𝑥 (5.6)

5.2.3 Strain theory

The strain means the relative displacement of an infinitesimal body from a reference state.

Generally, this displacement is usually caused by external forces applied to the element.

Therefore, the strain often shows the influence on an element exerted by the external force. The

strain change over time is called the strain rate.

The external force acting on an isotropic element will often result in an isotropic strain rate and

an anisotropic strain rate. An anisotropic stress (usually shear stress) applied on an infinitesimal

isotropic material element leads to a change in shape, which is referred to as a shear strain rate.

Conversely, an isotropic stress (such as static pressure, which is directionally independent),

acting on an infinitesimal isotropic material element, will create a change in volume but no

variation in the shape. This volume change constitutes an isotropic strain rate, which is also

referred to as a volumetric strain rate. An isotropic decrease in volume is known as

compression, while an increase in volume is referred to as dilation.

Herein, the total strain rate of an infinitesimal element at the condition of stress is to be derived.

As can be seen from Figure 5.3, considering the deformation rates along the x direction and the

y direction, the displacement gradient of the element in the x-y plane is simply adding the

change in angle between two originally orthogonal material lines (α and β), that is, when the

element is undergoing the velocity �⃗� = 𝑣𝑥⃗⃗⃗⃗⃗ + 𝑣𝑦⃗⃗⃗⃗⃗ , it can be transformed into a rhombus after

deformation.

Figure 5.3 Strain tensor rate theory of a 2D infinitesimal element under pure deformation

Thus, the infinitesimal strain rate of an element in three-dimensional Cartesian co-ordinates is

defined as:

117

[

�̇�𝑥𝑥 �̇�𝑥𝑦 �̇�𝑥𝑧�̇�𝑦𝑥 �̇�𝑦𝑦 �̇�𝑦𝑧�̇�𝑧𝑥 �̇�𝑧𝑦 �̇�𝑧𝑧

] =

[ 2𝜕𝑣𝑥𝜕𝑥

𝜕𝑣𝑥𝜕𝑦

+𝜕𝑣𝑦

𝜕𝑥

𝜕𝑣𝑥𝜕𝑧

+𝜕𝑣𝑧𝜕𝑥

𝑠𝑦𝑚 2𝜕𝑣𝑦

𝜕𝑦

𝜕𝑣𝑦

𝜕𝑧+𝜕𝑣𝑧𝜕𝑦

𝑠𝑦𝑚 𝑠𝑦𝑚 2𝜕𝑣𝑧𝜕𝑧 ]

(5.7)

This strain shows the total deformation result and contains the volumetric strain tensors

(diagonal parts) and shear strain tensors.

The isotropic part (volumetric strain rate) of the element can be analysed independently. In an

infinitesimal differential element within the continuous medium, it is subjected to a small

change in volume (e.g. dilation) by extension of all sides in a direction normal to all faces. The

dimension of the element can be seen in Figure 5.4, and the velocity of the element is �⃗� = 𝑣𝑥⃗⃗⃗⃗⃗ +

𝑣𝑦⃗⃗⃗⃗⃗ + 𝑣𝑧⃗⃗ ⃗⃗ . The original volume of the element is V.

Figure 5.4 Volumetric strain tensor rate

The total strain tensor is the sum of its isotropic part (volumetric strain rate) and the remaining

anisotropic part (shear strain rate). The anisotropic part can be got by the total deformation

subtracting the mean volumetric deformation in three directions (Bisplinghoff and Mar, 2002),

which is:

[Total strain rate]

= [Total volumetric strain rate]

+ [Total deformation strain rate – Mean volumetric strain rate]

(5.8)

With the shear strain rate and volumetric strain rate readily available, one can correlate the

strain rate and the stress applied on the system, which subsequently produces the rheological

characteristic for such a ‘fluid’. For instance, the rheology state of a Newtonian fluid can be

described using Eq.(5.9):

Rheology state:

118

[

𝜏𝑥𝑥 𝜏𝑥𝑦 𝜏𝑥𝑧𝜏𝑦𝑥 𝜏𝑦𝑦 𝜏𝑦𝑧𝜏𝑧𝑥 𝜏𝑧𝑦 𝜏𝑧𝑧

]

= 𝐾1 (𝜕𝑣𝑥𝜕𝑥

+𝜕𝑣𝑦

𝜕𝑦+𝜕𝑣𝑧𝜕𝑧) ∙ [

1 0 00 1 00 0 1

]

+ 𝜂

{

[ 2𝜕𝑣𝑥𝜕𝑥


+𝜕𝑣𝑦

𝜕𝑥




𝜕𝑦

𝜕𝑣𝑦



−2

3(𝜕𝑣𝑥𝜕𝑥

+𝜕𝑣𝑦

𝜕𝑦+𝜕𝑣𝑧𝜕𝑧) ∙ [

1 0 00 1 00 0 1

]

}

(5.9)

Because the deformation of a Newtonian fluid is pure shear deformation, Eq.(5.9) can be

simplified to Eq.(5.10) only if it considers the flow system in the x and z directions:

[0 0 𝜏𝑥𝑧0 0 0𝜏𝑧𝑥 0 0

] = 𝜂 [0 0


𝑠𝑦𝑚 0 0𝑠𝑦𝑚 𝑠𝑦𝑚 0

] (5.10)

Eq.(5.10) is equivalent to the rheology state equation previously described in Eq.(5.1).

5.3 Constitutive models of fine powder flows in a fluidised motion

conveyor

To develop a fluidised motion conveying model based on the rheology, the rheological

characteristics of the fluid must be initially established. According to previous studies on

fluidised bulk materials (Anjaneyulu and Khakhar, 1995; Chen, 2013), rheological

characteristics have been found to be a combination of a yield stress effect and a shear-thinning

effect. Meanwhile, the specific rheology type for the fine powder flow will be as dependent on

the bulk density as on aeration levels. Accordingly, the rheology state of such a fluid can be

subsequently proposed as:

𝜏 = 𝜏0𝜌 + 𝜂𝜌 ∙ �̇�𝑏𝜌 (𝜌 > 𝜌𝑐 , 0 < 𝑏𝜌 < 1) (5.11)

𝜏 = 𝜂𝜌 ∙ �̇�𝑏𝜌 (𝜌 ≤ 𝜌𝑐) (5.12)

where 𝜏0𝜌 is the yield stress, 𝜂𝜌 ∙ �̇�𝑏𝜌 embodies a power-law correlation which is commonly

used to describe the shear thinning effect, 𝜂𝜌 is consistency index and 𝑏𝜌 is the flow index. As

the properties of aerated materials are mostly dependent on the aeration level of the mixture,

these parameters have unique correlations with the bulk density. Moreover, when the aeration

119

levels increase and the flow transfers to dilute flow, the yield stress parameter will eventually

reduce to zero. According to the above assumptions, the constitutive equations governing the

flow system can be subsequently established. In terms of a pure power-law ‘fluid’ (i.e. no initial

yield value), its flow performance within a channel can be modelled by constitutive equations

discussed in Eq. (5.5) and Eq. (5.6). and its rheology state listed below:

Rheology state

[


]

= 𝐾1 (𝜕𝑣𝑥𝜕𝑥

+𝜕𝑣𝑦

𝜕𝑦+𝜕𝑣𝑧𝜕𝑧) ∙ [

1 0 00 1 00 0 1

]

+ 𝜂𝜌

{

[ 2𝜕𝑣𝑥𝜕𝑥


+𝜕𝑣𝑦

𝜕𝑥




𝜕𝑦

𝜕𝑣𝑦



𝑏𝜌

−2


+𝜕𝑣𝑦

𝜕𝑦+𝜕𝑣𝑧𝜕𝑧) ∙ [

1 0 00 1 00 0 1

]

}

(5.13)

Likewise, for a yield power-law fluid, its flow mechanism inside an air-gravity conveyor is

governed by constitutive equations. The following is its rheology state equation:

Rheology state

120

[


]

= 𝐾1 (𝜕𝑣𝑥𝜕𝑥

+𝜕𝑣𝑦

𝜕𝑦+𝜕𝑣𝑧𝜕𝑧) ∙ [

1 0 00 1 00 0 1

] + 𝜏0𝜌

+ 𝜂𝜌

{

[ 2𝜕𝑣𝑥𝜕𝑥


+𝜕𝑣𝑦

𝜕𝑥




𝜕𝑦

𝜕𝑣𝑦



𝑏𝜌

−2


+𝜕𝑣𝑦

𝜕𝑦+𝜕𝑣𝑧𝜕𝑧) ∙ [

1 0 00 1 00 0 1

]

}

(5.14)

Conveying models of both types of fluids can be obtained by solving all the constitutive

equations simultaneously. Nevertheless, it is not easy to solve the models above, and numerous

researchers have attempted to tackle such a problem with limited success. Due to this inherent

difficulty, these constitutive equations must to be simplified to ease the solving process, and this

is discussed below.

5.3.1 Incompressible approximation

Herein, an incompressible approximation technique is utilised in order to conduct the

simplification process. Though the fine powder fluidised flows showed volumetric variations

during the conveying process, which is mainly caused by the repeated fluidisation and

deaeration mechanism, such volumetric fluctuations are comparatively negligible to the shear

deformation along the channel axial direction (x). This is sensible, particularly when a large

channel length to width ratio is presented, which an air-gravity conveyor can easily satisfy.

Therefore, it is proposed in this thesis to model the fine powder fluidised motion conveying as

incompressible flows by neglecting the volumetric variation.

Under the above assumption, the volumetric parts in the constitutive models for both a power-

law fluid and a yield power-law fluid can be cancelled:

𝜕(𝜌𝑣𝑥)



𝜕𝑧≅ 0 (5.15)

As a result, the constitutive equations for the flow of a power-law fluid can be simplified to the

following by neglecting the volumetric strain and only considering the system in the x and z

dimensions:

121

Mass conservation

𝜕𝜌




𝜕𝑧= 0 (5.16)

Momentum conservation

x component: −𝜕𝑝

𝜕𝑥+𝜕𝜏𝑧𝑥𝜕𝑧

+ 𝜌g𝑥 = 0 (5.17)

Rheology state

[0 0 𝜏𝑥𝑧0 0 0𝜏𝑧𝑥 0 0

] = 𝜂𝜌

[ 0 0


0 0 0𝜕𝑣𝑥𝜕𝑧

0 0 ] 𝑏𝜌

(5.18)

Likewise, the constitutive equations for the yield power-law fluid can be simplified to

following:

Mass conservation

𝜕𝜌




𝜕𝑧= 0 (5.19)

Momentum conservation

x component: −𝜕𝑝

𝜕𝑥+𝜕𝜏𝑧𝑥𝜕𝑧

+ 𝜌g𝑥 = 0 (5.20)

Rheology state

[

0 0 𝜏𝑥𝑧0 0 0𝜏𝑧𝑥 0 0

] = 𝜏0𝜌 + 𝜂𝜌

[ 0 0


0 0 0𝜕𝑣𝑥𝜕𝑧

0 0 ] 𝑏𝜌

(5.21)

Although the incompressible assumption has simplified the solve process for the constitutive

equations of the two types of fluids, the material concentration profile during the actual

conveying process has also to be taken into account, which is discussed in the following

sections.

5.3.2 Fluidised motion conveying models (vent and non-vent)

Generally, a fluidised motion conveying system mainly includes two systems: vent and non-

vent. Essentially, the conveying technique is to maintain an aerated state in the bulk solid by

continuous introduction of air, from the moment that it is injected into the upper end of the

inclined channel, to the point at which it is discharged. In detail, compressed air is fed into the

122

lower chamber, which then permeates through the media and runs the length of the channel to

fluidise the particulate material. After fluidising the bed of granular material, these particulate

materials behave like a fluid and flow readily down the chute at angles much lower than the

angle of repose of the granular material.

For a vent fluidised flow system, the predominant factor causing flow is the gravitational force

on the material. The frictional stresses on the sidewalls tend to resist the motion, and the flow

will reach an equilibrium state when the frictional wall stresses are in balance with the

gravitational forces in the streamwise direction. This state corresponds to a fully developed

channel flow where the bed depth remains constant. Mathematical conveying models can be

developed based on the conservation of momentum considering the rheology of the gas-solid

mixture to describe the fully developed flow. Meanwhile, as for the velocity at bottom, no slip

and slip condition will be considered in the following models. In detail, there are six models for

the current flow system: 1. Combined conveying model (vent); 2. Power-law fluid conveying

model (vent); 3. Yield power-law fluid conveying model (vent); 4. Combined conveying model

with slip at bottom (vent); 5. Power-law fluid conveying model with slip at bottom (vent); 6.

Yield power-law fluid conveying model with slip at bottom (vent).

For a non-vent system, it is believed that there is the possibility of fluidised material being

transported by a force other than gravity (Gupta et al., 2006). Meanwhile, the no-slip and slip

condition has also been considered. Six flow models for non-vent system are shown below: 1.

Combined conveying model (non-vent); 2. Power-law fluid conveying model (non-vent); 3.

Yield power-law fluid conveying model (non-vent); 4. Combined conveying model with slip at

bottom (non-vent); 5. Power-law fluid conveying model with slip at bottom (non-vent); 6. Yield

power-law fluid conveying model with slip at bottom (non-vent).

5.3.2.1 Vent fluidised motion conveying models

According to the conservation of momentum considering the rheology of the gas-solid mixture,

six mathematical conveying models can be developed for the vent flow system and discussed

below.

5.3.2.1.1 Combined material conveying model (vent)

Considering a continuous incompressible flow as shown in Figure 5.5, the flow will exhibit the

stratification effect according to previous ECT-based research observations (Williams et al.,

2008). Similarly, such a channel flow is heterogeneous and its bulk density tends to increment

towards the channel bottom. As a result, the bulk density may exceed the critical bulk density at

a critical height (Hc) where the rheology of the aerated powder material alters from the dense

concentration levels described by the yield power-law fluid model to the more dilute flow

123

described by the power-law fluid model. Such a phenomenon results in stratified layers with

multiple rheological behaviours, which can be described as follows:

Firstly, in the region from the bottom to the height of Hc, the bulk density of the aerated powder

can be relatively high; this is modelled using the simplified constitutive equations for a yield

power-law fluid. A concentration factor fsy is devoted to this region.

Secondly, from the critical height Hc to H with a concentration factor of fsp, the aerated powder

undergoes further shear deformation. However, due to the lower bulk density, the rheology of

the gas-solids mixture is a power-law type. At the critical height Hc, the flow velocity is

consistent between the two layers

Figure 5.5 Mixed rheology behaviours of the material flow (vent)

Based on the above two material layers with different rheological forms, the following

conveying models were proposed:

At 0 < z < Hc, the velocity distribution of the flow can be solved by integrating Eq. (5.20) and

Eq. (5.21) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = Hc and 𝑣𝑥(0) = 0 at 𝑧 = 0.

Then, 𝑣𝑥 along the bed height 𝑣𝑥(𝑧𝑦) can be obtained as:

𝑣𝑥(𝑧𝑦) =𝑏𝜌

1 + 𝑏𝜌· (𝜌𝑦g𝑥

𝜂𝜌)

1𝑏𝜌· [𝐻𝑐

1+𝑏𝜌𝑏𝜌 − (𝐻𝑐 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] (𝑧 < 𝐻𝑐)

(5.22)

As a result, 𝑣𝑥(𝐻𝑐) =𝑏𝜌


𝜂𝜌)

1𝑏𝜌· 𝐻𝑐

1+𝑏𝜌𝑏𝜌 (5.23)

124

For Hc < z < H, solving the constitutive equations for the power-law fluid, by integrating Eq.

(5.17) and Eq.(5.18) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = H and 𝑣𝑥(𝐻𝑐) =𝑏𝜌

1+𝑏𝜌·

(𝜌𝑦g𝑥

𝜂𝜌)

1

𝑏𝜌· 𝐻𝑐

1+𝑏𝜌

𝑏𝜌 at 𝑧 = 𝐻𝑐.

The velocity 𝑣𝑥(𝑧𝑝) of fluid is obtained as:

𝑣𝑥(𝑧𝑝) =𝑏𝜌

1 + 𝑏𝜌· (𝜌𝑝g𝑥𝜂𝜌

)

1𝑏𝜌· [(𝐻 − 𝐻𝑐)

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ]

+𝑏𝜌


𝜂𝜌)


1+𝑏𝜌𝑏𝜌 (𝑧 ≥ 𝐻𝑐)

(5.24)

As a result, the total solids mass flow rate can be subsequently derived as:

𝑚𝑠 = 𝑚𝑠(power − law fluid) + 𝑚𝑠(yield power − law fluid)

= ∫ 𝜌𝑦 · 𝑤 · 𝑣𝑥(𝑧𝑦) · 𝑑𝑧𝐻𝑐

0

+∫ 𝜌𝑝 · 𝑤 · 𝑣𝑥(𝑧𝑝) · 𝑑𝑧 =𝐻

𝐻𝑐

𝜌𝑦 · 𝑤 · (𝜌𝑦g𝑥

𝜂𝜌)

1𝑏𝜌

·𝑏𝜌

1 + 2𝑏𝜌· 𝐻𝑐

1+2𝑏𝜌𝑏𝜌 + 𝜌𝑝 · 𝑤 · (

𝜌𝑝g𝑥𝜂𝜌

)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌

· (𝐻 − 𝐻𝑐)

1+2𝑏𝜌𝑏𝜌 + 𝜌𝑝 · 𝑤 ·

𝑏𝜌


𝜂𝜌)

1𝑏𝜌

· 𝐻𝑐

1+𝑏𝜌𝑏𝜌 (𝐻 − 𝐻𝑐)

(5.25)

However, there are also two extreme scenarios where the combined material conveying model

can be reduced into two models if either the power-law fluid alone or the yield power-law fluid

alone is modelled within the system.

5.3.2.1.2 Power-law fluid conveying model (vent)

For the vented system in this study, the fluidised air only plays the role of fluidising the

material, then the driving pressure gradient term in Eq. (5.17) equals zero as air vent to

atmosphere, i.e. −𝜕𝑃

𝜕𝑥= 0. The predominant factor causing flow is the streamwise gravitational

force on the material. Some previous studies (e.g. Botterill et al., 1972; Botterill and Bessant,

1976) have also established that the fluidised solids in an air-gravity conveyor are likely to

exhibit rheological behaviour. Hence, under the assumption of a homogeneous flow for well-

fluidised material, a power-law fluid model is applied to describe the material flow; also, the air

125

velocity at the material flow direction equals zero above the material layer, as shown below in

Figure 5.6.

Figure 5.6 Power-law fluid conveying model (vent)

Based on above assumptions, the following conveying models were subsequently proposed.

At 0 < z < H (H is bed height), solving the constitutive equations for the power-law fluid. Thus

Eq.(5.17) and Eq.(5.18) are transformed to:

𝜕𝜏𝑧𝑥𝜕𝑧

+ 𝜌g𝑥 = 0 (5.26)

𝜏𝑧𝑥 = 𝜂𝜌(𝜕𝑣𝑥𝜕𝑧)𝑏𝜌 (5.27)

g𝑥 = g ∙ sin𝜃, where 𝜃 is the inclination angle.

At 0 < z < H, the velocity distribution of the flow can be solved by integrating Eq. (5.26) and

Eq.(5.27) with the boundary conditions of 𝜏𝑧𝑥 =0 at z = H and 𝑣𝑥(0) = 0 at 𝑧 = 0.

Then, 𝑣𝑥 along the bed height 𝑣𝑥(𝑧) can be obtained as:

𝑣𝑥(𝑧) =𝑏𝜌

1 + 𝑏𝜌· (𝜌𝑝g𝑥

𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] (5.28)

The solids mass flow rate is subsequently derived as:

𝑚𝑠 = ∫ 𝜌𝑝 · 𝑤 · 𝑣𝑥(𝑧) · 𝑑𝑧𝐻

0

= 𝜌𝑝 · 𝑤 · (𝜌𝑝g𝑥

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

(5.29)

126

5.3.2.1.3 Yield power-law fluid conveying model (vent)

For modelling the yield power-law fluid, the bulk density 𝜌𝑦 may exceed the critical bulk

density 𝜌𝑐 where the rheology of the aerated powder material alters from the dense

concentration levels described by the yield power-law fluid model.

Figure 5.7 Yield power-law fluid conveying model (vent)

Similarly, at 0 < z < H (H is bed height), solving the constitutive equations for the yield power-

law fluid. Thus Eq.(5.20) and Eq.(5.21) are transformed to:

𝜕𝜏𝑧𝑥𝜕𝑧

+ 𝜌g𝑥 = 0 (5.30)

𝜏𝑧𝑥 = 𝜏0𝜌 + 𝜂𝜌(𝜕𝑣𝑥𝜕𝑧)𝑏𝜌 (5.31)


Eq.(5.31) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = H and 𝑣𝑥(0) = 0 at 𝑧 = 0.




𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] (5.32)


𝑚𝑠 = ∫ 𝜌𝑦 · 𝑤 · 𝑣𝑥(𝑧) · 𝑑𝑧𝐻

0

= 𝜌𝑦 · 𝑤 · (𝜌𝑦g𝑥

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

(5.33)

127

5.3.2.1.4 Combined conveying model with slip at bottom (vent)

Figure 5.8 Mixed rheology behaviours of the material flow with slip at bottom (vent)

Likewise, based on the above two material layers with different rheological forms, the following



Eq. (5.21) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = Hc and 𝑣𝑥(0) = 𝑣0 at 𝑧 = 0.


𝑣𝑥(𝑧𝑦) =

𝑏𝜌


𝜂𝜌)




+ 𝑣0 (𝑧 < 𝐻𝑐)

(5.34)



𝜂𝜌)


1+𝑏𝜌𝑏𝜌 + 𝑣0 (5.35)



1+𝑏𝜌·

(𝜌𝑦g𝑥

𝜂𝜌)

1

𝑏𝜌· 𝐻𝑐

1+𝑏𝜌

𝑏𝜌 + 𝑣0 at 𝑧 = 𝐻𝑐.


128



)

1𝑏𝜌· [(𝐻 − 𝐻𝑐)

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)


+𝑏𝜌


𝜂𝜌)


1+𝑏𝜌𝑏𝜌 + 𝑣0 (𝑧 ≥ 𝐻𝑐)

(5.36)




0

+∫ 𝜌𝑝 · 𝑤 · 𝑣𝑥(𝑧𝑝) · 𝑑𝑧 =𝐻

𝐻𝑐

𝜌𝑦 · 𝑤 · (𝜌𝑦g𝑥

𝜂𝜌)

1𝑏𝜌

·𝑏𝜌

1 + 2𝑏𝜌· 𝐻𝑐

1+2𝑏𝜌𝑏𝜌 + 𝜌𝑝 · 𝑤 · (


)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌

· (𝐻 − 𝐻𝑐)

1+2𝑏𝜌𝑏𝜌 + 𝜌𝑝 · 𝑤 ·

𝑏𝜌


𝜂𝜌)

1𝑏𝜌

· 𝐻𝑐

1+𝑏𝜌𝑏𝜌 (𝐻 − 𝐻𝑐) + 𝑣0𝐻

(5.37)

5.3.2.1.5 Power-law fluid conveying model with slip at bottom (vent)

Considering the velocity slip at the channel bottom condition, a similar power-law conveying

model can be seen in Figure 5.9.

Figure 5.9 Power-law fluid conveying model with slip at bottom (vent)


Eq.(5.18) with the boundary conditions of 𝜏𝑧𝑥 =0 at z = H and 𝑣𝑥(0) = 𝑣0 at 𝑧 = 0.

129



1 + 𝑏𝜌· (𝜌𝑝g𝑥

𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] + 𝑣0 (5.38)



0

= 𝜌𝑝 · 𝑤 · (𝜌𝑝g𝑥𝜂𝜌

)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌 + 𝑣0𝐻

(5.39)

5.3.2.1.6 Yield power-law fluid conveying model with slip at bottom (vent)

Considering the velocity slip at the channel bottom condition, a similar yield power-law

conveying model can be seen in Figure 5.10.

Figure 5.10 Yield power-law fluid conveying model with slip at bottom (vent)


Eq. (5.21) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = H and 𝑣𝑥(0) = 𝑣0 at 𝑧 = 0.




𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] + 𝑣0 (5.40)

130



0

= 𝜌𝑦 · 𝑤 · (𝜌𝑦g𝑥

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌 + 𝑣0𝐻

(5.41)

5.3.2.2 Non-vent fluidised motion conveying models

The difference between non-vent and vent fluidised motion conveying is that the fluidised air in

non-vent systems also contributes to the material flow. There is a significantly dispersed dilute

section or even an air-only phase from the material top surface (bed height of H) to the channel

top as the high air velocity tends to disperse the material dramatically. For simplification

purposes, air only is modelled in this section, as the pressure drop is caused by this air, and its

value equals −𝜕𝑝

𝜕𝑥. Here the pressure drop is replaced by 𝐴𝑠 =

1

2(−

𝜕𝑝

𝜕𝑥)𝑠 . Six models

corresponding to vent systems can be described as follows.

5.3.2.2.1 Combined material conveying model (non-vent)

Figure 5.11 Combined conveying model (non-vent)




Eq. (5.21) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = Hc and 𝑣𝑥(0) = 0 at 𝑧 = 0.


131


𝑏𝜌

1+𝑏𝜌· (𝜌𝑦g𝑥+2𝐴𝑠

𝜂𝜌)

1

𝑏𝜌· [𝐻𝑐

1+𝑏𝜌

𝑏𝜌 − (𝐻𝑐 − 𝑧)1+𝑏𝜌

𝑏𝜌 ]

(𝑧 < 𝐻𝑐)

(5.42)


1 + 𝑏𝜌· (𝜌𝑦g𝑥 + 2𝐴𝑠

𝜂𝜌)


1+𝑏𝜌𝑏𝜌 (5.43)



1+𝑏𝜌·

(𝜌𝑦g𝑥+2𝐴𝑠

𝜂𝜌)

1

𝑏𝜌· 𝐻𝑐

1+𝑏𝜌

𝑏𝜌 at 𝑧 = 𝐻𝑐.



1 + 𝑏𝜌· (𝜌𝑝g𝑥 + 2𝐴𝑠

𝜂𝜌)

1𝑏𝜌· [(𝐻 − 𝐻𝑐)

1+𝑏𝜌𝑏𝜌

− (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] +

𝑏𝜌


𝜂𝜌)

1𝑏𝜌

· 𝐻𝑐

1+𝑏𝜌𝑏𝜌 (𝑧 ≥ 𝐻𝑐)

(5.44)




0

+∫ 𝜌𝑝 · 𝑤 · 𝑣𝑥(𝑧𝑝) · 𝑑𝑧 =𝐻

𝐻𝑐

𝜌𝑦 · 𝑤

· (𝜌𝑦g𝑥 + 2𝐴𝑠

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻𝑐

1+2𝑏𝜌𝑏𝜌 + 𝜌𝑝 · 𝑤

· (𝜌𝑝g𝑥 + 2𝐴𝑠

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· (𝐻 − 𝐻𝑐)

1+2𝑏𝜌𝑏𝜌

+ 𝜌𝑝 · 𝑤 ·𝑏𝜌


𝜂𝜌)


1+𝑏𝜌𝑏𝜌 (𝐻

− 𝐻𝑐)

(5.45)

132

5.3.2.2.2 Power-law fluid conveying model (non-vent)

Figure 5.12 Power-law fluid conveying model (non-vent)

At 0 < z < H (H is bed height), solving the constitutive equations for the power-law fluid. Thus

Eq. (5.17) and Eq.(5.18) are transformed to:

2𝐴𝑠𝑝 +𝜕𝜏𝑧𝑥𝜕𝑧

+ 𝜌g𝑥 = 0 (5.46)

𝜏𝑧𝑥 = 𝜂𝜌(𝜕𝑣𝑥𝜕𝑧)𝑏𝜌 (5.47)


Eq.(5.47) with the boundary conditions of 𝜏𝑧𝑥 =0 at z = H and 𝑣𝑥(0) = 0 at 𝑧 = 0.



1 + 𝑏𝜌· (𝜌𝑝g𝑥 + 2𝐴𝑠𝑝

𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] (5.48)



0

= 𝜌𝑝 · 𝑤 · (𝜌𝑝g𝑥 + 2𝐴𝑠𝑝

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

(5.49)

133

5.3.2.2.3 Yield power-law fluid conveying model (non-vent)

Figure 5.13 Yield power-law fluid conveying model (non-vent)

Similarly, at 0 < z < H (H is bed height), solving the constitutive equations for the yield power-

law fluid. Thus Eq. (5.20) and Eq.(5.21) are transformed to:

2𝐴𝑠𝑦 +𝜕𝜏𝑧𝑥𝜕𝑧

+ 𝜌g𝑥 = 0 (5.50)

𝜏𝑧𝑥 = 𝜏0𝜌 + 𝜂𝜌(𝜕𝑣𝑥𝜕𝑧)𝑏𝜌 (5.51)


Eq.(5.51) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = H and 𝑣𝑥(0) = 0 at 𝑧 = 0.



1 + 𝑏𝜌· (𝜌𝑦g𝑥 + 2𝐴𝑠𝑦

𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] (5.52)



0

= 𝜌𝑦 · 𝑤 · (𝜌𝑦g𝑥 + 2𝐴𝑠𝑦

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

(5.53)

134

5.3.2.2.4 Combined conveying model with slip at bottom (non-vent)

Figure 5.14 Combined conveying model with slip at bottom (non-vent)

Likewise, based on the above two material layers with different rheological forms, the following



Eq. (5.21) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = Hc and 𝑣𝑥(0) = 𝑣0 at 𝑧 = 0.



𝑏𝜌


𝜂𝜌)




+ 𝑣0 (𝑧 < 𝐻𝑐)

(5.54)



𝜂𝜌)


1+𝑏𝜌𝑏𝜌 + 𝑣0 (5.55)


(5.17) and Eq. (5.18) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = H and 𝑣𝑥(𝐻𝑐) =𝑏𝜌

1+𝑏𝜌·

(𝜌𝑦g𝑥+2𝐴𝑠

𝜂𝜌)

1

𝑏𝜌· 𝐻𝑐

1+𝑏𝜌

𝑏𝜌 + 𝑣0 at 𝑧 = 𝐻𝑐.


135


1 + 𝑏𝜌· (𝜌𝑝g𝑥 + 2𝐴𝑠

𝜂𝜌)

1𝑏𝜌· [(𝐻 − 𝐻𝑐)

1+𝑏𝜌𝑏𝜌

− (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] +

𝑏𝜌


𝜂𝜌)

1𝑏𝜌

· 𝐻𝑐

1+𝑏𝜌𝑏𝜌 + 𝑣0 (𝑧 ≥ 𝐻𝑐)

(5.56)




0

+∫ 𝜌𝑝 · 𝑤 · 𝑣𝑥(𝑧𝑝) · 𝑑𝑧 =𝐻

𝐻𝑐

𝜌𝑦 · 𝑤

· (𝜌𝑦g𝑥 + 2𝐴𝑠

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻𝑐

1+2𝑏𝜌𝑏𝜌 + 𝜌𝑝 · 𝑤

· (𝜌𝑝g𝑥 + 2𝐴𝑠

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· (𝐻 − 𝐻𝑐)

1+2𝑏𝜌𝑏𝜌

+ 𝜌𝑝 · 𝑤 ·𝑏𝜌


𝜂𝜌)

1𝑏𝜌

· 𝐻𝑐

1+𝑏𝜌𝑏𝜌 (𝐻 − 𝐻𝑐) + 𝑣0𝐻

(5.57)

5.3.2.2.5 Power-law fluid conveying model with slip at bottom (non-vent)

Figure 5.15 Power-law fluid conveying model with slip at bottom (non-vent)

136


Eq. (5.18) with the boundary conditions of 𝜏𝑧𝑥 =0 at z = H and 𝑣𝑥(0) = 𝑣0 at 𝑧 = 0.




𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] + 𝑣0 (5.58)



0

= 𝜌𝑝 · 𝑤 · (𝜌𝑝g𝑥 + 2𝐴𝑠𝑝

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

+ 𝑣0𝐻

(5.59)

5.3.2.2.6 Yield power-law fluid conveying model with slip at bottom (non-vent)

Figure 5.16 Yield power-law fluid conveying model with slip at bottom (non-vent)


Eq. (5.21) with the boundary conditions of 𝜏𝑧𝑥 = 𝜏0𝜌 at z = H and 𝑣𝑥(0) = 𝑣0 at 𝑧 = 0.



1 + 𝑏𝜌· (𝜌𝑦g𝑥 + 2𝐴𝑠𝑦

𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 ] + 𝑣0 (5.60)


137


0

= 𝜌𝑦 · 𝑤 · (𝜌𝑦g𝑥 + 2𝐴𝑠𝑦

𝜂𝜌)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

+ 𝑣0𝐻

(5.61)

5.4 Conclusion

In this chapter, the flow mechanism of the fluidised material in an air-gravity conveyor has been

studied by utilising the analogy between a fluid and the aerated powder. The derivation of the

fundamental conveying models for fluidised motion conveying has been proposed with an

emphasis on its rheology. Particularly, 12 models for vent and non-vent fluidised motion flow

based on its rheology have been discussed in this chapter.

Firstly, to derive a rheology-based fluidised motion conveying model, the fundamental

continuous fluid mechanics approach has been adopted. The governing functions of continuous

flow systems, including conservation of mass and the conservation of momentum, were initially

developed by analysing an infinitesimal element within the system.

Secondly, when the material was subjected to external stresses, the strain theory was applied to

derive the total deformation. A shear component and a volumetric component contribute to

these deformations.

Thirdly, fundamental equations for the rheological state of the aerated powders were derived.

The rheological characteristics for aerated powders can be either a power-law type or a yield

power-law type depending on the aerated level (bulk density) within the system.

Subsequently, according to the above information, the constitutive equations which govern the

fluidised motion powder flow performance were then established. To obtain approximated

analytical results, an incompressible approximation technique was utilised in order to simplify

the constitutive equations, and the volumetric components within the constitutive equations

were eliminated.

Lastly, based on the stratification effect exerted by the material during the conveying process,

twelve conveying models were developed which consider the condition of vent and non-vent,

slip at bottom and no-slip at bottom. Also, these models embodied the components within the

flow of air only, power-law fluid and yield power-law fluid. All the models described above

require further study to examine the validities in the case of air-gravity conveying.

138

6 CHAPTER 6 Validation of air-gravity conveying model

6.1 Introduction

In order to predict the flow performance of the fluidised material being conveyed in air-gravity

conveyors using the flow models derived in Chapter 5, the adaptabilities of the rheology-based

flow models need to be investigated. The rheology parameters of consistency and flow index for

the proposed flow models have been studied in previous chapters. Therefore, the proposed

conveying model can be validated by comparing its predicted results with experimental results

from the air-gravity conveyor, which is the aim of this chapter. Sand and flyash powders were

selected to study their flow behaviours.

6.2 Flow model validation process

For the model derived from Chapter 5, the bed height is used to validate the accuracy of all the

proposed models. An air-gravity conveyor was developed to collect the experimental data

required in the validation process. In particular, basic conveying data like pressure drop along

the channel, material mass flow rate, airflow rate, conveying bulk densities, rheology

parameters and model selection are needed for the validation process.

6.2.1 Experimental steady flow bed height

During the air-gravity conveying testing, a steady flow state will be established for a vent

fluidised flow system. It is because the predominant factor causing flow is the gravitational

force on the material, that the frictional stresses on the sidewalls and channel bottom tend to

resist the motion, and the flow will reach an equilibrium state when the frictional wall stresses

are in balance with the gravitational forces in the streamwise direction. This state corresponds to

a fully developed channel flow where the bed depth remains constant. As for a non-vent flow

system, the fluidised material being transported by a force other than gravity, it is the shear

stress caused by excessive air in the conveying channel.

Based on the experimental behaviour investigated in the conveying test, a steady flow bed

height existed near the channel end (Observation window at 5 m) during the testing period,

which means that the full channel flow was developed. As a result, here the bed heights at the

location of 5 m were considered as the steady flow bed height. The bed height calculated by

different conveying models will be compared with the bed height at 5 m.

6.2.2 Fluidised bulk density and rheology parameters

As observed in the rheology testing and data analysing, the rheological parameters (consistency

and flow index) of an aerated material are bulk density dependent. Therefore, the conveying

bulk density within the air-gravity conveyor during the conveying process is essential to obtain

139

the relevant rheological properties. These parameters will all be applied to the conveying model

to investigating the relationship between bed height and material mass flow rate for every

typical air-gravity flow. To obtain the conveying bulk density, a fluidised bulk density at

minimum fluidised velocity was considered as the bulk density of aerated material within the

entire air-gravity conveyor channel when it was conveyed under certain air and solids mass flow

rates. Obviously, the average bulk density at lower fluidised velocity should be higher than the

fluidised bulk density. However, sand is easy to settle down during conveying and a static bed

was observed during testing at lower conveying velocity. When air flows through material, only

the top layers of particles become fluidised, the reminder acting as an additional distributor. As

a result, the fluidised bulk density is still used for calculating the bed height under lower

superficial air velocity, and an additional static bed height will be added for the bed height

model validation.

Once the conveying bulk density is obtained, the relevant rheological parameter consistency

(𝜂𝜌) and flow index (𝑏𝜌) can be calculated based on the empirical rheology correlations for sand

and flyash, as shown in Table 6.1.

Table 6.1 Empirical rheology correlations for sand and flyash

Parameter Sand Flyash

𝜂𝜌 𝜂𝜌 = 0.0202 × 𝜌𝐵 − 17.96 𝜂𝜌 = 0.0035 × 𝜌𝐵 − 1.3122

𝑏𝜌 𝑏𝜌 = −0.0017 × 𝜌𝐵 + 2.3085 𝑏𝜌 = −0.0016 × 𝜌𝐵 + 1.3115

6.2.3 Flow model selection

For different flow condition (vent and non-vent), the proper model should be selected to predict

the bed height under a steady flow state. In Chapter 5, conveying models based on different

solids concentration assumptions in the conveying channel were developed for the steady flow

state. However, for different flow conditions, those assumptions may not be reflective of the

actual flow characteristics during conveying. As a result, proper model selection processes and

simplifying the method should be considered in examining the applicability of each model,

which is conducted in detail for different flow condition below.

6.2.4 Validation process

In summary, the validation process for a combined material conveying model is described by

the flow chart shown in Figure 6.1. Generally, for a particular test case, the air and solids mass

flow rates were applied to calculate the corresponding conveying bulk density using the above

equation. After obtaining the conveying bulk density, rheological parameters of the material at

such a conveying bulk density can be subsequently determined by the empirical equations listed

140

in Table 6.1. Combined with the pressure drop measured in the experiment, the bed height is

obtained by incorporating the rheological parameters into the conveying model. Finally, the

predicted value is subsequently compared with the experimental result. The accuracy of the

model can be obtained by this validation process.

Figure 6.1 Flow chart of the power-law fluid conveying model algorithm

6.3 Validation of flow models

According to the validation process mentioned above, the bed heights of sand and flyash are

used to validate the model.

141

6.3.1 Vent flow of sand

Sand flow under the vent condition in a channel is heterogeneous and its bulk density tends to

increment towards the channel bottom. As a result, the bulk density may exceed the critical bulk

density at a critical height (Hc), where the rheology of the aerated powder material alters from

the dense concentration levels described by the yield power-law fluid model to the more dilute

flow described by the power-law fluid model. Such a phenomenon results in stratified layers

with multiple rheological behaviours, which can be described as follows:

Firstly, in the region from the bottom to the height of Hc, the bulk density of the aerated powder

can be relatively high; this is modelled using the simplified constitutive equations for a yield

power-law fluid.

Secondly, from the critical height Hc to H, the aerated powder undergoes further shear

deformation. However, due to the lower bulk density, the rheology of the gas-solids mixture is a

power-law type. At the critical height Hc, the flow velocity is consistent between the two layers.

Due to the easy settle down properties observed during the experiments, a thick layer of sand

will stay at the bottom with slight or no movement at lower superficial air velocity. Thus, the

yield power-law part can be considered as a not moving part for the model here. Meanwhile, the

power-law conveying part contributes the material mass flow rate during testing.

Figure 6.2 Combined material conveying model for sand flow (vent)


conveying models were proposed.

The velocity distribution at yield power-law part equal zero and velocity at power-law part

according to equation (5.24) becomes:

142

𝑣𝑥(𝑧) =

𝑏𝜌


)

1𝑏𝜌· [(𝐻−𝐻𝑐)

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝐻𝑐 − 𝑧)


(6.1)

The material mass flow rate is subsequently derived as:

𝑚𝑠 = 𝜌𝑝 · 𝑤 · (


)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· (𝐻−𝐻𝑐)

1+2𝑏𝜌𝑏𝜌

(6.2)

Following the flowchart in Figure 6.1, the predicted bed height for each test of sand under vent

condition was computed. Results were tabulated in Table 6.2 and shown in Figure 6.3 and

Figure 6.4. The error was calculated as the difference between mean experimental and predicted

bed heights.

Table 6.2 Model prediction results for all tests of sand (vent)

Velocity (mm/s) Material mass

flow rate (kg/s)

H-Hc

(mm)

Hc

(mm)

H

(mm)

Experimental bed

height (mm) Error %

58 0.63 15.99 36 51.99 50 3.98

72 1.32 17.52 30 47.52 45 5.59

85 1.67 18.03 24 42.03 43 2.25

96 1.72 18.32 14 32.32 35 7.65

106 1.76 18.15 6 24.15 20 20.75

128 1.70 18.20 0 18.20 19 4.21

140 1.70 18.07 0 18.07 19 4.88

72 0.30 14.19 30 44.19 56 21.08

85 0.30 14.76 24 38.76 45 13.86

96 0.30 14.76 14 28.76 36 20.10

106 0.30 14.59 6 20.59 28 26.46

117 0.30 14.19 0 14.19 18 21.14

128 0.30 14.87 0 14.87 17 12.53

143

Figure 6.3 Comparison between the Power-law model prediction and the experimental bed

height for sand (vent)

Figure 6.4 Comparison between the combined material conveying model prediction and

experimental bed height for sand (vent)

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Pulsatory

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Fluidisedflow

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144

As shown in Table 6.2, the largest difference between the experimental bed height and model

predicted values was 26.46%. It has been found that the static bed height reduced with the

increase in the airflow rate. When the superficial air velocity is high enough the material in the

conveying channel would be well fluidised and behave more like fluid and the static bed height

would reduce to zero. The power-law model dominated the flow performance and the material

mass flow rate increased with the increase in airflow. However, in this study the air velocity of

117 mm/s was lower than the minimum fluidisation velocity (128 mm/s). This indicated that the

conveying behaviour was dominated by the yield power-law flow. Only the top layer of the

material flew along the channel and the rest behaved like an additional porous medium.

Figure 6.3 presents the comparison between the power-law model prediction and the

experimental bed height for vent sand flow. The dash line in the figure is the 30% error line.

Only the bed height at the fluidised region fits well with the experimental measurement, which

means that the power-law model can predict the bed height well when the material is fully

fluidised. While for other regions, the power-law model underestimated the bed height as it

ignored the static bed height during material conveying. The combined material conveying

model considered the static bed height in the model and can predict the bed height at different

flow regions quite well, as shown in Figure 6.4. It was found that all the predicted bed height

and experimental data were in good agreement.

6.3.2 Non-vent flow of sand

Based on the flow behaviour observed during the conveying test, the model used to validate the

non-vent flow is the combined material conveying model (non-vent). In terms of this model, the

material flow in the conveying channel was described as a heterogeneous flow and its bulk

density tended to increment towards the channel bottom. This phenomenon was investigated by

ECT-based research observations (Williams et al., 2008) and also existed in current sand

fluidised flow.

145

Figure 6.5 Combined material conveying model for sand flow (non-vent)

As can be seen in Figure 6.5, the bulk density may exceed the critical bulk density at a critical

height (Hc), where the rheology of the sand alters from the dense concentration levels described

by the yield power-law fluid model to the more dilute flow described by the power-law fluid

model. Such a phenomenon results in stratified layers with multiple rheological behaviours,

which can be described as follows:

Firstly, in the region from the bottom to the height of Hc, the bulk density of the sand can be

relatively high; this is modelled using the simplified constitutive equations for a yield power-

law fluid. A concentration factor fsy is devoted to this region.

Secondly, from the critical height Hc to H with concentration factor of fsp, fluidised sand

undergoes further shear deformation. However, due to the lower bulk density, the rheology of

the gas-solids mixture is a power-law type. At the critical height Hc, the flow velocity is

consistent between the two layers.

Lastly, there is a dispersed dilute section or even an air-only phase from H to the channel top as

the high air velocity tends to disperse the material dramatically. In this case, air only is

considered in this region for simplification purposes.

As a result, the conveying bulk density obtained is the averaged value of these three phases. The

air phase is discarded and then the conveying density can be described below:

𝜌𝐵 = 𝜌𝑠𝑦𝑓𝑠𝑦 + 𝜌𝑠𝑝𝑓𝑠𝑝 (6.3)

Where 𝑓𝑠𝑦 =𝐻𝑐

𝐻, and 𝑓𝑠𝑝 = 1 −

𝐻𝑐

𝐻. H is the full bed height, Hc is the yield power-law fluid bed

height part and H-Hc is the power-law fluid bed height part.

146

As sand is easy to settle down at the bottom part of the conveying channel due to gravity, it

results in a thick layer that moves slightly forward under lower air velocity. Therefore, the yield

power-law part can be considered as a not moving part for model simplification purpose.

Meanwhile, the material mass flow rate is mostly contributed to by the power-law conveying

part.

Therefore, the velocity distribution at yield power-law part equal zero and velocity at power-law

part according to equation (5.44) becomes:



𝜂𝜌)

1𝑏𝜌· [(𝐻−𝐻𝑐)

1+𝑏𝜌𝑏𝜌

− (𝐻 − 𝐻𝑐 − 𝑧)


(6.4)


𝑚𝑠 = 𝜌𝑝 · 𝑤 · (

𝜌𝑝g𝑥 + 2𝐴𝑠𝑝𝜂𝜌

)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· (𝐻−𝐻𝑐)

1+2𝑏𝜌𝑏𝜌

(6.5)

Following the flowchart in Figure 6.1, predicted bed height for each test of sand was computed.

Results were tabulated in Table 6.3 and shown in Figure 6.6 and Figure 6.7. The error was

calculated as the difference between mean experimental and predicted bed heights.

Table 6.3 Model prediction results for all tests of sand (non-vent)

Velocity (mm/s) Material mass

flow rate (kg/s)

H-Hc

(mm)

Hc

(mm)

H

(mm)

Experimental bed

height (mm) Error %

36 0.15 12.24 50 62.24 63 1.21

47 0.47 14.12 42 56.12 48 16.92

58 1.34 16.83 36 52.83 42 25.78

72 1.32 16.09 22 38.09 36 5.81

85 1.52 17.63 15 32.63 26 25.52

96 1.72 17.71 6 23.71 22 7.75

106 2.06 18.09 0 18.09 18 0.52

128 2.09 18.04 0 18.04 17 6.14

140 2.08 18.04 0 18.04 17 6.12

72 0.30 14.20 22 36.20 42 13.81

85 0.30 13.17 15 28.17 38 25.86

147

96 0.28 14.24 6 20.24 28 27.72

106 0.38 14.18 0 14.18 17 16.61

128 0.30 14.34 0 14.34 16 10.39

Figure 6.6 Comparison between the Power-law model prediction and experimental bed height

for sand (non-vent)

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Transition


Pulsatory movementFluidised flow

-30% error

+30% error

148

Figure 6.7 Comparison between the combined material conveying model predictions and

experimental bed heights for sand (non-vent)

As shown in Table 6.3, the largest difference between the experimental bed height and model

predicted value is at 27.72%. The error mainly stems from the assumption of the velocity at

yield power-law part equals zero, which means that it simplifies the combined model into the

power-law model. Whereas, the flow is actually combined with the air, the power-law fluid and

the yield power-law fluid. Also, it can be found that the increase in the airflow rate reduces the

yield power-law part bed height. This is because at a larger airflow rate, material will be

fluidised better than lower airflow cases, as material behaved more like a fluid with a higher

fluidising airflow rate. The yield power-law part of the bed height will finally reduce to zero

when the airflow is strong enough to fluidise all the material in the conveying channel; in this

study, the value of this air velocity is 106 mm/s, lower than the minimum fluidisation velocity

(128 mm/s). As a result, it can be implied that at a low airflow rate, the conveying is dominated

by the yield power-law flow, and material flow rate is low because of the limited flow of

material. While at a higher airflow rate, the power-law model dominates the flow performance

and the material mass flow rate increases with the increase of airflow, finally reaching the

maximum value and becoming stable.

Figure 6.6 gives the comparison between the power-law model prediction and experimental bed

height. The dash line in the figure is the 30% error line. It can be seen that only the bed height

fall in the well-fluidised flow area are in good agreement with the experimental data. This is

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149

because, at this area, material was under a fluidised conveying condition without a static bed at

the bottom channel at higher superficial air velocity. But the power-law model cannot well

predict the bed height at the transition area and pulsatory movement area under lower air flow.

However, the combined material conveying model can be used to predict the material flow

behaviour at all flow ranges quite well. As shown in Figure 6.7, it was found that all the

predicted bed heights matched the value of experimental results very well. Overall, such a

combined material conveying model shows the potential of predicting fine powder air-gravity

flow performance.

6.3.3 Vent flow of flyash

Flyash air-gravity flow under the vent condition in the conveying channel is heterogeneous and

its bulk density tends to increment towards the channel bottom. Therefore, the bulk density may

exceed the critical bulk density, as shown in the sand flow model, where the rheology of the

aerated powder material at the bottom belongs to the dense phase model described by the yield

power-law fluid model, while the upper layer of flyash flow can be described by the power-law

fluid model. Such a phenomenon results in stratified layers with multiple rheological behaviours.

During the testing process, it is found that flyash can be fluidised better than sand flow.

Especially for the case of lower mass flow rate flow, most of the flyash in the conveying

channel flows freely after fluidisation. To simplify the calculation of flyash in the air-gravity

conveyor and study its flow behaviour, the vent power-law conveying model was used to first

validate the flow of flyash.

Figure 6.8 Power-law velocity conveying model for flyash flow (vent)

150

Based on the fluidised conveying property, the following conveying models were proposed. The

velocity distribution at the power-law part, according to equation (5.24), becomes the equation

below, and 𝑣𝑥 along with the bed height 𝑣𝑥(𝑧) can be obtained as:

𝑣𝑥(𝑧) =

𝑏𝜌


)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)


(6.6)


𝑚𝑠 = 𝜌𝑝 · 𝑤 · (


)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

(6.7)

Following the flowchart in Figure 6.1, the predicted bed height for each test of flyash under the

vent condition was computed. Results were tabulated in Table 6.4 and are shown in Figure 6.9.

The error was calculated as the difference between mean experimental and predicted bed

heights.

Table 6.4 Model prediction results for tests of flyash (vent)

Velocity (mm/s) Material mass flow

rate (kg/s)

Experimental bed

height (mm)

Model bed

height (mm) Error %

13.7 0.35 12.4 13.1 5.9

13.7 0.95 16.1 17.0 4.2

13.7 2.49 31.3 21.3 32.0

13.7 7.34 61.0 27.8 54.5

24.8 0.75 10.8 15.8 47.2

24.8 1.41 14.6 18.5 26.8

24.8 3.45 38.9 23.1 40.7

24.8 4.26 46.7 24.3 48.0

36.0 0.41 10.3 13.7 32.6

36.0 0.88 16.6 16.5 0.7

36.0 2.56 28.5 21.4 24.9

36.0 2.97 31.6 22.2 29.7

42.6 0.23 10.5 11.8 12.8

42.6 0.54 16.2 14.6 9.8

42.6 2.56 28.0 21.4 23.4

42.6 6.92 45.3 27.4 39.6

47.1 0.22 21.8 11.7 46.3

47.1 0.48 22.8 14.2 37.8

47.1 3.41 41.4 23.0 44.5

47.1 8.61 33.8 28.9 14.4

58.0 0.21 12.0 11.6 3.5

58.0 0.71 15.6 15.6 0.5

58.0 1.23 20.3 17.9 11.7

58.0 3.73 38.9 23.5 39.5

151

Figure 6.9 Comparison between Power-law model predictions and experimental bed heights for

sand (vent)

Table 6.4 presents the comparison between the power-law model prediction and experimental

bed height for vent flyash flow under the velocity measuring from 13.7 to 58.0 mm/s. Most of

the errors in the predicted values are lower than 30%, which means that the model can be used

to predict the vent flow of flyash quite well. Also, for a given velocity in this table, the predicted

bed height increases with the increase of mass flow rate. The smallest difference between the

experimental bed height and model predicted value was at 0.5% and the largest difference was

at 54.5%. The errors larger than 40% are caused by the larger flyash mass flow rate (> 3 kg/s),

which means that this power-law model is not good for predicting the testing data.

Figure 6.9 presents the comparison between the power-law model prediction and the

experimental bed height for vent flyash flow. Similarly, the dashed line in the figure is the 30%

error line. It was found that most of the predicted bed heights matched well with the value of the

experimental results, especially for the bed heights with values between 10 mm to 35 mm. It is

because the mass flow rates of flyash, which lead to the bed height in this region, are smaller

than 3 kg/s, that the conveying channels are sufficient to transport the flyash in the conveyor.

However, once the mass flow rate is higher than 5 kg/s, flyash sometimes will come out of the

top of the conveying channel during testing and the material in the channel is at a compressed

condition, which will affect the flow characteristics. As a result, it is not easy to decide the

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152

actual bed height during the conveying system; this is also why the predicted bed heights are not

good when the bed height is larger than 40 mm. Moreover, the rheology and fluidised density

used in the power-law conveying model are not good enough to describe the flow behaviour of

a dense phase flow with a high flyash mass flow rate. As a result, prediction deviations cannot

be ignored at those conditions. Except for this, this power-law conveying model is good for the

flyash air-gravity conveying system.

To improve the accuracy of prediction at the larger mass flow rate area, the yield power-law

model can be utilised for further validation. Similar to the validation process of sand vent flow,

the boundary between dense phase and fluidised phase flow is recorded by the high-speed

camera and the yield power-law bed height can be decided. As for the low mass flow rate tests,

the yield power-law model changes to the power-law model automatically as the yield power-

law bed height equals to zero, and the material mass flow rate is mostly contributed by the

power-law conveying part. As a result, the flow velocity of flyash at the bottom can be ignored

under the yield power-law flow mode. According to the vent flyash conveying results, for the

mass flow rate larger than 3 kg/s, the bulk density of flyash at the bottom of the channel will be

larger than the fluidised bulk density in general. As it is not possible to give rheology

parameters for those results, statistical bed heights based on 24 flyash conveying tests suggest

that a static bed height of 10 mm can be applied when comparing the fluidised testing, and this

10 mm bed height can also be measured at the end of every larger mass flow rate flyash

conveying test.

As can be seen in the predicted bed height and experimental bed height for vent flyash flow in

Figure 6.10, most of the data points fall into the error area lower than 30%, which means that

the predicted bed heights are in good agreement with the experimental data. Therefore, the yield

power-law conveying model is a good method to validate the vent flow of flyash in this study. It

also should be noted that the flyash bed height is not easy to decide using the window

observation method, as flyash is more likely to cover the observation window during the testing

process.

153

Figure 6.10 Comparison between Yield power-law model predictions and experimental bed

heights for flyash (vent)

6.3.4 Non-vent flow of flyash

As can be seen in the flow behaviour of flyash during the air-gravity conveying test, the model

used to validate the non-vent flow of flyash should be the combined material conveying model

(non-vent) as seen with the non-vent sand flow. The material flow in the conveying channel was

heterogeneous and an obvious bulk density difference can be seen from the testing observation.

The bulk density of flyash at the bottom is larger than the upper area, as the material layer is

thick at the bottom. However, it is difficult to tell the boundary between the power-law flow and

yield power-law flow area through the observation window because flyash will easily cover the

whole of the observation window during flyash conveying. Flyash fluidised better than sand

flow in the experimental testing, and most of the flyash in the conveying channel flows freely

after fluidisation. As a result, the power-law conveying model was used to validate the flow of

non-vent flyash flow.

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+30% error

154

Figure 6.11 Power-law fluid conveying model for flyash (non-vent)

As can be seen in Figure 6.11, the bulk density of flyash was considered as its fluidisation

density under fluidised condition. The rheology of the flyash was also based on the value at the

state of fluidisation, and the rheology of the gas-solids mixture is a power-law type.

Also, there is a dispersed dilute section or even an air-only phase from the flyash material layer

height H to the channel top as the high air velocity tends to disperse the material dramatically.

In this case, air only is not considered in this region for simplification purposes.

Therefore, the flow behaviour of flyash can be validated by the power-law conveying model.

The velocity distribution at the flyash material layer (power-law part) according to equation

(5.48) becomes:



𝜂𝜌)

1𝑏𝜌· [𝐻

1+𝑏𝜌𝑏𝜌 − (𝐻 − 𝑧)

1+𝑏𝜌𝑏𝜌 (6.8)


𝑚𝑠 == 𝜌𝑝 · 𝑤 · (

𝜌𝑝g𝑥 + 2𝐴𝑠𝑝𝜂𝜌

)

1𝑏𝜌·

𝑏𝜌

1 + 2𝑏𝜌· 𝐻

1+2𝑏𝜌𝑏𝜌

(6.9)

Following the flow chart in Figure 6.1, the predicted bed height for each test of flyash was

computed. Results were tabulated in Table 6.5, and shown in Figure 6.12. During the

calculation, the value of 𝐴𝑠𝑝 can be ignored, as there is almost no pressure drop along the

channel. The error was calculated as the difference between experimental and predicted bed

heights.

155

Table 6.5 Model prediction results for tests of flyash (non-vent)

Velocity (mm/s) Material mass flow

rate (kg/s)

Experimental bed

height (mm)

Model bed

height (mm) Error %

13.7 0.30 8.6 12.6 46.5

13.7 0.48 9.3 14.2 51.9

13.7 0.89 11.6 16.5 42.9

13.7 2.88 32.2 22.1 31.4

13.7 7.57 60.1 28.0 53.5

24.8 0.29 10.6 12.5 18.3

24.8 1.61 25.7 19.1 25.5

24.8 2.8 36.7 21.9 40.3

24.8 5.78 50.8 26.2 48.4

24.8 7.7 58.6 28.1 52.0

36.0 0.29 10.4 12.5 20.1

36.0 0.67 13.2 15.4 16.6

36.0 1.48 24.3 18.7 23.0

36.0 2.15 25.5 20.5 19.4

36.0 5.41 53.8 25.8 52.1

42.6 0.29 10.4 12.5 20.6

42.6 0.78 15.3 16.0 4.6

42.6 1.27 16.2 18.0 11.1

42.6 2.18 22.3 20.6 7.6

42.6 5.19 42.9 25.5 40.5

47.1 0.24 8.3 12.0 43.8

47.1 0.48 12.7 14.2 12.0

47.1 1.00 20.0 17.0 15.0

47.1 1.34 17.2 18.3 6.0

47.1 5.33 56.4 25.7 54.5

58.0 0.24 24.4 12.0 50.9

58.0 0.51 24.6 14.4 41.4

58.0 1.85 33.9 19.8 41.7

58.0 3.05 51.8 22.4 56.8

58.0 4.48 50.5 24.6 51.2

156

Figure 6.12 Comparison between the Power-law model prediction and experimental bed height

for flyash (non-vent)

As shown in Table 6.5, the model prediction results are given from the velocity of 13.7 to 58.0

mm/s. For a given velocity, bed heights are predicted under the different mass flow rate. Most

of the errors in predicted values are lower than 30%, which means that the model can predict the

non-vent flow of flyash quite well. However, the largest difference between the experimental

bed height and model-predicted values was at 56.8%. Figure 6.12 presents the comparison

between power-law model predictions and experimental bed heights. The dashed line in the

figure is the 30% error line. It can be seen in Figure 6.12 that the predicted bed heights are in

good agreement with the experimental data between the bed heights from 10 mm to 30 mm.

However, the predictions are not good when the bed heights increase to more than 40 mm,

which attributes to the higher mass flow rate. This is because at that higher flyash mass flow

rate, the flyash density in the conveying channel is actually not in a well fluidised state. That is

because the rheology parameters and fluidised density used in the model to predict the bed

height are not well enough able to describe the dense phase flow in the channel, which will lead

to the prediction deviations. Another reason for the bad prediction for the high mass flow rate

area is the possibility of an existing static bed height at the bottom of the conveying channel.

Though the flyash is easier to fluidise than sand in this air-gravity conveyor, and the static bed

height for flyash does not seem obvious, the thick layers at the channel bottom do exist.

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Pre

dic

ted b

ed h

eight

(mm

)


+30% error

-30% error

157

To improve the power-law model for flyash prediction, a yield power-law conveying model is

considered, as discussed in the vent flyash flow section. The 20 mm static bed height was added

to the flyash mass flow rate larger than 5 kg/s after 30 tests of non-vent flyash conveying. The

predicted bed height and experimental bed height for non-vent flyash flow is plotted in Figure

6.13. After applying the yield power-law model, those predicted bed heights at the condition of

high mass flow rate match well with the experimental data. Almost all the data fall into the 30%

error area and the accuracy of the testing as a whole obviously improved. Such a yield power-

law conveying model shows the potential for predicting flyash air-gravity flow performance.

Figure 6.13 Comparison between the Yield power-law model prediction and experimental bed

height for flyash (non-vent)

6.3.5 Velocity validation for sand and flyash

The model proposed by a new continuum approach can also be used to predict the velocity

distribution at the cross section of the channel for steady air-gravity flow. Here, the vent flow of

sand and flyash data are utilised to further validate the conveying model. This conveying

velocity distribution can be used for the velocity conveying design for air-gravity conveying

systems.

Figure 6.14 presents a comparison of experimental data points with the results of the conveying

model. The profile of the streamwise velocity is a typical velocity distribution for sand flow at

the vent condition. The data in the figure is from the test with a superficial air velocity of 127

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Pre

dic

ted b

ed h

eight

(mm

)


-30% error

+30% error

158

mm/s and mass flow rate of 1.70 kg/s. The velocity profile shows a power-law type and the

experimental velocity matches well with the velocity distribution.

Figure 6.14 Comparison between model velocity and experimental velocity of sand vent flow

Similarly, a typical example with a superficial air velocity of 36 mm/s and mass flow rate of

2.97 kg/s for model velocity distribution compared with the flyash experimental velocity can be

seen in Figure 6.15. The dashed line in the figure represents the power-law fluid calculation,

which shows the velocity distribution over the depth of flow at the centreline. The experimental

measurements are well represented by the curves corresponding to the power-law conveying

model. Therefore, the conveying model from the new continuum approach can be regarded as a

predictive model for air-gravity conveying systems.

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1

Hei

ght

(mm

)

Velocity (m/s)

Model velocity

Experimental velocity

159

Figure 6.15 Comparison between model velocity and experimental velocity of flyash vent flow

Here, only examples of the vent flow of sand and flyash are presented to extend the application

of the conveying model. It can not only be used to show the relationship between mass flow rate

and bed height, but also predict the velocity distribution for air-gravity conveying. Due to the

limitation of the image analysis method, the bed height of the flowing bed can be achieved, but

not the velocity distribution. It is difficult to trace all the particle flows in the observation

windows. Therefore, the image analysis method is not good enough to get the velocity

distribution for the conveying material. A better method is needed to obtain the flowing

velocity, such as a laser method, velocity sensors and so on. In any case, the example presented

here proves that the power-law and yield power-law conveying model is good enough to predict

the flow of the air-gravity conveyor. Once the velocity distribution is validated by further

research and more experimental data, the accuracy of model can be improved further.

6.4 Rheology-based air-gravity conveying system design protocol

According to the study and analysis in this thesis so far, it is suggested that an alternative

approach to the design of an air-gravity conveying system for fine material conveying can be

proposed based on a rheology method. However, further validation experiments with different

channel sizes and lengths are needed. Also, more testing on other materials should be conducted

before using this design chart.

0

4

8

12

16

20

24

28

32

36

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Hei

gh

t (m

m)

Velocity (m/s)

Model velocity

Experimental velocity

160

Figure 6.16 Rheology-based fine material air-gravity conveying system design chart

According to the flow chart in Figure 6.16, once the conveying candidate, the material mass

flow rate and the pipeline routing for a fine material air-gravity conveying system are

confirmed, a series of bench scale tests can be subsequently conducted.

The particle density and loose poured bulk density are used as supportive data for the air-gravity

conveying system. The fluidisation and De-aeration tests together can be utilised to determine

the minimum fluidisation bulk density, minimum fluidisation velocity and de-aeration factors,

which show the rheology properties of aerated fine powder materials.

The essential consistency and flow index for the rheological model are determined by the

rheology test. The relationship between these two parameters and bulk density can be decided

and further optimised by the modelling methods detailed in Chapter 3.

Bench scale testing results can be incorporated into conveying models for a particular air-

gravity conveyor design, including the vent and non-vent conveying systems.

The steady material conveying bed height can be calculated, which provides the flow behaviour

of the conveying material for further conveyor design. The suggested air supply for the

conveying system can be decided and used to estimate the overall power consumption.

161

6.5 Conclusion

This chapter presented the study of the initial validation process of the proposed conveying

models for predicting the steady flow bed height of an air-gravity conveyor. A 6 m downward

conveying channel was used to conduct the validation experiments. Sand and flyash used

previously in the rheology test were also selected as the conveying material. The experimental

data required in the validation process was collected by testing on the air-gravity conveyor. In

particular, basic conveying data like the pressure drop along the channel for a non-vent

conveying system, material mass flow rate, airflow rate, conveying bulk densities and rheology

parameters are needed for the validation process.

Selection of the conveying models was initially discussed. Results suggested that for sand flow,

the power-law conveying model was shown to have significantly under-estimated the conveying

bed height at the transition area and pulsatory movement area. The combined material

conveying model produced results comparable with the experimental values. The yield power-

law conveying part can be considered as a not moving part for model simplification purposes.

This combined model was selected for further comparative analysis, and final validation results

showed that the combined conveying model achieved 27.72% prediction error for non-vent sand

flow and 26.46%for vent sand flow.

For flyash, results showed that the combined material conveying model cannot be validated

because of the missing concentration profiles between the yield power-law and power-law

models. The power-law fluid conveying model was shown to agree with the experimental data

quite well, especially for the bed height having a value between 10 mm to 30 mm.

To conclude, in this study the rheology-based fine powder air-gravity conveying system

evaluation method was successfully developed. Also, according to some simple bench tests, this

approach enabled the system prediction of fine material flow behaviour and bed height in air-

gravity conveyors.

162

7 CHAPTER 7 CFD simulation on an air-gravity conveyor

7.1 Introduction

The computational fluid dynamic (CFD) approach is powerful in solving and analysing flow

behaviours when designing conveying systems for industrial applications. It is based on a fast

and reliable computational methodology that provides accurate and practical solutions for

reducing the risks of potential design flaws and optimizing engineering design. The gas-solid

two phase flow has been successfully simulated using CFD for a fluidised bed (Wang et al,

2010) and pneumatic conveying systems (Behera et al, 2013) as well as vent airslide flow (Oger

and Savage, 2013; Savage and Oger, 2013). Savage and Oger (2013) reviewed some selected

experimental studies of air-gravity conveyors and utilized a multiphase flow CFD program

MFIX to describe air-gravity flows (vent airslide flow). Their study was the first successful

attempt to model airslide that considered the detailed mechanics of fluid particles. Revisions

and additions to the governing multiphase flow equations used in the model were made, and the

model compared well with experimental velocity profiles and overall flow behaviour (Oger and

Savage, 2013). However, the periodic boundary conditions used in simulation meant that it

could only show the steady flow state of airslide, and the bed height along the airslide flow

channel could not be obtained in their study. Also, there has been no numerical simulation of

non-vent fluidised motion conveying found in the literature, and CFD could be an effective way

to study both the vent and non-vent air-gravity flow.

This chapter focuses on the fundamental CFD investigation of the gas-solid flow behaviour in

an air-gravity conveying system. Governing equations are firstly discussed, and then the effects

of modelling parameters including flow model, coefficient of restitution, specularity coefficient

and drag models of vent and non-vent fluidised motion conveying are examined. Experimental

results on bed height along the channel are used to compare with the simulation results to

validate the CFD model. The developed CFD model is also applied to understand and predict

material flow both in vent and non-vent air-gravity conveying, such as volume fraction and

velocity distribution along and cross the channel.

7.2 Governing equations for an air-gravity conveying system

The Eulerian-Eulerian model that incorporates the kinetic theory of granular flow was used to

describe the gas-solid two-phase flow in an air-gravity conveying system. In this study, air and

bulk material (sand and flyash) were used as the gas phase and the solid phase. The governing

equations for the conservation of mass, momentum and fluctuation kinetic energy are expressed

below.

163

7.2.1 Governing conservation equations

The volume fraction balance equation is given by:

∑𝛼𝑞

n

𝑞=1

= 1 (7.1)

where 𝛼𝑞 is the volume fraction of phase q, 𝑞 = g for gas, s for solid.

The continuity equations for gas and solid phase can be expressed as:

𝜕

𝜕𝑡(𝛼g𝜌g) + 𝛻 ∙ (𝛼g𝜌g 𝑣g⃗⃗ ⃗⃗ ) = 0 (7.2)

𝜕

𝜕𝑡(𝛼𝑠𝜌𝑠) + 𝛻 ∙ (𝛼𝑠𝜌𝑠 𝑣𝑠⃗⃗⃗⃗ ) = 0 (7.3)

where 𝜌g is the gas density, 𝜌s is the mass density of the individual solid particles, t is the time,

𝑣g is the gas velocity, and 𝑣𝑠 is the solid velocity.

The momentum conservation for the gas and solid phases can be described as:

𝜕

𝜕𝑡(𝛼g𝜌g 𝑣g⃗⃗ ⃗⃗ ) + 𝛻 ∙ (𝛼g𝜌g 𝑣g⃗⃗ ⃗⃗ 𝑣g⃗⃗ ⃗⃗ )

= −𝛼g𝛻𝑝 + 𝛻 ∙ �̿�g + 𝐾gs(𝑣𝑠⃗⃗⃗⃗ − 𝑣g⃗⃗ ⃗⃗ ) + 𝛼g𝜌g g⃗⃗

(7.4)

�̿�g = 𝛼g𝜇g(𝛻 𝑣g⃗⃗ ⃗⃗ +𝛻 𝑣g⃗⃗ ⃗⃗𝑇) + 𝛼g (𝜆g −

2

3𝜇g) 𝛻 ∙ 𝑣g⃗⃗ ⃗⃗ 𝐼 ̿ (7.5)

𝜕

𝜕𝑡(𝛼s𝜌s 𝑣s⃗⃗⃗⃗ ) + 𝛻 ∙ (𝛼s𝜌s 𝑣s⃗⃗⃗⃗ 𝑣s⃗⃗⃗⃗ )

= −𝛼s𝛻𝑝 − 𝛻𝑝s + 𝛻 ∙ �̿�s +𝐾sg(𝑣g⃗⃗ ⃗⃗ − 𝑣s⃗⃗⃗⃗ ) + 𝛼s𝜌s g⃗⃗

(7.6)

�̿�s = 𝛼s𝜇s(𝛻 𝑣s⃗⃗⃗⃗ +𝛻 𝑣s⃗⃗⃗⃗𝑇) + 𝛼s (𝜆s −

2

3𝜇s)𝛻 ∙ 𝑣s⃗⃗⃗⃗ 𝐼 ̿ (7.7)

where p is pressure, 𝑝𝑠 is the solid phase pressure, �̿�g is the stress-strain tensor of gas, �̿�s is the

stress-strain tensor of solid, 𝐾gs(= 𝐾sg) is the interphase exchange coefficient, 𝜇g and 𝜆g are the

shear and bulk viscosities of the gas phase, respectively, 𝜇s and 𝜆s are the shear and bulk

viscosity of the solid phase, and 𝐼 ̿is the unit tensor.

7.2.2 Kinetic theory of granular flow

For the granular flow in air-gravity conveyors, constitutive equations are required to describe

the rheology of the solid phase. For the granular flow in the compressible regime where the

solids volume fraction is less than the maximum allowed value, a solids pressure is calculated

independently and used for the pressure gradient term, ∇𝑝s , in Eq. (7.6). According to the

granular kinetic theory derived by Lun et al. (1984), the solids pressure composes a kinetic term

and a second term due to particle collisions, i.e.:

164

𝑝s = 𝛼s𝜌s 𝛩s+ 2𝜌s(1 + 𝑒s)𝛼s2g0 𝛩s (7.8)

where 𝑒s is the coefficient of restitution for particle collisions, g0 is the radial distribution

function, and 𝛩s is the granular temperature.

The radial distribution function, g0 , is a correction factor that modifies the probability of

collisions between particles and is given by Ding and Gidaspow (1990):

g0 = [1 − (αs

𝛼s,max)1 3⁄ ]

−1

(7.9)

where αs,max is the maximum particle packing.

The granular temperature, 𝛩s, is introduced into the model and can be defined as (Lun et al.,

1984):

𝛩s= ⟨𝑐2⟩ 3⁄ (7.10)

where c is the particle fluctuating velocity. Thus, for the solid phase, the granular temperature is

proportional to the kinetic energy of the random motion of the particles. The granular

temperature conservation equation developed by Ding and Gidaspow (1990), neglecting

convection and diffusion in the transport equation, has been used, i.e.:

3

2[𝜕

𝜕𝑡(𝛼s𝜌s 𝛩s) + 𝛻 ∙ (𝛼s𝜌s 𝑣s⃗⃗⃗⃗ 𝛩s)]

= (−𝑝s𝐼 + �̿�s): 𝛻𝑣s⃗⃗⃗⃗ + 𝛻 ∙ (𝑘𝛩s𝛻 𝛩s) − 𝛾𝛩s + 𝜙gs

(7.11)

where the first term on the right-hand side is the generation of energy by the solid stress tensor,

the second term represents the diffusion of the energy, the third term is the collisional

dissipation of energy and the fourth term is the energy exchange between gas and solid phase.

The diffusion coefficient for granular energy, 𝑘𝛩s, is defined by Gidaspow et al. (1992) :

𝑘𝛩s =25𝜌s𝑑s√𝛩s 𝜋

64(1 + 𝑒s)g0[1 +

6

5𝛼sg0(1 + 𝑒s)]

2 + 2𝜌s𝛼s2𝑑s(1

+ 𝑒s)g0√𝛩s𝜋

(7.12)

The collision dissipation of energy is given by Lun et al. (1984):

𝛾𝛩s =12(1 − 𝑒s

2)𝑔0

𝑑s√𝜋𝜌s𝛼s

2 𝛩s3 2⁄ (7.13)

The transfer of the kinetic energy can be expressed as (Lun et al., 1984):

𝜙gs = −3𝐾gs 𝛩s (7.14)

165

The solid stress tensor contains shear and bulk viscosities arising from particle momentum

exchange due to translation and collision. A frictional component of viscosity is also included to

express the viscous-plastic transition that occurs when particles reach their maximum solid

volume fraction. The sum of the collisional, kinetic and frictional terms gives the total solid

shear viscosity, i.e.:

𝜇s = 𝜇s,col + 𝜇s,kin + 𝜇s,fr (7.15)

where 𝜇s,col is the collision viscosity, which can be expressed as (Lun et al., 1984):

𝜇s,col =4

5𝛼s𝜌sg0(1 + 𝑒s)(

𝛩s𝜋)1 2⁄ (7.16)

The kinetic part of the shear viscosity proposed by Gidaspow et al. (1992) is:

𝜇s,kin =10𝜌s𝑑s√𝛩s 𝜋

96𝛼s(1 + 𝑒s)g0[1 +

4

5𝛼sg0(1 + 𝑒s)]

2 (7.17)

Schaeffer (1987) derived an equation for the frictional viscosity, 𝜇s,fr, which is given by:

𝜇s,fr =𝑝s 𝑠𝑖𝑛 𝜙

2√𝐼2𝐷 (7.18)

where 𝜙 is the angle of internal friction, and 𝐼2𝐷 is the second invariant of the deviatoric stress

tensor.

The bulk viscosity, 𝜆s, considering the resistance of the granular particles to compression and

expansion, can be expressed as (Lun et al., 1984):

𝜆s =4

3𝛼s𝜌s𝑑sg0(1 + 𝑒s)(

𝛩s𝜋)1 2⁄ (7.19)

7.2.3 Drag model

The drag force acting on a particle in gas-solid systems can be represented by the product of a

momentum transfer coefficient, 𝐾gs , and the slip velocity between the two phases, 𝑣g⃗⃗ ⃗⃗ − 𝑣s⃗⃗⃗⃗ .

Gidaspow et al. (1992) combined the model developed by Wen and Yu (1966) and the equation

derived by Ergun (1952) to compute the interphase momentum transfer coefficient between the

gas and solid phase. The gas-solid exchange coefficient, 𝐾gs, is given in the following form:

when 𝛼g > 0.8,

𝐾gs =3

4𝐶𝐷𝛼s𝛼g𝜌g|𝑣g⃗⃗ ⃗⃗ − 𝑣s⃗⃗⃗⃗ |

𝑑s𝛼g−2.65 (7.20)

when 𝛼g ≤ 0.8,

166

𝐾gs = 150𝛼s2𝜇s

𝛼g𝑑s2 + 1.75

𝛼s𝜌g|𝑣g⃗⃗ ⃗⃗ − 𝑣s⃗⃗⃗⃗ |

𝑑s (7.21)

Where

𝐶𝐷 =24

𝛼g𝑅𝑒s[1 + 0.15(𝛼g𝑅𝑒s)

0.687] (7.22)

and the relative Reynolds number, 𝑅𝑒s, is defined as:

𝑅𝑒s =𝜌s𝑑s|𝑣g⃗⃗ ⃗⃗ − 𝑣s⃗⃗⃗⃗ |

𝜇g (7.23)

7.2.4 Turbulence model

In this study, a standard k- ε model was used to solve the transport equations for k and ε. The k-

ε model is written as:

∇ ∙ (𝜌𝑚𝑘 𝑣𝑚⃗⃗⃗⃗⃗⃗ ) = ∇ ∙ (𝜇𝑡,𝑚𝜎𝜀

∇𝑘) + 𝐺𝑘,𝑚 − 𝜌𝑚𝜀 (7.24)

∇ ∙ (𝜌𝑚𝑘 𝑣𝑚⃗⃗⃗⃗⃗⃗ ) = ∇ ∙ (𝜇𝑡,𝑚𝜎𝜀

∇𝜀) +𝜀

𝑘(𝐶1𝜀𝐺𝑘,𝑚 − 𝐶2𝜀𝜌𝑚𝜀) (7.25)

where the mixture density and velocity are calculated as:

𝜌𝑚 =∑𝛼𝑖𝜌𝑖

𝑁

𝑖=1

(7.26)

𝑣𝑚⃗⃗⃗⃗⃗⃗ =∑ 𝛼𝑖𝜌𝑖𝑣𝑖⃗⃗⃗ ⃗𝑁𝑖=1

∑ 𝛼𝑖𝜌𝑖𝑁𝑖=1

(7.27)

The turbulent viscosity for the mixture is described as:

𝜇𝑡,𝑚 = 𝜌𝑚𝐶𝜇𝑘2

𝜀 (7.28)

7.3 Simulation conditions

Geometry and boundary conditions are discussed in this section and the solution procedure is

also presented.

7.3.1 Geometry and boundary conditions

In this chapter, the geometry of the air-gravity conveying system was based on the air-gravity

conveyor structure. The study by Gupta et al. (2010) was also initially used in order to compare

the model results with their measurements for the purpose of CFD model verification.

Therefore, in the CFD simulation a 6 m length channel with a 100×100 mm square cross-section

was chosen. The channel was simplified by taking into account the symmetry boundary

condition at the centreline of the channel, as shown in Figure 7.1, which was used to save the

167

simulation time. Thus, the cross section of the channel in our simulation is 100×50 mm.

Basically, a sweep method was used to mesh the channel from the inlet to the outlet face with a

gradually enlarged sweep type. Also, a local grid refinement method was applied to improve the

channel bottom. In total, 48000 cells with a minimum cell size of 8.136×10-8 m3 were employed

to simulate the fluidised motion flow.

At the inlet boundary, a velocity inlet condition was used with a given volume fraction for

conveying materials. At the bottom of the material bed, a velocity inlet was applied to simulate

the porous bed where the fluidising air was introduced. This method had been used by many

researchers (Wang et al, 2010; Anjaneyulu and Khakhar, 1995). A partial slip condition was

assumed for the side and top of walls with varying specularity coefficient values. At the outlet, a

pressure outlet boundary condition was specified, i.e. P=0 (relative to ambient pressure).

Figure 7.1 Meshing result of 3D computational geometry

7.3.2 Solution procedure

As described previously, the aim of this study is to develop approaches to predict the air-gravity

conveying behaviour from a fundamental perspective based on appropriate governing equations

for the gas-solid mixture. A Eulerian-Eulerian approach was used to study the gas-solid

interactions, and simulations were carried out using FLUENT (ANSYS 17.2) in double

precision mode. The standard k-ε dispersed model was employed to consider the turbulence

flow, whilst the kinetic theory of granular flow was applied to describe the momentum balance

equation for the solid phase. Air is taken as a continuous phase, while sand/flyash particles are

treated as continua, interpenetrating and interacting with each other and everywhere in the

computational domain. The frictional packing limit, which is the critical value of the solids

volume fraction when frictional stress can be added to the stress predicted by kinetic theory, was

168

modified to the value of 0.46 to fit the actual solid volume fraction distribution at a material

fluidised state for sand. Meanwhile, the packing limit can be calculated from the material tapped

bulk density to the value of 0.61 instead of the default value 0.63. As for flyash, the frictional

packing limit is 0.25, while the packing limit is 0.54. The phase coupled SIMPLE algorithm was

used to couple pressure and velocity. The convergence criteria for all the numerical simulations

were based on monitoring the residuals of all variables, i.e. 10-3 for the velocity residue whilst

10-4 for the mass flow continuity residual.

Table 7.1 Model parameters

Descriptions Values

Granular viscosity Gidaspow et al.

Granular bulk viscosity Lun et al.

Frictional viscosity Schaeffer

Angle of internal friction 30o

Granular temperature Algebraic

Drag law Gidaspow et al.

Coefficient of restitution for particle-particle collisions 0.9

Inlet boundary condition Velocity inlet

Outlet boundary condition Pressure outlet

Wall boundary condition No slip for air, specularity

coefficient 0 for solid phase

The simulation started with a given velocity of granular material at the inlet. Meanwhile, air

came from the bottom of the channel bed at a proper velocity to fluidise the material. The

inclination angle can be defined as the angle included by the gravity vector and the direction

that is normal to the channel bed. The gravitational forces at flow direction initially accelerated

the flow down the inclined channel and then the velocity and solid concentration profiles

gradually evolve as time proceeds. Meanwhile, the air from the bottom which is used to fluidise

the materials will provide an additional driving force due to interfacial shear stress in the non-

vent conveying system. As described above, the CFD model was solved using Fluent, and the

detailed settings in the software are listed in Table 7.1.

7.4 Investigation of model parameters

CFD modelling was first carried out to study the hydrodynamics of fluidised motion conveying

where flyash of particle size 108 µm is fluidised (Gupta, 2010). There are many factors and

parameters that determine the characteristics of flow in fluidised motion conveying. The

investigation into the effects of various model parameters, i.e., grid independency,

169

laminar/turbulence flow models, drag models, specularity coefficient and coefficient of

restitution, on model results are needed and conducted in this section.

7.4.1 Grid independency

A grid independent test has been performed in the CFD model with different mesh sizes, and

40000 (without refinement at the bottom), 48000 and 72000 numbers of hexahedral cells. Figure

7.2a shows the comparison of variations in the centreline volume fraction of material at the

position of 2.74 m for different mesh sizes. It can be seen that the volume fraction distribution

of 40000 cells had a similar type to that for the other two mesh sizes at the upper bed, the

materials all being transported at the channel bottom area and the material volume fraction

decreasing from 0.4 at a bed height of 30 mm to zero at above 50 mm. The material volume

fraction curve showed a sharp increase at the bottom material layer and then increased slowly as

the bed height increased before the fraction dropped. However, for the 40000 cells case, the

variation in volume fraction near the bed bottom is not shown, as there was not further

refinement of the cells at the bottom, unlike that seen in the other two cases. This indicates that

refinement is needed for the simulation cases to show better characteristics of flow. As seen in

Figure 7.2b, the velocity distribution nearly kept constant at the whole main material layer for

the 40000 cells case. But for the other two, the upper material velocity was larger than the

bottom, which generally matched the material flow characteristics in airslide flow (Oger and

Savage, 2013). From the simulation results using 48000 and 72000 cells, it has been observed

that the predicted curves for volume fraction and velocity distribution are comparable.

Moreover, they both show detailed features of the volume fraction on the bottom and the

velocity change at different heights of the material layer. However, the larger number of

computational cells will result in more simulation time. Thus, as a trade-off, 48000 cells are

deemed appropriate in the simulation at this flow condition.

(a) volume fraction (b) velocity distribution

Figure 7.2 Model results at the centreline when using different mesh sizes

170

7.4.2 Flow models (Laminar and Turbulence)

Generally, turbulent flow appears in most engineering problems. Reynolds numbers (Re) are

used to help predict flow patterns in different flow situations. Here in fluidization flow, the

value of Re numbers are around 4000 and belong to the transitional flow which is a mixture of

laminar and turbulent flow. With the increase of fluidising air velocity, the flow changes to

turbulent flow. Both the laminar and turbulent models are investigated and the comparison of

simulation results for laminar and turbulence models predictions are presented in Figure 4 for

profiles of solid volume fractions, particle velocity and granular temperature in the centreline at

the channel length of 2.74 m. It is observed that the bed expansion of the turbulence and laminar

model is similar; material gathers at the lower bed that results in a higher solid volume fraction

at the lower bed than the upper part. Also, the bed height in both models is the same (Figure

7.3a). However, the velocity distribution shows a much greater difference at the main material

layer in Figure 7.3b. The material velocity in the laminar model is uniform with a sharp increase

near the material surface, while the turbulence model experiences a gradual increase in velocity

from lower parts of the material layer to the material’s upper surface. Though a constant

velocity at each channel length is always used in industry to estimate the flow, a non-uniform

velocity profile actually exists in material flow in fluidised motion conveying. Savage and Oger

(2013) already provided a non-Newtonian viscosity model to describe the power-law velocity

distribution for a free surface flow in airslide. They also indicated that the velocity shapes

behaved with a significant change to the shape like the present velocity distribution in the

turbulent model, which they call a “lift-off” with slip at the bed (Oger and Savage, 2013).

In addition, the laminar flow model gives a similar granular temperature value as the turbulence

model in the centreline (Figure 7.3c), but a lower granular temperature value than the turbulent

model near the channel wall (Figure 7.3d). The maximum of the granular temperature means

that solid particles have much space to fluctuate. At the bottom the granular temperature (Figure

7.3c) is greater as the fluidised air comes from the bottom to fluidise the material in the channel.

At the wall the granular temperature is high in the turbulence model (Figure 7.3d) because of

the wall effects on the solid particles. At the centre of the flow channel, the granular temperature

is low because the particle-particle interactions caused by particle collisions are increased.

Therefore, taking into account the volume fraction and velocity distribution calculated by the

turbulent model and the turbulent interaction between phases, it can be concluded that the

turbulent model predictions are more realistic in fluidised motion conveying.

171

Figure 7.3 Comparison of laminar and turbulent models for centreline (a) volume fraction, (b)

velocity distribution, (c) Granular temperature and (d) cross section Granular temperature at the

bed of 0.03 m

7.4.3 Drag models

The drag force between the gas and solid particles is one of the dominant forces for a fluidised

motion conveyor, along with the gravitational force in the downward flow. There are three

models, i.e. Gidaspow (1992), Wen-Yu (1966) and Syamlal-O’Brien (Syamlal et al., 1993), that

are the most commonly used in CFD simulations for multiphase flow systems. The Gidaspow

model is a combination of the Wen and Yu model and the Ergun model, which is recommended

for fluidised flow by FLUENT and researchers (Behera et al., 2013). The Wen and Yu model is

applicable for dilute flow and the Syamlal-O’Brien model is better for use in dilute flow, as well

as in conjunction with its granular viscosity model.

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Figure 7.4 Centreline (a) volume fraction and (b) velocity distribution for different drag models

Estimated by these three drag models were the centreline solid volume fraction and particle

velocities as a function of channel height at the position of 2.74 m along the channel length, and

the results are plotted in Figure 7.4. It can be seen that the bed height predicted by the Gidaspow

and Syamlal-O’Brien models were almost the same, whilst the use of the Wen-Yu model gave a

lower bed height value. The particle velocity distribution derived by Wen-Yu and Syamlal-

O’Brien models shows a constant value. However, the Gidaspow model clearly gives an

increased velocity profile from the material bed bottom upwards, which has also been observed

in the study of airslide by Oger and Savage (2013), and they correspond to the non-Newtonian

power law viscosity model. The results obtained from these models indicate that the use of

Gidaspow’s (1992) drag model may be the most appropriate for a fluidised motion conveying

system and also be used in the simulation for the evaluation of other parameters.

7.4.4 Specularity coefficient

The specularity coefficient used in multiphase flow with granular temperature is a measure of

the fraction of collisions that transfer the momentum to the wall. The value of the specularity

coefficient can vary from zero (for smooth walls) to unity (for rough walls), in specifying the

level of roughness or shear to the wall. The zero specularity coefficient means a free-slip

boundary condition being equivalent to zero shear at the wall, whilst a value of unity

corresponds to diffuse collisions as would occur with a rough wall, and a significant amount of

momentum being transferred.

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Figure 7.5 Comparison of specularity coefficients for centreline (a) volume fraction, (b) velocity

distribution and (c) cross section velocity distribution, (d) granular temperature at the height of

0.03 m

The effect of the specularity coefficient on the flow behaviour in a fluidised motion conveying

system has been investigated by using the coefficient value of 0, 0.1, 0.5 and 1. The results are

plotted in Figure 7.5. At the same location of 2.74 m, it can be seen in Figure 7.5a that the larger

specularity coefficient has a higher bed height at the centreline. As expected, a higher value of

specularity coefficient leads to reduced particle flow velocities (shown in Figure 7.5b). The

curves for volume fraction and velocity distribution were comparable when using the larger

specularity coefficients of 0.5 and 1, and this may be because much more momentum

transferred to the wall compared to the smaller values of the specularity coefficient.

Figure 7.5c and 7.5d illustrate the velocity and granular temperature (at a height of 0.03 m)

distributions across the channel width. According to Figure 7.5c, the velocity almost kept

constant under free-slip conditions. However, all the other three velocity profiles appeared

parabolic, being similar to those presented by Oger and Savage (2013). The decrease in velocity

at the position from the centreline to the wall was due to the existence of shear conditions at the

wall. The velocity curves for specularity coefficient 0.5 and 1 were found to be the same, but

they reduced more than that for the coefficient of 0.1. This is because at a higher specularity

coefficient value the resistance is greater, so that the particles are more reluctant to move. It can

174

be seen in Figure 7.5d that the granular temperature was found higher closer to the channel wall

than the inside due to the wall effects on the solid particles. With a smaller specularity

coefficient (lower frictional factor), a higher velocity near the wall was observed in the present

study which shows a better agreement with the findings by others (Benyahia et al., 2005).

Therefore, the partial-slip boundary condition with a specularity coefficient of 0.1 will be used

in the simulation.

7.4.5 Coefficient of restitution

The coefficient of restitution expresses the energy dissipation due to the particle-particle

collision and particle-wall collision. A higher value of particle-particle restitution coefficient

describes a higher elasticity of collisions, and the value of 1 means that the particle-particle

collision is ideal and no energy dissipation generates due to the collision. On the other hand, the

value of 0 means that the particles stick together. In FLUENT, the default value for the

restitution coefficient is 0.9, but the actual particle-particle restitution coefficient is difficult to

measure for a given fluidised motion conveying system. Therefore, three different values of

restitution coefficients, i.e. 0.85, 0.9 and 0.99, are examined and the results are compared.

Figure 7.6 Centreline (a) volume fraction and (b) velocity distribution for different restitution

coefficients

It has been found that the variation in restitution coefficient does not affect the centreline solid

volume fraction (Figure 7.6a) simulation results significantly. Negligible difference in volume

fraction was observed when compared to the results obtained with these three values of

restitution coefficients while all other parameters remained constant. However, the average

velocity value at the restitution coefficient of 0.99 was largest among the three cases (Figure

7.6b). As explained previously, with the restitution coefficient increased to close to 1, the

collisions among particles become ideal, therefore the momentum loss reduces, resulting in a

larger conveying velocity. There was little difference in the simulation results for the restitution

of 0.85 and 0.9.

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7.5 Recommended parameters

The above verification process proves the best parameter choice for an air-gravity conveying

system. The basic model parameter choice can be the same as shown in Table 7.1. The

recommended parameters for further air-gravity conveying model applications are discussed and

the details can be seen below in Table 7.2.

Table 7.2 Optimum parameters

Descriptions Values

Grid independency 48000 cells with bottom refinement

Flow model Turbulent model

Drag model Gidaspow

Specularity coefficient 0.1

Coefficient of restitution 0.9

7.6 Verification of the model

The model was validated by comparing it with the data from the study by Gupta et al. (Gupta,

2010). In this study, the operating parameters in the simulations chosen were the same as those

in the paper (Table 7.3), and the resultant bed height along the conveying channel and the bed

height at different inclination angles were compared. Moreover, this section presents the results

of further computations to examine the effects of velocity distribution at cross sections of the

conveying channel.

Table 7.3 Properties of conveyed material

Material property Values

Fluidised density (kg/m3) 665.6

Minimum fluidising velocity (mm/s) 25.1

Median particle size (µm) 108

The solid volume fraction on the conveying channel was estimated using CFD for three

inclination angles of 1.07o (downward), 0o and -1.68o (upward). The results for 1.07o

(downward) are shown in Figure 7.7. It can be seen that flyash had a higher solid volume

fraction at the lower bed than at the upper part. The boundary of the material bed can be defined

as where the volume fraction is equal to or greater than 0.05. The predicted bed height has been

found to decrease along the channel.

176

Figure 7.7 Simulation results of solid volume fraction

Figure 7.8 shows the bed heights at three locations (0.91 m, 2.74 m and 4.57 m) for three

inclination angles. It can be seen that the computed bed heights by CFD are in good agreement

with the measurements by Gupta et al. (2010). For each location, the bed height was increased

by changing the inclination angle from downward to horizontal and the predicted trend was

consistent with that in the experimental study (Gupta et al., 2010). For a vent conveying system,

it is impossible to convey material in an upward inclined channel without any structural

modification because the gravitational component tends to resist the motion at the flow

direction. However, for a fluidised motion conveyor, the constructional change through

enclosing the conveying channel makes it feasible to transport the material upwards. The bed

heights near the feed end in an upwardly inclined channel were found to be greater than those

for the downward and horizontal channel cases. This was because there was permanent hold up

of fluidised material bed in the conveying section (Gupta et al., 2010). Meanwhile, the height of

the flyash bed at an upstream location is always higher than that at downstream locations. The

reason was because the continuous incoming air in the CFD simulation did not only fluidise the

material but also played an acceleration role in assisting the material’s flow along the channel in

the non-vent conveying system, which would cause the acceleration of flyash flow because of

the increased shear stress at the top surface of the moving material bed. Therefore, there was a

decrease in the material bed depth along the flow direction. Moreover, the higher velocity would

decrease the bed viscosity due to the decrease in the material bed height, which would further

contribute to the acceleration (Latkovic and Levy, 1991). Thus, the accelerated material flow

from the downstream locations of the conveyor resulted in the lower material bed depth at the

exit end and high material bed depth at the feed position.

177

Figure 7.8 Comparison of CFD and experimental bed heights along the channel with different

inclination angles

7.7 CFD model results of sand and flyash flow

According to the analysis process proposed above, the CFD method is used to predict the flow

behaviour of sand and flyash flow in our system. As for the time and resource problem, only the

typical fluidised flow of sand and flyash is simulated, with details shown below.

7.7.1 Sand (vent)

CFD results on fluidised conveying of sand at vent flow condition are discussed in this section.

The well fluidised case with the superficial velocity of 128 mm/s and mass flow rate of 1.70

kg/s is studied below to more deeply understand the flow behaviour for air-gravity conveying.

7.7.1.1 Bed height along the channel for vent sand flow

The solid volume fraction on the air-gravity conveying channel was calculated by CFD for vent

sand flow as shown in Figure 7.9. The colour bar shows the value of the sand volume fraction,

and here the value of 0.61 is the packing limit for sand instead of the default value 0.63. It can

be seen that sand has a higher solid volume fraction at the lower bed than at the upper part. The

predicted sand flow bed experienced a decrease trend along the channel. The bed height

decreased quickly at the inlet section and then decreased slowly, and then the bed height finally

stabilised at around 19 mm. The bed height along the channel compared well with the sand flow

observed in this vent flow under fluidised flow conditions.

178

Figure 7.9 Simulation results of the solid volume fraction for vent sand flow

7.7.1.2 Centreline volume fraction and velocity along the channel for vent sand flow

Figure 7.10 shows the centreline volume fraction at the location of 1, 2 and 5 m along the

channel for vent sand flow. The maximum volume fraction was in the middle of the middle of

conveying layer, because the fluidised velocity comes from the bottom to fluidise the material,

and then balances with gravity at the middle of the material layer. A layer of air was supposed

to remain at the bottom of the channel in the simulation with the air inlet boundary condition at

the channel bottom. However, it is difficult to form this ideal condition because of the existence

of a porous layer at the channel bottom. Material could stay at the bottom to act as an additional

porous medium in the conveying system; also, friction will resist the flow of fluidised material

and reduce its conveying velocity. The material bed height is 20 mm at 1 m, and higher than the

bed height at 2 m (19 mm) and 5 m (18 mm).

Figure 7.10 Centreline volume fraction at the location of 1, 2 and 5 m for vent sand flow

Figure 7.11 presents the velocity distribution at centreline at 1, 2 and 5 m for vent sand flow. It

can be seen that the velocity showed a slowly increasing trend from the bottom to the top

surface of the material layer. The velocity profiles were quite similar to the power law velocity

distribution for each location. Meanwhile, the velocity increased along the channel with the

acceleration of material under the condition of gravity and the continuous income of air from

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5 0.6

Hei

ght

(mm

)

Volume fraction

1 m

2 m

5 m

179

the channel bottom. The velocity at the channel bottom had a slip velocity smaller than the

material layer conveying velocity; this is because the velocity inlet condition used in the CFD

simulation resulted in the similar fluidised state for the material at the bottom.

Figure 7.11 Centreline velocity distribution at the location of 1, 2 and 5 m for vent sand flow

7.7.1.3 Velocity distribution at the cross section of the channel at the location of 5 for

vent sand flow

Figure 7.12 presents the cross section velocity distribution (here the symmetry velocity has been

added to show the whole channel width) at three different bed heights (5 mm, 10 m and 15 m) at

the location of 5 m. It is observed that the velocity profile shapes exhibit approximately a

constant value for each bed height, and the velocity quickly decreases to zero near the channel

side wall. It is also found that the velocity difference for each bed height is reduced close to the

wall of the channel. This is because of the wall resistance on flow materials and the velocity

profile which tends to be uniform near the wall finally reduced to zero.

0

20

40

60

80

100

0 0.5 1 1.5 2

Hie

gh

t (m

m)

Velocity (m/s)

1 m

2 m

5 m

180

Figure 7.12 Cross section velocity distribution for different bed height (5 mm, 10 mm and 15

mm)

7.7.1.4 CFD predicted bed height at 5 m for vent sand flow

The CFD model can be used to predict the material flow behaviour at all flow ranges quite well.

As shown in Figure 7.13, the bed heights at 5 m in the CFD simulation were used in comparison

with the experimental bed height. As for the fluidised flow region, the CFD bed heights are

quite close to the test bed heights. For the translation and pulsatory movement region, the static

bed height measured by the experiments are added into the CFD model, as the CFD method

cannot well simulate the fluid flow without any movement. It is found that all the predicted bed

heights matched the value of the experimental results at those regions very well. The error is

smaller than 10%. Therefore, such a CFD conveying model shows the potential of predicting

fine powder air-gravity flow performance.

0

0.4

0.8

1.2

1.6

2

0 20 40 60 80 100

Vel

oci

ty (

m/s

)

Channel width (mm)

5 mm

10 mm

15 mm

181

Figure 7.13 Comparison between CFD prediction (vent sand flow) and experimental bed height

7.7.2 Sand (non-vent)

CFD results on fluidised conveying of sand at non-vent flow condition are discussed below.

This case is based on the value obtained by the well-fluidised condition, the same as vent sand

flow with the mass flow rate of 2.06 kg/s.

7.7.2.1 Bed height along the channel for non-vent sand flow

The solid volume fraction of the air-gravity conveying channel was simulated by using CFD for

non-vent sand flow, as shown in Figure 7.14. Similarly, the colour bar shows the value of the

sand volume fraction, and the value of the packing limit is 0.61 for sand. It can be seen that sand

had a higher solid volume fraction at the lower bed than that at the upper part. The predicted bed

height has been found to decrease along the channel. The bed height decreased sharply at the

inlet section and then decreased slowly, finally stabilising at the bed height of around 18 mm.

The bed height along the channel compared well with the sand flow in this non-vent flow under

fluidised flow conditions.

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Pre

dic

ted b

ed h

eight

(mm

)


Transition


Pulsatory movement

Fluidisedflow

-30% error

+30% error

182

Figure 7.14 Simulation results of solid volume fraction for non-vent sand flow

7.7.2.2 Centreline volume fraction and velocity along the channel for non-vent sand flow

Figure 7.15 illustrates the centreline volume fraction at the location of 1, 2 and 5 m along the

channel. The bed height decreased along the channel length as can be seen in Figure 7.15 and

the maximum volume fraction occured in the middle of the conveying material layer. It is

because the fluidised velocity comes from the bottom to fluidise the material, that a layer of air

was supposed to remain at the bottom of the channel in the simulation. However, as in an air-

gravity conveyor, the existence of a porous membrane will not form the ideal condition as in the

CFD simulation. Material may stay at the bottom to act as an additional porous medium in the

conveying system; also, friction will resist the flow of fluidised material and reduce its

conveying velocity. The material bed height is 23 mm at 1 m, and higher than the bed height at

2 m (19 mm) and 5 m (18 mm).

Figure 7.15 Centreline volume fraction at the location of 1, 2 and 5 m for non-vent sand flow

Figure 7.16 presents the velocity distribution at the centreline at 1, 2 and 5 m. Obviously,

velocity almost kept a constant at the material layer under well-fluidised conditions at the

location of 1 m and 2 m, while for the location of 5 m, the velocity at the material layer behaved

like a power law velocity profile. The velocity increased along the channel with the acceleration

of material under the condition of gravity and air at the top of the channel. The velocity at the

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5 0.6

Hei

ght

(mm

)

Volume fraction

1 m

2 m

5 m

183

channel bottom had a slip velocity a little bit smaller than the material layer conveying velocity;

this is because the velocity inlet condition used in CFD simulation results in the similar

fluidised state for the material at the bottom. The friction forces acting on the powder were

reduced by the effect of air flow to the bottom of the channel.

Figure 7.16 Centreline velocity distribution at the location of 1, 2 and 5 m for non-vent sand

flow


non-vent sand flow

Figure 7.17 shows the cross section velocity distribution (here the symmetry velocity has been

added to show the whole channel width) at three different bed heights (5 mm, 10 m and 15 m) at

the location of 5 m. It is observed that the velocity profile shapes exhibit approximately

parabolic profiles for the height of 15 mm, while the velocity profile keeps a constant at the

lower bed height at the inner channel; the velocity quickly decreases to zero near the channel

side wall. Botterill and Bessant (1976) assumed that the fluidised materials behaved as a power-

law fluid and calculated approximately parabolic velocity profiles along the channel width.

Oger and Savage (2103) simulated some existing experiments (Botterill et al., 1976), and the

results of velocity profiles across the channel width at different distances from the bed showed

similar parabolic profile shapes, but the stable velocity distribution was found in the current

simulation. The velocity profiles calculated by present numerical simulations are able to give

reasonable predictions over the cross-section of the rectangular flow channel. It is also found

that the velocity at the upper bed is higher than the lower bed in the channel centre, with the

velocity difference for each bed height reduced close to the wall of the channel. This is because

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Hei

gh

t (m

m)

Velocity (m/s)

1 m

2 m

5 m

184

of the wall resistance on flow materials and the velocity profile tending to be uniform near the

wall finally reduced to zero.


mm)

7.7.2.4 CFD predicted bed height at 5 m for non-vent sand flow

The bed heights at 5 m in the CFD simulation were used to compare with the experimental bed

heights as shown in Figure 7.18. The static bed height was added into the CFD model, as the

CFD model cannot model its flow without any movement. It is found that all the predicted bed

heights matched the value of experimental results very well. The CFD model can be used to

predict the material flow behaviour at all flow ranges quite well. Overall, such a CFD conveying

model shows the potential of predicting fine powder air-gravity flow performance.

0

0.4

0.8

1.2

1.6

2

0 20 40 60 80 100

Vel

oci

ty (

m/s

)

Channel width (mm)

5 mm

10 mm

15 mm

185

Figure 7.18 Comparison between CFD prediction (non-vent sand flow) and experimental bed

height

7.7.3 Flyash (vent)

CFD results on fluidised conveying of flyash at vent flow conditions are presented in this

section. The superficial air velocity of this test is 42.6 mm/s and its mass flow rate is 2.56 kg/s.

7.7.3.1 Bed height along the channel for vent flyash flow

The results of vent flyash flow in the air-gravity conveying channel were simulated and can be

seen in Figure 7.19. The colour bar describes the value of the flyash volume fraction, and here

the value of 0.31 is the largest volume fraction for this case. The conveying flyash bed depth at

an upstream location is always higher than that at downstream locations. In detail, the flyash

bed height decreased quickly at the inlet area of the conveying channel and then more slowly at

the latter channel. Moreover, the volume fraction profiles at different distances from the bed

showed that the density of conveying material close to the channel bed is always larger than the

upper area. This is because the gravity force acting on the conveying material contributes to the

material coming down to the bottom bed. At the channel length close to the outlet, the solid

volume fraction is low and seems to be a constant for the whole bed height area. The bed height

along the channel compared well with the flyash flow in this vent flow testing under fluidised

flow condition.

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Pre

dic

ted b

ed h

eight

(mm

)


Transition



+30% error

-30% error

186

Figure 7.19 Simulation results of solid volume fraction for vent sand flow

7.7.3.2 Centreline volume fraction and velocity along the channel for vent flyash flow

Figure 7.20 provides the centreline volume fraction for flyash at the location of 1, 2 and 5 m

along the channel. Obviously, the volume fraction at the same height of the conveying channel

shows a decrease along the channel. The volume fraction at the channel length of 1 m is higher

than that of 2 m and 5 m. This is because the conveying flyash at the length of 1 m is still in

acceleration and the conveying velocity has not reached stable conveying velocity. The

maximum volume fraction does not exist in the bottom of the conveying material layer, but is a

little bit higher than the channel bed. It is because the fluidised velocity comes from the bottom

to fluidise the material; air was supposed to remain at the bottom of the channel in the

simulation, which would then reduce the volume fraction at the channel bottom. However, as in

an air-gravity conveyor, the existence of a porous membrane will not form the ideal condition,

as in the CFD simulation. Flyash tended to stay at the bottom of the channel, acting as an

additional porous medium in the conveying system. For the bed height at the channel length of 5

m, if the volume fraction near the channel bottom and top is ignored, the volume fraction of

fluidised flyash almost keeps constant at the conveying material layer, and this is the evidence

of a good fluidisation of flyash. Also, this condition will result in a uniform conveying velocity

for the whole moving material.

Figure 7.20 Centreline volume fraction at the location of 1, 2 and 5 m for vent flyash flow

0

20

40

60

80

100

0.00 0.05 0.10 0.15 0.20 0.25

Hei

gh

t (m

m)

Volume fraction

1 m

2 m

5 m

187

Figure 7.21 shows the velocity distribution at the centreline at 1, 2 and 5 m. The velocity almost

kept constant at the conveying material layer under well-fluidised conditions at the location of 1

m, 2 m and 5 m. While for the area near the channel bottom, the flyash velocity showed a linear

increase velocity profile from the channel bottom. Meanwhile, the velocity at the channel

bottom had a slip velocity, which is smaller than the conveying velocity for the fluidised

material layer. The slip velocity is caused by the velocity inlet condition used in the CFD

simulation, which will result in a fluidised state at the bottom of the channel. The friction forces

acting on the conveying flyash were reduced by the effect of aeration to the bottom of the

channel. Also, the velocity increased along the channel with the acceleration of material under

the conditions of gravity and aeration.

Figure 7.21 Centreline velocity distribution at the location of 1, 2 and 5 m for vent flyash flow

7.7.3.3 Velocity distribution at the cross section of the channel at the location of 5 m for

vent sand flow

Figure 7.22 shows the velocity distribution across the width of the channel (here the symmetry

velocity has been added to show the whole channel width) for different vertical distances from

the channel bed (10 mm, 20 mm and 30 mm) at the location of 5 m. The velocity profile shapes

from the present simulations and parabolic profile are seen to be similar. It can be seen in Figure

7.22 that the velocity at the middle of the channel cross section is almost a constant, while the

velocity quickly decreases to zero when the value of velocity is close to the channel side wall.

This is because of the wall resistance on the flow material, which reduces the conveying

velocity. Also, the velocity at the upper layer of conveying material is higher than the lower bed

height. The increase in the value of velocity from the bed height of 20 mm to 30 mm is smaller

0

20

40

60

80

100

0 0.5 1 1.5 2 2.5

Hei

ght

(mm

)

Velocity (m/s)

1 m

2 m

5 m

188

than the bed height from 10 mm to 20 mm. The reason for the smaller increase rate is that the

velocity at the upper layer tends to become the same velocity when the conveying flyash has

been well fluidised. Similarly, these predicted trends are consistent with the power-law flow

modelling (Savage and Oger, 2013) and the phenomenon observed during the air-gravity

conveying testing.


mm)

7.7.3.4 CFD-predicted bed height at 5 m for vent flyash flow

The CFD model is applied to predict the material flow behaviour along the channel. Here the

bed height at the length of 5 m is used to compare with the experimental results. As shown in

Figure 7.23, it was found that all the predicted bed heights are larger than the experimental

result except for one point. The reason for this is that the average particle diameter of flyash is

as small as 31.7 µm, which can be easily fluidised by adding fluidising air. As a result, flyash in

the conveying channel is in an expanded state, with fluid-like behaviour. While in the

experiments, the particles easily aggregate and the particle size will normally be larger than the

average particle size. Therefore, flyash cannot be fluidised perfectly and the bed height will be

lower than the value expected. So the simulated bed height will be higher than the experimental

results. However, all the errors are smaller than 30%, which still means that the CFD method is

good for air-gravity conveying predictions.

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Figure 7.23 Comparison between CFD prediction (vent flyash flow) and experimental bed

height

7.7.4 Flyash (non-vent)

The CFD results on fluidised conveying of flyash at non-vent flow condition are discussed in

this section. This case is under the superficial air velocity of 42.6 mm/s, with a mass flow rate of

2.18 kg/s.

7.7.4.1 Bed height along the channel for non-vent flyash flow

The results of non-vent flyash flow in the air-gravity conveying channel were simulated by

using CFD FLUENT. The colour bar shows the value of flyash volume fraction, as shown in

Figure 7.24. The flyash bed height decreased sharply at the inlet area of the conveying channel

and then become stable for the latter channel. Also, at the first two metres, it can be seen

obviously that flyash had a higher solid volume fraction at the lower bed than at the upper part.

While at the channel length close to the outlet, the solid volume fraction is low and seems to be

a constant. The predicted bed height has been found to decrease along the channel. The bed

height along the channel compared well with the sand flow in this non-vent flow under fluidised

flow conditions as well.

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Figure 7.24 Simulation results of solid volume fraction for non-vent flyash flow

7.7.4.2 Centreline volume fraction and velocity along the channel for non-vent sand flow

Figure 7.25 presents the centreline volume fraction for flyash at the location of 1, 2 and 5 m

along the channel. The bed height fluctuates but the average volume fraction decreases along

the channel length. For the first two metres, the maximum volume fraction existed in the middle

of the conveying material layer. Because the fluidised velocity comes from the bottom to

fluidise the material, air was supposed to remain at the bottom of channel in the simulation.

However, as in an air-gravity conveyor, the existence of a porous membrane will not form the

ideal condition as in the CFD simulation. Material may stay at the bottom to act as an additional

porous medium in the conveying system. For the bed height at the channel length of 5 m, the

volume fraction of fluidised flyash was almost kept constant at the upper material layer; this is

caused by the easy fluidisation of flyash. Also, this condition will result in the uniform

conveying velocity for the whole moving material.

Figure 7.25 Centreline volume fraction at the location of 1, 2 and 5 m for non-vent flyash flow

Figure 7.26 presents the velocity distribution at the centreline at 1, 2 and 5 m. Obviously,

velocity almost kept a constant at the material layer under well fluidised conditions at the

location of 1 m and 2 m, while for the location of 5 m, the velocity at the material layer showed

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a linear increase velocity profile from the channel bottom. The velocity increased along the

channel with the acceleration of material under the condition of gravity and air at the top of the

channel. The velocity at the channel bottom had a slip velocity a little bit smaller than the

material layer conveying velocity; this is because the velocity inlet condition used in the CFD

simulation resulted in a similar fluidised state for the material at the bottom. The friction forces

acting on the powder were reduced by the effect of air flow to the bottom of the channel.

Figure 7.26 Centreline velocity distribution at the location of 1, 2 and 5 m for non-vent flyash

flow


non-vent flyash flow

Figure 7.27 shows the profiles of the streamwise velocities across the width of the channel (here

the symmetry velocity has been added to show the whole channel width) for different vertical

distances from the channel bed (10 mm, 20 mm and 30 mm) at the location of 5 m. As would be

expected, a higher value of bed height will have higher particle flow velocities. The velocity

profiles indicated by the small dotted lines correspond to a constant flow velocity at the middle

of the conveying channel, and the velocity profile shapes from the present simulation show that

this is slightly higher than the velocities at the middle area of the channel. However, the velocity

profiles quickly decrease to zero near the channel side wall. This is because of the wall

resistance on flow materials and the velocity profile exhibits a reducing trend near the wall

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192

finally reduced to zero. These predicted trends are consistent with the power-law flow

modelling (Savage and Oger, 2013) and experimental observation during testing.

Figure 7.27 Cross section velocity distribution for different bed heights (10 mm, 20 mm and 30

mm)

7.7.4.4 CFD-predicted bed height at 5 m for non-vent flyash flow

Figure 7.23 presents the comparison between predicted bed heights and experimental bed

heights. All the bed heights are obtained at the length of 5 m as it is considered where the steady

flow is formed. Like the vent flyash flow, the CFD model is good at predicting the material flow

behaviour along the channel. It is also found that almost all the predicted bed heights are larger

than the experimental results. The reason, as discussed above, is that the average particle

diameter of flyash is too small, so that aggregation cannot be avoid during air-gravity conveying

testing. The particle aggregation will lead to the particle size enlarging, which will be larger

than the tested 31.7 µm. In other words, the particle size of flyash being conveyed in the

conveying channel become large and then the bed height during testing is lower than the CFD

predictions. It is also proved that an increase in the particle size will decrease the CFD bed

heights by simulation. In any case, all the errors fall into the 30% error region, and so this CFD

model is good for air-gravity conveying predictions.

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Figure 7.28 Comparison between CFD prediction (non-vent flyash flow) and experimental bed

height

7.8 Conclusion

In this study, a 3D CFD model was applied to describe the gas-solid flow in an air-gravity

conveying system. The effects of some important modelling parameters on the flow field were

examined. The model was validated by comparing the bed height along the channel with the

experimental results measured by Gupta et al. (Gupta, 2010). What’s more, the model can also

be used to provide the prediction of velocity distribution in vent and non-vent air-gravity

conveying. A good agreement relating to the prediction of material bed height along the channel

was found when comparing the simulated results with the bed depth in Gupta et al.’s study.

Following this, a CFD study of vent and non-vent air-gravity conveying was applied to simulate

the flow of sand and flyash flow based on the experiments. Bed height along the conveying

channel, centreline volume fraction and velocity along the channel, velocity distribution at the

cross section of channel and predicted bed height were investigated, and results show that the

CFD simulation predicted the flow behaviour of air-gravity conveying quite well. These

detailed investigations have improved the understanding of air-gravity conveying systems,

which have previously suffered from lack of numerical support. However, it must be noted that

the recommended parameters are not the optimum parameters for each case; these parameters

can just provide a good simulation of results close to the experimental data. Once the right

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parameters are selected, the CFD results could be better and fit better with the actual flow

behaviour.

Fortunately, the present study is the first successful attempt to model flows in a fluidised motion

conveyor considering the detailed mechanics of gas-solid interactions. However, these systems

are sensitive to the inlet conditions, which are to be set carefully or else they may lead to

process instability. Only the inlet boundary condition is applied at the porous bed, although the

bed of the transport channel acts both as an inlet and as a frictional bed. In addition, more

experimental works for measuring the material velocity and bed height on fluidised motion

conveying systems are needed for further model validation.

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8 CHAPTER 8 Recommended design protocol for an air-

gravity conveying system

8.1 Introduction

According to the analysis based on the mathematical conveying model and CFD simulation

from the above chapters, the flow behaviour of air-gravity conveying systems was studied

systematically. Both the mathematical conveying model and the CFD model can provide good

results on predicting air-gravity conveying. Moreover, other parameters like channel cross-

section, channel length, designed mass flow rate and recommended air supply can be decided

before conducting the rig design and fabrication.

8.2 Recommended design protocol

As per the study in this thesis so far, it is suggested that a new continuum approach combined

with CFD simulation be utilised to design an air-gravity conveying system for fine powder

material. Nevertheless, further validation experiments with different pipe geometries and

materials should be conducted before this design chart is used. The recommended design

protocol is presented below.

Figure 8.1 Recommended design protocol for an air-gravity conveying system

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As shown in the flow chart of Figure 8.1, the recommended design protocol for an air-gravity

conveying system is proposed here.

In stage one, for a given conveying material, its basic material properties, like particle density or

loose poured bulk density, can be decided by basic property testing. What’s more, the minimum

fluidisation bulk density, minimum fluidisation velocity and the de-aeration factor, which shows

the rheology property of aerated fine powder materials, can be investigated by fluidisation and

de-aeration tests.

Based on the particle property analysis, the mode of flow capability of the chosen materials can

be assessed by the flow chart discussed in Chapter 2. An initial prediction of the flow mode is

beneficial, as this can help provide clearer direction to the pneumatic conveying design process.

Generally, there are two types of predictive charts: basic particle-parameter-based (particle size

and density) and air-particle-parameter-based (permeability and de-aeration) predictive flow

models. With these particular parameters, the flow behaviour of this material can be basically

decided, and therefore, whether this material can be conveyed by an air-gravity conveying

system will be clear.

In stage two, once the conveying candidate, the tonnage rate, as well as the general pipeline

routing for an air-gravity conveying system are confirmed, its drawings can be figured out by

rig design and construction. Generally, the air-gravity conveying system mainly contains four

sections, namely the hopper feed section, the material conveying section, the material receiving

section and the return section. Instrumentation for measuring pressure and mass flow rates is

also important to study the flow along and across the channel, which rely on the data acquisition

system used in the LabVIEW software package to record the data. Finally, the data can be

recorded and solved fluently with the help of the LABVIEW and MATLAB programmes.

In stage three, the new continuum approach and CFD simulation method both have their

advantages and design tolerance. For the continuum approach, the essential consistency and

flow index for the rheological model are determined by the rheology test. This method is then

used to predict the steady flow of air-gravity conveying. In general, this method is supposed to

be better for industry use because it is easier and more time efficient. Moreover, the calculated

data can be used to obtain the optimum design of the conveying rig. However, it cannot be used

to predict the flow behaviour along the conveying channel, especially for the inlet area. This

means that the acceleration area of the conveying system was not considered in current study.

To predict the acceleration conveying parts, another model, called the acceleration model,

should be applied to improve the continuum model. In any case, this model is good enough for

normal air-gravity design where the steady flow can be formed quickly. The calculated steady

material conveying bed height provides the flow behaviour of the conveying material for further

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conveyor design. In addition, the suggested air supply for the conveying system can be decided

and used to estimate the overall power consumption. It can also be utilised to make the

conveying rig better with this conveying model. Therefore, an optimum parameter scheme can

then be proposed for the air-gravity system.

For the CFD simulation, this approach is powerful in solving and analysing flow behaviours of

the air-gravity conveyor. It is based on a fast and reliable computational methodology to provide

accurate and practical solutions for reducing the risks of potential design flaws and optimising

engineering design. Bed height along the conveying channel, centreline volume fraction and

velocity along the channel, velocity distribution at the cross section of the channel and predicted

bed height can be obtained from simulation. Results in this thesis show that the CFD simulation

predicted the flow behaviour of air-gravity conveying quite well. However, it suffers from many

kinds of parameters that affect the flow model selection. We note that the parameters chosen

may not be the best parameters for the conveying case of air-gravity conveying experiments; it

just provides a simulation of results close to the experimental data.

8.3 Comparison between the mathematical model and the CFD model

To support the recommended design protocol for an air-gravity conveying system, the accuracy

of the mathematical conveying model and the CFD model is important and discussed. Herein

for sand and flyash, the comparisons between predicted bed heights and experimental bed

heights at the condition of vent and non-vent flow are presented in the following figures.

Figure 8.2 to Figure 8.5 show the comparison between the mathematical conveying model and

the CFD model for sand and flyash. Both have been calculated at vent and non-vent flow

conditions. As shown in Figure 8.2 and Figure 8.3, both the mathematical and CFD model

predictions match well with the experimental bed heights. This means that for predicting sand

flow in an air-gravity conveying system, the models discussed above can be regarded as a good

predictive model, and parameters are linked to their fluidising air and fluidisation properties.

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Figure 8.2 Comparison between the mathematical conveying model and the CFD model for vent

flow of sand

Figure 8.3 Comparison between the mathematical conveying model and the CFD model for

non-vent flow of sand

0

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Mathematical model

Transition



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Figure 8.4 Comparison between the mathematical conveying model and the CFD model for vent

flow of flyash

Figure 8.5 Comparison between the mathematical conveying model and the CFD model for

non-vent flow of flyash

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As for the flyash flow in vent and non-vent conditions, both the mathematical model and CFD

model give good predictions at the bed height around 20 mm in Figure 8.4 and Figure 8.5.

However, for the bed heights larger than 30 mm, the mathematical model predictions are

smaller than the CFD model predictions of bed heights. It is difficult to tell which model is

better to present a result close to the experimental data, but with both models working together,

the flow behaviour in an air-gravity conveyor can be well-described and studied systematically.

8.4 Conclusion

In this Chapter, a new continuum approach combined with CFD simulation is discussed, which

can be utilised for an air-gravity conveying system design. The recommended design protocol

containing three stages is also presented, which is helpful for studying air-gravity conveying

systems. Furthermore, the comparison between the mathematical model and the CFD model are

discussed. Both the mathematical conveying model and the CFD model can provide good

results when predicting air-gravity conveying. It is difficult to tell which model’s predictions are

better, or the prediction closest to the experimental data, but the two models can work together

to research the flow behaviour of air-gravity conveying systems systematically.

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9 CHAPTER 9 Conclusion and future work

9.1 Conclusions

In this thesis, the fluidised conveying of fine powders in an air-gravity conveyor was

investigated systematically by conducting experiments, developing mathematic conveying

models and applying CFD-based simulation. The conveying models were derived using a

rheology-based approach to study the performance of fluidised flow, which stems from the

liquid-analogy characteristics of aerated bulk materials. Specific aspects of the flow were

investigated, including theoretical modelling of the fluidised flow conveying models based on

their rheology, design of the air-gravity conveyor, experimental determinations of the flow

behaviour of aerated materials, validation of the proposed conveying models and CFD

simulation of air-gravity fluidised conveying. The conclusions are summarised below, and

future work for more completely understanding fluidised flow behaviour in air-gravity

conveying systems, as well as further developments to the conveying model to predict bed

height along the channel, are also presented at the end of this chapter.

9.1.1 Experimental study on material properties and rheological parameters

The basic parameters including density parameters, particle size distribution and air-particle

parameters were described and characterised by basic parameter methods and air-particle

characterisation methods. Additionally, based on the parameters of the loose-poured bulk

density and particle diameter obtained above, the flow modes for different types of materials

were determined.

Essentially, the combination of a fluidisation chamber and a rotary viscometer was applied for

testing the shear stress and shear rate of fluidised materials, so that the parameters presented in

the rheology-state equations of aerated powders obtained in Chapter 2 could be determined.

Sand and flyash were selected as testing candidates, and the fluidised materials exhibited a

Pseudo-plastic type of fluidity. Experimental results indicated that the rheology flow

characteristics of aerated materials were predominantly non-Newtonian, and also bulk density

dependent. Moreover, based on the above rheology testing results analysis, the rheology of

fluidised bulk materials can be modelled by a power-law method. Model parameters such as the

consistency index and the flow index were shown to have linear correlations to variations in

bulk density.

9.1.2 Air-gravity conveyor design

The air-gravity conveyor was first designed to form a circulation system for future experimental

research. Essentially, the conveying system consists of four sections: the hopper feed section,

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the material conveying section, the material receive section and the material return section.

Detail drawings were described before fabricating the conveying rig.

Subsequently, instrumentation for measuring pressure and mass flow rates was installed in the

experimental area. The method used to measure the solid mass flow rate, pressure drop, bed

height and solid velocity were also discussed. The calibration of load cells and pressure

transducers was presented, then the calibration results were given for all of the sensors.

Additionally, a 3D printer was applied here to print the designed pressure sensor boxes to

protect them from dust.

Moreover, the experimental procedure was explained clearly. The material was firstly conveyed

back to the hopper through a vacuum conveying system. After filling the material in the supply

hopper, the knife gate valve was adjusted to a desired valve opening. Then the fluidising air was

injected into the plenum chamber after opening the pneumatic butterfly valve. Materials from

the supply hopper drop down into the conveying channel through the feed section, and then the

air that comes up through the porous membrane fluidises the material. The fluidised material

flows along the channel with the fluidised airflow and then falls into the receive box. A data

acquisition system was used and LABVIEW was utilised to record the change of mass flow rate

and pressures at different locations for the whole conveying process.

9.1.3 Experimental study on air-gravity conveying

The air-gravity conveying test was conducted on sand and flyash, with the material bed height,

material mass flow rate and pressure drop measured and analysed under vent and non-vent

conditions. Based on the experimental test procedure and test programme, the effect of air flow

rate, channel inclination and valve opening on the depth of flowing beds, material mass flow

rate and pressure drop along the channel (sidewall and top wall) were investigated and results

were discussed.

The flow behaviour was discussed based on the different phenomena observed visually during

the testing. Initial increases in the air flow rate will cause no change to the material bed. Further

increases in the air flow rate build up the material bed height in all the cases of conveying. The

material flow rate oscillations were observed as accumulation of sand in the conveying channel

for a certain period of time, followed by a sudden pulsatory flow of sand. After that, continually

increasing the air flow rate will cause a non-pulsatory movement of partial material bed at the

top layer of the bed. The flow bed height decreases and the flow accelerates after the bed starts

to flow. With further increases in air flow rate, a well fluidised state of sand is formed and

causes the total material bed to slide down through the channel. But when the air velocity

increases even more, air bubbles will occur and come out of the sliding material bed as the

excess air in the channel. This characteristic is also accompanied by vigorous particle agitation

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and the upper materials behave more like dilute flow, and thereafter the flow remains the same

with an increasing airflow rate.

It is found that the increase in the air flow rate increases the material mass flow rate of the air-

gravity conveying system initially, and thereafter steadies to a saturation level at a higher

airflow rate. It was also found that the bed height along the channel decreased with an

increasing air mass flow rate within different solid mass flow rate ranges for sand and flyash.

For a given airflow rate, pressure at the top of the conveying channel at five locations shows a

gradually reducing trend at different air flow rates. The existence of a pressure drop along the

channel validates the finding that in a non-vent air-gravity flow, the driving force to cause the

flow of material is not only the gravitational force at the flow direction but also the pressure

drop along the channel. In addition, for a given material mass flow rate and inclination angle,

the increase in the airflow rate decreases the bed height at a given location.

9.1.4 Fluidised motion conveying model development

To derive the fluidised motion conveying model based on its rheology, the continuous fluid

mechanics approach was used, and the analogy between a fluid and the aerated powder was

adopted in this study. Essentially, the governing function of continuous flow, that is, the

conservation of mass and the conservation of momentum, were initially developed by analysing

an infinitesimal element. Then, when the material was subjected to external stresses, the strain

theory was applied to derive the total deformation. Such a deformation comprised of both a

shear component and a volumetric component. Additionally, fundamental equations for the

rheological state of the aerated powders were derived. The rheological characteristics for

aerated powders can be either a power-law type or a yield power-law type, depending on the

aerated level (bulk density) within the system. According to the above models, constitutive

equations, which govern the fluidised motion conveying performance system, were then

established.

Subsequently, to obtain approximated analytical results, an incompressible approximation was

utilised to simplify the process of analysis on the constitutive equations, and the volumetric

components within the constitutive equations were eliminated. Based on the stratification effect

exerted by the material during the conveying process, twelve conveying models were developed

which consider the condition of vent and non-vent, slip at bottom and no-slip at bottom in air-

gravity conveying.

9.1.5 Conveying model validation

Validity for the proposed conveying models for predicting the steady flow bed heights was

examined in Chapter 6. Sand and flyash, used previously in the rheology tests, were selected as

the experimental materials. The experimental data required in the validation process was

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collected through testing carried out on the air-gravity conveyor. In particular, basic conveying

data like pressure drop along the channel, material mass flow rate, airflow rate, conveying bulk

densities, rheology parameters, and model selection were needed for the validation process.

The conveying bulk density in the channel was estimated by approximating the averaged bulk

density across the channel when conveying the material under certain air and solids mass flow

rates. After that, the rheological parameters in each test case were then determined. Selection of

the conveying models obtained in Chapter 5 was initially discussed. Results suggested that the

combined material conveying models are used to validate the model, and with recording of the

bed height profile for each fluid layer. The power-law fluid conveying model was more

applicable for extremely dilute phase conveying, as sand is easy to settle down at the bottom

part of the conveying channel due to gravity, which results in a thick layer that does not move

forward. Therefore, the yield power-law part can be considered as a not moving part for model

simplification purposes. Meanwhile, the material mass flow rate is mostly contributed to by the

power-law conveying part. For flyash, the combined material conveying model has shown that

it cannot be validated because of the missing concentration profiles between the yield power-

law and power-law models. The power-law fluid conveying model was applied to validate the

experimental behaviour, which agreed well with the experimental data.

To conclude, the rheology-based fine powder air-gravity conveying system evaluation method

was successfully developed in this research. Such an approach can well-predict fine powder

flow behaviour and steady flow bed height in air-gravity conveyors based on a simple series of

bench scale tests.

9.1.6 CFD study on air-gravity conveying

In Chapter 7, a 3D CFD model was applied to describe the gas-solid flow in air-gravity

conveyors. The effects of some important modelling parameters on the flow field were

examined. The model was validated by comparing the bed height along the channel with those

from experimental results. What’s more, the model can also be used to provide the prediction of

velocity distribution and pressure drop in air-gravity conveying. A good agreement relating to

the prediction of the material bed height along the channel was found when comparing the

simulated results with the bed depth in this study. These detailed investigations have improved

the understanding of air-gravity conveying systems, which were previously suffering from lack

of numerical support. Moreover, the CFD simulation was applied to compare with the

experimental results on sand and flyash in current air-gravity flow systems. Bed height along

the conveying channel, centreline volume fraction and velocity along the channel, velocity

distribution at the cross section of channel and predicted bed height were investigated, and

results show that the CFD simulation enables the system prediction of the fine powder flow

behaviour in the air-gravity conveying system.

205

Fortunately, the present thesis is the first successful attempt to model flows in vent and non-vent

air-gravity conveyors considering the detailed mechanics of gas-solid interactions. However,

these systems are sensitive to the inlet conditions, which are to be set carefully or else they may

lead to process instability. More experimental work measuring the material velocity and bed

height on air-gravity conveying systems is needed for further model validation.

9.2 Recommendation for future work

It is understood that there are still a number of aspects of this research topic in need of further

study. Some areas need further investigation to get a better understanding of fluidised flow, as

well as to further prove the applicability and validation of bed height prediction models with

various types of material in the air-gravity conveyor.

Firstly, during the air-gravity conveying model’s derivation process, an incompressible

approximation technique was applied in order to obtain analytical solutions for the constitutive

governing equations. For a small cross section air-gravity conveyor, this assumption is valid

enough to give good prediction results. However, for a large-size conveyor, the volumetric

deformation is potentially too significant to be neglected. As a result, an improved analysis

approach may be essential to get more reliable results.

Secondly, in order to obtain the acceptable rheology parameters for fluidised material, a rotary

viscometer was initially utilised for measuring the shear stress and shear rate at a fluidised bed.

In the case of material flow in the air-gravity conveyor, the flow is heterogeneous and always

presents a certain degree of turbulence, which is different from the behaviour on a fluidised bed.

Therefore, further modifications of the current resting apparatus should be conducted. Moreover,

the accuracy also should be improved for obtaining the value of consistency and the flow index.

Thirdly, the bed height recorded from the observation windows in the current air-gravity

conveyor needs to be improved. Especially for testing a material like flyash, it is difficult to

read the value of bed height precisely, as it will easily cover the whole of the observation

window. Moreover, the vent port on the air-gravity conveyor should be improved to reduce the

flow of material. Therefore, further modifications to the air-gravity conveyor should be

conducted as well.

Lastly, the particle properties of permeability, de-aeration, particle size distribution and particle

shape were generally neglected in CFD simulations for this thesis. These basic parameters for

particle properties play an important role in gas-solid flow behaviour in air-gravity conveying.

Therefore, the influence of these parameters should also be included to a greater extent in the

modified model for flow behaviour prediction in the air-gravity conveyor.

206

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212

10 Appendices

10.1 Appendix A - Airslide rig drawings

Figure 10.1 Flange connector 1

Figure 10.2 Flange connector 2

213

Figure 10.3 The conveying channel of air-gravity conveyor channel

Figure 10.4 The inlet of air-gravity conveyor

214

Figure 10.5 The discharge of air-gravity conveyor

Figure 10.6 Hopper support structure

215

Figure 10.7 Channel support structure

Figure 10.8 Gauge transducer protective box

216

Figure 10.9 Differential pressure transducer protective box

Table 10.1 Initial calibration

Sensor Cable Number Type Sensitivity O/P to NI Card NI I/P Sig Card I/P

P1 C1 0.5PSI (3.447KPa) gauge 17.5 mV/PSI @ 5 Vexc 4 mA = 0KPa 20mA=3.447KPa 0-10 V 43


P3 C1 1PSI (6.894KPa) gauge 22.5 mV/PSI @ 5 Vexc 0 mA = 0KPa 20mA=6.894KPa 0-10 V 45

DP4 C6 1PSI (6.894KPa) diff 16.7 mV/PSI @ 10 Vexc 4 mA = 0KPa 20mA=6.894KPa 0-10 V 58




DP8 C7 1PSI (6.894KPa) diff 16.7 mV/PSI @ 10Vexc 4 mA = 0KPa 20mA=6.894KPa 0-10 V 59




PD12 C8 1PSI (6.894KPa) diff 16.7mV/PSI @ 10Vexc 4 mA = 0KPa 20mA=6.894KPa 0-10 V 60









LC1, 2 ,3 C11 3 × 1000 kg load cells 20 mv/3000kg @ 10Vexc 4 mA = 0 kg 20 mA=3000 kg 0-10 V 63

LC4, 5, 6 C12 3 × 500 kg load cells 21 mv/1500kg @ 10Vexc 4 mA = 0 kg 20 mA=1500 kg 0-10 V 64

217

10.2 Appendix B - Pressure data analysis programmes

(1) Pressure data analysis programme 1

time=1:1:length(P1);time=0.001*time-0.001;time=time'; %P along the airslide channel P1c=P1*0.402 - 0.8107; P2c=P2*0.3687 - 0.9084; P3c=P3*0.6922 - 0.3233; P5c=P5*0.4424 - 0.8659; P6c=P6*0.3756 - 0.8618; P7c=P7*0.7049 - 0.691; P9c=P9*0.3686 - 0.8951; P10c=P10*0.3832 - 0.9144; P11c=P11*0.6853 - 0.3226; P13c=P13*0.3762 - 0.9261; P14c=P14*0.3644 - 0.7243; P15c=P15*0.6788 - 0.6398; P17c=P17*0.4157 - 0.8315; P18c=P18*0.3731 - 0.7322; P19c=P19*0.7182 - 0.3412; subplot(3,2,1);plot(time,P1c,'.',time,P2c,'.');legend('P1c','P2c');xlabel('time (s)');ylabel('kPa') subplot(3,2,2);plot(time,P5c,'.',time,P6c,'.');legend('P5c','P6c');xlabel('time (s)');ylabel('kPa') subplot(3,2,3);plot(time,P9c,'.',time,P10c,'.');legend('P9c','P10c');xlabel('time (s)');ylabel('kPa') subplot(3,2,4);plot(time,P13c,'.',time,P14c,'.');legend('P13c','P14c');xlabel('time (s)');ylabel('kPa') subplot(3,2,5);plot(time,P17c,'.',time,P18c,'.');legend('P17c','P18c');xlabel('time (s)');ylabel('kPa') subplot(3,2,6);plot(time,P3c,'.',time,P7c,'.',time,P11c,'.',time,P15c,'.',time,P19c,'.'); legend('P3c','P7c','P11c','P15c','P19c'); xlabel('Time (s)');ylabel('Pressure (kPa)') saveas(figure(1),'P_sidewall.jpg') saveas(figure(1),'P_sidewall.fig') %DP DP4c=DP4*0.8634 - 1.7366; DP8c=DP8*0.863 - 1.7353; DP12c=DP12*0.8658 - 1.7448; DP16c=DP16*0.8682 - 1.7404; DP20c=DP20*0.8666 - 1.7444; figure(2); plot(time,DP4c,'.',time,DP8c,'.',time,DP12c,'.',time,DP16c,'.',time,DP20c,'.'); legend('DP4c','DP8c','DP12c','DP16c','DP20c'); xlabel('Time (s)');ylabel('Pressure (kPa)') saveas(figure(2),'DP.jpg') saveas(figure(2),'DP.fig') %Ptop P3top=P3c-DP4c; P15top=P15c-DP16c; P19top=P19c-DP20c; figure(3); plot(time,P3top,'.',time,P15top,'.',time,P19top,'.'); legend('P3top','P15top','P19top');xlabel('time (s)');ylabel('kPa') saveas(figure(3),'P_top.jpg') saveas(figure(3),'P_top.fig') %Bin1 & Box2 Box2c=Box2*302.5-1.6225; Bin1c=Bin1*302.65-1.0059; figure(4); plot(time,Bin1c,'.',time,Box2c,'.');legend('Bin1c','Box2c'); xlabel('Time (s)');ylabel('Weight (kg)') saveas(figure(4),'Bin1&Box2.jpg') saveas(figure(4),'Bin1&Box2.fig')

218

(2) Pressure data analysis programme 2

range=input('range='); channel=[0.5,1.5,2.5,4.5,5]; range1=input('range Bin1&Box2 ='); %Bin1c & Box2c xlswrite('Bin1c&Box2c',time(range1),'Bin1c&Box2c','A2') xlswrite('Bin1c&Box2c',Bin1c(range1),'Bin1c&Box2c','B2') xlswrite('Bin1c&Box2c',Box2c(range1),'Bin1c&Box2c','C2') %P_sidewall & P_chamber P1m=mean(P1c(range)); P2m=mean(P2c(range)); P3m=mean(P3c(range)); P5m=mean(P5c(range)); P6m=mean(P6c(range)); P7m=mean(P7c(range)); P9m=mean(P9c(range)); P10m=mean(P10c(range)); P11m=mean(P11c(range)); P13m=mean(P13c(range)); P14m=mean(P14c(range)); P15m=mean(P15c(range)); P17m=mean(P17c(range)); P18m=mean(P18c(range)); P19m=mean(P19c(range)); %DP DP4m=mean(DP4c(range)); DP8m=mean(DP8c(range)); DP12m=mean(DP12c(range)); DP16m=mean(DP16c(range)); DP20m=mean(DP20c(range)); DP1=[DP20m,DP16m,DP12m,DP8m,DP4m] head={'Position(m)';'P_chamber(kPa)';'DP(kPa)';'P_top(kPa)';'P_sidewall1(kPa)';'P_sidewall2(kPa)'};

xlswrite('Sensors',head,'data'); xlswrite('Sensors',channel,'data','B1') xlswrite('Sensors',DP1,'data','B3') figure(1); plot(channel,DP1,'-d'); title('DP (chamber and top)') xlabel('Channel length (m)');ylabel('Pressure (kPa)') saveas(figure(1),'DP1.jpg') saveas(figure(1),'DP1.fig') %P_chamber P_chamber=mean([P19m,P15m,P3m]) xlswrite('Sensors',P_chamber,'data','B2') %P_top P_top4m=P_chamber-DP4m; P_top8m=P_chamber-DP8m; P_top12m=P_chamber-DP12m; P_top16m=P_chamber-DP16m; P_top20m=P_chamber-DP20m; P_top1=[P_top20m,P_top16m,P_top12m,P_top8m,P_top4m] figure(2); plot(channel,P_top1,'->'); title('P top') xlabel('Channel length (m)');ylabel('Pressure (kPa)') saveas(figure(2),'P_top1.jpg') saveas(figure(2),'P_top1.fig') xlswrite('Sensors',P_top1,'data','B4') % P_sidewall plot figure(3);

219

P_sidewall1=[P17m,P14m,P11m,P7m,P2m] P_sidewall2=[P18m,P13m,P9m,P5m,P1m] plot(channel,P_sidewall1,'-o',channel,P_sidewall2,'-*'); title('P sidewall') xlabel('Channel length (m)');ylabel('Pressure (kPa)') saveas(figure(3),'P_sidewall1.jpg') saveas(figure(3),'P_sidewall1.fig') xlswrite('Sensors',P_sidewall1,'data','B5') xlswrite('Sensors',P_sidewall2,'data','B6')

(3) Read frame file

fileName = 'name.avi';

obj = VideoReader(fileName);

numFrames = obj.NumberOfFrames;% Number of Frames

for k = 1 : numFrames % Read Frames

frame = read(obj,k);

imshow(frame); % Show Frames

imwrite(frame,strcat(num2str(k),'.jpg'),'jpg');% Save all the Frames

end

220

10.3 Appendix C - Experimental data for air-gravity conveying of sand and

flyash

(a) Experimental data for the vent air-gravity conveying of sand

(b) Experimental data for the non-vent air-gravity conveying of sand

0.5 m 1.5 m 2.5 m 4.5 m 5.5 m 1 m 2 m 5 m

1 58 0.63 5.00 2.471 2.448 2.498 2.456 2.469 2.495 80.0 75.0 50.0

2 72 1.32 5.00 3.154 3.082 3.086 3.082 3.073 3.086 48.0 46.0 45.0

3 85 1.68 5.00 3.488 3.340 3.436 3.444 3.428 3.330 47.0 46.0 43.0

4 96 1.72 5.00 3.946 3.818 3.840 3.854 3.831 3.787 36.0 35.0 35.0

5 106 1.76 5.00 4.387 4.281 4.261 4.292 4.272 4.251 21.0 20.0 20.0

6 127 1.70 5.00 5.135 5.082 5.133 5.094 5.098 5.132 20.0 20.0 19.0

7 140 1.70 5.00 5.719 5.657 5.714 5.674 5.685 5.700 19.0 19.0 19.0

8 96 1.48 2.50 4.197 4.351 4.353 4.361 4.351 4.377 50.0 42.0 32.0

9 106 1.11 2.50 4.652 4.662 4.669 4.668 4.665 4.684 50.0 45.0 36.0

10 127 1.52 2.50 5.635 5.683 5.703 5.715 5.694 5.732 42.0 36.0 30.0

11 96 1.56 3.75 4.184 4.126 4.091 4.129 4.095 4.069 50.0 43.0 42.0

12 106 1.53 3.75 4.602 4.530 4.534 4.537 4.519 4.479 48.0 37.0 36.0

13 127 1.69 3.75 5.510 5.451 5.472 5.483 5.463 5.455 45.0 40.0 40.0

14 72 0.30 5.00 3.508 3.146 3.225 3.338 3.368 3.332 100.0 90.0 56.0

15 85 0.30 5.00 3.923 3.633 3.677 3.784 3.780 3.776 90.0 75.0 42.0

16 96 0.30 5.00 4.028 3.973 4.024 4.001 4.002 4.034 40.0 38.0 32.0

17 106 0.30 5.00 4.383 4.334 4.391 4.360 4.367 4.401 38.0 30.0 18.0

18 117 0.30 5.00 4.906 4.609 4.615 4.657 4.681 4.666 20.0 19.0 18.0

19 127 0.30 5.00 5.241 5.119 5.114 5.125 5.105 5.121 19.0 18.0 17.0

Bed height (mm)DP along the channel (kPa)P_chambe

r average

(kPa)

No.Air velocity

(mm/s)Mass flow rate (kg/s)

Inclination

angle

(degree)

0.5 m 1.5 m 2.5 m 4.5 m 5.5 m 1 m 2 m 5 m

1 36 0.15 5.00 2.277 1.411 1.788 1.996 2.159 2.190 86.0 78.0 63.02 47 0.47 5.00 2.849 1.909 2.340 2.512 2.630 2.669 85.0 76.0 48.03 58 1.34 5.00 3.369 2.635 2.884 2.874 2.900 2.944 84.0 64.0 42.04 72 1.32 5.00 3.990 2.922 3.311 3.482 3.534 3.565 70.0 58.0 36.05 85 1.52 5.00 4.407 3.308 3.377 3.385 3.403 3.385 36.0 30.0 26.06 96 1.72 5.00 5.388 3.889 3.956 3.943 3.989 4.048 30.0 24.0 22.07 106 2.06 5.00 6.009 4.300 4.345 4.326 4.379 4.464 20.0 19.0 18.08 127 2.09 5.00 6.152 5.093 5.134 5.133 5.199 5.290 20.0 18.0 17.09 140 2.08 5.00 6.227 4.980 4.983 5.003 5.052 5.174 20.0 17.0 17.0

10 96 1.03 2.50 5.403 4.179 4.201 4.224 4.311 4.383 38.0 42.0 40.011 106 1.13 2.50 6.119 4.498 4.502 4.516 4.568 4.625 42.0 40.0 26.012 127 1.52 2.50 6.211 5.489 5.511 5.542 5.615 5.712 35.0 42.0 36.013 96 1.38 3.75 5.776 4.030 4.039 4.057 4.070 4.143 48.0 38.0 35.014 106 1.70 3.75 6.852 4.507 4.529 4.540 4.571 4.612 43.0 35.0 32.015 127 1.76 3.75 6.515 5.300 5.313 5.338 5.389 5.467 40.0 34.0 32.017 72 0.30 5.00 3.810 3.312 3.385 3.394 3.452 3.510 80.0 68.0 42.018 85 0.30 5.00 4.235 3.653 3.648 3.691 3.711 3.705 75.0 55.0 38.019 96 0.28 5.00 4.748 4.006 4.007 4.036 4.074 4.121 38.0 35.0 28.020 106 0.38 5.00 5.900 4.467 4.499 4.502 4.548 4.650 18.0 18.0 17.021 128 0.30 5.00 6.208 5.115 5.136 5.147 5.188 5.241 18.0 17.0 16.0

Bed height (mm)No.

Air velocity


Inclination

angle

(degree)

P_chambe

r average

(kPa)


221

(c) Experimental data for the vent air-gravity conveying of flyash

0.5 m 1.5 m 2.5 m 4.5 m 5.5 m

1 13.7 0.35 5.00 0.481 0.496 0.496 0.499 0.497 0.496 0.433 12.4

2 13.7 0.95 5.00 0.510 0.519 0.540 0.535 0.532 0.514 0.433 16.1

3 13.7 2.49 5.00 0.593 0.598 0.637 0.632 0.628 0.591 0.433 31.3

4 13.7 7.34 5.00 0.698 0.758 0.750 0.742 0.739 0.741 0.433 61.0

5 24.8 0.75 5.00 0.948 0.961 0.951 0.960 0.951 0.954 0.899 10.8

6 24.8 1.41 5.00 0.968 0.983 0.973 0.980 0.971 0.974 0.899 14.6

7 24.8 3.45 5.00 1.086 1.107 1.097 1.103 1.095 1.097 0.899 38.9

8 24.8 4.26 5.00 1.132 1.154 1.140 1.145 1.135 1.136 0.899 46.7

9 36.0 0.41 5.00 1.311 1.371 1.372 1.358 1.364 1.331 1.352 10.3

10 36.0 0.88 5.00 1.336 1.392 1.393 1.384 1.385 1.367 1.352 16.6

11 36.0 2.56 5.00 1.420 1.478 1.504 1.499 1.496 1.460 1.352 28.5

12 36.0 2.97 5.00 1.459 1.521 1.521 1.510 1.512 1.514 1.352 31.6

13 42.6 0.23 5.00 1.708 1.755 1.788 1.779 1.767 1.757 1.744 10.5

14 42.6 0.54 5.00 1.722 1.778 1.797 1.789 1.777 1.775 1.744 16.2

15 42.6 2.56 5.00 1.782 1.846 1.874 1.865 1.852 1.840 1.744 28.0

16 42.6 4.92 5.00 1.940 1.999 1.984 1.981 1.970 1.973 1.744 45.3

17 47.1 0.22 5.00 1.825 1.857 1.892 1.886 1.879 1.854 1.776 21.8

18 47.1 0.48 5.00 1.833 1.864 1.900 1.892 1.885 1.859 1.776 22.8

19 47.1 3.41 5.00 1.933 1.971 1.961 1.961 1.956 1.953 1.776 41.4

20 47.1 8.61 5.00 2.099 2.166 2.143 2.129 2.109 1.914 1.776 33.8

21 58.0 0.21 5.00 2.357 2.443 2.450 2.445 2.436 2.448 2.387 12.0

22 58.0 0.71 5.00 2.374 2.461 2.471 2.463 2.453 2.466 2.387 15.6

23 58.0 1.23 5.00 2.398 2.494 2.498 2.493 2.480 2.489 2.387 20.3

24 58.0 3.73 5.00 2.518 2.614 2.606 2.607 2.583 2.583 2.387 38.9

25 42.6 0.39 2.50 1.758 1.773 1.761 1.776 1.768 1.771 1.720 30.9

26 42.6 0.62 2.50 1.780 1.814 1.817 1.819 1.805 1.823 1.720 32.2

27 42.6 1.38 2.50 1.826 1.858 1.868 1.870 1.856 1.869 1.720 35.2

28 42.6 1.99 2.50 1.863 1.874 1.862 1.878 1.878 1.876 1.720 37.5

29 42.6 2.69 2.50 1.872 1.902 1.888 1.903 1.895 1.896 1.720 38.1

30 42.6 0.41 3.75 1.733 1.747 1.748 1.752 1.744 1.744 1.725 19.9

31 42.6 0.65 3.75 1.756 1.760 1.764 1.762 1.763 1.759 1.725 22.5

32 42.6 0.93 3.75 1.780 1.790 1.787 1.799 1.790 1.783 1.725 25.4

33 42.6 2.64 3.75 1.832 1.847 1.845 1.849 1.841 1.840 1.725 31.4

34 42.6 2.74 3.75 1.861 1.874 1.864 1.876 1.871 1.867 1.725 34.7

35 42.6 0.36 5.00 1.714 1.765 1.792 1.783 1.771 1.765 1.744 18.0

Steady bed

height

(mm)

DP along the channel (kPa)No.

Air velocity


Inclination

angle

(degree)

P_chambe

r average

(kPa)

P_filter

222

(d) Experimental data for the non-vent air-gravity conveying of flyash

0.5 m 1.5 m 2.5 m 4.5 m 5.5 m

1 13.7 0.30 5.00 0.481 0.483 0.484 0.479 0.480 0.477 0.431 8.6

2 13.7 0.48 5.00 0.493 0.485 0.486 0.483 0.483 0.480 0.431 9.3

3 13.7 0.89 5.00 0.541 0.490 0.491 0.498 0.490 0.491 0.431 11.6

4 13.7 2.88 5.00 0.623 0.602 0.602 0.599 0.598 0.595 0.431 32.2

5 13.7 7.57 5.00 0.762 0.893 0.741 0.748 0.733 0.737 0.431 60.1

6 24.8 0.29 5.00 1.007 0.980 0.981 0.976 0.977 0.928 0.900 10.6

7 24.8 1.61 5.00 1.179 1.026 1.023 1.028 1.027 1.030 0.900 25.7

8 24.8 2.80 5.00 1.492 1.085 1.087 1.089 1.076 1.085 0.900 36.7

9 24.8 5.78 5.00 1.546 1.164 1.164 1.164 1.147 1.156 0.900 50.8

10 24.8 7.70 5.00 1.732 1.213 1.200 1.200 1.194 1.196 0.900 58.6

11 36.0 0.29 5.00 1.449 1.374 1.376 1.371 1.371 1.369 1.316 10.4

12 36.0 0.67 5.00 1.533 1.383 1.384 1.383 1.388 1.383 1.316 13.2

13 36.0 1.48 5.00 1.643 1.482 1.451 1.447 1.437 1.439 1.316 24.3

14 36.0 2.15 5.00 1.826 1.463 1.444 1.444 1.438 1.445 1.316 25.5

15 36.0 5.41 5.00 2.614 1.647 1.640 1.630 1.627 1.588 1.316 53.8

16 42.6 0.29 5.00 1.943 1.753 1.757 1.763 1.745 1.762 1.657 10.4

17 42.6 0.78 5.00 2.009 1.762 1.767 1.764 1.765 1.767 1.657 15.3

18 42.6 1.27 5.00 2.239 1.793 1.797 1.802 1.787 1.802 1.657 16.2

19 42.6 2.18 5.00 2.459 1.820 1.828 1.823 1.826 1.833 1.657 22.3

20 42.6 5.19 5.00 3.283 1.928 1.962 1.964 1.958 1.936 1.657 42.9

21 47.1 0.24 5.00 2.050 1.813 1.813 1.814 1.812 1.780 1.770 8.3

22 47.1 0.48 5.00 2.064 1.840 1.837 1.838 1.834 1.835 1.770 12.7

23 47.1 1.00 5.00 2.282 1.878 1.877 1.877 1.871 1.874 1.770 20.0

24 47.1 1.34 5.00 2.413 1.859 1.859 1.860 1.857 1.742 1.770 17.2

25 47.1 5.33 5.00 3.654 2.063 2.057 2.057 2.055 2.080 1.770 56.4

26 58.0 0.24 5.00 2.776 2.336 2.352 2.357 2.359 2.353 2.230 24.4

27 58.0 0.51 5.00 2.871 2.336 2.367 2.375 2.376 2.354 2.230 24.6

28 58.0 1.85 5.00 3.420 2.378 2.385 2.386 2.387 2.401 2.230 33.9

29 58.0 3.05 5.00 3.699 2.463 2.464 2.472 2.475 2.491 2.230 51.8

30 58.0 4.48 5.00 4.111 2.466 2.473 2.474 2.480 2.485 2.230 50.5

31 36.0 0.27 3.75 1.607 1.474 1.468 1.467 1.469 1.464 1.316 21.0

32 36.0 0.36 3.75 1.678 1.480 1.471 1.472 1.473 1.472 1.316 21.0

33 36.0 0.99 3.75 1.785 1.509 1.497 1.498 1.498 1.497 1.316 26.0

34 36.0 1.61 3.75 1.899 1.463 1.464 1.472 1.459 1.444 1.316 30.0

35 36.0 2.24 3.75 2.080 1.582 1.571 1.572 1.571 1.570 1.316 32.0

36 36.0 0.38 2.50 1.620 1.400 1.427 1.441 1.428 1.406 1.316 20.0

37 36.0 0.67 2.50 1.574 1.431 1.435 1.448 1.434 1.432 1.316 26.0

38 36.0 0.86 2.50 1.688 1.446 1.440 1.449 1.443 1.456 1.316 28.0

39 36.0 1.30 2.50 1.789 1.444 1.470 1.483 1.471 1.449 1.316 30.0

40 36.0 4.57 2.50 2.596 1.686 1.726 1.736 1.733 1.725 1.316 43.0

Steady bed

height

(mm)

DP along the channel (kPa)P_filterNo.

Air velocity


Inclination

angle

(degree)

P_chambe

r average

(kPa)

Documents

Development of Design Models for Air-gravity Fine Powder