Analysis of radiation properties of gases and utilization

in a pulverised coal combustion simulation model

André Rocheta Mateus

Dissertação para obtenção do Grau de Mestre em Engenharia Mecânica

Júri Presidente: Prof. Luís Rego da Cunha de Eça Orientador: Prof. João Luís Toste de Azevedo Vogal: Prof. Viriato Sérgio de Almeida Semião

Outubro 2007

i

ACKNOWLEDGMENTS Thanks are due, first and foremost, to Professor João Luís Toste de Azevedo, for taking me on

as a student, for the enormously helpful advice on the content of the project and structuring of

the text, and the tireless availability he always showed.

Thanks to all my colleagues who helped me throughout the course with their companionship

and encouragement.

I would like also to thank Project BOFCOM, for the financial support of this project.

A very special thanks to my parents, and to all my friends and family, for their love and support.

Last but not least, thanks to my girlfriend Dorota for her love and inspiration.

ii

RESUMO Este trabalho tem como objectivo a simulação numérica de uma chama de carvão pulverizado

com oxi-combustão e recirculação de produtos de combustão e a sua comparação com a

combustão com ar atmosférico. Esta aplicação tem em vista a possibilidade de efectuar a

captura e sequestro das emissões de CO2 de centrais térmicas alimentadas a carvão.

Uma vez que a atmosfera no interior da fornalha tem uma elevada fracção de CO2 são

analisados métodos de cálculo das propriedades radiativas de gases, tendo em atenção as

condições em que vão ser utilizados. São comparados vários modelos de mistura de gases

cinzentos, incluindo modelos globais e outros desenvolvidos com base em modelos

detalhados. Para valores moderados do comprimento óptico os modelos permitem resultados

comparáveis, sendo favorecido o modelo SLW que utiliza como base de desenvolvimento

modelos espectrais.

São efectuadas simulações numéricas da combustão de carvão pulverizado em ar e em

atmosferas com injecção de oxigénio e produtos de combustão recirculados. Os resultados das

simulações são muito dependentes do escoamento que é previsto de uma forma mais realista

considerando condições isotérmicas (a alta temperatura) no interior da fornalha. Nessas

condições a distribuição da composição dos gases apresenta um bom acordo com os

resultados experimentais, enquanto com o cálculo da temperatura prevê-se um atraso na

ignição do combustível e o acordo com os resultados experimentais é limitado.

Palavras chave: Simulação Numérica, Propriedades Radiativas de Gases, SLW, Oxi-

Combustão, Recirculação de Produtos de Combustão.

iii

ABSTRACT The present work objective was the modelling of both a pulverized coal air-firing combustion

and pulverized coal oxy-fuel combustion tested in a single burner furnace. This application has

the potential for the separation and sequestration of CO2 from coal fired power plants.

Due to the very high concentrations of carbon dioxide in the oxy-fuel combustion, some

radiative models given in open literature were tested to establish which gave better results in

order to use it in the combustion modelling. Several gray gas models are compared including

global models as well as others developed from data obtained with detailed models. For

moderate values of the pressure path length all models presents comparable results, however

the SLW model is favoured once it is based on spectral model results.

Numerical simulations are performed of pulverised coal combustion in air and in a mixture of

oxygen and recirculated flue gases. The results from the simulations are strongly affected by

the predicted flow field that is more realistic in isothermal (high temperature) conditions inside

the furnace. In those conditions the distribution of the gas species concentrations present a

good agreement with the experimental results, while with the calculation of temperature a delay

in ignition is predicted and the comparison with the experimental results is limited.

Keywords: Numerical simulations, Radiative Gas Properties, SLW, Oxy-Fuel Combustion,

Recirculated Flue Gases.

iv

INDICE

ACKNOWLEDGMENTS................................................................................................................. i

RESUMO........................................................................................................................................ii

ABSTRACT ................................................................................................................................... iii

INDICE ..........................................................................................................................................iv

FIGURE LIST ................................................................................................................................ v

TABLE LIST..................................................................................................................................vii

NOMENCLATURE ...................................................................................................................... viii

SUBSCRIPTS................................................................................................................................ix

ACRONYMS.................................................................................................................................. x

1 INTRODUCTION .................................................................................................................. 1

1.1 COMBUSTION TECHNOLOGY WITH CARBON DIOXIDE CAPTURE ..................... 2

1.2 OXY-FUEL COMBUSTION WITH RFG....................................................................... 6

1.3 OBJECTIVES............................................................................................................... 9

1.4 STRUCTURE OF THE THESIS................................................................................. 10

2 CASE STUDY AND NUMERICAL MODEL........................................................................ 11

2.1 AVAILABLE EXPERIMENTAL RESULTS ................................................................. 11 2.1.1 FURNACE AND BURNER DESCRIPTION........................................................... 11 2.1.2 OPERATING CONDITIONS.................................................................................. 15

2.2 NUMERICAL MODELLING........................................................................................ 16 2.2.1 CONTINUOUS PHASE BALANCES..................................................................... 17 2.2.2 PARTICLE SIMULATION ...................................................................................... 21 2.2.3 BOUNDARY CONDITIONS................................................................................... 23

3 RADIATIVE PROPERTIES................................................................................................. 24

3.1 RADIATIVE INTERACTION WITH GASES............................................................... 24 3.1.1 WIDE BAND MODELS .......................................................................................... 27 3.1.2 GRAY GAS MIXTURE MODELS .......................................................................... 27

4 RESULTS ........................................................................................................................... 40

4.1 RADIATION MODELS ............................................................................................... 40

4.2 COMBUSTION RESULTS......................................................................................... 44 4.2.1 BASELINE CASE .................................................................................................. 44 4.2.2 FLAME C ............................................................................................................... 53

5 CONCLUSIONS ................................................................................................................. 61

6 FUTURE WORK................................................................................................................. 62

7 REFERENCES ................................................................................................................... 63

v

FIGURE LIST

Fig. 1.1 - Compiled by the Climatic Research Unit of the University of East Anglia and the

Hadley Centre of the UK Meteorological Office. Data set HadCRUT3 was used.

HadCRUT3 is a record of surface temperatures collected from land and ocean-based

stations.......................................................................................................................... 2

Fig. 1.2 – Monthly averaged carbon dioxide concentration. From Mauna Loa Observatory,

Hawaii............................................................................................................................ 2

Fig. 1.3 – Post-combustion capture [3] ......................................................................................... 3

Fig. 1.4 – Pre-combustion capture [3] ........................................................................................... 4

Fig. 1.5 – Oxyfuel combustion scheme [3] .................................................................................... 4

Fig. 1.6 – Conventional Pulverized Coal Fired Utility Boiler Retrofitted for Operation with the O2-

RFG Process [4]............................................................................................................ 5

Fig. 1.7 – Dependence of required recirculation amount and oxygen concentration on recycle

temperature and oxygen excess [6].............................................................................. 8

Fig. 1.8 – CO2 concentration in dry flue gas as a function of air ingress, oxygen excess and

oxygen purity from the ASU [6] ..................................................................................... 8

Fig. 1.9 – Dependence of the cryogenic liquefaction performance on pressure and temperature

[6] .................................................................................................................................. 9

Fig. 2.1 – Schematic of the O2-RFG combustion facility at IFRF [1]. ......................................... 12

Fig. 2.2 – IFRF Furnace #1 [1]. ................................................................................................... 13

Fig. 2.3 – Aerodynamically Air-Staged Burner [1] ....................................................................... 14

Fig. 3.1 – Spectral lines due to electronic, vibrational and rotational transitions in a gas molecule

[23] .............................................................................................................................. 25

Fig. 3.2 – Spectral absorptivity of an isothermal mixture of nitrogen and carbon dioxide [23]. .. 26

Fig. 4.1 - Comparison of emissivity of water vapour for all the models as a function of

temperature for different pressures and a path-length of 10m ................................... 40

Fig. 4.2 - Comparison of emissivity of water vapour for all the models as a function of molar

fraction at different temperatures and for length of 1m............................................... 41

Fig. 4.3 - Comparison of emissivity of carbon dioxide for all the models as a function of

temperature for different pressures and a path-length of 10m ................................... 42

Fig. 4.4 - Comparison of emissivity of carbon dioxide for all the models as a function of molar

fraction at different temperatures and for length of 10m............................................. 42

Fig. 4.5 – Comparison of emissivity of water vapour and carbon dioxide mixtures .................... 43

Fig. 4.6 – Comparison of the weight of CO in the emissivity of a mixture................................... 44

Fig. 4.7 – Baseline case flow for isothermal and with radiation solutions................................... 45

Fig. 4.8 – Baseline case mass release distribution for isothermal and with radiation solutions . 46

Fig. 4.9 - In-flame carbon dioxide profiles for the Baseline case for the different simulations.... 48

Fig. 4.10 -In-flame oxygen profiles for the Baseline case for the different simulations............... 49

vi

Fig. 4.11 - In-flame carbon monoxide profiles for the Baseline case for the different simulations

.................................................................................................................................... 50

Fig. 4.12 -In-flame temperature profiles for the Baseline case for the different simulations....... 52

Fig. 4.13 - Flame C flow for isothermal and with radiation solutions........................................... 53

Fig. 4.14 – Flame C mass release distribution for isothermal and with radiation solutions ........ 54

Fig. 4.15 - In-flame carbon dioxide profiles for the Flame C for the different simulations........... 55

Fig. 4.16 -In-flame oxygen profiles for the Flame C for the different simulations ....................... 56

Fig. 4.17 - In-flame carbon monoxide profiles for the Flame C for the different simulations ...... 57

Fig. 4.18 - In-flame temperature profiles for the Flame C for the different simulations............... 59

Fig. 4.19 – Absorption coefficient distribution for the SLW model and Leckner model. a)

Baseline Case. b) Flame C. ........................................................................................ 60

vii

TABLE LIST

Tab. 2.1– Proximate and Ultimate analysis of Göttelborn coal. From [3].................................... 15

Tab. 2.2 – Main combustion characteristics. From [3] ................................................................ 16

Tab. 2.3 – Rate equations and reaction parameters from the volatiles combustion model ........ 19

Tab. 3.1 – Coefficients blmn appearing in equation 3.4 for H2O. ............................................... 29

Tab. 3.2 – Coefficients clmn appearing in equation 3.5 for H2O ................................................ 30

Tab. 3.3 – The coefficients dlmn appearing in equation 3.6 for CO2.......................................... 32

Tab. 3.4 – Coefficients for equation 3.28 for water vapor ........................................................... 37

Tab. 3.5 – Coefficients for equation 3.28 for CO2....................................................................... 38

Tab. 3.6 – Coefficients for equation 3.42 for H2O and CO2 ....................................................... 39

Tab. 3.7 – Coefficients for equation 3.43 for CO......................................................................... 39

viii

NOMENCLATURE A – area [m2]

a – blackbody weight for the absorption coefficient in the SLW model [-]

A – EBU model empirical constant that typically is 4.0 [-]

B – EBU model empirical constant that usually is 0.5 [-]

Cabs - spectral absorption cross-section [m2 / mol]

CD –aerodynamic resistance coefficient [-]

cp – specific heat capacity [kJ / kg K]

E – fossil fuel input [kWth]

F – absorption-line distribution function [-]

Fext – external forces [N]

G – irradiation [W / m2]

h – convective heat transfer coefficient [W / m2K]

I – radiation intensity [W / m2Ω]

k - absorption coefficient [1 / m]

k – turbulent kinetic energy [m2 / s2]

L – length [m] .

m – mass flow [kg/s]

M – molar mass [kg / kmol]

mp – mass of particle [kg]

mR – mass fraction of R [-]

N – molar density [mol / m3]

P – pressure [bar]

Qa,p – absorption efficiency of particle [-]

r – radial coordinate [m]

R – reaction rate [kg / m3s]

R – recirculation ratio [-]

S – length [m]

SΦ – source term [UnitΦ / m3s]

T – temperature [K]

t – time [s] →

u – vectorial velocity [m / s]

v~ , u~ – Favre average velocity components [m / s]

V – volume [m3]

W – power [kW]

w – weights of discrete ordinate [-]

Y – molar fraction [-]

z – axial coordinate [m]

α – absorptivity [-]

ix

β – extinction coefficient [1 / m]

ε – emissivity [-]

ε – turbulent kinetic dissipation [m2 / s3]

η – efficiency [-]

λ – wavelength [µm]

ν – stoichiometric coefficient of specie i in reaction k [-]

µ, ξ – direction cosines [-]

ρ – density [kg / m3]

σ – Stefan-Boltzmann constant [W / m2K4]

τ – adimensional temperature for use in the Leckner model [-]

τ – transmissivity [-]

ГΦ – effective diffusion coefficient [kg / ms]

SUBSCRIPTS 0 – referring to low pressure conditions

a – absorption

b – blackbody

c – carbon dioxide

conv – convection

e – external surface area

g – gas

i – index of specie or coefficient or spectral segment

j – spectral interval (gray gas)

m – discrete ordinate index

max – maximum

min – minimum

mix – mixture

ov – overlap

p – particle

p – products

PFG – product flue gas

R – reactants

Rad – radiation

RFG – recycled flue gas

s – specie

sb – self-broadening

T – total

t – transversal projected area

w – water vapour

x

P – point of control volume considered

N – north

S – south

W – west

E – east

η – wave number

Φ – property

ACRONYMS

AASB – Aerodynamically Air-Staged Burner

ADF – Absorption Distribution Function Model

ADFF – Absorption Distribution Function Fictitious Gases Model

ANL – Argonne National Laboratory

APG – Advanced Power Generation

ASU – Air Separating Unit

CCS – Carbon Capture and Storage.

CFD – Computational Fluid Dynamics

CPD – Chemical Percolation Devolatilisation

EBU – Eddy Break-Up

EDC – Eddy Dissipation Concept

EOR – Enhanced Oil Recovery

ERZ – External Recirculation Zone

HVB – High-Volatile Bituminous

IFRF – International Flame Research Foundation

IGCC – Integrated coal Gasification Combined Cycle

IRZ – Internal Recirculation Zone

IST – Instituto Superior Técnico

LDV – Laser Doppler Velocimeter

MIT – Massachusetts Institute of Technology

NGCC – Natural Gas fired Combined Cycles

PC – Pulverized Coal Plants

PFG – Product Flue Gas

RFG – Recycled Flue Gas

SIMPLE – Semi-Implicit Method for Pressure-Linked Equations

SLW – Spectral-Line-based Weighted-sum-of-gray-gases Model

SOFC – Solid Oxide Fuel Cells

WSGG – Weighted-Sum-of-Gray-Gases Model

1

1 INTRODUCTION

Climate change is the greatest environmental challenge facing the world today. Gases like

carbon dioxide (CO2), nitrous oxide (N2O), chlorofluorocarbons (CFC’s), methane (CH4), low-

level ozone (O3) and water vapour, present in our atmosphere, are virtually transparent to

incident ultra-violet solar radiation. However these same gases are strong absorbers of

outgoing infrared terrestrial radiation, trapping and re-radiating energy that would otherwise

escape through our atmosphere. This energy has the effect of warming both the atmosphere

and earth’s surface. This process of global warming due to the increased concentration of

gases in the earth’s atmosphere is referred to as the “greenhouse effect”. Fig. 1.1 shows the

increase in the global average temperatures in the last century.

The most important greenhouse gas is CO2, although it has not the strongest global warming

potential, due to the enormous quantities emitted. These quantities of CO2 emitted into the

atmosphere lead to the greatest overall contribution to the enhancement of the greenhouse

effect. It is estimated that about 20% of the enhanced greenhouse effect can be attributed to

CO2 derived from coal use [1], and it is believed that the combustion of pulverized coal in

conventional utility boilers contributes with about 10% of the enhanced greenhouse effect.

CO2 concentrations have been increasing in the last decades, as is shown in Figure 1.2.

Nowadays CO2 emissions become a driving issue in the field of energy, and it is required to

reduce them. There are two possible ways to achieve the necessary reduction of CO2 emissions

in power generation based on fossil fuels: efficiency increase and CO2 capture and storage

(CCS).

For the last possibility the Oxy-fuel combustion is one of the promising options, since it provides

a flue gas containing up to 90% by volume of CO2 [2] making the capture process less energy

intensive.

2

Fig. 1.1 - Compiled by the Climatic Research Unit of the University

of East Anglia and the Hadley Centre of the UK Meteorological Office. Data set HadCRUT3 was used. HadCRUT3 is a record of

surface temperatures collected from land and ocean-based stations.

Fig. 1.2 – Monthly averaged carbon dioxide concentration. From Mauna Loa

Observatory, Hawaii.

1.1 COMBUSTION TECHNOLOGY WITH CARBON DIOXIDE CAPTURE

In the past years the Carbon Capture and Storage (CCS) chain with its processes and

components has been thoroughly investigated, practically and theoretically, which revealed

CCS as a valuable technology to reduce CO2 emissions.

3

Nowadays CO2 capture is already an industrial technology, and CO2 separation techniques are

commonplace in the oil and gas industries. The separation techniques used need to be adapted

and optimized for CCS.

In CCS, CO2 is extracted at some point in the energy conversion chain, depending on the type

of energy technology used. The CO2 capture processes or decarbonisation technologies are

usually divided into three main categories or general process routes:

• Post-combustion capture

• Pre-combustion capture

• Oxy-fuel (denitrogenated) combustion and post-combustion capture

In Post-combustion capture the CO2 is extracted from the combustion flue gas at low

pressure (atmospheric) and low CO2 concentration (3-20%), in a mixture of mainly nitrogen (N2)

and oxygen (O2). If integrated in existing facilities, it doesn’t demand any major modification.

The capture unit is an end-of-pipe unit, which can easily be added to the facility. This

technology can be used at large power plants, such as pulverized coal plants (PC), natural gas

fired combined cycles (NGCC), boilers, furnaces and stationary fuel cells such as solid oxide

fuel cells (SOFC). The general process is presented in Figure 1.3.

Fig. 1.3 – Post-combustion capture [3]

In Pre-combustion capture the fossil fuels are first converted at high pressure (20-80 bar,

depending on the technology used) in a reformer or gasification process, depending on the

fossil fuel, into a mixture of mainly carbon monoxide (CO) and hydrogen (H2) referred to as

syngas. Afterwards the mixture goes to a water-gas shift reactor, where CO reacts with steam,

producing CO2 and more H2. Due to the high pressure of this product gas stream and the higher

concentration, CO2 separation is less energy and cost intensive than post-combustion capture.

The H2 product can then be combusted in adapted turbines, or it can be used in fuel cells. This

technology can be used at integrated coal gasification combined cycle (IGCC) and NGCC. The

general process is presented in Figure 1.4.

4

Fig. 1.4 – Pre-combustion capture [3]

In Oxy-fuel (denitrogenated) combustion, the objective is to obtain a product flue gas with at

least 90% CO2 content, by using pure oxygen to perform the combustion, so that the flue gas

mainly consists of CO2 and water vapour, which are easily separated by condensation. O2 is

obtained in an air separation unit, normally using the cryogenic process, and the combustion is

carried out in an atmosphere of mainly O2/CO2. To limit the flame temperatures in the

combustion chamber, cold flue gas is partially recirculated, since the materials that are currently

used in the power industry cannot handle such high temperatures. There are various possible

configurations for the location of the recycle branching within the flue gas path. This technology

can be used in special designed gas turbines (NGCC), in adapted boilers and furnaces (PC).

The general process is presented in Figure 1.5.

Fig. 1.5 – Oxyfuel combustion scheme [3]

In order to capture CO2 from energy conversion process, generally at some point in the process

CO2 will need to be separated, this being the case for post-combustion and pre-combustion.

The energy conversion process can alternatively produce a concentrated CO2 stream, as long

as nitrogen is not present in the combustion (oxyfuel combustion).

Technologies are being developed to separate CO2 from the flue gas of fossil fuel fired

combustion systems. These technologies can be divided into four main categories [1]:

• Absorbent processes that rely on the dissolution of CO2 in a liquid solvent.

• Adsorption processes that involve a component in a gas mixture being selectively

transferred onto a batch of solid particles.

5

• Cryogenic separation that uses compression and refrigeration techniques. It is based on

the difference in boiling/condensation points.

• Membrane separation where gas permeation through a thin membrane barrier occurs.

The process of separating and recovering CO2 from the flue gas of coal fired combustion

systems is simplified if the CO2 concentration is increased, making of it a lower energy demand

process. A way of achieving this is to minimize the N2 concentration by eliminating it from the

comburent prior to combustion. To control the combustion temperature in oxy-fuel combustion it

is necessary to recirculate flue gases into the boiler, replacing the combustion air with a mixture

of O2 and recirculated flue gas (RFG). To make the steam cycle in the boiler comparable to the

air blown case, the adiabatic temperature in the furnace and the furnace exit temperature has to

be kept to a similar level. In the oxy-fuel process, although this temperature is dependent on the

recirculation ratio mainly, it also depends on the oxygen excess in the flue gases or gas

temperatures like in conventional boilers. In theory the pulverized coal combustion in an O2-

RFG comburent can produce a post-combustion gas with a 95% CO2 concentration [1]. A

possible configuration for a conventional pulverized coal fired utility boiler with O2-RFG process

is presented in Fig. 1.6.

Fig. 1.6 – Conventional Pulverized Coal Fired Utility Boiler Retrofitted for Operation with the O2-RFG

Process [4]. Currently, the most feasible technology to denitrogenate air is the cryogenic air separation [5].

Using this technology, air is cooled deeply. This process requires a pressure of 8-10 bar. To

achieve these conditions compression and heat exchange is required, and for that the cold

products (oxygen and nitrogen) exiting the distillation column are used to cool the air entering it.

6

Air separated this way is only economically feasible if a large amount is needed, due to the

price and size of a cryogenic separation unit.

Cryogenic separation can also be used for purification of the oxy-fuel combustion flue gas,

which consists mainly of CO2 and H2O, to separate CO2 from N2, Ar (due to the air leakage/

from the ASU), excess O2 and contaminants such as SO2 and NOx. This process is based on

condensation by lowering the temperature and increasing the pressure of the flue gas. Before

the CO2 liquefaction the water has to be removed completely. After the water removal, CO2 is

compressed to 30-40 bar and cooled to a temperature close to the triple point. Because non-

condensable gases (Ar, O2 and N2) will remain in the gaseous state, they can be easily

separated. There can be a further purification of CO2 by distillation separating CO2 from SO2

and NO2, which have higher boiling points, although NOx emissions are low since the missing

gaseous nitrogen in the combustion atmosphere prevents the formation of thermal NOx, and this

occurs mainly due to the nitrogen of the coal and also from air leakage. To this day as the

admissible levels of impurities for different geological storage sites are still not known, and limits

or critical impurities are not defined, it can be assumed that restrictions will be applied on the

permissible overall purity with particular regard to O2, SO2 and NOx.

A power plant using oxyfuel combustion has an efficiency reduction due to the energy

requirements of oxygen production and compression and CO2 compression. Lowering the

amount of impurities would lead to a decrease in power demand in CO2 compression.

EW

EW ncompressioO

referenceoxyfuel O−−η=η 2

2 (1.1)

where ηoxyfuel is the efficiency of the oxy-fuel power plant, ηreference O2 is the efficiency of a

reference plant with near stoichiometric combustion with O2, WO2 is the power requirement for

O2 production (ASU) and compression (MWe), Wcompression is the power requirement for CO2

compression (MWe) and E is the fossil fuel input (MWth).

1.2 OXY-FUEL COMBUSTION WITH RFG

Abraham in 1982 proposed the concept of burning pulverized coal in a mixture of O2 and RFG

to produce a high purity CO2 in conventional utility power plants [1]. It was considered an

attractive process due to the potential for using the CO2 product for enhanced oil recovery

(EOR). EOR uses CO2 to pump it into an existing oil well, where it dissolves in the oil,

expanding it and decreasing its viscosity and surface tension. The resulting product is therefore

more easily recovered from the oil wells. For this process it is required at least 90% pure CO2.

In these days there is another driving force for the implementation of the proposed project,

which is minimizing emissions of CO2 into the atmosphere because of the contribution to the

7

greenhouse effect. The oxy-fuel combustion technology is still under development. In order to

evaluate the feasibility of retrofitting a conventional coal fired utility boiler with this process

several techno-economic studies have been made and also experimental and mathematical

modelling work have been done.

An economic evaluation was conducted in the Massachusetts Institute of Technology (MIT) of

five alternative processes which could be used to retrofit a coal fired combustor, to minimize

CO2 emissions [1]. The most energy efficient process analyzed was the combustion of coal in a

mixture of O2 and RFG. They calculated that the process required 26-31% of the coal heating

value. It was also calculated that the thermal efficiency would be reduced from 35% to about

25%, because of the cost of the air separation plant to produce pure O2 and the final processing

of the product CO2, with an estimated increase in the electricity production costs of 80%.

The Argonne National Laboratory (ANL) in the United States conducted a significant

experimental work on the combustion of pulverized coal in a mixture of O2 and RFG [1] during

the mid 1980’s. In order to determine the potential for applying an O2-RFG combustion process

to a coal fired utility boiler, five research projects were carried out. These led to the conclusions

that optimum wet and dry recycle ratio existed for which the Tower Furnace performance was

similar to normal coal-air operation. The performance parameters studied were slagging and

fouling tendencies and carbon burnout. Flame stability performance was also reported to be

unchanged in spite of the use of O2 deficient RFG as the transport medium for the pulverized

coal.

A computationally efficient combustion model has been developed and validated against both

air and oxy-fuel flames at the Institute for Process Engineering and Power Plant Technology [4]

in Germany in 2007. In the cases studied the agreement between measured and calculated

properties is satisfactory.

The power plant efficiency was the objective of the recent research work made at Hamburg

University of Technology (TUHH) in 2007 [6], where it was aimed to identify the key factors

which cause the most significant impact. This research was based in the state-of-the-art

components and developments in power plant technologies, which are described in the so

called Reference Plant North-Rhine Westphalia, a study of an advanced plant in 2004. In this

work, the amount of residual oxygen, which represents an impurity, is recommended to be

reduced by lowering the excess oxygen rate from the 17% in modern hard coal to 15%, which

still yields a high oxygen concentration prior to combustion, as can be seen in Fig. 1.7.

8

Fig. 1.7 – Dependence of required recirculation amount and oxygen

concentration on recycle temperature and oxygen excess [6]

The air leakage is also studied, and it is noticed that even with a high oxygen concentration of

99.5% by volume attained from the ASU, an air leakage of 1% will already lead to a CO2 purity

bellow 90%, as it is shown in Fig. 1.8.

Fig. 1.8 – CO2 concentration in dry flue gas as a function of air ingress,

oxygen excess and oxygen purity from the ASU [6]

9

Another factor studied is the separation and liquefaction of CO2, where the combinations of

parameters able to operate condensation are shown in the white triangular region of Fig. 1.9.

Fig. 1.9 – Dependence of the cryogenic liquefaction performance on pressure

and temperature [6]

At RWTH Aachen University in Germany in 2007 [7] the parameters influencing the stability of

CO2/O2 pulverized coal flames were investigated. The burning mechanisms of pulverized coal in

a mixture of CO2/O2 are discussed and a method is provided to stabilize an oxycoal flame at low

O2 concentrations. While the usual approach is based on increasing the oxygen concentration

(around 27%) for stabilization of the combustion process, in this work a new approach for

oxycoal flame stabilization was developed, by adjusting the swirl burner design and its operating

conditions in order to enforce CO formation thus stabilizing the flame and obtaining a full

burnout at low oxygen concentrations in the CO2/O2 mixture. Numerical and experimental

results of a stable swirl oxycoal flame obtained with 21% oxygen concentration in the burning

mixture at the RWTH-Aachen test facility are presented.

1.3 OBJECTIVES

The objective in the present work was the simulation of an air-firing combustion and oxy-fuel

combustion from the APG2 (Advanced Power Generation) experiment using an existing

combustion model. Since for oxy-fuel combustion there is a much higher concentration of CO2

than for the air-firing combustion, studies were made with existing radiation models in the open

literature, some of which are already incorporated in the combustion model, to establish which

would be better for usage with the combustion model in the simulations.

The combustion model used in this work was the “Furnace” code [8]. The existing models in this

code were used as available, namely for flow, char oxidation, particle devolatilization and for

10

turbulent gas combustion. The contribution from the present thesis is the test and incorporation

of a different sub-model for radiation properties of gas mixtures.

1.4 STRUCTURE OF THE THESIS

In chapter 1 the background review for this work is presented, as well as the objectives

proposed for this work. The case study is introduced in chapter 2.1 where the composition and

mass flows of the primary and secondary inlet flows are presented as well as the burner and

furnace of the APG2 experiment. Chapter 2.2 presents the numerical model used in the

“Furnace” code. A brief presentation of the behaviour of radiation interaction with gases is

presented in chapter 3.1, as well as the radiation models studied in this work. The results for the

study on the radiation models are presented in chapter 4.1 and for the combustion simulations

in the chapter 4.2, where they are compared with the experimental results from the APG2

experiment. In chapter 5 the conclusions taken from this work are presented and in chapter 6

proposals for future work are identified.

11

2 CASE STUDY AND NUMERICAL MODEL

The case study in this work is the CFD simulation of two flames characterized at the

International Flame Research Foundation (IFRF) in the Advanced Power Generation (APG)

Research Project. The objective of the APG2 project was to evaluate the combustion of

pulverized coal in a mixture of O2 and RFG with primary consideration of retrofitting an existing

pulverized coal fired boiler, and defining an optimum mixture of O2 and RFG, by determining the

impact of the O2-RFG process on furnace performance, including changes in flame ignition and

stability, heat transfer, char reactivity and combustion efficiency, which would yield similar

combustion characteristics to normal air operation.

2.1 AVAILABLE EXPERIMENTAL RESULTS

This section presents the configuration of the burner and furnace and the specification of the

operating conditions considered in the experimental tests. Measured results [9] exist on the gas

composition and temperature obtained in radial profiles at six axial locations in the furnace.

2.1.1 FURNACE AND BURNER DESCRIPTION

The general layout of the combustion facility developed at the IFRF to burn pulverized coal in a

mixture of O2 and RFG is presented in Figure 2.1. The combustion facility recycles a controlled

mass fraction of the post-combustion gas back into the furnace by first mixing the RFG with O2

before combustion with the pulverized coal. This fraction is referred to as the recycle ratio and is

written as:

PFGRFG

RFG

mmm

R&&

&

+= (2.1)

where the sum of the recycled flue gas (RFG) and the product flue gas (PFG) is the total

combustion chamber mass throughput.

When leaving the furnace, the post-combustion gas is split into two streams, one to be recycled

(RFG) and the other to be processed and then exhausted (PFG). The RFG stream is cooled

and passes through a cyclone in order to remove as much of the recycled fly ash as possible.

Then it is directed through a stainless steel sectional heat exchanger to ensure that the recycle

fan inlet temperature is kept below the design temperature. After the recycle fans, the RFG is

12

split into two streams, the primary flue gas stream and the secondary flue gas stream. Both

streams mass flow rates are continuously monitored and controlled, to ensure the desired

recycle ratio.

Pure CO2 is used to transport the coal from the roto-feed unit to the burner, where it is mixed

with the primary flue gas and the primary O2 prior to the combustion.

The primary comburent is composed of the primary flue gas, the transport CO2 and the primary

O2 (if desired). In case of necessity the primary flue gas is cooled to maintain the nominal

primary comburent temperature of 100ºC. To ensure that the desired O2 concentration is

maintained, the primary flue gas before coal injection is periodically monitored.

The secondary comburent is composed of the secondary flue gas and the secondary O2. The

secondary flue gas is injected directly into a movable block swirl generator, where it is mixed

with pure O2 before being swirled and injected into the furnace. To ensure that the desired

secondary flue gas O2 concentration and temperature were maintained, continuous gas

sampling and temperature measurements inside the swirl generated are used. These are only

interrupted when primary comburent measurements are made.

Fig. 2.1 – Schematic of the O2-RFG combustion facility at IFRF [1].

The IFRF Furnace #1 was used in the APG experiments. This furnace has an internal square

cross-section of 2 × 2 m and is approximately 6.25 m long. It is constructed of 11 independently

13

water-cooled refractory-lined sections. To maintain a temperature history comparable to a

radiant section of a full-scale boiler operating with air, seven cooling loops were used to extract

energy from the combustion chamber. In order to determine the total heat extraction from the

furnace by calorimetry the cooling water flowrate and temperature for each section and loop

were continuously monitored. Fig. 2.2 presents a schematic detailing the location of the cooling

loops and measurement ports of Furnace #1.

Fig. 2.2 – IFRF Furnace #1 [1].

14

A standard IFRF aerodynamically air-staged burner (AASB) was used for the APG experiments.

In Fig. 2.3 a schematics of the burner and coal injector is presented. The AASB is specifically

designed to utilize a swirling combustion air stream which undergoes a defined flow transition

(vortex breakdown) within the burner quarl. The vortex breakdown can result in the formation of

an internal recirculation zone (IRZ), whose characteristics are critically influenced by swirl

generator type, swirl level and burner geometry.

The parameters used to design the AASB for the APG experiments are listed below:

-Thermal input: 2.5 MWt

-Primary velocity: 20 m/s

-Primary temperature: 100 ºC

-Secondary velocity: 40 m/s

-Secondary temperature: 300ºC

In order to obtain the burner dimensions it was assumed a burner quarl length to inlet diameter

ratio of 1.0, a quarl expansion ratio of 2.0, a bluff-body blockage ratio of 0.6, and zero inlet and

outlet angles. Subject to these conditions, the quarl profile was designed to fit a third order

polynomial.

To swirl the combustion air, an IFRF moveable block swirl generator was used, which was

calibrated using standard LDV techniques [1]. In order to maintain a nominal secondary

comburent velocity of 40 m/s while the RFG was varied inserts were used. The nominal primary

comburent velocity was maintained at 20 m/s.

Fig. 2.3 – Aerodynamically Air-Staged Burner [1]

15

2.1.2 OPERATING CONDITIONS

One coal tested in the APG2 experiment was the Göttelborn (HVB). Before being transported to

the burner by a roto-feed unit, it was dried crushed and milled to 75% < 75 µm. To transport the

coal in the flame C approximately 84 kg/h of pure CO2 was used. The results from a proximate

and an ultimate analysis of Göttelborn coal are presented in Tab. 2.1.

Tab. 2.1– Proximate and Ultimate analysis of Göttelborn coal. From [9] Proximate Analysis Mass Fraction (%dry)

volatiles 38.2 ash 7.5

Ultimate Analysis Mass Fraction (%dry)

carbon 74.42 hydrogen 4.79 nitrogen 1.51 sulphur 1.02

oxygen (by diff) 10.76 LCV 30 480 kJ / kg

Key recycle ratios determined from the APG1 experiment were evaluated in greater detail in the

APG2 experiment. Three flames were evaluated and compared to the baseline flame

(conventional air operation). The three O2-RFG flames investigated were identified as Flame A,

recycle ratio of 0.76, Flame B, recycle ratio of 0.73, and Flame C, recycle ratio of 0.58. In the

present work the flames that are simulated are the air firing combustion, here called as

Baseline, and Flame C. The main combustion characteristics of the baseline flame as well as

Flame C, including the complete flue gas composition are presented in Tab. 2.2. The conditions

of Flame C produce convection coefficients similar to the case of air firing.

16

Tab. 2.2 – Main combustion characteristics [9] Input

Baseline Flame C Göttelborn coal 276 kg/h 282 kg/h

Particle Size 75 % < 75 µm 75 % < 75 µm

Primary Transport Air 546 kg/h - Primary Transport CO2 - 84 kg/h

Secondary Combustion Air 2464 kg/h - Primary O2 0 kg/h 0 kg/h

Secondary O2 0 kg/h 646 kg/h Primary RFG - 414 kg/h

Secondary RFG - 1844 kg/h Swirl Number 1.03 0.84 Recycle Ratio - 0.58

Adiabatic Flame Temperature 2103 ºC 2087 ºC Thermal Input 2497 kW 2467 kW

Flue Gas Composition (dry basis) Baseline Flame C

O2 2.1 % 3.9 % CO 31 ppm 59 ppm

CO2 16.6 % 82.8 % NOx 819 ppm 1262 ppm SO2 753 ppm 1973 ppm

N2 (by difference) 81.1 % 13.0 % H2O (estimated) 6 % 25 %

NOx (0% O2) 913 ppm 1575 ppm NOx 321 mg/MJ 110 mg/MJ SO2 645 mg/MJ 375 mg/MJ Output

Baseline Flame C Flue Gas Temperature 1082 ºC 1129 ºC

Estimated PFG 3262 kg/h 1182 kg/h Combustion Efficiency 99.4 % 99.8 % Total Heat Extraction 1362 kW 1416 kW

Heat Extraction Efficiency 54.5 % 57.4 %

2.2 NUMERICAL MODELLING

The CFD simulations were carried out with the “Furnace” code [8]. The modelling of the gas flow

and of the coal particles are treated in different ways. The gas phase is treated accordingly to

the Euler method, and the solid phase (carbon particles) is treated with the Lagrange method.

17

2.2.1 CONTINUOUS PHASE BALANCES

The modelling of the gaseous phase is based on the resolution of balance equations. All these

equations are cast in the following general format:

P

~~~~

SSr

rrrzzr

v~r

rz

u~

φφφφφφ

φρφρ++

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∂∂

Γ∂∂

+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∂∂

Γ∂∂

=∂

⎟⎠⎞

⎜⎝⎛∂

+∂

⎟⎠⎞

⎜⎝⎛∂

11 (2.2)

where ГΦ is the effective diffusion coefficient of the Φ property, and SΦ + SPΦ the source term for

variable Φ with contributions respectively from the gas and disperse phase, in this case the coal

particles.

2.2.1.1 Flow

The flow is calculated through the solution of momentum balance equations, to the axial, radial

and tangential directions. Considering axial symmetry the problem is independent from the

tangential direction, allowing a bi-dimensional calculation in axial and radial directions where the

tangential velocity is also calculated.

To solve the momentum balance equations the distribution of pressure is necessary, which in

turn is obtained from the continuity equation. This equation is used with the Semi-Implicit

Method for Pressure-Linked Equations (SIMPLE) [10] algorithm to calculate pressure

corrections that are solved iteratively with the velocities. The standard wall function was used

[10].

The turbulence is modelled with the k-ε model that permits to estimate a turbulent viscosity used

to define the effective diffusion coefficients for the transport equations.

2.2.1.2 Combustion

Combustion reactions take place in the gas phase when volatile species are released from the

coal particles or when carbon monoxide resulting from the heterogeneous consumption of

carbon in the char mixes with oxygen. At microscopic level, the mixture is controlled by

turbulence, and therefore a model representing the interaction between turbulence and

combustion is necessary. Turbulence generates fluctuations in the concentrations and

consequently affects the combustion rate of the gaseous compounds.

There are two sets of methods to model the effects of turbulence in combustion, which includes

methods to represent the interaction with kinetic chemistry. One of those sets, based on the

mixture fraction, allows representing the gas composition in a certain point and instant. In order

18

to account for turbulence, a mixture fraction distribution is considered and its variance is

calculated. The kinetics are calculated taking into account the rate of turbulent deformation from

a pre-calculated “Flamelets” model. In these methods the fuel is considered with a uniform

composition, which is not very appropriate for coal combustion, since the actual gas species

depend on the devolatilisation conditions. There are ways of defining several mixture fractions,

but, since it complicates the method, generally is preferred to consider straightaway the mass

balances to several chemical species.

There are two models to handle the interaction of turbulence based on the mass balances to

individual species, the Eddy Break-Up (EBU) and the Eddy Dissipation Concept (EDC), having

as objective quantifying the mixture rate due to turbulence. Although it has been applied in IST

[11] presenting limitations due to the kinetic chemistry, originally the EBU method does not

considered the kinetic chemistry. The EDC method considers the interaction turbulence-

chemistry, defining perfect mixture reactors, where chemical kinetics are considered.

The mass balances for each species are defined from the equation 2.2, where the diffusion

coefficient used is the turbulent viscosity divided by the turbulent Schmidt number. The mass

source of each species due to the particle is the result of the application of the volatile release

model and char combustion, while, for the continuum phase is the result of applying the

turbulent combustion model, explained below.

Eddy Break-Up (EBU)

The EBU was originally proposed by Spalding [12] and later modified by Magnussen and

Hjertagar [13]. In this model, the combustion rate is determined by the mixture rate between the

reagents, estimated from the turbulent vortices dissipation rate. The vortices dissipation rate is

assumed as being proportional to the ratio between the turbulent kinetic dissipation and the

turbulent kinetic energy, ε/k. The reaction rate, Ri’,k, is given by the minimum value from the

following expression, applied to combustible and oxidant:

RkR

Rikiki Mv

mk

AMvR ',

'',','

ερ−= (2.3)

where mR is the reactants (R) specie mass fraction, and A is a model empirical constant that

typically has a value of 4.0.

To account the possibility of the chemical reaction not occurring when there is reactants mixture

at low temperatures, Magnussen and Hjertagar introduced an additional condition, in which the

rate must be larger than the value in the following expression:

∑∑=P PkP

P Pikiki M

mk

ABMR ´,

´´´,´, ν

ερν (2.4)

19

where mp represents the products (P) mass fraction, and B is another empirical constant that is

usually 0.5 . This last term is considered to account for the presence of whirls with thermal

energy, that allows the occurrence of the chemical reactions.

Another methodology to consider the possible limitation of kinetic chemistry, consists of taking

for the reaction rate the minimum between the mixture rate, calculated with the EBU model, and

the chemical kinetic rate calculated based of the average values of species concentrations and

temperature. In this approximation is considered that the methane, the tar and the carbon

monoxide oxidize through irreversible global reactions.

In the reaction R1, the methane oxidizes and originates carbon monoxide and water vapour,

while the tar converts in molecular hydrogen and carbon monoxide through reaction R2. The

carbon monoxide oxidizes (reaction R3) into carbon dioxide.

CH4 + 3/2 O2 1Ck⎯⎯→ CO + 2H2O (R1)

CxHyOz+ (x-z)/2 O2 2Ck⎯⎯→ x CO + y/2 H2 (R2)

CO + ½O2 3Ck⎯⎯→ CO2 (R3)

Tab. 2.3 – Rate equations and reaction parameters from the volatiles combustion model Reaction Reaction rates equation Constants References

(R.1) 3031110 42

.CH

.O

CC, YY

RTE

expk −⎟⎠⎞

⎜⎝⎛−−

K0,C1 = 1.15× 109 s-1

EC1/R = 24444. K

Westbrook and

Dryer (1981) [14]

(R.2) zyx OHCO

CC, YY

RTE

expk2

220 ρ⎟

⎠⎞

⎜⎝⎛−−

K0,C2 = 4.0× 105 s-1

EC2/R = 5771. K Shaw (1990) [15]

(R.3) 50350750330 22

.OH

.OCO

.CC, YYY

RTE

expk ρ⎟⎠⎞

⎜⎝⎛−−

K0,C3 = 5.42× 109 s-1

EC3/R = 15152. K

Dryer and

Glassman (1973)

[16]

It is assumed that all the oxygen and carbon present in tar forms carbon monoxide, and the

hydrogen forms H2. The stoichiometric coefficients for oxygen and heat reaction were defined

from the mass and energy balances.

2.2.1.3 Energy balance

The energy balance leads to an expression similar to equation 2.2 for the relative enthalpy. The

source terms SPΦ are the result of the energy exchange with particles during heating or char

20

combustion. The source term from the continuous phase is the result from the reactions in the

gas phase mentioned before and the radiative heat transfer rate.

Radiation heat transfer is calculated using the discrete ordinates method which calculates the

propagation of radiation intensities in pre-selected directions at the control volumes used for the

gas phase balances. The discrete ordinates equation for cylindrical coordinates (see e.g.

[17;18]) leads to diferential equations for the intensity of radiation in each direction (discrete

ordinate). The intensities are calculated from each corner of the domain in the quadrant where

the discrete ordinate is located, leading to a recursive calculation of the intensity as a function of

the neighbour values already calculated. For the positive direction of the axial and radial

direction the equation can be presented as:

2221

/VAA/SIIAIA

IPWEmSNm

P,/mmWWEmmSSNmP,m βξμ

ξμ+Γ++

+Γ++= − (2.5)

Where Im is the radiation intensity in the discrete ordinate m, µm and ξm are the cosines from the

direction and P, S, N, W, E refer to the control volume variables in the point and neighbours. S

is the source term that is the result from the gas and particle emission and the intensity from all

directions scattered in the direction considered and β is the extinction coefficient that includes

the contribution from the gas and the particles.

The source equation for the enthalpy is then obtained from:

⎟⎠

⎞⎜⎝

⎛−= ∑

mP,mmbg,aRad,h IwIkS π4 (2.6)

where wm is the weight factor for the direction. The calculation of the absorption coefficient of

the gases is further developed in chapter 3. This thesis contributed on testing different

approaches for the calculation of the radiative properties of gas mixtures as it will be presented.

2.2.1.4 Convergence criteria

The program iterates until the residues from the equations reach a prescribed value. For the

flow calculation (continuity and momentum equations) a maximum value of 1% was considered.

A maximum number of iterations is also specified and the final residues are reported for these

equations and for others.

21

2.2.2 PARTICLE SIMULATION

The particle evolution is calculated in a Lagrangian basis, tracking the particle trajectory in the

computational domain and solving an energy, a momentum and mass balance , accounting for

in sequence the drying, volatile release and char combustion.

Different initial positions are considered for the beginning of the trajectories, and to simulate the

diameter distribution, several diameter classes are considered according to the respective mass

fractions. The initial velocities were considered similar to the gas flow at the coal inlet. During

the calculation of the trajectories their influence in the gas phase is calculated through the

source terms for the balance equations of the gaseous phase.

2.2.2.1 Flow

The particles flow is obtained from the momentum equation balance for particles. The variation

of the particle momentum is equal to the sum of the forces applied to the particle. In the case of

solid particles in a gas, the main force is the aerodynamic resistance term [11].

( ) ( ) extppDp,tpp FuuuuCA

tum rrrrrr

+−⋅−⋅=∂

∂

2ρ

(2.7)

The particle trajectories will be influenced by the turbulence in the gaseous phase, which is

considered through the calculation of the particle velocity fluctuation. The velocity from the gas

phase in equation 2.2 is considered to be the sum of an average value with a fluctuation during

the life time of an eddy or during the time for a particle to cross the eddy.

2.2.2.2 Combustion

The coal combustion process can be divided into five different processes: coal particle heating,

drying, volatile release, volatile combustion and char combustion. The drying process is

assumed to occur at 100ºC and after the particle temperature increases again until reaching the

conditions to initiate the volatile release, which occurs significantly close to 600K. These

volatiles will burn subsequently in the gaseous phase, described in section 2.2.1.2.

The thermal decomposition of the particle leads to the release of the volatile matter. In most

cases the released volatiles consist in H2O, CO2, CO, H2, CH4 and tars. The released volatile

quantity strongly depends on the temperature, increasing with the increase of temperature [19].

Also important is the residence time of the particles at high temperatures, releasing more

volatiles for longer periods of time. Another important factor is the size of the particles, since for

smaller particles the heating rate increases and consequently, the release of volatiles also

increases [20].

22

In the modelling of volatiles release, the Chemical Percolation Devolatilisation (CPD) model,

proposed by Fletcher [21] is used. This model considers quantitatively the detail of the volatiles

mechanisms, including the breaking of bonds, rearranges, the releasing of light gases, the

evaporation of tar and cross-linking. This model predicts not only the volatile release rate, the

quantity of light gases released, tar and char, but also the distribution of light gases species in

the volatiles, namely CH4, CO, CO2, H2O and other light gases such as C2H4. This model was

linked with the kinetic chemistry for the combustion of gaseous species. After the volatile

release is close to completion the combustion of char initiates.

Char combustion is considered from a ½ order apparent kinetic rate defined in the CBK (Char

Burnout Kinetics) model [22]. This is one of the first models to propose the reactivity of coal

chars as a function of the coal rank.

2.2.2.3 Energy Balance

The energy balance to the particle represents the change in internal energy equal to the sum of

the heat exchanged with the gas phase with the heat released close to the particle that is

considered to remain in the particle. During the drying process heat is absorbed to vaporise the

water while during char burnout, the heat released in the combustion is included in the particle.

( ) ( ) ( )[ ]dt

dmh

dtdm

hTGQTThATcmdtd char

charOH

OHpp,apgconvp,eppp Δ+Δ−−+−= 2

2

4σ (2.8)

The heat exchange with the gas occurs due to convection and radiation. For the heat transfer

by radiation the particle absorption coefficient is calculated from correlations of the absorption

efficiency developed by Fiveland et al. [17].

2.2.2.4 Statistical representation of trajectories

To obtain a statistical representative value for the mass and energy sources from the particles,

a prescribed number of particles (from 2 to 5) were considered from each initial position and

particle diameter. Furthermore the contribution for the source terms from the particles,

calculated in iteration intervals from 50 to 200 was updated with a relaxation factor between 5

and 10%.

23

2.2.3 BOUNDARY CONDITIONS The inlet conditions used for both Baseline case and Flame C are presented in Tab. 2.4.

Baseline case Flame C Primary inlet Secondary inlet Primary inlet Secondary inlet

mgas (kg/s) 0.15167 0.68444 0.24339 0.68444 T (K) 353.15 475.15 363.15 475.15

mcoal (kg/s) 0.07667 - 0.07457 - Y_O2 (kg/kg) 0.23 0.23 0.02169 0.27347

Y_CO2 (kg/kg) 0.00035 0.00035 0.82611 0.46466 Y_CO (kg/kg) 0.0 0.0 0.00 0.00003 Y_H2O (kg/kg) 0.003 0.003 0.12325 0.18706 Y_N2 (kg/kg) 0.76365 0.76365 0.02761 0.07295 Y_NO (kg/kg) 0.0 0.0 0.0013 0.0007

Tab. 2.4 - Initial conditions used for both the Baseline case and Flame C in the simulations For the coal particles, the particle size distribution was specified by representative diameters with mass fractions presented in Tab. 2.5. Diameter

(µm) 3 5 7 10 15 20 40 50 60 80 100 200

mass fraction 0.005 0.055 0.04 0.05 0.08 0.17 0.20 0.10 0.05 0.05 0.10 0.10

Tab. 2.5 - Coal particles diameters and mass fractions

The furnace wall temperatures were initially set to 1100 K.

24

3 RADIATIVE PROPERTIES

Thermal radiative energy can be characterized by two theories, in one is viewed as consisting in

electromagnetic waves ( electromagnetic wave theory), and in the other as consisting of

massless energy parcels, called photons (quantum mechanics). According to Modest [23] the

electromagnetic wave theory is more often used to predict the radiative properties of liquids and

solids, while quantum mechanics is more convenient to obtain radiative properties of gases.

3.1 RADIATIVE INTERACTION WITH GASES

All gas atoms and molecules have an amount of energy, which consists of kinetic energy

(translational energy of a molecule) and internal energy. The internal energy of every atom and

molecule is dependent on the levels of electronic (energies associated with electrons spinning

at varying distances around the nucleus), rotational energy (atoms within a molecule spinning

around one another) and vibrational energy (atoms within a molecule vibrating against each

other). Quantum mechanics postulates that the levels for electronic, rotational and vibrational

energy are quantized, i.e., the electron orbits and rotational and vibrational frequencies can

change only with certain discrete amounts.

A photon (or electromagnetic wave) interacting with a gas molecule, may raise the molecule’s

energy level while being absorbed or may be scattered and change its direction of travel. On the

other hand the energy level of a molecule may be spontaneously lowered by the emission of an

appropriate photon. A change of the molecular energy level by emission or absorption of a

photon can be made by three different types of radiative transitions:

• bound-bound transitions – between nondissociated (“bound”) atomic or molecular states

• bound-free transitions – from a “bound” state to a free (dissociated) one (absorption) or

from “free” to “bound” (emission)

• free-free transitions – between two different “free” states

A relatively large amount of energy or a high frequency photon is required to change the orbit of

an electron, leading to absorption-emission lines at short wavelengths between the ultra-violet

and the near-infrared (10-2 µm and 1.5 µm). Less energy is required to change the vibrational

energy level, and so their spectral lines are encountered in the infrared (between 1.5 µm and 10

µm). The rotational energy level changes occur with the lowest amount of energy hence

rotational lines appear in the intermediate to far infrared (beyond 10 µm). It is usual for

vibrational energy changes to be simultaneously accompanied by changes in the rotational

energy levels, creating closely spaced groups of spectral lines that may partly overlap due to

the line broadening and create the so-called vibration-rotation bands in the infrared. The

spectral lines created by these transitions are illustrated in Fig. 3.1.

25

Fig. 3.1 – Spectral lines due to electronic, vibrational and rotational transitions in a gas molecule [23]

For bound-bound transitions to take place, discrete amounts of energy are necessary, since the

transitions for electronic, rotational and vibrational energy levels are quantized, leading to

discrete spectral lines, that in reality are slightly broadened due to the rotational lines

accompanying a vibrational transition usually overlap forming the vibration-rotation bands. A

typical absorption spectrum for a nitrogen-carbon dioxide mixture is shown in Figure 3.2, taken

from the early work of Edwards [23], where one can clearly see the formation of vibration-

rotation bands in the infrared due to bound-bound transitions separated by spectral windows.

26

Fig. 3.2 – Spectral absorptivity of an isothermal mixture of nitrogen and carbon dioxide [23].

Bound-free transitions occur when a photon is absorbed creating ionization and releasing an

electron, or a free electron combines with an ion producing a photon (free-bound transition).

Free-free transitions occur when a free electron emits or absorbs a photon. Electrons kinetic

energy levels are not quantized, hence the photons involved in transitions with free electrons

may have any frequency or wavelength and produce a continuous spectra.

The incident radiation in a gas layer is attenuated by absorption as it goes through the gas, and

the gas transmissivity can be written as:

se ⋅−= ηκ

ητ (3.1)

where κη is known as the absorption coefficient and s is the thickness of the gas layer. The

scattering from gas molecules is usually neglected. Scattering is only considered from the

particles. The incident radiation in a gas layer is either transmitted or absorbed, so the spectral

absorptivity is defined as:

se ⋅−−=−= ηκ

ηη τα 11 (3.2)

27

3.1.1 WIDE BAND MODELS Usually in heat transfer applications the objective is to obtain a heat flux over the entire

spectrum and it is advantageous to simplify heat transfer calculations to save computational

time. Therefore it is desirable to define models that can group the wavelengths over a spectral

range to calculate radiative emission or absorption of incoming radiation. The wide band model

allows determining the radiative properties from a volume gas over the spectral range of an

entire vibration-rotation band (hence the name), which are of special importance at combustion

temperatures for which the emissive power has its maximum in the infrared (between 1 µm and

6 µm) [23], using a single calculation in the process, assuming a distribution for the absorption

coefficient.

The most successful of the wide band models is the Exponential Wide Band Model, developed

by Edwards and Menard [23], where the smoothed absorption coefficient has an exponential

distribution, decreasing from the band centre. In this work this model was used to compare

against global models, and detailed information about this model can be found in Dinho [24].

3.1.2 GRAY GAS MIXTURE MODELS Gray gas mixture models are global models, in which the non gray medium is replaced by a

number of gray gases with different (but gray) absorption coefficients. The heat transfer rates

are calculated separately for each gray gas, and then the total heat flux is found by adding the

gray gas heat fluxes after being multiplied with weight factors, calculated to adjust existing data.

Some examples of these models that can be found in literature are the Weighted-Sum-of-Gray-

Gases (WSGG) Model, the Spectral-Line-based Weighted-sum-of-gray-gases (SLW) Model, the

Absorption Distribution Function (ADF) Model, and the Absorption Distribution Function

Fictitious Gases (ADFFG) Model. In this work comparisons were made with the SLW Model, the

Leckner Model and the TNF Model. Since in the “Furnace” code the Leckner and TNF model

are already incorporated, these will be tested and compared with the SLW model which is

incorporated into the code in this thesis. The Leckner Model was one of the earlier ones and

was included as it follows closely the data from Hottel [23]. The TNF was the only gray gas

model found that included the fitting to data for gas mixtures with CO that may be important for

the combustion configuration considered. The SLW Model is one of the newer gray gas models

based on information of the detailed line by line data basis that is explained in detail in the open

literature, while others do not present in detail [25]. The selected models are presented next.

3.1.2.1 SLW Model

The Spectral Line-based Weighted-sum-of-gray-gases (SLW) model is a gas radiative property

model that uses the absorption coefficient (normalized by the molar density) as the fundamental

parameter rather than absorptivity or band absorptance allowing arbitrary differential solution

28

methods of the RTE (Radiative Transfer Equation) in its fundamental method. This model is

developed from detailed line-by-line data.

Definition of the distribution function

The absorption-line blackbody distribution function is defined as that fraction of the blackbody

energy in the portions of the spectrum where the high-resolution spectral absorption cross-

section of the gas Cabs,η is less than the prescribed value Cabs. The distribution function for

species s is then expressed as:

∑ ∫Δ⋅

=i YPTC

bbb

STgbabss

STgabsi

dTET

YPTTCF),,,(

4 ),(1),,,,(η

η ηησ

(3.3)

where σ is the Stephan-Boltzmann constant and Ebη is Planck’s function evaluated at the wave

number η and blackbody (source) temperature Tb. The subscript i refers to the ith spectral

segment and the summation is performed over all segments covering the entire spectrum. The

dependence of the function on the spectrum is through the spectral interval of integration of

each segment Δηi which is dependent on the absorption cross-section, gas temperature Tg, the

total pressure PT, and species concentrations which affect line broadening.

Recommended Mathematical Correlations

H2O:

The following hyperbolic equation is recommended [26] for approximate calculations with H2O in

computer codes.

[ ]21),,(tanh

21

+= ξbgww TTPF (3.4a)

where the function Pw is given as

∑∑∑= = =

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

3

0

3

0

3

0 25002500l m

lm

b

n

n

glmnw

TTbP ξ (3.4b)

and

)ln( absC=ξ (3.4c)

Tg and Tb are in degrees Kelvin and Cabs has the units: m2/mole. The coefficients of the

correlation blmn, found in Table 3.1, were determined from a least squares fit of the distribution

29

function evaluated at 20 logarithmically spaced values of Cabs between 3x10-5 and 60 m2/mole,

and at the source and gas temperatures of 400, 500, 750, 1000, 1250, 1500, 1750, 2000, 2250,

and 2500 K. Equation 3.4 is applicable to the atmospheric pressure and in the limit of air-

broadening only (Yw→0).

Tab. 3.1 – Coefficients blmn appearing in equation 3.4 for H2O. l=0

m\n 0 1 2 3

0 1.6103 -4.0931 5.1435 -2.0857

1 -0.81812 15.5525 -21.819 9.8775

2 2.6001 -21.204 31.0828 -14.279

3 -1.3171 9.6524 -14.474 6.6747

l=1

m\n 0 1 2 3

0 0.440187 -0.63348 0.871627 -0.38798

1 -0.82164 5.0239 -5.9818 2.6355

2 1.5149 -7.8032 9.8642 -4.1931

3 -0.81023 3.727 -4.874 1.9868

l=2

m\n 0 1 2 3

0 0.106647 -0.43116 0.689598 -0.29831

1 -0.38573 1.8865 -2.9712 1.2834

2 0.578351 -2.6218 4.2698 -1.7929

3 -0.28014 1.1785 -1.9568 0.787249

l=3

m\n 0 1 2 3

0 8.25027E-03 -3.28556E-02 6.81563E-02 -3.04815E-02

1 -3.10578E-02 0.123369 -0.26154 0.117452

2 4.39319E-02 -0.15792 0.350948 -0.15308

3 -2.03699E-02 6.61142E-02 -0.15283 6.34035E-02

It’s recommended that the function is not used above 2500 K since extrapolating any correlation

beyond the data used in the fit is inappropriate.

To account for self-broadening, in equations 3.4 ξ should be replaced by ξ-ξsb:

[ ]21),,(tanh

21

+−= sbbgww TTPF ξξ (3.5a)

30

where

∑∑∑= =

+

=

⎟⎠⎞

⎜⎝⎛=

3

0

3

0

12

0)(

2500l m

lw

mn

n

blmnsb Y

Tc ξξ (3.5b)

Tb is in degrees Kelvin, ξ is given by equation 3.4c, and Yw is the mole fraction of H2O. The

coefficients clmn, found in Table 3.2, were obtained from a least squares fit with the distribution

function evaluated at the H2O mole fractions of 0, 0.05, 0.1, 0.2, 0.3, 0.45, 0.6, 0.8, and 1.0.

This function is not so accurate at absorption cross-sections below 0.1 m2/mole and at H2O

fractions above 30%.

Tab. 3.2 - Coefficients clmn appearing in equation 3.5 for H2O l=0

m\n 0 1 2

0 4.72 -8.5482 5.2394

1 -0.84969 0.312478 -0.13804

2 -3.47243E-02 4.02461E-02 -5.80104E-02

3 5.79830E-04 3.94125E-03 -5.29017E-03

l=1 m\n 0 1 2

0 -8.9615 16.9547 -10.76

1 1.5861 -2.0166 1.46

2 4.34730E-02 -0.67133 0.633231

3 2.87067E-03 -7.06830E-02 6.23710E-02

l=2 m\n 0 1 2

0 9.1461 -17.327 11.1864

1 -1.3975 1.9965 -1.6935

2 8.46419E-02 0.599994 -0.70054

3 7.14719E-03 6.62086E-02 -6.87294E-02

l=3 m\n 0 1 2

0 -3.5504 6.624 -4.3058

1 0.485392 -0.7071 0.689109

2 -6.77456E-02 -0.18179 0.269308

3 -5.92726E-03 -2.04694E-02 2.56411E-02

31

CO2:

The same hyperbolic tangent function as used for H2O is recommended for CO2:

[ ]21),,(tanh

21

+= ξbgcc TTPF (3.6a)

where

∑∑∑= = =

⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

3

0

3

0

3

0 25002500l m

lm

b

n

n

glmnc

TTdP ξ (3.6b)

and

)ln( absC=ξ (3.6c)

Tg and Tb are in degrees Kelvin and Cabs has the units m2/mole. The coefficients of the

correlation dlmn, found in Table 3.3, were determined from a least squares fit of the distribution

function evaluated at 20 logarithmically spaced values of Cabs between 3x10-5 and 600 m2/mole,

and at the same source and gas temperatures used for H2O. Equation 3.6 is applicable to one

atmosphere pressure. As with H2O, it is recommended that the function is not used above

2500K.

32

Tab. 3.3 -The coefficients dlmn appearing in equation 3.6 for CO2 l=0

m\n 0 1 2 3

0 2.45702 -5.45334 6.53751 -2.52344

1 -4.0232 15.67297 -24.3247 11.33757

2 7.54549 -23.8023 39.51896 -19.1137

3 -3.63104 11.9078 -20.3606 9.97877

l=1

m\n 0 1 2 3

0 7.65678E-02 2.36184 -3.95061 2.17482

1 0.2901819 -12.0041 22.44342 -13.0467

2 -0.64282 21.5003 -40.8667 23.66762

3 0.3942158 -11.5818 22.05176 -12.6536

l=2

m\n 0 1 2 3

0 -3.30582E-02 0.4367742 -0.725331 0.4138566

1 0.3672993 -3.52466 6.74885 -3.96295

2 -0.69811 6.60703 -12.9667 7.58713

3 0.3831158 -3.65683 7.19415 -4.16496

l=3

m\n 0 1 2 3

0 -1.87927E-03 1.92123E-02 -3.25863E-02 1.98493E-02

1 2.85033E-02 -0.223537 0.4402715 -0.26267

2 -5.49594E-02 0.4370937 -0.881494 0.521958

3 3.04198E-02 -0.247793 0.4990777 -0.291566

The absorption-line blackbody distribution function provides an efficient means of calculating

total radiative heat transfer rates with accuracy for problems of isothermal media with uniform

composition.

The fraction of the blackbody energy for a given source temperature in the spectral regions

where the absorption cross-section is between jabsC ,

~

and 1,

~

+jabsC may be found simply as the

difference of the distribution function evaluated at the two absorption cross-sections, which is

the blackbody weight of the absorption coefficient in the domain to calculate the emissivity.

),,,(),,,( ,

~

1,

~

sgbjabsssgbjabssj YTTCFYTTCFa −= + (3.7)

33

The jth gray gas absorption coefficient is defined as the product NCabs,j.

jabsj NCk ,= (3.8)

where N is the molar density of the gas evaluated from a equation of state, and Cabs,j is an

appropriate mean value of the absorption cross-sectional area between jabsC ,

~ and 1,

~

+jabsC .

In a numerical calculation, the absorption cross-section domain is divided into discrete

increments and a solution is carried out for each increment represented by a single value of the

absorption cross-section or a single gray gas. The total radiative heat transfer rates are found

simply by summing the resulting solutions. So, the total emissivity of one specie s for a given

temperature and at a path-length, L, is calculated as

[ ]∑ ⋅−−=j

jjs Lka )exp(1ε (3.9)

[ ])exp(1)()( ,,

~

1,

~LCNCFCF jabs

jjabssjabsss ⋅⋅−−⎥⎦⎤

⎢⎣⎡ −= ∑ +ε (3.10)

For brevity the dependence on the temperatures and composition is not shown, but is implied.

Cabs,j is given as the logarithmic average of the bounding supplemental absorption cross-

sections:

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ += +

2)ln()ln(exp 1,

~

,

~

,jabsjabs

jabsCCC (3.11)

Calculation of the total emissivity for gas mixtures

To this point, the SLW model has only considered the individual species H2O and CO2

independent of one another, but a mixture of the two must be considered in any practical gas

flame. The concept of the joint absorption-line blackbody distribution function is introduced and

to a good approximation the joint function is expressed in terms of the functions of the separate

species. In general total heat transfer rates in media of binary mixtures require a double

integration over the absorption cross-sections of the two species, but if the ratio of mole

fractions can be taken as spatially constant the number of gray gas solutions of the RTE can be

reduced to a single quadrature using a convolution approach which is an extension of that found

in the literature for the k-distribution method [26]. So two methods for calculating the emissivity

34

of an H2O and CO2 mixture are presented, the Double Summation Approach and the

Convolution Approach.

• The Double Summation Approach

To calculate total heat transfer rates in a mixture of H2O and CO2 an additional gray gas index k

is introduced to account for the second species. The absorption coefficients kj,k are given as the

sum of contributions of the two species:

kccjwwkj CNCNk ,,, += (3.12)

Where Nw and Nc are the molar densities of H2O and CO2, respectively.

The joint function may be expressed to a good approximation as the product of the individual

functions:

)()(),(, ccwwcwcw CFCFCCF = (3.13)

For brevity the dependence on temperatures and composition is not shown, but is implied.

The joint blackbody weights aj,k are obtained from the joint absorption-line distribution function:

kjkcckccjwwjwwkj aaCFCFCFCFa =⎥⎦⎤

⎢⎣⎡ −⎥⎦⎤

⎢⎣⎡ −= ++ )()()()( ,

~

1,

~

,

~

1,

~

, (3.14)

The emissivity is then calculated with:

[ ]∑∑ ⋅−−=j k

kjkjmix Lkaa )exp(1 ,ε (3.15)

• The Convolution Approach

The double integration involved in obtaining total heat transfer rates in a binary gas mixture is a

significant increase of computation over the single integration involved with a single specie but

still an immense decrease over line-by-line calculations. If the ratio of the mole fractions of the

two species is spatially constant then it is possible to construct a single absorption cross-section

spectrum with lines of both species. An absorption-line distribution function could then be

formulated in terms of a single absorption cross-section for the gas mixture in lieu of two

absorption cross-sections (one for each species). This would permit a single integration instead

of a double integration. If the CO2 to H2O molar density ratio is spatially constant one may

35

define a single absorption cross-section Cmix by factoring out the H2O molar density from

equation 3.12:

mixwcwwcw

cww CNrCCNC

NN

CNk =+=+= )()( (3.16)

where r is defined as the molar ratio Nc/Nw, and the mixture absorption cross-section is defined

in equation 3.16. The subscripts j and k have been deleted from equation 3.16 since ultimately

only a single index is required for Cmix.

Having defined Cmix for a given molar ratio it is possible to define a mixture absorption-line

blackbody distribution function Fmix. The mixture distribution function can be determined from

the individual distribution functions:

[ ]∑−

=++ −−=

1

1,1,1,

max

)()()()(n

kkcckcckcmixwmixmix CFCFrCCFCF (3.17)

where nmax is the index corresponding to Cc,max :

rCC

C wmixc

min,max,

−= (3.18)

The mixture blackbody weights are obtained from the mixture absorption-line blackbody

distribution function:

)()( ,1, jmixmixjmixmixj CFCFa −= + (3.19)

The emissivity is then calculated with:

[ ]∑ ⋅−−=j

jjmix Lka )exp(1ε (3.20)

where jmixwj CNk ,= , as stated above.

The Convolution Approach has a limited interest to apply in conditions where the molar

concentrations of water vapour and carbon dioxide are not correlated such as in the case of oxi-

combustion in a mixture containing CO2.

The SLW model is also extended to consider further grey gas to represent the absorption of

radiation by the particles [26].

36

3.1.2.2 Leckner’s Model

In the Leckner model [27], for the calculation of the emissivity of flue gas products, the

contribution from particles is combined with that of the gas mixture of CO2 and H2O in the form:

gsgs εεεεε ⋅−+= (3.21)

where εs is the total emissivity of the particles , εg the emissivity of the gas corresponding to the

addition of the absorption coefficients.

Considering only the contribution of the gas radiation from carbon dioxide and water vapour, the

emissivity is expressed as:

OVOHCOg εεεε Δ−+=22

(3.22)

The last subtracting term represents the correction by overlap.

The overlap factor is obtained by:

76.24.100089.01017.10 OVλζ

ζζε ⋅

⎭⎬⎫

⎩⎨⎧

⋅−⋅+

=Δ (3.23)

where,

( )[ ]OHCOcOV ppL22

log +⋅=λ (3.24)

pCO2 and pH2O are the partial pressures of the gaseous components, in bar, and Lc the path-

length in centimeters.

22

2

COOH

OH

ppp+

=ζ (3.25)

The expression used to the calculation of the total emissivity of each gaseous component is:

( )[ ] CexpBAPBPA

maxE

E ⋅ε=⎭⎬⎫

⎩⎨⎧

λ−λ⋅ξ−⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−

++++⋅

+⋅ε=ε 02

0 11

1 (3.26)

37

being,

∑=

⋅=M

i

iia

00ln λε (3.27)

∑=

⋅=N

j

jiji ca

0τ (3.28)

1000gT

=τ (3.29)

( )cLp ⋅= logλ (3.30)

where Tg is the gas temperature in Kelvin, and p represents the partial pressure for each

gaseous component in bar.

Following the factors and expressions for CO2 and H2O are presented

H2O: T> 400K; M=2 ; N=2

Tab. 3.4 - Coefficients for equation 3.28 for water vapour [27] i c0i c1i c2i

0 -2.2118 -1.1987 0.035596

1 0.85667 0.93048 -0.14391

2 -0.10838 -0.17156 0.045915

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅+⋅=

gTTE TP

pPP 2739.41 (3.31)

( )2max 2.13log τλ ⋅= (3.32)

5.0=ξ (3.33)

τlog053.2888.1 ⋅−=A (3.34)

4.11.1 −⋅= τB (3.35)

38

CO2: T> 400K; M=3; N=4

Tab. 3.5 - Coefficients for equation 3.28 for CO2 [27] i c0i c1i c2i c3i c4i

0 -3.9781 2.7353 -1.9882 0.31054 0.015719

1 1.9326 -3.5932 3.7247 -1.4535 0.20132

2 -0.35366 0.61766 -0.84207 0.39859 -0.063356

3 -0.080181 0.31466 -0.19973 0.046532 -0.0033086

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅=

TTE P

pPP 28.01 (3.36)

( )2max 225.0log τλ ⋅= (3.37)

47.1=ξ (3.38)

0.110.0 45.1 +⋅= −τA (3.39)

23.0=B (3.40)

3.1.2.3 TNF Model

The RADCAL model is used in the TNF model [28] from where it was adopted. The TNF model

was used to calculate optically thin flames. The absorption coefficient of the gas mixture is

calculated from:

∑ ⋅=i

pi )ap(ki

(3.41)

where ai is the mean absorption coefficient for H2O, CO2 and CO presented below.

For H2O and CO2:

A fifth order polynomial is used as a function of the inverse of temperature, for a temperature

range between 300K and 2500K in the form:

39

5

5

4

4

3

3

2

21010001000100010001000

⎟⎠⎞

⎜⎝⎛⋅+⎟

⎠⎞

⎜⎝⎛⋅+⎟

⎠⎞

⎜⎝⎛⋅+⎟

⎠⎞

⎜⎝⎛⋅+⎟

⎠⎞

⎜⎝⎛⋅+=

Tc

Tc

Tc

Tc

Tcca p (3.42)

where the coefficients are:

Tab. 3.6 – Coefficients for equation 3.42 for H2O and CO2 [28] c0 c1 c2 c3 c4 c5

H2O 0.23093 1.12390 9.41530 2.99880 0.51382 1.8684E-5

CO2 18.741 121.310 273.500 194.050 56.310 -5.8169

For CO: A fourth-order polynomial in temperature is used for CO, with coefficients for two temperature

ranges.

4

43

32

210, TcTcTcTcca COp ⋅+⋅+⋅+⋅+= (3.43)

where the coefficients are:

Tab. 3.7 – Coefficients for equation 3.43 for CO [28] c0 c1 c2 c3 c4

T < 750 K 4.7869 -0.06953 2.95775E-4 -4.25732E-7 2.02894E-10

T > 750 K 10.09 -0.01183 4.7753e-6 -5.87209E-10 -2.5334e-14

40

4 RESULTS

4.1 RADIATION MODELS

Some radiation models were tested previously to their use in CFD simulations, with the

objective of establishing which one gives better results, for usage in the “Furnace” code. Since

in CFD simulations the computing time is a key factor, only gray gas models, which take less

computing time, were tested and compared with the Exponential Wide Band model, which gives

more accurate results but takes more computation time. The SLW model is based on a further

detailed model (line by line integration) and was developed to allow for small calculation times,

and is incorporated in the “Furnace” code in the present work. The Leckner and TNF models

were already incorporated in the code, while in the present work the SLW model was

implemented in the “Furnace” code. All models were tested and compared with the Wide Band

model used as a reference as it was previously tested [24] and it is known to predict accurate

results [23].

In Fig. 4.1 the emissivities for water vapour for each model are presented and compared for

various values of pressure path-lengths. All models predict similar values at low partial pressure

path-lengths, but at high partial pressure path-length (600 bar cm) the TNF model leads to an

emissivity value equal to unity, while the other models continue to show the same tendencies

between them. When changing the molar fraction in Fig. 4.2 the TNF model generates much

different results compared to the other models, leading to much higher emissivities.

0,0001

0,001

0,01

0,1

1

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 T

εH2 O 0.05 bar cm - SLW0.3 bar cm - SLW4 bar cm - SLW600 bar cm - SLW0.05 bar cm - Leckner0.3 bar cm - Leckner4 bar cm - Leckner600 bar cm - Leckner0.05 bar cm - WB0.3 bar cm - WB4 bar cm - WB600 bar cm - WB0.05 bar cm - TNF0.3 bar cm - TNF4 bar cm - TNF600 bar cm - TNF

Fig. 4.1 - Comparison of emissivity of water vapour for all the models as a function of temperature for

different pressures and a path-length of 10m

41

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Yw

εH2 O 500 K - SLW1000 K - SLW1500 K - SLW2000 K - SLW500 K - Leckner1000 K - Leckner1500 K - Leckner2000 K - Leckner500 K -WB1000 K - WB1500 K - WB2000 K - WB500 K -TNF1000 K - TNF1500 K - TNF2000 K - TNF

Fig. 4.2 - Comparison of emissivity of water vapour for all the models as a function of molar fraction at

different temperatures and for length of 1m

The comparison of emissivity values for carbon dioxide shows even larger discrepancies

between the TNF model and the other models. Fig. 4.3 shows that the difference between the

TNF model and the other models increases with the pressure path-length, and again yields an

emissivity value equal to unity for high partial pressure path-lengths. In particular the molar

fraction influence for a path-length of 10m exhibits a strong deviation of the TNF model in Fig.

4.4 leading to values higher than 0.6 for the emissivity when the CO2 molar fraction reaches

20%. The conditions for the derivation of the TNF model are probably further from the

conditions considered and therefore it won’t be used.

When increasing the CO2 molar fraction in Figure 4.4 the Hottel model deviates from the results

of the wide band model, calculating higher emissivities. Although the Leckner model leads to

similar results of the Wide Band model at 500 K in Figure 4.4, at higher temperatures it leads to

much higher values for the emissivities. The SLW model predicts quite well all the ranges

tested when compared with the WB model, except at 500 K though it has not a considerable

deviation.

42

0,001

0,01

0,1

1

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 T

εCO2

0.05 bar cm - SLW0.3 bar cm - SLW4 bar cm - SLW600 bar cm - SLW0.05 bar cm - Leckner0.3 bar cm - Leckner4 bar cm - Leckner600 bar cm - Leckner0.05 bar cm - WB0.3 bar cm - WB4 bar cm - WB600 bar cm - WB0.05 bar cm - Hottel0.3 bar cm - Hottel4 bar cm - Hottel600 bar cm - Hottel0.05 bar cm - TNF0.3 bar cm - TNF4 bar cm - TNF600 bar cm - TNF

Fig. 4.3 - Comparison of emissivity of carbon dioxide for all the models as a function of temperature for

different pressures and a path-length of 10m

0

0,2

0,4

0,6

0 0,2 0,4 0,6 0,8 Yc

εCO2500 K - SLW1000 K - SLW1500 K - SLW2000 K - SLW500 K - Leckner1000 K - Leckner1500 K - Leckner2000 K - Leckner500 K - WB1000 K - WB1500 K - WB2000 K - WB500 K - Hottel1000 K - Hottel1500 K - Hottel2000 K - Hottel500 K - TNF1000 K - TNF1500 K - TNF2000 K - TNF

Fig. 4.4 - Comparison of emissivity of carbon dioxide for all the models as a function of molar fraction at

different temperatures and for length of 10m

Fig. 4.5 shows a comparison between the Leckner model and both approaches of the SLW

model against the WB model to calculate gas mixture emissivities. As it is observed, the double

summation approach leads to more similar results than the convolution approach and hence it

was adopted. The Leckner model presents large deviations for the larger path lengths but for

small lengths as those considered in grids for the numerical calculations the values seem

acceptable and therefore this model will also be considered in the numeric calculations.

43

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

400 600 800 1000 1200 1400 1600 1800 2000 2200 2400T

εWB - 1

SLWds - 1

SLWc -1

Leckner - 1

WB - 2

SLWds - 2

SLWc - 2

Leckner - 2

WB - 3

SLWds - 3

SLWc - 3

Leckner - 3

Fig. 4.5 – Comparison of emissivity of water vapour and carbon dioxide mixtures

Since in oxy-fuel combustion the higher concentration of carbon dioxide may also lead to larger

fractions of carbon monoxide, the emissivity of mixtures with large molar fractions of CO were

also compared. The SLW model was not fitted with CO and therefore the alternatives available

are the wide band model and the TNF models. Fig. 4.6 shows a comparison between these two

models replacing part of the CO2 by CO in a gas mixture emissivity as a function of

temperature. The results from the TNF model again lead to very large values. As it can be

observed replacing CO2 by CO increases the emissivity, however, since generally the molar

fractions of CO in combustion are much lower than the ones tested here, and even with these

the increase in the value for the emissivity is not high, CO won’t be considered in the radiation.

The final outcome of the review carried out is the suggestion to use the SLW model for the

calculations once is an accurate and fast model, yet the results with this model will be compared

against results with the Leckner model.

1-CO2 molar fraction = 0,1 ; H2O molar fraction = 0,1 ; L = 1 m 2-CO2 molar fraction = 0,7 ; H2O molar fraction = 0,15 ; L = 1 m 3-CO2 molar fraction = 0 8 ; H2O molar fraction = 0 15 ; L = 10 m

SLWds: Double Summation Approach SLWc: Convolution Approach

44

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

400 900 1400 1900 2400 T

ε WB 1 w ithout CO

WB 1 w ith CO

WB 2 w ithout CO

WB 2 w ith CO

TNF 1 w ithout CO

TNF 1 w ith CO

TNF 2 w ithout CO

TNF 2 w ith CO

Fig. 4.6 – Comparison of the weight of CO in the emissivity of a mixture

4.2 COMBUSTION RESULTS

The simulations using the “Furnace” code were carried in three stages:

• Isothermal, where the energy balances weren’t considered

• without radiation, where the energy balances were considered but without radiation

• with radiation, where the energy balances are considered with radiation

The calculations were performed initially considering a constant temperature of 1100 K similar

to wall temperatures, solving the equations of flow, particle trajectories and mass balances to

the gas phase with combustion. Then the final solution was used as initial approximation to

calculate the solution with the energy balance and all other equations including the particle

trajectories but without radiation and finally the solution was done with all sub-models.

Since the geometry has a square cross section it would require a three dimensional

representation but the main aerodynamic characteristics are associated with the circular burner,

so an equivalent cylinder was considered. Assuming axisymmetric conditions the domain was

represented by a representative plane. The numerical grid was prepared based on the position

of the inlet ports and fitting the quarl geometry with a total of 84 nodes in the axial direction and

86 in the radial direction.

4.2.1 BASELINE CASE

The flow for the baseline flame is presented in Fig. 4.7 for the isothermal and with radiation

simulations. For both cases it is seen that two recirculation zones are formed near the furnace

entrance, one in the corner (ERZ – External Recirculation Zone) and the other in the centre (IRZ

- Internal Recirculation Zone).There are in both cases also recirculations close to the furnace

45

exit due to the exit of flue gas in the centre of the furnace. There are main differences between

the flow fields obtained in the simulations, once in the isothermal case the ERZ is longer as well

as the IRZ leading to a smaller divergence of the flow entering the furnace. For the radiation

simulation the corner recirculation decreases and the centre recirculation increases

approaching the furnace wall, when compared to the isothermal simulation.

Fig. 4.7 – Baseline case flow for isothermal and with radiation solutions

The mass release distribution from the particles is shown in Fig. 4.8 again for the isothermal and

radiation simulations. It is observed that for the isothermal simulation the larger part of the mass

release occurs very close to the burner due to the higher temperature. Part of the mass sources

are released in the IRZ in the isothermal case, while for the radiation simulation the mass

release does not enter the IRZ at all. In the simulation with radiation the mass release occurs

farther away from the burner in the edge of the ERZ. This is one of the reasons why both cases

are presented.

46

Fig. 4.8 – Baseline case mass release distribution for isothermal and with radiation solutions

The converged results for the radiation simulation led to a colder recirculation zone and

therefore without ignition close to the burner. This may be partly a result from the initial particle

velocities which were considered to be equal to the flow velocity or can be attributed to the

limited performance of the k-ε turbulence model.

Fig. 4.9 shows the in-flame profiles for the CO2 concentration of the simulations and of the

experimental results. As it is observed, the isothermal solutions exhibit tendencies similar to the

experimental results. The combustion simulations with and without radiation predict much lower

values for the CO2 molar fractions than the experimental in the central region of the first profile.

In the ERZ the results from the isothermal simulation lead to higher values of CO2 in more

agreement with the experimental data that also suggests that the ERZ extends up to the fourth

profile. The results from the fifth profile for the simulation with radiation show lower values

associated with the gas from the secondary air stream with delayed combustion. With distance

from the burner the combustion simulation with and without radiation approaches the

experimental results, predicting similar results for the last two profiles.

The in-flame oxygen profiles for the simulations and for the experimental results are shown in

Fig. 4.10. The isothermal simulation results follow the tendencies of the experimental results

predicting similar results particularly in the external zone. The peak of oxygen in the first profiles

is predicted in similar radial positions as shown by the experimental results, suggesting that the

size of the recirculation zones in reality are similar to the ones predicted in the isothermal

simulation. The simulations with and without radiation present much higher values than the

experimental values in the central region near the burner, although the difference decreases

47

with distance from the burner. In the external zone the simulation without radiation shows a

good agreement with the experimental results and the simulation with radiation predicts higher

results, except in the last profile.

Fig. 4.11 presents the in-flame carbon monoxide profiles for the simulation and for the

experimental results. The isothermal simulation shows a similar behaviour to the experimental,

although with higher results near the burner, particularly in the first profile, and becomes more

similar with distance from the burner. The values close to the burner are a result of the volatile

release and the initial char burnout which is assumed to produce CO and the limited quantities

of oxygen. In the ERZ the values are low in line with the experimental observation. The results

from the simulation without radiation are lower than the experimental in the first profile near the

centre and much higher for x/D0=4. The high values of CO in this simulation may be a result of a

concentrated burnout in that area and then the values become low as expected. The simulation

with radiation exhibits virtually no CO in the first profile and higher values in the last profiles

showing a delayed combustion.

48

Fig. 4.9 - In-flame carbon dioxide profiles for the Baseline case for the different simulations

49

Fig. 4.10 -In-flame oxygen profiles for the Baseline case for the different simulations

50

Fig. 4.11 - In-flame carbon monoxide profiles for the Baseline case for the different simulations

51

The in-flame temperature profiles are presented in Fig. 4.12 for the combustion simulation

without radiation and for the simulations with radiation using the SLW model and the Leckner

model. All simulations lead to very low values in the furnace centre near the burner, which is in

accordance with the CO2, CO and O2 profiles. Since the temperature is very low in this region

and also due to the particles not entering in the IRZ, the mass release doesn’t take place in this

region and therefore there is no combustion here. The calculations are strongly coupled as can

be observed from the isothermal results. In this case there is some energy release from the

combustion of volatiles and char in the IRZ but these are lowered during the radiation

calculations. The simulation without radiation leads to results closer to the experimental values

in the external zone where the species profiles were also in line measurements. With distance

from the burner the values approach the experimental results, in accordance with the species

profiles.

Both models used in the simulation with radiation lead to very similar results. In these

simulations the temperature obtained is much lower than in the simulation without radiation. The

modification of temperature affects the flow that in turn lowers the amount of particles burned in

the ERZ.

52

Fig. 4.12 -In-flame temperature profiles for the Baseline case for the different simulations

53

4.2.2 FLAME C

The flow for flame C is presented in Fig. 4.13 for the isothermal and radiation simulations. The

simulations of the isothermal test case with the swirl number indicated in the experiments led to

a flow without IRZ and therefore of a flame with very different characteristics from the expected

situation. Therefore the simulations for the isothermal case were performed with a swirl number

similar to the case of air firing. For the simulations with and without radiation however the swirl

number was set to the test value and still the simulated flow presents an internal recirculation

zone as in the initial conditions for that simulation. The k-ε turbulence model used in the

simulations has strong limitations in the calculation of swirled flows [4] and further tests and

investigation are needed for the simulation of these flames. The flow results are quite similar to

the ones obtained for the case of air firing for the simulation with radiation despite the lower

swirl number.

Fig. 4.13 - Flame C flow for isothermal and with radiation solutions

The mass release for the oxy-fuel isothermal and radiation simulations is shown in Fig. 4.14. It

is seen that as the air firing combustion, in the isothermal simulation the majority of the mass

release does not enter the recirculations and only a small part enters the IRZ, while for the

simulation with radiaton the mass release does not enter the IRZ at all. This is probably due to

the parental use of the air firing case and with the calculation of heat transfer ignition is lost

close to the burner.

54

Fig. 4.14 – Flame C mass release distribution for isothermal and with radiation solutions

The in-flame carbon dioxide profiles are shown in Fig. 4.15, where it can be observed that the

isothermal simulation closely predicts the values of the experimental results. The simulation

without radiation as well as with radiation lead to lower values than the experimental results

near the burner in the furnace central zone. The values of CO2 volumetric fraction there are

close to the inlet values and little increase occurred in these values from the combustion

process. With distance to the burner the values for the simulations with and without radiation

tend to approximate the experimental results. In the external zone these simulations predict

values close to the experimental values.

Fig. 4.16 shows the in-flame oxygen profiles. Again the isothermal simulation leads to realistic

results, with the location of the border between the recirculations being predicted at the correct

radial positions. The simulations with and without radiation lead to higher values than the

experimental ones in the centre of the furnace close to the burner. In the external zone the

simulation without radiation shows results close to the experimental, and the simulation with

radiation higher results that are slowly mixed with the main combustion stream.

As it is seen in Fig. 4.17 the isothermal simulation predicts higher values for the carbon

monoxide concentration near the burner in the central zone than the experimental results. In the

external zone the results predicted by this simulation are close to the experimental. The

simulations with radiation and without radiation lead to lower values than the experimental

results in the central zone near the burner due to the delayed combustion. These tend to

increase, in particular for the simulation without radiation which leads to much higher values

than the experimental at x/D0=4. In the last profile the results for the simulation without radiation

are close to the experimental, although the simulation with radiation still yields larger values

than the experimental ones.

55

Fig. 4.15 - In-flame carbon dioxide profiles for the Flame C for the different simulations

56

Fig. 4.16 -In-flame oxygen profiles for the Flame C for the different simulations

57

Fig. 4.17 - In-flame carbon monoxide profiles for the Flame C for the different simulations

58

The in-flame temperature profiles are shown in Fig. 4.18 where, as in the air firing case, all the

simulations predict much lower values than the experimental in the furnace centre near the

burner, which here is also consistent with the species profiles. These values tend to approach

the experimental values later with the case without radiation leading to higher values compared

to experimental values and the results for air firing. When considering radiation, temperature is

much lower, due to the modifications on the solution with radiation including flow and mass

sources as discussed before. Again both simulations with radiation, using the Leckner’s and

SLW models, predict similar values.

As it was observed for each case the influence of the model for the calculation of the absorption

coefficient from the gas phase is small. Fig. 4.19 shows the calculated gas absorption

coefficients for the simulations with radiation with both models for radiation properties of gases

and for particles, for both the baseline case and flame C, The differences between the models

for the radiation gas properties are small due to the use of a small pressure path length. The

values are higher close to the furnace axis due to the smaller dimensions in the grid. The values

from the Leckner model are slightly higher. The contribution from the particles for both cases is

in general smaller than the gas contribution, except for the near burner zone. This is due to the

high particle loading close to the inlets and the lower temperature. Comparing the absorption

coefficients for flame C with those from the baseline case it can be observed that both the gas

and the particle contributions increase.

59

Fig. 4.18 - In-flame temperature profiles for the Flame C for the different simulations

60

Fig. 4.19 – Absorption coefficient distribution for the SLW model and

Leckner model. a) Baseline Case. b) Flame C.

61

5 CONCLUSIONS

This thesis presents numerical results for the simulation of pulverised coal combustion in

different atmospheres comparing the cases of air firing with the use of oxygen mixed with

recirculated flue gases. The application is presented for a single burner furnace for which

experimental data is available.

Models for the radiation properties of gases are reviewed and tested for a large range of

conditions including those likely to be met in the furnace. Several gray gas models are

considered and it is observed that all provide comparable results for small pressure path

lengths. However for more general conditions the TNF model is observed to lead to very large

values of emissivity and as it is a fitting from a detailed model it is suspected that is out of the

range of conditions used to prepare it. The Leckner model although developed for cases of air

firing conditions leads to reasonable results when increasing the pressure path-lengths and was

also considered in the numerical simulations. The SLW model led to the better agreement with

the calculations done with the wide band model and both are the more precise.

The inclusion of CO in the calculation of the radiant properties has a small contribution

according to the wide band model and the TNF model, that is the only gray gas model that

considers this species, leads to unrealistic values, so the presence of CO was not considered.

The simulations performed for pulverised coal combustion were done with a numerical model

developed at IST and the calculation of the radiation properties of gases was included in this

code. The results from the simulations are strongly affected by the predicted flow field that is

more realistic in isothermal (high temperature) conditions inside the furnace. In those conditions

the distribution of the gas species concentrations present a good agreement with the

experimental results, while with the calculation of temperature a delay in ignition is predicted

and the comparison with the experimental results is limited. The modification of the atmosphere

leads to higher values of the absorption coefficient when comparing the results for oxi-

combustion with air firing but no significant differences were obtained changing the Leckner by

the SLW model. Further work is required to examine the influence of the turbulence model and

inlet conditions in the flow calculation.

62

6 FUTURE WORK

The results obtained in the numerical simulations lead to the identification of a series of factors

that require further investigation and tests. The use of alternatives to the k-ε model should be

investigated by including corrections to this model in the code used. An alternative is the use of

a commercial software package (Fluent) where several turbulence models are implemented to

test the sensitivity of the calculations to this sub-model.

The radiative properties of the particles although have a lower weight in the final absorption

coefficient in the furnace should also be analysed. The importance of particles may increase if

one considers the possibility of using recirculated flue gases with ashes into the furnace

increasing the particle loading and participation of particles in the radiation.

The ignition conditions for the particles should also be examined and tests should be carried out

forcing the particles to penetrate into the internal recirculation zone, even if this condition is

relaxed later in the calculations to obtain more realistic results than the ones presented in this

thesis.

One should also consider possible modifications of the reaction mechanisms in the gas and for

the particle in the CO2 rich atmosphere, despite other authors have been using models similar

to the ones for air firing as it was considered in this work.

63

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