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Chemistry Reduction for Laminar Oxyfuel Combustion

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Chemistry Reduction for Laminar Oxyfuel Combustion Chemistry Reduction for Laminar Oxyfuel Combustion Dissertation zur Erlangung des Grades Doktor{Ingenieur der Fakult¨atf¨urMaschinenbau der Ruhr{Universit¨atBochum von Valentin N04 Bomba aus Yegue-Assi, Kamerun Bochum 2016 Dissertation eingereicht am: 15.12.2016 Tag der mündlichen Prüfung: 01.02.2017 Erstgutachter: Prof. Dr.-Ing. B. Rogg Zweitgutachter: Prof. Dr.-Ing. W. Eifler Contents Abstract iii 1 Introduction 1 1.1 Motivation for and Overview on the Reduction of Chemical Mechanisms 2 1.2 Previous Work . 5 1.2.1 Combustion in O2/CO2 Atmospheres . 5 1.2.2 Combustion in Pure Oxygen . 5 1.3 Outline of the Present Work . 7 2 Combustion Geometry and Governing Equations 8 2.1 Diffusion Flames in CounterFlow . 8 2.2 Higher-Order Effects . 13 3 Thermodynamics and Molecular Transport 15 3.1 Equations of State . 15 3.2 Phenomenological Relationships . 16 3.2.1 Stress Tensor . 16 3.2.2 Heat-Flux Vector . 17 3.2.3 Diffusion Velocities . 17 3.3 Transport Coefficients . 18 3.3.1 Simple Property and Data Models . 18 3.3.2 Detailed Property and Data Models . 19 3.3.2.1 Dynamic Viscosities . 20 3.3.2.2 Thermal Conductivities . 20 3.3.2.3 Ordinary-Diffusion Coefficients . 22 3.3.2.4 Thermal-Diffusion Coefficients . 23 3.4 Heat Capacities, Enthalpies and Entropies . 23 4 Chemistry 25 4.1 Ozone Chemistry as an Introductory Example . 25 i 4.2 Phenomenological Expressions of Chemical Kinetics . 25 4.3 Detailed Mechanisms of Elementary Reactions . 27 4.4 Partial Equilibria . 28 4.5 Steady States Species . 28 4.6 Global Reactions and Global Reaction Mechanisms . 30 5 Discretization and Numerical Methods 32 5.1 Formulation . 33 5.1.1 Differential Equations . 33 5.1.2 Finite Differences . 33 5.1.3 Differential Algebraic Systems . 35 5.2 Numerical Methods . 36 5.2.1 A Modified Newton Method . 36 5.2.2 An Extrapolation Method . 37 5.3 Adaptive Selection of Grid . 37 6 Methods of Reduction of Detailed Reaction Mechanisms to a Skeletal Mechanism 39 6.1 Basics . 39 6.2 Directed Relation Graph (DRG) . 40 6.3 DRG-Aided Sensitivity Analysis (DRGASA) . 42 6.4 Unimportant-Reaction Elimination . 43 6.5 Reaction Elimination Based on DRGASA . 44 6.6 Summary of Reduction Methods . 44 7 Derivation of Reduced Mechanisms of Global Reactions 47 7.1 Notational Issues . 47 7.2 Species Splitting . 48 7.3 Reaction Splitting . 49 7.4 Reduced Stoichiometric Matrix . 52 7.5 Global Reaction Rates Determined Systematically . 54 7.5.1 Theory of Derivation . 54 7.5.2 Sample Derivation . 58 7.6 Global Reaction Rates Determined Empirically . 60 8 Results for Detailed Mechanisms 64 9 Results for Skeletal Mechanisms 68 ii 9.1 Exploratory Reaction-Pathway Analysis . 68 9.2 Oxy-Methane Skeletal Mechanism Valid Over the Entire Strain Rate Range . 71 9.3 Oxy-Methane Skeletal Mechanism for Diffusion Flames at Low Strain Rates . 79 10 Results for Global, Systematically Reduced Mechanisms 83 10.1 Low Strain Rates . 83 10.2 Entire Strain Rate Range . 88 11 Results for Global, Empirically Reduced Mechanisms 92 12 Summary and Outlook 98 Appendix A Skeletal Mechanisms 100 A.1 Oxy-Methane Skeletal Mechanism for Counterflow Diffusion Flames . 100 A.2 Extremely Low Strained Oxy-Methane Skeletal Mechanism for Counter- flow Diffusion Flames . 102 Appendices 100 Appendix B Reactions, Their Rates, and Associated Quantities 104 B.1 Basic Reaction . 104 B.2 Third-Body Reaction . 105 B.3 Pressure-Dependent Reaction . 105 B.3.1 Unimolecular/Recombination Fall-Off Reactions . 105 B.3.1.1 Lindemann formulation . 106 B.3.1.2 Troe formulation . 106 B.3.1.3 SRI formulation . 107 B.3.2 Chemically Activated Bimolecular Reactions . 107 Bibliography 108 iii Abstract Combustion plays an important role in many practical engineering applications such as industrial furnaces, internal combustion engines and power trains, jet engines, and power plants. Today it has become vital for further environmentally responsible de- velopment of such combustion processes { e.g., for decreasing further the formation of pollutants in and hence the emission of pollutants from these processes { that engineers and scientists have available powerful chemistry models that they can employ in spa- tially and physically realistic and hence complex numerical simulations. To this end, realistic but computationally manageable chemistry models are required. The present thesis makes a contribution in this respect. Specifically, the thesis is concerned with the development of chemical reaction mechanisms for use in CFD codes that are powerful in the sense that they mimic combustion chemistry accurately but at the same time are efficient and hence affordable in terms of computational costs. The key results obtained in the research work for the present thesis include the deriva- tion of reduced chemistry models for non-premixed combustion of hydrocarbon fuels in pure oxygen rather than air, and the development of computer tools, or methods, that make that derivation possible in an efficient manner. Specifically, a new method for reaction elimination from detailed mechanisms is developed. The results obtained with the new method, combined with traditional methods, include powerful detailed reaction mechanisms for non-premixed oxyfuel combustion and even shorter, and hence ideal for CFD applications, reduced mechanisms consisting only of 11 global reactions steps. It is shown that with the reduced mechanisms developed in the present thesis non-premixed laminar flame structures are predicted that in detail and accuracy are comparable to truly detailed { but due to their shear size not CFD-capable { mecha- nisms of elementary reactions. iv Acknowledgments Fisrt and foremost, I sincerely thank my supervisor Prof. Dr-Ing. B. Rogg for his in- sightful comments, constructive feedback and recommendations throughout the present thesis. In addition, thank you Dear Prof. Rogg for the help provided beyond the aca- demic context. I am deeply indebted to Prof. Dr-Ing. W. Eifler for his constant support with respect to my scholarship extension requirements. Thanks to all my colleagues, namely, Dr-Ing. Yin, Shaheen, Baik, Lien, Azizi and Xie of the chair of fluid mechanics at the Ruhr-University Bochum for various form of assistance and the friendly atmosphere. Special thanks to Dr-Ing. Shaheen for the useful discussions about the directed relation graph reduction method. Thanks are also due to the successive secretaries of our chair, namely Ms S. Hentrich, S. Oltersdorf and U. Boehm for the help provided with respect to administrative issues. I gratefully acknowledge the financial support of the German Academic Exchange Ser- vice (DAAD). Special thanks to a friend, namely Father G. Chumacera and my family. Specifically, I thank my mother Albertine and my sister Sidonie for their constant encouragement. Finally, my heartfelt thanks to my wife Cristelle and our children Daniel and Anaelle for their patience and their exceptional support throughout the time I spent abroad for my PhD thesis. I owe you so much. v Nomenclature Roman Symbols Ai;b pre exponential factor in forward rate constant of reaction i Ai;f pre exponential factor in forward rate constant of reaction i 3 Ck molar concentration of species k [mol/m ] cp mixture (mass-based) specic heat capacity at constant pressure [J/(kg K)] cpk specific heat capacity of species k at constant pressure [J/(kg K)] D characteristic diffusion coefficient [C.m] T Dk thermal diffusion coefficient of species k [kg/(m s)] 2 Dk mixture-averaged diffusion coefficient of species k [m /s] 2 dk dipole moment of species k [m /s] Ek error induced to global target parameters due to the elimination of the interme- diate species k from the chemical mechanism Ei;b activation energy of backward step in reaction i [J/mol] Ei;f activation energy of forward step in reaction i [J/mol] Fi error induced to global target parameters due to the elimination of reaction i from the chemical mechanism h enthalpy (mass-based) of the gas mixture [J/kg] Hk molar enthalpy of species k [J/mol] Hk molar entropy of species k [J/(mol K)] hk enthalpy (mass-based) of species k [J/kg] vi I number of reactions in the system IA;i contribution of reaction i to the production rate of species A 2 jk; jkα diffusion flux vector of species k [kg/(m s)] K number of species in the system kB Boltzmann constant Kc;i equilibrium constant in concentration units for reaction i [depends on reaction] ki;b backward rate constant of reaction i [depends on reaction] ki;f forward rate constant of reaction i [depends on reaction] 3 Kp;i equilibrium constant in pressure units for reaction i [mol/cm ] Lek Lewis number of species k LeZ Lewis number of the mixture fraction [M] total molar concentration of a mixture [depends on reaction] mk mass of the molecule [kg] 3 !i rate of reaction i [mol/(cm s)] p pressure [Pa] Pr constant Prandtl number q; qα heat ux vector [W/m] Vk;Vkα diffusion velocity vector of species k [m/s] R Universal gas constant [J/(kmol K)] Rc Universal gas constant, in same units as activation energy [J/(kmol K] rAB measure for the deviation of the rate of production of species A if species B is removed from the chemical mechanism T temperature [K] t time [s] vii T 0 reference or standard-state temperature [K] u velocity components in the x direction [m/s] D D Vk ;Vkα mass diffusion velocity vector of species k [m/s] T D Vk ;Viα thermal diffusion velocity vector of species k [m/s] v velocity components in the y direction [m/s] W molecular weight (molar mass) of the mixture [kg/mol] Wk molecular weight (molar mass)of species k [kg/mol] x spatial coordinate [m] Xk mole fraction of species k y spatial coordinate
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