Investigation of the injection pressure impact on non-monotonic two-stage ignition delay of diesel engines under cold-start

•Simultaneous Shadowgraphy and high-speed natural luminosity methods are applied to investigate the ignition process of the fuel spray.•Increased injection pressure causes reduced low-temperature ignition delay and prolonged cool flame propagation time.•The combination of the two-stage ignition delay results in the non-monotonic trend of high-temperature ignition delay under a cold start.•An analytical model is established to quantitative explain the non-monotonic trend.