The present work is devoted to the 2D simulation of a point-to-plane Atmospheric Corona Discharge Reactor (ACDR) powered by a DC high voltage supply. The corona reactor is periodically crossed by thin mono filamentary streamers with a natural repetition frequency of some tens of kHz. The present study compares the results obtained in dry air and with a small amount of water vapour. The simulation involves the electro-dynamics, chemical kinetic and neutral gas hydrodynamic phenomena that influence the kinetics of the chemical species transformation. Each discharge stage lasts about one hundred of nanoseconds while the post-discharge stage occurring between two successive discharge phases lasts one hundred of microseconds. The ACDR is crossed by a lateral dry or humid air flow initially polluted with 400 ppm of NO.