Modelling of Biomass Combustion in Furnaces
Torbern Klason
May 2006
i
Doctoral Thesis.
ISBN 91-631-8870-8
ISRN LUTMDN/TMHP—06/1040–SE
ISSN 0282-1990
© Torbern Klason, May 2006
Division of Fluid Mechanics
Department of Energy Science
Lund Institute of Technology
Box 118
SE-221 00 Lund
Sweden
Printed by Media Tryck AB, Lund, May 2006
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Abstract
Biomass combustion in grate fired furnaces is an important approach to convert renewable
biomass fuel to heat and electricity. It is not only used in the Swedish energy industry but also
by a great number of Swedish households for domestic heating. Burning biomass has the
advantage of being CO2 neutral. However, it suffers from several difficulties, for example, the
poor combustion efficiency – there are considerable amount of emissions of unburned volatile
gases and solid fuel particles. The emission of pollutants such as NOx, CO, dioxin, and also
particulate matters, etc, damages our environment and has caused great public concern. To
meet the stringent legislation on environment protection, efficient and clean biomass
combustion furnaces must be developed. To achieve this goal, understanding of the biomass
combustion process must be improved by systematic scientific investigations on the
processes, and reliable simulation and design tools must be developed.
The aims of this thesis work are to study the fundamental details of biomass combustion
in grate-fired boilers by using computational methods, and to develop and validate modelling
tools to study biomass combustion. The three major aspects of biomass combustion in grate
fired boilers have been studied. They are the combustion process in the fuel bed, the volatile
combustion process in the free board and the radiation heat transfer process in the free board
and between the flames and the fuel bed. Sub-models for these different processes have been
developed and validated against available experimental data.
A two-zone and a three-zone bed model for biomass combustion are developed based on
the functional group concept and an existing coal combustion model. To account for the
spatial inhomogeneity of the fuel bed, a detailed quasi two-dimensional bed model
considering detailed transport inside each particle has been developed. The two-zone model
(for counter-current beds) and the three-zone model as well as the quasi two-dimensional
model (for cross-current beds) are applied to simulate the volatile compositions from the bed.
The gas phase combustion process in the free board is modelled using Favre averaged NavierStokes equations, together with transport equations for enthalpy and mass fractions of
different species. Turbulence is taken into account by the two-equation k-epsilon closure. The
chemical reactions are modelled using global mechanisms for both the oxidation of volatiles
and for the NOx emissions and re-burning. Different NOx models have been investigated.
Several different radiation models for the radiation heat transfer process in the free board have
been investigated, including the P1 model and the FVM model. In addition, assumptions of
optical thick and optically thin have been examined in different boiler applications. In
addition to the model development and validation, an efficient boundary correction method
has been developed to remedy the stiffness problem in modelling the various small secondary
air jets in large scale boilers.
Two large-scale grate-fired district heating boilers, one small-scale household heating
boiler and one laboratory scale pellets-fired reactor have been studied within the thesis work.
The studies have revealed the important features in grate fired biomass boilers. For example,
it was shown that turbulence plays important role in the volatile oxidation process – the
laboratory scale pellet reactor study showed that the turbulence level in the primary
combustion zone has a dominant influence on the temperature and species distributions. The
study of a large scale 50 MW industry boiler has demonstrated the advantage and potential of
the computational methods in future boiler analysis and design. The present thesis work has
also shown the complexity of the process and limitations of the models investigated. This lays
a solid ground for the future development of reliable tools for the computational analysis of
biomass combustion in grate fired furnaces.
Keywords: biomass combustion, grate fired boiler, volatile oxidation, NOx emissions,
thermal radiation, computational analysis of boiler performance
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This thesis deals with modelling of biomass combustion in grate fired boilers and it is based
on the following papers, included as appendices:
1. Klason T. & Bai X.S., ”Computational study of the combustion process and NO
formation in a wood pellet reactor”, manuscript submitted for publication, 2006.
2. Klason T. & Bai X.S., “FG-DVC modelling of biomass combustion in fixed bed”,
Proceeding of the Third Mediterranean Combustion Symposium, MCS 3, Marrakech,
Morocco, June 8-13, pp 188-194, 2003.
3. Klason T., Bahador M., Nilsson T.K., Bai X.S. & Sundén B., ”A study of radiation
heat transfer and biomass combustion in a large scale grate fired boiler”, manuscript
submitted for publication, 2006.
4. Klason T. & Bai X.S. “A CFD simulation of a 31 MW district heating boiler”,
Swedish-Finnish Flame Days in Borås, October 2005.
5. Klason T. & Bai X.S., “Combustion process in a biomass grate fired industry furnace:
a CFD study”, Progress in Computational Fluid Dynamics, PFCD, “A special issue on
biomass combustion”, in press, 2006.
6. Yu R.X., Klason T. & Bai X.S., “A boundary correction method for calculation of
turbulent reactive flows in furnaces”, manuscript submitted for publication, 2006.
Other papers not included here:
•
Nilsson T.K., Klason T., Bai X.S. & Sundén B., ”Thermal radiation heat transfer and
biomass combustion in a large-scale fixed bed boiler”, 2003 ASME International
Mechanical Engineering Congress & Exhibition, Washington D.C., November 16-21,
2003, Proceeding of IMECE’03, IMECE 2003-42249 (CD-ROM).
•
Elfasakhany A., Klason T. & Bai X.S., “Modeling of pulverized wood combustion
using a functional group model”, Submitted for publication.
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"The only wealth in this world is children. More than all the money, power on the earth."
Michael Corleone
“Children are one of the greatest gifts given to mankind; the joy of becoming a parent overshadows all the troubles, failures and problems of this world.”
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Table of Contents
1
2
Introduction ...................................................................................................................... 1
1.1
Background............................................................................................................... 1
1.2
Biomass Fuels............................................................................................................ 2
1.3
Technologies for Biomass Conversion.................................................................... 2
1.4
Problems related to Biomass Combustion in Grate Fired Boilers....................... 6
1.5
Studied Boilers.......................................................................................................... 8
1.6
Objectives and Scope of This Work...................................................................... 13
Modelling of Biomass Combustion in Grate-Fired Bed ............................................. 17
2.1
Physical and Chemical processes .......................................................................... 17
2.2
Review of Bed Models ............................................................................................ 18
2.3
Bed Models.............................................................................................................. 19
2.3.1
A Semi-Empirical Bed Model.......................................................................... 20
2.3.2
Bed Models with Comprehensive Chemistry................................................... 22
2.3.3
The Two-Zone Model ...................................................................................... 25
2.3.4
A Three Zone Cross-Current Bed Model......................................................... 27
2.3.5
A Quasi Two-Dimensional Bed Model............................................................ 29
2.3.6
Examples of Numerical Studies ....................................................................... 32
3
Modelling of Volatile Oxidation above the Fuel Bed .................................................. 37
3.1
Fundamental Equations for a Reacting Flow in an Industrial Furnace ........... 37
3.2
Turbulence .............................................................................................................. 39
3.2.1
Turbulent Eddy Scales ..................................................................................... 40
3.2.2
Reynolds Averaged Navier-Stokes Equations ................................................. 41
3.2.3
Two-Equation Model, k-ε ................................................................................ 43
3.2.4
Other Models.................................................................................................... 45
3.3
Modelling of Volatile Oxidation............................................................................ 46
3.3.1
Turbulence Chemistry Interaction.................................................................... 47
3.3.2
EDCM .............................................................................................................. 47
3.3.3
Other Models.................................................................................................... 48
3.4
Modelling of NOx Emission ................................................................................... 49
3.4.1
Models for Fuel-NO Simulations..................................................................... 50
3.4.2
Modelling of Thermal NO and NO from N2O-intermediate Mechanism ........ 53
4
Radiation Heat Transfer in Boilers .............................................................................. 55
4.1
Optically Thin Model ............................................................................................. 56
4.2
P1-Approximation................................................................................................... 57
4.3
The Finite Volume Method.................................................................................... 60
4.4
Radiative Properties............................................................................................... 62
4.4.1
Gas absorption.................................................................................................. 62
4.4.2
Particle Properties ............................................................................................ 65
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5
6
Numerical Methods ........................................................................................................ 73
5.1
Grid generation ...................................................................................................... 73
5.2
Spatial Discretisation Scheme ............................................................................... 73
5.3
A Boundary Correction Scheme (BCS) for Small Jet Inflow............................. 74
5.4
Solution Method ..................................................................................................... 78
5.5
Boundary Conditions ............................................................................................. 78
Summary of the Results................................................................................................. 81
6.1
Validation of the Volatile Combustion Model ..................................................... 81
6.2
Validation of the NO Emission Model.................................................................. 82
6.3
Simulation of the Bed Combustion using the Two-zone Model ......................... 82
6.4
Validation of the Thermal Radiation Models for Simulations of Wood
Combustion in Grate Fired Boilers .................................................................................. 83
6.5
Influence of Bed Combustion on the Emissions .................................................. 84
6.6
A CFD Study of the Air-staging unit in a Large Scale Boiler ............................ 86
6.7
A CFD Study of Flow Residence Time ................................................................. 87
6.8
An Area-correction Scheme for Boiler Simulations............................................ 88
7
Conclusions ..................................................................................................................... 91
8
Acknowledgement .......................................................................................................... 93
9
References ....................................................................................................................... 95
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List of Figures
Figure 1. The primary energy supply from 1971 to 2003 in Mtoe, [4]...................................... 1
Figure 2. Thermo-chemical conversion processes and their products. ...................................... 3
Figure 3. A schematic view of burners, their configuration in a suspension fired boiler (left)
and a circulating fluidised bed boiler (right).............................................................................. 4
Figure 4. Sketch of a crossfeed furnace. .................................................................................... 5
Figure 5. An overfeed stoker...................................................................................................... 6
Figure 6. An underfeed stoker for heat production. ................................................................... 6
Figure 7. Sketch of the 50 MW fixed bed boiler studied in this work. ...................................... 9
Figure 8. A sketch of the ECO-tubes (1 & 2), the angle of the air jets and the position of the
ECO tubes in the boiler. ........................................................................................................... 10
Figure 9. A schematic view of the ECO-tube system, seen from the top of the boiler............ 10
Figure 10. A sketch of the ECO-tubes with the hole diameters. B: blocked holes .................. 11
Figure 11. A two-dimensional sketch of the boiler.................................................................. 12
Figure 12. A sketch of the experimental reactor and the pellets burner, dimensions in mm. .. 13
Figure 13. Different aspects considered within the thesis work. ............................................. 14
Figure 14. A schematic view of a counter-current bed. ........................................................... 19
Figure 15. Progress of devolatilisation according to functional group model. ........................ 24
Figure 16. Adjustment of Functional Groups........................................................................... 25
Figure 17. Two-zone bed model for a counter-current bed...................................................... 26
Figure 18. Solution algorithm for the two-zone model............................................................ 27
Figure 19. The three-zone bed model....................................................................................... 27
Figure 20. The solution procedure of the 3-zone model. ......................................................... 28
Figure 21. The calculated temperature and shrinkage for different cells in a spherical particle.
.................................................................................................................................................. 29
Figure 22. The calculated species leaving a particle during its conversion. ............................ 30
Figure 23. A view of the 2-D bed computational domain........................................................ 31
Figure 24. Variation of CH4, H2O and tar as function of CO2, CO and O2.............................. 33
Figure 25. Sketch of the 50 kW bed......................................................................................... 33
Figure 26. The calculated concentration of species along the length of the 31 MW bed. ....... 35
Figure 27. A simplified reaction scheme of fuel NO. .............................................................. 50
Figure 28. The de Soete reaction model................................................................................... 51
Figure 29. Sketch of Mitchell and Tarbell model. ................................................................... 51
Figure 30. Conservation of radiant energy............................................................................... 56
Figure 31. A radiation ray travelling in space as a function of r, θ and φ ............................... 60
Figure 32. Radiant intensity field: (left) Actual, (right) 4 angle FVM discretisation. ............. 61
Figure 33. Band shapes for the exponential wide band model................................................. 63
Figure 34. Interaction between electromagnetic waves and spherical particles. ..................... 66
Figure 35.Total, fly-ash and char phase functions, calculated based on Mie theory. .............. 69
Figure 36. . u-control volume in a staggered grid .................................................................... 74
Figure 37. A schematical description of small jet in staggered grid ........................................ 75
Figure 38. Temperature at the centreline of the reactor for Cases I-IV. .................................. 81
Figure 39. O2 and CO2at the centreline of the reactor, for Cases I and II................................ 82
Figure 40. Calculated species concentrations for different moisture contents......................... 83
Figure 41. Comparison of species concentration and temperature along the furnace height at
z = 1.5 m and x = 3.9 m using P1. ............................................................................................ 84
Figure 42. Temperature and species molar percent at level 4, which is located near the outlet;
CO and CH4 multiplied with a factor 100. ............................................................................... 85
xi
Figure 43. Fuel-NO distributions for different values of γ at level 4....................................... 85
Figure 44. NO emissions at the outlet obtained from numerical simulations and measurements
.................................................................................................................................................. 86
Figure 45. The positions of the parcels in the boiler at different times after the injection from
the fuel bed. (50 MW, 40% moisture)...................................................................................... 88
Figure 46. Simulation of the distribution of turbulent kinetic energy in the FFC boiler: (a)
with the boundary correction method; (b) without the boundary correction method .............. 89
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List of Tables
Table 1. Common Functional Groups [41]. ............................................................................. 23
Table 2. Comparison between simulation and experimental data, n/a = not available. Species
concentration is in dry mole %................................................................................................. 34
Table 3. Calculated species mole fraction for different heat losses (dry mole %)................... 34
Table 4. Associated Legendre Polynomials, Pl m (cos θ ) . ......................................................... 57
Table 5. Log-normal parameters for fly-ash and char [67]. ..................................................... 67
Table 6. Particle concentrations [67]........................................................................................ 67
Table 7. Summary of the boundary correction scheme and a no-correction scheme............... 77
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Chapter 1: Introduction
1 Introduction
1.1 Background
Combustion, a phenomenon which to some is often connected with pollutant formation and to
some a source of destruction of the global environment. However, most of us know that
combustion is one of the most important discoveries ever made by man and it is a cornerstone
on which our modern society is built upon; in fact, without combustion little of our modern
society would exist today. Historically, combustion of solid played a key role in the
industrialization with the invention of the steam engine. The steam engine was fired with
solid fuel and it made way for expansion of mining, transportation, agriculture and mill
industries, just to mention a few. Nowadays combustion is still a most important process,
especially within heat and power, transport and other industry sectors (e.g. paper, pulp and
metal industry). Nevertheless, combustion is also a source to political and environmental
problems. As the world population is increasing and the third world countries need energy for
development, questions arise as how to meet this continuous demand of energy in the future.
There is a general agreement in the literature that oil and natural gas are expected to be
depleted or at least become too expensive to produce within this century [1-3]. Figure 1 shows
the global dependence of different fuels [4]. About 80% of the global energy demand is met
by fossil fuel and only 15% comes from renewable resources such as biomass, wind, hydro
and solar. Therefore, one of the major challenges for today’s scientist is to give answer and
find ways to meet the ever increasing energy demands and at the same time minimize the
side-effects of combustion such as global warming, acid rain, formation of dioxins, depletion
of ozone layer, etc. One way to meet a part of this need is to increase the use of renewable
energy sources like biomass, wind, solar, hydro and geothermal since neither of these sources
increases the atmospheric CO2 concentration, nor are they being depleted. Another positive
benefit with biomass fuels is that they produce oxygen through the photosynthetic process,
which is vital for all living species. This work focuses on the use of biomass fuel in grate fired
systems.
Figure 1. The primary energy supply from 1971 to 2003 in Mtoe1, [4].
1
Mtoe, Million ton oil equivalent, 1 Mtoe = 42 PJ
Chapter 1: Introduction
1.2 Biomass Fuels
Biomass fuel covers a large category of different living species, for example wood, grass,
straw, bagasse, sugarcane, stalks, food and agriculture residuals, etc. Biomass materials all
have their origin from the photosynthetic process. The photosynthetic process can occur in all
living green plants and some bacterias. In the photosynthetic process water and carbon
dioxide react with each other to form glucose (C6H12O6) and oxygen. The glucose is used by
the plant/or bacteria as “food” and oxygen is a “waste” product. The sunlight needed to run
the reaction is absorbed by the chlorophyll in the plants leafs. The same amount of CO2
absorbed by the plant during its growth, due to the photosynthetic process, is released when
the plant dies and decomposes or is combusted. Biomass can in that sense be considered to be
CO2 neutral (i.e. it does not add to the current CO2 level in the atmosphere, nor does it
decrease it).
The biomass fuel is normally classified into different classes depending on its origin. They are
woody (tree, bark), herbaceous (straw, grass), agriculture waste and residuals (sugarcane,
wheat, oats, corn) and refuse-derived fuels and organic waste materials (food, saw dust) [5].
Biomass is unlike coal a very highly volatile fuel with low ash content. The volatile content is
about 80-90 wt-% (dry-ash-free, DAF) for wood. The moisture content for wood can be up to
60 % of the total mass for a newly cut tree and works as heat sink when burning the fuel. For
air dried wood the moisture content is normally around 12-20 wt-%. Due to the high variation
of moisture content, the heating value can vary between 5 MJ/kg for “fresh, newly harvested”
biomass to 20 MJ/kg for dry wood briquettes. This can be compared to coal, whose low
heating value varies from about 22 MJ/kg for lignite to 34 MJ/kg for low volatile bituminous
coal.
1.3 Technologies for Biomass Conversion
There exist two different technologies for converting biomass into useful energy. It is done
either bio-chemical or thermo-chemical. Both processes convert the biomass to either an
energy carrier or to heat. Bio-chemical processes use bacterias to produce the energy carrier.
Examples of such processes are production of biogas, in which bacteria break down organic
waste material (e.g. garbage), which forms methane rich gases, or fermentation of wheat or
wood with ethanol and methanol as final product.
Thermo-chemical processes uses heat to produce the energy carrier. The conversion process is
either done indirectly by converting it to an energy carrier (i.e. liquid, gas or char) or by direct
combustion. The indirect processes are liquefaction, gasification and pyrolysis. Figure 2
shows the different thermo-chemical processes and some of its final products and usages.
Pyrolysis and Gasification
Pyrolysis is thermal decomposition of the wood structure without an externally added
oxidising agent. The pyrolysis products are mainly tar and char; however, due to the high
oxygen content in biomass, considerable amounts of CO and CO2 can be formed. In
gasification the thermal degradation takes place in presence of an externally supplied
oxidising agent. The oxidising agent is normally CO2, O2, H2O or air or a mixture of these.
The gasification products are CO, H2, H2O, CO2 and light hydrocarbons. The pyrolysis
2
Chapter 1: Introduction
process is attractive to use when high tar and char yield are of interest, while gasification are
more suited for gas production.
Liquefaction
Liquefaction is similar to pyrolysis; however, it is carried out at high pressure (100-200 atm)
and low temperatures ( ∼ 500 K) and often together with a catalyst. In the process the biomass
is converted to a liquid, which can be burned in a heat engine or a boiler.
Thermochemical conversion
Liquefaction
Pyrolysis
Liquid/oil
Char
Gasification
Combustion
Biogas
Heat
Propulsion
Electricity
Figure 2. Thermo-chemical conversion processes and their products.
Direct Combustion
Direct combustion of the fuel is the “simplest” way of biomass conversion. The biomass is
combusted in a combustion device where the chemical bond energy is converted to useful
heat. An example of such device is industrial boilers/furnaces.
Boilers for Direct Combustion
The design of a boiler differs depending on many things, for example, fuel type, ash
properties, moisture content, heating value. The combustion chamber in a boiler serves for
two purposes [6]:
1) It should accommodate the combustion process and achieve complete combustion
while at the same time minimize the harmful emissions.
2) It should receive the produced heat in the combustion gases by heat transfer and cool
them enough so ashes can form solid before they leave the combustion chamber.
There exist three main types of furnaces for direct combustion of biomass: fluidised bed,
suspension (pulverised combustion) and fixed bed systems.
In the fluidised bed system (FB), most of the bed material is inert (ashes, sand and sorbents)
only a few percent is fuel. The bed itself rests on a stationary air distributor grate through
which inlet air is injected with high velocity. The inlet air makes either the bed to bubble or
carry away considerable parts of the bed up in the over-fire compartment. In the first case the
3
Chapter 1: Introduction
bed is called a bubbling fluidised bed (BFB) and in the second case circulating fluidised bed
(CFB). A schematic view of the combustion systems can be seen in Figure 3. The inert
material that is carried away in the CFB boiler is recirculated to the combustor by passing
through a cyclone. The mixing in the FB-systems is generally good, which decreases the
amount of necessary excess air in order to ensure complete combustion. The combustion
temperatures are lower ( ∼ 800-950°C) than those in suspension and fixed bed systems. The
low combustion temperature is a result of on the large amount of inert material (ashes, sand
and eventual sorbents) inside the furnace and it is preferable to keep low temperatures to
avoid sintering of bed and ash material in the bed.
Suspension fired boilers have burners placed in the side-walls and the fuel is injected into the
boiler through a burner. A schematic view of a burner and its configuration in a suspension
fired boiler can be seen in Figure 3. The incoming particles are heated by thermal radiation
from the flame and by recirculating combustion gases. The recirculation zone can be created
either by a swirl-generator in the burner or by a bluff-body. The released volatiles are ignited
by the hot gases. Towards the end of devolatilisation the remaining char residual is oxidised
as it follows the flow. The size distribution, volatile fraction and moisture content of the fuel
are important in order to assure complete combustion. The particle sizes need to be small,
preferable below 100 µm, to ensure that the particle will burn out before leaving the boiler.
The moisture content should be low, otherwise it may delay the devolatilisation and char
combustion and lower the combustion temperature. High volatile fuels are preferable to use
since the ignition of volatile promotes the ignition of char, which results in high combustion
temperatures. Air supply is of importance both to secure complete particle burnout and also to
avoid formation of NOx.
Flame
Air
Fuel
Fuel
Air
Figure 3. A schematic view of burners, their configuration in a suspension fired boiler (left)
and a circulating fluidised bed boiler (right).
Fixed bed furnace has a fuel bed resting on a grate and the grate can be fixed, moving,
rotating, or vibrating. The simplest form of a fixed bed system is a campfire, where the
4
Chapter 1: Introduction
combustion air is fed through natural convection. However, for industry purposes the systems
are more sophisticated. Examples are wood stoves and pellets burner boilers for house heating
and stokers. Stokers are typical for heat and power production and can be divided into three
main categories: crossfeed, overfeed and underfeed [7]. The systems are designed in such a
way that drying, devolatilisation and char combustion take place in the bed.
In the crossfeed stoker the fuel is fed onto a horizontal or sloping grate where it is being
consumed as it travels along the grate, see Figure 4. Primary air is added from beneath the
grate and moves upward through the bed. The conditions in the bed are fuel-rich and the
volatiles leaving the bed react with secondary air and burns above the bed.
Figure 4. Sketch of a crossfeed furnace.
In an overfeed stoker the fuel is added on top of the grate. The fuel is moving downwards as it
is being consumed. Primary air moves upwards through the bed. The fresh fuel added at the
top of the bed is heated through thermal radiation coming from the volatile flame above the
bed and by hot gases coming from exothermic reactions taking place further down in the bed.
A schematic view of an overfeed stoker is seen in Figure 5.
5
Chapter 1: Introduction
CO, H2, CH4, Tar, …
Secondary air
Fuel
Drying
Devolatilisation
Gasification
Char oxidation
Ash
Grate
Primary air + Flue Gases
Figure 5. An overfeed stoker.
The underfeed stoker is different from the two other stokers in that the fuel and air are
supplied together to the bed, see Figure 6. The combustion takes place in the upper part of the
bed and the released volatiles and moisture pass through the reaction zone as they leave the
bed.
Secondary
air
Secondary
air
Primary
air
Figure 6. An underfeed stoker for heat production.
The main advantage with fixed bed combustion, compared to the other systems, is that it can
combust fuel with high moisture content ( ≤ 60 wt-%), varying size distribution, high ash
content and large variety in fuel mixture (i.e. mixture of different fuels). Other benefit with
grate fired combustion is that the technology is rather cheap compared with fluidised bed and
suspension combustion technology.
1.4 Problems related to Biomass Combustion in Grate Fired Boilers
The Fuel Bed Problem
Even though the grate fired bed is robust and well-proven technology it still suffers from
certain drawbacks. A common source of problem is the fuel bed. The drying, devolatilisation
and char oxidation processes occur irregularly along the grate. As a result the volatile
6
Chapter 1: Introduction
formation will be uneven and rich fuel volatile zones inside the boiler can be formed; the
secondary air may be unable to fully oxidise the volatiles before the flue gases leave the
boiler. In order to ensure acceptable oxidisation of the volatile is it necessary to add high
amount of excess air.
The char particle in the bed is another source of problem since it is sometimes difficult to
completely burn out the char before it leaves the grate. This leads to that significant amounts
of char can remain in the bottom ash. The small char and ash particles can also follow the gas
flow and cause erosion on heat exchangers and boiler walls.
Other bed related problems are burnouts and channel formations [8]. Burnouts cause damage
to the grate since they burns holes in the fuel-bed and exposes the grate to high surrounding
temperatures. This results in increased material wear and increased emissions of pollutants.
Channel-formation occurs over a part of the bed where the pressure drop is low. Most of the
primary air in that zone will then go through the channel. If the fuel is dry enough to burn
then it will result in a local burnout zone. Channel-formations are common to occur near the
furnace walls [8].
Pollutant Emissions
Practical combustion always involves emissions. The species that evolves not only depend on
the fuel but also depend on the combustion conditions, e.g. equivalence ratio, residence time,
temperature, air supply, etc. Some of the evolving species affect our environment and human
health negatively. It is therefore important to know how the pollutants are formed and find a
way to lower emissions of pollutants.
Emissions coming from renewable fuels, like biomass, can be divided into two different
groups: (1) emissions with origin from complete combustion and (2) emissions whose origin
comes from incomplete combustion. Emissions from the first group are CO2, NOx, SOx and
particle matter. Emissions from the second group are CO, unburned hydrocarbons (UHC),
particle matter and dioxins.
CO2 is a non-toxic and non-combustible gas, which is formed as a result of complete
combustion. It is the major source for global concern due to its green-house effect on the
environment. However, CO2 is also one of the essential gases for sustaining life due to its
importance in the photosynthesis reaction that produces oxygen. The main advantage with
biomass compared with fossil fuel, is that during its growth the plant/tree uses CO2 to make
glucose and thus when combusting the plant/tree it releases the same amount CO2 as it was
consumed during its growth.
NOx is a group name for different species of nitrogenous oxides. The most common of these
in combustion processes are NO and NO2 [9]. In the case of fluidized bed combustion
systems, significant emissions of N2O can be emitted as well [6, 9]. NOx is a green-house gas
and can also cause smog which is dangerous to the human body and the environment. It can
also deplete the ozone layer in the atmosphere and it can cause acid rain.
The main contribution of NOx emissions, in biomass combustion, comes from the nitrogen
bond to the fuel [10-13]. Thermal and prompt NOx occur at high combustion temperatures. In
biomass combustion the moisture content is often high and this works as a heat sink keeping
7
Chapter 1: Introduction
the combustion temperature low inside the boiler (800-1200°C) [10]. Thus the thermal and
prompt NOx emissions are low.
SOx is a group name for sulphur oxides (SO2 and SO3). It forms from sulphur compounds in
the fuel and the emitted sulphur oxides react with water vapour in the atmosphere, which
forms H2SO4 (sulphur acid). The sulphur content in biomass is rather low and it comes
mainly from sulphur compounds which have been absorbed during the growth of the tree.
CO and UHC are both formed as a result of incomplete combustion. CO is a toxic gas,
without colour or smell. It can be regarded as a good indicator of the combustion quality in
the combustion device. UHC is a group name for many different hydrocarbons; certain UHC
species like C6H6 are toxic, and others species like CH4 significantly adds to the greenhouse
effect.
Particle matter comes from both incomplete and complete combustion and it can consist of
both inorganic materials such as ashes and organic material such as char particle and soot.
The particles are small (0.1µm-10µm in diameter) and can interfere with the breathing system
and cause damages on the lungs.
Dioxin is referred to as a group of species consisting of two benzene rings which are
connected to each other by one or two oxygen atoms. The chloride atoms are then connected
on the benzene rings. Dioxin is very hazardous for the human body due to the fact that it
causes cancer, damages the immunity system and interferes with the hormonal system [14].
Dioxin is unstable and it easily breaks down to form other species above 800-850°C [6].
Therefore, the impact of dioxin can be greatly decreased by having a residence time of two
seconds above 850°C for the combustion gases. Even though biomass wood generally
contains trace elements of chlorine, it was found by Nussbaumer et al [12], that significant
concentrations of dioxin were formed when urban waste wood and demolition wood were
combusted.
1.5 Studied Boilers
Two grate-fired boilers and one pellets-fired reactor have been studied in this thesis work.
The grate-fired boilers are part of district heating plants and their thermal outputs are on 3050 MW. The pellets-fired reactor is an academic device, useful for validation of numerical
models. More details about the different cases can be found in [10, 15-20]
A 50 MW Grate-Fired Boiler
The investigated large-scale boiler is located at the Flintrännan Fjärrvärme Central (FFC)
plant, which belongs to E.ON. The fuel energy input is 50 MW based on the lower heating
value (LHV) and the power plant produces 55 MW of heat, which is used for district heating.
40 of the 55 MW comes from the boiler, an additional 15 MW comes from flue gas
condensation, where the heat from the steam is taken out. The overall efficiency of the plant is
107 % based on the higher heating value (HHV) and the boiler efficiency is 89 % [17]. A 2-D
view of the boiler can be seen in Figure 7. The dimension of the boiler is 12.15 meters in
height, 6.52 meters in width and 5.80 meters in depth. It is fired with wood chips with a high
moisture content (~40 wt-%). The fuel is fed mechanically into the bed and there it moves
slowly downward along the bed as it is consumed.
8
Chapter 1: Introduction
Figure 7. Sketch of the 50 MW fixed bed boiler studied in this work.
The boiler is constructed in such away that it will give low emissions, especially NOx. This is
achieved in two ways: (1) the high moisture content in the fuel works as a heat sink, thus
decreasing the temperature inside the boiler and (2) the use of flue gas recirculation to cool
the bed and combustion gases [15, 16]. The arrows in Figure 7 represent air and flue gas
inlets; each number represents a certain inlet. The roman numbers represent different bed
sections. Flue gas is injected together with air at inlet 1, 3, 6 and 7. Section I is a drying zone
and here hot flue gases, taken from above section 4, are injected to dry the wet fuel.
Devolatilisation takes place in section II and the remaining char is oxidised in section III and
IV. The remaining ash is removed from the bed after falling down through section IV. The
volatile matters leaving the bed move upward and are mixed with air as they pass through
inlet 6 and 7. The two inlets consist of six air jets that are placed on one side (inlet 6) and five
air jets on the opposite side (inlet 7). As the inlets blow towards each other they form a socalled “air curtain”. The volatiles are further oxidized as they pass through the air curtain.
Above the air curtain tertiary air is introduced through four air jets, one jet on each side of the
wall. The angle of these jets are so arranged that they form a strong swirling flow structure to
increase the mixing of volatile/air and to assist the combustion gases to form final products,
i.e. H2O and CO2. The swirler also enhances the residence time for the combustion gases and
eventual small char particle which might fly around in the boiler.
9
Chapter 1: Introduction
The points named M-2, M-3 and M-9 are measurement ports, from which experimental data
have been collected. At each port a probe has been used to measured temperature and species
concentrations at different positions along the z-direction, i.e. the depth direction in Figure 7.
The measured species are CO, unburned hydrocarbon (UHC) and oxygen. More details about
the experimental work and the equipment used can be found in [10, 15-17].
To further decrease NOx emissions from the FFC boiler, a system called ECO-tubes was
installed in 2001/2002. The ECO-tubes are two six meters long water cooled pipes which are
inserted 4.8 meters into the boiler. A sketch of the ECO-tubes can be seen in Figure 8 and
Figure 9.
Figure 8. A sketch of the ECO-tubes (1 & 2), the angle of the air jets and the position of the
ECO tubes in the boiler.
Outer row
Inner row
Figure 9. A schematic view of the ECO-tube system, seen from the top of the boiler.
Each of the ECO-tubes has two rows of small holes, each row consists of 20 holes, see Figure
10. The diameter of each hole can be varied. B stands for blocked; 13, 19 and 25 stand for the
hole-diameter in mm. The angle between Row 1 and Row 2 is fixed to be 150°. However, the
ECO-tubes can be rotated ± 45°and the angles on ECO-tube 1 and 2 are given by α and β
respectively, see Figure 8. α and β are changed depending on the load of the boiler. High
10
Chapter 1: Introduction
speed air flow (~100 m/s) is injected through the small holes on the ECO-tubes and it
increases the residence time and mixing of combustion gases.
Figure 10. A sketch of the ECO-tubes with the hole diameters. B: blocked holes
The ECO-tube system takes air from the air inlets to the bed and the lower regions of the
boiler. The removing of air from the bed and the lower parts of the boiler results in a low
oxygen concentration in the region. Thus, the ECO-tubes works like an air staging unit. The
lack of available oxygen prevents the NOx precursor compounds (i.e. HCN and NHi) from
reacting to form NOx. The increased mixing and gas residence time promote the reduction of
NOx since the formed NO can be reduced to N2 due to reaction between NO and NHi.
A negative effect of this air staging is the increased possibility of unburned volatile emissions.
This effect is avoided by optimizing the angle and air mass flow of ECO-tubes in order to
improve mixing and residence time of the reactants and thus maintaining low emissions of
NOx and unburned volatile.
A 31 MW Grate-Fired Boiler
A two dimensional sketch of the 31 MW furnace studied in this work is seen in Figure 11.
The furnace has the dimensions 9 x 12 x 5 meters (in x-, y-, z-direction) and it is an crossfeed stoker with a reciprocating sloping grate. The boiler is produced by Kvaerner and the
heat output of the district heating plant is 31 MW. Of the 31 MW 25 MW is taken from the
furnace (17 MW in the convection area and 8 MW from tube walls), the remaining 6 MW is
delivered from flue gas condensation [18, 19]. The furnace is fired with wet wood chips (a
moisture content of 35-55% on mass basis). The ultimate composition of the fuel is estimated
to 50%, 45% and 5% for C, O and H elements, respectively [18]. The fuel enters the bed from
the left side, see Figure 11 and the wet wood chips are dried and gasified into char and
volatile by heat from the flames, above the bed. The primary air is preheated to 150°C and
added from underneath the grate through five air zones. Above the bed recirculated flue gases
is injected, through 6 inlets, to both enhance the mixing between reactants and to decrease
combustion temperature and thereby lowering NOx production. The volatiles are oxidized to
final products, i.e. H2O and CO2 as they pass through the “neck”, where secondary air is
added from an air curtain. The air curtain is composed of two rows of each 21 air nozzles,
which inject high speed secondary air.
11
Chapter 1: Introduction
Measurements were carried out on four different heights (roman numbers I-IV in Figure 11)
and on each level temperature and species were measured at various horizontal depths. More
information about the measurement can be found in [19].
IV
Flue Gas
III
Sec. Air
Recirc. Flue Gas
Sec. Air
II
Fuel
I
Primary Air
Ash
Figure 11. A two-dimensional sketch of the boiler.
A 8 kW Pellets-Fired Reactor
The investigated system can be seen in Figure 12. It is an 8-11 kW updraft pellets fired
reactor and it consists of a 1.7 meter high cylinder that has a diameter of 0.2 meters. The first
1.2 meters of the rector is insulated, the remaining 0.5 meters has no insulation. At the bottom
of the cylinder a pellets burner is connected. The burner is supplied with wood pellets, which
are mechanically fed from one side of the cylinder and falls down on the grate. Primary air
enters through the grate, which consists of 32 holes with a diameter of 3 mm. Secondary and
tertiary air is supplied 60 and 75 mm above the grate, respectively. Both air inlets consist of
12 holes with a 4 mm diameter, placed symmetrically around the centreline. The secondary
air is injected with an angle of 30° to the horizontal plane. Numbers 1 to 9 represent
12
Chapter 1: Introduction
measurement ports where gas probes can be sidinserted. The first measurement port is located
145 mm above the grate. The distance between the first six ports is 100 mm, thereafter the
distance is increased to 200 mm between ports 6-8 and 400 mm between ports 8 and 9. More
details are found in [20].
10
Insulation
200
9
400
8
7
200
6
5
4
3
2
1
Fuel
Tertiary air
Secondary air
100
145
Inlet 3
Inlet 2
Grate
Primary air
Figure 12. A sketch of the experimental reactor and the pellets burner, dimensions in mm.
1.6 Objectives and Scope of This Work
Practical combustion for heat and power production always contains formation of pollutant
species. These species are of great concern due to their effect on the climate and on the public
health. The amount of emitted pollutants from combustion devices is continually being
limited due to stricter legislation. As a result the energy producer and boiler manufacturer, in
the heat and power sector, are forced to improve the combustion efficiency and furnace
operation on their plants continually. The improvement can be done either through
experiments or by using Computational Fluid Dynamics (CFD). The first method is necessary
but expensive and thus often limited to a few points inside the furnace, especially for largescale facilities and it can be difficult to study combustion processes inside the boiler. The
latter method, the usage of CFD, is cheaper and the combustion processes and pollutant
formation occurring inside the boiler can be studied more in detail. The effect of geometry
can also be studied, which makes it a useful tool for the boiler manufacturer, who can study
which geometry is preferable to use in terms of combustion efficiency and pollutant
formation. However, the success of CFD depends on the accuracy of the numerical methods
and the physical/chemical models employed. These models need to be validated against
measurement data and sometime tuned for each given problem.
13
Chapter 1: Introduction
The objectives for this work have been to study the combustion process phenomenon
involved in grate fired biomass boilers using CFD method. The aim is to increase the
understanding of the physical processes occurring inside a boiler and to be able to model them
in an accurate way. The work covers most of the processes occurring in a grate fired boiler,
the different aspects considered in this thesis work are summarised Figure 13.
Boiler
Design
Pollutant Emission
• Fuel-NOx
• Residence Time
Heat Transfer
by Radiation
Volatile oxidation
Wood chips
Bed Modelling
• Global Model
• Detailed Models
o Two-zone
o Three-zone
o Two-dimensional
I
II
III
Air/flue
gas
IV
Figure 13. Different aspects considered within the thesis work.
The goal of this work has been to develop reliable modelling tools, for simulation of grate
fired boilers. The work has been divided into the following areas:
•
•
•
•
•
•
Bed modelling
Radiation modelling
Modelling of boiler air staging
Modelling of pollutant emissions
Volatile oxidation modelling
Improvement of numerical methods
Bed modelling
The bed modelling has been carried out by first modifying an existing two-zone model for
counter-current coal gasifier to biomass combustion. The two-zone model assumes that drying
14
Chapter 1: Introduction
and devolatilisation take place in one zone and char oxidation/gasification in another zone.
The two-zone model is further extended into a three-zone model, where drying,
devolatilisation and char oxidation/gasification take place in separate zones and the bed is
changed from overfeed to crossfeed. A quasi two-dimensional bed model is developed
considering heat and mass transfer within the particles.
Radiation modelling
Considerable amounts of H2O and CO2 are formed during the combustion of wet biomass.
Small char particles and fly-ash may leave the bed and follow the flow up in the boiler and
participate in the thermal radiation, together with soot. The radiative effect of small particle,
soot and hot combustion gases, on the temperature predictions are evaluated using several
different radiation models.
Boiler design, Pollutant emissions & Volatile oxidation
An air-staging unit was installed in the FFC boiler and the effect of this new design on the
combustion process is studied, both experimentally and numerically. A numerical study of the
flow residence time has been carried out to examine whether it is possible to co-fire wood
chips together with refuse-derived fuels and organic waste materials. Different models for
calculation of NOx formation in boilers were tested and compared with measurement data.
Numerical methods
The area of the air-inlets in boilers is often small compared to the grid-size in boiler
calculations. As a result the momentum flux is often not properly modelled at the inlet. This
leads to erroneous flow field. An area correction method is proposed for adjustment of the lost
momentum and thereby improving the flow field and combustion simulations.
15
Chapter 1: Introduction
16
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
2 Modelling of Biomass Combustion in Grate-Fired Bed
Modelling of solid fuel conversion in a grate-fired bed is a complex problem involving not
only chemical (homogeneous and heterogeneous) reactions but also mass and heat transfer in
the solid particles and between solid particles and surrounding gas. The solid particles in the
bed have different properties, sizes and shapes and these have to be taken into account in the
modelling of the bed conversion. As the fuel burns, the thermo-chemical reactions occur
unevenly inside the bed. This leads to uneven gas distribution over the bed and it may lead to
cracks and channels through the bed. To model a full-scale bed in a boiler by taking into
account all processes occurring in the bed is not yet possible. It would require too much
storage and computational resources. Instead, certain simplifications and assumptions have to
be made.
2.1 Physical and Chemical processes
The biomass combustion process in grate fired bed can be divided into different sequences.
They are the drying, the volatile formation due to thermal decomposition, the reduction and
oxidation of volatile and finally the gasification and oxidisation of the char residual.
Solid fuel conversion process always starts with drying process. The fuel particle is heated up
through convection from the hot surrounding gases, conduction from neighbour particles and
through thermal radiation. The heat received by the particle is transported by conduction into
the particle. As the particle temperature reaches 100°C the particle is dried. The water leaves
the fuel as steam which cools down the outer surface of the wood. The drying needs heat to
proceed, and this in return lowers the temperature in the combustion device. As a “rule of the
thumb” is it not practically feasible to burn wood with moisture content above 60 wt-%. The
energy needed to evaporate the moisture would be more than the energy “produced” by the
combustion.
Volatile formation involves both pyrolysis and gasification and it can be called
devolatilisation for simplicity. The volatiles leave the fuel through pores and cracks in the
structure. As the volatiles reach the surface they react with the surrounding air and burn as a
diffusion flame. Heat from the gas combustion is transferred into the particle and supports and
enhances the drying and devolatilisation processes. The temperature of which devolatilisation
of wood takes place is between 200-500°C [5, 21, 22]. The degree of devolatilisation depends
on the final temperature and heating rate. If the final temperature is below 500°C, some
volatile will remain in the fuel and this will result in a greater char yield. However, with final
temperatures above 500°C devolatilisation becomes complete and what remains is a particle
of char and ash.
During devolatilisation is it difficult for the surrounding oxygen to reach the particle surface
due to the outgoing flow of volatiles. After devolatilisation is complete the oxygen molecules
can reach the particle surface and react with the char structure. Char evolves primary from
lignin, however, Svenson [23] showed that during fast pyrolysis of birch samples that even
hemi-cellulose can make large contributions to char evolution. The concentration of char
depends largely on the final temperature and heating rate. Slow heating rates gives enhanced
char yield since the evolving tar gets time to repolymerise and form char. High heating rates,
on other hand, drives out the volatile much faster and tar is cracked to lighter gases, thereby it
lowers the char yield. However, char yield depends mostly on the final temperature since a
17
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
high final temperature allows for more of the hydrocarbon structure to be broken down to
volatile.
Char oxidation is a often slow diffusion controlled process. The time it takes for the char to
oxidize depends on the surrounding temperature, char surface area and available oxygen. The
surface area depends on the porosity of the char residual since the oxygen diffuses into the
char through pores and cracks. The main products evolving during char oxidation is CO and
CO2.
2.2 Review of Bed Models
Much of the modeling done on fixed bed combustion in the past has been for coal
combustion. A comprehensive review of fixed bed coal models can be found in Hobbs et al.
[24]. In the review 37 different bed models are mentioned, of which six are zero dimensional,
27 are one dimensional and four are two dimensional. In recent years a number of fixed bed
models for biomass combustion have been developed [25-28]. All of these models are one
dimensional.
A steady state one dimensional model for downdraft biomass gasification was presented by
Giltrap et al. [25]. The model does not consider drying or devolatilisation, instead, it only
focus on combustion and gasification of char and volatiles. The volatile composition is
calculated by assuming that the biomass fuel has the formula of CH3.03O1.17 and it forms CO,
CH4 and H2O. Contribution from drying is considered by adding H2O to the product gases.
All oxygen is assumed to react with char to form CO and the remaining char is gasified by
CO2, H2O and H2, where H2 comes from reaction between CH4 and H2O. The model
considers no tar. When compared to experiments the results are reasonable for CO and CO2,
however, the other gases do not agree well, especially CH4 that is over-predicted by a factor
5.
Brunch et al. [26] presented a general model to cover the entire conversion process of biomass
fuel, from drying to char conversion. The bed is considered to be built up by a finite number
of packed particles, where each particle is modelled in one dimension. Heat transfer between
the particles is considered as well as particle shrinkage. However, shrinkage is assumed to
take place during char combustion and not during drying and devolatilisation. The volatile
that leaves the bed are assumed to be inert and not react with each other. When compared
with experiments it is found that the model works well for describing conversion of dry
particles at high heating rates. However, devolatilisation of wet particles is under-predicted.
Char conversion is well captured.
Shin and Choi [27] model the combustion of municipal solid waste (MSW) in a cross-current
bed using a one dimensional transient bed model and compared it with results from a one
dimensional wood gasifier. It was found the dominating mode of heat transfer in the bed was
due to radiation between particles. In the model drying, devolatilisation and char combustion
are assumed to occur in different stages where no stage can occur before the previous one is
finished. Unlike the Brunch et al model [26] the volatile and char from devolatilisation react
with surrounding oxygen to form products.
Thunman and Leckner [28] developed a one dimensional bed model to study the combustion
front in a countercurrent bed. The bed is built up by equally large particles and the conversion
of each particle is studied using a comprehensive particle model. The particle surface and the
18
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
gases flowing out from the surface are considered. The volatile species concentration is
estimated by energy, mass and species balance over the particle. Six volatile species are
considered. Empirical relations are used to calculate CO/CO2 and CiHj/CO2 ratios. The model
is very detailed and shows good comparison when it compared with experiment.
In many previous works the three dimensional bed has been approximated by a countercurrent gasifier where the fuel conversion are assumed to occur in stages as seen in Figure 14.
The gas composition, leaving the bed is distributed by the user and is often matched to
available experimental data. In this work four different bed models have been used. Three of
those are developed for counter-current gasifiers, similar to the one in Figure 14 and can be
used for over-feed stokers.
Wet fuel
Volatile
CO, H2, CH4, Tar, …
Drying
Tgas
H2O
Devolatilisation
Wood
dry wood
volatile + char
C+CO 2 → 2CO
Tsolid
Gasification
CO2
Char oxidation
Wet wood
H2O
C+H 2 O → CO+H 2
C+2H 2 → CH 4
λ C + O 2 → 2 ( λ − 1) CO + ( 2 − λ ) CO 2
Ash
O2
Primary air + Flue Gas
Figure 14. A schematic view of a counter-current bed.
2.3 Bed Models
Three different zero-dimensional bed models and one quasi two-dimensional bed model have
been examined in this work for determination of boundary conditions of the upper surface of
the bed. The first model, a semi-empirical model, is a rather simple model, which works well
for simple pellets burners. It adds the incoming fuel and air together and forms a fuel-species
in the form CaHbOcNd and assumes the fuel-species breaks down into a certain number of
gaseous species that leave the bed. The temperature of the gases leaving the bed is calculated
by energy conservation. The second and third models divided the bed into two respectively
three zones and assumes that drying, devolatilisation and char oxidation take place at different
zones and at different temperatures for each zone. The last model is a quasi two-dimensional
bed model, which assumes the bed to consist of a finite number of spherical particles.
19
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
2.3.1
A Semi-Empirical Bed Model
A semi-empirical model is used for modelling a pellets burner, where fuel is added from the
top and falls on a grate and primary air is added beneath the grate (cf. section 1.5, Figure 12).
The effluent gas compositions, mass flow and temperature from the bed conversion are
calculated by applying mass, element and energy conservation of incoming fuel and primary
air to the bed. First, the moisture flow and the mass flow of the dry ash free wood are
calculated.
mtot = m f + ma
(2.1)
mH 2O = Ym m f
(2.2)
m f , daf = (1 − Ym − Yash )m f
(2.3)
mtot : total mass flow to the burner [kg/s]
mH 2O : total mass flow of moisture in the fuel
m f : total mass flow of fuel to the burner
ma : total mass flow of primary air to the burner
m f , daf : total mass flow flow of dry ash free fuel to the burner
Yash : mass fraction of ash in the fuel
Ym : mass fraction of moisture in the fuel
The element composition of fuel and air are given. From element conservation the mass
fraction of C, H, O and N can be computed.
YC =
Y f ,C ⋅ m f , daf
Y f , H ⋅ m f , daf +
YH =
(2.4)
mtot
2 ⋅ wH
mH 2O
wH 2O
mtot
Y f ,O ⋅ m f ,daf + Ya ,O ⋅ ma +
YO =
wO
mH 2O
wH 2O
mtot
YN =
Y f , N ⋅ m f ,daf + Ya , N ⋅ mH 2O
mtot
(2.5)
(2.6)
(2.7)
Y f ,C : mass fraction of carbon in the fuel
Y f , H : mass fraction of hydrogen in the fuel
Y f ,O : mass fraction of oxygen in the fuel
Y f , N : mass fraction of nitrogen in the fuel
wi : molecular weight of species i [kg/kmole]
The volatile species are assumed to be CO, CO2, H2O, O2, N2, CH4 and tar. The number of
species is 7 and the number of equations is 4. This means that the system is not closed. To
20
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
simplify the problem it is assumed that nitrogen is inert it is in the form of N2. CO, O2 and
CO2 are assumed to be known from experiments. By applying element conservation for
oxygen H2O can be obtain from equation (2.8).
YH 2O =
wH 2O ⎛
2 ⋅ wO
2 ⋅ wO ⎞
w
− YO2
⎜ YO − YCO O − YCO2
⎟
wO ⎜⎝
wCO
wCO2
wO2 ⎟⎠
(2.8)
The mass fraction of unburned hydrocarbons (i.e. CH4 and tar) is calculated from the law of
mass conservation,
(
YUHC = 1 − YCO + YCO2 + YO2 + YN2 + YH 2O
)
(2.9)
From element conservation of carbon and hydrogen the carbon- and hydrogen-fraction in the
unburned hydrocarbons can be calculated, equations (2.10) and (2.11).
YCS = YC − YCO
wC
w
− YCO2 C
wCO
wCO2
YHS = YH − YH 2O
2 ⋅ wH
wH 2O
(2.10)
(2.11)
The amount of CH4 and tar can be obtained from calculating the quota between them,
equations (2.12) to (2.14). Tar is assumed to be composed of a mixture of C10H8 (67%), C6H6
(17%), C7H8 and C8H10 (each 8%) and it is represented as C9.2857H8.1429 [10].
YCS
x ⋅ wC
−
YCS + YHS
wTar
w
x ⋅ wC
X2 = C −
wCH 4
wTar
X1 =
QUHC =
X1
X2
(2.12)
(2.13)
(2.14)
x : number of carbon atoms in the tar, 9.2857
y : number of hydrogen atoms in the tar, 8.1429
wtar :12 x + y, 119.57 [kg/kmole]
Once the quota is known the mass fractions of CH4 and tar can be determined by multiplying
the quota with the amount of unburned hydrocarbons, equations (2.15) and (2.16).
YCH 4 = QUHC ⋅ YUHC
YTar = (1 − QUHC ) YUHC
(2.15)
(2.16)
Once the species composition leaving the bed is known, the enthalpy of the volatile gases can
be calculated by applying a heat balance over the bed, equation (2.17). The species enthalpy,
hi, is a polynomial function of temperature, equation (2.18). The temperature can be solved by
combining equations (2.17) and (2.18), which results in equation (2.19).
21
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
m f LHV + ma ha = mtot ∑ Yi hi
∑ Y h = aT
i i
(2.17)
i
2
+ bT + c
(2.18)
i
⎛ m LHV + ma ha
⎞
⎛ b ⎞ ⎛ 1 ⎞
T = − ⎜ ⎟ + ⎜ ⎟ b 2 − 4a ⎜ f
− c⎟
mtot
⎝ 2a ⎠ ⎝ 2a ⎠
⎝
⎠
(2.19)
LHV : lower heating value of the wet fuel [MJ/kg]
2.3.2
Bed Models with Comprehensive Chemistry
The two-zone, three-zone and quasi two-dimensional bed models are based on a
comprehensive chemistry. The fuel in the two-zone and three-zone model is thermally thin
and devolatilisation is modelled by the FG-DVC model. Char oxidation is modelled using
equilibrium calculations. The quasi two-dimensional model is a detailed model, which was
developed from the single particle model proposed by Thunman et al. [29]. The model
assumes the bed to consist of a number of thermally thick particles and it takes into account
the heat and mass transfer occurring inside each particle. A description of the different bed
models used in this work is given below.
FG-DVC model
The FG-DVC model was first developed for devolatilisation of coal [30-32]. It consists of two
different sub-models, a functional group model (FG) and Depolymerisation, vaporisation and
cross-linking model (DVC). The FG model predicts how the fuel decomposes to form light
gases and the concentration of these gases. At the same time, the DVC model treats the fuel as
a large network connected by breakable and unbreakable bridges. As decomposition starts the
network starts to break to form fragments through bridge breaking (depolymerisation) and
cross-linking (repolymerisation). The cross-linking and bridge breaking processes compete
with each other and the size of the fragments depends on competition between the two
processes. The lightest of these fragments evaporate as tar while the heavier forms char. In the
FG-DVC model the DVC-submodel [31, 33] predicts how much tar and char is formed and
supplies this data to the FG model [33-36]. The final amount of char is calculated in the FG
model by summing the loss of gases and tar and adding the amount of char coming from
cross-linking of tar.
The DVC sub-model may not be needed for devolatilisation of biomass [37, 38]. Tar may be
treated like other volatile species in the biomass FG-DVC model. It does not, like in the case
of coal, have to compete with other species about precursor material [38]. Therefore, only the
FG model will be described here. First, a brief introduction to the functional group theory will
be given below.
The Concept of Functional Groups
There exists a wide range of different organic compounds. Each of these compounds has
different chemical and physical properties. They can be categorized according to their
chemical reactivity into a few groups, where each group has a similar reactivity. Each of these
22
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
groups is called a Functional Group (FG). A functional group is an atom or a group of atoms,
which has a characteristic chemical behavior and is a part of a larger molecule [39]. One
expects that functional groups behave similarly for all molecules they are part of, during
thermal decomposition. When a piece of wood decomposes each FG is released at different
temperatures and forms certain gases. In coal conversion many different species can evolve
from decomposition of one functional group, however, for biomass each evolved species
often comes from decomposition of just one certain functional group [37].
In practise, the functional groups are not used explicitly. Instead, the product gases from the
decomposition of the functional groups are used. To obtain which gases evolve and their
kinetic data a pyrolysis experiment has to be carried out. A detailed description of the
procedure can be found in [40]. The evolution of the product gases is then described with
single step Arrhenius expressions. Some of the common functional groups are given in Table
1 [41].
Table 1. Common Functional Groups [41].
Functional Group
C=C
C ≡ CH
F, Cl, Br, or I
Name
Example
Alkane
CH3CH2CH3 (propane)
Alkene
Alkyne
Alkyl halide
Alcohol
Ether
Amine
CH3CH=CH2 (propene)
CH3C ≡ CH (propyne)
CH3Br (methyl bromide)
CH3CH2OH (ethanol)
CH3OCH3 (dimethyl ether)
CH3NH2 (methyl amine)
Aldehyde
CH3CHO (acetaldehyde)
Ketone
CH3COCH3 (acetone)
Acyl chloride
CH3COCl (acetyl chloride)
Carboxylic acid CH3CO2H (acetic acid)
Ester
CH3CO2CH3 (methyl acetate)
Amide
CH3NH2 (acetamide)
A Functional Group Model
The functional group model, FG, is based on the concept that the fuel consists of
combustibles, ash and moisture. Ash and moisture is assumed to be inert and can be left out
from the calculation. The combustibles (char and volatile) are seen as an organic material
consisting of a large number of functional groups that decompose at different rates [42]. As
the fuel decomposes due to thermal breakdown the functional groups detach from the fuel
23
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
molecule and decompose independently from one another to form certain product gases. This
can be illustrated by Figure 15.
(a)
(b)
Carboxyl
CO2
Carboxyl
(c)
CO2
Alcohol
H2O
Alcohol
H2O
Ketone
Ketone
CO
CO
Amine
Amine
HCN
HCN
Non volatile
carbon
Functional group
Composition of wood
Non volatile
carbon
Non volatile
carbon
Devolatilisation
Devolatilisation
complete
Figure 15. Progress of devolatilisation according to functional group model.
Figure 15a shows the functional group composition in the wood and initial devolatilisation
when carboxylic acid and alcohol form CO2 and H2O respectively. Figure 15b shows later
stage devolatilisation and Figure 15c shows complete devolatilisation where only char
remains, represented by the functional group non-volatile carbon. The decomposition of the
individual functional group, i, can be expressed by a rate constant, ki, which is given by an
Arrhenius expression:
ki = Ai exp((− Ei ± σ i ) / RT )
(2.20)
Ai : pre-exponential factor
E i : activation energy
σi : width of distribution of activation energy
The evolution of each gas species is calculated according to a first order reaction:
∂Yi
= kiYi
∂t
(2.21)
Yi : mass fraction functional group i
Initial value of Yi is obtained through experiment. The rate of char formation in the FG model
is opposite to that of gas formation, therefore, the rate of char formation can be written as
follows:
∂Y (char )
⎛ ∂Y ⎞
= −⎜ i ⎟
∂t
⎝ ∂t ⎠
(2.22)
A weakness with the FG model is that in order to use it one must know the initial functional
group composition (i.e. gas composition) and the kinetic data. If this is not known the
functional groups can be extracted from a similar fuel, (i.e. a fuel that has roughly the same
24
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
ratios of oxygen over carbon and hydrogen over carbon). The yields of the functional groups
of the unknown fuel are assumed to be similar to that of the similar fuel in the O/C vs H/C
plot [37], see Figure 16. The yields, from the known fuel, are adjusted by matching the
elements of the functional groups so the total sum matches the ultimate composition of the
unknown fuel. Further details about this procedure have been described elsewhere [43]. The
functional groups used in this work are those described by Chen et al [37] for populus
deltoides, which has an ultimate analysis similar to the fuel used in this work. Each functional
group has been adjusted to fit the ultimate composition of the known fuel.
Populus
deltoides
FG’s know
Yi
CO2
H2
CH4
CO
H/C
Wood chips
H2O
Tar
Unknown FG’s
O/C
Adjustment of
Pop. Delt. FG’s
Yi
Tar
CO2 H2
CO
H2O
CH4
Figure 16. Adjustment of Functional Groups.
2.3.3 The Two-Zone Model
The two-zone model, used in this work, was developed by Hobbs et al [42-44] for coal
conversion in a counter-current bed. It is more detailed compared with the semi-empirical
model. As seen in Figure 17, the bed is divided into two zones, a drying and devolatilisation
zone (DD) and an oxidation and gasification zone. The main assumption is that oxidation and
gasification occur at much higher temperature than drying and devolatilisation. This
temperature difference creates a natural border between the two zones. Therefore, the bed can
be divided into two zones with different temperatures. The temperature in the DD-zone is
referred to as Texit and in the oxidation and gasification zone it is referred to Teq. The high
temperature oxidation and gasification zone is called Equilibrium zone (EQ) and the gases
produced in this zone are assumed to be in chemical and thermal equilibrium. This can be
justified due to the fact that the high temperature in the zone favors chemical and thermal
equilibrium. The gases produced in the DD-zone are also assumed to be in chemical
equilibrium. It should be noted that in the case of the coal conversion tar was not in
equilibrium and therefore this zone was a partial equilibrium zone.
25
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
Product Gases
Texit
Wood
Drying & Devolatilisation
Texit
Q1
Char
Texit
Equilibrium T
eq.
Gases
Gasification & Oxidation
Q2
T
eq.
TGas
Ash
Flue Gas + Air
Figure 17. Two-zone bed model for a counter-current bed.
Devolatilisation and char formation is modelled by the FG model. The species composition
and temperature are determined by assuming chemical and thermal equilibrium, using
minimization of Gibbs free energy with given enthalpy and element composition of the gas
phase. This is performed by a generalized equilibrium code called CREE [43].
The mass and energy balances in the control volumes in Figure 17 are given by equations
(2.23) and (2.24).
ms ,in + m g ,in − ms ,out − m g ,out = 0
ms ,in hs ,in + mg ,in hg ,in + Q1 − ms ,out hs ,out − mg ,out hg ,out − Q2 = 0
(2.23)
(2.24)
m: mass flow [kg/s]
h: total enthalpy [J/kg]
Q: heat gain/loss to/from the bed [W]
The subscripts s, g, in and out refer to solid, gas, control volume in and control volume out.
Q1 represents heat coming from the over-fire compartment, to the bed that enhances the
drying and devolatilisation. Q2 represent heat lost from the bed to the walls from the high
temperature equilibrium zone.
The solution procedure for the two-zone model can be seen in Figure 18. First, the
temperature of the drying and devolatilisation zone is guessed. From the temperature the
drying and devolatilisation zone is calculated. Then, with the given char flow from the DDzone the temperature and gas composition are calculated in the EQ-zone. Finally, a new Texit
is calculated by solving an energy balance in the DD-zone with the given gas flow and
temperature from the EQ-zone. If the new Texit is equal to the guessed Texit within the given
tolerances, the solution has converged.
26
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
Start
Guess Texit
Calculate volatile yields and compositions in the DD-zone
Calculate temperature and gas composition in the EQ-zone
Solve energy balance around the DD-zone and get a new Texit
Calculated Texit equal to guessed Texit?
No
Yes
Solution converged
Figure 18. Solution algorithm for the two-zone model.
2.3.4 A Three Zone Cross-Current Bed Model
The three zone bed model is a developed for cross-current bed. The principles for the three
zone bed model can be seen in Figure 19.
Qin
Qin
Moisture + Flue gas
Wet
wood
Drying
Flue Gas
Dry
wood
Volatile + Air
Qout
Equilibrium Gas
Char Gasification
Devolatilisation Char
& Oxidation
Hot Air
Flue Gas + Air
Figure 19. The three-zone bed model.
The model assumes the bed to consist of three zones, a drying zone, a devolatilisation zone
and a char oxidation/gasification zone. Each zone is treated separately and the temperature of
the product gases leaving each zone is calculated by carrying out a mass and energy balance
over the zone, similarly to equations (2.22) and (2.23). The model has another option: that is
to give the zone temperature and then calculate the incoming/outgoing thermal radiation
to/from the each zone.
Drying is assumed to take place in the drying zone and all moisture leaves the fuel in this
zone. The dry fuel is then transported over to the devolatilisation zone, where the volatile
species composition and their amount is calculated using the FG model. The volatile species
27
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
leaving the fuel are assumed to be non-reactive in the bed and therefore the devolatilisation
zone can be considered to be a pure pyrolysis zone. After the devolatilisation is complete the
char is transported to the char oxidation/gasification zone. There the char is oxidized and/or
gasified depending on the incoming blast gas composition to the zone. The species
composition leaving the char oxidation zone is calculated using equilibrium assumptions, as
in the two-zone model. The temperature of the char oxidation zone is controlled by specifying
the amount of heat fluxes leaving the zone.
Fixed Drying &
Devolatilisation Temp
Start
Fixed Drying &
Devolatilisation heat fluxes
Guess temp of
drying zone
Calc. gas composition
& heat Flux to/from
drying zone
Temperature
not converged
Calc. gas composition
of drying zone
Calc. new temp of
drying zone
Calculate volatile
yields & compositions
Guess Temp of
devolatilisation zone
Temperature
not converged
Calculate volatile
yields & compositions
Calc. Heat Flux to/from
devolatilisation zone
Calc. new Temp of
devolatilisation zone
Calculate the species yields and the
temperature of char oxidation zone
Solution Converged
Figure 20. The solution procedure of the 3-zone model.
The solution procedure for the three-zone bed model can be seen in Figure 20 and it is slightly
different with the given heat fluxes to/from the zones and zone temperatures. With given
temperature the compositions in the drying and devolatilisation zones are determined directly.
With given heat flux to these zones, certain iterations are needed to calculate the temperature
and compositions in these zones. Once the final temperature of the devolatilisation zone is
28
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
known then the volatiles species composition are calculated. The remaining char goes to the
char oxidation zone where species and temperature is obtained from equilibrium calculations.
2.3.5 A Quasi Two-Dimensional Bed Model
Single Particle Model
The foundation for the quasi two-dimensional bed model is the single particle model of
Thunman et al. [5, 29]. The fuel particles are assumed to be of spherical shape. Detailed heat
and mass transport inside the particles are modelled using a system of spherical symmetric
one-dimensional transport equations. For a given surrounding air temperature that is higher
than the particle temperature, the fuel particles are heated up, followed by drying,
devolatilisation and char combustion of the particles. These processes are modelled using
chemical kinetic rate (Arrhenius expressions). The shrinking of the particles is taken into
account assuming the volume is a linear function of each released constituent [5]. More
detailed descriptions are referred to Thunman et al. [5, 29]. Here, to illustrate the physical
process and the model performance, the particle temperature, shrinkage and volatile gases
leaving the surface of a particle are shown in Figure 21 and Figure 22.
1000
0.8
Shrinkage coefficient [-]
1
Temperature [K]
1200
800
600
cell 1
cell 15
cell 25
cell 30
400
200
0
100
200
Time [s]
300
cell 1
cell 15
cell 25
cell 30
0.6
0.4
0.2
400
0
0
100
200
300
400
Time [s]
Figure 21. The calculated temperature and shrinkage for different cells in a spherical particle.
The wood particle in the calculations is spherical and is divided into 30 cells along the radial
direction. The first cell represents the centre of the particle and the 30th represent the particle
surface. The result shown in Figure 21 and Figure 22 are for a particle placed in 800 K hot air.
The initial particle temperature is 298 K. The temperature evolution for the particle as a
function of time in different computational cells shows plateaus of temperature at different
stages. The plateaus occurring at 398 K is due to the particle drying, in which the particle
temperature is nearly constant until the moisture has completely been evaporated. The time
interval of the drying period is shown by the length of the first temperature plateaus. As seen,
drying occurs quickly at the outer surface of the particle. The drying wave propagates towards
the centre of the particle. The entire drying period takes about 150 seconds. After the drying is
complete the particle is heated up quickly and devolatilisation finishes quickly. The formation
of volatile occurs approximately in the range of 473 K to 773 K. As the devolatilisation is
complete the char oxidation takes place, which increases the temperature of the particle to 150
to 200 K above the surrounding temperature as seen in Figure 21. It can also been seen in
Figure 21 that the transfer of heat inside the particle is rather slow before the char oxidation
takes place.
29
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
0.8
O2
H2O
CO
CO2
CH4
H2
N2
Molar fraction [-]
0.6
0.4
0.2
0
0
100
200
300
400
Time [s]
Figure 22. The calculated species leaving a particle during its conversion.
The computed mole fractions at surface of the single particle are seen in Figure 22. It can be
seen that the drying starts rather quickly and results in dilution of the O2 and N2 near the
particle. Due to the high surrounding temperature the devolatilisation starts before the drying
completely finished and it is seen that there are some overlapping of the different conversion
processes. This is followed by oxidation of the char, resulting in high concentrations of CO.
The zero concentration of O2 and no formation of CO2 are due to simplification of the char
oxidation, which assumes that only CO is formed during oxidation of char and that the
surrounding oxygen is not able to penetrate the char oxidation layer. However, towards the
end of the char oxidation the oxygen is able to penetrate the reaction layer, which is seen in
Figure 22. It can be noted that drying and devolatilisation times are rather short compared
with the oxidation of char. The drying time is about 150 seconds and the devolatilisation is
about 100 seconds. This can be compared to the char oxidation, which is about 250 seconds.
The shrinkage for different cells inside the particle is seen in Figure 21. It can be seen that the
particle losses 10% of its volume during drying. After devolatilisation is complete the particle
has shrinked to 40% of its originally volume. The little volume remaining after the shrinkage
is finished is due to the remaining ash.
A quasi two-dimensional description of the fuel bed
A schematic view of the fuel bed is seen in Figure 23. The bed is divided into a number of
computational cells. The fresh fuel particles are thrown to the bed from the left side of the
figure and the particles move in positive x-direction. The cells in the first row (j=0, i=1 to ii,
the shadow area) are boundary cells for the incoming primary air to the bed. The top row of
cells (j=jj, i=1, ii) represents the over-fire compartment above the bed.
30
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
Hx
y
∆x
jj
Feeding
Hy
i, j
ii
1
0
Primary air
Primary air
x
L
Figure 23. A view of the 2-D bed computational domain.
To simplify the computations, particles in each computational are assigned a residence time.
At cell (i,j) the coordinate (xi,yi) and the cell residence time are, respectively:
xi = (i / ii ) L, y j = ( j / jj ) H y ,
t ( xi , y j ) = ( H y − y j ) / v + ( H x + xi ) / u
where u is the speed of the particles moving in the horizontal direction. v is related to the
feeding rate of the particles to the bed ( m fuel ) and the bed moving speed u.
m fuel = ρ P H z H y u = ρ P H z H x v
where ρ P is the density of the fuel particle; H z is the width of the fuel bed (in the direction
perpendicular to the x-y plane). The time interval during which the particles stay in the cell
(i,j) is the same in every cells if the size of the cells are the same ( ∆x ):
∆t =
∆x
u
and the release rate of the total mass of the volatiles ( S P , j ) and release rate of species j ( S P ) in
the cell are respectively
SP =
SP, j =
nij
∆t
nij
∆t
t ( xi , y j ) +∆t
∫
mdt ,
t ( xi , y j )
t ( xi , y j ) +∆t
∫
mY j dt
t ( xi , y j )
31
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
where m is the mass release rate through the outer surface of the fuel particle; nij is the
number density (number of particles per volume) in the cell (i,j). Y j is the mass fraction of
species j in the volatile mixture released from the particles (as seen in Figure 22).
The transport equations for the species j can be written as
∂ρ gα gY j
∂t
+
∂
∂ ⎛ µ ∂Y j ⎞
ρ gα gY j ui ) = ⎜ t
(
⎟ + S p , j + ωgj
∂y
∂y ⎝ Sct ∂y ⎠
(2.25)
ρ g : density of gas [kg/m3 ]
Y j : species mass fraction of species j
α g : void fraction
ug : velocity of gas flow [m/s]
Sp : source term from single particle model
and the speed of the volatiles leaving the bed to the boiler ( ug ) is calculated with continuity
equation:
∂ρ gα g
∂t
+
∂
( ρ gα g u g ) = S p
∂y
(2.26)
The source terms ωgj represent the volatile oxidation rate in the bed. Since no volatile
oxidation is assumed to take place in the bed can ω gj have been neglected. The density of the
volatile gases in the bed is calculated using the equation of state and assuming a temperature
in each of the bed cell, for simplicity. The bed is assumed to be operating in stationary mode.
The time-dependent terms in equations (2.25) and (2.26) can be neglected, and the equations
become ordinary differential equations that can be integrated easily with given boundary
conditions at the bottom of the bed. The integration is done in y-direction and at all xposition.
2.3.6 Examples of Numerical Studies
Semi-Empirical Bed Model
Figure 24 show the possible volatile species for a given CO, CO2 and O2 using the semiempirical model. The semi-empirical model needs input of the mass fractions of three species
from the experiments. It is seen from the left figure that with given mass fraction of O2 about
0.0194 and CO mass fraction of 0.015, increasing the mass fraction CO2 would lead to an
increase of CH4, and decrease of H2O and Tar. Suppose that the mass fraction of CO2 is also
known from the experiments, then one can predict the mass fractions of CH4, H2O and Tar, by
using the semi-empirical model.
The model can predict the range of possible mass fractions of species. Take the left figure as
an example. The possible range of CO2 mass fraction is between 0.21 and 0.39, if the mass
32
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
fraction of O2 is 0.0194 and CO mass fraction is 0.015. Beyond this range either CH4 mass
fraction or H2O mass fraction becomes non-physical (less than zero).
O2 = 1.94 mass-%
CO2 = 26.4 mass-%
O2 = 1.94 mass-%
CO = 1.5 mass-%
10
5
30
25
CO2 [mass-%]
35
Species [mass-%]
15
0
20
20
20
Species [mass-%]
Species [mass-%]
20
CH4
H2O
Tar
15
10
5
0
0
10
5
CO [mass-%]
CO = 1.5 mass-%
CO2 = 26.4 mass-%
15
15
10
5
0
0
2
4
8
6
O2 [mass-%]
10
Figure 24. Variation of CH4, H2O and tar as function of CO2, CO and O2.
The semi-empirical model may used in cases where only part of the experiment data is
collected. The model has been tested in a large scale industry boiler (the Flintrännan boiler)
and a laboratory scale pellet reactor. More details are given later.
Two-Zone Bed Model
The two-zone bed model has been used to create the boundary conditions for simulations of
the laboratory scale pellet reactor and to study a small-scale 50 kW commercial house heating
boiler. The data for the pellet reactor can be found in Paper 1 of the Appendix to this thesis. A
sketch of the bed of the small-scale commercial boiler for domestic house heating is seen in
Figure 25.
Wood
Logs
Air
Air
Volatile
Figure 25. Sketch of the 50 kW bed.
Table 2 and Table 3 show the pyrolysis/gasification products as a function of heat-losses from
the bed to the wall. In Table 2 the simulated data is compared with experimental data, in
which mole fractions (on dry basis) of CO, CO2, and CH4 as well as temperature of volatile
gas were measured by Lönnermark [45]. The species concentrations agree well. The measured
temperature is difficult to compare with predicted temperatures since Texit and Teq are
33
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
calculated at different places from the location of the measured temperature. It was found that
the species concentrations agree well with measured data at a heat loss of 5.25%. The
calculated temperature is also reasonable since the measured data is between Texit and Teq. The
calculation is limited since the bed is simplified as zero-dimension with two different zones.
Table 2. Comparison between simulation and experimental data, n/a = not available. Species
concentration is in dry mole %.
Case
HT-loss [%] Texit [K] Teq [K] Tavg [K]
Simulations
5.25
821
1796
1309
Experiments
n/a
n/a
n/a
1183
CO
9.45
9.46
CO2
H2
20.12 15.31
20.5
n/a
CH4
4.53
4.32
Table 3 shows the predicted results from the heat loss study. The result shows an increase of
H2 and CO and a decrease of CH4 and CO2 with decreasing heat-loss. CO2, CH4 and CO are
found to agree best with experiment at the heat loss 5.25%. The variation of volatile
concentrations and temperature as a function the heat loss is reasonable. Heat loss
significantly reduces the temperature at the EQ zone. As a result, the forward reaction of the
‘water-gas shift reaction’ (5) is enhanced and its backward reaction is suppressed, thus it is in
favor of forming more CO2 and decreasing CO. The increase of CH4 may be due to the fact
that as temperature decreases, the chain of CH4 to CHO and CO will be suppressed, which
also leads to a low production of H2 from the hydrocarbons.
CO + OH ↔ CO 2 + H
(2.27)
Table 3. Calculated species mole fraction for different heat losses (dry mole %).
HT-loss [%] Texit [K]
1.81
857
3.53
839
5.25
821
6.97
803
8.7
784
10.42
762
12.14
738
Teq [K]
Tavg [K]
2010
1903
1796
1689
1580
1470
1360
1433
1371
1309
1246
1246
1170
1049
CO
12.62
11.05
9.45
7.82
6.2
4.62
3.14
CO 2
H2
CH4
17.66
18.87
20.12
21.37
22.63
23.86
25.09
18.15
16.78
15.31
13.74
12.09
10.36
8.52
2.66
3.57
4.53
5.52
6.55
7.6
8.65
Three-Zone bed and 2-D Bed Models
The tree-zone bed and the quasi two-dimensional bed models have been tested on the 31 MW
boiler and the calculated data was compared with measurement at level I and II for different
depths (i.e. z = 0.1, 0.98 and 2.26 m for level I and z =0.1 and 0.98 m for level II, Figure 11,
Chapter 1). The calculated results for CO, CH4, CO2 and O2 are seen in Figure 26. For the
three-zone model the bed was divided into three equally long zones. Drying took place in the
first zone, followed by devolatilisation in the second zone and char combustion in the last
zone. For the quasi two-dimensional model the bed was divided into 12 computational cells in
the bed length direction (x) and the incoming air to the bed was assumed to have a
temperature of 800 K. Considering the measurements it is seen that the amount of O2 and CO2
are rather constant across the grate (z-direction) and that O2 is high towards the end of the
grate. CO2, CO and CH4 show an opposite behaviour and are high at the middle of the bed (xdirection) and rather low toward the end of the bed. CO and CH4 are lower near the furnace
walls than in the middle of the boiler (z = 2.26 m). From the measurements, it can be seen that
34
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
20
2-D
3-zone
Exp y=1.4 z=0.1
Exp y=1.4 z=0.98
Exp y=1.4 z=2.26
Exp y=2.7 z=0.1
Exp y=2.7, x=0.98
18
2-D
3-zone
Exp y=1.4 z=0.1
Exp y=1.4 z=0.98
Exp y=1.4 z=2.26
Exp y=2.7 z=0.1
Exp y=2.7, z=0.98
16
CO2, Dry volume-%
CO, Dry volume-%
most of the conversion process takes place during the first 5-6 meters of the bed. Towards the
end of the grate, probably only ash remains. This hypothesis is supported by the low amount
of fuel species and of CO2. Oxidation of char would result in higher concentration of CO2
compared to the measured ones.
14
12
10
8
6
4
2
1
2
3
4
5
6
7
8
9
0
10
0
1
2
3
Bed length [m]
6
7
8
9
10
24
2-D
3-zone
Exp y=1.4 z=0.1
Exp y=1.4 z=0.98
Exp y=1.4 z=2.26
Exp y=2.7 z=0.1
Exp y=2.7, z=0.98
8
7
6
5
4
3
22
20
O2, Dry volume-%
9
CH4, Dry volume-%
5
Bed length [m]
10
18
16
14
12
10
2-D
3-zone
Exp y=1.4 z=0.1
Exp y=1.4 z=0.98
Exp y=1.4 z=1.86
Exp y=1.4 z=2.26
Exp y=2.7 z=0.1
Exp y =2.7, z=0.98
8
6
2
4
1
0
4
0
2
1
2
3
4
5
6
Bed length [m]
7
8
9
10
0
0
1
2
3
4
5
6
7
8
9
10
Bed length [m]
Figure 26. The calculated concentration of species along the length of the 31 MW bed.
The calculated results from the 2-D bed model show that the volatile and char oxidation starts
rather early. Most of the volatiles are released between 1.5 to 5 meters. After 5 meters the
devolatilisation process is complete and most of the char have been oxidized, which is
indicated by the low amount of released of CO. The oxygen concentration is rather high and
is constant over the entire grate except between 1.5 to 5 meters where it decreases due to
oxidation of the particles. Comparing with measurement it is shown that the trend of O2, CO
and CH4 is well predicted; however, the level of mass fractions of CH4 and O2 are overpredicted, and CO2 under-predicted. This is partially due to the fact that the measurement data
is collected between 0.4 to 1.2 meters above the grate for level I and this gives the volatile
time to be oxidised by the oxygen. Also, in the present quasi two-dimensional bed model,
oxidation of the volatile fuel in the bed has been neglected.
The calculated result from the three-zone model agrees less good with the measurement data
except CH4, which agree well with measurement data. The concentrations of CH4 and oxygen
are better predicted than the quasi two-dimensional model, since in the three zone bed model,
the oxidation of volatile fuel in the bed is taken into account by the chemical equilibrium
assumption. CO is reasonable for the devolatilisation zone but too high at the char oxidation
zone. CO2 show some agreement for char oxidation zone but under-predict at the
devolatilisation zone. O2 show agreement with the first measuring points at level II but fail to
capture the trend at the devolatilisation and char oxidation zone. Some of the poor agreement
35
Chapter 2: Modelling of Biomass Combustion in Grate-Fired Bed
with measurement data can be attributed to the fact that the location of measurement is 1.2 to
2.3 meters above the bed for level II.
To summarize, the investigated simple bed models can predict the physical and chemical
processes to certain extent. The variations of volatile gases along the bed can be
approximately simulated by the three-zone and the quasi two-dimensional bed model. The
model results can be a first approximation to bed combustion. In the present thesis, the model
results have been used as the boundary conditions for the simulation of the volatile
combustion in the free room. The sensitivity of the results to the bed models will be discussed
in the later chapters and papers in the appendix. However, it is rather clear that none of the
models can accurately predict the complex bed combustion process. More accurate treatment
of the transport processes and chemical reactions are needed to achieve better predictions. In
addition, well controlled experiments on the particles and volatile gases inside the bed are
desirable for future model validations.
36
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
3 Modelling of Volatile Oxidation above the Fuel Bed
The oxidisation of volatile species above the bed highly depends on the mixing between
reactants in the flow. Turbulence greatly enhances the heat and mass transfer and promotes
mixing of reactants. The mixing between the reactants occurs in a rather nonlinear manner
and it poses one of the challenges in simulation of engineering turbulent reacting.
3.1 Fundamental Equations for a Reacting Flow in an Industrial Furnace
A reacting flow can be described by a set of partial differential equations (PDE), which are
obtained from conservation laws of mass, momentum, energy and species. In industrial
boilers, the PDEs can be simplified based on the following assumptions.
•
•
gravitational force has negligible effect on the flow
the Mach number of the flow is low, Ma 0.3.
With the above assumptions the conservation equations for mass, momentum, energy and
species can be written as
∂ρ ∂ρ u j
+
=0
∂t
∂x j
(3.1)
∂ρ ui ∂ρ u j ui
∂P ∂τ ij
+
=−
+
∂t
∂x j
∂xi ∂x j
(3.2)
⎡ µ ∂h
∂Y ⎤
1⎞
⎛ 1
+ µ ⎜ − ⎟ ∑ hi i ⎥ + S R
⎢
∂x j ⎥⎦
⎝ Sc Pr ⎠ i
⎢⎣ Pr ∂x j
∂ρYi ∂ρ u jYi
∂ ⎛ µ ∂Yi ⎞
+
=
⎜
⎟ + ωR
∂t
∂x j
∂x j ⎜⎝ Sc ∂x j ⎟⎠
∂ρ h ∂ρ u j h ∂P ∂
+
=
+
∂t
∂x j
∂t ∂x j
(3.3)
(3.4)
t: time [s]
u j : velocity [m/s]
x j : cartesian coordinate [m]
P: pressure [N/m 2 ]
h: mixture enthalpy [J/kg]
Yi : mass fraction of species i
SR : thermal radiation source term [J/m3s]
ωi : rate of formation of species i [kg/m3s]
µ : molecular viscosity [kg/m s]
ρ: density [kg/m3 ]
Pr and Sc are the Prandtl and Schmidt numbers. The Prandtl number gives the ratio between
momentum and thermal diffusivity and it is defined as:
Pr=
µC p
kh
(3.5)
37
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
⎛ J ⎞
C p : specific heat ⎜
⎟
⎝ kg K ⎠
⎛ J ⎞
kh : heat conductivity ⎜
⎟
⎝ mK ⎠
The specific heat for a gas mixture at constant pressure can be defined as:
C p = ∑ C pi Yi
(3.6)
i
The Schmidt number, which defines the ratio between momentum and mass diffusivity is
defined as:
Sc=
⎛ m2
D : mass diffusion coefficient ⎜
⎜ s
⎝
µ
ρD
(3.7)
⎞
⎟⎟
⎠
From the Schmidt and Prandtl numbers the Lewis number can be defined and it gives the ratio
between thermal and mass diffusion:
Le =
kh
Sc
α
=
≡
Pr C p ρ D D
(3.8)
For most industry applications the Lewis number can be assumed to be equal to unity, which
simplifies equation (3.3) to
∂ρ h ∂ρ u j h ∂P ∂
+
=
+
∂t
∂x j
∂t ∂x j
⎛ µ ∂h ⎞
⎜⎜
⎟⎟ + S R
x
∂
Pr
j ⎠
⎝
(3.9)
The mixture enthalpy in the energy equation, h, is defined as
h = ∑ Yi hi
(3.10)
i
where the species enthalpy is given by:
T
hi = H i0 + ∫ C pi dT
T0
T : gas temperature [K]
T0 : gas reference temperature = 298 K
H i0 : heat of formation at reference temperature 298 K
The viscous stress tensor, τ i, j , in the momentum equation can be written as:
38
(3.11)
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
τ ij = 2µ sij − ζ
∂uk
δ ij
∂xk
(3.12)
δi,j : Kronecker delta
sij : flow strain tensor [s-1 ]
⎡ m2 ⎤
⎥
⎣⎢ s ⎦⎥
ζ : second viscosity ⎢
The second viscosity is often set to be equal to
2µ
. The flow strain rate tensor is given by
3
equation (3.13).
1 ⎛ ∂u ∂u j ⎞
sij = ⎜ i +
⎟
2 ⎜⎝ ∂x j ∂xi ⎟⎠
(3.13)
Equation of state is used to close the systems of PDEs.
P = ρ RT ∑
i
Yi
Mi
(3.14)
R: universal gas constant = 8.314 [kJ/mole K]
Mi : molecular weight of species i [kg/mole]
3.2 Turbulence
A flow is turbulent if Reynolds number is higher than a critical value, (≈ 2300 for pipe flows).
The Reynolds number is a non-dimensional quantity that gives the ratio between the inertial
forces over the viscous forces.
Re =
ρ ul
µ
(3.15)
ρ: density [kg/m3 ]
u: characteristic velocity [m/s]
l: characteristic length [m]
µ: dynamic viscosity [kg / m s]
Most of the flows occurring in nature and in industrial furnaces are turbulent. Turbulent flow
in industrial furnaces is a continuum phenomenon since the smallest scale of the flow is still
much larger than the molecule mean free path. The governing equations (3.1) to (3.14) are
valid for turbulent flows. However, the fluid motion is rather irregular and dissipative (energy
is needed to sustain turbulence, otherwise it decays quickly). An important character of
turbulence is that it greatly enhances mixing of mass, energy and momentum in all three
dimensions compared to a laminar flow. This is due to the eddy interaction on different
scales. In furnaces, intensive turbulence can be generated in the shear layers associated with a
number of high speed secondary air jets. Turbulence field depends also on the furnace
geometry. By optimizing the furnace geometry and secondary air supply, turbulence mixing
of fuel and air can be optimized.
39
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
3.2.1 Turbulent Eddy Scales
Turbulent flows contains a wide range of different length l, velocity u ( l ) and time
τ ( l ) ≡ l / u ( l ) scales and the flow is considered to be composed of eddies of various sizes.
The largest of these scales are called integral scale that is limited by the furnace geometry and
the smallest scales are named Kolmogorov scales and they are limited by the viscosity. The
large eddies contain most of the turbulent kinetic energy and these eddies are unstable and
tend to break up and transfer their energy to small eddies. These smaller eddies break up in a
similar manner and transfer their energy to even smaller eddies. This procedure continues
until the Kolmogorov scale is reached where the viscous forces dominating the flow and the
kinetic energy is dissipated into heat. This procedure, of which kinetic energy is continually
transferred from larger to smaller eddies, is called energy cascade. The scales of interest in
turbulent motion are the integral scale l0, and Kolmogorov microscale η.
The integral scale is, as mentioned above, the characteristic scale of the largest eddies in the
flow field and integral eddies contains most of the flows kinetic energy. The integral
timescale can be estimated by
τ0 =
τ 0 : integral time scale [s]
l0
u0
(3.16)
u0 : integral velocity scale [m/s]
l0 : integral length scale [m]
The Kolmogorov microscale is the smallest scale in the turbulent flow and on this level the
kinetic energy is dissipated to heat due to viscous dissipation. The Kolmogorov length,
velocity and timescales are expressed in terms of kinematic viscosity and dissipation rate, see
equations (3.17) to (3.19)
⎛υ3 ⎞
η ≡⎜ ⎟
⎝ε ⎠
uη ≡ (υε )
⎛υ ⎞
τη ≡ ⎜ ⎟
⎝ε ⎠
0.25
0.25
(3.17)
(3.18)
0.5
(3.19)
υ : kinematic viscosity [m 2 /s]
The dissipation rate, ε, of which energy is transferred from the Integral scale to the
Kolmogorov scale can be estimated by equation (3.20).
u03
ε∼
l0
(3.20)
A relationship between the largest and smallest scales can be obtained by combining
equations (3.17) to (3.19) with equation (3.20).
40
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
η
1 ⎛ υ3 ⎞
= ⎜ ⎟
l0 l0 ⎝ ε ⎠
0.25
1 ⎛ υ 3l ⎞
∼ ⎜ 30 ⎟
l0 ⎝ u0 ⎠
0.25
1
1 ⎛ υu 3 ⎞
0.25
= (υε ) ∼ ⎜ 0 ⎟
u0 u0
u0 ⎝ l0 ⎠
uη
τ η u0 ⎛ υ ⎞0.5 u0 ⎛ υ l0 ⎞
∼ ⎜ 3⎟
=
l0 ⎝ u0 ⎠
τ 0 l0 ⎜⎝ ε ⎟⎠
⎛ υ3 ⎞
=⎜ 3 3⎟
⎝ u0 l0 ⎠
0.25
0.5
0.25
⎛ υu 3 ⎞
=⎜ 40 ⎟
⎝ u0 l0 ⎠
⎛ υ u 2l ⎞
= ⎜ 30 20 ⎟
⎝ u0 l0 ⎠
⎛ υ ⎞
=⎜
⎟
⎝ u0l0 ⎠
0.25
0.5
0.75
⎛ υ ⎞
=⎜
⎟
⎝ u0l0 ⎠
⎛ υ ⎞
=⎜
⎟
⎝ u0l0 ⎠
= Re −0.75
(3.21)
0.25
= Re −0.25
(3.22)
0.5
= Re −0.5
(3.23)
It is shown in equations (3.21) to (3.23) above that the difference between the small scales
and large scales increases with increasing Reynolds number. This implies that the
Kolmogorov scales will become even smaller with increasing Reynolds number for a fixed
integral length scale.
3.2.2 Reynolds Averaged Navier-Stokes Equations
The Reynolds number is high in most industrial furnaces and since turbulent flow is a three
dimensional problem that involves many different scales it can not be resolved with CFD
calculations due to limitations of computational resources. Therefore, statistical methods and
approximations have to be introduced to solve the flow field. A common approach is to
average the governing equations and turbulent quantities. Averaging was introduced by
Reynolds in 1883 [46] by which he decomposed the variables into two parts, a mean value
and a fluctuating part. For a quantity φ the decomposition becomes:
φ = φ +φ '
(3.24)
φ : mean value of φ
φ ' : fluctuating part of φ
where the mean of the fluctuation ( φ ' ) is by definition zero. Several different kinds of
averaging are used for obtaining a mean value. For statistically stationary turbulent flows time
averaging can be appropriate to use and it is defined as:
φ=
1
tL
t0 + t L
∫ φ ( x, y, z, t ) dt
(3.25)
t0
Where t L is a large time scale. When t L is long enough (say 100 τ 0 ) φ is independent of τ 0
and t L . For flow experiments, which can be repeated or replicated N number of times,
ensemble averaging can be used and it is defined by:
φ=
1
N
N
∑ φ ( x, y , z , t )
n =1
n
(3.26)
where φ is equal to φn for the nth experiment. For homogeneous turbulence it is appropriate to
use spatial averaging since the turbulent flow is uniform in all directions. This is done by
using a volume integral of the domain of interest.
41
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
X Y Z
φ = ∫ ∫ ∫ φ ( x, y, z , t ) dxdydz
(3.27)
0 0 0
where X,Y and Z are the size of the domain in x,y and z-direction.
For reactive and compressible flows, the density is not constant but fluctuates. It is convenient
to decompose the variables with Favre averaging, i.e. density weighted averaging.
φ=
ρφ
ρ
(3.28)
where the decomposition of φ is done in a similar way as Reynolds decomposition:
φ = φ + φ ''
(3.29)
φ : density weighted mean value of φ
φ '': fluctuating part of φ
To determine the Favre averaged quantities, density is multiplied with equation (3.29) and the
expression can be rewritten as:
ρφ = ρφ + ρφ ''
(3.30)
The expression is then Reynolds averaged:
ρφ = ρφ + ρφ ''
(3.31)
φ ρ = ρφ
(3.32)
By rewriting equation (3.28) to
and considering (3.31) the ρφ '' is shown to be zero,
ρφ '' ρφ
=
−φ = 0
ρ
ρ
(3.33)
The reactive flow field, in this work, is treated by using the Favre averaged Navier-Stokes
equations with the k − ε turbulence closure model. Favre averaging removes the extra term
entering the continuity equations due to Reynolds averaging. In the following overbar means
Reynolds averaging and overtilde means Favre averaging. The Favre averaged conservation
of mass of a fluid can be expressed as follows:
∂ρ ∂ ρu j
+
=0
∂t
∂x j
42
(3.34)
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
The Favre averaged transport equations for momentum, energy and species conservation can
be expressed in the following way:
(
∂ ρ ui ∂ ρ u j ui
∂P ∂
τ ij − ρ ui''u ''j
+
=−
+
∂t
∂x j
∂xi ∂x j
)
(3.35)
⎛ µ ∂h ⎞ ∂
ρ h''u ''j + S R
⎜⎜
⎟⎟ −
⎝ Pr ∂x j ⎠ ∂x j
∂ ρ Y i ∂ ρ u j Yi
∂ ⎛ µ ∂Yi ⎞ ∂
+
=
ρYi ''u ''j + ω R
⎜⎜
⎟⎟ −
∂t
∂x j
∂x j ⎝ Sc ∂x j ⎠ ∂x j
(
∂ ρ h ∂ ρu j h ∂P ∂
+
=
+
∂t
∂x j
∂t ∂x j
(
)
(3.36)
)
(3.37)
The Favre averaged equation of state is:
N
P = ρ RT ∑
i =1
Yi
Mi
(3.38)
The viscous stress tensor τ ij in equation (3.35) after the Favre averaging can be written as:
⎛ ∂u i
τ ij = µ ⎜
⎜
⎝ ∂x j
+
∂u j
∂xi
⎞ 2 ∂u k
δ ij
⎟⎟ − µ
∂
x
3
k
⎠
(3.39)
For incompressible flows the second term on right hand side in equation (3.39) is zero, due to
continuity. The Favre averaged Navier-Stokes equations have the same form as the
fundamental governing equations for a reacting flow, however, three new terms appear in
(
)
equations (3.35) to (3.37) as a result of the averaging. The first of these terms − ρ ui''u ''j is the
(
so-called Reynolds stress tensor. This together with the turbulent transport fluxes, − ρ h''u ''j
(
and − ρYi ''u ''j
)
) are unknown and need to be modelled. The new unknown terms creates a
closure problem since there are more unknowns than knowns. To be able to close the system
it is necessary to introduce extra expressions. Several different models have been proposed to
close the system of equations.
3.2.3 Two-Equation Model, k-ε
An often used model for industrial furnace simulations is based on the turbulent eddy
viscosity hypothesis, proposed by Boussinesq in 1877. According to Bossinesq Reynolds
stress tensor can be related to the mean velocity gradient according to equation (3.40).
43
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
(
τ ij = − ρ ui ''u ''j
)
⎡ 1 ⎛ ∂u i ∂u j
= 2 µT ⎢ ⎜
+
⎜
2
∂
x
⎣⎢ ⎝ j ∂xi
⎞ 1 ∂u k ⎤ 2
δ ij ⎥ − ρkδ ij
⎟⎟ −
3
∂
x
⎥⎦ 3
k
⎠
(3.40)
τ ij : Reynolds stress tensor
1 '' ''
ρ uk uk / ρ , [m 2 /s 2 ]
2
µT : turbulent eddy viscosity [kg/m s]
k : turbulent kinetic energy =
The eddy viscosity does not depend on the fluid (as viscosity normally does). Instead, it is a
property of the flow. By using Boussinesqs hypothesis the problem of modelling Reynolds
stresses and the turbulent transport fluxes can be transformed to modelling of eddy viscosity.
The turbulent transport fluxes found in equations (3.35) to (3.37) are modelled using similar
gradient diffusion models, based on the eddy viscosity:
− ρ h''u ''j =
− ρY u =
'' ''
i j
µT ∂ h
PrT ∂x j
µT ∂Y i
(3.41)
ScT ∂x j
PrT : turbulent Prandtl number = 0.7
ScT : turbulent Schmidt number = 0.7
The eddy viscosity is modelled as follows.
µT = Cµ ρu *l *
(3.42)
Cµ : constant
u * : velocity scale
l * : length scale
The challenging task using Boussinesqs hypothesis is how to determine the turbulent length
and velocity scales, in equation (3.42). A large number of models have been given in the
literature for calculating the velocity and length scale. The simplest form of turbulence model
is to use algebraic expressions for u * and l * . This does not require any form of transport
equation. However, these models are rather crude, considering local turbulence effects only
and neglecting any history influence from turbulence convection. An example of such a
model is the Prandtl mixing length model [47]. Other models are one- and two-equation
models. One equation models use a transport equation for turbulent kinetic energy, k, from
which the velocity scale is estimated, u * ∼ k . The length scale is still obtained by an
algebraic expression. The two-equation models use two transport equations for calculation of
the velocity and the length scale. The two-equation model used in this work is the k-ε model.
In the k-ε model the turbulent kinetic energy (k) and the dissipation rate of it (ε) is defined as:
44
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
k=
11
ρ uk'' ul''
2ρ
(3.43)
ν ∂ui'' ∂ui''
ε= ρ
ρ ∂x j ∂x j
ν : kinematic viscosity [m 2 /s]
From equation (3.43) transport equations for k and ε can be derived, which was done by Jones
and Launder [48] shown below:
⎞ ∂k ⎤
'' ''
⎥ + − ρ ui u j
⎟
x
∂
⎠ j ⎦⎥
µT ⎞ ∂ε ⎤
ε
∂ ρε ∂ ρ u j ε
∂ ⎡⎛
'' ''
+
=
⎢⎜ µ +
⎥ + C1 − ρ ui u j
⎟
k
Prε ⎠ ∂x j ⎦⎥
∂t
∂x j
∂x j ⎢⎣⎝
∂ ρk ∂ ρ u j k
∂
+
=
∂t
∂x j
∂x j
⎡⎛
µT
⎢⎜ µ +
Prk
⎣⎢⎝
(
(
)
) ∂∂xu − ρε
(3.44)
ε2
∂u i
− C2 ρ
k
∂x j
(3.45)
i
j
Prk : constant turbulent Prandtl number = 1.0
Prε : constant turbulent Prandtl number = 1.3
C1: constant = 1.44
C2 : constant = 1.92
*
*
Using the dimensional relation, u ∼ k and l ∼
k
3
ε
2
, the eddy viscosity in equation (3.42)
can now be calculated by
µT = C µ ρ
k2
ε
(3.45)
where Cµ is an experimentally determined constant, often set to 0.09.
3.2.4 Other Models
Other models, which can be used for closing the system of equations, are the Reynolds Stress
Model (RSM) and Large Eddy Simulation (LES). The benefit with RSM is that it does not use
any turbulent viscosity for closing the system of equations. LES resolves most of the
turbulence scales (down to Taylor microscale) so that the results are not so sensitive to the
sub-grid scale models.
Reynolds stress model introduce six transport equations for calculation of Reynolds stress
tensor and each stress is calculated separately. An additional transport equation is needed for
ε. RSM is more computational demanding due to the five more transport equations; however,
it is generally more accurate than the k-ε model since it takes into account the anisotropy of
turbulence.
The Large Eddy Simulation approach divides the eddies into two different categories, large
eddies and small eddies. The procedure to separate a large eddy from a small eddy is done by
45
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
applying a filter. The large eddies are resolved “exactly”. Normally the grid-size is used as the
filter length and the eddies smaller than grid-size are modelled and taken into account by
different subgrid models. LES is unlike RANS not “case dependent”, i.e. there are no
constants which needs to be tuned for each particular case. LES solves the instantaneous
governing equations and therefore it can capture combustion and flow instabilities. The
benefits with LES is unfortunately at the cost that the approach is computational demanding
and generally require grid-size in the order of millimetres for engineering applications and it
is less used in large boiler simulations.
Another method, which does not require any modelling, is to use Direct Numerical
Simulation (DNS) of the transport equations. In this case all turbulence scales are fully
resolved, including the Kolmogorov scale. The approach is limited to simple flow with low
Reynolds numbers, because of the high computational effort.
3.3 Modelling of Volatile Oxidation
Combustion of biomass or any solid, gaseous or liquid fuels involves many different species
and reactions. Even when burning a “simple fuel” like methane it involves well over 270
reactions and 49 different species [9]. It is not possible to use these detailed species and
reactions to engineering combustion problems due to the fact that it is too computational
demanding. Instead, the volatile oxidation is often modelled using a global reaction
mechanism in which the elementary reactions are represented by a number of global
reactions. These reactions can be seen in equations (3.46) to (3.49) below. The major species
treated are CO, CO2, CH4, H2O, H2, O2, N2 and tar. Tar is assumed to consist of a mixture of
C10H8 (67%), C6H6 (17%), C7H8 and C8H10 (each 8%) and it is represented by CxHy where x =
9.2857 and y = 8.1429 [10].
y
⎛x y⎞
C x H y + ⎜ + ⎟ O2 → x CO + H 2O
2
⎝2 4⎠
3
CH 4 + O2 → CO + 2 H 2O
2
1
CO + O2 → CO2
2
1
H 2 + O2 → H 2O
2
(3.46)
(3.47)
(3.48)
(3.49)
Species transport equations for CO, CH4, H2, O2, tar, FC and GH are numerically solved. FC
and GH are conserved scalars for mass conservation of the elements C and H respectively.
They can be calculated in the following manner,
FC = YCH 4
Mc
M
Mc
x ⋅ MC
+ c YCO +
YCO2 +
Ytar
M CH 4 M CO
M CO2
M tar
12
12
12
111.43
Ytar
= YCH 4 + YCO + YCO2 +
16
28
44
119.57
46
(3.50)
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
GH = YCH 4
4M H 2M H
2M H
y⋅MH
+
YH 2 +
YH 2O +
Ytar
M CH 4 M H 2
M H 2O
M tar
4
2
8.1429
Ytar
= YCH 4 + YH 2 + YH 2O +
16
18
119.57
(3.51)
The mass fraction of CO2 and H2O can now be calculated as follows:
YCO2 =
YH 2O
44 ⎛
12
12
⎞
⎜ FC − YCH 4 − YCO − 0.932Ytar ⎟
12 ⎝
16
28
⎠
18 ⎛
4
⎞
= ⎜ GH − YCH 4 − YH 2 − 0.0681Ytar ⎟
2⎝
16
⎠
(3.52)
(3.53)
3.3.1 Turbulence Chemistry Interaction
The source term ω R in equation (3.37) represents the mean reaction rate of species i and it
takes into account the effects of turbulence. Turbulence has a large impact on the mixing of
reactants and affects the transport of heat and mass in a very non-linear manner. Therefore, it
is necessary to take into account the effects of turbulence on the reaction rate. In this work
these effects are taken into account based on the eddy dissipation combustion model (EDCM),
which was proposed by Magnussen and Hjertager [49].
3.3.2 EDCM
The EDCM assumes the reaction chemistry to be much faster than the mixing rate and the
combustion process is mixing controlled. The EDCM can be used when the Damköhler
number (Da) is large and the Karlovitz number (Ka) is small. The Damköhler number is the
ratio between the time scale for turbulent mixing and time scale for chemistry. The Karlovitz
number is the ratio between chemical time scale and Kolmogrov micro time-scale. In the case
of turbulent combustion of hydrocarbon fuels the Da number is often very large. The mean
reaction rate, for example the mean fuel consumption rate, will depend on the mixing rate of
oxidant and reactant on molecular level. By assuming that chemical reactions are mixing
controlled the mean fuel consumption rate can be written:
ω fu = m ρ min ⎛⎜ Y fuel , Y O 2 θ ⎞⎟
⎝
O2
⎠
(3.54)
Y fuel : mean concentration of fuel
Y O2 : mean concentration of oxygen
θO2 : stoichiometric oxygen required to burn a unit mass of fuel
where the mixing rate of reactants can be written as:
⎛ νε ⎞
m = 23.6 ⎜ 2 ⎟
⎝k ⎠
0.25
ε
k
(3.55)
47
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
To take into account that reactants may not react at molecular level due to low temperature a
correction factor is added to equation (3.54). This correction factor can be calculated based on
the combustion products and fuel:
YPr
ξ=
Y fuel +
θ Pr
YPr
(3.56)
θ Pr
YPr : Total mass fraction of products
θ Pr : stoichiometric product is formed when consuming a unit mass of fuel
The correction factor is multiplied to equation (3.54) and the mean fuel consumption rate
( ω R , in equation (3.37)) can then be written as:
⎛ νε ⎞
2 ⎟
⎝k ⎠
ω fu = 23.6ξ ⎜
0.25
⎛
ε
YO
ρ min ⎜ Y fuel ,
⎜
k
θO
⎝
2
2
⎞
⎟
⎟
⎠
(3.57)
0.25
⎛ νε ⎞
term may be set to a constant (the
When calculating the mean reaction rate the 23.6ξ ⎜ 2 ⎟
⎝k ⎠
so-called EDC-constant, CEDC). This constant needs to be calibrated for different problems.
For the present problems CEDC is set to 2.5.
3.3.3 Other Models
Other often used turbulence-chemistry interaction approaches are the Flamelet Library
approach [50] and probability density function (PDF) approach [51].
Flamelet Library Approach
The Flamelet Library Approach (FLA) assumes that the turbulent mean flame is an ensemble
of instantaneous locally laminar flames, called flamelets [50]. To use the flamelet library
approach the position of the flame front has to be found. For diffusion flames this can be done
by calculating the transport equation for mixture fraction, Z. The flame front is found where
the mixture fraction is equal to stoichiometry. Once the flame front is calculated the species
concentration and temperature can be obtained from a pre-calculated flamelet library. By
using the flamelet library approach detailed species such as soot can be calculated with
relatively low computational cost.
PDF Approach
In the PDF-approach the mean species mass fraction and temperature can be calculated using
a probability density function (PDF). This can be done by using a joint PDF.
ω (φ ) = ∫ ω (ψ )℘(ψ )dψ
48
(3.59)
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
ω (φ ) : mean reaction rate [kg/m3s]
℘ : probability function
ψ : scalar function
where the reaction rate is a function of all species and temperature.
ω = ω (Y1 , Y2 ,..., YN , T )
(3.60)
The method of using a joint PDF is computational demanding and the method can be
simplified by assuming that the PDF in equation (3.59) has a particular shape, a so-called
presumed PDF. An example of a normally used presumed PDF is the β-distribution, equation
(3.61)
P (ψ ) =
ψ a −1 (1 −ψ )
1
∫ψ (1 −ψ )
a −1
b −1
b −1
(3.61)
dψ
0
The only unknown variables in the presumed PDF are a and b. These parameters can be
determined from equation (3.62) and (3.63).
(
)
⎛ ψ 1 −ψ
⎞
⎜
− 1⎟⎟
a =ψ ⎜
2
⎜ ψ ''
⎟
⎝
⎠
a
b = −a
( )
ψ
(3.62)
(3.63)
3.4 Modelling of NOx Emission
Formation of NOx in biomass furnace may come from the following mechanisms:
•
Thermal or Zel’dovich mechanism. The extended Zel’dovich mechanism can be seen
in reaction N.1 to N.3. It plays important role at high temperatures and negligible
when temperature is below 1800 K [9, 11]. This is due to the fact that the nitrogen
atoms in the N2-molecule have a strong triple bond, which breaks first at very high
temperatures.
O + N 2 ⇔ NO + N
N + O2 ⇔ NO + O
N + OH ⇔ NO + H
•
(N.1)
(N.2)
(N.3)
Prompt or Fenimore mechanism. This mechanism occurs with combustion of
hydrocarbon fuels. The general scheme of the Fenimore mechanism is that
hydrocarbon radicals react with molecular nitrogen to form intermediate species like
HCN and NHi. These intermediate species (i.e. HCN and NHi) are then converted to
other intermediate compounds that ultimately form NO, see N.4-N.8, [9].
49
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
CH + N 2 ⇔ HCN + N
HCN + O ⇔ NCO + H
NCO + H ⇔ NH + CO
NH + H ⇔ N + H 2
N + OH ⇔ NO + H
•
(N.4)
(N.5)
(N.6)
(N.7)
(N.8)
Fuel-NO. The biomass fuel contains nitrogen that forms volatiles and some remain in
the solid char. The formation of NOx from the fuel nitrogen is called fuel-NO [11-13].
Most of the fuel bond nitrogen is released during devolatilisation as NH3, HCN and
HCNO in which NH3 is the predominant compound, only small amount of nitrogen
remains in the char [12, 13]. A simplified reaction scheme consisting of a few key
steps in fuel-N conversion to NO during biomass combustion can be seen in Figure
27.
Heterogeneous reactions
Char-N
+N
N2
HCNO
Fuel -N
NH3
HCN
+NO
+H
+H, OH
+H, OH
NO
NH2
+H
+OH, O2
CN
NH
+H
+OH, O2
N
+H
CNO
Figure 27. A simplified reaction scheme of fuel NO.
•
N2O intermediate mechanism. Malte and Pratt [52] showed that the following
reactions can be important in certain conditions:
N 2 + O + M ⇔ N 2O + M
N 2O + O ⇔ NO + NO
N 2O + O ⇔ N 2 + O 2
N 2O + H ⇔ N 2 + OH
(N.9)
(N.10)
(N.11)
(N.12)
In the present thesis, the thermal-NO mechanism, the N2O intermediate mechanism and the
Fuel-NO mechanism are applied to simulate NO formation in boilers. Prompt NO has been
neglected since the combustion in boilers is typically oxygen abundant.
3.4.1 Models for Fuel-NO Simulations
As previously discussed biomass fuels have more volatiles compared to coal and the main
part of the fuel bond nitrogen leaves as volatile compounds. Different studies have been
carried out in the literature to examine the amount of the different nitrogen species during
biomass conversion. Samuelsson [53] compared data gathered in the literature and found that
the ratio between released HCN and NH3 varied greatly depending fuel species. Fuels with
high O/N preferable formed NH3, compared to those with a low O/N ratio. The reason behind
50
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
the higher NH3 release was suggested to depend on reactions between HCN and OH- and Hradicals inside the particle, where HCN oxidises to NH3. de Jong et al. [38] reported
significant amounts of released HCN and HNCO during pyrolysis experiment of wood pellets
and Miscanthus Giganteus. In de Jongs studies the concentration of HCN was higher than
those of NH3. However, de Jong et al. explained that the high amount of HCN could be due to
the fact that the experiments did not allow for HCN to react to NH3.
There exist a number of different models for the fuel-NO mechanism. A short review of some
of them is given below. Among the more well-known ones are the de Soete model and the
Mitchell and Tarbell model [54, 55], both developed for coal combustion. The existing
models for biomass combustion are the Lindsjö et al., Brink et al. and Vilas et al. models [10,
56, 57].
The de Soete model [54] assumes all nitrogen is released through devolatilisation and forms
nitrogen intermediates, HCN, NH3 or C2N2 and that no heterogeneous reactions take place.
The nitrogen intermediate react with oxygen and form NO or reburn with NO to form N2, see
Figure 28.
N2
+NO
Fuel-N
Nitrogen intermediate
+O2
NO
Figure 28. The de Soete reaction model.
The Mitchell and Tarbell model [55] is derived for pulverised coal combustion. It consists of
three heterogeneous reactions (3.64) to (3.66) and four homogeneous reactions (3.67) to
(3.70). A schematic plot of the model can be seen in Figure 29.
Non-nitrogen volatile
Solid
Particle
Devolatilisation
Char
+CxHy
HCN
+H2O
+O2
NH3
NO
+O2
+NO
N2
Figure 29. Sketch of Mitchell and Tarbell model.
The solid particle devolatilises and form non-nitrogen volatile and HCN. HCN reacts with
H2O to form ammonia. The formed ammonia can react with oxygen to form NO or reburn
with NO to form N2. NO may also reburn with unburned hydrocarbons to from HCN. The
51
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
solid char releases the nitrogen by reacting with oxygen to form NO. The formed NO may
react with the solid surface to form CO and N2.
C(N)s +0.5O 2 → NO
C(N)s → HCN
Cs +NO → 0.5N 2 + CO
HCN+H 2 O → NH 3 + CO
NH3 +O 2 → NO + H 2 O + 0.5H 2
NH3 +NO → N 2 + H 2 O + 0.5H 2
1
⎛ 3-x/y ⎞
NO + C x H y + ⎜
⎟ H 2 → HCN + H 2 O
x
⎝ 2 ⎠
(3.64)
(3.65)
(3.66)
(3.67)
(3.68)
(3.69)
(3.70)
The Brink et al. model [56] does not consider heterogeneous reaction but assumes all nitrogen
in the fuel forms NH3. This hypothesis is based on pyrolysis and gasification studies of
biomass and peat, in which the amount of released NH3 was considerably greater than that of
HCN. The model uses the same 2-step global reaction mechanism, which was proposed by
Mitchell and Tarbell [55] for oxidation of NH3 and reburning of NO, reactions (3.68 and
3.69). The model performs rather well in fuel rich conditions and high temperatures.
However, when tested together with the de Soete and Mitchell and Tarbell models [54, 55] in
a recovery boiler for black liquor it severely under-predicted the emitted NO from the boiler,
while the de Soete model gave rather good agreement with measurements [58].
The Lindsjö et al. [10] model assumes the nitrogen in the fuel forms a mixture of HCN and
NH according to the reaction (3.71), in which γ is a distribution factor deciding the
distribution between HCN and NH. Similar to the Brink et al. model [56] it does not include
any heterogeneous reactions. The major species involved in NO calculations are NO, NH,
HCN and OH. The global reactions for fuel NO are assumed to be:
Fuel-N → γ HCN+ (1 − γ ) NH
HCN+0.5O 2 → CO+NH
NH+NO → N 2 +OH
NH+O 2 → NO+OH
(3.71)
(3.72)
(3.73)
(3.74)
The path of NO reburning with hydrocarbon radical to form HCN is neglected since it is less
important than NO reacting with NH. Since the reactions are assumed to be mixing controlled
the mean reaction rates are modelled with the EDCM.
The Villas et al. model [57] assumes that 80% of the fuel nitrogen is released during
devolatilisation and leaves as NH3. The oxygen and hydrogen in the fuel leaves during
volatile formation and the char matrix is assumed to consist of only carbon and the remaining
nitrogen. The volatile oxidation of the pyrolysis gases and their interaction with NO is
modelled by using a detailed chemical kinetic model. The char reactions for NO formation
and destruction are modelled with a simple two-step mechanism, (3.75 and 3.76).
⎡ ⎛ ψ⎞ ⎤
Cα Nδ (s)+ ⎢α ⎜ 1- ⎟ +δ ⎥ O 2 (g) → ψα CO(g)+ (1-ψ ) CO 2 (g)+δ NO(g)
⎣ ⎝ 2⎠ ⎦
52
(3.75)
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
⎛α +δ
Cα Nδ (s)+α NO(g) → α CO(g)+ ⎜
⎝ 2
⎞
⎟ N 2 (g)
⎠
(3.76)
The model was compared with experimental data obtained when burning wheat straw and
poplar wood. It shows good agreement compared to experimental data but over-predicts the
NO reduction for poplar wood under very rich conditions.
3.4.2 Modelling of Thermal NO and NO from N2O-intermediate
Mechanism
Thermal NO is modelled through Zel’dovich mechanism as described in the previous
subsection. To calculate rate of NO formation, the concentrations of O, N and OH radicals
need to be known. This is not possible if global mechanisms for the fuel oxidation are
employed. A simplified approach that is used here is to introduce steady-state approximation
to the O-radicals and partial equilibrium for the shuffle steps OH + H2 = H2O + H, H + O2 =
O + OH [59]. This leads to the overall reaction rate of NO formation as the following.
d [ NO]
⎛ 38440 ⎞
= 9.0 ⋅1012 T 0.3 exp ⎜ −
⎟ [ N 2 ][O2 ]
dt
T ⎠
⎝
(3.77)
The units are in mole, cm, s and K. Since thermal NO is a slow process it can not be modelled
using the EDC model. Instead, it is modelled by using a presumed PDF approach. A βdistribution PDF is used. More information about the presumed PDF model can be found in
[59, 60].
Similarly, Rokke et al. [61] showed that NO from the N2O-intermediate mechanism can be
calculated by the following rate:
d [ NO]
= 2.65 ⋅ 1012 exp ( −13160 / T ) [ N 2 ][ O2 ][ M ]
dt
(3.78)
where [M] is the third body mole concentration (in mole/cm3).
53
Chapter 3: Modelling of Volatile Oxidation above the Fuel Bed
54
Chapter 4: Radiation Heat Transfer in Boilers
4 Radiation Heat Transfer in Boilers
When modelling biomass combustion inside fixed bed boilers it is important to take into
account the effects of thermal radiation. At high temperatures, as in combustion, thermal
radiation is the dominating heat transfer mode. This is due to the dependence of radiation on
the temperature to the power of four, the low flow speed in the boiler and the large combustor
volume. Radiation is included in the calculation through the source term in the energy
equation (3.11), SR.
()
∞ 4π
S R = −∇ ⋅ q r = − ∫
∫
0 0
dI λ
∂Ω∂λ
ds
(4.1)
()
q r : radiative heat flux vector [W/m 2 ]
r : position vector [m]
s : coordinate along the path of a radiation ray [m]
I λ : intensity of radiation at the wave length λ [W/m 2 ⋅ sr ⋅ µm]
The Radiation Transfer Equation (RTE) for an absorbing, emitting and scattering medium can
be written as:
σ
dI λ
= s ⋅∇I λ = −κ λ I λ r , s − σ s ,λ I λ r , s + κ λ I b ,λ r + s ,λ
ds
4π
( )
( )
()
∫
4π
0
( ) ( )
I λ r , s i Φ λ s i , s ∂Ωi (4.2)
λ : wavelength [µm]
κ : absorption coefficient
σ s : scattering coefficient
I b : black body radiation
Ωi : solid angle in s direction [sr]
Φ : scattering phase function
r : position vector
s : direction vector
The terms in RTE can be easier understood by considering Figure 30, which shows a radiation
beam travelling along direction s in an absorbing, emitting and scattering media. As the beam
passes through the medium, some energy is lost due to absorption of the media and scattering.
The beam may also gain energy from incoming scattering and energy emitted from the media
to the beam. The first two terms on the right hand side of equation (4.2) represent losses due
to absorption and scattering. The last two terms represent gains due to energy emitted from
the media and incoming scattering.
The RTE is a differential-integration equation and it can only be solved exactly for a few
limited cases. Since it can not be solved analytically in its general form, simplifications need
to be done. By assuming the gas medium to be grey (i.e. independent of the wave length) and
adding κ and σs into β (extinction coefficient), equations (4.2) and (4.3) can be simplified to:
55
Chapter 4: Radiation Heat Transfer in Boilers
σ
dI
= s ⋅∇I = − β I r , s + κ I b r + s
ds
4π
4π
dI
∂Ω
S R = −∇ ⋅ q r = − ∫
ds
0
( )
()
∫
4π
0
( ) ( )
I r , s i Φ s i , s ∂Ωi
()
(4.3)
(4.4)
There exist a number of different numerical methods to solve the RTE. The methods
considered in this work are Optically Thin model (OT), P1-approximation model and Finite
Volume Method (FVM).
Absorption and
scattering losses
I (κ + σ s ) ds
Incoming
Radiation I
Outgoing
Radiation
⎛ dI ⎞
I + ⎜ ⎟ ds
⎝ ds ⎠
Scattering
addition
Gas emission
(κ I b ) ds
ds
Figure 30. Conservation of radiant energy.
4.1 Optically Thin Model
The optically thin model [62] is a simple model that does not need to solve the RTE. Instead,
it calculates the radiation source term from gas temperature and its absorption coefficient,
based on the assumption that the medium is only radiating heat (no absorption). It can be
useful to use when the optical thickness2 of the medium is much smaller than unity. The
source term can be seen in equation (4.5):
()
S R = −∇ ⋅ q r = −4σ T 4 (κ soot + κ P , gas )
(4.5)
κ P,gas : Planck mean absorption coefficient of the gas mixture [1/m]
κ soot : soot absorption coeffient [1/m]
In the present thesis, the Planck mean absorption coefficient for the gases has been calculated
by using the Exponential Wide Band Model (EWBM) given in Nilsson and Sundén [63]. If
soot is not important, the first term on the right hand side of equation (4.5) is neglected.
2
Optical thickness is defined as absorption coefficient time a characteristic length (κ*L), for example the
diameter of a combustor or mean beam length of a boiler.
56
Chapter 4: Radiation Heat Transfer in Boilers
4.2 P1-Approximation
The P1-approximation [64] is the simplest case of spherical harmonics, or P-N radiation
approximation. A derivation is given below, following Modest [65]. The radiation intensity is
expanded in terms of a two dimensional general Fourier series:
( )
∞
l
() ()
I r , s = ∑ ∑ I lm r Yl m s
l = 0 m =−1
(4.6)
r : position vector [m]
s : unit vector in given direction
()
I lm r
()
are position dependent coefficients and Yl m s
are spherical harmonics given by
equation (4.7):
Yl
m
( s ) = ( −1)
(
)⎥
⎢
⎢⎣ ( l + m ) !⎥⎦
( m + m ) / 2 ⎡ l − m !⎤
0.5
eimψ Pl (cos θ )
m
(4.7)
θ : polar angle of the unit vector s
ψ : azimuthal angle of the unit vector s
m
which satisfy the Laplace’s equation in spherical coordinates. Pl are associated Legendre
polynomials, defined as:
(1 − µ )
(µ ) =
2 m/2
Pl
m
2l l !
l
d l +m
µ 2 − 1)
l +m (
dµ
(4.8)
µ : cos θ
For the P1-approximation the series in equation (4.6) is truncated after l = 1 (i.e. llm ≡ 0 for
l ≥ 2 ), and thus the lowest order of P-N approximation is obtained:
( )
I r , s = I 00Y00 + I1−1Y1−1 + I10Y10 + I11Y11
(4.9)
where the associated Legendre polynomials are given in Table 4.
Table 4. Associated Legendre Polynomials, Pl m (cosθ ) .
l
0
1
m=0
1
cos θ
M=1
---sin θ
Combining equations (4.7-4.9) with the data given in Table 4 the radiation intensity can now
be expressed as follows:
57
Chapter 4: Radiation Heat Transfer in Boilers
(
)
1 1 iψ
I1 e − I1−1e − iψ ) sin θ
(
2
i
1 −1 1
= I 00 + I10 cos θ +
I1 − I1 ) sin θ cosψ −
I1−1 + I11 ) sin θ sinψ
(
(
2
2
I r ,θ ,ψ = I 00 + I10 cos θ −
(4.10)
Equation (4.10) can be rewritten in a more compact form by introducing two new functions, a
scalar function a r and a vector b r .
()
()
( ) () ()
I r, s = a r + b r s
(4.11)
By substituting equation (4.11) in the expression for incident radiation (G), equation (4.12) is
obtained.
( ) ∫ I ( r, s )d Ω = a ( r ) ∫ d Ω + b ( r ) ∫ s ⋅ d Ω
⎫
⎪
4π
4π
4π
⎪⎪
⎛ sin θ cosψ ⎞
⎛ 0⎞
⇒ G r = 4π a r
⎬
2π π ⎜
⎟
⎜ ⎟
⎪
∫ s ⋅ d Ω = ∫0 ∫0 ⎜ sin θ sinψ ⎟ sin θ dθ dψ = ⎜ 0 ⎟ = 0⎪
4π
⎜ cosθ ⎟
⎜ 0⎟
⎝
⎠
⎝ ⎠
⎭⎪
G r =
()
()
(4.12)
()
By similarly inserting equation (4.11) into the definition for the radiative heat flux, q r , the
following expression is obtained.
( ) ∫ I ( r, s ) s d Ω = a ( r ) ∫ s d Ω + b ( r ) ∫ ss d Ω = ... = 43π b ( r )
q r =
4π
since the term
∫π ssd Ω is equal to
4
4π
(4.13)
4π
4
πδ , as shown in equation (4.14), and δ is a unit tensor.
3
⎛ sin 2 θ cos 2 ψ
sin 2 θ sin ψ cosψ
2π π ⎜
2
2
2
∫4π ssd Ω = ∫0 ∫0 ⎜ sin θ sinψ cosψ sin θ sin ψ
⎜ sin θ cosθ cosψ sin θ cos θ sinψ
⎝
sin θ cosθ cosψ ⎞
⎟
sin θ cosθ sinψ ⎟ × sin θ dθ dψ
⎟
cos 2 θ
⎠
⎛ π sin 2 θ 0
⎞
0
⎛1 0 0 ⎞
π⎜
⎟
4π ⎜
⎟
2
π sin θ 0
0 1 0⎟
=∫ ⎜ 0
⎟ sin θ dθ =
⎜
0
3 ⎜
⎟
⎜ 0
⎟
2
π
θ
0
2
cos
⎝ 0 0 1⎠
⎝
⎠
(4.14)
Equation (4.11) can be rewritten in terms of incident radiation (G) and radiative heat flux
( q ( r )) .
( )
I r, s =
58
()
()
1 ⎡
G r + 3 q r ⋅ s⎤
⎦
4π ⎣
(4.15)
Chapter 4: Radiation Heat Transfer in Boilers
Equation (4.15) can now be used to obtain an expression of incoming scattering. This is done
by substituting equation (4.15) into equation (4.3) and assuming linear anisotropic scattering,
( )
Φ s ⋅ s i = 1 + A1 s ⋅ s i
(4.16)
The incoming scattering can then be written as:
∫π I ( s ) Φ ( s ⋅ s ) d Ω
i
i
4
=
i
=
1
4π
∫ ( G + 3q ( r ) ⋅ s ) (1 + A s ⋅ s ) d Ω
i
4π
1
i
i
()
⎤ 3q r ⎡
⎛
⎞ ⎤
G ⎡
Ω
+
⋅
Ω
+
Ω
+
⋅
Ω
d
A
s
s
d
s
d
A
s
s
d
i
i
i
⎢
⎜
⎢
i
i⎥
i
i ⎟ ⋅ s ⎥ (4.17)
1
1 ∫
∫
4π ⎣ 4∫π
4π ⎢⎣ 4∫π
4π
⎦
⎝ 4π
⎠ ⎦⎥
()
()
= G + A1 q r ⋅ δ ⋅ s = G + A1 q r ⋅ s
The RTE (equation 4.3) can be written as follows by inserting equations (4.15) and (4.17) in
equation (4.3):
( ()
() )
(
() )
σ
1
1 ⎡
G r + 3 q r ⋅ s ⎤ ( I b − κ − σ s ) + s G + A1 q r ⋅ s
∇ ⋅ ⎡⎢ s G r + 3 q r ⋅ s ⎤⎥ =
⎦
⎣
⎦ 4π ⎣
4π
4π
()
()
(4.18)
By multiplying equation (4.18) with Y00 = 1 and integrating over all solid angles the following
expression can be obtained, which is the divergence of radiative heat flux:
()
∇ ⋅ q r = κ ( 4π I b − G )
I b : black body radiation,
(4.19)
σT 4
π
σ: Stefan-Boltzmann constant = 5.67×10-8 [W/m 2 K 4 ]
By multiplying equation (4.18) with the components of the direction vector s and integrating
over all directions the following expression can be obtained.
()
∇G = − ( 3β − A1σ s ) q r
(4.20)
Equation (4.20) can be further simplified by eliminating the heat flux by taking the
divergence of the equation and dividing it with 3β − A1σ s
⎛
⎞
1
∇ ⋅⎜
∇G ⎟ = −∇ ⋅ q r = −κ ( 4σ T 4 − G )
⎝ 3β − A1σ s
⎠
()
(4.21)
β: extinction coefficient (κ+σs )
A1: linear anisotropic scattering phase function coefficient
σs : scattering coefficient
κ: total absorption coefficient (κ p,gas +κ soot ) [1/m]
59
Chapter 4: Radiation Heat Transfer in Boilers
Equations (4.19) and (4.21) are a complete set of one scalar and one vector equation and are
the governing equations in the P1-approximation. The problem can be further simplified by
assuming isotropic scattering, i.e. A1 may be set to zero. When the incident radiation is solved
the radiation source term in equation (4.4) can be calculated according to:
()
S R = −∇ ⋅ q r = −κ ( 4σ T 4 − G )
(4.22)
4.3 The Finite Volume Method
In the Finite Volume Method, FVM [66], the directional effect of radiation is considered. The
direction is described by an azimuthal angle, θ, and a polar angle, φ , see Figure 31.
φ
I
r
θ
Figure 31. A radiation ray travelling in space as a function of r, θ and φ .
The 4π solid angles are discretized into a finite number of discrete solid angles and in each
solid angle the radiation intensity is assumed to be uniform. The numbers of solid angle
directions are given by equation (4.24).
φi =
π
nφ
, 0<φ <π
2π
, 0 < θ < 2π
θi =
nθ
(4.24)
nφ : number of polar angles
nθ : number of azimuthal angles
The angular space consists of nφ × nθ control angles. A two dimensional example is shown in
Figure 32 to explain how the real intensity field (left) can be approximated by a four
discretized solid angles in FVM (right).
60
Chapter 4: Radiation Heat Transfer in Boilers
Figure 32. Radiant intensity field: (left) Actual, (right) 4 angle FVM discretisation.
Below follows a short derivation of FVM. The RTE for a grey absorbing, emitting and
scattering medium can be written as:
σ (r)
dI
= − β ( r ) I ( r,sˆ ) + κ ( r ) I b ( r ) + s
I ( r,sˆ i ) Φ ( sˆ i ,sˆ ) d Ωi
ds
4π 4∫π
(4.25)
By applying Gauss’s theorem equation (4.25) one obtain
⎧
∫ ∆∫A Ii ( sˆi ⋅ nˆ ) dAd Ωi = ∆Ω∫ ∆∫V ( −β Ii + Si ) dVd Ωi
⎪ ∆Ω
i
⎪ i
⎨
M
⎪ I i = I ( r , sˆi ) Si = κ I b + σ s ∑ I j Φ ij ∆Ω j
⎪⎩
4π j =1
(4.26)
where i is the direction (under consideration) and j is the incoming direction to volume (or
surface). If one has a Cartesian coordinate system with parallelepiped control volumes, then
the control volume has six surface areas and equation (4.27) will result. In order to separate
the direction under consideration from all incoming directions, a modified extinction and
source term is introduced, see equation (4.28).
6
⎛
∑ ⎜⎜ I
k ,i
∆Ak
⎞
∫ ( sˆi ⋅ nˆk ) d Ωi ⎟⎟ = ( − β Ii + Si ) ∆V ∆Ωi
∆Ωi
⎝
⎠
⎧ 6 ⎛
⎞
⎪∑ ⎜ I k ,i ∆Ak ∫ ( sˆi ⋅ nˆk ) d Ωi ⎟ = ( − β m ,i I i + S m,i ) ∆V ∆Ωi
⎟
⎪⎪ k =1 ⎜⎝
∆Ωi
⎠
⎨
M
⎪ β = β − σ s Φ ∆Ω , S = κ I + σ s
∑ I j Φij ∆Ω j
ii
i
m ,i
b
⎪ m ,i
4π
4π j =1
⎪⎩
j ≠i
k =1
(4.27)
(4.28)
Expanding the sum over the surfaces in equation (4.28), equations (4.29) to (4.31) will result.
Indicies used are: w=west, e=east, s=south, n=north, l=low, and h=high. The expressions of
Dci in equation (4.31) is similar to the ordinates in DOM (µi, ξi and ηi), and ∆Ω j in equation
(4.28) is similar to the quadrature weights in DOM. The difference between DOM and FVM
is the factor ∆Ωi in equation (4.28), which is not used in DOM.
61
Chapter 4: Radiation Heat Transfer in Boilers
(I
i ,e
− I i , w ) ∆Ax Dcxi + ( I i , n − I i , s ) ∆Ay Dcyi + ( I i ,h − I i ,l ) ∆Az Dczi =
(−( β )
m ,i P
)
I i , P + ( Sm ,i ) P ∆V ∆Ωi
⎧∆Ax ,in = ∆Ax ,out = ∆Ax = ∆y∆z
⎪
⎪∆Ay ,in = ∆Ay ,out = ∆Ay = ∆x∆z
⎨
⎪∆Az ,in = ∆Az ,out = ∆Az = ∆x∆y
⎪∆V = ∆x∆y∆z
⎩
⎧ Dcxi = ( sˆi ⋅ nˆ x ) d Ωi
∫
⎪
∆Ωi
⎪
⎨
⎪ Dczi = ( sˆi ⋅ nˆ z ) d Ωi
∫
⎪⎩
∆Ωi
Dcyi =
(4.30)
∫ ( sˆ ⋅ nˆ ) d Ω
i
y
i
∆Ωi
∆Ωi =
(4.29)
φi + θi+
∫ d Ω = φ∫ θ∫ sinθ dθ dφ
(4.31)
i
∆Ωi
i−
i−
The intensity is discretized and calculated in each computational cell and in each direction.
When the intensity is known the incident radiation can be calculated according to:
G=
∫ I dΩ
(4.32)
4π
After the incident radiation is known the radiation source term can be calculated in the same
way as for P1-approximation:
()
S R = −∇ ⋅ q r = −κ ( 4σ T 4 − G )
(4.33)
4.4 Radiative Properties
To be able to calculate the RTE it is needed to supply detailed information about the radiative
properties of the combustion gas. The radiation properties include gas and soot absorption and
particle absorption and scattering.
4.4.1 Gas absorption
Gaseous species can both absorb and emitted radiative energy. When a ray of radiative energy
passes through a gas layer with thickness s it gradually becomes diminished through
absorption. The absorption leads to an exponential decay of incident radiation and the
transmissivity of a homogeneous isothermal gas layer may be written as:
τ λ = e −κ λ s
(4.34)
The exponential decay is also known as Beer-Lamberts law. Based on the fact that the gas
layer either transmits or absorbs radiative energy an expression for spectral absorbtivity can
be defined.
α λ = 1 − τ λ = 1 − e −κ λ s
τ : transmissivity
α : absorptivity
62
(4.35)
Chapter 4: Radiation Heat Transfer in Boilers
Depending on molecular structure some gases absorb and emit energy in specific wave
lengths or bands and in between the gas is transparent, i.e. no energy is absorbed or emitted.
The bands, in which the gases absorbs, depends not only on the gas species but also on
temperature and pressure. In the case of biomass combustion considerable amounts of CO2
and H2O are formed together with some amount of CO, and CH4. To make detailed
calculation of these species would be rather complicated and unsuitable for engineering
calculations such as boiler calculations. Instead different kinds of models for the gas
absorption coefficient can be used. There exist a large number of models, which can be
divided into the three following groups:
1. Empirical models
2. Band models
3. Correlation models
These groups will not be discussed here but more details can be found in Modest [65]. The
model used in this work belongs to the band model group. The used band model is the
exponential wide band model (EWBM) [63]. Another gas absorption model used is the
spectral line based weighted sum of grey gas model (SLW) [65]
4.4.1.1 Exponential Wide Band Model
The EBWM builds on the fact that gases generally absorb and emit energy within several
bands. The main idea with wide band models is to use a simple function to represent the gas
absorption over a wide band. In the case with the EWBM the function is exponential.
Depending on the band shape, the mean line intensity to spectral line spacing ratio S/d can be
found by one of the following exponential functions, which can also be seen in Figure 33:
S/d
(S/d)0
(1/e)*(S/d)0
ω
ηu
ω
ω
ηc
ηl
Figure 33. Band shapes for the exponential wide band model.
63
Chapter 4: Radiation Heat Transfer in Boilers
S ⎛ α ⎞ −(ηu −η ) / ω
upper limit
= ⎜ ⎟e
d ⎝ω ⎠
S ⎛ α ⎞ −(η −ηl ) / ω
lower limit
= ⎜ ⎟e
d ⎝ω ⎠
(4.36)
S ⎛ α ⎞ −2(ηc −η ) / ω
band centre
= ⎜ ⎟e
d ⎝ω ⎠
α : integrated band intensity [m/kg]
ω : band width [1/m]
η : wave number
ηu : wave number for upper band head
ηc : wave number for central band head
ηl : wave number for lower band head
S / d : smoothed absorption coefficient [1/m]
The radiative properties are obtained from the integrated absorption coefficient α, line overlap
parameter β and band width parameter ω. The band correlation parameters (α, β and ω) are
calculated using polynomial fits of α/α0 and γ/γ0.
α
= a0 + a1T + a2T 2 + a3T 3 + a4T 4 + a5T 5 + a6T 6
α0
γ
= b0 + b1T + b2T 2 + b3T 3 + b4T 4 + b5T 5 + b6T 6
γ0
(4.37)
The band width parameter is calculated from equation (4.38).
ω
T
=
ω0
To
(4.38)
When the above parameters are known β can be calculated using equation (4.39).
⎛ p⎛
p ⎞⎞
β = γ Pe = γ ⎜ ⎜1 + ( b − 1) a ⎟ ⎟
p ⎠⎠
⎝ p0 ⎝
n
(4.39)
pe : effective pressure
po : 1 atm
pa : partial pressure [atm]
T0 : 100 K
When band correlation parameters3 are known can the absorbtivity of the gas, αg, be
calculated. Details about this can be found in [63]. The local gas absorption coefficient is
calculated from the absorbtivity according to equation (4.40).
The pressure parameters (n and b in equation (4.39)) and band correlation parameters α 0 , β 0 and ω 0 depends
on gas species and wavelength and can be found in [63].
3
64
Chapter 4: Radiation Heat Transfer in Boilers
κ=
Lm : mean beam length, 3.6 ⋅
1 ⎛ 1
ln ⎜
Lm ⎜⎝ 1 − α g
⎞
⎟⎟
⎠
(4.40)
furnace volume
[m]
furnace area
The species, which are taking into consideration when calculating the gas absorption
coefficient are CO, CO2, H2O and CH4 and their data can be found in [63]. It should be noted
that the EWBM is much more computational efficient compared to accurate and
computational demanding line-by-line calculations (LBL). However, the gain in efficiency is
at the cost of accuracy. Modest [65] estimated the averaged error to be approximately ±20% .
4.4.1.2 The Spectral Line Based Weighted Sum of Grey Gas Model
The SLW model, which uses an accurate and compact database, is reliable and applicable
model in engineering calculations. In this model the weight of grey gases is interpreted as the
fraction of the blackbody radiation. Details about this model can be found in [65]. For using
of the SLW model similar to weighted sum of grey gas model, the RTE should be solved for
each of the selected gray gases. This model will be more expensive when is used in mixture of
several gases. In the case of two different gases, for example CO2 and H2O, the RTE for an
emitting and absorbing media, may be written as follows:
dI jk
ds
= −κ jk I jk + a jkκ jk I b
(4.41)
a j ,k : blackbody weight [-]
where Ijk is the radiation intensity for the jth grey gas component of H2O and kth grey gas
component of CO2. The SLW model, in this study has been used for the mixture of CO2 and
H2O gases. The convolution approach was used to calculate the total blackbody weight of the
mixture. Several numbers of absorption cross sections were checked and finally 15
logarithmically spaced intervals from 3e-5 up to 200 were used.
4.4.2 Particle Properties
Combustion in grate fired furnace often includes small particles leaving the bed and following
the flow. These particles may be fly ash, wood or char particles. The interaction between
particles and electromagnetic waves (i.e. thermal radiation) is somehow different compared
with homogeneous gas. In the case of radiation in a homogeneous medium the radiation ray is
transmitted, absorbed or reflected. However, particles (depending on their size) may interfere
with the travelling radiation ray and change its direction. The direction can be changed
through three mechanisms, see Figure 34.
1. Diffraction
2. Reflection
3. Refraction
65
Chapter 4: Radiation Heat Transfer in Boilers
Refraction
Iin
θ
θ
c
θ
Reflection
2 ⋅ rp
Diffraction
λ
Figure 34. Interaction between electromagnetic waves and spherical particles.
Scattering is an encounter between a radiation wave and one or more particles, in which the
ray undergoes a change of direction and loss/gain energy in the process. In diffraction the path
of the radiation ray is changed without it colliding with the particle. In reflection the ray is
reflected as it hits the surface of the particle. Refraction is similar to reflection except that the
ray is not reflected, as it hits the particle, but it travels through the particle. As the ray moves
through the particle some energy may be absorbed and it direction is altered. These three
phenomena is better known as scattering. When a scattering media is considered then the
effect of scattering is added to equation (4.34), see equation (4.41).
−σ
τλ = e (
s ,λ
+κ λ ) s
(4.41)
Scattering can be classified into three different regimes. The regimes are defined by the size
parameter, equation (4.42).
x=
2π rp
λ
(4.42)
where rp is the effective radius of the particle. The three regimes are:
1. x 1, Rayleigh scattering and it is proportional to 1/λ4.
2. x ≈ 1, Mie scattering.
3. x 1, Geometrical optics. The surface of the particle is treated like a normal surface.
In grate fired boilers both soot and fly-ash/char particles are present. The size parameter, x,
varies from 10-4 for soot to about 100 for char and fly-ash particles. Thus, can radiative
parameters for soot be calculated using Rayleigh scattering. The fly-ash and char have bigger
particle diameter and falls in the Mie regime. Only Mie and Rayleigh scattering will be
mentioned briefly in the following part and how the effect of scattering affect the extinction
coefficient, β, for particle clouds of non-uniform size distribution. Further information about
geometrical optics can found in Modest [65].
66
Chapter 4: Radiation Heat Transfer in Boilers
Mie Scattering
For Mie calculations carried out in this work it is assumed that the participating particles
consist of a cloud of fly-ash and char particles with non-uniform sizes. The data of the
particles are taken from [67] and the particle size is expressed with log-normal distribution,
which has the following form:
2
− ln ( D ) − µ ) / 2σ 2
e(
f ( D) =
2π σ D
(4.43)
µ and σ are logarithmic mean and standard deviation and their values for fly-ash and char can
be seen in Table 5.
Table 5. Log-normal parameters for fly-ash and char [67].
Particle type
fly-ash
char
µ
3.89
5.63
σ
1.34
1.17
Based on the work carried out in [67] two different cases of particle concentration have been
computed in this work. The particle concentrations are seen in Table 6 and are calculated
from a study done by on biomass fired grate boilers [68].
Table 6. Particle concentrations [67].
Particle type
fly-ash
char
Low conc. [g/Nm3]
3.89
5.63
High conc. [g/Nm3]
1.34
1.17
The spectral scattering, absorption and extinction coefficients per kg/Nm3 of particles with a
diameter D and wavelength λ is given by:
σ s ,i , λ , D =
κ i ,λ , D =
β i ,λ , D =
3Qscat ,i ,λ , D
2 ρi D
3Qabs ,i ,λ , D
2 ρi D
3Qext ,i ,λ , D
2 ρi D
(4.44)
(4.45)
(4.46)
ρi : density of fly-ash and char [kg/m3 ]
D : diameter of particle [m]
67
Chapter 4: Radiation Heat Transfer in Boilers
The density of the char and fly-ash is assumed to be 150 [69] and 283 [16] kg/m3 respectively.
By integration over the mass size distribution the total spectral scattering, absorption and
extinction coefficients can be obtained.
Dmax
∫
σ s ,i , λ = M i
σ s ,i ,λ , D f ( D ) dD
(4.47)
0
Dmax
∫
κ i ,λ = M i
κ i ,λ , D f ( D ) dD
(4.48)
β i ,λ , D f ( D ) dD
(4.49)
0
β i ,λ = M i
Dmax
∫
0
M i : mass of particles per unit volume, char & fly-ash
Dmax : maximum diameter of particle = 300 µ m
The mean Planck scattering, absorption and extinction coefficient is obtained by averaging
the spectral results, where i stands for fly-ash and char.
∫
σ s ,i =
∞
0
σ s ,i , λ I b , λ d λ
∫
∞
I b ,λ d λ
0
κi =
∫
∞
0
κ i ,λ I b ,λ d λ
∫
∞
I b ,λ d λ
0
βi =
∫
∞
0
β i ,λ I b ,λ d λ
∫
∞
I b ,λ d λ
0
(4.50)
(4.51)
(4.52)
The phase function is then given by equation (4.53).
∞
Φ i (θ ) =
∫σ
i ,λ
0
Φ i ,λ (θ ) I b ,λ d λ
∞
∫σ
(4.53)
I dλ
i ,λ b ,λ
0
where Φ i ,λ (θ ) is given by equation (4.54).
Dmax
Φ i ,λ (θ ) =
∫
σ i ,λ , D Φ i ,λ , D (θ ) f ( D ) dD
0
Dmax
∫
(4.54)
σ i ,λ , D f ( D ) dD
0
The phase function is related to the number of particles and for a particle cloud, consisting of
different types of particles the phase function is calculated according to equation (4.55).
68
Chapter 4: Radiation Heat Transfer in Boilers
∑ Φ (θ ) N
Φ (θ ) =
∑N
i
i
i
(4.55)
i
i
N i : number of particles per unit volume, char & fly-ash
The calculated phase function, used in this work, for fly-ash and char are seen in Figure 35.
Due to the large number of fly-ash particles compared to char particles is the total phase
function similar to the one of fly-ash. It is seen in Figure 35 that the calculated phase
functions for fly-ash and char show strong forward scattering, especially for cos (θ ) close to
1. Fly-ash also show some backward scattering for −0.8 ≤ cos (θ ) .
1000
Ash
Char
Total
Phase Function
100
10
1
0.1
0.01
-1
-0.5
0
cos φ
0.5
1
Figure 35.Total, fly-ash and char phase functions, calculated based on Mie theory.
Rayleigh Scattering
In Rayleigh scattering is the diameter of the particle considerably much smaller than the
wavelength of the radiation within the particle. An example of solid particles, which falls into
the Rayleigh scattering regime is soot. Soot has a small diameter, which often is less than 10
nm. Due to the small diameter of soot can scattering be neglected in comparison to emission
and absorption and this results in that the extinction coefficient only depend on absorption.
This in return simplifies the phase function in Rayleigh scattering and it can be written as
[65]:
69
Chapter 4: Radiation Heat Transfer in Boilers
Φ (θ ) =
3
(1 + cos2 θ )
4
(4.56)
The absorption coefficient for a particle cloud of non-uniform size can be written as [65]:
⎧ m 2 − 1 ⎫ ∞ ⎛ 2π r ⎞ 2
⎬∫ ⎜
⎟ π r n ( r ) dr
2
⎩m + 2⎭ 0 ⎝ λ ⎠
∞
κ λ = π ∫ Qabs r 2 n ( r ) dr = −4 J ⎨
0
(4.57)
Equation (4.57) can be simplified further by introducing the expression for volume
fraction f v .
∞⎛ 4
⎞
f v = ∫ ⎜ π r 3 ⎟ n ( r ) dr
0
⎝3
⎠
(4.58)
By now rewriting equation (4.57) together with equation (4.58) will the expression for
absorption coefficient (and also extinction coefficient) be reduced to equation (4.59).
κ λ = βλ = −
24π ⎧ m 2 − 1 ⎫ ∞ 4 3
J⎨ 2
⎬ ∫0 π r n ( r ) dr ⇒ κ λ = − J
4
2
+
m
⎩
⎭ 3
⎧ m 2 − 1 ⎫ 6π f v
⎨ 2
⎬
⎩m + 2⎭ λ
(4.59)
By expanding the complex index of refraction, m = n − ik , may the absorption coefficient be
written as
κλ =
(n
36π nk
2
fv
− k + 2 ) + 4n k λ
2
2
2
2
(4.60)
From equation (4.60) can it be seen that the absorption coefficient does not depend on the
particle size distribution but it depend volume fraction, i.e. the total volume occupied by all
particles. Therefore equation (4.60) can be written as a constant C0 times volume fraction and
wavelength.
κ λ = C0
C0 :
(n
36π nk
2
2
fv
λ
(4.61)
)
− k + 2 + 4n 2 k 2
The constant C0 depend only on the refraction index. If an average value of the Plank-mean
and Rosseland-mean absorption coefficients are used then equation (4.62) will result.
κ = κ Plank + κ Rosseland
where κ Plank and κ Rosseland are given by equations (4.63) and (4.64).
70
(4.62)
Chapter 4: Radiation Heat Transfer in Boilers
κ Plank = 3.83
f v C0T
C2
κ Rosseland = 3.60
f v C0T
C2
(4.63)
(4.64)
C2 is a second Plank function and has the value 1.4388 ⋅10−2 m K [65]. In the case of when
soot is included in the calculations then the refraction index for soot is given a constant value
of m = 1.57 − 0.56i [70]. This results in equation (4.65).
κ soot = 1265 f v T
(4.65)
A constant soot volume fraction has been used in this work.
71
Chapter 4: Radiation Heat Transfer in Boilers
72
Chapter 5: Numerical Methods
5 Numerical Methods
Since there exist no analytical solutions to the governing equations, the turbulent reacting
flow field has to be solved numerically. This means that the geometry has to be divided into a
fine grid and the governing equations has to be discretized. In this work finite difference
method has been used for discretisation. The system of discrete equations is solved in an
iterative manner until convergence is reach, i.e. the errors become small enough to be
negligible.
The solution procedure can be divided into the following steps:
1. Grid generation
2. Discretisation of the governing equation and setting of boundary conditions
3. Iterative solution
5.1 Grid generation
The discretisation of the governing equations is based on a uniform staggered rectangular grid
system. In each mesh cell scalar quantities such as pressure, temperature, density and species
mass fractions are defined at the cell centre whereas components of velocity vector are
defined at the cell surface centre [71]. This will result in a “coupling” of the dependent
variables, preventing high frequency (odd-even) oscillations in the numerical solution.
5.2 Spatial Discretisation Scheme
A general form of the governing equations can be written as, in terms of φ ,
∂ρu j φ
∂x j
=
∂
∂x j
⎛ µ eff ∂φ ⎞
⎜
⎟ + Sφ
⎜ σ ∂x ⎟
j
φ
⎝
⎠
(5.1)
Hereafter, the over-bars and over-tildes have been omitted in the governing equations for
simplicity. Second order central difference is used to discretize the diffusion terms; the
convection terms are discretized by a second order upwind scheme to ensure numerical
stability. The discretized algebraic equation (for simplicity in a two dimensional form) can be
written as:
1
1
1
1
Feφe − Fwφw + Fnφn − Fsφs
hx
hx
hy
hy
(5.2)
1
1
1
1
= 2 De (φx )e − 2 Dw (φx ) w + 2 De (φ y ) − 2 De (φ y ) + Sφ
n
s
hx
hx
hy
hy
where Fφ and D∇φ are the local convection and diffusion fluxes, respectively. These fluxes
may be viewed as surface averaged, for example on the w-cell surface (Figure 36):
Fwφw ≡
1
hy hz
∫
w − surface
ρ uφ dS , Dw (φx ) w ≡
1
hy hz
∫
Dwφx dS
(5.3)
w − surface
73
Chapter 5: Numerical Methods
The fluxes are estimated by a linear interpolation between the two neighbour interfaces. The
derivatives φ x , φ y are estimated using second order central differences. Take u-velocity
component momentum equation as an example (see Figure 36 for the u-control volume). Fe
is the flux through face e of the u-control volume, and Fe = ρ e ⋅ 12 (u E + u P ) . The estimation
for u will decide the discretization precision of the convective term. For example, if we take
⎧u
ue = ⎨ P
⎩u E
Fe > 0
Fw > 0
⎧u
, uw = ⎨ W
Fe < 0
⎩u P
(5.4)
Fw < 0
then a first order upwind scheme is obtained; if we set
⎧⎪ 3 u − 1 u
u e = ⎨ 32 P 12 W
⎪⎩ 2 u E − 2 u EE
3
1
Fe > 0
Fw > 0
⎪⎧ u − u
, u w = ⎨ 2 3 W 21 WW
Fe < 0
⎪⎩ 2 u P − 2 u E Fw < 0
(5.5)
a second order upwind scheme is obtained. It is clear that more points are needed in second
order schemes than the first order one. So when the control volume is near the boundary, the
points required by the second order scheme are not all available. In these boundary cells, the
first order upwind scheme is kept. If the cell Peclet number near the boundary Pe ∼ Fe hx / µeff ,e
is less than 2, a second order central difference scheme can be used. More detail can be found
in [72, 73].
y
N
WW
u
W
n
w
P
e
E
EE
s
S
hy
hx
x
Figure 36. . u-control volume in a staggered grid
5.3
A Boundary Correction Scheme (BCS) for Small Jet Inflow
Consider a small air jet on the left boundary of a staggered grid system, Figure 37. The width
of the jet is less than the size of a mesh cell. It is impossible to set a uniform u -velocity
component ( u jet ) at the cell surface containing the jet since this would enlarge the inlet area
numerically. To retain the correct mass flux of the jet inflow, uB3 must be set as the cell area
averaged velocity, umass
74
Chapter 5: Numerical Methods
umass = u jet Ajet ,u / Acell ≡ ξu u jet
(5.6)
where u jet is the velocity component of the jet inflow in the x-direction; Ajet ,u is the area of
the small jet in the surface A1-B1; Acell = hy hz is the area of the cell surface A1-B1.
ξu ≡ Ajet ,u / Acell is the area ratio. Equation (5.6) ensures that the fluxes of mass, energy, k and
ε are identical to the physical fluxes through the small jet inflow, given that correct boundary
conditions for the enthalpy, k and ε are provided. However, the momentum flux on the cell
surface is different from that of the small jet inflow, since
2
2
ρ umass
Acell = ρ u 2 A2 / Acell ≠ ρ u jet
Ajet ,u
jet
(5.7)
jet ,u
Another option is to set a uniform velocity umom = u jetξu1/ 2 on the cell surface; this ensures the
momentum flux at the cell surface being equal to the momentum flux of the small jet inflow.
However, the fluxes of mass, energy, k and ε are different from the corresponding physical
fluxes through the small jet inflow.
y
A
umass
v jet
C
v A2
A
A2
C
C
u jet
u D3
B3 uB3
P
D
E
B1
B2
D
D
hy
Jet
hx
'
B
'
D3
x
Figure 37. A schematical description of small jet in staggered grid
To preserve all the fluxes through the cell surface containing the small jet, we propose a
boundary correction scheme as described below. Consider the control volume for the scalars
A1B1C1D1, the control volume of the axial velocity ( u ) A2B2C2D2, and the control volume for
the vertical velocity component ( v ) A3B3C3D3 (see Figure 37). Corrections are made on the
cell surface A1-B1 of the mass/scalar control volume, A2-B2 of u-control volume, and A3-B3 of
v-control volume.
75
Chapter 5: Numerical Methods
First, we consider the discretized continuity equation and scalar transport equations in the
control volume A1B1C1D1 (with continuity equation one sets φ ≡ 1 in equation (5.2)). To
preserve the mass of the inflow from the small jet one sets
Fw ≡
1
hy hz
∫
ρ udS = ρ umass = ξu ρ u jet
(5.8)
A1 − B1
The convective fluxes of scalars through the inflow boundary are simply
Fwφw =
1
hy hz
∫
ρ uφ dS = ρ wφwξu u jet
(5.9)
A1 − B1
where ρ w and φw are taken from the inflow conditions. The diffusive fluxes of scalars are
evaluated as
Dw (φx ) w ≡
Dw
hy hz
⎛
⎞
⎜ ∫ φx dS ⎟
⎜ A −B
⎟
⎝ 1 1
⎠
Dw
hx hy hz
⎛
⎞
⎜ ∫ φ dS − ∫ φ dS ⎟
⎜ A −B
⎟
jet − exit
⎝ 2 2
⎠
Dw
(φP − ξuφ jet )
hx
(5.10)
Without correcting the small jet area the diffusive flux is calculated as
Dw
(φP − φ jet )
hx
Dw (φx ) w
(5.11)
Consider the discretized momentum equation for the u-component in the control volume
A2B2C2D2. Two fluxes, the convective and diffusive momentum fluxes through A2-B2 are to
be defined. The convective flux is calculated as
Fwuw ≡
1
hy hz
∫
ρ uudS
A2 − B2
ρ PuP ( uD + umass ) / 2 ρ P u jet ( uD + umass ) / 2
3
(5.12)
3
Here a first order upwind scheme has been used to evaluate uP . An alternative scheme is
Fwuw
ρ P umass ( uD + umass ) / 2
(5.13)
3
The diffusive flux is evaluated as
Dw ( u x ) w ≡
Dw
hy hz
⎛
⎞
⎜ ∫ u x dS ⎟
⎜ A −B
⎟
⎝ 2 2
⎠
Dw
hx hy hz
⎛
⎞
⎜ ∫ udS − ∫ udS ⎟
⎜ C −D
⎟
A1 − B1
⎝ 1 1
⎠
Dw
uD3 − umass
hx
(
)
(5.14)
Consider the discretized momentum equation for the v-component in the control volume
A3B3C3D3. The convective momentum flux at the boundary containing the small jet inflow is
Fwvw ≡
76
1
hy hz
∫
A3 − B3
ρ uvdS
ρ w vw
hy hz
(u
A3
)
(
hy hz / 2 + u jet Ajet ,v = ρ wvw u A3 / 2 + ξ v u jet
)
(5.15)
Chapter 5: Numerical Methods
where ρ w and vw are taken from the inflow boundary condition. ξ v is the ratio of the area of
the small inflow jet in the v-control volume to area of the A3-B3 cell surface:
ξv =
Ajet ,v
(5.16)
hy hz
If the small jet is assumed to be in the centre of the A1-B1 surface then the convective flux is
simply
Fwvw ≡
1
hy hz
∫
ρ uvdS
ρ wvw ( u A + umass ) / 2
(5.17)
Dw
v A2 − ξ v v jet
hx
(5.18)
3
A3 − B3
The diffusive flux is evaluated as
Dw ( vx ) w ≡
Dw
hz hy
∫
vx dS
A3 − B3
(
)
Without correcting the small jet area the diffusive flux is evaluated as
Dw ( vx ) w
Dw
v A2 − v jet
hx
(
)
(5.19)
To evaluate the performance of the boundary correction method, we will compare the
numerical results from two schemes. One is the scheme presented above, and the other is a
‘no-correction’ scheme. Details of these two schemes are summarized in Table 7. For
simplicity, only two-dimensional formulation is shown. For three dimensional flows, wvelocity component is discretized in a similar way to the v-velocity component.
Table 7. Summary of the boundary correction scheme and a no-correction scheme.
Boundary fluxes
Boundary Correction Scheme
(BCS)
No-Correction Scheme
(without BCS)
Fwφw
Equation (5.9)
Equation (5.9)
Dw (φx ) w
Equation (5.10)
Equation (5.11)
Fwuw
Equation (5.12)
Equation (5.13)
Dw ( u x ) w
Equation (5.14)
Equation (5.14)
Fwvw
Equation (5.15)
Equation (5.17)
Dw ( vx ) w
Equation (5.18)
Equation (5.20)
kw , ε w
Equation (5.21) with U = V jet Equation (5.21) with U = umass
The boundary correction scheme has been implemented using a ‘correction source (CS) term’.
The ‘no-correction’ scheme is chosen as the base scheme. The CS term is the difference
between the selected BCS and the base scheme. For example, the CS term for the umomentum equation is
77
Chapter 5: Numerical Methods
CSu =
ρP
2hx
(1 − ξu ) u jet ( uD
3
+ umass
)
(5.20)
CSu is added to the right hand side of equation (5.2). When ξu (the area ratio) is unity, no
correction is needed and the CS term is zero. With the mesh size continuously refined, the
small inflow jet is gradually resolved, and the area ratio such as ξu approaches to unity
gradually. This shows that the boundary correction scheme satisfies the consistency criterion.
The scheme is of first order accuracy.
With the boundary correction scheme, the computational effort is increased only slightly.
Since all the modification operation has been considered in the source terms, numerical
features such as the convergence rate and numerical stability with the boundary correction
scheme are similar to those with the base scheme.
5.4 Solution Method
The velocity components and pressure are coupled in the discretized momentum equations. A
distributive relaxation scheme [74, 75] is used here. The scheme is to diagonalize the iteration
matrix so that the three velocity components and pressure can be computed sequentially. The
resulting equation for the pressure is a Poisson equation that is similar to the one obtained
from the SIMPLE scheme [73]. A pointwise symmetric Gauss-Siedel iteration scheme is used
to solve the discretized equations. The method is simple, but the information propagation per
iteration is only one grid point, so the convergence to the final solution is slow, especially
when fine mesh is used. Multi-grid method is used to accelerate the convergence. The
solution procedure employs V-cycles in the fully approximate storage (FAS) mode. Further
details of the Multi-Grid method are referred to [74, 75].
5.5 Boundary Conditions
The governing equations are closed with the equation of state that relates the gas pressure
with the species mass fractions, temperature and density.
Wall boundary. Non-slip wall conditions are used for the velocity components. k and ε at
the walls are determined from wall functions [76, 77]. Species mass fractions at the wall are
assumed to have zero normal gradients. The furnace wall temperature is typically given and it
is used to determine the condition of the specific enthalpy at the wall.
Inlet and outlet boundaries. Mass conserved zero velocity gradient condition is used at
outflow boundary. At the outflow boundary all the scalars are assumed to have zero second
derivatives. The mean velocity components, k , ε and the mean mass fraction fractions of
different species as well as the mean enthalpy at the flow inlets are given from the furnace
operation conditions. In case the values of k and ε are not known at the inflow, they are
estimated as
3
3 2 2
2
3
k = ( u′ )
I U , ε = ( u′ ) /
I 3U 3 /
(5.21)
2
2
78
Chapter 5: Numerical Methods
where u ′ is the characteristic turbulent velocity fluctuation; U is the inflow speed; I is the
turbulence intensity, and is the characteristic turbulence length scale.
79
Chapter 5: Numerical Methods
80
Chapter 6: Summary of the Results
6 Summary of the Results
As discussed in the previous chapters, to model the combustion process of biomass in grate
fired furnaces, different sub-models have to be employed. A first question is how accurate is
each of this sub-models? To investigate this, comparison with experimental data is needed.
Several boilers are considered to validate the models and a brief summary of the survey is
given below. More details are given in the papers listed as the Appendix to this thesis. The
model is then applied to study the performance of the biomass boilers. This includes the effect
of secondary air supply, the effect of fuel moisture, effect of turbulence mixing, etc. The
results are also summarized below.
6.1 Validation of the Volatile Combustion Model
A laboratory-scale pellet reactor is considered to validate the models for the oxidation of
volatile gases in a turbulent flow. The flow-field is modelled using Favre averaged NavierStokes equations together with the k-ε turbulence model. Volatile oxidations and fuel-NOx
chemistry is computed using global mechanisms with the eddy dissipation combustion model
(EDCM). The models were validated against measurement data collected along the axis of the
pellets fired reactor [20]. The fuel bed was modelled using the semi-empirical model and
alternatively the two-zone FG bed model. A sensitivity study of the result to the bed model
was carried out. It was shown that the bed models affected the prediction of the species and
temperature only in a small region near the bed. The models had rather little influence on the
main flame structures. On the other hand, the mixing of volatile fuel and the secondary and
tertiary air plays an important in the combustion process. Shown in the figures are numerical
tests with different turbulence intensity at the fuel bed and secondary/tertiary air inlets. The
turbulence intensity I for the secondary and tertiary air inlets is 0.06 and 0.23 (secondary) and
0.14 and 0.58 (tertiary) for Case I and II respectively. With higher turbulence level the
combustion rate is higher and the consumption rate of oxygen and fuel is higher. The peak
flame temperature is also higher. The rather simple combustion model with the global
combustion chemistry and EDCM for turbulence/chemistry interaction gave rather reasonable
prediction of the mean flame structure. More results are found in paper 1.
1600
Exp
I
II
1400
Temperature [C]
Increasing I
1200
1000
800
600
400
0
0.1 0.2
0.3
0.4
0.5 0.6
x [m]
0.7
0.8
0.9
1
1.1
Figure 38. Temperature at the centreline of the reactor for Cases I-IV.
81
Chapter 6: Summary of the Results
26
10
Exp
I
II
9
8
Exp
I
II
24
Increasing I
Increasing I
22
CO2 [vol-%]
O2 [vol-%]
7
20
6
18
5
4
16
3
14
2
12
1
0
0
0.1 0.2
0.3
0.4
0.5 0.6
x [m]
0.7
0.8
0.9
1
1.1
10
0
0.1 0.2
0.3
0.4
0.5 0.6
x [m]
0.7
0.8
0.9
1
1.1
Figure 39. O2 and CO2at the centreline of the reactor, for Cases I and II.
6.2 Validation of the NO Emission Model
Investigation of the NO formation in the laboratory scale pellet reactor was carried out. The
fuel nitrogen content is less than 0.1%, from the fuel analysis [20]. The fuel-NO model that
was used previously for the large scale FFC boiler simulation showed has applied to the
present case. It was shown that high amount of fuel-NO was formed near the bed; NO was
consumed considerably along the axial downstream by reaction with NH3 (modelled with
NH). The numerical model of fuel-NO correctly predict the experimental observed NO
decrease along reactor axis. At far downstream, the experimental measure NO reaches to an
constant level about 100 ppm. The fuel-NO predicted by the model is about 25 ppm by
assuming the fuel N is about 0.1% of the dry ash-free pellet fuel. Numerical study showed
that the measured high level NO came from two other mechanisms, the Zel’dovich thermal
NO, about 20 ppm and N2O-intermediate mechanism, about 60 ppm. The sum of the total NO
from these two mechanisms and fuel-NO mechanism is fairly close to the measured data. The
influence of turbulence on the thermal NO and NO from the N2O-intermediate mechanism are
taken into account using a presumed PDF with a Gaussian distribution. With higher
fluctuation of the flame temperature, the level of predicted NO is higher. More details about
the NO studies can be found in Paper 1.
Further validation of the fuel-NO model has been carried out on the large scale FFC furnace
where wet wood-chips were used as the fuel. The fuel-N content is about 0.6% (on dry ash
free basis) that is much higher than the fuel used in the pellet reactor. The main source of NO
is therefore from the fuel-NO, that is about 80 – 120 ppm at the outlet of the furnace. It was
shown that air distribution in the furnace could affect the fuel-NO formation considerably. In
Paper 5, a systematic study of the air distribution on the NO formation is presented.
6.3 Simulation of the Bed Combustion using the Two-zone Model
Three different fuel beds were simulated using the two-zone functional group model. The
result from FFC boiler is presented in Figure 40. The calculated light UHC (methane) and CO
at moisture content of 42 wt.% are shown to be higher than the measured data, owing to the
fact that the measurement data was collected in the free board above (but close to) the bed.
82
Chapter 6: Summary of the Results
35
9
CO2
H2
7
Dry Mole %
Dry Mole %
8
6
5
4
CO
CH4
CO exp.
30
25
3
2
30
CH4 exp.
40
35
45
Fuel Moisture Content [wt.%]
50
20
30
40
35
45
Fuel Moisture Content [wt.%]
50
Figure 40. Calculated species concentrations for different moisture contents.
The bed model was used to study the effect of moisture content on the combustion in the bed.
Figure 40 shows an increase of CO2 and H2 and a decrease of CO as the moisture content in
the fuel increases. This may be explained by using the water-gas shift reaction (I) and reaction
(II). With high temperature and concentrations of H2O in the EQ-zone OH-radicals is
enriched. They react with CO and oxidize it to CO2. The forward reactions of (I) and (II) are
enhanced, which leads to the increasing concentrations of H2 and CO2.
CO + OH
H2O + H
CO 2 + H
H 2 + OH
(I)
(II)
The numerical results on the large-scale boilers are qualitatively reasonable. However, in
order to properly validate the model more experimental data about the pyrolysis/gasification
products and temperature at different operation conditions (such as the change of moisture
content studied here) should be carried out. Heat transfer through radiation to the bed is also
of importance to know. More details are found in Paper 2.
6.4 Validation of the Thermal Radiation Models for Simulations of Wood
Combustion in Grate Fired Boilers
The performance of two radiation models on the thermal radiative heat transfer calculations in
a 50 MW grate fired FFC boiler is investigated. The computationally simple optically thin
model, the P1-approximation and the more computational demanding Finite Volume model
(FVM) were utilised in the investigation. The radiative properties of the combustion gases
were calculated by an optimised version of the exponential wide band model (EWBM) and by
the spectral line based weighted sum of grey gases model (SLW). Since combustion of wood
in boilers involves the presence of small particles in the flow field the influence of the
participating particles (i.e. fly-ash and char) on the radiative results is investigated.
The calculated temperature showed that the difference between the P1 and FVM radiation
models were small. The optically thin model predicted temperatures considerably much lower
compared to the two other models. The presence of scattering particles had fairly small
influence of the calculated temperature; the peak temperature is slightly lower with scattering
particles.
83
Chapter 6: Summary of the Results
Figure 41 show the results calculated using the P1-approximation, together with the
measurement data from M-9 (cf. Chapter 1). The species are in mole fraction, on dry basis. In
the calculation the boiler size was used as the mean beam length and the agreement between
the measurement and the calculations is reasonably good. As seen from the figure the
temperature and oxygen levels change rapidly at a furnace height of 6 m. At this location the
four secondary air jets supply air, which leads to the rapid increase of O2 concentration. The
air jet is cold compared to the hot gases and as a consequence the temperature decreases while
oxygen concentration increases. More results are found in Paper 3.
Mole fraction (dry basis)
0.12
0.1
0.08
0.06
0.04
0.02
0
3
6
1800
UHC
CO
O2
UHC. Exp.
CO Exp
O2 9Exp
T (K)
1600
Calc.
Exp.
1400
1200
1000
800
3
6
Furnace height (m)
9
Figure 41. Comparison of species concentration and temperature along the furnace height at
z = 1.5 m and x = 3.9 m using P1.
6.5 Influence of Bed Combustion on the Emissions
A study of how the combustion process (gas temperature and species distributions in the
furnaces) is affected by the use of different inflow boundaries conditions above the fuel bed is
carried out on a 31 MW grate fired industry furnace. Two different bed inflow boundaries
conditions were tested, one simplified uniform bed and one distributed bed. The computation
was focused on the turbulent combustion process above the bed. The result was compared
with available experimental data at different locations and with calculated data from Fluent
6.1.
In the lower parts of the boiler the distributed bed was able to capture the trends of some
species, while the simplified bed condition also showed fair agreement. After injection of
secondary air most of the bed history was destroyed and ‘forgotten’. The numerical results
near the outlet from the Fluent simulation and simulations with both “beds conditions” were
rather similar, see Figure 42. This is consistent with the finding in the study of the laboratory
scale pellet reactor. The bed combustion models affect the combustion near the bed. With
very strong secondary air flow, the combustion of volatile in the furnaces is more sensitive to
the turbulence mixing, and less sensitive to the bed combustion.
84
Chapter 6: Summary of the Results
Level 4, Species by distributed bed, in-house code
Level 4
1000
900
700
Dry Volume %
Temperature (C)
800
600
500
400
Temp, exp
Simplified
Distributed
Fluent
300
200
100
0
1
1.5
2
3
4
2.5
3.5
<- fuel in x (m) ash out ->
4.5
5
22
20
18
16
14
12
10
8
6
4
2
0
1
CH4, exp
O2, exp
CO2, exp
CO, exp
CO, calc
O2, calc
CH4, calc
CO2, calc
1.5
CH4, exp
O2, exp
CO2, exp
CO, exp
CH4, calc
CO, calc
O2, calc
CO2, calc
1.5
4.5
5
Level 4, Species by simplifed bed
2
3
4
2.5
3.5
<- fuel in x (m) ash out ->
4.5
5
Dry Volume %
Dry Volume %
Level 4, Species by Fluent
22
20
18
16
14
12
10
8
6
4
2
0
1
2
3
4
2.5
3.5
<- fuel in x (m) ash out ->
22
20
18
16
14
12
10
8
6
4
2
0
1
CH4, exp
O2, exp
CO2, exp
CO, exp
O2, calc
CO, calc
CO2, calc
CH4, calc
1.5
2
3
4
2.5
3.5
<- fuel in x (m) ash out ->
4.5
5
NO (ppm)
Figure 42. Temperature and species molar percent at level 4, which is located near the outlet;
CO and CH4 multiplied with a factor 100.
200
180
160
140
120
100
80
60
40
20
0
1
Level 4
measured
γ =0.3
γ =0.5
γ =0.7
Simplified
1.5
2
2.5
3
3.5
x (m)
4
4.5
5
Figure 43. Fuel-NO distributions for different values of γ at level 4.
NO was only computed for the simplified and distributed bed by the in-house code. ThermalNO was not calculated due to the low temperatures inside the boiler. The nitrogen in the fuel
is assumed to be converted to HCN and NH3 during pyrolysis and char oxidation and the
molar ratio of HCN/NH3 is γ /(1 − γ ) . The value of γ for the distributed bed is varied between
0.3 and 0.7 and HCN and NH3 are and follow the distribution of CH4. For the simplified bed γ
is set to 0.5. The results from the calculations can be seen in Figure 43. It can be noted that
the amount of NO from fuel-NO is rather sensitive to γ. Compared to the case where γ=0.5,
85
Chapter 6: Summary of the Results
the result differ about ± 15% by varying γ. The numerical calculations capture the formed NO
rather well for the distributed bed. In case of the simplified bed NO is over-predicted. This
shows that the bed history in terms of NO is not forgotten by the secondary air. More details
and discussions are found in Paper 4.
6.6 A CFD Study of the Air-staging unit in a Large Scale Boiler
An air-staging unit (called ECO-tubes) for reduction of NOx emissions was installed on the
FFC plant 2001. A numerical and experimental study was carried out to study the effect of the
ECO-tube system on the emission of NO at the furnace outlet. The study was aimed to find an
optimum configuration of both the ECO-tube angle α and mass flow of air from the system.
The different configurations were compared against a case where no ECO-tubes were in use.
The numerical results and experimental data are shown in Figure 44.
Without the ECO tubes, the numerically predicted NO emission is about 98 mg/MJ; with a
low air flow rate through the ECO-tubes ( m = 0.986 kg/s), numerically predicted NO
emission is about 88 mg/MJ; a 10% reduction of NO emission is predicted (measured NO is a
little lower, about 74 mg/MJ). The ECO-tube angle α is 45o in this low flow rate case. If α
is kept as 45o and further increasing the mass flow rate in the ECO-tubes to m = 2.64 kg/s,
the predicted NO emission is reduced to 69 mg/MJ, about 30% reduction of NO emission is
predicted as compared to the case without the ECO-tube system. The reduction of NO
emission is due to the fact that by increasing the airflow rate in ECO-tubes, the airflow rate at
the lower part of the furnace is decreased (since the total airflow to the furnace is the same in
these experiments). As a result, the oxygen concentration decreases in the lower part of the
furnace and the oxidation of HCN and NH3 to NO paths are suppressed.
120
Numerical
Experimental
100
NOx [mg/MJ]
80
60
40
20
0
.
.
.
.
.
.
m=0 m=0.986 m=1.816 m=1.816 m=1.816 m=2.64
α
=15
α
=45
α =25
α =45
α =15
.
m=2.64
α =25
.
m=2.64 Mass flow [kg/s]
Angle α
α =45
Figure 44. NO emissions at the outlet obtained from numerical simulations and measurements
One may also see the effect of ECO-tube angle α on the NO emission in Figure 44. The
variation of ECO tube angle changes the large scale flow structure and thereby it affects the
oxygen and temperature distributions and the NO emission. From the numerical simulations,
86
Chapter 6: Summary of the Results
it is shown that the optimal angle is α = 25o . At this angle the level of NO emission is lower.
The experiment showed that the optimal angle is α = 25o for the case of m = 1.816 kg/s; for
the high mass flow rate case ( m = 2.64 kg/s) the optimal angle is α = 15o . In general, the
numerical simulations are in fairly close agreement with the experimental data for all test
cases. More details about the work are found in Paper 5.
6.7 A CFD Study of Flow Residence Time
The current legislation states that an energy producer must have a gas residence time of at
least two seconds above 850°C when co-firing garbage with biomass fuels in a boiler [78].
CFD calculations were used to investigate whether it was possible to achieve the “two
seconds” rule in the FFC boiler at different load and moisture content of the fuel. The flow
residence time is calculated based on CFD calculations, which give the mean fields of
temperature, species concentration and the flow velocity:
t
⎧
⎪ x = x0 + ∫ u ( x, y, z ,τ )∂τ
o
⎪
t
⎪⎪
y
y
=
+
⎨
0
∫o v ( x, y, z,τ )∂τ
⎪
t
⎪
⎪ z = z0 + ∫ w( x, y, z ,τ )∂τ
⎪⎩
o
(6.1)
where u, v and w are calculated flow velocity components at the flowfield point (x,y,z). τ is
parcel residence time. The residence time of the gases are calculated by releasing gas parcels
that follow the local mean flow. The motion of parcels is governed by the following
integration equations. The original position of the parcel (x0, y0, z0) is at the fuel bed. This
procedure is similar to the PIV measurement where seeding of small particles is made,
followed by tracking of the particles. The residence time defined in equation (6.1) is different
from the real residence time of fuel molecules. The residence time of fuel molecule is shorter
since it reacts with oxygen and radicals (H, O, OH) and it disappears quickly once the
reaction starts. The calculated residence time (using equation (6.1)) is also different from the
real residence time of a wood or char particle since they are affected by the shape and size of
the particles. Nevertheless the present residence time gives a good estimation of the time scale
in which the fuel and very small particles may stay in the furnace.
The parcel distribution for the flow residence time from one to two seconds for the standard
operation conditions are shown in Figure 45. The flow speed below the air curtain is low and
the fuel parcels travels slowly during the first second. After 1.5 second, most fuel parcels have
passed the air curtains, as shown by the parcels in Figure 45. The parcels follow the flow
streamlines, and mostly concentrated in the narrow zone in the middle of the furnace. After
1.75 seconds, the fuel parcels start to spread wider in the furnace due to the two large
recirculation zones above the air curtain. After 2 second some parcels have reached to a
height of 9 m in the furnace, and the spreading of the parcels is even wider. It should be noted
that the parcels shown in Figure 45 are all the parcels in the furnace; they are not only in the
middle x-y plane. Thus, it is seen that after 2 seconds the parcels spread to rather large
domain of the furnaces – this is an effect of the three dimensional plot. More results are found
in Paper 5.
87
Chapter 6: Summary of the Results
t=1s
t=1.75s
t=1.5s
t=2s
Figure 45. The positions of the parcels in the boiler at different times after the injection from
the fuel bed. (50 MW, 40% moisture).
6.8 An Area-correction Scheme for Boiler Simulations
Computational analysis of boiler performance and design is becoming a useful technique in
the boiler manufactures and utility industry. However, a severe drawback with the method is
that the computation can be very expensive and difficult to use. One particular problem is the
grid generation that describes the boilers and the small secondary air jets. The grid sizes used
to capture the combustion field are often larger compared to the area of the air-inlets in
boilers. This leads to that either very fine grid is used to resolve the air jets thus the
computational cost is very high, or rather coarse grid is used with an unresolved air jets. In the
latter case, the mass flow is conserved but the momentum fluxes are under-predicted at the
air-inlets. As a result, the flow field inside the boiler can not be modelled correctly. An area
correction method is proposed for the adjustment of the lost momentum and thereby
88
Chapter 6: Summary of the Results
improving the flow field and combustion simulations. Figure 46 show the turbulent kinetic
energy with the modification (a) and without modification (b). With the newly developed
boundary correction method, the accuracy of the computation is significantly improved
without a significant increase of the computational cost. More results are found in paper 6.
Figure 46. Simulation of the distribution of turbulent kinetic energy in the FFC boiler: (a)
with the boundary correction method; (b) without the boundary correction method
89
Chapter 6: Summary of the Results
90
Chapter7: Conclusions
7 Conclusions
The aims of this work were to study biomass conversion in fixed bed boilers and to develop
reliable modelling tools for simulation of grate-fired boilers. Modelling of a boiler is complex
and it involves many different fields such as turbulence modelling, numerical methods, heat
and mass transfer, chemical kinetics, two-phase flows.
The thesis has made contribution on the following aspects:
Development and validation of bed modelling
An existing two-zone bed model for coal conversion in counter-currents beds was modified to
biomass conversion. The two-zone model was also extended to a three-zone bed model where
drying, devolatilisation and char combustion occurs separate from each other in each zone. A
quasi two-dimensional bed model based on a single particle model was developed. The twozone model was tested on two beds, a 50 kW small-scale bed and a 50 MW bed. The
calculated results showed reasonable agreement with measurement data. The three-zone and
the quasi two-dimensional models were tested on the 31 MW bed. The calculated results from
the three-zone model and the quasi two-dimensional bed model were generally good, yet
further development of the models is needed to account for more details such as coupling with
radiation heat transfer, inhomogeneity of the bed (channel formation, collapse of the bed).
New well defined experiment measurement of the particles and gases inside the fuel bed is
needed to validate the models.
Evaluation of new boiler design
An air-staging unit (ECO-tubes) were installed in a 50 MW boiler in the Malmö FFC plant. A
numerical and experimental study was carried out with emphasis on lowering NOx emissions.
The emissions of NOx were simulated for different ECO-tube angles and mass flux of air
from these tubes. The numerical results were compared with the experiments. The trend of
NOx variation could be predicted to a fairly satisfactory extent by the present model. An
optimum angle for the air-staging unit was found to be between 15-25° depending on how
much air that was bypassed to the air-staging unit from the other air inlets in the boiler. This
study demonstrated the usefulness of the computational analysis method on the boiler
performance and design.
Study of flow residence time
A numerical study was carried out to examine whether it was possible to co-fire wood chips
with refuse derived fuel (garbage). The current legislation states that the energy producer need
to have a flow residence time of at least two seconds above 850°C [78]. The mean flow,
temperature and species concentration fields were first calculated. Then gas parcels were
released that followed the mean flow. The influence of the load and moisture content of the
fuel on the flow residence time was systematically investigated. The results showed that when
operating at the full load and normal condition, the flow residence time was sufficiently long
to meet the demands given in the current legislation. Decreasing the load gave increased
parcel residence time due to decrease of flow speed. The reduced load also resulted in a
decrease of the hot 850°C zone. Reducing moisture content had two different effects: one was
that the total rate of mass flow, which decreased due to the removal of water vapour in fuel.
This decreased the parcel speed, especially in the lower part of the furnace below the air
91
Chapter7: Conclusions
curtain. The other effect was the increase of combustion temperature, which decreased the
parcel residence time due to acceleration of the combustion gases especially in the upper part
of the furnace. The residence time of the gas parcels depends on the competition between
these two opposite effects.
Evaluation of different radiation and gas absorption models in boiler calculations
Boiler calculations can often be computational demanding since many processes occur in the
boiler. In order to simplify the numerical studies and decrease the computational effort it is of
interest to know if a simple radiation model can give reasonable results compared to a more
computational demanding and advanced model. Three different radiation models and two gas
absorption models were evaluated and compared with available measurement data. The effect
of particle scattering was also studied and it was found that a rather simple model such as the
P1-approximation using the EWBM model gave results similar to those of the more advanced
FVM model using the SLW gas absorption model. However, the P1 model predicted negative
heat fluxes to the bed compared to FVM, which yields positive ones. The effect of particle
scattering was seen at temperature above 1300 K, where the peak temperature is lower
compared to cases without scattering. Particle scattering modelling also significantly
increased the computational time, although it improved computed heat fluxes to the bed.
Investigation of the sensitivity of simulated combustion process in the free board to the bed
modelling
A study was carried out to examine how the results in the free board of a boiler are affect by
the combustion process in the fuel bed. The studied boiler was a 31 MW grate-fired boiler.
Two boundary conditions above the fuel bed were tested. One simplified condition assuming
a uniform distribution of species and temperature along the bed and one condition with nonuniform distributions of the species and temperature. The simplified condition gave results
that were less good in comparison with measurement data; the non-uniform bed condition
showed fairly good agreement with measurement near the bed. However, above the air curtain
where secondary air was injected, all models gave rather similar results that are in fairly good
agreement with measurement. The bed history is ‘forgotten’ after injection of secondary air
and therefore matching of bed data against measurement data near the bed was rather
unimportant for the results after the secondary air injection.
Development of an area correction method for adjustment of the lost momentum in boiler
calculations
The boilers are often very large compared to the size of the secondary air jets. The cell size to
capture the combustion process is often larger than the diameter of the air-inlets for secondary
air. Due to the large ratio of the length scales, the air inlets may be represented by only a few
grids and thereby the area of the discretized air inlets is not equal to the area of physical air
inlets. This results in that the momentum of the air jet is different from the physical one. As a
result the flow field will not be captured correctly. To compensate for this deficit an area
correction method has been developed. The method is tested on three cases, a laminar and a
turbulent isothermal flow in a model combustion chamber and a turbulent reactive flow in a
50 MW grate fired biomass furnace. The results show that the boundary correction method
can give significantly improved numerical solution with low computational cost.
92
Chapter 8: Acknowledgement
8
Acknowledgement
This work supported by STEM, the Swedish National Energy Administration
(Energimyndigheten), within the programme “småskalig förbränning av biobränslen” and
from the LTH KC-FP ‘biolåg’ project and Malmö Värme Syd AB, Sydkraft, now more
known as E.ON.
I would like to thank my supervisor, Professor Xue-Song Bai for introducing and given me
the opportunity to work with such an interesting and challenging field as biomass combustion.
I also would like to give thanks for the nice collaboration and for taking and investing so
much time and effort discussing and explaining many confusing matters.
A very special thanks goes to Mats Åbjörnsson, Mats Renntun and Magnus Axelsson at
E.ON. (former Sydkraft) for the fun projects we been involved in and for the useful
discussions of what is relevant to the industry. Another thank you goes to Dr Henrik
Thunman, Dr Federico Ghirelli and Professor Bo Leckner at Chalmers and Dr Henrik
Wiinikka at ETC for sharing numerical and experimental data with me.
A special thanks goes to Thomas Nilsson and Mehdi Bahador for their cooperation and help
with explaining thermal radiation. Thank you for all the help and explanations of different
radiation models. I especially want to extend my gratefulness to Mehdi for his continual help
with particle scattering and for reading the radiation chapter both one and two times.
I would like to thank Ping Wang for fruitful discussions about turbulence modelling. I also
thank Rixin Yu for all debugging help. A thanks goes to “Kalle” and Per for all the fun and
help I got during the biofuel course. Kalle, the matlab program would never work without
your help, nor would the car be running without your skilful technical hands. Thank you also
to Professor Laszlo Fuchs.
A thank you goes to Jacob Nilsson and for the fun discussions we had during the solar power
course. I hope you make it become a professional football player in the big international
leagues and become a cornerstone in the Swedish team.
Then I would like to thank Krister Olsson, Johan Revstedt and Robert Szasz for fixing all my
computer problems.
A thanks to all my colleagues, especially those in the football team. The list can not be
complete without mentioning Christophe “det är gott” Duwig for all the discussion of which
food ingredients that can and can not be eaten together at the same time. Further on Göran
Grönhammar should be mentioned for all the entertaining stories about construction of the
Swedish nuclear power plants. I never grow tired of listening to your stories.
I also would like to thank my family and friends for all the help and support, there are too
many to mention here; I hope you all understand this.
Finally I would like to give a big thank you to my two flowers, which are my dear and lovely
wife Pamela and our daughter Melissa. Thank you so much for allowing me to work over and
even working during weekends. Thanks for your BIG patience with me and thank you for all
the nice and warm food you always had ready for me when I came home. Thanks for also
93
Chapter 8: Acknowledgement
doing most of the “domestic” work at home. So now when “pappa” is finished he can play
with you much more, my dear Melissa.
I also want to thank those people who took themselves the time to read through the entire
thesis until here and I end with the final words:”Dixit ei Iesus ego sum resurrectio et vita qui
credit in me et si mortuus fuerit vivet et omnis qui vivit et credit in me non morietur in
aeternum credis hoc”.
Torbern Klason, May 2006, Lund.
94
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