Purging valve in a primary duct of a compressor and corresponding process to suppress the surge effect

The insert (2) has a hollow portion inserted through an aperture in a wall (12). A membrane is arranged at one end of the hollow portion. The membrane comprises an outer surface that defines a fluid stream within a turbomachine along an inner surface of the wall, and an inner surface that is in communication with a leakage channel. The membrane deforms vicinity of a notch in presence of pressure difference between outer and inner surfaces. The membrane is made of material that is same as material of an insert. The membrane is united with the insert. An independent claim is also included for a method for diminishing and suppressing a surging phenomenon in an axial compressor of a double-flow turbomachine.