Abstract
In this chapter we present in detail the equations governing multicomponent reactive flows. The derivation of these equations from the kinetic theory of gases can be found in classical textbooks, usually for nonreactive and/or monatomic mixtures [CC70] [FK72] [WT62], and is summarized in Chapter 4 in the general situation of polyatomic reactive gas mixtures [EG94].
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References
A. Amsden, P. J. O’Rourke, and T. D. Butler, KIVA-II: A Computer Program for Chemically Reactive Flows with Sprays, Los Alamos National Laboratory Report, LA-11560-MS, May, (1989).
J. D. Anderson, Jr., Hypersonics and High Temperature Gas Dynamics, McGraw-Hill Book Company, New York, (1989).
G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, (1967).
D. L. Baulch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, T. Just, J. A. Kerr, M. J. Pilling, J. Troe, R. J. Walker, and J. Warnatz, Evaluated Kinetic Data for Combustion Modelling, J. Phys. Chem. Ref. Data, 21, (1992), pp. 411–734.
S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, Cambridge, (1970).
S. M. Candel, Mécanique des Fluides, Dunod, Paris, (1990).
G. V. Candler, J. Olejniczak, and B. Harrold, Detailed Simulation of Nitrogen Dissociation in Stagnation Regions, Phys. Fluids, 9, (1997), pp. 2108–2117.
M. Capitelli, I. Armenise, and C. Gorse, State-to-State Approach in the Kinetics of Air Components Under Re-Entry Conditions, J. Thermophys. Heat Transfer, 11, (1997), pp. 570–578.
M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J. Frurip, R. A. McDonald, and A. N. Syverud, JANAF Thermochemical Tables, Third Edition, J. Phys. Chem. Ref. Data, 14, Suppl. 1, (1985), pp. 1–1856.
G. M. Come, V. Warth, P. A. Glaude, R. Fournet, F. Battin-Leclerc, and G. Sacchi, Computer—Aided Design of Gas-Phase Oxidation Mechanisms, Application to the Modeling of n-Heptane and Iso-Octane Oxidation, 26th Symposium International on Combustion, The Combustion Institute, Pittsburgh, (1996), pp. 755–762.
C. F. Curtiss, Symmetric Gaseous Diffusion Coefficients, J.Chem. Phys., 49, (1968), pp. 2917–2919.
N. Darabiha, S. Candel, V. Giovangigli, and Smooke M., Extinction of Strained Premixed Propane-Air Flames with Complex Chemistry, Comb. Sci. Tech., 60, (1988), pp. 267–284.
G. Dixon-Lewis, Computer Modeling of Combustion Reactions in Flowing Systems with Transport, in W. C. Gardiner, Ed., Combustion Chemistry. Springer, New York, (1984), pp. 21–125.
J. P. Drumond and M. Y. Hussaini, Numerical Simulation of a Supersonic Reacting Mixing Layer, AIAA 19th Fluid Dynamics, Plasma Physics and Laser Conference, Honolulu, Hawaii, Paper AIAA-87-1325, (1987).
J. P. Drumond and H. S. Mukunda, A Numerical Study of Mixing Enhancement in Supersonic Reacting Flow Fields, 3rd International Conference on Numerical Combustion, Sophia-Antipolis (Antibes), A. Dervieux and B. Larouturrou, Eds., Lecture Notes in Physics, Springer-Verlag, 351, (1989), pp. 36–64.
A. Ern and V. Giovangigli, Multicomponent Transport Algorithms, Lecture Notes in Physics, New Series “Monographs”, m 24, Springer-Verlag, Berlin, (1994).
A. Ern and V. Giovangigli, Fast and Accurate Multicomponent Property Evaluations, J. Comp. Phys., 120, (1995), pp. 105–116.
A. Ern and V. Giovangigli, The Kinetic Equilibrium Regime, Physica-A, 260, (1998), pp. 49–72.
A. Ern and V. Giovangigli Thermal Diffusion Effects in Hydrogen/Air and Methane/Air Flames, Comb. Theor. Mod., 2, (1998), pp. 349–372.
A. Ern, V. Giovangigli, and M. Smooke, Numerical Study of a Three-Dimensional Chemical Vapor Deposition Reactor with Detailed Chemistry, J. Comp. Phys., 126, (1996), pp. 21–39.
M. Feinberg, The Existence and Uniqueness of Steady States for a Class of Chemical Reaction Networks, Arkiv Rat. Mech. Anal, 132, (1995), pp. 311–370.
J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases, North Holland Publishing Company, Amsterdam, (1972).
M. Frenklach, D. W. Clary, T. Yuan, W. C. Gardiner, and S. E. Stein, Mechanism of Soot Formation in Acetylene-Oxygen Mixtures, Comb. Sci. Tech., 50, (1986), pp. 79–115.
W. C. Gardiner, Jr., Combustion Chemistry, Springer-Verlag, New York, (1984).
V. Giovangigli, Convergent Iterative Methods for Multicomponent Diffusion, IMPACT Comput. Sci. Eng., 3, (1991), pp. 244–276.
V. Giovangigli and M. Massot, Asymptotic Stability of Equilibrium States for Multicomponent Reactive Flows, Math. Mod. Meth. Appl. Sci., 8, (1998), pp. 251–297.
V. Giovangigli and M. Massot, The Local Cauchy Problem for Multicomponent Reactive Flows in Full Vibrational Nonequilibrium, Math. Meth. Appl. Sci., 21, (1998), pp. 1415–1439.
V. Giovangigli and M. Smooke, Extinction Limits of Strained Premixed Laminar Flames with Complex Chemistry, Comb. Sci. Tech., 53, (1987), pp. 23–49.
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, John Wiley & Sons, Inc., New York, (1954).
K. Kailasanath, E. S. Oran, and J. P. Boris, Numerical Simulation of Flames and Detonations, 3rd International Conference on Numerical Combustion, Sophia-Antipolis (Antibes), A. Dervieux and B. Larouturrou, Eds., Lecture Notes in Physics, Springer-Verlag, 351, (1989), pp. 82–97.
R. J. Kee, G. H. Evans, and M. E. Coltrin, Application of Supercomputers to Model Fluid Transport and Chemical Kinetics in Chemical Vapor Deposition Reactors, Supercomputer Research in Chemistry and Chemical Engineering, K. F. Jensen and D. G. Truhlar, Eds., ACS Symposium Series, 353, (1987), pp. 334–352.
R. Kubo, Statistical Mechanics, North Holland Publishing Company, Amsterdam, (1965).
B. Laboudigue, V. Giovangigli, and S. Candel, Numerical Solution of a Free-Boundary Problem in Hypersonic Flow Theory: Nonequilibrium Viscous Shock Layers, J. Comp. Phys., 102, (1992), pp. 297–309.
M. Massot, Modélisation Mathématique et Numérique de la Combustion des mélanges Gazeux, Thèse, École Polytechnique, (1996).
T. Poinsot, S. Candel, and A. Trouvé, Application of Direct Numerical Simulation to Premized Turbulent Combustion, Prog. Ener. Comb. Sci., 21, (1996), pp. 531–576.
K. F. Roenigk and K. F. Jensen, Low Pressure CVD of Silicon Nitride, J. Electrochem. Soc., 134, (1987), pp. 1777–1785.
D. E. Rosner, Transport Processes in Chemically Reacting Flow Systems, Butterworths, Boston, (1986).
L. Sainsaulieu, Equilibrium Velocity Distribution Functions for a Kinetic Model of Two-Phase Fluid Flow, Math. Mod. Meth. Appl. Sci., 5, (1995), pp. 191–211.
J. H. Scinfeld and S. N. Pandis, Atmospheric Chemistry and Physics, John Wiley & Sons, Inc., New York, (1998).
M. D. Smooke, Solution of Burner Stabilized Premixed Laminar Flames by Boundary Value Methods, J. Comp. Phys., 48, (1982), pp. 72–105.
D. R. Stull and H. Prophet, JANAF Thermochemical Tables, Second ed., Washington, NBS NSRDS-NBS37 (1971).
J. Van de Ree, On the Definition of the Diffusion Coefficients in Reacting Gases, Physica, 36, (1967), pp. 118–126.
L. Waldmann, Transporterscheinungen in Gasen von Mittlerem Druck, Handbuch der Physik, S. Flügge, Ed., 12, Springer-Verlag, Berlin, (1958), pp. 295–514.
L. Waldmann und E. Trübenbacher, Formale Kinetische Theorie von Gasgemischen aus Anregbaren Molekülen, Zeitschr. Naturforschg., 17a, (1962), pp. 363–376.
J. Warnatz, M. D. Allendorf, R. J. Kee, and M. E. Coltrin, A Model of Elementary Chemistry and Fluid Mechanics in the Combustion of Hydrogen on Platinum Surfaces, Comb. Flame, 96, (1994), pp. 393–406.
F. A. Williams, Spray Combustion and Atomization, Phys. Fluids, 1, (1958), pp. 541–545.
F. A. Williams, Combustion Theory, Second ed., The Benjamin/Cummings Publishing Company, Inc., Menlo Park, (1985).
Y. B. Zeldovitch, G. I. Barenblat, V. B. Librovitch, and G. M. Makhviladze, The Mathematical Theory of Combustion and Explosions, Consultants Bureau, New York, (1985).
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Giovangigli, V. (1999). Fundamental Equations. In: Multicomponent Flow Modeling. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1580-6_2
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DOI: https://doi.org/10.1007/978-1-4612-1580-6_2
Publisher Name: Birkhäuser, Boston, MA
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