Abstract:

Sensitivity analysis is an important tool in model validation and evaluation that has been employed extensively in the analysis of chemical kinetic models of combustion processes. The input parameters of a chemical kinetic model are always associated with some uncertainties, and the effects of these uncertainties on the predicted combustion properties can be determined through sensitivity analysis. In this work, first- and second-order global and local sensitivity coefficients of ignition delay time with respect to the scaling factor for reaction rate constants in chemical kinetic mechanisms for combustion of H₂, methane, n-butane, and n-heptane are examined. In the sensitivity analysis performed here, the output of the model is taken to be natural logarithm of ignition delay time and the input parameters are the natural logarithms of the factors that scale the reaction rate constants. The output of the model is expressed as a polynomial function of the input parameters, with up to coupling between two input parameters in the present sensitivity analysis. This polynomial function is determined by varying one or two input parameters, and allows the determination of both local and global sensitivity coefficients. The order of the polynomial function in the present work is four, and the factor that scales the reaction rate constant is in the range from 1/e to e, where e is the base of the natural logarithm. A relatively small number of sample runs are required in this approach compared to the global sensitivity analysis based on the highly dimensional model representation method, which utilizes random sampling of input (RS-HDMR). In RS-HDMR, sensitivity coefficients are determined only for the rate constants of a limited number of reactions; the present approach, by contrast, affords sensitivity coefficients for a larger number of reactions. Reactions and reaction pairs with the largest sensitivity coefficients are listed for ignition delay times of four typical fuels. Global sensitivity coefficients are always positive, while local sensitivity coefficients can be either positive or negative. A negative local sensitivity coefficient indicates that the reaction promotes ignition, while a positive local sensitivity coefficient suggests that the reaction actually suppresses ignition. Our results show that important reactions or reaction pairs identified by global sensitivity analysis are usually rather similar to those based on local sensitivity analysis. This finding can probably be attributed to the fact that the values of input parameters are within a rather small range in the sensitivity analysis, and nonlinear effects for such a small range of parameters are negligible. It is possible to determine global sensitivity coefficients by varying the input parameters over a larger range using the present approach. Such analysis shows that correlation effects between an important reaction and a minor reaction can have relatively sizable second-order sensitivity coefficient in some cases. On the other hand, first-order global sensitivity coefficients in the present approach will be affected by coupling between two reactions, and some results of the first-order global sensitivity analysis will be different from those determined by local sensitivity analysis or global sensitivity analysis under conditions where the correlation effects of two reactions are neglected. The present sensitivity analysis approach provides valuable information on important reactions as well as correlated effects of two reactions on the combustion characteristics of a chemical kinetic mechanism. In addition, the analysis can also be employed to aid global sensitivity analysis using RS-HDMR, where global sensitivity coefficients are determined more reliably.

Key words: Global sensitivity analysis, Local sensitivity analysis, Ignition delay time, Chemical mechanism for combustion