Uncertainty-quantification analysis of the effects of residual impurities on hydrogen–oxygen ignition in shock tubes

Abstract

This study addresses the influences of residual radical impurities on the computation and experimental determination of ignition times in H2/O2 mixtures. Particular emphasis is made on the often-times encountered problem of the presence of H-atoms in the initial composition of H2/O2 mixtures in shock tubes. Two methods are proposed for quantifying experimentally H-residual impurities in shock tubes, namely, an a priori method that consists of detecting OH traces upon shocking unfueled mixtures, and a posteriori method in which the amount of impurities is inferred by comparing fueled experimental autoignition data with calculations. A stochastic Arrhenius model that describes the amount of H-radical impurities in shock tubes is proposed on the basis of experimental measurements as a function of the test temperature. It is suggested that this statistical model yields a probability density function for the residual concentration of hydrogen radicals in standard shock tubes. Theoretical quantifications of the uncertainties induced by the impurities on autoignition times are provided by using the 5-step short chemistry of Del Álamo et al. [1]. The analysis shows that the relative effects of H-impurities on delay times above crossover become more important as the dilution increases and as the temperature and pressure decrease. Below crossover, the effects of H-impurities on the ignition delay vanish rapidly, and are negligible compared to the departures produced by the non-ideal pressure rise that is seen in some shock-tube experiments at such low temperatures. The influences of kinetic uncertainties on the ignition time are typically negligible compared to the effects of the uncertainties induced by H-impurities when the short mechanism is used, except for air at high temperatures for which kinetic uncertainties dominate. Furthermore, calculations performed with the short mechanism show that correlations between the uncertainties in the rates of branching and termination steps have only some small influences on the ignition-time variabilities near crossover, where a global sensitivity analysis shows an increasing importance of the recombining kinetics. Computational quantifications of uncertainties are carried out by using numerical simulations of homogeneous ignition subject to Monte-Carlo sampling of the concentration of impurities. For the conditions analyzed, these computations show that the variabilities produced in ignition delays by the uncertainties in H-impurities are comparable to the experimental data scatter and to the effects of typical uncertainties of the test temperature when the Stanford chemical mechanism [2] is used. The calculations also unveil that the utilization of two other different chemical mechanisms, namely San Diego [3] and GRI v3.0 [4], yields variations in the ignition delays which are within the range of the uncertainties induced by the H-impurities. Finally, the effects of residual impurities in kinetic-isolation experiments and in supersonic-combustion ramjets are briefly discussed.