Predicting cell size from chemical kinetics calculations is based on the concept of the finite reaction-zone thickness of a detonation wave. Historically, the relationship between reaction zone thickness and cell size has often been taken to be a simple linear proportionality [Westbrook and Urtiew (1983)], although this is valid only within limited ranges of conditions. An empirically based extension of this theory suggests that the ratio of cell size to reaction zone thickness is a function of equivalence ratio [Shepherd (1986)]. While this theory is more successful at describing observed trends, it is still limited to specific mixtures and conditions, and does not address the functional form of the relationship.
Two steps are critical in developing reliable predictions of cell size from chemical kinetics calculations: 1) developing a validated reaction mechanism for the compositions of interest, and 2) correlating the computed reaction zone lengths to the cell size. Our validation testing is described in Section 3.1 and the correlations are presented in Sections 3.2 and 3.3.
For this report, two classes of chemical kinetics calculations were performed: constant volume explosion, and one-dimensional steady flow. In addition, purely equilibrium calculations were performed with a thermochemical solver (STANJAN, [Reynolds (1986)]). Numerically, the kinetics calculations consist of integrating forward in time the appropriate ordinary differential equations. The initial conditions were obtained by using STANJAN to solve the frozen shock jump conditions.
Reaction rate and property calculations were performed with the Sandia gas phase chemical kinetics subroutine library [Kee et al. (1989)]. The primary limitation on the accuracy of these calculations is the reaction mechanism and rate constants. We tested several different published mechanisms as part of our study. Thermodynamic data for all kinetics calculations were taken from the thermodynamic database distributed with the Sandia chemical kinetics package. The thermodynamic database distributed with the GRI mechanism [Frenklach et al. (1995)] was not used except where data were not available in the Sandia database.
Modeling of finite-rate chemical reactions is a standard practice, but compiling a list of the relevant elementary reactions and corresponding rate parameters is still a challenge for novel mixtures. Much published work in this area is aimed at finding the most important elementary reactions and parameters to allow stripped down or reduced (and therefore computationally faster) mechanisms to yield accurate solutions. This is generally successful only for simple reactions and within limited ranges of conditions. Since our mixtures of interest involve many reactants, we are focusing on comprehensive, rather than fast, mechanisms. The mechanisms listed in Appendix E have been selected to be as comprehensive as possible. For calculations that do not use some of the reactions in these mechanisms, the unnecessary reactions can be removed to reduce solution time.
Furthermore, while there are mechanisms available containing all the elementary reactions we need, they are tuned for conditions quite different from ours. Namely, atmospheric flame modeling is more common than detonation modeling, and hydrocarbon combustion in air is far more studied than oxidation of NH3 or by N2O.
The reactions of interest in this study involve the oxidation of H2, CH4, and NH3 by N2O and air. The chemistry of the individual fuel-oxidizer combinations have been studied and reported in some detail in the literature, but few studies are available with combinations of these fuels and oxidizers. The number of relevant studies is further reduced by the limited conditions considered in each. Generally, mechanisms can be built and expanded from the simpler and better understood reactions to the more complicated systems of interest. However, an assembly of simpler mechanisms may omit reactions that are not important in the constituent mechanisms but that become important in the mixture. Also, some reactions may proceed through various sequences of elementary reactions, and the importance of each path may vary with the addition of other reactants. A mechanism that successfully models a simple mixture while ignoring certain routes will perform poorly when those routes become important.