Information-Driven Design for Shock Tube / Laser Absorption Studies of Fundamental Rate Constants in Combustion, with Application to Methanol Pyrolysis

Abstract

Shock tube experiments, paired with precision laser diagnostics, are ideal venues to provide kinetics data critically needed for the development, validation and optimization of modern combustion kinetics models. However, to design sensitive, accurate, feasible and information-rich experiments that may yield such data often requires sophisticated planning. This study presents a mathematical framework and quantitative approach to guide such experimental design, namely a method to pin-point the optimal conditions for specific experimentation under realistic constraints of the shock tubes and diagnostic tools involved. For demonstration purpose, the current work is focused on a key type of shock tube kinetic experiments -- direct determination of fundamental reaction rate constants. Specifically, this study utilizes a Bayesian approach to maximize the prior-posterior gain in Shannon information of the rate constants to be inferred from the intended experiment. Example application of this method to the experimental determination of the CH$_3$OH + H (k$_1$) and CH$_2$O + H (k$_2$) rate constants is demonstrated in shock tube/laser absorption studies of the CH$_3$OH pyrolysis system, yielding new recommended rate constant expressions (over 1287 K - 1537 K) as: k$_1$ = $ 2.50 \times 10^6 (T/K)^{2.35} exp(-2975 K /T) \, cm^3mol^{-1}s^{-1} \pm 11.4\%$ and k$_2$ = $7.06 \times 10^7 (T/K)^{1.9} exp(-1380 K/T) \, cm^3mol^{-1}s^{-1} \pm 9.7 \%$. Potential extension to other types of kinetic studies, e.g. prediction of combustion benchmarks such as ignition delay times and species yields, and global uncertainty minimization of generic reaction models, are also briefly discussed.