Investigation Into the Erosion Modelling and Design of Tubular Air Pre

7/30/2019 Investigation Into the Erosion Modelling and Design of Tubular Air Pre

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INVESTIGATION INTO THE EROSION MODELLING AND

DESIGN OF TUBULAR AIR PRE-HEATER ENTRANCE

ISSUES

A THESIS SUBMITTED IN PARTIAL FULFILMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

POWER PLANT TECHNOLOGIES

BY

UGONNA CHIDERA MBAEZUE

REG. NO: 201189490

Department of Mechanical and Aerospace Engineering

University of Strathclyde

Glasgow

2012

SUPERVISOR: DR. WILLIAM DEMPSTER


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Copyright Declaration

To the best of my knowledge and belief this thesis contains no material previously published

by any other person except where due acknowledgment has been made.

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

diploma in any university.

Signature:

Date:


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AcknowledgementI would like to express sincere gratitude to my project supervisor, Dr. William Dempster for

the assistance he gave me through the course of this project. Without his guidance and

assistance, the progress of this thesis would have been stalled. I would also like to express my

gratitude to Dr. William Nicholls, who endured and patiently answered all the questions that

gave me cause for concern during the course of this thesis. My gratitude also goes to my

course director, Dr. Matthew Stickland, for his assistance throughout the period of this

postgraduate degree. To all my tutors, I thank you all for having the patience to clarify

problems that I had in your modules. I also want to thank the security personnel stationed at

Livingston tower who endured my late hours and movements in and out of the building at

very odd hours without complaints.

To Sri Harold Klemp and his crew of 973, I sincerely express my gratitude to you guys for all

the help you gave me from start to finish of this degree. I could not have made it this far

without your ever present presence. Thank you.

Finally, I would like to say thank you to the ones I live for; my parents, brothers and sister.


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AbstractThe erosive effect of particles transported by flue gas has always been a major concern in the

power generation industry. The ash particles in the flue gas tend to impinge on the wall

surface of the tubes in which they are transported causing significant erosion. The intensity of

this erosion is felt most at the inlet region of the tube, where due to the difference in areas

between the open area and the tube inlet, the incoming flow separates from the tube wall. In

the process of reattachment to the wall surface, the fluid and its entrained particles strike the

tube surface at an elevated angle causing bits of the tube to be removed. A cumulative effect

of this surface removal is the failure of the tube in that region. In this project, the CFD

software FLUENT was used in modelling a single phase flow using the Eulerian approach.

The geometry created was similar to that of a heat exchanger common in power plants. Upon

validation of the flow model, the Lagrangian approach was used to specify the discrete phase

representing the ash particles entrained in the single phase flow. The erosive effect of the

discrete phase in tube geometries with different design modifications made at the tube inlet

and the regions surrounding it was then analysed. The goal was to determine the efficacy of

the design modifications in the reduction of the rate of erosion by impingement of the tube

wall by ash particles. Results showed that although the modifications reduced the erosive

effects of the flue gas on the tube wall, in none of the cases was it completely eliminated. It

was also discovered that some of the modifications produced adverse effects in the tube

which would render them unsuitable for use in erosion mitigation.


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Table of ContentINVESTIGATION INTO THE EROSION MODELLING AND DESIGN OF TUBULAR AIR PRE-HEATER

ENTRANCE ISSUES .................................................................................................................................... i

Copyright Declaration ............................................................................................................................. ii

Acknowledgement ................................................................................................................................. iii

Abstract .................................................................................................................................................. iv

Table of Content ..................................................................................................................................... v

List of Figures ........................................................................................................................................ vii

List of Tables .......................................................................................................................................... ix

Notations and Units: ............................................................................................................................... x

Chapter 1 ................................................................................................................................................. 1

1.0 Introduction: ........................................................................................................................... 1

1.1 Background: ............................................................................................................................ 1

1.2 Objectives of thesis: ................................................................................................................ 3

1.3 Outline of thesis: ..................................................................................................................... 3

Chapter 2 ................................................................................................................................................. 5

Literature Review .................................................................................................................................... 5

2.0 Introduction: ........................................................................................................................... 5

2.1 Coal combustion: .................................................................................................................... 5

2.2 Air Pre-heaters: ....................................................................................................................... 8

2.3 Erosion: ................................................................................................................................. 10

2.4 Mechanisms of erosion: ........................................................................................................ 11

2.5 Factors influencing erosion: .................................................................................................. 13

2.6 Design to mitigate effects of erosion: ................................................................................... 17

2.7 CFD and Erosion Modelling: .................................................................................................. 19

2.7 Summary of literature review ............................................................................................... 21

Chapter 3 ............................................................................................................................................... 22

Methodology ......................................................................................................................................... 22

3.0 Introduction: ......................................................................................................................... 22

3.1 General Overview of Computational Fluid Dynamics (CFD): ................................................ 22

3.2 Components of ANSYS-FLUENT: ........................................................................................... 24

3.2.1 Basic Flow Equations: .................................................................................................... 24

3.2.2 Discrete Phase Tracking: ............................................................................................... 29

Conclusion: ........................................................................................................................................ 32


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Chapter 4 ............................................................................................................................................... 33

Single Phase Flow Validation ................................................................................................................ 33

4.0 Introduction: ......................................................................................................................... 33

4.1 Geometry Creation: .............................................................................................................. 33

4.1.1 Procedure: ..................................................................................................................... 33

Geometry: ..................................................................................................................................... 33

Meshing: ....................................................................................................................................... 37

4.2 Pre-processing:...................................................................................................................... 38

4.2.1 Procedure: ..................................................................................................................... 38

4.3 Post-processing ........................................................................................................................... 39

4.3.1. ............................................................................................................................................. 39

4.3.2 Single phase flow model validation: ............................................................................. 40

4.3.3 Test for mesh sensitivity: .............................................................................................. 41

4.3.4 Test for turbulence model sensitivity: .......................................................................... 42

Chapter 5 ............................................................................................................................................... 44

Results and Analysis .............................................................................................................................. 44

5.0 Introduction: ......................................................................................................................... 44

5.1 Results: .................................................................................................................................. 44

5.1.1 Empirical results: ........................................................................................................... 44

5.1.2 Simulation Data: ............................................................................................................ 46

5.2 Comparison of erosion rates by particle size, for cases studied: .......................................... 76

5.3 Suggested design modifications at the tube inlet. ............................................................... 79

5.4 Validation for coefficients of restitution ............................................................................... 81

Test for coefficients of restitution sensitivity: .............................................................................. 81

Chapter 6:.............................................................................................................................................. 88

Conclusion and Recommendations: ..................................................................................................... 886.0 Introduction: ......................................................................................................................... 88

6.1 Conclusion: ............................................................................................................................ 88

6.2 Recommendations: ............................................................................................................... 91

References ............................................................................................................................................ 92

Appendix A ............................................................................................................................................ 97

Model validation: .......................................................................................................................... 97

Appendix B .......................................................................................................................................... 101


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List of FiguresFigure 1. 1: Cross section of a pulverised power plant ........................................................................... 2

Figure 2. 1 Structural model of high volatile bituminous coal....6

Figure 2. 2 : Diagrammatic representation of ash formation during high temperature combustion ofcoal .......................................................................................................................................................... 7

Figure 2. 3 Tube bank of air preheater. .................................................................................................. 9

Figure 2. 4 Flow separation at tube inlet. Courtesy .............................................................................. 10

Figure 2. 5 Typical location of erosion at the inlet of air heater tube .................................................. 11

Figure 2. 6 Erosion by plastic deformation. .......................................................................................... 13

Figure 4. 1: Plain tube inlet without modifications............................................................................... 34

Figure 4. 2: Addition of sleeve insert at tube inlet. ............................................................................... 35

Figure 4. 3: Design modification with perforated plate with the same diameter as the tube. ............... 35

Figure 4. 4: Design modification with pore plate of diameter 1.2D. .................................................... 36

Figure 4. 5: Design modification with smooth transition at the tube inlet. ........................................... 36

Figure 4. 6: Meshed Geometry in Gambit ............................................................................................ 37

Figure 4. 7: Meshed Geometry in Gambit ............................................................................................ 38

Figure 4. 8: Stream function of single phase fluid showing point of separation................................... 39

Figure 4. 9: Vector representation of single phase flow of fluid, showing recirculation zone. ............ 39

Figure 4. 10: Y-Plus value at the tube wall........................................................................................... 40

Figure 4. 11: Location of pressure drop as a result of contraction at tube inlet. ................................... 41

Figure 5. 1: Graph of erosion intensity relative to impingement angle................................................. 45

Figure 5. 2: Plain pre-heater tube without modifications...................................................................... 49

Figure 5. 3: Flow contraction or vena contracta formation at tube inlet. .............................................. 50

Figure 5. 4: Location of erosion occurrence on the tube plate and the tube wall. ................................ 50

Figure 5. 5: Graphical representation of maximum erosion location from the tube inlet ..................... 51

Figure 5. 6: Vectors showing flow motion within the recirculation zone. (a) ...................................... 51

Figure 5. 7: Vectors showing flow motion within the recirculation zone. (b) ...................................... 52

Figure 5. 8: Zone of maximum turbulence in the tube.......................................................................... 52

Figure 5. 9: Design modification with sleeve insert at tube inlet.......................................................... 54Figure 5. 10: Recirculation zone location at tube inlet after flow contraction. ..................................... 55

Figure 5. 11: Vectors showing flow motion within the recirculation zone at tube inlet. ...................... 55

Figure 5. 12: Recirculation zone location along tube wall after flow expansion.................................. 56

Figure 5. 13: Vectors showing flow motion within the recirculation zone after flow expansion. (b) .. 56

Figure 5. 14: Locations of erosion occurrence on the tube plate and the inserted sleeve. .................... 57

Figure 5. 15: Shear stress occurrence along inserted sleeve. ................................................................ 57

Figure 5. 16: Location of maximum turbulent intensity at tube inlet. .................................................. 58

Figure 5. 17: Graph showing drop in total pressure after flow expansion from sleeve contraction. .... 58

Figure 5. 18: Graph showing rise in static after flow expansion from sleeve contraction. ................... 59

Figure 5. 19: Design modification with perforated plate of same diameter as pre-heater tube located

before tube inlet. ................................................................................................................................... 61
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Figure 5.20: Vector representation of recirculation zone formed between perforated plate and tube

plate. (a) ................................................................................................................................................ 61

Figure 5.21: Velocity profile of flow within tube. ................................................................................ 62

Figure 5.22: Locations of erosion occurrence on the tube plate and the inserted sleeve. ..................... 62

Figure 5. 23: Location of maximum turbulent intensity at tube between perforated plate and tube

plate....................................................................................................................................................... 63

Figure 5.24: Wall Shear stress occurrence along perforated plate wall, tube plate and tube inlet........ 63

Figure 5.25: Vector representation of flow reversal at tube inlet.......................................................... 64

Figure 5.26: Magnified vector representation of recirculation zone formed between perforated plate

and tube plate. ....................................................................................................................................... 64

Figure 5.27: Design modification with perforated plate of diameter 1.2D of pre-heater tube inlet...... 66

Figure 5.28: Locations of erosion occurrence along pore plate wall and tube plate. ............................ 67

Figure 5.29: Graph identifying location of maximum erosion from tube inlet. .................................... 67

Figure 5.30: Shear stress occurrence along pore plate, tube plate and tube inlet.................................. 68

Figure 5.31: Recirculation zone location between pore plate and tube plate........................................ 68Figure 5. 32: Vector representation of recirculation zone between the pore plate and the tube plate. . 69

Figure 5. 33: Location of maximum turbulent intensity occurring at the tube inlet. ............................ 69

Figure 5. 34: Design modification with smooth transition introduced at pre-heater tube inlet. ........... 71

Figure 5. 35: Stream function of fluid flow at the tube inlet................................................................. 71

Figure 5. 36: Location of maximum flow velocity at tube inlet. .......................................................... 72

Figure 5. 37: Vector representation of flow velocity at tube inlet. ....................................................... 72

Figure 5. 38: Wall shear stress occurrence at tube inlet........................................................................ 73

Figure 5. 39: Location of erosion occurrence along tube plate and tube inlet. ..................................... 73

Figure 5. 40: Graph showing location of maximum erosion from tube inlet ........................................ 74

Figure 5. 41: Location of maximum turbulent intensity occurring at the tube inlet. ............................ 74Figure 5. 42: Vector representation of erosion at the tube inlet. ........................................................... 75

Figure 5. 43: Variation of erosion rates for particle size of 50-microns for cases considered.............. 76




Figure 5. 47: Variation of erosion rates for particle size of 100-microns for cases considered ............ 78

Figure 5. 48: Further possibilities of design modifications to mitigate erosion.................................... 79

Figure 5. 49: Prediction of locations of erosion occurrence by coefficients of restitution used in

simulation.............................................................................................................................................. 82

Figure 5. 50: Location of maximum erosion from tube inlet ................................................................ 82

Figure 5. 51: Prediction of locations of erosion occurrence by altered coefficients of restitution. ...... 83


Figure 5. 53: Prediction of locations of erosion occurrence by altered coefficients of restitution. ...... 85


Figure 5. 55 : Location of maximum erosion intensity in geometry used in simulation. Geometry 1.. 86

Figure 5. 56: Location of maximum erosion intensity for geometry with further refinement applied to

the mesh. Geometry 2 ........................................................................................................................... 87

Figure 5. 57: Location of maximum erosion intensity for geometry with further refinement applied to

the mesh. Geometry 3........................................................................................................................... 87
http://e/INVESTIGATION%20INTO%20THE%20EROSION%20MODELLING%20AND%20DESIGN%20OF%20TUBULAR%20AIR%20PRE.docx%23_Toc335048133http://e/INVESTIGATION%20INTO%20THE%20EROSION%20MODELLING%20AND%20DESIGN%20OF%20TUBULAR%20AIR%20PRE.docx%23_Toc335048133http://e/INVESTIGATION%20INTO%20THE%20EROSION%20MODELLING%20AND%20DESIGN%20OF%20TUBULAR%20AIR%20PRE.docx%23_Toc335048133


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List of Tables

Table 2. 1 Elemental composition of minerals found in coal fly ash. ..................................................... 7

Table 4. 1: Variations in results observed with increased mesh refinement ......................................... 42

Table 4. 2: Variations in results observed with different turbulence models........................................ 43

Table 5. 1: Impingement angle coefficients used in the simulation...................................................... 47

Table 5. 2: Coefficients of restitution used in the simulation. .............................................................. 47

Table 5. 3: Erosion rate dependency on size of particle ....................................................................... 48

Table 5. 4: Erosion rate dependency on particle size............................................................................ 53




Table 5. 8: Coefficients of restitution applied in the simulation showing erosion rates obtained

according to particle size. ..................................................................................................................... 81

Table 5. 9: Altered Coefficients of restitution applied in the simulation showing erosion rates obtained

according to particle size. ..................................................................................................................... 83

Table 5. 10: Altered Coefficients of restitution applied in the simulation showing erosion rates

obtained according to particle size........................................................................................................ 84

Table 5. 11: Geometries tested with different levels of refinement applied to the mesh ...................... 86


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Notations and Units:

Cell face area at the wall boundary -

Constant (

) -

Coefficient of particle size -CD Drag Coefficient -

Cp , Cq Concentrations of pyrite & quartz -

dh, Hydraulic diameter - m

Diameter of particle - m

Cross-diffusion term - Volume of surface removed - gms , p Rate of erosion - mg/kg

Coefficient of particle impact angle - Function of angle of impact - External body forces - Turbulent kinetic energy - Generation of - Vickers hardness of material surface -Hm Melting enthalpy of material -

Iq Quartz abrasiveness -

Ie Erosion index of ash -

KT Kinetic energy transfer as a result of impact - cm-2

sec-2

Kp, Km, Mechanical and physical constants of particle & material - Downstream separation length - m Downstream separation height - mM Summation of mass of particles -

Mass of erodent - kg

Mass of material removed - mg


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Mass flow rate of particle - Static pressure of flow -Qp Particle loading rate - gms/s

Material surface condition - m Reynolds number -R Geometry of particle -

, Radial & axial coordinates - Mass of entrained particles -

&

User-defined functions -

Tm Melting temperature of material - K

, Velocity of impact of particle - m/s Volume of material removed by deformation mechanism - & Dispersion of k and -Greek letters:

,

Density of particle & material - g/cm3

Yield stress of material - kgf/mm2 Energy to extract unit volume from the component surface - Angle of impingement of particle - Stress tensor - Gravitational body forces -

Molecular viscosity -, Effective diffusivity of k and -Subscripts: Particlem Material

q Quartz Kinetic energySuperscripts:

,

Velocity exponent


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Chapter 1

1.0 Introduction:

This chapter will give a brief explanation of the working principles of a power plant and theprocess of flue gas production. It also outlines the objectives of the thesis and concludes with

a layout of the thesis with regards to chapter arrangement and content.

1.1 Background:

The recent explosion in world population has led to an increase in demand for energy and

electricity. It is projected that by the year 2035, the world would require 769.8 Quadrillion

Btu of energy to sustain it. This represents a significant rise from the total consumption of

504.7 Quadrillion Btu in 2008 (U.S. DOE, 2011). Of this vast quantity, fossil fuels are

expected to provide over 80% of resources required for power generation (U.S. DOE, 2011).

These fossil fuels come in the form of Liquids, Coal and Natural gas. In this same order, they

also represent the divisions from where the largest quantities are mined and delivered. Hence

the importance of coal to the future of the human race in terms of energy production and

consumption cannot be taken for granted. Factors contributing to the frequent choice of coal

as a source of energy include its wide availability and relative cheapness (Beer, 2000).

Coal is used in the boiler/furnace of a power plant to produce thermal energy which in turn is

used to generate steam to rotate turbines. The journey of coal begins in the crushing facility

where it is crushed and reduced to the particular size required. From this facility, it is

transported to the pulveriser where its size is further reduced to a finer form and then, it is

finally transported to the burners. A mixture of both air and the macerated coal are fed into

the furnace where coal is completely combusted. A significant portion of the ash produced

from this process drops to the bottom of the furnace and there it is extracted while the other

portion is engulfed by the flue gases and carried away. The ash entrained in the flue gas is

referred to as fly-ash (Basu et al., 2000). The flue gas is usually channelled through many

sections of the plant in a bid to extract as much heat energy as possible from it before it is

finally exhausted into the atmosphere. Some of these sections include the air pre-heater,

where the temperature of the combustion air is raised as a result of the heat exchange between

the two fluids. Also included, are the super-heater and the re-heater surfaces through which

the flue gas is also channelled. The energy from the flue gas is also absorbed in the

economiser, where it is used to preheat the water before it enters the drum and the evaporatortubes of the boiler. Before final exhaust, the gas is passed through a gas-solid separator where


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a large quantity of the ash is collected in devices such as bag-houses or an electrostatic

precipitator. To reduce its nitric oxide and sulphur dioxide content, a selective catalytic

reducer and a flue gas desulfurizer is usually employed. An induced draft fan then extracts

the gas and exhausts it through the stack.

Figure 1. 1: Cross section of a pulverised power plant

Source: (Termuehlen & Emsperger, 2003)

Asides the environmental concern of exhausting flue gas into the atmosphere, the ash

produced during the combustion process has been identified as one of the drawbacks of coal

use as a fuel. This is as a result of the detrimental effects the fly-ash has on the heat

exchanger tubes, as the flue gas in which it is entrained flows through the tubes. It is stated by

Das et al., (2006) that up to 20% of the ash produced during coal combustion cause an

erosive effect on different components of the boiler. Some of the contributing factors to this

erosive effect of the fly ash include its particle size, velocity of flow, angle of impact on

component surface, material surface composition and temperature of the carrier gas (Tylczak,

Adler, & Rawers, 2003). Extensive research has been carried out by various scholars, to

relate resultant erosion to these determinant factors and some of these results are detailed in

subsequent chapters.

Erosion and its location of maximum intensity is another data required from this process, to

enable the engineer to properly design for and mitigate the effects (Bremhorst & Brennan,


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2011). General available data explains that this location is usually at the inlet of tubes but the

exact location has hardly been explored.

Another area that has received very little attention is the exploration of possible designs that

could mitigate the effects of flue gas erosion at the inlet of air-pre-heater tubes.

Computational Fluid Dynamics (CFD) since its development has enabled the accurate

simulation of flow for different components of which physical visualization or a physical

model set-up would have been difficult, hence earning its title of being cost effective and

highly efficient (Vuthaluru & Vuthaluru, 2006). Different CFD software packages are readily

available and some of them include: FLUENT, PHOENICS, FG-DVC, FLASH CHAIN,

CINAR, CFX etc. (Korytnyi et al., 2008). Though different, the principles of their operation

are still basically governed by the use of a series of complex numerical equations to simulate

the interaction between flow and its constituent particles; such that certain inferences as heat

transfer, amount of material wear, efficiency of the system etc. can be drawn.

1.2 Objectives of thesis:

Investigation of erosion and causes of erosion to include a review of availableliterature on erosion & CFD modelling of erosion with the investigation & assessment

of current designs to mitigate erosion

Development of air pre-heater tube geometry in 2D using GAMBIT, simulation ofsingle-phase gas flow in this geometry using ANSYS-FLUENT and finally, its

validation

Implementation of gas particles Euler-Lagrange flow models to predict erosion at thetube entrance and an analysis of the erosion rates.

Investigation of the efficacy of certain designs to mitigate erosion within the pre-heater tube.

1.3 Outline of thesis:

Chapter 2: Literature review of past works of knowledge covering the issues ofinterest, a comprehensive study of erosion, erosion mechanisms and its engendering

factors.

Chapter 3: Detailed explanation of Computational Fluid Dynamics (CFD) as a flowsimulation tool, with a concentration in ANSYS-FLUENT.

Chapter 4: Creation of the pre-heater tube geometry, simulation of the single phaseflow, and its validation.


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Chapter 5: Analysis of results Chapter 6: Conclusions and recommendations.


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Chapter 2

Literature Review

2.0 Introduction:

This chapter presents a summary of research carried out by different scholars exploring

erosion mechanism and its effect on different material components. It was observed that quite

a lot of research documentation containing results that detail the factors that enhance the

detrimental effects of erosion already exists. Some researchers however, went further to

develop empirical or semi-empirical mathematical models in a bid to relate the variables

which they discovered escalate erosion to the process of erosion itself. These models were

meant to act as guides in accurately predicting the process by which erosion occurs in order

to reduce it.

This chapter begins with a general description of coal and the plant component (air pre-

heater) in question. Erosion mechanisms and prediction models derived from experiments

carried out through extensive laboratory work and simulation of the working environment is

then detailed. The chapter is concluded by examining the different proposals suggested by

researchers as to the modification of pipes/tubes to mitigate the effects of material wear by

solid particles.It was discovered that little literature exists detailing a model, whether empirical or semi-

empirical to pinpoint the exact location erosion intensity is expected to be greatest in a pre-

heater tube. The absence of sufficient research in this area forms a part of this thesis.

2.1 Coal combustion:

Basu et al., (2000) describes coal as a heterogeneous material composed of fossilized

carbonaceous material with dispersed mineral inclusion (Flagan & Seinfield, 1988). Coal is

produced as a result of the transformation in plant and material structure over a long period of

time, usually over millions of years in the presence of high temperature and pressure present

below the earth surface. As a result of this lengthy period of formation referred to as

coalification, a class division in which coals can be categorised has been developed. These

include in order of oldest coal: anthracite, bituminous coal, subbituminous coal, lignite and

peat. The physical structure of coal is basically made up of two categories of materials:

organic or macerals and inorganic or mineral matter (Ward, 2002). The inorganic materials

have very little significance when combusted while on the other hand, its mineral or

inorganic materials are associated with the erosion, corrosion or stickiness in components


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parts producing the detrimental effects associated with coal combustion (Gupta, Wall, &

Baxter, 1999)

Upon heating to extract latent energy, coal particles as a result of reactions within its internal

structure disintegrate into tiny pieces (Flagan & Friedlander, 1978). Its combustion is

triggered by the reaction of the volatile materials forming part of the coals chemical structure

at high temperatures. Thermal stresses develop within its structure and a build-up of these

stresses eventually lead to the breakdown of the pulverised coal chunk. Flagan & Seinfield

(1988), explain that two mechanisms exist through which ash is formed during coal

combustion. In the first mechanism, as carbon within the coal combusts, constituent mineral

compounds upon contact bond to form large ash clusters. High temperatures emanating from

the coal would lead to a breakdown of these clusters into globules of ash which settle on the

shell of the char. The char then further combusts leading to the formation of what is referred

to as residue ash. Further breakdown of the residual ash at high temperatures would lead to

the transformation in its physical structure from its round structure, to one of a spherical

nature. These new ash particles are known as cenospheres and their sizes range from a few

micrometres, to several micrometres. In the second mechanism of ash formation, only a small

percentage (1%) (Flagan & Seinfield, 1988) of the ash melts as a result of high temperatures.

A fraction of the melted ash then coalesces to form minute particles. The size diameter of

these particles increase as additional volatilized ash particles condense on its surface.

Figure 2. 1 Structural model of high volatile bituminous coalSource:(Shinn, 1984)


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Figure 2. 2 : Diagrammatic representation of ash formation during high temperature combustion of coal

Courtesy (Flagan & Seinfield, 1988)

Table 2. 1 Elemental composition of minerals found in coal fly ash.

Element Compound in ash % composition

Silicon Silica (SiO2) 55.20

Aluminium Aluminium oxide (Al2O3) 30.80

Iron Iron oxide (Fe2O3) 3.67

Titanium Titanium oxide (TiO2) 1.61

Phosphorous Phosphorous pentoxide (P2O5) 0.35

Calcium Calcium oxide (CaO) 5.01

Magnesium Magnesium oxide (MgO) 1.40

Sodium Sodium oxide (Na2O) 0.20

Potassium Potassium oxide (K2O) 0.73

Sulphur Sulphur (S) 0.20

Manganese Manganese oxide (MnO) 0.03

Total SiO + Al2O3 + Fe2O3 89.67Courtesy (Das et al., 2006)


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2.2 Air Pre-heaters:

An air pre-heater usually made of ductile material can be described as a heat exchanger

designed to facilitate the transfer of heat energy between flue gases and incoming combustion

air. They may be designed in any of the following forms as noted by Kakac & Liu (2002):

i. Regenerativetype: are air pre-heaters designed for continuous heating operationssuch that the heating matrix alternates between the gases where heat transfer is

required. They are further sub-divided into two;

a. Rotating plate type: in this design, the component rotor is installed withthe plate heating surfaces and contained by box housing. As the rotor

spins, the plates are exposed to both the flue gas and the incoming

combustion air in an alternating cycle. The design allows for the transferof heat energy to the plate surface when exposed to the flue gases and then

a final transfer of the stored heat energy to the incoming air.

b. Stationary plate type: in this design, the plates are fixed while the air/gassections circle around it. Its working principle is similar to that of the

rotating plate. Component parts include a stator, seal system and an air

hood (Basu Kefa, & Jestin, 2000).

ii. Recuperative-type: in these air pre-heaters, heat transfer is carried out acrossplates or the tube walls. They have neither rotating nor moving components, and

are usually larger that the regenerative types (Basu Kefa, & Jestin, 2000). Their

weights double that of the regenerative type and occupy about nine times the

volume of its counterpart. They are further subdivided into two;

a. Tubulartype: For this air heater type, its design is such that the hot flue gasstreams in the longitudinal direction within the tubes while the combustion air

flows in the crosswise direction. The flue gases make a single pass through the

tubes but the combustion air is required to make a number of passes before it

exits the heat exchanger. An increase in its number of passes, usually results in

a lower temperature difference between the two fluids and also a drop in

combustion air velocity as a result of the resistance presented by the increased

number of pipes. The arrangement of multiple passes is common in large

capacity boilers (Basu Kefa, & Jestin, 2000). Tubular-type air pre-heater

geometries constitute the major part of this thesis.


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Figure 2. 3 Tube bank of air preheater.

b. Plate-type: in this arrangement, parallel-lined plates are used to channel fluidflow, and replace the use of pipes/tubes.

iii. Heat pipe.In coal fired power plants, a mixture of air and macerated coal pieces is fed into the furnace

to generate heat energy which is absorbed through radiation by the evaporator tubes lining the

furnace surface. Upon combustion, some of the ash produced by the coal drops to the bottom

and is extracted while the flue gas bearing the remainder of the ash begins its journey towards

the plant stack. Along the way, the entrained ash referred to as fly ash1

is deposited on plant

components such as the walls, pipe surfaces etc. To increase plant efficiency, the flue gas

usually still at a very high temperature is passed through several types of heat exchangers of

which one is the air pre-heater where it mixes with the incoming combustion air and in the

process transfers heat to it. These air pre-heaters are usually in the form of gas-in/air-over

configuration where the flue gas flows inside the tubes while air flows over it.

As the flue gas flows from the large open area into the constricted and smaller area of the pre-

heater tube inlet, a pressure drop occurs at the tube entrance which is followed by a shift in

flow pattern from an axial pattern to one of a cross-patterned nature (Bremhorst & Lai, 1979).

The separation in flow pattern usually stems from flow entering the tube at an angle larger

than the angle of the tube inlet axis (Bremhorst & Brennan, 2011). Takahashi & Horiuchi

(1969) examined the hydrodynamic interaction between tube inlets and fluids approaching it.

1The term fly ash first appeared in Journal Proceedings of the American Concrete Institute in 1937

(www.undeerc.org).


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Their experiments showed that at the inlet of water bearing pipes of high pressured feed

water heaters, two strong eddies are formed which transformed the nature of the fluid flow to

one of a highly turbulent nature. At the other end the tube outlet, the flow turbulence had

disappeared containing no vortex. The separation of the incoming flow coupled with the

increased acceleration of the flow, would lead to the entrained fly-ash particles striking the

tube wall at an angle causing gradual surface removal. A build-up of this would ultimately

lead to the complete failure of the tube in that region (Basu Kefa, & Jestin, 2000).

2.3 Erosion:Basu, Kefa, & Jestin, (2000) describes erosion as the wear of any solid plane as a result of

repeated impingement by hard particles while Hutchings & Winter (1974) describe erosion as

the resultant detrimental effect of minute particles which are entrained in a flowing fluid

striking a material surface and leading to its wear by abrasion. The detrimental effects of

erosion, is felt across all industries where fluid is transported in confined conduits such as

pipes or tubes. This abrasion generally leads to the failure of components and the loss of

millions in revenue each year, as plants have to be shut down for either maintenance or

replacement purposes. The effects of erosion are so prominent that the DOE (Materials &

Components, 1998), recognised erosion by fly-ash present in flue gas as the second most

important cause of tube failures in power plants and Basu, Kefa, & Jestin, (2000) concur that

in certain instances, one-third of all tube failures in power plants could be traced to fly-ash

erosion.

Figure 2. 4 Flow separation at tube inlet. Courtesy

Source: (Bremhorst & Lai. 1979)


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Figure 2. 5 Typical location of erosion at the inlet of air heater tube

2.4 Mechanisms of erosion:

Das et al., (2006), explains that there are 3 major mechanisms by which metal surface

removal occurs:

1. Cutting wear mechanism: in which particles of ash impinge the material surface at anacute angle with a velocity much more than that required for the material surface to be

penetrated. Coupled with the velocity, is the transfer of heat energy from the particle

to the material surface upon impact leading to an increase in shear strain at that

location. When strain build-up surpasses the elastic strain boundary of the material,

the ash particle penetrates the material surface removing a portion of it. Raask (1969)

explains that this mechanism is predominant in ductile materials as the action of

cutting depends on how ductile the impinging surface is.

Kragelsky et al., (1982) developed an erosion model to this effect but it was modified

by Das et al., (2006) to produce an erosion model based on the cutting action of the

ash- particles:

2.1

Bitter (1963) also observed that erosion wear occurred by two mechanisms, by the

deformation of the component surface as a result of repeated impact by the solid

particles and by an acerbic attack of the flow constituent particles. He derived an

erosion prediction model for wear by deformation based on the kinetic energy

transferred on impact.


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2.22. Plastic deformation mechanism: In this mechanism, wear occurs as a result of the

combined effects of extrusion and forging. Upon impingement by ash particles, highly

strained lip-shaped (Hutchings & Winter, 1974) forms are developed by the surface

which is susceptible to easy removal by particles either by adhesion to the ash

particles, or through a process of extrusion between the particle and the material

surface. Adiabatic shear heating is generated in the vicinity of the impact and just

below the material surface, a work hardened layer is formed. This layer develops

owing to the fact that velocity of ash particle impact is much more than required to

strain the surface. When the surface of the component is completely covered by these

distorted forms and the work hardened layer attains a level of stability and appreciable

thickness, erosion sets in. Maximum erosion occurs as the work hardened layer

functions as an anvil hence increasing the ease with which the impinging particles

extrude-forge the surface of the material. Sheldon & Kanhere (1972) developed a

model relating the indentation formed by a surface upon impingement by a particle:

2.3Das et al., (2006) also proposed an erosion prediction model:

2.4

Levy (1986) examined the surface of an eroded metal using high magnification

electron scanning microscope and discovered that the eroded surface bore a close

resemblance to that of a surface which had experienced a combined effect of

extrusion and forging. The visual examination corroborates the proposition by Raask

(1969) that for ductile materials, wear occurred by a combination of both plastic

deformation & cutting while for brittle materials, erosion occurred predominantly by

the action of plastic deformation.


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Figure 2. 6 Erosion by plastic deformation.

Source: Levy (1986)

3. Erosion as a function of temperature: occurs as a combined effort of both plastic andcutting wear. Sheldon & Kanhere (1972), Sheldon et al., (1977) Sheldon et al., (1977),

Fan et al., (1990) and Jun & Tabakoff, (1994), Das et al., (2006) all document an

erosion rate, based on this mechanism.

2.5The temperature function was developed into a polynomial equation, relating it to the

yield stress of the different materials considered by (Lee et al.,1999).

2.5 Factors influencing erosion:

The intensity of erosion of a material surface is dependent on many factors surrounding the

impinging particle. Some of these factors are discussed:

1. Particle impingement velocity: plays an important role in deciding the extent towhich a material surface is deformed. The erosion rate (E) was proposed by Basu,

Kefa, & Jestin, (2000) to be directly related to velocity at an exponent;

= 2.3 - 2.7

for ductile components, and = 2 - 4 for brittle components.


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2.6Researchers after considerable experiments have attributed different constants to the

value of but a common trend is found in their discoveries; they agree that theparticles travel at a different velocity from the flow in which they are entrained.Finnie (1960) asides from being one of the pioneers in the field of prediction of

erosion models also recognized difficulties that might hinder the correct prediction of

this process, the difficulty of accurately predicting entrained particle velocity. In his

experiments, he explored erosion mechanism on both brittle and ductile materials.

These he notes are not without difficulties in parameter identification which he

identifies before building a mathematical model based on the cutting effect of a single

grain. Finnie scaled his calculated values up and then compared them with values

obtained experimentally for cutting wear of multiple grains acting on a surface. He

found a close relationship between the two. In conclusion, he infers that the amount of

surface wear of a material is related to the velocity conditions of flow of the fluid with

respect to its constituent particles as well as the nature of the impingement surface and

its reaction when hit by the abrasive particles. He based this upon the observation that

surfaces bruised by solid particles were more likely to cause an increase in turbulence

of the fluid flow, and therefore invariably increase the speed of surface removal. He

verifies this theory for ductile materials, but warns that it does not hold true for brittle

materials. Raask (1969) after due examination of the different factors (angle of

impact, abrasiveness of ash, temperature of metal surface, etc.) that contribute to

erosion intensity, also agreed that velocity of flow was the most important parameter

to consider when designing to mitigate erosion.

2. Flow conditions: the relationship between amount of surface removal and conditionof flow was studied by Dosanjh & Humphrey, (1985). Their experiment results

showed that an increase in flow turbulence had an inverse relationship with the rate at

which erosion occurred. Basu, Kefa, & Jestin, (2000) explains that this phenomenon

could be partially attributed to the decrease in particle impact speed and flux in

relation to the material surface, with increase in turbulence of the gas phase.

3. Particle impingement angle: Haller, (1939) examined the influence of wear on metalsurfaces and discovered upon examination of his specimen surfaces after impact that

for high impact angles, a flat and distorted surface was formed while for low

impingement angles, a grazed and less distorted surface was formed. His conclusion


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was that erosion could only be as a result of the angle of particle impact. Wellinger

(1949) also experimented with a view to determining the influence impact angle had

on erosion mechanism. His results showed that erosion as a function of impingement

angle had a more severe effect at lower angles for low carbon steel which is soft and

ductile when compared to hardened high-carbon steel which is brittle. At high

impingement angles, he observed that the reverse occurred. His results also showed

that the mechanical properties of the component played a huge part in its resistance to

erosion. Nagarajan et al., (2009) developed an erosion model predicting with an

accuracy of >90%, the dependence of erosion on fly-ash impact angle. Their report

presents an experiment which used 3 types of low-alloy steels, 3 ash samples obtained

from power stations, impingement angles of 150, 30

0& 45

0and a velocity of flow

varied by using compressed air pressure which was then measured using the rotating-

double-disk technique. Using High Level Analysis (HLA), their results showed and

verified past well documented experimental data that the rate of erosion was directly

related to increased particle flow velocity, but that as a function of impingement

angle, the rate of erosion increased up to a certain value then decreased or flattened

out. In addition, they documented other factors which might affect the rate of erosion

such as the effect of particle size where they recorded a direct relationship between

erosion rate and particle size up to a size of 120m, and a levelling effect afterwards.

Mechanical properties of the test samples such as hardness and composition were

found to play a minor role in material erosion when compared to the surface condition

of the material (roughness) which was a major decider in the susceptibility of the

material to erosion. With all the data gathered and sorted, a mathematical model was

developed, which when they compared to values measured in real life situations,

showed an accuracy of >90%. They however note that these results are only

obtainable at room temperature conditions in which the experiments were conducted

and for elevated temperatures, the results would be quite different.

2.7

For Oka et al., (1997) the approach was to test the effect of varied impingement

angles on rate of erosion for different materials which included metals, ceramics and

plastics. For their experiments, a sand blast rig was used at low impingement angles


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and observations suggested that striking velocity of particles and rate of surface

removal were directly related while erosion rates varied for different classes of metal

at lower angles of impingement. Their erosion model was derived based on

trigonometric functions of both impingement angle and the materials hardness. They

also discovered that the hardness of the components played a role in its erosion. For

example, softer materials experienced more erosion at shallower angles than their

tougher counterparts.

2.8Mbabazi, et al., (2004) also discovered that erosion intensity attained a maximum

value at angles between 250

& 300

for mild steel tubes and afterwards the rate fell

sharply.

4. Ash particle size: Nagarajan et al., (2009), investigated the influence of particle sizeon erosion and observed that erosion rose steadily as particle size increased towards

120m. Sizes larger than 120m produced a constant value in the plot. Basu, Kefa, &

Jestin, (2000), also investigated this factor, and noted that erosion rates increased

steadily for particle sizes between 10m and 100m, but that above this value,

volume of material removed was independent of the size of the impinging particles.

5. Temperature of flue gas: when a particle impinges upon a surface at a high velocity,heat energy is transferred form the particle to the material surface. This would usually

result in the intermittent melting and re-solidification of the extruded portion. Upon

further impact, the extruded portion is easily removed by the impinging particle.

Jennings et al., (1976) investigated the consequence of transfer of heat energy as a

result of impact by dust particles which results in the melting of the impacted surface.

They were able to develop a mathematical model for predicting erosion mechanism

based on the heat energy transferred between the particle and the material surface as

they interacted. The model was developed using dimensional analysis obtained from

an experiment which employed alloys (aluminium, beryllium copper and titanium)

and stainless steels as the material surfaces and dust samples (2 specimens with

angular shaped specks and the other specimen spherically shaped).

ZT = 2.9Y= G

1/3/R

1/3KTTmHm 2.10


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Xie & Walsh (1995) also explored the influence of nitrogen and oxygen

concentrations in conjunction with temperature on the rate of erosion. Their results

showed that low erosion rates were directly related to low temperatures irrespective of

oxygen concentrations at that temperature. They were also able to show that erosion

progressed slowly at greatly oxidized high temperature, with erosion rates being

highest at low oxygen concentrations in the presence of high temperatures. Where the

incident ash particles were accelerated by a nitrogen stream jet, they observed that

metal wear steadily increased with increasing temperature. Experiment temperature

ranges, were between 4500K and 600

0K.

Yong & Ruff (1977) however proffered the theory that high temperatures could lessen

the effects of erosion as a result of increase in ductility of the material. This would

cause the impinging particles to embed themselves in its surface hence providing a

form of surface protection for the component. Sense can be seen in this theory as

observations by Raask (1969) suggest that erosion intensity was observed only in

plants that had little or no deposit.

6. Abrasiveness of ash content: as mentioned earlier, the organic contents of coalhardly contribute to its erosive effects. Hence the detrimental effects of coal can be

traced to its inorganic material make up. Borio & Levasseur, (1984) note that the

influence of quartz and its size distribution could be the most damaging characteristic

of coal. A mathematical relationship was developed by (DOE, Materials &

Components, 1992), to relate the ash quartz and pyrite content to the abrasiveness

expected from the coal.

Ic = [Cq + (0.2 to 0.5) Cp] Iq 2.11

2.6 Design to mitigate effects of erosion:

To properly design for erosion mitigation, the location at which its intensity is maximum,

needs to be predicted with near accuracy. A few researchers have taken steps beyond erosion

prediction modelling, to propose where the effect of erosion is expected to be greatest in a

fluid bearing tube. For example, Bremhorst & Lai (1979), utilized flow visualization and

velocity distribution studies to determine the flow characteristics obtained at the inlet of shell

and tube heat exchangers. From their studies, they were able to describe this flow as cross-

patterned in nature and that its intensity was greatest a location approximately 3-4D from the

pipe inlet, where D represents the diameter of the pipe. With reference to size of particles,


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they were able to prove that particles less than 1mm in diameter were likely to separate from

the flow and impinge directly on the pipe walls. Tucker (1967) also studied flow patterns

obtained at the inlet of condensers and observed that erosion was most intense at a distance

2in from the tube inlet and could be attributed to the cross flow pattern generated at the pipe

inlet. In his experiments, he also discovered that cross flow of fluids led to flow separation at

the tube inlets which subsequently led to particle impingement. He suggested tube

modifications such as the attachment of bell-mouths to the pipe inlets to eliminate pressure

drops responsible for generating cross flows at the tube inlets. Other modifications include;

the attachment of a deflector plate in the cooling water feed pipe. Basu, Kefa, & Jestin,

(2000) specifically studied the mechanisms of erosion in air pre-heater tubes. They worked

with the erosion model proposed by (CBSC, 1973) and deduced that the location of

maximum wear occurred at the inlet, at a point;

X= 2d, where d is the pipe diameter

They went ahead to prescribe design modifications at the pre-heater tube inlet region to

reduce the rate at which this area is attacked; these measures were derived from conclusions

that particle velocity was the most influential factor in the determining the rate at which metal

surfaces are eroded. Some of the modifications include; the attachment of sleeve tubes 2-4d

long, at pipe entrances such that the sleeves are eroded rather than the pipe itself. The use of a

pore plate placed at about 0.26d from the tube inlet with diameter 1.2d; of which its function

is to force gas contraction in order to reduce swirl at the tube inlet. Others include a smooth

transition at the inlet of the tube, and the use of a perforated plate of same diameter as the

tube, such that flow contraction occurs between the plate and a normalized axial flow enters

the tube. Fan et al., (2001) also explored design enhancements of pipe bends to mitigate the

resulting erosion caused by incoming gas streams. They discovered that the attachment of

fins to the outer side surface of the pipe bend reduced the amount of material eroded by a

significant value. Fan et al., (1999) also proposed design modification to straight pipes to

reduce the velocity of incoming gas streams. They attached fins to both sides of the tube with

a view to reducing wall-particle interaction by reducing gas flow which consequently changes

the constituent particle trajectory. Although this method is riddled with complexities such as

increasing the weight and length of the pipe and causing a possible reduction in heat transfer

efficiency (especially for heat exchangers), they conclude that the final decision would rest

with the designer as to how to balance these effects while still achieving optimised

conditions. Lai & Bremhorst (1979) carried out the most extensive studies in the design of


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parts with which the tube inlet and its surrounding regions are modified in order to mitigate

erosion. They examined the efficacy of flow rectification devices such as perforated plates,

deflector plates or fences and a prismatic flow corrector in the mitigation of erosion. These

devices were designed with different specifications and placed at different locations from the

tube inlet. They came to the conclusion that the perforated plated device produced the best

and most desirable results.

2.7 CFD and Erosion Modelling:

The development of fluid simulation software computational fluid dynamics CFD has greatly

enhanced the ease with which experiments are carried out. Real life situations can now be

replicated without the rigours of acquiring and setting up equipment to simulate operation

conditions. Results obtained from these computer simulations are also found to have goodaccuracy in their result prediction. Hence in recent years, they have gained popularity in their

use to model interaction between components and their constituent elements. Researchers in

the field of erosion have greatly utilized this benefit to revalidate empirical models developed

through physical experiments and data collection by past researchers. For example, Wang &

Yang (2008) examined the theory that observed erosion effects varied for both ductile and

brittle materials with the use of Finite Element Modelling (FEM). They discovered that for

ductile materials, erosion occurred as a result of micro-cutting and micro-ploughing of the

surface by the abrasive particles; while for brittle components a transfer of energy upon

impact from the particles to the component surface was the source of crack generation and

subsequent spread. This further strengthens observations made through physical experiments.

They developed a Finite Element model using the CFD software code ANSYS/LS-DYNA

and the erosion models proposed by (Johnson & Cook, 1983) and

(Johnson & Holmiquist,1999). Hence with Finite Element Analysis (FEA), they were able to

study the effects obtained when flow conditions and impingement angle were varied and their

results tallied with those achieved through experimental means. Their experiments produced

results which examined and correctly predicted the behaviour of both ductile and brittle

materials in an erosive environment. Das et al. (2006) developed an erosion model with a

computer code EROSIM-1 as a predictive tool for studying erosion mechanisms on metal

surfaces. With this code, they explored the effects of varying temperature conditions on the

tensile properties of the metal and its ability to render a metal surface susceptible to erosion.

Their observations suggested that under elevated temperature conditions and at angles less

than 900, metal surface erosion increased considerably and at high impingement angles,


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temperature had no significant effect. This signified that steels exhibit characteristics typical

of ductile materials at high temperatures. They calibrated their model by juxtaposing the

results it produced with those obtained experimentally by other researchers. These results

were found to agree and hence proved the capability of their code to accurately predict

erosion mechanisms at room and elevated temperatures. Dhamangaonkar et al., (2011)

utilized the Cold Air Velocity Test (CAVT) technique to determine the velocity of flow in

different sections of the boiler in order to correctly predict erosion occurrence. Fly-ash

velocity can be directly linked to the velocity of the flue gas in which it is entrenched and

although the two components might have different velocities, a correlation could still be

established between the two. They used the CFD code FLUENT to simulate the CAVT in the

boiler for different zones, and found that the results were in appreciable agreement with a

deviation of 23%. Wallace et al., (2004) in an attempt to determine the accuracy to which

CFD models could predict erosion, also discovered that for choke valves which were their

material specimens, material wear was most intense at the entrance. This intensity dwindled

as length increased within the choke as rightly predicted by (Bremhorst & Lai, 1979). Habib

et al., (2005) examined factors that engender erosion at the tube inlet region of shell and tube

heat exchangers. Using the Langrangian model to predict particle velocity and the empirical

erosion equations proposed by Wallace., (2000), their results showed that particle size and

velocity magnitude escalated erosion at the entrance of tubes. When the particle sizes were

large and flowed at low velocities, the erosion intensity was minimal as eddies created at the

tube entrances by pressure drops at the tube inlet were too low to increase particle

acceleration. Lee et al., (2000), developed a predictive model to compare the Eulerian

approach of modelling flow conditions, to the commonly used Lagrangian method. They

compared parameters such as impact velocity, impact angle and particulate concentration for

both approaches, and concluded that the Euler method produced slightly more accurate

results than the Lagrangian method. Model results, also proved that the Eulerian approach

required much less data input to achieve even better results than the Lagrangian method.

They calibrated their results with experimental results obtained by Bauver et al., (1984) and

found them to be in sound agreement. Mohanarangam et al., (2007), also compares the

efficiency of the Eulerian and Lagrangian approaches to fluid modelling when they

numerically simulated a turbulent gas-particle flow in a 900

bend pipe. The results obtained

for both models, were calibrated against experimental results produced by (Kliafas & Holt,

1987); while the Eulerian model showed good agreement with the yardstick data, the


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Lagrangian model showed considerable discrepancies, requiring more computational mesh

and time. They recommend that for complex flows, the Eulerian model should be employed.

2.7 Summary of literature review

Literature studied showed that quite a lot of time and resources has been spent researching

and detailing erosive effects in different components of the boiler. Focus has been more on

verification of empirical models and detailing factors that could encourage pipe degradation

by particle impingement. A few researchers have indicated that the inlet of pipes suffers most

from particle impingement effects, while even fewer have been able to indicate the exact

location it is to be expected. Research has also been limited in the area of design of parts used

in the modification of tubes, whether at the inlet or the surrounding regions to mitigate the

erosive effects of the fly-ash particles.

CFD as a simulation tool has been proven to show sensible accuracy and efficacy in the

execution of fluid flow scenarios or models in order to study them. This is evident in the

pivotal roles it has played in several empirical formulae validations.


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Chapter 3

Methodology

3.0 Introduction:

This chapter presents an in-depth description of the principles governing the equations

employed in the analysis of erosion by flue gas flow in air pre-heater tubes using the CFD

package ANSYS-FLUENT. The rationale behind the selection of the simulation models, are

also outlined.

3.1 General Overview of Computational Fluid Dynamics (CFD):

The influence offluid and its dynamics in our everyday lives can hardly be ignored from

the aerodynamics generated when we drive our cars, to the ventilation flow of our cooling

systems; it is obvious that we live in a fluid world. Fluid dynamics covers all applications

that involve fluid flow or heat transfer. It can then be correctly said that the principles of

fluid dynamics govern all aspects of product manufacture intended for human use. Therefore

the accurate knowledge of the fluid dynamics involved in any system or component would

ensure that the component or system is designed to perform at optimal efficiency. To achieve

this, a high degree of complexity both in design and functionality has to be introduced and

this invariably introduces an equal degree of complexity in the fluid dynamics of the

component or system. Test runs on potential prototypes or product efficiency modelling is

usually hindered by the need to set up physical models to visualize or obtain accurate results

which would mean accurately modelling the fluid flow involved.

Since the development computational fluid dynamics (CFD), product design, operation and

analysis have all become easily obtainable as a result of the use of a virtual simulation

platform. Problems involving complex motion requiring transient analysis e.g. the internal

components of an engine, phase change as a result of cooling or heating and multi-physics

phenomenon such as the interaction of fluids and its constituent elements are now easily

solved and accurate results obtained without the need for the set-up of physical structures.

CFD has thus been able to save the designer costs usually incurred during the

design/production life of a component or system.

CFD packages although numerous and commercially available, all have an underlying

principle which is the use of mathematical equations to model transport phenomenon in


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complex shapes or geometries. This process is accomplished in a particular order which is

described below:

Pre-processing: enables the designer to reproduce geometry similar to that ofinterest. It provides an option of either a 2-D or 3-D structure. Meshes are also

generated and deployed in the pre-processor interface. Meshes used, are classified

into two categories, namely:

o Structured mesho Unstructured mesh.

Variables related to the model geometry such as its boundary conditions and their

numerical parameters are all produced from the pre-processor interface. The

boundary conditions may involve laminar or turbulent types of flow and FLUENT

lists models which govern them. If flow involves particle tracking (particles

entrenched in a fluid) or multiphase flows, the desired governing equations are

specified.

Solver:once geometry, boundary and flow conditions are specified, it is solved.The function of the solver is to solve the equations in each of the mesh grids, hence

ensuring that the model is harmonised with its boundary conditions. This solution

follows a technique called Discretisation, and is carried out by either of thefollowing methods:

o Finite Difference Method (FDM): utilizes the Taylor series expansions(Smith G.D., 1985) to solve complex flow equations. This is achieved by

dividing the flow region into small elements and a variable for the dependent

quantity is assumed. Different numerical analysis procedures (Zienkiewicz

& Taylor, 1989) are then used to develop expressions for the first and

second order derivatives of the sought variable. This value is computed for

each element on the meshed surface of the geometry, after which all the

equations are gathered and solved for.

o Finite Volume Method (FVM): splits the flow region into different controlvolumes which were generated by the mesh function. Conservation

equations are applied and solved by method of integration in each volume

(Patankar, 1980) and (Versteeg & Malalasekera, 1995). ANSYS-FLUENT,

utilizes this discretization technique in its numerical analysis.

o Finite Element Method:


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Post-processing: includes the section of CFD dedicated to the analysis of generatedresults. Visual representation in the form of graphs, contour plots etc. are usually

generated from the post-processor which enable easy interpretation of data.

A typical CFD package used in this thesis is called ANSYS-Workbench which comprises of a

host of simulation packages which include Analysis systems, Component systems, Custom

systems and Design exploration. These have their respective sub-divisions designed to model

and analyse various conditions in different components. One of its design suites FLUENT, is

the fluid flow package used for this analysis.

3.2 Components of ANSYS-FLUENT:

As stated earlier, this thesis employs the use of the CFD software ANSYS-FLUENT which is

one of the many design suites available in ANSYS-WORKBENCH. A description of the

mathematical equations governing its fluid flow modelling and analysis will be described.

This will be done, with a bias for the topic of interest which is the analysis of erosion effects

in air pre-heater tubes.

3.2.1 Basic Flow Equations:

The first solution of ANSYS-FLUENT is directed towards resolving the conservation

equations for mass and momentum for all flows. This is done regardless of the nature of flow

whether laminar or turbulent. Additional equations are then provided to cater for such

conditions as heat transfer, particle tracking, turbulence etc. within the fluid flow.

Mass conservation equation:

3.1Eqn. above describes the general equation of mass conservation used to solve incompressible

flows as well as compressible flows.

Continuity equation for 2D axisymmetric geometry is defined by:

3.2


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Conservation of momentum equations, specifically for non-accelerating frames of reference

is represented by the following equation:

3.3

Equation of stress tensor is represented by: = * + 3.4 Represent molecular viscosity,Irepresents unit tensor.

3.2.1.1 Turbulence flow model:

ANSYS-FLUENT provides a series of turbulence models meant to assist the designer

correctly represent the fluctuations in velocity prevalent in turbulent or laminar flows.

Turbulence models available were designed based on the physics governing the flow, degree

of accuracy desired, computational power at the designers disposal, available time needed

for result production and the stipulated guidelines for the resolution of a specific type of

problem. Examples of some of the models provided are listed below:

Spalart-Allmaras model.

k- models, further sub-divided into the following sub-modelso Standard k- modelo Renormalization-group (RNG) k- modelo Realizable k- model

k- modelso Standard k- modelo Shear-Stress Transport (SST) k- model

Transition k-kl-w model

Transition SST model model (add-on) Reynolds Stress Models (RSM)

o Linear pressure-strain RSM modelo Quadratic pressure-strain RSM modelo Low-Re stress-omega RSM model

Detached Eddy Simulation (DES) model, which also covers the RANS models

o Spalart-Allmaras RANS model


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o Realizable k- RANS modelo SST k-w RANS model

Large Eddy Simulation (LES) model, further divided into the following sub-modelso Smagorinsky-Lilly subgrid-scale modelo WALE subgrid-scale modelo Dynamic Smargorinsky modelo Kinetic-energy transport subgrid-scale model.

The turbulence model used in this simulation and analysis was selected from the k- model

group with Shear-Stress Transport (SST) k- model being preferred over the Standard

version. This was done in accordance with the stipulated guidelines of the Engineering

Sciences Data Unit (ESDU) for the accurate prediction of the extent of pressure drop across

tube contractions. Pressure drop prediction across the tube inlet was chosen as a yardstick to

validate the single-phase flow model. The equations involved in the depiction of turbulence

in fluid flow when the SST k- model is used is further described in detail below

The k- turbulence model: consists of the Standard and the Shear-Stress Transport

(SST) turbulence models.

The Standard version of the model is based on the same principles as the Wilcox k- model

(Wilcox, 1998) which accounts for low-Reynolds number effects, compressibility and shearflow spreading. Its suitability for modelling wall-bounded flows is based on its accuracy in

predicting free shear flows spreading rates with similar results obtained in the measurement

of far wakes, mixing layers, plane, round and radial jets.

The Shear Stress Transport version was developed by Menter (1994) and is a more accurate

version of the two turbulence models, producing better accuracy for near-wall region models.

This accuracy is as a result of the incorporation or the modification of the standard model, to

include:

- A damped cross-diffusion derivative term in the -equation.- Different model constants- Modification of the turbulent viscosity, to recognise turbulent shear stress

transportation.

- Addition of an appropriate blending function to increase model stability in near-walland far-field regions.

- Cross diffusion term incorporation in the -equation.


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k-(SST ) transport models.

3.5and

3.6Equation for the effective diffusivity is given as:

3.7

3.8and represent the turbulent Prandtl numbers for the k and constants respectively. * + 3.9S accounts for the strain rate magnitude, and

3.10

3.11F1 & F2 denote the blending functions, and are given as:

3.11a

3.11b


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is the distance to the next surface, while represents the positive portion of the cross-diffusion term.

For the turbulence production;

, represents the turbulence kinetic energy 3.12 , represents the production 3.13The equations above, are represented differently in the Standard model, and form part of the

dissimilarities between the two models.

For turbulence dissipation,

3.14 3.15For Cross-Diffusion equation,

3.16Model constants are represented by,

= 1.176, , = 1.0, , , 3.2.1.2 Flow solvers:

The equation solvers used by ANSYS-FLUENT flow analysis are divided into two namely:

i. The Pressure-based solver;ii. The Density-based solver.

The two numerical approaches have a few similarities which include; the solution of the

velocity field from the momentum equation, use of a comparable discretization method

Investigation Into the Erosion Modelling and Design of Tubular Air Pre

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