Analysis of the spatio-temporal scales of laminar premixed flames near equilibrium

References

• Sportisse , B. 2000 . An analysis of operator splitting techniques in the stiff case . J. Comput. Phys. , 161 : 140 – 168 . doi: 10.1006/jcph.2000.6495
   Web of Science ®Google Scholar
• Ropp , D. L. , Shadid , J. N. and Ober , C. C. 2004 . Studies of the accuracy of time integration methods for reaction–diffusion equations . J. Comput. Phys. , 194 : 544 – 574 . doi: 10.1016/j.jcp.2003.08.033
   Web of Science ®Google Scholar
• Hundsdorfer , W. and Verwer , J. G. 2003 . Numerical Solution of Time-Dependent Advection–Reaction–Diffusion Equations , Berlin : Springer-Verlag .
   Google Scholar
• Peletier , M.A. , Savare , G. and Veneroni , M. 2012 . Chemical reactions as Γ-limit of diffusion . SIAM Rev. , 54 : 327 – 352 . doi: 10.1137/110858781
   Web of Science ®Google Scholar
• Al-Khateeb , A. N. , Powers , J. M. and Paolucci , S. 2010 . On the necessary grid resolution for verified calculation of premixed laminar flames . Commun. Comput. Phys. , 8 : 304 – 326 .
   Web of Science ®Google Scholar
• Lu , T. F. , Yoo , C. S. , Chen , J. H. and Law , C. K. 2010 . Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis . J. Fluid Mech. , 652 : 45 – 64 . doi: 10.1017/S002211201000039X
   Web of Science ®Google Scholar
• Ziegler , J. L. , Deiterding , R. , Shepherd , J. E. and Pullin , D. I. 2011 . An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry . J. Comput. Phys. , 230 : 7598 – 7630 . doi: 10.1016/j.jcp.2011.06.016
   Web of Science ®Google Scholar
• Martelli , E. , Valorani , M. , Paolucci , S. and Zikoski , Z. 2012 . Numerical simulation of edge flames initiation and propagation using an adaptive wavelet collocation method . Proc. Combust. Inst. , 34 Proceedings of the Combustion Institute 34 (2013) doi: 10.1016/j.proci.2012.06.139
   Google Scholar
• Sharpe , G. J. and Falle , S.A.E.G. 2011 . Numerical simulations of premixed flame cellular instability for a simple chain-branching model . Combust. Flame , 158 : 925 – 934 . doi: 10.1016/j.combustflame.2011.01.026
   Web of Science ®Google Scholar
• Al-Khateeb , A.N. and Powers , J.M. “ Analysis of the reaction–advection–diffusion spectrum of laminar premixed flames ” . In 48th AIAA Aerospace Sciences Meeting , Orlando , FL : 4–7 January 2010 . AIAA 2010-0954.
   Google Scholar
• Landau , L.D. and Lifshitz , E.M. 1959 . Fluid Mechanics , 475 London : Pergamon Press .
   Google Scholar
• Al-Khateeb , A. N. 2010 . Fine scale phenomena in reacting systems: identification and analysis for their reduction , Dame , IN : Ph.D. diss. University of Notre .
   Google Scholar
• Paolucci , S. 1982 . On the filtering of sound from the Navier–Stokes equations , Livermore, CA : Rep. SAND82-8257 Sandia National Laboratories .
   Google Scholar
• Maas , U. and Pope , S. B. 1992 . Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space . Combust. Flame , 88 : 239 – 264 . doi: 10.1016/0010-2180(92)90034-M
   Web of Science ®Google Scholar
• Warnatz , J. , Maas , U. and Dibble , R. W. 1996 . Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation , Berlin , , Germany : Springer-Verlag .
   Google Scholar
• Lam , S. H. and Goussis , D. A. 1988 . Understanding complex chemical kinetics with computational singular perturbation . Proc. Combust. Inst. , 22 : 931 – 941 .
   Google Scholar
• Al-Khateeb , A. N. , Powers , J. M. , Paolucci , S. , Sommese , A. J. , Diller , J. A. , Hauenstein , J. D. and Mengers , J. D. 2009 . One-dimensional slow invariant manifolds for spatially homogenous reactive systems . J. Chem. Phys. , 131 : 024118 doi: 10.1063/1.3171613
   Web of Science ®Google Scholar
• Kee , R. J. , Coltrin , M. E. and Glarborg , P. 2003 . Chemically Reactive Flow: Theory and Practice , Hoboken , NJ : Wiley .
   Google Scholar
• Smooke , M. D. , Miller , J. A. and Kee , R. J. 1983 . Determination of adiabatic flame speeds by boundary value methods . Combust. Sci. Technol. , 34 : 79 – 90 . doi: 10.1080/00102208308923688
   Web of Science ®Google Scholar
• Hirschfelder , J. O. , Curtiss , C. F. and Campbell , D. E. 1953 . The theory of flame propagation. IV . J. Phys. Chem. , 57 : 403 – 414 . doi: 10.1021/j150505a004
   Web of Science ®Google Scholar
• Kee , R. J. , Grcar , J. F. , Smooke , M. D. and Miller , J. A. 1992 . A FORTRAN program for modeling steady laminar one dimensional premixed flames , CA : Rep. SAND85-8240 Sandia National Laboratories, Livermore .
   Google Scholar
• Kirkby , L. L. and Schmitz , R. A. 1966 . An analytical study of stability of a laminar diffusion flame . Combust. Flame , 10 : 205 – 220 . doi: 10.1016/0010-2180(66)90077-0
   Web of Science ®Google Scholar
• Sharpe , G. J. 2003 . Linear stability of planar premixed flames: reactive Navier–Stokes equations with finite activation energy and arbitrary Lewis number . Combust. Theory Model. , 7 : 45 – 65 . doi: 10.1088/1364-7830/7/1/303
   Web of Science ®Google Scholar
• Golub , G. H. and Van Loan , C. F. 1983 . Matrix Computations , Baltimore , MD : Johns Hopkins University Press .
   Google Scholar
• Kee , R. J. , Rupley , F. M. and Miller , J. A. 1992 . CHEMKIN-II: a FORTRAN chemical kinetics package for the analysis of gas phase chemical kinetics , Livermore, CA : Rep. SAND89-8009B Sandia National Laboratories .
   Google Scholar
• Kee , R. J. , Dixon-Lewis , G. , Warnatz , J. , Coltrin , M. E. and Miller , J. A. 1991 . A FORTRAN computer code package for the evaluation of gas-phase multicomponent transport properties , Livermore, CA : Rep. SAND86-8246 Sandia National Laboratories .
   Google Scholar
• Kee , R. J. , Rupley , F. M. and Miller , J. A. 1992 . The CHEMKIN thermodynamic data base , Livermore, CA : Rep. SAND87-8215B Sandia National Laboratories .
   Google Scholar
• Miller , J. A. , Mitchell , R. E. , Smooke , M. D. and Kee , R. J. 1982 . Toward a comprehensive chemical kinetic mechanism for the oxidation of acetylene: comparison of model predictions with results from flame and shock tube experiments . Proc. Combust. Inst. , 19 : 181 – 196 .
   Google Scholar
• Dabireau , F. , Cuenot , B. , Vermorel , O. and Poinsot , T. 2003 . Interactions of flames of H2+O2 with inert walls . Combust. Flame , 135 : 123 – 133 . doi: 10.1016/S0010-2180(03)00154-8
   Web of Science ®Google Scholar
• Powers , J. M. and Paolucci , S. 2005 . Accurate spatial resolution estimates for reactive supersonic flow with detailed chemistry . AIAA J. , 43 : 1088 – 1099 . doi: 10.2514/1.11641
   Google Scholar
• Hindmarsh , A. C. 1983 . “ ODEPACK, a systematized collection of ODE solvers ” . In Scientific Computing , Edited by: Stepleman , R. S. 55 – 64 . Amsterdam , , The Netherlands : North-Holland .
   Google Scholar
• Mazaheri , K. , Mahmoudi , Y. and Radulescu , M.I. 2012 . Diffusion and hydrodynamic instabilities in gaseous detonations . Combust. Flame 159 , : 2138 – 2154 . doi: 10.1016/j.combustflame.2012.01.024
   Google Scholar
• Baulch , D. L. , Bowman , C. T. , Cobos , C. J. , Cox , R. A. , Just , T. , Kerr , J. A. , Pilling , M. J. , Stocker , D. , Troe , J. , Tsang , W. , Walker , R. W. and Warnatz , J. 2005 . Evaluated kinetic data for combustion modeling: supplement II . J. Phys. Chem. Ref. Data , 34 : 757 – 1357 . doi: 10.1063/1.1748524
   Web of Science ®Google Scholar
• Margolis , S. B. 1978 . Time-dependent solution of a premixed laminar flame . J. Comput. Phys. , 27 : 410 – 427 . doi: 10.1016/0021-9991(78)90018-9
   Web of Science ®Google Scholar
• Singh , S. , Powers , J. M. and Paolucci , S. 2002 . On slow manifolds of chemically reactive systems . J. Chem. Phys. , 117 : 1482 – 1496 . doi: 10.1063/1.1485959
   Web of Science ®Google Scholar
• Heimerl , J.M. and Coffee , T.P. 1980 . The detailed modeling of premixed, laminar steady-state flames. I. Ozone . Combust. Flame 39 , : 301 – 315 . doi: 10.1016/0010-2180(80)90026-7
   Google Scholar
• Maas , U. , Raffel , B. , Wolfrum , J. and Warnatz , J. 1986 . Observation and simulation of laser induced ignition processes in O2–O3 and H2+O2 mixtures . Proc. Combust. Inst. 21 , : 1869 – 1876 .
   Google Scholar