Two-dimensional numerical simulations of rotating detonation engine are carried out with detailed chemical kinetic mechanism using detoFoam, a custom solver based on OpenFOAM7. The results show the transition process from single wave with counter-rotating components mode to two counter-rotating waves at equal speed mode. Counter-rotating components are weak waves propagating in the opposite direction against the primary detonation wave. The mechanism behind the transition process is that the counter-rotating components gain energy from collisions with detonation waves and the fresh gas region. When counter-rotating components gain more energy than they lose in one cycle, they become stronger until the peak pressure reaches a threshold value. When a counter-rotating component is strong enough, its collision with fresh gas region will ignite a detonation wave, breaking the steady state. The new detonation wave propagates in the opposite direction against the original detonation wave, leading to the formation of two counter-rotating detonation waves. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.