Non-uniform ignition behind a reflected shock and its influence on ignition delay measured in a shock tube

Accurate measurement of ignition delay in a shock tube is extremely important for developing chemical mechanisms of different fuels. In ideal shock-tube experiments, the test gas behind the reflected shock is expected to ignite uniformly. However, in practical shock-tube experiments, non-uniform ignition occurs due to different factors such as boundary layer growth and boundary layer-reflected shock interaction. Such non-uniform ignition greatly complicates the interpretation of measurements and affects the accuracy of ignition delay measurement. Even without boundary layer and multi-dimensional effects, non-uniform ignition can still happen since the reflected shock itself can induce the spatial gradient of ignition delay. This was first studied numerically by Melguizo-Gavilanes and Bauwens (Shock Waves 23(3):221-231, 2013) using a simplified three-step chemical mechanism. They found that non-uniform ignition can greatly affect the determination of ignition delay in a shock tube. As an extension of Melguizo-Gavilanes and Bauwens' work, in the present study we conduct simulations considering detailed chemistry for two fuels, hydrogen and n-heptane, without and with low-temperature chemistry. Moreover, the detonation development for different mixtures is interpreted through comparing the local sound speed and reaction front propagation speed. The ignition delay recorded at different positions away from the end wall is compared to that in a homogeneous system. A large deviation in ignition delay is observed. The deviation is shown to change linearly with the distance away from the end wall, and a correlation is proposed to accurately describe such deviations.