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A novel method in combustion modeling for 2D numerical study of a two-stage porous burner

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Title:
A novel method in combustion modeling for 2D numerical study of a two-stage porous burner
Creator:
Dabbagh, Mohammad ( author )
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
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1 electronic file (73 pages) : ;

Thesis/Dissertation Information

Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Electrical Engineering, CU Denver
Degree Disciplines:
Electrical engineering
Committee Chair:
Jenkins, Peter
Committee Members:
Darbeshti, Kannan
Premnath, Kannan

Subjects

Subjects / Keywords:
Porosity -- Mathematical models ( lcsh )
Permeability -- Mathematical models ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
Currently, the treatments used to diminish the emissions of combustion processes has become a controversial issue. Except for catalytic treatments of the exhaust gases- which are very costly and have a low conversion efficiency- utilizing porous media (PM) in the combustion process is one of the most effective techniques. In this research, the method of applying porous media in burners is investigated using a numerical simulation code. Combustion in porous media has interesting advantages compared with free flame combustion because of an increased power dynamic range, higher burning rates and low pollutant emissions. ( ,, )
Abstract:
A numerical code was developed to investigate the effect of different parameters on the combustion in a porous media. The Navier-Stokes and energy equations for solids and gases in a two-stage porous burner were considered. The effects on the combustion by adding a heat source term to the gas phase energy equation were considered. The governing equations are discrete in a non-uniform structured mesh by using the finite volume method. The hybrid differencing scheme (HDS) was used for the convection terms. A SIMPLE algorithm was used for solving the conservation equations. The temperature, velocity, and equivalence ratios were known at the inlet. At the outlet, for the gas phase the flow was assumed to be fully developed and for the solid phase a boundary condition similar to that of inlet was considered.
Abstract:
Results show that by adding the heat source parameter the model has a close agreement with existing numerical simulations that solve the chemical equations for combustion in porous burners. The numerical results in this work were compared with those of A.J. Barra et al. The parametric study showed that by increasing the mixture equivalence ratio or inlet velocity, the gas phase temperature increases and is directly related to the pollution from the products of combustion. The reduction of porosity in the preheating and combustion zone lead to changes in the solid phase temperatures. Increasing the solid conductivity in the two zones caused an increase in the gas and solid phase temperatures.
Thesis:
Thesis (M.S.)--University of Colorado Denver
Bibliography:
Includes bibliographical references.
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Embargo ended 05/12/2019
General Note:
n3p
Statement of Responsibility:
by Mohammad Dabbagh.

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University of Colorado Denver
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Auraria Library
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999609638 ( OCLC )
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A NOVEL METHOD IN COMBUSTION MODELING FOR 2D NUMERICAL STUDY
OF A TWO-STAGE POROUS BURNER by
MOHAMMAD DABBAGH B.S., Yazd University, 2007
A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Mechanical Engineering Program
2017
1


This thesis for the Master of Science degree by Mohammad Dabbagh has been approved for the Mechanical Engineering Program by
Peter Jenkins, Advisor Maryam Darbeheshti Kannan Premnath


Dabbagh, Mohammad (M.S., Mechanical Engineering)
A Novel Method in Combustion Modeling for 2D Numerical Study of a Two-Stage Porous
Burner
Thesis directed by Professor Peter Jenkins
ABSTRACT
Currently, the treatments used to diminish the emissions of combustion processes has become a controversial issue. Except for catalytic treatments of the exhaust gases- which are very costly and have a low conversion efficiency- utilizing porous media (PM) in the combustion process is one of the most effective techniques. In this research, the method of applying porous media in burners is investigated using a numerical simulation code. Combustion in porous media has interesting advantages compared with free flame combustion because of an increased power dynamic range, higher burning rates and low pollutant emissions.
A numerical code was developed to investigate the effect of different parameters on the combustion in a porous media. The Navier-Stokes and energy equations for solids and gases in a two-stage porous burner were considered. The effects on the combustion by adding a heat source term to the gas phase energy equation were considered. The governing equations are discrete in a non-uniform structured mesh by using the finite volume method. The hybrid differencing scheme (HDS) was used for the convection terms. A SIMPLE algorithm was used for solving the conservation equations. The temperature, velocity, and equivalence ratios were known at the inlet. At the outlet, for the gas phase the flow was assumed to be fully developed and for the solid phase a boundary condition similar to that of inlet was
m
considered.


Results show that by adding the heat source parameter the model has a close agreement with existing numerical simulations that solve the chemical equations for combustion in porous burners. The numerical results in this work were compared with those of A. J. Barra et al. The parametric study showed that by increasing the mixture equivalence ratio or inlet velocity, the gas phase temperature increases and is directly related to the pollution from the products of combustion. The reduction of porosity in the preheating and combustion zone lead to changes in the solid phase temperatures. Increasing the solid conductivity in the two zones caused an increase in the gas and solid phase temperatures.
The form and content of this abstract are approved. I recommend its publication.
Approved: Peter Jenkins


DEDICATION
This thesis is dedicated to my wife, Fatemehsadat, who has supported everything I have pursued and scarified her life for me. I am truly thankful for having you in my life. Also, I am proud to dedicate this thesis to my parents, who have taught me what hard work is, allowed me to find my interests, and have been my main source of encouragement and inspiration throughout my life. Nothing I have accomplished would have been possible without their endless advice, love, support, and dedication to being the best role models possible.
v


ACKNOWLEDGMENTS
This research would not have been possible without the opportunities that my advisor, Dr. Peter Jenkins, presented to me. His knowledge, support, kindness, and positive attitude were key factors in my graduate career.
I also want to thank Dr. Darbeheshti and Dr. Premnath for their introduction to this research. Their knowledge on the topic made it possible for me to continue through difficult times. They asked the right questions and pointed me in the direction of several sources of information that were essential to this thesis.
vi


TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION
1.1 Introduction.......................................................1
1.2 Literature Review.................................................2
1.3 Atmosphere........................................................5
1.4 Combustion Exhaust Gas............................................6
II. POROUS BURNERS
2.1 Definition.......................................................16
2.2 Fundamentals of Porous Burners...................................17
2.3 Flame Propagation in Porous Burners..............................21
2.4 Emissions in Porous Burners......................................22
2.5 Technical and Economic Advantages of Porous Burners..............22
2.6 Porous Burners Geometrical Structure.............................23
2.7 Materials and Structures Used in Porous Burners..................25
2.8 Porous Burners Application.......................................27
III. NUMERICAL SIMULATIONS29
3.1 Introduction.....................................................30
3.2 Physical Model...................................................30
3.3 Governing Equations..............................................31
3.3.1 Navier-Stokes Equations........................................34
3.3.2 Energy Conservation Equation...................................35
3.4 Heat Transfer Modeling in Porous Burners.........................36


3.5 Combustion Modeling in Porous Burners................................37
3.6 Temperature Variable Coefficients in the Energy Equations............39
3.7 Boundary Conditions..................................................40
3.8 Numerical Method.....................................................41
3.8.1 Hybrid Differencing Scheme.........................................41
3.9 Computational Grid...................................................42
3.10 Incompressible Field Solution by Simple Algorithm...................43
3.10.1 The Simple Algorithm..............................................44
IV. RESULTS
4.1 Results ..........................................................48
4.2 Temperature and Velocity Contours....................................48
4.3 Fuel-Air ratio effects...............................................51
4.4 Porosity and Porous Bores Diameter Effects on the Temperature........53
4.5 Emissivity Effects on the Temperature................................55
4.6 Mixture Inlet Velocity Effects on the Temperature....................56
4.7 Effective Conduction Coefficient Effects on the Temperature..........58
4.8 Conclusion...........................................................60
viii
REFRENCES
62


CHAPTER I INTRODUCTION
1.1 Introduction
The increased population and economic growth in countries increases the amount of pollution gases from combustion processes. These gases have devastating effects on the environment, humans, and their climate. The effects of this phenomenon on geothermal gases, acid rain, and thick fog of smoke that is caused by chemical fumes cause respiratory problems for humans. For example, the effects of CO gases on human health can be seen in Figure 1.1. The first and foremost step to control and reduce this pollution is to recognize the
sources of these pollutants; such as burners, vehicles, and engines.
100
50
10
%CO
5
0.1 1 10 Exposure (hr)
Figure 1.1: CO effects on human health
The second step is to become familiar with the details of these gases and to understand the chemical processes leading to these emissions. The emissions consist of unburned hydrocarbons (CH4, C2H2, C2H4, ....), carbon oxides (CO, CO2), nitrogen oxides (NO, NO2, N2O), sulfur oxides (SO, SO2, CS2, OCS), and solid particles such as soot. These gases are called primary pollutants. Meanwhile, there are some other gases which are called secondary emissions and
1


they are the result of reactions between primary pollutants and airborne elements, such as SO3, HNO3, H2SO4, and O3.
This research evaluated the methods which are used to reduce the emission of these gases and to control the reactions that lead to the production of such gases. The second and third steps are discussed in this chapter. The disadvantages of those methods that are applied to reform the process of combustion and to reduce emissions from combustion encourage researchers to find new processes. One of those methods is that of using porous medium in the combustion chamber. There are several studies of the application of porous media in a combustion chamber and a short summary is provided in the next section.
1.2 Literature Review
Using porous media (PM) in combustion processes has two important advantages. As Mahdi et al (2015) mentioned, the first and foremost effect is its heat dissipation characteristics, which are greater than that of conventional fins and results in greater convection heat transfer [1], In porous medium, the regular motion of the fluid flow forms a mixture of the fluid around the individual porous beads. Studying the treatment of fluid flow and heat transfer in porous media is based on both empirical and fundamental approach. As Kaviany (1995) mentioned in the “Principal of Heat Transfer in Porous Media” the study of the heat transport in porous media has a long history [2], Regarding Darcy's book written in 1856, the effects of porous media were analyzed using his work on water flow through beds of sands (a water filtration application). By that time,
2


the single-phase flow through pipes was already evaluated by Hagen and Poiseuille. The effects of transport in porous media during that time could be assessed in two ways: direct (e.g., studies directed by Darcy, Carman, Leverett) and indirect (e.g., studies directed by Hagen, Knudsen, Taylor). Thus, when it came to the utilization of the porous media in the combustion, it had already been investigated by several scientists. The most basic investigations were found in the early twentieth century. In 1912, Bone invented the first porous boiler and heater [3], One year later, Lucke did research on radiative heaters, furnaces and cooking stoves. In 1933, Hays reported a new invention of heating water using the combustion in porous medium [4], Babkin et al (1991) studied the propagation of combustion flame of premixed mixture in porous combustion chamber [5], In the study done by Trimis in 2002, an experimental comparison was made between the free flame and combustion processes in porous inert media [6], In that research, the pros and also the procedures of using the porous media in internal combustion engines were assessed. Also, he and his associates, developed the thermodynamics and the environmental advantages of this method. In addition, they invented an external engine that had very low emissions. In that model, porous burners were used to heat the working fluid. Kumar did a thermodynamic evaluation of these combustion characteristics with an open combustion chamber [7], Also, Weclas et al (2001), investigated the use of a porous combustion chamber in an internal combustion engine [8], As Trimis claimed (2002), it was possible to design a porous combustion chamber by considering some advantages, such as increasing the stability, improving the rate
3


of energy release, and reducing the distribution of pollutants [9], The main idea of designing these chambers was based on the optimal limit of the temperature to be maintained for the combustion process and the reduction of NOx and CO. The main reason was that the porous media chamber caused homogeneous combustion. Increasing the efficiency and increasing the rate of the combustion are two of the most significant consequences of using PM in combustion chambers.
Also, the effects of radiation and combustion in porous chambers have been studied. Kaviany, in 1993, examined the dependent and independent scattering effects based on the “Monte Carlo” simulation method and compared the numerical results to experimental results [2], In the research which is presented by Trimis and Drust, an experimental comparison between free flame and the flame inside the porous chamber was done. In this study, the burner dimension, the burner thermal power, the extent of the exhaust emissions, and its stability have been examined [9], Howell et. Al. (1995) investigated some characteristics, such as the effective conduction coefficient, impermeability coefficient, and extinction coefficient, all for porous media and based on experimental results [10], Brenner, in 2000, presented diffusion coefficients and impermeability coefficients for laminar flow as functions of temperature [11]. Hsu et al (1993) developed convection and radiation coefficients based on the prediction of gas and solid phase temperatures [12], Malico and Pereira, in 2001, evaluated the radiation effects on the 2D combustion in porous medium [13],
4


Finally, Barra et al presented results from his simulation of ID two-stage porous burners in two different studies, in 2003 and 2004 [14] [15], They evaluated, by using numerical analysis, the effects of changing the porous bore diameter, convection coefficient, and the inlet fuel jet velocity on the gas and solid profiles.
In this research, I compared my results with Barra’s results. Their research results are used as a benchmark of my research.
1.3 Atmosphere
To determine the extent of air pollution and how to control it, it is necessary to have a basic analysis of the atmosphere. Atmosphere is composed of 78% N2, 21% O2, and 1% other gases. There are four different layers in atmosphere, and the first one, the Troposphere, is explained as follows.
• Troposphere
This is the main part of the atmosphere and it makes up 90% of mass of the atmosphere. Gases resulting from combustion immediately affect this layer. As Mishra has written in “Fundamental Combustion” in 2008, almost all the chemical reactions in atmosphere start in this layer, in the presence of ozone and in wavelength less than 320 nm [16], The following reactions happen in this layer.
Generated OH in reaction 1-2 could be used in the other reactions as follow.
O3+ UV(Sunlight) -> O2+O
Eq.1.1
O+H2O—>20H
Eq. 1.2
oh+co^h+co2
Eq. 1.3
5


h+o2+m^ho2+m
Eq. 1.4
H02could be used to regenerate OH.
H02+03—►0H+202 Eq. 1.5
Since there are emission gases in this layer of atmosphere, a considerable amount of N02exists, which results in a reduction in the H02generation. Instead, nitric acid is generated as shown in the following equation:
0H+N02^HN03 Eq. 1.6
1.4 Combustion Exhaust Gases
Identifying the origin of emissions produced by combustion helps to lead to the control and reduction of such emissions. The most important ones are as follow:
• Unburned Hydrocarbons (UHCs)
As Charles E. Baukal mentioned in the “Industrial Burners Handbook”, by increasing the excess air rate, UHCs decrease [17], Actually, the largest portion of UHCs in the exhaust gases result from the thermal cracking phenomena. In this process, large HC molecules are cracked to smaller ones, which are effected by the high temperature of combustion chamber. The UHCs structure is dependent on the makeup of the fuel, combustion chamber geometry, and parameters associated with the engine. In all fuel combustion cases, except methane combustion, the reaction of UHCs with air causes photochemical smog.
6


• Photochemical smog
Ulraviolet rays
Figure. 1.2: Photochemical smog formation
Photochemical smog is a secondary emission that is formed by combination of Nitrogen oxide, sunlight, and UHCs, and creates harmful components such as Ozone, Aldehyde, and Peroxyacetyle Nitrate (PAN). These components cause headaches, eye irritation, respiratory problems, and premature skin aging. This pollution is evident in the sky as a brown layer. This phenomenon is explained well in Figure 1.2.
The following reactions forms emissions as described below:
N2+O2—>-2NO Eq. 1.7
2N0+02—>-2N02 Eq. 1.8
If the NO2 concentration in the atmosphere is high, the air is clear, and there are no clouds, then sunlight would cause the following reactions:
NCh+sunlight—>-N0+0 Eq. 1.9
0+02-^03 Eq. 1.10
N0+03^N02+02 Eq. 1.11
7


If the NO concentration is greater than the NO2, reaction in Eq.1-11 occurs and the ozone level remains constant. However, the effect of UHCs increases the NO2 concentration and, as a result, ozone forms.
• UHCs creating factors
There are some processes that create UHCs. First is Air-fuel ratio. In the case of a rich mixture, there is not enough oxygen for all hydrocarbons, and as a result there would be more UHCs. On the other hand, by leaning the mixture results in reduced amount of UHCs. However, if the leaning of the mixture is continued, the result would be an incomplete combustion, UHCs would be increased and the thermal efficiency would decrease. Pulkrabek, w., in Engineering Fundamental of the Internal Combustion Engine, in 2005, discussed this effect as shown in Figure 1.3. Hence, in this case, finding the optimum operating point is vital to an efficient and clean combustion process [18],
Fieure. 1.3: Amount of emission in education flow inresoect of Eauivalence ratio
8


Incomplete combustion

There are several factors relating to incomplete combustion. First is not having a stoichiometric mixture. In this case, there is not enough Oxygen molecules and the combustion would be incomplete. Also, to reduce the onset of incomplete combustion, quench zones are created in the combustion chamber by creating swirl or turbulent flow in the combustion chamber to provide better mixing of the fuel and air.
• Deposition of fuel on the combustion chamber walls
The deposition of fuel on the combustion chamber walls is a function of mixture pressure and mostly occurs in internal combustion engines as Pulkrabek, w., explained in Engineering Fundamental of the Internal Combustion Engine [18].
• Carbon monoxide (CO)
Carbon monoxide is colorless, odorless and very toxic. If, during the
Table. 1.1: CO sources
Source
Gasoline motor vehicles
Aircraft, trains, ships, etc.
Off-highway vehicles
Coal
Fuel oil
Natural gas
Wood
Total fuel combustion Industrial processes Agricultural burning Solid waste disposal Miscellaneous Total
Emissions (million tons per year) %
7.8 34.2
2.0 8.8
1.9 8.3
3.9 17.1
1.3 5.7
4.7 20.6
0.1 0.4
21.7 95.1
0.2 0.9
0.3 1.3
0.4 1.8
0.2 0.9
22.8 100.0
9


combustion process, there is not enough oxygen to convert all the carbon to carbon dioxide, then CO forms as can be seen in Figure 1.3. In other words, CO is one of the products of incomplete combustion. The main sources of CO are shown in Table 1.1, as Strehlow, R.A., explained in Combustion Fundamental, McGraw-Hill, Singapore, 1985 [19], The most important factor to reduce CO is having a lean mixture.
• Nitrogen oxide (NOx)
Having nitrogen oxide emissions in the atmosphere and combining them with
elements of air increases the concentration of ozone and results in the formation
Table. 1.2: NOx sources
Source Emissions (million tons per year) %
Gasoline motor vehicles 95.8 64.3
Diesel, aircraft, trains, vessels 5.6 3.8
Off-highway vehicles 9.5 6.4
Coal 0.5 0.3
Fuel oil 0.1 0.1
Natural gas 0.1 0.1
Wood 0.1 0.1
Total stationary sources 0.8 0.6
Total fuel combustion 111.7 75.1
Industrial processes 11.4 7.7
Agricultural burning 13.8 9.3
Solid waste disposal 7.2 4.9
Miscellaneous 4.5 3.0
Total 148.6 100.0
of photochemical smog. The two main sources of this gas are specified in Table 1.2, as Strehlow, R.A., showed in Combustion Fundamental, 1985 [19],
• NOx formation mechanisms in combustion process
As Kuo, K., explained in Principles of Combustion (2005), there are three
mechanisms of NOX formation in a combustion process [20],
10


The first one is Zeldovich mechanism. In this mechanism, which is the most
active mechanism in combustion processes, NOx is formed behind the combustion zone. The following reactions occur:
0+N2^N0+N Eq. 1.12
N+02^N0+0 Eq. 1.13
N+OH—►NO+H Eq. 1.14
NO forms N02 in a reaction with water and oxygen, as the following reaction shows:
N0+H20^N02+H2 Eq. 1.15
N0+02^N02+0 Eq.1.16
The other mechanism is the Prompt mechanism, which NOx forms very rapidly within the flame while reacting with the hydrocarbons of fuel. The following reactions occur in this method:
CH+N2^HCN+N Eq.1.17
HCN+O—►NCO+H Eq. 1.18
NCO+H—►NH+CO Eq.1.19
NH+H^N+H2 Eq. 1.20
N+OH—►NO+H Eq.1.21
The other mechanism is called Fuel mechanism. In this mechanism, which is mostly represented in coal combustion, the fuel itself includes Nitrogen. This Nitrogen reacts with existing Oxygen in the air and forms NOx. Houghton, J.T., (1997) compared these three mechanisms in the Global Warming: The Complete Briefing, Cambridge Press, as shown in following diagram (Figure 1.4) [21]:
11


—'----‘----1----■---1----■---1----.---1____,___I I I
1000 1100 1200 1300 1400 1500 1600
Temperature °C
Figure 1.4: NOx formation compression during different mechanism • NOx control mechanisms during combustion process
There are some important solutions to reduce the NOx emission resulting from combustion. The first is by reducing the excess air. Generally, it is common to have excess air in boilers and burners in order to have a complete combustion. But, this excess air causes more NOx. There are some disadvantages to reducing the excess air, such as increasing the formation of CO and UHC, and decreasing the thermal efficiency, as shown by Mishra, P., in Fundamental of Combustion, in 2008, and is shown in the Figure 1.5 [22], The other method to control NOx is called the staged combustion. As Baukal has mentioned in Industrial Burners Handbooks, 2004, by having this kind of combustion, the flame length and the heat transferred would be increased, which results in a decrease in the flame temperature. Hence, the thermal NOx formation would decrease. This result is shown in the following Figure 1.6 [17]
12


AIR
FUEL
AIR
Figure. 1.5: NOx control technology
Diffusion burner
AIR
FUEL
AIR
FUEL
AIR
Partially premixed burner.
AIR -
FUEL-AIR -FUEL-AIR -
Schematic of a staged-air burner.
Figure.1.6: Comparison of flame length


• NOx control mechanisms after combustion process
There are several ways to reduce NOx emission effects in the post combustion process. The most effective way is using “thermal convertors”. In this process, exhaust gases would be directed through a thermal convertor, allowing high temperature secondary reactions to occur easily; as described in the following:
CO+I/2O2—>C02 Eq.1.22
CXHY+z02—>zC02+l/2yH20 Eq.1.23
Also, it is possible to use “particulate traps”, which work as filters and are applied at the exit of burners. A disadvantage of using these traps is the possibility of getting filters blocked by carbon particles during the combustion process.
• Carbon dioxide (CO2)
Although C02 is not considered a toxic emission, it has a damaging role as Greenhouse gas. This greenhouse effect causes a temperature increase and results in a climate change over a long period of time.
• Sulfur
As Strehlow, R.A., explained in Combustion Fundamental, in 1985, the main resource of sulfurs is fossil fuels (Table 1.3), which cause acidic rain [19],
14


Table 1.3: SO2 sources
Source S02 (million tons per year)
Fossil fuel 80
Metal smelting 8
Biomass burning 2
Natural sources (ocean, vegetables, oil and volcano) 25
15


CHAPTER II
Porous Burners
Optimizing the efficiency and reducing the pollution in combustion emissions is an ongoing challenge. One solution to reduce combustion emissions is by providing the necessary conditions for having a homogeneous combustion. In this chapter, porous burner characteristics, the application of porous media in burners, the porous burner geometrical structure, and the industrial use of porous burners have been studied.
2.1 Definition
As Kaviany stated in the “principles of heat transfer in porous media”, the porosity is: “The volume fraction occupied by voids, i.e., the total void volume divided by the total occupied by the solid matrix and void volumes” [2], Pores are three-dimensional and of three types. If each void is connected to more than one other pore it is called “interconnected”. “Dead end” is defined for the cores that are connected only to one other pore, and “isolated” for those that are not connected to any other pore, while the fluid flow passes through the interconnected pores. “Effective porosity” is the volume fraction of the interconnected pores. The porosity is a function of pressure gradient for the deformable matrixes. Generally, the pores do not have a typical size and distribution. Regarding the size, some pores are very large and some others are very small (micropores or ultramicropores). The most common structures for the matrix are “very long straight cylinders”, “spheres”, and “short and long fibers” such as circular sections.
16


2.2 Fundamentals of Porous Burners
There are two functions for using porous medium in a combustion chamber. The first, as Ferrenberg suggested in 1988, PM has the role of thermal storage and a heat exchanger, and there is no combustion within a porous medium [23], As the second function, the porous medium could be used as a combustion chamber, as introduced by Zhou et al (2014), or by using the medium in the piston bowl or in the cylinder head, as Durst and Weclas proposed [24],
The porous media is a solid material. Generally, its structure is a honeycomb structure. Such a honeycomb structure, by itself, could be classified by two methods. It could have a random structure or, it could be in a packing structure, which is called a regular structure. Fluid passing through this media have specific characteristics. As Weclas explained (2010), the distinction of combustion in this medium in respect to a medium without any porosity is the lack of formation of a free flame [25], The reason is as follows; the flame is formed in a 3-dimentional porous chamber which look like a wasp nest. The second difference is related to the preheating of inlet mixture gases. Generally, flame propagation in premixed burners could be controlled by the upstream heat transfer. The thermal conductivity of the laminar flow of gas in the laminar flame or the advanced heat transfer in turbulent flames are the factors that limit flame propagation in conventional burners. Limiting the flame speed provides stability and maximizes the energy release rate.
17


The temperature of the flame in porous burners can be kept within acceptable limits due to the solid phase of the burning media and the high coefficient of heat conduction and radiation that exists in this phase compared to gas phase. Premixed burners with an open flame have very low flame thickness due to very low conductivity of the gas mixture. Hence, reactions occur in a very small part of the chamber, and the rest of the combustion chamber remains unused, as it is shown in Figure 2.1.
Figure 2.1: Combustion thickness in premix burner
Combustion in porous media provides a way of expanding the combustion thickness to the entire combustion chamber, due to its high coefficient of heat conduction and its radiation characteristics.
The other important application of porous burners is the stability range. As Mishra in 2006 explained, porous burners have a broad stability range in comparison to conventional burners, specifically in the case of increased flame speed [16], In conventional burners, flame stability exists in a very limited flame speed range, while in porous burners, the flame is much more stable. The reason is that the heat transfer in the opposite direction of the flow of the air-fuel mixture causes that area to reach ignition temperature and stabilizes the flame and combustion. In conventional burners, if the flame speed exceeds the design
18


6
§
O
600 800 1000 1200 1400 Velocity gradient (1/s)
1600
Figure 2.2: Stable zone respecting to velocity gradient and fuel ratio speed, it causes flame flashback or blow-off (Figure 2.2). This does not occur in
porous burners.
These changes lead to stable combustion, as Mishra explained in his book (Fundamental of Combustion, 2008- Figure 2.3) [22],
Figure 2.3: Flame speed and fuel jet velocity in a stable combustion In porous burners, air-fuel mixture enters in the preheat area at first. Any
chemical reaction occurs in this area, where is usually heated by heat conduction and heat radiation coming from the reaction zone. This area could be extended to the inlet, depending on the thickness of the porous burner. By approaching this area of combustion and with the sharp rise in the temperature gradient, heat
19


conduction will occur. In this area, due to conduction and radiation induced by combustion chamber gases, the temperature of the solid is above the temperature of the combustion gas mixture and heat transfer occurs by conduction from the solid phase to the gas phase.
After this preheat zone, the gas temperature reaches a temperature which causes the formation of a combustion zone. The thickness of this zone is very small, and within this zone, gas temperatures are higher than in the solid zone. Also, heat is transferred to the solid by conduction.
After combustion, there is another zone which is called by MoBbauer S. and Trimis (in 2001) as the post flame zone (Figure 2.4 & Figure 2.5).
fuel/air
mixture
U . . i,. i
heat removal from the reaction zone by convection, radiation, and conduction
Figure 2.4: Heat removal within burner zones
In this zone, heat is transferred to the outside of combustion chamber, which
creates a negative temperature gradient. Hence, having the temperature increase
20


in the upstream and reduced reduction in the downstream is the characteristic of these kind of burners.
Waste gas
Heat transport for the stabilization of the combustion process \
Heat removal by radiation and conduction of the solid, conductive heat transfer of the gas phase and dispersion
Large pores region (region C)
Small pores region (region A)
Heat transfer in the axial direction by radiation, conduction, dispersion and convection
Combustion zone
Ignition temperature Preheating zone
ttttttmtt
Gas mixture (fuel and oxidant)
Figure 2.5 Main heat transfer mechanisms in a porous burner
2.3 Flame Propagation in Porous Burners
As mentioned earlier, the controlled flame propagation in premixed burners is a limiting factor to the flame rate and results in flame stabilization and maximizes the energy release rate. The practical constraint in the utilization of combustion in porous burners is the reduction in the combustion rate, which results from the reduction in the gas mixture velocity. This occurs due to the small dimensions of porous medium. It has been shown that the flame propagation that occurs in porous burners is a function of the Peclet number. Weclas defined the Peclet number as:
Pe = WS&L
g
f
S,dm
Ctr
Eq. 2.1
In this formula, Si is the laminar flame velocity, dm is the equivalent pore diameter, and af is the diffusivity factor for the combustion products. This formula relates the portion of heat released from the combustion to the heat conducted out of porous chamber. Flame propagation is possible when the heat
21


release rate is larger than the heat transfers to the outside. Hence, if the size of voids is smaller than critical, flame growth would be stopped and the flame would be quenched. Alternatively, if the voids are greater than the critical size, flame propagation could be possible. Babkin et al in 1991 determined the Peclet number for Methane as 65 [4],
2.4 Emissions in Porous Burners
Carbon monoxide (CO) and unburned hydrocarbons (HC) are formed due to an incomplete combustion process. Also, they are created as a result of cold spots in the combustion chamber. NOx production is also dependent on the temperature of combustion products. In these kind of burners, because of the high heat transfer rate, especially radiation heat transfer, the combustion chamber temperature is reduced. Also, hot and cold spots occur during the combustion process due to the structure of porous medium and as a consequence of having a homogeneous combustion.
2.5 Technical and economic advantages of porous burners
Most of the advantages of porous burners result from having efficient heat transfer in the combustion zone and also having flame stability at high burning speeds. The most important advantages are as follows:
• High thermal efficiency by taking advantage of the preheat zone. This kind of burner is clearly much more efficient.
• Very low emission (CCCK7 mg/kwh) (CNCK25 mg/kwh)
• Stable combustion: for lean air-gas mixture, with a fuel-air ratio between 0.53- 0.91
22


• Fuel flexibility: porous burners have fuel flexibility in the range of 1-20, that is much higher than common burners in the range of 1-3.
• High power density: These burners are 10 times smaller in comparison to common burners which reduces the materials cost.
• Compact shape
• Fast flame response time
• Variable dynamic power range
2.6 Porous Burners Geometrical Structure
These type of burners generally have a two-phase structure. First, the air-fuel mixture enters from bottom zone, as shown in Figure 2.6.
exhaust gases
stabilisation
ignition
fuel/air-mixture
Figure 2.6: Porous burner geometrical structure
A compressed porous structure exists in this area. This results in a reduction of the diameter of the bores which results in a lowering in the Peclet number from the critical level. As a result, the flame is not formed in this zone, as it has not been conditioned for combustion. In other words, the main goal of preheat zone is just to preheat the fuel-air mixture. The second zone is called the
23


combustion zone. Flame propagation occurs in this zone and results in combustion. Using porous material in the combustion zone results in a higher Peclet number.
2.7 Materials and Structures Used in Porous Burners
Porous matrix performance used in burners is dependent on the materials used and the form of matrix grid. Generally, the material has a high resistance to high temperatures, high mechanical resistance, heat shock resistance, and high conductive and radiation heat transfer properties. As MoBbauer et al. explained in 1999, in the preheat zone, because of lower temperature, it is preferred to use these materials to protect against elevated temperature and thermal shock [26], This is why low porosity material is suggested for this zone, while for the heating zone, it has been recommended to choose materials with high resistance against elevated temperature and thermal shock, as shown in Figure 2.7
Figure 2.7: Porous structure
The best materials suggested for this medium are A1203, SiC, ZrC>2. The most important characteristics of these materials are as follows:
24


• A1203
The temperature range of this structure is about 1950 degrees C. The conductivity coefficient is about 5-30 w/mk (in the temperature range of 20-30°C). The coefficient of thermal expansion is average, while the radiation coefficient is about 0.28 at 2000°C. Also, its porosity is high (0.9(s(0.99). Such structures have a high heat transfer due to structure due to having a high internal surface.
Figure 2.8: A1203 Structure used in porous burner
• SiC
This structure has unique features. Its maximum allowable operating temperature is 1600 °C. It has a radiation coefficient between 0.8-0.9 (in the temperature of 2000°C and a high porosity (0.7(s(0.9). High heat shock resistance, low thermal expansion coefficient, and a conduction coefficient in
Figure 2.9 Sic structure
25


the range of 20-150 are some its’ other characteristics. Figure 2.9 shows this structure.
• ZrC>2
This structure is recommended for use in high temperatures, such as in a combustion zone, since it has a maximum allowable temperature of 2300°C. Some other characteristics of this medium are having a low thermal conductivity coefficient between 2-5 w/mk, and radiation coefficient of 0.31. Also, a high heat shock resistance is one of its important features. (Figure 2.10).
Figure 2.10: ZrO: structure
In the next table (Table2.1), all these three materials features are compared. Table 2.1 Comparison between A1203, SiC, and Zr02 characteristics
Parameter Dimensions AI2O3 SiC Zr02
Maximum Allowable temperature in air °C 1900 1600 1800
Thermal expansion coefficient a (20-1000° C) 10'6 1/K 8 4-5 10-13
Thermal conductivity X at 1000° C W/mK 20-30 8-150 2-5
Thermal conductivity X at 1000° C W/mK 5-6 20-50 2-4
Specific thermal capacity J/gK 09-1 0.7-0.8 0.5- 0.6
Thermal stress resistance parameter, hard shock R (a/Ea) K 100 230 230
Thermal stress resistance parameter, mild shock R (RA) 10"3 W/m 3 23 1
Total emissivity at 2000 K - 0.28 0.9 0.31
26


2.8 Porous Burners Application
As Advic. F mentioned in 2004, there are several applications for these kind of burners. The figures below show some of the most important applications of these types of burners.
• Household burners
By having a wide dynamic power range, there is not necessary to have repetitive starts in these kinds of burners. This characteristic causes a significant reduction in emission production, since the main emission formation occurs during the starting process. Also, by having higher heat transfer rates, fewer emissions occur. Advic compared the emission of burners in household
applications as shown in the Figure 2.11 [27],
Emissions (in mg/kWh)
Figure 2.11: Emission comparison between Porous burners and standard burners The other benefit of using this type of burner in the household is the limited
space needed for installation, due to its compressed shape, as shown in Figure 2.12.
27


Figure 2.12: Household porous burner
• Gas turbine combustion chambers
Gas turbines usually work with pre-heated gases in order to reduce the thermal NOx. Although, if 50% of the nominal power is obtained, unstable combustion occurs and leads to NOx and CO generation. This could be resolved easily by applying porous burners in gas turbines.
• Internal combustion engines
The treatments to reduce the emissions of internal combustion engines (ICE) have become controversial issues. Except for catalytic treatments of the exhaust gases- which are high costly and low conversion efficiency - utilizing the porous media in the combustion process is one of the best alternative techniques. By adding porous media to ICEs, it is possible to approach a homogeneous combustion level and by controlling the temperature, less emissions are produced, as Mujeebu et al proved in 2009 [28], Furthermore, using this medium to preheat the gases results in an increase in the efficiency. Weclas found that the best performance of this medium is achieved by utilizing an open-cell structure of PM, without any valve in the cylinder head, to separate the cylinder head from the cylinder chamber [25],
28


• Steam engines
One of the other applications of porous burners is in steam engines. Generally, steam engines are very large. But there are two excellent feature in porous burners that are applicable to steam engines - compact shape and high power density. These characteristics allows steam engine designers to reduce the size of the steam engine. As an example, the porous steam engines could be used as a heat source in the Sterling engine.
29


CHAPTER III Numerical Analysis of A 2-D Porous Burners
3.1 Introduction
In this chapter, the combustion in a porous burner has been analyzed. In this combustion simulation, the solid phase radiation effects are assumed by applying an effective conduction term. Also, the combustion process was modeled by adding a constant heat source of energy in the conservation of species equation. Initially, the mass conservation, momentum conservation, and energy conservation equations are derived. Then, the results are compared to Barra’s study.
3.2 Physical model
The computational area is a two-stage tetrahedral burner. As presented in Figure 3.1, the burner length is 6.05 cm (included 3.5 cm preheat zone and 2.55 cm combustion zone) and the width is 1 cm.
3.5 cm 2.55 cm
Preheating
Zone
Methane/Air,
Combustion
Zone
Methane/air V. 0, T —>
25.6 ppc PSZ 3-9 PF PSZ â–  A 5C

â–º
Products
3.5
6.05
Figure 3.1: Burner’s geometry
For both zones partially stabilized Zirconia has been used (Table 3.1) and the porosity of each zone was different.
30


Table 3.1: PSZ Thermo-Physical
Combustion zone Preheat zone
Pore diameter 0.152 cm 0.029 cm
Porosity 0.87 0.835
Conductivity 1.21 W/mK 0.77 W/mK
Pore density 25.6 ppc 3.9 ppc
C 0.638 0.146
M 0.42 0.96
Density 510 kg/m3
Specific heat 824 kg/m3
3.3 Governing Equations
Some assumptions were made in deriving the equations. First, assume all porous materials are neutral and are not involved in any chemical reaction. The other assumption is that the porous material was considered as a continuum material. Also, the fluid velocity and porous permeability is high enough that the fluid pressure loss and boundary layer effects can be ignored in this medium.
As in the porous burners, both the gas and solid phases exist. The governing equations are not the same as in the conventional equations. For example, in the momentum equation, the pressure loss caused by the fluid passing in the porous medium should be considered. Generally, the pressure loss of a passing fluid is obtained using Darcy’s law.
• Darcy’s law
As Nield and Bejan (2013) mentioned in the “Convection in Porous Media”, in the fluid mechanics of porous media, the momentum equations or force balances are presented by numerous experimental observations which are summarized mathematically as the Darcy Law [29], In other words, in fluid dynamics and hydrology, the total discharge in a porous medium is expressed by
31


Darcy’s law. This law is based on the experimental results of the flow of water through sand beds (Figure 3.2). This law also applies to the oil and gas governing equations. This law is based on a simple proportional relationship between pressure loss, permeability, viscosity, flow cross- sectional area, and the total fluid discharge, and given by the following equation (Eq. 3.1)
-KA (Pb-Pa)
Q =
Eq. 3.1
L

tz :::: y b
Figure 3.2: Darcy’s law
In this equation, K is the intrinsic permeability of the medium. This coefficient is a function of the inlet fluid, and the porous medium network structure, specifically, the bore diameters. One of the most common equations for this coefficient is the Carman-Kozeny equation, as Vafi proposed in “hand book of porous media” in 2000 [30]:
s3d2
k = â– 
Ck{\-sf
Eq. 3.2
In this equation, Ck is a dimensionless coefficient and is equal to 180 for spherical particles, s is the porosity of the porous medium, while dp is the spherical bore diameter. By dividing Eq. 3.1 by area, the volumetric flux could be obtained by using Eq. 3.3:
32


q = ——AP /uL
Eq. 3.3
Fluids always flow from a high to low pressure, this is why the negative sign
is used in the above equation. Darcy’s law is valid for fluids with low velocity,
which is why fluids with Reynolds number less than 10 are usually considered
as Darcy’s fluids, as Carman-Kozeny claimed. The Reynolds number for a porous
medium is defined by Equation 3.4 or either 3.5. pvdi0
Re = -
Re =
U
qdp
d
Eq. 3.4 Eq. 3.5
In the Eq. 3.4, v is the fluid velocity at the outlet and d3o is a parameter which is defined as 30% of the average bore diameter. In Figure 3.3, the range of application of Darcy’s law is shown,
As Zhengwen mentioned in 2006, many attempts have been made to correct
the Darcy equation [31], Finally, Forchheimer (1901) suggested a second order
33


of the velocity term to represent the microscopic inertial effect, and corrected the Darcy equation using the following equation [30]:
- dp/dX = pv/k +Ppv2 Eq. 3.6
In this equation, P is the non-Darcy coefficient and p is the fluid density. The Forchheimer equation was corrected in 1947 by Brinkman [31], In the corrected equation, second-order derivatives of the velocity were added to the Darcy equation as shown in following equation, where X, Y, and Z directions are mutually perpendicular.
- dp/dX = pv/k - (d2v/dY2+ d2v/dZ2) Eq. 3.7
In the numerical simulation which was done in this study, it was impossible to use Darcy’s model due to the high fluid velocity. Also, if the pressure drop was calculated using Brinkman model, it was negligible as well. The reason was that the first term is almost zero since there is a high permeability and, as a result, the K coefficient was large. Also, referring to the second term, by having a very small pore diameter, the change of velocity across the pore throat was negligible, while there is no pressure loss in Y direction (as a 2D problem). As a result, the second term was approximately zero. Because of this, the mass conservation and momentum conservation were used as the common equations.
3.3.1 Navier-Stokes Equations
The mass conservation equation and the momentum conservation equation are given as follows:
• Mass conservation equation:
8(pUj)
dx,
= 0
Eq.3.8
34


Momentum conservation equation:
d , duf. dP
----(puui - fj.—L) =-------
dx. dx. dxi
J J ‘
Eq. 3.9
3.3.2 Energy conservation equation:
To use the energy conservation equation in a porous burner, a volume-averaged model was used. In this approach, the energy equation was solved for both the gas and solid phases, as given in equations 3.10 and 3.11:
• Gas phase energy equation
dx,
f»fpT'-eKt
dTg
dx
j /
ns ^ cjy ^
-i (n-r,)
' &A'
Solid phase energy equation
Eq. 3.10
_d_
dx,
(l-e)K,
K
dx,
-H{T,-TS)-
dq,
dx.
rad
Eq. 3.11
On the right hand side of Eq. 3.10, first term represents the chemical energy release during N chemical reactions, while the second term represents the species distribution. The third term represents the conduction between the gas and solid phases. It is noted that the solid radiation is much greater than the gas radiation, and, as a result the gas radiation flux is negligible in gas phase energy equation.
On the right hand side of Eq. 3.11, first term shows the heat conduction between the gas and solid phases, while the second term represents the radiation flux from the porous medium.
In this study, porous medium radiation was modeled as an effective conductive term. Also, instead of solving the species transport equation, the
35


combustion was modeled by adding a constant heat source of energy to the gas phase energy equation, Eqn. 3.10, rather than solving the first and second terms, which are chemical energy release and species distribution terms.
3.4 Heat Transfer Modeling in Porous Burners
In this study, an effective conductive term was used in order to model the porous medium radiation, as Saidi mentioned in “A 3D Modeling of Static and Forward Smoldering Combustion in a Packed bed of Materials” (2007) [32], Using this technique and as the first step in the modeling process, the effective conduction coefficient was defined. While there are several definitions for this coefficient, in this study the coefficient which is defined by Cheng G.J. A in 1999 was used [33],
Kff=ks(fr9 Eq. 3.12
As the second step, the effective conduction coefficient was defined for both the gas and solid phases separately, as given in Eq. 3.13 and Eq.3.14.
Q--e)K
k -k
“'s.eff Keff
sk-(l-s)ks
Eq. 3.13
skg
k‘-«=k«sk _(!_„)*
Eq. 3.14
As the third step, it was essential to consider the radiation effects on the effective conduction coefficient. In order to do that, as Kaviany defined in 1995, the other coefficient should be defined as Kr (Eq. 3.15 and Eq. 3.16) [35], The total effective conduction coefficient would be the sum of these two coefficients (Eq. 3.17).
36


K =4FdpoT?
Eq. 3.15
F = 0.1843 + 0.5765 tan-
k „ =k „+k
s,ejf,r s.eff r
1.535
(-

Eq. 3.16 Eq. 3.17
As the final step (step 4), the energy equation was rewritten. In the new energy equation (Eq. 3.18), ksejf r, represented the radiation effects.
k —
a*
â– i v ^ y
+ hv(T-T,= 0
Eq. 3.18
3.5 Combustion Modeling in Porous Burners
As explained earlier, in this study the species transport equation was not solved and the combustion was modeled by adding a constant heat source in the gas phase energy equation. Hence, the new gas phase energy equation was changed to the following, Eq.3.19,
aTi a
p‘c‘£u'l^ = el^,
dT ^
â– ,eff^-yK(Tg-Ts) + sS(x)Q(x)
Eq. 3.19
In this simulation, adding the heat source was very important to the combustion process. In porous burners, the mixture of fuel and air was initially preheated in the preheating zone. The heat source was added just before the interface, 0.075 cm before the border between the two regions (preheating zone and combustion zone). This heat source increased linearly and was at its
maximum value in the border, which was equal to 2.5*106 . Then, the value
m
decreased to zero in 0.11 cm after the interface. In order to being able to show
37


the heat source placement, the Dirac delta function, 8, was defined as shown in
the Figure 3.4.
X
Figure 3.4: Heat source placement
To determine the heat source value, first it was necessary to evaluate the combustion equation. If the fuel is Methane, the combustion equation is shown by Eq. 3.20 (without any excess air):
CH4+2(02+3.76N2) -> C02+2H20+7.52N2 Eq.3.20
As a result, the molar fuel-air ratio would be:
Eq. 3.21
Air 2
To have a complete combustion, excess air was required. In this case, Eq. 3.22 shows the actual molar and mass fuel-air ratio:
( j . )act, mol ~ $
Air 2
(—) t =-(/>* —
Air' ’mass 2 29
Hence, the mixture mass flow rate was:
Eq. 3. 22 Eq. 3. 23
38


On the other hand, the mass flow rate, by its definition, was related to the
gas velocity, as Eq. 3.25 shows:
m . = p. A.u -»w . cc u
mix rin mg mix g
Eq. 3.25
Now, by setting Qcxmfuel, the final relationship for Qcis given in Eq. 3.26:
1 + — 1 +
1 + —

\ 8 Eq. 3. 26
In the Eq. 3.26, kc is a constant. As Barra et al claimed in 2003, this constant could be 27.4*106Aw/m2s (ug = 60 cm!s, = 0.65) [13],
3.6 Temperature Variable Coefficients in the Energy Equations
Three different coefficients used in both gas and solid phase energy equations vary by temperature. These coefficients are the gas density (pg), gas
viscosity (/jg), and the volumetric heat transfer coefficient. As Barra suggested in 2003, these coefficients are calculated as follow [14],
Regarding gas density (pg), Barra proposed to use the values given in Eq.
3.27. In this equation, /?gis gas density, a is thermal diffusivity coefficient, and cgis the specific heat of gas mixture (Eq. 3.28),
Eq. 3. 27
cg = a exp( BTg )
Eq. 3.28


To find the “a” and “B” values for Methane gas, Eq. 3.29 and 3.30 are used: a = 947 + 0.095^ Eq. 3.29
5 = 1.83*10^[a:1] Eq. 3.30
Viscosity is varying with temperature, as shown by Eq. 3.31,
ju=3.371 *10“7r°-7 Eq. 3.31
Finally, the correlation for volumetric Nusselt number was given by the following correlation (Eq. 3.32):
Nu=c Re"
Eq. 3.32
Where the “c” and “m” values are given for PSZ material in the Table 4.1. By considering Eq. 3.32 and also Eq. 3.33, which represents the Reynolds number, the volumetric heat coefficient was calculated. This coefficient relates the energy and solid phase equations to each other.
Re =
Pg£udp
Ps
Eq. 3.33
3.7 Boundary Conditions
The inlet boundary conditions follow (Eq. 3.34, 3.35, and 3.36):
Momentum: | Uiniet I Vinlet =0
Eq. 3.34 Gas energy: T — T ± g,inlet ^0
Eq. 3.35
Solid energy: k s’in=ea(TA T ) \ Sdn SUr / Eq. 3.36
The outlet boundary conditions are given as (Eq. 3.37, 3.38, and 3.39):
40


Momentum:
fop*
dx dv,
Out
dx
= 0
= 0
Eq. 3.37
Gas energy:
dT
g,Out
dx
= 0
Eq. 3.38
Solid energy: -k-
dT
dx
= £ (t* -T4 )
\ s,out sur I
Eq. 3.39
Pressure: Pw =
Also, the walls in the combustion chamber are considered adiabatic for both the gas and solid phases. E was assumed to be 0.8.
3.8 Numerical Method
The governing equations were solved using the finite element method (FEM). In this method, a non-uniform grid with variable spacing (variable mesh size) was used to discrete the governing equations, while the pressure and velocity fields were related by using a “Simple algorithm” (Figure. 3.5).
o.oi
___I__I_____i__i__I__I__L_
J____!___I__I__;___I__I__I___I__i__I______I__I___L.
0.01
0,02
0,03
X
0.04 0.05
o.oe
Figure 3.5: Computational Grid
In the FEM analysis, the convection terms were discretized by a “Hybrid Differencing Scheme”.
3.8.1 Hybrid differencing scheme
This scheme was a combination of a “Central Differencing Scheme” and an “Upwind Differencing Scheme”. This scheme takes advantage of the piecewise
41


formula based on the local Peclet number in order to evaluate the net flux through each control volume face. If the general form of the discretized equation was like Eq. 3.39, then the coefficients would be given in Eq. 3.40-43, with variables F and D representing the convection mass flux and diffusion conductance at cell
F
faces respectively, so that Pe = — .
aA=aJy,+aE$E Eq. 3.40
ap=aw+aE+{FE-Fw) Eq. 3.41
aw=Dw+max
F ,(D +5l),0
W ^ V W ry / ?
Eq. 3.42
aE = De+ max
Fe,(£,e+y'>’°
Eq. 3.43
3.9 Computational Grid
In this numerical study, the convergence criteria were assumed based on the mass residual, first-order pressure norm, and also the first-order gas phase temperature norm, which all should be less than 10"6, 10"4, and 10"4 respectively. In the Table 3.2, the error percentage was presented for three different grid cells (74*15, 148*30, and 296*60).
Table 3.2 Error percentage due to change in the number of computational grid cells
Total number of grid cells Gas phase temperature change percentage Solid phase temperature change percentage
74*15
148*30 11.05 4.95
296*60 2.53 2.66
42


There was not a significant change in the gas and solid phase temperature between these two grids, which is why 148*30 was selected as the grid size.
3.10 Incompressible Field Solution by Simple Algorithm
To solve the incompressible field, the Navier-Stokes equations had to be solved. As Pantkar proposed in 1980, a good method to solve the non-linear N-S equations was using the Simple algorithm, which is one of the finite element methods to discrete the equations. The acronym simply stands for Semi-Implicit Method for Pressure-Linked Equations. This algorithm could be solved for both the “Collocated grid” or “Staggered grid”.
For collocated grids, all the variables (including vector variables and scalar variables) were stored at the same locations. For the staggered grids, variables were stored at different locations and were shifted to a half of the control volume in each coordinate direction. The collocated grid approach was applicable when the geometry was complicated, while the staggered grid approach was preferred when using the Cartesian coordinates. Although it was much simpler to use the collocated grids, the issue was that if this method was used to solve N-S equations, it was hardly possible to have a proper coupling between the pressure and velocity fields. In the Figure 3.6, the backward staggered grid is shown.
43


Figure 3.6: The arrangement for the two-dimensional flow
While all the scalar variables (including pressure) are stored at the nodes
marked as (•), the velocities are defined at the scalar cell faces between the nodes and are indicated by arrows (—») for u-velocities and (T) for v-velocities, as Versteeg proposed in “An Introduction to Computational Fluid Dynamics: the finite volume method” (1995). It is worth mentioning that in the border, nodal points to calculate velocities, the length of each node were 1.5 times the other nodes.
3.10.1 The Simple algorithm
This Simple algorithm was based on the guess-and-correct procedure. To initiate this process, a pressure field p* was guessed. In addition, an initial guess for the velocity field was required. By these initial guesses, the discretized momentum equations (Eq.3.44) were solved.
ai,Jlli,J ~'^janbllnb + (PI-\,J ~ PI ,j) A ,J +
_ ' ' Eq. 3.44
=HanbAb+(Pij-1 ~PI,j)AI,j +bI,j
44


Now, defining p and v as the difference between the corrected p and v and
initial guesses, follows:
P = P*+P' u = u* +ur
* f
V = V + V
Eq. 3.45
Substituting the corrected values into the momentum equations yield to corrected equations.
PAj =YjanbU'nb+{ r.-u-Fv. )4,
ai,JVI,J=HanbV'nb+{ p.A-p.'j] )A
Eq. 3.46
At this point, an approximation was introduced by neglecting '^janbu’nb and ^janbv'nb resulting in Eq. 3.47 as follow:
'■;J“i,Ap;^-ph)
Eq. 3.47
where the coefficients were calculated as given by equation Eq. 3.48:
d
Ui,J
a
dTi=^L
"ij
Eq. 3.48
“I,j
By substituting these corrected values into the Eq. 3.45, the final values for
a,
pressure and velocity are:
u,,j =u,j
+d:J(p;-,J-p;J)
v:j =v'.j +d, j (p/j-i -P,'j )
Eq. 3.49
To check the velocity values, these values should be able to satisfy continuity equation as well. Those ones reach out to the Eq. 3.50.
45


(^A bur ~(^A ),v ] + \(f»A )/.,+i ~(f»A )jj Eq. 3.50
= 0
Substituting the velocity values from eq. 3.49 into the continuity equation (Eq. 3.50) gives:
n P' =a P' +ct P' +ci P' +ci P' +b'
“u1 I,J “i+XJ1 I+\,J I-\,J1 I-\,J IJ+1 lj-\1 I,J-1 ^UI,J
Eq. 3.51
where the coefficients are as follows:
Table 3.3: Corrected pressure coefficients
aI+l,J al-\,J aI,J+1 al ,J-1 bij
(pU buf (pdA)lJ (pdA)rJ
By substituting the corrected pressure terms into equation 3.47 gives the corrected velocity terms. The b'jjterm was obtained from the continuity equation
for a single node. If the velocity terms calculated using the momentum equation are correct, this term should be equal to zero. The simple flowchart was developed as shown in Figure 3.7.
The simple algorithm needs an under-relaxation in order to converge (Eq. 3.52). These new values were used to update the pressure and velocity. In these equations, the coefficients are au,av< 0.8 and a <0.5. Usually, the equation of
au =1—ap is used with apandap .
Pmw =P* + apP'
U- =a„u+(l-a„)u-' v""=a„v+(l-a,)./-1 Eq 3.52
46


Figure 3.7: Simple algorithm flowchart


4.1 Introduction
CHAPTER IV RESULTS
In this chapter, the results of the simulation of combustion in the area of solution are discussed. Also, changes in the velocity, fuel-air ratio, conduction coefficient, porosity, porous bores diameter, and the radiation coefficient for both the gas and solid temperatures are discussed Then, the gas and solid medianl-D temperature diagrams are presented and the effects of changes made are evaluated.
4.2 Temperature and Velocity Contours
In the Figures 4.1 and 4.2, the gas and solid phase temperature are presented respectively.
O CD CD CD O CD O â–¡ CD O
ounoLnoLnoLnot-nocDocncDCD
■ST CN ■'— CD CD CD LO CO CM CD O tO O LO □ CD
CO CD CD LTJ TO CN O â–¡ Ifl â–¡ LD â–¡ tn
T-r— t- «— cd h- co m r- a
TG
1
0.01 -
>-
0
0
___I_______:_:__I____i_______I_i__!__,_!__I_;__;_!__I_I__I__I_I__I_I
0.01 0.02 0.03 0.04 0.05 0.06
X
X
Figure 4.1: Gas phase temperature contour
48


Figure 4.2: Solid phase temperature contour
Also, in the Figure 4.3, velocity contour is provided. In these three diagrams, through the boundary area between the two zones (preheating zone and combustion zone), the walls velocity decreases and gas temperature increases.
â– 
Figure 4.3: Velocity contour
49


By reducing the velocity, the conduction coefficient decreases and the time duration of the heat transfer between two phases increases, and the temperature differences between gas and solid increases (Figure 4.4).
Figure 4.4: Gas and solid temperature and convection coefficient along central line of the solution area In the preheating zone, the solid temperature is higher than the gas
temperature by having both conduction and radiation heat transfer. Although, by having a high conduction, the temperature difference between these two phases is not significant. In the combustion zone, by having the combustion and the released energy, both phase temperatures increases. At first, the gas temperature is higher, but eventually, by having the heat transfer from the gases close to wall to the solid, the solid temperature increases. Finally, by having radiation emission to the ambient air, the solid temperature decreases. The gas temperature increases and the convection heat transfer decreases in the combustion zone as a result of its low velocity.
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4.3 Fuel-Air Ratio Effects
As shown in t Figure 4-5, by increasing in the fuel-air ratio, the gas temperature and the solid temperature increases, while a reduction in this ratio leads to reduction in the temperature of both phases.
Figure 4.5 Fuel-Air effects on the temperature in 2 millimeters away from the walls This ratio does not affect the preheating zone, since there is no reaction in
this zone. By having a higher fuel-air ratio more energy is released in the combustion zone. Although using a richer fuel and air mixture leads to higher temperature and more thermal NOx, using a porous medium results in a higher heat transfer rate, and a decrease in thermal NOx. (Figures 4.6 and 4.7).
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Figure 4.6: Fuel-Air ratio effects on the temperature along the central line of the combustion zone
Figure 4.7: 1-D effect of Fuel-Air ratio on the gas and solid phases temperature
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4.4 Porosity and Porous Bores Diameter Effects on the Temperature
Any change in the porosity affects both the temperature of the gas and solid phases (Figures 4.8 and 4.9). Increasing the porosity, that means neglecting the porous media effects, leads to temperature increase in both phases. This is why in these kinds of burners, it is possible to reduce the temperature for maximum power and to reduce the pollution and thermal NOx, which is not permitted in common burners, as any temperature reduction causes an efficiency loss. In other words, with porous burners, reducing the temperature without any efficiency loss is feasible. The preheating zone temperature is not affected, as the porosity of this zone is assumed to be constant. Also, using porous media in the combustion zone causes a temperature reduction after the combustion zone and an increase in the porosity heat transfer rate which results in a reduction in temperature in that zone.
1 500
-â– ----- Tg , Porousity= 0.95 j ;
------T,, Porousity= 0.95
1250
1000
750
500
0 0.01 0.02 0.03 0.04 0,05 0.06
X
Figure 4.8 1-D effects of porosity on the temperature
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Figure 4.9 Porosity effects on the temperature along the central line
By increasing the bore diameter, the volume convection coefficient drops. As a result, the difference between the gas and the solid phase coefficient increases. Although the gas temperature would not be affected by this coefficient, the solid temperature drops significantly- as the solid temperature is influenced by convection heat transfer from the gas side (Figure 4.10).
Figure 4.10 1-D effects of porosity on both gas and solid phases temperature
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4.5 Emissivity Effects on the Temperature
By having a higher emissivity, the radiation rate increases. Also, by having a very low emissivity (£• = 0.01), as seen in Figure 4.5, the temperature diagram is perpendicular relative to the outlet cross section. This shows that by reducing the emissivity and having a very small radiation, the adiabatic assumption is close to reality (Figures 4.11 and 4.12).
Figure 4.11: Emissivity effects on the temperature along the central line
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4.6 Mixture Inlet Velocity Effects on the Temperature
Any change in the mixture velocity effects the temperature. By having a higher velocity, volumetric convection coefficient increases, which results in a decrease in temperature difference between gas and solid. Also, the released heat coming from the heat source increases (Figures 4.13, 4.14. 4.15, and 4.16). However, in the preheating zone, it has the opposite effect; with a lower mixture velocity more time would be available for transferring the heat from the combustion zone to the preheating zone. In other words, a reduction in the velocity leads to an increase in the preheat zone temperature (both the gas and solid temperature increase, if the inlet velocity of the fuel and air mixture increases, by getting more heat from the combustion zone).
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Figure 4.14: Enlarging the effect of mixture velocity on the temperature
Figure 4.13: Mixture velocity effects on the temperature along the central line
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Figure
temperature
X
Figure 4.16: 1-D effects of changing mixture velocity on the gas and solid temperature
4.7 Effective Conduction Coefficient Effects on the Temperature
By increasing the effective conduction coefficient, the heat transfer originated in the solid side increases, which leads to a solid phase temperature
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decrease. Also, this energy would be transferred to the gas and increase the gas
phase temperature (Figures 4.17, 4.18, and 4.19).
Figure
in the central line
As this coefficient is constant in the preheating zone, the combustion zone temperature would not be affected by any change of this coefficient.
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Figure 4.18: 1-D effects of efficient conduction coefficient on the gas and solid phase temperature
Figure 4.19: Effective conduction coefficient effects on the temperature along the central line
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The numerical results in this research are compared with those of 1-D numerical analysis done by A.J. Barra et al., that solves chemical equations for combustion in porous burner. In order to being able to compare the results, averaging is done on the cross section of the burner (Figures 4.20 and 4.21).
Figure 4.20: Comparing gas phase temperature with Barra's results
Figure 4.21: Comparing solid phase temperature with Bara's results
As can be seen from the above diagrams, there is a good agreement with the numerical simulations that solve chemical equations for combustion in a porous
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burner. Due to the wall temperature effects which affects the temperature, the simulated gas and solid temperature are higher in some points. It is worth mentioning that in Barra’s one dimensional analysis these effects are not visible.
Also, the parametric study shows that by increasing the mixture equivalence ratio or inlet velocity, the gas phase temperature increases. This effect is directly related to the pollution products of combustion. The reduction of porosity in the preheating and combustion zone leads to an increasing and decreasing solid phase temperature. Increasing the solid conductivity in the two zones will cause an increase in the gas and solid phase temperatures.
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REFRENCES
[1] Mahdi. A. R., et al., Review of Convection Heat Transfer and Fluid Flow in Porous Media with Nanofluid, Renewable and Sustainable Energy Reviews, 41, pp. 715-734,
[2] Kaviany, M., Principles of Heat Transfer in Porous Media, Springer, 1995.
[3] Ingham, D.,B., Transport Phenomena in Porous Media III, Elsevier, 2005.
[4] Pickenacker, O., Resting A. & Trimis D., Novel Low NOx Burner Designs for Boilers and Furnaces by using Staged Combustion in Inert Porous Media, ETATS-UNIS, 2000.
[5] Babkin, V.S., Filtrational combustion of gases. Present state of affairs and prospects. Pure and Applied Chemistry 65 (2), 335344, 1993.
[6] MoBbauer S., Trimis, D., Drust, F.& Hass, T., Zero Emission Engine- A Novel Steam Engine for Automotive Applications, The Fifth International Symposium on Diagnostics and Modeling of Combustion in Internal Combustion Engine, Nagoya, 2001.
[7] Kumar, N.R., Exergy Analysis of porous medium combustion engine cycle, International Scholarly Research Network, 542840, 2011.
[8] Drust, F., Weclas M., A New Concept I.C. Engine with Homogeneous Combustion in a Porous Medium, The Fifth International Symposium on Diagnostics and Modeling of Combustion in Internal Combustion Engine, Nagoya, 2001.
[9] Trimis, D., Drust, F., Pickenacker, 0.& Pickenacker, K., Porous Medium Combustion versus Combustion Systems with Free Flames, Clean Air, Vol. 3, pp.1-20, 2002.
[10] Howell, J.R., Hall, M.J., & Ellazy, J.L., Combustion within Porous Inert Medium, ASME HTD, Heat Transfer in Porous Media and Two-Phase Flow, 302:1-21, 1995. [7]
[11] Brenner, G., Pickenacker, O., Pickenacker, K., Trimis, D., Wawrzinke, K. & Weber, T., Numerical and Experimental Investigation of Matrix-Stabilized Methane/Air Combustion in Porous Media, Combust Flame, 123:201-213, 2000.
[12] Hus, P.F., Howell, J.R., & Mettews, R.D., A Numerical Investigation of Premixed Within Porous Inert Media, ASME J, of Heat transfer, 115:744-750, 1993.
[13] Malico, I. &Pereira, J.C.F., Numerical Study on the Influence of Radiative Properties in Porous Media Combustion, ASME Journal of Heat transfer, 123:951-957,2001.
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[14] Barra, J., Ellzey L., Diepvens, G.& Michael R., Numerical Study of the Effect of Material Properties on Flame Stabilization in Porous Burners, Combustion and Flame, 134:369-379, 2003.
[15] Barra, J. & Ellzey L., Heat Recirculation and Heat Transfer in Porous Burners, Combustion and Flame, 137:230-241, 2004.
[16] Mishra, S.C., Steven, M., Nemoda, S., Talukdar, P., Trimis, D.& Drust, F., Heat Transfer Analysis of a Two-Dimensional Rectangular Porous Radiant Burner, International Communications in Heat and Mass Transfer ,33:467-474, 2006.
[17] Baukal, E., Industrial Burners Handbooks, CRC, 2004.
[18] Pulkrabek, w., Engineering Fundamental of the Internal Combustion Engine, Pearson Prentice-Hall, University of Wisconsin-Platteville, 2005.
[19] Strehlow, R.A., Combustion Fundamental, McGraw-Hill, Singapore, 1985.
[20] Kuo, K., Principles of Combustion, John Wiley& Sons, New Jersey, 2005.
[21] Houghton, J.T., Global Warming: The Complete Briefing, Cambridge Press, 1997.
[22] Mishra, P., Fundamental of Combustion, Prentice Hall of India, New Delhi, 2008.
[23] A. J. Ferrenberg, “Regenerative internal combustion engine,” US Patent no. 4,790,284, 1988.
[24] Zhou, J.H., Cheung, C.S. & Leung, C.W., Combustion, performance and emissions of a diesel engine with H2, CH4 and H2 CH4 addition. International Journal of Hydrogen Energy, 39(9), pp.4611 4621, 2014.
[25] Weclas M., Potential of Porous-Media Combustion technology as Applied to internal Combustion Engines, 2010.
[26] MoBbauer, S., Pickenacker, O., Pickenacker, K., & Trimis, D., Application of the Porous Burner Technology in Energy- and Heat-Engineering, the Fifth International Conference on Technologies and Combustion for a Clean Environment, Portugal, 1999.
[27] Advic. F., Application of the Porous Medium Gas Combustion Technique to Household Heating Systems with Additional Energy Sources, Erlangen, 2004.
[28] Mujeebu. M. A, et al, A review of Investigations on Liquid Fuel Combustion in Porous Inert Media, Progress in Energy and Combustion Science, pp. 216-230, 2009.
[29] Nield D.A., Bejan, A., Convection in Porous Media, Springer, 2013.
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[30] Vafai, H., Handbook of Porous Media, CRC Press, New York, 2000.
[31] Zhengwen, z., Reid, G., A Criterion for Non-Darcy Flow in Porous Media, Transport in Porous Media, 63: 57-69, 2006.
[32] Saidi, M.S., Hajaligol, M.R., Mhaisekar, A.&Subbiah, M., A 3D Modeling of Static and Forward Smoldering Combustion in a Packed bed of Materials, Applied Mathematical Modelling, 31:1970-1996,2007.
[33] Cheng G.J.A., Yu, B.& Zulli, P., Evaluation of Effective Thermal Conductivity from the Structure of a Packed bed, Chem.Eng. Sci., 54, 4199-4209,1999.
[34] Patankar, S. V., Numerical Heat transfer and Fluid Flow, Taylor & Francis ,1st ed. 1980.
[35] Singh, B.P.& Kaviany, M., Effect of Solid Conductivity on Radiative Heat Transfer in Packed Beds, Int.J. Heat Mass Transfer, 16:2579-2583, 1994.
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Full Text

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i A NOVEL METHOD IN COMBUSTION MODELING FOR 2D NUMERICAL STUDY OF A TWO STAGE POROUS BURNER by MOHAMMAD DABBAGH B.S., Yazd University, 2007 A thesis submitted to the F acul t y of the Graduate S c h o ol of the Uni v ersi t y of Colorado in p artial fulfillme n t of the requirem e n ts for the degree of Master of Science Mechanical Engineering Program 2017

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ii This thesis for the Master of Science degree b y Mohammad Dabbagh has b een appr o v ed for the Me c hanical Engineering Program b y Peter Jenkins, Advisor Maryam Dar b ehes h ti Kannan Premnath May 1 3 , 2017

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iii Dabbagh, Mohammad (M.S. , Mechanical Engineering) A Novel Method in Combustion Modeling for 2D Numerical Study of a Two Stage Porous Burner Thesis directed b y Professo r Peter Jenkins ABSTRACT Currently, the treatments used to diminish the emissions of combustion processes has become a controversial issue. Except for catalytic treatments of the exhaust gases which are very costly and have a low conversion efficiency ut ilizing porous media (PM) in the combustion process is one of the most effective techniques. In this research, the method of applying porous media in burners is investigated using a numerical simulation code. Combustion in porous media has interesting adva ntages compared with free flame combustion because of an increased power dynamic range, higher burning rates and low pollutant emissions . A numerical code was developed to investigate the effect of different parameters on the combustion in a porous media. The Navier Stokes and energy equations for solids and gases in a two stage porous burner were considered. The effects on the combustion by adding a heat source term to the gas phase energy equation were considered. The governing equations are discrete in a non uniform structured mesh by using the finite volume method. The hybrid differencing scheme (HDS) was used for the convection terms. A SIMPLE algorithm was used for solving the conservation equations. The temperature, velocity, and equivalence ratios w ere known at the inlet. At the outlet, for the gas phase the flow was assumed to be fully developed and for the solid phase a boundary condition similar to that of inlet was considered .

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iv Results show that by adding the heat source parameter the model has a close agreement with existing numerical simulations that solve the chemical equations for combustion in porous burners. The numerical results in this work were compared with those of A.J. Barra et al. The parametric study showed that by increasing the mixt ure equivalence ratio or inlet velocity, the gas phase temperature increases and is directly related to the pollution from the products of combustion. The reduction of porosity in the preheating and combustion zone lead to changes in the solid phase temper atures. Increasing the solid conductivity in the two zones caused an increase in the gas and solid phase temperatures . The form and co n te n t of this abstract are appr o v ed. I recommend its publi c ation. Approved: Peter Jenkins

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v DED ICATION This thesis is dedicated to my wife, Fatemehsadat, who has supported everything I have pursued and scarified her life for me. I am truly thankful for having you in my life. Also, I am proud to dedicate this thesis to my parents, who have taught me what hard work is, allowed me to find my interests, and have been my main source of encouragement and inspiration throughout my life. Nothing I have accomplished would h ave been possible without their endless advice, love, support, and dedication to bein g the best role models possible .

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vi ACKNOWLEDGMENTS This research would not have been possible without the opportunities that my advisor, Dr. Peter Jenkins, presented to me. His knowledge, support, kindness, and positive attitude were key factors in my gradua te career. I also want to thank Dr. Darbeheshti and Dr. Premnath for their introduction to this research. Their knowledge on the topic made it possible for me to continue through difficult times. They asked the right questions and pointed me in the directi on of several sources of information that were essential to this thesis .

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vii T ABLE OF CONTENTS CHAPTER I . INTRODUCTION 1.1 Introduction ................................ ................................ ................................ .............. 1 1.2 Literature Review ................................ ................................ ................................ ..... 2 1.3 Atmosphere ................................ ................................ ................................ .............. 5 1.4 Combustion Exhaust Gas ................................ ................................ ......................... 6 I I. POROUS BURNERS 2.1 Definition ................................ ................................ ................................ ............... 1 6 2.2 Fundam entals o f Porous Burners ................................ ................................ ........... 1 7 2.3 Flame Propagation i n Porous Burners ................................ ................................ .. 2 1 2.4 Emissions in P orous B urners ................................ ................................ ................. 2 2 2.5 Technical and E conomic A dvantages of P orous B urners ................................ ...... 2 2 2.6 Porous Burners Geometrical Structure ................................ ................................ .. 2 3 2.7 Materials and S tructures U sed in P orous B ur ners ................................ ................. 2 5 2.8 Porous Burners Application ................................ ................................ ................... 2 7 II I. NUMERICAL SIMUL A TIONS 29 3.1 Introduction ................................ ................................ ................................ .......... 30 3.2 Physical Model ................................ ................................ ................................ ..... 30 3.3 Governing Equations ................................ ................................ ............................ 31 3.3.1 Navier Stokes Equations ................................ ................................ ................... 34 3.3.2 Energy C onservation Equation ................................ ................................ .......... 35 3.4 Heat Transfer Modeling in Porous Burne rs ................................ ......................... 36

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viii 3.5 Combustion Modeling in Porous Burners ................................ ............................ 3 7 3.6 Temperature Variable Coefficients in the Energy Equations ............................... 3 9 3.7 Boundary Conditions ................................ ................................ ............................ 4 0 3.8 Numerical Method ................................ ................................ ................................ 4 1 3.8.1 Hybrid Differencing Scheme ................................ ................................ ............. 4 1 3.9 Computational Grid ................................ ................................ .............................. 4 2 3.10 Incompressible Field Solution by Simple Algorithm ................................ ......... 4 3 3.10.1 The Simple Algorithm ................................ ................................ ..................... 4 4 IV . RESULTS 4.1 Results ................................ ................................ ................................ ................. 4 8 4.2 Temperature and V elocity C ontours ................................ ................................ .... 4 8 4.3 Fuel Air ratio effects ................................ ................................ ............................ 5 1 4.4 Porosity and Porous B ores D iameter E ffects on the T emperature ....................... 5 3 4.5 Emissivity E ffects o n the T emperature ................................ ................................ 5 5 4.6 Mixture I nlet V elocity E ffects on the T emperature ................................ ............. 5 6 4.7 Effective C onduction C oefficient E ffects on the Te mperature ............................ 5 8 4.8 Conclusion ................................ ................................ ................................ ............ 60 REFRENCES ................................ ................................ ................................ .................... 6 2

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1 CHAPTER I INTRODUCTION 1.1 Introduction The i ncreased population and ec onomic growth in countries increase s the amount of pollution gases from combustion processes . These gases have devastating effects on the environment, humans, and their climate. The effects of this phenomenon on geothermal gases, acid rain, and thick fog o f smoke that is caused by chemical fumes cause respiratory problems for humans. For example, the effects of CO gases on human health can be seen in Figure 1.1. The first and foremost step to control and reduce this pollution is to recognize the sources of these pollutants; such as burners, vehicles, and engines. The second step is to become familiar with the details of these gases and to understand the chemical processes leading to these emissions. The e missions consist of unburned hydrocarbons (CH 4 , C 2 H 2 , C 2 H 4 , ....), carbon oxides (CO, CO 2 ), nitrogen oxides (NO, NO 2 , N 2 O), sulfur oxides (SO, SO 2 , CS 2 , OCS), and solid particles such as soot. These gases are called primary pollutants. Meanwhile, there are some other gases which are called secondary emissions and Figure 1 .1 CO effects on human health Figure 1 .1 : CO effects on human health

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2 they are the result of reactions between primary pollutants and airborne elements, such as SO 3 , HNO 3 , H 2 SO 4 , and O 3 . This research evaluated the methods which are used to reduce the emission of these gases and to control the reactions that lead to the production of such gases. The second and third steps are discussed in this chapter. The disadvantages of those methods that are applied to reform the process of combustion and to reduce emissions from combustion encourage researchers to find new processes . One of those methods is that of using porous medium in the combustion chamber. There are several studies of the application of porous media in a combustion chamber and a short summary is provided in the next section . 1.2 Literature Review Using porous media (PM) in combustion processes has two important advantages. As Mahdi et al (2015) mentioned, the first and foremost effect is its heat dissipation characteristics, which are greater than that of conventional fins and results in greater convection hea t transfer [1]. In porous medium, the regular motion of the fluid flow forms a mixture of the fluid around the individual porous beads. Studying the treatment of fluid flow and heat transfer in porous media is based on both empirical and fundamental approa ch. As Kaviany (1995) heat transport in porous media has a long history [2]. Regarding Darcy's book written in 1856, the effects of porous media were analyzed using his work on water flow through beds of sands (a water filtration application). By that time,

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3 the single phase flow through pipes was already evaluated by Hagen and Poiseuille. The effects of transport in porous media during that time could be assessed in two ways: dir ect (e.g., studies directed by Darcy, Carman, Leverett) and indirect (e.g., studies directed by Hagen, Knudsen, Taylor). Thus, when it came to the utilization of the porous media in the combustion, it had already been investigated by several scientists. Th e most basic investigations were found in the early twentieth century. In 1912, Bone invented the first porous boiler and heater [3]. One year later, Lucke did research on radiative heaters, furnaces and cooking stoves. In 1933, Hays reported a new inventi on of heating water using the combustion in porous medium [4]. Babkin et al (1991) studied the propagation of combustion flame of premixed mixture in porous combustion chamber [5]. In the study done by Trimis in 2002, an experimental comparison was made be tween the free flame and combustion processes in porous inert media [6]. In that research, the pros and also the procedures of using the porous media in internal combustion engines were assessed. Also, he and his associates, developed the thermodynamics an d the environmental advantages of this method. In addition, they invented an external engine that had very low emissions. In that model, porous burners were used to heat the working fluid. Kumar did a thermodynamic evaluation of these combustion characteri stics with an open combustion chamber [7]. Also, Weclas et al (2001), investigated the use of a porous combustion chamber in an internal combustion engine [8]. As Trimis claimed (2002), it was possible to design a porous combustion chamber by considering s ome advantages, such as increasing the stability, improving the rate

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4 of energy release, and reducing the distribution of pollutants [9]. The main idea of designing these chambers was based on the optimal limit of the temperature to be maintained for the co mbustion process and the reduction of NOx and CO. The main reason was that the porous media chamber caused homogeneous combustion. Increasing the efficiency and increasing the rate of the combustion are two of the most significant consequences of using PM in combustion chambers. Also, the effects of radiation and combustion in porous chambers have been studied. Kaviany, in 1993, examined the dependent and independent scattering numerical results to experimental results [2]. In the research which is presented by Trimis and Drust, an experimental comparison between free flame and the flame inside the porous chamber was done. In this study, the burner dimension, the burner thermal power, the extent of the exhaust emissions, and its stability have been examined [9]. Howell et. Al. (1995) investigated some characteristics, such as the effective conduction coefficient, impermeability coefficient, and extinction coefficient, all for porous media and based on experimental results [10]. Brenner, in 2000, presented diffusion coefficients and impermeability coefficients for laminar flow as functions of temperature [11]. Hsu et al (1993) developed convection and radiation coefficients based on the pred iction of gas and solid phase temperatures [12]. Malico and Pereira, in 2001, evaluated the radiation effects on the 2D combustion in porous medium [13].

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5 Finally, Barra et al presented results from his simulation of 1D two stage porous burners in two diff erent studies, in 2003 and 2004 [14] [15]. They evaluated, by using numerical analysis, the effects of changing the porous bore diameter, convection coefficient, and the inlet fuel jet velocity on the gas and solid profiles. In this research, I compared my results are used as a benchmark of my research. 1. 3 Atmosphere To determine the extent of air pollution and how to control it, it is necessary to have a basic analysis of the atmosphere. Atmosphere is composed of 78% N 2 , 21% O 2 , and 1% other gases. There are four different layers in atmosphere, and the first one , the Troposphere, is explained as follows . Troposphere This is the main part of the atmosphere and it makes up 90% of mass of the atmosphere. Gases res ulting from combustion immediately affect this layer. As chemical reactions in atmosphere start in this layer, in the presence of ozone and in wavelength less than 320 nm [16]. The foll owing reactions happen in this layer. O 3 2 +O Eq. 1 . 1 O+H 2 Eq. 1 . 2 Generated OH in reactio n 1 2 could be used in the other reactions as follow . 2 Eq. 1 . 3

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6 H+O 2 2 +M Eq. 1 . 4 HO 2 coul d be used to regenerate OH. HO 2 +O 3 2 Eq. 1 . 5 Since there are emission gases in this layer of atmosp here, a considerable amount of NO 2 exists, which results in a reduction in th e HO 2 generation. Instead, nitric acid is generated as shown in the following equation: OH+NO 2 3 Eq. 1 . 6 1. 4 Combustion E xhaust G ases Identifying the origin of emissions produced by combustion helps to lead to the control and reduction of such emissions. The mo st important ones are as follow : Unburned Hydrocarbons ( U HC s ) increasing the excess air rate, UHCs decrease [17]. Actually, the largest portion of UHCs in the exhaust gases result from the thermal cracking phenomena. In this process, large HC molecules are cracked to smaller ones, whic h are effected by the high temperature of combustion chamber. The UHCs structure is dependent on the makeup of the fuel, combustion chamber geometry, and parameters associated with the engine. In all fuel combustion cases, except methane combustion, the re action of UHCs with air causes photochemical smog.

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7 Photochemical smog Photochemical smog is a secondary emission that is formed by combination of Nitrogen oxide, sunlight, and UHCs, and creates harmful components such as Ozone, Aldehyde, and Peroxyacetyl e Nitrate (PAN). These components cause headaches, eye irritation, respiratory problems, and premature skin aging. This pollution is evident in the sky as a brown layer. This phenomenon is explained well in Figure 1.2. The following reacti ons forms emissio ns as described below : N 2 +O 2 Eq. 1 . 7 2NO+O 2 2 Eq. 1 . 8 If the NO 2 concentration in the atmosphere is high, the air is clear, and there are no clouds, then sunlight would cause the following reactions: NO 2 Eq. 1 . 9 O+O 2 3 Eq. 1 . 10 NO+O 3 2 +O 2 Eq . 1 . 11 Figure.1.2: Photochemical smog formation

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8 If the NO concentration is greater than the NO 2 , reaction in Eq.1 11 oc curs and the ozone level remains constant. However, the effect of UHCs increases the NO 2 concentration and, as a result, ozone forms . UHC s creating factors There are some processes that create UHCs. First is Air fuel ratio. In the case of a rich mixture, there is not enough oxygen for all hydrocarbons, and as a result there would be more UHCs. On the other hand, by leaning the mixture results in reduced amount of UHCs. However, if the leaning of the mixture is continued, the result would be an incomplete combustion, UHCs would be increased and the thermal efficiency would decrease. Pulkrabek, w., in Engineering Fundamental of the Internal Combustion Engine, in 2005, discussed this effect as shown in Figure 1.3. Hence, in this case, finding the optimum oper ating point is vital to an efficient and clean combustion process [18]. Figure.1.3: Amount of emission in education flow in respect of Equivalence ratio

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9 Incomplete combustion There are several factors relating to incomplete combustion. First is not having a stoichiometric mixture. In this case, there is not enough Oxygen molecules and the combustion would be incomplete. Also, to reduce the onset of incomplete combustion, quench zones are created in the combustion chamber by creating swirl or turbulent flow in the combustion chamber to provide better mixing of the fuel and air . Depositio n of fuel on the combustion chamber walls The deposition of fuel on the combustion chamber walls is a function of mixture pressure and mostly occurs in internal combustion engines as Pulkrabek, w., explained in Engineering Fundamental of the Internal Combu stion Engine [18]. Carbon monoxide (CO) Carbon monoxide is colorless, odorless and very toxic. If, during the Table.1.1: CO sources

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10 combustion process, there is not enough oxygen to convert all the carbon to carbon dioxide, then CO forms as can be seen in Figure 1.3. In oth er words, CO is one of the products of incomple te combustion . The main sources of CO are shown in T able 1.1, as Strehlow, R.A., explained in Combustion Fundamental, McGraw Hill, Singapore, 1985 [19]. The most important factor to redu ce CO is having a lean mixture. Nitrogen oxide (NOx) Having nitrogen oxide emissions in the atmosphere and combining them with elements of air increases the concentration of ozone and results in the formation of photochemical smog. The two main sources of this gas are specifie d in Table 1.2, as Strehlow, R.A., showed in Combustion Fundamental, 1985 [19]. NOx formation mechanisms in combustion process As Kuo, K., explained in Principles of Combustion (2005) , there are three mechanisms of NOX formation in a combustion process [2 0].

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11 The first one is Zeldovich mechanism. In this mechanism, which is the most active mechanism in combustion processes, NOx is formed behind the combustion zone. The following reactions occur: O+N 2 Eq. 1 . 12 N+O 2 Eq. 1 . 13 Eq. 1 . 14 NO forms NO 2 i n a reaction with water and oxygen, as the following reaction shows: NO+H 2 2 +H 2 Eq . 1 . 15 NO+O 2 2 +O Eq . 1 . 16 The other mechanism is the Prompt mechanism, which NOx forms very rapidly within the flame while reacting with the hydrocarbons of fuel. The following reactions occur in this method: CH+N 2 Eq . 1 . 17 Eq. 1 . 18 NC Eq . 1 . 19 2 Eq. 1 . 20 N+O Eq . 1 . 21 The other mechanism is called Fuel mechanism. In this mechanism, which is mostly represented in coal combustion, the fuel itself includes Nitrog en. This Nitrogen reacts with existing Oxygen in the air and forms NOx. Houghton, J.T., (1997) compared these three mechanisms in the Global Warming: The Complete Briefing, Cambridge Press, as shown in following diagram (Figure 1.4) [21]:

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12 NOx control mec hanisms during combustion process There are some important solutions to reduce the NOx emission resulting from combustion. The first is by reducing the excess air. Generally, it is common to have excess air in boilers and burners in order to have a complet e combustion. But, this excess air causes more NOx. There are some disadvantages to reducing the excess air, such as increasing the formation of CO and UHC, and decreasing the thermal efficiency, as shown by Mishra, P., in Fundamental of Combustion, in 200 8, and is shown in the F igure 1. 5 [22 ]. The other method to control NOx is called the staged combustion. As Baukal has mentioned in Industrial Burners Handbooks, 2004, by having this kind of combustion, the flame length and the heat transferred would be in creased, which result s in a decrease in the flame temperature. Hence, the thermal NOx formation would decrease. This result is shown in the following Figure 1.6 [17] Figure 1. 4: NOx formation compression during different mechanism

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13 Figure.1.5: NOx control technology Figure.1.6: Comparison of flame length

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14 NOx control mechanisms after combustion process There are several ways to reduce NO x emission effects in the post this process, exhaust gases would be directed through a thermal convertor, allowing high temperature secondary reactions to occur easily; as describ ed in the following: CO+1/2O 2 2 Eq . 1 . 22 CXHY+zO 2 2 +1/2yH 2 O Eq. 1 . 23 Also, it is applied at the exit of burners. A disadvantage of using these traps is the possibility of getting filters blocked by carbon particles during the combustion process. Carbon dioxide (CO 2 ) Alt hough CO2 is not considered a toxic emission, it has a damaging role as Greenhouse gas. This greenhouse effect causes a temperature increase and results in a climate change over a long period of time. Sulfur As Strehlow, R.A., explained in Combustion Fund amental, in 1985, the main resource of sulfurs is fossil fuels (Tabl e 1.3), which cause acidic rain [19].

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15 Source So 2 (million tons per year) Fossil fuel 80 Metal smelting 8 Biomass burning 2 Natural sources (ocean, vegetables, oil and volcano) 25 sources 2 : SO Table 1.3

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16 CHAPTER II Porous Burners Optimizing the efficiency and reducing the pollution in combustion emissions is an ongoing challenge. One solution to reduce combustion emissions is by providing the necessary conditions for having a homogeneous combustion. In this chapter, porous burner characteristics, the application of porous media in burners, the porous burner geometrical structure, and the industrial use of porous burners have been studied. 2 . 1 Definition Pores are three dimensional and of three types. If each void is connected to more than connected to any other pore, while the fluid flow passes through the interconnecte interconnected pores. The porosity is a function of pressure gradient for the deformable matrixes. Generally, the pores do not have a typical size and distribution. Regarding the size, some pores are very large and some others are very small (micropores or ultramicropores). The most common structures for the such as circular sections.

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17 2.2 Fundamentals o f P orous B urne rs There are two functions for using porous medium in a combustion chamber. The first, as Ferrenberg suggested in 1988, PM has the role of thermal storage and a heat exchanger, and there is no combustion within a porous medium [23]. As the second function, the porous medium could be used as a combustion chamber, as introduced by Zhou et al (2014), or by using the medium in the piston bowl or in the cylinder head, as Durst and Weclas proposed [24]. The porous media is a solid material. Generally, its struct ure is a honeycomb structure. Such a honeycomb structure, by itself, could be classified by two methods. It could have a random structure or, it could be in a packing structure, which is called a regular structure. Fluid passing through this media have spe cific characteristics. As Weclas explained (2010), the distinction of combustion in this medium in respect to a medium without any porosity is the lack of formation of a free flame [25]. The reason is as follows; the flame is formed in a 3 dimentional poro us chamber which look like a wasp nest. The second difference is related to the preheating of inlet mixture gases. Generally, flame propagation in premixed burners could be controlled by the upstream heat transfer. The thermal conductivity of the laminar f low of gas in the laminar flame or the advanced heat transfer in turbulent flames are the factors that limit flame propagation in conventional burners. Limiting the flame speed provides stability and maximizes the energy release rate.

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18 The temperature of the flame in porous burners can be kept within acceptable limits due to the solid phase of the burning media and the high coefficient of heat conduction and radiation that exists in this phase compared to gas phase. Premixed burners with an open flame have very low flame thickness due to very low conductivity of the gas mixture. Hence, reactions occur in a very small part of the chamber, and the rest of the combustion chamber remains unused, as it is shown in F igure 2.1. Combustion in porous media provides a way of expanding the combustion thickness to the entire combustion chamber, due to its high coefficient of heat conduction and its radiation characteristics. The other important application of porous burners is the stability range. As Mishra in 2006 exp lained, porous burners have a broad stability range in comparison to conventional burners, specifically in the case of increased flame speed [16]. In conventional burners, flame stability exists in a very limited flame speed range, while in porous burners, the flame is much more stable. The reason is that the heat transfer in the opposite direction of the flow of the air fuel mixture causes that area to reach ignition temperature and stabilizes the flame and combustion. In conventional burners, if the flame speed exceeds the design Figure 2 .1 : C ombustion thickness in premix burner

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19 speed, it causes flame flashback or blow off (Figure 2.2). This does not occur in porous burners. These changes lead to stable combustion, as Mishra explained in his book (Fundamental of Combustion, 2008 Figure 2.3) [22]. Fi gure 2.3 : Flame speed and fuel jet velocity in a stable combustion In porous burners, air fuel mixture enters in the preheat area at first. Any chemical reaction occurs in this area, where is usually heated by heat conduction and heat radiation coming from the reaction zone. This area could be extended to the inlet, depending on the thickness of the porous burner. By approaching this area of combustion and with the sharp rise in the temperature gradient, heat Figure 2.2 : Stable zone respecting to velocity gradient and fuel ratio

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20 conduction will occur. In this area, due to cond uction and radiation induced by combustion chamber gases, the temperature of the solid is above the temperature of the combustion gas mixture and heat transfer occurs by conduction from the solid phase to the gas phase. After this preheat zone, the gas tem perature reaches a temperature which causes the formation of a combustion zone. The thickness of this zone is very small, and within this zone, gas temperatures are higher than in the solid zone. Also, heat is transferred to the solid by conduction . Afte r combustion, there is another zone which is called by Mößbauer S. and Trimis (in 2001) as the post flame zone (Figure 2.4 & Figure 2.5). In this zone, heat is transferred to the outside of combustion chamber, which creates a negative temperature gradient . Hence, having the temperature increase Figure 2.4: Heat removal within burner zones

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21 in the upstream and reduced reduction in the downstre am is the characteristic of these kind of burners . 2.3 Flame P ropagation in P orous B urners As mentioned earlier, the controlled flame propagation in pre mixed burners is a limiting factor to the flame rate and results in flame stabilization and maximizes the energy release rate. The practical constraint in the utilization of combustion in porous burners is the reduction in the combustion rate, which result s from the reduction in the gas mixture velocity. This occurs due to the small dimensions of porous medium. It has been shown that the flame propagation that occurs in porous burners is a function of the Peclet number. Weclas defined the Peclet number as : Eq. 2 .1 In this formula, S l m is the equivalent pore diameter, and a f is the diffusivity factor for the combustion products. This formula relates the portion of heat released from the combustion to the heat conducted out of porous chamber. Flame propag ation is possible when the heat Figure 2.5 Main heat transfer mechanisms in a porous burner

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22 release rate is larger than the heat transfers to the outside. Hence, if the size of voids is smaller than critical, flame growth would be stopped and the flame would be quenched. Alternatively, if the voids are greater than the critical size, flame propagation could be possible. Babkin et al in 1991 determined the Peclet number for Methane as 65 [4]. 2.4 Emissions in P orous B urners Carbon monoxide (CO) and unburned hydrocarbons (HC) are formed due to an incomplete combusti on process. Also, they are created as a result of cold spots in the combustion chamber. NOx production is also dependent on the temperature of combustion products. In these kind of burners, because of the high heat transfer rate, especially radiation heat transfer, the combustion chamber temperature is reduced. Also, hot and cold spots occur during the combustion process due to the structure of porous medium and as a consequence of having a homogeneous combustion. 2.5 Technical and economic advantages of po rous burners Most of the advantages of porous burners result from having efficient heat transfer in the combustion zone and also having flame stability at high burning speeds. The most important advantages are as follows: High thermal efficiency by taking advantage of the preheat zone. This kind of burner is clearly much more efficient. Very low emission (CCO<7 mg/kwh) (CNO<25 mg/kwh) Stable combustion: for lean air gas mixture, with a fuel air ratio between 0.53 0.91

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23 Fuel flexibility: porous burners have fuel flexibility in the range of 1 20, that is much higher than common burners in the range of 1 3. High power density: These burners are 10 times smaller in comparison to common burners which reduces the materials cost. Compact shape Fast flame response time Variable dynamic power range 2.6 Porous Burners Geometrical Structure These type of burners generally have a two phase structure. First, the air fuel mixture enters from bottom zone, as shown in Figure 2.6. A compressed porous structure exists in this area. This results in a reduction of the diameter of the bores which results in a lowering in the Peclet number from the critical level. As a result, the flame is not formed in this zone, as it has not been conditioned for combustion. In other words, the main goal of preheat zone is just to preheat the fuel air mixture. The second zone is called the Figure 2.6: Porous burner geometrical structure

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24 combustion zone. Flame propagation occurs in this z one and results in combustion. Using porous material in the combustion zone results in a higher Peclet number. 2.7 Materials and S tructures U sed in P orous B urners Porous matrix performance used in burners is dependent on the materials used and the form of matrix grid. Generally, the material has a high resistance to high temperatures, high mechanical res istance, heat shock resistance, and high conductive and radiation heat transfer properties. As Mößbauer et al. explained in 1999, in the preheat zone, because of lower temperature, it is preferred to use these materials to protect against elevated temperat ure and thermal shock [26]. This is why low porosity material is suggested for this zone, while for the heating zone, it has been recommended to choose materials with high resistance against elevated temperature and thermal shock, as shown in F igure 2.7 T he best materials suggested for this medium are Al2O3, SiC, ZrO 2 . The most important characteristics of these materials are as follows: Figure 2.7: Porous structure

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25 Al 2 O 3 The temperature range of this structure is about 1950 degrees C. The conductivity coefficient is about 5 30 w/mk (in the temperature range of 20 30°C). The coefficient of thermal expansion is average, while the radiation coefficient is about 0.28 at 2000°C. Also, its porosity is high (0.9 0.99). Such structures have a high heat transfer due to structure due to hav ing a high internal surface. SiC This structure has unique features. Its maximum allowable operating temperature is 1600 °C. It has a radiation coefficient between 0.8 0.9 (in the temperature of 2000°C and a high porosity (0.7 0.9). High heat shock r esistance, low thermal expansion coefficient, and a conduction coefficient in Figure 2.8 : Al2O3 Stru cture used in porous burner Figure 2.9 Sic structure

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26 the range of 20 structure. ZrO 2 This structure is recommended for use in high temperatures, such as in a combus tion zone, since it has a maximum allowable temperature of 2300°C. Some other characteristics of this medium are having a low thermal conductivity coefficient between 2 5 w/mk, and radiation coefficient of 0.31. Also, a high heat shock resistance is one of its important features. ( Figure 2.10 ) . In the next table ( T able 2.1) , all these three materials features are compared. Table 2.1 Comparison between Al2O3, SiC, and ZrO2 characteristics Parameter Dimensions Al 2 O 3 SiC ZrO 2 Maximum Allowable temperature in air °C 1900 1600 1800 Thermal expansion coefficient (20 1000° C) 10 6 1/K 8 4 5 10 13 Thermal conductivity at 1000° C W/mK 20 30 8 150 2 5 Thermal conductivity at 1000° C W/mK 5 6 20 50 2 4 Specific thermal capacity J/gK 09 1 0.7 0.8 0.5 0.6 The rmal stress resistance parameter, hard shock R ( /E ) K 100 230 230 Thermal stress resistance parameter, mild shock R (R/ ) 10 3 W/m 3 23 1 Total emissivity at 2000 K 0.28 0.9 0.31 Figure 2.10: ZrO 2 structure

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27 2.8 Porous B urners A pplication As Advic. F mentioned in 2004, there a re several applications for these kind of burners. The figures below show some of the most important applications of these types of burners. Household burners By having a wide dynamic power range, there is not necessary to have repetitive starts in the se kinds of burners. This characteristic causes a significant reduction in emission production, since the main emission formation occurs during the starting process. Also, by having higher heat transfer rates, fewer emissions occur. Advic compared the emis sion of burners in household applications as shown in the F igure 2.11 [27]. The other benefit of using this type of burner in the household is the limited space needed for installation, due to its compressed shape, as shown in Figure 2.12. Figure 2. 11: Emission comparison between Porous burners and standard burners

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28 Gas turbine c ombustion chambers Gas turbines usually work with pre heated gases in order to reduce the thermal NOx. Although, if 50% of the nominal power is obtained, unstable combustion occurs and leads to NOx and CO generation. This could be resolved easily by applyi ng porous burners in gas turbines. Internal combustion engines The treatments to reduce the emissions of internal combustion engines (ICE) have become controversial issues. Except for catalytic treatments of the exhaust gases which are high costly and lo w conversion efficiency utilizing the porous media in the combustion process is one of the best alternative techniques. By adding porous media to ICEs, it is possible to approach a homogeneous combustion level and by controlling the temperature, less emi ssions are produced, as Mujeebu et al proved in 2009 [28]. Furthermore, using this medium to preheat the gases results in an increase in the efficiency. Weclas found that the best performance of this medium is achieved by utilizing an open cell structure o f PM, without any valve in the cylinder head, to separate the cylinder head from the cylinder chamber [25]. Figure 2. 12: Household porous bu rner

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29 Steam engines One of the other applications of porous burners is in steam engines. Generally, steam engines are very large. But there are two excell ent feature in porous burners that are applicable to steam engines compact shape and high power density. These characteristics allows steam engine designers to reduce the size of the steam engine. As an example, the porous steam engines could be used as a heat source in the Sterling engine.

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30 CHAPTER III Numerical Analysis of A 2 D Porous Burners 3.1 Introduction In this chapter, the combustion in a porous burner has been analyzed. In this combustion simulation, the solid phase radiation effects are assu med by applying an effective conduction term. Also, the combustion process was modeled by adding a constant heat source of energy in the conservation of species equation. Initially, the mass conservation, momentum conservation, and energy conservation equa study. 3.2 Physical model The c omputational area is a two stage tetrahedral burner. As presented in F igure 3.1, the burner length is 6.05 cm (included 3.5 cm preheat zone and 2.55 cm combustion z one) and the width is 1 cm. For both zones partially stabilized Zirconia has been used (Table 3.1) and the porosi ty of each zone was different. Figure

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31 3.3 Governing E quations Some assumptions were made in deriving the equations. First, assume all porous materials are neutral and are not involved in any chemical reaction. The other assumption is that the porous material was considered as a continuum material. Also, the fluid velocity and porous permeability is high enough that the fluid pressure loss and boundary layer effects can be ignored in this medium. As in the porous burners, both the gas and solid phases exist. The governing equations are not the same as in the conventional equations. For example, in the momentum equation, the pressure loss caused by the fluid passing in the porous medium should be conside red. Generally, the pressure loss of a passing fluid is law in the fluid mechanics of porous media, the mome ntum equations or force balances are pr esented by numerous experimental observations which are summarized mathematically as the Darcy Law [29] . In other words, i n fluid dynamics and hydrology, the total discharge in a porous medium is expressed by Preheat zone Combustion zone Pore diameter Porosity Conductivity Pore density 0.146 0.638 C 0.96 0.42 M Densi ty Specific heat Table 3.1 : PSZ Thermo Physical characteristics

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32 . This law is based on the experimen tal results of the flow of water through sand beds (Figure 3.2) . This law also applies to the oil and gas governing equations. This law is based on a simple proportional relationship between pressure loss, permeability, viscosity, flow cross sectional are a, and the total fluid discharge, and given by the following equation (Eq. 3.1) Eq. 3.1 In this equation, K is the intrinsic permeability of the medium. This coefficient is a function of the inlet fluid, and the porous medium network structure, specifically, the bore diameters. One of the most common equations for this coefficient is the Carman book o Eq. 3.2 In this equation, C k is a dimensionless coefficient and is equal to 180 for spherical particles. is the porosity of the porous medium, while d p is the spherical bore diameter. By dividing Eq. 3.1 by area, the volumetric flux could be obtained by using Eq. 3.3 : Figure

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33 Eq. 3.3 Fluids always flow from a high to low pressure, this is why the negative sign which is why fluids with Reynolds number less than 10 are usually considered ds, as Carman Kozeny claimed. The Reynolds number for a porous medium is defi ned by Equation 3.4 or either 3.5. Eq. 3.4 Eq. 3.5 In the Eq. 3.4, v is the fluid velocity at the outlet and d 30 is a parameter which is defined as 30% of the average bore diameter. In Figure 3.3, the range of app As Zhengwen mentioned in 2006, m any attempts have been made to correct the Darcy equation [31] . Finally, Forchheimer (1901) suggested a second order Figure

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34 of the velocity term to represent the microscopic inertial effect, and co rrected the Darcy equation using the following equation [30] : /k + v 2 Eq. 3.6 Forchheimer equation was corrected in 1947 by Brinkman [31]. In the co rrected equation, second order derivatives of the velocity were added to the Darcy equation as shown in following equation, where X, Y, and Z directions are mutually perpendicular. /k 2 2 2 2 ) Eq. 3.7 In the numerical simulation which was done in this study, it was impossible was calculated using Brinkman model, it was negligible as well. The reason was that th e first term is almost zero since there is a high permeability and, as a result, the K coefficient was large. Also, referring to the second term, by having a very small pore diameter, the change of velocity across the pore throat was negligible , while ther e is no pressure loss in Y direction (as a 2D problem) . As a result, the second term was approximately zero. Because of this, the mass conservation and momentum conservation were used as the common equations. 3.3.1 Navier Stokes Equations The mass conserva tion equation and the momentum conservation equation are given as follows: Mass conservation equation: Eq.3.8

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35 Momentum conservation equation: Eq. 3.9 3.3.2 Energy conservation equation : To use the energy conservation equation in a porous burner, a volume averaged model was used. In this approach, the energy equation was solved for both the gas and solid phases, a s given in equations 3.10 and 3.11: Gas phase energy equation Eq. 3.10 Solid phase energy equation Eq. 3.11 On the right hand side of Eq. 3.10, first term repr esents the chemical energy release during N chemical reactions, while the second term represents the species distribution. The third term represents the conduction between the gas and solid phases. It is noted that the solid radiation is much greater than the gas radiation, and, as a result the gas radiation flux is negligible in gas phase energy equation. On the right hand side of Eq. 3.11, first term shows the heat conduction between the gas and solid phases, while the second term represents the radiatio n flux from the porous medium. In this study, porous medium radiation was modeled as an effective conductive term. Also, instead of solving the species transport equation, the

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36 combustion was modeled by adding a constant heat source of energy to the gas ph ase energy equation, Eqn. 3.10, rather than solving the first and second terms, which are chemical energy release and species distribution terms . 3.4 Heat T ransfer M odeling in P orous B urners In this study, an effective conductive term was used in order to model the porous medium radiation, as Saidi mentioned [32] . Using this technique and as the first step in the modeling process, the effective conduction co efficient was defined. While there are several definitions for this coefficient, in this study the coefficient which is defined by Cheng G.J.A in 1999 was used [33]. Eq. 3.12 As the second step, the effective conduction coefficient was defined for both the gas and solid phases separately, as given in Eq. 3.13 and Eq.3.14. Eq. 3.13 Eq. 3.14 As the third step, it was essential to consider the radiation effects on the effective conduction coefficient. In order to do that, as Kaviany defined in 199 5 , the othe r coefficient should be defined as K r (Eq. 3.15 and Eq. 3.16) [ 35 ] . The total effective conduction coefficient would be the sum of these two coefficients (Eq. 3.17).

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37 Eq. 3.15 Eq. 3.16 Eq. 3.17 As the final step (step 4), the energy equation was rewritten. In the n ew energy equation (Eq. 3.18), , represented the radiation effects. Eq. 3.18 3.5 Combustion M odeling i n P orous B ur ners As explained earlier, in this study the species transport equation was not solved and the combustion was modeled by adding a constant heat source in the gas phase energy equation. Hence, the new gas phase energy equation was c hanged to the following , Eq.3.19, Eq. 3.19 In this simulation, adding the heat source was very important to the combustion process. In porous burners, the mixture of fuel and air was initially preheated in the preheating zone. Th e heat source was added just before the interface, 0.075 cm before the border between the two regions (prehea ting zone and combustion zone). This heat source increased linearly and was at its maximum value in the border, which was equal to . Then, the value decreased to zero in 0.11 cm after the interface. In order to being able to show

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38 the heat source placement, the Dirac the Figure 3.4. To determine the heat source value, first it was necessary to evaluate the combustion equation. If the fuel is Methane, the combustion equation is shown by Eq. 3.20 (without any excess air): CH 4 +2(O 2 +3.76N 2 2 +2H 2 O+7.52N 2 Eq.3.20 As a result, the molar fuel a ir ratio would be: Eq. 3. 21 T o have a complete combustion, excess air was required. In this case, Eq. 3.22 shows the actual molar and mass fuel air ratio: Eq. 3. 22 Eq. 3. 23 Hence, the mixture mass flow rate was : Figure 3.4 : Heat source placement

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39 Eq. 3.24 On the other hand, the mass flow rate, by its definition, was related to the gas velocity, as Eq. 3.25 shows: Eq. 3.25 Now, by setting , the final relationship for is given in Eq. 3.26: Eq. 3. 26 In the Eq. 3.26, is a constant. As Barra et al claimed in 2003, this constant could be [13] . 3.6 Temperature V ariabl e C oefficients in the E nergy E quations Three different co efficients used in both gas an d solid phase energy equations vary by temperature. These coefficients are the gas density , gas viscosity , and the volumetric heat transfer coefficient. As Barra suggested in 2003, these coefficients are calculated as follow [14]. Regarding gas density , Barra proposed to use the values given in Eq. 3.27. In this equation, is gas density is thermal diffusivity coefficient , and is the specific heat of gas mixture (Eq. 3.28) , Eq. 3. 27 Eq. 3.28

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40 To find the used : Eq. 3.29 Eq. 3.30 Viscosity is varying with temperature, as shown by Eq. 3.31, Eq. 3.31 Finally, th e correlation for volumetric Nusselt number was giv en by the following correlation (Eq. 3.32) : Eq. 3.32 By considering Eq. 3.32 and also Eq. 3.33, which represents the Reynolds number, the volumetric heat coefficient was calculated. This coefficient relat es the energy and solid phase equations to each other. Eq. 3.33 3.7 Boundary C onditions The i nlet boundary conditions f ollow (Eq. 3.34, 3.35, and 3.36): Eq. 3.34 Eq. 3.35 Eq. 3.36 The outlet boundary conditions are given as (Eq. 3.37, 3.38, and 3.39):

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41 Eq. 3.37 Eq. 3.38 Eq. 3.39 Also, the walls in the combustion chamber are considered adiabatic for both d to be 0.8. 3. 8 Numerical M ethod The governing equations were solved using the finite element method (FEM). In this method, a non uniform grid with variable spacing (variable mesh size) was used to discrete the governing equat ions, while the pressure and velocity 3 . 8 .1 Hybrid differencing s cheme This scheme was a combina and Figure 3.5: Computational Grid

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42 formula based on the local Peclet number in order to evaluate the net flux through each control volume face. If the general form of th e discretized equation was like Eq. 3.39, then the coefficients would be given in Eq. 3.40 4 3 , with variables F and D representing the convection mass flux and diffusion conductance at cell faces respectively , so that . Eq. 3. 40 Eq. 3.4 1 Eq. 3.4 2 Eq. 3.4 3 3. 9 Computational G rid In this numerical study, the convergence criteria were assumed based on the mass residual, first order pressur e norm, and also the first order gas phase temperature norm, which all should be less than 10 6 , 10 4 , and 10 4 respectively. In the Table 3.2, the error percentage was presented for three different grid cells (74*15, 148*30, and 296*60). Table 3.2 Error percentage due to change in the number of computational grid cells Solid phase temperature change percentage Gas phase temperature change percentage Total number of grid cells 74*15 4.95 11.05 *30 2.66 2.53 296*60

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43 T here was not a significan t change in the gas and solid phase temperature between these two grids, which is why 148*30 was selected as the grid size. 3.1 0 Incompressible Fi eld S olution by Simple A lgorithm To solve the incompressible field, the Navier Stokes equations had to be solv ed. As Pantkar proposed in 1980, a good method to solve the non linear N S equations was using the Simple algorithm, which is one of the finite element methods to discrete the equations. The acronym simply stands for Semi Implicit Method for Pressure Linked Equations. This algorithm could be solved for both For collocated grids, all the variables (including vector variables and scalar variables) were stored at the same locations. For the staggered grids, var iables were stored at different locations and were shifted to a half of the control volume in each coordinate direction. The collocated grid approach was applicable when the geometry was complicated, while the staggered grid approach was preferred when u si ng the Cartesian coordinates. Although it was much simpler to use the collocated grids, the issue was that if this method was used to solve N S equations, it was hardly possible to have a proper coupling between the pressure and velocity fields. In the Fig ure 3.6, the backward staggered grid is shown.

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44 While all the scalar variables (including pressure) are stored at the nodes marked as , the velocities are defined at the scalar cell faces between the nodes and are indicated by arrows ( ) for u velocities and ( ) for v velocities, points to calculate velocities, the length of each node were 1.5 times the other nodes. 3.1 0 .1 The Simple algorithm This Simple algorithm was based on the guess and correct procedure. To initiate this process, a pressure field p * was guessed. In addition, an initial guess for the velocity field was r equired. By these initial guesses, the discretized momentum equations (Eq.3.4 4 ) were solved. Eq. 3.4 4 Figure 3.6: The arrangement for the two dimensional flo w

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45 Now, defining p and v as the difference between the corrected p and v and init ial gues ses, fo llow s : Eq. 3.4 5 Substituting the corrected values into the momentum equation s yield to correct ed equations . Eq. 3.4 6 At this point, an approximation was introduced by neglecting and .., resulting in Eq. 3.4 7 as follow: Eq. 3.4 7 where the coefficients were calculated as given by e quation Eq. 3.4 8 : Eq. 3.4 8 By substituting these corrected values into the Eq. 3.4 5 , the final values for pressure and velocity are : Eq. 3.4 9 To check the velocity values, th e se values should be able to satisfy continuity equation as well. Tho se ones reach out to the Eq. 3.50 .

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46 Eq. 3. 50 Substituting the velocity values from eq. 3.4 9 into the continuity equation (Eq. 3. 50 ) gives: Eq. 3.5 1 w here the coefficients are as follows : By substituting the corrected pressure terms into equation 3.4 7 gives the corrected velocity terms. The term was obtained from the continuity equation for a single node. If the velocity terms calcu lated using the momentum equation are correct, this term should be equal to zero. The simple flowchart was developed as shown in Figure 3. 7. The simple algorithm needs an under relaxation in order to converge (Eq. 3.5 2 ). These new values were used to upda te the pressure and velocity. In these equations, the coefficients are and . Usually, the equation of is used with . Eq. 3.5 2 Table 3.3: Corrected pressure coefficients

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47 Figure 3.7: Simple algorithm flowchart

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48 CHAPTER IV . RESULTS 4.1 Introduction In this chapter, the results of the simulation of combustion in the area of solution are discussed. Also, changes in the v elocity, fuel air ratio, conduction coefficient, porosity, porous bores diameter, and the radiation coefficient for both the gas and solid temperatures are discussed Then, the gas and solid median1 D temperature diagrams are presented and the effects of ch anges made are evaluated. 4.2 Temperature and V elocity C ontours In the Figure s 4.1 and 4.2 , the gas and solid phase temperature are presented respectively. Figure 4.1: Gas phase temperature contour

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49 Also, in the Figure 4.3, velocity contour is provided. In these three diagrams, through the boundary area between the two zones (preheating zone and combustion zone), the walls velocity decreases and gas temperature increases. Figure 4.2 : Solid phase temperature contour Figure 4.3: Velocity contour

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50 By reducing the velocity, the conduction coefficient decreases and the time duration of the heat transfer between two phases increases, and the temperature differences between gas and solid increases (Figure 4.4). In the preheating zone, the solid temperature is higher than the gas temperature by having both conductio n and radiation heat transfer. Although, by havi ng a high conduction, the temperature difference between these two phases is not significant. In the combustion zone, by having the combustion and the released energy, both phase temperatures increases. At first, the gas temperature is higher, but eventual ly, by having the heat transfer from the gases close to wall to the solid, the solid temperature increases. Finally, by having radiation emission to the ambient air, the solid temperature decreases. The gas temperature increases and the convection heat tra nsfer decreases in the combustion zone as a result of its low velocity. Figure 4.4: Gas and solid temperature and convect ion coefficient along central line of the solution area

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51 4.3 Fuel Air R atio E ffects As shown in t Figure 4 5, by increasing in the fuel air ratio, the gas temperature and the solid temperature increases, while a reduction in this ratio lea ds to reduction in the temperature of both phases. Figure 4.5 Fuel Air effects on the temperature in 2 millimeters away from the walls This ratio does not affect the preheating zone, since there is no reaction in this zone. By having a higher fuel air ra tio more energy is released in the combustion zone. Although using a r ich er fuel and air mixture leads to higher temperature and more thermal NOx, using a porous medium results in a higher heat transfer rate, and a decrease in thermal NOx. (Figures 4.6 and 4.7).

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52 Figure 4.6: Fuel Air ratio effects on the temperature along the central line of the combustion zone Figure 4.7 : 1 D effect of Fuel Air ratio on the gas and solid phases temperature

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53 4.4 Porosity and Porous B ores D iameter E ffects on the T emperature Any change in the porosity affects both the temperature of the gas and solid phases (Figures 4.8 and 4.9). Increasing the porosity , that means neglecting the porous media e ffects, leads to temperature increase in both phases. This is why in these kinds of burners, it is possible to reduce the temperature for maximum power and to reduce the pollution and thermal NOx, which is not permitted in common burners, as any temperatur e reduction causes an efficiency loss. In other words, with porous burners, reducing the temperature without any efficiency loss is feasible. The preheating zone temperature is not affected, as the porosity of this zone is assumed to be constant. Also, usi ng porous media in the combustion zone causes a temperature reduction after the combustion zone and an increase in the porosity heat transfer rate which results in a reduction in temperature in that zone. Figure 4.8 1 D e ffects of porosity on the temperature

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54 By increasing the bore diameter, the volume c onvection coefficient drops. As a result, the difference between the gas and the solid phase coefficient increases. Although the gas temperature would not be affected by this coefficient, the solid temperature drops significantly as the solid temperature is influenced by convection heat transfer from the gas side (Figure 4. 10 ). Figure 4.9 Poro sity effects on the temperature along the central line Figure 4.10 1 D effects of porosity on both gas and solid phases temperature

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55 4.5 Emissivity E ffects on the T emperature By having a higher emissivity, the radiation rate increases . Also, by having a very low emissivity , as seen in Figure 4.5, the temperature diagram is perpendicular relative to the outlet cross section. This shows that by reducing the emissivity and having a very small radiation, the adiabatic assumption is close to reality (Figures 4.1 1 and 4.1 2 ). Figure 4.11: Emissivity effects on the temperature along the central line Figure 4.12: 1 D emissivity effects on the gas and solid temperature

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56 4.6 Mixture I nlet V elocity E ffects on the T emperature Any change in the mixture velocity effects the temperature. By having a higher velocity, volumetric convection coefficien t increases, which results in a decrease in temperature difference between gas and solid. Als o, the released heat coming from the heat source increases (Figures 4.1 3 , 4.1 4 . 4.1 5 , and 4.1 6 ). However, in the preheating zone, it has the opposite effect; with a lower mixture velocity more time would be available for transferring the heat from the comb ustion zone to the preheating zone. In other words, a reduction in the velocity leads to an increase in the preheat zone temperature (both the gas and solid temperature increase, if the inlet velocity of the fuel and air mixture increases, by getting more heat from the combustion zone).

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57 Figure 4.13: Mixture velocity effects on the temperature along the central line Figure 4.14: Enlarging the effect of mixture velocity on the temperature

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58 4.7 Effective C onduction C oefficient E ffects on the T emperature By increasing the effective conduction coeff icient, the heat transfer originated in the solid side increases, which leads to a solid phase temperature Figure 4.15: Effects of significant change in the inlet mixture velocity on the temperature along the central line Figure 4.16: 1 D effects of changing mixture velocity on the gas and solid temperature

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59 decrease. Also, this energy would be transferred to the gas and increase the gas phase temperature (Figures 4.17, 4.18 , and 4.19 ). As this coefficient is constant in the preheating zone, the combustion zone temperature would not be affected by any change of this coefficient. Figure 4.17: Effective conduction coefficient effect on the gas and temperat ure in the central line

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60 4. 8 Conclusion Figure 4.18: 1 D effects of efficient conduction coefficient on the gas and solid phase temperature Figure 4.19: Effective conduction coefficient effects on the temperature along the central line

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61 The numerical results in this research are comp ared with those of 1 D numerical analysis done by A.J. Barra et al., that solves chemical equations for combustion in porous burner . I n order to being able to compare the results, averaging is done on the cross section of the burner (Figures 4.20 and 4.21 ) . Figure 4. 20: Comparing gas phase temperature with Barra 's results 1 As can be seen from the above diagrams, there is a good agreement with the numerical simulations that solve chemical equations for combustion in a porous Figure 4.2 1: Comparing solid phas e temperature with Bara's results

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62 burner. Due to the wall tem perature effects which affects the temperature, the simulated gas and solid temperature are higher in some points. It is worth Also, the parametric study shows that by incre asing the mixture equivalence ratio or inlet velocity, the gas phase temperature increases . This effect is directly related to the pollution products of combustion. The reduction of porosity in the preheating and combustion zone leads to an increasing and dec reasing solid phase temperature . Increasing the solid conductivity in the two zones will cause an increase in the gas and solid phase temperatures.

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63 REFRENCES [1] Mahdi. A. R., et al., Review of Convection Heat Transfer and Fluid Flow in Porous Medi a with Nanofluid, Renewable and Sustainable Energy Reviews, 41, pp. 715 734, [2] Kaviany, M., Principles of Heat Transfer in Porous Media, Springer, 1995. [ 3 ] Ingham, D.,B., Transport Phenomena in Porous Media III , Elsevier, 2005. [ 4 ] Pickenacker, O., Kesting A. & Trimis D., Novel Low NOx Burner Designs for B oilers and Furnaces by using Staged Combustion in Inert Porous Media, ETATS UNIS, 2000. [ 5 ] Babkin, V.S., Filtrational combustion of gases. Present state of affairs and prospects. Pure and Applied Chemistry 65 (2), 335344, 1993. [ 6 ] Mößbauer S., Trimis, D., Drust, F.& Hass, T., Zero Emission Engine A Novel Steam Engine for Automotive Applications, The Fifth International Symposium on Diagnostics and Modeling of Combustion in Internal Combustion Engine, Nagoya, 2001 . [ 7 ] Kumar, N.R., Exergy Analysis o f porous medium combustion engine cycle, International Scholarly Research Network, 542840, 2011. [ 8 ] Drust, F., Weclas M., A New Concept I.C. Engine with Homogeneous Combustion in a Porous Medium, The Fifth International Symposium on Diagnostics and Mode ling of Combustion in Internal Combustion Engine, Nagoya, 2001 . [ 9 ] Trimis, D., Drust, F., Pickenacker, O.& Pickenacker, K., Porous Medium Combustion versus Combustion Systems with Free Flames, Clean Air, Vol. 3, pp.1 20, 2002. [1 0 ] Howell, J.R., Hall, M.J., & Ellazy, J.L., Combustion within Porous Inert Medium, ASME HTD, Heat Transfer in Porous Media and Two Phase Flow, 302:1 21, 1995. [7] [1 1 ] Brenner, G., Pickenäcker, O., Pickenäcker, K., Trimis, D., Wawrzinke , K. & Weber, T., Numerical and Experim ental Investigation of Matrix Stabilized Methane/Air Combustion in Porous Media, Combust Flame, 123:201 213, 2000. [1 2 ] Hus, P.F., Howell, J.R., & Mettews, R.D., A Numerical Investigation of Premixed Within Porous Inert Media, ASME J, of Heat transfer, 11 5:744 750, 1993. [1 3 ] Malico, I. &Pereira, J.C.F., Numerical Study on the Influence of Radiative Properties in Porous Media Combustion, ASME Journal of Heat transfer, 123:951 957,2001.

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65 [30] Vafai, H., Handbook of Porous Media, CRC Press, New York, 2000. [31] Zhengwen, z., Reid, G., A Criterion for Non Darcy Flow in Porous Media, Transport in Porous Media, 63: 57 69 , 2006. [32] Saidi, M.S., Hajaligol, M.R., Mhaise kar, A.&Subbiah, M., A 3D Modeling of Static and Forward Smoldering Combustion in a Packed bed of Materials, Applied Mathematical Modelling, 31:1970 1996,2007. [33] Cheng G.J.A., Yu, B.& Zulli, P., Evaluation of Effective Thermal Conductivity from the Str ucture of a Packed bed, Chem.Eng. Sci., 54, 4199 4209,1999. [34] Patankar, S. V., Numerical Heat transfer and Fluid Flow, Taylor & Francis ,1st ed. 1980. [35] Singh, B.P.& Kaviany, M., Effect of Solid Conductivity on Radiative Heat Transfer in Packed Be ds, Int.J. Heat Mass Transfer, 16:2579 2583, 1994.