The rotating detonation wave (RDW) propagation processes and influence factors are simulated in the plane-radial structure. The effects of inner radii of curvature, domain widths and stagnation pressures on propagation mode are studied. The RDW is initiated, and two kinds of propagation mode are obtained and analyzed. The flow field structure, parameters variation and influence factors on unstable propagation mode are explored in depth, and the geometrical and injection conditions of the unstable propagation are obtained. Results indicate that the decoupling and re-initiation occur repeatedly during the unstable propagation mode of the RDW, and the angular velocities of leading shock wave vary accordingly. When the domain width remains constant, the range of stagnation pressure under unstable propagation mode increases as the inner radius increases. But the RDW propagates steadily when the inner radius increases to a certain value (Larger than 40 mm in this study). The effect of curvature radius and initial pressure ahead of detonation wave on the unstable propagation mode in this calculation model is similar to that in a curved channel. When r(i) +0.464p(a) > 80.932 or r(i) >= 40 mm, the detonation wave can propagate steadily in the annular domain. When the curvature radius remains constant, the stagnation-pressure range of the unstable propagation mode decreases as the domain width increases. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.