A trapped vortex combustor for use in a gas turbine engine includes an outer vortex chamber wall and a dome attached to, or formed integrally with, the outer vortex chamber wall. The dome, the outer vortex chamber wall, or both define at least in part an outer trapped vortex chamber and a channel. The channel extends along the circumferential direction at a forward end of the outer vortex chamber wall, the channel configured to receive an airflow through or around the outer vortex chamber wall, the dome, or both and provide such airflow as a continuous annular airflow to the inner surface of the outer vortex chamber wall. The dome further defines a fuel nozzle opening, with all openings in the dome outward of the fuel nozzle opening along the radial direction, excepting any effusion cooling holes having a diameter less than about 0.035 inches, being in airflow communication with the channel.