An aircraft engine, comprising a thermal engine, an axial turbine having a turbine inlet, and an exhaust assembly fluidly connecting the thermal engine to the axial turbine. The exhaust assembly includes a housing and a deflector removably mounted within the housing. The deflector has circumferentially distributed vanes. The deflector is a first deflector, having a first set of geometric characteristics, that is removable from the housing and replaceable by a second deflector having a second set of geometric characteristics different from the first set of geometric characteristics. The first deflector is one of a first class of deflectors and the second deflector is one of a second class of deflectors, the first and second class of deflectors respectively defining first and second exhaust flow profiles that differ from each other.