Numerical Technique

The numerical model used to simulate the shock tube data is an adiabatic, constant-volume process with finite rate chemical kinetics. The initial conditions are the pre-shock chemical concentrations and the post-shock thermal conditions. This model isolates the chemical kinetics from fluid dynamical considerations. The appropriateness of the constant volume approximation is limited to reflected shock experiments and compositions with small heat release (effectively high dilution). Another limitation of the constant-volume analysis is that the fluid between the reflected shock and the endwall can be nonuniform due to shock-wave boundary layer interaction [Bradley (1962)]. Neither of these effects are considered in the present study.

Some published mechanisms specify pressure fall-off relations that are not standard within the Sandia package [Kee et al. (1989)]. In some cases, the published relation is found to be a special case of a Sandia relation, but in others, an approximation is the best that can be achieved. In the Sandia package, the rate constant for a reaction that includes fall-off effects is given by a function that blends a low pressure limit to a high pressure limit:

$$k = k_\infty\left(\frac{P_r}{1+P_r}\right)F$$

where

$$P_r = \frac{k_0[M]}{k_\infty}$$

The Lindemann form results when F is unity, and the code then requires 6 rate parameters - three for the low pressure limit and three for the high pressure limit. In the Troe form, F is a function of P_r and F_cent, where

$$F_{cent} = (1-a)\exp\left(-\frac{T}{T^{***}}\right)+a\exp\left( -\frac{T}{T^*}\right)+\exp\left(-\frac{T^{**}}{T}\right)$$

and the code then uses the four additional parameters a, T^***, T^*, and T^**, where T^** is optional. In the SRI form, Fis a function of P_r and 5 additional parameters:

$$F = \left[a\exp\left(\frac{-b}{T}\right)+\exp\left(\frac{-T}{c}\right) \right]^XdT^e$$

$$X = \frac{1}{1+\log^2P_r}$$

Where fall-off relations are specified in a published mechanism but are not standard relations in the Sandia code, approximations have been made (see Appendix E).