Chemical kinetics uncertainty quantification on the dynamic detonation parameters for hydrogen–air mixtures

Abstract

This study aims at (i) presenting detail reaction kinetics and corresponding reduced model which include nitrogen species chemistry for conditions relevant to H${}_2$-air detonations, (ii) based on the obtained kinetics, conducting the quantification of the uncertainty induced by the uncertainty of the rate constants on the dynamic detonation parameters (DDP) predicted using various semi-empirical and theoretical models, and (iii) investigating the impact of the induction length uncertainty on the 2-D detonation simulations. To achieve the first goal, a total of 72 detailed reaction models were compiled and quantitatively evaluated based on (a) shock tube ignition delay-time ($\tau$) data under detonation-relevant conditions in H${}_2$-O${}_2$-diluent(-nitrogen oxide) mixtures, and (b) DDP data. The two evaluation approaches lead to the selection of two different reaction models. For both selected mechanisms, a Monte Carlo method was adopted to statistically identify the uncertainty on the dynamic detonation parameters induced by the uncertainty of rate constants. Reactions R1: H+O${}_2$=OH +O and R2: H+O${}_2$(+M)=HO${}_2$(+M) were shown to induce the largest uncertainty on the predicted DDP for initial conditions of 300 K and 101 kPa. Furthermore, the uncertainty bands of cell size for a range of equivalence ratios obtained by perturbing R1 and R2 were illustrated. The distribution type of the DDP induced by sampling the rate constant $k$ was investigated. To estimate the maximum possible uncertainty of cell size induced from rate constants, two extreme mechanisms were developed by perturbing the rate constants to their 3$\sigma$ limits. For a stoichiometric mixture, these extreme mechanisms present a variation of the induction zone length by a factor of 15, which results in a change in the predicted cell size by 10.7 times. The difference in cell size can be even larger for off-stoichiometric mixtures. Concerning the third goal of the current study, we varied the rate constant of H+O${}_2$=H+OH, the most sensitive reaction for the induction length, to its 3$\sigma$ limits to study the corresponding influence in 2-D unsteady simulations characteristics, i.e., soot foil, shock velocity profile, and temperature field, for a stoichiometric hydrogen–air mixture. A reduced mechanism was developed based on the selected kinetics to minimize the computational cost related to 2-D simulations. An average cell size 2.08 times larger was obtained when using the model with the -3$\sigma$ perturbation on R1 rather than when using the model with the +3$\sigma$ perturbation. Our results demonstrate that the uncertainties on the rate constants constitute an essential aspect to consider for DDP prediction and cell size prediction in 2-D unsteady simulation.

Novelty and significance Statement

1. Two detailed reaction models with nitrogen-species chemistry were selected using a very wide range of conditions. 2. A reduced reaction model was developed for detonation relevant conditions. 3. The first uncertainty quantification study under detonation-relevant conditions was performed. 4. The effect of the rate constant uncertainty of H+O${}_2$=H+OH, the most sensitive reaction for the induction length, in 2-D simulations was determined. 5. The uncertainty on chemical kinetics is of primary importance for detonation modeling.