An aircraft turbomachine, comprising: - a centrifugal compressor extending around an axis A, - an annular combustion chamber extending around the axis A, - a system for diffusing and rectifying an air flow leaving the centrifugal compressor to supply the combustion chamber, this system comprising: ▪ an annular diffuser which is oriented substantially radially and which comprises an inlet supplied by the centrifugal compressor, and ▪ an annular rectifier which comprises an outlet for supplying the combustion chamber, and - a heat exchanger, this exchanger comprising: ▪ a first circuit supplied with exhaust gases from the turbomachine, and ▪ a second circuit comprising an inlet connected by a first volute to an outlet of the diffuser, and an outlet connected by a second volute to an inlet of the rectifier, the first and second volutes being joined together and each comprising an annular conduit wound around the axis A and connected to a first port located at the external periphery of the conduit and oriented in a tangential direction, and a second port located at the internal periphery of the conduit and oriented in a radial direction, the conduit of each of the volutes having an evolving passage cross-section which is maximum at the level of the first port and minimum at a circumferential end of the conduit opposite the first port, characterised in that the volutes (40a, 40b) have reversed winding directions so that their first ports are formed by conduit portions spaced apart from each other and the minimum cross-section of each conduit is located at the level of a larger cross-section of the other conduit. - a centrifugal compressor extending around an axis A, - an annular combustion chamber extending around the axis A, - a system for diffusing and rectifying an air flow leaving the centrifugal compressor to supply the combustion chamber, this system comprising: ▪ an annular diffuser which is oriented substantially radially and which comprises an inlet supplied by the centrifugal compressor, and ▪ an annular rectifier which comprises an outlet for supplying the combustion chamber, and ▪ an annular diffuser which is oriented substantially radially and which comprises an inlet supplied by the centrifugal compressor, and ▪ an annular rectifier which comprises an outlet for supplying the combustion chamber, and - a heat exchanger, this exchanger comprising: ▪ a first circuit supplied with exhaust gases from the turbomachine, and ▪ a second circuit comprising an inlet connected by a first volute to an outlet of the diffuser, and an outlet connected by a second volute to an inlet of the rectifier, the first and second volutes being joined together and each comprising an annular conduit wound around the axis A and connected to a first port located at the external periphery of the conduit and oriented in a tangential direction, and a second port located at the internal periphery of the conduit and oriented in a radial direction, the conduit of each of the volutes having an evolving passage cross-section which is maximum at the level of the first port and minimum at a circumferential end of the conduit opposite the first port, ▪ a first circuit supplied with exhaust gases from the turbomachine, and ▪ a second circuit comprising an inlet connected by a first volute to an outlet of the diffuser, and an outlet connected by a second volute to an inlet of the rectifier, the first and second volutes being joined together and each comprising an annular conduit wound around the axis A and connected to a first port located at the external periphery of the conduit and oriented in a tangential direction, and a second port located at the internal periphery of the conduit and oriented in a radial direction, the conduit of each of the volutes having an evolving passage cross-section which is maximum at the level of the first port and minimum at a circumferential end of the conduit opposite the first port,