An aircraft turbomachine having a centrifugal compressor, an annular combustion chamber, an annular casing extending around the chamber and delimiting an annular space (E) in which the chamber is situated, and a heat exchanger. The heat exchanger can include a first circuit supplied with exhaust gas from the turbomachine, and a second circuit connected by first and second volutes respectively to an outlet of the compressor and to the annular space. The first and second volutes can be positioned at an axial distance from one another, and the second volute is can be connected to the annular space by a straightener which is situated at least in part outside the casing and which is integrated into an annular connecting pipe which connects the second volute to this casing.