Master of Science Thesis
KTH School of Industrial Engineering and Management Energy Technology EGI-2016-006MSC EKV1124
Division of Heat and Power Technology Stockholm, Sweden
2015-2016
Multi-energy well kinetic modeling of novel PAH formation pathways in flames
Nicola Giramondi
Multi-energy well kinetic modeling of novel PAH formation pathways in flames
Nicola Giramondi
Approved Examiner Supervisors
14/03/2016 Prof. Tosten Fransson Dr. Bj¨orn Waldheim CFD Engineer at Scania CV AB (Industrial Master Thesis Supervisor)
Dr. Jeevan Jayasuriya (EGI supervisor)
Abstract
Polycyclic Aromatic Hydrocarbons (PAHs) are harmful by-products formed during com- bustion of hydrocarbons under locally fuel-rich conditions followed by incomplete com- bustion. PAHs act as precursors during the formation of soot. PAHs and soot are harmful for human health and legislation limits the emission of unburned hydrocarbons and soot. Consequently, other measures are necessary in order to limit the production of PAHs and soot in internal combustion engines applications, entailing a possible de- crease of fuel efficiency and higher technical requirements for automotive manufactures.
The combustion chemistry of PAHs is not fully understood, which prompts the need of further investigations. The chemical dynamics shown by novel pathways of PAH for- mation involving vinylacetylene addition to the phenyl radical opens up new horizons for the potential contribution to PAH formation through this class of reactions. In the present work novel pathways of the formation of naphthalene and phenanthrene are in- vestigated for a laminar premixed benzene flame and a laminar ethylene diffusion flame.
The purpose is to improve the prediction of the aromatic species concentration in the flames. A pathway chosen due the high potential aromatic yield is assessed through preliminary flame calculations relying on simplifying assumptions concerning reaction rates. Certain isomerisation steps of the pathway occur within a time-scale characteris- tic of thermal relaxation processes. Therefore, the solution of the energy grained master equation is necessary in order to calculate the phenomenological reaction rates resulting from a non-equilibrium kinetic modeling. Quantum chemical calculations are performed in order to calculate molecular properties of the species involved. These properties are
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effect of temperature and pressure on the kinetic parameters is investigated. Despite of the potential yield demonstrated through the preliminary flame calculations, the com- puted rate constants show that the studied reactions are insignificant for the formation of naphthalene and phenanthrene in the studied flames. An effort is put on evaluating if the non-equilibrium kinetic modeling adopted for the calculation of the kinetic parame- ters is consistent with the kinetic modeling used in the flame calculations. The current work provides an efficient method to compute rate constants of multi-energy well reac- tions at different thermodynamic conditions, characteristic of flames and of combustion in commercial devices or in internal combustion engines. Pathways with a slightly dif- ferent chemical dynamics should be tested applying the current methodology. Moreover, further studies should be aimed at overcoming possible limits of the kinetic modeling of multi-energy well reactions occurring in combustion environments.
Key words: Polycyclic Aromatic Hydrocarbons, soot, laminar flame, flame calcu- lation, quantum chemical calculation, non-equilibrium kinetic modeling.
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I am sincerely grateful to Dr. Bj¨orn Waldheim, my industrial supervisor at the NMTD department at Scania. His support, guidance and trust gave me an extraordinary moti- vation and allowed an outstanding professional and personal development. I could not expect a better supervision, that I will always gratefully acknowledge. I would also like to thank all the coworkers of the NMTD department, whose cordiality and helpfulness allowed a great work environment. Moreover, I consider myself privileged for the guid- ance and the helpfulness of Prof. Peter Lindstedt from Imperial College London. My academic supervisor at KTH, Prof. Jeevan Jayasuriya, has always supported me and my interest for the field of combustion has grown while attending his lectures at KTH. I would also like to thank my academic supervisor at Politecnico di Milano, Prof. Alessio Frassoldati, for his prompt replies despite the distance and for having demonstrated a motivating interest for this project.
I am grateful to my friends at KTH and at Politecnico di Milano, for their advices and the good time spent together. Thanks to Carolina, who has never missed to support and encourage me throughout this period.
My exceptional mother Gabriella has allowed me to give my best despite the sacri- fices and the difficulties faced together. I am forever in her debt.
My beloved father Gino gave me incomparable love and handed down his precious knowledge and experience to me. His example will guide me for life. All my efforts and results are dedicated to him.
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Abstract i
Acknowledgements iii
Contents iv
List of Figures viii
List of Tables xiv
Nomenclature xvi
1 Introduction 1
1.1 Background . . . 1
1.2 Motivation . . . 2
2 Objectives 4 3 Methodology 6 4 Literature Review 9 4.1 PAH chemistry . . . 9
4.1.1 Introduction to PAH chemistry . . . 9
4.1.2 The formation of the first aromatic ring . . . 9
4.1.3 The HACA mechanism of aromatic growth . . . 10
4.1.4 Consumption of benzene . . . 12
4.2 Sectional soot modeling . . . 14
4.3 Modeling of general reacting flows . . . 18
4.3.1 Introduction to the modeling of general reacting flows . . . 18
4.3.2 The physics of general reacting flows . . . 18
4.3.2.1 Momentum equation . . . 18
4.3.2.2 Species conservation equation . . . 19
4.3.2.3 Enthalpy conservation equation . . . 20
4.3.3 Transport properties . . . 21
4.3.4 Determination of thermodynamic properties . . . 23
4.4 Kinetics of chemical reactions . . . 24
4.4.1 Introduction to the kinetics of chemical reactions . . . 24
4.4.2 Reaction rates . . . 24
4.4.3 Reactions that involve a third body . . . 25 iv
4.4.4 Reactions with pressure-dependent kinetics . . . 25
4.4.5 The estimation of reaction rates . . . 27
4.4.5.1 Estimations based on equilibrium considerations . . . 27
4.4.5.2 Estimations based on reaction class considerations . . . . 28
4.5 Overview of the flame systems studied in this work . . . 28
4.5.1 The laminar premixed benzene flame of Bittner and Howard . . . 28
4.5.1.1 Flame chemistry . . . 31
4.5.1.2 Physics of a free-flowing laminar flat flame . . . 34
4.5.2 The laminar ethylene diffusion flame of Olten and Senkan . . . 36
4.5.2.1 Flame chemistry . . . 37
4.5.2.2 Physics of a laminar counter-flow diffusion flame . . . 40
5 Novel pathways of naphthalene formation 44 5.1 Prediction of aromatic species concentrations in the flames studied in this work . . . 44
5.2 Pathways of napthalene formation involving vinylacetylene addition to the phenyl radical . . . 46
5.2.1 Previous investigations . . . 46
5.2.1.1 The addition of the phenyl radical to vinylacetylene triple bond . . . 46
5.2.1.2 The addition of the phenyl radical to vinylacetylene dou- ble bond . . . 48
5.2.2 Inspiration from the studies of astrochemical evolution of the in- terstellar medium . . . 49
6 Preliminary flame calculations 53 6.1 Introduction to the preliminary flame calculations . . . 53
6.2 Testing a PAH formation pathway from a previous literature study . . . . 53
6.3 Testing the novel PAH formation pathways . . . 54
6.3.1 Interpolation of the low temperature kinetic rate constants of the barrier-less pathway . . . 54
6.3.2 Testing the barrier-less pathway assuming the rate of collisions as an estimate of the pre-exponential factor . . . 57
6.3.3 Testing the pathway with a 5 kJ/mol barrier at the entrance . . . 59
6.3.4 Testing the pathway with a 17 kJ/mol barrier at the entrance . . . 61
6.4 Considerations on the preliminary flame calculations . . . 63
6.5 A note on the subsequent analysis and on nomenclature . . . 64
7 Quantum chemical calculations 65 7.1 Introduction to quantum chemical calculations . . . 65
7.1.1 A note on the tools used for the quantum chemical calculations . . 66
7.2 The Schr¨odinger equation . . . 66
7.3 The Hartree-Fock method . . . 67
7.4 Basis set . . . 69
7.5 Density Functional Theory . . . 70
7.6 Single point energies . . . 71
7.7 Vibrational frequencies and Intrinsic Reaction Coordinate . . . 72
8 Pathway analysis for the estimation of kinetic parameters 74
8.1 Introduction to nonequilibrium reaction pathways . . . 74
8.2 The Energy Grained Master Equation . . . 75
8.2.1 Introduction to the Energy Grained Master Equation . . . 75
8.2.2 Energy transfer model . . . 77
8.2.3 Energy discretization . . . 78
8.2.4 Statistical mechanics and partition functions . . . 78
8.2.4.1 Rotational energy levels and partition function . . . 80
8.2.4.2 Vibrational energy levels and partition function . . . 81
8.2.5 Microcanonical rate coefficients . . . 82
8.3 MESMER input specifications . . . 83
8.3.1 Introduction to MESMER input specifications . . . 83
8.3.2 Single point energies . . . 83
8.3.3 Rotational constants . . . 83
8.3.4 Symmetry numbers . . . 83
8.3.5 Vibrational Frequencies . . . 84
8.3.6 Lennard-Jones parameters . . . 84
8.3.7 Energy transfer parameters . . . 85
8.3.8 Energy discretization parameters . . . 86
8.3.9 Ensure energetic consistency . . . 86
8.4 Deriving reaction rates constants from the solution of the Energy Grained Master Equation . . . 87
8.4.1 Time scale separation . . . 87
8.4.2 Conservative master equations and phenomenological modeling of the chemical system . . . 89
8.4.3 Non-conservative master equation . . . 92
8.5 Preliminary considerations for a consistent kinetic modeling of the pathway 92 8.5.1 CSEs analysis . . . 93
8.5.2 A note on well skipping . . . 96
8.5.3 Species profiles analysis . . . 97
9 Results of the computation of molecular properties and kinetic param- eters 102 9.1 Computed molecular properties . . . 102
9.1.1 Single point energies . . . 102
9.1.2 Vibrational frequencies . . . 106
9.1.3 Rotational constants . . . 106
9.2 Computed reaction rates . . . 108
9.2.1 Reactions implemented into the chemical mechanism of the flames 108 9.2.2 Canonical reaction rates . . . 109
9.2.3 Phenomenological reaction rates . . . 110
9.3 Computing the species profiles by replicating the kinetic modeling of the flames . . . 116
10 Final flame calculations 120 10.1 Introduction to the final flames calculations . . . 120 10.2 Flame calculations based on the canonical reaction rates currently computed120
10.2.1 Case a: the focus on naphthalene formation . . . 120 10.2.1.1 Results of the calculation for the ethylene diffusion flame
of Olten and Senkan . . . 121 10.2.1.2 Results of the calculation for the premixed benzene flame
of Bittner and Howard . . . 123 10.2.2 Case b: the extension to phenanthrene formation . . . 125
10.2.2.1 Results of the calculation for the ethylene diffusion flame of Olten and Senkan . . . 125 10.2.2.2 Results of the calculation for the premixed benzene flame
of Bittner and Howard . . . 126 10.3 Flame calculations based on the phenomenological reaction rates cur-
rently computed . . . 127 10.3.1 Case c: the application of the phenomenological reaction rate con-
stants currently computed and the extension to phenanthrene for- mation . . . 127 10.3.1.1 Results of the calculation for the ethylene diffusion flame
of Olten and Senkan . . . 129 10.3.1.2 Results of the calculation for the premixed benzene flame
of Bittner and Howard . . . 130 10.4 Factors affecting the relevance of the added pathway of formation of naph-
thalene . . . 131
11 Conclusions and future work 133
Bibliography 136
A GAMESS calculations I
A.1 GAMESS calculations settings . . . I A.1.1 The Hartree-Fock method . . . I A.1.2 Basis set . . . II A.1.3 Optimization process . . . II A.1.4 Density functional theory . . . IV A.1.5 Single point energies . . . IV A.1.6 Vibrational frequencies . . . V A.2 Molecular properties resulting from GAMESS calculations . . . VI B Additional kinetic parameters from MESMER calculations XII
2.1 A group of measured and calculated species mass fractions of the lami- nar ethylene diffusion flame of Olten and Senkan investigated by Wald- heim [6]. The measured values are identified by circles, the computed profiles by the solid line and the ones represented by dashed and dotted lines corresponds to computation with an 100 K increase and decrease respectively. The figure is taken from the doctoral thesis of Waldheim [6]. 4 3.1 Schematic representation of the methodology adopted in the current work. 7 4.1 Major benzene oxidation pathways investigated in a jet-stirred reactor at
1000K, 10 atm and Φ = 1.5. The width of the arrows is proportional to the relevance of the reaction [1] . . . 13 4.2 Major benzene oxidation pathways investigated in the Princeton reactor
at Φ = 1.36. The width of the arrows is proportional to the relevance of the reaction [1] . . . 13 4.3 The NIST experimental system [17] . . . 15 4.4 Rate constant of the methyl recombination as a function of the pressure
at a fixed temperature [21] . . . 27 4.5 Species involved in the reactions in Eqs. 4.64, 4.65, 4.66 and 4.67. . . 29 4.6 Experimental setup of the premixed benzene flame of Bittner and Howard [10] 30 4.7 Mole fractions of relevant species, flux and mole fraction of benzene as
a function of the distance from the burner in the flame of Bittner and Howard [10] . . . 31 4.8 Main formation pathway of Phenantrene in the flame of Bittner and
Howard [6] . . . 33 4.9 Relevant formation pathway of Pyrene in the flame of Bittner and Howard
[6] . . . 33 4.10 Formation of Pyrene from cyclopenta[def]phenanthrene in the flame of
Bittner and Howard [6] . . . 34 4.11 Structure of the species relevant for the mechanisms of PAHs growth in
the flame of Bittner and Howard . . . 34 4.12 Experimental set-up adopted by Olten and Senkan for the study of an
ethylene diffusion flame [11] . . . 36 4.13 Temperature profile and mass fraction profiles of the major species of the
laminar ethylene diffusion flame of Olten and Senkan [11] . . . 38 4.14 Streamlines of a counter-flow diffusion flame [24] . . . 40
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4.15 Measured and calculated temperature profiles of the laminar ethylene diffusion flame of Olten and Senkan. The measured temperature val- ues are identified by circles, the radiation corrected temperature profile by squares, the computed temperature profile by the solid line and the temperature profile calculated after reducing the fuel stream velocity of 25% by dash-dotted line. The figure is taken from the doctoral thesis of Waldheim [6]. . . 42 5.1 Relevant measured (circles) and calculated (dash dotted lines) species
profiles of the laminar ethylene diffusion flame of Olten and Senkan in- vestigated by Waldheim [6] . . . 45 5.2 Relevant measured (circles) and calculated (dash dotted lines) species
profiles of the laminar premixed benzene flame Bittner and Howard in- vestigated by Waldheim [6]. . . 45 5.3 Pathway of naphthalene formation involving the addition of the phenyl
radical to the vinylacetylene triple bond involving. Two subsequent rota- tions occur around the single and double bond within the side chainr [25]. 46 5.4 Pathway of naphthalene formation involving the addition of the phenyl
radical to the vinylacetylene triple bond.Only one rotation occurs around the single bond within the side chain [25]. . . 47 5.5 Planar representations of C10H8(G), C10H8(J) and C10H9(L) consistent
with the study of Moriarty and Frenklach [25]. . . 47 5.6 Pathway of naphthalene formation involving the addition of the phenyl
radical to vinylacetylene double bond studied by Moriarty and Fren- klach [25] . . . 48 5.7 The dominant pathway of naphthalene formation subsequent to viny-
lacetylene addition to the phenyl radical investigated by Moriarty and Frenklach [25]. . . 49 5.8 Potential energy surface of the barrier-less pathway involving the phenyl
radical addition to C1 of vinylacetylene [27] . . . 50 5.9 Potential energy surface of the pathway involving the phenyl radical ad-
dition to C4 of vinylacetylene with a 5 kJ/mol barrier at the entrance [27] 51 5.10 Potential energy surface of the pathway involving the phenyl radical ad-
dition to C2 of vinylacetylene with a 17 kJ/mol barrier at the entrance [27] 51 5.11 Hydrogen migration from the side chain to the aromatic ring [25] . . . 52 6.1 Species profiles of the premixed benzene flame of Bittner and Howard.
The circles and the dash dotted curve represent the measured species concentrations and the species profiles computed by Waldheim [6], re- spectively. The solid curve represents the currently computed species profiles based on the low temperature rate constants interpolation of the barrier-less pathway of Parker et al. [27]. . . 54 6.2 Species profiles of the ethylene diffusion flame of Olten and Senkan. The
circles and the dash dotted curve represent the measured species concen- trations and the species profiles computed by Waldheim [6], respectively.
The solid curve represents the currently computed species profiles based on the low temperature rate constants interpolation of the barrier-less pathway of Parker et al. [27]. . . 55 6.3 Molecular structures of 1-C10H7, 2-C10H7 and A3H . . . 56
6.4 Species profiles of the benzene premixed flame of Bittner and Howard.
The circles and the dash dotted curve represent the measured species concentrations and the species profiles computed by Waldheim [6], re- spectively. The solid curve represents the currently computed species profiles based on an approximate theoretical collision rate of the barrier- less pathway of Parker et al. [27]. . . 57 6.5 Species profiles of the ethylene diffusion flame of Olten and Senkan. The
circles and the dash dotted curve represent the measured species concen- trations and the species profiles computed by Waldheim [6]. The solid curve represents the currently computed species profiles based on an ap- proximate theoretical collision rate of the barrier-less pathway of Parker et al. [27]. . . 58 6.6 Species profiles of the premixed benzene flame of Bittner and Howard.
The circles and the dash dotted curve represent the measured species concentrations and the species profiles computed by Waldheim [6], re- spectively. The solid curve represents the currently computed species profiles based on an approximate theoretical collision rate of the reaction pathway with a 5 kJ/mol barrier at the entrance. . . 59 6.7 Species profiles of the ethylene diffusion flame of Olten and Senkan. The
circles and the dash dotted curve represent the measured species concen- trations and the species profiles computed by Waldheim [6], respectively.
The solid curve represents the currently computed species profiles based on an approximate theoretical collision rate of the reaction pathway with a 5 kJ/mol barrier at the entrance. . . 60 6.8 Species profiles of the premixed benzene flame of Bittner and Howard.
The circles and the dash dotted curve represent the measured species concentrations and the species profiles computed by Waldheim [6], re- spectively. The solid curve represents the currently computed species profiles based on an approximate theoretical collision rate of the reaction pathway with a 17 kJ/mol barrier at the entrance. . . 61 6.9 Species profiles of the ethylene diffusion flame of Olten and Senkan. The
circles and the dash dotted curve represent the measured species concen- trations and the species profiles computed by Waldheim [6], respectively.
The solid curve represents the currently computed species profiles based on an approximate theoretical collision rate of the reaction pathway with a 17 kJ/mol barrier at the entrance. . . 62 8.1 Potential energy diagram of the pathway in analysis. The energy levels
are expressed in kJ/mol. . . 93 8.2 Spectrum of the eigenvalues of the pathway in Fig. 8.1. The black solid
curve represent the boundary of the IEREs, the black dotted curve is the boundary of the region close to the IEREs within which the criterion adopted by MESMER is not fulfilled. The two colored curves approaching the IEREs and the non-monotonic one are the CSEs. . . 94 8.3 Spectrum of the eigenvalues obtained by Miller and Klippenstein [43]
for an irreversible exchange reaction pathway involving 3 wells with a Potential Energy diagram qualitatively similar to the current case 8.1. . . 94 8.4 Potential energy diagram of the pathway with the Minimum 2 skipped.
The energy levels indicated are expressed in kJ/mol. . . 95
8.5 Spectrum of the eigenvalues of the pathway with the Minimum 2 skipped.
The black solid curve represent the boundary of the IEREs, the black dotted curve is the boundary of the region close to the IEREs within which the criterion adopted by MESMER in not fulfilled. The colored curves approaching the IEREs and the non-monotonic one are the CSEs. . 95 8.6 Potential energy diagram of the pathway with both Minimum 2 and Min-
imum 3 skipped. are expressed in kJ/mol. . . 96 8.7 Spectrum of the eigenvalues of the pathwaywith both Minimum 2 and
Minimum 3 skipped. The black solid curve represent the boundary of the IEREs, the black dotted curve is the boundary of the region close to the IEREs within which the criterion adopted by MESMER in not fulfilled.
The colored curve approaching the IEREs and the non-monotonic one are the CSEs. . . 96 8.8 Fractional species profiles as a function of time computed by MESMER for
the complete pathway in Fig. 8.1. The subsequent diagrams correspond to the different temperatures indicated and to ambient pressure. The dashed curve corresponds to reactants, the red one with circular icons to Minimum 1, the yellow one with triangular icons to Minimum 2, the green one with squared icons to Minimum 3 and the solid curve to products. . . 99 8.9 Fractional species profiles as a function of time computed by MESMER for
the pathway in Fig. 8.4. The subsequent diagrams correspond to different temperatures and to ambient pressure. The dashed curve corresponds to reactants, the red one with circular icons to Minimum 1, the green one with squared icons to Minimum 3 and the solid curve to products. . . 100 8.10 Fractional species profiles as a function of time computed by MESMER
for the pathway in Figure 8.4 The subsequent diagrams correspond to different temperatures at a pressure of 106 atm. The characterization of the different curves is consistent with Fig. 8.9. . . 101 9.1 Reaction Coordinate of the Transition States of the pathway. . . 105 9.2 Potential Energy Surface of the pathway with a 5 kJ/mol energy barrier
at the entrance investigated by Parker et al. [27]. The solid line represents the PES obtain by the authors [27], whereas the other lines are the results of the current quantum chemical calculations, applying different DFT methods and basis sets as indicated in the legend. . . 107 9.3 Canonical reaction rates of reactions RI, RII and RIII. The solid line
corresponds to the values computed by MESMER and the dash-dotted line to the correspondent interpolations. . . 111 9.4 Reaction rates as a function of temperature at ambient pressure. The
green solid curves with squared icons and the red dash-dotted curves with rhomboidal icons are the phenomenological reaction rates (listed in Table B.2) and the correspondent interpolations (shown in Table 9.7), respectively. When present, the black dashed curve represent the trend of the correspondent rate constants previously used into the chemical mechanism. . . 112 9.5 Phenomenological forward and backward reaction rate constants of the
reaction in Eq. 9.1 at different temperatures and at ambient pressure.
The former is represented by the blue solid line with squared icons and the latter is the red solid line with rhomboidal icons. . . 113
9.6 Equilibrium constant of the reaction in Eq. 9.1 at different temperatures and at ambient pressure. . . 113 9.7 Reaction rates in m3/(kmol · s) trends as a function of temperature at
2.67 kPa. The light blue solid curves with circular icons and the red dash-dotted curves with rhomboidal icons are the phenomenological re- action rates (listed in Table B.3) and the correspondent interpolations (shown in Table 9.8), respectively. The green solid lines with squared icons are the correspondent phenomenological reaction rates at ambient pressure of Table B.2. When present, the black dashed curve represents the trend of the correspondent rate constants previously implemented into the chemical mechanism. . . 114 9.8 Canonical and corresponding phenomenological reaction rates leading to
products at different temperatures for reactions RI, RII and RIII. The blue curves with squared icons are the canonical reaction rates. The red curves with circular icons, the green curves with rhomboidal icons and the orange curve with triangular icons are the phenomenological reaction rates computed at 106, 1 atm and 2.67 kPa respectively. . . 118 9.9 Fractional species profiles as a function of time of the pathway in Fig-
ure 8.4. The subsequent diagrams correspond to different temperatures at ambient pressure. The dashed curve, the red one with circular icons, the green one with squared icons and the solid curve are the fractional profiles shown in Fig 8.9. The correspondent thinner curves are the frac- tional profiles computed as a result of the system in Eq. 9.8. . . 119 10.1 Species profiles of the ethylene diffusion flame of Olten and Senkan. The
circles and the solid curves represent the measured concentrations and the currently computed species profiles for case a. The dash dotted curves represents the correspondent species profiles computed by Waldheim [6]. . 122 10.2 Planar representation of C10H8(L) and of the C10H9(L) radical. . . 123 10.3 Formation of C10H9(T) radical through C10H9(M) isomerization. . . 123 10.4 Chemical structures of the species involved in the reaction in Eq. 10.6. . . 123 10.5 Species profiles of the premixed benzene flame of Bittner and Howard.
The circles and the solid curves represent the measured concentrations and the currently computed species profiles for case a. The dash dotted curves represents the correspondent species profiles computed by Waldheim [6]. . 124 10.6 Species profiles of the ethylene diffusion flame of Olten and Senkan. The
circles and the solid curves represent the measured concentrations and the currently computed species profiles for case b. The dash dotted curves represents the correspondent species profiles computed by Waldheim [6]. . 126 10.7 Species profiles of the premixed benzene flame of Bittner and Howard.
The circles and the solid curves represent the measured concentrations and the currently computed species profiles for case b. The dash dotted curves represents the correspondent species profiles computed by Waldheim [6]. . 127 10.8 Species profiles of the ethylene diffusion flame of Olten and Senkan. The
circles and the solid curves represent the measured concentrations and the currently computed species profiles for case c. The dash dotted curves represents the correspondent species profiles computed by Waldheim [6]. . 129
10.9 Species profiles of the premixed benzene flame of Bittner and Howard.
The circles and the solid curves represent the measured concentrations and the currently computed species profiles for case c. The dash dotted curves represents the correspondent species profiles computed by Waldheim [6]. . 130
6.1 Significance of the reactions currently applied to the premixed benzene flame kinetic scheme based on the low temperature rate constants inter- polation of the barrier-less pathway of Parker et al. [27]. When the minus sign is indicated into brackets, the correspondent reaction turned reverse. 56 6.2 Significance of the reactions currently applied to the ethylene diffusion
flame kinetic scheme based on the low temperature rate constants inter- polation of the barrier-less pathway of Parker et al. [27]. . . 56 6.3 Significance of the reactions currently applied to the premixed benzene
flame kinetic scheme based on an approximate theoretical collision rate of the barrier-less pathway of Parker et al. [27]. . . 58 6.4 Significance of the reactions currently applied to the ethylene diffusion
flame kinetic schem based on an approximate theoretical collision rate of the barrier-less pathway of Parker et al. [27]. . . 59 6.5 Significance of the reactions currently applied to the premixed benzene
flame kinetic scheme, testing the pathway with a 5 kJ/mol barrier at the entrance . . . 60 6.6 Significance of the reactions currently applied to the ethylene diffusion
flame kinetic scheme, testing the pathway with a 5 kJ/mol barrier at the entrance . . . 61 6.7 Significance of the reactions currently applied to the premixed benzene
flame kinetic scheme, testing the pathway with a 17 kJ/mol barrier at the entrance. When the minus sign is indicated into brackets, the correspon- dent reaction turned reverse. . . 62 6.8 Significance of the reactions currently applied to the ethylene diffusion
flame kinetic scheme, testing the pathway with a 17 kJ/mol barrier at the entrance. . . 62 8.1 Rotational symmetry numbers of all the species of the pathway . . . 83 9.1 Ground single point energies for the different species from B3LYP cal-
culations adopting 6-311G basis set. ∆E0 is the difference between E0
of each species and the sum of E0 of the reactants (vinylacetylene + the phenyl radical). . . 103 9.2 Ground single point energies for the different species from B3LYP calcu-
lations adopting 6-311G(d,p) basis set. ∆E0 is the difference between E0
of each species and the sum of E0 of the reactants (vinylacetylene + the phenyl radical). . . 103
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9.3 Ground single point energies for the different species according to the values of Parker et al. [27]. ∆E0 is the difference between E0 of each species and the sum of E0 of the reactants (vinylacetylene + the phenyl radical). . . 104 9.4 Ground single point energies for the different species from M06-2X calcu-
lations adopting 6-311G(d,p) basis set. ∆E0 is the difference between E0
of each species and the sum of E0 of the reactants (vinylacetylene + the phenyl radical). . . 104 9.5 Rotational constants [cm−1] of all the species of the pathway . . . 106 9.6 Interpolated expressions of the canonical reaction rates listed in Tab. B.1
within Appendix A. Units are m3, kmol, s and K. . . 109 9.7 Interpolated expressions of the phenomenological reaction rates computed
at ambient pressure and listed in Tab. B.2. Units are m3, kmol, s and K. 110 9.8 Interpolated expressions of the phenomenological reaction rates computed
at a pressure of 2.67 kPa and listed in Tab. B.3. Units are m3, kmol, s and K. . . 115 A.1 Vibrational frequencies [s−1] of the transition sstates of the pathway. . . . VI A.2 Vibrational frequencies [s−1] of reactants, minima and products of the
pathway. . . VII A.3 Reaction coordinates [˚A] of the transition states of the pathway. The
data below relate to the current orientation of the transition states in the coordinate system. . . IX B.1 Canonical reaction rates computed at different temperatures for the re-
actions RI, RII and RIII. Units are m3, kmol, s. . . XII B.2 Phenomenological reaction rates computed on the chemical system with
Minimum 2 skipped (see Fig. 8.4) at different temperatures and ambient pressure. Units are m3, kmol, s. . . XIII B.3 Phenomenological reaction rates computed on the chemical system with
Minimum 2 skipped (see Fig. 8.4) at different temperatures and 2.67 kPa.
Units are m3, kmol, s. . . XIV
Abbreviations
Abbreviation Description
PAH Polycyclic Aromatic Hydrocarbon
PM Particulate Matter
FORTRAN FORmula TRANslation programming language
DFT Density Functional Theory
B3LYP Electronic density functional ab initio method M06-2X Electronic density functional ab initio method CCSD(T) Coupled Cluster ab initio method
6-311G Basis set
6-311G(d,p) Polarized basis set
ZPE Zero Point Energy
ME Master Equation
EGME Energy Grained Master Equation CSE Chemically Significant Eigenvalue IERE Internal-Energy-Relaxation Eigenmode RRKM Rice-Ramsperger-Kassel-Marcus theory
GAMESS General Atomic and Molecular Electronic Structure System MESMER Master Equation Solver for Multi-Energy Well Reactions
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Parameters
Alphabetic
Designation Description SI units
m Mass kg
x, y Space coordinate m
t Time s
T Temperature K
u, v Velocity m/s
p Pressure P a
E Energy J , Ha
h Specific enthalpy J/kg
cp Specific heat capacity at constant pressure J/(kg · K) Cv Molar specific heat capacity at constant volume J/(mol · K)
X Molar fraction -
Y Mass fraction -
f Volumetric force N/m3
W Molar mass kg/mol
Kn Dimensionless Knudsen number -
Sc Dimensionless Schmidt number -
Vi Diffusion velocity m/s
D Diffusion coefficient m2/s
n Inverse of the molecular weight mol/kg
Dk Diffusion coefficient parameter m2/s
Vc Velocity correction m/s
W1,2(1) Dimensionless function of the reduced temperature - W(2) Dimensionless function of the reduced temperature - F Dimensionless function for estimating the specific
heat capacity
-
R Reaction rate mol/s
k Reaction rate constant [m3; kmol; s]
Ea Activation energy J/mol
A Pre-exponential factor [m3; kmol; s]
Keq Equilibrium constant [m3; kmol]
VL,J Lennard-Jones potential V
a Strain rate 1/s
J Molecular flux kg/(m2· s)
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J0 Dimensionless molecular flux -
V Dimensionless density-weighted velocity -
< ∆Ed> Energy transferred on average in a collision J Evib Energy contribution of the molecular vibrational
modes
J
Erot Energy contribution of the molecular rotational modes
J
I Moment of Intertia kg · m2
A, B, C Rotational constants cm−1
Concluded from last page
Greek
Description SI units
Designation
ρ Mass density kg/m3
µ Viscosity kg/(m · s)
τ Viscous stress tensor N/m2
β Rate of attachment of soot particles m3/s
σ Collision diameter m
φm Well depth of the Lennard-Jones potential V
λ Thermal conductivity W/(m · K)
δj,k Kronecker delta -
γ Ratio of the molar specific heat capacities - ηi,j,k Parameter ensuring the conservation of mass -
ψ Stream function kg/m2
ω Cross-stream function -
Φ0 Dimensionless velocity -
η Dimensionless density-weighted space variable - µ0 Dimensionless density-weighted viscosity -
ρ0 Dimensionless density -
ζ Distance parameter of an atomic orbital 1/m2
νi Molecular vibrational frequency 1/s
ωLJ Lennard-Jones frequency of collisions 1/s
βT Parameter proportional to temperature m2· kg/s2
grain,i Average energy grain J
τj Time of relaxation s
Symbols
Alphabetic
Designation Description
ai Coefficient of the polynomial interpolation of the specific enthalpy ni Number of soot particles of size class i
Zrot Number of molecular collisions
H Hamiltonian operator
V Potential energy operator T Kinetic energy operator
r Particle position
N Number of particles
cn Atomic oribital linear combination coefficient nbasis Number of basis functions
Nnorm Atomic orbital normalization constant l Coordinate parameter of an atomic orbital
f˜ Generic function
F Generic electronic density functional
F Force constant matrix
x Space coordinate vector
yi Mass-weighted space coordinate Gi,j Mass-weight factor
qi Eigenvector of the mass-weighted force constant matrix ei Eigenvalue of the mass-weighted force constant matrix p Vector of the grained energy distribution
M Grained energy distribution change matrix P Collision probability
qV ibrationalM ode Contribution of a single mode to the vibrational partition function qvib Vibrational partition function
qrot Rotational partition function qrv Roto-vibrational partition function gi,j Relative speed of collision
EJdiatomic Rotational energy level of a diatomic molecule
J Rotational quantum number
nvibi Vibrational quantum number
W (E − E0) Sum of roto-vibrational energy states gj Eigenvector of the EGME
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Tˆ Operator describing the time evolution of the energy distributions Nchem Number of chemically significant eigenvectors of the EGME nspecies Number of chemical species involved in a pathway
nwells Number of intermediates of a pathway
S Number of species with an energy distribution ci,j(E) Energy population linear combination coefficient ai,j(E) Molar fraction linear combination coefficient
Concluded from last page
Greek
Description Designation
νA Stoichiometric coefficient αk,i Third body enhancement factor Φi,j Mixing coefficient
ξ Heat loss factor
Ψ Wave function
φ Molecular orbital
χ Atomic orbital
ρel Electronic density
ρDOS Roto-vibrational density of state
σrot Number of rotational symmetry operations Ω∗ Reduced collosion integral
λj Eigenvalue of the EGME
Physical Constants
Designation Description Value
R Gas constant 8.314 J/(mol · K)
kb Boltzmann constant 1.381 · 10−23 J/K
h Planck constant 6.626 · 10−34 J · s
Introduction
1.1 Background
Polycyclic aromatic hydrocarbons (PAH) are by-products formed in all the commercial combustion devices running on hydrocarbons under locally fuel-rich conditions. Even though their concentration is generally low, they act as precursors during soot formation and are harmful to human health. Aromatic species are also contained in a wide range of hydrocarbon fuels for automotive, industrial and aeronautic applications e.g. diesel, gasoline and kerosene. Despite the issues connected to PAH, the presence of aromatic species is favored in the application of spark ignition engines as there are evidences that they decrease the phenomena of knock and auto-ignition [1]. Moreover, despite the presence of aromatic compounds in the fuel, aromatic formation and growth also occurs during combustion of aliphatic fuels [2, 3].
During the last decades, one of the main topics within the research in the field of com- bustion has been the relation between PAH formation and oxidation in the combustion of hydrocarbons and the formation of soot. It has been demonstrated that PAH forma- tion and subsequent growth connects the main combustion chemistry of the flames to the chemistry and the dynamics of soot formation [4].
PAH and soot emissions are harmful both for human health and for the environment.
Furthermore, they may cause a reduction of combustion efficiency as well as fouling and deterioration of the combustion devices. Soot generated from automotive engines and other commercial combustion devices leads to hazardous exposure of particulate matter (PM) in populated areas. Even a short term exposure to aerosol containing PM may cause respiratory problems varying from asthma to chronic bronchitis and emphysema.
There are evidences that a long term exposure to aerosols containing relevant soot concentrations may lead to cancer and heart problems [5].
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These critical issues made the European Union legislators introduce stricter limit values of PM and PAHs emissions with consequentially higher technical requirements for au- tomotive manufactures [6]. The Euro VI Particulate Matter mass emission limit is 10 mg/kWh for heavy-duty compression ignited diesel engines on world harmonized station- ary and transient test cycle [7]. Concerning the Particulate Matter number, the limits correspond to 8.0 · 1011and 6.0 · 1011particles/kWh for the world harmonized stationary and transient test cycle, respectively [6]. In order to achieve the above mentioned tech- nical requirements the approach of the automotive companies regarding soot emissions has to prevent soot formation in the end of the combustion and/or the oxidation of soot through the exhaust aftertreatment system.
The European Union emission limits legislation is coupled with local policies which have in common with the former one the aim of reducing the concentration of hazardous pollutants in densely populated areas: They are named low emission zones (LEZ) [6].
The case of the region of Lombardia in Italy and of the municipality of Milan are considered: The use of 2-stroke motorcycles below Euro 1 and public Diesel buses below Euro 3 are permanently banned. Moreover, in sub areas like the one comprising the municipality of Milan, the use of all the other petrol vehicles below Euro 1 and Diesel vehicles below Euro 3 are banned except in winter daily hours [8].
It has been demonstrated [9] that heavy duty diesel vehicles play a dominant role in the emissions of P M < 2.5, whose quantity can be one order of magnitude higher compared to the PM emissions from light duty gasoline vehicles. Moreover, diesel engines emit on average PM with a greater mass and a higher amount of ultra-fine particles, if compared to gasoline engines. Further investigations [9] have demonstrated that PAH emitted from vehicles are mainly in the PM fraction below 0.4 µm and heavy PAHs have been traced in PM fractions of a larger size. These observations represent a straightforward experimental proof of the relationship between PAH and soot formation.
1.2 Motivation
The purpose of the present work is to provide an additional contribution to the doctoral thesis “Modelling of soot formation and aromatic growth in laminar flames and reactor systems” developed by B. B. O. Waldheim [6] from Imperial College between 2010 and 2014 in collaboration with Scania. In the doctoral work, Waldheim applied a sectional soot model to combustion processes in laboratory devices under conditions where soot measurements have been previously carried out. Moreover, he included a thorough preliminary investigation of both the aromatic and the soot chemistry involved in the systems analyzed. In the present work, the analysis will be focused on the chemistry of
the aromatic species included in the soot model mentioned above. New PAHs formation pathways will be investigated for the laminar premixed benzene flame of Bittner and Howard [10] and the laminar ethylene diffusion flame of Olten and Senkan [11] studied by Waldheim [6].
Within the process of soot formation occurring during combustion of hydrocarbons, the chemistry of the polycyclic aromatic hydrocarbons concerns the gas-phase part of the flame. More precisely, the latter represents the stage of formation of soot precursors, preliminary to soot inception and growth. Depending on the composition of the fuel and on the flame type, the pathways involved in the fuel consumption are different. As it will be shown in the course of this work, different chemical routes become relevant in the formation, growth and oxidation of PAHs [1, 3, 6]. Commercial fuels are a complex mixture of both aromatic and aliphatic hydrocarbons and depending on the relative concentration of these classes of compounds, the pathways of formations of PAHs and their subsequent growth and oxidation are different. Depending on the thermodynamic conditions of the flame, certain pathways prevail over other ones and occur in different zones of the flame [1, 6]. In order to evaluate the relevance of a particular pathway different studies can be developed. Among them, studies of laminar flames - either diffusive and premixed of aromatic or aliphatic fuels - will be quoted. The choice to in- vestigate laminar flames is made in order to focus on the chemistry of the flames. In the kinetic mechanisms a broad range of chemical species are taken into account and mea- surements of the concentration of the minor species would be too technically challenging if a turbulent flame was investigated. Moreover, the implementation of comprehensive kinetic mechanisms in simulations of turbulent flames makes the computational cost too high and this is a reason why modeling of commercial combustion devices adopt re- duced mechanisms. The current objective is to investigate the pathways of formation of polycyclic aromatic species under certain chemical conditions, not considering the real structure of commercial combustion devices: This clarifies the decision to investigate laminar flames modeled as one-dimensional systems.
Moreover, several experiments have been conducted using different reactors for the study of the partial oxidation and combustion of fuel under different operative conditions [1].
The motivation behind the reactor studies is to focus on particular pathways occur- ring in different zones of the flames, with certain local equivalence ratios, temperature and pressure, as well as to validate computational results with a broader amount of experimental measurements under a wide rage of physical and chemical conditions.
Objectives
The aim of the current M.Sc. thesis project is to enhance the accuracy of the prediction of PAH and soot formation in laminar flames of aliphatic and aromatic hydrocarbons, by applying novel pathways of PAH formation to the correspondent kinetic mechanisms.
This work is focused on the simulation of flames where the application of the current PAH chemistry models fails in the prediction of the amount of PAHs formed and oxi- dized. In particular, the main goal is to improve the prediction of PAH concentration
Figure 2.1: A group of measured and calculated species mass fractions of the lam- inar ethylene diffusion flame of Olten and Senkan investigated by Waldheim [6]. The measured values are identified by circles, the computed profiles by the solid line and the ones represented by dashed and dotted lines corresponds to computation with an 100 K increase and decrease respectively. The figure is taken from the doctoral thesis
of Waldheim [6].
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in the ethylene diffusion flame of Olten and Senkan [11], where the molar fractions of aromatic species such as naphthalene (C10H8), phenanthrene (A3) and pyrene (A4) are underestimated. Figure 2.1 shows the underestimation of phenanthrene and pyrene in the ethylene diffusion flame investigated by Waldheim [6]. Hence, the objective will be to find reasonable agreement between the computational and the experimental PAH molar fraction profiles as a function of the distance from the burner.
In order to achieve the main, general goal of this project, the following intermediate objectives have to be fulfilled:
• Novel pathways of PAH formation, significant in terms of aromatic growth when applied to the studied flames, have to be identified;
• Depending on the features of the identified PAH formation pathways, different molecular properties of the involved species have to be preliminarly calculated in order to determine the correspondent kinetic parameters;
• The reaction rate constants of the identified pathways have to be computed at the thermodynamic conditions of interest for the studied flames;
• The reliability and robustness of the method adopted for computing the reaction rate constants have to be demonstrated;
• The influence of the thermodinamic conditions on the computed kinetic parameters have to be clarified;
• The significance of the identified PAH formation pathways in terms of aromatic growth in the studied flames have to be confirmed.
Methodology
The aim of this chapter is to give the reader an overview of the workflow characterizing the current project. A schematic representation of the methdology adopted in this work is shown in Fig. 3.1.
First, a thorough literature review is done in order to:
• Outline the fundamentals of the aromatic chemistry in the framework of flame and reactor studies;
• Introduce soot modeling, within which the current study is contextualized;
• Give an overview of the physics and of the chemistry of the studied flames, together with the tools adopted for performing the flame calculations.
A further literature search is performed in order to identify novel PAH formation path- ways potentially significant in terms of aromatic growth in the studied flames. The features of the novel pathways are outlined in comparison to analogous pathways, pre- viously extensively investigated in the literature. In particular, the Potential Energy Surfaces of the correspondent pathways are considered.
The potential significance of the novel pathways is subsequently assessed through prelim- inary flame calculations relying on available simplified kinetic parameters, either found in the literature or estimated. The pathway showing the highest potential in terms of aromatic yield is selected for a more refined investigation.
Due to the topology of the Potential Energy Surfaces of the selected PAH formation pathway, the solution of an energy density population balance between the involved chemical species is required for computing accurate reaction rate constants. In order to
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Figure 3.1: Schematic representation of the methodology adopted in the current work.
deremine the energy distributions of the involved species, various molecular properties are calculated through quantum chemical calculations.
The energy density population balance is subsequently solved for the energy distributions of the species involved in the pathway. A preliminary analysis of the chemical system represented by the single pathway is performed in order to ensure reliability for the computation of the correspondent reaction rate constants. In particular, the time-scales of the chemical reactions involved in the pathway are compared to the time-scales of the processes of achievement of thermal equilibrium within the studied chemical system.
The need to introduce approximations to the pathway is outlined, since features of the correspondent Potental Energy Surface make it not suitable for the computation of reli- able rate constants with the available tools. The effect of the introduced approximations on the computation of the reaction rate constants is investigated.
Reaction rate constants are computed for a broad range of thermodynamic conditions:
The effect of pressure and temperature on the kinetic parameters of the pathway is investigated. In particular, the rate constants of the reactions involved in the pathway are computed for the temperature range of interest and at the correspondent pressures of the studied flames. The rate constants are interpolated as a function of the temperature
fitting a modified Arrhenius expression. The latter is the expression applied to the kinetic scheme of the flames.
Final flame calculations relying on the refined kinetic parameters are performed in order to confirm the significance of the identified pathway. Different assumptions are adopted and discussed in order to further investigate the influence of the thermodynamic condi- tions.
The organization of the report is consistent with the methodology adopted in this work:
Each chapter corresponds to a different phase among the ones previously depicted. The computed molecular properties and reaction rate constants are listed within a single chapter aiming at resuming the macro-phase of the computation of the kinetic parame- ters shown in Fig. 3.1. This macro-phase represents the main contribution of the current work.
Literature Review
4.1 PAH chemistry
4.1.1 Introduction to PAH chemistry
The aim of this section is to give an overview of the complexity of the chemistry involved in the combustion of hydrocarbons: PAHs formation and oxidation pathways contribute to the chemistry of hydrocarbon flames. When considering PAHs formation pathways, it will be taken into account the formation and consumption of the first aromatic ring, its growth as well as the role of minor species in their development. The first step to consider within the chemistry of Polycyclic Aromatic Hydrocarbons is the formation of the first aromatic ring.
4.1.2 The formation of the first aromatic ring
The first aromatic ring formation through the combination of aliphatic compounds often represents the rate-limiting step in PAH formation pathways [4]. During combustion of real fuels, the reactions involved in the formation of the first aromatic ring contribute to different processes within the flame, such as the consumption of the aliphatic fractions of the fuel. The first aromatic ring formation may also occur subsequently to the ring opening of the aromatic fractions of the fuel. The current discussion is mainly focused on reactions involving aliphatic radicals. Both even- and odd- carbon-atom-pathways have been investigated for a broad selection of flames and fuels at different physical conditions [4]. Among them, the role or resonance stabilized radicals like n- and iso- C4H3 and C4H5, as well as of the propargyl radical are relevant [4].
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As an example, the role of the propargyl radical in benzene formation in a near soot- ing acetylene premixed flame diluted in Ar (equivalence ratio equals to 2.5) has been investigated [3]:
C3H3+ C3H3 → C6H6 (4.1)
There are evidences that the reaction in Eq. 4.1 represents the dominant pathway of benzene formation in the main reaction zone of the flame. However, it has to be pointed out that the reaction in Eq. 4.1 is likely to be a global mechanism, representative of a series of elementary reactions. First, a linear C6H6 isomer is formed and subsequently, either isomerises to benzene or reacts with other radicals to form benzene [3]. The propargyl radical is a highly-stable hydrocarbon radical and several studies show that, once the activation of the adduct is reached, the energy barrier of the cyclization of the linear isomer of benzene is overcome [4].
The parameters that play a role in the first aromatic formation are several. The pres- sure of the system influences the kinetic parameters of many reactions so that, when varying the pressure, the dominant pathways may change and additional pathways may become significant. For instance, increasing the pressure, the relevance of ring-ring re- actions increases and tends to prevail over the reactions involving the C4 and propargyl radicals mentioned above. Similarly, other species besides resonantly stabilized radicals gain a more relevant role in the formation of the first aromatic ring, e.g. C6Hx linear compounds [4].
4.1.3 The HACA mechanism of aromatic growth
Another species that plays a key role both in the formation of the first aromatic ring and in PAH growth is acetylene. Gaseous acetylene is considered the “building block”
through which the main mechanism of aromatic growth proceeds in hydrocarbon flames [4].
Acetylene is involved in the second step of the well-known mechanism of Hydrogen- Abstraction-C2H2-Addition. First, a hydrogen atom activates an aromatic hydrocarbon molecule by abstracting one hydrogen atom from its structure:
Ai+ H → Ai−+ H2 (4.2)
Then, gaseous acetylene is added to the activated aromatic hydrocarbon radical:
Ai−+ C2H2→ AiC2H2 (4.3) Even though this mechanism could appear straightforward, particular kinetic and ther- modynamic conditions are required to make it predominant.
Concerning the first step of activation of the aromatic molecule, many reactions can prevent the HACA mechanism to proceed, like the reverse of the hydrogen abstraction or the recombination of the activated radical with a hydrogen atom [4]. Among these two reactions, the former one plays a more significant role with decreasing pressure and molecular size of the aromatic molecule Ai [4]. Furthermore, the formation of the activated radical (Ai−) may proceed through different reactions involving other types of radicals instead of the hydrogen atom. However, many investigations on shock-tubes and flames have demonstrated the H abstraction, shown in the reaction in Eq. 4.2, is predominant under several thermodynamic conditions [4]. In any case, the outcome with respect to activation of aromatic molecule precursors in the second step of the HACA machanism is the same.
In order for the acetylene addition to complete the aromatic growth, two conditions have to be fulfilled [4]:
• The thermodynamic irreversibility of the two steps.
• The enhancement of the kinetics of the forward reactions in Eqs. 4.2 and 4.3.
The simple acetylene addition
Ai−+ C2H2→ AiC2H2 (4.4) has a high reversibility and even in the case of release of H, following the reaction
Ai−+ C2H2 → AiC2H + H (4.5) the reversibility may still prevail. The irreversibility of the acetylene addition, named re- action “affinity” (the opposite of the so-called reaction “resistance”) is achieved through an entropy recovery and energy decrease of the system, that leads to the formation of highly stable hydrocarbons called stabilomers [4]. Depending on the temperature level, different kinetic regimes of the HACA mechanism establish and either the thermody- namic resistance or the rate of one or more sub-steps may control the PAH growth [4].
The sequences of reactions occurring in the process of PAHs growth terminates with irreversible steps involving ring closure which lead to the formation of stabilomers. An appropriate example is the following reaction of acetylene addition [4]:
AiC2H2+ C2H2 → Ai+1+ H (4.6)
4.1.4 Consumption of benzene
Depending whether the flame is a premixed or a diffusion flame as well as on the equiva- lence ratio and on the pressure of the system, the consumption of benzene occurs either through oxidation reactions and through pyrolysis reactions.
Several experimental studies on the pyrolysis of benzene [12] both at high and low temperatures have shown the production of diacetylene (C4H2) and acetylene as by- products which are subsequently involved in the HACA mechanism. The pyrolysis of benzene is described by the mechanism of Bauer-Aten [13]:
C6H6(+M) C6H5+ H(+M) (4.7)
C6H6+ H C6H5+ H2 (4.8)
C6H5(+M) n-C4H3+ C2H2(+M) (4.9) n-C4H3(+M) C4H2+ H(+M) (4.10) Acetylene is the by-product of a sequence of reactions that starts with the formation of the phenyl radical through the scission of a CH bond of the benzene ring. The latter is the rate limiting step in all conditions [14]. Through RRKM calculations [13] the formation of o-benzyne from the phenyl radical has been demonstrated to be relevant in the pyrolysis of benzene at temperatures higher than 1250 K:
C6H5(+M) o-C6H4+ H(+M) (4.11) The formation of acetylene and diacetylene was suggested to follow the decomposition of o-benzyne [13]:
o-C6H4(+M) C4H2+ C2H2(+M) (4.12) As stated above, the consumption of the fuel occur through reaction of both pyrolysis and oxidation. Relying on the investigation on the premixed benzene flame of Bittner and Howard [10] and on the subsequent study of Waldheim [6], the thermal decomposition of benzene shown in Eqs. 4.7-4.10 contributes 44% to benzene consumption. The second and third reaction of benzene consumption in order of importance are [6]:
C6H6+ OH C6H5+ H2O (4.13)
C6H6+ O C6H5O + H (4.14)
Figure 4.1: Major benzene oxidation pathways investigated in a jet-stirred reactor at 1000K, 10 atm and Φ = 1.5. The width of the arrows is proportional to the relevance
of the reaction [1].
Figure 4.2: Major benzene oxidation pathways investigated in the Princeton reactor at Φ = 1.36. The width of the arrows is proportional to the relevance of the reaction [1].
The three main reactions consuming the phenyl radical are [6]:
C6H5+ O2 C6H5O + H2 (4.15)
C6H5O C5H5+ CO (4.16)
C6H5+ H C6H4+ H2 (4.17)
More precisely, the reaction in Eq. 4.15 is the main channel of formation of the phenoxy radical, that subsequently almost completely (90%) decomposes to cyclopendadienyl radical through the reaction in Eq. 4.16 [6]. The remaining phenoxy radical is converted to phenol [6]. The reaction in Eq. 4.17 shows that benzyne (C6H4) formation contributes to the phenyl radical consumption. However, benzyne mainly undergoes hydrogenation (62%), forming the phenyl radical again [6].
As previously mentioned, in order to further investigate the mechanism of aromatic fuels consumption and to validate the computational results with a sufficient amount of experimental measurements at different physical conditions, experiments have been
conducted using shock tubes for fuel pyrolysis, flow reactors for both fuel pyrolysis and oxidation and jet stirred reactors for fuel partial oxidation and combustion [1].
Studies on benzene oxidation conducted in the Princeton flow reactor at Φ = 1, 36 and in a pressurized jet-stirred reactor at 10 atm and 1000 K confirmed phenoxy radical to be a relevant intermediate in the pathway of benzene oxidation at different physical and chemical conditions [1]. Further investigations on benzene premixed flames with air at ambient pressure and temperature as well as on pressurized laminar premixed benzene flames over different equivalence ratios confirmed the central role of phenoxy radical in the oxidation of benzene, together with its dominant influence on the flame speed. In fact, the phenoxy recombination with H atoms to form phenol reduces the benzene flame speed [1].
In order to give to the reader an overview of the complexity of benzene oxidation in aro- matic flames, Figures 4.1 and 4.2 show several major pathways under different physical and chemical conditions, investigated through reactor studies [1].
4.2 Sectional soot modeling
Even though a thorough description of the modeling of soot formation and oxidation ex- ceeds the objectives of the current work, giving an overview of the methodology involved is important in order to properly contextualize the study of the aromatic chemistry of flames. The first soot models were approximated numerical methods for the solution of the master equations concerning particle coagulation. Among the latter ones, the method of moments relies on the assumption that knowing all the particle moments implies having the knowledge of the distribution function of the particles size [15]. The approximation necessary in order to achieve a reasonable computational effort, while determining the properties of the system with a sufficient accuracy, is to consider only the first few moments of the particle size distribution [15]. A further step has been represented by the introduction of discrete sectional models. They overcame the first approximate models since the particle size distribution is obtained by discretizing the particle sizes into classes of surrogate species referred as to bins with a fixed size re- lation between each other. More precisely, the classes of PAHs and soot particles are differentiated either basing on the number of carbon atoms or on the atomic mass [2].
The following digression relies on the works of Bhatt and Lindstedt [16] - concerning the sectional soot model subsequently improved by Waldheim [6] and used in the current work - and of Saggese et al. [2] - concerning the determination of particle size distribution of soot in a premixed ethylene flame applying another sectional soot model. The aerosol
Figure 4.3: The NIST experimental system [17]
dynamics modeling of the flame is subsequent to the gas phase modeling. The former is coupled with the gas-surface reactions responsible of the inception and growth of soot particles. Considering the surface chemistry involved in the soot growth, several heterogeneous reactions are taken into account, such as [2]:
• The HACA mechanism.
• The addition of resonantly stabilized radicals.
• The oxidation of soot particles.
The first two classes in the list both occur in the gas-phase chemistry of the flame and involve solid soot particles as reactants. The boundary between the gas-phase chemistry and the chemistry of the soot solid particles is not sharp. In the modular discrete sectional approach [2], the first class of soot particles incepted is chosen to be a bin characterized by a certain mass or a certain number of carbon atoms, that is formed through the growth of PAHs in the gas-phase chemistry step. The choice of this smallest soot bin is arbitrary, however, in the soot model used by Saggese et al. [2] it is consistent with experimental measurements both concerning PAHs emission from sooting flames and concerning soot measured particle sizes. Another approach, adopted by Bhatt and Lindstedt [16], is to consider pyrene as the incepting species, i.e. as the zeroth bin.
As previousely mentioned, the soot model used in the current work was developed by Bhatt and Lindstedt [16] and subsequently improved by Waldheim [6]. The model was first applied to the combustion of ethylene in the NIST reactor system in Fig.4.3. The
