Some interpretive aspects of elementary sensitivity gradients in combustion kinetics modeling

Abstract The applications of sensitivity analysis by gradient techniques to study detailed combustion chemistry will soon become more common as a result of the recent availability of increasingly efficient computer codes. This paper provides a compendium of the various uses and interpretive aspects of sensitivity gradient techniques applied to chemical kinetics. Illustrations are provided through analysis of the frequently studied elementary kinetic mechanism for the CO/H 2 O/O 2 system. Elementary first and second order sensitivity coefficients, obtained by the Green's function method, are interpreted and discussed in detail for a fuel lean and dilute system reacting in N 2 at 1100K and 1 atm. From the results of linear sensitivities, the effects of variations in initial conditions and uncertainties in rate constants and equilibrium constants on the model predictions are determined. Second order sensitivities are shown to yield valuable information on how these linear sensitivities vary when an initial condition or rate constant is varied. Elements of the Green's function matrix are shown to have a memory function interpretation, and results of small perturbations in each species concentration at various times during the kinetics on all other species concentrations at later times are presented. These latter sensitivities are unique in that they, in principle, are measurable in the laboratory. The results of feature sensitivity analysis (i.e., the effects of variations in input parameters on specific kinetic predictions, such as induction and kinetic periods) are presented for a wide range of equivalence ratios. Finally, elementary sensitivity analysis is shown to be extremely useful in experimental design as well as model development and evaluation.

[1]  M. Kramer,et al.  Sensitivity Analysis in Chemical Kinetics , 1983 .

[2]  Eugene P. Dougherty,et al.  Further developments and applications of the Green’s function method of sensitivity analysis in chemical kinetics , 1979 .

[3]  Herschel Rabitz,et al.  Chemical sensitivity analysis theory with applications to molecular dynamics and kinetics , 1981, Comput. Chem..

[4]  C. M. Lund,et al.  A numerical model of chemical kinetics of combustion in a turbulent flow reactor , 1977 .

[5]  W. C. Gardiner,et al.  An evaluation of methane combustion mechanisms , 1977 .

[6]  Metin Demiralp,et al.  Chemical kinetic functional sensitivity analysis: Derived sensitivities and general applications , 1981 .

[7]  D. Allara,et al.  A computational analysis of the alkane pyrolysis mechanism: Sensitivity analysis of individual reaction steps , 1980 .

[8]  Richard A. Yetter,et al.  Elementary and derived sensitivity information in chemical kinetics , 1984 .

[9]  Robert J. Gelinas,et al.  Sensitivity analysis of ordinary differential equation systems—A direct method , 1976 .

[10]  C. Westbrook,et al.  Chemical kinetic modeling of hydrocarbon combustion , 1984 .

[11]  R. Stolarski,et al.  Uncertainty propagation in a stratospheric model 2. Monte Carlo analysis of imprecisions due to reaction rates , 1978 .

[12]  Joseph M. Calo,et al.  An improved computational method for sensitivity analysis: Green's function method with ‘AIM’ , 1981 .

[13]  D. Edelson.  Mechanistic details of the Belousov–Zhabotinsky oscillations IV. Sensitivity analysis , 1981 .

[14]  R. Schainker,et al.  On the statistical sensitivity analysis of models for chemical kinetics , 1975 .

[15]  J. E. Hardy,et al.  Isothermal quenching of the oxidation of wet CO , 1980 .

[16]  D. R. Stull.  JANAF thermochemical tables , 1966 .

[17]  Eugene P. Dougherty,et al.  Computational kinetics and sensitivity analysis of hydrogen–oxygen combustion , 1980 .

[18]  and W C Gardiner,et al.  Chemical Kinetics of High Temperature Combustion , 1980 .

[19]  Herschel Rabitz,et al.  The Green’s function method of sensitivity analysis in chemical kinetics , 1978 .

[20]  Metin Demiralp,et al.  Chemical kinetic functional sensitivity analysis: Elementary sensitivities , 1981 .

[21]  C. Fortuin,et al.  Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory , 1973 .