A self-cooled orifice structure, that may be for a combustor of a gas turbine engine includes a hot side panel, a cold side panel spaced from the hot side panel, and a continuous first wall extending axially between the hot and cold side panels and spaced radially outward from a centerline. The structure may further include a first plurality of helical vanes projecting laterally, radially, inward from the first wall for flowing cooling air in a spiraling fashion through the cold side panel, then through the hot side panel.