Stator structure (22) extending around an axis of the turbomachine and comprising: —a support (50) having an inner surface centred on the axis and—a flange (60) defining an air chamber (A2) and having an outer surface centred on the axis, the support (50) extending around the flange (60) such that the inner and outer surfaces are opposite to each other, the structure (22) defining an oil circuit and an air circuit which are formed by upstream channels (64, 65) and downstream channels (54, 55), —each upstream channel (64, 65) defining an outer opening in the outer surface, —each downstream channel (54, 55) defining an inner opening in the inner surface, each circuit being oriented between the outer and inner openings in a direction comprising a component radial to the axis.