Combustion Properties of Biologically Sourced Alternative Fuels

Transcription

1 Combustion Properties of Biologically Sourced Alternative Fuels by Abhishek Barnwal A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science Graduate Department of Aerospace Engineering University of Toronto Copyright 212 by Abhishek Barnwal

2 Abstract Combustion Properties of Biologically Sourced Alternative Fuels Abhishek Barnwal Masters of Applied Science Graduate Department of Aerospace Engineering University of Toronto 212 The effects of pressure on various properties of ten different syngas fueled flames were analyzed using one and two dimensional simulations. One-dimensional premixed flames were modeled in CANTERA. Flame speed, adiabatic flame temperature and thermal diffusivity as functions of equivalence ratio and pressure were quantified for the fuels using four chemical kinetic mechanisms. Data from the different mechanisms displayed good agreement with data from previous experimental benchmarks. Two-dimensional axisymmetric co-flow flames were simulated in a state of the art computational framework for modeling laminar flames. Flame structure comparisons were made with past experimental and numerical results as well as with theoretical predictions. Good agreement in stoichiometric flame height was observed with past theoretical and numerical flame height measurements. Visible flame heights had little correlation with the stoichiometric flame heights. The flame radius was also noted to be proportional to p.35 at high pressures instead of p.5 as predicted by theory. ii

3 Acknowledgements I would like to sincerely thank Professor C.P.T. Groth for giving me the chance to study at the University of Toronto s Insitute for Aerospace Studies under his direction. His guidance and support through the course of my studies has been greatly appreciated. Furthermore, I would like thank the efforts of Dr. Marc Charest in helping me understand the code and for bearing with all of my questions during the various stages of my research work. Lastly, I would like to thank my parents for their endless support and for nurturing my dreams over all these years. None of this would have been possible without them. This thesis is dedicated to them. Financial support for the research described herein was provided by the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ), the Natural Sciences and Engineering Research Council (NSERC) in the form of Collaborative Reseach and Development Grant, and Rolls-Royce Canada Inc. Computational resources for performing all of the calculations reported herein were provided by the SciNet High Performance Computing Consortium at the University of Toronto and Compute/Calcul Canada through funding from the Canada Foundation for Innovation (CFI) and the Province of Ontario, Canada. Toronto, 212 Abhishek Barnwal iii

4 Contents Abstract ii Acknowledgements iii Contents iv List of Tables vii List of Figures viii 1 Introduction Motivation Background Fuel Compositions Soot Formation Effects of Pressure Objectives Numerical Studies of Unstrained Planar One-Dimensional Laminar Premixed Flames Numerical Studies of Two-Dimensional Axisymmetric Laminar Co-Flow Diffusion Flames iv

5 2 Numerical Solution Methods One-Dimensional Laminar Premixed Flame Modelling CANTERA Solution Method - Flame Speed and Temperature CANTERA Solution Method - Thermal Diffusivity Axisymmetric Laminar Co-Flow Diffusion Flame Modelling Governing Equations Finite-Volume Solution Technique Low-Mach-Number Preconditioning Round-Off Error Control Inviscid Flux Evaluation Higher-Order Spatial Accuracy for Inviscid Fluxes Viscous Flux Evaluation Steady State Relaxation Method Results I: One-Dimensional Laminar Premixed Flames Validation Study for H 2 -CO Mixture Laminar Flame Speed Effects of the Chemical Kinetic Mechanism Effects of Stoichiometry and Pressure Adiabatic Flame Temperature Thermal Diffusivities Thermal Diffusivities of Reactants v

6 3.4.2 Thermal Diffusivities of Products Results II: Laminar Co-Flow Diffusion Flames Introduction Experimental Methodology Discretization and Boundary Conditions Solution Procedure for Simulations Comparison with Experiments Prediction of Flame Heights Predictions of Flame Radius Conclusions and Future Research Conclusions I: One-Dimensional Laminar Premixed Flames Conclusions II: Axisymmetric Laminar Co-Flow Diffusion Flames Recommendations for Future Research References 71 vi

7 List of Tables 1.1 Biogas and Syngas Fuel Compositions of Interest S1 flame heights S2 flame heights S5 flame heights vii

8 List of Figures 1.1 University of Toronto Institute for Aerospace Studies (UTIAS) high-pressure laminar co-flow diffusion flame burner apparatus Schematic showing overview of CANTERA Modules D computational domain for laminar premixed flame simulations Illustration of pseudo transient method Schematic diagram showing generic 2D quadrilateral computational cell Schematic diagram showing diamond path viscous flux reconstruction stencil for a quadrilateral computational cell Comparison of experimental measurements of laminar flame speed to predicted values from CANTERA for 5:5 mixture by mole fraction of H 2 and CO as a function of equivalence ratio Influence of chemical kinetic mechanism on predicted laminar flame speeds for the B1 biogas-air, and S1 syngas-air flames at pressures of 1 and 25 atmospheres Influence of chemical kinetic mechanism on predicted laminar flame speeds for the and S2-S3 syngas-air flames at pressures of 1 and 25 atmospheres Influence of chemical kinetic mechanism on predicted laminar flame speeds for the S4, S5, S5M25 and S5M5 syngas-air flames at pressures of 1 and 25 atmospheres viii

9 3.5 Influence of chemical kinetic mechanism on predicted laminar flame speeds for the S6 and S14 syngas-air flames at pressures of 1 and 25 atmospheres Effect of equivalence ratio and pressure on laminar flame speeds for S2-S3 syngas-air flames. Results were obtained by using the Curran mechanism Effect of equivalence ratio and pressure on laminar flame speeds for the S4, S5, S5M25 and S5M5 syngas-air flames. Results were obtained by using the Curran mechanism Effect of equivalence ratio and pressure on laminar flame speeds for the S6 and S14 syngas-air flames. Results were obtained by using the Curran mechanism Effect of pressure on laminar flame speeds for B1 biogas-air, and S1-S3 syngas-air flames. Results were obtained by using the Curran mechanism Effect of pressure on laminar flame speeds for the S4, S5, S5M25 and S5M5 syngas-air flames. Results were obtained by using the Curran mechanism Effect of pressure on laminar flame speeds for the S6 and S14 syngas-air flames. Results were obtained by using the Curran mechanism Effect of composition and pressure on the adiabatic flame temperature at 1 and 25 atmospheres pressure. Results were obtained by using the Slavinskaya mechanism Effect of equivalence ratio and pressure on thermal diffusivities for B1 biogas-air, and S1 syngas-air flames. Results were obtained by using the Curran mechanism Effect of equivalence ratio and pressure on thermal diffusivities for the S2- S5 syngas-air flames. Results were obtained by using the Curran mechanism Effect of equivalence ratio and pressure on thermal diffusivities for the S6, S5M25, S5M5 and S14 syngas-air flames. Results were obtained by using the Curran mechanism ix

10 3.16 Effect of composition and pressure on the post-combustion mixture thermal diffusivity at 1 and 25 atmospheres pressure. Results were obtained by using the Curran mechanism University of Toronto Institute for Aerospace Studies (UTIAS) high-pressure laminar co-flow diffusion flame burner apparatus Schematic of modelled computational domain D computational grid (mirrored) showing both the grid blocks and computational cells. The mesh contains 512 (12 1)-cell blocks and a total of 61,44 cells Convergence history for the S1 syngas-air flame at 1 atm. The normalized L 2 norm of the continuity equation is shown Visible flames for the S1 composition. The flame heights in order are 25.2 mm, 14. mm, 6. mm and 5.14 mm Visible flames for the S2 composition. The flame heights in order are 9.5 mm, 4. mm, 9.7 mm and 1.4 mm Visible flames for the S5 composition. The flame heights in order are 7.3 mm, 5.5 mm, 4.8 mm, 4.7 mm and 4.5 mm. The fuel flow rate was constant at 9 ccm (cm 3 /minute) Effect of reaction mechanism and pressure on flame structure for the S1 composition at pressures of 1, 5, 1 and 15 atmospheres. Peak temperature is indicated on the bottom right and left corners of each plot Effect of reaction mechanism and pressure on flame structure for the S2 composition at pressures of 1, 5, 1, and 15 atmospheres. Peak temperature is indicated on the bottom right and left corners of each plot Effect of reaction mechanism and pressure on flame structure for the S5 composition at pressures of 1, 5, 1, and 15 atmospheres. Peak temperature is indicated on the bottom right and left corners of each plot x

11 4.11 Effect of reaction mechanism and pressure on flame structure for the S5 composition at a pressure of 2 atmospheres. Peak temperature is indicated on the bottom right and left corners of the plot Effect of reaction mechanism and pressure on OH mass fraction for the S1 composition at pressures of 1, 5, 1 and 15 atmospheres Flame radius as a function of pressure for the S1 and S5 compositions.. 58 xi

12 Chapter 1 Introduction 1.1 Motivation As the world s sources of fossil fuels diminish, energy security, self-reliance and environmental impact of combustion have become important issues for the combustion science community as well as the common population [1]. To remedy those issues, several alternative, biologically sourced fuels (such as syngas, biogas, biodiesel, ethanol, etc.) have been identified as suitable candidates to be used in combustion devices due to their favourable availability and emissions profile [2]. Such biologically derived fuels are more sustainable since their sources can be grown, making their use an excellent way to offset the carbon emitted due to combustion activities [3]. Over the past few decades of combustion research, a good knowledge base has been assembled for conventional fossil fuels with regards to combustion characteristics. A similar such knowledge base for biologically sourced fuels is now required. While some previous experimental and numerical studies of laminar biofuel (primarily syngas, a mixture of carbon monoxide, CO and hydrogen, H 2 ) flames have been conducted under atmospheric or near atmospheric conditions [4 9], the range of possible combinations studied is rather minimal. Consequently, a knowledge base, much like the one developed for conventional fossil fuels, is lacking for alternative fuels, particularly at elevated pressures. Without such a knowledge base, it is impossible to design a combustion device that uses the above mentioned alternative fuels efficiently while producing fewer pollutants than devices fuelled by fossil fuels [1, 11]. 1

13 Chapter 1. Introduction 2 While multiple experiments can be conducted to create the above mentioned knowledge base, it can also be very useful to corroborate the experimental results with results obtained from the use of Computational Fluid Dynamics (CFD). Such complementary studies are useful in the further development and refinement of combustion CFD and pollutant emission models, which can subsequently be used for practical combustor design. 1.2 Background Fuel Compositions The combustion properties of bio-based alternative fuels is expected to be directly influenced by the possible variations in feedstock. This thesis research has therefore concentrated on a computational study of the effects of fuel composition on the combustion properties of both syngas and biogas gaseous biofuels. Syngas, in its simplest form is composed of carbon monoxide (CO) and hydrogen (H 2 ). Various diluents and impurities can also be part of the mixture, depending on the source of the fuel and its intended use [12]. One popular way of producing syngas is through gasifying biological refuse such as wood or wood waste products. While not arising from bio-based sources, other well known methods for producing syngas are steam methane reformation and coal gasification. The relative proportions of carbon, hydrogen, nitrogen, moisture content, and impurities in the feedstock or source have a direct impact on the final syngas composition [13 15]. The choice of oxidant used in the gasification process (air, pure oxygen, steam or a mixture of these gases are generally used) obviously has an important effect on the nitrogen (N 2 ) content of the product syngas. When air is used as the oxidant, the product syngas typically contains about 5% N 2, and when pure oxygen (O 2 ) is the oxidant there is generally negligible N 2 in the syngas (often less than 1% by volume). Syngas produced with steam as the oxidant also has low nitrogen content. While many typical syngas sources have values of the volume of hydrogen to carbon monoxide ratio near unity (i.e., H 2 /CO = 1), syngas mixtures can have a wide range of values for this ratio with.3 H 2 /CO 5 and this variation is expected to greatly affect the combustion properties of syngas. Some sources of syngas, depending on feedstock, can also contain some amount

14 Chapter 1. Introduction 3 of methane (CH 4 ) as well. While it can be filtered out, it usually is not and as such many syngas compositions contain an average of 5% methane by volume. Biogas composition also depends directly on the source. Biogas from landfill gas (i.e., biogas produced by a combination of aerobic and anaerobic decomposition of solid waste in landfills) is typically about 45-55% methane (CH 4 ), 3-4% carbon dioxide (CO 2 ), and 5-15% nitrogen, N 2 by volume [16]. Biogas from mechanically controlled digesters is produced in a completely anaerobic environment and is rarely if ever exposed to air. This reduces the nitrogen concentration to negligible amounts. Biogas sourced from digesters is typically composed of 55-7% CH 4 and 3-45% CO 2. Based on the preceding observations and with a desire to consider a wide range of biobased gaseous fuels, ten different fuel compositions were considered in this thesis study. The ten compositions considered are listed in Table 1.1. The compositions include one biogas composition (B1), seven syngas compositions with H2/CO ratios ranging from.5 to 2 (S1-S6, S14), and two syngas/methane blends with 25% and 5% by volume methane (S5M25 75% S5 with 25% CH 4, S5M5 5% S5 with 5% CH 4 ). The biogas, B1, contains 6% CH 4 and 4% CO 2 and is typical of biogas from digesters. The three syngas compositions S1, S2, and S3 all have a fixed CO 2 content (25%) and no methane, but the H 2 /CO ratio varies from.5 to 2. The syngas compositions S4, S5, and S6 are similar to S1, S2, and S3, but 5% methane is added (close to the average content of methane for most sources of syngas) and the CO 2 content is reduced slightly to allow for this. The S14 syngas composition has a reduced CO 2 content (15%) and contains no methane. The S5 syngas composition, having 5% methane and a H2/CO ratio of unity was blended to ratios of 75:25 and 5:5 with pure methane leading to the S5M25 and S5M5 compositions. These selected compositions allow for the effects of hydrogen, methane, and carbon dioxide content to be explored and the role of the constituents on syngas combustion to be examined. Moreover, as syngas can be blended with natural gas in many applications, the selected blends with methane also allow for combustion properties of syngas/natural gas blends to be examined. It should be expected each of these gaseous biofuels will burn in a unique way and generate a range of combustion products of varying composition [17]. It is important to note that the selected biogas/syngas compositions listed in Table 1.1 do not allow for the effects of nitrogen content on fuel combustion properties to be explored.

15 Chapter 1. Introduction 4 Table 1.1: Biogas and Syngas Fuel Compositions of Interest Name H 2 /CO CO (% vol) H 2 (% vol) CH 4 (% vol) CO 2 (% vol) N 2 (% vol) B1-6 4 S S S S S S S S5M S5M However, the effects of nitrogen dilution are more or less understood and, furthermore, for most combustion applications, the nitrogen in the air or oxidizer will dominate any amount of nitrogen that is generally present in the biogas/syngas fuel. Some syngas compositions may also contain water vapour which may vary in content from -4% and, in many applications, water vapour can also be added to syngas prior to combustion to lower flame temperatures and thereby reduce emissions. However, the influence of water vapour on the combustion properties of gaseous biofuels was deemed to be beyond the scope of the present study Soot Formation Soot is a common and in most cases undesirable combustion by product. It is especially important to quantify soot production in new fuel compositions because of the many negative effects it has on the environment around it. Soot is produced due to the incomplete combustion of hydrocarbons in diffusion type flames and is responsible for giving flames a characteristic yellow color [18]. It is a known carcinogen due to the organic compounds present within it and due to its ability to penetrate deep into the respiratory system of all living creatures [19, 2]. The formation of soot not only negatively affects the efficiency of the combustion de-

16 Chapter 1. Introduction 5 vice [2], but also contributes to global warming [21]. Soot deposits inside combustion chambers of turbines and reciprocating engines are troublesome to clean, adding extra downtime to engines that could be doing useful work [2]. It is due to the above reasons and many recent governmental regulations that there has been a drive in the combustion community to try and minimize soot production in the next generation of practical devices. However, soot formation in hydrocarbon fuelled flames, is an inherently complex process that is still not completely understood [2 22]. An investigation of sooting propensity of gaseous biofuels as a function of pressure was initially in the scope of this present study for the B1, S5, 5M25,and S5M5 fuel compositions as outlined in Table 1.1. However, time constraints and the author s difficulties with accurately modelling the other non-sooting gaseous biofuels led to the soot modelling being postponed and left for other future follow on studies Effects of Pressure Pressure is an important parameter that influences flame structure and other flame properties in all types of flames. Understanding of pressure s influence flame structure is still limited even though most practical combustion devices operate at elevated pressures [23]. In laminar premixed flames, an increase in pressure limits diffusive processes and increases the density of the mixture which thereby reduces the flame speed and thermal diffusivity of the fuel [24, 25]. The adiabatic flame temperature however is rather independent of pressure and is therefore unaffected, except near stoichiometric conditions where the temperature can go up by approximately 5-1 K for a significant increase in pressure. In laminar diffusion flames, pressure affects the shape and structure of the flame. This effect is realized through the influence of pressure and gravity on the buoyant forces which accelerate the hot gases. Since buoyancy induced acceleration is proportional to pressure squared, an increase in pressure will change the shape of the flame. In high pressure laminar diffusion flames, the streamlines contract towards the center, due to buoyancy effects, thereby decreasing the diameter of the flame [26]. It has also been suggested that the decrease in flame diameter at elevated pressures could be due to increases in reaction rates which in turn are caused by higher temperatures and steeper concentration gradients [26, 27].

17 Chapter 1. Introduction 6 Past theoretical studies have shown that to a first-order approximation, flame height should be independent of pressure and should only depend on mass flow rate [28, 29]. It was thought that residence time, and thereby the axial velocity along the flame centreline was independent of pressure, based on experimental [27] and numerical predictions [3]. The predictions were based on findings that the flame radius is proportional to p.5 [31,32], which implies that centreline velocity and thereby residence time should be independent of pressure. If the residence time is indeed not dependent on pressure, then flame height should be constant at all pressures. While many previous experimental studies have indicated that this may not be true (Roberts and McCrain [27], and Miller and Maahs [26] observed that flame heights initially increased with pressure at low pressures, then decreased slightly with further increases in pressure), Gulder and Joo [33] and Bento et al. [34] have clearly demonstrated that the visible flame heights are indeed constant across a wide range of pressures. Numerically, Charest et al. [22, 35] as well as Liu et al. [3] have also shown that flame heights are essentially constant with pressure. 1.3 Objectives Numerical Studies of Unstrained Planar One-Dimensional Laminar Premixed Flames As part of this assessment of biogas and syngas fuels for practical devices, it is useful to first determine the basic combustion characteristics of the fuel. A preliminary investigation of the fuels listed in Table 1.1 was therefore carried out in which solutions of unstrained, planar, one-dimensional (1D), laminar, premixed flames were computed and studied using a software package known as CANTERA [36]. Chemical kinetic mechansims of varying levels of detail designed for modelling the combustion of biogas and syngas fuels were considered as described in 2. The premixed flames solutions were determined and predictions of the laminar flame speeds and adiabatic flame temperatures were obtained for each biofuel composition as a function of mixture equivalence ratio and pressure. The flame speed and temperature are important and key combustion properties to examine as they reveal much about the nature of the fuel combustion properties. Knowledge of flame speed gives an overall summary of some of the important charac-

18 Chapter 1. Introduction 7 teristics of the fuel such as reactivity, diffusivity and exothermicity and is useful in the optimal design of combustion devices [12, 37]. The value of the flame speed also reveals much about the susceptibility of a flame fed by a particular fuel mixture to flashback or extinguish [6, 9]. A recent and complementary experimental study of laminar flame speeds for gaseous biofuels is described by Lapalme et al. [38]. The adiabatic flame temperature, the equilibrium temperature of the combustion products assuming that no work is done at constant pressure, is an important parameter in quantifying the heat release associated with the combustion of the fuel. The flame temperature can also be a useful indicator of pollutant formation. The production of nitrogen oxides, NO x, is highly dependent on the flame temperature through the Zeldovich mechanism, which has been shown to dominate NO x production for temperatures above 18 K [15]. The adiabatic flame temperature also has an influence on flame propagation and extinction. Fuels with high flame temperatures have higher heating values, which consequently raises the flame speed of the fuel [25]. Numerical predictions of the 1D premixed flames and the resulting flame speeds and temperatures also provide an excellent way of examining proposed chemical kinetic mechanisms, both detailed and reduced, and validating them against experimental data as well as other previous, more established, kinetic mechanisms [39]. Converged solutions for the 1D premixed flame simulations provided values for the following properties as a function of equivalence ratio and for a range of pressures from 1 to 25 atm for all the fuels outlined in Table 1.1: ˆ flame speed; ˆ adiabatic flame temperature; ˆ species mass fractions along the grid; and ˆ thermal diffusivity. CANTERA was used in evaluating all of these quantities and its usage is further detailed in Chapter 2 while the results of the numerical computations for the premixed flames described above are presented and discussed in Chapter 3.

19 Chapter 1. Introduction 8 Figure 1.1: University of Toronto Institute for Aerospace Studies (UTIAS) high-pressure laminar co-flow diffusion flame burner apparatus Numerical Studies of Two-Dimensional Axisymmetric Laminar Co-Flow Diffusion Flames Although most practical combustion devices employ high-pressure turbulent flames, flames in the turbulent regime cannot be easily studied because of experimental limitations related to optical accessibility, complex flame geometries, and the wide range of time and length scales. It is difficult to relate the small changes in flame structure or pollutant emissions to small scale processes such as chemistry or fluid interactions. For this reason, simple laminar flames are commonly studied even though most practical combustion devices use high-pressure turbulent flames [4]. Laminar flames are easily controlled in laboratory experiments yet still share many similar features with turbulent flames. Their detailed study is both essential and helpful to advancing combustion science [35, 41]. Axisymmetric laminar diffusion flame simulations of the University of Toronto Institute for Aerospace Studies (UTIAS) high-pressure co-flow burner (shown in Figure 1.1) as used in the experiments by Joo and Gulder [33] were carried out as part of the study using an advanced, state of the art two-dimensional computational framework for modelling laminar flames, which was developed by Charest et al. [22,35] which in turn was built upon the previous work of Northrup and Groth [42]. The framework features detailed treatments of chemical kinetics, radiation transport and soot formation and transport. This

20 Chapter 1. Introduction 9 new computational framework is a highly-scalable combustion modelling tool which has been developed specifically for use on large multi-processor, high-performance and parallel computer systems. A parallel-implicit time-marching scheme with a Newton-Krylov iterative solution procedure, a second-order-accurate, finite-volume, spatial-discretization scheme, and a block-based adaptive mesh refinement (AMR) are all utilized to solve, in a fully-coupled manner, the unmodified compressible form of the Navier-Stokes equations governing multi-species reactive flows on both two-dimensional planer and axisymmetric domains using multi-block, body-fitted, quadrilateral meshes. Piecewise linear limited reconstruction and Riemann-solver-based flux functions are used to ensure robust and accurate solutions for a wide range of flow conditions [43]. Low-Mach-number preconditioning of both the inviscid flux and the temporal derivative are applied in order to permit the efficient and accurate solution of the conservation equations for low-speed flows associated with laminar flames [44]. While not considered in the the present work, radiation can be modelled using the discrete ordinates method (DOM) [45] to solve the radiative transfer equation and spectral absorption coefficients for gas band absorption are approximated using the wide-band model developed by Liu et al. [46] which is based on the statistical narrow-band correlated-k (SNBCK) method [46, 47]. Furthermore, a simplified semi-empirical model can be used to predict chemistry, nucleation, surface growth, coagulation, and oxidation of soot particles [48, 49]. The latter assumes that acetylene is the only precursor leading to the formation of soot particles. In this thesis work, numerical simulations of laminar co-flow diffusion flames were performed for the S1, S2 and S5 fuels as shown in Table 1.1 at pressures of 1, 5, 1, and 15 atmospheres using several chemical kinetic mechanisms. The Slavinskaya [5] and GRI-Mech 3. [51] chemical kinetic mechanisms as described in section 2.1 were both considered. The Slavinskaya mechanism is a reduced form of the GRI-Mech 3. mechanism and as such the results from both mechanisms were used to assess the effectiveness of the reduced mechanism. The numerical solutions for the axisymmetric flames were compared against experimental data from the thesis work of Barua [52] to assess and quantify the differences between the model and actual experiments. Converged solutions provided quantitative measurements of the following properties for each fuel at any of the pressures mentioned above: ˆ flame structure (height, width, streamlines etc.);

21 Chapter 1. Introduction 1 ˆ temperature contours; and ˆ mass fraction contours of participating species (reaction mechanism dependent). The computational framework for laminar flames and its usage are discussed in further detailed in Section 2.2, while the data and results of the laminar co-flow diffusion flame computations are presented in Chapter 4.

22 Chapter 2 Numerical Solution Methods 2.1 One-Dimensional Laminar Premixed Flame Modelling As mentioned in Chapter 1 of this thesis, CANTERA was used to calculate the flame speeds and adiabatic temperatures of the biogas and syngas mixtures outlined in Table 1.1. CANTERA is an open-source object-oriented software tool kit for chemical kinetics, thermodynamics, and transport processes [36] written in C++. Some capabilities of CANTERA are as follows: ˆ computation of thermodynamic properties; ˆ computation of transport properties; ˆ solution of Chemical equilibrium; ˆ implementation of homogeneous and heterogeneous chemistry; ˆ simulation of reactor networks; and ˆ numerical simulation of one-dimensional flames. Figure 2.1 [53] provides a summary of how CANTERA interfaces with a user s C++ code. Four reaction mechanisms, some more detailed than others, were considered in the present work when computing solutions to the laminar premixed flames for the bio-based fuels of interest. The mechanisms that were considered herein are as follows: 11

23 Chapter 2. Numerical Solution Methods 12 Figure 2.1: Schematic showing overview of CANTERA Modules. ˆ the GRI-Mech 3. mechanism [51]; reactions - 53 species ˆ the mechanism of Slavinskaya et al. (Slavinskaya mechanism) [5]; - 86 reactions - 19 species - derived from the GRI-Mech 3. mechanism ˆ the mechanism of Le Cong et al. (Dagaut mechanism) [54]; and reactions - 99 species ˆ the NUIG C5 version 52 mechanism, of Metcalfe et al. (Curran mechanism) [11] reactions species Although the GRI-Mech 3. mechanism was developed explicitly for describing methaneair combustion under atmospheric conditions, it contains both hydrogen and CO chemistry; it is not, however, tuned for bio-based gaseous fuel chemistry. The mechanism of Slavinskaya et al., referred to here as the Slavinskaya mechanism, is a reduced form of the GRI-Mech 3. specific for H 2 -CO combustion while the mechanism of Le Cong et al., here

24 Chapter 2. Numerical Solution Methods 13 referred to as the Dagaut mechanism, is a mechanism developed specifically for CH 4 syngas mixtures at gas-turbine operating conditions. The NUIG-C5-v52. or so-called Curran mechanism includes both low- and high-temperature versions, with the former being suited for ignition studies. The high-temperature version of the NUIG-C5-v52. mechanism was considered here as ignition was not of concern CANTERA Solution Method - Flame Speed and Temperature When solving for the laminar flame speed, CANTERA computes the steady state solutions to the conservation equations shown for a reactive gaseous mixture with simplification for the one-dimensional flame geometry [24]. In order, the conservation equations of concern are the continuity, species conservation and energy conservation equations in steady state form for a one dimensional laminar premixed flame. The conservation equations can be expressed as: dṁ dx =, (2.1a) ṁ dy i dx + d dx (ρy iv i,diff ) = ω i MW i, for i = 1, 2,.., N species, (2.1b) ṁ dt c p dx + d N dt ( k dx dx ) + N dt ρy i v i,diff c p,i dx = h i ωmw i. i=1 i=1 (2.1c) Here ṁ i is the mass flux, Y i is the species mass fraction, v i,diff is the species diffusional velocity, ω i is the species reaction rate and lastly MW i is the species molar mass. The flame speed S l is related to ṁ by S l = ṁ /ρ. Along with the governing equations, CANTERA also uses the ideal-gas equation of state and temperature dependent polynomials for species properties as closure equations. A chemical kinetic mechanism is also required to provide the values for ω i. First the problem is split into domains as Figure 2.2 shows. The cells within each domain are refined independently of other cells in other domains as solution resolution requires. Within each cell, the discretized form of the governing equations as shown above are solved using a hybrid Newton/time-stepping algorithm to accelerate convergence [55]. Given an initial 1D mesh, will authomatically refine the mesh locally until an accurate steady-state premixed flame solution is achieved. In the present work, the mechanism

25 Chapter 2. Numerical Solution Methods 14 Figure 2.2: 1D computational domain for laminar premixed flame simulations. of Slavinskaya typically required 15 5 non-uniformly spaced cells for a steady state solution, with the number of cells being higher for the high pressure cases. Similarly the GRI-Mech 3. mechanism required 2 45 cells, the Curran NUIG mechanism required cells, and finally the Dagaut mechanism required around 15 3 cells for a successful calculation. The n th equation in the j th point of the one dimensional domain is of the form F j,n (φ) =, (2.2) where F j,n only depends on the solution at the points j-1, j, j+1 thereby making the system Jacobian banded [55], which are nothing more than a coupled non-linear system of algebraic equations. The resulting residual equations are solved with a modified Newton s method. Starting from classical Newton s method, which linearises around an initial solution estimate, φ, and is given by F lin,n = F i (φ ) + j F i φ j j φ φ=φ (φ j), (2.3) then the linear problem is solved to generate a new estimate for φ given by F lin (φ 1 ) =, φ 1 = φ [J ] 1 F, (2.4a) (2.4b) where J is the system Jacobian, F i / φ j. If the Newton iterations fail to find a steady-state solution to the premixed flame of interest, an attempt is made to solve a pseudo-transient problem, which has a larger

26 Chapter 2. Numerical Solution Methods 15 Figure 2.3: Illustration of pseudo transient method. domain of convergence [55]. The pseudo-transient problem is created by adding transient terms in each conservation equation, where physically reasonable, as shown below: A dφ dt = F (φ), (2.5a) F (φ n+1 ) A φn+1 φ n =. (2.5b) t The quantity A in Equation 2.5a is a diagonal matrix with entries of 1 on the diagonal for the equations with a transient term, and for the constraint equations. With the pseudotransient added, the modified problem becomes as shown in Equation 2.5b. Figure 2.3 illustrates how the pseudo-transient addition method can aid in the convergence to steady state. It is worth nothing that if A is the identity matrix in Equation 2.5a, then for a sufficiently small time step, the transient residual function will approach a linear problem [55]. If on the other hand, A contains zeros on the main diagonal, then there is no guarantee of the transient Newton problem converging, regardless of the time step size. If convergence is not achieved, all that can be tried is a better starting estimate for the solution of the non-linear problem. The C++ program that solves for the flames speed and temperature proceeds as follows when compiled and executed with one of the chemical kinetic mechanisms mentioned above:

27 Chapter 2. Numerical Solution Methods load mechanism, fuel-oxidizer mixture and environment condition data; 2. calculate unburned mixture properties; 3. determine equilibrium conditions and burned gas properties; 4. create the grid; 5. use provided initial guess of temperature and velocity profiles; 6. call inbuilt newton solver subroutine to iteratively improve upon the initial guess; 7. refine grid and call solver subroutine again if necessary; and 8. output to tecplot data format CANTERA Solution Method - Thermal Diffusivity Thermal diffusivity can be defined as follows: α = k ρc p, (2.6) where α is the mixture thermal diffusivity, k is the mixture thermal conductivity, ρ is the mixture density and c p is the mixture specific heat capacity at constant pressure. To calculate the mixture properties as outlined above, the solution results from the flame speed calculations are used. CANTERA as used in this study was modified to output the mass fractions of all of the species involved at every grid point. Using these mass fractions and some additional built-in subroutines, it is possible to calculate the mixture properties and thereby the thermal diffusivity at each grid point in the computational mesh. The values of thermal diffusivity for the biofuels outlined in Table 1.1 will be presented and discussed in Chapter Axisymmetric Laminar Co-Flow Diffusion Flame Modelling As mentioned earlier, numerical modelling is a very powerful tool that can be used to design more efficient and lower pollutant emitting combustion devices, avoiding the often

28 Chapter 2. Numerical Solution Methods 17 costly trial and error of approaches of conventional design procedures. Unfortunately, hydrocarbon combustion is an inherently complex process that is still not fully understood. Processes such as detailed gas-phase chemistry, radiation, multiphase diffusion and soot formation and oxidation remain a challenge to model. As such many models that are currently in use employ significant engineering approximations to ensure that simulations remain relatively easy to solve in a finite amount of time. To further the development of a state of the art and efficient combustion modelling tool that uses the latest higher-order schemes, domain-decomposition methods and non-linear implicit relaxation methods, along with the latest models that account for multi-phase transport, chemistry, soot production and radiation transport, Charest et al. [22, 35] recently developed an advanced computational framework for the numerical simulation of laminar flames. The framework features detailed treatments of chemical kinetics, radiation transport and soot formation and transport. This new computational framework is a highly-scalable combustion modelling tool which has been developed specifically for use on large multi-processor high-performance parallel computer systems and is used herein for the simulation of the laminar co-flow diffusion flames. The computational framework for laminar flames of Charest et al. [22,35] uses a parallelimplicit time-marching scheme with a Newton-Krylov iterative solution procedure, a second-order-accurate, finite-volume, spatial-discretization scheme, and block-based adaptive mesh refinement to solve, in a fully-coupled manner, the unmodified compressible form of the Navier-Stokes equations governing multi-species reactive flows on both twodimensional planer and axisymmetric domains using multi-block, body-fitted, quadrilateral meshes. Piecewise linear limited reconstruction and Riemann-solver-based flux functions are used to ensure robust and accurate solutions for a wide range of flow conditions [43]. Low-Mach-number preconditioning of both the inviscid flux and the temporal derivative are applied in order to permit the efficient and accurate solution of the conservation equations for low-speed flows associated with laminar flames [44]. While not considered in the the present work, radiation can be modelled using the discrete ordinates method [45] to solve the radiative transfer equation and spectral absorption coefficients for gas band absorption are approximated using the wide-band model developed by Liu et al. [46] which is based on the statistical narrow-band correlated-k method [46,47]. Furthermore, a simplified semi-empirical model can be used to predict chemistry, nucleation, surface growth, coagulation, and oxidation of soot particles [48, 49]. The latter assumes

29 Chapter 2. Numerical Solution Methods 18 that acetylene is the only precursor leading to the formation of soot particles Governing Equations As mentioned above, the computational framework used in the present study solves the compressible, 2D axisymmetric form of the Navier-Stokes equations for a reactive gaseous mixture. In the absence of soot, the governing conservation equations are as follows: ρ t + (ρv) =, (2.7a) (ρv) + (ρvv + pi) = τ + ρg, t (2.7b) t (ρe) + [ρv(e + p )] = (v τ ) q + ρg v, ρ (2.7c) t (ρy k) + [ρy k (v + V k )] = ω k, for k = 1,..., N species, (2.7d) here t is the time, ρ is the density of the mixture, p is the mixture pressure, e is the mixture energy, v is the velocity vector, τ is the fluid stress tensor, g is the gravitational acceleration vector, q is the heat flux vector, Y k is the mass fraction of the k th species, V k is the diffusional velocity of the k th species and ω k is the time rate of change of the k th species. The ideal gas law is used to calculate the mixture density. The heat flux vector q is shown below. q = κ T + ρ N h k Y k V k, (2.8) where κ is the thermal conductivity of the mixture, h and Y are the individual species enthalpy and mass fractions respectively. The gas phase diffusion velocity vector for the k th species is calculated by k=1 where D k is the species averaged diffusion coefficient. V k = D k Y k Y k, (2.9) Finite-Volume Solution Technique Equations 2.7a - 2.7d governing the reactive gas phase are solved numerically using the parallel, implicit and finite-volume based scheme developed previously by Groth et

30 Chapter 2. Numerical Solution Methods 19 Figure 2.4: Schematic diagram showing generic 2D quadrilateral computational cell. al. [56, 57] and subsequently improved by Charest et al. [22, 35]. In this approach, the domain of the physical problem is discretized into a number of finite-size computational cells and the integral form of the conservation equations shown earlier is then applied to and solved for the cells. For a generic quadrilateral cell, (i, j), in a two-dimensional domain as shown in Figure 2.4, the semi-discrete, non-linear and coupled form of the governing equations for the primitive, cell-averaged solution quantities, W, are as follows: dw i,j = W [ ] dt U 1 (F k ˆn k l k ) ij + S ij (2.1) ij A ij faces,k where U ij and W ij are the cell averaged conserved and primitive form of the solution vectors. In Equation 2.1 A ij is the cell area, ˆn k and l k are the normal vector and edge length for the k th face respectively, and S ij is the source term that includes contributions from chemistry, gravity and boundary conditions. The flux, F k, includes both the inviscid and viscous fluxes (F and F v respectively) Low-Mach-Number Preconditioning Finding a solution of the non-linear ODEs resulting from the finite-volume spatial discretization and given in Equation 2.1 at low mach numbers can be very challenging due

31 Chapter 2. Numerical Solution Methods 2 to the stiffness created by the disparate velocity scales of the acoustic and convective waves [58]. Therefore preconditioning is used to lessen the overall numerical stiffness of the problem. Preconditioning replaces the physical time derivatives with adjusted artificial derivatives to better match the magnitudes of the acoustic and convective waves (the eigenvalues of the Jacobian). The computational framework used herein adopts the preconditioning scheme developed by Weiss and Smith [44]. The modified conservation equations for an axisymmetric co-ordinate system can be written as: Γ W + F t r + G z = F v r + G v + S, (2.11) z where Γ is the preconditioning matrix as developed by Weiss and Smith. The eigenvalues 1 F of the preconditioned Jacobian matrix in the r-direction, Γ, are as follows: W λ = [u a, u, u, u + a, u,..., u] T, (2.12) for which u = u(1 α), a = α 2 u 2 + Vp 2, α =.5(1 βv 2 p ), (2.13a) (2.13b) (2.13c) β = ρ p + ρ T (1 h p ) ρh T. (2.13d) The subscripts in the expressions above represent partial derivatives of the quantities of interest. For a perfect gas, ρ T = ρ/t, ρ p = 1/(RT ), h p =, and h T = c p. The so-called preconditioned sound speed, V p, can be defined as where a is the sound of speed and M ref V p = min[max(v inv, V pgr, V vis, M ref a), a], (2.14) is a reference Mach number used to prevent singularities at stagnation points. A value of 1 4 for M ref was used in all the simulations conducted. The remaining subscripted terms are the inviscid, pressure-gradient, and viscous velocity scales as derived in [44] and given by V inv = u 2 + v 2, (2.15a) p V pgr = ρ, (2.15b) V vis = µ ρ x, (2.15c) where p is the pressure gradient within the cell and x is the length of the computational cell.

32 Chapter 2. Numerical Solution Methods Round-Off Error Control Charest et al. noted that below Mach numbers of 1 3, machine round-off errors began to contaminate the solutions for pressure. To remedy the problem, the solution method was modified to use the procedure developed by Choi and Merkle [59]. A reference pressure, p, is used to reduce the influence of round-off errors in pressure at low Mach numbers. Due to the modification, the new overall pressure, p, is given by p = p + p, (2.16) where p is the reference pressure and p is the deviation from the local pressure from p. The reference pressure is subtracted from Equation 2.7b and p is replaced by p in the numerical solution vector, W Inviscid Flux Evaluation A higher-order upwind Godunov-type scheme is used to resolve the numerical fluxes at cell interfaces. Godunov s method assumes that the solution within each computational cell is piecewise constant and that the solution at the cell interface can be approximated via upwinding [6]. Upwinding also preserves the monotonicity of the solution. Given left and right solutions states, W L and W R, the flux at a cell interface is defined in terms of a function that involves the solution of a Riemann problem, R, in a direction along the cell interface normal, ˆn. The numerical flux is given by F ˆn = F(W L, W R, ˆn), (2.17) where the evaluation of F requires the solution of the Riemann problem. Roe s approximate Riemann solver [61] is used in the current solution method to solve the Riemann problem and evaluate the fluxes. Harten s correction [62] is also employed with the solver to rectify violations of the entropy condition at sonic points. The flux in one direction at a cell interface is given by F (R (W L, W R )) = 1 2 (F R + F L ) 1 Â W, (2.18) 2 where F L and F R are the left and right fluxes as functions of the left and right primitive solution states W L and W R, W = W R - W L. Â = ˆR ˆΛ ˆR 1 where ˆR is a matrix

33 Chapter 2. Numerical Solution Methods 22 composed of primitive right eigenvectors and ˆΛ is the eigenvalue matrix. The matrix  is the linearised flux Jacobian evaluated at a reference state Ŵ. The reference state is typically chosen such that Roe s conditions are relaxed for reacting flows [63]. Therefore, the Roe-averaged flow variables are given by û = ρr u R + ρ L u L ρ R + ρ L, (2.19) where u R and u L are either of the flow variables u, v, h, Y k. ˆρ, the Roe averaged density, is given by ρ R ρ L. To control the dissipation at low Mach numbers that results with the use of upwind methods, Equation 2.18 can be re- derived by using the pre-conditioned wave speeds as shown by Weiss and Smith [44]. The linearised flux Jacobian term (with the  matrix) in Equation 2.18 is modified as shown below.  W  W = Γ ( Γ 1 F W ) W = Γ A Γ W, (2.2) where A Γ = R Γ Λ Γ R Γ 1. The subscript Γ shows that the matrix eigenvectors and eigenvalues were derived using the preconditioned system Higher-Order Spatial Accuracy for Inviscid Fluxes Godunov s method is first-order accurate by nature and therefore is excessively dissipative. To extend Godunov s method to second or higher orders can be challenging since simple schemes with constant coefficients will introduce non-monotonic behaviour near solution discontinuities [43]. Godunov s method is first-order due to the projection of the actual solutions on to piecewise constant states in the cell-averaged solution. Since this projection is not related to the upwinding process, modifying the spatial approximation to the solution is all that is required to increase solution accuracy. In the computational framework of Charest et al. [22,35] the solution at the cell interface between two adjacent cells is represented by a piecewise linear function to achieve second-order spatial accuracy. Slope limiters are employed to ensure that monotonic behaviour of the solution is preserved at discontinuities. The slope limiters function by locally reducing the reconstructed solution to first-order, thereby damping out any over- or under-shooting behaviour at discontinuities. The

34 Chapter 2. Numerical Solution Methods 23 reconstructed left and right solution values at a cell interface given by the piecewise linear limited representation for an interface (i + 1, j) are given by 2 [ W W L = W ij + φ ij r (r i+.5,j r ij ) + W ] ij z (z i+.5,j z ij ), (2.21) ij [ W W R = W i+1,j + φ i+1,j r (r i+.5,j r i+1,j ) + W ] i+1,j z (z i+.5,j z i+1,j ), i+1,j (2.22) where φ is the slope limiter. Slope limiting is performed using methods designed especially for multiple dimensions [43]. The cell gradients are calculated using linear reconstruction from Green-Gauss theory as discussed by Barth and Jespersen [64] Viscous Flux Evaluation The computational framework for laminar flames adopted herein uses the centrallyweighted diamond-path method, as developed by Coirier and Powell [65], to evaluate the viscous fluxes at the cell boundaries. The viscous flux for a cell face is given by F v n = G(W, W, n), (2.23) where G is the viscous flux function. Figure 2.5 shows the diamond-path method. Gradients at each face are calculated by applying the divergence theorem along the path. The solution is known at the cellcentred vertices, however the solution state at the vertices (nodes) of the cell must be interpolated. A weighting scheme developed by Zingg and Yarrow [66] that linearly reconstructs nodal data using cell-centred solution data of the neighbouring cells is used Steady State Relaxation Method The computational framework for laminar flames uses Newton s method to numerically solve the governing equations shown earlier. The semi-discrete form of the governing equations are iteratively relaxed to converge to a steady-state solution of the form R(W ) = dw dt =. (2.24)

35 Chapter 2. Numerical Solution Methods 24 Figure 2.5: Schematic diagram showing diamond path viscous flux reconstruction stencil for a quadrilateral computational cell. Charest et al. [22, 35] developed the Newton algorithm used within the computational framework for laminar flames. Their approach follows the scheme developed by Groth and Northrup [67]. The implementation of the algorithm makes use of a Jacobian matrix free, inexact Newton method along with an iterative Krylov subspace linear solver. The equation above is solved starting from an estimate W. The estimates are improved upon by solving ( ) n R W n = J(W n ) W n = R(W n ), (2.25) W where J is the residual Jacobian and n is the step number. The improved solution for step n + 1 is found by using W n+1 = W n + W n. (2.26) The overall process runs until a suitable reduction in the residual norm is achieved and the condition R(W n ) = ɛ R(W ) is satisfied; ɛ is a tolerance that is set to 1 7 in the solution method. Newton s method, at each step, requires the solution of the system Jx = b where x = W and b = R(W ). For a system of non-linear, coupled ODEs, the Jx = b system is large, sparse and asymmetric. Such a system can be solved by using the generalized

36 Chapter 2. Numerical Solution Methods 25 minimal residual (GMRES) technique as developed by Saad and Schultz [68,69]. GMRES is an Arnoldi-based solution method which generates orthogonal bases of the Krylov subspace to construct the solution. GMRES is a useful technique since the Jacobian matrix, J, is not explicitly formed. GMRES only uses matrix vector products at each step to create the new trial Krylov vectors thereby greatly reducing the storage requirements for forming J [7]. The GMRES iterations can be terminated by solving the system to some previously specified tolerance, R n + J n W n ) < χ R(W n ), where χ is set to.1 in the solution method. Finally, to further lower memory requirements, the computational framework uses a modified version of GMRES, GMRES(m), that restarts and refreshes the search directions every m iterations.

37 Chapter 3 Results I: One-Dimensional Laminar Premixed Flames 3.1 Validation Study for H 2 -CO Mixture Prior to commencing the premixed flame simulations for all of the fuels listed in Table 1.1, a limited but still useful validation study of CANTERA and the four chemical kinetic mechanisms for gaseous biofuels of interest was conducted by comparing predicted laminar flame speeds to the existing experimental data of McLean et al. [71]. The experimental flame speed data was generated from flames fuelled by a mixture of H 2 and CO at mole fractions of 5% each. The laminar flame speeds as a function of equivalence ratio were then computed for this same fuel using the four mechanisms given in Section 2.1 of Chapter 2: the GRI-Mech 3., Slavinskaya, Dagaut, and Curran mechanisms. A comparison of the predicted laminar flame speeds to the experimental measurements of McLean et al. [71] is depicted in Figure 3.1 for the H 2 -CO mixture. Before describing the results shown in Figure 3.1, it should be pointed out that the mechanism of Le Cong et al. (i.e., the Dagaut mechanism) proved to be extremely problematic when obtaining premixed flame solutions with CANTERA and as such numerical solutions were not obtained in all cases. It would seem that one or more of the reaction rates results in extreme numerical stiffness that CANTERA is not able to overcome. The numerical stiffness therefore results in a failure of the Newton solver without yielding a 26

38 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames McLean et al. Dagaut Curran GRI 3. Slavinskaya Laminar Flame Speed (m/s) Equivalence Ratio Figure 3.1: Comparison of experimental measurements of laminar flame speed to predicted values from CANTERA for 5:5 mixture by mole fraction of H 2 and CO as a function of equivalence ratio. valid premixed flame solution. Having said that, the predictions given in Figure 3.1 for all four mechanisms are generally in good agreement with each other and the experimental measurements; if experimental error is taken into account then it can be conclusively said that the results from all four mechanisms are in extremely good agreement with the experimental data. Data from the GRI-Mech 3. and Dagaut mechanisms deviates the most from the experimental data, which is understandable since they were both originally derived for combustion

39 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 28 simulations of fuels with significant quantities of methane (CH 4 ). At high equivalence ratios (equivalence ratio > 2), the mechanism of Slavinskaya et al. under predicts the experimental results by approximately 1%. The GRI-Mech 3. mechanism over predicts by approximately 1% until an equivalence ratio of about 3.5. After that point it starts to under predict the results. The Curran mechanism tracks the experimental data points the most closely with deviations starting to become significant only at extremely fuel rich conditions (i.e., for equivalence ratios, φ, φ > 3.7). The comparisons of Figure 3.1 and the generally good agreement between the four chemical kinetic mechanisms and experiment provide some level of confidence in the laminar premixed flame predictions which now follow. At least for pressures near atmospheric, the predicted results are expected to lie within typical experimental errors for measuring such quantities. 3.2 Laminar Flame Speed Effects of the Chemical Kinetic Mechanism Comparisons of the predicted flame speeds for the ten biogas and syngas compositions are shown in Figures 3.2, 3.3, 3.4, and 3.5. The figures show the predicted flame speeds for the B1, S1-S5, S5M25, S5M5, S6 and S14 fuel compositions (as described in Table 1.1), for equivalence ratios between and at pressures of 1 and 25 atmospheres using all four reaction mechanisms. Note that all of the corresponding premixed flame simulations were conducted with an initial unburned mixture (reactants) temperature of 3 K. At a cursory glance, it would appear that all of the mechanisms do a reasonable job of predicting the laminar flame speed, and provide generally similar results. Notably, the mechanisms of Slavinskaya, Curran, and Dagaut produce similar results for the propagation speed of a one-dimensional laminar flame to within 5% or less from 1 to 25 atm. The GRI-Mech 3. mechanism almost always overshoots the results of the other mechanisms, sometimes by more than 1%. This over-prediction is especially apparent for the flame speeds calculated at 1 atm.

40 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames B1 Dagaut Curran GRI 3. Slavinskaya 1.8 Dagaut Curran GRI 3. Slavinskaya S1 Laminar Flame Speed (m/s) atm 25 atm Laminar Flame Speed (m/s) atm 1 atm Equivalence Ratio Equivalence Ratio Figure 3.2: Influence of chemical kinetic mechanism on predicted laminar flame speeds for the B1 biogas-air, and S1 syngas-air flames at pressures of 1 and 25 atmospheres. 1.2 Dagaut Curran GRI 3. Slavinskaya 1 S Dagaut Curran GRI 3. Slavinskaya S3 Laminar Flame Speed (m/s) atm 25 atm Laminar Flame Speed (m/s) atm 25 atm Equivalence Ratio Equivalence Ratio Figure 3.3: Influence of chemical kinetic mechanism on predicted laminar flame speeds for the and S2-S3 syngas-air flames at pressures of 1 and 25 atmospheres. The discrepancies between the Slavinskaya, Curran and Dagaut mechanisms are most apparent for methane rich fuels (B1, S5M25 and S5M5). For these fuel compositions, the results from the GRI-Mech 3. mechanism are generally in much better agreement with the other mechanisms. There are also some significant differences between the predicted flame speeds of the four mechanisms for fuel rich conditions in the case of these

41 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 3 Laminar Flame Speed (m/s) Dagaut Curran GRI 3. Slavinskaya 1 atm 25 atm S4 Laminar Flame Speed (m/s) Dagaut Curran GRI 3. Slavinskaya 1 atm 25 atm S Equivalence Ratio Equivalence Ratio.6.5 Dagaut Curran GRI 3. Slavinskaya S5M S5M5 Dagaut Curran GRI 3. Slavinskaya Laminar Flame Speed (m/s) atm 25 atm Laminar Flame Speed (m/s) atm 1 atm Equivalence Ratio Equivalence Ratio Figure 3.4: Influence of chemical kinetic mechanism on predicted laminar flame speeds for the S4, S5, S5M25 and S5M5 syngas-air flames at pressures of 1 and 25 atmospheres. methane rich fuels. In some cases, the differences can be as high as 5% for high values of equivalence ratios Effects of Stoichiometry and Pressure Based on the findings of the validation study discussed above and the comparisons of the predicted flame speeds for the ten biogas and syngas compositions as shown in Figures 3.2, 3.3, 3.4, and 3.5, in general it was found that the Slavinskaya, Curran and Dagaut

42 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames Dagaut Curran GRI 3. Slavinskaya 1 S Dagaut Curran GRI 3. Slavinskaya Laminar Flame Speed (m/s) atm 25 atm Laminar Flame Speed (m/s) atm atm S Equivalence Ratio Equivalence Ratio Figure 3.5: Influence of chemical kinetic mechanism on predicted laminar flame speeds for the S6 and S14 syngas-air flames at pressures of 1 and 25 atmospheres. mechanisms yield rather similar results. With this in mind, the effects of fuel/air stoichiometry and pressure on the predicted laminar flame speeds are examined here using the results obtained with the Curran mechanism. The predicted laminar flame speeds for equivalence ratios ranging from.5 to 1.8 and at pressures of 1, 5, 1, 15, 2 and 25 atm are shown in Figures 3.6, 3.7, and 3.8. To begin with, the influence of stoichiometry on the flame speeds of the biogas and syngas compositions is evident in the results of Figures 3.6, 3.7, and 3.8. For the five syngas fuels composed entirely of H 2, CO and CO 2 (S1, S2, S3, S4 and S14), the flame speed generally increases with equivalence ratio from lean to rich condtions and reaches peak values under fuel rich conditions close φ = 1.7. This is a well known and expected effect and occurs because of hydrogen s extremely high mass diffusivity [24]. The high mass diffusivity implies that hydrogen s Lewis number (Le) is above unity; since flame speed is proportional to Le and since free stream Lewis numbers for lean and rich hydrogen enriched mixtures are.33 and 2.3, the effect of Le is to reduce flame speed under lean conditions and increase it for rich conditions [25]. Another factor in the high flame speed of hydrogen enriched fuels is the availability of free hydrogen related radicals. The more hydrogen there is in the fuel, the more chain-propagating hydrogen radicals are created, which makes the overall reaction propagate faster [15, 72]. If the above did not occur, then the expected peak flame speed for any hydrogen enriched fuel would be found close

43 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 32 Laminar Flame Speed (m/s) B1 1 atm 5 atm 1 atm 15 atm 2atm 25 atm Laminar Flame Speed (m/s) S1 1 atm 5 atm 1 atm 15 atm 2atm 25 atm Equivalence Ratio Equivalence Ratio Laminar Flame Speed (m/s) atm 5 atm 1 atm 15 atm 2atm 25 atm S2 Laminar Flame Speed (m/s) atm 5 atm 1 atm 15 atm 2atm 25 atm S Equivalence Ratio Equivalence Ratio Figure 3.6: Effect of equivalence ratio and pressure on laminar flame speeds for S2-S3 syngas-air flames. Results were obtained by using the Curran mechanism. to an equivalence ratio of unity. Hydrogen s effect is especially visible in the flame speed of the S14 composition as seen in Figure 3.8. The S14 composition contains the most hydrogen after the S6 composition, no methane and low amounts of CO 2. CO 2 does not participate in the combustion reactions and acts as an inert diluent due to its high molar heat capacity. A high heat capacity suppresses temperature and reduces the rate of carbon monoxide and hydrogen oxidation, thereby also reducing the flame speed [6,15]. This not only explains why the flame speed

44 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 33 Laminar Flame Speed (m/s) atm 5 atm 1 atm 15 atm 2atm 25 atm S4 Laminar Flame Speed (m/s) atm 5 atm 1 atm 15 atm 2atm 25 atm S Equivalence Ratio Equivalence Ratio Laminar Flame Speed (m/s) S5M25 1 atm 5 atm 1 atm 15 atm 2atm 25 atm Laminar Flame Speed (m/s) S5M5 1 atm 5 atm 1 atm 15 atm 2atm 25 atm Equivalence Ratio Equivalence Ratio Figure 3.7: Effect of equivalence ratio and pressure on laminar flame speeds for the S4, S5, S5M25 and S5M5 syngas-air flames. Results were obtained by using the Curran mechanism. of the S14 composition is high, but also why its shifted the most towards the fuel rich side of the plot. In general, the data show that the equivalence ratio that the maximum flame speed is achieved at is dependent on the fuel species with the highest concentration. Lapalme et al. [38] arrived at the same conclusion from experimental and numerical observations using the same fuels as described in Table 1.1. McLean et al. [71] also observed similar results in the past for various hydrogen and carbon monoxide mixtures. For the S14

45 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 34 Laminar Flame Speed (m/s) atm 5 atm atm 15 atm 1 2atm 25 atm S6 Laminar Flame Speed (m/s) atm 5 atm 1 atm 15 atm 2atm 25 atm S Equivalence Ratio Equivalence Ratio Figure 3.8: Effect of equivalence ratio and pressure on laminar flame speeds for the S6 and S14 syngas-air flames. Results were obtained by using the Curran mechanism. composition the maximum flame speed approaches 1.4 m/s with H 2 /CO = 1.. For the syngas compositions containing 5% methane (S4 and S5), peak flame speeds are achieved between equivalence ratios of 1.2 and 1.4 after which the flame speeds decrease as the fuel rich limit is approached. For the syngas-methane blends, the flame speed maximum is achieved near φ = 1.1, which is consistent with the increased CH 4 content in the fuel. The flame speed maximum for the biogas (B1) composition occurs near stoichiometric conditions and the flame speed decreases for both lean and rich conditions. Figures 3.6, 3.7, 3.8 show that any increase in pressure results in a significant reduction in the flame speed. For the syngas compositions, the flame speed is reduced from maximum values near 1.2 m/s at 1 atmosphere to maximum values of around.1 m/s at 25 atmospheres. For the biogas composition, the flame speed is reduced from about.25 m/s at stoichiometric conditions and 1 atmosphere to.3 m/s at 25 atmospheres. For the two syngas-methane blends (S5M25 and S5M5), the maximum flame speed falls from approximately.4 m/s to.8 m/s when the pressure is increased from 1 atmosphere to 25 atmospheres. Theoretical considerations [24] as well as previous experimental [73] and numerical [74] research suggest that the laminar flame speed, s L, is proportional to p.5 for conventional hydrocarbon fuels. To assess the validity of this result for the fuels in question, the

46 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 35 laminar flame speed data has been re-plotted as a function of pressure using log-log scales for the plots. The results are shown in Figures 3.9, 3.1 and 3.11 below. A line representing the expected theoretical behaviour that s L p.5 is also shown in each plot for reference purposes Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Laminar Flame Speed (m/s).1.5 S L p.5 Laminar Flame Speed (m/s).4.2 S L p.5 B1 S Pressure (atm) Pressure (atm) Laminar Flame Speed (m/s) S L p.5 Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Laminar Flame Speed (m/s) S L p.5 Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical S2 S Pressure (atm) Pressure (atm) Figure 3.9: Effect of pressure on laminar flame speeds for B1 biogas-air, and S1-S3 syngas-air flames. Results were obtained by using the Curran mechanism.

47 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Laminar Flame Speed (m/s).4.2 S L p.5 Laminar Flame Speed (m/s).4.2 S L p.5 S4 S Pressure (atm) Pressure (atm) Laminar Flame Speed (m/s) S L p.5 Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Laminar Flame Speed (m/s) S L p.5 Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical.5.5 S5M25 S5M Pressure (atm) Pressure (atm) Figure 3.1: Effect of pressure on laminar flame speeds for the S4, S5, S5M25 and S5M5 syngas-air flames. Results were obtained by using the Curran mechanism.

48 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Φ=.8 Φ=1. Φ=1.4 Φ=1.8 Theoretical Laminar Flame Speed (m/s) S L p.5 Laminar Flame Speed (m/s).5 S L p.5 S6 S Pressure (atm) Pressure (atm) Figure 3.11: Effect of pressure on laminar flame speeds for the S6 and S14 syngas-air flames. Results were obtained by using the Curran mechanism. As evident from the plots of the flame speeds for the ten fuel compositions as a function of pressure, the expectation that the flame speed is indeed proportional to p.5 would also seem valid here, at least for the fuels with little H 2 and/or relatively high CH 4 content (e.g., the B1, S5M25, and S5M5 compositions). The numerical curves for each equivalence ratio in these cases are in relatively good agreement with the expected theoretical result. The agreement is best represented for pressures between 1 1 atm and for leaner flames. At high pressures and equivalence ratios, the exponent seems to become slightly higher for all of the fuels, which has been observed in past experimental research by Okajima et al. [73]. As the H 2 content of the biofuel increases, the flame speed behaviour deviates more significantly from the expected theoretical result. The presence of the hydrogen and its relatively high diffusivity are the main reasons attributed to this observed behaviour. 3.3 Adiabatic Flame Temperature The effect of fuel composition and pressure on the adiabatic flame temperature is depicted in Figure 3.12 for all ten compositions as described in Table 1.1. In general, the flame temperature is maximum for slightly fuel rich conditions for all compositions with values

49 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames atm atm Flame Temperature (K) B1 S1 S2 S3 S4 S5 S6 S14 S5M25 S5M Equivalence Ratio Flame Temperature (K) B1 S1 S2 S3 S4 S5 S6 S14 S5M25 S5M Equivalence Ratio Figure 3.12: Effect of composition and pressure on the adiabatic flame temperature at 1 and 25 atmospheres pressure. Results were obtained by using the Slavinskaya mechanism. ranging from 21 K to 23 K at 1 atmosphere. This is explained by taking into account the balance of energy required to increase the temperature of the combustion products (depending on the molar specific heat of the products) and the energy lost during dissociation of the products at high temperatures [25]. If dissociation were ignored, the peak of the flame temperature curve would be found at the stoichiometric point. Since dissociation is inhibited at high pressures, the temperature peak at 25 atmospheres pressure corresponds with the stoichiometric point, as shown in Figure The flame temperature increase with pressure is minimal even at 25 atmospheres; the increase in temperature was noted to be less than 1 K. Finally, the B1 composition was noted to have the lowest flame temperature at all pressures, owing to the lack of H 2. The S14 composition, on the other hand, has the highest flame temperature at all pressures, which can be attributed to an abundance of H 2, no CH 4 and little CO Thermal Diffusivities Thermal diffusivity is an often undervalued parameter that is important to quantify for any new fuel composition. Thermal diffusivity measures the change in temperature in a unit volume of the gas by heat that flows in unit time through a unit area of unit

50 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 39 thickness with unit temperature difference between its faces [24, 75]. In the context of combustion, it is a measure of how rapidly any energy absorbed from a thermal heat source is diffused through the entire volume of the gas Thermal Diffusivities of Reactants First, the thermal diffusivities of the reactants (i.e., cold air and fuel mixture) will be discussed. Since the mixture is not reacting at this point, it is not necessary to compare the results from the difference mechanisms since they will all be identical. With the above in mind, consider Figures shown below with the predicted thermal diffusivities for the fuel compositions as described in Table 1.1, for equivalence ratios between and at pressures of 1, 5, 1, 15, 2 and 25 atmospheres. 2E 5 B1 3E 5 S1 2.5E 5 Thermal Diffusivity (m 2 /s) 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm Thermal Diffusivity (m 2 /s) 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm 5E 6 5E Equivalence Ratio Equivalence Ratio Figure 3.13: Effect of equivalence ratio and pressure on thermal diffusivities for B1 biogasair, and S1 syngas-air flames. Results were obtained by using the Curran mechanism.

51 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 4 3.5E 5 S2 4E 5 S3 Thermal Diffusivity (m 2 /s) 3E 5 2.5E 5 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm Thermal Diffusivity (m 2 /s) 3.5E 5 3E 5 2.5E 5 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm 5E 6 5E Equivalence Ratio Equivalence Ratio 3E 5 S4 3.5E 5 S5 2.5E 5 3E 5 Thermal Diffusivity (m 2 /s) 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm Thermal Diffusivity (m 2 /s) 2.5E 5 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm 5E 6 5E Equivalence Ratio Equivalence Ratio Figure 3.14: Effect of equivalence ratio and pressure on thermal diffusivities for the S2-S5 syngas-air flames. Results were obtained by using the Curran mechanism.

52 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 41 3E 5 S5M25 2.5E 5 S5M5 2.5E 5 Thermal Diffusivity (m 2 /s) 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm Thermal Diffusivity (m 2 /s) 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm 5E 6 5E Equivalence Ratio Equivalence Ratio 4E 5 S6 4E 5 S14 3.5E 5 3.5E 5 Thermal Diffusivity (m 2 /s) 3E 5 2.5E 5 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm Thermal Diffusivity (m 2 /s) 3E 5 2.5E 5 2E 5 1.5E 5 1E 5 1 atm 5 atm 1 atm 15 atm 2 atm 25 atm 5E 6 5E Equivalence Ratio Equivalence Ratio Figure 3.15: Effect of equivalence ratio and pressure on thermal diffusivities for the S6, S5M25, S5M5 and S14 syngas-air flames. Results were obtained by using the Curran mechanism. The effects of pressure and equivalence ratio on the thermal diffusivities are evident for the range of fuel compositions of interest. Increased pressure results in a significant reduction of the thermal diffusivity across all the fuels of interest. This is in agreement with the observed reduction in flame speed with an increase in pressure mentioned earlier. For the syngas compositions, the thermal diffusivity is reduced from maximum values, at rich conditions, near 3.8(1) 5 m 2 /s at 1 atmosphere to maximum values of around.15(1) 5 m 2 /s at 25 atmospheres. For the biogas composition, the thermal diffusivity

53 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 42 is reduced from about 2.2(1) 5 m 2 /s at lean conditions and 1 atmosphere to.1(1) 5 m 2 /s at 25 atmospheres. For the two syngas-methane blends (S5M25 and S5M5), the maximum thermal diffusivity, at rich conditions falls from approximately 2.8(1) 5 m 2 /s to.1(1) 5 m 2 /s when the pressure is increased from 1 atmosphere to 25 atmospheres. The thermal diffusivity of the biogas compositions decreases monotonically as equivalence ratio is increased. This means that the thermal diffusivity of the biogas composition as a mixture is lower than that of the air which is slowly replaced by the fuel as the mixture becomes fuel rich. The thermal diffusivities of the syngas and syngas-methane blended compositions on the other hand increases monotonically with equivalence ratio. This means that the thermal diffusivity of the fuel itself is higher than that of air. Therefore as the fuel-air mixture becomes richer, the mixture s thermal diffusivity increases. This trend was also observed by Prathap et al. [76] when they calculated thermal diffusivities for a fuel composition of 5% H 2 and 5% CO as a function of equivalence ratio. Notably, the S6 composition has the highest thermal diffusivity and the steepest slope as the equivalence ratio is increased. This is expected since it has the highest concentration of hydrogen at 5%. It is also worth noting that all the compositions with significant quantities of hydrogen start with a higher thermal diffusivity than the methane enriched compositions. This confirms that hydrogen s thermal diffusivity is also higher than that of other compounds (CO, CH 4, CO 2 ) found in the compositions examined [24] Thermal Diffusivities of Products The thermal diffusivities of the products (i.e., hot post-combustion gas mixture) were also calculated and analysed. It was observed that the difference in the results from the Slavinskaya, Curran and GRI-Mech 3. mechanisms were largely negligible. Results are therefore considered for the Curran mechanism here. Figure 3.16 illustrates the differences between the thermal diffusivities of the hot post-combustion gases from the ten biogas and syngas fuel compositions as shown in Table 1.1. It is immediately evident that as pressure is increased from 1 to 25 atmospheres, the thermal diffusivity of all the post combustion mixtures decreases by approximately 9%; the same effect was also observed for the cold inlet mixtures. Another prominent effect is the peak thermal diffusivity corresponding with the peak adiabatic flame temperature

54 Chapter 3. Results I: One-Dimensional Laminar Premixed Flames 43 Maximum Thermal Diffusivity (m 2 /s) B1 S1 S2 S3 S4 S5 S6 S14 S5M25 S5M Equivalence Ratio 1 atm Maximum Thermal Diffusivity (m 2 /s) 2.8E 5 2.6E 5 2.4E 5 2.2E 5 2E 5 1.8E 5 1.6E 5 1.4E 5 1.2E 5 B1 S1 S2 S3 S4 S5 S6 S14 S5M25 S5M5 1E Equivalence Ratio 25 atm Figure 3.16: Effect of composition and pressure on the post-combustion mixture thermal diffusivity at 1 and 25 atmospheres pressure. Results were obtained by using the Curran mechanism near the stoichiometric point, as seen in Figure This is an expected effect since the higher the temperature of a gaseous mixture, the better it is able to transport via diffusional processes thermal energy.

55 Chapter 4 Results II: Laminar Co-Flow Diffusion Flames 4.1 Introduction As previously outlined in Section of Chapter 1, one of the objective of this study was to study the combustion characteristics of the S1, S2 and S5 fuel compositions as shown in Table 1.1 by considering laminar co-flow diffusion flames for these gaseous biofuels as a function of pressure. The combustion of the fuels was simulated using a stateof-the-art laminar combustion modelling framework developed by Charest et al. [22, 35]. Numerical results were obtained for both GRI-Mech 3. and Slavinskaya chemical kinetic mechanisms. The structure of the numerically simulated flames was compared against recent experimental data obtained by Barua [52]. A discussion of the numerical results for the co-flow flames along with comparisons to the available experimental results follows in the remainder of this chapter. 4.2 Experimental Methodology The laboratory-scale, high-pressure axisymmetric co-flow burner was developed at UTIAS [32 34] and the experimental measurements were made by Barua [52]. As shown in Figure 4.1, the UTIAS burner consists of a central fuel tube with 3 mm inner diameter and a 44

56 Chapter 4. Results II: Laminar Co-Flow Diffusion Flames 45 Figure 4.1: University of Toronto Institute for Aerospace Studies (UTIAS) high-pressure laminar co-flow diffusion flame burner apparatus. concentric tube of 25.4 mm inner diameter that supplies the co-flow air. The outer surface of the stainless steel fuel nozzle is tapered to minimize the formation of wakes behind the tube walls and improve overall flame stability. Sintered metal foam is inserted in the fuel and air nozzles to straighten the flow and provide a more uniform velocity profile at the nozzle exit. 4.3 Discretization and Boundary Conditions An illustration of the modelled computational domain for the co-flow diffusion flame is shown in Figure 4.2. The fuel jet is emitted from the center of the annular ring while the air mixture is emitted from the outer ring. The computational domain extends radially outwards 12.7 mm and 4 mm downstream of the fuel nozzle exit. The far-field boundary was treated using a free-slip condition which neglects any shear imparted to the co-flow air by the chimney walls. The modelled domain is also extended 5 mm upstream into the fuel and air tubes to account for the effects of fuel preheating observed by Guo et al. [77] and better represent the inflow velocity distribution. At the outlet, temperature, velocity and species mass fractions are extrapolated while the pressure is held fixed. The mixture is specified at the inlet along with velocity and temperature while the pressure

57 Chapter 4. Results II: Laminar Co-Flow Diffusion Flames 46 Figure 4.2: Schematic of modelled computational domain. is extrapolated. Uniform velocity and temperature profiles were specified for both the fuel and air inlet boundaries. A simplified representation of the fuel tube geometry was used. The tapered edge of the fuel tube was approximated by a tube with.4 mm thick walls. The three surfaces that lie along the tube wall were modelled as adiabatic walls with zero-slip conditions. The computational domain was divided into 192 cells and 16 blocks in the radial and 32 cells and 32 blocks in the axial direction. The resulting computational mesh (as shown in Figure 4.3) contained 61,44 cells that were structured and non-uniformly spaced. These cells were clustered towards the burner exit plane to capture interactions near the fuel tube walls and towards the centreline to capture the core flow of the flame. Charest et al. [22,35] have previously shown that this level of mesh resolution is more than sufficient to accurately represent the laminar co-flow diffusion flames associated with the UTIAS high-pressure burner. 4.4 Solution Procedure for Simulations The following sequence of steps were taken when obtaining solutions for the syngas fuelled laminar co-flow flames using the computational framework developed by Charest et al. [22, 35]:

58 Chapter 4. Results II: Laminar Co-Flow Diffusion Flames Height (mm) Radius (mm) Figure 4.3: 2D computational grid (mirrored) showing both the grid blocks and computational cells. The mesh contains 512 (12 1)-cell blocks and a total of 61,44 cells. Step 1: The domain as shown in Figures 4.2 and 4.3 is initialized with cold air, fuel, and a small rectangular region above the fuel exit plane is used as an igniter to start the chemical reactions. The igniter region is initialized with an unburnt fuel-air mixture of stoichiometric proportions set to a temperature of 18 K. Step 2: Ignition is an inherently chaotic period that includes many transients that have to be overcome. A semi-implicit relaxation scheme is used within the computational framework [42] to partially solve Equations 2.7a 2.7d and find an initial guess for Newton s method. The partial solution is found after approximately 2, iterations using a CFL of.2 and for M ref =.1. Step 3: The solution from step 2 is used as an initial guess to solve Equations 2.7a 2.7d using the implicit algorithm as described in Section 2.2. As the algorithm converges to the final solution, the value for M ref is decreased to 1 4 while the CFL value is slowly increased to between 2 5. Convergence was said to be achieved when the mass, momentum and energy residual L 2 norms were reduced by at least six orders of magnitude. Figure 4.4 shows an example of a typical convergence history for a solution at atmospheric pressure. The convergence

59 Chapter 4. Results II: Laminar Co-Flow Diffusion Flames Density L 2 norm Thousands of Iterations Figure 4.4: Convergence history for the S1 syngas-air flame at 1 atm. The normalized L 2 norm of the continuity equation is shown. histories for the higher pressure cases were similar, albeit the solutions took longer to converge. Generally, for every increase in pressure of 5 atmospheres, the number of iterations required to achieve convergence increased by approximately 1, iterations. 4.5 Comparison with Experiments Barua [52] measured the visible flame height of non-sooting flames fuelled by the S1, S2 and S5 fuel compositions as described in Table 1.1. Barua s experimental images and results are shown in Figures 4.5, 4.6, and 4.7. The fuel flow rate was measured in cubic centimetres per minute (ccm) and was set as described in the figures. The air flow rate was set to 1 litres per minutes for all cases. Since the visible flame height changed drastically with each increment in pressure, the fuel flow rate had to be increased at

60 Chapter 4. Results II: Laminar Co-Flow Diffusion Flames 49 higher pressures to obtain flame heights equivalent to those at lower pressures Prediction of Flame Heights Since making a comparable visible flame height measurement from a numerical standpoint is difficult without modelling the chemiluminescence of the various intermediate reaction species involved, the stoichiometric mixture fraction was used to calculate the flame height of the numerical solutions. Given a steady state solution, the mixture fraction of the fuel can be calculated for the entire domain by using the following equation [78]: Z = Y C Y C,2 mw C + Y H Y H,2 nw H + Y O Y O,2 αw O Y C,1 Y C,2 mw C + Y H,1 Y H,2 nw H + Y O,1 Y O,2 αw O, (4.1) where Y and W are the mass fraction and atomic weights of the carbon, hydrogen and oxygen atoms, m and n are the number of carbon and hydrogen atoms in the fuel, 1 and 2 signify the fuel and air inlets, and α is the stoichiometric fuel-air ratio. stoichiometric mixture fraction can be calculated by calculating the mass fraction of the fuel at stoichiometric conditions with the oxidizer (air) [24], as the following equation shows: Z stoich = Y F,stoich = The W C + W H + W O W C + W H + W O + α(2w O (2W N )). (4.2) Given the above equations, consider the data shown in Tables 4.1, 4.2 and 4.3 as well as the plots shown in Figures 4.8, 4.9, 4.1 and 4.11 comparing the stoichiometric flame Figure 4.5: Visible flames for the S1 composition. The flame heights in order are 25.2 mm, 14. mm, 6. mm and 5.14 mm.

61 Chapter 4. Results II: Laminar Co-Flow Diffusion Flames 5 Figure 4.6: Visible flames for the S2 composition. The flame heights in order are 9.5 mm, 4. mm, 9.7 mm and 1.4 mm. heights from the Slavinskaya and the GRI-Mech 3. mechanisms. The peak temperatures are indicated by the numbers on the lower left and right corners of the plots. The stoichiometric flame height contour has also been imposed on top of the false-colour temperature contours for the S1, S2 and S5 fuelled flames. Figure 4.7: Visible flames for the S5 composition. The flame heights in order are 7.3 mm, 5.5 mm, 4.8 mm, 4.7 mm and 4.5 mm. The fuel flow rate was constant at 9 ccm (cm 3 /minute).