Dynamic stiffness removal for direct numerical simulations

Abstract A systematic approach was developed to derive non-stiff reduced mechanisms for direct numerical simulations (DNS) with explicit integration solvers. The stiffness reduction was achieved through on-the-fly elimination of short time-scales induced by two features of fast chemical reactivity, namely quasi-steady-state (QSS) species and partial-equilibrium (PE) reactions. The sparse algebraic equations resulting from QSS and PE approximations were utilized such that the efficiency of the dynamic stiffness reduction is high compared with general methods of time-scale reduction based on Jacobian decomposition. Using the dimension reduction strategies developed in our previous work, a reduced mechanism with 52 species was first derived from a detailed mechanism with 561 species. The reduced mechanism was validated for ignition and extinction applications over the parameter range of equivalence ratio between 0.5 and 1.5, pressure between 10 and 50 atm, and initial temperature between 700 and 1600 K for ignition, and worst-case errors of approximately 30% were observed. The reduced mechanism with dynamic stiffness removal was then applied in homogeneous and 1-D ignition applications, as well as a 2-D direct numerical simulation of ignition with temperature inhomogeneities at constant volume with integration time-steps of 5–10 ns. The integration was numerically stable and good accuracy was achieved.

[1]  Jacqueline H. Chen,et al.  Direct numerical simulation of hydrogen-enriched lean premixed methane–air flames , 2004 .

[2]  M. Bodenstein,et al.  Eine Theorie der photochemischen Reaktionsgeschwindigkeiten , 1913 .

[3]  Habib N. Najm,et al.  Modeling unsteady reacting flow with operator splitting and ISAT , 2006 .

[4]  Tianfeng Lu,et al.  Systematic approach to obtain analytic solutions of quasi steady state species in reduced mechanisms. , 2006, The journal of physical chemistry. A.

[5]  C. Law,et al.  Complex CSP for chemistry reduction and analysis , 2001 .

[6]  N. Peters,et al.  Asymptotic structure and extinction of methaneair diffusion flames , 1988 .

[7]  Tamás Turányi,et al.  Reduction of large reaction mechanisms , 1990 .

[8]  Pierre-Alexandre Glaude,et al.  Automatic reduction of detailed mechanisms of combustion of alkanes by chemical lumping , 2000 .

[9]  Neil Shenvi,et al.  Efficient chemical kinetic modeling through neural network maps. , 2004, The Journal of chemical physics.

[10]  Zhuyin Ren,et al.  The use of slow manifolds in reactive flows , 2006 .

[11]  Zhuyin Ren,et al.  Reduced description of complex dynamics in reactive systems. , 2007, The journal of physical chemistry. A.

[12]  Habib N. Najm,et al.  An automatic procedure for the simplification of chemical kinetic mechanisms based on CSP , 2006 .

[13]  Tianfeng Lu,et al.  A criterion based on computational singular perturbation for the identification of quasi steady state species: A reduced mechanism for methane oxidation with NO chemistry , 2008 .

[14]  M. Carpenter,et al.  Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .

[15]  C. Westbrook,et al.  A Comprehensive Modeling Study of iso-Octane Oxidation , 2002 .

[16]  Michael Frenklach,et al.  Detailed reduction of reaction mechanisms for flame modeling , 1991 .

[17]  C. Sung,et al.  Augmented reduced mechanisms for NO emission in methane oxidation , 2001 .

[18]  Tianfeng Lu,et al.  Diffusion coefficient reduction through species bundling , 2007 .

[19]  Habib N. Najm,et al.  A CSP and tabulation-based adaptive chemistry model , 2007 .

[20]  S. Lam,et al.  The CSP method for simplifying kinetics , 1994 .

[21]  S. H. Lam,et al.  Using CSP to Understand Complex Chemical Kinetics , 1993 .

[22]  Harsha K. Chelliah,et al.  Explicit reduced reaction models for ignition, flame propagation, and extinction of C2H4/CH4/H2 and air systems , 2007 .

[23]  H. Pitsch,et al.  An efficient error-propagation-based reduction method for large chemical kinetic mechanisms , 2008 .

[24]  Forman A. Williams,et al.  The asymptotic structure of stoichiometric methaneair flames , 1987 .

[25]  Ramanan Sankaran,et al.  Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: flame stabilization and structure , 2009, Journal of Fluid Mechanics.

[26]  C. Westbrook,et al.  A Comprehensive Modeling Study of n-Heptane Oxidation , 1998 .

[27]  H. Im,et al.  Direct numerical simulation of ignition front propagation in a constant volume with temperature inhomogeneities: I. Fundamental analysis and diagnostics , 2006 .

[28]  Philippe Pierre Pebay,et al.  Direct numerical simulation of ignition front propagation in a constant volume with temperature inhomogeneities. II. Parametric study , 2006 .

[29]  M. Carpenter,et al.  Several new numerical methods for compressible shear-layer simulations , 1994 .

[30]  Herschel Rabitz,et al.  A general analysis of exact lumping in chemical kinetics , 1989 .

[31]  Tianfeng Lu,et al.  Strategies for mechanism reduction for large hydrocarbons: n-heptane , 2008 .

[32]  Ulrich Maas,et al.  Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space , 1992 .

[33]  S. H. Lam,et al.  REDUCED CHEMISTRY-DIFFUSION COUPLING , 2007 .

[34]  Bruno Sportisse,et al.  Reduction of chemical kinectics in air pollution modeling , 2000 .

[35]  D. Chapman,et al.  LV.—The interaction of chlorine and hydrogen. The influence of mass , 1913 .

[36]  Epaminondas Mastorakos,et al.  An algorithm for the construction of global reduced mechanisms with CSP data , 1999 .

[37]  Jacqueline H. Chen,et al.  Three-dimensional direct numerical simulation of soot formation and transport in a temporally evolving nonpremixed ethylene jet flame , 2008 .

[38]  Tianfeng Lu,et al.  Linear time reduction of large kinetic mechanisms with directed relation graph: N-Heptane and iso-octane , 2006 .

[39]  Habib N. Najm,et al.  Regular Article: A Semi-implicit Numerical Scheme for Reacting Flow , 1999 .