Turbine engine for an aircraft

A turbomachine for aircraft, the turbomachine being intended to propel, towards a downstream side, a flow of air entering from an upstream side, said turbomachine having a primary annular flow path and a cold flow channel extending around the primary annular flow path, said turbomachine comprising:

• an impeller arranged upstream of a first annular wall, the first annular wall separating the primary annular flow path from the cold flow channel,
• in the primary annular flow path, from upstream to downstream, a compressor, a combustion chamber, a first turbine and a second turbine, the compressor having an input stage and an output stage, the first turbine having a first turbine rotor and the second turbine having a second turbine rotor,
• a shaft assembly for rotating the compressor and the impeller about an axis of rotation, the shaft assembly comprising a first connecting shaft and a second connecting shaft, the first connecting shaft being rotatably connected to the second turbine rotor, the second connecting shaft being rotatably connected to the first turbine rotor and rotating the compressor,
• an inter-turbine stator disposed between the first turbine and the second turbine, the inter-turbine stator comprising a plurality of arms extending between an inner end and an outer end, the plurality of arms extending through the primary annular flow path,
• a cooling assembly comprising a first cooling circuit having successively:
• a first cooling inlet located between the impeller and the compressor,
• a first passage extending through the primary annular flow path into the inter-turbine stator from the inner end to the outer end, and
• a first cooling outlet extending into the cold flow channel.