Gas turbine engines having cryogenic fuel systems

A propulsion system, comprising:

• a turbine engine having a combustor arranged along a core flow path of the turbine engine;
• an auxiliary power unit;
• a cryogenic fuel tank configured to supply a fuel to at least one of the combustor and the auxiliary power unit;
• a fuel supply line having a first flow supply line, a second flow supply line, and a third flow supply line, wherein the first flow supply line fluidly connects the cryogenic fuel tank to the combustor through a first core flow path heat exchanger, the second flow supply line fluidly connects the cryogenic fuel tank to the combustor through a second core flow path heat exchanger, and the third flow supply line fluidly connects the cryogenic fuel tank to the auxiliary power unit to supply fuel to the auxiliary power unit;
• a first flow controller arranged along the fuel supply line and configured to respectively control a flow of fuel into at least one of the first flow supply line during a first operational parameter of the propulsion system, the second flow supply line during a second operational parameter of the propulsion system that is different from the first operational parameter, and the third flow supply line during a first third operational parameter of the propulsion system that is different from the first operational parameter and the second operational parameter,
• an expansion turbine configured to receive fuel from at least one of the first flow supply line and the second flow supply line downstream of the respective first core flow path heat exchanger and second core flow path heat exchanger and upstream of the combustor;
• and
• a second flow controller arranged between the expansion turbine and the combustor and configured to selectively divert at least a portion of fuel that exits the expansion turbine to the auxiliary power unit.