Supercritical carbon dioxide-cooled generator and turbine

An aircraft comprising:

• a gas turbine engine;
• and
• power generation system operably coupled to the gas turbine engine, the power generation system comprising:
• a shaft having an internal fluid conduit;
• a compressor operably coupled to a first end of the shaft and having an internal bore fluidly connected to the internal fluid conduit of the shaft;
• a turbine operably coupled to a second end of the shaft and having a hub with one or more hub fluid conduits fluidly connected to the internal fluid conduit of the shaft;
• a generator operably coupled to the shaft between the compressor and the turbine, wherein the shaft is a common shaft with the compressor, the turbine, and the generator coaxially mounted on the common shaft;
• and
• a working fluid arranged in a closed-loop flow path having a primary flow path that flows through each of the compressor and the turbine to drive rotation of the shaft,
• wherein a portion of the working fluid is extracted from the primary flow path and directed into the internal fluid conduit at the first end of the shaft to provide cooling to the compressor, then directed through the internal fluid conduit and the generator to provide cooling to the generator, and then into the hub and hub conduits of the turbine to provide cooling to the turbine, wherein the portion of the working fluid is rejoined with a primary flow path of the working fluid.