Compressor and a turbine engine with optimized efficiency

An axial flow turbine engine compressor comprising:

• a casing presenting an inside wall of general shape that defines an aerodynamic reference surface defining a gas-passing passage;
• a rotor wheel mounted to rotate relative to the casing in the passage;
• the rotor wheel carrying a plurality of radial blades, each having a tip, a leading edge, and a trailing edge;
• a circumferential trench being formed in the inside wall of the casing;
• a shape of the trench being defined essentially by three substantially conical surfaces, of an upstream surface, a middle surface, and a downstream surface, the surfaces following one after another from upstream to downstream;
• the middle surface being substantially parallel to the aerodynamic reference surface;
• the downstream surface extending downstream at least as far as the trailing edges of the blades;
• the upstream surface extending upstream from the leading edges of the blades;
• and
• the junction between the middle and downstream surfaces is situated in a range of 30% to 80% or in a range of 50% to 65% of the axial length of the blades starting from the leading edge.